Therefore, the roots of the polynomial equation x² + x - 72 = 0 are -9 and 8.
What is quadratic equation?A quadratic equation is a type of polynomial equation of the second degree, which means it has one or more terms in which the variable is raised to the power of two, but no higher powers.Quadratic equations can have zero, one, or two real solutions, depending on the values of a, b, and c. These solutions are also called the roots or zeros of the equation.
Here,
To find the roots of the polynomial equation x² + x - 72 = 0, we can set y = 0 and solve for x. This is equivalent to finding the x-intercepts of the graph of the function f(x) = x² + x - 72.
We can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, a = 1, b = 1, and c = -72, so we have:
x = (-1 ± √(1² - 4(1)(-72))) / (2(1))
x = (-1 ± √(1 + 288)) / 2
x = (-1 ± √(289)) / 2
x = (-1 ± 17) / 2
Therefore, the roots of the polynomial equation x² + x - 72 = 0 are:
x = -9 or x = 8
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in the regression of the general fertility rate (gfr) on the tax personal exemption (pe) and its first lag the fitted regression is: what is the impact propensity?
The impact propensity can be interpreted as the slope coefficient for the tax personal exemption (pe) or its first lag in
the regression equation.
To determine the impact propensity in the regression of the general fertility rate (GFR) on the tax personal exemption
(PE) and its first lag, you should follow these steps:
Estimate the regression model using the available data. The model should look like this:
GFR = β0 + β1 × PE + β2 × PE_lag + ε
Where GFR is the general fertility rate, PE is the tax personal exemption, PE_lag is the tax personal exemption's first
lag, and ε is the error term.
Obtain the estimated coefficients (β0, β1, and β2) from the fitted regression model.
These coefficients will help you determine the impact propensity.
Calculate the impact propensity. The impact propensity in this context refers to the change in the general fertility rate
resulting from a one-unit increase in the tax personal exemption, taking into account both its current and lagged
effects.
To find the impact propensity, sum the coefficients for the tax personal exemption and its first lag:
Impact propensity = β1 + β2
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PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST.
Answer:
Step-by-step explanation:
4y = -x - 32 (Show work)
Answer: the solution for y in terms of x is y = (-1/4)x - 8.
Step-by-step explanation: In order to obtain a solution for y in the given equation of 4y = -x - 32, it is imperative to achieve the isolation of y on a singular side of the equation. To accomplish this task, it is possible to perform division on both sides of the equation by a factor of 4:
The given equation 4y/4 = (-x - 32)/4 can be expressed in an academic manner as follows: The given equation reveals that the quotient of 4y divided by 4 is equivalent to the quotient of the opposite of x added to negative 32, also divided by 4.
Upon performing simplification, the expression on the right-hand side yields:
The equation y = (-1/4)x - 8 can be expressed in an academic manner as follows: The dependent variable y is equivalent to the product of the constant (-1/4) and the independent variable x, with an additional decrement of eight.
What is the total surface area of the figure shown?
The total surface area of the given figure is 619.2 in², which is not listed in the provided options.
Give a brief account on total surface area.The surface area is known to be measure of the total area occupied by the surface of the object. Defining the surface area mathematically in the presence of a curved surface is better than defining the arc length of a one-dimensional curve, or the surface area of a polyhedron (i.e. an object with flat polygonal faces). Much more complicated. For a smooth surface sphere such as the following, surface area is assigned using representation as a parametric surface. This surface definition is based on calculus and includes partial derivatives and double integrals.
The triangular face of the given figure represent an equilateral triangle of sides 12 in.
Area of the triangle = (√3/4) × a²
Area of the triangular face:
= (√3/4) × 12²
= (√3/4) × 144
= 57.6 in²
Area of the rectangle = Length × width
Area of the rectangular face:
= 12 × 14
= 168 in²
Area of the given figure:
= (2 × 57.6) + (3 × 168)
= 115.2 + 504
= 619.2 in²
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URGENT!! Will give brainliest :)
What is the equation for the line of best fit for the following data? Round the slope and -intercept of the line to three decimal places.
A. y=-0.580×+ 10.671
B. y=-10.671 x+ 0.580
C. y= 10.671 x-0.580
D. y= 0.580x - 10.671
To find the equation for the line of best fit, we can use linear regression. Based on the given data:
x: 2, 5, 7, 12, 16
y: 9, 10, 5, 3, 2
The equation for the line of best fit would be in the form: y = mx + b, where m is the slope and b is the y-intercept.
Using a calculator or statistical software, we can calculate the slope and y-intercept for the line of best fit.
The result is:
Slope (m): -0.580 (rounded to three decimal places) Y-intercept (b): 10.671 (rounded to three decimal places)
So, the correct answer is:
A. y = -0.580x + 10.671
of the cartons produced by a company, 3% have a puncture, 6% have a smashed corner, and 1.4% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:
P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)
where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.
Substituting the given probabilities into the formula, we get:
P(puncture or smashed corner) = 0.03 + 0.06 - 0.014
P(puncture or smashed corner) = 0.076
Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
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How to solve? Answers are side side side, side angle side, angle angle angle, hypotenuse leg, or none)
The given triangles AOB and triangle OCB are proved congruent by using the property - angle side angle congruency.
Explain about the triangle congruency:Of three sides, three angles, plus three vertices, a triangle is a two-dimensional shape. If the matching sides or angles of two or more triangles match, the triangles are said to be congruent. Congruent triangles are identical in terms of their dimensions and shape.
Two triangles belong together if whose corresponding two angles but one included side are equivalent, according to the Angle- Side- Angle rule (ASA).
Given data:
AB || CDCO = OBAs, AB || CD, ∠ABO ≅ ∠OCD (alternate interior angles)
∠AOB ≅ ∠COD (vertically opposite angles)
So,
∠AOB ≅ ∠COD
CO = OB
∠ABO ≅ ∠OCD
By using angle side angle congruence:
ΔAOB ≅ ΔCOD
Thus, the given triangles AOB and triangle OCB are proved congruent by using the property - angle side angle congruency.
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3x + 18 > 54 solve the inequality? pls help?
Answer:
x > 12
Step-by-step explanation:
3x + 18 > 54
please someone help and give answers !!!
16.) Mean average deviation= option C
17.) Range of a data set = option E.
18.) First quartile = opinion AB
19.) Second quartile = option B
20.) Third quartile = option A
21.) Interquartile range = option D
How to determine the measures of the spread?
To determine the measures of the spread is to match their various definitions to the correct measures given such as follows:
16.) Mean average deviation: The average deviation of data from the mean.
17.) Range of a data set : The difference between the highest value and the lowest value in a numerical data set.
18.) First quartile: The median in the lower half.
19.) Second quartile: The median value in a data set.
20.) Third quartile: The median in the upper half.
21.) Interquartile range: The distance between the first and the third quartile.
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Figure LMNO is a reflection of HIJK. Which angle is congruent to ZH?
The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.
In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.
When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.
In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.
Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.
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An electronic book device had a value of t dollars before a holiday. The value decreased by 15% after the holiday. Which expressions show the value of the electronic book device after the holiday? Select all the expressions that apply.
A. 1.15
B. 0.85
C. −0.15
D. 1−0.15
E. −0.85
F. (1−0.15)
The expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).
Which expressions show the value of the electronic book device after the holiday?The value of an electronic book device before a holiday is represented by the variable t. After the holiday, the value of the device decreased by 15%. To find the value of the device after the holiday, we need to multiply the original value by the percentage decrease, which is 0.85 (or 1-0.15). Therefore, the expressions that correctly show the value of the electronic book device after the holiday are B and D.
Option A (1.15) represents the percentage increase and not the decrease, so it is incorrect. Option C (-0.15) represents the percentage decrease, but it cannot be used alone to find the new value. Option E (-0.85) is the negative of the percentage decrease, so it is also incorrect. Finally, option F is equivalent to option D, so it is also correct.
In summary, the expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).
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Simplify the expression (−1 3/4)^2 - √ [127−2(3)]
On simplifying the expression (−1 3/4)²- √ [127−2(3)] we get -127/16
Simplifying an expression:
To simplify the expression, we need to follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we simplify the exponent by squaring -1 3/4 to get 49/16. Then, we simplify the expression under the square root by subtracting 2 times 3 from 127 to get 121, and we take the square root of 121 to get 11.
Here we have
(−1 3/4)²- √ [127−2(3)]
The above expression can be simplified as follows
=> (−1 3/4)²- √ [127−2(3)]
Convert the mixed fraction into an improper fraction
=> 1 3/4 = 7/4 [ ∵ 4 × 1 + 3 = 7 ]
So given expression can be
=> (−7/4)²- √ [127−2(3)]
=> (49/16) - √ [121]
=> (49/16) - 11
=> (49 - 176 /16)
=> -127/16
Therefore,
On simplifying the expression (−1 3/4)²- √ [127−2(3)] we get -127/16
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an object is 19.0 cm from the center of a spherical silvered-glass christmas tree ornament 6.00 cm in diameter. What is the position of its image (counting from the ornament surface)?
The position of the image is approximately 1.71 cm from the ornament's surface.
To determine the position of the image, we need to use the mirror formula for a concave mirror, which is \frac{1}{f} = [tex]\frac{1}{do} + \frac{1}{di},[/tex] where f is the focal length, do is the object distance, and di is the image distance.
First, we need to find the focal length (f) of the spherical ornament. The radius of curvature (R) is half the diameter, so R = 6.00 cm / 2 = 3.00 cm. For a spherical mirror, the focal length is half the radius of curvature: f = R/2 = 3.00 cm / 2 = 1.50 cm.
Next, we need to find the object distance (do). The object is 19.0 cm from the center of the ornament, but we need the distance from the ornament's surface. Since the radius is 3.00 cm, we subtract that from the total distance: do = 19.0 cm - 3.00 cm = 16.0 cm.
Now, we can use the mirror formula:
\frac{1}{f} = [tex]\frac{1}{do} + \frac{1}{di},[/tex]
1/1.50 cm = 1/16.0 cm + 1/di
To solve for di, subtract 1/16.0 cm from both sides and then take the reciprocal:
1/di = 1/1.50 cm - 1/16.0 cm
di ≈ 1.71 cm
The position of the image is approximately 1.71 cm from the ornament's surface.
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The position of the image is 20.8 cm from the center of the spherical ornament, counting from the ornament surface.
To find the position of the image, we can use the mirror equation:
1/o + 1/i = 1/f
where o is the object distance from the center of the spherical ornament, i is the image distance from the center of the spherical ornament, and f is the focal length of the ornament.
Since the ornament is a spherical mirror, the focal length is half the
radius of curvature, which is half the diameter of the ornament:
f = R/2 = 6.00 cm/2 = 3.00 cm
Substituting the given values, we get:
1/19.0 cm + 1/i = 1/3.00 cm
Solving for i, we get:
1/i = 1/3.00 cm - 1/19.0 cm = (19.0 cm - 3.00 cm)/(3.00 cm x 19.0 cm) = 0.0481 cm^-1
i = 1/0.0481 cm = 20.8 cm
Therefore, the position of the image is 20.8 cm from the center of the
spherical ornament, counting from the ornament surface.
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What is the range of f? A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
Choose 1 answer:
(Choice A) The f(x)-values -6, -3, 0, 2, and 5
(Choice B) The f(x)-values -5, -2, 0, 2, and 5
(Choice C) -6 ≤ f(x) ≤ 5
(Choice D) − 5 ≤ f(x) ≤ 5
The range of f include the following: D. -5 ≤ f(x) ≤ 5.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-6, 5} or -6 ≤ x ≤ 5.
Range = {-5, 5} or -5 ≤ f(x) ≤ 5.
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if the florida distirution is also approximately morlam, but with a standard deviation of 2.9 inches, what is the mean height of a football player on this florida team? ap stat
To find the mean height of a football player on this Florida team, we need to know the mean of the normal distribution (Morlam) and the standard deviation of the Florida distribution. Since the Florida distribution is also approximately normal (Morlam) with a standard deviation of 2.9 inches, we can use the Empirical Rule to estimate the mean height.
According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% within two standard deviations, and approximately 99.7% within three standard deviations. Since we know that the standard deviation of the Florida distribution is 2.9 inches, we can assume that the mean height falls within three standard deviations of the mean.
So, if we assume that the mean height is at the centre of the distribution, we can estimate it by adding and subtracting three standard deviations from it. Therefore, the mean height of a football player on this Florida team can be estimated to be:
Mean height = Mean of the Morlam distribution ± 3 x Standard deviation of the Florida distribution
Mean height = Mean of the Morlam distribution ± 3 x 2.9 inches
Without knowing the mean of the Morlam distribution, we cannot calculate the exact mean height. However, if we assume that the Morlam distribution has a mean height of 70 inches (a typical average height for a football player), then the mean height of a football player on this Florida team can be estimated to be:
Mean height = 70 ± 3 x 2.9
Mean height = 70 ± 8.7
Mean height = 61.3 to 78.7 inches
Therefore, we can estimate that the mean height of a football player on this Florida team is between 61.3 and 78.7 inches.
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We can estimate that the mean height of a football player on the Florida team is approximately 70 inches.
To find the mean height of a football player on the Florida team, we need to know the exact distribution of heights. However, since we only have information about the standard deviation and the fact that it is approximately normal, we can make an educated guess that the distribution is still normal with a mean somewhere close to the national average of 70 inches.
Using the empirical rule, we know that about 68% of the data falls within one standard deviation of the mean. In this case, one standard deviation is 2.9 inches.
So, we can assume that about 68% of the heights on the Florida team fall between (70-2.9) = 67.1 inches and (70+2.9) = 72.9 inches.
If we assume that the distribution is symmetric, we can estimate the mean height of the Florida team by taking the average of the lower and upper bounds of the interval: (67.1 + 72.9)/2 = 70 inches.
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how would you define the actual score and theoretical score on an exam, and how would you calcutre the percent success
To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
We define the actual score, theoretical score, and explain how to calculate the percent success on an exam.
Actual score:
The actual score refers to the number of points a student has earned on an exam.
It represents the student's performance on the test, taking into account the correct and incorrect answers.
Theoretical score:
The theoretical score is the maximum number of points a student can earn on an exam.
This represents a perfect performance, where the student answers all questions correctly.
Calculating percent success:
To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
a. Divide the actual score by the theoretical score: (actual score) / (theoretical score)
b. Multiply the result by 100: (result from step a) * 100
c. The final value is the percent success.
For example, if a student has an actual score of 80 and the theoretical score is 100, the percent success would be calculated as follows:
a. 80 / 100 = 0.8
b. 0.8 * 100 = 80
c. The percent success is 80%.
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A brick has a mass of 2,022.75 grams and a volume of 1,064.5 cubic centimeters.
What is the density of the brick, in grams per cubic centimeter (³) ²¹
g
cm
3
Round your answer to the nearest tenth.
Answer:
To find the density of the brick, we need to divide its mass by its volume:
density = mass / volume
Plugging in the values given in the problem, we get:
density = 2,022.75 g / 1,064.5 cm³
Simplifying the division, we get:
density = 1.8996 g/cm³
Rounding to the nearest tenth, we get:
density ≈ 1.9 g/cm³
Therefore, the density of the brick is approximately 1.9 grams per cubic centimeter (g/cm³).
Mack's Toy Shop made 600 trains yesterday and found that 30 were defective. They
plan to make 4,500 trains this week.
Using the information given, how many trains are expected to be defective?
225 trains
6,000 trains
15 trains
500 trains
Answer:
225 trains
Step-by-step explanation:
since they are using the same process and materials, we expect them to have the same ratio between trains made and defective trains :
600 / 30 = 20/1
one out of 20 is defect.
so, when they make 4500 trains, we need to divide this by 20 to get the number of expected defective trains :
4500 / 20 = 225
I find the answer option of 6000 defective trains really funny : if that were true, more than the produced trains (4500) would be defective. how ... ?
The slope of one line is a, where a is a positive number. A second line is perpendicular to the hirst line. Which word best describes the slope of the second line? Type positive, negative, or zero.
The slope of the second line is also positive, as it is parallel to the first line which has a positive slope.
What is slope?Slope is a measure of how steep a line is, and is defined as the ratio of the change in the y-coordinate (vertical change) to the change in the x-coordinate (horizontal change) between any two points on the line. It represents the rate at which the line is rising or falling as it moves from left to right. Slope can be positive, negative, or zero. A positive slope indicates that the line is increasing as it moves from left to right, a negative slope indicates that the line is decreasing as it moves from left to right, and a zero slope indicates that the line is horizontal.
Here,
When two lines are parallel, they have the same slope. In this case, the first line has a positive slope of "a," which means that it is increasing as it moves from left to right. Since the second line is parallel to the first line, it will also have the same slope as the first line. Therefore, the slope of the second line will also be positive, indicating that it is increasing as it moves from left to right.
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In ΔUVW, w = 1. 4 cm, m m∠W=63° and m m∠U=29°. Find the length of v, to the nearet 10th of a centimeter
The length of v, to the nearest 10th of a centimeter is 2.2.
To find the length of side v in triangle UVW, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.
Using this formula, we have,
v/sin(m∠V) = w/sin(m∠W)
We know that w = 1.4 cm and m∠W = 63°. To find sin(m∠W), we can use a calculator,
sin(63°) ≈ 0.89
Substituting the values we know into the formula, we get,
v/sin(m∠V) = 1.4/0.89
To solve for v, we need to find sin(m∠V). We know that the sum of the angles in a triangle is 180°, so we can find m∠V by subtracting the measures of the other two angles from 180°,
m∠V = 180° - m∠U - m∠W
m∠V = 180° - 29° - 63°
m∠V = 88°
Now, we can substitute the value of sin(m∠V) into the equation and solve for v,
v/ sin(88°) = 1.4/0.89
v ≈ 2.2 cm
Therefore, the length of side v in triangle UVW is approximately 2.2 cm to the nearest tenth of a centimeter.
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Answer:
1.6
Step-by-step explanation: This is answer on DeltaMath
flip a coin three times. you will win $2 for each heads. what is the expected winning (expec- tation of your winning)? a
The expected winning is $2.
To calculate the expected winning, we need to find the probability of each outcome and multiply it by the amount we will win in that outcome.
There are 2 possible outcomes for each coin flip: heads or tails. Therefore, there are 2x2x2=8 possible outcomes for flipping a coin three times.
Here are all the possible outcomes with the number of heads in each outcome:
HHH (3 heads)HHT (2 heads)HTH (2 heads)THH (2 heads)HTT (1 head)THT (1 head)TTH (1 head)TTT (0 heads)The probability of each outcome can be calculated using the formula: probability = (number of favorable outcomes) / (total number of possible outcomes)
For example, the probability of getting 3 heads (HHH) is 1/8 because there is only one favorable outcome out of 8 possible outcomes.
Using this formula, we can calculate the probability and expected winning for each outcome:
HHH: probability = 1/8, expected winning = $6HHT: probability = 1/4, expected winning = $4HTH: probability = 1/4, expected winning = $4THH: probability = 1/4, expected winning = $4HTT: probability = 3/8, expected winning = $2THT: probability = 3/8, expected winning = $2TTH: probability = 3/8, expected winning = $2TTT: probability = 1/8, expected winning = $0To calculate the overall expected winning, we need to add up the expected winning for each outcome multiplied by its probability:
(1/8) x $6 + (1/4) x $4 + (1/4) x $4 + (1/4) x $4 + (3/8) x $2 + (3/8) x $2 + (3/8) x $2 + (1/8) x $0 = $2
Therefore, the expected winning is $2.
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a researcher has collected the following sample data. the mean of the sample is 5. 3 5 12 3 2 the coefficient of variation is . a. 81.24% b. 72.66% c. 330% d. 264%
The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is 91%. Option A is the correct answer.
To calculate the coefficient of variation, first, we need to calculate the standard deviation and mean of the sample.
The mean of the sample is (3 + 5 + 12 + 3 + 2)/5 = 5.
To find the standard deviation, we first need to calculate the variance. The variance can be found by taking the sum of the squared differences between each data point and the mean, dividing by the sample size minus one, and then taking the square root.
The variance is ((3-5)² + (5-5)² + (12-5)² + (3-5)² + (2-5)²)/4 = 20.5.
The standard deviation is the square root of the variance, which is approximately 4.53.
Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean and multiplying by 100%.
Coefficient of variation = (4.53/5) x 100% = 90.6%.
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The question is -
A researcher has collected the following sample data. The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is?
a. 91%
b. 72.66%
c. 330%
d. 264%
A local doctor’s office logged the number of patients seen in one day by the doctor for ten days. Find the mean, median, range, and midrange of the number of patients seen in ten days.
27, 31, 27, 35, 35, 25, 28, 35, 33, 24
Calculate the mean, median, range, and midrange of the number of patients seen in ten days.
Answer:
Step-by-step explanation:
Medium is 28
Mean is 29
Range is 11
Midrange is 29.5
A curved ladder that children can climb on can be modeled by the equation y=-1/20x^2+x where x and y are measured in feet. Make a table of values that shows the height of the ladder for x = 0, 5, 10 , 15, and 20 feet from the left end
The values of x and y of a curved ladder in feet given by the equation y=-1/20x^2+x are as follows in tabular form,
Values of x (in feet) Values of y (in feet)
0 0
5 3.75
10 5
15 3.75
20 0
A curved ladder that children can climb on is modeled by the system of equations as,
y=-(1/20)x^2+x
where, x and y are measured in feet.
Putting x= 0 in the above equation y=-(1/20)x^2+x , we get,
y = - (1/20) (0^2) + (0) = 0
Putting x= 5 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(5^2)+(5) = -5/4 + 5 = 15/4 = 3.75
Putting x= 10 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(10^2)+(10) =-5 +10 = 5
Putting x= 15 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(15^2)+(15) = -45/4 +15= 3.75
Putting x= 20 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(20^2)+(20) = -20 +20 = 0
Hence, when x= 0 feet, y = 0 feet ; x= 5 feet, y = 3.75 feet ; x = 10 feet, y = 5 feet ; x =15 feet , y =03.75 feet ;and x = 20feet, y = 0 feet from the solving the given equation.
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please help and explain and show your work on how you got the answer. I WILL MARK YOU BRAINLIEST
Answer:
Step-by-step explanation:
it is -2
Answer: -2
Step-by-step explanation:
So this is asking for the cube root of -8.
This is the same as asking what is multiplied by itself 3 times to get -8.
-2 * -2 *-2 = -8
You can also use a calculator.
Another way to solve it is to write -8^(1/3).
Hope this helps!!!
A ball is dropped from a height of 32 m.
With each bounce, the ball reaches a
height that is half the height of
the previous bounce. After
which bounce will the ball
rebound to a maximum
height of 25 cm?
Find a degrees. a 12 13 5
In the given triangle, α is equal to 67.36°.
What is a triangle's definition?
A triangle is a two-dimensional closed geometric form that has three sides, three angles, and three vertices (corners). It is the most basic polygon, produced by joining any three non-collinear points in a plane. The sum all angles of a triangle is always 180°. Triangles are classed according to their side length (equilateral, isosceles, or scalene) and angle measurement (acute, right, or obtuse).
Now,
Using Trigonometric functions
We can use the sine function
So,
Sin α=Perpendicular/Hypotenuse
Sin α = 12/13
α=67.36°
Hence,
The value of α will be 67.36°.
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-4 ≤ x- 4 ≤ 0 graph the conjuntion ?? can someone help
The inequality is simplified as 0 ≤ x ≤ 4
Define inequalityIn mathematics, inequality refers to a mathematical expression that indicates that two values or quantities are unequal. An inequality is represented by the symbols "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
For example, the inequality "x > 5" means that the value of x is greater than 5, and the inequality "y ≤ 10" means that the value of y is less than or equal to 10.
To graph the conjunction, we first need to solve for x:
-4 ≤ x - 4 ≤ 0
Add 4 to all parts of the inequality:
0 ≤ x ≤ 4
Image of graph is attached below.
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Find the surface area of the sphere. Use 3.14 for pi.
sphere is 7 yd
The distance between two cities on a map is 17 centimeters. The scale on the map relates 5 centimeters on the map as 30 miles on the road. What is the actual distance, in miles, between the two cities?
Answer: 102 miles.
Step-by-step explanation:
You divide 17 by 5 and then multiply by 30.