[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 900\\ P=\textit{initial amount}\dotfill &700\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\\\ \end{cases} \\\\\\ 900 = 700(1 + 0.06)^{t} \implies 900=700(1.06)^t[/tex]
The ratio of boys to girls is 4to3 how many boys are there
The ratio of boys to girls is 4:3 boys are there of 5 boys were more than girls.
Most of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.
Formula used:
No. of Object= Total No of abject. x Given ratio/Sum of ratios
No. of Boys = 35 x 4 /7
No. of Boys = 140 / 7
No of Boys = 20
And No. of Girls = 35 x 3/7
No. of Girls = 105 /7
No. of Girls = 15
Final answer:
No. of boys - No. of girls
20-15= 5
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Draw a number line and show the following numbers. positive proper fractions with a denominator of 6
The fraction 1/6 is closer to 0, while the fraction 5/6 is closer to 1.
What does the denominator represent?A horizontal bar between two numbers and, on occasion, the symbol "/" can be used to identify a fraction. The term "fractional bar" refers to this bar or symbol. The "denominator" is the number below the fractional bar, while the "numerator" is the number at the top.
Indeed, the following number line displays positive proper fractions with the denominator 6:
0 1 2 3 4 5
|------------|------------|------------|------------|------------|
0 1/6 1/3 1/2 2/3 5/6
The complete numbers are represented by tick marks, while the fractions are displayed in between. The fractions 1/6 and 5/6 are closer to the numbers 0 and 1, respectively.
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PLS HELP! I WILL MAKE U BRAINLIST! LATE WORK
Step-by-step explanation:
to graph a line always find 2 points out has to go through. that means the points' coordinates make the equation true.
I usually start with x = 0.
point 1 of equation 1 is then
y = -2×0 + 6 = 6
(0, 6)
point 1 of equation 2 is then
y = (3/2)×0 - 1 = -1
(0, -1)
then I pick a value for x that makes the handling of any fractions easier. like in our case x = 2.
point 2 of equation 1 is then
y = -2×2 + 6 = -4 + 6 = 2
(2, 2)
point 2 of equation 2 is then
y = (3/2)×2 - 1 = 3 - 1 = 2
(2, 2)
oh, so I have found the intersection point right away (point 2 of both equations).
so, let's pick a different point 2 for equation 1, like x = 4
y = -2×4 + 6 = -8 + 6 = -2
(4, -2)
with these 4 points you define the 2 lines, and you have the intersection point at (2, 2).
PLEASE HELP ASAP !!!!!!!!!!!!!
The length of the x is 9 units.
Describe Triangle?Triangles can be classified based on the lengths of their sides and the sizes of their angles. The three most common types of triangles are equilateral, isosceles, and scalene. In an equilateral triangle, all sides and angles are equal. In an isosceles triangle, two sides and two angles are equal. In a scalene triangle, all three sides and angles are different.
Let's call the two sides of the triangle that the median divides into 9 and 10 "a" and "b", respectively. Then, we can use the formula for the length of a median in a triangle:
median = 1/2 * √(2a² + 2b² - c²)
where c is the length of the third side of the triangle. However, we don't know the length of the third side, so we need to find it. We can use the fact that the median divides the third side into two equal parts:
c/2 = (a + b)/2
c = a + b
Now we can substitute this into the formula for the length of the median:
x = 1/2 * √(2a² + 2b² - (a + b)²)
Simplifying:
x = 1/2 * √(2a² + 2b² - a² - 2ab - b²)
x = 1/2 * √(a² + 2ab + b²)
x = 1/2 * √((a + b)²)
x = 1/2 * (a + b)
x = 1/2 * (9 + 10)
x = 9
So the length of the median is 9 units.
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On a hot summer day in Death Valley, the amount of water in a swimming pool is 4000 gallons. 30 Days later, the amount of water in the pool is 3500 gallons. If the evaporation follows a continuous exponential model for decay, find k, the constant of proportionality in the equation A=Av0e^kt. Round to 4 decimal places.
Write a function that models the amount of water in the pool A(t), t days after the original measurement
The half-life of the radioactive substance,1/2 = 18.905 years.
What is half-life of the radioactive substance?The half-life of a radioactive atom or substance
A radioactive element's half life is the amount of time it takes for its atoms to split in h-alf from their initial number.
nuclear decay
The process of a heavy radioactive element's nucleus disintegrating and emitting alpha, beta, and gamma rays is known as radioactive decay.
Radioactivity law
According to the law, when a radioactive element decays or disintegrates, a new element two places below the original element in the periodic table with alpha particle emission or two places above the original element with beta particle emission results.
Hence, The half-life of the radioactive substance,1/2 = 18.905 years.
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Which statement is not true about the absolute value of -6?
It equals the absolute value of 6.
It can be expressed as |-61.
It describes the distance between -6 and 0 on the number line.
It describes the distance between 6 and -6 on the number line.
My Progress
Done →
out express written consent of Curricu
Answer:6
Step-by-step explanation:
Absolute value is just how many units, it is away from 0.
A population of values has a normal distribution withμ=178andσ=75.2. You intend to draw a random sample of sizen=48. Find the probability that a sample of sizen=48is randomly selected with a mean between182.3and 198.6.P(182.3×M<198.6)=Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exactz-scores orzscores rounded to 3 decimal places are accepted.
The probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.
The central limit theorem: what is it?The behaviour of sample means and sums in sizable random samples is described by the central limit theorem, a statistical concept. It asserts that regardless of how the underlying population is distributed, as the sample size grows, the distribution of the sample means and sums will converge to a normal distribution. This theorem is crucial because it enables us to extrapolate population parameters from sample data. Because sample means and variances are simpler to gather and evaluate, we may use them to estimate population means, variances, and other characteristics. Several study fields, including the social sciences, the natural sciences, and business, frequently employ the central limit theorem.
Given that the sample size n = 48.
The mean between 182.3and 198.6 is calculated using the central limit theorem.
The sample mean is given as:
Z = (M - μ) / (σ / √(n))
Substituting the values we have:
Z = (198.6 - 178) / (75.2 / √(48)) - (182.3 - 178) / (75.2 / √(48))
Z = 1.62
Now, Z-score less than 1.62 is approximately 0.9474.
Hence, the probability that a sample of size n=48 has a mean between 182.3 and 198.6 is approximately 0.9474.
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Homework Progress
79/99 Marks
If £2000 is placed into a bank account that pays 3% compound interest per year.
how much will be in the account after 2 years?
Optional working
3
78%
Answer
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2 \implies A = 2121.8[/tex]
If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is
The end behavior of a polynomial function is to decrease without bound as x approaches negative infinity, and to increase without bound as x approaches positive infinity.
If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is as follows:
As x approaches negative infinity, the value of the function decreases without bound.
As x approaches positive infinity, the value of the function increases without bound.
To understand why this is the case, consider a polynomial function of the form:
f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0
where n is odd and a_n < 0.
As x approaches negative infinity, the dominant term in the polynomial is a_n x^n, and since n is odd and a_n is negative, the value of the dominant term approaches negative infinity as x approaches negative infinity.
Similarly, as x approaches positive infinity, the dominant term in the polynomial is again a_n x^n, but this time the value of the dominant term approaches negative infinity as x approaches positive infinity.
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At a local car dealership a particular salesperson sells an average of 3. 1 cars per week with a standard
deviation of 1. 1 cars. The dealership pays her $300 a week plus a commission of $250 for each car that
she sells. What are the mean and standard deviation, respectively, of her total weekly pay? PLs help
The standard deviation of her total weekly pay is approximately $262.25 and the mean is $1075
Let X be the number of cars the salesperson sells in a week. Then, X follows a normal distribution with mean μ = 3.1 and standard deviation σ = 1.1.
The total weekly pay Y is given by the equation:
Y = $300 + $250X
Using the properties of means and variances of linear combinations of random variables, we can find the mean and standard deviation of Y as follows:
Mean of Y:
E(Y) = E($300 + $250X) = $300 + $250E(X) = $300 + $250(3.1) = $1075
Therefore, the mean of her total weekly pay is $1075.
Standard deviation of Y:
Var(Y) = Var($250X) = $250^2Var(X) = $250^2(1.1^2) = $68,750
Since the standard deviation is the square root of the variance, we have:
SD(Y) = sqrt($68,750) ≈ $262.25
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This composite figure is created by placing a sector of a circle on a triangle. What is the area of this
composite figure? Use 3.14 for . Round to the nearest hundredth. Show your work
As a result, the answer to the following question, When we round to the area nearest hundredth, we get: 42.84 square units in total.
What is area?An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.
The formula for a sector's area is:
Sector area = (central angle/360) x pi x radius2
When we plug in the values we know, we get:
Sector area = (60/360) x 3.14 x 62
Sector area = 18.84 square units
Triangle area = (base x height)/2
When we plug in the values we know, we get:
Triangle area = (8 x 6)/2 Triangle area = 24 square units
Total area Equals sector area + triangle area
18.84 + 24 = total area
42.84 square units in total
When we round to the nearest hundredth, we get:
42.84 square units in total.
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Diego applied to x colleges. If Nikki applied to 3 times as many colleges as Diego did, how many colleges did Nikki apply to?
3
x + 3
3x
3x + 3
Nikki applied to 3x colleges.
To determine the number of colleges Nikki applied to, we need to multiply the number of colleges Diego applied to by 3. Hence, the answer is represented by the mathematical expression 3x.
Explanation:In this problem, 'x' represents the number of colleges Diego applied to. Nikki, on the other hand, applied to 3 times as many colleges as Diego did.
So, to find out the total number of colleges Nikki applied to, we multiply the number of colleges Diego applied to ('x') by 3.
Hence, the correct mathematical expression for the number of colleges Nikki applied to would be 3x.
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Mixes two varieties of saffron X and y the ratio 3:8 if the cost of X is rupees 154 per g and that of y is rupees 121 per gram at what price should he sell the mixture make a profit of 25%
The seller should sell the mixture at Rs. 162.5 per gram to make a profit of 25%.
Let's assume that the quantity of variety X in the mixture is 3x and the quantity of variety Y is 8x. Therefore, the total quantity of the mixture will be 3x + 8x = 11x.
The cost of variety X is Rs. 154 per gram. Therefore, the cost of 3x grams of variety X will be 3x × Rs. 154 = Rs. 462x.
Similarly, the cost of variety Y is Rs. 121 per gram. Therefore, the cost of 8x grams of variety Y will be 8x × Rs. 121 = Rs. 968x.
The total cost of the mixture will be the sum of the costs of the individual varieties:
Total cost = Rs. 462x + Rs. 968x = Rs. 1430x
To make a profit of 25%, the selling price of the mixture should be 1.25 times the cost price:
Selling price = 1.25 × Total cost
= 1.25 × Rs. 1430x
= Rs. 1787.5x
Therefore, the selling price of the mixture should be Rs. 1787.5x to make a profit of 25%. To find the price per gram of the mixture, we need to divide this selling price by the total quantity of the mixture:
Price per gram of mixture = Selling price / Total quantity
= Rs. 1787.5x / 11x
= Rs. 162.5 per gram (approx.)
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Do what the photo says.
The area of the composite figure is 186.5 m².
How to find the area of a composite figure?The figure above is a composite figure. A composite figure is a shape that has two or more shapes in it.
Hence, the area of the composite figure is the sum of the whole individuals area of the shapes.
The composite figure can be divided into rectangles, square and quarter circle.
area of the composite figure = area of rectangle + area of square + area of quarter circle
area of the composite figure = 8 × 9 + 6 × 6 + 1 / 4 × 3.14 × 10²
area of the composite figure = 72 + 36 + 1 / 4 × 3.14 × 100
area of the composite figure = 108 + 314 / 4
area of the composite figure = 108 + 78.5
area of the composite figure = 186.5 m²
Therefore, the composite figure with different shapes has an area of 186.5 metres squared.
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benny makes $20 an hour babysiting. he can make 35% more per hour if he babysits an extra kid what could his new hourly wage be.
Answer:
If Benny makes $20 an hour babysitting, his 35% increase would be:
35% of $20 = 0.35 x $20 = $7
This means that Benny could make an extra $7 per hour if he babysits an extra kid. Therefore, his new hourly wage would be:
$20 + $7 = $27
So, if Benny babysits an extra kid, he could make $27 per hour.
Step-by-step explanation:
An object with a mass of 7.5kg accelerates 8.3m/s2 when an unknown force is applied to it. What is the amount of force
Answer: The amount of force (F) can be calculated using Newton's second law of motion, which states that force is equal to mass times acceleration:
F = m*a
where F is the force, m is the mass, and a is the acceleration.
Plugging in the given values, we get:
F = 7.5kg * 8.3m/s^2
F = 62.25 N
Therefore, the amount of force applied to the object is 62.25 Newtons.
Step-by-step explanation:
Which statements about liquid volume are true
The statements that are cοrrect based οn unit cοnversiοn is -
A - One milliliter is 100 times smaller than οne liter.
C - Milliliters are smaller units than liters.
D - One liter is 1,000 times larger than οne milliliter.
What is unit cοnversiοn?Unit cοnversiοn is a prοcess with multiple steps that invοlves multiplicatiοn οr divisiοn by a numerical factοr οr, particularly a cοnversiοn factοr. The prοcess may alsο require selectiοn οf the cοrrect number οf significant digits, and rοunding.
On the basis οf unit cοnversiοn methοds -
These three statements are true -
One milliliter is 100 times smaller than οne liter.
Milliliters are smaller units than liters.
One liter is 1,000 times larger than οne milliliter.
The οther statements are incοrrect -
Liters are nοt smaller units than milliliters.
One milliliter cannοt be 100 times larger than οne liter, as it is a smaller unit οf vοlume.
One liter cannοt be 1,000 times smaller than οne milliliter, as it is a larger unit οf vοlume.
Therefοre, the statements A, C and D are cοrrect.
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Which statements about liquid volume are true?
Select each correct answer.
One milliliter is 100 times smaller than one liter.
Liters are smaller units than milliliters.
Milliliters are smaller units than liters.
One liter is 1,000 times larger than one milliliter.
One milliliter is 100 times larger than one liter.
One liter is 1,000 times smaller than one milliliter.
Using the graph answer the following questions What is the slope of the function What is the y intercept of the function What is the slope intercept form of the function?
Answer: what's the queston?
Step-by-step explanation:
Answer:
um question ?
Step-by-step explanation:
Write 27^2/9^4 as a power of 3
Answer: We can simplify 27 as 3^3 and 9 as 3^2. Then, we have:
27^2/9^4 = (3^3)^2/(3^2)^4
Using the power of a power rule, we can simplify:
= 3^(3x2)/(3^2x4)
= 3^6/3^8
Using the quotient rule, we can subtract the exponents:
= 3^(6-8)
= 3^-2
Therefore, 27^2/9^4 can be expressed as 3^-2 in terms of a power of 3.
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The measures of the angles of a triangle are shown in the figure below. Find the measure of the largest angle.
(5x+14)°
(6x+17)°
105°
Answer:
105° is the largest angle
Step-by-step explanation:
All angles add up to 180°
Find the value of x
105 + 6x + 17 + 5x + 14 = 180
Combine like terms
136 + 11x =180
Isolate the x ( subtract 136 from both sides)
11x = 44
Divide both sides by 11
x = 4
Now substitute the value of x into each expression to find the largest angle
5(4) + 14 = 20 + 14 = 34°
6(4) + 17 = 24 + 17 = 41°
105 > 41 > 34
A triangular piece of fabric has side lengths of 3 inches, 4 inches, and 5 inches. Will it fit in the corner of a rectangular quilt? Explain.
Yes, because it is a right triangle.
Yes, because it is an isosceles triangle.
No, because it is an equilateral triangle.
No, because it is an obtuse triangle.
Answer:
yes because it is a right triangle
Step-by-step explanation:
if you apply the pythagorean theorem a squared plus b squared equals c squared. c being the hypotenuse, the longest side. so 3x3 + 4x4 = 25 and 5x5 is 25. This confirms that it is a right triangle because pythagoras's theorem only works with right triangles. Also, every angle of a rectangle is a right angle (90 degrees) meaning that the triangle will fit in any and every corner! Hope this helped!
Find the values of variables and the measures of the indicated angles.
Using the angle of intersecting chords theorem, the measure of x = 175°.
What is the Angle of Intersecting Chords Theorem?The angle of intersecting chords theorem states that when two chords intersect within a circle, the angle that they form is equal to half the sum of the measures of the intercepted arcs and the vertical angle opposite to the angle.
Therefore, based on the theorem, we would have:
180 - 60 = 1/2(x + 65)
120 = 1/2(x + 65)
Multiply both sides by 2:
240 = x + 65
subtract 65 from both sides:
240 - 65 = x
x = 175°
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Someone help me solve this!
Based on the information provided, the true sentences are that route B has a more consistent number of rides (B), and the typical number of riders is greater on route A (D).
How can the graphs be interpreted?To begin, these whisker plots compare the number of riders in two routes. In this context, the graph shows the median for route A is 40 and for the route, B is 35, which means the "typical number of riders is greater on route" (option D). Besides this, it can be observed that the number of riders varies more for route A than for route B, which makes B to be true.
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Use the triangle below to write the given ratios.
In the given triangle the value of the ratios are Sin (P) = 5/13. tan (T) = 12 /5. cos (T) = 5/13.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to determine each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
Using the trigonometric identities we can write the ratios as follows:
Sin (P) = Opposite side to P / Hypotenuse= 5/13
tan (T) = Opposite side to T / Adjacent side to T = 12 /5
cos (T) = adjacent side to T / Hypotenuse = 5/13.
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For a measurement project in math class, students measured the lengths of their pinky fingers. Alex's measured 2 inches long. Jerimiah's pinky finger was (7)/(4) inches long. Whose finger is longer? Draw a number line to help prove your answer.
Jerimiah's finger is longer. A number line can be drawn from 0 to 8 inches with 2 inches marked for Alex's finger and 7/4 inches marked for Jerimiah's finger. Since 7/4 is greater than 2, Jerimiah's finger is longer.
To prove that Jerimiah's finger is longer than Alex's, we can use a number line. On this number line, we start with 0 inches at one end and 8 inches at the other. We mark 2 inches for Alex's finger and 7/4 inches for Jerimiah's finger. Since 7/4 inches is greater than 2 inches, Jerimiah's finger is longer than Alex's. To further prove this, we can convert the fraction 7/4 into a decimal. 7/4 = 1.75, which is greater than 2. Therefore, Jerimiah's finger is longer than Alex's.
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Find the surface area of the cube shown below?
The surface area οf the cube with sides οf 25 cm is 3750 square centimeters.
What is Surface Area?Surface area is the measure οf the tοtal area that the surface οf a three-dimensiοnal οbject οccupies, including all οf its faces, sides, and curves. It is οften expressed in square units such as square meters οr square feet, and is an impοrtant parameter fοr determining prοperties such as heat transfer, frictiοn, and οptical prοperties οf an οbject.
The surface area οf a cube with sides οf length "a" can be fοund by using the fοrmula:
Surface area[tex]= 6a^2[/tex]
Substituting the given value οf "a" intο the fοrmula, we get:
Surface area [tex]= 6(25 cm)^2[/tex]
Surface area[tex]= 6(625 cm^2)[/tex]
Surface area [tex]= 3750 cm^2[/tex]
Therefοre, the surface area οf the cube with sides οf 25 cm is 3750 square centimeters.
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The question was incomplete, the complete question is mentioned here:
Find the surface area of the cube with side 25cm?
can anyone help me please
The interval of the expression x ≤ 3 and x ≥ -3 is (-3, 3).
How to graph equations?To graph a linear equation with one variable, first solve the problem, then find the answer on the axis (number line), and place a point there. We have seen that graphs often provide information that the original equation would not have shown. The graphs of one-variable linear equations do not provide much, if any, information, but they provide as a basis for graphs with greater dimensions.
The given inequality is x ≤ 3 and x ≥ -3.
Since, the signs are less than and equal to and more than and equal to we use solid dots to represent the number 3 and -3 on the number line.
Also, the expression requires all the numbers between 3 and -3. Thus, the interval is:
(-3, 3).
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This is 4/6 problems finish them all each is 10 points 60 total.
The trigonometric ratios for cosines indicates that the measure of angle B, m∠B, in the right triangle with hypotenuse side length of 15 units and adjacent leg to ∠B of 12 units, obtained using the trigonometric ratios for cosines is; m∠B ≈ 36.9°
What are trigonometric ratios?Trigonometric ratios relate the lengths of two side lengths of a right triangle and the interior angles of the right triangle.
The cosine of an angle can be obtained from the ratio of the adjacent side to the angle to the hypotenuse side of the right triangle in which the angle is an acute angle, therefore;
cos(θ) = Adjacent side to the angle ÷ Hypotenuse side of the angle
The measure of the length of the adjacent side to the angle x = 12 units
The measure of the hypotenuse side of the right triangle = 15 units, therefore;
cos(x°) = 12/15 = 4/5 = 0.8
The measure of the angle x therefore can be obtained using the arccos function, (cos⁻¹ function) in a scientific calculator as follows;
x = arccos(0.8) ≈ 36.9°
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The function f(x) = –5x2 + 13x + 6 represents the height, in meters, of a coin x seconds after it is thrown into the air. What is the maximum height of the coin
The maximum height of the coin is approximately 14.825 meters.
To find the maximum height of the coin, we need to find the vertex of the parabolic function. The x-coordinate of the vertex is given by:
x = -b/2a
where a = -5 and b = 13 are the coefficients of the quadratic function f(x) = -5x^2 + 13x + 6.
Plugging these values into the formula, we get:
x = -13/(2×(-5)) = 13/10
Now we can find the y-coordinate of the vertex by plugging in x = 13/10 into the function:
f(13/10) = -5(13/10)^2 + 13(13/10) + 6
Do the arithmetic operations
≈ 14.825 meters
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Find the HCF of:
x²+5x+6, x²-4 and x³+8
Answer:
x²+5x+6 can be factored as (x+2)(x+3)
x²-4 can be factored as (x+2)(x-2)
x³+8 can be factored as (x+2)(x²-2x+4)
The common factor of all three expressions is (x+2). Therefore, the HCF of x²+5x+6, x²-4, and x³+8 is (x+2).
Step-by-step explanation:
Answer: To find the highest common factor (HCF) of these three polynomials, we can factor each polynomial and then look for the factors that they have in common.
First, let's factor each polynomial:
x² + 5x + 6 = (x + 2)(x + 3)
x² - 4 = (x + 2)(x - 2)
x³ + 8 = (x + 2)(x² - 2x + 4)
Now, we can see that all three polynomials have a factor of (x + 2). Therefore, the HCF of these three polynomials is (x + 2).
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