Answer:
(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52
Step-by-step explanation:
i literally just learned this today so here we go:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:
(x - (-7))^2 + (y - (-4))^2 = r^2
(x + 7)^2 + (y + 4)^2 = r^2
We also know that the circle contains the point (-1, -8).
We can substitute these values for x and y, and solve for r:
(-1 + 7)^2 + (-8 + 4)^2 = r^2
36 + 16 = r^2
r^2 = 52
Substituting this value of r^2 into the equation for the circle, we get:
(x + 7)^2 + (y + 4)^2 = 52
Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52
Becky ate 7.5 x 10^5 milligrams of rice. Carter ate 3.1 x 10^6 milligrams of rice. who ate more?
Answer:
The Correct answer is Carter
3. Find the probability of randomly entering each room in the maze shown at right.
a. P(A)
b. P(B)
The probabilities of randomly entering each room in the maze shown at right are:
P(A) = 5/18
P(B) = 1
What is the probability?The probabilities can be determined from the formulas below:
P(A) = 1/3 * 1/2 * 1 + 1/3 * 1/3
P(B) = 1/3 * 1 + 1/3 * 1 + 1/3 *1
To calculate the probabilities, we need to simplify the expressions and do the arithmetic.
Using the formulas you provided:
P(A) = (1/3 * 1/2 * 1) + (1/3 * 1/3) = 1/6 + 1/9 = 5/18
P(B) = (1/3 * 1) + (1/3 * 1) + (1/3 * 1) = 1
Therefore, the probabilities, evaluated to their simplest form, are:
P(A) = 5/18
P(B) = 1
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50 Points! Multiple choice algebra question. If r(x)=x^3-2x+1, find r(2a^3). Photo attached. Thank you!
Answer:
D
Step-by-step explanation:
Answer:
D. [tex]8a^{9} -4a^{3} +1[/tex]
Step-by-step explanation:
Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :
[tex]r(2a^{3} )[/tex] is the same as saying [tex]x=2a^{3}[/tex]So, we have [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]Solve for [tex]r(2a^{3} )[/tex] :
1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]
Start with simplifying [tex](2a^{3})^{3}[/tex][tex](2a^{3})^{3}=2^{3}*(a^{3})^{3}=8*a^{3*3}=8a^{9}[/tex]When you have a quantity raised to a power, or an exponent, you have to distribute the exponent to each term multiplied.When you multiply two terms that are raised to a power, you add the powers.When you divide two terms that are raised to a power, you subtract the power in the numerator from the power in the denominator.When you have a power raised to a power, you multiply the powers.2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]
Simplify [tex]2(2a^{3})[/tex]Multiply two times the quantity[tex]2(2a^{3})=4a^{3}[/tex]3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]
Answer:
So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].
Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]
The supply and demand for a product are related to price by the following equations, where y is the price, in dollars, and x is the number of units, in thousands. Find the equilibrium point for this product.
y=300+40x
y=9300-50x
helpp..
Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:
300 + 40x = 9300 - 50x
Simplifying and solving for x:
90x = 9000
x = 100
Now that we know x, we can use either equation to find y:
y = 300 + 40(100) = 4300
So the equilibrium point is when x = 100 and y = 4300.
Step-by-step explanation:
Could someone help me find the answers and show me how they got it it’s a review for a quiz I have to take for tomorrow
Area of composite shape = 12 + 9
= 21 cm²
How to solve
Area of composite shapes:
13) Figure 1:
Figure1 is a rectangle.
l = 4 cm & w = 2 cm
Area of figure1 = l * w
= 4 * 2
= 8 cm²
Figure2:
Figure2 is a parallelogram
base = b = 4 cm
h = 4 cm
Area of figure2 = b * h
= 4 * 4
= 16 cm²
Area of composite shape = 8 + 16
= 24 cm²
14) Figure1:
Figure 1 is a trapezium. a & b are parallel sides and h is the height
a = 4 cm ; b = 6 cm; h = 4 -2 = 2 cm
Figure2:
Figure2 is a rectangle. l = 6 cm ; w = 2 cm
Area of figure2 = 6*2
= 12 cm²
Area of composite shape = 10 + 12
= 22 cm²
15) Figure 1 & figure 2:
Figure 1 and figure 2 are congruent triangles
base = b = 3 cm & h= 4 cm
= b *h
= 3 * 4
= 12 cm²
Figure3:
Figure 3 is a square.
side = 3 cm
Area of figure3 = side *side
= 3 * 3
= 9 cm²
Area of composite shape = 12 + 9
= 21 cm²
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If you are performing a right-tailed z-statistic test with a sample size n = 100 and a 0.01 significance level, what is the critical value?
If your calculated value of the z-statistic is z = 2.88, what is your conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)?
1. The critical value, according to the z-table, is roughly 2.33. 2. There is enough data to support the alternative hypothesis and reject the null hypothesis.
What is null hypothesis?A null hypothesis is a claim that assumes there is no meaningful difference between two or more variables in a population or that any difference that is detected is the result of chance in statistical hypothesis testing. Typically, it is indicated by H0. A statement that rejects the null hypothesis and assumes that the variables being compared have a substantial difference is known as an alternative hypothesis, or Ha. In contrast to the null hypothesis, which the researcher is attempting to refute, the alternative hypothesis is what the researcher is attempting to prove.
1. We can use a z-table or a calculator to determine the critical value for a right-tailed z-statistic test with a sample size of 100 and a significance level of 0.01. The z-score that equates to the 0.99 probability level, which is the complement of the 0.01 significance level, is the critical value. The crucial value, according to the z-table, is roughly 2.33.
2. We compare the estimated z-statistic value, z = 2.88, to the crucial value, 2.33. The estimated value of z falls in the rejection zone of the null hypothesis because it exceeds the crucial value. As a result, we find that there is enough data to support the alternative hypothesis and reject the null hypothesis.
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What is M in triangle properties
I hope this helps you.
A car park changes £1.50 to each car entering.
The payment station only accepts £1 coins and 50p coins.
Here are the coins collected from the payment station on particular day:
Number of £1 coins 172
Number of 50p coins 256
Assuming each driver paid the exact amount due on that day, work out the percentage of the drivers that paid with three 50p coins.
Answer:
84 paid with three 50p coins.
A container in the shape of a rectangular prism has a height of 2 feet. Its length is four
times its width. The volume of the container is 200 cubic feet. Find the length and width of
the container.
Answer: length = 20 feet and width = 5 feet
Step-by-step explanation: Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.
Find the equation of the linear function
represented by the table below in slope-intercept
form.
X: -3,1,5,9
y: -8,0,8,16
By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.
what is slope?A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).
To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.
With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:
slope = (y change) / (change in x)
slope = (16 - (-8)) / (9 - (-3))
slope = 24 / 12
slope = 2
We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:
y = mx + b 0 + b b = 2(1) + b b = -2
Hence the linear function's slope-intercept equation is:
y = 2x - 2
As a result, the linear function denoted by the table is y = 2x - 2.
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PLEASE HELP !!
(Do not guess please and thank you )
Step-by-step explanation:
A = π r²
r = 3 inches
A = 3.14 × (3)²
A = 3.14 × 9
A = 28.29 square inches
60°
y
Find the value of y.
A. y = 2
B.
4√√3
3
y = 4
C.
D. y = 4√3
8
30°
The value of y is 4, so the answer is option A: y = 4.
What is trigonometric ratios ?
Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
Using the given diagram, we can use the trigonometric ratios to find the value of y.
First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:
sin(30°) = opposite/hypotenuse
sin(30°) = y/8
y/8 = 1/2
y = 8/2
y = 4
Therefore, the value of y is 4, so the answer is option A: y = 4.
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The expression 12x +8 is equivalent to the expression a(bc+c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4). Which statement best explains whether the students answer is correct or incorrect
The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
What is expression?Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.
This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.
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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).
Which statement best explains whether the student's answer is correct or incorrect?
OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).
C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).
OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).
What is the average of these numbers?
45 46 50 52 51 59 55 51 42 44
51 55 60 62 52 54 47 74 52 52
59 52 65 45 58 59 59 52 54 65
50 Points! 2 Multiple choice algebra questions. Photo attached. For questions 5 and 6, use the graph. Determine the values of x between which a real zero is located. Estimate the x-coordinate at which a relative minimum occurs. Thank you!
5. The real zero occurs located
C. between -2 and -16. The x-coordinate at which a relative minimum occurs is at
B. 2What is real zero and relative minimum in a graphIn the context of a graph of a function
A real zero, also known as a root or a solution, is a value of the independent variable (usually denoted as x) for which the value of the dependent variable (usually denoted as y) is equal to zero.
Geometrically, a real zero corresponds to the x-coordinate of a point where the graph of the function intersects the x-axis.
A relative minimum, on the other hand, is a point on the graph where the function has a local minimum value.
Geometrically, a relative minimum corresponds to a point where the graph changes from decreasing to increasing, and is located at the bottom of a valley or a trough.
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Colleen is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Hartford was $250. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer: Increase in percentage by 42% and with baggage 43.2%.
Step-by-step explanation:
we know that the price is increased from $250 to $ 335
the percentage change by increasing the price is
$355 - $ 250 = $105
percentage change will be change/original = 105/250*100 = 42%
additional charges $ 50, $105+ $50 = 155
percentage change = 155/355*100 = 43.2%
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A rectangular pyramid is shown in the figure.
A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
What is the surface area of the pyramid?
The surface area of the pyramid is 113 cm².
What is rectangular pyramid?A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.
The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.
To find the surface area of the pyramid, we need to find the area of each face and then add them up.
Area of the base:
The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:
Area of base = length × width = 7 cm × 5 cm = 35 cm²
Area of the four triangular faces:
Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:
Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²
Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²
There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:
Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face
= 2 × 19 cm² + 2 × 20 cm²
= 78 cm²
Total surface area:
Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:
Total surface area = area of base + total area of four triangular faces
= 35 cm² + 78 cm²
= 113 cm²
Therefore, the surface area of the pyramid is 113 cm²
.
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how long does it take for a deposit of $1300 to double at 9% compounded continuously?
how many years does it take to double? years _ days _
What is the perimeter of the triangle?
Answer:
40 units
Step-by-step explanation:
a = 8
b = 15
To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]8^{2} +15^{2} =x^{2}[/tex]
64 + 225 = c^2
289 = c^2
c = 17
a + b + c = perimeter
8 + 15 + 17 = 40
Answer:
40 units
Step-by-step explanation:
You want the perimeter of the triangle shown in the graph.
DimensionsYou can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.
The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:
c² = a² +b²
c² = 8² +15² = 64 +225 = 289
c = √289 = 17
The long side of the triangle is 17 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:
P = 8 + 15 + 17 = 40
The perimeter is 40 units.
__
Additional comment
A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.
The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)
4)
Northbrook Middle School surveyed 325 students to learn more about their after-schoo
activities. They found that 90 students are in a club and play a sport. 140 total students
play a sport and 200 total students are in a club. Construct a two-way relative freques
table summarizing the data.
Plays a Sport
In a Club
Not In a Club
Total
Doesn't Play a
Sport
Total
Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).
What is frequency?Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.
90 students are in a club and play a sport.
140 total students play a sport.
Therefore, 140 - 90 = 50 students play a sport but are not in a club.
The total number of students who play a sport is 140 + 50 = 190.
200 total students are in a club.
Therefore, 200 - 90 = 110 students are in a club but do not play a sport.
The total number of students who do not play a sport is 325 - 190 = 135.
The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.
This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.
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When two sample means are significantly different
Group of answer choices
The pooled variance estimate should not be used
The difference is too great to attribute to chance
The corresponding population means are significantly different
The difference is of practical importance
When two sample means are significantly different, "the difference is too great to attribute to chance".
What is statistical significance?The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).
Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.
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A man bought two pencils and three biros at a cost of 50, Again he bought three pencils and four biros for 70. find the cost of a pencil and a biro
A quadrilateral is shown.
H
6.5
5.51
What is the area of the quadrilateral? Enter the answer in the box.
The calculated area of the quadrilateral is 35.82 square units.
What is the area of the quadrilateral?Given that
BAse = 6.5
Height = 5.51
To find the area of a quadrilateral, we need to multiply the base by the height.
Area of quadrilateral = base x height
Substituting the given values, we get:
Area = 6.5 x 5.51
Area = 35.815
Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.
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When an athlete hits a ball all of the following would make a difference in the height and distance that the ball goes. ball How hard you hit the swing ● The angle of the is blowing air Which way the wind How hard the wind is blowing Temperature of the Humidity of the air How high you hit the ball
All options except "How high you hit the ball" would affect the ball's height and distance.
Selecting which would make a difference in the height and distanceThe following factors would make a difference in the height and distance that the ball goes when an athlete hits a ball:
How hard you hit the swingThe angle of the swingWhich way the wind is blowingHow hard the wind is blowingTemperature of the airHumidity of the airTherefore, all options except "How high you hit the ball" would affect the ball's height and distance.
When an athlete hits a ball, there are several factors that can affect the ball's trajectory, including the force and angle of the swing, as well as external environmental factors such as wind, temperature, and humidity.
The harder the athlete hits the ball, the more force will be imparted to the ball, and the farther it will travel.
Similarly, the angle of the swing can affect the trajectory of the ball, with a higher or lower angle resulting in different heights and distances traveled.
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What is the solution to the equation 3/5x-4-3√7x+8?
A x = -6
B x=-1
C x = 1
D x = 2
The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To solve the equation 3/5x - 4 - 3√7x + 8 = 0:
First, simplify the expression by combining like terms:
3/5x - 3√7x + 4 = 0 + 8
3/5x - 3√7x + 4 = 8
Next, move the constant term to the right side:
3/5x - 3√7x = 8 - 4
3/5x - 3√7x = 4
Factor out x from the left side:
x(3/5 - 3√7) = 4
Divide both sides by (3/5 - 3√7):
x = 4 / (3/5 - 3√7)
To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):
x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]
x = 12/5 + 12√7/5 / (9/25 - 63/25)
x = 12/5 + 12√7/5 / (-54/25)
x = -10√7/9
Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
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solve for r if $425.83=400(1+r)^5 ? (show explanation please)
Answer: 0.0295
Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.
Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:
$1+r=\sqrt[5]{1.064575}$.
Subtracting 1 from both sides gives $r\approx 0.0295$.
Therefore, your answer would be 0.0295.
3. In a sports centre, the ages of 100 people were recorded as follows: Age Under 20 years 20 to 29 years 30 t0 39 years 40 to 59 years 60 years and over Number of people 30 15 12 14 29 Fri, 24 Mar 2023 Angle (i) complete the table above to show the angle for each categ rounded off to the nearest degree. (ii) construct a pie chart using the circle below.
100 people = 360° of circle
For n people, the degree for the circle is (n×360)÷100
30 people = (30×360)÷100 = 108°
15 people = 54°
12 people = 43.2° ≅ 43°
14 people = 50.4° ≅ 50°
29 people = 104.4° ≅ 104°
Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS
The missing step in the proof is: D. ADCA
What is the missing step and reason of the proof?In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).
Therefore, we have the following proportional sides:
DC/AC = AC/BC
Given that DC = BA (given statement), we can substitute BA for DC in the proportion:
BA/AC = AC/BC
Now, we can cross-multiply to get:
BA * BC = AC²
Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:
BA * BC = AC * AC
Use the definition of congruent sides to replace BA with DC:
DC * BC = AC * AC
And finally, use the substitution property of equality to replace BC with 6 units (given statement):
DC * 6 = AC * AC
From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.
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Mohal plans to repaint some classroom bookcases. He has 1 1/8 gallons of paint. All of the bookcases are the same size and each requires 1/8 gallon of paint. How many bookcases will he be able to paint?
Mohal will be able to paint 9 bookcases for the amount of paint.
What is fraction?An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.
Given that, he has 1 1 /8 gallons of paint.
Thus, number of bookcases are:
1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9
Hence, Mohal will be able to paint 9 bookcases for the amount of paint.
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Given f’(x)=4x-3 compute f(5)-f(-1)
Answer:
To solve this problem, we need to integrate the derivative f'(x) to obtain the function f(x).
∫f'(x) dx = ∫(4x - 3) dx
f(x) = 2x^2 - 3x + C
where C is the constant of integration.
To find the value of C, we need to use the fact that f(0) = 5. Substituting x = 0 into the above equation, we get:
f(0) = 2(0)^2 - 3(0) + C = C
Therefore, C = 5.
Hence, the function f(x) is:
f(x) = 2x^2 - 3x + 5
Now, we can find f(5) and f(-1) and compute their difference:
f(5) - f(-1) = (2(5)^2 - 3(5) + 5) - (2(-1)^2 - 3(-1) + 5)
f(5) - f(-1) = (50 - 15 + 5) - (2 + 3 + 5)
f(5) - f(-1) = 35 - 10
f(5) - f(-1) = 25
Therefore, f(5) - f(-1) = 25.