A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00. If the collection contains 25 quarters, how many nickels can be in the collection?

Answers

Answer 1

The total number of nickels that can be collected is 17 and this can be determined by forming the inequality.

Given :

A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00.

The inequality can be formed in order to determine the total number of nickels that can be collected.

Let the total number of quarters be 'x' and the total number of nickels be 'y'. Then the inequality that represents the total number of quarters and nickels contained in the collection is at least 42 is given by:

x + y [tex]\geq[/tex] 42 --- (1)

The inequality that represents that the worth of the coins is at most $8 is given by:

0.25x + 0.5y [tex]\leq[/tex] 8 --- (2)

Now, according to the given data there are a total of 25 quarters in the collection, so, the number of nickels contained in the collection is:

x + y [tex]\geq[/tex] 42

25 + y [tex]\geq[/tex] 42

y [tex]\geq[/tex] 17

So, the total number of nickels that can be collected is 17.

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Answer 2

Final answer:

The collection can contain up to 35 nickels, given that it already includes 25 quarters and the total value does not exceed $8.00.

Explanation:

To determine how many nickels can be in the collection, we must first calculate the total value of the 25 quarters. Since each quarter is worth 25 cents, we multiply 25 quarters by 25 cents to get 625 cents, which is $6.25. The maximum value of the entire collection is $8.00. Thus, we subtract $6.25 from $8.00 to find the remaining value that can be occupied by nickels, which is $1.75. Each nickel is worth 5 cents, so we divide $1.75 by 0.05 (5 cents) to find the maximum number of nickels. $1.75 divided by 0.05 equals 35. Therefore, the collection can contain up to 35 nickels.

Related Questions

A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12 respectively. the probability that the sample mean is larger than 70 equals:

Answers

To solve this problem, we can use the z statistic to find for the probability. The formula for z score is:

z = (x – u) / s

Where,

u = the sample mean = 68

s = standard deviation of the samples = 12

x = sample value = 70

In this case, what is asked is the probability that the sample mean is larger than 70, therefore this corresponds to the right of z on the graph of normal distribution.

z = (70 – 68) / 12

z = 2 / 12

z = 0.17

Therefore finding for P at z ≥ 0.17 using the standard distribution tables:

P (z = 0.17) = 0.5675

But this is not the answer yet since this is the P to the left of z. Therefore the correct one is:

P (z ≥ 0.17) = 1 - 0.5675

P (z ≥ 0.17) = 0.4325 = 43.25%

The probability that the sample mean is larger than 70 is 43.25%

The probability that the sample mean is larger than 70 for a sample size of 40 from a population with a mean of 68 and standard deviation of 12 is approximately 14.69%.

To determine this probability, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means will be approximately normal if the sample size is large enough (n ≥ 30 is a common benchmark).

The standard error of the mean is calculated using the formula:

SE = σ / √n

Where σ is the population standard deviation and n is the sample size.

In this case:
σ = 12
n = 40

Therefore,

SE = 12 / √40 ≈ 1.8974

The z-score is calculated using the formula:

z = (M - μ) / SE

Where M is the sample mean,
μ is the population mean,
SE is the standard error.

Given,
μ = 68
M = 70

Therefore,

z = (70 - 68) / 1.8974 ≈ 1.054

Using the z-table, we find the probability that a z-score is less than 1.054 is approximately 0.8531.

However, we need the probability that the sample mean is greater than 70, so we subtract this from 1,

1 - 0.8531 ≈ 0.1469

Thus, the probability that the sample mean is larger than 70 is approximately 0.1469, or 14.69%.

Express the number as a ratio of integers. 7.5336

Answers

75336 / 10000

division gives you 7.5336

How many cubic feet of space is there in a warehouse that is 610 feet wide by 140 feet deep and has an 18 foot ceiling?

Answers

To solve:
Find the volume by multiplying the length, width, and height together.

(610)(140)(18)=1537200

Answer: 1,537,200 ft^3

Final answer:

The warehouse has a volume of 252,000 cubic feet, calculated using the corrected dimensions of 140 feet in length, 100 feet in width, and an 18-foot ceiling.

Explanation:

To calculate the volume of a warehouse, we use the formula for the volume of a rectangular prism, which is length × width × height. However, the question contains a typo about the width of the warehouse.

We are informed that the correct width is 100 feet, not 610 feet.

Given the corrected dimensions (140 feet by 100 feet with an 18 foot ceiling), we can now calculate the volume of the warehouse.

Volume = length × width × height
= 140 feet × 100 feet × 18 feet
= 252,000 cubic feet.

Therefore, the warehouse has a volume of 252,000 cubic feet of space.

What is the next number in the sequence 5 10 3 15 20 13 25 30?

Answers

We are asked to determine the next numbers in the given sequence such as 5 10 3 15 20 13 25 30. In order for us to answer this problem, we need to find the difference between the two consecutive number and perform subtraction such as shown below:
For 5 and 10, the difference is -5
For 10 and 3, the difference is 7
For 3 and 15, the difference is -12
For 15 and 20, the difference is -5
For 20 and 13, the difference is 7
For 13 and 25, the difference is -12
For 25 and 30, the difference is -5

Now, we can identify the next two numbers in the sequence since we already know that the format of the difference is -5, 7 and -12. So the next numbers are the following:
30 - 7 = 23
23- (-12) = 35

Therefore, the sequence is 5 10 3 15 20 13 25 30 23 35

You are required to take five courses, one each in humanities, sociology, science, math, and music. you have a choice of 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses. how many different sets of five courses are possible?

Answers

Final answer:

By multiplying the course options together for Humanities, Sociology, Science, Math and Music (2*2*6*6*8), we found that there are a total of 576 different sets of five courses.

Explanation:

To answer this question, we have to calculate the number of different sets of five courses. This can be done by multiplying the number of choices available for each requirement. So, if you have 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses to decide from, the calculation would be as follows:

We then multiply these options together (2*2*6*6*8) to get the total number of different sets of courses possible, which is 576.

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To find the total number of different sets of five courses, multiply the number of choices for each course category: 2 (Humanities) × 2 (Sociology) × 6 (Science) × 6 (Math) × 8 (Music). This results in 1152 different sets of five courses.

To determine the number of different sets of five courses possible, we need to consider the choices available for each category:

- Humanities: 2 choices

- Sociology: 2 choices

- Science: 6 choices

- Math: 6 choices

- Music: 8 choices

The total number of different sets of five courses can be found by multiplying the number of choices in each category together. Here is the calculation:

2 × 2 × 6 × 6 × 8

Let's calculate this step-by-step:

1. 2 × 2 = 4

2. 4 × 6 = 24

3. 24 × 6 = 144

4. 144 × 8 = 1152

Therefore, the number of different sets of five courses possible is: 1152

midpoint of 4 – 3i and –2 + 7i please help!!!!!

Answers

hello :
let : z = 4-3ii z' = -2+7i
the distance between the points 4-3i and -2+7i is : |z - z' |
|z - z' | = |4-3i+2-7i| = |6-10i | =√(6²+(-10)²) =√136

PLEASE HELP 50 POINTS
A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.

Team Low High Range Mean Median IQR σ
Team A 22 58 36 42.1 44 18.25 10.35
Team B 38 49 11 43.9 44.5 3.5 2.97
Team C 27 36 9 31.8 32 3.75 2.55

Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)

Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically. (5 points)

Answers

Part A: Team C should be chosen if the club wants to award the team that has the most consistent scoring among its team members
Part B: Team B should be chosen if the club wants to award the team w/ the highest average score
hope this helps:)
please mark thanks and brainliest:)

Part A: Team A, because they constantly win and have the most wins.

Part B: Team A, because they have the highest median.

Your welcome:)

if it was wrong I am sorry:(

What reference angle in the first quadrant corresponds to theta = -120? Answer in radians.

Answers

To draw theta=-120° in the unit circle, we move clockwise 90°, then another 30°.

This means that we pass the fourth quadrant and stop in the third quadrant.

The reference angle of an angle theta in the third quadrant, is theta + 180°.

So the reference angle of -120° is -120°+180°=60°.

360° are 2π Radians
then 60° are 1/6 of 2π Radians = π/3 Radians

Answer: Reference angle is π/3 Radians

Answer:

Answer: Reference angle is π/3 Radians

Step-by-step explanation:

linear function graph express in slope intercept form

Answers

The slope intercept form is y=(1/4)x-4

To the nearest degree what is the measure of each exterior angle of a regular hexagon ?

a.60°
b.45°
c.30°
d.51°

Answers

This is the concept of geometry, the total sum of angles in a hexagon is given by:
(n-2)*180
=(6-2)*180
=720
the size of each interior angle will be:
120°
N/B
the exterior and interior angles are supplementary to each other.
Therefore the size of the exterior angle will be:
180-120
=60°
the answer is A

Answer:

Step-by-step explanation:

The sum of measures of all the exterior angles of ANY POLYGON is 360°.

The measure of each exterior angle of ANY POLYGON is [tex]\frac{360}{n}[/tex]

where [tex]n[/tex] is the number of sides of the polygon

A hexagon has 6 sides, thus the measure of each exterior angle of a hexagon is:

[tex]\frac{360}{6}=60[/tex] degrees

Answer choice A is correct.

Find the period of the function. y = 5 cos one divided by twox

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\\\ f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\ f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}} \end{array} \\\\ -------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ [/tex]

[tex]\bf \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\[/tex]

[tex]\bf \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]

so.. with that template in mind, let's see

[tex]\bf \begin{array}{llll} y=5cos&\left(\frac{1}{2}x\right)\\ &\ \uparrow \\ &\ B \end{array}\qquad period\qquad \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{1}{2}}\implies \cfrac{2\pi }{1}\cdot \cfrac{2}{1}\implies 4\pi [/tex]

How many square meters are in 350 square centimeters?

Answers

There are 3.5 square meters in 350 square centimeters. A way to help remember this is that the prefix "centi" means one hundred, and there are a hundred centimeters in one meter. Hope this helps:)

~Ash

Final answer:

To convert 350 square centimeters to square meters, divide by the conversion factor that 1 square meter equals 10,000 square centimeters, resulting in 0.035 square meters.

Explanation:

To convert 350 square centimeters to square meters, we should remember that 1 square meter is equal to 10,000 square centimeters because 1 meter is equal to 100 centimeters and for area, we need to square that conversion (100 cm × 100 cm).

We start with the given quantity of 350 square centimeters. Then, we use the conversion factor 1 square meter is 10,000 square centimeters to perform the calculation, which gives us:

350 cm² × (1 m² / 10,000 cm²) = 0.035 m².

Therefore, 350 square centimeters is equal to 0.035 square meters.

In science class, Savannah measures the temperature of a liquid to be 50∘ Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit. What is the temperature of Savannah's liquid to the nearest degree Fahrenheit

Answers

Final answer:

To convert the temperature of Savannah's liquid from Celsius to Fahrenheit, use the equation °F = (°C × 9/5) + 32. Savannah's temperature in Celsius is 50°, so her temperature in Fahrenheit is 122°F.

Explanation:

To convert the temperature from Celsius to Fahrenheit, you can use the equation:
°F = (°C × 9/5) + 32.
In this case, Savannah's temperature in Celsius is 50°. Using the equation, we can calculate her temperature in Fahrenheit as:
°F = (50 × 9/5) + 32 = 122°F.
Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.

Final answer:

Savannah's liquid, initially measured at 50°C, converts to 122°F using the formula F = C x (9/5) + 32.

Explanation:Converting Celsius to Fahrenheit

To convert the temperature from degrees Celsius to degrees Fahrenheit, we use the conversion formula: F = $ C \times \frac{9}{5} + 32 $, where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.

In Savannah's case, she measured the temperature as 50°C. Applying the conversion formula:

First, multiply the Celsius temperature by $ \frac{9}{5} $50 \times \frac{9}{5} = 90Then, add 32 to this result to find the Fahrenheit temperature.90 + 32 = 122

Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.

Outside a home there is a keypad that will open the garage if the correct four digit code is entered.? How many codes are possible?

Answers

Assume that none of the digits on the keypad are repeated. This means that we have 10 digits: 0,1,2,3,4,5,6,7,8,9.

The number of ways to arrange 10 distinct digits is
10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800

Answer: 3,628,800
That is 3 million, 628 thousand, and 800.

Final answer:

There are 10,000 possible codes that can be entered into the keypad to open the garage.

Explanation:

The number of possible codes is determined by the number of choices for each digit of the code. In this case, there are 10 possible choices for each digit (0-9). Since there are 4 digits in the code, we can multiply the number of choices for each digit together to find the total number of possible codes: 10 x 10 x 10 x 10 = 10,000. Therefore, there are 10,000 possible codes that can be entered into the keypad to open the garage.

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What is the value of 10 C 2

Answers

The formula to use is the nCr combination formula
n C r = (n!)/(r!*(n-r)!)
where the exclamation marks indicate factorial notation

Plug n = 10 and r = 2 into the formula
n C r = (n!)/(r!*(n-r)!)
10 C 2 = (10!)/(2!*(10-2)!)
10 C 2 = (10!)/(2!*8!)
10 C 2 = (10*9*8!)/(2!*8!)
10 C 2 = (10*9)/(2!)
10 C 2 = (10*9)/(2*1)
10 C 2 = 90/2
10 C 2 = 45

Answer: 45

What equation results from completing the square and then factoring? x2 + 6x = 13

Answers

Step 1: Subtract 13 from both sides.
x^2+6x−13=13−13x^2+6x−13=0
Step 2: Use quadratic formula with a=1, b=6, c=-13.
x=−b±√b2−4ac2ax=−(6)±√(6)2−4(1)(−13)2(1)
x=−6±√882
x=−3+√22 or x=−3−√22
Answer would be
x=−3+√22 or x=−3−√22

WILL GIVE BRAINLIEST PLEASE HELP!!

What is the fifth term of the recursive formula an=2an-1 with the first term of 3?

A.
7
B.
17
C.
33
D.
65

Answers

Hi.

Your answer is going to be

C.) 33

Hope this helps! :)

Find the volume of a sphere that has a surface area of 16 sq. in.
A. (32/3) cubic inches
B.8 cubic inches
C.(4/3) cubic inches

Answers

Given the surface area of the sphere, for us to obtain the volume we need to get the value of the radius. The surface area of the sphere is given by:
S.A=4πr^2
hence the radius can be calculated as follows;
16=4πr^2
4=πr^2
r=(4/π)^(1/2)
volume of a sphere is given by:
V=4/3πr^3
=4/3*π*(4/π)^(1/2))^3
=32/3 cubic inches

Answer:

A is the answer

Use the equation and type the ordered-pairs.

y = log 3 x

{(1/3,____,)(1,___), (3,___),(9,____),(27,____),(81,___)}

Answers

I don't know if the equation is log of 3 x or natural log( log of 10) so I'll just assume that it is log of 3

-1,0,1,2,3,4 is the answer for y according to order

Answer:

[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]

Step-by-step explanation:

Here the "X" Values are given, thus the corresponding "Y" values will be

[tex]Y = log (3 X)\\a) X = \frac{1}{1} , Y = log (3 * \frac{1}{3} ) = log (1) = 0\\b) X = 1, Y = log (3*1) = log (3) = 0.477\\c) X = 3, Y = log (3*3) = log (9) = 0.954\\d) X = 9, Y = log (3*9) = log (27) = 1.43\\e) X = 27, Y = log (3* 27) = log (81) = 1.90\\f) X = 81, Y = log (3 * 81) = log (243) = 2.385\\[/tex]

So the pattern would be

[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]

the ratio of the corresponding side of two regular polygons is 3:4 the area of the larger polygon is 320 m squared what is the area of the smaller polygon?

Answers

The area of the smaller polygon with a side ratio of 3:4 is 180 m2 for the smaller polygon.

When dealing with the areas of similar polygons, if the ratio of corresponding sides is given, such as 3:4 in this case, the ratio of their areas is the square of the ratio of their sides. This is because the area is a two-dimensional measure, so each dimension is scaled by the ratio.

Given that the area of the larger polygon is 320 , we establish that the scale factor is 3 for the smaller polygon and 4 for the larger one.

To find the area of the smaller polygon, we use the fact that the ratio of the areas is (3/4)2 = 9/16.

This means that the area of the smaller polygon is 9/16 times the area of the larger polygon. Therefore, focusing on the comparison of areas, we calculate:

Area of smaller polygon = (9/16) x Area of larger polygon

= (9/16) x 320

Area of smaller polygon = 180

geometry. helppp!!! please explain this

Answers

Answer: 10

----------------------------------------------

Explanation:

Segment TU must be congruent (equal in length) to segment UV in order for the angle TSV to be bisected by segment SU

Bisected = cut in half

So because TU = UV, we can say,

TU = UV
3x+18 = 4x+8
3x+18-3x = 4x+8-3x
18 = x+8
18-8 = x+8-8
x = 10

An electronic device that previously sold for $21 has been reduced to 17.43. the price reduction, rounded to the nearest whole percent is

Answers

percent decrease = (new number - original number) / original number...* 100
= (21 - 17.43) / 21....* 100
= 3.57 / 21....* 100
= 0.17 * 100
= 17%.....the price reduction was 17%

The price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.

What is whole number?

The whole numbers are the part of the number system which includes all the positive integers from 0 to infinity. These numbers exist in the number line.

What is Percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

According to question, an electronic device that previously sold for $[tex]21[/tex] has been reduced to [tex]17.43[/tex]

We have to find the price reduction, rounded to the nearest whole percent .

So percentage reduction

[tex]=\frac{21-17.43}{21}[/tex]×[tex]100[/tex]%

[tex]=0.17[/tex]×[tex]100[/tex]%

[tex]=17[/tex]%

Hence, price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.

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Find 3 consecutive even intergers if the sum is 108

Answers

x+ (x+2)+(x+4)= 108
3x+6= 108
3x=102
x= 34

Final answer: 34, 36, 38

please help, show me the steps

Answers

let's say, the number is "a".

what's three times "a"? well, 3*a or 3a.

ok... what's four more than that? well, 3a + 4

what's the square root of that? well, [tex]\bf \sqrt{3a+4}[/tex]

alrite, and we know that's equal to 7...so

[tex]\bf \sqrt{3a+4}=7\impliedby \textit{squaring both sides} \\\\\\ (\sqrt{3a+4})^2=7^2\implies 3a+4=49\implies 3a=45\implies a=\cfrac{45}{3} \\\\\\ \boxed{a=15}[/tex]

Please Help!! Find the measure of angle 2. Image Attached

Answers

opposite angles = 180 degrees

180-111 = 69

angle 2 = 69 degrees

Foe the AP given by a1,a2,......,an,...with non zero common difference, the equation satisfied are

Answers

The given sequence is
a₁, a₂, ..., [tex] a_{n} [/tex]

Because the given sequence is an arithmetic progression (AP), the equation satisfied is
[tex] a_{n}=a_{1}+(n-1)d [/tex]
where
d = the common difference.

The common difference may be determined as
d = a₂ - a₁

The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..

The sum of the first n terms is
[tex]S_{n}= \frac{n}{2} (a_{1}+a_{n})[/tex]

Example:
For the arithmetic sequence
1,3,5, ...,
the common difference is d= 3 - 1 = 2.
The n-th term is
[tex]a_{n}=1+2(n-1)[/tex]

For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100

In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).

Answers

When you have a set of data points and you want to get a model out of it, you do data fitting. The first thing to do is plot the points using a scatter plot type of chart as shown in the picture. I used MS Excel as a tool for data fitting. On the left side of the picture, I used linear fitting. Then, it gives you the linear equation y=0.2907x + 2.2643. It has a correlation coefficient, R^2, of 0.9595. This measures how good your data fits the model equation. The closer it is to 1, the better. However, it is rare to get 1 because that is very ideal. A R^2 of 0.9595 is very satisfactory already. But if you want an even better model, the right side of the picture shows data fitting on a quadratic equation with an equation of y=0.0209x^2 +0.506x+2.0232 with R^2 of 0.9992.

Answer:

The closer this value is to 1 or -1, the better the fit. For linear, the correlation coefficient R2=.96. For quadratic, the R2=.99. For exponential, the R2=.91. This means quadratic is the best fit, very good actually since .99 is very close to 1.

Step-by-step explanation:

Write the equation in exponential form.

Answers

the answer is D. ( btw,the picture quality sucks,try cropping it)

andy states, " if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."

A.True
B.False

Answers

A. True, to bisect is to divide into equal or congruent halves. Because you can do so it means its going to be a parallelogram.

The statement "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram." is True .

What is parallelogram?

"It is a quadrilateral whose opposite sides are parallel and equal in length."

What is diagonal?

"It is a straight line that connects the opposite corners of a polygon through its vertices."

According to the question

The statement states that

"if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."

Now ,

As per properties of parallelogram

In any quadrilateral the two diagonals bisect each other is a parallelogram .

Hence, The statement is True .

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If f(x)=x-7 and g(x)=x^3, what is G(f(x))?

A. x^3+x-7
B. x^3(x-7)
C. X^3-7
D. (x-7)^3

Answers

replace the 'x' in the formula for g(x) by f(x):-

g(f(x)) = (x-7)^3

Its D

Answer:

D. [tex](x-7)^3[/tex]

Step-by-step explanation:

Given functions are,

[tex]f(x) = x-7-----(1)[/tex]

[tex]g(x)=x^3-----(2)[/tex]

Now,

[tex]g(f(x))=g(x-7)[/tex] ( From equation (1) ),

[tex]=(x-7)^3[/tex] ( From equation (2) ),

[tex]\implies g(f(x)) = (x-7)^3[/tex]

Hence, Option D is correct.

Other Questions

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