Use the rational zeros theorem to list all possible rational zeros of the following.
h(x)= 7x^4+7x^3-2x^2-5x-5

The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

Learn more about Rotation here:

https://brainly.com/question/1571997

#SPJ1

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

​for such more question on parabola

https://brainly.com/question/9201543

#SPJ8

The number of Cheetos you can buy in the supermarket is 7.

You have $16 and a coupon for a five dollar discount at a local

supermarket . One bag of hot Cheetos cost 3 dollars. Therefore, the

number  of bag of Cheetos you can buy can be calculated as follows:

Therefore, altogether he has 16 + 5(coupon discount)  = 21 dollars to spend

in the super market.

Therefore,

number of Cheetos worth 3 dollars one can buy = 21 / 3

number of Cheetos worth 3 dollars one can buy = 7

learn more on discount here: https://brainly.com/question/28971646

#SPJ1

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

Read more on graphs:

https://brainly.com/question/19040584

#SPJ1

Answer:

Susan has a total of 660 nails

Step-by-step explanation:

John box contains 65 small nails, 40 medium nails, and 45 large nails.

The proportion of John nails is

65/5:40/5:45/5

13:8:9

Total = 30

If Susan has 176 medium nails and same proportion to John's nails

8/30(x) = 176

Where x is the total number of nails for Susan box

X= (176*30)/8

X= 22*30

X= 660 nails

Susan has a total of 660 nails

Answer:

Standard form for straight line

y = m x + b

If x = 0 then y = b = 3

y = m x + 3

Since m is the slope the requested equation is y = x + 3

Answer:

Step-by-step explanation:

y = mx + b for line through (7, 4) and perpendicular to -5x + 9y = - 71

perpendicular lines have negative reciprocal slopes

-5x + 9y = - 71

9y = 5x - 71

y = (5/9)x - 71/9

so a perpendicular line will have slope -9/5

y = (-9/5)x + b

plug in our desired point

4 = (-9/5)7 + b

4 = -63/5 + b

20/5 = -63/5 + b

b = 83/5

y = (-9/5)x + 83/5

5y = -9x + 83

Answer:

A

Step-by-step explanation:

The line is shaded above, so eliminate C and D.

Also, the line has negative slope, so eliminate B.

Thus, the answer is A

Answer:

C.

Step-by-step explanation:

Choose two points on the line and find the slope. For example, let's use coordinates (0,2) and (5,4).

Use the slope formula to find the slope between these points.

y2-y1/x2-x1

4-2/5-0 = 2/5

Slope of the new line is 2/5.

With the slope, compare the two fractions. Set them up side by side and cross multiply. Whichever one gives you the larger number is the larger fraction. Larger slopes are going to be steeper. So, C is right.

Refer to my picture to see what I mean by cross multiplying.

Answer:49

Step-by-step explanation:

A = \(\frac{3+11}{2}\) · 7

= \(\frac{14}{2} \\\) · 7

= 7·7

=49

Answer:

the correct answer is: n ∈ R

Answer:

$14.034

Step-by-step explanation:

40/10 means that the price has a 40% discount and then, a 10% discount from what is left. To calculate the net price, first you have to calculate the price with the 40% discount:

25.99*(1-0.4)= 15.594

Then, you have to calculate the price with the 10% discount:

15.594*(1-0.1)= 14.034

According to this, the net price is $14.034.

Answer:

Step-by-step explanation:

The missing information includes finding the volume of the circle x² + y² = 4 from the x-axis of the squares and the equilateral triangles.

\(x^2 + y^2 = 4\)

Perpendicular to x-axis

\(y = \sqrt{4 -x^2}\)

Area of the square = \(( \sqrt{4-x^2}+ \sqrt{4-x^2})^2\)

\(= (2 \sqrt{4 -x^2})^2 \\ \\ = 4(4-x^2) \\ \\ = 16 - 4x^2\)

Volume  V = \(\int ^2_{-2} (16 -4x^2) \ dx\)

\(= \Big [ 16x - \dfrac{4x^3}{3} \Big]^2_{-2}\)

\(= \Big [32 - \dfrac{32}{3} \Big] - \Big[-32 +\dfrac{32}{3} \Big]\)

\(= \dfrac{128}{3}\)

Area of Equilateral triangle

\(= \dfrac{1}{2}\times 2 \sqrt{4-x^2}\times \sqrt{3}\sqrt{4-x^2}\)

\(= \sqrt{3}(\sqrt{4-x^2})^2\)

\(Volume (V )= \int ^2_{-2}\sqrt{3} (4 -x^2) \ dx\)

\(= 4\sqrt{3} \ x - \dfrac{\sqrt{3} \ x^3 }{3} \Big|^2_{-2} \\ \\ = 16 \sqrt{3} - \dfrac{16\sqrt{3}}{3} \\ \\ = \dfrac{32\sqrt{2}}{3}\)

The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

Learn more about distance here:

https://brainly.com/question/26046491

#SPJ1

Given

A ratio is a _____ of two quantities



A ratio can be expressed as a _______ description, with a ________, or as a ________​

Procedure

A ratio is a comparison of two quantities.

A ratio can be expressed as a word description, with a colon between two quantities, or as a fraction

​

true census  is most likely to be based on a census There are many benefits to choosing a portion of the population selected to represent the population.

• Reducing the cost and time needed to conduct research. Researchers will save more time and money analyzing sample than the whole population.  

• Reducing resource deployment. The manpower needed to analyze a sample is less than the manpower needed to analyze the whole population.  

• Increasing data accuracy. Data taken from the sample will be more accurate than data taken from the whole population because the sample is more willing to join the research.  

• Creating an intensive and exhaustive data. The data taken from a sample will be more intensive and exhaustive because the respondents are minimum.  

learn more about of census here

https://brainly.com/question/1211838

#SPJ4

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

Learn more on age word problems here;

https://brainly.com/question/17043336

#SPJ1

The width of the rectangle is 1/9 cm.

The perimeter of the rectangle is 3.2 cm.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Area = 1/6 cm²

Length = 1.5 cm

Width = w

Now,

Area = length x width

Perimeter = 2 (length + width)

So,

1/6 = 1.5 x w

w = 1/(6 x 1.5)

w = 1/9 cm

And,

Perimeter.

= 2 (1.5 + 1/9)

= 2 x (13.5 + 1)/9

= 29/9

= 3.2 cm

Thus,

The width of the rectangle is 1/9 cm.

The perimeter of the rectangle is 3.2 cm.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ1

With some rewriting, you get

\(\displaystyle \sum_{k=0}^\infty (-1)^k\frac{x^{k+2}}{4^k} = x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k\)

Recall that for |x| < 1, you have

\(\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k\)

So as long as |-x/4| = |x/4| < 1, or |x| < 4, your series converges to

\(\displaystyle x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k = \frac{x^2}{1-\left(-\frac x4\right)} = \frac{x^2}{1+\frac x4} = \boxed{\frac{4x^2}{4+x}}\)

Based on known expressions from Taylor series, the power series \(\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}\)Taylor series-derived formula of the rational function \(\frac{4\cdot x^{2}}{4+x}\).

Taylor series are polynomic approximations used to estimate values both from trascendental and non-trascendental functions. It is commonly used in trigonometric, potential, logarithmic and even rational functions.

In this question we must use series properties and common Taylor series-derived formulas to infer the expression behind the given series. Now we proceed to find the expression:

\(\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}\)

\(x^{2}\cdot \sum\limits_{k = 0}^{\infty} \left(-\frac{x}{4} \right)^{k}\)

\(x^{2}\cdot \left(\frac{1}{1+\frac{x}{4} } \right)\)

\(\frac{4\cdot x^{2}}{4+x}\)

Based on power and series properties and most common Taylor series- derived formulas, the power series \(\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}\) represents a Taylor series-derived formula of the rational function \(\frac{4\cdot x^{2}}{4+x}\). \(\blacksquare\)

To learn more on Taylor series, we kindly invite to check this verified question: https://brainly.com/question/12800011

Answer: x = 2 or x = -2

Step-by-step explanation:

I presume the question is asking for the equation of x^2 - 4 = 0

x^2 - 4 = 0

add 4 to both sides

x^2 = 4

square root both sides

x = sqrt(4)

which is +/- 2

Step-by-step explanation:

If this were to make a triangle, then 30.1 and 0.8 would be the shorter sides and 31 would be the longest side.

The sum of the lengths of the shorter sides is 30.1+0

8=30.9.

Since this is less than the length of the segment that would be the longest side, by the triangle inequality theorem, these side lengths would not make a triangle.

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

Read more on time and maximum height here: https://brainly.com/question/30145152

#SPJ1

-56x + 49y= -14

- 56x + 56y=64

105y=50

y=0.48

-8x+7(0.48)=-2

-8x+3.36=-2

-8x=-5.36

x=0.67

Answer:

(x, y) = (9, 10)

Step-by-step explanation:

-8x + 7y = -2...... (1)

- 8x + 8y = 8......(2)

Multiplying on both sides of the equations (1) & (2) by 8 and 7 respectively, we find:

-64x + 56y = - 16...(3)

-56x + 56y = 56.....(4)

Subtracting equation (4) from equation (3), we find:

-64x + 56y = - 16

-56x + 56y = 56

+ - -

_____________

- 8x = - 72

x = - 72/-8

x = 9

Substituting x = 9 in equation (1), we find:

-8(9) +7y = - 2

-72 +7y = - 2

7y = 72 - 2

7y = 70

y = 70/7

y = 10

(x, y) = (9, 10)

Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

For more such questions on combinations

https://brainly.com/question/28065038

#SPJ8

Answer:

There is no problem stated, but here is the x's for every equations provided:

Step-by-step explanation:

a.) x²+2=36

x²=34

x=√34

b.) 2x + 2 =36

2x= 34

x= 17

c.)2x=36

x= 18

d.) 2x+1=36

2x=35

x=35/2

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

A similar problem, also featuring proportional relationships, is presented at https://brainly.com/question/7723640

#SPJ1