Which explains how to show that
X=-8/3
is a root of
9×^2+48×+64=0?

a. Graph
9x^2 + 48x + 64 = 0
to show that
x=-8/3
is where the parabola crosses the y axis.

b. Graph
9x^2 + 48x +64 = 0
to show that the parabola's vertex is just above the value
x=-8/3

c. Substitute
x=-8/3
back into
9x^2 + 48x + 64 =0
and simplify to show that a true statement
results.

d. Substitute
x=-8/3
back into
9x^2 + 48x + 64 = 0
and simplify to show the values of
a
c
remain perfect squares.

If the length,breadth, height of cuboid are 16 m, 5 m,4 m , slant height of pyramid is 10m,  height be 6 m then the surface area of composite figure be 444 [tex]m^{2}[/tex].

Given that the length,breadth,height of cuboid are 16m,5 m, 4m and slant height be 10 m and height be 6 m.

Surface area is basically sum of area of all the sides of a figure.

Surface area of composite figure =  area of cuboid less area of common side + area of 2 slant sides of pyramid+area of two triangles.

=2(lb+bh+hl)-(lb)+2(slant height*breadth of cuboid)+2[1/2* length of cuboid* height of triangle)

=2(16*5+5*4+4*16)-16*5+2(10*5)+2[1/2*16*6]

=2(80+20+64)-80+2*50+2(48)

=2(164)-80+100+96

=328-80+196

=248+196

=444[tex]m^{2}[/tex]

Hence the surface area of composite figure having a cuboid and pyramid on top is 444[tex]m^{2}[/tex].

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The example on direct variation is illustrated below based on the information given.

An example will be:

When x = 2, y = 10. Find the value of y when x is 6.

In this case, this will be calculated thus:

y = kx

10 = 2k

k = 10/2

k = 5

Since y = kx.

y = 5 × 6

y = 30

The value of y is 30.

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Answer:

20 + 4y

Step-by-step explanation:

The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).

Answer-4,5

Step-by-step explanation:

Answer:

35%

Step-by-step explanation:

She is saving $0.70/$2.00 weekly.

To convert this into a percentage we covert it to decimal then multiply by 100 :

$0.70/$2.00 = 0.35

0.35 × 100 = 35%

Our final answer is 35%.

Hope this helped and have a good day

The area of the reduced rug is 25 square feet

The dimensions are given as:

Length = 12.5 feet

Width = 10 feet

The area is calculated as:
Area = Length * Width

So, we have:

Area = 12.5 * 10

Evaluate

Area = 125

When reduced by one-fifth, we have:

Area =1/5 * 125

Evaluate

Area = 25

Hence, the area of the reduced rug is 25 square feet

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Answer:

In total she got $555 so we have to divide that to see how much she got per hour.

Step-by-step explanation:

y/x=?

$555/15= $37

Now how much money multiplied by how many hours

$37 X 15 = $555

I hope this helps, if you need any more information just comment!

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Of students in the sample, 90/200 fraction of the students were male.

To find the fraction of male students:

Number of male students = 90

Number of female students = 110

So, total students = 90 + 110 = 200

Fraction of students who were male =  male students / total students

Fraction of students who were male = 90/200

So, 90/200 fraction of the students were male.

Therefore, 90/200 fraction of the students were male.

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The question you are looking for is given here:

A university surveyed its students on their opinions of campus housing. The following two-way table displays data for the sample of

200 students responded to the survey.

Answer:

y = -3x + 4

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y = -3x + 4

Answer:

x < 7

Step-by-step explanation:

The domain encompasses all the "x" values (or inputs) of a function.

The arrow on the left line symbolizes that the function continues into the negative region for infinity. As such, this eliminates option C.

Closed dots are points whose "x" values are included in the function. Open-dots are on points whose "x" values are not included in the function. Although the open-dot on the left line at x = -1 generally means it is not included in the function, the closed dot on the right line overrides this. Therefore, x = -1 is in the domain. The value x = 7 is not within the domain of the function due to the open-dot. This eliminates option B and option D.

With this said, the domain of the function is x < 7.

The expected outcome of spins based on the probability information is 60.

From the information, Joey decides to spin the wheel 60 times. Therefore, the expected outcome of spins is 60.

The thing that the booth owner can do to make the wheel more profitable for himself is to make winning probability less than that of losing.

Here, the booth owner do makes the wheel more profitable for himself as the winning is smaller.

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Answer:

4

Step-by-step explanation:

Slope=rise/run

there is a increase of 4 in y for every increase of 1 in x

Answer:

x < - 9

Step-by-step explanation:

- 4x > 36

divide both sides by - 4 , reversing the symbol as a result of dividing by a negative quantity.

x < - 9

[tex]\boldsymbol{\sf{-4x > 36 }}[/tex]

Divide both sides by −4. Since −4 is <0, the inequality direction is changed.

[tex]\boldsymbol{\sf{x < \dfrac{36}{-4} }}[/tex]

Divide 36 by −4 to get −9.

[tex]\boxed{\boldsymbol{\sf{x < -9}}}[/tex]

The total amount of Chandra's investments after 8 years is $110.03

The formula for calculating the compound interest is expressed as;

A = P(1+r/n)^nt

where

P is the amount invested = $75

r is the rate. = 0.048

t is the time =8years

n = 12 (monthly)

Substitute

A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03

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Answer:

36

Step-by-step explanation:

To answer this question, we need to first understand the notation (f · x)(-2). This is a composite function, and another way to write this is f(g(-2)). This means that we have to find g(-2) and apply the function f to whatever this value is. Let's start by finding g(-2):

[tex]g(x)=x-2\\g(-2)=-2-2\\g(-2)=-4[/tex]

Now that we know g(-2) is -4, we can apply this to f:

[tex]f(x)=x^2-4x+4\\f(-4)=(-4)^2-4(-4)+4\\f(-4)=16-(-16)+4\\f(-4)=16+16+4\\f(-4)=36[/tex]

Therefore, our answer is 36

The design of the experiment above will center around:

The aim of this study is to know  and compare student's level of satisfaction with school cafeteria food services so as to improve the quality of food served at school meal service.

Hence The design of the experiment above will center around:

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the maximum height is 180ft.

The height of the equation is modeled by:

[tex]y = 60t - 5t^2[/tex]

Notice that this is a quadratic equation with a negative leading coefficient, which means that the maximum is at the vertex, then the maximum is at:

[tex]t = -60/(2*-5) = 6[/tex]

To get the maximum height, we need to evaluate the function in t = 6, we will get:

[tex]y = 60*6 - 5*6^2 = 180[/tex]

This means that the maximum height is 180ft.

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Answer:

3x^2 - 7x =0

x(3x-7) = 0

3x - 7 = 0

3x =7

x= 7/3

Answer:  0.6

Explanation:   You need to divide 3 by 5 and it will give you the answer of 0.6

The expression 3 - 7p² + 11(4 + n) to find an example of each kind of expression is;

3 - 7p² + 11(4 + n)

The expression has 3 parts

3 - 7p² + 11(4 + n)

= 3 - 7p² + 44 + 11n

= 47 + 7p² + 11n

Complete question:

Use the expression 3 — 7p2 + 11(4 + n ) to find an example of each kind of expression

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Answer:

True

Step-by-step explanation:

We got the formula for that:

F=ma

now if you replace the given data, it's gonna be

F=5 kg×3m/s²====> F=15kg.m/s²

Based on the calculations, the ratio of AD to DB ​ is equal to 0.6.

A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

From the graph, we have:

Length of AD = 1.5

Length of DB = 2.5

Ratio = AD/DB

Ratio = 1.5/2.5

Ratio = 0.6.

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The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

The equation is given as:

3x+9+4x+x=

Represent the blank with y

So, we have:

3x + 9 + 4x + x = y

Evaluate the like terms

8x + 9 = y

For the equation to have no solution the value of y and 8x + 9 must not be equal.

Take for instance

y = 8x + 1

So, we have:

8x + 9 = 8x + 1

Subtract 8x from both sides

9 = 1

The above equation is false because 1 and 9 are not equal

Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

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Complete question

Use the drop-down menus to complete each equation so the statement about its solution is true.

No Solutions

3x+9+4x+x=

Using the given recipe, he will need 6 cups of milk to make 18 servings.

We know that the recipe for 6 servings, calls for 2 cups of milk.

Miguel wants to do 18 servings, Then he needs to use the recipe:

18 = x*6

Solving the linear equation for x:

x = 18/6 = 3

So he needs to use his recipe 3 times.

And we know that for 6 servings he needs 2 cups of milk, then for 18 he needs:

3*(2 cups) = 6 cups of milk.

Using the given recipe, he will need 6 cups of milk to make 18 servings.

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For the function g(x) we have:

The function g(x) is given by applying transformations to f(x), the transformations are:

The function is:

[tex]g(x) = -(x + 2)^2 + 5[/tex]

The graph is the one you can see below:

There you can see that the vertex is at (-2, 5), then the line of symmetry is:

x = -2.

And we have a maximum at the vertex, which is y = 5.

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Using the quadratic formula, the solutions are:

a) [tex]x = \frac{3 \pm \sqrt{41}}{4}[/tex]

b) [tex]x = 1 \pm 2i[/tex]

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

Item a:

The coefficients are a = 2, b = -3, c = -4, hence:

Item b:

The coefficients are a = 1, b = 2, c = 2, hence:

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Answer:

2.0

Step-by-step explanation:

The work done in lifting the block is 3430 J

From the question, we are to determine the work done in lifting the block

Using the formula,

Work done = mgh

Where m is the mass

g is the acceleration due to gravity

and h is the height

From the question,

m = 50.0 kg

g = 9.81 m/s²

h = 7.00 m

Putting the parameters into the formula,

Work done = 50.0 ×9.8 × 7.00

Work done = 3430 J

Hence, the work done in lifting the block is 3430 J

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