i need help with this question parts c d and e

Solution:

Suppose you are measuring a moving box to see if it has enough room in it.

The moving box is a cube.

Given that the length of one side is 2 ft. long, i.e.

To find the volume of a cube, the formula is

Substitute for l into the formula above

Hence, the volume of the box is 8 ft³

Direct Variation is of the form (directly proportional);

While indirect variation (inversely proportional) is of the form;

So, for each of the given question we want to determine if they are direct or indirect variation;

1.

Therefore, this is a Direct variation with proportionality constant;

2.

Therefore, this is a Direct variation with proportionality constant;

We can see the problem states that P = 2(x+3) and also states that P=4x

Those equations lead to the expression

2(x+3)=4x

Operating

2x+6=4x

Subtracting 2x

6 = 2x

Solving for x

x = 6/2 = 3

Thus, the perimeter is

P = 2(3+3) = 12 units

Answer

x = 6

Explanation:

m<3 and m<4 are supplementary angles

supplementarrh angles is 180 degrees

m<3 + m<4 = 180

13x - 13 + 8x + 67 = 180

collect the like terms

13x + 8x - 13 + 67 = 180

21x + 54= 180

Isolate 21x

21x = 180 - 54

21x = 126

divide both sides by 21

21x/21 = 126/21

x = 6.

Therefore, x = 6

[tex]\left(\cfrac{8}{3}\right)^{-2} \left(\cfrac{3}{4}\right)^{-3}\implies \left(\cfrac{3}{8}\right)^{+2} \left(\cfrac{4}{3}\right)^{+3}\implies \cfrac{3^2}{8^2}\cdot \cfrac{4^3}{3^3}\implies \cfrac{4^3}{8^2}\cdot \cfrac{3^2}{3^3} \\\\\\ \cfrac{64}{64}\cdot \cfrac{1}{3}\implies 1\cdot \cfrac{1}{3}\implies \cfrac{1}{3}[/tex]

Given:

Using the trigonometric identity:

We have the following:

replacing:

P (2,13) = (x1,y1)

Q(7,1) = (x2,y2)

The answer is 13 units

SOLUTION

Given the equation as seen below, we can use the following steps to get the factors

Step 1: Remove the bracket by multiplying the value outside the bracket with the one inside the bracket using the distributive law. We have:

Step 2: Now that we have a quadratic equation, we solve for x using the quadratic formula:

Hence, it can be seen from above that the factors will be -7 or 11/3.

The question is given to be:

Step 1

Multiply every number by 100:

Step 2

Subtract 370 from both sides:

Step 3

Subtract 175x from both sides:

Step 4

Divide both sides by 200:

ANSWER

The correct option is OPTION B, the SECOND OPTION.

Solution:

The first set given as;

Then in list form, the set is;

Also, the second set given as;

Then, in list form, the set is;

The intersection of the two sets is;

Thus, the solution in interval notation is;

ANSWER: (-3,-1)

Answer:

The number of years you should invest the principal is;

Explanation:

Given;

Recall that the formula for simple interest is;

substituting the given values;

Therefore, the number of years you should invest the principal is;

We can also solve as;

then we can divide both sides by 21.98;

60

1) Considerando que 57 es 95% de algun numero, vamos escribir esta ecuacion

0.95x = 57 Escribindo 95% como 0.95, dividir los dos lados por 0.95

x =57/0.95

x=60

2) Asi 57 es 95% de 60.

In order to find the minimum and maximum value in the given interval, first let's find the vertex coordinates:

Since the coefficient a is positive, so the y-coordinate of the vertex is a minimum point, therefore the absolute minimum is (4,-48).

Then, to find the maximum, we need the x-coordinate that is further away from the vertex.

Since 0 is further away from 4 than 7, let's use x = 0:

Therefore the absolute maximum is (0,0).

To solve a literal equation means to express one variable with respect to the other variables in the equation. The most important part of a literal equation is to isolate or keep by itself a certain variable on one side of the variable (either left or right) and the rest on the other side

Solving multistep equations takes more time and more operations compared to solving a literal equation.

∠2 and ∠3 are alternate interior angles. In order to A II B, the alternate interior angles must be equal.

Then,

To find x, subtract x from both sides of the equation:

Now, add 10 to both sides of the equation:

Finally, divide both sides by 2:

Answer: x = 20.

The given expression is

y + y - (y - x)

We would substitute x = 1 and y = 4 into the expression. it becomes

4 + 4 - (4 - 1)

8 - 3

= 5

the correct answer is 5

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

small rectangle

length = 4

perimeter = 28

big rectangle

length = 12

perimeter = ?

Step 02:

small rectangle

perimeter = 2l + 2w

28 = 2 * 4 + 2 w

28 - 8 = 2w

20 / 2 = w

10 = w

big rectangle

4 w = 10 * 12

w = 120 / 4 = 30

Perimeter = 2*12 + 2*30

= 24 + 60 = 84

The answer is:

The perimeter of the big rectangle is 84.

we have the inequality

12x > 3(5x-2)-15

step 1

apply distributive property right side

12x > 15x-6-15

combine like terms right side

12x > 15x-21

step 2

Adds both sides 21

12x+21 > 15x-21+21

simplify

12x+21 > 15x

step 3

subtract 12x both sides

12x+21-12x > 15x-12x

21 > 3x

step 4

Divide by 3 both sides

21/3 > 3x/3

7 > x

Rewrite

STEP 1:

We'll derive an expression for the width and the length

STEP 2:

Next, We then derive an expression for the perimeter substituting w as a function of l

STEP 3:

Solve for l and subsequently w

Therefore, length = 72 ft and width = 48ft

Let the total number of marbles in the bag be 'x'.

Given that exactly 25% of the total marbles are black,

Also, given that there are total 8 marbles in the bag,

Then the number of black marbles will be obtained by substituting x=8,

Thus, there are 2 black marbles in the bag.

Answer:

2 cats and 2 dogs

Explanation:

Representations:

x = number of cats sold

y = number of dogs sold

Equations:

We know that it sells a total of 4 pets, so the sum of the number of cats and dogs is 4. So:

x + y = 4

On the other hand, they make $300, and they make $50 for each cat and $100 for each dog, so:

$50x + $100y = $300

So, the system of equation is:

x + y = 4

50x + 100y = 300

Graph:

Now, we need to graph the equations, so we need to identify two points for each equation:

For x + y = 4

If x = 0, then:

0 + y = 4

y = 4

If x = 4, then:

4 + y = 4

4 + y - 4 = 4 - 4

y = 0

For 50x + 100y = 300

If x = 0, then:

50(0) + 100y = 300

100y = 300

100y/100 = 300/100

y = 3

If x = 4, then:

50(4) + 100y = 300

200 + 100y = 300

200 + 100y - 200 = 300 - 200

100y = 100

100y/100 = 100/100

y = 1

Therefore, we have the points (0, 4) and (4, 0) to graph the line of the first equation and the points (0, 3) and (4, 1) to graph the line of the second equation.

So, the graph of the system is:

Therefore, the solution is the intersection point (2, 2), so they sold 2 cats and 2 dogs that day.

EXPLANATION

The transformations that would map Figure 1 onto Figure J are:

A rotation followed by a translation

Given:

Base of a triangle 24m and height = 30m

Required:

Find the area of a triangle.

Explanation:

We have formula for area of triangle

Now,

Answer:

The area of triangle is 360 meter square.

Morgan wants to order at least $45 worth of merchandise.

She spent $8 and $19. m represents the amount of money she needs to spend to get free shipping. The inequality is:

8 + 19 + m ≥ 45

m ≥ 45 - 8 - 19

m ≥ 18

Answer:

x = 10

Explanation:

Because the transverse lines are parralell, the following must be true

cross multipication gives

which simplifies to give

subtracting 2x from both sides gives

subtracting 6 from both sides gives

Hence the value of x is 10.

In this case, we'll have to carry out several steps to find the solution.

Step 01

Data:

Graph:

Height of Golf Ball

Step 02:

functions:

We must analyze the graph to find the solution.

Function:

Non linear

intercepts:

x-intercepts: 0 and 120

y-intercept: 0

symmetry:

x = 50

positive:

domain: (0 , 120)

negative:

there are no negative values

increasing:

interval on x: (0 , 50)

decreasing:

interval on x: (50, 120)

That is the full solution.

Given:

To find: The value of x when

Explanation:

Since,

We can write it as,

Hence, the solution is x = -5, and 3.

Final answer: The solution is,

1) Notice that:

Grouping like terms we get:

Therefore:

Then the zeros of h(r) are:

2) Notice that:

Therefore the vertex of the given parabola is:

Answer:

1)

2) Vertex:

As a general rule, we know that the area of a dilated figure is the area of the original figure multiplied by the square of the scale factor. We can see this in the following formula:

where A is the area of the original figure, A' is the area of the dilated figure and k is the scale factor.

In this case, we have that the area of the dilated figure (trapezoid A'B'C') is 12 square units, and the scale factor is k = 2/3. Then, using the equation we get the following:

therefore, the area of trapezoid ABCD is 5 1/3 square units

A cosine function is given in the form:

where |A| is the amplitude, h is the horizontal shift (also called a phase shift) and k is the vertical shift.

The function is given to be:

Therefore, the amplitude is 8.