We are reviewing a module and I don't remember how to do it.

1. If the cake rises by ¹/₃ as it bakes, the number of cups of cake batter needed for the four cakes is 140.

2. If ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides, the number of cups of icing needed for the four cakes is 47.

The number of cups of cake batter and icing can be determined using the mathematical operations of multiplication, addition, division, and subtraction.

First, the volumes of each cake and its batter are calculated using the given dimensions and the rise.

Using the division operation, the number of cups of cake batter for each cake is determined and multiplied by four.

We understand that the normal volume of the cake will increase with the icing, helping us to calculate the increased volume after the icing.

The difference between the two volumes becomes the volume of the icing required, which is divided by 14.4 in³ to get the number of cups of icing required.

The volume of each cake = Length x Width x Height

Length = 14 inches

Width = 12 inches

Height = 4 inches (2 x 2)

= 12 x 14 x 4

= 672 in³.

Rise of the cake as it bakes =  ¹/₃

The normal volume before rising = 1

Risen volume = 1¹/₃

1¹/₃ = 672 in³

The normal volume of cake batter before the ¹/₃ rise = 504 in³ (672/1¹/₃).

1 cup = 14.4 in³, the total cups for each cake = 35 cups (504 in³/14.4 in³).

The total cups of cake batter for the 4 cakes = 140 cups (35 x 4).

The total quantity of icing = 1¹/₄ (¹/₄ + ¹/₂ + ¹/₂).

The new volume after the icing = 840 in³ (672 x 1¹/₄)

The difference in volume after the icing = 168 in³ in (840 in³ - 672 in³)

If 1 cup = 14.4 in³, the cups of icing for each cake = 11.67 cups (168 in³/14.4 in³).

The total cups of icing for the 4 cakes = 47 cups (11.67 x 4).

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Four double-layered cakes, each 12.0 in. x 14.0 in., have been ordered for a special event.  Each layer is 2.0 in. high.

a) If the cake rises by ¹/₃ as it bakes, how many cups of cake batter are needed? (1 cup = 14.4 in³.  Hint: The ¹/₃ rise should be treated as a constant.)

b) How many cups of icing are needed if ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides? (Assume icing is not layered on top of the icing. 1 cup = 14.4 in³.)

The slope-intercept form is an equation as follows:

Then, we need to change the original equation in this equivalent:

Dividing the total equation by 7, we have:

Therefore, the slope-intercept form is:

We have to find the value of z and x.

We assume that lines g and h are parallel.

Then, z and the angle with measure 85° are consecutive interior angles.

As they are conscutive interior angles, their measures add 180°.

Then, we can write:

Then, we can relate the angle with measure z with the angle with measure (6x-109). They are vertical angles and, therefore, they have the same measure.

Then, we can write:

Answer: z = 95 and x = 34.

S = 2(a*b + a*c + b*c)

= 2 (12*15 + 12*6 + 15*6)

= 2 (342)

= 684 ft^2

       A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

f(x)=3(x−1)2

Find the given parabola's characteristics.

Lessen the steps you tap...

Vertex form is to be used, y=a(x−h)2+k,

to calculate the values of a, h, and k.

a=3

h=1

k=0

The parabola widens because the value of an is positive.

opens up

Find the (h,k) vertex. ( 1 , 0 )

Calculate p, the distance between the focus and the vertex.

To continue, tap...

1/ 12

Locate your focus.

To continue, tap... ( 1 , 1/ 12 )

By identifying the line that connects the vertex with the focus, you may determine the axis of symmetry.

x = 1

 The horizontal line that results from deducting p from the vertex's y-coordinate k depends on whether the parabola opens up or down. This line is known as the directrix.

y = k − p

Simplify the formula after substituting the known p and k values.

y = − 1 /12

Analyze and graph the parabola using its characteristics.

Direction: opens up

vertices: ( 1, 0 )

Focus: ( 1 , 1 /12 )

x = 1 is the symmetry axis.

Direction: y = /1 12.

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Answer: 71.25

This is not of of the options, but is the right answer.

Step-by-step explanation:

7 x 5 + 42 - 23 / 4 =

Step 1: Make parentheses

(( 7 x 5 ) + 42) - ( 23 / 4) =

Step 2: Solve parentheses ( Multiplication and division first )

(35 + 42) - 5.75 =

Step 3: Solve parentheses ( Addition )

77 - 5.75 =

Step 4: Subtract

= 71.25

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The linear function to represent the number of mulch delivered to a site  is y = 29x + 35

In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

For this question, we can represent the cost of having x cubic yards of mulch delivered to a site. For a standard linear function, it can be represented as y = mx + c

m = slope

c = intercept

We can use this concept to write a linear function to represent this problem:

y = mx + c

y = 29x + 35

In this case, the slope is 29 and the intercept is 35. The slope in this situation is the cost of the mulch and the amount charged by the business is the intercept.

The equation representing this problem is y = 29x + 35

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The number of miles that she need to bike on the last day so that her average (mean) is 63 miles per day is 62 miles.

The mean is the average of a set of numbers. Let the biking of the last day be represented as x. This will be:

(61 + 67 + 66 + x) / 4 = 64

(194 + x) / 4 = 64

Cross Multiply

194 + x = 64 × 4

194 + x = 256

Collect like terms

x = 256 - 194

x = 62

The miles is 62 miles.

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The equation of a line in slope-intercept form can be written like this:

y = mx + b

Where m is the slope and b is the y-intercept of the line.

In this case, the slope of the line is 1/2, then we can rewrite the above equation like this:

y = (1/2)x + b

We are also told that this line passes through (2, -4), by replacing 2 for x and -4 for y into the above equation, we can solve for the value of b, like this:

-4 = 2(1/2) + b

-4 = 1 + b

-4 - 1 = 1 - 1 + b

-5 = b

b = -5

Then, we can rewrite the equation of the line, like this:

y = (1/2)x - 5

Then, the last option is the correct answer

Given the quadratic equation:

Let's solve for the following:

• (a) g(-3)

To solve for g(-3), substitute -3 for x and evaluate.

Thus, we have:

Hence, we have:

g(-3) = 46

• (b) To determine the coordinates of the point given in question (a).

In the function, g(x) can also be written as y.

Thus, from g(-3), we have the following:

x = -3

y = 46

When x = -3, the value of y = 46

In point form, we have the coordinates:

(x, y) ==> (-3, 46)

Therefore, the coordinates of the given point by the answer in (a) is:

(-3, 46)

• (c) Evaluate g(2a).

To evaluate g(2a), substitute 2a for x in the equation and evaluate.

Thus, we have:

ANSWERS:

• (a) g(-3) = 46

• (b) (-3, 46)

• (c) g(2a) = 12a² - 10a + 4

The Solution:

The given inequality is

Clearing the brackets, we get

Collecting the like terms, we get

So, the solution is true for all real values of x.

The interval notation of the solution is

It is expected that the cost of gas will increase as the number of gallons increases and decrease as the number of gallons decrease. This is a direct proportion

As such, if

12 gallons of gas cost $26.68

15 gallons will cost 15/12 * $26.68

= $33.35

15 gallons of gas will cost $33.35

Let's begin by listing out the information given to us:

Cost of Radio (c) = $20

Jane's saving (s) = $15

% of radio cost saved = (Jane's saving / Cost of Radio) * 100%

Jane has saved 75% of the radio cost

Answer:

3

Step-by-step explanation:

Given expression:

[tex]\dfrac{(14^2-13^2)^{\frac{2}{3}}}{(15^2-12^2)^{\frac{1}{4}}}[/tex]

Following the order of operations, carry out the operations inside the parentheses first.

Apply the Difference of Two Square formula  [tex]x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]

to the operations inside the parentheses in both the numerator and denominator:

[tex]\implies \dfrac{((14+13)(14-13))^{\frac{2}{3}}}{((15+12)(15-12))^{\frac{1}{4}}}[/tex]

Carry out the operations inside the parentheses:

[tex]\implies \dfrac{((27)(1))^{\frac{2}{3}}}{((27)(3))^{\frac{1}{4}}}[/tex]

[tex]\implies \dfrac{(27)^{\frac{2}{3}}}{(81)^{\frac{1}{4}}}[/tex]

Carry out the prime factorization of 27 and 81.

Therefore, rewrite 27 as 3³ and 81 as 3⁴:

[tex]\implies \dfrac{(3^3)^{\frac{2}{3}}}{(3^4)^{\frac{1}{4}}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{3^{(3 \cdot \frac{2}{3})}}{3^{(4 \cdot \frac{1}{4})}}[/tex]

[tex]\implies \dfrac{3^2}{3^1}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 3^{(2-1)}[/tex]

[tex]\implies 3^1[/tex]

[tex]\implies 3[/tex]

Given that,

→ ((14² - 13²)^⅔)/((15² - 12²)^¼)

Evaluating the problem,

→ ((14² - 13²)^⅔)/((15² - 12²)^¼)

→ ((196 - 169)^⅔)/((225 - 144)^¼)

→ (27^⅔)/(81^¼)

→ ((3³)^⅔)/((3⁴)^¼)

→ (3²)/3

→ 9/3 = 3

Therefore, the solution is 3.

SP = 2a+5

RQ= 5a-1

ST = 3b-3

SQ = 7b-9

RQ=?

TQ=?

SP = RQ

2a+5 = 5a-1

Solve for a

5+1 = 5a-2a

6 = 3a

6/3 = a

2=a

RQ= 5a-1 = 5(2)-1 = 10-1 = 9

RQ= 9

ST + TQ = SQ

ST= TQ

TQ= 3b-3

3b-3+3b-3= 7b-9

Solve for b

6b-6 = 7b-9

-6+9 = 7b-6b

3=b

TQ = 3b-3= 3(3)-3= 9-3 =6

TQ= 6

Notice that the x coordinate of both points is the same, therefore the line is a vertical line.

Answer: The slope is undefined.

Solution:

For this case we know that the width is given by:

w = 6x +8

The lenght is given by:

l= 12x +16

And the perimeter would be given by:

P= 2l +2w = 2(12x+16)+ 2(6x+8)= 24x+32 +12x+16=36x + 48

And then the ratio would be:

Answer

The two coordinates on the line include

(0, -1.5) and (-4.5, 0)

The graph of the line is presented below

Explanation

We are asked to plot the grap of the given equation of a straight line.

To do that, we will obtainthe coordinates of two points on the line.

These two points will preferrably be the intercepts of the line.

y = (-x/3) - (3/2)

when x = 0

y = 0 - (3/2)

y = -(3/2)

y = -1.5

First coordinate and first point on the line is (0, -1.5)

when y = 0

0 = (-x/3) - (3/2)

(x/3) = -(3/2)

x = (-3) (3/2)

x = -(9/2)

x = -4.5

Second coordinate and second point on the line is thus (-4.5, 0)

So, to plot the line, we just mark these two points and connect them to each other.

The graph of this line is presented under 'Answer' above.

Hope this Helps!!!

100,000π ft³

1) Let's find the volume of that Cylinder using this formula:

Note that the volume is the area of the base (a circle) times the height

2) Also, notice that in the picture we have the diameter, the radius is half the Diameter:

3) So the volume is 100,000π ft³

Let's recall one of the properties of exponents:

Therefore, in our exercise we have:

we have that

the volume of the cube is equal to

V=b^3

64=b^3

b^3=4^3

b=4 unit

see the attached figure

the surface area of the new figure is equal to

SA=2B+PH

where

B is the area of the base

P is the perimeter of the base

H is the height

we have

B=4*8=32 unit2

P=2(4+8)=24 unit

H=2 unit

so

SA=2(32)+24*2

SA=64+48

SA=112 unit2

In order to find the values of f(0), f(1) and f(2), we just need to find in the graph for the value of the function (that is, the value of y) for the values of x equal to 0, 1 and 2 respectively.

Looking at the graph, for x = 0 we have y = -7, therefore f(0) = -7

For x = 1 we have y = -2, therefore f(1) = -2

For x = 2 we have y = -5, therefore f(2) = -5

The profit on one standard DVD player is $59 and on one portable DVD player is $69.

If there are s number of standard DVD player then total profit on standard DVD players is $59s. Simillarly total profit on portable DVD players is $69p.

The total profit on DVD player shoul be at least $345, which means total profit on DVD players is $345 or more than $345.

The linear inequalty for total profit is,

The graph of the linear inequality is,

In graph, lines pointing away the origin represent the region for the equation.

We will have the following:

*Initially, as x increases, y decreases.

*The slope of the graph is equal to -1 for all x between x = 0 & x = 3.

*Starting at x = 3, the function value y increases as x increases.

*The slope of the graph is equal to 3 for x between x = 3 & x = 5.

*For x between x = 0 & x = 4, the function value y ≤ 0.

*For x between x = 4 & x = 8, the function value y ≥ 0.

Step 1 : To determine the area of the rhombus

Therefore the area of the rhombus = 112m²

FOR THE PAIRS TO BE OPPOSITE IT MEANS THE NUMBERS SHOULD ALSO CONTRAST IN SIGNS.

47 AND -47 ARE OPPOSITE

74 AND - 74 ARE OPPOSITE

|4|=4 AND -4 ARR OPPOSITE

47 AND |-47|=47 ARE NOT OPPOSITE BECAUSE THEY BOTH HAVE THE SAME SIGNS.

THE LAST OPTION IS THE ANSWER.

The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.

According to the question,

We have the following information:

f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]

Now, to find the value of f(0), we will put 0 in place of x.

f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]

f(0) = 0+7*0-0+12

(When a number has some power then it means that in order to solve this we have expand the expression and multiply the number as many times as the power is given. For example, in the case of 3 as power, we will multiply any number 3 times and in case of 2 as power, we will multiply the given number 2 times.)

f(0) = 0+0-0+12

f(0) = 12

Now, to find the value of f(2), we will put 1 in place of x:

f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]

f(2) = -8+7*4-4+12

f(2) = -8+28-4+12

f(2) = 40 -12

f(2) = 28

Now, to find the value of f(2), we will put -2 in place of x:

f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]

f(-2) = -(-8) + 7*4+4+12

f(-2) = 8+28+4+12

f(-2) = 52

Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.

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The factors are -3 and -1

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is,

2x² + 8x + 6

Put it equal to 0 so that we can solve for 'x'

2x² + 8x + 6 = 0

Now, its factors are 6x and 2x

2x² + 6x + 2x + 6 = 0

2x(x + 3) + 2(x + 3) = 0

To cross check your solution is correct or not. You've to just see the the brackets value should be same after taking common. Here the bracket value is (x+3) which is same.

(2x + 2) (x+3) = 0

split the values to solve further,

2x + 2 = 0                |         x + 3 = 0

2x = -2                     |          x = -3

x = -2/2

x = -1

Hence, the factors are -3 and -1

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Answer: You need to spend more than $5.00

Step-by-step explanation: