Guided Problem Solving You have a class photo that is 10 in. long and 8 in. wide. If you want to enlarge your photo to be 15 in. long, how wide will the photo be?

Understand the Problem You know the dimensions of the original photo and the length of the enlarged photo. Find the width of the enlarged photo.
Make a Plan Draw the figures and label their sides.

Answer:

3.7 n^2 + 4n + 2.1

Step-by-step explanation:

2.7 n^2 + n^2 = 3.7 n^2

6n - 2n = 4n

7.8 - 5.7 = 2.1

Answer:

1

5z + 6z = 11z

2

9y + -6y = 3y

3

ANSWER ( 11z + 3y)

well, we had a cylinder with 7mL of water, in the rock goes and kaboom the volume for the cylinder and its contents is 9 mL, well, the displaced water from the rock is equivalent to its volume, as Archimedes would properly point out, so since it was 7mL and now is 9mL well, the extra 2mL is the volume of the rock :).

sidenote:  Archimedes is Da Bomb!!!!

now, we know the rock weights 24 grams, and we also know its volume is 2mL, so its density is simply g/mL, or [tex]\cfrac{24g}{2mL}\implies 12~\frac{g}{mL}[/tex]

Answer:

see explanation

Step-by-step explanation:

(j + k)²

= (j + k)(j + k)

each term in the second factor is multiplied by each term in the first factor , that is

j(j + k) + k(j + k) ← distribute parenthesis

= j² + jk + jk + k² ← collect like terms

= j² + 2jk + k²

The sales tax is $1.2  and the total cost of the item is  $21.2   .

In the question,

it is given that ,

the selling price of the item is $20.

the rate of sales tax is = 6^ ,

so the sales tax can be calculated using the formula

sales tax = 6% of selling price

So , sales tax = 6% of 20

= 0.06 * 20

= 1.2

so , the sales tax is $1.2

the total cost of the item will be = selling price + sales tax

= 20 + 1.2

= 21.2

Therefore , The sales tax is $1.2  and the total cost of the item is  $21.2   .

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Answer:

  P'(-16, 0)

Step-by-step explanation:

You want the coordinates of the image of P(-4, 0) when the figure is dilated by a factor of 4 about the origin.

Dilation about the origin multiplies each coordinate by the dilation factor:

  P' = 4P

  P' = 4(-4, 0) = (-16, 0)

The coordinate of the image point are (-16, 0).

Answer:

h=6+(2t)

Step-by-step explanation:

The words that describe the pattern that can be used to complete the table is that the number of lines is double the number of figures, which indicates that the correct option is option A

A. The total number of lines y is two times the figure number x

An equation is a mathematical statement that connects two expression with an equals sign.

The pattern that can be used to complete the table is therefore;

The number of lines, y, is twice the number of figures, x

The relationship expressed mathematically as an equation is presented as follows;

y = 2·x

The completed table is presented as follows;

Figure Number, x   [tex]{}[/tex] Total Lines, y                        [tex]{}[/tex] Ordered pair

1                         [tex]{}[/tex]            2                                          (1, 2)

2                         [tex]{}[/tex]           4                                          (2, 4)

3                         [tex]{}[/tex]           6                                          (3, 6)

4                         [tex]{}[/tex]           8                                          (4, 8)

5                         [tex]{}[/tex]           10                                        (10, 5)

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Answer:

y=-7

Step-by-step explanation:

just simplify it

4+y=-3

y=-3-4

y=-7

Answer:2

Step-by-step explanation:

Answer:

Part A: C

Part B: T shirt = $20, hat = $12

Step-by-step explanation:

Part A:

He buy 8 T-Shirts and 5 hats for $220.

He buy another buys 5 T-shirts and 1 hat for $112.

assuming t = tshirt, h = hat, C is the correct answer

Part B:

8t + 5h = 220

5t + h = 112

1. Use second equation to represent h in term of t

h = 112 -5t

2. Replace h in first equation with h from 1.

8t + 5(112 -5t) = 220

8t + 560 - 25t = 220

-17t + 560 = 220

-17t = 220 - 560

-17t = -340

t = -340/-17 = 20

3. Replace t in equation from 1. with t from 2.

h = 112 -5(20) = 112 - 100 = 12

Check the picture below.

Option C is correct which is dC/dt = π (dd/dt).

According to the question,

We know that the diameter of the circle is half the radius of the circle.

d = r/2

By transferring r to the left-hand side and d to the right-hand side

r = d/2

We also know that circumference of the circle is

C=2πr

C=2πd/2

C=πd

Now we will differentiate on both the side with respect to t and we will get,

dC/dt = π (dd/dt)

Differentiation is a technique for tracking down the subordinate of a capability. Differentiation is a process, where we find the momentary rate of change in capability in light of one of its variables. We usually differentiate with respect to time which is represented as ds/dt.

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The statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.

Let us understand about the given graph:

The given graph is a graph of a cube root function.

So, the statement of Noelle, “The graph represents the function [tex]f(x)=\sqrt[3]{x}[/tex]." is correct.

So, option A is not correct.

The inverse of a cube root function is a cubic function.

So, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect.

So, option B is correct.

The domain and range of the cube root function are all real numbers.

So, the statement of Julian, “The domain and range of the function is all real numbers.” is correct.

So, option C is not correct.

From the graph, we can see f(-1) = -1.

So, the statement of Yemen, “The value of f(-1) = -1.” is correct.

So, option D is not correct.

Thus, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.

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The point (-2, 6) is reflected across the y-axis then the new coordinates of the point are (2, 6).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

We know when a point (x, y) is reflected along the y-axis (x, y) becomes

(- x, y).

Given, A point (-2, 6) is reflected across the y-axis.

∴The new coordinates of the point are (2, 6).

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The correct response variable is the amount of pain relief.

Given that,

A tall glass of ice water, according to some, can help migraine sufferers find relief. Multiple migraine sufferers will be recruited by researchers to participate in a test. The individual will either take a placebo pill or a common painkiller when they get a migraine. Additionally, only half of each group will take the pill with water; the other half will sip on a small amount of water. The quantity of pain relief is then reported by participants.

To find :  What is the response variable in this experiment.

Explanation :

Response variable or study variable, in general called as dependent variable  is the variable of main focus in study. We want to study the changes in explanatory or independent variables are associated with response variable. Sometimes we want to measure the effect of predictors i.e explanatory variables on response variable.

For example in hand, we want to determine whether the drinking ice water is associated with amount of pain relief. Hence in this study, response variable is the amount of pain relief.

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To calculate the distance between two points, we have to:

[tex]\large\displaystyle\text{$\begin{gathered}\sf The \ points\ are \left \{ {{A=(x_1,y_1)} \atop {B=(x_2,y_2)}} -\to\boldsymbol{\sf{m=\frac{\Delta y}{\Delta x }\iff \ m=\frac{y_2-y_1}{x_2-x_1} }} \right. \end{gathered}$}[/tex]

We have that the points to calculate the slope are:  (x₁ = -4, y₁ = 4) and (x₂ = -15, y₂ = 2)

Add the data in the formula:              

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}} \\ \\ \boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{2-4}{-5-(-4) } } \end{gathered}$}} \\ \\ \boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2}{-11} } \end{gathered}$} }}[/tex]

Answer:

Step-by-step explanation:

2y=-3x-5

y=-3/2x-5/2

Answer:

Y= -2.5

X= -1.6

Step-by-step explanation:

2y+3x= -5

2y+3(0)= -5

2y= -5

2y÷2=y

-5÷2= -2.5

Y=-2.5

2y+3x= -5

2(0)+3x= -5

3x= -5

3x÷3=x

-5÷3= -1.6

X= -1.6

The amount in grams of food A and B she feeds this group of rats each day will be 2200003.84 gm and 1100006.4 gm respectively.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Given that, she provides a certain set of lab rats with a daily meal that contains exactly 32 units of niacin and 22000 units of retinol. She uses two different brands of industrial pellet food.

If food A has 100 units of retinol and 0,12 units of niacin per gram.Niacin 0.20 units and retinol 50 units are both included in Food B per gram. The grams of each food she feeds this group A of rats each day is,

=32×0.12+22000×100

=2200003.84 gm

If food B contains 0,20 units of niacin and 50 units of retinol per gram.The grams of each food she feeds this group A of rats each day is,

=32×0.20+22000×50

=1100006.4

Thus, the amount in grams of food A and B she feeds this group of rats each day will be 2200003.84 gm and 1100006.4 gm respectively.

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On 6th day the Blake and Nicole will be on same page

Consider the case of Blake

The initial page number = 40

Number of pages per day = 10

Consider the B is the page number and t is the number day

Then the function will be

B = 40 + 10t

Consider the case of Nicole

The initial page number = 10

Number of pages per day = 15

Consider the N is the page number and t is the number day

Then the function will be

N = 10 + 15t

Draw the graph using the functions

Hence, on 6th day the Blake and Nicole will be on same page

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The quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

Given:

f(x) = 2(x+1)^2 - 8

= 2(x^2+1+2x) - 8

= 2x^2 + 2 +4x - 8

= 2x^2+4x-6(standard form)

Intercept form:

= 2x^2+4x-6

= (x-1)(x+3)

x-1 = 0

x = 1

x+3 = 0

x = -3

(1,0) and(-3,0).

Therefore the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

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The value of the variable m in the rectangle is given as follows:

m = 12.5.

The segments from the rectangle, and their lengths, are given as follows:

They are opposite vertices of the rectangle, as they do not have any common vertex.

Since they are opposite vertex, it doesn't matter if these segments are bases, heights or diagonals, they will have the same length.

Thus the numeric value of variable m is obtained as follows:

WY = XZ

(as they have the same length).

Replacing the measures of each of these segments:

12m + 7 = 16m - 43

12m - 16m = -43 -7

-4m = -50

4m = 50 (multiplication by -1).

m = 50/4

m = 12.5.

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Answer:it will take him roughly 75 minutes or an hour and 15 minutes:)

Step-by-step explanation:

so you take 2 and multiply it by the 30 minuets and then divide 30 by 2 so it will look like this

2x30=60(1 hour)

30÷2=15

now add 60 + 15 and you get

75

Answer:

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

Step-by-step explanation:

The vertex is at [tex](0,3)[/tex], so the equation is of the form [tex]f(x)=ax^2+3[/tex].

Using the point [tex](1,1)[/tex] to solve for [tex]a[/tex],

[tex]1=a+3 \implies a=-2 \\ \\ \therefore f(x)=-2x^2+3[/tex]

Answer:

x=22

Step-by-step explanation:

5x+6+3x-2=180

8x+4=180

8x=176

x=22