Ms. Peterson wrote the expression below on the chalkboard for her class. She asked the students to write an equivalent expression using no more than one set of parentheses. 4(3x + 5y + 2z) + 3(x-z)
Tom wrote 12x + 20y + 8z
Jenna wrote 5(3x + 4y + z)
Chris wrote 15x + 20y − 5z
Which, if any, of the three students wrote an expression that is equivalent to Ms. Peterson’s expression?

Answers

Answer 1

The answer would be Jenna's answer. If you distribute the teachers original expression you get 15x + 20y + 5. If you distribute Jenna's answer you get just that.

Related Questions

What if mac bought8pack of toy boats and then he gave his friend 3boats? If mac has 13 boats now,how many boats were in each pack?

Answers

There were two boats in each car.

To solve for this, we need to set up an algebraic equation.
We have 8 packs of toy boats, meaning there are a specific amount of toy boats per pack, so we have to multiply 8 by a variable, x. Considering this is the total, too, we should let this sit at the end of the equation (=8x). Mac gave his friend 3 toy boats, meaning we will be subtracting 3 from our equation, but this will be on the other side of the equation with 8x (-3). We also have a current total of 13 toy boats after Mac gave away 3 boats, meaning that 13 will have to sit alone (+13).
With this information, let's set up an equation. With what we have, the equation will look like this:
8x - 3 = 13
Now all we have to do is solve for x. To start this off, we should add 3 to both sides to isolate the variable.
8x = 13 + 3; simplify.
8x = 16; All that is left is to divide both sides by 8 and we will have figured out how many toy boats were in each pack.
8x / 8 = x; 16 / 8 = 2.

We are left with our answer, x = 2. That being said, there were 2 toy boats per pack.

I hope this helps!

how many times does a person blink in 1.5 min

Answers

About 22-30 times in 1.5 minutes

Which expression is equivalent to 1/4(2−5x+6) ?
Please answer fast!

Answers

The equivalent expression for the given expression is 2-5x/8.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 1/4(2-5x+6).

The equivalent expression is

1/4(8-5x)

=8/4 -5x/8

= 2-5x/8

Therefore, the equivalent expression is 2-5x/8.

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To find the equivalent expression to 1/4(2−5x+6), distribute 1/4 to each term inside the parentheses to get 1/2 - 5/4x + 3/2.

To simplify the expression 1/4(2−5x+6), you need to distribute the 1/4 to each term inside the parentheses:

1/4 * 2 = 1/21/4 * (-5x) = -5/4x1/4 * 6 = 3/2

Putting it all together, the equivalent expression is 1/2 - 5/4x + 3/2.

This semicircle has a diameter of 5 meters.

What is the area of this figure?

Use 3.14 to for pi.

Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.

Answers

Area of semicircle is given by:
[tex]A_sc = \frac{1}{2} \pi r^2 [/tex]

r is the radius, and we are given the diameter. Radius is half the diameter, so it's 2.5m. Let's plug that into the formula (using 3.14 as an estimation for pi):
[tex]A_t = \frac{1}{2}(3.14)(2.5)^2 = 9.81m^2 [/tex]

So, the area of this semicircle is 9.81m².

What is 20 percent of 60

Answers

Hello!

20 percent of 60 we can setup like this.

.20*60=x

x=12

Hope this helps. Questions please just ask. Thank you

20\100=1\5
1\5*60=
12
you multiply 1\5*60\1 to get the answer 12

Amount Saved = Original Price x Discount % / 100. So,

Amount Saved = 60 x 20 / 100

Amount Saved = 1200 / 100

Amount Saved = $12 (answer)

the length of bill's backyard swimming pool is 60 ft longer than the width if the pool. The surface area of the water is 1600 square ft. What is the width of the pool?

Answers

Given data:
Surface Area of water = A = 1600[tex]ft^{2}[/tex]
Length of the swimming pool = L = 60[tex]ft[/tex] + W
Width of the swimming pool = W =?

Since,
Area = Length * Width
A = L * W

Therefore,
1600 = (60 + W) * W
1600 = 60W + W*W

=> [tex]W^{2} + 60W - 1600 = 0[/tex]

In the above equation(in terms of quadratic formula),
a = 1
b = 60
c = -1600
x = W

Use,

x(for positive) = [tex]x =\frac{ -b + \sqrt{ b^{2} - 4*a*c } }{2*a} [/tex]
Plug-in the values you would get:
x = (-60 + 100) / 2
x = 20 --- (1)

x(for negative) = [tex]x =\frac{ -b - \sqrt{ b^{2} - 4*a*c } }{2*a} [/tex]
Plug-in the values you would get:
x = (-60 - 100) / 2
x = -80 --- (2)

Since x = W = Width, and width CANNOT be negative, therefore, the correct answer is (1):

Ans: Width = 20ft

To find the width of Bill's rectangular pool, set up an equation with 'x' as the width, resulting in x(x + 60) = 1600. Solving this quadratic equation, the width of the pool is found to be 20 feet.

The question asks us to determine the width of Bill's backyard swimming pool given that the pool's length is 60 feet longer than its width and the surface area of the water is 1600 square feet. To solve this, we can set up an equation where the width of the pool is x feet and the length is x + 60 feet. Because surface area is found by multiplying the length by the width for a rectangular object, our equation is x(x + 60) = 1600.

Now, solve for x:

x^2 + 60x = 1600x^2 + 60x - 1600 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. In this case, the equation factors nicely:

(x + 80)(x - 20) = 0

Setting each factor equal to zero gives us:

x + 80 = 0 or x - 20 = 0x = -80 or x = 20

Since a negative width doesn't make sense for a physical object, we discard x = -80 and the width of the pool is 20 feet.

A triangle and a rectangle are drawn. The triangle's base is equal to the rectangle's length. The triangle's height is equal to the rectangle's width. Which sentence is true?

A.)exactly 1 of these rectangle's can fit inside this triangle.
B.)2 of these rectangles can fit inside this triangle
C.)exactly 1 of these triangle's can fit inside this rectangle
D.)2 of these triangles can fit inside this rectangle

Answers

c is the correct answer

Final answer:

Exactly 1 of these triangles can fit inside this rectangle.

Explanation:

The sentence that is true is exactly 1 of these triangles can fit inside this rectangle. To understand why, let's analyze the dimensions of the triangle and the rectangle. Suppose the base of the triangle is 4 units and the height is 3 units. If the length of the rectangle is also 4 units and the width is 3 units, the triangle will perfectly fit inside the rectangle. However, if the length or width of the rectangle is different from the corresponding dimensions of the triangle, it will not be possible to fit the triangle inside the rectangle without overlapping.

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Work out the area of a triangle of base 7.5m and height 6cm

Answers

1/2 times 7.5 times 6 = 22.5. That is your area. Hope it helps! :)

Hello there!

To start, the formula to calculate the area of a triangle is:
A=[tex] \frac{B*H}{2} [/tex]

B is the value of the base and H is the value of the height.

Knowing this formula, you can solve for the values of the area of the triangle by plugging the value of your base and height into the formula and solve for A, the area.

A=[tex] \frac{7.5*6}{2} [/tex]

Now, simplify this equation:
A=[tex] \frac{7.5*6}{2} [/tex]
A=[tex] \frac{45}{2} [/tex]
A=45÷2
A=22.5

Therefore, the area of your triangle would be 22.5 meters squared.

Hope this helps and have a marvelous day! :)

A rectangular prism has a length of 3 1/2 inches, a width of 3 1/2 inches, and a height of 7 inches. Danny has a storage container for the prism that has a volume of 90 cubic inches.

What is the difference in volume between the prism and the storage container?

PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!

Answers

To find the volume of the prism you multiply
length x width x height. So for the prism you multiply 3 1/2 x 3 1/2 x 7. Which gives you the answer of 85.75, or rounded it’ll give you 86.
Now to find the difference you subtract the volume of the prism from the container which will give you your final answer

4.25
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Cameron has clear container in the shape of a cube.Each egde 9 centimeters long.He found the volume of the container in cubic centimeters by multiplying the egde length by itself 3 times.What is the volume of the container in the cubic

Answers

Just find the volume 9*9*9 or 9^3 = 729cm^3

What is the period of the function f(x) shown in the graph?

Answers

For this case what you should see is when the value "y" of any point of the graph is repeated again.
In this case we have that the period will be given by:
T = ((3/4) pi) - ((- 1/4) pi)
T = ((3/4) pi) + ((1/4) pi)
T = ((3 + 1/4) pi)
T = ((4/4) pi)
T = pi
Answer:
the period of the function f(x) shown in the graph is
T = pi

What is the volume of a right circular cylinder with a radius of 4 m and a height of 4 m?

Answers

The volume of a cylinder by definition is given by:
V = ((pi) * (r ^ 2)) * (h)
Where,
r: radio
h: height.
We have then:
V = ((pi) * ((4) ^ 2)) * (4)
V = 64 * pi m^3
Answer:
The volume of a right circular cylinder is
V = 64 * pi m^3

A pair of running shoes costs five dollars more than a pair of regular tennis shoes .. the total cost for both is one 115 $ What is the price of the regular tennis shoes?

Answers

115-5=110/2=55

$55 for the pair of Regular

Renee is making a scale diagram of her mp3 player. The length of her scale drawing is 8 inches, and the width is 14 inches. The actual length of the mp3 player is 4 centimeters, and the width is 7 centimeters. what is the scale factor?

Answers

Answer: 2

Explanation:

The scale factor is the ratio between the scale drawing measures and the actual measures.

                                   scale drawing length            8 inches
scale factor = ratio = -------------------------------- =   --------------- = 2
                                        actual length                    4 inches

Also,
                                   scale drawing width             14 inches
scale factor = ratio = ----------------------------- =       --------------- = 2
                                     actual width                      7 inces

As seen the scale factor is 2.

The scale factor is 1:2 or 1/2.

To determine the scale factor between the actual dimensions and the scale drawing, divide the actual length and width by the corresponding values in the scale drawing dimensions. In this case, the scale factor is 1:2 or 1/2.

To find the scale factor:

Calculate the ratio of the actual length to the scale length: 4 cm / 8 in = 0.5Calculate the ratio of the actual width to the scale width: 7 cm / 14 in = 0.5Since both ratios are the same, the scale factor is 1:2 or 1/2.

Write the resultant if the 2 vectors as an ordered pair.

<5, -2> and <0,0>

Answers

To find the resultant vector, you need to base the solution from the Pythagorean Theorem.

Step 1. Find z1 by adding x1^2 and y1^2.
z1= 5^2 + 0^2 = 5

Step 2. Find z2 by adding x2^2 and y2^2.
z2= -2^2 + 0^2 = 2

Step 3. Find c.
5^2 + 2^2 = c^2
c=square root of 29
c=5.39

The final answer is 5.39.

The bottom shape is a square prism with base edges of 3 cm and a height of 10 cm. What is the volume of the composite figure if the top shape is a right pyramid with a height of 2 cm?
90 cm3
60 cm3
6 cm3
96 cm3

please i really need help on this

Answers

Answer: 96 cm^3

To answer this, start by finding the volume of the square prism. The formula is L x W x H, therefore the volume is 3 x 3 x 10 = 90.

Then, find the volume of the pyramid on the top. Use the same formula but divide it by 3 because it is a pyramid. 3 x 3 x 2 / 3 = 6

Add 90 and 6 to get 96.

what is 9,750,000,000 in scientific notation

Answers

Hey there mate!

So, when doing this kind of notation (scientific notation), this is pretty much like braking down the number,and trying to make it more simple.

[tex]\boxed{9,750,000,000} \ in \ scientific \ notation... \\ \\ \Longrightarrow\boxed{\boxed{9.75*10^9}} \Longleftarrow[/tex]

I hope this helps you! :)

9.75 x 10[9 exponent]

420% of what number is 26,565

Answers

26,565 divided by 4.20 = 6,325

the answer is 6325 because if u divide 26565 by 420% u get 6325
to check u can multipley 6325 by 420% u get 26565

if the r-value, or correlation coefficient, of a data set is 0.854, what is the coefficient of determination to three decimal places?

Answers

To find the coefficient of determination, square the correlation coefficient:
(0.854)² = 0.729316. To three decimal places, this would be 0.729.

Answer with explanation:

Coefficient of determination(r²), is defined as, how well the data values are associated with each other when Regression line is drawn. In regression analysis, the coefficient of determination measures , how well the regression predictions approximate the real data points, means it measures the closeness between two variables.The Value of r², lies between 0 to 1. If value of r²=1, it shows ,regression line that is data values are Perfectly associated with each other.

If ,r²=0, it means there is no variation between two variables.There is 0% variation between two variables.

→Coefficient of Variation=[Correlation coefficient]²

=r²

=(0.854)²

=0.854 × 0.854

=0.729316

=0.730(Approx)

Explain how you would use a number line to find to find the absolute value of-12

Answers

So a absolute value is just the opposite of the value given, (unless it is a positive number) so you start on -12 and count 24 units to the right so it would make positive 12

The absolute value of -12 is 12 and we can find it on the number line by going 24 times right from -12.

What is absolute value?

The absolute value or modulus of a real number x, and we know that modulas always gives a positive number.

How to determine absolute value?

The number which is given in the question is -12 and we have to find the absolute value of this number. To find out the absolute value we have to put this number in modulas.

I -12 I =it will give us 12

to make -12 to 12 we need to first take it to 0 by adding 12 and then from 0 to 12 by adding another 12. We have added 24 to-12 to reach 12.

In this way we can find the absolute value of -12 on number line.

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Ramona is asked to draw a tree using a scale of 1 inch:3 meters.She draws a 4-inch tree.How tall is the tree?

Answers

She increased 1 inch to 4 inches, which was done by multiplying by four. All you have to do is just multiply 3 meters by 4 to get 12 meters. :) The tree is 12 meters long.

The tree is 12m tall

A rectangle 7 feet longer than it is wide find the dimensions of the rectangle if its area is one 198 sq ft.

Answers

w=width l=length
l=w+7

w(w+7)=198
w^2+7w-198=0
(w-11)(w+18)=0
w=11 or -18

w=11 and l=18

Find the balance in the account after the given period.
$4,200 deposit earning 4.2% compounded monthly, after 2 years. Use the direction in the pic plz.

Answers

Substituting our values into the formula we get
[tex]A=4200(1+ \frac{0.042}{12})^1^2^*^2 \\ = 4200(1+0.0035)^2^4 \\ = 4200(1.0035)^2^4 \\ = 4567.37[/tex]

if triangle rst is an acute angle then m

Answers

Less than 90 degrees

The state capitol building in Baton Rouge, Louisiana, is 450 feet tall. Ella’s scale model of the building uses the scale 25 feet = 10 inches. How tall is Ella’s model? 18 inches 180 inches 1,125 inches 425 inches

Answers

We can use a proportion to solve problems that involve scale factors. Every 25 feet equals 10 inches, according to Ella's scale model. The building is actually 450 feet tall, so feet and inches are our units for the proportion. The first step is to set up the proportion:

[tex] \frac{450}{x} [/tex] = [tex] \frac{25}{10} [/tex]

Notice the feet (450 and 25) are lined up next to each other, and the inches (x and 10) are lined up as well. Next, we solve by cross multiplying and dividing. 450 times 10 gives us 4500. Then, we divide by the remaining number,25. 4500/25 equals 180. So, Ella's model is 180 inches tall.

do anyone know how to solve this? need the answer fast.

Answers

The value of g^-1(-3) is the value of x that makes g(x) = -3. To find it, we can solve
.. (x +4)/(2x -5) = -3
.. x +4 = -3(2x -5)
.. 7x = 11
.. x = 11/7

The desired value is
.. (3/11)*g^-1(-3)
.. = (3/11)*(11/7)
.. = 3/7

[tex] \frac{3}{11} g^{-1}(-3) = \frac{3}{7}[/tex]

what is the inverse of the conditional statement? If a polygon the has five angles, then it is a Pentagon

Answers

Answer: The inverse f the given statement is

"If a polygon is not a Pentagon, then it does not have five sides".

Step-by-step explanation: We are given to write the inverse of the following conditional statement:

"If a polygon the has five angles, then it is a Pentagon".

INVERSE of a conditional statement :

If the conditional statement is

"If p, then q",

then its inverse statement is given by

"If not q, then not p".

Therefore, the inverse of the given statement is

"If a polygon is not a Pentagon, then it does not have five sides".

Answer:

It is Option C If a polygon does not have five angles then it is not a pentagon.

Step-by-step explanation:

A news anchorman can read 7.5 lines in 0.5 minutes. How many lines can he read in 8.5 minutes? Round the answer to the nearest tenth, if necessary.

A. 15.0 lines B. 127.5 lines
C. 31.9 lines D. 2.7 lines

Answers

The answer is 127.5 Lines.

beer Bottles are filled so that they contain an average of 475 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml.

Answers

I attached the rest of your question in the image below.
We use the normal distribution density function f(z) to find the probability of a specific range of values.
Z= ((X-μ)/σ)
μ = 475σ = 8
a) X< 470 ml
P[X<470] = P[Z<(470-475)/8] = P[Z<(470-475)/8] = P[Z<-0.625] = 0.2659

b) 6 pack with a mean of less than 470ml
Z = ((X-μ)/(σ/√n))
Z = (470-475)/(8/√6)
P [Z<-1.53] = 0.063
c) 12 pack with a mean of less than 470ml
Z = ((X-μ)/(σ/√n))
Z = (470-475)/(8/√12)
P [Z<-2.165] = 0.0152

Use the parabola tool to graph the quadratic function f(x)=x2−12x+27.

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answers

Remember that for a quadratic function of the form [tex]a x^{2} +bx+c[/tex] we can find its vertex with formula: [tex]h= \frac{-b}{2a} [/tex] where [tex]h[/tex] is the x-coordinate of the vertex; then we will find the y-coordinate by replacing [tex]h[/tex] in our original function.

From the question know that [tex]a=1[/tex] and [tex]b=-12[/tex], so lets replace those values in our vertex formula to find the x-coordinate of our vertex:
[tex]h= \frac{-(-12)}{2(1)} [/tex]
[tex]h= \frac{12}{2} [/tex]
[tex]h=6[/tex]
Now lets replace that value into our original function to find the y-coordinate of our vertex:
[tex]f(6)=6^{2} -12(6)+27[/tex]
[tex]f(6)=36-72+27[/tex]
[tex]f(6)=-9[/tex]
Finally, we have our vertex (6,-9)

Now to graph our function we are going to take advantage of its line of symmetry; if the vertex is (6,-9) the line of symmetry of the parabola is x=6, so if we chose the point (6,0), our second point will have coordinates (3,0) as you can see in the picture.

The vertex of a parabola is the minimum or the maximum point of the parabola

The equation of the parabola is given as:

[tex]f(x) = x^2 + 12x + 27[/tex]

The x-coordinate of the vertex is calculated using:

[tex]x = -\frac{b}{2a}[/tex]

So, we have:

[tex]x = -\frac{12}{2 \times 1}[/tex]

[tex]x = -\frac{12}{2}[/tex]

[tex]x = -6[/tex]

Substitute -6 for x in f(x)

[tex]f(-6) = (-6)^2 + 12(-6) + 27[/tex]

[tex]f(-6) =-9[/tex]

So, the vertex of the parabola is (-6,-9)

Let x = 0.

So, we calculate f(0) as follows:

[tex]f(0) = (0)^2 + 12(0) + 27[/tex]

[tex]f(0) = 27[/tex]

This means that f(x) passes through (0,27)

See attachment of the parabola