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Part 2 - Writing Equivalent Expressions - You will now use mathematical properties to create two expressions that are equivalent to Sara’s expression.
Property Used
Original/Changed Expression
New expression with property used
Commutative Property of Addition (rearrange the added terms in the parentheses to group like terms together.)
5(2j + 3 + j)

Combine Like terms after rearranging them
(put your answer from the previous row here)

Distributive Property of multiplication over addition (multiply the number outside the parentheses)
(put your answer from the previous row here)
(Use this final expression that you write in this box on the next slide.)

Answer:

A

Step-by-step explanation:

It is th eonly one with a asquare base and it maches the net.

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PLEASE RATE!

Option A is correct!

The value of the function [tex]\frac{f}{g} (5)[/tex] is 270.

Given functions are:

[tex]f(x) = 7+4x\\\\g(x) = \frac{1}{2x}[/tex]

[tex]\frac{f}{g} (x)[/tex] is the ratio of functions f(x) and g(x) i.e. [tex]\frac{f(x)}{g(x)}[/tex].

So, [tex]\frac{f}{g} (x) =\frac{7+4x}{\frac{1}{2x} }[/tex]

[tex]\frac{f}{g} (x) =2x(7+4x)[/tex]

[tex]\frac{f}{g} (5) =2*5(7+4*5)[/tex]

[tex]\frac{f}{g} (5) =270[/tex]

Therefore, the value of the function [tex]\frac{f}{g} (5)[/tex] is 270.

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Answer:

270

Step-by-step explanation:

edge2022

Answer:

It guess it should be 95158398

Why?

Because we have two right triangles with the same shared leg (the L of HL) and the hypotenuses are the same length (the H of HL). The tickmarks tell us those segments are the same.

HL only applies to right triangles because the hypotenuse is only found in right triangles. If we didn't have those 90 degree square markers, then this would be an SSA case, but that's not a valid congruence theorem.

Answer:

15

Step-by-step explanation:

To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula

[tex]x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x= \frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}[/tex]

[tex]x= \frac{-700+\sqrt{530000} }{2}; x= \frac{-700-\sqrt{530000} }{2}[/tex]

[tex]x=\frac{-700+100\sqrt{53} }{2}; x=\frac{-700-100\sqrt{53} }{2};[/tex]

[tex]x=-350 + 50\sqrt53 = 14.005; x = -350 - 50\sqrt53 = -714.005[/tex]

In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.

[tex](-714.005)^2+700(-714.005)-10000=-0.360[/tex]

Furthermore, we must round to the nearest whole number, as you cannot make part of an item.

Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:

[tex](14)^2+700(14)-10000=-4\\\\(15)^2+700(15)-10000=725[/tex]

Answer:

x^2 -1

Step-by-step explanation:

-1×x + -1×1 + x×1 + x×x

= x^2 -x +x -1

= x^2 -1

[tex] {x}^{2} - 1[/tex]

Answer:

wars the graph

Step-by-step explanation:

The mole ratio of the oxygen to pentane will be 8:1

A mole ratio is ​a ratio between the amounts in moles of any two compounds involved in a chemical reaction

A chemical equation is said to be a balanced chemical equation if it has an equal number of all the constituent atoms on both sides of the reaction arrow.

The balanced chemical reaction for the combustion of pentane is as follows:

[tex]\rm C_5H_{12}+8O_2--- > 5CO_2+6H_2O[/tex]

From the above-balanced chemical equation, it is clear that 1 mol of [tex]C_5H_{12}[/tex] reacts with 8 moles  [tex]O_2[/tex] to form 5 moles of [tex]CO_2[/tex]

Thus the mole ratio of the oxygen to pentane will be 8:1

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Answer:

8:1

Step-by-step explanation:

edge

Answer:

5+5 = 10

6x5=30

I hope it works for you

Answer:

10 , 30

Step-by-step explanation:

5 + 5 = 10

6 * 5 = 30

Answer:

447 people

Step-by-step explanation:

382 plus 65 is 447.

Answer:

8v3

Step-by-step explanation:

phythagorean theorm

The measure of x from the triangle is x = 4

A planar figure or polygon having three sides and three angles is called a triangle.

The internal angles of a triangle, which has three vertices, add up to 180 degrees.

Assume the triangle is ABC, with A + B + C equaling 180 degrees.

Triangle area equals (1/2) × Length x Base.

About a right triangle

According to the Pythagoras Theorem, If a2 + b2 = c2, then the hypotenuse2 = base 2 + height 2, making it a right triangle.

If a2 + b2 c2, the triangle is an acute triangle.

If a2 + b2 > c2, the triangle is sharp.

Given the data,

Let's use ABC to depict the triangle.

Now, the triangle's sides are measured in units of AB and y.

x units = BC

Moreover, AC = 8 units.

The trigonometric relationships show that sin = opposite / hypotenuse.

Hence, the definition of sin 30° is x / 8

With simplification, we have (1/2) = x / 8

8 is multiplied twice, giving us x = 8/2 x = 4 units.

Hence , the sides of the triangle are solved

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Answer:

4.5 Games

Step-by-step explanation:

42 Minus 6 (shoes)= 36

36 divided by 8 (each game) would equals 4.5

Answer:

above is the solution to the question

Answer:

36 passengers

Step-by-step explanation:

Maria averages 20 passengers every 20 minutes, so she places 1 passenger per minute.

Sal averages 20 passengers every 25 minutes, so he places 0.8 passenger per minute.

If they work together, they can place (1 + 0.8) passengers = 1.8 passengers per minute.

In 20 minutes, they can load

1.8 passengers/minute * 20 minutes = 36 passengers

It took both Maria and Sal 11.1 minutes to load 20 passengers

The number of passenger Maria loads each minute = 20 passengers/20 minutes = 1 passenger per minute

The number of passenger Sal loads each minute = 20 passengers/25 minutes = 0.8 passenger per minute

Let t represent the total time taken to load the 20 passengers, hence:

(1 passenger per minute × t minutes) + (1 passenger per minute × t minutes) = 20 passengers

t + 0.8t = 20

1.8t = 20

t =  11.11 minutes

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Answer:

d

Step-by-step explanation:

Answer:

maybe a or b but to me it's a

Answer:

105. Alternate Interior Angles are Congruent. <3

Step-by-step explanation:

Alternate Interior Angles are Congruent <3 .In geometric terms, two sides of a polygon that share an endpoint make up an angle.

In geometric terms, two sides of a polygon that share an endpoint make up an angle. This angle is known as an internal angle for a simple polygon if a point within it is located inside the polygon, regardless of whether the polygon is convex or not. the inner of the two angles created where two polygonal sides meet, according to Wikipedia. any one of the four angles created when a third line cuts a pair of parallel lines.

inside angles The angles created within or inside of a shape are called interior angles. The interior angles in this case are ABC, BCA, and CAB.

Given ,

m<4=105

m<5=105

Therefore alternate interior angles is congruent to<3

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Answer:

Midline will be at -13 which is your vertical shift(d)

Amplitude (a) -s 13 si will move up to 0, back to midline(-13), down to -26, and then back to midline to complete the cycle. This would conform to a sine graph

There is no phase shift

The period is 6 minutes so b= 2pi/6 or pi/3

Equation therefor is y= 13sin[(pi/3)x] -13

[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Number \: of \:terms \: in \: A.P,n = 30[/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Fourth \: term ,a_4 = 11 [/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf last\:term, a_{30} = 89 [/tex]

[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]

[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf The \: A.P. [/tex]

[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf 23rd\: term, a_{23} [/tex]

[tex]\\[/tex]

[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]

The nth term of A.P is determined by the formula-

[tex]\green{ \underline { \boxed{ \sf{a_n = a+(n-1)d}}}}[/tex]

where

Since ,

[tex]\sf a_4 = 11 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+(4-1) d= 11 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+3d= 11\_\_\_(1) [/tex]

[tex]\sf a_{30}= 89 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+(30-1)d=89[/tex]

[tex]\longrightarrow[/tex][tex]\sf a+29d= 89\_\_\_(2)[/tex]

Subtracting equation (1) from equation(2)

[tex]\begin{gathered}\\\implies\quad \sf a+29d-(a+3d) = 89-11 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a+29d-a-3d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a-a+29d-3d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 26d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf d = \frac{78}{26} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf d = 3 \\\end{gathered} [/tex]

Putting the value of d in equation (1) -

[tex]\begin{gathered}\\\implies\quad \sf a+3(3) = 11 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a = 11-9 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a = 2 \\\end{gathered} [/tex]

[tex]\quad\quad\quad\sf =2+3[/tex]

[tex]\quad\quad\quad\sf =5 [/tex]

[tex]\quad\quad\quad\sf =2+6[/tex]

[tex]\quad\quad\quad\sf =8 [/tex]

[tex]\longrightarrow[/tex]Thus , The A.P is 2,5,8,. . . . . .

Now,

[tex]\begin{gathered}\\\implies\quad \sf a_n = a+(n-1)d \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23 }= 2+(23-1)\times 3 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+22 \times 3 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+66 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 68 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Thus , 23rd term is 68.

Answer:

x=56/66

Step-by-step explanation:

Answer:

The formula should be the change in y-values with respect to the change in the x-values. She used an incorrect formula

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Anya found the slope of the line that passes through the points (–7, 4) and (2, –3). Her work is shown below. Let (x2, y2) be (–7, 4) and (x1, y1) be (2, –3). m = = = The slope is . What error did she make? She simplified the denominator incorrectly. The denominator simplifies to –7. She labeled the points incorrectly. The point (–7, 4) should be (x1, y1). She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values. She used an incorrect formula. The formula should be the sum of the x-values with respect to the sum of the y-values.

Slope of a line is expressed according to the formula;

Slope m = Δy/Δx

Slope = y2-y1/x2-x1

Given the coordinates (–7, 4) and (2, –3), from the coordinates;

x1 = -7, y1 = 4, x2 = 3, y2 = -3

Substitute into the formula;

Slope = -3-4/3-(-7)

Slope = -7/3+7

Slope = -7/10

Based on Anya workings, it can be concluded that Anya used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values

By what the question asks, I assume that this refers to getting the slope in a linear equation.

The correct option is:

She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values.

A general linear equation is given by:

y = a*x + b

where a is the slope and b is the y-intercept.

We know that for a line that passes through points (x₁, y₁) and (x₂, y₂) then the slope can be computed as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Notice that the formula is the change in y-values with respect to the x-values,

So we can conclude that the correct option is:

"She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values."

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Using the normal distribution, it is found that:

1. His z-score was of Z = -1.88.

2. There is a 0.0301 = 3.01% probability that a randomly selected person has a smaller E/A ratio than the patient in question 1.

3. Z-score of z = 1.85, there is a 0.0322 = 3.22% probability that a randomly selected patient has a higher E/A ratio.

4. Due to the higher absolute value of the z-score, the first patient had a more extraordinary result.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item 1:

Considering his ratio, we have that X = 0.73, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.73 - 1.35}{0.33}[/tex]

[tex]Z = -1.88[/tex]

His z-score was of Z = -1.88.

Item 2:

The probability is the p-value of Z = -1.88, hence, there is a 0.0301 = 3.01% probability that a randomly selected person has a smaller E/A ratio than the patient in question 1.

Item 3:

Score of X = 1.96, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.96 - 1.35}{0.33}[/tex]

[tex]Z = 1.85[/tex]

The probability is 1 subtracted by the p-value of Z = 1.85, hence, 1 - 0.9678 = 0.0322 = 3.22% probability that a randomly selected patient has a higher E/A ratio.

Item 4:

Due to the higher absolute value of the z-score, the first patient had a more extraordinary result.

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Answer: Im trying to find out the same thing oh no!

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. What is the range of hours Troy spent at play rehearsal? Explain how to find the range of a data set. (3 points)

To find the range, subtract the smallest value from the largestvalue. For Troy’s  time, the range = 10 - 4 = 6 hours.

2. What is the range of hours Ronnie spent at play rehearsal? (3 points)

Ronnie’s range = 7 - 3 = 4 hours 

3. Who had a greater range of hours spent at rehearsal? (4 points)Troy had a bigger range.

Answer:

m∠A = 150°

m∠B = 30°

m∠E = 110°

Step-by-step explanation:

Linear pair:

⇒ m∠A + 30° = 180°

⇒ m∠A = 150°

Alternate interior angles:

⇒ m∠B = 30°

Sum of interior angles of a triangle is 180°:

⇒ m∠C + 30° + 40° = 180°

⇒ m∠C = 110°

Linear pair:

⇒ m∠C + m∠D = 180°

⇒ 110° + m∠D = 180°

⇒ m∠D = 70°

Alternate interior angles:

⇒ m∠E = m∠C

⇒ m∠E = 110°

Answer:

making x=0

Step-by-step explanation:

it gives you the points where the point intersects the y-axis

Answer:

A: Making x = 0

Step-by-step explanation:

The y-intercept of a function is where x is zero (i.e. [tex]f(0)[/tex])

Answer:

zero and one-hundred eighteen-thousandths

Answer: 18.4 inches

Step-by-step explanation: