Three students were given the expression shown and were asked to take a common factor out of two of the terms. Use the drop-down menus to complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent.

Answer:

Hello

Step-by-step explanation:

955÷35

27.2857142857

Or

35/955

35)955(27

-945

________

10

I hope this works♥️

Answer: {5 ± 2√10, 5 - 2√10}

Step-by-step explanation: First isolate the binomial squared by adding 40 to both sides to get (x - 5)² = 40.

Next, square root both sides to get x - 5 = ± √40.

Notice that root of 40 can be broken down to 2√10.

So we have x - 5 = ± 2√10.

To get x by itself, add 5 to both sides to get x = 5 ± 2√10.

So our answer is just {5 ± 2√10, 5 - 2√10}.

As a matter of form, the number will always come before the

radical term in your answer to these types of problems.

In other words, we use 5 ± 2√10 instead of ± 2√10 + 5.

Answer:

Question 1 = D) Acute

Question 2 = C)3 feet

Question 3 = D) Obtuse

Question 4 = C)27.73 ft.

Step-by-step explanation:

Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?

In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem

Where:

If a² + b² = c² = Right angle triangle

If a² +b² > c² = Acute triangle.

If a² +b² < c² = Obtuse triangle.

It is important to note that the length ‘‘c′′ is always the longest.

Therefore, for the above question, we have lengths

5 = a, 6 = b and c = 7

a² + b² = c²

5² + 6² = 7²

25 + 36 = 49

61 = 49

61 ≠ 49, Hence 61 > 49

Therefore, this is an Acute Triangle

Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?

This is question that deals with proportion.

The formula to solve for this:

Height of the statue/ Length of the shadow of the person = Height of the person/ Length of the shadow of the person

Height of the statue = 15 feet

Length of the shadow of the person = 20 feet

Height of the person = unknown

Length of the shadow of the person = 4

15/ 20 = Height of the person/4

Cross Multiply

15 × 4 = 20 × Height of the person

Height of the person = 15 × 4/20

= 60/20

Height of the person = 3 feet

Therefore, the person is 3 feet tall.

Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?

In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem

Where:

If a² + b² = c² = Right angle triangle

If a² +b² > c² = Acute triangle.

If a² +b² < c² = Obtuse triangle.

It is important to note that the length ‘‘c′′ is always the longest.

Therefore, for the above question, we have lengths 17, 12, 9

9 = a, 12 = b and c = 17

a² + b² = c²

9² + 12² = 17²

81 + 144 = 289

225 = 289

225 ≠ 289

225 < 289

Hence, This is an Obtuse Triangle.

Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?

To calculate how far apart the two friends are we use the formula

Distance = √ ( Length² + Breadth²)

We are given dimensions: 12ft by 25ft

Length = 12ft

Breadth = 25ft

Distance = √(12ft)² + (25ft)²

Distance = √144ft²+ 625ft²

Distance = √769ft²

Distance = 27.730849248ft

Approximately ≈27.73ft

Therefore, the friends are 27.73ft apart.

Answer:

a)

H₀ : µd = 0  

H₁ : µd < 0  

b)

The test statistic is

tₙ₋₁ = α / s√n

c)

at 0.10 level of significance,

tₙ₋₁ , ₐ

t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311

d)

given that  T(critical) = 1.62

∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311

at 10% level of significance,

REJECT H₀

Since 1.62 > 1.311, we can reject the null hypothesis.

Answer:

Step-by-step explanation:

The correct answer is q

Because we have been given the equation p + q already so if we observe the equation carefully we see that if we add the variable q to the variable p we get the answer p + q

Answer:

12 units

Step-by-step explanation:

Since all of the sides of a rhombus are congruent, JK = JM which means:

2x + 4 = 3x

-x = -4

x = 4 so 3x = 3 * 4 = 12

Answer:

The two choices are true by CPCTC. Are there other choices that were not posted?

Answer: 0.418 < p < 0.512

Step-by-step explanation: A 95% conifdence interval for a population proportion is given by:

[tex]p + z\sqrt{\frac{p(1-p)}{n} }[/tex]

where:

p is the proportion

z is score in z-table

n is sample size

The proportion for people who said "yes" is

[tex]p=\frac{202}{434}[/tex] = 0.465

For a 95% confidence interval, z = 1.96.

Calculating

[tex]0.465 + 1.96*\sqrt{\frac{0.465(0.535)}{434} }[/tex]

[tex]0.465 + 1.96*\sqrt{0.00057}[/tex]

0.465 ± 1.96*0.024

0.465 ± 0.047

Interval is between:

0.465 - 0.047 = 0.418

0.465 + 0.047 = 0.512

The interval with 95% of confidence is between 0.418 and 0.512.

The perimeter of the swimming pool is 15m

A swimming pool is rectangular in nature. The perimeter of the rectangular pool is expressed using the formula;

[tex]P=2(L+W)[/tex]

Given that

Length L = 4.5m

Width W = 3m

Get the perimeter

[tex]Perimeter = 2(4.5+3)\\Perimeter = 2(7.5)\\Perimeter = 15m[/tex]

Hence the perimeter of the pool is 15m

1.1.4 Rate is defined as the ratio between two quantities with a different unit. Examples of rates are;

The ratio is simply defined as the ordered pair between two variables x and y, For instance,

Learn more on ratio and rate here: https://brainly.com/question/24325733

Answer:

$800

Step-by-step explanation:

Let the original price be $x.

75% reduction ----- 100% -75%= 25%

25%x= 200

[tex] \frac{25}{100} x = 200 \\ x = 200 \div \frac{25}{100} \\ x = 200 \times \frac{100}{25} \\ x = 800[/tex]

Thus, the original price of the clothes dryer is $800.

Answer:

$800

Step-by-step explanation:

Let the original price be x.

Final price=100%-75%

                  =25%

x-75%=200

x=200 x 100/75

x=8 x 100

x=800

Thank you!

Answer:

step 2

Step-by-step explanation:

9 = -3(e - 2)

9 = -3e + 6

9-6 = -3e

3 = -3e

divide both sides by -3

-1 = e

Answer:

The answer is 55, -275, 1375, -6875......

Step-by-step explanation:

Answer:

C. [tex] y = 3\sqrt{7} [/tex]

Step-by-step explanation:

Based on the right triangle altitude theorem, the altitude, y, in the diagram above, equals the geometric mean of 9 and 7.

This implies => [tex] y = \sqrt{9*7} [/tex]

Thus, solve for y.

[tex] y = \sqrt{9} * \sqrt{7} [/tex]

[tex] y = 3\sqrt{7} [/tex]

The answer is C. [tex] y = 3\sqrt{7} [/tex]

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find GV

To find GV we use cosine

cos∅ = adjacent / hypotenuse

From the question

GV is the adjacent

GC is the hypotenuse

So we have

GC = 55°

GV = 55 cos 37

GV = 43.92495

We have the final answer as

Hope this helps you

Answer:

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Step-by-step explanation:

For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,

( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.

( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120

Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )

_________________________________

So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Answer:

[tex] \frac{1}{3} [/tex]Rational number as denominator is not equal to zero and numerator is a integer.

Rational numbers. denoted by [tex] \mathbb Q[/tex]

1/3 is clearly not a natural number or integer.

it is a fraction, =0.333 , it fits the definition of rational number ([tex] \frac pq [/tex]).

Answer:

Circle Equation : x² + y² = 21

Step-by-step explanation:

So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.

The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,

( √5 )² + ( 4 )² = r²,

5 + 16 = r²,

r = √21

In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -

( x - 0 )² + ( y - 0 )² = (√21 )²

Circle Equation : x² + y² = 21

Answer:

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

Step-by-step explanation:

The remainder is the value of the subtraction of the last 2 lines in the procedure.

  5x - 9

- (5x - 10)

That is

5x - 5x = 0 and - 9 - (- 10) = - 9 + 10 = 1

over the divisor x- 2 , gives

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

Answer:

Step-by-step explanation:

f(g(0))=

g(0)= 6(0) + 4 = 0 + 4 = 4

f(4)= 4(4)+5 = 16 + 5 = 21

g(f(0))=

f(0)= 4(0)+5 = 0+5 = 5

g(5)= 6(5)+4 = 30+4= 34

Answer:

204/1015 (irreducible) = 20.1%

1/8120 (irreducible) = 0.01232%

1/5832 (irreducible) = 0.01715%

1/6 (irreducible) = 16.67%

Step-by-step explanation:

Domain of a any cubic function [tex]f(x)=ax^3+bx^2+cx+d[/tex] is defined to be always [tex]\mathbb{R}[/tex].

The derivative with respect to x of your cubic function is,

[tex]\dfrac{d}{dx}f(x)=f'(x)[/tex]

to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,

[tex]\dfrac{d}{dx}x^3=3x^2[/tex] by the rule [tex]\dfrac{d}{dx}x^m=mx^{m-1}[/tex] where [tex]m\in\mathbb{R}[/tex]

[tex]\dfrac{d}{dx}-6x=-6[/tex]

[tex]\dfrac{d}{dx}3=0[/tex]

So the derivative is,

[tex]f'(x)=3x^2-6[/tex]

both derivative and the original function have equal domain.

Hope this helps :)

Step-by-step explanation:

[tex]thank \: you[/tex]

The answer is the first choice. If every 2 cm. is 4 cm., that means that the dimensions' values are doubled. Then, you can just double the dimensions. Preferably, in my opinion, this is the easier way to go. By your preference, though, you can do it the longer way as well.

There are 4 2s in the number 8.

There are 3 2s in the number 6.

If each of the 2s are 4s,

So, therefore,

Transforming the 2s to 4s,

4x4=16 cm.

3x4=12 cm.

So, this means that the final answer is the first choice. I hoped that this helped  answer your question. Enjoy your day, and take care!

Answer:

`Length=16 feet, width=12 feet

Image result for how to  use scale model step by step'

Divide the real life dimension of either length or width by that of the model. So the real life object had a length of 32m, and the model had a length of 8, then do 8(4). This is equal to 32, then divide by 2.

Hope this helps love <3

Answer:

Step-by-step explanation:

  tan(A) = a/b = 3.3/1.7

  A = arctan(33/17) ≈ 62.7°

  B = 90° -A = 27.3°

  c = √(a²+b²) = √(3.3² +1.7²) = √13.78

  c ≈ 3.7

Answer:

[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]

Step-by-step explanation:

Given that:

[tex]cosA=-\dfrac{1}3[/tex]

and

[tex]tanA > 0[/tex]

To find:

[tex]cos\dfrac{A}{2} = ?[/tex]

Solution:

First of all,we have cos value as negative and tan value as positive.

It is possible in the 3rd quadrant only.

[tex]\dfrac{A}{2}[/tex] will lie in the 2nd quadrant so [tex]cos\dfrac{A}{2}[/tex] will be negative again.

Because Cosine is positive in 1st and 4th quadrant.

Formula:

[tex]cos2\theta =2cos^2(\theta) - 1[/tex]

Here [tex]\theta = \frac{A}{2}[/tex]

[tex]cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}[/tex]

But as we have discussed, [tex]cos\dfrac{A}{2}[/tex] will be negative.

So, answer is:

[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]

Answer:

She can put the rocks into groups of 19.

That would give her 2 groups.

Step-by-step explanation:

The mean of the exam score is 65.56

The given exam data is as follows;

Possible Score range ----------- frequency (f) -------- score (x) -----------(fx)

40 - 50   -------------------------  21 ------------------- -----45 -------------- 945

50 - 60  --------------------------- 39------------------------55 ---------------2145

60 - 70 ----------------------------- 40---------------------- 65 ---------------- 2600

70 - 80 ------------------------------ 34 --------------------- 75 ----------------- 2550

80 - 90 ------------------------------ 28 --------------------- 85 ---------------- 2380

Note:[tex]score (x) = \frac{sum \ of \ the \ range }{2} , \ example \ \frac{40+49.99}{2} \approx 45[/tex]

The sum of the frequency (f) = 162

The sum of fx, ∑fx = 10620

The mean of the exam score:

[tex]\bar x = \frac{\Sigma fx }{\Sigma f} = \frac{10620}{162} = 65.56[/tex]

Therefore, the mean of the exam score is 65.56

To learn more about grouped mean calculation please visit: https://brainly.in/question/20735794

Step-by-step explanation:

28000 ÷ 100

=280

280 × 5

=1400

Answer:

255.8

Step-by-step explanation:

first

1/6*1535

=255.8