Which shows two expressions that are equivalent to (-8)(-12)(2)

Answer:

  65 miles

Step-by-step explanation:

The straight line distance between two points can be considered to be the hypotenuse of a right triangle. In this case, the legs of the triangle are the distance east and the distance north. The Pythagorean theorem describes the relation between the legs (a, b) and the hypotenuse (c).

  c² = a² +b²

  c² = 60² +25² = 3600 +625 = 4225

  c = √4225 = 65

The two airports are 65 miles apart.

__

Additional comment

You may recognize that the greatest common factor of 25 and 60 is 5, which means these numbers have the ratio 5 : 12. You may also recognize these as being the two smaller numbers in the Pythagorean triple {5, 12, 13}. That is, you expect the airports to be 5×13 = 65 miles apart.

The distance between the two airports is 65 miles.

Let's denote the distance east as [tex]$d_e = 60$[/tex] miles and the distance north as [tex]$d_n = 25$[/tex] miles. The distance between the two airports, which is the hypotenuse of the right-angled triangle formed by the two distances, can be calculated as follows:

[tex]\[ d = \sqrt{d_e^2 + d_n^2} \][/tex]

Substituting the given values:

[tex]\[ d = \sqrt{60^2 + 25^2} \] \[ d = \sqrt{3600 + 625} \] \[ d = \sqrt{4225} \] \[ d = 65 \][/tex]

Therefore, the distance between the two airports is 65 miles.

Answer:

f(x)-g(x)= 4x²-3x-10

Step-by-step explanation:

(6x²-9x-17) - (2x²-6x-7)

use distributive property

6x²-9x-17-2x²+6x+7

combine like terms

4x²-3x-10

Answer:

a = 15

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

a +25+140 = 180

Combine like terms

a +165 = 180

Subtract 165 from each side

a+165-165 = 180-165

a = 15

Answer:

15 degrees

Step-by-step explanation:

In order to have a triangle, all the angles must add up to 180. Since we already have 2 or the three angles, we just add the two angles we have and subtract by 180 (working backwards!). 140 + 25 is equal to 165, and 180 - 165 is 15. Thus, 15 must be your answer.

The mode is the most frequently occurring number in a data set. In this case, there doesn't appear to be a mode, as each number only appears once.

To find the mode, we need to identify which age appears most frequently in the dataset. Given the data you provided - 28 years old, 48 years old, 55 years old, 64 years old - it seems every age only appears once and none of them repeat. Hence, in this case, we can not find a mode because there are no repeating numbers.

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Answer:

Add all the average amounts of items in each bag and you should get 23. Then, divide it by 3 since you are working with 3 numbers.

Answers for different places you have to round to:

Ones: 8

Tenths: 7.7

Hundredths: 7.67

Thousandths: 7.667

The average number of items in all the gift bags is [tex]7.4[/tex].

To find the average number of items in all the gift bags, we need to consider the distribution of the bags and their respective average items.

Given:

50% of the bags are green with an average of 8 items per bag.

20% of the bags are yellow with an average of 5 items per bag.

30% of the bags are blue with an average of 8 items per bag.

Let's calculate the average number of items across all gift bags:

1. Calculate the total number of bags:

Total bags = 50% (green) + 20% (yellow) + 30% (blue) = 100%

2. Calculate the weighted average of items:

[tex]\[ \text{Average items per bag} = \left(0.50 \times 8\right) + \left(0.20 \times 5\right) + \left(0.30 \times 8\right) \][/tex]

Green bags contribute [tex]\( 0.50 \times 8 = 4 \)[/tex] items on average.

Yellow bags contribute [tex]\( 0.20 \times 5 = 1 \)[/tex] item on average.

Blue bags contribute [tex]\( 0.30 \times 8 = 2.4 \)[/tex] items on average.

[tex]\[ \text{Average items per bag} = 4 + 1 + 2.4 \][/tex]

[tex]\[ \text{Average items per bag} = 7.4 \][/tex].

Answer:

8^4

Step-by-step explanation:

Here we have:

8^6 · 8³

-------------

   8^5

That's multiplication in the numerator.  The appropriate rule of exponents states that:

8^a·8^b = 8^(a+b), so the numerator is equivalent to 8^(6 + 3) = 8^9.

Now we have

8^9

------

8^5

and the appropriate rule for division here is

8^a / 8^b = 8^(a - b)

So our:

 8^9

---------  8^(9-5) = 8^4

  8^5

Answer:

We can say that the graph g(x) is obtained by shifting the grapf f(x) by 2 units up.

Step-by-step explanation:

[tex]f(x) = 2^x[/tex]

[tex]g(x) = f(x) + k[/tex]

Rule : f(x)→f(x)+k

graph f(x) shifts upward by k units

Since we are given that [tex]g(x) = f(x) + k[/tex]

So, this means when graph f(x) shifts upward by k units then g(x) is obtained

We are given that k = 2

So, when graph f(x) shifts upward by 2 units then g(x) is obtained .

Thus we can say that the graph g(x) is obtained by shifting the grapf f(x) by 2 units up.

15*18+12/3+9=103

(15*18=270)

(270+12=282)

(282/3=94)

(94+9=103)

Answer: 84

Simplify it to 14x6

Answer:

I think it's -5x

Step-by-step explanation:

I'm assuming the zero pair is simply adding

The answer to your question is 82%

The stadium is 87% filled with 13,920 people attending out of a maximum capacity of 16,000 seats.

To find out what percentage of the stadium's capacity is filled, we can use the formula: (Number of people in the stadium / Capacity of the stadium) × 100%. In this case, the stadium currently has 13,920 people and its capacity is 16,000 seats. We calculate the percentage like this:

(13,920 / 16,000) × 100% = 0.87 × 100% = 87%

Therefore, 87% of the stadium's capacity is filled.

Answer:

18

Step-by-step explanation:

Remark

This is one of those questions that can throw you. The problem is that do you include the original rectangle or not. The way it is written it sounds like you shouldn't

However if you don't the question gives you 2 complex answers. (answers with the sqrt( - 1) in them.

Solution

Let the width = x

Let the length = x + 5

Area of the rectangle: L * w = x * (x + 5)

Area of the smaller squares (there are 2)

Area = 2*s^2

x = s

Area = 2 * x^2

Area of the larger squares = 2 * (x+5)^2

Total Area

x*(x + 5) + 2x^2 + 2(x + 5)^2 = 120                 Expand

x^2 + 5x + 2x^2 + 2(x^2 + 10x + 25) = 120     Remove the brackets

x^2 + 5x + 2x^2 + 2x^2 + 20x + 50 = 120      collect the like terms on the left

5x^2 + 25x +  50 = 120                                   Subtract 120 from both sides.

5x^2 + 25x - 70 = 0                                         Divide through by 5

x^2 + 5x - 14 = 0                                               Factor

(x + 7)(x - 2) = 0                                                 x + 7 has no meaning  

x - 2 =  0

x = 2                                                              

Perimeter

P = 2*w + 2*L

w = 2

L = 2 + 5

L = 7

P = 2*2 + 2 * 7

P = 4 + 14

P = 18

Answer:

Part a) The scale of the new blueprint is [tex]\frac{5}{8} \frac{in}{ft}[/tex]    

Part b) The width of the living room in the new blueprint is [tex]9.4\ in[/tex]

Step-by-step explanation:

we know that

The scale of the original blueprint is

[tex]\frac{2}{5}\frac{in}{ft}[/tex]

and

the width of the living room on the original blueprint is 6 inches

so

Find the actual width of the living room, using proportion

[tex]\frac{2}{5}\frac{in}{ft}=\frac{6}{x}\frac{in}{ft}\\ \\x=5*6/2\\ \\x=15\ ft[/tex]

Find the actual length of the living room, using proportion

[tex]\frac{2}{5}\frac{in}{ft}=\frac{9.6}{x}\frac{in}{ft}\\ \\x=5*9.6/2\\ \\x=24\ ft[/tex]

Find the scale of the new blueprint, divide the length of the living room on the new blueprint by the actual length of the living room

[tex]\frac{15}{24} \frac{in}{ft}[/tex]

simplify  

[tex]\frac{5}{8} \frac{in}{ft}[/tex]      

Find the width of the living room in the new blueprint, using proportion

[tex]\frac{5}{8}\frac{in}{ft}=\frac{x}{15}\frac{in}{ft}\\ \\x=15*5/8\\ \\x=9.4\ in[/tex]

Final answer:

The scale of the new blueprint is 1.5625, and the width of the new blueprint is 9.375 inches.

Explanation:

The original blueprint of the Moreno’s’ living room has a scale of 2 inches= 5 feet.

The family wants to use a new blueprint that shows the length of the living room to be 15 inches. If the width of the living room on the original blueprint is 6 inches and the length is 9.6 inches, what are the scale and the width of the new blueprint.

Calculate the scale using the original blueprint scale and the new length provided:

Scale = (New Length)/(Original Length) = 15/9.6 = 1.5625.

Calculate the width of the new blueprint using the original width and the scale:

Width of new blueprint = (Original Width) * (Scale) = 6 * 1.5625 = 9.375 inches.

Yes! This is true. line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2

This can be confirmed by the concept of similar triangles. The proportions of the sides are used to confirm this

The proportion used is: LQ / L'Q = 4 / (4 + 4 ) = 1/2

The scale factor is 2.

Hence L'M' / LM = 2

Answer:

0 your asking the following right? -8-8?  If yes, its 0 if you substitute m.

:) hope that helped

Answer:

Which equations are true?

There is more than one correct answer choice. Select all that apply.

4⋅5m+4⋅7=20m+47

14+21w=7(2+3w)

49r+35=7(7r+35)

9(8h−3)=72h−27

5⋅2+5⋅3t=10+15t

3⋅6f+3⋅11=18f−33

Step-by-step explanation:

Once you expand the brackets on the left hand side you should get get the answers on the right hand side

The overall temperature would be 3.6°F as this is how much it was changed by

Answer=3.6°F

[tex]13 + 9 + 10 = 33[/tex]

Diego's neighbors paid him $33.

X= 9/2

X= 4.5

X= 4 1/2

Answer: 9/2

Step-by-step explanation:

1.Break down the problem into these 2 equations.

x+4=3x−5

−(x+4)=3x−5

2. Solve the 1st equation: x+4=3x−5.

x=9/2

3. Solve the 2nd equation: −(x+4)=3x−5

x=1/4

4. Collect all solutions.

x=1/4,9/2

5. Check solution

When x=1/4​​, the original equation ∣x+4∣=3x−5 does not hold true.

We will drop x=1/4​​ from the solution set.

6. Therefore,

x=9/2

Answer:

The inverse function is f(x) = (x + 7)/2

Step-by-step explanation:

To find the inverse of any function, start by switching the x and f(x) values.

f(x) = 2x -7

x = 2f(x) - 7

Now solve for the new f(x). The result will be your inverse function.

x = 2f(x) - 7

x + 7 = 2f(x)

(x + 7)/2 = f(x)

The inverse of Y = 2x - 7 can be found by swapping the x and y variables and then solving for y, which gives the inverse function y = (x + 7) / 2.

To find the inverse of the function Y = 2x - 7, you can follow these steps:

So, the inverse of Y = 2x - 7 is y = (x + 7) / 2.

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Answer:  The correct option is (C) $342.

Step-by-step explanation:  Given that Mr. Williams is building a sand box for his children and is costs $228 for the sand if he builds a rectangular-sand box with dimensions 9 ft by 6 ft.

We are to find the cost of the sand if he decides to increase the size to [tex]13\frac{1}{2}~\textup{ft by }9~\textup{ft}.[/tex]

Since the box is empty from inside, so we will be considering the perimeter of the box, not area.

The perimeter of the rectangular-sand box with dimensions 9 ft by 6 ft is

[tex]P_1=2(9+6)=30~\textup{ft},[/tex]

and the perimeter of the rectangular-sand box with dimensions [tex]13\frac{1}{2}~\textup{ft by }9~\textup{ft}.[/tex] is

[tex]P_2=2\left(13\dfrac{1}{2}\times9\right)=2(13.5\times9)=45~\textup{ft}.[/tex]

Now, we will be using the UNITARY method.

Cost of sand for building rectangular-sand box with perimeter 30ft = $228.

So, cost of  sand for building rectangular-sand box with perimeter 1 ft will be

[tex]\$\dfrac{228}{30}.[/tex]

Therefore, the cost of sand for building rectangular-sand box with perimeter 45 ft is given by

[tex]\$\dfrac{228}{30}\times45=\$342.[/tex]

Thus, the required cost of the sand is $342.

Option (C) is CORRECT.

Answer:

A. $513

Step-by-step explanation:

Find the area of the boxes by multiplying the sides.

The first box is 54 ft sq.

The second box is 121.5 ft sq.

So

[tex]\\\frac{54}{121.5} =\frac{228}{x}[/tex]

cross mult.

27702 = 54x

513 = x

Answer: --42

Step-by-step explanation:

All that you have to do in this equation is substitute the value of x given with the x's in the expression. SO...

Expression: -4(5x+2) - 6(x-3)

Substitute: -4(5(2)+2) - 6((2)-3)

Solve: -4(10+2) - 6(-1)

-4(12) - 6(-1)

-48 +6

Answer: -42

Hope this helps!

Answer:

What is the simplified expression?

✔ –26x + 10

What is the value for both expressions when x = 2

✔ –42

Step-by-step explanation:

I just got it correct

Answer:

Least positive angle measurement = 280°

Step-by-step explanation:

Given in the question

angle = -80°

Co terminal angles are angles whose difference differs by multiple of 360°

To solve this all we have to do is add or subtract 360° over and over again until we get answer between 0° and 360°

Answer:

280 is the answer.

Step-by-step explanation:

Angles are said to be coterminal when the sum of angles 360 degrees.

-80 ± 360

Since its asking for positive angle ,therefore

-80+360 = 280 degrees

Answer:

there are thirty kids in the class

Step-by-step explanation:

there are two boys to three girls so 18 divided by 3 is 6. 2 times 6 is 12. 12 plus 18 is 30.

The total number of students that are in Ms. Cunningham's class is 30 students.

Let the number of boys be represented by x.

2/3 = x/18

Cross multiply.

3 × x = 2 × 18

3x = 36

x = 36/2

x = 12

Boys = 12

Girls = 18

Total number of students = 12 + 18 = 30

Therefore, the total number of students that are in Ms. Cunningham's class is 30 students.

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Answer:

x = 7

Step-by-step explanation:

The triangles are similar, and they have a scale factor of 1/7 because 14 / 7 = 2.

Following the scale factor, you divide 49 by 7 to get 7.

The value of x in the second triangle is 7.

To determine the value of x in the diagram, we need to use the concept of similar triangles.

Two triangles are similar if their corresponding angles are equal and their sides are in proportion.

In this case, we have two triangles:

Triangle with sides 14 and 49.

Triangle with sides 2 and x.

Since both triangles are similar, we can set up a proportion using their corresponding sides:

(14 / 2) = (49 / x)

Now, we can solve for x:

(14 / 2) = (49 / x)

7 = 49 / x

To solve for x, we can multiply both sides of the equation by x:

7x = 49

Now, divide both sides by 7 to isolate x:

x = 49 / 7

x = 7

So, the value of x in the second triangle is 7.

for such more question on triangle

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u don't multiple u divide 3 and u do the same for 9 divide it by 3

Answer:

31.702 inches (C)

Step-by-step explanation:

Here we need to calculate the circumference of the bike tire.  

The formula for Circumference is C = πd, where d is the diameter.

Here, C = π(26 in), or 26π in.  Every time the wheel rotates, the bike covers  26π in.  If one tire completed 388 full rotations, then the distance Marc traveled was (26π inches/rotation)(388 rotations), or, to the nearest inch,

31,692 inches.  This corresponds to (C) of the given possible answer choices.

Answer:

c.) on edg.

Step-by-step explanation:

Answer:  3, -3, 3i, -3i

Step-by-step explanation:

[tex]x^4-81=0\\\\Factor:\\(x^2-9)(x^2+9)=0\\(x-3)(x+3)(x^2+9)=0\\\\\text{Apply the Zero Product Property:}\\x-3=0\qquad x+3=0\qquad x^2+9=0\\\boxed{x=3}\qquad \qquad \boxed{x=-3}\qquad \quad x^2=-9\\.\qquad \qquad \qquad \qquad \qquad \qquad x=\sqrt{-9}\\.\qquad \qquad \qquad \qquad \qquad \qquad \boxed{x=\pm 3i}[/tex]

B. the answer would be hyperbola

Answer:

Option 2 - Hyperbola

Step-by-step explanation:

Given : The polar equation [tex]r=\frac{1}{4-6\cos\theta}[/tex]

To find : What conic section is represented by the polar equation?

Solution :

To find the conic section first we convert the polar into Cartesian equation    

We know,  [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]x=r\cos\theta[/tex]              

[tex]r=\frac{1}{4-6\cos\theta}[/tex]

[tex]4r-6r\cos\theta=1[/tex]      

Substitute the value of r,

[tex]4(\sqrt{x^2+y^2})-6x=1[/tex]      

[tex]4\sqrt{x^2+y^2}=1+6x[/tex]        

Squaring both side,

[tex]16(x^2+y^2)=(1+6x)^2[/tex]      

[tex]16x^2+16y^2=1+36x^2+12x[/tex]      

[tex]16y^2=20x^2+12x+1[/tex]      

Applying completing the square we get,

[tex]16y^2=20(x+\frac{3}{10})^2-\frac{4}{5}[/tex]

[tex]16y^2-20(x+\frac{3}{10})^2=-\frac{4}{5}[/tex]

[tex]\frac{16y^2}{-\frac{4}{5}}-{20(x+\frac{3}{10})^2}{-\frac{4}{5}}=1[/tex]

[tex]-\frac{y^2}{\frac{1}{4}}+{(x+\frac{3}{10})^2}{\frac{1}{25}}=1[/tex]

[tex]{(x+\frac{3}{10})^2}{\frac{1}{25}}-\frac{y^2}{\frac{1}{4}}=1[/tex]

This is in the form of hyperbola equation i.e. [tex]\frac{x^2}{a^2}-\frac{y^2}{b^2} =1[/tex]

Therefore, The given conic section is a hyperbola.

Hence, Option 2 is correct.

[tex]\bf (-3v)^5\implies \stackrel{\textit{distributing the exponent}}{(-3)^5(v)^5}\implies -243v^5[/tex]

To simplify (-3v)^5, raise the absolute value to the power of 5 and keep the negative sign. The simplified expression is -243v^5.

To simplify the expression −3v5, raise the absolute value of -3v to the power of 5 and keep the negative sign. Since v is a variable, we cannot simplify it further.

The simplified expression is:

−35v5 = −243v5