What is the domain of the relation?

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.

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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.

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]5(2x + 7) = 10x + 35[/tex]

The given expression 5(2x+7) is equivalent to (10x+35).

The distributive property is the property that expresses the distributive law of algebraic multiplication. similarly, in polynomial expression we can use the distributive property for example we can write a(c+b)  in the form of (ac+bc).

We have a polynomial expression:

= 5(2x+7)

By using the distributive property we get

=(5×2x+5×7)

= (10x+35)

Thus, the given expression 5(2x+7) is equivalent to (10x+35).

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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

Gallons would provide a more precise measurement when measuring water evaporation from a swimming pool.

If you are measuring the amount of water evaporated from a swimming pool, gallons would give you a more precise measurement. Gallons is a larger unit of measurement than quarts and therefore provides a more accurate representation of the amount of water evaporated from a swimming pool due to its larger capacity.

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

15*18+12/3+9=103

(15*18=270)

(270+12=282)

(282/3=94)

(94+9=103)

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

I say 8 is the answer.

Proof:

[tex]3 + 2 + 3 = 8[/tex]

So 8ft is my answer.

Answer:

36 square feet outdoor carpet will be required for this hole.

Step-by-step explanation:

A triangle colored in green with a rectangular hole has been given in the figure.

Area of the outdoor carpet will be calculated by the expression,

Area of the carpet = Area of the right triangle - Area of the rectangle removed from the triangle

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}\times (12)\times (7)[/tex]

                                         = 42 square ft

Area of the rectangle = Length × Width

                                   = 3×2

                                   = 6 square ft

Area of the remaining area to be covered with the carpet = 42 - 6

= 36 square feet

Therefore, area of the outdoor carpet required for the hole = 36 feet²

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:

  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:

Step-by-step explanation:

yes i did and it was sad because it was so hard mabey some questions where easy but other than that it was hard i whould cry throught the whole pert test but nah i didint

The PERT test's Math portion mainly covers algebra and geometry. It includes topics such as fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts. Preparation, practice, and study guides are recommended to perform well.

The PERT (Postsecondary Education Readiness Test) is a placement test used by colleges in Florida to assess a students' college readiness in Reading, Writing, and Mathematics. If you're concerned about the Math section, understanding the content breakdown can be very helpful.

The Math portion of the PERT test primarily includes algebraic and geometry questions, with the main focus being algebra. Topics include but aren't limited to fractions, decimals, percentages, ratios and proportions, linear equations, inequalities, polynomials, quadratic equations, and basic geometry concepts.

Preparing for this test may include using study guides, practice tests, and brushing up on your algebra and geometry skills. Remember utilizing all available resources and allotting ample time to study can greatly help you perform better on the test.

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Answer:

I think it's -5x

Step-by-step explanation:

I'm assuming the zero pair is simply adding

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:

B: 192pi - 144

Step-by-step explanation:

Area of the sector = (120/360) * pi * r^2

Area of the sector = 1/3 * pi * 24 * 24

Area of the sector = 192 * pi

Now to find the area of the triangle.

The triangle is an isosceles triangle That means two of its sides are equal. They are equal to the radius of the circle, which is 24.

the small angles are equal to

2x + 120 = 180    Subtract 120 from both sides

2x = 60               Divide by 2

x = 60/2

x = 30

The height of the triangle is derived from sin(30) = opposite / hypotenuse

sin(30) = 1/2

hypotenuse = 24

1/2 = opposite / hypotenuse

1/2 = opposite / 24                      Multiply both sides by 24

1/2 * 24 = opposite

opposite = 12

The height = 12

r = 24

Area of the triangle = 1/2 * 12 * 24

Area of the triangle = 144

So the area of the shaded area = 192*pi - 144 which looks like B

The area of the shaded region of the circle in terms of pi is 192π - 144√3 m².

The correct option is B) 192π - 144√3 m².

The shaded area of the circle is a segment, to determine the area of the segment, we simply subtract the area of the triangle from the area of the sector.

Note that; the area of a sector is expressed as:

Area = (θ/360) × πr²

Area of a triangle can be expressed as:

Area = ab × (sinθ)/2

Hence, the area of the shaded region will be:

Area = ( (θ/360) × πr² ) - ( ab × (sinθ)/2 )

Plug in the values and simplify:

Area = ( (120/360) × π × 24² ) - ( 24 × 24 × (sin120)/2 )

Area = ( 192π ) - ( 144√3 )

Area = 192π - 144√3

Therefore, the shaded area measures 192π - 144√3 square meters.

Option B) 192π - 144√3 m² is the correct answer.

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Answer: 84

Simplify it to 14x6

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

Hello.

To find our answer we need to do .25 x 100.

      0.25

x      1 00

_________     STEP 1: Calculate 5 x 1 to get 5.

      5 00

    --

    0.25

x    1 00

_______     STEP 2: Multiply 2 x 1 to get 2.

   2 5 00

We've simply have our answer, but are not done.

We have 2500 but we cannot forget about the decimal.

We need to move it over 2 times.

Our final answer is 25.00

So she will pay $25.00 total for 100 apples.

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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].

The rule is add 3. The next three terms are 36, 39, 42

Answer:

A

Step-by-step explanation:

x^2 +8X = 33

x^2 +8X +(8/2)^2 = 33 + (8/2)^2

(x + 8/2)^2 = 49

(x +4)^2 = 49

x = -11

x = 3

The values of x in the given quadratic equation by completing the square are -11 and 3.

Hence, option A)-11,3 is the correct answer.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

Given th equation in the question;

x² + 8x = 33

Using completing the square method

First we take the half of the x term and square it

( 8/2 )² = 16

Now we add 16 to both sides

x² + 8x + 16 = 33 + 16

Next, we rewrite the perfect square on the left

( x + 4 )² = 33 + 16

( x + 4 )² = 49

We take square root of both sides

x + 4 = √49

x = -4 ± √49

x = -4 ± 7

x = -4 - 7 or -4 + 7

x = -11 or 3

x = -11, 3

The values of x in the given quadratic equation by completing the square are -11 and 3.

Hence, option A)-11,3 is the correct answer.

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

Diego's neighbors paid him $33.

Answer:

76.16

Step-by-step explanation:8 multiplied by 9.52

Answer: 5.6?

Step-by-step explanation:

x^= 16+16

x^= 32

find the square root of 32 which is 5.6 pretty sure

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:

[tex]49,987.24\ ft[/tex]

Step-by-step explanation:

Let

x-----> distance from the two towns

we know that

In the right triangle ABC

[tex]tan(32\°)=37,000/(x+y)\\x+y=37,000/tan(32\°)[/tex]

In the right triangle ABD

[tex]tan(76\°)=37,000/(y)\\y=37,000/tan(76\°)[/tex]

see the attached figure to better understand the problem

Remember that

(x+y)-y=x

so

[tex]x=\frac{37,000}{tan(32\°)} -\frac{37,000}{tan(76\°)}[/tex]

[tex]x=49,987.24\ ft[/tex]

Answer:

3 x 5 = 15

4 x 7 = 28

the answer is 15/28

;)

Answer:

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

:) hope that helped

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