f(x) = x − 8, g(x) = x2 Find (f + g)(x)

(1)   x = 12,   (2)   [tex]x=3\frac{1 }{2}[/tex]

Solution:

(1)     If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.

⇒ [tex]\frac{25}{10}=\frac{30}{x}[/tex]

Do cross multiply.

⇒ [tex]25 \times x=30 \times 10[/tex]

Divide both sides of the equation by 25 to equal the expression.

⇒ [tex]x=\frac{30 \times 10}{25}[/tex]

⇒ x = 12

(2)   Side of triangle = [tex]4\frac{1}{3} =\frac{13}{3}[/tex]

If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.

⇒ [tex]\frac{26}{\frac{13}{3} }=\frac{21}{x}[/tex]

Do cross multiply.

⇒ [tex]26 \times x=21 \times \frac{13}{3}[/tex]

⇒ [tex]26 \times x=7 \times 13[/tex]

Divide both sides of the equation by 26 to equal the expression.

⇒ [tex]x=\frac{7 \times 13}{26}[/tex]

⇒ [tex]x=\frac{7 }{2}[/tex]

⇒ [tex]x=3\frac{1 }{2}[/tex]

Answer:

w=9

Step-by-step explanation:

I hope this image is helpful to you.

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The student's algebra problem is solved by gathering like terms, simplifying the equation, and then isolating 'w'. The solution to the equation is 'w = 9'.

The subject of this question is mathematics, specifically, the topic is algebra. The equation given is -4+w+17-2/3w=16. We need to solve this equation for 'w'.

To start, we should gather like terms. Therefore, -4 + 17 becomes 13, making our equation 13 + w - 2/3w = 16. We can also rearrange this to w - 2/3w instead, which results in 1/3w = 16 - 13, therefore, 1/3w = 3. To solve for w, we can multiply the both sides of the equation by 3, which leads to w = 3 * 3 or w = 9.

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Answer:

7. [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]

8. [tex]0.1+0.15>0.2[/tex]

Step-by-step explanation:

Given:

Three sides of the triangles are given.

For Question 7

1/2 _ 1/3 _1/5

For Question 8

0.1 _ 0.15 _ 0.2

We need to use >, <, and + signs to write inequalities for the relationships among  the sides of the triangles.

Solution:

Part 7.

Property of the triangles.

Sum of two side of triangles must be greater than third side.

So, first, second and third side of the triangle is [tex]\frac{1}{2}, \frac{1}{3}\ and\ \frac{1}{5}[/tex]

[tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]

[tex]\frac{5}{6}>\frac{1}{5}[/tex]

So, its satisfy the triangle rule.

Therefore, Inequality is [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]

Part 8.

Property of the triangles.

Sum of two side of triangles must be greater than third side.

So, first, second and third side of the triangle is [tex]0.1, 0.15\ and\ 0.2[/tex]

[tex]0.1+0.15>0.2[/tex]

[tex]0.25>0.2[/tex]

So, its satisfy the triangle rule.

Therefore, Inequality is [tex]0.1+0.15>0.2[/tex]

Use inequalities to compare sides of triangles with >, <, and + signs.

For 7:

1/2 > 1/3

1/3 > 1/5

1/2 + 1/3 > 1/3 + 1/5

For 8:

0.1 < 0.15

0.15 < 0.2

0.1 + 0.15 < 0.15 + 0.2

Step-by-step explanation:

The area of a cirkel is calculated with the formula \pi×r^2. Using the 15 inch radius given we get \pi×15^2=706.5 inches squared.

Answer:

The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.

Step-by-step explanation:

Let's find out the pattern Zack is using to water his garden, this way:

First week =  1 3/8  gallons of water

Second week = 1 3/4 gallons of water = 1 3/8 + 3/8 = 1 6/8 = 1 3/4

Third week = 2 1/8 gallons of water = 1 3/4 + 3/8 = 1 6/8 + 3/8 = 2 1/8

The constant of adding every week is 3/8 gallons, therefore,

Fourth week = 2 1/8 + 3/8 = 2 4/8 = 2 1/2 gallons of water

Fifth week = 2 1/2 + 3/8 = 2 4/8 + 3/8 = 2 7/8 gallons of water

The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.

Following the pattern of increasing water usage by 3/8 gallons each week, Zack will use 2 7/8 gallons of water in the fifth week.

Zack watered his garden with increasing amounts of water over the first three weeks. Since there is a pattern, we can deduce the amount of water he will use in the fifth week by identifying the pattern and then continuing it.

Observing the pattern, we see that Zack is increasing the amount of water by 3/8 gallons each week. The progression in gallons is:

Continuing this pattern:

Therefore, Zack will use 2 7/8 gallons of water on the fifth week.

Answer:

Step-by-step explanation:

12 inch = 1 ft.

12 inch can be be written as (5 + 5 + 2) inch.

It is given that, 5 inches require for 12 beads.

Hence, (12 + 12) = 24 beads will take up (5 + 5) = 10 inches.

There are 2 inches more to fill.

5 inches required for 12 beads.

1 inch required for [tex]\frac{12}{5}[/tex] beads.

2 inches will be required for [tex]\frac{24}{5}[/tex] beads.

[tex]\frac{24}{5} = 4.8[/tex].

Hence, there will 24 + 4 = 28 beads in total. (Only 4 is added instead of 4.8 because, the number can not be in fraction and there is no space for 29 beads in total).

Here is the equation:

43.25 = 1.25t + 7 where t is the number of minutes he was on the trampoline.

Answer:

Step-by-step explanation:it is the second option. :)

Answer:

Top right = second choose

Step-by-step explanation:

Will drank [tex]8\frac{1}{3}[/tex] grams of sugar.

Step-by-step explanation:

Given,

Amount of sugar in one bottle = [tex]3\frac{3}{9}=\frac{30}{9}\ grams[/tex]

Amount of bottles drank by Will = [tex]2+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}\ bottles[/tex]

Total sugar drank by Will = Amount of sugar in one bottle * Amount of bottles drank by Will

Total sugar drank by Will = [tex]\frac{30}{9}*\frac{5}{2}[/tex]

Total sugar drank by Will = [tex]\frac{150}{18}=\frac{25}{3}[/tex]

Total sugar drank by Will = [tex]8\frac{1}{3}[/tex]

Will drank [tex]8\frac{1}{3}[/tex] grams of sugar.

Keywords: fraction, multiplication

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Answer: Here dimension of bigger triangle = 10

Dimension of smaller triangle = 5

Scale factor = 10/5 =2

Therefore

Center C and scale factor 2

Answer:

Answer:

The relationship between the number of months after the first year and the amount remaining on the card is discrete

The independent variable is the

number of months after the first year

The dependent variable is the

amount remaining on the card.

Answer: [tex]x=-25[/tex]

Step-by-step explanation:

For this exercise it is necessary to remember the multiplication of signs:

[tex](+)(+)+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]

Then, having the following equation provided in the exercise:

[tex]4 + \frac{1}{5}x = -1[/tex]

You need to solve for the variable "x" in order to find its value.

To solve the equation, you can follow the steps shown below:

Step 1: You need to subtract 4 from both sides of the equation. Then:

[tex]4 + \frac{1}{5}x-(4) = -1-(4)\\\\ \frac{1}{5}x=-1-4\\\\ \frac{1}{5}x=-5[/tex]

Step 2: This is the final step. You must multiply both sides of the equation by 5 in order to find the value of the variable "x".

Then, you get the following result:

[tex](5)( \frac{1}{5}x)=(-5)(5)\\\\x=-25[/tex]

Answer:

2

Step-by-step explanation:

There are 2 units of distance separating -5 and -3.

Answer:

- 2

Step-by-step explanation:

I think this right!! Hope it helps!!

The complete set of ordered pairs for the relation y = 2(x + 11), where x belongs to the set (-2, -1, 0, 1, 2), is {(-2, 18), (-1, 20), (0, 22), (1, 24), (2, 26)}.

The given equation is y = 2(x + 11), where x takes values from the set (-2, -1, 0, 1, 2). To find the corresponding y-values for each x-value, we substitute the given x-values into the equation and calculate the y-values.

For x = -2:

y = 2(-2 + 11) = 2 * 9 = 18

So, the ordered pair is (-2, 18).

For x = -1:

y = 2(-1 + 11) = 2 * 10 = 20

Ordered pair: (-1, 20).

For x = 0:

y = 2(0 + 11) = 2 * 11 = 22

Ordered pair: (0, 22).

For x = 1:

y = 2(1 + 11) = 2 * 12 = 24

Ordered pair: (1, 24).

For x = 2:

y = 2(2 + 11) = 2 * 13 = 26

Ordered pair: (2, 26).

Combining all these ordered pairs, we have the complete set of ordered pairs for the given relation:

{(-2, 18), (-1, 20), (0, 22), (1, 24), (2, 26)}.

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Answer:

Square

Got it correct on my test just now

Answer:

12.6

Step-by-step explanation:

plug in 5 for b

5*5 = 25

25-12.4=12.6

Answer:

B= -2.48

Step-by-step explanation:

Divide 5 and -12.4 both by 5 then B=-2.48

Answer:

6

Step-by-step explanation:

16/4=4 (to brother) 16-4=12 (whats remaining) 12/2=6 (to sister)

Ruby gives her sister 6 animals.

To find out how many animals Ruby gives her sister, we need to follow the instructions step by step. Ruby starts with 16 stuffed animals. She gives 1/4 of her collection to her brother, which is equal to 16 * 1/4 = 4. Now Ruby has 16 - 4 = 12 stuffed animals left. Then she gives half of the remaining animals to her sister, which is equal to 12 * 1/2 = 6. So Ruby gives her sister 6 animals.

Answer:

If each grid square represents one block, then the number of box he walked will be 30 blocks.

Step-by-step explanation:

Tommy walks from his home to the mall and then walks to a movie theater.

His home is at (0,0), the mall is at (0,8) and the movie theater is at (7,8).

Now, distance from (0,0) to (0,8) is 8 units and the distance from (0,8) to (7,8) is 7 units.

So, total distance covered is (8 + 7) = 15 units.

After leaving the theater Tommy walks to the store before returning home.

The store is at (7,0).

Now, the distance from (7,8) to (7,0) is 8 units and the distance from (7,0) to (0,0) is 7 units.

So, total distance covered is (8 + 7) = 15 units.

If each grid square represents one block, then the number of the box he walked will be (15 + 15) = 30 blocks. (Answer)

The height of a parallelogram can be found by solving the equation 'Area = base × height' given the area is 175 square centimeters and the height is 18 centimeters less than the base. The base 'b' and the height 'b - 18' form a quadratic equation that can be solved to find 'b', after which subtracting 18 will give the height.

The question is asking to find the height of a parallelogram given its area and a relationship between the base and the height. The area of a parallelogram is found using the formula Area = base × height. According to the given information, we know that the area is 175 square centimeters. The relationship between the base and the height of the parallelogram is such that the height is 18 centimeters less than the base. Therefore, we can denote the base as 'b' and the height as 'b - 18'. Plugging these into the formula for the area we get 175 = b × (b - 18).

To solve for 'b', we can set up and solve a quadratic equation. After finding the value of 'b', we can calculate the height by subtracting 18 centimeters from our value for 'b'. Let's go through the steps:

After solving the quadratic equation, we would get the value of 'b' and accordingly the value of 'b - 18' which is the height of the parallelogram in centimeters.

Answer:3√(p/q)3

Step-by-step explanation: Find the cube root .

The law used to simplify the expression [tex]( (p/q)^3 \)[/tex] is the "Power of a Quotient" rule.

The correct option is (b).

The "Power of a Quotient" rule states that when a fraction is raised to a power, we can raise both the numerator and denominator to that power individually. Mathematically, it is represented as:

[tex]\[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \][/tex]

Applied to the expression [tex]\( (p/q)^3 \)[/tex], we raise both[tex]\( p \) and \( q \)[/tex] to the power of 3:

[tex]\[ \left(\frac{p}{q}\right)^3 = \frac{p^3}{q^3} \][/tex]

This simplification allows us to express the original expression in terms of powers of the numerator and denominator separately. In other words, the exponent 3 is distributed to both [tex]\( p \) and \( q \), resulting in \( p^3 \)[/tex]in the numerator and [tex]\( q^3 \)[/tex] in the denominator.

Using this rule, we can handle expressions involving powers of fractions efficiently, breaking them down into simpler terms that are easier to work with or evaluate. It's particularly useful when dealing with algebraic expressions or equations where fractions with powers are involved, providing a systematic approach to simplification.

complete question given below:

Which law would you use to simplify the expression

[tex](p\q)^3[/tex]?

a.power of a power

b.power of a quotient

c.quotient of powers

d.power of a product

Answer:

Darius needs [tex]26\frac{2}{3}[/tex] cups of bread cubes to make four batches of stuffing for a family reunion.

Step-by-step explanation:

Given:

bread cubes to make a batch of stuffing  =   6 2/3 cup

To Find:

Number of cups of bread cubes needed to make four batches of stuffing for a family reunion = ?

Solution:

According to the question, to make one batch of stuffing Darius needs [tex]6\frac{2}{3}[/tex] cups of bread cubes

So if he wants to make four batched, then the number of cups of bread cubes  will be four times  as needed for making one batch

Then

Number of cups of bread cubes needed to make four batches = 4 x  bread cubes needed to make a batch of stuffing

Number of cups of bread cubes needed to make four batches

=  [tex]4 \times 6\frac{2}{3}[/tex]

=>[tex]4 \times \frac{18+2}{3}[/tex]

=> [tex]4 \times \frac{20}{3}[/tex]

=>[tex]\frac{80}{3}[/tex]

=>[tex]26\frac{2}{3}[/tex]

Darius will need 80/3 cups of bread cubes to make four batches of stuffing for a family reunion.

To find out how many cups of bread cubes Darius will need to make four batches of stuffing for a family reunion, we need to multiply the amount of bread cubes used in one batch by the number of batches he wants to make. Darius uses 6 2/3 cups of bread cubes in one batch. So, to find the total amount of bread cubes needed for four batches, we can multiply 6 2/3 cups by 4.

First, we convert the mixed number into an improper fraction: 6 2/3 = (6 * 3 + 2)/3 = 20/3.

Next, multiply the improper fraction by 4: (20/3) * 4 = 80/3 cups.

Therefore, Darius will need 80/3 cups of bread cubes to make four batches of stuffing for a family reunion.

================================

Work Shown:

C = 44 is the circumference

in general, the circumference of a circle is

C = 2*pi*r

Plug in C = 44 and solve for r.

C = 2*pi*r

44 = 2*pi*r

2*pi*r = 44

r = 44/(2pi)

r = 7.0028175 which is approximate

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

Now plug this into the formula for the area of a circle

A = pi*r^2

A = pi*(7.0028175)^2

A = 154.061985

A = 154 rounding to the nearest whole number

Answer:

B

Step-by-step explanation:

Circumference = 2πr

And circumference = 44 m

44 = 2πr

so, r = 44/2π

r = 22/π

Radius is 22/π

Area of circle = πr²

Area of circle = π × (22/π)²

Area of circle = π × 22²/π²

Area of circle = 22²/π

Area of circle = 484/π

Area of circle = 154.14m²

Answer: ( -6 , -6.5 )

Step-by-step explanation:

The formula for calculating Mid - point is given by

M = ([tex]\frac{x_{1}+x_{2}}{2}[/tex] , [tex]\frac{y_{1}+y_{2}}{2}[/tex] )

[tex]x_{1}[/tex] = -5

[tex]x_{2}[/tex] = -7

[tex]y_{1}[/tex] = -9

[tex]y_{2}[/tex] = -4

substituting into the formula , we have

M = [tex]\frac{-5-7}{2}[/tex] , [tex]\frac{-9-4}{2}[/tex]

M = [tex]\frac{-12}{2}[/tex] , [tex]\frac{-13}{2}[/tex]

Therefore : mid point = ( -6 , -6.5 )

Answer:

Infinitely many

Step-by-step explanation:

To read 43.106 correctly, say 'forty-three point one zero six'

To read the number 43.106 correctly, we start by reading the whole number part, which is 43. This is read as 'forty-three'.

Next, we read the decimal part. The first digit after the decimal point is read as 'one', the second digit as 'zero', and the third digit as 'six'. Finally, we put all the parts together and read the number as 'forty-three point one zero six'.

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Answer:

The length of the shadow the telephone booth is 12 ft.

Step-by-step explanation:

Given:

An adult elephant that is 10 ft tall casts a shadow that is 15 ft long.

The length of the telephone booth is 8 ft.

Now, to find the length of the shadow the telephone booth casts.

Let the length of the shadow the telephone booth be [tex]x.[/tex]

As given, an adult elephant that is 10 ft tall casts a shadow that is 15 ft long.

So, 10 ft is equivalent to 15 ft.

Thus, 8 ft is equivalent to [tex]x.[/tex]

Now, to get the length of the shadow of the booth we get cross multiplication method:

[tex]\frac{10}{15} =\frac{8}{x}[/tex]

By cross multiplying we get:

[tex]10x=120[/tex]

Dividing both sides by 10 we get:

[tex]x=12.[/tex]

Therefore, the length of the shadow the telephone booth is 12 ft.

Answer:

60 degrees

Step-by-step explanation:

180-90=90

90-30=60

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Work Shown:

125 = 5*5*5 = (5)^3

x^12 = (x^4)*(x^4)*(x^4) = (x^4)^3

125x^12 = (5x^4)^3

[tex]\large \sqrt[3]{125x^{12}} = \left(125x^{12}\right)^{1/3}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = \left((5x^4)^3\right)^{1/3}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = (5x^4)^{3*(1/3)}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = (5x^4)^{1}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = \textbf{5x}^{\textbf{4}}[/tex]

Answer:

Step-by-step explanation:

[tex]125=5*5*5=5^{3}\\\\\ \sqrt[3]{125x^{12}}=\sqrt[3]{125*x^{4*3}}\\\\=\sqrt[3]{5^{3}*(x^{4})^{3}}=5*x^{4}=5x^{4}[/tex]