a. Using parallel line relationships, find the value of
x. Use the relationship between the two marked
angles to set up your equation.
Show your work to support your answer. (4 pts)
x =
b. Find the measure of each of the angles. Don’t forget to label your answers.

The required state income tax owed on a $90,000 per year salary is $4950.

Given that,
A table shows the income tax owed by the state on the particularar salary,
Income Range ($)      Tax Rate

0 - 10,000                     3%
10,001 - 50,000             5%
50,001 - 100,000           5.5%

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
on $90,000
Tax owed = 5.5% of 90000, because this salary lies in the segment 50,001 - 100,000.
Tax owed = 0.055[90000] = $4950

Thus, the required state income tax owed on a $90,000 per year salary is $4950.

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Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

Given that, it takes Zach 10 minutes to paint [tex]40\frac{1}{2}[/tex] square feet of his bedroom wall.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,  square feet = 40.5 square feet

Rate at which he paints the wall =40.5/10

= 4.05 square feet per minute

As we know 1 hour =60 minutes

Now, number of square feet

= 4.05×60

= 243 square feet

Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

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Answer:

2.8 Miles in 24 minutes

Step-by-step explanation:

60 / 24 = 2.5

2.5 / 7 = 2.8

Answer:

17.5mi

Step-by-step explanation:

7mi = 17.5mi

60min = 24min

60/24=2.5

2.5*7=17.5

Answer:

A/ $4 for 1 gallon

B/ $48

Step-by-step explanation:

Take 24 divided by 6 = $4 per gallon

Then take 4 times 12 = $48 for 12 gallons

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The product of A x B of matrix is

a)  [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]

b) [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]

c) [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]

d) [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the 2 matrices be A and B

The value of matrix A is

[tex]A = \left[\begin{array}{ccc}4\\5\\\end{array}\right][/tex]

The value of matrix B is

[tex]B = \left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]

Now , the dimensions of matrix A is 2 x 1 and of matrix B is 1 x 2

So , matrix multiplication is possible

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}4\\5\\\end{array}\right] *\left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]

So  , the value of matrix C is calculated as

[tex]C = \left[\begin{array}{ccc}( 4 * 2 ) &( 4 * 3 )\\( 5 * 2 ) &(5 * 3 )\\\end{array}\right][/tex]

On simplifying the matrix , we get

[tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]

Therefore , the value of matrix C is   [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]

b)

C be the result of A x B

The value of matrix A

[tex]A = \left[\begin{array}{ccc}3\\4\\\end{array}\right][/tex]

The value of matrix B is

[tex]B = \left[\begin{array}{ccc}1&2\\\end{array}\right][/tex]

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}( 3 * 1 ) &( 3 * 2 )\\( 4 * 1 ) &(4 * 2 )\\\end{array}\right][/tex]

On simplifying the matrix , we get

[tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]

Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]

c)

C be the result of A x B

The value of matrix A

[tex]A = \left[\begin{array}{ccc}-1\\6\\\end{array}\right]\\[/tex]

The value of matrix B

[tex]B = \left[\begin{array}{ccc}7&2\\\end{array}\right][/tex]

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]

Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]

d)

C be the result of A x B

The value of matrix A

[tex]A = \left[\begin{array}{ccc}8\\5\\\end{array}\right]\\[/tex]

The value of matrix B

[tex]B = \left[\begin{array}{ccc}3&-12\\\end{array}\right][/tex]

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]

Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]

Hence , the matrix multiplication is done and the results are given

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5 children can share all parts of the bread if each child takes 0.2 parts.

Fraction are numbers of the form [tex]\frac{a}{b}[/tex] where a and b are real numbers. It is represented as a portion or part of a whole.

The number on the top is called numerator and the number on the bottom is called denominator.

There are 10 equal parts of bread and each child takes 0.2 part.

Total parts of the bread = 10

Part each child takes = 0.2 = [tex]\frac{2}{10}[/tex]

2 parts out of 10 are taken by each child.

Remaining are  [tex]\frac{8}{10}[/tex] parts.

[tex]\frac{2}{10}[/tex] × 4 =  [tex]\frac{8}{10}[/tex]

Remaining parts can be shared by 4 children.

Hence number of children who can share the bread if each takes 0.2 parts = 5

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Answer:

1. 3/10

2. 19/12

3. 35/36

4. 1/3

Step-by-step explanation:

Answer:

2 rows on each page equals 104, which means that there would be 3 non-used photos

Step-by-step explanation:

Answer:

Answer: 200x + 25y <= 6000

Step-by-step explanation:

He started out with 47 balls after winning 2 blue balls and losing 3 red balls.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party.

Here,

Let the number of blue balls be x and the number of red balls be y,

after 5 days ,

x + 10 = y - 15      

after 9 days ,

x + 18 = 2 * ( y - 27 )  

subtracting both,

8 = y - 39

y = 47

The number of red balls in beginning is 47.

He had 47 balls in the beginning as he win 2 blue ball and lose 3 red balls.

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As per the given equation, the resulting conversion is written as,

13.6g/cm³ x 1kg/1000 x 10⁶cm³/m³ = 13600kg/m³

Equation:

An equation consist the value of the variable, numbers and the constants.

Given,

Here we have the density of mercury is 13.6 grams per cubic centimeter.

Now, we have to convert this one into kg/m3.

Here the process of conversion of  13.6 g/cm3 to kg/m3

We know that, 1 Kg of weight is equal to 1000 grams of weight

Then it can be written as

=> 1 g = 1 kg/1000

Then the first blank (numerator) will be filled with 1 Kg

Similarly, 1 meter is equal to 100 centimeter

So, for cubic unit it can be written as,

=> 1 cm³ = 1m³/100³

It can be simplified as,

=> 1 cm³ = 1m³/10⁶

Now, the second blank (numerator) will be filled with 10⁶

Finally, the third blank (denominator) will be filled with 1m³

Therefore, the last blank will be 13600

Hence, we have find the all the values on the blanks.

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Circle B will have larger circumference by 3.14 centimeter

The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle.

The circumference of the circle is = 2пr where r is radius

According to the information

Circle A has diameter = 9 cm

Radius of circle A = [tex]\frac{9}{2}[/tex] cm

Circumference of Circle A = 2пr

                                            = 2 × 22/7 × 9/2

                                            = 28.28 centimeter  

Circle B has radius = 5 cm

Circumference of circle B = 2 × 22/7 × 5

                                             = 31.42 centimeter

Circle B will have larger circumference by 3.14 centimeter

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The base length of the isosceles triangle is 23. Therefore, the correct option is C.

An isosceles triangle is a triangle with (at least) two equal sides. It also has two angles equal to each other.

The base angle of an isosceles triangle is equal in length.

The legs of an isosceles triangle are equal. Therefore,

3x - 1 = - 3x + 41

3x + 3x = 41 + 1

6x = 42

divide both sides by 6

x = 42  /6

x = 7

Let's find the length of the base side.

Therefore,

4x - 5

where

x = 7

4(7) - 5 = 28 - 5 = 23

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The graph's intersection with the x-axis is known as the x-intercept. The graph's intersection with the y-axis is known as the y-intercept.The y-intercept is (0,-4).

To find Y intercept substitute x=0;

here X interept is (1,-1)

Y intercept (0,-4)

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Answer:

the slope is -1/9

Step-by-step explanation:

The first thing to do is use the slope formula y^1 - y^2 over x^1 - x^2. You substitute each value into these variables and solve, which will then give you a negative slope of -1/9.

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The food will be needed to feed all the cub for one year is 1825 kg.

Given :

A lion ha 4 cubs that weigh 1. 7 kg, 2. 1 kg, 3 kg, and 2. 7 kg. Each cub eat 1. 25 kg of food a day.

one cub eats food = 1.25 kg

4 cubs eats food = 1.25 kg * 4

= 125 / 100 * 4 kg

= 500 / 100 kg

= 5 kg

5 kg for one day.

cub eats food for one year = 365 * 5 kg

= 1825 kg.

Therefore the food will be needed to feed all the cub for one year is 1825 kg.

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Answer:

x+5 or 5+x

Step-by-step explanation:

It seems we are looking for a math expression that is the same as English expression you wrote.The sum is what we get when we add numbers. Therefore, we could restate the English expression as what do we get when we add 5 to the number x? While we do not know what specific number x represents, we do know that if we add 5 to the number x we get 5 plus x. Now the question can be restated as, "How do we write 5 plus the number x?" Do you know the answer now? Does 5 + x sound right? How about x + 5? Both of these expressions are correct as they both represent the sum of 5 and the number x.

There were 1080 seats in the theater.

In this question, we have been given that the 6th grade students went on a field trip to see a ballet.

The students filled 702 seats leaving 35% vacant.

We need to find the total seats in the theater.

Let there were n seats in the theater.

Given that 35 percent of total seats were vacant.

So, we get an equation,

702 + (35% of n) = n

702 + 0.35n = n

(1 - 0.35)n = 702

0.65n = 702

n = 1080

Therefore, the total seats in the theater = 1080

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Answer:

A

Step-by-step explanation:

mass / volume

m/v

Answer: d = m/V

Step-by-step explanation: density is the mass divided by volume or d= m/V

Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

What is a Pythagoras theorem?

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:

a² + b² = c²

To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:

KL² = KM² + KN²

Substituting the given values, we get:

24² = 10² + KN²

Solving for KN, we get:

KN² = 24² - 10²

= 576 - 100

= 476

KN = √476

= 21.84

Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

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Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

What is a Pythagoras theorem?

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:

a² + b² = c²

To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:

KL² = KM² + KN²

Substituting the given values, we get:

24² = 10² + KN²

Solving for KN, we get:

KN² = 24² - 10²

= 576 - 100

= 476

KN = √476

= 21.84

Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

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The percent of increase is 4.761 %

Given :

A laptop computer originally priced at $2100 now and sell for $2,200.

Percentage :

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Difference = sell price - original price

= 2200 - 2100

= 100

Percent of increase = 100 * 100 / 2100

= 100 * 1 / 21

= 100 / 21

= 4.761 %

Therefore 4.761 % increase in percent.

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Answer:

Step-by-step explanation:

Square, Irregular shape

The value of a , b and c are 7, 11 and 1 respectively.

173a is divisible by 9.

Rule of divisible by 9 is:

The number itself is divisible by 9 if its digit sum is also divisible by 9.

digits sum  =  1+7+3+a  = 11+a.

11+a is divisible by 9. a can be 7 so that 11+7 = 18 is divisible by 9.

minimum positive value of a = 7.

173b is divisible by 11

Rule of divisible by 11 is:

A number is completely divisible by 11 if the difference between the sum of its alternative digits is divisible by 11.

sum of its alterative digits:

1+3 =4  

7+b =7+b

difference of alternative digits sum = 7+b-4 = b+3 is divisible by 11 b = 8

so that 8+3 = 11 is divisible by 11.

minimum positive value of b = 11.

173c is divisible by 6.

Rule of divisible by 11 is:

Any number that can be divided by both 2 and 3 is also divisible by 6.

sum of digits of number = 1+7+3+c = 11 + c if divisible by 2 then it should be even if we put c = 1  , 11+1 = 12 which is divisible by both 2 and 3.

minimum positive value of c = 1.

So the value of a ,b and c are 7, 11 and 1 respectively.

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Answer:

1.03% of 0.054=0.0005562

Answer:

42

Step-by-step explanation:

Given function:

[tex]f(x)=4x^4-2x^3-3x^2+3x[/tex]

Use the method of synthetic substitution to find the value of the function when x = 2.

Place the value of x in the left box and write the coefficients of the function in descending order, remembering to write a zero for the coefficient of any missing term.  

(As there is no constant term in this function, the last coefficient should be written as zero).

       [tex]4x^4-2x^3-3x^2+3x[/tex]

[tex]\begin{array}{c|ccccc}2&4&\:\:-2&\;\;-3&\;\:\:\:\:3&\;\;0\\\cline{1-1} \end{array}[/tex]

Bring the leading coefficient down:

[tex]\begin{array}{c|ccccc}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &&&\\\cline{2-6}&4\end{array}[/tex]

Multiply the number you brought down with the number in the box and put the result in the next column (under the -2):

[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&&\\\cline{2-6}&4\end{array}[/tex]

Add the two numbers in the second column together and put the result under them in the bottom row:

[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&&\\\cline{2-6}&4&6\end{array}[/tex]

Repeat:

[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&12&\\\cline{2-6}&4&6&9\end{array}[/tex]

[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&12&18\\\cline{2-6}&4&6&9&21\end{array}[/tex]

[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&12&18&42\\\cline{2-6}&4&6&9&21&42\end{array}[/tex]

The last value, 42, is the value of the function when x is 2.

Therefore,

[tex]f(2)=4x^4-2x^3-3x^2+3x=42[/tex]

180 ft2 be the area of the rectangular  sheep pen .

What is rectangle?

A quadrilateral is a shape with two opposed sides that are equal and parallel.

                     There are four 90-degree angles on its four sides, making it a four-sided polygon. The shape of a rectangle is two dimensional.

Length of the sheep pen =60ft

150 ft of fencing bought

One side of rectangular sheep pen is covered with barn which is equaling the  width

perimeter of rectangular sheep pen = 2(length +width)

length need to covered is 2 Length+ width

150 =2 length+width

150 = 2 x60 +width

150-120= width

30= width

Area of rectangle = 60 x 30

                         =      180 ft2

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Answer:332

Step-by-step explanation:Solution for 161 is what percent of 200:

161:200*100 =

(161*100):200 =

16100:200 = 80.5

Now we have: 161 is what percent of 200 = 80.5

Question: 161 is what percent of 200?

Percentage solution with steps:

Step 1: We make the assumption that 200 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $100\%=200$.

Step 4: In the same vein, $x\%=161$.

Step 5: This gives us a pair of simple equations:

$100\%=200(1)$.

$x\%=161(2)$.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{200}{161}$

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{161}{200}$

$\Rightarrow x=80.5\%$

Therefore, $161$ is $80.5\%$ of $200$.

Answer:

  3⁰ = 1

  x⁰ = 1

Step-by-step explanation:

You want powers of 3 filled in your table from an exponent of 4 down to an exponent of 0.

3⁴ = 3·3·3·3 = 81 . . . . . . 3 is a factor 4 times

3³ = 3·3·3 = 27 . . . . . . .  3 is a factor 3 times

Each row of the table has 3 being a factor of 3^x one fewer times, so each value of 3^x is 1/3 of the previous value.

The last two rows of the table are ...

  3¹ = 3

  3⁰ = 1

See the attachment for the whole table.

In general, the meaning of x⁰ is ...

  x⁰ = 1

__

Additional comment

In algebra, 0⁰ = 1 is the usual definition. In some contexts (mathematical analysis, calculus), it may be "undefined."

That means x⁰ = 1 for all real numbers x, including x = 0.