Find the value of x .. assume that segments that appear to be tangent are tangent .

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}[/tex]

so we're really looking for the equation of a line whose slope is -5 and that it passes through (-4 , 0)

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\hspace{10em} \stackrel{slope}{m} ~=~ - 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 5}(x-\stackrel{x_1}{(-4)}) \\\\\\ y -0= -5 (x +4) \implies {\Large \begin{array}{llll} y=-5x-20 \end{array}}[/tex]

The simple interest is $420 and the maturity value is $$6,720

Using this formula to find the simple interest

Simple interest = Principal  × Interest rate × Time

Where:

Principal = $6300

Interest rate =4% or 0.04

Time = 20 month = 20/12 = 1.6666666

Let plug in the formula

Simple interest = $6,300 × 0.04 × 1.6666666

Simple interest = $420

Using this formula to find the maturity value

Maturity value = Principal + Interest

Maturity value = $6,300 + $420

Maturity value = $6,720

Therefore the interest is $420.

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Answer:

Step-by-step explanation:

1 and 2 are supplementary angles and hence sum to 180°.

Answer:

Step-by-step explanation:

1. List out the numbers and divide

-1/6/2/9=

2. In division for fractions, the number or numbers on the right of the division side flip and change to multiply!

-1/6/2/9= -1/6*9/2= -9/12

3. Simplify!

-9/12= -3/4

Answer:

-3/4

Step-by-step explanation:

so you leave -1/6 but then you change the sign to multiply and the other fraction change it so if you had 2/9 it will be 9/2

so we get -1/6×9/2.

if you don't know how to multiply fractions i can explain just ask.

Answer:

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

A and C are congruent angles opposite to congruent sides of the isosceles triangle.

Find the measure of ∠A

Answer:

The angle A is 55°.

Step-by-step explanation:

We know that,

→ <A = <C

Now the value of x will be,

→ 3x + 40 = x + 50

→ 3x - x = 50 - 40

→ 2x = 10

→ x = 10/2

→ [ x = 5 ]

Then the value of m<A is,

→ A = 3x + 40

→ A = 3(5) + 40

→ A = 15 + 40

→ [ A = 55° ]

Hence, the answer is 55°.

The shape has a surface area of: Surface Area = 282.6 in²

The given parameter is represented on the figure

In this case, the figure is a cone with the following parameters

Radius, r = 5 inches

Height, h = 12 inches

The surface area of the cone is then calculated as

A = πr * (r + √(h² + r²))

Substitute the known values in the above equation, so, we have the following representation

A = 3.14 * 5 * (5 + √(12² + 5²))

Evaluate the expression

A = 282.6

Hence, the surface area is 282.6 square inches

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Answer:

{-9,-8,7,8,10}

The required equation  can be used to determine the pounds of laundry the customer brought in is A. 0.61x + 28.00 = 41.42

An equation is a mathematical expression that shows the relationship between two variables.

To find the given equation,

Let x be the number of pounds of clothes washed and folded at the laundromat.

Given that the laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service, the total amount paid for the number of poundsof clothes is P = rate × number of pounds = $0.61 × x = 0.61x

Also, the laundromat has a wash-and-fold service for a monthly fee of $28.00.

So, the total amount paid is T = P + $28.00 = $0.61x + $28.00

Now, since one customer paid $41.42 in total for the month, since this is the total amount paid, then T = $41.42

So, $0.61x + $28.00 = $41.42

So, the required equation is A. 0.61x + 28.00 = 41.42

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When is a standard normal random variable, the probability of P(–1.20 ≤ z ≤ 1.50) is 0.8181.

The probability illustrates the likelihood of events.

From the information, it's important to note that P(–1.20 ≤ z ≤ 1.50) will be:

= P(Z ≤ 1.50) - P(Z ≤ -1.20)

= P(Z ≤ 1.50) - [1 - P(Z ≤ -1.20)]

It should be noted that by using the normal z table, the probability of the corresponding z score will be 0.9332 and 0.8849.

This will be:

= 0.9332 - (1 - 0.8849)

= 0.8181

Therefore, the probability is 0.8181.

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The set of information that is true about the relation is:

Domain: {3, 4, 5, 6}

Range: {-8, -1, 2, 7}

The relation is not a function.

A relation that represents a function will have each of its domain elements related to exactly one range element.

All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,

Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.

Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:

The domain of the relation is: {3, 4, 5, 6}

The range of the relation is: {-8, -1, 2, 7}

The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.

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From the equation E(d) = 38d + 500, The initial electricity is 500W and the build up is 38W per day

An equation is an expression showing the relationship between two or more numbers and variables.

The standard equation of a straight line is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let E represent the electricity from the solar panels after d days.

Since:

E(d) = 38d + 500

The y intercept is 500 and the slope is 38

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Answer:

80

Step-by-step explanation:

the mean of a data set is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{88+72+68+78+94}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80

1. 35 signed up for only mathematics

2. 20 signed up for only English

3. 85 or 70 is English or mathematics

4. Neither math or English is 45

5. English and Math is 50

1. How many signed for only mathematics

We have to define only mathematics as x

while we have math = m

English as E

Math and English as ME

only math

X = M - ME

= 85 - 50

= 35

2. Only English

E - ME

= 70 - 50

= 20

3. English or mathematics =

85 or 75

4. Neither English nor Mathematics

150 - (85 + 70 - 50)

= 45

5. The number for math and English is what is the intersection = 50

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Vertex of g(x) is: (-2, -4)

acc to our question:

Vertex form of a quadratic function:

f(x) = (x - h)² + k

We have (h, k) = (3, -4)

The function f(x) is:

f(x) = (x - 3)² - 4

The function g(x) is: g(x) = f(x + 5) =

Vertex of g(x) is:(-2, -4)

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Answer:

a) He obviously used 7 liters of cooking oil.

b) He has 24 liters of cooking oil left.

A total of 9 workers are needed to finish the same task in 4 days

From the question, we understand that:

3 workers can complete a certain task in 12 days

This means that

3 workers = 12 days

The proportionality constant is then calculated as

Proportionality constant = Number of workers x Number of days

Substitute the known values in the above equation So, we have the following equation

Proportionality constant = 3 * 12

Evaluate

Proportionality constant = 36

When the number of days is 4, we have

Days = 4

So, we have

Proportionality constant = Number of workers x Number of days

This gives

36 = Number of workers x 4

Divide both sides by 4

Number of workers = 9

Hence, the number of workers is 9

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Answer:

B

Step-by-step explanation:

Combine 2x^2 and 3x^2 to get 5x^2.

Combine x and 2x to get 3x.

Add 3 and 1 to get 4.

After solving the Algebraic expression we gets Tim needs 3.05 lbs. and 2.95 lbs. Metal.

Algebraic expressions are constructed using integer constants, variables, and the addition, subtraction, multiplication, and division operations of basic arithmetic.

To form the Algebraic expression

Let x be the quantity of silver at 29% and y the quantity at 80%

Then x*28% + y*61% = 6*54%

and x + y = 6

 Let y = 6-x then

29*x + (6-x)*80= 324

29*x + 480- 80*x = 324

51*x = 156 and x = 156/51 = 3.05 lbs.

so y = 6 - x = 2.95 lbs.

Hence,

Tim needs 3.05 lbs. and 2.95 lbs. Metal.

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Answer:

1.6 kg = $2.96

Step-by-step explanation:

The given statement is,

→ 1 kg of apple = $1.85

→ a = 1.85

Now the cost of 1.6 kg of apple is,

→ 1.6 × a

→ 1.6 × 1.85

→ $2.96

Hence, 1.6 kg of apple is $2.96.

Answer:

Answer is 0. If you have to owe someone 9 dollars and they give you nine back it is 0. You can also rearrange the problem to 9-9 (same thing) which is 0

The division of the given polynomial is [tex]13q - 9 + \frac{8}{q+7}[/tex].

What is the quotient of polynomials?

Any quotient of polynomials a(x)/b(x) can be expressed as q(x)+r(x)/b(x), where r(x) is a real number and b is a real number (x). For instance, x-2+3 can be used to represent (x2-3x+5)/(x-1) (x-1).

We have,

              [tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]

By dividing,

           [tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)} / \frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]

                  [tex]= 13q + \frac{-9q - 55)}{ (q + 7)}[/tex]

                   [tex]\frac{-9q - 55}{q+7} / \frac{-9q - 55}{q+7}[/tex]

                   [tex]= 13q - 9 + \frac{8}{q+7}[/tex]

Hence, the division of the given polynomial is  [tex]13q - 9 + \frac{8}{q+7}[/tex].

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The number of possible different votes for Milan, based on the list of bands is 60 different votes.

There are 5 lists of bands that Milan has to choose from to place a vote and there are only 3 bands to be chosen out of the 5 lists.

The total number of different votes possible is therefore possible by performing a permutation:

= 5! / ( 5 - 3) !

= 5 ! / 2 !

= (5 x 4 x 3 x 2 x 1) / (2 x 1)

= 60 different votes

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A.The length of each path is 130 meters.

Given:

The park resembles an isosceles trapezoid.

Figure shows a trapezium . AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.

we know that:

Diagonals are equal in isosceles trapezoid.

14x + 4 = 11x + 31

14x - 11x = 31 - 4

3x = 27

divide by 3 on both sides

3x/3 = 27/3

x = 9

Diagonal length = 14x + 4.

= 14*9 + 4

= 126 + 4

= 130 meters.

Therefore The length of each path is 130 meters.

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The factorization of the expression  [tex]x^3+3x^2+9x+27[/tex] is  [tex](x+3)(x^2+9)[/tex].

What is factorization?

  The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. A factorization is just the procedure by which an algebraic expression gets expanded in the opposite direction. The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. Factorization is the reverse process of expansion of an algebraic statement. If an algebraic expression is a product of prime factors, it has undergone complete factorization.

Here the given polynomial expression is ,

=> [tex]x^3+3x^2+9x+27[/tex]

=> [tex]x^2(x+3)+9(x+3)[/tex]

=> [tex](x+3)(x^2+9)[/tex]

Hence the complete factorization of the given expression is [tex](x+3)(x^2+9)[/tex].

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After solving, 50% is her hourly overtime rate.

In the given question,

India works overtime, she receives an hourly rate of 1-times her regular hourly 1/2 rate.

We have to find her hourly overtime rate.

India is working overtime so her regular hourly rate is 1/2.

Evaluating the expression

We find her hourly overtime rate in percentage.

She receive overtime rate for 1 time is 1/2 rate.

We can write 1/2 as 0.5.

To express it as percentage we multiply and divide by 100.

= 0.5 × 100/100

= 50%

Hence, 50% is her hourly overtime rate.

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Answer:

Step-by-step explanation

so basically you need to see what m<I equals and do the same for the rest of them and you should get your answer and that would be let me see and m<k= -44 degrees and m<I and J= -10 degrees and there you have if this is not right i tried have the same step and ask another person

Answer:

The height is 12ft

Step-by-step explanation:

In order to find the height, you have to divide the area by the width which is 180ft divided by 15ft, you get 12ft, and if you double-check 15 x 12 gets you 180, which is the area.

The correct expression of the inequality expression is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

From the question, the expression is given as

18 ÷ 6 + 3 □ 6 + 12 ÷ 3

We start by converting the above expression to the same form

So, we start by solving the quotients

This gives

3 + 3 □ 6 + 4

Next, we evaluate the sum

So, we have

6 □ 10

In the above expression, we have

6 and 10

By convention, the number 6 is less than the number 10

This is so because 6 has a smaller value and 10 has a higher value

When the above numbers are compared, we have

6 is less than 10

This means that we make use of the inequality symbol <

So, we have

18 ÷ 6 + 3 < 6 + 12 ÷ 3

Hence, the complete inequality is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

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Based on the definition of perpendicular bisector, the value of b = 5.

A perpendicular bisector can be described as any line that bisects another line segment at right angles.

This means, the measure of the angles at the point of bisection are right angles (90 degrees).

Therefore:

12b + 30 = 90 [definition of perpendicular bisector]

Solve for b

12b + 30 - 30 = 90 - 30

12b = 60

Divide both sides by 12

12b/12 = 60/12

b = 5

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