What is the value of x and y of the parallelogram?

Answer:

Option A: 12.5

Step-by-step explanation:

We use trigonometric ratios on this right angled triangle.

[tex]$ cos \hspace{1mm} \theta = \frac{adj}{hyp} $[/tex]

we get:

[tex]$ cos \hspace{1mm} 28^{\circ} = \frac{11}{x} $[/tex]

Also cos 28° = 0.88

Therefore, x = [tex]$ \frac{11}{0.88} $[/tex]

[tex]$ = \frac{100}{8} =\textbf{12.5} $[/tex]

OPTION A is the answer.

The value of k that makes the polynomial k^2x^3 - 6kz + 9 divisible by x-1 is 3. This is found using the Remainder Theorem and substituting x=1 into the polynomial and solving the resulting equation.

The question asks for the value of k such that the polynomial k2x3 - 6kz + 9 is divisible by x-1. To find the value of k, we use the Remainder Theorem, which states: if a polynomial f(x) is divisible by x-c, then f(c) = 0.

Applying this theorem, we set x=1 and solve for k:

Therefore, the value of k that makes the polynomial divisible by x-1 is 3.

Mikes repair shop $100 service charge plus $65 per hour Amys auto repair $40 service charge plus $80 per hour write an equation for each repair shop to represent the total cost of a car repair as a function of the number of hours worked let C = total cost to you let h = number of hours worked. Suppose you need to get the dent in your car repaired you see the ads above in the newspaper your father who knows a bit about cars said it would take no more than 3 hours for the repair person to fix your car how do you determine where you should take your car to get it repaired

-Mike Cost:: M(3) = 100 +65*3 = $295

-Amy Cost:: A(3) = 40 + 80*3 = $280

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-Mike charges 100 dollars service charge plus 65 dollars per hour.

-Amy charges 40 dollars service charge plus 80 dollars per hour.

-The cost to repair from mike is 100 + 65 * x.

-The cost to repair from amy is 40 + 80 * x.

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Let x = 3 and you get:

The cost to repair from mike is 100 + 65 * 3 = 295 dollars.

The cost to repaid from amy is 40 + 80 * 3 = 280 dollars.

As long as the time to repair is 3 hours or less, the cost to repair will be cheaper from Amy.

Answer:

$32,577.89

Step-by-step explanation:

Use the formula for amount after compound interest. A = P(1 + i)ⁿ

'P' is the principal, meaning starting amount. P = $20,000

'i' is the interest per compounding period in decimal form. Since the compounding period is annual, just like the interest rate is given as, i = 0.05. If  the compounding period was not annual: then i = r/c (annual interest rate divided by number of compounding periods in a year).

'n' is the number of compounding periods, or the number of times the interest increases. n = 10. Calculate 'n' using n = tc (number of years times number of compounding periods in a year). Since c=1, n = t. ('t' is the number of years).

'A' is the amount after 'n' years. We need to find A.

Use all of the numbers that we know for the variables, replace the variables with the numbers in the formula. Solve for 'A'.

A = P(1 + i)ⁿ

A = $20,000(1 + 0.05)¹⁰     Add inside brackets first

A = $20,000(1.05)¹⁰       Do (1.05)¹⁰ then multiply by 20,000

A = $32,577.89           Answer

Therefore the balance will be $32,577.89 after 10 years.

Answer:

[tex]x = \frac{1}{4} y + \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]y = 4x - 2[/tex]

first flip

[tex]4x - 2 = y[/tex]

now add 2 to each side

[tex]4x + 2 = y + 2[/tex]

now

[tex]4x = y + 2[/tex]

divide by 4

[tex]4x \div 4 = 4 + 2 \div 4[/tex]

so

[tex]x = \frac{1}{4} y + \frac{1}{2} [/tex]

Answer:

x-20

Step-by-step explanation:

x+4=y+24

x=y+24-4

x=y+20

y=x-20

Answer:

Step-by-step explanation:

Mean= 10+2+5+2+6+7+9+2+3/9

=46/9 = 5.11

Arrange in Ascending order:

2,2,2,3,5,6,7,9,10

Mode = 2     ( that occurs most number of times)

Median = 5   ( median is the middle term)

Answer: -2

Step-by-step explanation:

Let the number be x , then twice the number is 2x.

Twelve decreased by twice the number = 12 - ( 2x )

8 times the sum of the number and 4 = 8 ( x + 4 )

combining the two , we have

12 - 2x = 8 ( x + 4 )

12 - 2x = 8x + 32

12 - 32 = 8x + 2x

-20 = 10x

x = -20/10

x = -2

Answer:

m=-7

Step-by-step explanation:

The slope intercept form is y=mx+b.

So, the variable that represents slope is x.

If your plug your equation in, -7 would be the slope.

Answer:

x = 111

Step-by-step explanation:

Sum of interior angles= (n-2)*180= (7-2)*180 = 5*180 = 900

x + 139 + 121 + 125 + 126 + 158 + 120 = 900

x + 789 = 900

x = 900 - 789 = 111

x = 111

Answer:

Step-by-step explanation:

F(x) = 2x + 6

G(x) = - 5x - 9

product of F and G .....the product is the result of multiplication

(2x + 6)(-5x - 9) =

-10x^2 - 18x - 30x - 54 =

-10x^2 - 48x - 54 <====

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, 11)

m = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

3

Step-by-step explanation:

y2 - y1/ X2 - X1

11 - 2/ 4-1

9/3

= 3

Answer:

n = 17.6

Step-by-step explanation:

Cross-multiply and you have:

5 * n = 11 * 8

5n = 88

n = 88/5 = 17.6

Answer:

LN = 13 units.

Step-by-step explanation:

If LMNP is a rectangle, then LN and MP are the two diagonals of the rectangle and they are equal.

Now, given that LN = 7x - 8 and MP = 4x + 1

So, 7x - 8 = 4x + 1

⇒ 3x = 9

⇒ x = 3

Therefore, LN = 7x - 8 = 7(3) - 8 = 13 units. (Answer)

This is an equation representing the ellipse

Explanation:

Answer:

Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (=  -3.4 cm)

Step-by-step explanation:

i) change in water level over the course of 9 months =

   [tex]- \frac{5}{8} - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6\frac{5}{8} - 3.2 + 0.3[/tex]

 = [tex]-0.625 - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6.625 - 3.2 + 0.3[/tex]

= -3.4

Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= - 3.4 cm)

Answer:

D) y= -3x + 6

Step-by-step explanation:

y = mx + p

m = slope = (0-6)/(2-0) = -6/2 = -3

p = y-intercept = 6  ,because the line passes through points (0,6)

Answer:

D) y= -3x + 6

Using the associative property of addition, two equivalent expressions to find the total cost are: (1) ($12 + $24) + $6 and (2) $12 + ($24 + $6). Both expressions will yield the same result due to the associative property.

The question involves using the associative property of addition to find equivalent expressions for the total cost of items bought for Anita's mother's party. The total costs given are for three items: cake ($12), hot dogs and hamburgers ($24), and drinks ($6). To demonstrate the associative property, we can group the costs in different ways before adding them.

Both expressions will yield the same total cost when calculated, which shows the associative property of addition in action.

Answer:

6

Step-by-step explanation:

hold up hold up so you are saying 60 less than what quotient I'm guessing 68 divided by 12 so the answer would be 6

Step-by-step explanation:

The slope is described by the the initial and final value of one quantity over the difference between the initial and final of the other

Rate: for points on a Cartesian plane,(x1, y1) and (x2, y2)

the slope, m= (y2 - y1)/(x2 - x1)

The rate of change on the other hand is mostly refers to how much a quantity is changing with time i.e the rate of change of y from y1 to y2 can be expressed as

rate = (y2 - y1)/(t2 - t1)...where t1 and t2 are the various time in y1 and y2 respectively...

The transformed function after reflecting f(x)=|x| across the x-axis, moving it 2 units to the right, and 7 units down is f(x)=-|x-2|-7.

The original function is f(x)=|x|.

When the graph of the function is reflected across the x-axis, it changes the sign of the output or y-coordinate.

Thus, the absolute value function becomes f(x)=-|x|.

When this function is moved 2 units to the right, it results in a shift in the coordinate of x within the function, thus becoming f(x)=-|x-2|.

Lastly, when the function is moved 7 units down, 7 is subtracted from the function, resulting in the final equation of f(x)=-|x-2|-7.

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Answer: y-intercept

Explanation The "b" or the constant term represents the y-intercept which is the point where the line crosses the y-axis.

Answer:

2p+5=n

(p = Jake's points)  (n = Nate's points)

The relationship between Nate's and Jake's scores can be expressed by the expression N = 2p + 5.

The relationship between the number of points Nate scored (represented by N) and the number of points Jake scored (represented by p) can be expressed as:

N = 2p + 5

This expression represents that Nate's score is equal to twice the number of points Jake scored, plus 5.

Answer:

Therefore the maximum number of video games that we can purchase  

is 6.

Step-by-step explanation:

i) Let us say the number of video game system we can buy that costs $185

 is x and the number of video games of cost $14.95 is y.

ii) The total amount we can spend on the purchase of the video game

   system is $280.

iii) Now with the amount of $280 mentioned in ii) we can see that the

   number  of game systems that can be bought is 1.

 Therefore x = 1.

 Therefore the equation we can write to equate the number of video

  games  and video game system is given by $185 + $14.95 × y ≤ 280

  Therefore 14.95 × y ≤ 280 - 185 = 95

  Therefore y ≤   95 ÷ 14.95 = 6.355

  Therefore the maximum number of video games that we can purchase  

   is 6.

Answer:

Step-by-step explanation:

Since both points have their y coordinate as -6, and this is a line,

Then your answer would be y = -6

Answer:

The n th of the given sequence is [tex]t_{n} = 26-6 n[/tex]

Step-by-step explanation:

Step 1 :-

Given sequence is 20,14,8,2,.......this sequence in arithmetic progression but this sequence is decreasing sequence.

given first term is 20 and difference is[tex]d = second term- first term = 14-20=-6[/tex]

now the nth term of given sequence is

by using formula [tex]t_{n}=a+(n-1)d[/tex]

[tex]t_{n}= 20+(n-1)(-6)[/tex]

[tex]t_{n}= 20-6 n+6[/tex]

final answer:-

[tex]t_{n} = 26-6 n[/tex]

verification:-

[tex]t_{n} = 26-6 n[/tex]

put n=1 we get first term is 20

put n=2 we get second term is 14

put n=3 we get third term is 8

put n=4 we get fourth term is 2

so the n th term of sequence is

[tex]t_{n} = 26-6 n[/tex]

Answer:

Step-by-step explanation:

4x² - 8x= 0​

4x(x -2) = 0

: 4x = 0 or x - 2 = 0

4x = 0

Dividing by 4

x = 0/4

x = 0

And

x - 2 = 0

x = 2

Answer:

12

Step-by-step explanation:

I calbvkjy

The answer is 3 :)

Have a nice day!

1/2(3^3-1)

1/2(27-1)

1/2(26)

13

Answer:

13

Step-by-step explanation:

Replace b with 3, then multiply 3^3 get the answer then subtract by 1, last multiply what u got from the paranthesis by 1/2