A(5, 10) and B(13,-2) are two points on the line AB.
The perpendicular bisector of the line AB has gradient
Find the equation of the perpendicular bisector of AB

Answer: \sqrt[4]{xy^{2} }

Step-by-step explanation: Siplified

Answer:

31.25 k

Step-by-step explanation:

80 %   *  x = 25 k

.80  x    = 25 k

x   = 25 k / .80 = 31.25 k

Answer:

  125k

Step-by-step explanation:

You want to know Ola's daily allowance if 25k remained after 80% was spent.

The fraction remaining was 100% -80% = 20%. If that fraction of Ola's allowance (a) is 25k, we have ...

  0.20a = 25k

Dividing by 0.20, the value of 'a' is shown to be ...

  a = 25k/0.20 = 125k

Ola's total daily allowance was 125k.

Answer: -5

Step-by-step explanation:

2(0)-5

0-5 = -5

Answer:

Kayla , why do you find the question tricky?  :/

Step-by-step explanation:

HP total = 3*3/4 +  5*1/4  + 6*3_1/3  + 8* 1/2

HP total = 9/4 + 5/4 + 18_6/3 + 8/2

HP total = 9/4 + 5/4 + 60/3 + 16/4

HP total = 27/12 + 15/12 + 240/12 +48/12

HP total = 330/12

HP total = 165/6

HP total = 55/2

HP total = 27_1/2

Answer:

27.5 HP

Step-by-step explanation:

Sum

Answer:

  30√3 ≈ 51.96 miles

Step-by-step explanation:

The distance between the two ships can be found using the Law of Cosines, or using your knowledge of the side relationships in special triangles.

__

Each ship is traveling at 10 mph, so after 3 hours will have traveled 30 miles.

The triangle OS1S2 formed by the harbor and the two ship locations is an isosceles triangle with base angles of 30°. Each half of OS1S2 is a 30-60-90 triangle whose longer leg is √3 times half the hypotenuse. The sum of those two "longer legs" is the distance between the ships.

The distance between ships is 2×15√3 = 30√3 ≈ 51.96 miles.

_____

Additional comment

If you prefer to use the Law of Cosines, you are looking for the length of the side opposite the 120° angle in a triangle with sides of 30 miles.

  c² = 30² +30² -2·30·30·cos(120°) = 30²(2-2·(-0.5)) = 3·30²

  c = 30√3 . . . . . take the square root (miles)

New price = 90 dollars

25% of 120 = 30

Price is reduced 25% from 120 so,

120 - 30 = 90

Amount of discount = 30

Answer: A

Step-by-step explanation: I hate when theres problems like this, considering theres celcius and fahrenheit but the correct answer is A

The amount of the profit at x = -2 can not be determined because the number of the shirt can not be negative. Then the amount of the profit at x = 12 is $ 2 and at x = 17.5 is $ 35.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A company manufactures and sells shirts.

The daily profit the company makes depends on how many shirts they sell.

The profit, in dollars, when the company sells x shirts can be found using the function f(x) = 6x − 70.

Find and interpret the given function values and determine an appropriate domain for the function.

Then at x = −2, then the profit will be

For this condition, the amount of the profit can not be determined because the number of the shirt can not be negative.

Then at x = 12, then the profit will be

f(12) = 6 × 12 − 70

f(12) = 72 − 70

f(12) = $ 2

Then at x = 17.5, then the profit will be

f(17.5) = 6 × 17.5 − 70

f(17.5) = 105− 70

f(17.5) = $ 35

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Answer:

Hamburgers and Tacos.

Step-by-step explanation:

If you divide 6 by 3 you get 2, and if you divide 9 by 3 you get 3.

2:3

Answer:

3x +2y = 11 .... 1

x +5y = 8....2

x + 5y = 8

multiply by -3 on both sides

-3x - 15y = -24

-3x - 15y = - 24

3x +2y = 11

-13y = -13

y = 1

substitute the value of y in 1 or 2

3x +2y = 11

3x = 11 - 2y

3x = 11 - 2(1)

3x = 9

x = 3

(x;y) ( 3 ; 1)

eq(2)×3

eq(1)-eq(3)

Putting in eq(2)

Pair

Answer: 18

Step-by-step explanation:

By the consecutive interior angles theorem, [tex]5x+7x+24=180 \longrightarrow x=13[/tex].

So, this means that using the corresponding angles theorem, [tex]7x+24=6y+7[/tex], and since [tex]x=13[/tex], this means that [tex]7x+24=115[/tex].

So, [tex]6y+7=115 \longrightarrow \boxed{y=18}[/tex]

Answer

North of the box plot speed over 72 is the answer because it is a very high speed of the chart and it shows that the its going over the average speed

Answer:

-9.25

Step-by-step explanation:

Answer: Heyaa! ~

Your Exact Answer is... - 37/4 but your Decimal form is -9.25

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Hopefully this helps you!

-Matthew ~

Step 1

Find the area of the Square in the middle

Formula for finding square:

[tex]A = L*W[/tex]

Let's apply the formula and find our answer:

[tex]A = 2*2\\=4[/tex]

The area of the square is 4 units

Step 2

Find the area of all 4 triangles around the square

As you know, the formula for finding 1 triangle is as follows:

[tex]A = \frac{1}{2} *B*H[/tex]

But, to find the area of 2 triangles, we can use this formula:

[tex]A=B*H[/tex]

And to find 4 of them (with same dimensions;as required here), we can use this one:

[tex]A=2*B*H[/tex]

Let's apply the formula then! What are we waiting for!!!!

[tex]A=2*2*2\\=2*4\\=8[/tex]

The area of ALL of the triangles around the square is 8 units

Step 3

Add all areas to find FINAL ANSWER!

Easy!

4+8=12

Answer:

12 is the answer because 2 x 2 = 4 but since it is a triangular face we half it and end up with 2, 2 x 4 is 8, the square it 2 x 2 = 4 so we add 4 and 8 which equals 12  

Check the picture below.

Answer:

the pattern is going in the form of 1³ , 2³ , 3³ , 4³

therefore next term should be 5³ which is equal to 125. So the missing term is 125

I hope you got that.

By : Modern Einstein

The cubic regression function of the points (1,-1), (2,-13), (3,-45), (-1,11) is y = -2x³ + 2x² - 4x + 3

The points are given as:

(x,y) = (1,-1), (2,-13), (3,-45), (-1,11)

A cubic regression function is represented as:

y = ax³ + bx² + cx + d

Next, we determine the cubic function using a graphing calculator.

From the graphing calculator, we have the following coefficients:

Recall that:

y = ax³ + bx² + cx + d

So, we have:

y = -2x³ + 2x² - 4x + 3

Hence, the cubic regression function of the points is y = -2x³ + 2x² - 4x + 3

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The person must leave the money in the bank for about 10.1 years at interest 4.25% to reach $11200 when compounded annually.

Compound interest is when interest is added to the principal of an investment, allowing the interest to compound over time. In other words, the beginning principal as well as the total interest from prior periods are both used to compute interest. In contrast to simple interest, which only affects the initial capital, this causes the investment to expand exponentially over time. Often utilised in banking and investment, compound interest is sometimes defined in terms of a yearly interest rate and the frequency with which it is compounded.

Given that, bank pays 4.25% interest compounded annually on the invested amount.

The compound interest is given as:

[tex]A = P(1 + r/n)^{(n*t)}[/tex]

Substituting the values of P = $5500, r = 4.25% = 0.0425, A = $11200, and n = 1.

[tex]11200 = $5500(1 + 0.0425/1)^{(1*t)}\\t = log(11200/5500)/log(1.0425) = 10.1 years[/tex]

Hence, the person must leave the money in the bank for about 10.1 years to reach $11200.

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Answer:

+ 5, - 5

Step-by-step explanation:

p^2 - 8 = 17

p^2 = 17 + 8

p^2 = 25

      = 5 x 5

p^2 = 5^2

p = ± 5

Answer:

Step-by-step explanation:

Let the amount of rent is R

Calculate the value of R in reverse order of spending

Correct choice is B

Answer:

B. $466

Step-by-step explanation:

[tex]\textsf{let}\: x= \textsf{Lydia's salary}[/tex]

[tex]\implies \textsf{rent}=\dfrac{1}{2}x[/tex]

Modelling the given information to find the total salary:

[tex]\implies \left(x-\dfrac{1}{2}x-168\right)-\dfrac{x-\frac{1}{2}x-168}{2}-57=92[/tex]

[tex]\implies \dfrac{1}{2}x-168-\dfrac{\frac{1}{2}x-168}{2}-57=92[/tex]

[tex]\implies \dfrac{1}{2}x-\dfrac{\frac{1}{2}x-168}{2}=317[/tex]

[tex]\implies x-(\frac{1}{2}x-168)=634[/tex]

[tex]\implies x-\frac{1}{2}x+168=634[/tex]

[tex]\implies \dfrac{1}{2}x=466[/tex]

[tex]\implies x=932[/tex]

Therefore, Lydia's total salary was $932

[tex]\implies \textsf{rent}=\dfrac{1}{2}(932)=\$466[/tex]

Answer:

-1

Step-by-step explanation:

perpendicular = always has a slope of neg 1

Answer:

-1

Step-by-step explanation:

It is -1. I can't explain, I just did it in my head, so sorry!

Using the binomial distribution, it is found that the probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, we have that:

The probability that he hits fewer than 8 of the bottles is given by:

[tex]P(X < 8) = 1 - P(X \geq 8)[/tex]

In which:

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{10,8}.(0.95)^{8}.(0.05)^{2} = 0.0746[/tex]

[tex]P(X = 9) = C_{10,9}.(0.95)^{9}.(0.05)^{1} = 0.3151[/tex]

[tex]P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987[/tex]

Hence:

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.0746 + 0.3151 + 0.5987 = 0.988[/tex]

[tex]P(X < 8) = 1 - P(X \geq 8) = 0.012[/tex]

The probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.

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Answer:

see explanation

Step-by-step explanation:

the arc length of a circle is calculated as

arc = circumference of circle × fraction of circle

(5)

circumference (C) is calculated as

C = 2πr ( r is the radius )

here diameter = 12 , then r = 12 ÷ 2 = 6

C = 2π × 6 = 12π ≈ 37.7 m ( to the nearest tenth )

(6)

JK = 2πr × [tex]\frac{75}{360}[/tex]

    = 2π × 7 × [tex]\frac{5}{24}[/tex]

    = 14π × [tex]\frac{5}{24}[/tex]

    = [tex]\frac{14\pi (5)}{24}[/tex] ≈ 9.2 in ( to the nearest tenth )

(7)

7.5 = 2πr × [tex]\frac{120}{360}[/tex]

7.5 = 2πr × [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

22.5 = 2πr ( divide both sides by 2π )

r = [tex]\frac{22.5}{2\pi }[/tex] ≈ 3.6 ft

Answer:

44 inches

Step-by-step explanation:

perimeter of triangle = length of side 1 + length of side 2 + length of side 3

length of side 1 = 26

length of side 2 = 55

125 = 26 + 55 + length of side 3 = 81 + length of side 3

subtract 81 from both sides to get the length of side 3

length of side 3 = 44 inches

When observing a performance or movement pattern, you should break down the complex skills into component parts.

Complex skills are skills that are composed of many parts. This makes it difficult  to engage in these sort of skills without a rigorous training.

Thus, when observing a performance or movement pattern, you should break down the complex skills into component parts.

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The tower is 260 feet away from the fire.

The height of the tower is the opposite side while the distance from the tower to the fire is the adjacent side.

Given:

Angle of depression = 30°.

Opposite side = 150 feet.

Now,

tan [tex]\thtea\\[/tex][tex]\theta[/tex]= P/B

tan 30 [tex]\thtea\\[/tex]= 150/B

1/√3= 150/B

B=  150*√3

B= 150*1.732

B= 259.8

B= 260 feet.

Hence, the tower is 260 feet away from the fire.

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