Use the Pythagorean theorem to find x. Enter the answer in simplified form.
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Answer:

y=-1/4x+9/4

Step-by-step explanation:

Get slope of the line first (to find slope that is perpendicular, get the negative reciprocal)

4 turns into -1/4

To get the y-intercept, plug in the given coordinate values into this formula:

y=mx+b

3=-3(-1/4)+b

3-3/4=b

b=9/4

b is our y-intercept

9/4 is our y-intercept

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

[tex]y = 4 + x\implies y = \stackrel{\stackrel{m}{\downarrow }}{1}x+4\qquad \impliedby \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}[/tex]

so therefore

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

so we're really looking for the equation of a line whose slope is -1 and passes through (-3 , 3)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -1 \\\\\\ \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}{3}=\stackrel{m}{-1}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-3=-(x+3)\implies y-3 = -x-3\implies y = -x[/tex]

Answer:

the question is asking what it is the segment between HB,HG and CG

Step-by-step explanation:

Answer:

So that it can run faster

Answer:

[tex]a = change \: in \: v \div time[/tex]

Step-by-step explanation:

Change in V =28-0

=28

time =4 sec

Therefore acceleration =28 ÷4

7m/s^-2

Answer:

0.015 m²

Step-by-step explanation:

Since we need the area in square meters, we need to first convert our centimeter values into meters.

[tex]\frac{1m}{100cm} =10cm[/tex]

1 · 10 = 10
10/100 = 0.1 m

[tex]\frac{1m}{100cm} =15cm[/tex]

1 · 15 = 15
15/100 = 0.15 m

The area of a rectangle is a = l · w. Plugging in the given values, we get:

a = 0.1 × 0.15

a = 0.015 m²

hope this helps!

The value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 approximately.

If we're given that:

Then, we get:

[tex]z = \dfrac{\overline{x} - \mu}{s}[/tex]

If the sample standard deviation is not given, then we can estimate it by:

[tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]

where [tex]\sigma[/tex] = population standard deviation

For this case, since the sample size is 81 > 30, and we want to compare the mean (population mean) with some hypothesized mean (3.5 here), therefore, we can use one-sample z-test, which has the aforesaid test statistic.

We're provided that:

Thus, we get:

[tex]z = \dfrac{\overline{x} - \mu}{s} = \dfrac{3.25 - 3.5}{0.3} \approx -0.83[/tex]

Thus, the value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 approximately.

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Answer:

5

Step-by-step explanation:

A=a+b/2 x h

4 = a

5 = b

8 = h

4 + 5 / 2 = 4.5

4.5 x 8 = 36

So the other base length is 5

Answer:

1:8

Step-by-step explanation:

First, you must find the scale factor. Because you are given the area of the base, you must take the square root of 49 and 196. That leaves you with 7:14, and that simplifies to 1:2. To find the ratio of the volumes, you must cube both. That leaves you with a 1:8 ratio.

the standard form of that graph is ax squared +bx+c

Answer:

30

Step-by-step explanation:

[tex] - 6(x - 16) = - 84[/tex]

[tex]x - 16 = 14[/tex]

[tex]x = 30[/tex]

Answer:

x= 2, x= -12

Step-by-step explanation:

cuz i said so

first move the 24 to the other side of the equation by subtracting it from both side's

now the equation looks like this

x^2+10x-24

then find values that add to equal 10 and that also multiply to equal -24

this works out to (x-2) (x+12)

which means that x is equal to 2 and -12

The number of ways to elect a Chair and a Vice Chair is 156.

Given that the Board of directories has 13 members, to determine how many ways are there to elect a Chair and a Vice-Chair, the following calculation must be made:

As the rule does not affect, because in the two years that have elapsed a different election will be held, the number of ways to elect a Chair and a Vice Chair is 156.

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Answer:The number of ways to elect a Chair and a Vice Chair is 156.

Step-by-step explanation:

The equation of k is 13/7.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

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.

Given:

7k+17=30

Now, solving for k

Subtract both side 17

7k + 17 - 17 = 30 - 17

7k = 13

k= 13/7

Hence, the equation of k is 13/7.

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Answer:

Equation B is the same as Equation A + 2

Step-by-step explanation:

To be able to get equation B from equation A, we have to compare equation A with equation B. Given that equation A. is 5x-2+x=x-4 and equation B is 5x+x=x-4.

Equation B: 5x+x=x-4.

Equation A: 5x-2+x=x-4.

Simplifying equation A to be in the form of equation B:

5x -2 + x = x - 4

Adding 2 to both sides:

5x + x -2 + 2 = x - 4 + 2

5x + x = x - 4 + (+2)

= equation A + 2

But 5x+x=x-4 = equation A

Therefore Equation B is the same as Equation A + 2

Answer:

AB is chord

GF is tangent

DE is diameter

HJ is secant

C is center of the circle

DC is radius

K is point of tangency

AB is arc

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

3 green   for  5   red

then   3 out of (3+5)   are green   ... or  3/8 are green

3/8 * 160 = green         = 60 green

Answer:

60 green candies

Step-by-step explanation:

We know the proportion :

Let's make a linear equation where candies is denoted by x.

Number of green

Answer: I got you

The values are:

a = 6

b = 2

c = 6

d = 2

e = 6

f = 6

g = 1

Step-by-step explanation: Hope this helps

The values for the highlighted variables that show how to subtract the rational expressions are; a = 6, x^2 + 6x is equal to x(x+6), and b=2.

From the information, the denominator and numerator of the first term are multiplied by x.

The difference of squares is factored as (a² -b²) = (a +b)(a -b), so the denominator of the first term can be factored.

The common factor x can be factored out of the denominator of the second term which gives ...

[tex]\dfrac{2}{x^2-36}-\dfrac{1}{x^2+6x}= \dfrac{2}{(x+6)(x-6)}-\dfrac{1}{x(x+6)}\quad a=6[/tex]

Now Multiplying the first term by x/x and the second term by (x-6)/(x-6) gives ...

[tex]\dfrac{2x}{(x+6)(x-6)x}-\dfrac{x-6}{(x+6)(x-6)x}\quad b=2,\ c=6[/tex]

Writing the sum over the common denominator, we have;

[tex]\dfrac{2x-x+6}{(x+6)(x-6)x}\quad d=2,\ e=6[/tex]

Collecting terms in the numerator gives ...

[tex]\dfrac{x+6}{(x+6)(x-6)x}\quad f=6[/tex]

Finally, canceling the common factor we get;

1/(x-6)x

The values of the letters are;  a=6, b=2, c=6, d=2, e=6, f=6, g=1

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Answer:

A pie in maths have a degree of 360 degrees

Answer:

Less than(<)

55% of 60 is 33

60% of 65 is 39

when solving problems with percentage, always multiply x, your decimal form of the percentage, by y, the often whole number part you are multiplying the percentage by.

[tex]0.55 * 60 = 33\\0.60 * 65 = 39[/tex]

note that if the percentage is for example 30%, it will be 0.3, while if it were 3%, it would be 0.03 to avoid confusion.

That said, the answer is less than.

Answer:

1) {y,x}={-3,-23}

2) {x,y}={7,-9/2}

Step-by-step explanation:

Required:

1) y - x = 20, 2x - 15y = -1

Equations Simplified or Rearranged :

[1]    y - x = 20

  [2]    -15y + 2x = -1

Graphic Representation of the Equations :

x + y = 20        2x - 15y = -1  

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = x + 20

// Plug this in for variable  y  in equation [2]

  [2]    -15•(x +20) + 2x = -1

  [2]     - 13x = 299

// Solve equation [2] for the variable  x

[2]    13x = - 299

  [2]    x = - 23

// By now we know this much :

  y = x+20

   x = -23

// Use the  x  value to solve for  y

   y = (-23)+20 = -3

Solution :

{y,x} = {-3,-23}

2) 25-x=-4y,3x-2y=30

Equations Simplified or Rearranged :

  [1]    -x + 4y = -25

  [2]    3x - 2y = 30

Graphic Representation of the Equations :

   4y - x = -25        -2y + 3x = 30  

Solve by Substitution :

// Solve equation [1] for the variable  x

  [1]    x = 4y + 25

// Plug this in for variable  x  in equation [2]

 [2]    3•(4y+25) - 2y = 30

  [2]    10y = -45

// Solve equation [2] for the variable  y

  [2]    10y = - 45

  [2]    y = - 9/2

// By now we know this much :

  x = 4y+25

   y = -9/2

// Use the  y  value to solve for  x

  x = 4(-9/2)+25 = 7

Solution :

{x,y} = {7,-9/2}

Answer:

Write your question.

Step-by-step explanation:

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Answer:

whats the question?

Step-by-step explanation:

Answer:

A. Answer is 2263.

Checkpoint 1 is -86 Checkpoint 4 is 2177

Subtract -86 from 2177....2177-(-86)   

=2263

2263 is how much higher checkpoint 1 (-86) is from checkpoint 4 (2177)

B. 239 FEET.

the altitude of the hill must be subtracted by the depth of the ckeckpoint(2)(-189)

therefore the altitude of the hill comes out to be 428-189=239feet.

therefore,the actual altitude of the hill is 239 feet.

Answer:

d) 729cm^3

Step-by-step explanation:

Length =27cm

Width = 1/3 of length

= 1/3 of 27cm = 1/3 × 27cm = 9cm

Height = 1/3 of width

= 1/3 of 9cm = 1/3 × 9cm = 3cm

So, length = 27cm; width = 9cm; height = 3cm

So, volume = length × width × height

= 27cm × 9cm × 3cm = 729cm^3

Given that X varies inversely as Y, the value of Y when the number of X is increased to the given value is -6.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Inverse variation It is expressed as;

x ∝ 1/r then x = k/y

Where k is the proportionality constant.

Given the data in the question;

First we find the proportionality constant.

x = k/y

4 = k / -9

k = -36

Now, If x = 6 then y = ?

x = k/y

6 = -36 / y

6y = -36

y = -36 / 6

y = -6

Given that X varies inversely as Y, the value of Y when the number of X is increased to the given value is -6.

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Answer:

The answer is A.

Step-by-step explanation:

I used an online Calculator to calculate it for you.

(x + 4) * (x - 4) * (x + 2)
(x^2 - 4^2) * (x+2)
x^3 + 2x^2 - 16x^2 - 32

Answer:

19). V = 381.51 cubic inches

20) The cylindrical box has a greater volume so Lin would prefer getting it.

Step-by-step explanation:

Assuming that the plastic bag filled with water was shaped like a sphere (bc there's not enough context to make it anything other than a sphere), the solution lies within an equation:

V = 4/3πr^3

This is the equation for finding the volume of sphere.

Hint: diameter = radius/2

V = 4/3π(4.5)^3

V = 4/3π(91.125)

V = 4.19(91.125)

V = 381.51 cubic inches

______________________________________________________

Equation of a rectangular prism: V = L * W * H

Equation of cylinder: V = πr^2h

Rectangle box:

V = 12 * 9 * 10

V = 120 * 9

V = 1080

Cylinder box:

V = π5^2(14)

V = π(25)(14)

V = 350 * 3.14

V = 1099

1080 < 1099

Answer:

a2−b2=(a−b)(a+b) is correct.

Step-by-step explanation:

(a+b)3=a3+3a²b+3ab²+b3

(a−b)3=a3-3a²b+3ab²−b3

Answer:

1550 miles

Step-by-step explanation:

rate * time = distance

620 m/hr  *  2.5 hr = 1550 miles

(Note that   2 hr and 30 min is 2 and 1/2 hours = 2.5 hours)

Answer:

6.54498

Step-by-step explanation:

The formula that you use to solve this is (0/360)pi*radius2. You have to plug in the information that you are already given.