Determine whether the vectors in each pair are normal to each other. (8,-4) and (-2,4)

a) The Linear equation is,

y = 13.5x + 119.5

b) The annual membership fee at this club is $119.5.

c) The fee that is charged each time a member plays racquetball is $13.5.

What is Linear equation?

The linear equation of a line with slope m is defined as;

y = mx + b

Now, Let the linear equation is;

y = mx + b

For, Jay played racquetball 77 times and payed a total of $1159.

1159 = 77m + b  .... (i)

And, For Sammy played racquetball 37 times and payed a total of $619.

619 = 37m + b ... (ii)

Solve both equation as;

1159 - 619 = 77m - 37m

40 m = 540

m = 13.5

And, b = 119.5

Hence, The Linear equation is,

y = 13.5x + 119.5

So, The annual membership fee at this club is $119.5

The fee that is charged each time a member plays racquetball is $13.5.

Hence,

a) The Linear equation is,

y = 13.5x + 119.5

b) The annual membership fee at this club is $119.5.

c) The fee that is charged each time a member plays racquetball is $13.5.

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the formula for the parabola that passes through the points, y = ax2 + bx + c. The values of a, b, and c are -9, -19,32 respectively.

The intersection of a right circular cone with a plane parallel to an element of the cone creates a plane curve, which is equivalent to a point moving so that its distance from a given point equals its distance from a fixed line.

based on the available facts;

Parabola fundamental: y = ax2 + bx + c

We can plug in three locations for (x, y) to get three equations at once.

(-4, -40):  40 = 4a - 2b + c   {equation 1}

(-3, -13):   -13 = 9a + 3b + c    {equation 2}

(-2,4): 4 = a - b + c        {equation 3}

Solve this system to find the values of a, b, c

Let's first eliminate variable c:

4a - 2b + c = -40   {equation 1}

 a -  b + c = 4   {equation 3}

---------------------  subtract

3a - b = -44

9a + 3b + c = -13    {equation 2}

 a -  b + c = 4   {equation 3}

--------------------  subtract

8a + 4b = -17

We now have two equations with 2 unknowns we can use to find a, b

3a - b = -44         {equation 4}

8a + 4b = -4   {equation 5}

Multiply equation 4 through by 4 and add equations

12a - 4b = -176

8a + 4b = -4

-----------------   add

20a = -180

a = 180/20

a = -9

8a + 4b = -4

4b = -76

b = -19

Plug these 2 values into one of the original equations and solve for c

4 = a - b + c        {equation 3}

4 = -9-19 + c

4 = -28 + c

4+28= c

c = 32

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the option tray days subtract 4 from both sides.

Answer:

S = 350T - 130, where T is the number of hours and S is the number of pounds.

If T = 11, then S = 3,720 pounds.

Step-by-step explanation:

[tex]m = \frac{2320 - 1445}{7 - 4.5} = 350[/tex]

[tex]2320 = 350(7) + b[/tex]

[tex]2320 = 2450 - b[/tex]

[tex]b = - 130[/tex]

So we have S = 350T - 130. Substituting 11 for T, we have S = 3,720 pounds.

Answer:

11

Step-by-step explanation:

If three integers have a mean of 9, a median of 12, and a range of 13, then the three integers are 1, 12, and 14.

As the median is the value that's exactly in the center of a set of values, one of the three integers is 12.

Considering the first and third integers to be x and y, the range can be given as

x - y = 13

x = 13 + y

As mean can be given as,

x + 12 + y / 3 = 9

Putting x = 13 + y in this equation,

13 + y + 12 + y / 3 = 9

25 + 2y = 9 × 3

25 + 2y = 27

2y = 27 - 25

2y = 2

y = 2/2

y = 1

As,

x = 13 + y

x = 13 + 1

x = 14

Hence the three integers are calculated to be 1, 12, and 14.

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The statement employs that Because b > 1, the function shows  exponential growth. We calculate the y-intercept by substituting 0 for x and afterward solving for y.

Exponential growth is the process by which quantity rises over time. It happens when the instantaneous rate of alteration of a quantity with regard to time is proportionate to the amount itself.

As a result, the exponential growth formula is: x(t) = 10,000 * (1 + 0.05)t = 10,000 * 1.05t. Here is the amount of years that have gone since 2019. In our situation, t = 11 should be used for the year 2030 because that is the lot of years between 2030 as well as the initial year 2019.

y=0.1(10)ˣ

y = 0.1(10)⁰

y = 0.1(1)

y = 0.1

Because b > 1, the function shows exponential growth. We calculate the y-intercept by substituting 0 for x and afterward solving for y.

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Using the Pythagorean Theorem, the values of x are given as follows:

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Hence, in the first triangle:

x² + 35² = 37²

x² = 37² - 35²

x² = 144

x = sqrt(144)

x = 12.

On the second triangle, we have two right triangles, hence:

x = a + b.

a² + 8² = 10²

a² = 36

a = sqrt(36)

a = 6.

b² + 8² = 17²

b² = 225

b = sqrt(225)

b = 15.

Hence the value of x is given as follows:

x = a + b = 6 + 15 = 21.

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The equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.

A bisector divides segments or angles into two equal halves.

Given the data in the question;

Since AC is bisected at point E and we know that a bisector divides segments or angles into two equal halves.

AC = 2 × AE

Hence

40 = 2( 4x + 2 )

Rewrite the equation such that x will be at the left side.

2( 4x + 2 ) = 40

To solve for x, remove the parenthesis using distributive property.

2( 4x + 2 ) = 40

2×4x + 2×2 = 40

Rewrite the equation such that x will be at the left side.

8x + 4 = 40

Subtract 4 from both sides.

8x + 4 - 4 = 40 - 4

8x = 36

Divide both sides by 8

8x/8 = 36/8

x = 36/8

x = 4.5

Therefore, the equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.

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Answer:

19

Step-by-step explanation:

The answer stays the same

Answer:

|19|

Step-by-step explanation:

The absolute value of a positive number stays positive.

Answer:

Step-by-step explanation saz mix dururtuuuutruturutrutrtru

The measure of the angles are  ∠A = 33°  ,   ∠B = 33° and   ∠C = 114°

Supplementary angles are the angles whose sum is equal to [tex]180^{o}[/tex].

According to the question we have been given that the three angles that is ∠A , ∠B and ∠C are the supplementary angles that is their sum is 180°.

Let the measure of ∠A = x = ∠B

and the measure of ∠C = 81 + x

Now,

      ∠A + ∠B + ∠C = 180°

Putting the required values we get

        x° + x° + (81 +x )° = 180°

        2x° + 81° + x° = 180°

             3x° = 99°

               x° = 33°

Hence the measure of three angles are

       ∠A = 33°  ,   ∠B = 33° and   ∠C = 114°

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If the equation of the parent graph, shown in the reference picture attached hereby, is [f(x) = |x|], then the equation of the translated graph will be [f(x) = (|x-2| + 1)].

Along with the question statement, we are provided with a reference attachment, which is a grid, consisting of two graphs, and the equation of the parent graph is [f(x) = |x|].

We are required to calculate the equation of the other graph, which is a translated version of the parent graph.

From the reference grid, we can clearly see that, the vertex of the parent graph is at the origin (0, 0) while that of the translated graph is at (-2, 1), i.e., the vertex translated by 2 units to the left along the x-axis and then, 1 unit upwards along the y-axis. And this translation will be followed by every point of the daughter graph.

Hence, the equation of the translated graph will be [f(x) = (|x-2| + 1)].

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Answer: x = 61

Step-by-step explanation:

combine both angles to equal 180 in one formula

2x+3+x-6=180

then add the sides up

3x-3=180

add 3 to both sides

3x=183

divide

x=61

Answer:

33

Step-by-step explanation:

You do 6 x 2 and you get 12 times that by 3 and get 36 and subtract that by 3 and get 33.

Answer:

Step-by-step explanation:

6 x 6 = 36
3(4) is just 3x4 which is 12
so 36 - 12 = 24

Answer:

(-∞, 4]

Step-by-step explanation:

Domain: x-axis

(-∞, 4]

Graph type: √-x

I hope this helps!

Step-by-step explanation:

let's write it a little bit nicer

5.7 + 67v = -9.3 + 65v | subtract 65v on both sides

5.7 + 2v = -9.3 | subtract 5.7 on both sides

2v = -9.3 - 5.7 = -15 | divide both sides by 2

v = -7.5

An algebra word problem that can be used to explain the given expression is;

If the cost of a box is $16 and the cost of a bag is $14. Peter decides to buy x number of boxes. If his brother wants to buy bags to be same number as the number of boxes bought by his brother and he spends $8 more than the cost of the bags, how many boxes did peter buy?

We are given the algebraic expression as;

16x = 14x + 8

Algebraic word problems are defined as questions that need translation of sentences to equations, and then solving those equations. It usually has a single variable that represents a quantity in a real-life scenario that is  unknown.

Now, an algebra word problem that can be used to explain the given expression is;

If the cost of a box is $16 and the cost of a bag is $14. Peter decides to buy x number of boxes. If his brother wants to buy bags to be same number as the number of boxes bought by his brother and he spends $8 more than the cost of the bags, how many boxes did peter buy?

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The profit for 33 sales is $145

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

f(x) = 5x is the  revenue (in dollars) for selling x hamburgers.

profit = $20 less than revenue

So, the equation for the profit is

profit = 5x - 20

Now, if sales is 33 i.e., x=33 then profit will be

profit = 5(33) - 20

profit = 165-20

profit = $145

Hence, the profit is $145

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Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit. If Khalid makes an investment at 4% simple interest. at the end of 1 year, the total value of the investment is $1560. Then the original investment is $1500.

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit.

Percent to decimal 4%=4/100=0.04

A=P(1+rt)

where A is the final amount

P is initial principle balance, t is time and r rate of interest.

1560=P(1+0.04)

1560=1.04P

P=1560/1.04

P=1500

Therefore $1500 is originally invested.

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Solve for x by factoring. Obtain the roots of the expression. Solve the quadratic form and obtain the complex solutions. Equate the expression to zero and divide by the common factor 4, and factor out x.

4x^3-8x^2+16x

4x^3-8x^2+16x = 0

x(x^2-2x+4) = 0

x =0

x^2-2x+4 = 0

by quadratic formula,

x =  (-b±√(b²-4ac))/(2a)

x= (--2±√((-2)²-4(1x4))/(2)

x =  (2±√(4-16))/(2)

x =  (2±√-12)/(2)

Let √-12 = i , a complex root

x =   (2±i)/(2)

x =  (2+i)/(2)

x =  (2-i)/(2)

Thus,

x = 0

x =  (2+i)/(2)

x =  (2-i)/(2)

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The average weekly change in your running time bases on the information will be 4 seconds.

It should be noted that the mean simply means the average of the numbers that are given.

It should be noted that in this case, the person approve your time running a course by 5 seconds in week one, by three seconds in week two in by four seconds in week three.

Therefore, the average weekly change in your running time will be:

= Total seconds / Number of weeks

= (5 + 3 + 4) / 3

= 12 / 3.

= 4 seconds

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Step-by-step explanation:

I don't know what the equations are, but I'll do my best to help

ax² + bx + c

"a" is multiplied by (-4) and (c), as well as 2 in the denominator

"b" is put in front of the equation so, hypothetically speaking, b = -1

-b = -(-1) = 1 so it would turn a positive into a negative and a negative into a positive number.

b is also squared so no matter what it will be positive in √b² - 4ac

"c" is multiplied by (-4) and (a)

If I knew the equations I could help more but this is probably the best I can do.

I hope this helps!

Answer:

(a + b) = 9

Step-by-step explanation:

The a² - b² formula is also known as "the difference of squares formula"

It can be decomposed as follows:
a² - b²  = (a - b)(a + b)

Since we are given a + b = 5 and a² - b² = 45

we have

45 = 5 (a + b)

Dividing by 5 both sides
45/5 = (a + b)

9 = (a + b)

or,

(a + b) = 9

Answer:

328 Posters

Step-by-step explanation:

$1000-$180 = $820

$820/$2.50 = $328

To Check Answer:

328 x 2.50 = 820

820 + 180 = 1000

Answer:

8x^2 + 13.

Step-by-step explanation:

(f o g)(x) is found by replacing the x in f(x) by g(x).

= 4(2x^2 + 3) + 1

= 8x^2 + 12 + 1

= 8x^2 + 13.

Answer:

It is 6×x 6x-18=45

6x=45-18

=27

6x=27

27 divided by 6 = 4.5

Answer:

3/8 is a proper fraction which means it can't be written as a mixed number

Step-by-step explanation:

If the numerator is bigger than the denominator then you can convert it to a mixed number.

Answer:

3/8 is equal to 0.375

i dont think this can be turned into a mixed number becuase the fraction isn't over 8

example: 18/8 can be changed into the mixed number 2 3/8

Step-by-step explanation: