10. Find point W on the y-axis so that VW + XW is a minimum given V(2, 3) and
X(-2, -1).

Answer:1. 2

2. 20

3. 5499999.5 or5500000

Step-by-step explanation:

Answer:

1. 2

2. 20

3. 5,499,999.5 = 5,500,000

Each year Adam have to contribute $9486.68  to reach his goal of $750000 .

In the question ,

it is given that ,

Adam wants to have $75000 at the end of 30 years .

So ,the future value (FV) = 75000

the interest rate compounded annually = 6%

So , i = 6% = 0.06

given n = 30 , where n is the number of periods in which payments will be made .

we know , that the formula to calculate the Future value of the Annuity is

[tex]FV=PMT\times(\frac{(1+i)^{n}-1) }{i} )[/tex]

where ,

FV = Future Value

PMT = Periodic Payment

i = interest rate

n [tex]=[/tex] number of periods in which payments will be made .

Substituting the values in the formula ,

we get ,

75000 = PMT×((1+0.06)³⁰-1)/0.06)

75000×0.06 = PMT×(1+0.06)³⁰-1)

PMT = 45000/(1+0.06)³⁰-1)

PMT = 9486.6836

PMT ≈ 9486.68

Therefore , Each year Adam have to contribute $9486.68  to reach his goal of $750000 .

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Answer:

113 crates

Step-by-step explanation:

hope it helped :)

Originally, Stefan how much spent in the bicycle and helmet is $247.5

information from the problem

Stefan sells Jin a bicycle for ​$147 and a helmet for ​$18

The total cost for Jin is 150​% of what Stefan spent originally to buy the bike and helmet

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

150%

= 150 / 100

= 1.5

Total amount Jin spent

= 147 + 18

= 165

Original amount spent by Stefan

The factor 1.5 of what Jin spent is calculated

= 1.5 * 165

= 247.5

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By evaluating the linear function we will get the 3 points:

A. (-2, 8)

B. (2, -4)

C. (7, -19)

You can see the graph on the image at the end.

Well, the first thing we need to do is get these points, to do so, we need to evaluate the linear function in the given values.

We have f(x) = -3x + 2

if x = 2

f(2) = -3*2 + 2 = -4

if x = -2

f(-2) = -3*-2 + 2 = 8

if x = 7

f(7) = -3*7 + 2 = -19

So we have the points (-2, 8), (2, -4), and (7, -19)

The graph of these 3 points can be seen in the image below.

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The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

(a) 6 + 7(b - 1) = 5 + b

6 + 7b - 7 = 5 + b

7b - 1 = 5 + b

7b - b = 5 + 1

6b = 6

b = 1

(b) x/3 + 5 = 6 has the solution x = 3

as, 3/3 + 5 = 6

1 + 5 = 6

6 = 6

also, 9 - 3x = 0 has the solution x = 3

as, 9 - 3(3) = 0

9 - 9 = 0

0 = 0

also, 2x + 4 = 10 has the solution x = 3

as, 2(3) + 4 = 10

6 + 4 = 10

10 = 10

(c) 7x - 4 = 3x + 8

7x - 3x = 8 + 4

4x = 12

x = 3

(d) 6x - 9 = 15

6x = 15 + 9

6x = 24

x = 4

(e) 9 - x = 14/x has the solution x = 7

as, 9 - 7 = 14/7

2 = 2

also, 65 - 2x = 6x + 9 has the solution x = 7

as, 65 - 2(7) = 6(7) + 9

65 - 14 = 42 + 9

51 = 51

also, 3 + 4x = 5x - 4 has the solution x = 7

as, 3 + 4(7) = 5(7) - 4

3 + 28 = 35 - 4

31 = 31

Hence, The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

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ANSWER

The Fundamental Theorem of Algebra states that when we work.There are 1 zero in f(x) = 3x4 + x + 2 .

According to the fundamental theorem of algebra, the equation [tex]f(x) = 3x^4+x+2[/tex] has 4 solutions.

Given equation;

[tex]f(x) = 3x^4+x+2[/tex]

Fundamental theorem of algebra:

The following is another way to phrase the theorem: Every non-zero, single-variable, degree n polynomial with complex coefficients has precisely 'n' complex roots, counted with multiplicity. Using repeated polynomial division, it can be shown that the two claims are equivalent.

A (single-variable) polynomial's number of solutions is equal to its highest exponent, or the polynomial's "degree," according to the fundamental theorem of algebra.

So, there are four solutions because this polynomial is of the fourth degree.

The algebraic fundamental theorem states that there are four solutions to the equation [tex]f(x) = 3x^4+x+2[/tex] .

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Answer:

lines are perpendicular

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

line 1

4x + 2y = 12 ( subtract 4x from both sides )

2y = - 4x + 12 ( divide through by 2 )

y = - 2x + 6 ← in slope- intercept form

slope of line 1 = - 2

line 2

3x - 6y = 18 ( subtract 3x from both sides )

- 6y = - 3x + 18 ( divide through by - 6 )

y = [tex]\frac{1}{2}[/tex] x - 3 ← in slope- intercept form

slope of line 2 = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

Clearly the lines are not parallel

• the product of the slopes of perpendicular lines = - 1

- 2 × [tex]\frac{1}{2}[/tex] = - 1

then Line 1 and Line 2 are perpendicular to each other

The equations represents regular prices and sale prices of items in the store during the sale are

A) regular price: $29.99, sale price: $24.59

B) regular price: $55.43, sale price: $45.45

D) regular price: $652.30, sale price: $534.89

E) regular price: $849.50, sale price: $679.60

What means percent off?

A product's price is decreased by the percentage indicated by a product's percentage off.

We have,

A regular price: $29.99, sale price: $24.59

B regular price: $55.43, sale price: $45.45

C regular price: $215.33, sale price: $172.26

D regular price: $652.30, sale price: $534.89

E regular price: $849.50, sale price: $679.60

Hence, by calculating discount & subtracting it from original prince we get sale price.

Discount = Original Price x Discount %/100

Final Price = Original Price - Discount

A)

Discount = 29.99 × 18/100

Discount = 29.99 x 0.18 = $5.40

Final Price = 29.99 - 5.3982 = $24.59

B)

Discount = 55.43 × 18/100

Discount = 55.43 x 0.18 = $9.98

Final Price = 55.43 - 9.9774 = $45.45

C)

Discount = 215.33 × 18/100

Discount = 215.33 x 0.18 = $38.76

Final Price = 215.33 - 38.7594 = $176.57

D)

Discount = 652.3 × 18/100

Discount = 652.3 x 0.18 = $117.41

Final Price = 652.3 - 117.414 = $534.89

E)

Discount = 849.5 × 18/100

Discount = 849.5 x 0.18 = $152.91

Final Price = 849.5 - 152.91 = $696.59

Hence by comparing the original price with the final price we can identify the equation represents regular prices and sale prices of items in the store during the sale are

A) regular price: $29.99, sale price: $24.59

B) regular price: $55.43, sale price: $45.45

D) regular price: $652.30, sale price: $534.89

E) regular price: $849.50, sale price: $679.60

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Answer:

.....................................

Step-by-step explanation:

Answer: 4x+1

Step-by-step explanation:

1.  5(2x-3)-2(3x-8)

2. 10x-15-2(3x-8)

3. 10x-15-6x+16

4. 10x+1-6x

5. 4x+1

Answer:

4x+1

Step-by-step explanation:

First you have to expand it like 10x-15-2(3x-8) Basically multiplying 5 with 2x and -3.

Then take -2 multiply with 3x and -8  which will make it  10x-15-6x+16

Now Put together the like terms 10x-6x -15+16

Which makes it 4x+1

Hope it helped! I am a student too.

Brainly wont be there to help you in life its better to study.

Answer: -6a^2+4a

Step-by-step explanation: simplify

It is true that the confidence intervals for the mean provide an estimate for where the true mean lies.

In statistics, a confidence interval denotes the likelihood that a population parameter will fall between a set of values for a given proportion of the time. A confidence interval depicts the likelihood that a parameter will fall between two values near the mean. Confidence intervals quantify the degree of uncertainty or certainty in a sampling procedure.

The mean is a basic mathematical average of two or more values. There are two sorts of means that may be calculated: the arithmetic mean and the geometric mean. A mean tells you the average of a bunch of values, which helps you contextualize each data point.

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Answer:

7

Step-by-step explanation:

First distribute 3 into (x-10)

this will get you 3x-30=-9

then since 30 is negative, you do the opposite and add 30 to -9

-9+30 is 21 (when you add the 30 you are adding it to both sides, this will remove the original -30 because they are opposites)

You are left with 3x=21

Currently x is being multiplied by 3. Do the opposite and divide 21 by 3

21 divided by 3 is 7.

x=7

Answer:

x = 7

Step-by-step explanation:

1. Distribute

3(x - 10) = -9

3x - 30 = -9

2. Add 30 to both sides

3x - 30 = -9

3x - 30 + 30 = -9 + 30

3. Simplify

Add the numbers:

3x - 30 + 30 = -9 + 30

3x = -9  + 30

Add the numbers:

3x = -9 + 30

3x = 21

4. Divide both sides by the same factor

3x = 21

3x/3 = 21/3

Simplify

3x/3 = x

21/3 = 7

x = 7

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The equation of the straight line passing through two points (-2,-6) and (10,0) is y = x/2-11/2.

According to the question,

We have the following information:

We have two points: (-2,-6) and (10,0)

Now, first we will find slope of this equation:

(Slope is denoted by m.)

m = (y2-y1)/(x2-x1)

In this case, we have x1 = -2, y1 = -6, x2 = 10 and y2 = 0.

m = {0-(-6)}/{10-(-2)}

m = (0+6)/(10+2)

m = 6/12

m = 1/2

Now, the following formula will be used to find the equation of the straight line:

(y-y1) = m(x-x1)

y-(-6) = 1/2{x-(-1)}

y+6 = 1/2(x+1)

y+6 = x/2+1/2

y = x/2+1/2-6

y = x/2-11/2

Hence, the equation of the straight line passing through two points (-2,-6) and (10,0) is y = x/2-11/2.

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Ken will run 3 laps and Hamid will run 4 laps in 80 and 60 seconds.

To find this, we first find the number of seconds that will have passed when they meet again.  We use the LCM, or least common multiple, for this.  First we find the prime factorization of each number:

LCM of 80 and 60 = 2X2X5X4X3

                             = 4X5X4X3

                             = 240

Now, divide the respective seconds from the total 240, we get

for Ken, 240÷ 80 = 3 laps

For Hamid, 240÷ 60 = 4 laps

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Arrangement of the cards with six number -5,-2, -3 , 2, 0, -1 into three pairs such that they have same total are given by :

( -5 ,2) , (-2, -1) , (-3, 0)

As given in the question,

Given cards with six numbers are as follow:

-5,-2, -3 , 2, 0, -1

Arrangement of six cards in such a way that they have a same total is given by:

-5 + 2 = -3

-3 + 0 = -3

-2 + (-1) = -3

These pairs have the same total which is equal to -3.

Required pairs can be written as follow:

( -5 , 2) , ( -3 , 0) , ( -2 , -1)

Therefore , arrangement of the cards with six number -5,-2, -3 , 2, 0, -1 into three pairs such that they have same total are given by :

( -5 ,2) , (-2, -1) , (-3, 0)

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As per the unitary method, the time taken by Dave and joe work together to wash 20 cars is 125 minutes.

Unitary method:

In math, the method in which first we find the value of one unit and then the value of the required number of units is referred as unitary method.

Given,

10 cars are washed in 75 minutes by Dave. joe can wash 6 cars in 30 minutes.

Now, we need to find the time taken to wash 20 cars if Dave and joe work together.

Here we know that,

10 cars are washed in 75 minutes by Dave. joe can wash 6 cars in 30 minutes.

So, for 1 minute, the can wash,

Dave's works for 1 car  = 75/10 =  7.5

And Joe's time for one car = 30/6 = 5

So, together they can wash the car at,

=> (7.5 + 5)/2

=> 6.25 minutes.

So, for 20 cars they take the time,

=> 6.25 x 20

=> 125

Therefore, they take 125 minute to wash 20 cars.

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71 Hours

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The system of inequalities is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

A relationship between two expressions or values that are not equal to each other is called 'inequality'.

Given that, for a concert event, there are 30 reserved seat tickets and 20 general admission tickets. There are 1,900 reserved seats available, and fire regulations limit the number of paid ticket holders to 2,800.

The system of inequalities can be explained as follows:

30x + 20y ≥ 63,000 → Indicating a take in of at least $63,000 in ticket sales.

x ≤ 1900  → Indicating that 500 reserved seats are available.

x + y ≤ 2800 → Indicating limits of the paid ticket holders to 2800.

x ≥ 0  → Indicating ticket x must be equal or greater than 0.

y ≥ 0  → Indicating ticket y must be equal or greater than 0.

Hence, The system of inequalities is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

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Answer:

f(- 4) = 22

Step-by-step explanation:

substitute x = = - 4 into f(x)

f(- 4) = 2(- 4)² + 7(- 4) + 18 = 2(16) - 28 + 18 = 32 - 10 = 22

Answer: 10.5 > v

Step-by-step explanation:

Add both sides by 8 to isolate the right side to just v. You would get 10.5 > v as a result.

Answer:

She bought 5 chocolate bars.

Step-by-step explanation:

let x = number of chocolate bars

let y = number of gummy bears

[tex]\begin{cases}x + y = 7\\1.5x + 3y = 13.5\end{cases}\\\\\\\to - \begin{cases}3x + 3y = 21\\1.5x + 3y = 13.5\end{cases}\\\\\\\to 1.5x = 7.5\\\to x = 5\\\\[/tex]

Answer:

she purchased 3 chocolate bars

Step-by-step explanation:

hope this helps :)

what i did to find this problem is that i multiplied 3 x 3, which is 9, and then multiplied 1.50 x 3, which was 4.50. i added 9 + 4.50 and i got the answer!

Answer:

1. TPR

2.NM

3. 6

Step-by-step explanation:

1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.

2.  If you flip PRT then TR will match with NM

3. 4x-3=21

4x-3+3=21+3

Simplify: 4x=24

4x/4=24/4

x=6

Answer:

TPR

NM

6

The triangle NKM matcheswith TPR. We also already knew KMN= PRT. Now it was just a matter of aligning the order. 

 If you would like just basically flip the following: PRT then TR would match with NM which is what we need.

Finding: 4x - 3= 214x - 3 + 3 = 21 + 3

Simplify: 4x= 244x/ 4= 24/ 4x = 6

Answering: x = 6

Answer:

5

Step-by-step explanation:

By the Pythagorean Theorem:

[tex] {x}^{2} + {10}^{2} = {(5 \sqrt{5} )}^{2} [/tex]

[tex] {x}^{2} + 100 = 125[/tex]

[tex] {x}^{2} = 25[/tex]

[tex]x = 5[/tex]

Answer:

representative sample

Step-by-step explanation:

ik things

The equivalent expression is;

⇒ ln (e⁴) = 4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ ln (e⁴)

Now,

Since, We know that;

ln (eˣ) = x

So, We can apply the above rule, we get;

⇒ ln (e⁴) = 4

Thus, The equivalent expression is;

⇒ ln (e⁴) = 4

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The simplified form of this expression is x^4y-3x+y^2x^3-3y

From the question, we have

(x+y)(x^3 y-3)

= xx^3 y-x⋅3+yx^3 y-y⋅3

=x^4y-3x+y^(1+1) x^3-3y

=x^4y-3x+y^2 x^3-3y

The simplified form of this expression is x^4y-3x+y^2 x^3-3y

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The scale of increase in the drawing to inches in the actual room is 18

A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches

1 feet = 12 inches

Initially the room's length = 15 feet = 15 x 12 = 180 inches

On scale drawing the length = 10 inches

Let the  scale of inc in the drawing to inches in the actual room be k

10 x k = 180

k = 180 / 10 = 18

Initially the room's width = 12 feet = 12 x 12 =144 inches

On scale drawing the width = 8inches

8 x k = 144

k = 18

Therefore,  the  scale of inc in the drawing to inches in the actual room is 18

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