Solve the simultaneous equation
-4x+3y=1
6x-y=2

The equation of the perpendicular line is y = x + 15.

In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:

y = m · x + b      

Where:

The first line has a slope - 1 and the slope of the second line is:

m' = - 1 / m

m' = 1

Then, the intercept of the second line is:

b = y - m · x

b = 10 - (- 5)

b = 15

The equation of the perpendicular line is y = x + 15.

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Answer:

D

Step-by-step explanation:

The number of questions is 20; it's the total points that are worth 50 and the question is asking for number of questions

The binomial expression in simplest form which represents three times this quantity is; 3n +45.

Which expression, in simplest form, represents three times this quantity?

According to the task content, it follows that the expression which represents the quantity as defined is to be expressed, in simplest form binomial.

Since the word phrase given in the task content is represented as; n +3.

Hence, three times this quantity as required in the task content is;

3(n +15).

Ultimately, when expressed as a binomial expression by expansion; we have;

(3×n) + (3×15)

=3n +45.

Therefore, the binomial expression in simplest form which represents three times this quantity as required is; 3n +45.

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Using the quartiles of the data-set, it is found that there is one high outlier in the data-set.

The dot plot shows the frequency of each observation, hence the complete data-set is given by:

4, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 14, 16, 18, 20.

The quartiles are found as follows:

The IQR is given by:

IQR = Q3 - Q1 = 13 - 9 = 4.

The high outliers are the values that are more than 1.5 IQR above Q3, hence the threshold is given by:

13 + 1.5 x 4 = 19.

There is only value greater than 19, which is of 20, hence there is one high outlier in the data-set.

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Answer:

answer was 0

Step-by-step explanation:

The greatest value in range of work situation is $200.

For the given question;

The one time bonus is $40.

Amount earned by Kara per hour is $8.

The range of working hours lies between 16 to 20 hours in a week.

Let 'x' be the number of hours Kara worked.

The the inequality will be;Then, the equation for the amount earned in a week is;

Total pay = one time pay + 8×number of hours

Total pay = one time pay + 8x

The greatest value will be earned by the kara when she will work for 20 hours.

Thus, put x = 20.

Total pay = one time pay + 8×20

Total pay = 40 + 8×20

Total pay = 200

Therefore, the total greatest pay earned by the Kara is $200.

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He will earn 2603.16 dollar in one year.

An expression is a collection of terms that have been joined together using the operations +, -, or x, such as 4 x 3 or x 2 - x y + 17.

Two expressions are said to be equal in value by an equation, such as 4 b 2 = 6.

Given:

A copy of the entire query is provided below:

45w+ 155

He will therefore save

=45*6+155

=270+155 =425 dollars

so,  w=6.

Knowing that a year equals 52 weeks

Also,

w=52 and

w²/25+45w+155

Thus,

=52*52/25+45*52+155

=108.1602340+155

= $263.16

Hence, he will make $2603.16 in a year.

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Answer: There are 12 volleyball players

Step-by-step explanation:

If the ratio of basket to volleyball players is 5:2 and there are 30 known basket ball players that means the ratio can be written as 30:x.

If 30 is 5 parts (5x) and volleyball players is 2 parts (2x)  we need to figure out the value of 1 part (x)

This can be done by

5x=30

x=6

Now we know what 1 part is, we can now use that two figure out 2 parts

2x or 2(6)

2(6) = 12

So the ratio is 30:12. This can be confirmed by dividing both sides of the radio by 6 to get 5:2

The given algebraic equation  formula i.e., [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b of -3 and -5 respectively.

As per the question statement, we are supposed to verify the algebraic equation formula

[tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex]

We are given that a = -3 and b = -5

Now substituting the values of a and b in the  algebraic equation formula

[tex](a^{2} -b^{2} )=(a+b)(a-b)\\LHS = (a^{2} -b^{2} )\\LHS= ([-3]^{2} -[-5]^{2} )\\LHS=(9-25)\\LHS = -16[/tex]

LHS = Left hand side of the equation

Now considering RHS i.e., Right hand side

[tex]RHS = (a+b)(a-b)\\RHS = ([-3]+[-5])([-3]-[-5])\\RHS= (-8)(2)\\RHS = -16[/tex]

As Left Hand Side LHS = Right Hand Side RHS

Hence the equation, [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b and is true for all real values of a and b.

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x+2x+x=d is solution set of a linear system whose augmented matrix.

What does matrix mean?

First statement

[ 1 2 3 | d][x]

[ 1 2 3]x=d

x+2x+3x=d

Second statement

Ax=d

Given that A = [ 1 2 3]

[ 1 2 3]x=d

x+2x+3x=d

x+2x+x=d

Then, they are going to have the same solution

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Answer:  A

Step-by-step explanation: A because you have to find the total amount of money so you a X

i think/ hope

Answer:

the coordinates of BB would be: B(8,1)

Answer:

23

Step-by-step explanation:

You have to do the division first unless it is a fraction.

14/2 = 7

30 - 7 = 23

If it was a fraction (with 30 - 14 on top and 2 on the bottom) Then the answer would be 8 > 30 - 14 = 16/2 = 8

Hope this helps.

Answer:

x - 7 = -25

Step-by-step explanation:

The value of x is,

→ x = -18

Then the value of x - 7 will be,

→ x - 7

→ -18 - 7

→ -25

Hence, the answer is -25.

Answer:

just put out + from the question.

Answer:

sqrt of 49 is simplified as 7 so its a rational that can be put in all the rows

Step-by-step explanation:

Rational numbers: -1.3, 2.7777.., 25/2 also known as 12.5, O

Integers: sqrt of 49 also known as 7, 0

Whole numbers: sqrt of 49 also known as 7, 0

Natural numbers: sqrt of 49 also known as 7, 0

Irrational numbers: sqrt of 2, Pi,

Answer:

#1 = -2

Step-by-step explanation:

First, we need to make -2 2/3 an improper fraction. An improper fraction is a fraction whose numerator is bigger than its denominator.

you first multiply the whole number (ignoring the negative sign for now) by the denominator:

2*3=6

then you add the numerator:

6+2=8

finally you put that number over the denominator and then put the negative sign back:

-8/3

Next, you can use keep change flip to solve the division

You keep the first fraction, change the division sign to a multiplication sign, and flip the numerator and the denominator of the second fraction:

-8/3 divided by 4/3 becomes -8/3 x 3/4

finally you multiply across as you would normally and simplify

-8/3 x 3/4= -24/12

-24/12 simplified is -2

:D

if you need help with the rest just comment on this response and I'll try to answer as soon as I can

The time when the two total costs would be equal is 6 hours.

The equation that can be used to represent the total cost of renting a canoe is a linear function. A linear equation is an equation that has a single variable raised to the power of 1.  A linear equation increases by a predetermined constant. An example of a linear equation is 2x + 2.

The form that the equation would be is:

Total cost = rental fee + (cost per hour x number of hours)

Total cost at Shop A = $2 + $5h

Total cost Shop B = $8 + $4h

When the total costs are equal, the two above equations would be equal.

$2 + $5h = $8 + $4h

Combine similar terms: $$5h - $4h=  $8 - $2

Add similar terms: h = 6 hours

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-2 9 2 is the change in points from Tuesday to Wednesday in stock market.

What does the term "stock market" mean?

What does the stock market represent?

The stock market closed on Tuesday = -284 points

On Wednesday  it closed = -8

the change in points from Tuesday to Wednesday = -284 - 8 =   -2 9 2

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Using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.

Given the problem above, we would do the following:

Using the information given, we would form two equations for the system as shown below:

2v + 3d = 90 ---> equation 1

v + 2d = 51.5 ---> equation 2

Multiply equation 2 by 2 to get equation 3

2v + 4d = 103 ---> equation 3

Subtract equation 1 from equation 3

d = 13

The cost of one DVD = d = $13.00

Substitute d = 13 into equation 2

v + 2d = 51.5 ---> equation 2

v + 2(13) = 51.5

v + 26 = 51.5

v = 51.5 - 26

v = 25.5

The cost of one video game = v = $25.50.

Therefore, using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.

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The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.

From the question, we are to graph the given inequality

The given inequality is

1 < y + 7x ≤ 12

First, we will separate the inequality

1 < y + 7x and y + 7x ≤ 12

1 < y + 7x

We will determine two points on the line

1 = y + 7x

When x = 0

1 = y + 7(0)

1 = y

y = 1

(0, 1)

When y = 8

1 = y + 7x

1 = 8 + 7x

1 -8 = 7x

-7 = 7x

x = -7/7

x = -1

(-1, 8)

We can use these two points to plot the line of 1 < y + 7x

Also,

We will determine two points on line y + 7x ≤ 12

y + 7x = 12

When x = 0

y + 7(0) = 12

y + 0 = 12

y = 12

(0, 12)

When y = 5

5 + 7x = 12

7x = 12 - 5

7x = 7

x = 7/7

x = 1

(1, 5)

We can use these two points to plot the line of y + 7x ≤ 12

The graph of the combined inequality, 1 < y + 7x ≤ 12, is shown below. The correct graph is graph b.

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Answer:

0.012÷2=12 thousandths ÷ 2

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = [tex]\int_a^b \delta\left|r^{\prime}(t)\right| d t[/tex]

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

[tex]\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}[/tex]

Further simplifying;

[tex]\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}[/tex]

Now, use integration to find the mass of the wire;

       [tex]\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}[/tex]

Therefore, the mass of the wire is estimated as 40π√2 units.

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The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

The number can be -3, -2, -1, 0 ,1

Here, we are given that twice a number is increased by three and the result is between negative three and seven.

Let the number be x

Twice of the number = 2x

Four more than twice the number = 2x + 4

This number is between -3, 7

⇒ -3 < 2x +4 < 7

subtracting 4 from both sides we get

-3 -4 < 2x < 7 - 4

-7 < 2x < 3

Dividing both sides by 2 we get

-7/2 < x < 3/2

- 3.5 < x < 1.5

Thus the original number lies between -3.5 and 1.5

This means that it can take 5 values-

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

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Answer:

123

Step-by-step explanation:

supplementary angles add up to 180

(5x - 22) + (x + 28) = 180

5x - 22 + x + 28 = 180

6x + 6 = 180

6x = 180 - 6

6x = 174

x = 174/6

x = 29

<A = 5x - 22 = 5(29) - 22 = 123