What is the solution to the system of equations y 2x 3. 5 x 2y 14?.

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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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:

representative sample

Step-by-step explanation:

ik things

For the given triangle the value of y would be 55°.

What are the angles in a linear pair?

When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°.

In the given triangle, x and 100° forms angles in a linear pair,

by using the property of angles in a linear pair,

               x + 100 = 180

               x = 180 - 100

               x = 80°.

Now by using the property of angles of a triangle.

Sum of all angles of a triangle = 180

45 + y + 80 = 180

y + 125 = 180

y = 180 - 125

y = 55°.

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Answer:

113 crates

Step-by-step explanation:

hope it helped :)

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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The equation:

1/3y = -1

Is equivalent to a horizontal line, so the equation is linear.

A general linear equation is written as:

y = m*x + b

Where m is the slope of the line and b is the y-intercept

In this case, we have the equation:

1/(3y) = -1

So "y" is on the denominator, if we multiply both sides by y, we get:

1/3 = -y

Now we can multiply both sides by -1:

-1/3 = y

So we have a linear equation with a slope equal to zero:

y = 0*x - 1/3 = -1/3

This is a horizontal line.

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The ramp would be 5.4 inches high

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Length of fiber board = 19 inches

Angle of elevation of ramp = 16°

Height of ramp = h

The height of the ramp, length off fiber board and length of ramp form a right angle triangle with acute angle 16°

tan 16 = opposite/adjacent

tan 16 = h /19

By cross multiplying,

h = 19 tan 16

but tan 16 = 0.2867

h = 19 x 0.2867

h = 5.4 inches

In conclusion the height of the rise of the ramp would be 5.4 inches

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Answer:5.2

Step-by-step explanation:

hard way

Answer:

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

Step-by-step explanation:

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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The sum of the interior angles for a pentagon is 540°

Sum of Interior Angles of a Pentagon :

The interior angles of a pentagon sum up to 540 degrees.. Regardless of how regular or irregular the pentagon is, this is true. By dividing the whole amount by 5, we can calculate the size of each internal angle in the case of regular pentagons. To determine the measure of a missing angle in the situation of irregular pentagons, we must first know the measurements of other angles.

Any pentagon's internal angles add up to 540° in the same way. This holds true regardless of how regular or irregular the pentagon is. By using the polygon angle sum formula, the following sum is obtained:

(n-2)180(n−2)×180°

where n represents the polygon's number of sides. We have n = 5 in the case of a pentagon. Consequently, utilizing the formula:

=(n-2)180=(n−2) ×180°

= (5-2) 180= (5−2) ×180°

= (3) 180= (3) ×180°

= 540=540°

Consequently, a pentagon's interior angles add up to 540 degrees.

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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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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.

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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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:

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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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:

Below

Step-by-step explanation:

100t = 1491.48     divide both sides of the equation by 100 to get

t = 14.9148        round

t = 14. 91

Answer:

t = 14. 91

Step-by-step explanation:

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:

(0, 0)

Step-by-step explanation:

Step 1: Define a Function

Recall that a graphed relation can only be a function if every input (x-value) has exactly one output (y-value), and not the other way around. That is, a function can have the points (2, 3) and (3, 3), but not (2, 3) and (2, 4), for example. This information will be very useful in solving this problem.

Step 2: Take Inventory of the Current Points

Let's first take into account what points we already have plotted. Using the graph, we can see that our current 4 points are (-3, 0), (-1, 1), (1, 2), and (3, 3). Again, the y-values do not really matter here as they can be repeated, but the x-values are what we need to pay attention to, so let's disregard the y-values of the points and just list the x-values as x = -3, -1, 1, and 3.

Step 3: Use this Information to Choose the Correct Answer

We know that in order to still be a function, the point we add must have an x-value that is not among the above list (and if it is, it must be the same exact point - e.g. if one of the options was (-3, 0), then it would technically work, but that is not the case with any of these points so we can ignore this possibility).

We can see that the x-values of the options are x = 1, 3, -3, and 0. Of these options, 1, 3, and -3 are already in our list, so those are not correct. Therefore, the only point that will keep the graphed relation a function is (0, 0). (Don't worry that the graph doesn't look like a straight line, a function is defined as any set of points that has exactly one output for every input - this does not necessarily mean the function follows an equation as we may normally think!)

Answer:

(0,0)

Step-by-step explanation:

All of the other choices would result in there being two values of y for a given x (thus NOT a function)

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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a. The number of teenagers that like hard rock is of: 272.

b. The number of teenagers surveyed is of: 200.

c. A percentage greater than 100% is when the percentage of an amount is calculated relative to an smaller amount.

The measures are obtained applying the given proportions and percentages in the context of the problem.

For item a, the amount is of 32% of 850, hence:

0.32 x 850 = 272 teenagers like hard rock.

For item b, we have that 75% = 0.75 of the amount x is of 150, hence the total amount of teenagers surveyed is obtained as follows:

0.75x = 150

x = 150/0.75

x = 200 teenagers were surveyed.

A percentage is calculated as the division of an amount a by an amount b. Hence, if the amount a is greater than the amount b, the percentage will be greater than 100%.

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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

The coordinates  of the image of (5, 2) if it was reflected over the x-axis and then that image was reflected over the y-axis. is (-5, -2)

We need to find the coordinates of the image of (5, 2) if it was reflected over the x-axis and then that image was reflected over the y-axis.

When an object is reflected over the x axis, the y coordinate changes

(x, y) reflected in x axis gives (x, -y)

So, the point (5, 2) is reflected over x axis, it becomes (5, -2)

Now this image is gain reflected over y axis

When an object is reflected over the y axis, the y coordinate changes

(x, y) reflected in y axis gives (-x, y)

So, the point (5, -2) is reflected over y axis, it becomes (-5, -2)

Therefore, the coordinates  of the image of (5, 2) if it was reflected over the x-axis and then that image was reflected over the y-axis. is (-5, -2)

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Answer: -6a^2+4a

Step-by-step explanation: simplify

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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The vertex form of the parabola is y = a[tex](x-h)^2[/tex]+ k.

What is vertex form ?

            When a graph crosses its symmetry axis, the vertex formula in mathematics aids in determining the parabola's vertex coordinate. The typical representation of the vertex point is (h, k). We are aware that y=a[tex]x^2[/tex]+bx+c is the typical equation for a parabola. The vertex in this case, if the coefficient of [tex]x^2[/tex] is positive, should be at the base of the U-shaped curve. The vertex of a U-shaped curve should be at the top if the coefficient of [tex]x^2[/tex] is negative.

Here We know that the standard form of the parabola is y=a[tex]x^2[/tex]+bx+c.

Thus, the vertex form of a parabola is y = a[tex](x-h)^2[/tex]+ k.

The vertex formula is used to find the vertex of a parabola. There are two ways to find the vertex of a parabola.

Vertex, (h, k) = (-b/2a, -D/4a)

Where “D” is the discriminant where D = [tex]b^2[/tex] – 4ac.

“h” and “k” are the coordinates of the vertex.

Hence the vertex form of the parabola is y = a[tex](x-h)^2[/tex]+ k.

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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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