Question 5 of 10
In the diagram below, 30 is parallel to XY. What is the value of x?
769

Answer:

(1, -2), (4, 1)

Step-by-step explanation:

Here we want to solve the system of equations:

y = x^2 - 4*x + 1

y = x - 3

First, we can see that in both parts we have isolated the variable "y", so we can just write:

x - 3 = y = x^2 - 4*x + 1 = y

removing the "y"s, we get:

x - 3 = x^2 - 4*x + 1

Now we can solve this for x

0 = x^2 - 4*x + 1 - x + 3

0 = x^2 - 5*x + 4

This is a quadratic equation, the solutions are given by the Bhaskara's formula, that says that for a general quadratic equation:

0 = a*x^2 + b*x + c

The solutions are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

So for the case of our equation:

0 =x^2 - 5*x + 4

The solutions are given by:

[tex]x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*1*4} }{2*1} = \frac{5 \pm 3}{2}[/tex]

So the two solutions are:

x₁ = (5 + 3)/2 = 4

x₂ = (5 - 3)/2 = 1

To find the ordered pair, we need to replace these values in one of the equations of the system, let's use the second:

y = x₁ - 3 = 4 - 3 = 1

Then we have one solution at (4, 1)

And for the other:

y = x₂ - 3 = 1 - 3 = -2

then the ordered pair is (1, -2)

Now we want to write from least to greatest with respect to the x-coordinate, then the correct order is:

(1, -2), (4, 1)

Answer:

hope it is helpful to you

Answer:

Rs.1772624

Step-by-step explanation:

Multiply 52,236 by 34

Answer:

x = 15

Step-by-step explanation:

The two angles add to a straight line, so they add to 180

6x-5 + 6x+5 = 180

Combine like terms

12x = 180

Divide by 12

12x/12 =180/12

x =15

Answer:

x = 15

Step-by-step explanation:

Two angles are supplementary and their sum is 180

6x + 5 + 6x - 5 = 180 add like terms

12x = 180 divide both sides by 12

x = 15

Given:

The equation is:

[tex]30n-C+200=0[/tex]

To find:

The slope intercept form of the given equation.

Solution:

We have,

[tex]30n-C+200=0[/tex]

We need to write the given equation in the form of [tex]C=mn+b[/tex].

Adding C on both sides, we get

[tex]30n-C+200+C=0+C[/tex]

[tex]30n+200=C[/tex]

Interchanging the sides, we get

[tex]C=30n+200[/tex]

This equation is in the form of [tex]C=mn+b[/tex], where m is 30 and b is 200.

Therefore, the slope intercept form of the given equation is [tex]30n-C+200=0[/tex].

The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

Answer:

Answer B

3 non collinear point

Answer:

The rate of change is 3.5

Step-by-step explanation:

Really? Like this is easy.

Answer:

$250*C + $180*G = $950

Step-by-step explanation:

Solving for G, it is G = (950 - 250C)/180

Solving for C, it is C = (950 - 180G)/250

Answer:

D. all real numbers greater than or equal to 2

Step-by-step explanation:

Range values consists of all possible set of y-value plotted on the vertical axis. So, we are looking at the y-values on the y-axis (vertical axis).

The line starts at 2 on the y-axis. The shaded "o" means that 2 is included or the range of the function is 2 or above.

Thus, this means that:

the range of the function of the graph are "all real numbers greater than or equal to 2."

The Range of the function are all real numbers greater than or equal to 2

The Range of a function is the output values or values of the dependent variable of a function.

Since the y - axis represents the dependent variable, the Range of the function is the values of y given from the graph. The values of y given from the graph range from and include 2 to ∞. The value 2 is included since it is shaded.

So, the Range of the function are all real numbers greater than or equal to 2

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Answer: Perimeter: 28 units

Area: 32 square units

Step-by-step explanation:

Answer:

Perimeter = 24

Area =32

Step-by-step explanation:

To find the perimeter, add up the number of outside edges

4+ 2+2+2+2+2+4+2+2+2+2+2 =24 units

To find the area, count the number of boxes in each row

4 + 4+ 8+8+4+4 = 32 units^2

Answer:

$461

Step-by-step explanation:

First, find the cost with the daily charge of $29.

Multiply 14 by 29, since the car was rented for 14 days:

14(29)

= 406

Find the cost with the distance traveled. Since there is only a charge after the first 100 km, subtract 100 from 320.

320 - 100

= 220

Find the charge by multiplying this by 0.25:

220(0.25)

= 55

Add this to the daily charge:

55 + 406

= 461

So, the cost will be $461

Answer:

The probability is 32/81

Step-by-step explanation:

We know that:

The probability that the team wins is p = 2/3

Then the probability of not winning is q = 1 - p = 1 - 2/3 = 1/3

The team plays 4 matches.

We want to find the probability that the team wins 1 more than half of the number of matches played.

So if there are 4 matches, the half is 2 matches

one more than half is then 3 matches.

Let's assume that the team wins the first 3 matches, and does not win the last match.

match one, the team wins with prob: P₁ = 2/3

match two, the team wins with prob: P₂ = 2/3

match three, the team wins with prob: P₃ = 2/3

match four, the team wins with prob: P₄ = 1/3

The joint probability is the product of all the individual probabilities:

P = (2/3)*(2/3)*(2/3)*(1/3)

Now we must also considerate the permutations, we have the cases:

the team does not win the fourth match

the team does not win the third match

the team does not win the second match

the team does not win the first match

So we have just four permutations, then the total probability is:

probability = 4*P = 4*(2/3)*(2/3)*(2/3)*(1/3) = 4*(8/81) = (32/81)

Answer:

x = -4

Step-by-step explanation:

y = 3x - 1

Replace all instances of Y into the second quation.

2x - (3x-1) = 5

2x -3x +1 = 5

-x = 4

x= -4

Answer:

11

Step-by-step explanation:

15-12=3

so

x-8=3

x=11

Answer:

22.5 in.

Step-by-step explanation:

Both triangles have 110º so that means they are equal.

12x15=180 inches

So, X=22.5 inches

Answer:

1115.8

Step-by-step explanation:

Answer:

20/3

Step-by-step explanation:

The Other guy is wrong, this is the correct answer from Plato

The rate of change in a direct variation relationship is the same as the constant of proportionality. The rate of change is the change in the dependent value, y, over the change in the independent value, x.

In this case, the number of tickets sold is the independent variable and the amount of money raised from ticket sales is the dependent variable. The ratio of money raised per ticket sold is the constant of proportionality.

Since 3 tickets are sold for $20, the rate of change, or slope, is 20/3

Answer:

20/3 I mean imI'm doing it rn and..... the plug

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

11 times 11 = 121

11 times 12 equals 132

11 times 13 = 143

Answer:

13

Step-by-step explanation:

11x13 is 143 heidnehf

Answer:

60

Step-by-step explanation:

The system of equation to find the number of apples and number of granola bars is: [0.75x + (9 - 0.15x)] = 21.00

The number of apples is 20 and the number of granola bars is 40.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."

George will bring 60 total items to school

Let, George will bring 'x' apples.

Therefore, he will bring (60 - x) granola bars.

Given, apples cost $0.75 each, and granola bars cost $0.15 each.

Therefore, cost of all apples is $0.75x.

Cost of all granola bars is:

= $(60 - x) × 0.15

= $(9 - 0.15x)

The system of equation to find the number of apples and number of granola bars is: [0.75x + (9 - 0.15x)] = 21.00

Now, [0.75x + (9 - 0.15x)] = 21.00

⇒ [0.75x - 0.15x] = 21.00 - 9

⇒ 0.6x = 12.00

⇒ x = (12.00 ÷ 0.6)

⇒ x = 20

Therefore, the number of apples George will bring to school is 20.

Now, the number of granola bars George will bring to school is (60 - 20) = 40.

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Answer:

m= -6

Step-by-step explanation:

:]

Answer:

C

Step-by-step explanation:

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

Given the slope of the red line is 4 , then the slope of the green line is

m = - [tex]\frac{1}{4}[/tex] → C

The slope of the green line is C (m = -1/4 )

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

The slope of the line is calculated as follows:

m = Δy/Δx

We are Given a line with slope m then the slope of a line perpendicular to it is m

m (perpendicular) = -1/m

Given the slope of the red line is 4 , then the slope of the green line is;

m = -1/4

Therefore the slope of the green line m = -1/4.

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Answer:

[tex]2.50[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-1,0.8)[/tex]

[tex](x_2,y_2) = (0,2)[/tex]

[tex](x_3,y_3) = (1,5)[/tex]

[tex](x_4,y_4) = (2,12.5)[/tex]

Required

The rate of change (b)

The above graph is represented as:

[tex]y = ab^x[/tex]

For: [tex](x_2,y_2) = (0,2)[/tex];

We have:

[tex]y = ab^x[/tex]

[tex]2 = a * b^0[/tex]

[tex]2 = a *1[/tex]

[tex]2 = a[/tex]

[tex]a = 2[/tex]

For [tex](x_3,y_3) = (1,5)[/tex],

We have:

[tex]y = ab^x[/tex]

[tex]5 = a * b^1[/tex]

[tex]5 = a * b[/tex]

Substitute [tex]a = 2[/tex]

[tex]5 = 2 * b[/tex]

Divide by 2

[tex]2.5 = b[/tex]

[tex]b = 2.5[/tex]

Hence, the rate of change is 2.50

Answer:

or, 2x-x^2+2x^2=1

or,2x+x^2=1

or,x^2+2x-1=0

or,x^2+x+x-1=0

or,x(x+1)+1(x-1)=0

or,(x+1)(x-1)=0

therefore x=(-1,+1)

Answer:

y = 2x + 5

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 )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, so

y = 2x + c ← is the partial equation

To find c substitute (- 3, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = 2x + 5 ← equation of parallel line

The Equation of line is y = 2x + 5.

The ratio of a line's change in y coordinate to its change in x coordinate is known as its slope.

Both the net change in the x-coordinate  is Δx and the net change in the y-coordinate are represented by Δy.

Given Equation

y = 2x + 3

and line passes through (-3, -1)

equation of line is given by,

y =mx + c

where m is slope,  given equation is parallel to graph the value of slope is equal for both

m = 2 from given equation

new equation is y = 2x + c

substitute values of x and y

-1 = 2(-3) + c

c = -1 + 6

c = 5

Equation of line is y = 2x + 5

Therefore the equation represents,

the line in slope-intercept form is y = 2x + 5

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An equation of the line through the point (-4, -2) parallel to y = 14x - 3 is 14x - y = 54.

To find an equation of a line through the point (-4, -2) that is parallel to the line y = 14x - 3, we can use the fact that parallel lines have the same slope.

The given line y = 14x - 3 is in slope-intercept form, y = mx + b,

where m represents the slope.

In this case, the slope is 14.

Since the desired line is parallel to the given line, it will also have a slope of 14.

Therefore, the equation of the line can be written as:

y - y1 = m(x - x1),

where (x1, y1) represents the coordinates of the given point (-4, -2), and m represents the slope.

Substituting the values into the equation, we have:

y - (-2) = 14(x - (-4)).

Simplifying this equation gives:

y + 2 = 14(x + 4).

Expanding the right side of the equation:

y + 2 = 14x + 56.

Finally, rearranging the equation to the standard form, we have:

14x - y = 54.

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Answer:

The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.

Step-by-step explanation:

Let be the following system of equations:

[tex]2\cdot x + 3\cdot y = 12[/tex] (1)

[tex]x\cdot y = 6[/tex] (2)

Then, we solve both for [tex]x[/tex] and [tex]y[/tex]:

From (1):

[tex]2\cdot x + 3\cdot y = 12[/tex]

[tex]2\cdot x = 12- 3\cdot y[/tex]

[tex]x = 6 - \frac{3}{2}\cdot y[/tex]

(1) in (2):

[tex]\left(6-\frac{3}{2}\cdot y \right)\cdot y = 6[/tex]

[tex]6\cdot y-\frac{3}{2}\cdot y^{2} = 6[/tex]

[tex]\frac{3}{2}\cdot y^{2}-6\cdot y + 6 = 0[/tex]

The roots of the polynomial are determined by the Quadratic Formula:

[tex]y_{1} = y_{2} = 2[/tex]

By (1):

[tex]x = 6 - \frac{3}{2}\cdot (2)[/tex]

[tex]x = 3[/tex]

If we know that [tex]x = 3[/tex] and [tex]y = 2[/tex], then the final value is:

[tex]z = 8\cdot x^{3}+27\cdot y^{3}[/tex]

[tex]z = 8\cdot 3^{3}+27\cdot 2^{3}[/tex]

[tex]z = 432[/tex]

The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.