How many solutions does 3(4x - 8) = -24 + 12x have?
Group of answer choices
a. infinitely many solutions
b. no solution
c. one solution
d. two solutions

The rquired equation of the line is x + 2y = - 10

The slope-intercept form of a line is given by

Where m = slope and c = y-intercept  

Note: The slope of two parallel lines will have the same slope

Here we have

The point (-6, -8) and the line x - 2y = 6 --- (1)

Let the equation y = mx + c ---- (2)  is the equation of the line  that passes through (-6, -8) and parallel to x - 2y = 6  

As we know the parallel  lines will have the same slope

=> Slope of line (1) = Slope of line (2)

Here x - 2y = 6

=> 2y = - x + 6

=>  y = -x/2 + 3  which is in the form of y = mx + c

=> Slope of line = - 1/2

Therefore, the Slope of lines (2) = -1/2

=> y = (-1/2)x + c

=> 2y = -x + 2c --- (3)

Given that line passes through (-6, -8)

=> 2(-8) = - (-6) + 2c

=> - 16 = + 6 + 2c

=> 2c = -10

=> c = -5

=>  y = -x/2 + (-5)

=>  y = -x/2 - 5

=> 2y = - x - 10

=> x + 2y = - 10

Therefore,

The required equation of the line is x + 2y = - 10  

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A graph of the solution to this system of inequalities on a coordinate plane is shown in the image attached below.

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

y ≥ x²

y ≤ x + 2

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (2, 4) and ordered pair (-1, 1).

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The height of the riders above the Colorado River at the peak of the arc shown will be 3,064.73 feet.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

The length of the variable 'y' is given as,

sin (212° - 180°) = y / 41

0.5299 = y / 41

y = 21.73 feet

The height of the riders above the Colorado River is given as,

⇒ 21.73 + 43 + 3,000

⇒ 3,064.73 feet

The height of the riders above the Colorado River at the peak of the arc shown will be 3,064.73 feet.

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The missing part is given below.

The equation's directrix of [tex]y^{2}-6y-2x+19=0[/tex]. is 4.5 since this parabola's directrix's equation is x + a = 0.

The statistic is said to be in a simplified sense when divided into its smallest equivalent fraction. What to do to determine the most basic form. Look for common factors in the denominators and numerators.  A statement having two equal sides and then an equal sign in the midpoint is called an equation in mathematics. The conceptual model of any formula contains the degrees of all the variables given descending order. The typical form of a linear equation is an x + b = 0. This same general form of a mathematical expression with two variables is an x + b y + c = 0. (or something similar). Inequalities can be categorized either identities or dependent equations. An id holds true regardless of the value given to the variables.

given

Knowing the axis and vertex of a parabola allows one to determine the directrix of the curve.

The equation of the directrix of this parabola is x + a = 0 for an equation of the parabola in standard form [tex]y^{2} = 4ax[/tex], with focus at (a, 0) axis as the x-axis.

equation = [tex]y^{2}-6y-2x+19[/tex]=0

directrix  x = h−p

(y−k)2 = 4p(x−h),p≠0

Directrix: x=4.5

The equation's directrix of [tex]y^{2}-6y-2x+19=0[/tex]. is 4.5 since this parabola's directrix's equation is x + a = 0.

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The complete question is:-

Find the directrix of this equation of y2-6y-2x+19=0

To find the mean of a given set of data, you divide the sum of all the values and divide it by the number of values.

[tex]9,-2,9,9,-2,-2,14[/tex]

[tex]9+-2+9+9+-2+-2+14\\=35[/tex]

There are a total of 7 values that are given. So, to find the mean, we simply must divide 35(the sum of all values) by 7(the number of values).

[tex]35\div7=5[/tex]

Therefore, the mean of our given set of data is 5.

Answer:

450 plus whatever other costs there are if there are any

Step-by-step explanation:

300+150=450 so it is 450 plus any other ammount of money you must pay if any

Answer and Explanation:

To calculate the total value of the loan with simple interest, we can use the formula:

Loan amount x (Interest rate x Time in years) = Simple interest

Where,

Loan amount = $50,000

Interest rate = 6.15%

Time in years = 3 years + 7 months / 12 months/year = 3.58 years

So,

Simple interest = $50,000 x (6.15% x 3.58) = $10,439

Therefore, the total value of the loan with simple interest would be $50,000 + $10,439 = $60,439.

The required median of the given data set 11, 13, 24, 28, 30, and 47 is 24.

When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top 50% of data.

The median of a set of numbers is the middle value when the numbers are arranged in order.

First, we need to arrange the numbers in ascending order:

11, 13, 24, 28, 30, 47

For an even number of values, the median is given as
Median = n  / 2 th terms

Median = 6 / 2 = 3rd term

Median = 24

So, the median of 11, 13, 24, 28, 30, and 47 is 24.

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The amount of outdoor carpet that will be needed for the hole in square feet will be = 40ft²

To calculate the quantity of outdoor carpet needed is to subtract the square and the rectangular areas that were not covered from the whole rectangular area that was covered.

The area of the square = length×width = 3×2 = 6ft²

The area of the rectangule = length×width = 1×2 =2ft²

The area of the whole hole = l×w = 4× 12= 48ft²

Therefore, the area of the outdoor carpet that will be needed for the hole in square feet would be;

= 48 - ( 2+6)

= 48 - 8

= 40 ft²

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The value of the x for the given triangle is 30.67.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given a right triangle,

the base angle is 61° and the length of the base is 17

using tangent to find the value of x

tanФ = perpendicular/base

here base = 17

perpendicular = x

Ф = 61°

tan61 = x/17

x = 17tan61

x = 30.67

Hence the value of x is 30.67.

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Answer:

B.    175.84 square inches

Step-by-step explanation:

The pizza is shaped like a circle

Area of a circle = π r² where r is the radius

r = d/2 where d = diameter

Here d = 16 in

r = 16/2 = 8

Total area of pizza = π · 8² = 64 π

If 1/8th of the pizza was consumed balance = 1-1/8 = 7/8

7/8 of the total area = 7/8 x 64π = 56π = 175.84 square inches

This is the area of the remaining portion of the pizza

The end behavior of the graphed function is defined by:

To identify the end behavior, we need to look how the function behaves as the independent variable tends to ±∞.

Here we can see that in both ends, the function tends asymptotically to y = 1, then the end behavior is:

as x → ∞, f(x) → 1

as x → -∞, f(x) → 1

And we also can see that when x = 1 the function tends to infinity, then:

as x → 1, f(x) → ∞

These are the 3 correct options.

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slope

it has 3 on side and i have done this plenty of tjmes to know

Answer:

Based on the angles of elevation and the distance between Susan and Mark, the bird is likely at a height of approximately 1.95 kilometers from the ground. This is based on calculations using the Pythagorean theorem and the law of cosines.

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

20/4=5

The reciprocal of 5 = 1/5

The profit of the unit is £410

Profit is the revenue remaining after all costs are paid. Profit is the difference between business income (revenue) and business expenses (costs

To get the unit profit;

unit profit = Price - production cost

From the question,

The unit production cost is 740 while the price is 1150

using the formula above,

Unit profit  = 1150 - 740

Unit profit = £410

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La expresión se puede simplificar para obtener:

7a - 9b + 6a - 4b = 13a - 13b

Queremos simplificar la siguiente expresión:

7a - 9b + 6a - 4b

Primero, podemos reordenar los terminos así obtenemos:

7a - 9b + 6a - 4b = 7a + 6a - 9b - 4b

Ahora podemos usar a y b como factores comunes, entonces obtendremos:

7a + 6a - 9b - 4b = (7 + 6)a + (-9 - 4)b

                            = 13a - 13b

Esa es la opcion correcta.

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Answer:

secΘ = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

using the identity

• secΘ = [tex]\frac{1}{coa0}[/tex] = [tex]\frac{1}{\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex]

The value of w = 16. The number 24 has a place value of two due to the presence of two full sets of tens.

Let the be ST = RU = PQ

S T = w,  RU= -3w + 44,  and  PQ = -5w + 68

Then by simplifying the above equation we get,

(w) + (-3w + 44) + (-5w + 68) = 0

w - 3w + 44 - 5w + 68 = 0

Group like terms

w - 3w - 5w + 44 + 68 = 0

Add similar elements: w - 3w - 5w = -7w

-7w + 44 + 68 = 0

Add the numbers: 44 + 68 = 112

-7w + 112 = 0

Move 112 to the right side

-7w = -112

Divide both sides by -7

[tex]$\frac{-7 w}{-7}=\frac{-112}{-7}[/tex]

Then we get,

w = 16

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The value of w in the given trapezoid is 18.4.

The following characteristics apply to a trapezium:

Similar to other quadrilaterals, the trapezium's four angles add up to 360°.

Two of a trapezium's sides are parallel, whereas the other two aren't.

Regular trapezium diagonals are divided by one another.

In a trapezium, the mid-length segment's is equal to half the total length of the parallel bases.

A trapezium created by two parallel sides and one non-parallel side has two pairs of neighbouring angles that add up to 180 degrees.

We know that the length of the mid-segment is equal to half the sum of the parallel bases, in a trapezium.

Thus,

TS +PQ = 1/2 (UR)

w - 5w + 68 = 1/2 (-3w + 44)

2(-4w + 68) = -3w + 44

-8w + 136 = -3w + 44

136 - 44 = -3w + 8w

92 = 5w

w = 18.4

Hence, the value of w in the given trapezoid is 18.4.

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Answer: irrational numbers

Step-by-step explanation:

By definition, natural numbers are rational numbers.

The equivalent fraction to 10/2 are 5/1, 20/4, 30/6, 40/8, 50/10 and so on.

10/2

The equivalent fraction can be determined by division method or multiplication method

Division method:

10/2

divide both numerator and denominator by 2

= 5/1

Multiplication method:

10/2

multiply numerator and denominator by 2

= 20/4

multiply numerator and denominator by 3

= 30/6

multiply numerator and denominator by 4

= 40/8

Therefore, equivalent fractions are fractions which have equal numerator and denominator in its simplest form.

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The required trasformation is given as,
(A) Function f translated 4 units down.
(B) Function f translated 3 units left.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here.
Given function

f(x) = ∛[x + 1]

put x = -3 and y = y - 4
f(x) = ∛[x - 3 + 1]  - 4
f(x) = ∛[x - 2]  - 4

Thus, the required trasformation is given as,
(A) Function f translated 4 units down.
(B) Function f translated 2 units left.

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The number of hits by each player are 1195 and 1470 hits, respectively

Let's call the number of hits that Ricky got "x".

Then, Pedro got x + 275 hits.

The total number of hits for both players is x + (x + 275) = 2665

Solving for x, we get 2x + 275 = 2665

Subtracting 275 from both sides,

We get 2x = 2665 - 275 = 2390

Dividing both sides by 2,

We get x = 2390 / 2 = 1195

So Ricky got 1195 hits and Pedro got 1195 + 275 = 1470 hits.

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Answer:

The probability is 0.33

Step-by-step explanation:

Please find the attachment for detail

Answer:

Answers Below

Step-by-step explanation:

[tex]area = \frac{1}{2} (p \times a)[/tex]

[tex]perimeter = 5s[/tex]

The ratio of the side lengths, yellow to green

We see yellow is 36 and green is 60, so we just put that slash mark in between as indicated in the directions, giving us

36/60. We can reduce this to it's simplistic form of 3/5

The ratio of the perimeters, yellow to green.

To find the perimeter, we multiply the side by 5

Yellow; 36x5= 180

Green; 60x5= 300

We put that ratio slash... 180/300. Reducing it comes out to 90/150 > 30/50 > 3/5 also...

And that's because the polygons are similar.

Since the polygons are similar... what would be the ratio for the areas...

Yep, 3/5

Last is to find the area of the green.

The yellow is 45 and the ratio is 3/5. We can write the equation as a ratio

[tex] \frac{45}{x} = \frac{3}{5} [/tex]

Now if we cross multiply;

[tex](45)(5) = 3x > 3x = 225[/tex]

Last but not least, divide by 3

[tex]x = 75[/tex]

Making the area of the green 75

The value of x is 24.2.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

Base = 22

Hypotenuse = x

Cos Ф = Base / Hypotenuse

Now,

Cos 24 = 22 / x

0.91 = 22/x

x = 22/0.91

x = 24.18

x = 24.2

Thus,

x is 24.2.

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''The planets farthest from the Sun have the coolest surface temperatures" is the accurate statement.

The amount of energy received from the Sun decreases with increasing distance, so the planets farthest from the Sun receive the least energy and therefore have the coolest surface temperatures.

This can be seen in our solar system, where the outer planets (Mars, Jupiter, Saturn, Uranus, and Neptune) are colder than the inner planets(Mercury, Venus, and Earth)

Therefore, the statement "The planets farthest from the Sun have the coolest surface temperatures" is accurate.

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The greatest common factor is 3x.

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common.

For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.

Given:

3x³+18x²-12x

First, factorize each term of Expression

3x³ = 3. x . x . x

18x² = 3 . 3 . 2. x .x

12x =

So, 3x³+18x²-12x

= 3. x . x . x + ( 3 . 3 . 2. x .x ) - (2 . 2. 3 . x)

= 3x ( 3x² + 6x - 4)

Hence, the GCF is 3x.

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The measure of the angles of the parallelogram are: x = 90 degrees, y=   122degress and z=90 degrees

A parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides

Remember that the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

This implies that y + 58 = 180

Making y the subject of the relation

y=180-58

y=122⁰

Also, since the other two opposite angles are not given, then it means that x=y = 180/2 = 90

this therefore means that x= 90, y= 122 and z= 90 degrees

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The interest charge after one month can be calculated by multiplying the balance by the monthly interest rate, which is 12% divided by 12 months, or 0.12 / 12 = 0.01. The balance after one month would be:

$800 * (1 + 0.01) = $808

The total balance after one month and after making a $200 payment would be:

$808 - $200 = $608

So, the answer is $608.