What is the solution of the equation 6x − 3 = -51? A. -9 B. -8 C. 8 D. 9

Answer:

(-7,8)

Step-by-step explanation:

The coordinates of the points dividing the line segment in ratio m:n can be calculated as:

[tex](\frac{mx_{1}+nx_{2}}{m+n} ,\frac{my_{1}+ny_{2}}{m+n} )[/tex]

Here x1, y1 are the coordinates of first point J (-10, 12) and x2, y2 are the coordinates of second point K(8, -12).

In this case m will be 5 and n will be 1 as the ratio is 5:1

Using all these values we can find the coordinates of point L

[tex]( \frac{5(-10)+1(8)}{5+1},\frac{5(12)+1(-12)}{5+1} )\\\\ = (\frac{-42}{6} ,\frac{48}{6} )\\\\ =(-7,8)[/tex]

Thus, the coordinates of point L which divides the line segment JK in 5:1 are (-7,8)

The coordinates of point L, which divides the line segment JK in the ratio 5:1, are (5,-8).

To find the coordinates of point L that divides the line segment JK in the ratio 5:1, we use the formula for section formula in coordinate geometry. This formula provides the coordinates of a point that divides a line segment into a specific ratio. The formula is X = (m1*x2 + m2*x1) / (m1+m2), Y = (m1*y2 + m2*y1) / (m1+m2), where m1 and m2 are the ratios.

Here, J(-10,12) is x1,y1 and K(8,-12) is x2,y2. The point L is dividing JK in the ratio 5:1, so m1=5 and m2=1. Substituting these values:

X = (5*8 + 1*-10) / (5 + 1) = 30 / 6 = 5, Y = (5*-12 + 1*12) / (5 + 1) = -48 / 6 = -8.

Therefore, the coordinates of point L are (5,-8).

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ANSWER

[tex]y= -3{(x + 4)}^{2} + 2[/tex]

EXPLANATION

The given function is:

[tex]y= -3x^2-24x-46[/tex]

Factor -3 for the first 2 terms.

[tex]y= -3(x^2 + 8x)-46[/tex]

We add and subtract the square of the coefficient of x.

[tex]y= -3(x^2 + 8x + {(4)}^{2} ) - - 3( {4)}^{2} -46[/tex]

Factor the perfect square trinomial.

[tex]y= -3 {(x + 4)}^{2} ) + 48 -46[/tex]

The vertex form is:

[tex]y= -3{(x + 4)}^{2} + 2[/tex]

This is an exponential decay problem.

Using the equation Y = a *(1-rate)^time

where Y is the future value given as 12,000 and a is the starting value given as 13,000.

The rate is also given as 5%.

The equation becomes:

12,000 = 13,000(1-0.05)^x

12,000 = 13,000(0.95)^x

Divide each side by 13000:

12000/13000 = 0.95^x/13000

12/13 = 0.95^x

Use the natural log function:

x = ln(12/13) / ln(0.95)

x = 1.56 years. ( this will equal 12,000

Round to 2 years it will be less than 12000.

Answer:

-5 < x <=-2

Step-by-step explanation:

9<=1-4x<21

Subtract 1 from each side

9 -1<=1-1-4x<21-1

8 <= -4x < 20

Divide each side by -4.  That means to flip all inequalities

8/-4 >= -4x/-4 >20/-4

-2 >=x > -5

-5 < x <=-2

Answer:

93

Step-by-step explanation:

180-25=155

155÷5=31

31×3=93

A triangle is a three-edged polygon with three vertices. The measurement of the largest angle of the triangle is 93°.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Let the measure of the smallest angle be x. And as it is given that the measure of the second angle is 3 times the smallest, while the measure of the third angle is 25 more than the smallest angle. Therefore, the measure of the angles can be written as,

∠1 = x

∠2 = 3x

∠3 = x + 25

Since the sum of all the angles of a triangle is 180°, therefore, the sum can be written as,

∠1 + ∠2 + ∠3 = 180°

x + 3x + (x+25) = 180°

x + 3x + x + 25 = 180°

5x + 25 = 180°

5x = 180° - 25°

5x = 155°

x = 31°

Now, the measurement of all the angles is,

∠1 = x = 31°

∠2 = 3x = 3(31°) = 93°

∠3 = x + 25 = (31+25)° = 56°

Hence, the measurement of the largest angle of the triangle is 93°.

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R; all quadratic functions are going to have ranges and domains of *ALL REAL NUMBERS* [(-∞, ∞)].

Answer: the domain is all real numbers. the range is {y|y ≤ 16}

Step-by-step explanation:

Don’t have trust issues

No a triangle equals to be 180 degrees not 190 degrees

No, a triangle cannot be drawn with the following angles.

On a triangle, all angles will add up to 180º.

These angles add up to 190º so it would not work.

Answer:

you need to add the picture

Step-by-step explanation:

Answer:add the picture

Step-by-step explanation:

The equation in slope-intercept form for the line with slope -7 and y-intercept 8 is y = -7x + 8. To graph the line, plot the y-intercept and use the slope to find other points on the line, connecting them to create the line.

To write an equation in slope-intercept form, we use the formula y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -7 and the y-intercept is 8, so the equation is y = -7x + 8.

To graph the line, first plot the y-intercept, which is the point (0,8). Then, use the slope to find other points on the line. Since the slope is -7, for every increase of 1 on the horizontal axis, the line decreases by 7 on the vertical axis. So, for example, if we move 1 unit to the right from the y-intercept, we go down 7 units. Plot these additional points and connect them to create the line.

$400 + (74.00 * 24) = $2,176.

The cash price is $191.00 less.

Answer:

bedroom furniture for $1,985.00 cash  

or  

bedroom furniture for $400 down  payment and $74.00 per month for 24 months

so, calculating the total money  

             = down payment + monthly payment × number of months

             =   $400 + $74.00 × 24

             =  $ 2176

hence, paying bedroom furniture for  $1,985.00 cash  will be the appropriate option for the payment.

Answer:

1.68

Step-by-step explanation:

1. Move all of the terms to the left side and set the problem equal to zero.

2. Set each factor equal to zero.

For this case we have the following equation:

[tex]6 ^ {- x} + 4 = 3x-1[/tex]

We must clear the value of x, we follow the steps below:

We subtract 3x on both sides of the equation:[tex]6 ^ {- x} -3x + 4 = -1[/tex]

Add 1 to both sides of the equation:

[tex]6 ^ {- x} - 3x + 4 + 1 = -1 + 1\\6 ^ {- x} - 3x + 5 = 0[/tex]

Each side of the equation is drawn, then the solution is the x value of the intersection point.

[tex]x = 1.68[/tex]

Answer:

See attached image

[tex]x = 1.68[/tex]

Answer:

k=2

Step-by-step explanation:

[tex]\frac{k}{3} = \frac{16}{24}[/tex]            Set up your equation

24k=48                                                      Cross multiply

k=2                                                             Divide 24 from both sides

You answer is k=2

For this case we have the following equation:

[tex]\frac {k} {3} = \frac {16} {24}[/tex]

We must find the value of the variable "k":

Simplifying the right side of the equation we have:

[tex]\frac {k} {3} = \frac {8} {12}\\\frac {k} {3} = \frac {4} {6}\\\frac {k} {3} = \frac {2} {3}[/tex]

We multiply by 3 on both sides of the equation:

[tex]k = \frac {2} {3} * 3\\k = 2[/tex]

Answer:

[tex]k = 2[/tex]

also the direction is anti clockwise

I hope it could help you :)

To draw a 30° angle in standard position on the coordinate plane, start by drawing the initial side of the angle which is the positive x-axis. Use a protractor to measure a 30° angle counterclockwise from the initial side. Then draw a line from the origin to the endpoint of the angle to represent the terminal side. Label the angle measure as 30° and label the terminal side accordingly. Indicate the direction of rotation by drawing an arrow showing the counterclockwise direction.

To draw a 30° angle in standard position on the coordinate plane, follow these steps:

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[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=\stackrel{\times 6}{6r} \end{cases}\implies V=\pi (6r)^2 h\implies V=\pi (6^2r^2) h \\\\\\ V=36~~\pi r^2 h\impliedby \textit{36 times the original volume}[/tex]

The effect that multiplying the radius by 6 would have on the volume of the cylinder is the volume would increase by a factor of 36

From the question, we are to determine what effect multiplying radius by 6 would have on the cylinder

Using the formula for calculating the volume of a cylinder

V = πr²h

Where V is the volume of the cylinder

r is the radius

and h is the height

If the r is the radius and h is the height of the first cylinder,

Then, volume of the first cylinder will be

V = πr²h

For the new cylinder

radius = 6r

and h = h

Then, volume of the new cylinder will be

V₂ = π × (6r)² × h

V₂ = π × 36r² × h

V₂ = 36πr²h

The new volume is multiplied by a factor of 36

Hence, the effect that multiplying the radius by 6 would have on the volume of the cylinder is the volume would increase by a factor of 36.

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I am pretty sure you would do it like that!!! Hope this helps :)

Answer:

1

Step-by-step explanation:

Answer:

y = 40 + 0.35x

y = 50 + 0.1x

Step-by-step explanation:

Talk A Lot Company

$40 for 600 mins

$0.35 for each extra min

Total cost = y

Number of extra minutes after 600 mins = x

y = 40 + 0.35x

Chat Away Company

$50 for 600 mins

$0.10 for each extra mins

Total cost = y

Number of extra minutes after 600 mins = x

y = 50 + 0.1x

Answer:

D. Reciprocal parent function

Step-by-step explanation:

The given function has the x-axis as the horizontal asymptote

The vertical asymptote is the line x=0, which is the y-axis.

This means that the function has x, in the denominator.

Therefore, the function represented by the graph is [tex]\frac{1}{x}[/tex].

This is the parent reciprocal function.

The correct choice is D

Answer:

89,400 was the population in 2016

Step-by-step explanation:

Answer:

graph B

Step-by-step explanation:

if we mention x =0 then y=-12 and we do the same with y if we mention y=0 then x=6 and x=-2 and we will find thes cases only in graph B

The solution is Option B.

The graph of the equation of line y = x² - 4x - 12 is given below , where the values of y = 0 at x = -2 and x = 6

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be A

Now , the value of A is given as

y = x² - 4x - 12   be equation (1)

On factorizing the equation (1) , we get

y = x² + 2x - 6x - 12

So , on grouping the common terms , we get

y = x ( x + 2 ) - 6 ( x + 2 )

y = ( x + 2 ) ( x - 6 )

when y = 0

x + 2 = 0

On subtracting 2 on both sides , we get

x = -2

when y = 0

x - 6 = 0

On adding 6 on both sides , we get

x = 6

So , the value of y = 0 , when x = -2 and when x = 6

Substituting the values in the equation,we get the following graph

Therefore , the equation of line is y = ( x + 2 ) ( x - 6 )

Hence , The graph of the equation of line y = x² - 4x - 12 is given below , where the values of y = 0 at x = -2 and x = 6

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Answer:

if -196 was positive, it could be 14 or -14, but because it is negative, it is considered infinity or unknown

Hm..Maybe so that when they give birth the stretch Mark's on their body wont be so bad.

Because it provides the child with nutrition to sustain life in the mother’s stomach

Final answer:

In mathematics, the right triangle definition of tan theta is the ratio of the length of the side opposite to theta (y) to the length of the side adjacent to theta (x).

Explanation:

The right triangle definition of tan theta (tan θ) involves the ratio of the lengths of two specific sides of the triangle. According to SOHCAHTOA, a mnemonic used to remember the definitions of the sine, cosine, and tangent functions, tan theta is the ratio of the opposite side (y) to the adjacent side (x) of the right triangle, where theta (θ) is one of the non-right angles. This can be written as tan(θ) = y/x.

In other words, the tangent of an angle θ in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

This can be represented as:

tan(θ) = Opposite side / Adjacent side = y / x

For example, if the opposite side y is 5 units and the adjacent side x is 3 units, then tan(θ) = 5 / 3

The Pythagorean Theorem may be applied in conjunction with the definitions of trigonometric functions to solve various problems involving right triangles, but it specifically relates to the relationship between the sides of a right triangle: a² + b² = c², where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.

When solving problems related to right triangles, it is beneficial to remember that the sum of the angles of a triangle is always equal to two right angles (or 180 degrees).

Answer:

can't help you sorry

Step-by-step explanation:

can't help you sorry!

Answer:

yes

Step-by-step explanation:

The answer is the graph has a relative maximum

Answer:

x<\frac{-y+4}{2}

Step-by-step explanation:

Hope this helps!!!

can i get brainliest plzzz thx

Answer: the answer is A

Step-by-step explanation:

We'll assume that the CPI is given for the END of the year.

Then 2014's rate is the change in price from 2013 in percent,

r = 180/125 - 1 = 36/25 - 1 = 11/25 = 44 %

Answer: choice c

----------

This is a pretty poor question.  The questioner should clarify the exact dates of the given values of the CPI, and use the actual values.   44% is an alarming inflation rate, but fortunately a fictitious one here in the US.  US inflation in 2014 was around 0.7% so the number the student was asked to compute was off by more than a factor of sixty.

Answer:

C

Step-by-step explanation:

The answer would be d- tossing s coin, tossing a second coin, and tossing a third coin

Option: D is the correct answer

D. Tossing a coin, tossing a second coin and tossing a third coin.

We know that when a coin is tossed then there are only two possible outcomes i.e. either a head or a tail.

Now, when a second coin is tossed then again we have two possible outcomes i.e. head and a tail.

and the total sample space of the two events is given by:

HH    HT   TT     TH

Now, when a coin is tossed third time then in than two outcomes are possible on the coin i.e. a head and a tail.

Hence, the total number of outcomes are:

HHH    HTH    TTH   THH

HHT     HTT     TTT    THT

i.e. when a coin is tossed n times that the total possible outcomes are:

                           [tex]2^n[/tex]

Here the coin is tossed three times.

Hence, the total possible outcomes are:  [tex]2^3=8[/tex]

Answer:

D

Step-by-step explanation:

First of all, a very easy way is to count all the rectangles and then count the squares that are shaded and have balloons.

You'll get 7 squares that are shaded and have balloons and 16 rectangles in total.

So the fraction will be [tex]\frac{7}{16}[/tex]

Another simple way is to just multiply [tex]\frac{7}{8}[/tex] and [tex]\frac{1}{2}[/tex]

[tex]\frac{7}{8}*\frac{1}{2}=\frac{7}{16}[/tex]

Answer:

Mean: 116

Median: 115

Mode: 115

Step-by-step explanation:

Mean is the average of the data set; it’s found by adding up all the numbers and dividing that sum by the number of numbers there are

(114 + 120 + 115 + 114 + 118 + 117 + 114)/7 = 812/7 = 116

Median is found out by ordering the given numbers from largest to smallest and finding the middle number; if there are an even number of given numbers, you add them up and divide by two.

In this case, you are lucky enough to be given an odd numbers of given numbers

Ordering (smallest to largest):

114, 114, 114, 115, 117, 118, 120

Median is 115

(this is the number in the middle of the data set)

Mode is the most frequently occurring number in the data set

In this case, the

Mode is 114

The mean of the data is 116, the median is 115, and the mode is 114. All three measures offer insights into the dataset's central tendencies.

To find the mean, median, and mode of the given data: 114, 120, 115, 114, 118, 117, 114, let's follow these steps:

Mean: Add all the numbers together and divide by the number of data points.

Median: Arrange the numbers in ascending order and find the middle value. If there is an even number of observations, calculate the average of the two middle values.

Mode: The most frequently occurring value in the dataset.

Thus, the mean is 116, the median is 115, and the mode is 114.