Write the equation of the line that passes through the points (6,-3) and (1,7) in the form y = mx + b.

m=
b=​

Answer:

123 people

Step-by-step explanation:

60 + 36x ≤ 4500  x is  the number of people

36x ≤ 4440  Subtract 60 from both sides of the equation

x ≤ 123.333...  Divide both sides  by 36.

We cannot have a portion of a person, so we would round down to the next person which would be 123.

Main Answer:

Mars is bigger than Pluto by 27 times.

Explanation:

Given: Volume of Mars = [tex]1.31[/tex] × [tex]10^{21} m^{3}[/tex]

            Volume of Pluto = [tex]4.93[/tex] × [tex]10^{19} m^{3}[/tex]

To find: Determine how many times bigger is Mars than Pluto.

No. of times bigger = [tex]\frac{Volume of Mars}{Volume of Pluto}[/tex]

                              = [tex]\frac{1.31 * 10^{21} m^{3} }{4.93 * 10^{19}m^{3} }[/tex]

                              = [tex]\frac{131}{493} * 10^{2}[/tex]

                              =0.2657 × 100

                              = 26.57

                              =27

Final Answer:

Therefore, 27 times bigger is Mars than Pluto.

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There are a two solutions of the given quadratic equation.

According to the statement

We have to find that the number of solutions of the equation.

So, For this purpose, we know that the

Quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power

From the given information:

The given equation is a:

-16=16x^2

It becomes

16x^2 = -16

Then solve it with the help of the rearrange the terms

x^2 = -16/16

x^2 = -1

x = (-1)^1/2

x = +i , -i

There is a two solutions of the quadratic equation.

So, There are a two solutions of the given quadratic equation.

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Answer

i.d.k anformation in the table and i.d.k maria's worth

Step-by-step explanation:

The equation for the vertical translation of y=f(x). 4 units up is y=f(x)+4.

Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of modifications/transformations to change it to the desired function.

A point on the graph of y=f(x) has the shape (x,f(x)).

The points on the graph of y=f(x)+4 are of the form (x,f(x)+4).

So, the graph for y=f(x) +4 is the same as the graph for y=f(x) shifted up by 4 units.

The new equation is:

y=f(x)+4

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Answer:

Below in bold.

Step-by-step explanation:

81^2/3

= 81^2 = 6561

6561^1/3

= ∛(6561)

= 18.72

√18.72

= 4.33 to nearest hundredth.

The property of real numbers illustrated by the equation is commutative property of multiplication.

The basic properties of real numbers are used to determine the sequence of simplifying mathematical expressions.

Commutative property of multiplication states that change order of factors does not change the product. i.e. a*b=b*a.

In the given equation, to determine if the property is applicable, we need to rewrite the equation:

97(7)=100(7)-3(7)

Taking the common factor out on the right side:

97(7)=7(100-3)

Simplifying,

97(7)=7(97)

Both sides of the equation will give the same answer of 679.

Hence, in this form it is evident that commutative property of multiplication is illustrated by the equation 97(7)=100(7)-3(7)

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At 2 % annual interest, the amount invested was $ 7,000 and at 5 % annual interest, the amount invested was $ 3,000.

Total amount invested = $ 10, 000

interest earned = $ 290

Let amount invested for 2 % annual interest = x

Let amount invested for 5 % annual interest = 10,000 - x

so, we get that:

2 % x + 5 % (10,000 - x) = 290

0.02 x + 500 - 0.05 x = 290

500 - 0.03 x = 290

0.03 x = 500 - 290

0.03 x = 210

3 x = 21000

x = 21000 / 3

x = 7,000

10,000 - x = 3,000

Therefore, at 2 % annual interest, the amount invested was $ 7,000 and at 5 % annual interest, the amount invested was $ 3,000.

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Answer:

$138

Step-by-step explanation:

%15 -> .15

120×.15=18

$120 + $18 = $138

A triangle's altitude is the perpendicular segment from the triangle's vertex to the opposite side (or the line containing the opposite side).

BD is an altitude here because is it perpendicular to AC.

A triangle's altitude is the perpendicular segment from the triangle's vertex to the opposite side (or the line containing the opposite side).

An altitude of a triangle is a line segment through a vertex that is perpendicular to a line containing the base in geometry. The extended base of the altitude is the line that contains the opposite side. The intersection of the extended base and the altitude is known as the altitude's foot.

A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.

BD is an altitude here because is it perpendicular to AC.

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Answer:

first to get a 60 sided figure we know there if 360 degrees in a full rotation so let's simply divide it by 60

360÷60= 60 degrees

Answer:

im pretty sure it's

Step-by-step explanation:

all the angles added should be 180, so you subtract 62 and 94 from 180 to get 24.

The equation x = 2

is the slope-intercept form of the line passing through the points (2,-1) and (2,6)

It is given that, the line is passing through two points (2, -1) and (2, 6)

The formula to find the equation of a line in two point form is

(y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)

where m = [tex]\frac{y2 - y1}{x2 - x1 }[/tex] is the slope of the line

Slope is the measurement of the level of steepness of the line

We need to find the Two- Point form of the line

Using the above formula we get, where

x1 = 2 , x2 = 2, y1 = -1, y2 = 6

m = [tex]\frac{(6-(-1))}{(2-2)}[/tex]= [tex]\frac{7}{0}[/tex]

The equation of the line = (y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)

[y - (-1)] = [tex]\frac{7}{0}[/tex] (x - 2)

0. [y - (-1)] = 7(x-2)

7x - 14 = 0

x = 2

Hence, x =2 is the slope-intercept form of the line passing through the points (2,-1) and (2,6)

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The equation be I = √W/R  

Where I is the current.

W stands for electrical power.

R stands for resistance in ohms then the value of I = 0.5.

A circuit's ability to transport electrical energy is referred to as its electric power. One joule per second, or one watt, is the SI unit of power. Similar to other SI units, watts have standard suffixes that refer to thousands, millions, and billions of watts as kilowatts, megawatts, and gigawatts, respectively.

Let the equation be I = √W/R

Where, I is the current.

W stands for electrical power.

R stands for resistance in ohms.

Simply enter the values of W and R into the equation, i.e.,

When W = 50, R = 200, to solve for the value of I for each set.

I = √50/ 200

The square root of I = √0.25

W = 50, R = 200, I = 0.5.

I = √50/ 200

The square root of I = √0.25

I = 0.5

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the independent variable is the one that's squared, namely the "x", that means that the parabola is a vertically opening parabola, so its axis of symmetry will simply be the equation of the vertical line that passes through the vertex, hmmm what's its vertex anyway?

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{-38} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 12}{2(-1)}~~~~ ,~~~~ -38-\cfrac{ (12)^2}{4(-1)}\right) \implies \left( - \cfrac{ 12 }{ -2 }~~,~~-38 - \cfrac{ 144 }{ -4 } \right) \\\\\\ (6~~,~~-38+36)\implies (\stackrel{x}{6}~~,~~-2)~\hfill \stackrel{\textit{axis of symmetry}}{x=6}[/tex]

Check the picture below.

Answer: All answers are correct

Step-by-step explanation: ur really smart congrats

Answer: x=-15

Step-by-step explanation:

-1 = 4 + x/3

-1-4=4-4+x/3

-5=x/3

-5*3=x*3/3

-15=x*1

x=-15

[tex]-1=4+\frac{x}{3}\\ \\-1(-4)=4+\frac{x}{3}-4\ \ \ \ \ \ \ \ \ \ justify:subtract\ by\ 4\ on\ both\ sides\\\\(3)-5=x/3(3)\ \ \ \ \ \ \ \ \ justify:\ multiply\ by\ 3\ on both sides\\\boxed{x=-15}[/tex]

Answer:

a score of 100 is required

Step-by-step explanation:

the average is calculated as

average = [tex]\frac{sum}{count}[/tex]

given her average for 4 subjects is 80 , then

[tex]\frac{sum}{4}[/tex] = 80 ( multiply both sides by 4 to clear the fraction )

sum = 320

let x be the score required to raise average to 84 , then

[tex]\frac{320+x}{5}[/tex] = 84 ( multiply both sides by 5 )

320 + x = 420 ( subtract 320 from both sides )

x = 100

she requires to score 100 in her fifth subject

Answer: she needs score 100 in the fifth subject.

Step-by-step explanation:

Let a subject is nₓ

Hence,

[tex]\displaystyle\\\frac{n_1+n_2+n_3+n_4}{4} =80\\[/tex]

Multiply both parts of the equation by 4:

[tex]n_1+n_2+n_3+n_4=(80)(4)\\n_1+n_2+n_3+n_4=320[/tex]

[tex]\displaystyle\\\frac{n_1+n_2+n_3+n_4+n_5}{5}=84[/tex]

Multiply both parts of the equation by 5:

[tex]n_1+n_2+n_3+n_4+n_5=(84)(5)\\(n_1+n_2+n_3+n_4)+n_5=420\\320+n_5=420\\320+n_5-320=420-320\\n_5=100[/tex]

The number of kilometers are 1,3.5,0.5,0.075,0.001.

Meters are 1000,3500,500,75,1.

The number of meters is x.

The number of kilometers is y.

kilometer = 1/1000×meter

y = 1/1000×x

The units of length and distance are meters and kilometers, respectively. The kilometer, or 1,000 meters, serves as the unit of distance measurement in the metric system. Therefore, one meter is equivalent to a thousandth of a kilometer.

A meter is denoted by the letter m, whereas a kilometer is denoted by the letter km. The default unit of length measurement in the metric system. Between the length of a ruler and the spacing between objects in a room, meters are used to measure everything.

Therefore the number of kilometers are 1,3.5,0.5,0.075,0.001.

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The measure of m (arc ACD) is 180°

Here,

AD and CG are diameter of circle B.

We have to find the measure of m ACD.

What is Diameter of a circle?

A line that passes through the center and meets the circumference at opposite ends is called diameter of a circle.

Now,

Since, AD is a diameter.

Therefore, ACD is a semicircle.

The measure of a semicircle is 180.

So, The measure of m (arc ACD) is 180°.

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Answer:

Step-by-step explanation:

x= -2

y=2

Answer:

y= -4

Step-by-step explanation:

3-4y=19

-3      -3

-4y=16/-4

y=-4

The equation in point-slope form of the line having the slope m=0 that contains the points (-2,6) is y-6=0(x+2)

Given,

The slope m= 0

The points =(-2,6)

We know the point-slope form,

[tex]y-y_{1}=m(x-x_{1} )[/tex]

Substitute the values in the equation

y-6=0(x-(-2))

y-6=0(x+2)

Hence, the equation in point-slope form of the line having the slope m=0 that contains the points (-2,6) is y-6=0(x+2)

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Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

Answer:

2

Step-by-step explanation:

just did it on khan acadmey.

The required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

Translation means the displacement of a figure or a shape from one place to another. In translation a figure can move upward, downward, vertical and horizontal.

Some of the Translation are,

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Rotation means the circular movement of an object around a centre. It is possible to rotate different shapes by an angle around the centre point.

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system.

Thus, the required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.

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The complete question image is attached.

The slope of the line 5y + 3 = (2/5)x is 2 .

The equation of a straight line can be written as follows,

y = mx + c                                         equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 5y + 3 = (2/5)x .

To get the slope of this given equation we need to convert the given equation in the format of equation of a straight line i.e., equation1.

So, now we will rearrange the given equation as,

 5y + 3 = (2/5)x

⇒ 5y = (2/5)x - 3

Now on dividing this equation by 5 on both sides, we will get

⇒ y = 2x + (-3/5)                                               equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 2

Intercept = c = (-3/5)

The slope of the line 5y + 3 = (2/5)x  is 2 .

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Answer:

$300

Step-by-step explanation:

subtract $200 by $50= $150, then $150 to $100.

Answer: Scale factor = 5/4 and this is a fraction number.

Step-by-step explanation:

Given Data,

find the question in the attachment.

Scale factor = (Dimensions of image) / (corresponding dimensions of preimage)

Let us assume,

         Dimensions of image = B

       corresponding dimensions of preimage = A

So,

we can write,

             Length of rectangle B = 45/2

             Length of rectangle A =18

Then,

                Scale factor = B/A

                                     = (45/2) / (18)

                                     =  22.5 / 18

                                     = 5/4

                                     = 1.25

Therefore, image rectangle A is dilated with by a scale factor of  1.25

In order to express 1.25 as a fraction, we will first try to remove the decimal.

As 1.25 has 2 numbers after the decimal point, we will divide it by 100 in order to remove the decimal.

Hence, we get: 1.25 = 125/100

Now, dividing both sides by a common factor of 25, we will get:

125/100 = 5/4

Thus, 1.25 a as a fraction is 5/4.

Therefore,

Scale factor = 5/4 and this is a fraction number.

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The properties used in the the simplification of the expression is:

step 1: Inverse multiplication property

step 2: Commutative property

step 3: Associative property

step 4:  Commutative property

step 5: Identity property

Given the expression is:

1 ÷ 2/3 × (₋5) × 3 ÷ (₋1/4)

step 1: 1 × 3/2 × (₋5)  × 3 × (₋4)

Inverse multiplication property is applied.

The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.

step 2: 1 × (₋4) × 3/2 × (₋5) × 3

Commutative property is applied.

Mathematical addition and multiplication operations are covered under the commutative property. In other words, adding or multiplying two integers does not change the outcome if the order or location of the numbers is changed.

step 3: 1 × [(₋4) × 3/2] × (₋5) × 3

Associative property is applied.

According to the associative feature of multiplication, the outcome of a multiplication problem is unaffected by the arrangement of the numbers in the problem's constituent parts.

step 4: 1 ×[-6] × (₋5) × 3

commutative property is applied.

step 5: (-6) × (₋5) × 3

Identity property is applied.

Multiplying 1 by any number yields the number itself, according to the Multiplicative Identity Property, commonly known as the Identity Property of Multiplication. This is because any time a number is multiplied by 1, it retains its identity and does not change.

Hence we have applied the above mentioned properties of multiplication.

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