The points (3,6) and (5,12) lie on the graph of a linear equation. Is (4,8) a solution of the same linear
equation? Explain.

Answers

Answer 1

After finding the equation of the line, it is found that:

Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear  equation.

------------------------

Equation of a line:

The equation of a line is given by:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

------------------------

Finding the slope:

Given two points (x,y), the slope is given by change in y divided by change in x.

Points (3,6) and (5,12)Change in y: 12 - 6 = 6Change in x: 5 - 3 = 2Slope: [tex]m = \frac{6}{2} = 3[/tex]

Thus:

[tex]y = 3x + b[/tex]

------------------------

To find the y-intercept, we replace one of the points into the equation. I will replace (3,6). Thus:

[tex]6 = 3(3) + b[/tex]

[tex]b = 6 - 9 = -3[/tex]

Thus, the equation of the line is:

[tex]y = 3x - 3[/tex]

------------------------

Is (4,8) a solution of the same linear  equation?

We have to replace x by 4 and y by 8, and see if it results in an identity. So

[tex]8 = 3(4) - 3[/tex]

[tex]8 = 12 - 3[/tex]

[tex]8 \neq 9[/tex]

Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear  equation.

A similar problem is given at https://brainly.com/question/16024991


Related Questions

Pls pls pls pls help me

Answers

Answer:

96 cm²

Step-by-step explanation:

Triangular face:

base = 8 cm

height = 6 cm

Area of triangle = [tex]\dfrac{1}{2}*b*h[/tex]

              [tex]= \dfrac{1}{2}*8*6\\\\=4*6\\\\= 24 \ cm^{2}[/tex]

Area of 4 triangular faces = 4 * 24 = 96 cm²

The graph of y vx is translated 5 units to the left and 7
units up. What is the equation of the graph that results from
this translation?

Answers

y=-1.4x

Step-by-step explanation:

divide the change in y by the change in x to find the gradient,

7 divided by -5 [as the translation is to the left].

there might be a y intercept value, c as in

y=mx + c but with the given information without  thee starting points it is hard to find

The required equation of the graph that results from the translation is y = √(x + 5) + 7.

What is translation on the coordinate plane?

Translation on a coordinate plane is a transformation that moves an object or figure from its original position to a new position in a straight line. It is also called a "slide." In translation, all points of the object are moved by the same distance in the same direction.

Here,
To shift the graph of the function y = √x to the left by 5 units, we need to replace x with x + 5 in the equation. This will give us the graph of y = √(x + 5).

To shift the graph 7 units up, we need to add 7 to the entire function. This will give us the final equation of the translated graph:

y = √(x + 5) + 7.

Therefore, the equation of the graph that results from the translation is y = √(x + 5) + 7.

Learn more about translation here:

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Match the arc or central angle to the correct measure based on the figure below.

Answers

Answer:

a. 50 degrees

b. 130 degrees

c. 180 degrees

d. 230 degrees

a. 50°

b. 130°

c. 180°

d. 230°

what is geometry?

geometry, the department of mathematics deals with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

various shapes in geometry have different angle measures. as an example: A triangle is a 3-sided shape and the sum of its 3 interior angles is 180˚ A square, rectangle or quadrilateral are 4-sided shapes, and the sum of their four interior angles is 360˚

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1. Ms. Rogers earns $___ each month. She pays 25% of her earnings, or $____ in federal taxes and 6% of her earnings, or $____ in state taxes. She pays ____ % of her earnings, or $____ for insurance. After these deductions, Ms. Rogers takes home $_____

131.76
8
175.68
549
2,196
1,339.56​

Answers

Answer:

2,196;    549;     131.76;     8;     175.68;      1339.56

Step-by-step explanation:

2,196 is the biggest number, so use that as the first number.

.25x2196=549

.06x2196=131.76

.08x2196=175.68

2196-(549+131.76+175.68)=1339.56

NEED HELP ASAP!
Slove for x.

A.4
B.10
C.8
D.7

Answers

i think it 10 because the angle your looking at is x is 7

What is the value of c ?

Answers

Answer:

the value of c is 70

a circle has a radius of 8.5cm correct to the nearest 0.1cm.
the lower bound of the area of the circle is pπ cm².
the upper bound of the area of the circle is qπ cm².

find the value of p and the value of q.

Answers

Answer:

The area of the circle is exactly π times the square of its radius. If you are given that the radius is within 0.1cm of 8.5cm, i.e. lies between 8.4 cm and 8.6 cm, its square will lie between p=8.4² = 70.56 and q=8.6² = 73.96 cm².

Answer:

The area of the circle is exactly π times the square of its radius. If you are given that the radius is within 0.1cm of 8.5cm, i.e. lies between 8.4 cm and 8.6 cm, its square will lie between p=8.4² = 70.56 and q=8.6² = 73.96 cm².

Step-by-step explanation:

thanks for question dear

Find the positive difference between -8 and -14

Answers

Answer:

I'm pretty sure its 6

Step-by-step explanation:

14-8 is equal to 6 so I'm pretty sure it would be six.

an agent receives a commission of d% of the selling price of a house. if the commission amounted to 600, the selling price, in dollars was


Need help brainlist and will mark brainlist

Answers

Answer:

Selling price is $60000/d

Step-by-step explanation:

Let the selling price be say $x. Now the commission is d% of x, that is (d/100)*x=600. x=60000/d

Commission of d% amounts to 600 the selling price in dollers will be

Selling price = 600 * [tex]\frac{100}{d}[/tex] = 6000/d $

What are Selling price, Cost price, Profit &Loss ?

The price of an item which i have sold to someone is my selling price and for the person it is his/her cost price.

When my selling price is more than my cost price I make profit.

When my selling price is less than my cost price i make loss.

In the given question d% of commision amounts to 600$. Let us assume d% = 10 % for easy understanding.

[tex]\frac{percentage}{100}[/tex] * selling price = 600

[tex]\frac{d}{100}[/tex] * selling price = 600

Selling price = 600 * [tex]\frac{100}{d}[/tex] = 6000/d $

or, 60000/10 = 6000 $

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I’m sure this is easy but I hateeee geometry. help ASAP plsssss

Answers

Given points

(-4,3)(2,5)

Distance:-

[tex]\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(2+4)^2+(5-3)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(6)^2+(2)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{36+4}[/tex]

[tex]\\ \sf\longmapsto \sqrt{40}[/tex]

[tex]\\ \sf\longmapsto 6.2[/tex]

3 cm
20 cm
4 cm
Find the volume of the rectangular prism.
[?] cm
Enter

Answers

Answer:

240cm^3

Step-by-step explanation:

3cmx20cmx4cm=240cm^3

Lucia quiere repartir 4/5 litros de leche entre sus dos hijos en partes iguales. ¿Cuánto le dará a cada hijo?

Answers

Maybe speak American

Someone please helppp

Answers

Answer:

true

Step-by-step explanation:

y = 5x+6

To find the inverse, exchange x and y

x = 5y+6

Solve for y

x-6 = 5x+6-6

x-6 = 5x

Divide by 5

x/5 - 6/5 = 5y/5

1/5x - 6/5 = y

The inverse is (x-6)/5

monday through friday a baker uses 1 1/4 sacks of flour when baking cakes. will the baker use more than or less than 5 sacks of flour from monday through friday?

Answers

Answer:

more than 5 sacks

Step-by-step explanation:

1 1/4 sack of flour per day

5 days

5 * 1 1/4

Change to an improper fraction

5 * (4*1+1)/4

5 * 5/4

25/4

Change to a mixed number

6 1/4 sacks

Answer:

more than

Step-by-step explanation:

1 1/4 = mon - fri

1 1/4 * 5 (days) = 6.25

I hope this helped !

6.25 > 5

For the function y = (4x - 3)(x + 7)
the 2 x-intercepts are?

Answers

Answer:

3/4 =x        -7=x

Step-by-step explanation:

y = (4x - 3)(x + 7)

To find the x intercepts, set y=0

0 = (4x - 3)(x + 7)

Using the zero product property

0 = 4x-3    0=x+7

3 = 4x           -7=x

3/4 =x        -7=x

Answer:

x - intercepts are (3/4 , 0) &  (-7 , 0)

Step-by-step explanation:

y = (4x - 3)(x + 7)

At x-intercept, y=0

(4x - 3)(x + 7) = 0

4x - 3 = 0    ;  x + 7 = 0

  4x = 3       ; x = -7

    x = [tex]\dfrac{3}{4}[/tex]      ; x = -7

The height of a triangle is 5cm more than half the base of the triangle. The area of the triangle is 6cm^2. Find the base and height of the triangle

Answers

Answer:

Base = 2 cm and height = 6 cm.

Step-by-step explanation:

Area = 1/2 * base + height

Let b be the base and h = height of the given triangle, then

6 = b/2 * h

6 = b/2(b/2 + 5)

b^2/4 + 5b/2 - 6 = 0

b^2 + 10b - 24 = 0

(b + 12)(b - 2) = 0

b = 2  (we neglect the negative b = -12)

So h = b/2 + 5 = 2/2 + 5 = 6.

the perimeter of a right angled triangle is 60 cm and its area is 120cm².find the lengths of the triangle.​

Answers

Step-by-step explanation:

The area of triangle given as 120 cm2

Area of Triangle = 1/2 x b x h = 120

therefore bxh = 240

240 can be factorized as 10 x 24

The perimeter of the triangle is given as 60

so the other side has to be 26 cm

As this is a right angle triangle it should satisfy pythagoras theorem

(10)2 + (24)2 = (26)2

100+576 =676

Hence the sides of the triangle are 10 cm, 24 cm and 26 cm

At the beginning of the year, Ian had $30 in savings and saved an additional $15 each week thereafter. Brayden started the year with $70 and saved $5 every week. Let II represent the amount of money Ian has saved tt weeks after the beginning of the year and let BB represent the amount of money Brayden has saved tt weeks after the beginning of the year. Graph each function and determine the amount of money Ian and Brayden have saved in the week that they have the same amount of money saved.

Answers

A linear equation can be written as:

[tex]y = a*x + b[/tex]

Where a is the slope and b is the y-intercept.

Defining x as the number of weeks since the start of the year, we can write the linear equations I and B as:

[tex]B(x) =\$70 + \$5*x[/tex]

(initial amount plus the amount that he saves each week times the number of weeks)

Similarly, for Ian we have:

[tex]I(x) = \$30 + \$15*x[/tex]

The graph of these lines can be seen below, where the blue one is I(x) and the green one is B(x).

Now we want to determine how much they had when they had the same amount.

This means that we need to solve:

B(x) = I(x)

Replacing the equations we get:

[tex]\$70 + \$5*x = \$30 + \$15*x[/tex]

Now we can solve this for x:

[tex]\$70 - \$30 = \$15*x - \$5*x[/tex]

[tex]\$40 = \$10*x[/tex]

[tex]\$40/\$10 = x[/tex]

[tex]4 = x[/tex]

So they have the same amount of money in week 4, and each one of them has:

[tex]B(4) = I(4) = \$70 + \$5*4 = \$70 + \$20 = \$90[/tex]

If you want to learn more about this, you can read:

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Can anyone please help?

Answers

Answer:

i don't know

( lol )

heheeeee

Find th slope of the line passing through the points (5,8) and (6,12)

Answers

Answer:

Slope= 4

Step-by-step explanation:

y2-y1/x2-x1

5=x1 8=y1 etc.

12-8/6-5

=4/1

Answer:

The slope of the line is 4.

Step-by-step explanation:

To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex].

For finding the slope of this line with the points (5,8) and (6,12), start by writing down the information given from the question.

[tex]y_2=12[/tex]

[tex]y_1=8[/tex]

[tex]x_2=6[/tex]

[tex]x_1=5[/tex]

Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{12-8}{6-5}[/tex]. Then, simplify the equation, which will look like [tex]\frac{4}{1}=4[/tex]. The final answer will be 4.


17. Test Practice which represents the number that is ten more than two
thousand, seventy?
A 280
® 2,008
© 2,080
0 2,800

Answers

Answer:

2,080

Step-by-step explanation:

Two thousand and seventy is written as 2,070.

Ten more than 2,070 would be 2,080 as you're just adding on 10.

Hope this helps :)

Zero is_______greater than any negative integer.

always

never

sometimes

Answers

Answer:

always

Step-by-step explanation:

Zero is always greater than any negative integer.

All the negative integers lie to the left of 0 on the number line. This implies that zero is always greater than any negative integer.

Zero is always greater than any negative integer

What is the perimeter of a square which has the same area as a circle with circumfrence of 4π

Answers

Answer:

Perimeter square = 8 sqrt(pi)

Step-by-step explanation:

The perimeter of a square is 4*s

The area of a circle is Area = pi * r^2

The circumference of a circle is C = 2*pi * r

C = 4 pi

4pi = 2*pi * r

r = 2

So the area of the circle is pi * r^2 = pi * 2^2 = 4pi

The square has the same area

Area = 4*pi

Square = 4*pi

s^2 = 4*pi

s = sqrt(4*pi)

s = 2*sqrt(pi)

The perimeter = 4 * 2 * sqrt(pi)

The perimeter = 8 * sqrt(pi)

Please help explanation if possible

Answers

Answer:

y = | x-5|

Step-by-step explanation:

y = |x-h| +k  where (h,k) is the center of the "v"

The "v" is located at (5,) so h=5 and k = 0

y = | x-5| +0

(ii) Differentiate x2 + 3x -4.​

Answers

Answer:

2x +3

Step-by-step explanation:

d/dx(x2 + 3x -4)

d/dx (x^2) + d/dx(3x)- d/dx(4)

2x +3 -0

2x +3

Find the measure of the missing angles.


b =
C=

Answers

Answer:

Angle C and Angle B 61 degree as Angle 119 is supplementary to angle B and C (180-119=61)

if the area of square is 2401 sqaure metre,find the perimeter of the sqaure​

Answers

Answer

P=196                        

P=4A=4·2401=196                                  

Answer:

196m

Step-by-step explanation:

[tex] \sqrt{2401} = 49[/tex]

[tex]49 + 49 + 49 + 49 = 196[/tex]

4(v+4)–7=17 please help me

Answers

Answer:

v = 2

Step-by-step explanation:

4(v+4)–7=17

=> 4(v + 4) = 17 + 7

=> 4v + 16 = 24

=> 4v = 24 - 16

=> 4v = 8

[tex] = > v = \frac{8}{4} [/tex]

=> v = 2 (Ans)

Answer:

v=2

Step-by-step explanation:

4(v+4)–7=17

Distribute

4v+16 -7 = 17

Combine like terms

4v +9 =17

Subtract 9 from each side

4v+9-9=17-9

4v = 8

Divide by 4

4v/4 = 8/4

v=2

Non right angled triangle

Answers

Answer:

18.06

Step-by-step explanation:

law of cos()

b^2 = (16.5)^2 + (17.1)^2 - 2(16.5)(17.1)cos(65)

[tex]\frac{3\sqrt{2}\sqrt{-3135\cos \left(65^{\circ \:}\right)+3137}}{10}\quad \begin{pmatrix}\mathrm{Decimal:}&18.06035\dots \end{pmatrix}[/tex]

I need help please and thank you!​

Answers

Answer:

v is 198 m/s

Step-by-step explanation:

[tex]v = \sqrt{gh} \\ v = \sqrt{9.8 \times 4000} \\ v = 198 \: m {s}^{ - 1} [/tex]

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Is there one network president in this room who claims he can't do better?[4] The best estimates indicate that during the hours of 5 to 6 P.M. sixty percent of your audience is composed of children under twelve. And most young children today, believe it or not, spend as much time watching television as they do in the schoolroom. I repeatlet that sink in, ladies and gentlemenmost young children today spend as much time watching television as they do in the schoolroom. It used to be said that there were three great influences on a child: home, school, and church. Today, there is a fourth great influence, and you ladies and gentlemen in this room control it.[5] If parents, teachers, and ministers conducted their responsibilities by following the ratings, children would have a steady diet of ice cream, school holidays, and no Sunday school. What about your responsibilities? Is there no room on television to teach, to inform, to uplift, to stretch, to enlarge the capacities of our children? Is there no room for programs deepening their understanding of children in other lands? There are some fine children's shows, but they are drowned out in the massive doses of cartoons, violence, and more violence. Must these be your trademarks? Search your consciences and see if you cannot offer more to your young beneficiaries whose future you guide so many hours each and every day [6] You must provide a wider range of choices, more diversity, more alternatives. It is not enough to cater to the nation's whims; you must also serve the nation's needs. And I would add this: that if some of you persist in a relentless search for the highest rating and the lowest common denominator, you may very well lose your audience. 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(paragraph 6) please answer thissimplify it too