Find the equation of a line containing the given points (4,3) and (8,1). Write the equation in slope-intercept form. Please give step by step explanation.

Answer: (7, 2.5)

Step-by-step explanation:

Midpoint formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]

(x1, y1)= (4, 8)

(x2, y2)= (10, -3)

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

 [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]

=[tex](\frac{4+10}{2}, \frac{8-3}{2} )[/tex]

=[tex](\frac{14}{2}, \frac{5}{2} )[/tex]

=[tex](7, 2.5)[/tex]

Hope this helps!! :)

Please let me know if you have any question

Answer:

Step-by-step explanation:

1.) angle 1 and angle to form a linear pair (given)

2.) angle 1 and 2 are supplementary (supplement theorem)

3.) measure of angle 1 + measure of angle 2 = 180 degrees (def. of supplementary angles)

4.) angle 1 and 3 are supplementary (given)

5.)measure of angle 1 + measure of angle 3 = 180 degrees (def. of supplementary angles)

6.) measure of angle 1+ measure of angle 2 = measure of angle one + measure of angle 3 (congruent supplements theorem)

7.) measure of angle 2 = measure of angle 3 (subtraction property of equality)

8.) angle 2 is congruent to angle 3 (definition of congruence)

Answer:

a+3

Step-by-step explanation:

You cannot go any further in answering this question.  These two terms are not like terms so they cannot be combined.  Therefore, the answer is just a+3 itself.

Answer:

9656.064 rounded its 9656

Step-by-step explanation:

multiply the length value by 1.609344

6000*1.609344

Answer:

  a) (3, -4), (2, 4), (-5, -6)

  b) (4, 3), (-4, 2), (6, -5)

Step-by-step explanation:

a) Reflection in the x-axis negates the y-coordinate:

  (x, y) ⇒ (x, -y)

  (3, 4) ⇒ (3, -4)

  (2, -4) ⇒ (2, 4)

  (-5, 6) ⇒ (-5, -6)

__

b) Reflection in the line y=x swaps the x- and y-coordinates:

  (x, y) ⇒ (y, x)

  (3, 4) ⇒ (4, 3)

  (2, -4) ⇒ (-4, 2)

  (-5, 6) ⇒ (6, -5)

Answer:

line AC

Step-by-step explanation:

because those are two points along line r

it can't be line AB because that would make it a line segment

Answer:

Line ac

Step-by-step explanation:

Answer:

5.00 +12.00=17.00

Step-by-step explanation:

specify whether the money is in pounds like $12 for a pound of cashews I can't tell what you need

Answer:

2nd option= 0.5608

3rd option=0.5608

6th option=0.5608

7th option=0.5608

Answer:

[tex]11 {w}^{2}u \sqrt{2w}[/tex]

Step-by-step explanation:

I'm never sure how far to go on these questions but I think what I'e done looks pretty nice. Essentially I simplified each radical, factored out each variable, combined the radicals after more simplification, and then picked the answer you were most likely looking for. I gave some alternatives in my work that are "simple" too, but the answer above is most likely I'd say.

Work is in the attachment, comment with any questions.

Answer:

[tex]q(x)=2x-5,x\neq-2[/tex]

Step-by-step explanation:

So we have:

[tex]a(x)=2x^2-x-10\\b(x)=x+2[/tex]

And we want to find the quotient q(x). Thus:

[tex]q(x)=\frac{a(x)}{b(x)}[/tex]

Substitute:

[tex]q(x)=\frac{2x^2-x-10}{x+2}[/tex]

Factor the numerator:

[tex]2x^2-x-10\\=2x^2+4x-5x-10\\=2x(x+2)-5(x+2)\\=(2x-5)(x+2)[/tex]

Substitute:

[tex]q(x)=\frac{(2x-5)(x+2)}{x+2}[/tex]

The (x+2)s cancel out. Therefore:

[tex]q(x)=2x-5[/tex]

However, we must restrict x such that it cannot equal -2.

In the original equation, if it did, our answer would be undefined. Thus, our final answer is:

[tex]q(x)=2x-5,x\neq-2[/tex]

And we are done :)

Edit: Typo

Answer:

The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].

Step-by-step explanation:

Let be [tex]\vec u = (2,-3)[/tex], its unit vector is determined by following expression:

[tex]\hat {u} = \frac{\vec u}{\|\vec u \|}[/tex]

Where [tex]\|\vec u \|[/tex] is the norm of [tex]\vec u[/tex], which is found by Pythagorean Theorem:

[tex]\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}[/tex]

[tex]\|\vec u\| = \sqrt{13}[/tex]

Then, the unit vector is:

[tex]\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)[/tex]

[tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex]

The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].

Answer:

x = 5 +/- 4 ([tex]\sqrt{16}[/tex])

so the answer is 1 and 9

Step-by-step explanatio:

The values of x can be 1 or 9.

The correct option is (B) and (C).

A statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of a mathematics has been driven by attempts to find answers to those questions in a systematic way.

For example

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

Given:

x= 5 ± √16

Now, taking the root of 16 which is +4 and -4.

So, x= 5 ± 4

We have two values ,

x= 5+4 or x= 5-4

x=9 or 1

Hence, the solution to x= 5 ± √16 is B. 1 and C. 9.

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Answer:

1st Slot: f(-3)

2nd Slot: -3

3rd Slot: is not

Step-by-step explanation:

Using the Remainder Theorem, we plug in the root of x + 3 (which is x = -3) and see the remainder.

If the remainder = 0, it is a factor

If the remainder ≠ 0, it is NOT a factor

f(-3) = -2(-3)⁴ - 8(-3)³ - 2(-3) - 63

f(-3) = -3

So, x + 3 is NOT a factor.

We then have our 3 answers.

Answer:

length= 24cm

Step-by-step explanation:

interpreting the question

L=3w

perimeter=2(l+w)

64=2(3w+w)

64=2(4w)

64=8w, Divide both sides by 8

w= 8cm

since w= 8

L=3w

L=3×8

L=24cm

Step-by-step explanation:

Hey, there!!

[tex] = \frac{43}{7} [/tex]

Divide 43 by 7.

you will get quotient as 6 and remainder is 1.

so,

The proper fraction is:

[tex] = 6 \frac{1}{7} [/tex]

Hope it helps...

First must do the division:

43 : 7 = 6 with 1 of rest

so 43 = 6 * 7 + 1

with the denominator:

[tex]\frac{43}{7} = \frac{6*7+1 }{7}[/tex]

[tex]\frac{43}{7} = \frac{6*7 }{7}+\frac{1}{7}[/tex]

semplify:

[tex]\frac{43}{7} = 6+\frac{1 }{7}[/tex]

Answer:

DY

Step-by-step explanation:

TO ENCRYPT TO USING CAESAR ALPHABETIC SHIFT CIPHER OF 10. THIS MEANS WE'RE EXPECTED TO LOOP EVERY ALPHABET BY 10, SKIPPING EVERYONE TILL WE GET TO THE TENTH.

TO ENCRYPT T, WE HAVE

T = U - V - W - X - Y - Z - A - B - C - D

THEREFORE, T WILL BE ENCRYPTED AS D

TO ENCRYPT O, WE HAVE

O = P - Q - R - S - T - U - V - W - X - Y

HENCE, O WILL BE ENCRYPTED AS Y.

THIS MEANS THAT OUR QUESTION, TO, WILL BE ENCRYPTED AS DY

Answer:

chemical formula for silver sulfate Ag2SO4

Answer:

Ag2SO4

Step-by-step explanation:

..............

Answer:

Step-by-step explanation:

assume the coin is circular.

i think radius=2.0 cm

∵ 20 cm is too big for a coin.

i have calculated the area of both the surfaces.

area =2×πr²=2×π×2.0²=8 π=8×3.14=25.12 cm²

if only one surface then area=π×2²=4π≈12.57 cm²

Answer:

[tex]f(x) = 1588.4x + 39000[/tex]

[tex]f(15) = 62826[/tex]

Step-by-step explanation:

Given

In 1990; Income= $39000

In 2010; Income= $70768

Solving (a): An equation in form of f(x) = ax + b

First, we need to determine the slope, a

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Taking y as income and x as year index.

When x = 0; y = 39000

When x = 20; y = 70768

Substitute these values in the above formula

[tex]a = \frac{70768 - 39000}{20 - 0}[/tex]

[tex]a = \frac{31768}{20}[/tex]

[tex]a = 1588.4[/tex]

Next, is to determine the formula using:

[tex]y - y_1 = a(x - x_1)[/tex]

Considering :When x = 0; y = 39000, we have

[tex]y - 39000 = 1588.4(x - 0)[/tex]

[tex]y - 39000 = 1588.4x[/tex]

Make y the subject of formula

[tex]y = 1588.4x + 39000[/tex]

Express y as a function of x

[tex]f(x) = 1588.4x + 39000[/tex]

Solving (b): Income in 2005

In 2005, x = 15

So:

[tex]f(x) = 1588.4x + 39000[/tex] becomes

[tex]f(15) = 1588.4 * 15 + 39000[/tex]

[tex]f(15) = 62826[/tex]

Answer:

1/3 is 33.33%

1299.99 x 33.33 =433.286

1299.99 - 433.286= 866.704

Step-by-step explanation:

$866.704 is what she paid

Discount was $433.286

Answer:

7.5%

Step-by-step explanation:

Approximate distance = 180 miles

Actual distance = 167.5 miles

Percent error = { (approximate value - actual value) / actual value } × 100

= { (180 - 167.5) / 167.5 } × 100

= (12.5 / 167.5) × 100

= 0.075 × 100

= 7.5%

Answer:

4w + 6

Step-by-step explanation:

Group like terms

7w - 3w + 6 = 4w + 6

Hope this Helps :)

Answer:

<c=152°

Step-by-step explanation:

We know that A and B are equal because it's an isosceles triangle.

x-14=x/2

2(x-14)=x

2x-28=x

x=28

<A=x-14=28-14=14

<B=x/2=28/2=14

<C=180-14-14=152°

B. (3, -7)

When the equation is graphed, the vertex is at the point (3,-7). I hope this helps!!!

The vertex of the quadratic expression g(x) = 8x² - 48x + 65 is (3, -7).

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The vertex of a quadratic function f(x) = ax² + b x + c is,

(-b/2a, f(-b/2a)).

Here the function is,

g(x) = 8x² - 48x + 65

b = -48 and a = 8.

Vertex = (-(-48) / 16, g(-(-48) / 16))

           = (3, g(3))

g(3) = 8(3)² - 48(3) + 65 = 0

g(3) = -7

Hence the correct option is B.

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Answer:

The opposite of the number 1/4 is equal to -1/4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number is 1/4 and the opposite of the number will be calculated as,

The opposite will be the negative value of 1/4.

Positive value = 1/4

Negative value = -1/4

Therefore, the opposite of the number 1/4 is equal to -1/4.

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Answer:

The width of the poster will be 17 inches

Step-by-step explanation:

The area = 204  square inches

Note:

- both length and width are whole numbers

- The width of the poster is greater than 11 inches

- The width is a prime

The prime numbers greater than 11 are

13, 17, 19, 23, 29, ...,

all these numbers divide 204 with a remainder except for 17

Therefore, the width will be 17 inches, and the length will be 12

since 17 divides 204 into 12 places

Answer:

The answer is 29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

first make into improper fraction then mulityply and then simplify