Find the slope of the line that passes through each
pair of points. Express as a fraction in simplest
form. (-2,6), (1,15)

Answer:

1. -9/20

2.  1  7/12

3.  -4  1/3

Step-by-step explanation:

When adding and subtracting fractions with unlike denominators, you must first make them like denominators. To do this we must:

1. Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).

2. Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.

3. Then add (or subtract) the fractions, as we wish!

The easiest way to this is by multiplying the denominators. Remember that whatever you do to the bottom, you also do to the top

1. -5/4 +4/5

if we multiply 4 and 5, we get 20. Our denominator will be 20 before we simplify.

our new equation is going to be -25/20 + 16/20. Now we can add these together to get an answer of -9/20. Which is in the simplist form.

One more thing: to make a mixed number an improper fraction, you multiply the whole number by the denominator, and add the numerator.

1X4=4

4+1=5

The improper fraction is 5/4.

To make a Whole number a fraction, multiply the number by the denominator

-5x3=15

The improper is -15/3.

To go from an improper to a mixed, divide the numerator by the denominator. The remainders are going to be the fraction attached.

Answer:

a = [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

To find the value of a, find the Slope of both the equations.

For lines to be perpendicular to each other    [tex]m_{1}m_{2} = - 1[/tex]

For line 1:

2x + 3y − 6 = 0 represent the line in y=mx +c form

3y = -2x + 6

y = [tex]\frac{-2}{3} x[/tex] + [tex]\frac{6}{3}[/tex]

y = [tex]\frac{-2}{3} x[/tex] + 2

[tex]m_{1}[/tex] = [tex]\frac{-2}{3}[/tex]

For line 2:

ax - 3y = 5

ax = 5 + 3y

ax - 5 = 3y

y = [tex]\frac{ax}{3} - \frac{5}{3}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{a}{3}[/tex]

Apply the condition of perpendicularity:

[tex]\frac{-2}{3}[/tex] * [tex]\frac{a}{3}[/tex] = - 1

[tex]\frac{2a}{9} = 1[/tex]

a = [tex]\frac{9}{2}[/tex]

Answer:

  53.3

Step-by-step explanation:

One way to do this is to add half a tenth, 0.05, then drop all the digits of the result to the right of the tenths digit.

  53.2785 +0.05 = 53.3285

Dropping digits to the right of the tenths place, we have ...

  53.3

_____

The effect of this is to increase the tenths digit by 1 if the hundredths digit is 5 or more. That is the usual instruction given for rounding to tenths. (Then drop hundredths and digits to the right.)

Answer:

B

Step-by-step explanation:

I've taken a picture of the way I solved it.

The required simplified solution of the given expression is x=21/4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
-4 + 5x - 7 = 10 + 3x - 2x,

Adding alike terms and And isolate the terms containing variable x,
-11 + 5x = 10 +x
5x - x = 10 + 11
4x = 21
x = 21 / 4

Thus, the required simplified solution of the given expression is x=21/4. Option B is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

Answer:

x = ±4

Step-by-step explanation:

Step 1: Write out quadratic

2x² - 5 = 27

Step 2: Add 5 to both sides

2x² = 32

Step 3: Divide both sides by 2

x² = 16

Step 4: Take the square root of both sides

x = ±4

∴ x can equal -4 or 4

Answer:

[tex] \boxed{ \bf \huge \: x =4}[/tex]

[tex] \rm \: Or,[/tex]

[tex] \boxed{\bf \huge \: x = - 4}[/tex]

Step by step explanation:

Given Equation is :-

[tex]\sf \implies \: 2 {x}^{2} - 5 = 27[/tex]

We need to find the value of [tex]x[/tex] using Quadric formula.

Firstly, Subtract 27 from both of the side(s):-

[tex]\sf \implies2 {x}^{2} - 5 - 27 = 27 - 27[/tex]

On Simplification:-

Add -5-27 as (-) and (-) equals to (+). -5-27 would be represented as 5+27, which results to 32.

[tex]\sf\sf \implies2 {x}^{2} - 32 = 0[/tex]

Then, for this equation , a=2, b=0, c=-32.

Put the values :-

That is,

[tex]\sf \implies2 {x}^{2} + 0x + ( - 32) = 0[/tex]

As we know, that the quadratic formula is:-

[tex]\sf \implies \: x = \dfrac{ -b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

Put the values :-

[tex]\sf \implies \: x = \dfrac{ - 0 \pm \sqrt{0 {}^{2} \: - 4(2) ( - 32)} }{2(2)} [/tex]

On Simplification:-

[tex]\sf \implies \: x = \dfrac{ - 0 {}^{} \pm \sqrt{ {0 } - \: 8 \times - 32}}{2 \times 2} [/tex]

[tex]\sf \implies \: x = \dfrac{ - 0 \pm \: \sqrt{ - 8 \times - 32} }{4}[/tex]

[tex]\sf \implies x = \dfrac{ - {0}^{}\pm \: \sqrt{ + 256} }{4} [/tex]

As 0 has no value here,

[tex]\sf \implies \: x = \dfrac{ \pm \sqrt{256} }{4} [/tex]

On cancelling,

Remove the square of 256 ( √256)

[tex]\sf \implies \: x = \dfrac{ \pm \cancel{ \: 256}}{ \cancel4} [/tex]

[tex]\sf \implies \: x = ± + 4[/tex]

It may be represented as,

[tex]\sf \implies \: x = - 4[/tex]

Or,

[tex]\sf \implies \: x = 4[/tex]

_______________________________

I hope this helps!

Please let me know if you have any questions.

~MisterBrian

Answer:

4

Step-by-step explanation:

3³=27

6-³=1/216

2^5=32

27X1/216x32

=4

Answer:

-7 + 4 = -3

Step-by-step explanation:

So you start at -7 and if you add a positive number to a negative number you basically subtract from the negative number, so you would do -7 + 4 which equals -3

Answer:

50

Step-by-step explanation:

Answer:

[tex]2\sqrt7,-2\sqrt7[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=4x^2-6[/tex]

And we want to find all x such that f(x) is 106. So, substitute 106 for f(x):

[tex]106=4x^2-6[/tex]

Add 6 to both sides:

[tex]112=4x^2[/tex]

Divide both sides by 4:

[tex]x^2=28[/tex]

Take the square root of both sides:

[tex]x=\pm\sqrt{28}[/tex]

Simplify the square root:

[tex]x=\pm\sqrt{28}=\pm\sqrt{4\cdot 7}=\pm2\sqrt7[/tex]

So, those are the two values that will satisfy our requirement.

And we're done!

Answer:

324 teachers

Step-by-step explanation:

3 teachers of every 50 students

__ teachers of 5400 students

so,

[tex]5400 \div 50 = 108[/tex]

therefore,

[tex]3 \times 108 = 324[/tex]

Answer:

5u-25

Step-by-step explanation:

We have to simplify by distributing 5 to the variable and the number.

5(u-5)

5(u)5(-5)

5u-25

Answer:

each friend gets 1/36 of the loaf of pumpkin bread

Step-by-step explanation:

1/6 of a loaf

1/6 divided by 6

turn 6 into a fraction → 6/1

1/6 ÷6/1

to divide multiply the reciprocal 6/1 → 1/6

1/6 x 1/6 = 1/36

each friend get 1/36

OR

6/x = 1/6

x= 36

6/36

[tex]3d=n[/tex]

[tex]10d+5n=325[/tex]

[tex]10d+15d=325[/tex]

[tex]25d=325[/tex]

[tex]d=13[/tex]

[tex]n=39[/tex]

Hope this helps.

頑張って!

Answer:

(y^3)(z^2)

Step-by-step explanation:

subtract the common based exponents

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]\sf{\dfrac{y^7z^3}{y^4z}}\\\\=\tt{\dfrac{y^7}{y^4}×\dfrac{z^3}{z^1}}\\\\=\tt{y^{(7-4)}×z^{(3-1)}}\\\\=\tt{(y^3)×(z^2)}\\\\\pmb{\green{\boxed{\bold{y^3z^2}}}}[/tex] 

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

GK = 9x-5

Step-by-step explanation:

GK = GH +HJ + JK

= (GJ - HJ) + (HJ) + (HK - HJ)

= (4x-3-x) + (x) + (6x-2-x)

= 3x-3 + x + 5x-2

= (3x+5x+x)+(-3-2)

GK = 9x-5

Answer:

$8.75

Step-by-step explanation:

If you do

$3.50 x 2.5 you get

$8.75

Answer:

Triangle

Step-by-step explanation:

Basically, you have to multiply the base and the height of the triangle, and then divide it by two.

Answer:

O triangle

Step-by-step explanation:

Triangle area = (base*heigth)/2

Answer:

3 hours

Step-by-step explanation:

$20 + $16 = $36 base

$36 + $16 = $52

$52 + $16 = $68

3 HOURS

Answer:

domain is x

range is y

Step-by-step explanation:

The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

The range is the interval where the function f(x) is defined whereas the domain is the input interval of the independent variable (x).

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

Hence "The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis".

For more details about the range and domain of the function,

brainly.com/question/28135761

#SPJ2

Answer:

7X+7=2(X+1)

7X+7=2X+2

7x-2X =2-7

5X/5 =-5/5

. X =-1

Hey there! I'm happy to help!

Let's call our number n. Here is the information we have.

n×12=84

We want to figure out what n equals. To do this, we have to get it by itself in the equation. What we will do is cancel out the 12 by dividing both sides by 12.

n×12/12=84/12

n=7

Therefore, our number is 7.

Have a wonderful day! :D

Answer:

0.025 l

Hope it helped u if yes mark me BRAINLIEST

Answer:

Distance traveled= 41968.4 km

The domain of the function is t

t(h)= 478

h = hours

Step-by-step explanation:

the distance that they traveled in kilometers, d, can be modeled by

d(t) = 97.8t

where t is the time in hours

They traveled a total of 478 hours.

Distance traveled d(t)

d(t) = 87.8(478)

d(t) = 41968.4

Distance traveled= 41968.4 km

The domain of the function is t

t(h)= 478

Solution for 6x^2+9x=0 equation:

Simplifying

6x2 + 9x = 0

Reorder the terms:

9x + 6x2 = 0

Solving

9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.

3x(3 + 2x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying

3 + 2x = 0

Solving

3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0

0 + 2x = 0 + -3

2x = 0 + -3

Combine like terms: 0 + -3 = -3

2x = -3

Divide each side by '2'.

x = -1.5

Simplifying

x = -1.5

Solution

x = {0, -1.5}

Answer:

100 cups of food is for a 25 pound dog

Answer:

(C) 3 feet

Step-by-step explanation:

We have a function of f(x) here. When Sarina throws the ball, it has been 0 seconds since she threw it.

Since x represents the amount of seconds, we can find the height of the ball (f(x)) by substituting x in as 0.

[tex]-0^2 - 0 + 3[/tex]

0 squared is 0, 0 minus zero is 0, and 0+3 = 3, so

[tex]f(x) = 3[/tex]

Meaning that when Sarina threw the ball, it's height was 3 feet.

Hope this helped!