Solve the equation. Check the solution.
8- 2x - 5- 13x = 6

Answer:

y=-2x-3

Step-by-step explanation:

y-y1=m(x-x1)

Answer:

  6) y = -7x +11

  8) y = -1/3x -1

  10) y = 5/4x -2

Step-by-step explanation:

It is convenient to start with a point-slope form of the equation.

  y = m(x -h) +k . . . . . line with slope m through point (h, k)

__

6) m = -7, (h, k) = (2, -3)

  y = -7(x -2) -3 = -7x +14 -3

  y = -7x +11

__

8) m = -1/3, (h, k) = (-3, 0)

  y = (-1/3)(x -(-3)) +0

  y = -1/3x -1

__

10) m = 5/4, (h, k) = (4, 3)

  y = 5/4(x -4) +3 = 5/4x -5 +3

  y = 5/4x -2

Answer:

Both functions must be linear. The y-intercepts of f(x) and g(x) must be opposites.

Step-by-step explanation:

First we need to solve.

h(x) = 10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16

It seems tricky at first but we know a couple things. When we add the factors of h(x) together we get j(x) = 7[tex]x[/tex] so we know that when we multiply 2 numbers together it should equal 10 but add up to 7.

Lets write the possible combinations of 10:

1 x 10 = 10

2 x 5 = 10

5 x 2 = 10

10 x 1 = 10

Now which combination will add or subtract to 7?

1 - 10 = 9    1 + 10 = 11  

2 - 5 = -7    2 + 5 = 7   We can stop here!

2 and 5 are in our factor, so let's write it down.

(2x      ) (5x        )     We know there will one + and one - because the -16. If we had two + it would be positive 16, and is we had two - it would also be positive 16 because a    - x - = +

Now the last number is 16. Let's find the possible combinations of 16.

1 x 16 = 16

2 x 8 = 16

4 x 4 = 16  We will stop here because we end up repeating posibilities.

Here is where we think critically. Whichever combination we choose has to be multiplied by 2 and 5 and end up equaling 12. I think 16 is too high so let's try 2 and 8.

2x * 2 = 4x     5x * 8 = 40x    Now one is positive and the other is negative. Let's try each combination.

4x - 40x = -36x   -4x + 40x = 36x     Neither of those are 12x. So let's Try 4 and 4.

2x * 4 = 8x       5x * 4 = 20x  One will be positive and the other will be negative. Let's try each combination.

8x - 20x = -12x    -8x + 20x = 12x There is our combination!  Remeber when you mutiply together you have to multiply the opposite factor. Here are the combinations:

(Ax + B )(Cx + D) = (Ax*Cx) + (Ax*D) + (B*Cx) + (B*D)

(Ax - B )(Cx + D) = (Ax*Cx) + (Ax*D) - (B*Cx) - (B*D)

(Ax + B )(Cx - D) = (Ax*Cx) - (Ax*D) + (B*Cx) - (B*D)

(Ax - B )(Cx - D) = (Ax*Cx) - (Ax*D) - (B*Cx) + (B*D)

So we have:

(2x + 4) (5x - 4)

Let's prove is and multiply it back out.

2x*5x - 2x*4 + 4*5x - 4*4

10[tex]x^{2}[/tex] - 8[tex]x[/tex] + 20

10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16  So we got it right!

Now let's see if they really add up to 7x.

(2x + 4) (5x - 4)  which we now need to add together

2x + 4 + 5x - 4   Rearrange

2x + 5x + 4 - 4   Combine like terms

7x + 0  or 7x  It works!

So our original functions are f(x) = 2x + 4   and g(x) = 5x - 4

Now to answer the question. Select 2 options.

Both functions must be linear. Yes, because an equation with only an [tex]x[/tex] will be a straight line, if we graph both functions they are both straight lines.

Both functions must be quadratic. No, because a quadratic equation is any equation that can be rearranged in standard form as [tex]ax^{2} + bx +c = 0[/tex] Neither f(x) or g(x) can be rearranged to fit that.

Both functions must have a y-intercept of 0. No, to find the y intercept we set x to 0 and solve for y.

2x + 4 = y                    5x - 4 = y

2(0) + 4 = y                  5(0) - 4 = y

0 + 4 = y                        0 - 4 = y

y = 4                                y = -4

Neither are 0.  

The rate of change of either f(x) or g(x) must be 0. Let's find the rate of change for each equation.

We need an interval so we have to find one. Let's use 1 and 2 for x, but we have to solve for y to get the coordinate.

f(x[tex]_{1}[/tex]) = 2x + 4       f(x[tex]_{2}[/tex]) = 2x + 4         g(x1) = 5x - 4        g(x2) = 5x - 4

x[tex]_{1}[/tex] = 1                     x[tex]_{2}[/tex] = 2                      x

y[tex]_{1}[/tex] = 2(1) + 4           y[tex]_{2}[/tex] = 2(2) + 4           y

y[tex]_{1}[/tex] = 2 + 4              y[tex]_{2}[/tex] = 4 + 4                y

y[tex]_{1}[/tex] = 6                    y[tex]_{2}[/tex] = 8                      y

( 1 , 6 )                  ( 2 , 8 )                     ( 1 , 1 )                   ( 2 , 6 )

Rate of change formula is:

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Now we just plug in for each function.

f(x) = 2x + 4                                      g(x) = 5x - 4

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{8 - 6}{2 - 1}[/tex] = [tex]\frac{2}{1}[/tex] = 2                            

You can see the rate of change is not 0 for either function.

The y-intercepts of f(x) and g(x) must be opposites. Yes, we solved for the y intercepts earlier.

To find the y intercept we set x to 0 and solve for y.

2x + 4 = y                    5x - 4 = y

2(0) + 4 = y                  5(0) - 4 = y

0 + 4 = y                      0 - 4 = y

y = 4                             y = - 4

4 and - 4 are opposites, so this statement is also true.

Answer:

y=3b + 6 ................ . ..

The answer is 3b + 6 in Khan Accademy

Answer:

D.

Step-by-step explanation:

[tex] \sqrt{-75} = \sqrt{-1 \times 75} = \sqrt{-1 \times 25 \times 3} = 5i\sqrt{3} [/tex]

The square root of the given number is 5i√3. Therefore, option D is the correct answer.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

The given number is √(-75).

Here, √(-75) can be written as √(-25×3)

= 5i√3

Therefore, option D is the correct answer.

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Answer:

x=13

Step-by-step explanation:

Q is the midpoint of PR

PQ + QR = PR

PQ= QR

PQ+QR = PR

QF + QR = PR

2QR = PR

2*43 = 9x-31

86 = 9x-31

Add 31 to each side

86+31 = 9x-31+31

117 = 9x

Divide each side by 9

117/9 = 9x/9

13 =x

Answer:

x = 13

Step-by-step explanation:

since Q is the midpoint of PR and QR is 43, then

PR = QR * 2 ⇒ 43 * 2 = 86

PR = 9x - 31

⇒ 9x - 31 = 86

⇒ 9x = 86 + 31

⇒ 9x = 117

Divide both sides by 9 ⇒ [tex]\frac{9x}{9} = \frac{117}{9}[/tex]

⇒ x = 13

40

2 + 10 = 24

2(2 + 10) = 2×12 = 24

3 + 6 = 27

3(3 + 6) = 3×9 = 27

7 + 2 = 63

7(7 + 2) = 7×9 = 63

5 + 3 = 40

5(5 + 3) = 5×8 = 40

Answer:

d linear

Step-by-step explanation:

It looks a bit like a linear equation

The function g(x) = 5x - 3 is a linear function as the degree of x is one.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

g(x) = 5x - 3 is not a constant it is a function in x.

g(x) = 5x - 3 is not a quadratic function as the degree of x is one.

g(x) = 5x - 3 is also not an absolute function as we can see.

Hence g(x) = 5x - 3 is a linear function as the highest power of x or the degree of x is 1 and it is a linear function in variable x.

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Step-by-step explanation:

pls make me as brainliest

Answer: The equation 3x + 2 = 3x - 2 has no solutions.

Step-by-step explanation:

So far, we know that we have four equations, and we have to find one that has no solutions. We can first examine them like Jubal did:

7x + 1 = 7x+ 1

3x + 2 = 3x - 2

4x + 1 = 3x + 8

-2x + 1 = -2x + 1

Just by looking at this, we see here that two of these equations look exactly the same even on the other side of the equation sign:

7x + 1 is the same as 7x + 1       AND

-2x + 1 is the same as -2x + 1

So we know that these are identities, meaning, they have infinitely many solutions. So, they cannot have no solutions because they are the ultimate opposite of that.

Next, looking at the other problems, we see that:

4x + 1 = 3x + 8       AND

3x + 2 = 3x - 2

Let's just take a look at the second equation from this selection. We see that this equation looks almost exactly the same on both sides of the equation sign, EXCEPT that the constants are different ( I mean 2 and -2 ). IF we WERE to add/subtract two from both sides, they wouldn't cancel out but instead leave you with 4. If you had subtracted the 3xs, then you would have been left with 0. So, 0 does NOT equal 6, so therefore, this has no solutions.

And what about 4x + 1 = 3x + 8?

If you just take a look at it, it only has one solution.

Hence, 3x + 2 = 3x - 2 has no solutions.

Answer:

h=8cm

Step-by-step explanation:

V= πr^2h/3

Where

V=volume of a cone

π=pi= 3.14

r= radius=4cm

h= height = ?

V= πr^2h/3

134= 3.14*4*4*h/3

134= 50.24h/3

Divide both sides by 50.24

h/3= 134 / 50.24

h/3= 2.67

Cross product

h= 2.67*3

h= 8.01

Approximately h= 8cm

The best estimate of the cone's height is 8cm

Answer:

tan^2 theta - tan^2 phi = (sin^2 theta- sin^2 phi) /(cos^2 theta cos^2phi) (identity has been verified)

Step-by-step explanation:

Verify the following identity:

tan(θ)^2 - tan(ϕ)^2 = (sin(θ)^2 - sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2)

Hint: | Eliminate the denominator on the right hand side.

Multiply both sides by cos(θ)^2 cos(ϕ)^2:

cos(θ)^2 cos(ϕ)^2 (tan(θ)^2 - tan(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Express the left hand side in terms of sine and cosine.

Write tangent as sine/cosine:

cos(θ)^2 cos(ϕ)^2 ((sin(θ)/cos(θ))^2 - (sin(ϕ)/cos(ϕ))^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Simplify the left hand side.

cos(θ)^2 cos(ϕ)^2 ((sin(θ)/cos(θ))^2 - (sin(ϕ)/cos(ϕ))^2) = cos(θ)^2 cos(ϕ)^2 ((sin(θ)^2)/(cos(θ)^2) - (sin(ϕ)^2)/(cos(ϕ)^2)):

cos(θ)^2 cos(ϕ)^2 (sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Put the fractions in sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 over a common denominator.

Put sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 over the common denominator cos(θ)^2 cos(ϕ)^2: sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 = (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2):

cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Cancel down (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2).

Cancel cos(θ)^2 cos(ϕ)^2 from the numerator and denominator. (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2) = (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2) = cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2:

cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Express cos(ϕ)^2 in terms of sine via the Pythagorean identity.

cos(ϕ)^2 = 1 - sin(ϕ)^2:

1 - sin(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Express cos(θ)^2 in terms of sine via the Pythagorean identity.

cos(θ)^2 = 1 - sin(θ)^2:

sin(θ)^2 (1 - sin(ϕ)^2) - 1 - sin(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Expand (1 - sin(ϕ)^2) sin(θ)^2.

(1 - sin(ϕ)^2) sin(θ)^2 = sin(θ)^2 - sin(θ)^2 sin(ϕ)^2:

sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 (1 - sin(θ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Expand -(1 - sin(θ)^2) sin(ϕ)^2.

-(1 - sin(θ)^2) sin(ϕ)^2 = sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2:

sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Evaluate sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2.

sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2 = sin(θ)^2 - sin(ϕ)^2:

sin(θ)^2 - sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Come to a conclusion.

The left hand side and right hand side are identical:

Answer: (identity has been verified)

Step-by-step explanation:

this is solutions of your questions

Answer:

x = 15

Step-by-step explanation:

4x - 3 ( x - 2 ) = 21

Distribute

4x -3x +6 = 21

Combine like terms

x+6 = 21

Subtract 6 from each side

x+6-6=21-6

x = 15

Answer:

$0.43

Step-by-step explanation:

Preston adopted a cat from a rescue shelter

He needs to buy food for his new cat so he compared the price of cat litter at different stores

Preston gets the best deal at fluffy felines pet shop

They sell 20 pound jug litter for $8.60

Therefore the cost of the cat litter per pound can be calculated as follows

= 8.60/20

= 0.43

Hence the cost of the cat litter per pound is $0.43

Answer:

Division property of equality

Step-by-step explanation:

What she did was ;

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

Answer:

-2(3v - 6) = 0

-6v + 12 = 0

-6v = -12

v = -12/-6

v = 2 answer

Step-by-step explanation:

Answer:

b BA→  and e BC→

Step-by-step explanation:

< ABC

The vertex is B

The angle is formed by rays BA→  and ray BC→

Answer: V = 4500 cubic units or units^3

Step-by-step explanation:

So far, we know that the givens are:

a height of 30cm, a length of 15cm, and a width of 10cm

So we have to find the volume. The formula for volume is just V = lwh which means that the volume equals the length times the width times the height.

V  = (l)(w)(h)

Now, all you have to do is to substitute the given numbers into the equation:

V = (15)(10)(30)

Simplify that:

V = 4500

Put it in the terms:

V = 4500 cubic units or units^3

Hence your answer!

Answer:

129 is yr ANSWER........

Answer:

[tex]\huge \boxed{\mathrm{129\° }}[/tex]

Step-by-step explanation:

Adjacent angles in a parallelogram add up to 180 degrees.

[tex]\mathrm{m \angle A + m \angle B=180}[/tex]

Solving for [tex]\mathrm{m \angle B}[/tex].

[tex]\mathrm{m \angle B=180-m \angle A}[/tex]

[tex]\mathrm{m \angle B}=180-51[/tex]

[tex]\mathrm{m \angle B=129}[/tex]

Answer:

x = 14

Step-by-step explanation:

comp = add up to be 90

3x + 14 + 2x + 6 = 90

5x + 20 = 90

5x = 70

x = 14

Answer:

123.60$

Step-by-step explanation:

Step 1: 24 x 5 = $120

step 2: 18 x .20 = $3.60

step 3: $120 + $3.60 = $123.60

$123.6

Step-by-step explanation:

5 dozen= 5×$24=$120

18 miles=18×$0.20=$3.6

$120+$3.6=$123.6

thus, she charged the customer $123.6

gronala bars:18

energy drinks:9

Step-by-step explanation:

$0.50 •18= $9

$2.00•9=$18

$9+$18=$27

Answer:

[tex]Speed = \frac{3}{2}[/tex]mph

Step-by-step explanation:

Given

Distance = [tex]\frac{1}{2}[/tex] mile

Time = [tex]\frac{1}{3}[/tex] hour

Required

Determine the speed

To do this, we simply divide distance by time

[tex]Speed= \frac{Distance}{Time}[/tex]

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

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

[tex]Speed = \frac{3}{2}[/tex]

Hence, the speed is [tex]\frac{3}{2}[/tex] mile per hour

Tyler's speed is 1.5 miles per hour.

The formula for speed is:

= Distance / Time

Distance = 1/2 miles

Time = 1/3 hours

Tyler's speed is therefore:

= 1/2 ÷ 1/3

= 1 / 2 x 3/1

= 3/2 miles per hour or.

= 1.5 miles per hour

Tyler's speed is therefore 1.5 miles per hour.

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Answer:

y= 1-x

Step-by-step explanation:

● (a^2x)/a^(x-y) = a

This means that:

● 2x-(x-y) = 1

● 2x - x +y = 1

● x + y = 1

Substract x from both sides

● x+y -x = 1-x

● y = 1-x

She should score more than 77 on the fifth quiz to have an average of at least 84 .

The average is the middle value of a set of numbers. This isn't to be confused with the median, which is the middle of a set of numbers. The average is the middle value of the numbers. If you need to find the average of a set of numbers, you add them all together and divide by the amount of numbers.

Formula of average:

[tex]Average = \frac{Sum of terms }{Number of terms }[/tex]

According to the question

A student has scores on four quizzes : 85,83,98,77

she score on the fifth quiz to have an average of at least 84

Let fifth quiz score = x

By using formula of average:

[tex]Average = \frac{Sum of terms }{Number of terms }[/tex]

As average should be at least 84

[tex]84 < \frac{85+83+98+77+x }{5 }[/tex]

420 < 343+x  

420 - 343 < x

77< x

Therefore,

x should be greater than 77 .

Hence, she should score more than 77 on the fifth quiz to have an average of at least 84 .

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Answer:

With both ratio= 3

The ratio are equivalent

Step-by-step explanation:

Ratio= number of balloons/ number of centerpieces

For

18 balloons for every 6 centerpieces

Ratio= 18/6

Ratio= 3

For

27 balloons for every 9 centerpieces

Ratio= 27/9

Ratio= 3

Value of each ratio= 3 and 3

3=3

So they are eqtand equivalent

Answer:

The measure of ∠TSU = 65°

Step-by-step explanation:

Since RST is a right-angled triangle and RS and ST connect to form a right angle, ∠RST = 90°. Also, since RS and ST connect to form a right angle, ∠RST = ∠RSU + ∠TSU.

We make ∠TSU subject of the formula. So,

∠TSU = ∠RST - ∠RSU

Given that angle ∠RSU = 25° and ∠RST = 90°, substituting these values into he expression for ∠TSU, we have

∠TSU = ∠RST - ∠RSU

∠TSU = 90° - 25°

∠TSU = 65°

So, ∠TSU = 65°

The measure of ∠TSU = 65°

Answer:

65

Step-by-step explanation:

you know it forms a right angle because of the marking on it

so take 90 because thats the degree of a right angle, and subtract 25 from it and you will get your other side

90-25=x

65=x

check by adding both angles

65+25=90

Answer:

division property of equality.

Step-by-step explanation:

Answer:

[tex]g(x)=2\,|x-5|[/tex]

Step-by-step explanation:

Recall that a horizontal translation (shift) in 3 units to the right involves directly subtracting 3 from the variable x (horizontal axis variable) , and that moving the function up 5 units involves adding to the whole function 5 units. That is:

[tex]g(x)=2\,|x-3-2|- 5+ 5\\g(x)=2\,|x-5|+0\\g(x)=2\,|x-5|[/tex]

Answer:

12x +54

Step-by-step explanation:

3x + 9(X+6) =

Distribute

3x+9x +54

12x +54

Answer:

[tex] 12x + 54[/tex]

Step-by-step explanation:

[tex]3x + 9(x + 6) \\ 3x + 9x + 54 \\ = 12x + 54[/tex]