A line includes the points (4, – 6) and (8, – 4). What is its equation in point-slope form

Answer:

As

[tex]\:\left(\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right)^2=x^4y^{-14}z^{-4}[/tex]

Step-by-step explanation:

Given the expression

[tex]\left[\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right]^2[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]

[tex]\left(\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right)^2=\frac{\left(\left(x^2y^3\right)^{-1}\right)^2}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]

                      [tex]=\frac{\left(\left(x^2y^3\right)^{-1}\right)^2}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}[/tex]

so the expression becomes

                       [tex]=\frac{\frac{1}{x^4y^6}}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]       ∵ [tex]\left(x^2y^3\right)^{-1}=\frac{1}{x^2y^3}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]

so the expression becomes

                      [tex]=\frac{\frac{1}{x^4y^6}}{\frac{y^8z^4}{x^8}}[/tex]                    ∵ [tex]\left(x^{-2}y^2z\right)^2=\frac{y^4z^2}{x^4}[/tex]

as

[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

so the expression becomes

                          [tex]=\frac{1\cdot \:x^8}{x^4y^6y^8z^4}[/tex]

                         [tex]=\frac{x^8}{x^4y^6y^8z^4}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]

so the expression becomes

                        [tex]=\frac{x^{8-4}}{y^8y^6z^4}[/tex]

                        [tex]=\frac{x^4}{y^8y^6z^4}[/tex]

                        [tex]=\frac{x^4}{y^{14}z^4}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}[/tex]

so the expression becomes

                           [tex]=x^4y^{-14}z^{-4}[/tex]

Therefore,

Answer:

"Your grade, g, must be at least  75 to pass this class'' is translated as:

Step-by-step explanation:

Given the grade is denoted by 'g'.

In algebra '≥︎' denotes that something must be 'greater than or equal to'. In other words, it means 'at least'.

As the gade must be at least 75, it means it can be greater than 75, but it can not be less than 75.

Therefore, "Your grade, g, must be at least  75 to pass this class'' is translated as:

Answer:

The third choice

Step-by-step explanation:

We need to find the slope and y-intercept of the line and then put it into y = mx = b form. To find the slope, pick a point on the line; I will use (-2, 5); count how many units up you need to go to get to the next point on the line, which in this case it would be 3. The count how many to the right or left you would need to go, which is 1 to the left. Moving left means a negative, so it is -1. Your slope fraction would be [tex]\frac{3}{-1}[/tex] , since slope is rise over run. You can sub this fraction in for m in y = mx + b, which will give you a revised equation of y = -3x = b. To find the y intercept, or b, just find the point where the line crosses the y-axis, which is -1. So, the equation is now y = -3x - 1.The correct answer is third choice.

Answer:

The required distance away from the foot of the tree is 238.0 feet.

Step-by-step explanation:

The height of the redwood tree = 340 feet, and the angle of elevation to its top = [tex]55^{o}[/tex].

let the required distance be represented by x, applying the appropriate trigonometry function, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan [tex]55^{o}[/tex] = [tex]\frac{340}{x}[/tex]

⇒ x = [tex]\frac{340}{Tan 55^{o} }[/tex]

      = [tex]\frac{340}{1.4282}[/tex]

      = 238.062

x = 238.0 feet

The required distance away from the foot of the tree is 238.0 feet.

Answer:

Option D StartFraction w Over 6 EndFraction is correct option.

Step-by-step explanation:

We need to find algebraic expression that represents “the class was divided into six equal groups”

Let complete class strength is w

Dividing into six equal groups we get w/6

The algebraic expression that represents “the class was divided into six equal groups” is w/6

So, Option D StartFraction w Over 6 EndFraction is correct option.

Answer:

d

Step-by-step explanation:

i got it right

Answer:

Let the numbers be x and y

x+y=100

x-y=95

taking x-y=95

x=95+y

x+y=100

95 + y +y = 100

2y=100-95

y=5/2

y=2.5

x=95+y

x=95+2.5

x= 97.5

Hope it helps...............

The two numbers are 97.5 and 2.5.

Subtraction is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Let x and y be the two numbers.

The sum is 100 and the difference is 95.

x + y = 100 ⇒ x = 100 - y

x - y = 95

Substituting x = 100 - y in the second equation,

100 - y - y = 95

100 - 2y = 95

2y = 100 - 95

2y = 5

y = 5/2 = 2.5

x = 100 - y = 100 - 2.5 = 97.5

Hence the numbers are 97.5 and 2.5.

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Answer:

$59.40

Step-by-step explanation:

8% is equal to 0.08

since you are adding the tax to the original cost you will multiply 55 by 1.08 to get the cost of the shoes plus the tax.

Answer:

55 times .8 =44$

Step-by-step explanation:

Answer:

You input the equation they give you into the table to get an outcome. The Equation they gave you is x=y. simply, what ever X is, thats what y is. x=y. On the table it says that X is 3. If x is 3 then y is three because they are equal. if X is 7 then Y is 7. its the same throughout the whole table. To write it as an ordered pair you write (X,Y) if x is three y is three so the ordered pair would look like (3,3)

Answer:

it depends how many hours both of them make but here is what you can do:

Valeria needs to do 2 hours more than Daniel. This is because Daniel makes $18 and hour and Valeria makes only 10. If you do 10*2 or 10+10 you get 20 which is greater than 18. I hope this helps and good luck!

Answer: Natalia answered 11 questions while Daphne answered 6

Step-by-step explanation:

Well... 17-5 (the total amount of questions minus the number of more questions Natalie answered) equals 12 which you will divide by 2 because there are 2 girls, will get Daphnes amount of questions answered (6) and then basically Natalia answered 11

Answer:

147 cm³

71 cm³

54 cm³

1403π cm³

523π cm³

683π cm³

Answer:

4 × 3 - 2 × 5 = 12 - 10 = 2

2x² + 3y² = 2 × 9 + 3 × 25 = 18 + 75 = 93

Answer:

Both have important predecessors—our Constitution was influenced by the Magna Carta and the English Bill of Rights of 1689, and the Declaration by John Locke's writings on the consent of the governed and by a document close to home for Thomas Jefferson, the draft version by George Mason of Virginia's Declaration of ...

Step-by-step explanation:

thats what I could find

Answer

x is 1.62 or -0.62

Step-by-step explanation:

Quadratic Formula:

[tex] \boxed{ \bf{x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}}[/tex]

Given Quadratic Equation:

x² + x - 1 = 0

a = 1 (Quadratic coefficient)

b = 1 (Linear coefficient)

c = -1 (Constant coefficient)

By substituting values in the formula, we get:

[tex] \rm \longrightarrow x = \dfrac{-1 \pm \sqrt{1^2 - 4(1)( - 1)}}{2 \times 1} \\ \\ \rm \longrightarrow x = \dfrac{ - 1 \pm \sqrt{1 + 4} }{2} \\ \\ \rm \longrightarrow x = \dfrac{ - 1 \pm \sqrt{5} }{2} [/tex]

Answer:

(p + 6)(p + 2)

Step-by-step explanation:

I believe you meant  p^2 + 8p + 12 = 0, in which " ^ " indicates exponentiation.

Note that 12 = 2*6, and that these two factors, 2 and 6, add up to 8.  Thus,

p^2 + 8p + 12 = 0 = (p + 6)(p + 2)

Answer:

b  is the correct answer

Answer:

C

Step-by-step explanation:

Its not A because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its not B because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its C because The left side 5 is less than the right side 6, which means that the given statement is always true.

Its not D because The left side is 5 is not less than the right side 6, which means that the given statement is false.

Answer:

x+y=41

x=2y+14

by solving eq

2y+14+y=41

y=27

×=68

Answer:

the answer is 40

Step-by-step explanation:

because when you estimate 1 it will give you zero for example from 1234=0 56789 =1 so 1=to zero so the answer is 40

Answer:

Step-by-step explanation

The shortest length of the right-angled triangle is 4 cm.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angles is a right angle.

Given is, the diagram shows a right-angle triangle.

We have area of the right-angle triangle = 18 cm²

We know that area of a right-angle triangle = 1/2(base)(height)

18 =  1/2(x - 1)(x + 4)

36 = (x - 1)(x + 4)

x² + 4x - x - 4 = 36

x² + 3x - 4 = 36

x² + 3x - 4 - 36 = 0

x² + 3x - 40 = 0

x² - 5x + 8x - 40 = 0

x(x - 5) + 8(x - 5) = 0

x + 8)(x - 5) = 0

x = -8 or 5

we can only use positive numbers because length can't be negative,

Thus, x = 5

The shortest side is definitely one of the 2 legs. The hypotenuse of a triangle is the longest side.

Therefore,

height = x - 1 = 5 - 1 = 4 cm

base = x + 4 = 5 + 4 = 9 cm

Hence, the shortest length of the right-angled triangle is 4 cm.

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Answer:

68

Step-by-step explanation:

Given is an isosceles triangle, therefore measures angles opposite to equal sides would be equal.

Hence,

56° + 56° + x° = 180°

112° + x° = 180°

x° = 180° - 112°

x° = 68°

x = 68

Answer:

Step-by-step explanation:

The triangle is isosceles as two sides have same length

Angles opposite to same sides have same value, therefore two of them  equal to 56°

Answer:

C

Step-by-step explanation:

You have to add the whole equation not only a part of it.

Answer:

the answer is A

Answer:

option 1

Step-by-step explanation:

y = -2  ;   x = -4

Therefore, y = (1/2)x

When x = 8,

[tex]y = \frac{1}{2}*8\\\\\y = 4[/tex]

5 + 2x ≤ 30

2x ≤ 25

x ≤ 12.5

Did this help? I hope it did! Pls tell me if it helped!

Answer:

the y-intercept is 0

Step-by-step explanation:

it goes straight through the origin