For what value of x will the line passing through the following pairs of points be
vertical?
F(3-2x, 12) and G(x +9, 7)

Answer:

13

Step-by-step explanation:

Divide 12 by 3 first because of (PEMDAS) you get 4 tge add that to the 9 the you get 13.

P = parentheses

E = exponent

M = multiplication

D = division

A = addition

S = subtraction

Using a geometric sequence, it is found that the maximum height reached after the 5th bounce is of 43.48 feet.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the ball is dropped from a height of 101.00 inches onto a hard flat floor, and after each bounce, the height is 19% less, that is, 81% of the previous height, hence the first term and the common ratio are given by:

[tex]a_1 = 101, q = 0.81[/tex]

Then, the height of the nth bounce is given by:

[tex]a_n = 101(0.81)^{n-1}[/tex]

And the height of the 5th bounce is:

[tex]a_5 = 101(0.81)^{5-1} = 43.48[/tex]

The maximum height reached after the 5th bounce is of 43.48 feet.

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How to solve your problem

x^{2}-21=100

Quadratic formula

Factor

1

Move terms to the left side

x^{2}-21=100

x^{2}-21-100=0

2

Subtract the numbers

x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0

x^{2}\textcolor{#C58AF9}{-121}=0

3

Use the quadratic formula

x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x^{2}-121=0

a=\textcolor{#C58AF9}{1}

b=\textcolor{#F28B82}{0}

c=\textcolor{#8AB4F8}{-121}

x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}

4

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Add zero

Multiply the numbers

x=\frac{\pm 22}{2}

5

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x=\frac{22}{2}

x=\frac{-22}{2}

6

Solve

Rearrange and isolate the variable to find each solution

x=11

x=-11

Answer:

3

Step-by-step explanation:

Answer:

  318

Step-by-step explanation:

The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.

__

The amount of the penalty is 5.3% of 6000:

  0.053 × 6000 = 318

Wendy paid a penalty of 318 for her early withdrawal.

The number of miles between the two cities is 8.13 miles.

In order to determine  the number of miles between the two cities, we would have to divide 13 kilometers by 1.6 miles. Division is when a number is grouped into equal numbers using another number.

Number of miles = 13 / 1.6 = 8.13 miles

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Answer:

x = 3

Step-by-step explanation:

Hello!

We can distribute the parenthesis and solve for x.

The value of x is 3.

We can plug it back in to check if it works.

Correct!

Answer:

[tex]\huge\boxed{\sf x = 3}[/tex]

Step-by-step explanation:

9 - 2(x - 5) = x + 10

Distribute

9 - 2x + 10 = x + 10

Subtract 10 to both sides

9 - 2x = x

Add 2x to both sides

9 = x + 2x

9 = 3x

Divide 3 to both sides

9/3 = 3x/3

3 = x

OR

[tex]\rule[225]{225}{2}[/tex]

Answer:

2.25or21/4

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

Expression:

Simplify it in below steps:

Answer:

8x

Step-by-step explanation:

We can add all of the side lengths of the triangle to figure out the perimeter. 3x-1+3x+1=6x+2x=8x

Answer:

3/10

Step-by-step explanation:

So you have 2/5 left in your cupboard. Say the amount of chips originally in your cupboard would be 30. 2/5 of 30 would be 12.

Then multiply 12 by 3/4 so it would be 3/4 of 12.

The result would be 9

9/30 = 3/10

this is complicated explanation

there are much easier explanations tho

It looks like the differential equation is

[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]

Factorize the right side by grouping.

[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]

[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]

Now we can separate variables as

[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]

[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]

[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]

You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

Answer:

x = 3.4

Step-by-step explanation:

Use the sin formula, due to the fact of the hypotenuse being known, and the variable being across 70.

Sin(70) = x / 3.6

Sin(70) * 3.6 = x

3.3828934 = x

Round to nearest tenth, as question asked

3.4 = x

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

Answer:

-10

Step-by-step explanation:

if we put f(n)=3 , Then

f(3)=f(3-2) + f(3-1)

= f(1) + f(2)

= -6+(-4). [since f(1)= -6 and f(2) = -4)

= -6-4

= -10

Answer:

[tex]a. {( \sqrt{36} )}^{2} = 36[/tex]

[tex]b. ({ \sqrt{ \frac{25}{81} } })^{2} = \frac{25}{81} = 0.3086[/tex]

[tex]c. {( \sqrt{1.99} )}^{2} = 1.99[/tex]

[tex]d. {( \sqrt{x} })^{2} = x[/tex]

The square exponent is removed with the root .

The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4

let

x = cost of the meal

Both = 2x - 3

3/4x + 1/2x = 2x - 3

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

5/4x = 2x - 3

5/4x - 2x = - 3

(5-8)x/ 4 = -3

-3/4x = -3

x = -3 ÷ -3/4

= -3 × -4/3

= 12/3

x = $4

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Answer:

Acute Triangle.

Explanation:

The figure shows an equilateral triangle which has all the angles equal.

Acute Triangles are those who has angles less than 90°

Hence, an equilateral triangle is always an acute triangle.

Additional,

A right angle triangle has 90° angle.

An obtuse triangle has greater than 90° angle.

Answer:

48.57 USD

Step-by-step explanation:

Just subtract 3500 from 1800 you get 1700

then

1700 divided by 35

The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x  for finding the values of y.

Thus,

       16*(-2)+4y=12

      -32+4y=12

      4y=12+32

     4y=44

      y=11

         16*(-1)+4y=12

         16*(0)+4y=12

         16*(1)+4y=12

         16*(2)+4y=12

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Answer:

4

Step-by-step explanation:

8/2 is 4

A triangle is a three-edged polygon with three vertices. The measure of ∠C is 18°.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Let the measure of ∠C be represented by x. Given the measure of ∠A= 2(∠B), while the measure of ∠B=3(∠C). Therefore, the measure of angles can be written as,

∠A = 2(∠B) = 2[3(∠C)] = 6x

∠B = 3x

∠C = x

Now, since the sum of all the angles of a triangle is 180°. Therefore,

∠A + ∠B + ∠C = 180°

6x + 3x + x = 180°

10x = 180°

x = 18°

Hence, the measure of ∠C is 18°.

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Answer:

-ax² + bx + c and satisfies the condition b² = 4ac

Step-by-step explanation:

that's my answer

{Correct me if I'm not correct}

Keep safe|

x=4

Step-by-step explanation:

4x=16y

x=16divide4

x=4

Answer:

y = 4x

Step-by-step explanation:

Take a pair of coordinates, like

(8,32) ; (4,16)

m = (Δy):(Δx)

   = (32-16) : (8 - 4) = 4

y = mx + c

  = 4x +c

Now substitute the values from one of the 2 coordinates' pair.

16 = 16 + c

c = 0

Therefore,

y = 4x

Answer: 121.375

Step-by-step explanation:

[tex]2^4=16[/tex]

[tex]\frac{1942}{2^4}[/tex]

[tex]\frac{1942}{16}=121.375[/tex]

Answer:

(2.405, 1.537)

Step-by-step explanation:

When you graph these, they intersect at (2.405, 1.537).

You can use desmos as a graphing calculator, it is extremely helpful.

Hope this helps!

Any line with a slope different than 3 will intercept the given line only once.

The answer will be any line that is not parallel (nor the same) to the given line.

Remember two lines are parallel if the lines have the same slope and different y-intercept

In this case, the given linear equation is:

6x - 2y = 10

y = 3x - 5

So the slope is 3 and the y-intercept is -5.

Then, any line with a slope different than 3 will intercept this line only once.

An example can be:

y = 314*x

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Step-by-step explanation:

please can you divide it will give you the answer

Answer:

6 m²

Step-by-step explanation:

Original area :

12 × 14 = 168 m²

New area :

(12-3) × (14+4) =  

9 × 18 = 162 m²

168 - 162 = 6

Area would change by 6 m²

Step-by-step explanation:

[tex] ln(x) + ln(y) + ln(3) [/tex]

[tex] ln(3xy) [/tex]