Which of the following is the result of rewriting the formula to solve for l

A.
B.
C.
D.

Answer:

5.08

Step-by-step explanation:

2.17+2.91 = 5.08

The correct form of the expression is x² -9

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y = (x − 3)(x + 3) =

This can be done by opening the brackets

x²+3x-3x-9

⇒x²-9

Therefore, the correct form of the equation is x²-9

The x-intercept  = 1 and the y intercept is -9

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Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3  transformed .

Mathematics includes the study of numbers, various variable, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship between the number of inputs and the corresponding outputs for each. Simply explained, a function range is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a realm. The letter f is frequently used to denote functions (x).

Here,

Given :

=>  f(x) = log x

=> g(x) = log (x) - 3

So , it is transformed as logx = f(x)

it is transformed as :

=> g(x) = f(x) - 3

Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3  transformed .

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Answer:

Supplementary angles are angles that add up to 180 degrees, or on a straight line. If one angle is 163.6 degrees less than its supplementary, then all you have to do is subtract that number from 180. The angles are

180 - 163.6 = 16.4

180 - 16.4 = 163.6

One angle is 16.4 degrees, the other is 163.6. They both add up to make 180.

Answer:

28

Step-by-step explanation:

The constant variation, a, is equal to the product of x and y when they are both known. In this case, when x = 7 and y = 4, the constant variation is 4 * 7 = 28. So, the equation for the inverse variation is y = 28 / x.

The correct sample space for the gumballs in her bag is;

A: Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape

The sample space of an experiment is defined as the set of all the possible outcomes. For example, when we toss a coin, the sample space is; {head, tail}.

Now, the parameters for the bag filled with gumballs are;

1 watermelon.

2 lemon-lime.

3 grape gumballs.

Therefore the sample space is the different types of gumballs there and it is; {Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape}

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Answer:

He is incorrect

Step-by-step explanation:

7n = 49

Isolate variable "n" by dividing both sides by 7:

n = 7

Since doing this step makes n to equal 7, [Ben is incorrect to say that n = 6]

The solution is, she got commission of 2%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission.

so, she got commission = 1200/60000 * 100

                                        =2%

Hence, The solution is, she got commission of 2%.

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The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.

B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.

D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.

E. lim t→∞ P(t) = 740, so the answer is 740.

F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.

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Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

Answer:

4,080,000,000,000

Step-by-step explanation:

1,200 * 3.4*10⁹

=4080*10⁹

=4,080,000,000,000

The given function is continuous at  x = 3,  RHL = LHL = F(2)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  (x²-9)/(x² - x -6)(x² + 6x +9)

To check whether it is continuous at x = 2

First taking LHL,

[tex]\lim_{h \to \ 0}[/tex]  ((2-h)²-9)/((2-h)² - (2-h) -6)((2-h)² + 6(2-h) +9)

⇒  -5/(-4x25)

⇒   1/20

Now, taking RHL

[tex]\lim_{h \to \ 0}[/tex]  ((2+h)²-9)/((2+h)² - (2+h) -6)((2+h)² + 6(2+h) +9)

⇒  -5/(-4x25)

⇒   1/20

The value at x = 3

F(3)  =   ((2)²-9)/((2)² - (2) -6)((2)² + 6(2) +9)

       =  -5/(-4x25)

       =   1/20

Hence Proved,   RHL = LHL = F(2)

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The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Note that in question 28 above:

X = 56° (Alternative Angles)

Y = 124° (Angles in a straight line)

Z = 81° (Sum of angles in an irregular parallelogram).

in Question 29,
x = 126° (Co-interior angles and Bisector theorem).

Question 28: Note that the sum of angles in an irregular parallelogram always equal 360°. Since X and 56° are alternate angles and are therefore congruent, and Y and 56° are on the same line and therefore sum up to 180°, resulting in Y being equal to 124°, then we have three interior angles of an irregular parallelogram:

∠X = 56°

∠Y = 124°; and

∠99° (As given), which is co-interior with ∠Z

Thus whether by the Co-interior principle where two co-interior angels sum up to 180° or by sum of angles in an irregular parallelogram, we will still obtain a result where:

∠Z = 81°. That is

360° = 56 + 124 + 99 + ∠Z

∠Z = 360 - (56 + 124 + 99)
∠Z = 81°

OR

Using the Co-Interior angles theorem, we can state that:

∠Z = 180 - 99
∠Z = 81°

Question 29:
Recall that an angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.

Thus, we can state that 27° is half of the angle whose Co-interior is x.

Thus ∠x = 180 - (27*2)

∠x = 180 -54
∠x = 126°


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Answer:

A. 1436.03 ft³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(7 ft)³

V = 1436.03 ft³

Answer:

d. x = 7

Step-by-step explanation:

To find the value of x, you can cross multiply the fractions to get 32 * x = 8 * 28, then simplify:

32x = 224

x = 7.

Lisa's remaining of her monthly income is $490. Her net worth is $142.980. Her saving ratio is 17%, liquidity ratio is 23% and Debt-to-asset ratio is 63%.

Based on the given data, we can construct Lisa's personal cash flow statement and personal balance sheet as:

Personal Cash Flow Statement

Cash Inflow:

Cash Outflow:

Debts:

Living expenses:

Total cash = $490

Personal Balance Sheet

Assets:

Total Assets = $383,140

Liabiities:

Total Liabilties = $240,160

Net worth = $142,980

Saving ratio can be calculated by assuming that the amount of Lisa's cash on bank is her saving. Then:

saving ratio = saving : net income

Saving ratio = cash in bank : net income

Saving ratio = $600 : $3,600

Saving ratio = 17%

Liquidity ratio is calculated by comparing Lisa's current assets with her net worth. Hence:
Liquidity ratio = Current assets : Net worth

Liquidity ratio = (Cash in bank + Car + Clothing owned + Furniture) : Net worth

Liquidity ratio = ($600 + $18,000 + $540 + $14,000) : $142,980

Liquidity ratio = 23%

Debt-to-asset ratio = Total Liabilities  : Total Assets

Debt-to-asset ratio = $383,140 : $240,160

Debt-to-asset ratio = 63%

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Answer:

Student most likely forgot to form 2nd equation.

Step-by-step explanation:

The answers appear to be cut off, but I can clearly see that the other solution isn't considered. When solving an absolute value equation, you form two equations. In this case, we have x-3=4 and x-3=-4 as our equations because |-4|=|4|=4 so this is accounted for. Hence, the two solutions should be x=7 AND x=-1.

The car can travel 528 miles on a one full tank gas that averages 44 miles per gallon.

In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data.

Given that, Juanita has a hybrid car that averages 44 miles per gallon.

Her car has a 12-gallon tank.

So, the car travels:

(12) (44) = 528 miles.

Hence, the car can travel 528 miles on a one full tank gas.

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Answer: false

Step-by-step explanation:

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 7x^2-6 \qquad \begin{cases} x_1=4\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(4)}{b - 4} \\\\\\ \cfrac{(7b^2-6)~~ - ~~(7(4)^2-6)}{b-4}\implies \cfrac{7b^2-6~~ - ~~(112-6)}{b-4} \implies \cfrac{7b^2-112}{b-4}[/tex]

[tex]\cfrac{7(b^2-16)}{b-4}\implies \cfrac{7(b^2-4^2)}{b-4}\implies \cfrac{7~~\begin{matrix} (b-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(b+4)}{~~\begin{matrix} b-4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \boxed{7(b+4)}[/tex]

This expression gives the average rate of change of the function over the interval [4, b].

The average rate of change of a function on an interval is equal to the rise (change in the y-value) divided by the run (change in the x-value) over that interval.

For f(x) = 7x² - 6 on the interval [4, b], the average rate of change can be found by calculating the slope of the secant line connecting the points (4, f(4)) and (b, f(b)).

Therefore, the average rate of change of f(x) = 7x² - 6 on the interval [4, b] is:

(7b² - 6 - (7(4)² - 6)) / (b - 4) = (7b² - 28) / (b - 4)

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There are 50 hundredths in the fraction 5/10.

In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

From the information provided about the numerical value, we have:

5/10 = 0.5.

Note: 1 hundredth is equal to 1/100 = 0.01.

Therefore, by dividing 0.5 by 0.01 we have:

Number of hundredths = 0.5/0.01 = 50.

In conclusion, 5 tenths or 5/10 is equivalent to 50 hundredths.

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The shortest distance  from A to B in the figure is length AB, So Option A is correct

The smallest (straight line) distance between a body's beginning position and its final location—represented by an arrow pointing from starting position to final position—is referred to as a body's displacement as it moves from one position to another. Being a vector quantity, it.

Given that,

A quadrilateral figure ABCD

and it has one diagonal BD

Shortest distance from A to B  =?

Possible paths, For A to B

1. Directly A to B

Distance = AB

2. A to D then D to B

Distance =  AD + DB

3.   A to D then D to C and then C to A

Distance =  AD + DC + CA

It can be seen that distance covered is lesser in case 1 in compare to case 2 & 3

Hence, the shortest distance is  AB

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The measure of HG is 12

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.

The opposite sides of a parallelogram are equal. This means that 3y = y+8

3y = y+8

3y-y = 8

2y = 8

divide both sides by 2

y = 8/2

y = 4

if y = 4 and HG is y+8

therefore

the measure of HG = 4+8

= 12

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The equation is $230,000 x 0.97^5.

The worth of the house in five years is  $197,508.83.

Depreciation is the decline in the carrying value of an asset. Depreciation occurs as a result of wear and tear.

The equation that would be used to determine the worth of the house in 5 years is

Worth of the house = cost of the house x (1 - depreciation/100)^number of years

= $230,000 x (1 - 3/100)^5

$230,000 x (1 - 0.03)^5

$230,000 x 0.97^5  = $197,508.83

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Answer:

C. 5

D. 5√3*

*Check the last one - choice D - make sure it is 5√3 not 53–√ before marking it correct.

Otherwise only choice C is the correct answer

Step-by-step explanation:

The sides of a 30-60-90 triangle are always in the ratio of 1 : √3 : 2.

If the side opposite the 90° angle(the hypotenuse)  = a

If the side opposite the 30° angle: PQ = a

Then the side opposite the 90° angle = 2a

The side opposite the 60° angle = √3a

Since here we are given the hypotenuse = 10

Side opposite the 30° angle = 2a/2 = 10/2 = 5

Side opposite the 60° angle = √3a = √3 · 5 = 5√3

I believe in your choice for D it should be 5√3 but not sure about that so check if it is before marking it correct

Answer:

Options C) and D) are correct

Step-by-step explanation:

Given:  The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To choose: the correct option

Solution:

ΔKBO is a right-angled triangle.

[tex]sinO=\frac{side opposite to angle}{sideadjacent to angle}[/tex]

[tex]= \frac{BK}{KO} \\= \frac{BK}{10}[/tex]

⇒ sin 60°= [tex]\frac{BK}{10}[/tex]

[tex]\frac{\sqrt{3} }{2} = \frac{BK}{10}[/tex]

BK = [tex]\frac{\sqrt{3} }{2} (10) = 5\sqrt{3}[/tex]

CosO = [tex]\frac{side adjacent to angle}{side opposite to angle}[/tex]

          [tex]= \frac{BK}{KO} \\= \frac{BO}{10}[/tex]

          ⇒ cos 60° = [tex]\frac{BO}{10}[/tex]

            [tex]\frac{1}{2}= \frac{BO}{10} \\BO = \frac{10}{2} = 5[/tex]

Solving the provided question, we can say that Using quadratic formula, x = 19 or x = 3; Sum of the 2 numbers = 3 + 19 = 22

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

Let x represent a number that is twice as far away from 5 than 17.

|x - 5| = 2|x - 17|

(x - 5)² = 4(x - 17)²

[tex]x^2 + 25 - 10x = 4(x^2 + 49 - 14x)\\x^2 + 25 - 10x = 4x^2 + 196 - 56x\\3x^2 - 46x + 171 = 0\\[/tex]

Using quadratic formula,

x = 19 or x = 3

Sum of the 2 numbers = 3 + 19 = 22

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The required equation is y = -9x - 65.

What is a slope intercept form?

One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

Here, we have

Given: the equation of a line parallel to y =-9x + 8, that passes through the point P(-8, 7).

The slope of y = -9x+8.... (1)

can be found as

compare with the standard equation

y = mx+c.... (2)

where m is the slope so

Comparing (1) and (2)

slope = m = -9

So the slope of the parallel line will also be -9

So in order to find the equation we need a point and a slope to put in the point-slope formula

y-y₁ = m(x-x₁)

Point (x,y) = (-8,7) slope m = -9

y-7 = -9(x+8)

y = -9x - 72 + 7

y = -9x - 65

Hence, the required equation is y = -9x - 65.

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The length of the line segment QM which is half the diagonal MP is equal to 21 in the parallelogram LMNP.

A parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.

For the parallelogram LMNP; the lines MP and LN are its diagonals, and the both bisect each other, that is they cut each other to form two equal parts.

So QM and PQ are equal halves of the line MP

Therefore, since PQ = 21 then QM = 21 because they form a diagonal of the parallelogram LMNP bisected by the diagonal LN.

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