3/2 x 7/2= 2^x

A. X= 1

B. X= 3

C. X= 5

D. X= 8

The rules of the calculation are:

The complete question is added as an attachment

The equation is given as:

0.738 × 0.28 = 0.20664

When approximated, we have:

0.738 × 0.28 ≈ 0.21

The above approximation can mean any of the following:

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Answer:

The point-slope form is y - 8 = 4(x - 2)

Step-by-step explanation:

Given:

the point-slope form is y - y1 = m(x - x1)

Hence the point-slope form is y - 8 = 4(x - 2)

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Answer:

f(x) = 7.5x

Step-by-step explanation:

you can find the slope by using the slope formula (y2-y1)/(x2-x1). you can use any of the values but for this example I'll be using (2, 15) and (4, 30).

(30-15)/(4-2) = 15/2 = 7.5.

now we can use one of the coordinates to find the y-intercept by plugging the known values in the equation y=mx+b where m is the slope and b is the y-intercept.

for this example I'll be using (2, 15) but you could use any of the values you gave.

15 = 7.5(2) + b

15 = 15 + b

0 = b

so now we have the function rule

f(x) = 7.5x + 0 or just f(x) = 7.5x

Step-by-step explanation:

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Answer:

f^-1(x)=8x/5

Step-by-step explanation:

The inverse of f(x)=5x/3+5 is 8x/5

The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15

We have:

f(x)=5x/3+5

Rewrite as:

y=5x/3+5

Swap x and y

x = 5y/3 + 5

Subtract 5 from both sides

5y/3 = x - 5

Multiply through by 3

5y = 3x - 15

Divide through by 5

y = 3x/5 - 15

Rewrite as:

f-1(x) = 3x/5 - 15

Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15

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The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression  [tex](\sqrt[4]{16})^{3x[/tex].

The rules of the exponent are

(a) [tex]a^m*a^n=a^{m+n[/tex]

(b)[tex]a^m/a^n=a^{m-n[/tex]

(c)[tex](a^b)^c=a^{bc}[/tex]

(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]

here the given expression is [tex]16^{3x/4}[/tex]

we can rewrite the expression as

[tex]16^{3x/4}[/tex]

as we know by the rule of the exponent that    [tex](a^b)^c=a^{bc}[/tex]

=[tex](16^{1/4})^{3x[/tex]

as we know by the rule of the exponent  [tex]\sqrt[n]{a}=a^{1/n[/tex]

=[tex](\sqrt[4]{16})^{3x[/tex]

Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]

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Answer:

66560 pairs

Step-by-step explanation:

let the number of pairs of boots the company makes in 260 days = X

1day -----------------256pairs

260days-------------X

cross multiplying

1×X = 260×256

X= 66560

therefore, in 260days, he makes 66560 pairs

Answer:

C is the answers for the question

Step-by-step explanation:

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The compound inequality can be expressed as "x > -4 or x ≤ 4."

The correct graph of the solution is:

OC. Solution: x > -4 and x ≤ 4

Let's solve the compound inequality step by step:

x + 7 > 3

Subtract 7 from both sides to isolate x:

x > 3 - 7

x > -4

and, we have,

x - 5 ≤ -1

Add 5 to both sides to isolate x:

x ≤ -1 + 5

x ≤ 4

Now, we have two inequalities for x:

x > -4

x ≤ 4

The compound inequality can be expressed as "x > -4 or x ≤ 4."

The correct graph of the solution is:

OC. Solution: x > -4 and x ≤ 4

The graph will include all values greater than -4 (open circle) and all values less than or equal to 4 (closed circle) on the number line.

The correct representation is:

OC. Solution: x > -4 and x ≤ 4

Graph:

-5 -4 -3 -2 -1 0 1 2 3 4 5

+---|---|---|---|---|---|---|---|---|---+

-4 0 4

The open circle at -4 indicates that x is greater than -4, and the closed circle at 4 indicates that x is less than or equal to 4.

The shaded area between -4 and 4 represents the solution to the compound inequality.

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Answer:

(f-g)(x) = 7x+5

Step-by-step explanation:

Given that,

f(x)=2x+2 and g(x) =-5x-3

To Find:

Solution:

[tex](f - g)(x)[/tex]

Re-write as:

Now substitute the values on the polynomial/function:

Simplify using this order:BPEMDAS

Hence,(f-g)(x) = 7x+5.

Answer:

? = 26

Step-by-step explanation:

Challenge accepted!

For the bottom left corner:

[tex]10^{2} + 6^{2} \\= 100 + 36\\= 136[/tex]

Now, 10 - 6 = 4

136 / 4 = 34

For the top left corner:

[tex]7^{2} + 5^{2} \\= 49 + 25\\= 74[/tex]

Now, 7 - 5 = 2

74 / 2 = 37

For the top right corner:

[tex]8^{2} + 4^{2} \\= 64 + 16\\= 80[/tex]

Now, 8 - 4 = 4

80 / 4 = 20

For the bottom right corner:

[tex]6^{2} + 4^{2} \\= 36 + 16\\= 52[/tex]

Now, 6 - 4 = 2

52 / 2 = 26

Another method:

5×6+7=37

7×6-5=37

6×4+10=34

10×4-6=34

4×3+8=20

8×3-4=20

So, 4×5+6=26

6×5-4=26

Firstly we have to multiply number with smaller number from the both number, then, multiply that constant number with larger number and then subtract smaller number you will get same number, in this with 4 only 5 constant number following this rule 4×5+6=26, 6×5-4=26, if you multiply 4 with 6, then, 4×6+6=30, 6×6-4=32, and with 7, 4×7+6=34, 6×7-4=38. So, 26 is the right answer of this question

Answer:

Scale factor is 3

The equation of the line of best fit is y = -0.03x + 69.94

The column headers are given as:

Year    Time(s)

To enter the data values in a graphing calculator, we use the following representations:

x ⇒ Year

y ⇒ Time (s)

Using the above representations, we have the following calculation summary from a graphing calculator:

The equation of the line of best fit is:

y = bx + a

Where

b = SP/SSX = -514.6/17242.92 = -0.02984 ≈ -0.03

a = MY - bMX = 11.7 - (-0.03*1951.59) = 69.94497 ≈ 69.94

So, we have:

y = -0.03x + 69.94

A linear equation is represented as:

y = Slope * x + y intercept

So, we have:

Slope = -0.03

y intercept = 69.94

The y-intercept implies that the initial time is 69.94 seconds, while the slope implies that the time decreases by 0.03 seconds each year

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Approximate value of √17

So the point is (8,4)

As we can see in graph the point is contained by the circle

Hence the distance

Approximately 9 units

Option D

Answer:

Yes, the distance from the origin to the point (8, √17) is 9 units

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given:

Substitute the given values into the formula to create the equation of the circle:

[tex]\implies (x-0)^2+(y-0)^2=9^2[/tex]

[tex]\implies x^2+y^2=81[/tex]

To find if point [tex]\sf (8, \sqrt{17})[/tex] lies on the circle, substitute x = 8 into the found equation and solve for y:

[tex]\implies 8^2+y^2=81[/tex]

[tex]\implies 64+y^2=81[/tex]

[tex]\implies y^2=81-64[/tex]

[tex]\implies y^2=17[/tex]

[tex]\implies y=\sqrt{17}[/tex]

As y = √17  when x = 8, this proves that point (8, √17) lies on the circle.

The distance from the origin to any point on the circle is the radius.

Therefore, as the radius is 9 units, the distance from the origin to the point (8, √17) is 9 units.

Answer: same slope, y int are different

Step-by-step explanation:

Both these lines never intersect because they have the same slope.

they both go down 1 over 1, and also their y interecepts are different

Answer:

y = 5z

Step-by-step explanation:

added in the picture

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[ let the point at which line segments SV and RT intersects be O ]

[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]

[ linear pair ]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]

[ Exterior angle = sum of opposite interior angles ]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]

( let it be equation 1 )

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]

[ Sum of angles of Triangle ]

[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]

( let it be equation 2 )

____________________________________

By comparing both equations :

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]

[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]

( Add 180° on both sides )

[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]

[tex]\qquad \tt \rightarrow \: y = 5z[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

5700000

Step-by-step explanation:

Answer:

A. 84x - 16y - 10.6

Explanation:

[tex]\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)[/tex]

[tex]\sf \rightarrow 2 (42x-8y-5.3)[/tex]

apply distributive method: a(b + c) = ab + ac

[tex]\sf \rightarrow 2 (42x) -2(8y)-2(5.3)[/tex]

[tex]\sf \rightarrow 84x -16y-10.6[/tex]

The given radical root 84, the simplification is option B; [tex]2\sqrt{21}[/tex].

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given radical;

[tex]\sqrt{84} \\\\\sqrt{42 \times 2} \\\\\sqrt{7\times3\times 2 \times 2} \\\\2\sqrt{21} \\[/tex]

Thus, the correct option is B; [tex]2\sqrt{21}[/tex].

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Answer:

The ratio of decay rates is 3:4. So, option D is correct.

Step-by-step explanation:

Concept: The Decay rate for any  function can be calculated by the formula Decay rate = Difference in y values / Difference in x values in given interval

Decay Rate for the exponential function in the interval -2 ≤ x ≤ 0 is (4-1) / (-2-0) = 3/2.

Decay rate for quadratic function in same interval = [(4-0) ÷ -(-2-0)] = 2.

Ratio of decay rates = (3/2) : (2) = 3:4

Option D, the exponential function decays at three-fourths the rate of the quadratic function is the correct answer.

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By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:

k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week

By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

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As IJK is isosceles

Hypotenuse must not counted counted among equal sides so

Apply roots

Option C

The number of units sold in 2021 = 13,300 units.

The number of units that would have to be sold in 2022 to reach the stockholder's desired profit level = 15,200 units.

Assuming that Cullumber company sells the same number of units in 2022 as it did in 2021, the selling price in order to reach the stockholder's desired profit level = $160.

The net income of a company is its profit function, derived by the formula:

Profit = Sales - Cost.

Sales are the product of the number of units sold and per unit selling price.

Cost is the sum of fixed costs and the product of the number of units produced to the variable cost per unit.

Assuming the number of units sold in 2021 to be x,

we can say sales = $152x, and

cost = ${574800 + 96x}.

Therefore, profit = sales - cost,

or, 170000 = 152x - {574800 + 96x},

or, 170000 = 56x - 574800

or, 56x = 574800 + 170000 = 744800,

or, x = 744800/56 = 13300.

Therefore, the number of units sold in 2021 was 13,300.

In 2022, the desired profit = $170,000 + $106,400 = $276,400.

Assuming the number of units sold in 2022 to be n, at the same unit data and fixed cost, we can say that:

Sales = $152n, and

Cost = ${574800 + 96n}.

Therefore, profit  sales - cost,

or, 276400 = 152n - {574800 + 96n},

or, 276400 = 56n - 574800,

or, 56n = 574800 + 276400 = 851200,

or, n = 851200/56 = 15200.

Therefore, the number of units sold in 2022 should be 15,200 to reach the desired profit of the stakeholders.

When the number of units sold in 2022 is the same as in 2021, that is, the number of units = 13,300, we assume the per unit selling price to be $P.

Now we can say that,

Sales = $13300P.

Costs = ${574800 + 96*13300} = ${574800 + 1276800} = $1851600.

Therefore, profit = sales - cost,

or, 276400 = 13300P - 1851600,

or, 13300P = 1851600 + 276400 = 2128000,

or, P = 2128000/13300 = 160.

Therefore, the new selling price per unit to reach stockholders' desired profit, assuming the number of units sold in 2022 to be the same as in 2021 is $160.

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It should be noted that a reflection is known as a flip and it's a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.

In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.

The reflection is attached.

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Answer:

Adjacent sides are in the ratio 5 : 12

That means,

Let length = 12x and breadth = 5x

Perimeter = 34

2(l+b) = 34

12x + 5x = 17

17x = 17

x = 1

Lenth =12 cm

Breadth = 5 cm

By Pythagorean theorem

The length of the diagonal of rectangle = 13 cm

Answer:

w≈7.6in

Step-by-step explanation:

L= 7.25

D= 10.5

Answer:-

The width of this rectangle is = 7.59

Given:-

In this question, it is given that -

The diagonal of this rectangle is = 10.5

the length of this rectangle is = 7.25

To find:-

We have to find the width of this rectangle.

Solution:-

We can easily solve this problem using the Pythagorean theorem.

In this problem, it is given that the length of this rectangle is = 7.25 and the diagonal is =10.5

so by the Pythagorean theorem, we can get-

(length)² + (width)² = (diagonal)²

or, (7.25)² + (width)² = (10.5)²

or, (width)² = (10.5)² - (7.25)²

= 17.75 × 3.25

= 57.6875

or, width = 7.59

So, the width of the rectangle is 7.59.

-5≥

so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)

Answer:

x> -6

Step-by-step explanation:

Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6

The arc length of the semicircle is 5π units

From the question, we are to calculate the arc length of the semicircle

Arc length of a semicircle = 1/2 the circumference of the circle

∴ Arc length of a semicircle = 1/2 × 2πr

Arc length of a semicircle = πr

Where r is the radius

From the given information,

r = 5

∴ Arc length of the semicircle = 5 × π

Arc length of the semicircle = 5π units

Hence, the arc length of the semicircle is 5π units

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