Solve each equation. Round to the nearest ten-thousandth. 7 x⁻³=25

The missing value of inverse variation is 0.5

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the given question,

Take the order pair (4,1.5)

As it is an inverse variation, we can substitute it

y=k/x  

1.5=k/4

K=6

Now find the inverse variation equation

y=k/x

Also, k=6

Solve this equation for the second pair (x,12)

As, y=6/x

   x = 6/12 = 1/2 = 0.5

Therefore, missing value is 0.5

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On simplifying the expression √5 x³ . √40 x y⁷ we get 10√2 x⁴y⁷

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

Given,

√5 x³ . √40 x y⁷

⇒ √5 × √40 × x⁴ × y⁷

⇒ √200 × x⁴y⁷

⇒ 10√2 x⁴y⁷

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Answer:

Hope this helps with your question :)

B

Step-by-step explanation:

This is because in the slope-intercept form,

y = mx + b, the m = slope, and the b = y-intercept. So the final answer would be

y = 1/2x - 5

Answer: the length is 23 feet     the width is 14 feet

Step-by-step explanation:

Let  the length is x feet

Hence, the width is (x-9) feet

The perimeter of a rectangular pool is:

P=(2)(x+(x-9))

74=(2)*(2x-9)

74=(2)(2x)-(2)(9)

74=4x-18

74+18=4x-18+18

92=4x

(4)(23)=(4)(x)

Divide both parts of the equation by 4:

23 feet=x

23-9=x-9

14 feet=x-9

The required expression that is equivalent to (6^-3/3^-2x6^2) to the 3rd power is 3^3/2^3.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now the given expression is,

(6^-3/3^-2x6^2)to the 3rd power

or, we can write

(6^-3/3^-2x6^2)^3

Since, a^-1 = /a

Therefore we have

6^-3 = 1/6^3

3^-2 = 1/3^2

Therefore we get,

{(1/6^3)/(1/3^2) x 6^2}^3

Simplifying we get

{(3^2/6^3) x 6^2}^3

or, {(3^2  x 6^2)/6^3}^3

Solving we get

(3^2/6)^3

Now since,

3^2 = 9

Put in expression we get

(9/6)^3

or, (3/2)^3

therefore we get,

3^3/2^3

this is the required expression that is equivalent.

Thus, the required expression that is equivalent to (6^-3/3^-2x6^2) to the 3rd power is 3^3/2^3.

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The distance, d = v²/64.

Let 'v' denote the velocity of an object dropped from a tall building.

Let 'd' be the distance the object has dropped.

Given that the relation between v and d is, v =√(64d)

This equation gives 'v' in terms of 'd'.

We need to solve this formula for d.

For this, consider v =√(64d)

We square on both sides to get rid of the square root.

⇒ v² = 64d

Now isolating d to one side of the equation,

⇒ d = v²/64 is the formula for d

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Answer:

[tex]h = G + \frac pf[/tex]

Step-by-step explanation:

[tex]G = h - \frac pf \text{ / Add }\frac pf \text{ to both sides}\\\\G + \frac pf = h - \frac pf + \frac pf\\\\G + \frac pf = h[/tex]

Answer:

24

Step-by-step explanation:

8 * 12 = 96

96 / 4 = 24

Have a great night! :D

Hope this helps.

Answer:

hatch

Step-by-step explanation:

the hatch marks on the triangle represent the same length

if a side has one hatch mark it has the same length as the other side with one hatch mask

the same goes for the one with two hatch marks

The factors of 2 x²-19 x+24 are x = 3/2 and x = 8

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of a number into its factors or divisors. The factorization of the integer 12, for instance, may appear as 3 times 4.

Given,

2 x²-19 x+24

By factorization,

⇒ 2x² - 16 x - 3x + 24

⇒ 2x (x-8) - 3 (x - 8)

⇒ (2x - 3) (x-8)

⇒ x = 3/2 and x = 8

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The statements which must be true of triangle RST are;

According to the stated premises;

m∠R > m∠S + m∠T

This in turn means that the angle measure of ∠R > angle measure of ∠S and ∠T.

Therefore, we can conclude that; m∠R > 90° and m∠S + m∠T < 90°

As such, certainly, m∠R > m∠T and m∠R > m∠S

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Using inverse variation, the function model will be y = 48. 1/x and the value of y at x = -5 will be -48/5

Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.

Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.

Inverse variation is y = k. 1/x

given y = 4

x = 12

So, 4 = k. 1/12

So, the value of k = 48

We can conclude that the value of constant variation is 48

when x = -5, the value of y will be -

y = k.1/x

y = 48 . 1/-5

y = -48/5

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Answer:

use an app for it.

Answer:

cos4θ=8cos^4θ−8cos^2θ+1

Step-by-step explanation:

Answer:

So when you add 2 plus to it equals 2 adrew tates kissing.

Step-by-step explanation:

Neither of Nicole and Kiri are correct that evaluating the conditional If 15 is a prime number, then 20 is divisible by 4.

Nicole reasoning is incorrect because despite the fact that 20 is divisible by 4, it does not mean the conditional is true. The conditional states that “15 is a prime number”- this is incorrect. Because this is incorrect the validity of the conclusion does not justify the validity of the hypothesis. Kiri’s reasoning is inaccurate despite the fact that his explanation of the hypothesis is correct, the hypothesis has no direct implication on the conclusion.

Hence, their belief that the conditional is true are both wrong. A conditional is only true if the premise for that conditional is first true in itself and also directly affects the conclusion.

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The equivalent expression of the expression given as 0.75/9 * 0.75/3 is 1/48

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

0.75/9 * 0.75/3

Evaluate the product of the numerators

So, we have

0.75/9 * 0.75/3 = 0.5625/9 * 1/3

Evaluate the product of the denominators

So, we have

0.75/9 * 0.75/3 = 0.5625/27

Simplify the fraction

So, we have

0.75/9 * 0.75/3 = 0.0625/3

Further simplify

So, we have

0.75/9 * 0.75/3 = 625/30000

Further simplify

So, we have

0.75/9 * 0.75/3 = 1/48

Hence, the equivalent expression of the expression given as 0.75/9 * 0.75/3 is 1/48

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The radius of the new parking area is 71cm. (option b)

The liters of sporting drinks they have with them is 30 liters (option d).

A circle is a bounded figure which points from its center to its circumference is equidistant. The area of a circle is the area that is bounded in a circle.

Area of a circle = πr²

Where :

22/7 x 123² = 47,548.286 m²

When the parking area is reduced by 1/3. its new area is: 1/3 x 47,548.286 m² = 15,849.429 m²

The radius of the reduced parking lot:√ (7/22 x 15,849.429 m²) = 71m

The first step is to determine the volume of one of the packages.

Volume of a rectangular prism = length x width x height

6 x 4 x 10.5 = 252 cm³

Now, the volume of the 120 packs of sports drinks have to be determined:

120 x 252 cm³ = 30,240cm³

The last step is to convert cm to liters

1 cm = 1 /1000 liters

30,240 / 1000 = 30 liters

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Answer:

a.

D=[-6,4)

R=(-3,4]

b.

D=[-6,7)

R=[-1,6)

Step-by-step explanation:

[,] <-- used for when the point is included in the answer (closed circle or greater than/less than or equal to sign)

(,) <-- used for when the answer does not include point (open circle or greater than/less than sign   not equal to)

Plug in the points where shown on each line.

Hey again! Just answered your last domain and range question so I hope I helped again!

Answer:

the arithmatic mean of 5 and 19 is: 5,7,9,11,13,15,17,19.

Step-by-step explanation:

hope this helps

Answer: y = x + 4.

Reason: -2 + 4 = 2 and -1 + 4 = 3 so, any equation added with 4 would be y or x + 4 = y.

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ln e⁸³ = 83, by definition and properties of logarithm.

Now,

In the question, ln (e)⁸³, a = e

By property of logarithms, [tex]log_b(a)^{m}=m(log_b(a))[/tex],

=> 83 (ln (e)) = 83 [tex]log_e(e)[/tex]

Since, [tex]log_e(e)[/tex] = 1, ln (e)⁸³ = 83 (1) = 83.

Hence, ln e⁸³ = 83, by definition and properties of logarithm.

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Approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.

The perpendicular line to a point is the path that travels the shortest distance between them.

The equation for the indicated line is -x + 2y = 14, which can be expressed as the following in slope and intercept form:

The y-intercept is 7, and the slope, m1, is 1/2.

Consequently, the line's equation is:

Therefore, the coordinates of the point on line A(-1/4, 5) that coincides with the perpendicular from the line -x + 2y = 14 (y = x/2 + 7) are as follows:

The location on the line -x + 2y = 14 (y = x/2 + 7) that is perpendicular to the point A(-1/4, 5) has the coordinates: (-1, 6.5)

The following formula is used to calculate the distance between points A and B:

Where: (x₁, y₁) = (-1/4, 5), and (x₂, y₂) = B(-1, 6.5)

Using the values as plug-ins, we have;

[tex]\begin{aligned}&I_{A B}=\sqrt{(6.5-5)^2+((-1)-(-1 / 4))^2}=\sqrt{(-0.75)^2+(1.5)^2}=\sqrt{\frac{45}{16}}=\frac{3}{4} \cdot \sqrt{5} \\&l_{A B}=\frac{3}{4} \cdot \sqrt{5} \approx 1.677\end{aligned}[/tex]

Therefore, approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.

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Answer:

m<1 = 148

m<4 = 32

Step-by-step explanation:

<1 and <7 are alternate exterior angles. By the Alternate Exterior Angle Theorem, <1 and <7 are congruent and therefore m<1 = m<7. So m<1 = 148 degrees.

<3 and <7 are corresponding angles. By the Corresponding Angles Postulate, <3 and <7 are congruent and therefore m<3 = m<7. So m<3 = 148 degrees. <3 and <4 form a linear pair, and by the Linear Pair Postulate, <3 and <4 are supplementary and therefore m<3 + m<4 = 180. So m<4 = 180 - m<3 = 180 - 148 = 32 degrees.

The solution for x in the equation -128 = 4x is -32

The collection of values used to replace the unknowns in an equation to make it true is known as the solution. Two fundamental algebraic laws, the additive property and the multiplicative property, are utilized to find the solutions to equations with a single unknown raised to a single power.

Given that,

The equation: -128 = 4x

We have to find x:

That is:

-128 = 4x

x = ( -128 / 4 )

x = -32.

Therefore, the solution for the given equation -128 = 4x is -32.

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[tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.

Given: [tex]6^{2x} = 10[/tex]

Taking logarithm on both sides:

=> log ([tex]6^{2x}[/tex]) = log 10

=> 2x (log 6) = log 10 ( as [tex]log_b(a)^m = m (log_b(a))[/tex])

=> 2x = [tex]\frac{log10}{log6}[/tex]

=> 2x = [tex]\frac{1}{0.778}[/tex]

=> 2x = 1.285

=> x = 0.642

Hence, [tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.

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