Simplify each expression.
ln e²

Answer:

Step-by-step explanation:

1 1/2 cups = 1.05

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: 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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The expression has to be written in it's prime factor form. 27 = 3x3x3 = 3^3 in index form. 3=3^1 . By power rule (a^m)^n = a^mn.

(3^1)^1/4+(3^3)^1/4

3^1/4 + (3^2x3^1)^1/4

3^1/4+3^2/4x3^1/4

3^1/4(1+3^1/2)

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The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office

Given data

Zarah's office is 2 cm wide and 4 cm long

Another office is 8 cm long and 4 cm wide

Area of an office = length * width = long * wide

Area of Zarah's office = 4 cm * 2 cm = 8 cm2

Area of another office = 8 cm * 4 cm = 32 cm2

comparing the two areas

say by how much is 32 cm2 greater than 8 cm2

32 cm2 / 8 cm2 = 4

The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office.

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Answer:

8.4

Step-by-step explanation:

7 x .2 is the increase 1.4

Add 1.4 to 7 to get 8.4

Answer:

30

Step-by-step explanation:

Quadratic Formula

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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log (2x) = -1 => x = 0.05, by properties of logarithm.

Given: log (2x) = -1

Raising both sides to 10, in order to remove the logarithm:

=> [tex]10^{log_{10}(2x)} = 10^{-1}[/tex]

=> 2x = [tex]\frac{1}{10}[/tex] ( as [tex]a^{log_a(x)} = x[/tex])

=> x = [tex]\frac{1}{20} =[/tex] 0.05

Hence, log (2x) = -1 => x = 0.05, by properties of logarithm.

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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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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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The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage at which the dress was sold from its original price is 28%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The selling price of the dress = $56

The original price of the dress = $200

The percentage at which the dress was sold from its original price.

= 56/200 x 100

= 56/2

= 28 %

Thus,

The percentage at which the dress was sold from its original price is 28%.

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Possible coordinates for points B  (-3, 13)

Given that

point A (5 , -7)

and there are 8 points between A and B.

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

The equation of a circle centerd in the point (x0, y0) is:

(x - x0)² + (y - y0)² = r²

where r = radius of the circle

So we can draw a circle of 8 units around A, and get:

(X - 5)² + (Y - (-7))² = 8²

So from this equation we can find all the possible values of B.

Y = √(8² - (X- 5)²) - 7

So for a given value of X, you can find the value of Y. where (8² - (X-5)²) can not be a negative number, so

8² ≥ (X - 5)²

So X = -3 (because (-3 - 5)² = 8²)

to X = 13 (because (13 - 5)² = 8²)

So X is in the range (-3, 13)

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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:

No solution

Step-by-step explanation:

Given equation:

[tex]w+5w+4=3(2w-1)[/tex]

Distribute the parentheses:

[tex]\implies w+5w+4=3 \cdot 2w- 3 \cdot 1[/tex]

[tex]\implies w+5w+4=6w- 3[/tex]

Combine like terms:

[tex]\implies 6w+4=6w-3[/tex]

Add 3 to both sides:

[tex]\implies 6w+4+3=6w-3+3[/tex]

[tex]\implies 6w+7=6w[/tex]

Subtract 6w from both sides:

[tex]\implies 6w+7-6w=6w-6w[/tex]

[tex]\implies 7=0[/tex]

As 7 ≠ 0 there is no solution.

Cost of 25 pound flour is $30.75.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Price of 3 pound flour = $3.69

She needs 25 pounds of flour to make enough cookies for a bake sale.

Now, Price of 3 pound flour = $3.69

Hence, Cost of 1 pound flour = $3.69 ÷ 3 = $1.23

So, Cost of 25 pound flour = 25 x $1.23

                                          = $30.75

Therefore, Cost of 25 pound flour is $30.75.

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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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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:

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!

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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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

Answer:

24

Step-by-step explanation:

8 * 12 = 96

96 / 4 = 24

Have a great night! :D

Hope this helps.

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

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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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:

for (a) i got 15

Step-by-step explanation:

AE=17, AB=16 which makes AM=8

so from there u do pythagorean theorem

17^2 - 8^2 = 225

√255= 15

Answer:

26.565⁰

Step-by-step explanation:

Triangles AEM and BEM are congruent since
AE = BE
m∠AME = m∠BME=90°
and EM is the common side

So AM = BM = AB/2 = 16/2 = 8

Triangle EAM is a right triangle with hypotenuse AE = 17 and AM = 8

So EM² = (17² - 8²) by the Pythagorean theorem
EM² = 289 - 64 = 225
EM = √225 = 15 cm

To find m∠ECM, note that triangle ECM is a right triangle with m∠EMC = 90° and the side opposite ∠EMC = EC, the side opposite ∠ECM is EM

By the law of sines

EC/sin90 = EM/sin(∠ECM)

So,

sin(∠ECM) = EM/EC since sin 90 = 1

So we have to compute EC

Again note that the triangle MCB with sides BM, MC and BC is a right triangle with m∠CBM = 90°

The hypotenuse is MC

So MC ² = MB² + BC² = 15² + 30² = 1125

MC = √1125 = 33.54 cm

Therefore
sin(∠ECM) = EM/MC = 15/33.54 = 0.4472

m∠ECM = sin⁻¹ (0.4472)

= 26.565⁰

To be honest I am not 100% sure of this answer, please check and see if this works. Thanks

The standard form for the equation of this line is equal to 3A - 4B = 12.

A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

In Mathematics, the standard form of a linear equation is given by the following:

Ax + By = C.

When C = 24, the line passes through point (4, 0) and we have;

Ax + By = C.

4A + B(0) = 24.

4A = 24

A = 24/4

A = 6

When C = 24, the line passes through point (0, -3) and we have;

A(0) + B(-3) = 24

-3B = 24

B = -24/3

B = -8

Therefore, the standard form for the equation of this line is given by:

6A - 8B = 24

Dividing all through by 2, we have:

3A - 4B = 12

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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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