Part A: If (7^2)^x = 1, what is the value of x? Explain your answer. ( How did you get your answer?)

Part B: If (7^0)^x = 1, what are the possible values of x? Explain your answer. ( How did you get your answer?)

Answer:

24

Step-by-step explanation:

to solve this you should first write it out

-8 * -3

now multiply them

the negatives cancel each other out

so

you can just do 8 * 3

and get 24

Answer:

[tex](x-6)^2=-1[/tex]

Step-by-step explanation:

Given equation:

[tex]-6x^2+64x-222=-8x[/tex]

When completing the square, first move the terms in x to the left and the constant to the right of the equation:

[tex]\implies -6x^2+64x-222=-8x[/tex]

[tex]\implies -6x^2+64x-222+222=-8x+222[/tex]

[tex]\implies -6x^2+64x=-8x+222[/tex]

[tex]\implies -6x^2+64x+8x=-8x+222+8x[/tex]

[tex]\implies -6x^2+72x=222[/tex]

Factor out the leading coefficient -6 from the left side, then divide both sides by -6:

[tex]\implies -6(x^2-12x)=222[/tex]

[tex]\implies \dfrac{-6(x^2-12x)}{-6}=\dfrac{222}{-6}[/tex]

[tex]\implies x^2-12x=-37[/tex]

Add the square of half the coefficient of the term in x to both sides, forming a perfect square trinomial on the left side:

[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2=-37+\left(\dfrac{-12}{2}\right)^2[/tex]

[tex]\implies x^2-12x+\left(-6\right)^2=-37+\left(-6\right)^2[/tex]

[tex]\implies x^2-12x+36=-37+36[/tex]

[tex]\implies x^2-12x+36=-1[/tex]

Factor the perfect square trinomial on the left side:

[tex]\implies (x-6)^2=-1[/tex]

To solve:

[tex]\implies \sqrt{(x-6)^2}=\sqrt{-1}[/tex]

[tex]\implies x-6=\pm i[/tex]

[tex]\implies x-6+6=\pm i+6[/tex]

[tex]\implies x=6 \pm i[/tex]

Therefore, the solutions are:

[tex]x=6+i, \quad x=6-i[/tex]

Answer:

$30.00

Step-by-step explanation:

$25.50 = y(1 - 0.15)

$25.50 = y(0.85)

($25.50) / (0.85) = y

y = $30

Answer:

$30

Step-by-step explanation:

let x = the original price

x - .15x = 25.50  

The original price - .15 of the original price is 25.25

.85x = 25.25  Divide both sides by .85

x = 30

Check:

30 - .15(30) = 25.25

30 - 4.50 = 25.25

25.25 = 25.25

The original price is $623.51.

Let the original price be represented by x.

Since the appliance store decreases the price of a 19-In television set 29%, that means the percentage of the sales price will be:

= 100 - 29

= 71%

Therefore, the original price will be:

= 71% of x = $442.69

0.71x = $442.69

x = $442.69/0.71

x = $623.51

The price is $623.51.

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The day of the month is nominal (option c).

Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable.  A nominal variable is a categorical variable that is qualitative.

A ratio scale is quantitative. A ratio scale is a variable with a true zero. An example is weight. An interval variable is a variable where each value is measured along a scale. An example of an interval variable is credit score.

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Answer:

[tex]m∠1 = 64°[/tex]

[tex]m∠2 = 26°[/tex]

[tex]m∠3 = 36°[/tex]

Step-by-step explanation:

[tex]m∠1→75° + 41° + m∠1 = 180° \\ m∠1 = 180 - 116[/tex]

[tex]m∠1 = 64°[/tex]

[tex]m∠2→64° + m∠2 = 90° \\ m∠2 = 90 - 64[/tex]

[tex]m∠2 = 26°[/tex]

[tex]m∠3→m∠3 + 54° = 90° \\ m∠3 = 90 - 54[/tex]

[tex]m∠ 3 = 36°[/tex]

Answer:

VAT = R239.85

Step-by-step explanation:

VAT = 15%

15/100 = 0.15

R1599 × 0.15 = 239.85

VAT = R239.85

Answer:

The volume of a cube is the edge length cubed (S^3)

To find the edge length when the volume is known find the cubic root of the volume.

Step-by-step explanation:

Edge = ∛1/27

Edge = 1/3 ft.

Answer:

The first option

Step-by-step explanation:

Step-by-step explanation:

3800 is the general amount, but before he can touch it, 800 and 200 are taken away from it for the described purposes.

so, what is left is

3800 - 800 - 200 = 2800

this is then the real amount he can do something with.

The percentage saved if the customer purchases the shirt today will be 18%.

The percentage of the original price which is the sale price will be 82%.

The percent discount offered on the shirt is 18%.

From the information, the men’s dress shirt costs $45, but it is $8.1 off today, the percentage saved if the customer purchases the shirt today will be:

= Amount off / Cost × 100

= 8.1/45 × 100

= 18%

The percentage of the original price that is the sale price will be:

= ($45 - $8.1) / $45 × 100

= 36.9/45 × 100

= 82%

The percent discount offered on the shirt is 18%.

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When the storage unit is 8 ft high, the volume of the storage unit is C. 192ft³

To determine the volume, V,

= Area of the rectangle ABCG + Area of the rectangle CDEF

Area of the rectangle ABCG =2 x 2 = 4 square feet.

Area of the rectangle CDEF = 6 x 3 = 18 square feet.

So, the area of the base ABCDEFG, A = 18+4 = 22 square feet.

The given height, h= 8 feet

Volume = 22 x 8 = 192 cubic feet.

Therefore, it should be noted that when the storage unit is 8 ft high, the volume of the storage unit is 192ft

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The flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.

From the information, it was stated that the recipe for cookies calls for 3 cups of flour for every 4 cups of oatmeal.

Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be:

= 3/4 × 16

= 12

Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.

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The roots of the function  x⁴+ x² = 4 x²  + 4 are ±2 or x = ±i.

A Complex number is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a function as x⁴+ x² = 4 x²  + 4

x⁴+ x² - 4 x²  - 4 = 0

x⁴+ - 3 x²  - 4 = 0

Assume u = x²

x⁴+ - 3 x²  - 4 = 0

Now using the substitution u = x² , then

u² - 3u - 4= 0 ← in standard form

(u - 4)(u + 1) = 0 ← in factored form

Then equate each factor to zero and solve for u

u - 4 = 0 ⇒ u = 4

u + 1 = 0 ⇒ u = - 1

Then convert u back into terms of x

x² = 4 ( take square root of both sides )

x = ± 2

x² = - 1 ( take square root of both sides )

⇒ x = ±i

Thus, The roots of the function  x⁴+ x² = 4 x²  + 4 are ±2 or x = ±i.

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y + 1/4x - 9/4 is an equation of a line passing through the point (-1, 2) that is parallel to the line y = -4x + 5

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that y = -4x + 5

Here -4 is the slope and 5 is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 1/4, x₁ = -1 and y₁ = 2

y - 2 = 1/4(x - (-1))

y - 2 = 1/4(x + 1)

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

y + 1/4x - 9/4

You can use the point-slope form calculator to determine the equation of a line given its slope and a point on the line. You will soon understand what the point-slope form equation is and how it differs from the slope-intercept form equation.

The point-slope formula is expressed as

y - y₁ = m(x - x₁)

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The 120 feet point to point displacement and the 80° angle formed at the vertex A by the control line, AC = AB, Charlie is holding, gives the length of the control line as about 93 feet.

The given parameters are;

The distance (displacement) traveled by the plane = 120 feet (point to point)

The points on the circle, flown by the model plane = C and B

The center of the circle = A

The angle formed by AC and AB = 80°

Required;

The length of the control line.

Solution:

The control line in the description of the diagram is the line AC or AB

Therefore;

AC = AB

Taking the points C and B as the point the plane flew through, we have;

BC = 120 feet

Which gives

‹ABC = ‹ACB = (180° - 80°)/2 = 50°

From the law of sines, we have;

Which gives;

120/(sin(80°)) = AC/(sin(50°))

AC = 120×(sin(50°))/(sin(80°)) ≈ 93

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Answer:

The control line is about 86 feet long.

Hope this helps!

Step-by-step explanation:

Answer: [tex]3^{14}[/tex]

Step-by-step explanation:

[tex]\frac{3^{9} }{3^{-5} }[/tex]

Properties of exponents (negative exponent) says that a term can be moved from the numerator to the denominator and vice versa by flipping the sign.

So,

[tex]\frac{1}{3^{-5} } =3^{5}[/tex]

Properties of exponents (Product Rule) also say that

[tex]a^{x} *a^{y} = a^{x+y}[/tex]

So,

[tex]3^9*3^5=3^{9+5} =3^{14}[/tex]

Another way to solve this is simply using the Properties of exponents (Quotient Rule) which states

[tex]a^{x} /a^{y} =a^{x-y}[/tex]

So,

[tex]\frac{3^{9} }{3^{-5} }=3^{9-(-5)} =3^{14}[/tex]

Answer:

[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]

Step-by-step explanation:

there is a common ratio between consecutive terms, that is

[tex]\frac{24}{96}[/tex] = [tex]\frac{6}{24}[/tex] = [tex]\frac{1}{4}[/tex]

this indicates the sequence is geometric with explicit formula

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 96 and r = [tex]\frac{1}{4}[/tex] , then explicit formula is

[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]

Bank account with an interest rate of r% per year = 2.5%

Simple Interest :

Simple interest paid or received over a certain period is a fixed percentage of the principal amount.

Simple Interest=P×[tex]\frac{r}{100} }[/tex]×T

where:

P=Principal

r= interest rate on a certain period

T= Time

Given :

Principal(P)=  £1000

Time (T)= 1 Year

Find :

the interest rate per year = r%

Now,  

Interest earned on account =  £1025 - £1000

Simple Interest= £ 25

Simple Interest=P×[tex]\frac{r}{100}[/tex]×T

25= 1000×[tex]\frac{r}{100}[/tex]×1

25×100=1000r

2500=1000r

[tex]\frac{2500}{1000} =r\\\frac{25}{10} =r\\\frac{5}{2} =r\\2.5=r[/tex]

r= 2.5%

the interest rate of r% per year. after one year the value of the account=2.5%

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​

Answer:

It's C, a function cannot have an x paired with 2 different y's

Usando la fórmula del valor futuro, se encuentra que el valor acumulado en su cuenta al final de los dos años es de $110,615.

La formula es dada por:

[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]

En que:

En este problema, hay que:

Así:

[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]

[tex]V(24) = 1600\left[\frac{(1 + 0.02625)^{23}}{0.02625}\right][/tex]

V(24) = $110,615.

El valor acumulado en su cuenta al final de los dos años es de $110,615.

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The addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.

Given 3 1/2 + 2 3/4

= 7/2 + 11/4

= (14+11) / 4

= 25/4

= 6 1/4

Given 3 1/2 - 2 3/4

= 7/2 - 11/4

Find the LCM of both denominators

= (14-11) / 4

= 3/4

Therefore, the addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.

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Answer

59,000+1,700=60,000

Step-by-step explanation:

The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value. In the graphically representation we can see the line intersect each other at point (12,6).

Given that,

The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value.

We have to create a graphic representation of this inequality system and choose a potential resolution.

x + y ≤18----->equation(1)

Amount in pennies: 5x+10y≥110------>equation(2)

solves by eq2 - 5×eq(1)

5x+10y - 5(x+y) = 120 - 5×18

5x + 10y -5x-5y  = 120 - 90

5y = 30

y=6

Then x=12

Therefore, x=12, y=6 is the point where two lines converge.

In the graphically representation we can see the equation (1) line and equation (2) line intersect each other at point (12,6).

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Using the given information, the value of the variable x is equal to -0.125.

The given question can easily be solved using the constraints given in the question. It is given that B is between A and C. Also, the given question is in the form of Linear equation in one variable. Linear equation in one variable is the one which is of the form ax+b=0 where a and b are real numbers and x is the variable.

So, this implies that AB+BC=AC

Also, AB=4x-7 and BC=20x-5 and it is given that AB=BC

Thus, this implies that:

AB=BC

4x-7=20x-5

Taking 20x from Right hand side to Left hand side and -7 from Left hand side to Right hand side.

4x-20x=-5+7

-16x=2

x=-2/16

=>x=-1/8

=>x=-0.125

Thus, the value of x is equal to -0.125.

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The equation of the CD in slope-intercept form is: C. y = -4x + 2.

The equation of a line in slope-intercept form can be written as y = mx + b. In this form, m represents the slope and b represents the y-intercept.

The slopes of lines that are parallel are equal, while the slopes of the lines that are perpendicular to each other are negative reciprocals of each other.

The slope (m) of the graph y = 1/4x - 3 is 1/4. Since AB of rectangle ABCD is perpendicular to the graph, then the slope (m) of AB would be the negative reciprocal of 1/4 which is: -4.

Also, since CD is parallel to AB, they would have the same slope, m = -4.

To find the equation of CD that is parallel to AB, substitute m = -4 and (a, b) = (-1, 6) into y - b = m(x - a):

y - 6 = -4(x - (-1))

y - 6 = -4(x + 1)

y - 6 = -4x - 4

y = -4x - 4 + 6

y = -4x + 2

Therefore, the equation of the CD in slope-intercept form is: C. y = -4x + 2.

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