Which expression is equivalent to: (x^1/4 y^16)^1/2 ?

A. X^1/2 Y^4
B. X^1/8 Y^8
C. X^1/4 Y^8
D. X^1/4 Y^4

Answer:

D

Step-by-step explanation:

Lets look at the numbers

sqrt(4) = 2  which is a rational number

sqrt(5)   cannot be simplified, it is an irrational number

-6/5  a ratio of integers, which is the definition of a rational number, so it is a rational number

3.5 = 35/10  a ratio of integers, which is the definition of a rational number, so it is a rational number

.555555 = 5/9   a ratio of integers, which is the definition of a rational number, so it is a rational number

Rational numbers:  sqrt(4), -6/5, 3.5  , .5555(repeating)

Irrational numbers: sqrt(5)

Answer: D

Step-by-step explanation:

Answer:

Cathy has read 3/6 or 1/2 of her book.

Step-by-step explanation:

1/6+2/6=3/6 or 1/2

Answer:

$33 336

Step-by-step explanation:

Increase = 30 000 × 0.112

Increase = $3336

New salary = 30 000 + 3336

New salary = $33 336

Answer:

Pitcher 1/3 gallon = 4/12 gallon

Jug 3/4 = 9/12 gallon

So, it will take 2 pitchers plus 1/12 of a gallon to fill the jug.

Step-by-step explanation:

The formula of a slope m:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (0, -1) and (5, -2). Substitute:

[tex]m=\dfrac{-2-(-1)}{5-0}=\dfrac{-2+1}{5}=-\dfrac{1}{5}[/tex]

Answer:

Option A is correct

[tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]

Step-by-step explanation:

Given that:

70% of x.

⇒[tex]\frac{70}{100} \times x[/tex]

⇒[tex]\frac{7x}{10}[/tex]

Option A:

[tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]

⇒[tex]\frac{3x}{4}-\frac{x}{20}[/tex]

⇒[tex]\frac{60x-4x}{80}[/tex]

⇒[tex]\frac{56x}{80}[/tex]

Simplify:

⇒[tex]\frac{7x}{10}[/tex]

Option B:

[tex]3(\frac{x}{4})-(\frac{x}{10})[/tex]

⇒[tex]\frac{3x}{4}-\frac{x}{10}[/tex]

⇒[tex]\frac{30x-4x}{40}[/tex]

⇒[tex]\frac{26x}{40}[/tex]

Simplify:

⇒[tex]\frac{13x}{20}[/tex]

Option C:

[tex](\frac{x}{2})+(\frac{x}{10})[/tex]

⇒[tex]\frac{6x}{10}[/tex]

Simplify:

⇒[tex]\frac{3x}{5}[/tex]

Option D:

[tex](\frac{x}{2})+\frac{1}{2}(\frac{x}{4})[/tex]

⇒[tex]\frac{x}{2}+\frac{x}{8}[/tex]

⇒[tex]\frac{5x}{8}[/tex]

Therefore, only option which is equivalent to 70% of x is, Option A i.e  [tex]3(\frac{x}{4})-\frac{1}{2}(\frac{x}{10})[/tex]

Answer:

a

Step-by-step explanation:

Answer:

D. log (x-2)

Step-by-step explanation:

We can see that in the graph of the function g(x), the graph is shifted toward the right.

We know that, to shift a graph to the right, we subtract that number of units inside the function.

For example if we are plotting a graph of F(x) and if we have to shift the function to the right by 2 units, we can write it as, [tex]F(x-2)[/tex].

Similarly, here the graph of log (x) is shifted 2 units to the right so we can write the function as,

[tex]log (x-2)[/tex] (we subtract inside the function).

Answer:

D. [tex]log(x-2)[/tex]

Step-by-step explanation:

We have been given function's [tex]f(x)=log(x)[/tex] graph and graph of function g(x). We are asked to choose the correct function formula for g(x).

We can see that our parent function f(x) is translated to right to get function g(x).  

The rule for translating a function to right by k units is:      

[tex]f(x)\rightarrow f(x-k)[/tex]

We can see that our parent function is shifted 2 units to right as our parent function crosses x-axis at x equals 1, while our new function crosses x-axis at x equals 3. So our new function g(x) will be:

[tex]g(x)=log(x-2)[/tex]

Therefore, the expression [tex]log(x-2)[/tex] is equal to g(x) and option D is the correct choice.

Answer:

[tex]2.6334 \cdot 10^{-5}[/tex]

Step-by-step explanation:

[tex](46.2 \cdot 10^{-1})(5.7 \cdot 10^{-6})[/tex]

To multiply it , first we multiply the numbers.

46.2  times 5.7 is 263.34

Now we multiply the exponents. To multiply exponents we apply exponential property.

[tex]a^m \cdot a^n= a^{m+n}[/tex]

When the exponents with same base are in multiplication then we add the exponents

[tex]10^{-1} \cdot 10^{-6}=10^{-7}[/tex]

[tex](46.2 \cdot 10^{-1})(5.7 \cdot 10^{-6})[/tex]

[tex]263.34 \cdot 10^{-7}[/tex]

Now we write it in scientific notation. Move the decimal point after the first number. So we move decimal point 2 places to the left

[tex]2.6334 \cdot 10^2 \cdot 10^{-7}[/tex]

[tex]2.6334 \cdot 10^{-5}[/tex]

Answer:

BC < ED ⇒ answer A

Step-by-step explanation:

* Lets revise some facts in the triangle

- If one side of a triangle is longer than another side, then the angle

 opposite the longer side will be larger than the angle opposite the

 shorter side

- If one angle in a triangle is larger than another angle in a triangle,

 then the side opposite the larger angle will be longer than the side

 opposite the smaller angle

* Lets solve the problem

- In the two triangles BCD and DEB

∵ CD = 8 and BE = 8

∴ CD = BE

∵ Side BD is a common side in the two triangles

- The third side in Δ BCD is BC and the third side in DEB is DE

∵ BC is the opposite side to the angle of measure 24°

∵ ED is the opposite side to the angle of measure 30°

∵ The measure 24° < the measure 30°

∴ The side opposite to the angle of measure 24° < the side opposite

   to the angle of measure 30°

∵ The other two sides of the 2 triangles BCD and DEB are equal

∴ We can compare between the 3rd sides in the Δ BCD and Δ DEB

∴ BC < ED

Answer:

A) X = -5,  Y = 1

B) X = -2, Y = 4

C) X = -5 , Y = 4  

Step-by-step explanation:

The reflection over an x-axis means the values associated with the x remains same while y-axis variable change their sign.  

The three co-ordinates of this figure are  

A) X = -5,  Y = -1

B) X = -2, Y = -4

C) X = -5 , Y = -4  

Now going by the above rule to determine the co-ordinates when the image is reflected over x-axis, the new co-ordinates are:

A) X = -5,  Y = 1

B) X = -2, Y = 4

C) X = -5 , Y = 4  

Step-by-step explanation:

Please find the attachment.  

We have been given an image on coordinate plane and we are asked to reflect our given image over the x-axis.

The rule for reflection for an image over x axis is: [tex](x,y)\rightarrow(x,-y)[/tex]. This means that after reflection about x axis, x coordinates remain same but y-coordinates are transformed into their opposite sign.

Let us give names to vertices of our pre-image. A(-5,-1), B(-5,-4) and C(-2,-4).

When we will reflect our pre-image (ABC) about x-axis, x coordinates will remain same, so x coordinates will remain negative.

Since y-coordinates will change into their opposite sign, so coordinates of y will be positive for our image as y-coordinates of pre-image are negative.

A                    A'

(-5,-1)            (-5,1)

B                    B'

(-5,-4)           (-5,4)

C                    C'

(-2,-4)            (-2,4)  

Therefore, coordinates of our image A'B'C' will be: A'(-5,1), B'(-5,4) and C'(-2,4).

Answer:

144

Step-by-step explanation:

36 ÷ 1/4

We will use copy dot flip

36 * 4

144

The next term is double the previous term, so that the [tex]n[/tex]-th term is given recursively by

[tex]\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}[/tex]

This rule tells us that

[tex]a_2=2a_1[/tex]

[tex]a_3=2a_2=2^2a_1[/tex]

[tex]a_4=2a_3=2^3a_1[/tex]

and so on, with the explicit rule

[tex]a_n=2^{n-1}a_1=2^{n-1}[/tex]

for [tex]n\ge1[/tex].

If 512 is the [tex]k[/tex]-th term in the sequence, then

[tex]512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10[/tex]

Final answer:

In the geometric progression 1, 2, 4, ..., the 9th term is 512, determined by the formula for the nth term of a geometric progression.

Explanation:

The question asks us to find the term in a geometric progression where the value is 512. A geometric progression (GP) is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the ratio. In the given geometric progression 1, 2, 4, ..., each term is obtained by multiplying the previous term by 2. To find which term is 512, we can use the formula for the nth term of a GP, which is a_n = a_1 × r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

Since a_1 is 1 and r is 2, we have: 512 = 1 × 2^(n-1). Simplifying this gives us 2^9 = 512, which means the 9th term of the sequence is 512. Therefore, 512 is the 9th term in the given geometrical progression.

The distance between points PQ is [tex]2\sqrt{10}[/tex].

The midpoint of PQ is [tex]( 4, 3)[/tex].

Given that,

The points are P(7, 4) and Q(1, 2).

We have to determine,

The distance between the points and,

The midpoint of PQ.

According to the question,

To calculate the distance between two points by using distance formula;

[tex]Distance \ formula = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }[/tex]

Where,  [tex]x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2[/tex]

Substitute the values in the formula;

[tex]PQ = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }\\\\PQ = \sqrt{(1-7)^2 + (2-4)^2 }\\\\PQ = \sqrt{(-6)^2 + (-2)^2 }\\\\PQ = \sqrt{36+ 4 }\\\\PQ = \sqrt{40}\\\\PQ = 2\sqrt{10}[/tex]

And, The midpoint of PQ calculated by using formula;

[tex]Midpoint \ of \ PQ = (\dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2} )[/tex]

Where,  [tex]x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2[/tex]

Substitute the values in the formula;

[tex]Midpoint \ of \ PQ = (\dfrac{7+1}{2} ,\dfrac{4+2}{2} )\\\\Midpoint \ of \ PQ = (\dfrac{8}{2} ,\dfrac{6}{2} )\\\\Midpoint \ of \ PQ = (4,3)[/tex]

Hence, The distance between points PQ is [tex]2\sqrt{10}[/tex].

The midpoint of PQ is [tex]( 4, 3)[/tex].

To know more about Distance Formula click the link given below.

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Answer:

4.5%

Step-by-step explanation:

Find interest rate by using the formula I=P⋅i⋅t, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

I = $720, P = $2000 and t = 8 years, so

I = P*i*t

i = I/P*t

i = 720 / 2000 * 8

i = 0.045 = 4.5% per year

The interest rate, calculated with the simple interest formula, for an investment of $2000 that grows to $2720 over 8 years is 4.5%.

The subject is about determining the interest rate for an investment in a simple interest account. The formula for calculating simple interest is: Interest = Principal x Rate x Time (I = PRT). In this case, the principal (P) is $2000, the time (T) is 8 years, and the interest (I) earned is the difference between the final balance and the initial deposit, which is $2720 - $2000 = $720.

To find the rate (R), we rearrange the formula to: R = I / (P x T). Plugging in the numbers, we get: R = $720 / ($2000 x 8) = 0.045, or 4.5% when expressed as a percentage.

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Question:

what are your choices?

Answer:

He translated them the wrong way.

It should of gone up 2 and right 2 not down 2 and left 2.

The correct coordinates would be (A' = 3,0) (B' = 3, -3) (C' = 2, -2)

Please mark brainliest would rly help.

Step-by-step explanation:

Answer:

60 child tickets were sold

Step-by-step explanation:

Let no of children tickets sold that day be c and adult tickets be a

Then since total number of tickets sold is 148, we have

c+a = 148  ... i

Also given that admission fee is 6.00 for children and 9.70 for adults

So for c children tickets sold value= 6c and for adults it is 9.7a

total revenue = 6c+9.7a=1213.60 ... ii

We got two equations in two variables c and a

Let us solve this

a =148-c. substitute this in ii

6c+9.7(148-c) = 1213.60

Simplify the above to have

222 = 3.7c

Or c = 60

No of child tickets sold = 60

The width of the rectangle is 5.55 ft and the length is 19.425 ft. The perimeter of the rectangle is 25.95 ft and the area is 107.95875 sq ft.

To find the width of the rectangle, we can set up the equation

5/2 = 13.875 / width

Solving for width gives us width = 5.55 ft. Therefore, the length of the rectangle is 13.875 + 5.55 = 19.425 ft.

The perimeter of a rectangle is given by the formula 2(length + width). Substituting the given values, we get the perimeter to be 2(19.425 + 5.55) = 25.95 ft.

The area of the rectangle is given by the formula length * width. Substituting the given values, we get the area to be 19.425 * 5.55 = 107.95875 square feet.

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Answer: 585.15

Step-by-step explanation:

Subtract 20 from 169

Once you do so you should get 149%

figure out what $235 + 149% is then you should get five hundred eighty five dollars and fifteen cents ($585.15)

Answer:

Probability of rolling an even number then rolling an odd number = 1/4

Step-by-step explanation:

When we roll a fair six-sided die twice,

The pair of combinations are

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(5,1),(6,2),(6,3),(6,4),(6,5),(6,6)

There are 36 possibilities

The odd numbers are 1,3 and 5

even numbers are 2,4 and 6

Possibilities of rolling an even number then rolling an odd number

(2,1),(2,3),(25)

(4,1),(4,3),(4,5)

(6,1),(6,3),(6,5)

There are 9 possibilities

Probability of rolling an even number then rolling an odd number = 9/36 = 1/4

Answer:

To save 6 months' worth in a fund would be $2858.59.

Step-by-step explanation:

At a wage of $13.70 per hour for a 40 hour work week, your gross pay (not including any taxes or deductions) is $548 per week, or $2192 per month.  Deductions and taxes are 7.65% + 11.55% + 8.35%, for a total of 27.55% that comes out of your gross pay.  $2192 multiplied by 27.55%, or .2755, is $603.90, therefore, in order to find your realized income per month, you must subtract your gross pay by the amount of deductions and tax withholdings:  $2192 - $603.90 = 1588.10.  Another 30% of your realized income is for housing and fixed expenses, or $1588.10 multiplied by 30%, or 0.30, which comes to $476.43.  If you want to save 6 months' of expenses in an emergency fund, simply take your monthly expenses, $476.43, and multiply by 6 = $2,858.59.  

The correct answer is option d. $2,858.59

1. Monthly gross income should be calculated using the exact number of days in the month, which can vary. However, since we are given 4 weeks per month, we will continue with that assumption.

2. The tax rates are percentages, so we need to convert them to decimals for calculation:

Total tax rate = 0.0765 + 0.1155 + 0.0835 = 0.2755.

3. The realized income after taxes should be calculated as follows:

Realized income after taxes = [tex]\$2,192 \times (1 - 0.2755) = \$2,192 \times 0.7245 = \$1,588.53.[/tex]

4. The monthly housing and fixed expenses are correct at $476.56.

5. The emergency fund calculation is also correct:

Emergency fund = [tex]6 \times \$476.56 = \$2,859.36.[/tex]

Upon re-evaluation, the correct calculation for the emergency fund is $2,859.36, which should be rounded down to $2,858. However, the options provided suggest that the correct answer is $3,277.17. This indicates that there may be an error in the provided options or in the interpretation of the question.

Given the calculations above, none of the provided options match the calculated emergency fund. The closest option is d) $2,858.59.

Answer:

Toner = $45.00; ink = $25.50

Step-by-step explanation:

Let T = the cost of a toner cartridge and I = the cost of an ink cartridge

We have two conditions:

(1)                      T = I + 19.50

(2)           4T + 11I = 460.50     Substitute (1) into (2)

4(I + 19.50) + 11I = 460.50     Remove parentheses

 4I + 78.00 + 11I = 460.50     Combine like terms

      15 I + 78.00 = 460.50     Subtract 78.00 from each side

                    15I = 382.50      Divide each side by 15

(3)                  I = 25.50

=====

Substitute (3) into (1)

T = 25.50 + 19.50

T = 45.00

=====

Check:

(1)                         45.00 = 25.50 + 19.50

                           45.00 = 45.00

(2) 4×45.00 + 11×25.50 = 460.50

         180.00 + 280.50 = 460.50

                        460.50 = 460.50

Answer:

slope = 0

Step-by-step explanation:

To find the slope when you have 2 points, we use the formula

m = (y2-y1)/(x2-x1)

m = (-5--5)/(18--2)

   = (-5+5)/(18+2)

   = 0/20

The slope is zero

This a horizontal line, because the y values do not change

The correct answers are:

Box-1: [tex]\frac{3\thinspace ft}{1\thinspace yd}[/tex]

Box-2: [tex]\frac{12\thinspace \thinspace in}{1\thinspace ft}[/tex]

Box-3: [tex]\frac{1\thinspace stud}{15\thinspace in}[/tex]

Box-4: 42 studs

Explanation:

Given:

Wall is 17.5 yds long.

In 1 yard, there are 3 feet.

Therefore,

[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}[/tex]

In Box-1, you should put [tex]\frac{3\thinspace ft}{1\thinspace yd}[/tex].

In 1 foot, there are 12 inches.

Therefore,

[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}[/tex]

In Box-2, you should put [tex]\frac{12\thinspace \thinspace in}{1\thinspace ft}[/tex].

He needs to place 1 stud every 15 inches.

Therefore,

[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}*\frac{1\thinspace stud}{15\thinspace in}[/tex]

In Box-3, you should put [tex]\frac{1\thinspace stud}{15\thinspace in}[/tex].

Now multiple all the numbers, you will get the number of studs.

[tex]\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}*\frac{1\thinspace stud}{15\thinspace in} = 42\thinspace studs[/tex]

In Box-4, write 42 studs.

-i

To calculate the number of additional studs needed, convert the length of the wall to inches and divide by the interval between each stud. Subtract 1 from the total number of intervals to find the number of additional studs needed.

To determine the number of additional studs needed, we need to calculate the number of intervals between studs. First, we need to convert the length of the wall to inches, which is 17.5 yds * 3 ft/yd * 12 in/ft = 630 inches. Next, we divide the length of the wall by the interval between each stud, 630 inches / 15 inches = 42 intervals. Since the first stud has already been placed, we subtract 1 from the total number of intervals to find the number of additional studs needed: 42 - 1 = 41 additional studs.

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Answer:

4a - 3

Step-by-step explanation:

"four times a" = 4 * a = 4a

"3 less than" = -3

Combine the terms: 4a - 3

~

ANSWER: SSS, SAS, ASA, AAS, or HL

EXPLANATION:

SAS: Three congruent sides on both triangles.

SAS: Two congruent sides and a congruent included angle on both triangles.

ASA: Two congruent angles and a congruent included side on both triangles.

AAS: Two congruent angles and a congruent side on both triangles.

HL: Two right triangles with one congruent leg and congruent hypotenuses.

Hey there!

Answer: 6*Q= 6Q or 6*Q= y

Step-by-step explanation:

The product is the answer to a multiplication problem, therefore 6*Q will be the first part.

The second part will be the answer. Normally, this would be represented just by 6Q, but you can use another letter to represent it. We'll use y for an example.

6*Q= 6Q

or

6*Q= y

Step-by-step explanation:

ANSWER: 6*q