Use properties of exponents to write an equivalent expression. Write the correct exponent for each box.
(6 to the 7th power over 6 to the 5th power)

Step-by-step explanation:

a || b means that a is parallel with b.

a ≅ b means a is congruent with b. that mags that if you orient a and b alike and then put them on top of each other, there is nothing that stands out. they perfectly cover each other.

for angles alone this simply means they have the same size.

A true.

when a line (like in this case r) intersects parallel lines (like in this case p and q), then the angles at the intersections must be the same for p and q.

after all, parallel means that both lines emulate each other's behavior exactly - except for the physical location itself.

B in general is not true. it would only be true, if also r || s.

C true. for the same reasons as A.

D true. for the same reasons as A.

Answer:

150x8=1,200 so that much more

Step-by-step explanation:

Darryl will need to save an additional $187.50 per month for the next 8 months in order to accomplish his original goal of saving $150 per month for 18 months.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a quantity.

Expressions can be simple or complex, and they can be used to perform mathematical operations, make comparisons, or evaluate functions.

An expression can contain any combination of numbers, variables, and operators, such as addition, subtraction, multiplication, division, and exponentiation.

For example, 3 + 5, 2x - 7, and (4a + 2b) / (3c - d) are all examples of expressions.

We have,

Darryl intended to save $150 a month for 18 months, which would have given him a total savings of:

$150/month x 18 months

= $2,700

However, after 10 months, he has only managed to save $1,200.

This means he fell short of his goal by:

$2,700 - $1,200

= $1,500

To accomplish his original goal, he will need to save an additional $1,500. Since he has 8 months left to save, he will need to save:

$1,500 / 8 months

= $187.50 per month

Therefore,

Darryl will need to save an additional $187.50 per month for the next 8 months in order to accomplish his original goal of saving $150 per month for 18 months.

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Answer:

27(-⁴)

³

= 3³(-⁴/³)

= 3(-⁴)

= 1

81

Answer:

there is a 5 by 5 square

Step-by-step explanation:

Answer:

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equalStep-by-step explanation:

Answer:

1

5

3

in order

Step-by-step explanation:

First, note that the degree of a polynomial is the value of the highest exponent in the polynomial

There will be as many solutions as there are degrees

1.  - 6x − 9y = 2 has degree 1 since x == x¹ so 1 solution

2. [tex]2x^5-x^4+2x^3-6x^2+2x\:+\:4=0[/tex] has degree 5 so 5 solutions

3. [tex]-4x^3 - 10x^2+7x+5[/tex] has degree 3 so 3 solutions

Answer:

It would be A

Step-by-step explanation:

The correct way to find the sum p+q, where p is positive and q is negative, is to start from the point representing p on the number line and move to the left by the magnitude of q.

Let's place the positive number p on the number line, starting from the origin (0) and moving to the right by p units. Now, let's place the negative number q on the number line by moving q units to the left from the origin.

To find the sum p+q, we need to consider the relative positions of p and q. Since p is positive, we have moved to the right on the number line. However, since q is negative, it is also positioned to the left of the origin. To add p and q, we need to consider their magnitudes and the direction they point in.

The correct way to find the sum p+q is to start from the point representing p and then move to the left by the magnitude of q. This corresponds to moving p units to the right and then q units to the left. The endpoint of this combined movement represents the sum p+q on the number line.

Hence the correct option is (a).

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Answer:

14 girls divided by their percentage 0.4 the result will be

35 students

The extra calories that you are consuming per year is 182,500 calories.

The number of miles that you should walk to burn the extra calories is 1,825 miles.

You are consuming 20 oz of Dr. Pepper each meal. You take Dr. Pepper twice in a day. To determine the total extra calories that is being consumed, multiply the calories consumed per month by the number of times in a day you consume Dr. Pepper and by the number of days in a week.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

Extra calories consumed in a year = calories per meal x 2 x number of days in a year

250 x 2 x 365 = 182,500 calories

In order to determine the number of miles you have to walk to lose the extra calories, divide the extra calories by the calories lost per mile

Number of miles to walk = 182,500 / 100 = 1825 miles

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Answer:

The system consists

Step-by-step explanation:

The amount he put into the first account at 2% interest will be $8,000 and into the second account at 7% interest will be $42,000.

Given that,

Amount invested by Alex = $50,000,

Total interest earned = 6.2%,

Now,

Let,

Amount invested at 2% = x,

So,

Amount invested at 7% = (50,000 - x),

So,

According to the question,

7%(50000 - x) + 2%(x) = 6.2% * 50,000

we get,

0.07(50000 - x) + 0.02(x) = 0.062 * 50,000

3500 - 0.07x + 0.02x = 3100

3500 - 0.05x = 3100

We  get,

0.05x = 3500 - 3100

0.05x = 400

x = 8000,

So,

Amount invested at 2% = $8000,

So,

Amount invested at 7% = (50,000 - 8000) = $42,000,

Hence we can say that the amount he put into the first account at 2% interest will be $8,000 and into the second account at 7% interest will be $42,000.

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The correct answer will be option b

let x= 5.764764               (1)

multiply both the sides by 1000

1000x = 5764.764              (2)

now substract equation one from equation (2)

999x =  5764

x = 5764/999  

In mathematics, a rational number is a number that can be expressed as the quotient or fraction

p

/

q

of two integers, a numerator p and a non-zero denominator q.[1] For example,

−3

/

7

is a rational number, as is every integer (e.g. 5 =

5

/

1

). The set of all rational numbers, also referred to as "the rationals",[2]

A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example:

3

/

4

= 0.75), or eventually begins to repeat the same finite sequence of digits over and over (example:

9

/

44

= 0.20454545...).[6] This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones

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Solve for [tex]t[/tex] when [tex]h=0[/tex], given [tex]v_0=0[/tex] and [tex]h_0 = 4[/tex].

[tex]0 = -16t^2 + 4 \implies 16t^2 = 4 \implies t^2 = \dfrac14 \implies t = \dfrac12[/tex]

so it will take half a second for the ball to hit the ground.

Answer:4

Step-by-step explanation:

dilation

In a plane, a transformation in which each point on the image lies on the same line as the corresponding point on the preimage and a fixed point called the center of dilation; the ratio between the distance from the center of dilation to a point on the image and the distance from the center of dilation to the corresponding point on the preimage remains constant.

Answer:

  (c)  -19 + x = -21

Step-by-step explanation:

You want the mathematical expression equivalent to the English sentence "a number added to -19 is -21."

Addition is written using the math plus symbol (+).

The English word "is" usually signifies sameness or equality, expressed using the math equal sign (=).

The variable x is often used to represent "a number."

When a number is added to -19, we start with -19, then, using the plus symbol, we add x:

  "a number added to -19"   ⇒   -19 + x

  "is"   ⇒   =

   "-21"   ⇒   -21

So, the translated description is ...

  -19 + x = -21

Simplification - The process of making something less complicated and therefore easier to do or understand, or the thing that results from this process .

What is the simplification rule?

The general rule to simplify expressions is PEMDAS - stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Replace Question mark .

1.) 1/2 = 1× x / 2 ×10

     1/2 = x / 20

     x = 20 / 2

      x = 10.

2.) 3/4 = 3 x 5 / 4× x

     3/4 = 15 / 4x

     12x = 60

x = 60 / 12

x = 5

3.) 7/8 = 7× 3 / x × 3

     7/8 = 21 / 3x

      21x = 21 × 8

        x = 8

4.) 2/3 = x×4 / 3  × 4

2/3 = 4x / 12

12x = 24

x =2 .

5.) 6/12 = (6/6) / (12/x)

1/2 = 1 / (12/x)

1/2 = x/12

2x = 12

x = 6.

6.) 3 / 15 = (3 /x) /(15 / 3)

3/15 = (3/x) / 5

3/15 = 3/5x

15x = 15× 3

x =3.

7.) 175/250 = (x/25) / (250/25)

taking LHS

175/250 = 7/ 10

Solve RHS

(x/25) / (250/25)

(x/25) / (10) = x/250

x/250 = 7/10

x = 175.

8.) 28 /56 = (28/28) / (x/28)

28/56 = 1/ (x/28)

28 / 56 = 28 /x

x =56 .

9.) 14/16 =(14/x) / (x/2)

14/16 = 14/x × 2/x

14 /16 = 28  /x²

1 /16 = 2/ x²

x² =32 .

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The value of the account is $47226.73.

The compound interest formula is equal to  

A = P( 1 + r/n )^{nt}

where  A is the Final Investment Value, P is the Principal amount of money that is to be invested, r is the rate of interest, t is the Number of Time Periods, and n is the number of times interest is compounded per year.

Now, we have:

t = 21 years

Principal amount, P = $9000

Rate, r = 8% = 0.08 and

n = 12 as a year has 12 months.

Substituting these values in the formula,

[tex]A = P( 1 + \frac{r}{n} )^{nt}[/tex]

A = 9000 × ( 1 + 0.08/12)²⁵²

A = 9000 × ( 1 + 0.0066)²⁵²

A = 9000 × ( 1.0066)²⁵²

A = 9000 × 5.247

A = 47226.73

The value of the account will be $47226.73.

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Answer:$195.70

Step-by-step explanation:

Starting price is : $248.50

Price with 25% off :

$248.50 x ( 1 - 0.25 ) = $248.50 x 0.75 = $186.375

After that she has to pay 5 % sales tax:

$186.375  x 1.05 = $195.70

Answer:

The total cost of the items is $195.70.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 5 and that it passes through (-1 , 2)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-1)}) \implies y -2= 5 (x +1) \\\\\\ y-2=5x+5\implies {\LARGE \begin{array}{llll} y=5x+7 \end{array}}[/tex]

Answer:

Step-by-step explanation:

each side of square=10/4=2.5

because all the vertices are in quarter |||

so all the coordinates are negative.

x coordinate=-0.5-2.5=-3

y coordinate=-2-2.5=-4.5

all the coordinates are (-3,-2) ,(-0.5,-2)

and (-3,-4.5),(-0.5,-4.5)

Answer:

3 miles

Step-by-step explanation:

Cost of 20 yards of ribbon is $13.32.

Given,

The cost of 6 ½ yards of ribbon = $9.75

We have to find the cost of 20 yards of ribbon.

First of all we have to find the cost of 1 yard of ribbon:

Cost of 1 yard of ribbon = ( 6 ½ yards of ribbon) / (cost of 6 ½ yards of ribbon)

Cost of 1 yard of ribbon = 6 ½ / 9.75 = 6.5 / 9.75 = 0.66666

That is cost of 1 yard of ribbon is $0.666 approximately.

Now, we have to find the cost of 20 yards of ribbon:

Cost of 20 yards of ribbon = (cost of 1 yard of ribbon) x 20

Cost of 20 yards of ribbon = 0.666 x 20 = 13.32

That is cost of 20 yards of ribbon is $13.32.

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The value of x from the triangle is 12

Given the sides as;

Using the Pythagorean theorem

Hypotenuse square = opposite square + adjacent square

Substitute the value, we have;

15² = x ² + 9²²

Find the squares

225= x² + 81

collect like terms

225 - 81 = x²

144 = x²

Take the square root of both sides

x √144

x = 12

Thus, the value of x from the triangle is 12

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In the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.

We are given that Zachery has to write a total of 95,234 words.

Total words to be written = 95,234 words.

Words already written in the first month = 35,295 words.

Words already written in the second month = 19,240 words.

Words written in total = 35,295 words + 19,240 words.

= 54,535 words

Words left for writing = 95,234 words - 54,535 words

= 39,699 words

months left = 4

Average Words written in remaining month = 39,699 words / 4

= 9924.75 words.

= 10,000 words.

Therefore, in the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.

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After the evaluation of the given expression n² + 4, the correct option is (3) 85, 68, and 40.

So, n² + 4:

Therefore, after the evaluation of the given expression, the correct option is (3) 85, 68, and 40.

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The final endpoint values are: (12,-6)

The midway point of a line or segment is referred to as the midpoint. It creates an evenly spaced division in the line. In essence, it divides the lines into two.

According to the question, the coordinates of a line LN is given as:  N (-8,2) and Midpoint M M(2,-4).

To calculate the midpoint, use the standard midpoint formula which is represented as below:

Midpoint =[tex]\frac{x1 + x2 }{2}[/tex] and [tex]\frac{y1 + y2 }{2}[/tex]

From the given data, the values are:

X1 = -8; Y1 = 2; X = 2; Y = -4

Therefore, the calculated midpoint is:

2 = -8 + [tex]\frac{x2}{2}[/tex] = 12

4 = 2 + [tex]\frac{y2}{2}[/tex] = -6

Hence, the final endpoint values are (12,-6)

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The function written in vertex form is

[tex]g(x) =4x^2+88x =4(x+ 11)^2 - 484[/tex]

This is further explained below.

Generally, the equation for the function is  mathematically given as

g(x) = 4x2 + 88x

Therefore,

g(x) = a(x +11)2 + k

[tex](x +11)x^{2} as\ x^2 + 22x +121[/tex]

[tex]g(x) = a(x^2 +22x +121) + k\\\\g(x) = ax^2+ 22ax +121a + k[/tex]

Equate eq(a) with eq(b) We obtain,

[tex]4x^2 + 88x = ax^2 + 22ax +121a + k[/tex]

Examine the x coefficients on both sides of the equation.

a=4 and 22a= 88 ; 121a + k = 0

121(4) = -k

k = -484

[tex]g(x) =4x^2+88x =4(x+ 11)^2 - 484[/tex]

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CQ

Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = ___ (x +11)² +____.

Answer:

Jade Howey

Step-by-step explanation:

Answer:

Maria

Step-by-step explanation:

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