simplify 5 x 5^2 in index form

Answer:

G

Step-by-step explanation:

let his fixed price be x and his hourly fee be y;

270 = 4y + x

420 = 7y + x

x is common in both equations

equate the two;

x = 270-4y and x = 420-7y

270-4y = 420-7y

3y = 150

y = 50

x = 270-4*50

x = 70

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

Answer:

The correct option is;

B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t

Step-by-step explanation:

The given parameters are;

The number of T-shirts, t, and shorts, s, Tim must design a day = 12

The maximum number of T-shirts and shorts Tim can design a day = 30

The maximum number of hours Tim can work = 18 hours

Therefore, we have;

The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs

Which gives;

s ≥ 12 - t

Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs

Which gives;

s ≤ 30 - t

The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24

The fraction of 36 minutes in 45 minutes = 36/45 = 0.667

Therefore we have;

The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts

Which gives;

s ≤ 24 - 0.66·t

The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.

Answer:

B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0

Step-by-step explanation:

Hope this helps!!

Answer:

I hope this helps!

Answer D

Step-by-step explanation:

Step-by-step explanation:

salary per day =$140

bonus on sales =14%

sales on Saturday =$600

bonus on Saturday sales=14/100*$600

=$84

sales on Sunday =$1200

bonus on Sunday sales=14/100*$1200

=$168

total amount she earned over the two days=$140+$84+$168

=$532

Answer:

m = -9

Step-by-step explanation:

2m-10=44+8m

Subtract 2m from each side

2m-2m-10=44+8m-2m

-10 = 44+6m

Subtract 44 from each side

-10-44 = 44-44+6m

-54 = 6m

Divide by 6

-54/6 = 6m/6

-9 = m

Answer:

solve by solving the salvation for equation don't be a slave get educated from what's gave

Answer: x = 3

Step-by-step explanation:

Sqrt(x+7) - 1  = x

Sqrt(x+7) = x + 1

x+7 = x^2 + 1

x = x^2 - 6

x=3

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

Answer: Brian invested $16000 in Fund B .

Step-by-step explanation:

Let x be the amount Brian invested in Fund B.

Given, The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit.

i.e. profit on Fund A = 4% of 8000 = 0.04 ×8000 = $320

Profit on Fund B = 1% of x = 0.01x

Together they earn 1% profit, i.e. Combined profit = 2% of (8000+x)

= 0.02(8000+x)

As per question,

Combined profit=Profit on Fund A+Profit on Fund B

[tex]\Rightarrow\ 0.02(8000+x) =320+0.01x\\\\\Rightarrow\ 0.02(8000) +0.02x=320+0.01x\\\\\Rightarrow\ 160+0.02x=320+0.01x\\\\\Rightarrow\ 0.02x-0.01x=320-160\\\\\Rightarrow\ 0.01x=160\\\\\Rightarrow\ x=\dfrac{160}{0.01}\\\\\Rightarrow\ x=16000[/tex]

Hence, Brian invested $16000 in Fund B .

Answer:

Option B.

Step-by-step explanation:

Consider the correct question is "Which statement correctly compares

1. -201  and  151

-201 = 151

-201 < 51

-201 > 151"

The given numbers are -201 and 151. We need to compare these numbers.

We know that all negative numbers are less than positive numbers.

So,

-201 < 151

If both numbers are negative, then the larger negative number is the smaller number.

Therefore, the correct option is B.

Answer:

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours

Step-by-step explanation:

Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:

Speed = distance / time

The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.

For running:

Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:

5 = p / x

p = 5x

For biking:

Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:

12 = q / y

q = 12y

The total distance ran and biked by Suzette (d) = Distance biked + distance ran

d = p + q

80 = p + q

80 = 5x + 12y                 (1)

The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run

t = x + y

9 = x + y                         (2)

Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:

7y = 35

y = 35/7

y = 5 hours

Put y = 5 in equation 2:

9 = x + 5

x = 9 -5

x = 4 hours

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours

3x^2 - x - 2

What are some ways to solve an equation?

Different ways to solve equations. We have 4 ways of solving one-step equations: Adding, Substracting, multiplication, and division. If we add the same number to both sides of an equation, both sides will remain equal.

How do you evaluate an equation?

= (x - 1)(3x + 2)

= 3x^2 + 2x - 3x - 2

= 3x^2 - x - 2

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Answer:

Each slice of pizza cost:

$1.63

Step-by-step explanation:

4.89/3 = 1.63

Answer:

$1.63

Step-by-step explanation:

We want to find the cost per slice of pizza. Therefore, we must divide the total cost by the number of slices of pizza.

cost / slices

It costs $4.89 for 3 slices.

$4.89 / 3 slices

Divide 4.89 by 3 (4.89/3=1.63)

$1.63 / slice

The cost of each slice of pizza is $1.63

Answer:

x = 3

Step-by-step explanation:

j(x) = 4/5(-5) + 7

= -4 + 7

= 3

Answer:

15

Step-by-step explanation: -4/5 x has to be -12 because -12+7 equals 5. Since we want to figure out x, we have to flip -4/5 x to 4/5x which would change the -12 to 12. What is a fourth of 12? It is three. 12+3 equals 15. This is the first right answer on all of the internet for this question!

Answer:

x= -11

Step-by-step explanation:

the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .

the value of x is:

>32+2x=10

>2x=10-32

>2x= -22

>x= -11

Answer:

Step-by-step explanation:

Coefficient of x = 2

32 + 2x  = 10

Subtract 32 from both side

32 + 2x -32 = 10 - 32

              2x =  - 22

Divide both sides by 2

            2x/2 = -22/2

x = -11

Answer:

358.125

Step-by-step explanation:

Answer:

358 3/24

Step-by-step explanation:  

The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:

It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.

Based on the information given, the correct expression that can be used to solve the question should be:

65 - (5.50b + 7.5)

In conclusion, the correct options are B and C.

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Answer:

B and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

2√24 + 5√54

To combine the radicals first make sure the radicals have the same square root

That's

Since they have the same square root we can combine them

That's

We have the final answer as

Hope this helps you

Answer:

B. 1/2

Step-by-step explanation:

y = ax^2 + bx + c

14 = a(0)^2 + b(0) + c

c = 14

10.5 = a(1)^2 + b(1) + 14

10.5 = a + b + 14 ____(i)

8 = a(2)^2 + b(2) + 14

8 = 4a + 2b + 14

4 = 2a + b + 7 ___ (ii)

i - ii

10.5 - 4 = -a + 7

6.5 = -a + 7

a = 7- 6.5

a = 0.5

Value of a in the quadratic function is 0.5

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree

Given,

Quadratic function

y = [tex]ax^{2}+bx+c[/tex]

Consider values in the table x= 0 and  y =14

[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]

Consider x=1 and y = 10.5

[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]

Consider x=2 and y =8

[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]

Subtract a + b= -3.5 from 2a + b= -3

a=-3--3.5=0.5

Hence, the Value of a in the quadratic function is 0.5

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Answer:

n = 24

Step-by-step explanation:

Given the fraction:

[tex]$\frac{n}{n+101}$[/tex]

To find:

Smallest positive integer [tex]$n$[/tex] such that the fraction is equal to a terminating decimal.

Solution:

The rule that a fraction is equal to a terminating decimal states that, the denominator must contain factors of only 2 and 5.

i.e. Denominator must look like [tex]2^m\times 5^n[/tex], only then the fraction will be equal to a terminating decimal.

Now, let us have a look at the denominator, [tex]n+101[/tex]

Let us use hit and trial method to find the value of [tex]n[/tex] as positive integer.

n = 1, denominator becomes 102 = [tex]2 \times 3 \times 17[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 4, denominator becomes 105 = [tex]5 \times 3 \times 7[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 9, denominator becomes 110 = [tex]2 \times 5 \times 11[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 14, denominator becomes 115 = [tex]5 \times 23[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 19, denominator becomes 120 = [tex]5 \times 3 \times 2^3[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 24, denominator becomes 125 = [tex]2^0 \times 5 ^3[/tex] It is of the form [tex]2^m\times 5^n[/tex].

So, the answer is n = 24

Answer: 2

Step-by-step explanation:

Given: Shaquira has made 86  chocolate chip cookies and 42 sugar cookies.

Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.

Now, the greatest number of identical packages that Shaquira can make= GCD of 86 and 42

Prime factorization of 86 and 42:

86 = 2 ×43

42 = 2 × 3 × 7

GCD of 86 and 42 = 2   [GCD = greatest common factor]

Hence, the greatest number of identical packages that Shaquira can make =2

Answer:

Step-by-step explanation:

Area of a rectangle = Length * Width

Given parameters

Area A = 8x2 – 10x – 12

Length of the rectangle = 4x+3

Required

Width of the rectangle.

Substituting the given parameters into the formula

8x2 – 10x – 12  = (4x+3)*width

width = 8x2 – 10x – 12 /4x+3

S

Factorizing the numerator

8x² – 10x – 12

= 2(4x²-5x-6)

= 2(4x²-8x+3x-6)

= 2(4x(x-2)+3(x-2))

= 2(4x+3)(x-2)

Width = 2(4x+3)(x-2)/4x+3

Width = 2(x-2)

Width = 2x-4

Hence the width of the rectangle is 2x-4

Answer:

i think its very interesting and pretty cool,  because there is so much to learn  and so much to explore

i wouldn't like the fact that you have to study so much though

Step-by-step explanation:

Answer:

perimeter is  4 sqrt(29) + 4pi  cm

area is 40 + 8pi cm^2

Step-by-step explanation:

We have a semicircle and a triangle

First the semicircle with diameter 8

A = 1/2 pi r^2 for a semicircle

r = d/2 = 8/2 =4

A = 1/2 pi ( 4)^2

  =1/2 pi *16

  = 8pi

Now the triangle with base 8 and height 10

A = 1/2 bh

  =1/2 8*10

  = 40

Add the areas together

A = 40 + 8pi cm^2

Now the perimeter

We have 1/2 of the circumference

1/2 C =1/2 pi *d

         = 1/2 pi 8

        = 4pi

Now we need to find the length of the hypotenuse of the right triangles

using the pythagorean theorem

a^2+b^2 = c^2

The base is 4 ( 1/2 of the diameter) and the height is 10

4^2 + 10 ^2 = c^2

16 + 100 = c^2

116 = c^2

sqrt(116) = c

2 sqrt(29) = c

Each hypotenuse is the same so we have

hypotenuse + hypotenuse + 1/2 circumference

2 sqrt(29) + 2 sqrt(29) + 4 pi

4 sqrt(29) + 4pi  cm

Step-by-step explanation:

First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.

2pi4 so the perimeter for the half circle would be 8pi/2.

The area of that half circle would be piR^2 so 16pi/2.

Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2

16+100=C^2

116=C^2

C=sqrt(116)

making the perimeter of this triangle 2×sqrt(116)

The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.

We than just need to add up the perimeters and areas for both the half circle and triangle.

The area would be equal to 8pi+40

The perimeter would be equal to 4pi+4(sqrt(29))

Answer:

2p + 12

2 (p = +6) + 12 = 20

Answer:

I think its 6

Step-by-step explanation:

because you have to add 9 and 3 together then you get 12 and you have to divide 2p with 12 and you'll get 6

Answer:

-3=x <13

Step-by-step explanation:

[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]

Multiply through by 3

[tex] - 27 = 2x - 21 < 15[/tex]

Add 21 to all sides

[tex] - 6 = 2x < 36[/tex]

Divide through by 2

[tex] - 3 = x < 18[/tex]

The solutin set is

[tex]{- 3 = x < 18}[/tex]

Answer:

18 inches by 36 inches.

Step-by-step explanation:

Since we have given that

The generic version was basedOn the brand name and was 2/3

And given Dimensions of generic version is given by 12inches ×24inches

If we use the first dimensions of 12inches we have

12=2/3 × brand

12×3/2 = brand

=18inches= brand

we use the first dimensions of 24 inches we have

24=2/3 × brand

24×3/2 = brand

=36 inches= brand

brand= 36 inches

Therefore,the dimensions of brand name will be 18 inches by 36 inches.

Answer:

0

Step-by-step explanation:

Notice that the last factor is null (9×0)

So the result will be null since any number that is multiplied by 0 equals 0.

Answer:

D. zero

Step-by-step explanation:

Since the graphs do not intersect, there are zero solutions.

The number of solutions on the graph is zero

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

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Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation: