1. Approximate using perfect squares.
<78 <
<√78<
<√78 <
So V78 is between
and

Based on the distance between Cities A and B and also cities A and C, and the fact that the cities are on a straight line, the distance between City B and City C can be found to be 10 miles

The distance between cities A and B and cities A and C are related because they are on a straight line.

This means that the distance between  cities A and B and cities A and C can be used to find the distance between  cities B and C and also the distance between cities A and B and cities B and C can be used to find the distance between A and C.

To find the distance between cities B and C, formula is:

= Distance between cities A and C - Distance between cities A and B

= 110 - 100

= 10 miles

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We can solve the quadratic equation using factorization method.

First, let's re-write the equation:

Next, we try to factorize the expression by the left:

Next, we equate each factor to zero to find the value of x

We can conclude that :

We can also do a check by substituting the value of x back into the equation:

The sides of the triangle whose perimeter is 30 are given by-

[a] = 9 , [b] = 10 , [c] = 11.

The perimeter of triangle is the sum of its sides. Mathematically -

Perimeter [P] = a + b + c

Given is a triangle whose side measurements are x, x + 1, and 11. The perimeter of triangle is 30 inches.

From the definition of the perimeter of a triangle -

Perimeter = sum of its sides

x + (x + 1) + 11 = 30

x + x + 1 + 11 = 30

2x + 12 = 30

2x = 18

x = 9

Now -

Length of side 1 = [a] = 9

Length of side 2 = [b] = 10

Length of side 3 =  [c] = 11

Therefore, the sides of the triangle whose perimeter is 30 are given by-

[a] = 9 , [b] = 10 , [c] = 11.

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Answer:

You're question is incomplete.Please try to make it more clear

Answer: (A)

Step-by-step explanation:

By elimination, none of the other answers choices fit the lines; B, C, and D all have at least one positive slope. Both lines shown in the graph have negative slopes, so both equations have to have a negative x value when simplified, so it's A.

Polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).

As given,

Polynomial function f with real coefficients for the given degree, zeros, and solution point is:

Degree 4

Solution Point f(0) = -8

Zeros -4, 1, i

f(x)=k(x +4)(x -1)(x -i)(x +i)

     =k (x² + 3x -4) (x² -i²)

    =k(x² + 3x -4) (x² +1)   ___(1)

Solution point f(0) =-8

-8 =k(0² +3(0) -4)(0² +1)

⇒ k=2

Substitute k=2 in (1)

f(x) =2(x² + 3x -4) (x² +1)

     =2(x⁴ +3x³ -3x²+3x-4)

Therefore, polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).

The complete question is:

Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.

Degree 4

Solution Point f(0) = -8

Zeros -4, 1, i

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Answer:

4 1x4=4 so 4 is ur answer

Step-by-step explanation:

If the number of miles driven is 'x', then the weekly cost to rent a car f(x) is:

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{45 = 3(4b - 1)}[/tex]

[tex]\mathsf{3(4b - 1) = 45}[/tex]

[tex]\mathsf{3(4b) + 3(-1) = 45}[/tex]

[tex]\mathsf{12b - 3 = 45}[/tex]

[tex]\large\textsf{ADD 3 to BOTH SIDES}[/tex]

[tex]\mathsf{12b - 3 + 3 = 45 + 3}[/tex]

[tex]\large\textsf{Simplify it}[/tex]

[tex]\mathsf{12b = 45 + 3}[/tex]

[tex]\mathsf{12b = 48}[/tex]

[tex]\large\textsf{DIVIDE 12 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{12b}{12} = \dfrac{48}{12}}[/tex]

[tex]\large\textsf{Simplify it}[/tex]

[tex]\mathsf{b = \dfrac{48}{12}}[/tex]

[tex]\mathsf{b = 4}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{b = 4}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

SolutionSoltuion:

From the question, the given value id

By applying the theorem above, we will have the value of XY be

Hence,

The final answer = 6

Answer:

The scale factor for the square LMNO to L'M'N'O' is k = 1/2.

Remember that for any length L, a dilation of scale factor k gives a new length L' such that:

L' = k*L

Look at line LM, it has a length:

L = √(6^2 + 2^2) = √40

Now line L'M' has a length:

L' = √(1^2 + 3^2) = √10

Then we can see that:

L' = k*L

√10 = k*√40

√10/√40 = k

√(1/4) = k

1/2 = k

The scale factor is 1/2.

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The voltage E of the electrical appliance using a power of 1000 watts is 50 Volts.

Power is simply the quantity of energy transferred per unit time. It can be expressed as;

P = E × I

Where E is voltage and I is current.

Given the data in the question;

To determine the voltage of the appliance, plug in the given values into the formula above and solve for E.

P = E × I

1000W = E × 20A

E = 1000 / 20

E = 50V

Therefore, the missing value voltage E is 50 volts.

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Answer:

88

Explanation:

Let us call the number NUMBER, then we know that

The above says that 75% of the number is 66.

Then how do we find the value of NUMBER?

Multiplying both sides by 100/75 gives

Answer: n = 8

Step-by-step explanation:

Let the number be n:

The equation is:

[tex]\frac{3}{4}[/tex]n - 14 = -8

Now to solve:

[tex]\frac{3}{4}[/tex]n - 14 + 14 = -8 + 14

[tex]\frac{3}{4}[/tex]n = 6

[tex]\frac{4}{3}[/tex]×[tex]\frac{3}{4}[/tex]n = 6×[tex]\frac{4}{3}[/tex]

n = 8

a. A has 64 subsets.

b. A has 63 proper subsets.

If all of the items of Set A are also present in Set B, Set A is said to be a subset of Set B. Set A is, in other words, contained within Set B.

If Set B has at least one element that is not present in Set A, Set A is considered a proper subset of Set B.

If a set has "n" members, the number of subsets of that set is 2ⁿ, and the number of proper subsets of that subset is 2ⁿ-1.

Given:

Set A=(8,9,10,11,12,13)

Number of elements in the given set,n = 6

a. Number of subsets of A = 2ⁿ = 2⁶ = 64

b. Number of proper subsets of A = 2ⁿ-1 = 2⁶-1 =63

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When solving for the lengths of the sides of a right triangle, we can make use of the acronym SOH-CAH-TOA. In this problem, because x is adjacent to the 52-degree angle and we are also given the length of the hypotenuse, we can use the "CAH" part, which stands for cosine x = adjacent/hypotenuse.

So the answer is x = 11.08.

SOLUTION

From the question,

We have that the equation of the line is 5x + 2y = 9.

2y = - 5 x + 9

Divide both sides by 2, we have :

y = 1/ 2 ( -5x + 9 )

The slope of this line = -5 / 2

The complete expansion of the expression would give; 60x^3 -  11x^2 - 74x + 24

To expand an expression means that we should be able to obtain the original long expression that was factorized in order to get it. In this case, the expression that we have is  (3x+4)(5x-2)(4x-3). We would now have to carry out the expansion in stages.

1)  (3x+4)(5x-2)

15x^2 - 6x + 20x - 8

2) We can now carry out the next step in the expansion as we multiply the bracket with the last term in the expression;

15x^2 - 6x + 20x - 8(4x-3)

60x^3 - 45x^2 - 24x^2 + 18x + 80x^2 - 60x -32x + 24

We can now collect the like terms;

60x^3 -  45x^2 - 24x^2 + 80x^2 + 18x - 60x - 32x + 24

60x^3 -  11x^2 - 74x + 24

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Answer: -82.2

Step-by-step explanation:

Since the price paid got 30% discount from the original price, so this price represents 70% of the original price.

Using the variable x to represent the original price, we can write the following equation and solve it for x:

Therefore the original price is $19.

In a week, a student exercise 2 hours at school and another 1/4 of an hour at home.

The total exercise of the students came plain soccer

The total hour a student exercise both home and school is

2 + 1/4

Our LCM is 4

4x2/1 + 4*1/4 /4

8 + 1 / 4

9/4 hours

A student exercise a total of 9/4 hours in a week

If one student exercise a total of 9/4 hours in a week then how many hours will 16 students exercise in a week

Mthematically,

1 student ========= 9/4 hours

16 students ======= x hours

Introduce cross multiplication

1 * x = 16 x 9/4

x = 16 x 9/4

x = 144/4

x = 36 hours

Therefore, 16 students exercise a total of 36 hours in a week

The answer is 36 hours

x = 144 / 4 hours

The correct statement regarding Isaiah is that A. His gross pay is $3,000 and net pay is $2,500

Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay. Net pay, often known as take-home pay, is the amount that is left after all withholdings have been taken into account. Determining the number of pay periods you have throughout the year is the first step in calculating the gross compensation for a salaried employee.

The time range for which you pay your employee is known as a pay period. You must first determine your employee's gross compensation before you can determine their net pay. This is where you should start. The next thing you need to know is what payroll deductions your employee receives.

Since the take-home pay is $2,500, this is the net pay.

In conclusion, the correct option is A.

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Isaiah works at a technology company in the summer and earns

$3000. After federal, state, and Social Security/Medicare taxes are

deducted, his take-home pay is $2,500. Which of the statements

below is CORRECT? *

His gross pay is $3,000 and net pay is $2,500

His gross and net pay are $3,000

His gross and net pay are $2,500

His gross pay is $2,500 and net pay is $3,000

The standard form of the expression 25×10 to the power of -3 is 2.5×10⁻⁴

The Index Power Rule:

For the given expression;

25×10 to the power of -3

This can be written as follows;

= 25×10⁻³

To write the expression in standard form, shift the decimal to the  left of the number and add one more power to base 10.

= 2.5×10⁻⁴

Thus, the expression in the standard form becomes  2.5×10⁻⁴.

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ANSWER

100.5 feet

EXPLANATION

The radius of the circular garden is 16 feet.

To find how much wood she would need to make a fence around the garden, we need to find the circumference of the garden.

Circumference can be found using the formula:

where r = radius

Therefore:

She would need 100.5 ft length of wood to enclose the garden.

Radius = 6 cm

The area of circle is given by:

A = 113.04 cm^2

The average rate of change of helicopters height when it starts  descending is : - 630.01 ft/min

Rate of change between two points,

Follow these steps to calculate the rate of change on a graph when given two points on the graph:

Here in the question ,

Given two points (0 , 8400) and (13.333 , 0)

to find the average rate of change ,

Average rate of change = y2 - y1/ x2 - x1

by substituting values,

Average rate of change = 0 - 8400/ 13.333 - 0

                                        = - 8400 / 13.333

                                        = - 630.01 ft/min

since the helicopter is descending the rate of change will be negative

so the rate of change of helicopters height is - 630.015 ft/min

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Answer:

x = 3.4

Step-by-step explanation:

18x - 44 = 8x - 10

       +10

18x - 34 = 8x

               -18x

       -34  = -10x

         / 10

               x = 3.4

Proof:

18 x 3.4 = 61.2 - ( 44 ) = 17.2

8 x 3.4 = 27.2 - ( 10 ) = 17.2