What is the length, in feet, of the hypotenuse of a right triangle with legs that are 3 feet long and 4 feet long? Question 10 options: 25 5 7 7√

Given

Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4%.

Total interest paid was $475

Find out  he invest in each.

To proof

Let us assume that Paul invested  in an account paying 4% be = x

As given in the question

Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4%.

Let us assume that Paul invested  in an account paying 5% be = 3x

Total interest paid = $475

First convert 4% in the decimal form

[tex]=\frac{4}{100}[/tex]

= 0.04

First convert 5% in the decimal form

[tex]=\frac{5}{100}[/tex]

= 0.05

Than the equation become in the form

0.04x + 0.05 × 3x = 475

0.04x + 0.15x = 475

0.19x = 475

x = $2500

Paul invested  in an account paying 4% be = $2500

Paul invested  in an account paying 5% be = $7500

Hence proved

Answer 5/14

Step-by-step explanation:

The simplest form of the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] is [tex]\frac{5}{14}[/tex].

An expression is a combination of numbers, variables, operations, functions, and often symbols that are combined according to particular rules to represent a mathematical computation or relation.

Expressions can be both simple as a single number or variable and complex by involving multiple variables and operations.

Some examples of Expressions are x, 4, x² + 6y + 2xy +6, [tex]\frac{x}{y}[/tex], [tex]\frac{x}{y} \times \frac{p}{q} \div e^7[/tex] etcectra.

The given expression is

[tex]\frac{5}{8} \times \frac{4}{7}[/tex] [tex]= \frac{5}{2}\times \frac{1}{7}[/tex]

        [tex]= \frac{5\times1}{2\times7}\\ = \frac{5}{14}[/tex].

Hence the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] can be simplified as [tex]\frac{5}{14}[/tex].

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Answer:

(-6, 36)

Step-by-step explanation:

The standard form: ax^2 + bx + c

In this case:

a is 1

b is 12

c is 0

Calculate -b / 2a. This is the x-coordinate of the vertex.

To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

-12 / ( 2 x 1 )

-12 / 2

-6

You log -6 in the function

f(x) = x^2 + 12x

f(-6) = (-6)^2 + 12(-6)

      = 36 +  (-72)

      = 36 - 72

      = 36

I hope this

Answer: A (-6, -36)

Step-by-step explanation:

Answer:

Value of house before Increase = $700000.

Step-by-step explanation:

Let the value of house before increase be $x.

Increase in value = 7%of x= .07x

Value of house before increase+ Increase in value = Total value.

x+.07x=749000

Adding like terms,

1.07x=749000

Dividing both sides by 1.07.

x=700000.

Value of house before Increase = $700000.

Answer: 280 Miles.

Step-by-step explanation: 60 x 4 = 240 + 40 = 280 Miles.

Answer:

[tex]r(x)=(4x)^7[/tex]

Step-by-step explanation:

For example,

If we wanted to horizontally compress [tex]y=x^2[/tex], we would multiply by 4 to get [tex]y=(4x)^2[/tex], and

if we wante to horizontally expand [tex]y=x^2[/tex], we would multiply by [tex]\frac{1}{4}[/tex] to get [tex]y=(\frac{1}{4}x)^2[/tex]

Since this question asks for horizontal compression, we multiply the [tex]x[/tex] of the function by 4. So the function we need is [tex]f(x)=(4x)^7[/tex]. The second choice is correct.

I only get one (2, 11)

to find the points which are solutions, substitute the x-coordinate into the equation and if the value obtained equals the y-coordinate of the point then it is a solution

(7, 16) : y = (3 × 7 ) + 5 = 21 + 5 = 26 ≠ 16

( - 2, 1): y = (3 × - 2) + 5 = - 6 + 5 = - 1 ≠ 1

(2, 11) : y = (2 × 3) + 5 = 6 + 5 = 11

( - 7,16 ): y = (3 × - 7) + 5 = - 21 + 5 = - 16 ≠ 16

the only point from the given list that is a solution is (2 , 11)

By substituting the x and y values of the given points into the equation 'y = 3x + 5', we can determine that the only solution from the given points is (2,11).

The given equation is y = 3x + 5. We can find out which of the points are solutions to the equation by substituting the x-coordinate and y-coordinate of each point into the equation. If the equation holds true, then the point is a solution.

So, the points that are solutions to the equation y = 3x + 5 are (2,11).

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The next number would be 6.

The pattern is add 3, then subtract two.

The next number in the series 3 6 4 7 5 8 is 6.

The next number in the series 3 6 4 7 5 8 is 6.

This is an alternating pattern where the first number increases by 1, the second number stays the same, and the third number increases by 1. So, starting with 3, the next number after 8 should be 9. However, since 9 is not given in the options, we can look for the closest number that follows the pattern, which is 6.

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12x^2-44x+7 = (6x - 1)(2x - 7)

35x^2-27x-18 = (7x - 9)(5x +2)

[tex]f(x)=3x+5,\ g(x)=-2x^2-5x+3\\\\(f+g)(x)=f(x)+g(x)=(3x+5)+(-2x^2-5x+3)\\\\=3x+5-2x^2-5x+3=-2x^2+(3x-5x)+(5+3)=-2x^2-2x+8\to\boxed{C.}[/tex]

Answer:

C.your GPA

Step-by-step explanation:

In general, employment applications require all of the following except:

C.your GPA

The GPA is not as important as the references, ones employment history and the highest level of education.

These information gives an overview about your history like if you are a fresher or an experienced person. And what education have you got, or who referred you to this particular company.

The GPA's are not considered at the first place. When a person progresses in an interview, then GPA might be considered to gather information like the person is how much efficient in that particular subject.

x=-64/35

-6/5x+2= 21/25

Do fraction cross multiply

(-6*25=(5x+2)21

Then swap the sides (5x+2) *21 = (-6)*25

multiply(5x+2)21= -150/21

simplify

5x+2=- 50/7

subtact 2

5x+2-2=- 50/7-2

silmplify 5x=-64/7

divide by 5

5x/5=-64/7/5

simplify

x= -64/35

Solve:

-6/5x    +     2     =     21/25

Steps:

Solution      -6/5x    +     2     =     21/25      =======>   29/30,    Decimal  =====>   x   =   0.96667

Subtract  2 from both sides:

-6/5x    +     2     -   2    =     21/25     -    2

Simplify:

-6/5x      =     -29/25

Multiply both sides by   -25:

(-6/5x )(-5)     =     (-29/25 )(-5)

Simplify:

6x    =   29/5

Divide both sides by 6:

6x/6         =     29/5/6

Simplify:

Answer        x        =    29/30         Decimal:     0.96667....

Hope that helps!!!!                                      : )

Answer: The area of the mobile is 140.4 m².

Step-by-step explanation:

Hi to solve this problem we have to analyze the information given:

Width : 7.2 meters (a)

Length : 19.5 meters (b)

The mobile is rectangular. So, we have to apply the area of a rectangle formula.

The area of the mobile is 140.4 m².

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

Option C

Step-by-step explanation:

given two equations

6m-5n= 14   ... i

2m+2n= -10  ...ii

We can solve this by elimination.

For elimination consider the coefficients of m.

They are 6 and 2, with LCD 6

You multiply 2nd equation by 3 to have

6m+6n =-30 ... iii and

6m-5n  = 14  ... i

Subtract i from iii

11n = -44

Divide by 11 to get n

n = -4

Substitute in I equation

6m-5(-4) =14

6m +20 = 14

subtract 20

6m =14-20 =-6

divide by 6

m =-1

Hence answer is m=-1 and n=-4

(-1,-4)

Option C is the answer.

First we have to change 7 1/5 into an improper fraction. 7 1/5 converted to an improper fraction is 36/5. Now, to divide this by 1/8, we need to multiply it by 8 (multiplying by the reciprocal). 36/5 * 8/1 = 288/5. In simplest form, this is 57 3/5.

The division problem 7 1/5 divided by 1/8 is solved by converting the mixed number to an improper fraction, converting the division problem to a multiplication problem by multiplying by the reciprocal, and then simplifying the resulting fraction. The final answer is 57.6.

To solve the problem 7 1/5 divided by 1/8, we first need to convert the mixed number 7 1/5 into an improper fraction. We do this by multiplying the whole number 7 by the denominator of the fraction 5 and then adding the numerator 1. So, 7 * 5 + 1 = 36.

So, 7 1/5 becomes 36/5. Now, we have 36/5 divided by 1/8.

When we are dividing by a fraction, we need to multiply by its reciprocal. The reciprocal of 1/8 is 8/1. So the problem becomes 36/5 multiplied by 8/1.

When multiplying fractions, we simply multiply the numerators and the denominators together. So, 36 * 8 = 288 and

5 * 1 = 5. Therefore, our answer is 288/5. Lastly, when we simplify this, it becomes 57.6.

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A.1/16 of a pound. Hope i helped

Answer:

A

Step-by-step explanation:

Use the value for the variable to solve for the other unknowns.  Substitute the value for the variable into the expression for the number of seats on the middle level.  Substitute the value for the variable into the expression for the number of seats on the lower level.

Use the value for the variable to solve for the other unknowns.  Substitute the value for the variable into the expression for the number of seats on the middle level.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Use the value for the variable to solve for the other unknowns.  Substitute the value for the variable into the expression for the number of seats on the middle level.  Substitute the value for the variable into the expression for the number of seats on the lower level.

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A. hope this helps. Mark as Brainliest.

Answer:

b.14.2 mph

Step-by-step explanation:

Answer:

The cart’s speed in miles per hour is 14.2 miles per hour .

Option (B) is correct .

Step-by-step explanation:

As given

Rob measures his go-cart’s speed to be 250 inches per second.

As

[tex]1\ inch = \frac{1}{63360}\ miles[/tex]

[tex]1\ second = \frac{1}{3600}\ hours[/tex]

Now convert 250 inches per second into miles per hour .

[tex]250 inches\ per\ second = \frac{250\times \frac{1}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]

[tex]250 inches\ per\ second = \frac{\frac{250}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]

[tex]250 inches\ per\ second = \frac{250\times 3600}{63360}\ miles\ per\ hour[/tex]

[tex]250 inches\ per\ second = \frac{900000}{63360}\ miles\ per\ hour[/tex]

250 inches per second = 14.2(Approx) miles per hour.

Therefore the cart’s speed in miles per hour is 14.2 miles per hour .

Option (B) is correct .

ANSWER

[tex]x=-2\pm 2\sqrt{2}[/tex]

EXPLANATION

Given:

[tex]x^2+4x-4=0[/tex]

We complete the square as follows;

Add 4 to both sides of the equation:

[tex]x^2+4x=4[/tex]

Add half the coefficient of [tex]x[/tex] to both sides of the equation.

[tex]x^2+4x+(2)^2=4+(2)^2[/tex]

The Left Hand Side of the equation is now a perfect square.

[tex](x+2)^2=4+4[/tex]

[tex](x+2)^2=8[/tex]

Take the square root of both sides

[tex]x+2=\pm \sqrt{8}[/tex]

[tex]x=-2\pm 2\sqrt{2}[/tex]

Hence the correct answer is option C

Given equation is [tex]x^2+4x-4=0[/tex]

compare with [tex]ax^2+bx+c=0[/tex]

we get: a=1, b=4, c=-4

plug these values into quadratic formula:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-4 \pm \sqrt{4^2-4(1)(-4)}}{2(1)}[/tex]

[tex]x=\frac{-4 \pm \sqrt{16-4(-4)}}{2}[/tex]

[tex]x=\frac{-4 \pm \sqrt{16+16}}{2}[/tex]

[tex]x=\frac{-4 \pm \sqrt{32}}{2}[/tex]

[tex]x=\frac{-4 \pm 4\sqrt{2}}{2}[/tex]

[tex]x=-2 \pm 2\sqrt{2}[/tex]

Hence finall answer is:

[tex]x=-2+2\sqrt{2}[/tex] and [tex]x=-2-2\sqrt{2}[/tex]

2(x + 3) ≥ -10 - 4x

2x + 6 ≥ -10 - 4x

+4x               +4x

6x + 6 ≥ -10

      -6   -6  

6x       ≥ -16

      [tex]\frac{6x}{6} \geq \frac{-16}{6}[/tex]

      [tex]x \geq -\frac{8}{3}[/tex]        reduced fraction

2(x+3) greater than or equal to -10 - 4x

So

2(x+3) >= -10 - 4x

2x + 6 >= -10 - 4x

2x + 4x >= -10 - 6

6x >= - 16

 x >= - 16/6

 x >= - 8/3

[tex]\sqrt{63} = \sqrt{9*7} = \sqrt{3*3*7}  = 3\sqrt{7}[/tex]

The simplified form of √(63) after removing all perfect squares from inside the square root is 3√(7).

To simplify the square root of 63 and remove perfect squares, we start by finding the prime factorization of 63. The prime factorization of 63 can be obtained by dividing the number by its smallest prime factor, which is 3, and then continuing the process for each quotient until we get a prime number. The prime factorization of 63 is:

63 = 3 * 3 * 7.

Now, we look for any perfect square factors within the square root of 63. In this case, the perfect square factor is 3 * 3 (3 squared). We can remove this perfect square from the square root, leaving us with:

√(63) = √(3 * 3 * 7).

Since we removed one pair of 3's (3 * 3), the simplified square root of 63 becomes:

√(63) = 3√(7).

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Answer:

You need annual gross pay of 20000.

Step-by-step explanation:

Suppose, your annual gross pay is  [tex]x[/tex]

You estimate that the net pay will be 65% of your gross pay. So, the annual net pay will be:  [tex]x*65\% = 0.65x[/tex]

As there are 52 weeks in 1 year, so your weekly net pay will be:  [tex]\frac{0.65x}{52}[/tex]

Given that, you will need 250 per week after taxes to get by. So, the equation will be......

[tex]\frac{0.65x}{52}=250\\ \\ 0.65x= 52*250=13000\\ \\ x=\frac{13000}{0.65}=20000[/tex]

So, you need annual gross pay of 20000.

ASNSWER

[tex]Perimeter=\frac{5x-16}{2}[/tex]

EXPLANATION

Let [tex]w=x[/tex] represent the width of the rectangle.

One-fourth of the width will be,

[tex]\frac{1}{4}x[/tex]

Let [tex]l[/tex] represent the length of the rectangle.

Then, subtracting 4 units from one-fourth the width gives us the length

[tex]\Rightarrow l=\frac{1}{4}x-4[/tex]

Perimeter[tex]=2x+2l[/tex]

[tex]\Rightarrow Perimeter=2x+2(\frac{1}{4}x-4)[/tex]

We expand to obtain;

[tex]Perimeter=2x+\frac{x}{2}-8[/tex]

[tex]Perimeter=\frac{x+4x-16}{2}[/tex]

[tex]Perimeter=\frac{5x-16}{2}[/tex]

toby will reach more people in 40 phone calls

The way to solve this problem is to turn both denominators into 40

4 * 4        16

_          =  ---       so Clara will reach 16 people in 40 phone calls

10 * 4       40

3  * 5       15

_           = ----        so Toby will reach 15 people in 40 phone calls

8 * 5         40

Therefore Clara will reach more people in 40 phone calls than Toby.

Answer:

c = 3 oil changes

Step-by-step explanation:

The fixed rate for oil change is $ 40

The surplus rate for miles outside the radius is $ 2.25

Josh lives 7 miles of the radius

Therefore an equation for c: The largest number of oil changes that can be scheduled and maintained within the budget for the year is:

[tex]\\40c + 2.25 * 7c = 200\\c (40 + 2.25 * 7) = 200\\c =\frac{200}{40 + 2.25 * 7}\\c = 3,578\\c = 3[/tex] oil changes

Therefore, with the budget set Josh can make a maximum of 3 oil changes per year

Answer:

The answer is 3

Step-by-step explanation

mileage fee for each oil change: 7(2.25) = $15.75

service call + mileage fee = total for each oil change

$40 + $15.75 = $55.75

c = number of oil changes

55.75c = total amount for all oil changes

55.75c ≤ 200

c ≤ 3.59

Therefore, the greatest number of oil changes that Josh can schedule without exceeding his budget is 3.

F(x) = 1/2x^2 is a variation of the basic graph y = x^2 (the squaring function).

The graph of the squaring function has the shape of a parabola that opens up.  Its vertex is at (0,0).

The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).   The vertex of F(x) = (1/2)x^2 is still (0,0).  That eliminates the first 2 possible answers.  Note that F(1) = (1/2)(1)^2 = 1/2.  The point (1, 1/2) is on the third graph, but not on the fourth.  Thus, the third graph is correct.

Only the third graph (option C) represents the graph of [tex]F(x) = \frac{1}{2} x^2[/tex]

The given function is:

[tex]F(x) = \frac{1}{2} x^2[/tex]

This graph is of the form [tex]y = ax^2[/tex] and it takes the shape of a parabola with center at (0, 0)

Only two of the graphs shown among the options have the center at the origin (0, 0), but only one is scaled by 0.5

Therefore, the graph of the function [tex]F(x) = \frac{1}{2} x^2[/tex] is plotted below

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