50 POINTS!

David borrowed money from a credit union for 5 years and was charged simple interest of 6%. The total interest that he paid was $2,100. How much money did he borrow?​

How many  cups of water do you need to make lemonade? 9/4 cups

How is the number of cups calculated?

Given:

8 lemons need =18 cups of water

1 lemon needs= x cups of water

By cross- multiplication method,

[tex]\frac{8}{1} =\frac{18}{x}[/tex]

8x = 18

x = 18/8

 = 9/4 cups of water is needed to make lemonade

What is the cross- multiplication method?

To learn more about cross- multiplication method, refer:

https://brainly.com/question/294036

#SPJ13

Answer: 3x

Step-by-step explanation:

5x-2x=

5*x-2*x=

x(5-2)=

x*3=3x

Answer:3x

Step-by-step explanation:

combine like terms

5x-2x

2x is a negative

so 5-2=3

so in conclusion 3x

Consider the formulae from Inverse Trigonometry,

Solve for the first angle as,

Thus, the required angle measure is 82 degrees approximately.

Solve for the second angle as,

Thus, the required angle measure is 14 degrees approximately.

Solve for the third angle as,

Thus, the required angle measure is 28degrees approximately.

Solve for the fourth angle as,

Thus, the required angle measure is 47 degrees approximately.

Solve for the fifth angle as,

Thus, the required angle measure is 58 degrees approximately.

Answer: y = x^2 - 2x - 8

Step-by-step explanation:

An estimate of the real height of the lamp post is 9m.

The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm

Scale = length of the lamp post / height of the car

10.8 / 1.8 = 6

Now, multiply the scale by the width of the car.

The real height of the lamp post = 6 x 1.5 = 9m

To learn more about scale drawings, please check: https://brainly.com/question/26388230

#SPJ1

The account balance is $883.264 after 5 years.

The Principal amount is $800, the time given is 5 years and the rate of interest is 2%.

We have to find the account balance after 5 years.

Formula to find the amount

Amount = Principal × [tex](1 +\frac{rate}{100}) ^{time}[/tex]

Now putting the value we get,

Amount = 800 × [tex](1 + \frac{2}{100} )^{5}[/tex]

             = 800 × [tex]\frac{102}{100 } ^{5}[/tex]

             = 800  ×[tex]1.02^{5}[/tex]

             = 800× 1.104

             = 883.264

Therefore the amount is $883.264 that is the account balance after 5 years.

To know more about compound interest and its amount refer to the link given below:

https://brainly.com/question/12325365

#SPJ1

Answer:

Step-by-step explanation:

Triangles ADC and BDC are right triangles, since CD⊥AB.

Use Pythagorean to find the length of CD:

Use trigonometry to find the angle ABC:

Answer:

Here is your answer So I did the Step for you and By the way I'm from South Africa

Answer: 7

Step-by-step explanation:
5*⁵(22-²9*¹2)-⁷2*⁶(3*³2+⁴4)+⁸7=7

1)9*2=18
2)22-18=4
3)3*2=6
4)6+4=10
5)5*4=20
6)2*10=20
7)20-20=0
8)0+7=7

Answer:

w = 5

Step-by-step explanation:

2w - 15w - 18 = -83

combine w on left side:

-13w - 18 = -83

add 18 to both sides:

-13w - 18 + 18 = -83 + 18

-13w = -65

divide both sides by -13:

-13w/-13 = -65/-13

w = 5

The percentage increase is 7.9 %.

The given numbers are 68 and 63.

Percentage change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.

Here, old value = 63 and new value = 68

Difference = 68-63 =5

Percentage increase = Difference of old value and new value ÷ old value

= 5/63 × 100

= 0.0793 × 100

= 7.93 %

≈ 7.9 %

Therefore, the percentage increase is 7.9 %.

To learn more about the percentage increase visit:

https://brainly.com/question/20818421.

#SPJ1

Answer:

-12 is the answer

Step-by-step explanation:

Substitute 1/4 for a and 6 for b in the equation

-8ab

-8(1/4)(6) Multiply

-8(1.5) Multiply

-12

Using given area and base length of a rectangle we got that the height of the given rectangle is 6.5 inches.

Rectangle is closed geometric figure that has four perpendicular sides with opposite sides equal.

The formula for the area of the rectangle :

Area of the rectangle = Length × Breadth

Given that the area of a rectangle is 45.5 square inches.

The base of the rectangle is given 7 inches

To find : Height of the rectangle

Let the base length is the length of the rectangle and height is the Breadth of the rectangle.

Then, Area of the rectangle = Length × Breadth

⇒ 45.5 = 7 × Height

⇒ 45.5 /7 = Height

⇒ 6.5 = Height  of the rectangle

Therefore, the height of the rectangle is 6.5 inches.

Also, Learn more about the area of rectangle from below link:

https://brainly.com/question/8663941

#SPJ1

This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t2 + 45.

How can one determine a function's maximum height?

The vertex, which is a maximum (or minimum) in a parabola, can be located by solving the square (yuck!) or by using the formula x = -b/2a. By re-entering the original equation with this x value as the vertex's x, we can determine the appropriate maximum height.

By multiplying "D * tan (theta)," where "tan" is the tangent of angle theta, you can get the height of the item of interest. For instance, rounding up, the height is 40 tan 50 = 47.7 meters if theta is 50 degrees and D is 40 meters.

To learn more about function's maximum heigh refer to:

https://brainly.com/question/12446886

#SPJ13

Answer:

| 56x² + 14xy

Step-by-step explanation:

14x(4x + y)

Apply the Distributive Property

14x x 4x + 14xy

Multiply the monomials

56x² + 14xy

Apply the distributive property on 4x + y, distributing 14x.

14x(4x + y)
(14x x 4x) + (14x x y)
56x + 14xy

Answer:

(f∘g)(12) = 24

Step-by-step explanation:

We are given the functions f(x)=4x+8 and [tex]g(x)=\sqrt{x+4}[/tex]. We want to find (f∘g)(12).

(f∘g)(12) means that we first find the value of g(12), and then plug that value into f(x).

First, we find g(12). To do this, substitute x as 12.

[tex]g(12) = \sqrt{12 + 4}[/tex]

Add 12 and 4 together under the radical.

[tex]g(12) = \sqrt{16}[/tex]

Take the square root of 16.

g(12) = 4

Now, substitute 4 as x in f(x) = 4x + 8.

f(4) = 4(4) + 8

Multiply.

f(4) = 16 + 8

Add 16 and 8 together.

f(4) = 24

f(4) has the same value as (f∘g)(12), since 4 is the value of (g)(12), and then the value of g(12) was plugged in as x in f(x).

Therefore, (f∘g)(12) is 24.

Answer:

144

Step-by-step explanation:

12 * 12 = 144

Answer:

It's 144.

..............

36.

When you divide powers with the same base (in this case, 6), you subtract the exponents.

See details:

[tex]\frac{6^{8} }{6^{6} } \\8-6=2\\6^{2}=36[/tex]

Answer:

-7/4 seeing how the line touches -3,4 and 1, -3 only it goes down 7 and 3 to the right

Step-by-step explanation:

sub to imagine fn

The number of vowels is:

The total number of tiles is:

Therefore, the total number of letters not vowels is given by:

Hence, the probability of picking a letter that is not a vowel:

Therefore the required probability is 4/5

The number that makes the mixed fraction equation true is -1.

The number that makes the equation true is calculated by applying the following formula as follows;

The given equation;

-7 ¹/₂ + ? = - 8 ¹/₂

The solution of the equation is calculated as follows;

Convert each mixed fraction into improper fraction;

-7 ¹/₂ = -15/2

-8 ¹/₂ = -17/2

-15/2 + ? = -17/2

Collect the similar terms together as follows;

? = -17/2 + 15/2

? = (-17 + 15) / 2

? = -2/2

? = - 1

Thus, the number that makes the equation true is -1.

Learn more about mixed fraction equations here: https://brainly.com/question/9932338

#SPJ1

The absolute value equation which correctly represents the situation as described is; | x- 3.5 | = 0.8.

The values which are 0.8 units from 3.5 as given are therefore; 4.3 and 2.7.

It follows from the task content that the numbers which are 0.8 units away from 3.5 on the number line be determined.

On this note, the correct representation of the situation above involves an absolute value equation such that;

| x- 3.5 | = 0.8

Hence, to solve the equation; (x- 3.5) = 0.8 OR (x- 3.5) = -0.8.

x = 0.8 + 3.5. OR. x = -0.8 + 3.5

x = 4.3 OR x = 2.7.

Ultimately, the required values are; 4.3 and 2.7.

Read more on absolute value equations;

https://brainly.com/question/28782154

#SPJ1

If  Tia rounds a number, x, to 3 sf and the result is 7.68. the error interval for x in the form a ≤ x < b is 7.685  ≤ x ≤ 7.684

The accuracy thresholds that apply when a number has been rounded or truncated are known as error intervals. In other words, they represent the range of values that a number might have taken had it not been rounded off or truncated.

To do this, we consider the smallest and largest numbers that could be rounded or truncated to a value while maintaining a certain level of accuracy.

We know that if this digit is smaller than 5, then we round down.

Then the largest number that can be rounded down to 7.68 is:

7.684

Now we want to find the smallest number that can be rounded up to 7.68

We know that if the next digit is 5 or bigger, then we round up.

Then the number 7.685 is rounded up to 7.68

Then the error interval is:

7.685  ≤ x ≤ 7.684

Learn more about error interval

https://brainly.com/question/22444784

#SPJ9

Answer:

I believe that it should be less than 2,000.

Step-by-step explanation:

11038 < 11405 = 9405 + 2000

11038 - 9405 < 2000

Answer:

y =-0.25x + (-6)

Step-by-step explanation:

crosses y axis at -6 so that's your y-intercept

to find gradient use change in y / change in x

so make a triangle -1 / 4 = -0.25

Prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called extrapolation of data.

In statistics and mathematics, especially in the branch of data-science it is quite common to use a range of values from a parameter to predict the values of the dependent variable.

One of the most common applications of this is regression equations, when pairs of one of the independent variables with the dependent variable are used to predict the dependent variable.

In the case of this problem, we want to predict the dependent variable, but with values that are outside the experimental range, hence we extrapolate the data inside the experimental range for values that are outside the experimental range.

More can be learned about extrapolation of data at https://brainly.com/question/14446380

#SPJ1

Answer: he could have gotten 100 or 0

Step-by-step explanation: he could have had alot of tests and gotten 100 on all of them to even out the one zero.

The coordinates of the image of any point P(x, y), from any geometric locus, after being reflected over the x-axis.

Geometric loci are geometrical constructions formed by one or more points, these may represent a point or a figure formed by finite or infinite set of points.

Let P(x, y) = (x, y) a point of the geometric locus, which has to be modified by using reflection over the x-axis. This can done by adding the vector (- 2 · x, 0) to the vector P(x, y):

P'(x, y) = P(x, y) + (- 2 · x, 0)

P'(x, y) = (x, y) + (- 2 · x, 0)

P'(x, y) = (- x, y)

Where P'(x, y) is the image of point P, from any geometric locus, after making the reflection over the x-axis.

To learn more on reflections: https://brainly.com/question/15487308

#SPJ1

According to the given figure, angles GHE and DFH are corresponding angles, which are equal because GH and DF are parallels. So, we can express the following

Replacing the given expressions, we have

Let's solve for x

Then, we find the measure of the angle DFH