Find the amount that results from a $900 investment invested at 7% interest,
compounded continuously, after 4 years.

Answer:

Let's neaten up that equation a bit:

trapezoid area = height * (sum of the bases) / 2

height = 2 * area / (short base + long base)

height = 2 * 78 / (5 + 8)

height = 156 / 13

height = 12 inches

Source: https://www.1728.org/quadtrap.htm

Step-by-step explanation:

The formula for the height is h = (b1+b2)/2A and the height of the trapezoid is 12 inches

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.

The area of a trapezoid is expressed as;

A = 1/2( a +b) h

where a and b are the parallel sides and h is the height.

Making h the subject

(a+b)h = 2A

h = 2A/( a+b)

h = 2A( b1 + b2)

A = 78 in²

a = 5 in

b = 8 in

h = 2 × 78/( 8+5)

h = 156/13

h = 12 in

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Answer:

$319

Step-by-step explanation:

Usually, sales tax is proportional to the amount of the sale, so if the sales tax is a factor of 22/16 times the original tax, then the sale amount must be 22/16 times the original item cost:

 (22/16)·$232 = $319

Answer:

y=1, x=5

Step-by-step explanation:

Since x-5=0 is given already, give the x a value and switch the 5 to the other side x-5=0 ----> x=5

Now we have a value for x, so plug x into the original equation,

4(5)+3y=23,

20+3y=23

Subtract both sides by 20

20-20+3y=23-20

3y=3

dvide both sides by 3

y=1

use the value for x we got earlier

y=1, x=5

Hi!

I will write it like this to make it easier to see:

[tex]\frac{0}{35} - \frac{31}{35} - \frac{2}{35}[/tex]

Seeing this, we can right away take the [tex]\frac{0}{35}[/tex] away to make it easier, because 0/35 is 0. Now, we are left with:

[tex]-\frac{31}{35} - \frac{2}{35}[/tex]

Since the denominators (the 35s) are the same, we do not have to mess with those. We simply subtract the numerators (-31 - 2) and we get -33. Therefore, your answer is :

[tex]-\frac{33}{35}[/tex]

Hope this helps! Have a great day! :D

Answer:

OK okokokokokokokokokokokok

Answer:

Step-by-step explanation:

Answer:

See image

Step-by-step explanation:

Look at the front side of the building. It's a triangle, with the height given. We can see a right triangle here which means we can use the Pythagorean theorem. a^2 + b^2 = c^2 (a and b are the shorter sides called legs and c is the longest side called the hypotenuse)

20^2 + 13^2 = c^2

400 + 169 = c^2

569 = c^2 square root both sides

Sqrt 569 is approximately 23.85 ft. This is the length from the roof peak down the front edge to the bottom front right corner in the image.

Now, if we consider the roof itself. That edge is now a leg (on the front face it was the hypotenuse). The other leg is the 35 ft width given. So we'll use pythagorean theorem again to find the diagonal

23.85^2 + 35^2 = c^2

568.8 + 1225 = c^2

1793.8 = c^2

Square root both sides of the equation.

Sqrt 1793.8 = c

42.35 ft = c

The diagonal of the roof is just over 42 feet, that is 42.35 feet.

Answer:

8/15

Step-by-step explanation:

1/5 + 1/3 = 3/15 + 5/15 = 8/15

Answer:

$2.72

Step-by-step explanation:

2.74x0.89=2.4475

0.8x0.34=0.272

2.447+0.272=2.719, rounded is 2.72

I think the y=ab^x goes with the first graph and the y=logbc goes with the second

Step-by-step explanation:

pictures

Answer:

ehhh Pfouto math ni

dali raka AA yooo

Answer:

$ 156.86

Step-by-step explanation:

We have been given that the bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip.

The total bill including tip would 136.40 plus 15% of136.40plus15136.40.

\text{Total bill}=\$136.40+\frac{15}{100}\times \$136.40Total bill=$136.40+10015×$136.40

\text{Total bill}=\$136.40+0.15\times \$136.40Total bill=$136.40+0.15×$136.40

\text{Total bill}=\$136.40+\$20.46Total bill=$136.40+$20.46

\text{Total bill}=\$156.86Total bill=$156.86

Therefore, the total cost of bill including tip would be $156.86.

Answer:

Option D

Step-by-step explanation:

[tex]\\ \sf\longmapsto 2(4^x)[/tex]

Not like this

[tex]\\ \sf\longmapsto 2(4^x)=8^x [/tex](×)

Hence the variable has coefficient 4 as 4^x is multiplied.

Since nothing is shown, you can infer.

First to solve the expression:

1) Expand by distributing terms.

[tex]7-(2y-2)[/tex]

2) 2 Remove parentheses.

[tex]7 - 2y + 2[/tex]

3)  Collect like terms.

[tex]-2y+(7+2)\\[/tex]

4) Simplify.

[tex]-2y + 9[/tex]

The expression that is equivalent to [tex]7-2(y-1)[/tex] is [tex]-2y + 9[/tex].

Hope this helps,

- Recordofraganrok

Answer:

answer choice is B

Step-by-step explanation:

Use mathaway and scan the problem

Answer: For in the inequality to be true, X must be less than or equal to 1. That represented as an in equality is X < 1.

x<1 true

Step-by-step explanation:

3(1+x)<+6= 3×1+3×X<+6=3+3x<6 then3x=6-3 solution 3x=3 devide by 3 both sides the answer is x=1 hence x<1 verified

Answer:

Step-by-step explanation:

6x + 10 + 2x + 26 = 180

8x + 36 = 180

8x = 144

x = 18

Answer:

y = 1/2x - 8

Step-by-step explanation:

Assuming that they want the equation in slope intercept form we would use the following form: y = mx + b

where m = slope and b = y intercept.

We are given the slope and a point on the line. We need to find the y intercept. We can do this by plugging in what we are given and then solving for b.

y = mx + b

slope (m) = 1/2

x value of given point (x) = 8

y value of given point (y) = -4

- plug in these values -

-4 = (1/2)(8) + b

now solve for b

multiply 1/2 and 8

-4 = 4 + b

subtract 4 from both sides

-8 = b

So the y intercept (b) is -8

We now plug in the slope and y intercept into slope intercept form

y = mx + b

m = 1/2 and b = -8

y = 1/2x - 8 is the equation of the line that passes through the point (8,-4) and has a slope of 1/2

For more validation refer to the attached image.

[tex]\text{Given that,}\\\\(x_1,y_1) = (8,-4), ~~ \text{and slope, m} = \dfrac 12\\\\\text{Equation with given points,}\\\\y -y_1 = m(x-x_1)\\\\\implies y -(-4) = \dfrac 12 (x-8)\\\\\implies y+4 = \dfrac 12 x - 4\\\\\implies y= \dfrac 12x -4 -4 \\\\\implies y = \dfrac 12 x -8\\\\\implies y = \dfrac{x-16}2\\\\\implies 2y = x -16\\\\\implies x -2y = 16[/tex]

Answer:

Step-by-step explanation:

1) 11 + 11

2) 17 - n

3) x^2

4) 3^3

5) 88 / 8

6) 6 + 11

7) the quotient of 35 and 5

8) the sum of 4 and 5

9) 10 squared

10) 3 less than x

13) p^3 + qp

2^3 + 4(2)

8 + 8 + 16

14) (y^3)z / 3

(5^3)3 / 3

125(3) / 3

375 / 3

125

15) 2 + (j - h)^2

2 + (5 - 3)^2

2 + (2)^2

2 + 4

6

Answer:

between midnight and 3am i think

Step-by-step explanation:

Answer:

no correlation

Step-by-step explanation:

they arent in a line

The phrase that best describes the relationship indicated by the scatter plot is D. No correlation

This refers to the use of dots to represent values for two different numeric variables.

Hence, we can see that the best description that can be used to show the relationship in the scatter plot is option D which is no correlation because they are not in a line.

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The exponential equation used to represent the population of the town is given by y = 5655(1.026)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population remaining after x years.

The population grow at the rate of 2.6% annually. Hence:

b = 100% + 2.6% = 1.026

There are initially 5655 people, hence a = 5655.

The equation becomes:

y = 5655(1.026)ˣ

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Answer:

Unit 4- Expressions and Equations: In this unit, students build on their knowledge from unit 2, where they extended the laws of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and exponential expressions.

Answer:

D

Step-by-step explanation:

Answer:

[tex] \frac{5(x + y)}{ - 8x} [/tex]

Step-by-step explanation:

quotient means division

numerator is the top

denominator is the bottom

product means multiply

sum means add

Answer: C

Step-by-step explanation:

Answer huuhHH

Step-by-step explanation: