What is the area of the shaded region?

Similar terms in this expression are those associated with the variable x.

In this case, they would be the following:

Using simple interest, it is found that Ellie borrowed 150 units of money.

Simple interest is used when there is a single compounding per time period.

The amount of interest after t years in is modeled by:

\(I = Prt\)

In which:

In this problem:

Then, solving for P, we find the amount she borrowed.

\(I = Prt\)

\(39 = P(0.065)(4)\)

\(P = \frac{39}{0.065(4)}\)

\(P = 150\)

Ellie borrowed 150 units of money.

To learn more about simple interest, you can take a look at https://brainly.com/question/25296782

Answer:

-20x

Step-by-step explanation:

Let the number be x.

The product of -4 and this number is -4x.

5 times this is 5(-4x), which simplfiies to -20x.

Answer:

- 6

Step-by-step explanation:

Rate of change over the interval 1 ≤ x ≤3 is given by
\(\dfrac{f(3) - f(1)}{3-1} \\\\= \dfrac{66- 78}{2}\\ \\= \dfrac{-12}{2}\\\\= -6\)

We can see from the table that the function value drops by 6 for every 1 unit increase in x

The graph of the function is attached below.

The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.

Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.

We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.

In the given problem;

The graph of the function f(x) = 1 + x / x² - 1 is attached below;

Learn more on graph of a function here;

https://brainly.com/question/7807573

#SPJ1

You have to divide 27 by 100 and that gives you .27.

If you multiply until you reach 32.13 with different numbers you get 19. It is a 19% increase.

Answer:

103 degrees

Step-by-step explanation:

The angles in a triangle always add up to 180 degrees

so 62+15=77

180-77=103

hope it helps :)

Answer:

103º

Step-by-step explanation:

All angles of a triangle add up to 180º

This means:

62º + 15º + the third angle = 180º

Then you just solve:

180º - 77º = 103º

Hope this helps :)

Answer:

The missing factor is 1.

\(28=7\times(4\times1)\)

Step-by-step explanation:

\(28=7\times(4\times y)\), where y is the unknown factor.

You can solve this equation for y.

Divide both sides by 7:

\(\rightarrow 28\div7=(7\times(4\times y))\div7\\\rightarrow4=4\times y\)

Divide both sides by 4:

\(\rightarrow4\div4=(4\times y)\div4\\\rightarrow1=y\\\rightarrow y=1\)

The missing factor is 1.

\(28=7\times(4\times1)\)

You can also tell just by looking on this particular problem. \(7\times4=28\), so the missing factor can't be anything other than 1.

◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦

                             \(HELLO! :)\)

Answer:

The X would have to be 12!

Step-by-step explanation:

Because 2/3 is 6, 6 x 2 = 12 - 6 = 6

Answer:

15

Step-by-step explanation:

Using gemdas you would have to work in the parenthesis first and 15-6 is 9 multiplied by 2/3 is 6

Answer:

(3, -2) is the correct choice.

Answer:

7*3=21

21*2=42

42 units^3

Step-by-step explanation:

brainliest

The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

Learn more on Solving linear inequalities here: https://brainly.com/question/24372553

#SPJ1

Answer:

4 pizzas for 10

Step-by-step explanation:

Divide the prices by the number of pizzas and you will get the prices per pizza.

2.50$ per pizza for 4

2.75$ per pizza for 7

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

Answer: 7/16 of a yard

Step-by-step explanation:

first we have to find common denominators. 3x=7/8, or 3x=14/16

1/4=4/16 then 14-4-3=7, all over 16.

We need a work of 294210 watts to pump the water over the top. \(\blacksquare\)

Since the cross section area of the trough (\(A\)), in square meters, varies with the height of the water (\(h\)), in meters, and considering that pumping system extracts water at constant rate, then the work needed to pump all the water (\(W\)), in joules, is:

\(W = \int\limits^{V_{max}}_0 {p} \, dV\) (1)

Where:

The infinitesimal volume is equivalent to the following expression:

\(dV = A\, dh\) (2)

Since the area is directly proportional to the height of the water, we have the following expression:

\(A = \frac{A_{max}}{H_{max}}\cdot h\) (3)

Where:

In addition, we know that pressure of the water is entirely hydrostatic:

\(p = \rho \cdot g \cdot h\) (4)

Where:

By (2), (3) and (4) in (1):

\(W = \frac{\rho\cdot g\cdot W_{max}\cdot L_{max}}{H_{max}} \int\limits^{H_{max}}_{0} {h^{2}} \, dh\)   (5)

Where:

The resulting expression is:

\(W = \frac{\rho\cdot g\cdot W_{max}\cdot L_{max}\cdot H_{max}^{2}}{3}\)   (5b)

If we know that \(\rho = 1000\,\frac{kg}{m^{3}}\), \(g = 9.807\,\frac{m}{s^{2}}\), \(W_{max} = 2\,m\), \(L_{max} = 5\,m\) and \(H_{max} = 3\,m\), then the work needed to pump the water is:

\(W = \frac{(1000)\cdot (9.807)\cdot (2)\cdot (5)\cdot (3)^{2}}{3}\)

\(W = 294210\,W\)

We need a work of 294210 watts to pump the water over the top. \(\blacksquare\)

To learn more on work, we kindly invite to check this verified question: https://brainly.com/question/17290830

(b) The transformation stretches the graph by a factor of 5 describes the effect of this transformation on the graph of the quadratic function along the y-axis.

The transformation from y = 2x² to y = 10x² changes the coefficient of the x² term from 2 to 10. This change in the coefficient affects the vertical scaling of the graph of the quadratic function along the y-axis. When we multiply the entire function by a constant, it causes a vertical stretch or compression of the graph depending on the magnitude of the constant.

In this case, the transformation stretches the graph along the y-axis by a factor of 5 since 10 is 5 times greater than 2. This means that the vertical distance between the points on the graph of the function is now 5 times greater than before the transformation.

Therefore, the correct option is (b) - The transformation stretches the graph by a factor of 5.

Correct Question :

If you transform y = 2x2 into y = 10x2, which option below describes the effect of this transformation on the graph of the quadratic function along the y-axis?

a) The transformation shrinks the graph by a factor of 25.

b) The transformation stretches the graph by a factor of 5.

c) The transformation stretches the graph by a factor of 25.

d) The transformation shrinks the graph by a factor of 5.

To learn more about graph here:

https://brainly.com/question/17267403

#SPJ1

The sales after 5 months is 36,000 units (since f(t) is given in thousands of units).

The given function f(t) represents the sales of a gaming product in thousands of units after t months. To find the sales after 5 months, we need to substitute t = 5 in the function f(t) and evaluate the expression. f(5) = 5(5) + 11

= 25 + 11

= 36

Therefore, the sales of the gaming product after 5 months is 36 thousand units. This means that the company has sold 36 thousand units of the gaming product within the first 5 months since the launch of the product. It also indicates that the sales are increasing by 5 thousand units every month.

To know more about sales here

https://brainly.com/question/14647090

#SPJ1

-- The given question is incomplete, the complete question is

"Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11. Find the sales after 5 months."

Answer:

There are 153 combinations

Combinations - any two from eighteen is given by the formula 18C2 or 18! / (2!*16!)

= 18 * 17 / 2 = 153

OK that is the maths - now the explanation

The first sock can be any of 18

The second sock can be any of 17 (one already been selected and they must be mismatched)

Therefore there are 18*17 = 306 permutations she could make

However the question asks for "combinations" not "permutations"

A green sock on the right foot and a yellow sock on the left foot is deemed to be a different "permutation" to a yellow sock on the right foot and a green sock on the left foot. HOWEVER, they are regarded as the same "combination" in both cases you have one green and one yellow sock.

Therefore for combinations we must divide the 306 permutations calculated above by 2 = 153

FYI Walton has incorrectly given you the value of 18!. That would only apply if Martha Mathy had 18 feet!

The density of the Machu Picchu place is 3586.14 visitor per square miles

He currently has about 18000 visitors daily.

This means for each day his visitors are 18000.

The area of his apartment is 13 km square.

The daily visitor density can be calculated as follows:

Therefore,

number of visitor daily = 18000

area of the place = 13 km square

13 km² = 5.01933 miles²

Hence,

How crowded or density of the place = 18000 / 5.01933

How crowded or density of the place = 3586.13599823

How crowded or density of the place = 3586.14 visitor per square miles

learn more on density here:https://brainly.com/question/16894337

#SPJ1

Answer: C

Step-by-step explanation:

1.2x-10=0.2x+14

subtract 0.2x

1.0x-10=14

add 10

x=24

Answer:

Step-by-step explanation:

We can solve this problem by finding all the perfect squares with square roots that can be expressed in the form a√b, where a and b are integers, and n is greater than or equal to 10, and b is as small as possible.

The first few perfect squares with roots that can be expressed in this form are:

10^2 = 100 = 10√1

13^2 = 169 = 13√1

17^2 = 289 = 17√1

19^2 = 361 = 19√1

23^2 = 529 = 23√1

There are 5 perfect squares in the range n <= 500 with roots that can be expressed in the form a√b. So, the answer is 5.

answer:

you would have to subtract the 15 from 25

then divide 25 by 5

your answer should be 5

38 cupcakes can Eric make.  

percentage, a relative value indicating hundredth parts of any quantity.

According to the recipe, one cupcake requires 25% sugar, 25% egg, and 50% flour.

To convert the percentages to actual quantities, we can multiply the amount of each ingredient by 20 (the weight of one cupcake) and divide by 100.

Sugar: 25% × 20g = 5g

Egg: 25% × 20g = 5g

Flour: 50% × 20g = 10g

Eric has 200 grams of egg,

200g / 5g = 40 cupcakes.

Eric has 380 grams of flour

380g / 10g = 38 cupcakes.

Hence, 38 cupcakes can Eric make.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

The amount it would cost to put a new floor in the closet is $76.00

From the question, we are to calculate how much it would cost to put a new floor in the closet

From the given information,

A closet in the house is 2 yards by 1 yard.

To determine how much it would cost to put a new floor in the closet,

First,

We calculate the area of the closet

Area of the closet = 2 yard × 1 yard

Area of the closet = 2 square yards

Now,

From the given information,

The flooring costs $38.00 per square yard

Thus,

The amount it would cost to put a new floor in the closet is

2 × $38.00

= $76.00

Hence,

The amount it would cost is $76.00

Learn more on Calculating cost here: https://brainly.com/question/1662561

#SPJ1

The answer to this question that density = 0.755 but after rounding it to nearest hundred we get \(kg/cm^3\)

What is density?

Density of any substance is defined as the mass of substance divided by the volume of the substance

generally denoted by d

mass of brick  = 9.44kg

volume of brick = (length)(breadth)(height)

volume = (5)(5)(5)

\(= 125 cm^3\)

density d = \(\frac{9.44kg}{125cm^3}\)

which after calculation comes out to be d = 0.755 now rounding off till hundredth place we get

\(d = 0.8kg/cm^3\)

to learn more about density click the link

https://brainly.com/question/1354972

#SPJ9

1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x

2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x

3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1

4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x

5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x

6.  When we simplify cos x + sin xtan x, the result obtained is sec x

We can simplify the trig identities as follow:

1. Simplification of sec² x + tan² xsec² x

sec² x + tan² xsec² x = sec² x(1 + tan² x)

Recall

sec² x = 1 + tan² x

Thus,

sec² x(1 + tan² x) = sec² x × sec² x

sec² x(1 + tan² x) = sec⁴x

Therefore, the simplified is written as

sec² x + tan² xsec² x = sec⁴x

2. Simplification of (sec² x - 1) / sin² x

(sec² x - 1) / sin² x

Recall,

sec² x - 1 = tan² x

Thus,

(sec² x - 1) / sin² x = tan² x / sin² x

Recall

tan² x = sin² x / cos² x

Thus,

tan² x / sin² x = (sin² x / cos² x) / sin² x

tan² x / sin² x = 1/ cos² x

Recall

1/ cos² x = sec² x

Therefore, the simplified expression is written as:

(sec² x - 1) / sin² x = sec² x

3. Simplification of (1/sec² x) + (1/csc² x)

(1/sec² x) + (1/csc² x)

Recall

sec² x = 1/cos² x

Thus,

cos² x = 1/sec² x

Also,

csc² x = 1/sin² x

Thus,

sin² x = 1/csc² x

Therefore, we have

(1/sec² x) + (1/csc² x) = cos² x + sin² x

Recall

cos² x + sin² x = 1

Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:

(1/sec² x) + (1/csc² x)  = 1

4. Simplification of (sec x / sin x) - (sin x / cos x)

(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x

Recall

sec x = 1/cos x

sinx sinx = sin² x

Thus,

(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x

(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x

Recall

1  - sin² x = cos² x

Thus, we have

[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x

[1 - sin² x] / sinx cos x = cos x / sin x

Recall

cos x / sin x = cot x

Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:

(sec x / sin x) - (sin x / cos x) = cot x

5. Simplification of (1 + sin x)(1 - sin x)

(1 + sin x)(1 - sin x)

Clear bracket

1 - sin x + sin x - sin² x

1 - sin² x

Recall

1 - sin² x = cos² x

Thus, we have

(1 + sin x)(1 - sin x) = cos² x

6. Simplification of cos x + sin xtan x

cos x + sin xtan x

Recall

tan x = sin x / cos x

cos x + sin xtan x = cos x + sin x (sin x / cos x)

cos x + sin xtan x = cos x + (sin² x / cos x)

cos x + sin xtan x = (cos² x + sin² x) / cos x

Recall

cos² x + sin² x = 1

cos x + sin xtan x = 1 / cos x

1/cos x = sec x

Thus,

cos x + sin xtan x = sec x

The simplified expression of cos x + sin xtan x is sec x

Learn more about simplification of trig:

https://brainly.com/question/31193285

#SPJ1