The perimeter of an isosceles triangle is 45 inches. Two sides of the triangle are congruent,
and the third side is twice as long as the sum of the congruent sides. What is the length of the
third side of the triangle in inches?

Option C is correct, the value of x in the triangle is 10.28 units.

The given triangle is right angled triangle.

We know that the sine function is a ratio of opposite side and hypotenuse.

To the angle 40 degrees the opposite side is x.

The hypotenuse is 16.

Sin 40 degrees=x/16

0.6428=x/16

Apply cross multiplication:

x=16×0.6428

x=10.28

Hence, the value of x in the triangle is 10.28 units.

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All the solutions are,

g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }

h⁻¹ (x) = 5x - 13

⇒ (h⁻¹ о h ) (- 3) = 3

We have to given that,

Functions g and f are defined as,

g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)

And, h (x) = (x + 13) / 5

Now, We can simplify for inverse function as,

For inverse function of g,

g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)

g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }

And, Inverse function of h is,

h (x) = (x + 13) / 5

y = (x + 13) / 5

Solve for x,

5y = x + 13

x = 5y - 13

h⁻¹ (x) = 5x - 13

So, We get;

⇒ (h⁻¹ о h ) (- 3)

⇒ (h⁻¹ (h (- 3))

⇒ (h⁻¹ (- 3 + 13)/5)

⇒ (h⁻¹ (2))

⇒ 5 (2) - 13

⇒ 10 - 13

⇒ - 3

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The value of x in triangle STU is given as follows:

b) 8.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

Applying the Pythagorean Theorem for this problem, the value of x is obtained as follows:

x² + 15² = 17²

x² = 17² - 15²

x² = 64.

x = 8.

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Answer: To calculate the distance the beetle walks diagonally across the table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the two sides of the right triangle formed by the table are 160 cm and 90 cm. Let's call the hypotenuse (the distance the beetle walks) "d."

So, applying the Pythagorean theorem, we have:

d^2 = 160^2 + 90^2

Simplifying:

d^2 = 25600 + 8100

d^2 = 33700

Taking the square root of both sides:

d ≈ √33700

d ≈ 183.54 cm

Therefore, the beetle walks approximately 183.54 cm diagonally across the kitchen table.

Answer: There are 16 fluid ounces in 1 pint. To determine the number of pints in the jug, we need to divide the total number of fluid ounces by 16.

Given that the jug contains 36 fluid ounces of apple juice, we divide 36 by 16:

36 fluid ounces ÷ 16 fluid ounces/pint = 2.25 pints

Therefore, the jug contains 2.25 pints of apple juice.

Answer: A

Step-by-step explanation:

The probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.

If the student randomly orders the events, there is only one correct order out of all possible permutations.

Hence, the likelihood of selecting the accurate sequence is equal to 1 over the total count of potential arrangements.

As there are 5 occurrences, the overall count of conceivable sequences is equivalent to 5 factorial (5!), amounting to 120.

Therefore, the probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.

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On an exam, students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. What is the probability that the student chooses the correct order?

The remaining credit after 65 minutes of calls is approximately $15.45.

To find the remaining credit after 65 minutes of calls, we can use the given information to determine the linear function that relates the remaining credit to the total calling time.

Let's assume the total calling time in minutes is represented by the variable "x," and the remaining credit in dollars is represented by the variable "y."

We are given two data points:

When x = 43, y = $19.41.

When x = 56, y = $17.72.

We can use these data points to form a system of linear equations.

Let's solve it to find the equation of the linear function.

Using the point-slope form of a linear equation:

y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values:

For the first data point:

x1 = 43

y1 = 19.41

Using the second data point:

x2 = 56

y2 = 17.72

The slope (m) can be calculated as:

m = (y2 - y1) / (x2 - x1)

m = (17.72 - 19.41) / (56 - 43)

m = -1.69 / 13

m ≈ -0.13

Now, we can use the point-slope form with one of the data points to find the equation of the linear function:

Using (x1, y1) = (43, 19.41):

y - 19.41 = -0.13(x - 43)

Simplifying the equation:

y - 19.41 = -0.13x + 5.59

y = -0.13x + 24

Now that we have the equation of the linear function, we can substitute x = 65 to find the remaining credit after 65 minutes:

y = -0.13(65) + 24

y ≈ $15.45

Therefore, the remaining credit after 65 minutes of calls is approximately $15.45.

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==============================================

Explanation:

The formula to use is n*(n-1)/2

Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66

That formula is from the nCr combination formula when r = 2.

---------------------

Here's a visual way to see why that rule works.

Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]

In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]

Let's also cross out any cell below the main diagonal.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]

We do this because a mirrored copy is found above the diagonal.

We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.

Those 6 matchups are:

The order doesn't matter. A matchup like "A vs B" is the same as "B vs A".

We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.

Then we split that in half to get the formula n(n-1)/2.

Autumn's bank registry will be :

Transaction Amount Balance

Paycheck $1275.00 $1275.00

Rent $400.00 $875.00

Utilities $75.00 $800.00

Cell Phone $80.00 $720.00

Subway Pass $120.00 $600.00

Groceries $200.00 $400.00

Work Clothes $100.00 $300.00

Entertainment $100.00 $200.00

Savings $200.00 $0.00

As you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:

Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.

By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.

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Using the bearing and trigonometry in the problem, the distance of the waterfall from the lake is 7.94km

To determine the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the distance in a south direction.

To find the distance between the waterfall and the lake, we can use the concept of right triangles and trigonometric functions.

Since the bearing is given as 236°, we can subtract this angle from 180° to find the angle formed by the south direction and the line connecting the lake and the waterfall:

180° - 236° = -56°

Now, we can consider the south direction as the reference direction (0°) and the line connecting the lake and the waterfall as the hypotenuse of a right triangle.

Using the cosine function, we can calculate the length of the side adjacent to the angle (-56°), which represents the distance between the waterfall and the lake:

cos θ = adjacent / hypothenuse

Adjacent = Hypotenuse * cosθ

Let's substitute the values into the formula:

Adjacent  = 14.2 km * cos(-56°)

To calculate the cosine of -56°, we can use the fact that the cosine function is an even function:

cos(-56°) = cos(56°)

Adjacent side = 14.2 cos(56)

Adjacent side = 7.94km

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Answer:

The waterfall is approximately 8.91 km away from the lake

Step-by-step explanation:

To find the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the southward direction.

Since the waterfall is 14.2 km south of the lake, the line connecting the waterfall and the lake forms a right triangle with the south direction being the adjacent side, the distance between them being the hypotenuse, and the angle formed between them being the bearing of 236°.

To find the distance between the waterfall and the lake, we can use the cosine function, which relates the adjacent side, hypotenuse, and angle:

cos(236°) = adjacent side / hypotenuse

Let's denote the distance between the waterfall and the lake as "d." The adjacent side represents the southward direction.

cos(236°) = d / 14.2 km

Solving for "d":

d = cos(236°) * 14.2 km

Using a calculator:

d ≈ -8.91 km

Since distance cannot be negative, we take the absolute value:

|d| ≈ 8.91 km

Therefore, the waterfall is approximately 8.91 km away from the lake.

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Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = [tex]\frac{1}{2}[/tex] × 100° = 50°

Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

:)

There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.

To construct a 90% confidence interval for the mean number of books people read, we can use the following formula:

Confidence Interval = x ± (Z * (s / √n))

Where:

x = sample mean (12.4 books)

s = sample standard deviation (16.6 books)

n = sample size (1017)

Z = Z-score

Since the sample size is large (n > 30), we can assume the sampling distribution is approximately normal.

We can use the standard normal distribution to find the Z-score for a 90% confidence level.

The Z-score for a 90% confidence level is approximately 1.645.

Now we can calculate the confidence interval:

Confidence Interval = 12.4 ± (1.645  (16.6 / √1017))

Confidence Interval ≈ 12.4 ± (1.645  (16.6 / √1017))

Confidence Interval ≈ 12.4 ± (1.645  (16.6 / 31.95))

Confidence Interval ≈ 12.4 ± (1.645 x 0.518)

Confidence Interval ≈ 12.4 ± 0.85

There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.

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Hello!

A = 115° => opposite

B = 115° => corresponding angles

C = 65° => 180° - 115°

Answer:

A = 115 degrees

B = 115 degrees

C = 65 degrees

Step-by-step explanation:

A is opposite of 115 so it is 115 degrees.

B is 115 because it is on a parellel line to the one of 115

C is 180 minus B, which is 180 - 115 = 65

The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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The value of measure of angle 1, angle 2, and angle 3 are,

⇒ ∠1 = 106 degree

⇒ ∠2 = 74°

⇒ ∠3 = 74°

We have to given that;

Angle in figure is,

⇒ 74°

Since, From figure,

angle 1 is,

⇒ ∠1 = 180 - 74

⇒ ∠1 = 106 degree

Hence, We get;

Measure of angle 2 is,

⇒ ∠2 = 180 - 106

⇒ ∠2 = 74°

And, Measure of angle 3 is,

⇒ ∠ 3 = ∠ 2

By definition of alternate interior angle.

⇒ ∠3 = 74°

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The measure of ∠1 is 106 because it is a straight angle with 74° angles.

The measure of ∠2 is 74 because it is a vertical angle with 74° angles.

The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.

We have,

The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.

Corresponding angles are always equal.

Now,

∠1 + 74 = 180

∠1 = 180 - 74

∠1 = 106

And,

∠2 and 74 are vertical angles.

So,

∠2 = 74

And,

∠3 and 74 are corresponding angles.

So,

∠3 = 74

Thus,

The measure of ∠1 is 106 because it is a straight angle with 74° angles.

The measure of ∠2 is 74 because it is a vertical angle with 74° angles.

The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.

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This is a simple one.

All you need to do is find the scale factor of the shapes. (How much has it decreased by?)

Wecan find this by doing 15 ÷ 20 (not the other way round because we want to find the scale factor for the bigger rectangle to the smaller)

15 ÷ 20 = 0.75

So to find the area all you need to do is times the area with the scale factor which is 0.75

500 x 0.75 = 375cm²

So the answer is

(A) 375cm²

Step-by-step explanation:

This is the equation for a circle in the form :

(x-h)^2 + (y-k)^2  =   r^2     where h,k is the center and r is the radius

center = 5.2,-3.7    and radius = sqrt (49) = 7

Given statement solution is :- The Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.

To find the inverse function of f(x) = (x - 4)/3, we need to swap the roles of x and y and solve for y. Let's start by writing the equation with y instead of f(x):

y = (x - 4)/3

Now, let's interchange x and y:

x = (y - 4)/3

To solve for y, we can isolate it by multiplying both sides of the equation by 3:

3x = y - 4

Next, let's add 4 to both sides:

3x + 4 = y

Finally, we can write the inverse function as:

[tex]f^(-1)(x)[/tex] = 3x + 4

So, the Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.

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Answer:

[tex]\textsf{a)} \quad x = 17[/tex]

[tex]\textsf{b)} \quad T_n=3n^2-3n-1[/tex]

[tex]\textsf{a)} \quad x = 20[/tex]

[tex]\textsf{b)} \quad T_n=3n^2-4n+5[/tex]

Step-by-step explanation:

Given quadratic number pattern:

To find the equation for the nth term, we can use the general form of a quadratic equation:

[tex]\boxed{T_n=an^2 + bn + c}[/tex]

where n is the position of the term.

Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:

[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=-1\\a+b+c&=-1\end{aligned}[/tex]

[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=5\\4a+2b+c&=5\end{aligned}[/tex]

[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=35\\16a+4b+c&=35\end{aligned}[/tex]

Rearrange the first equation to isolate c:

[tex]c=-a-b-1[/tex]

Substitute this into the second and third equations:

[tex]\begin{aligned}4a+2b+(-a-b-1)&=5\\3a+b&=6\end{ailgned}[/tex]

[tex]\begin{aligned}16a+4b+(-a-b-1)&=35\\15a+3b&=36\end{ailgned}[/tex]

Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:

[tex]b=-3a+6[/tex]

[tex]\begin{aligned}15a+3(-3a+6)&=36 \\15a-9a+18&=36\\6a&=18\\a&=3 \end{aligned}[/tex]

Substitute the found value of a into the equation for b and solve for b:

[tex]\begin{aligned}b&=-3a+6\\&=-3(3)+6\\&=-9+6\\&=-3\end{aligned}[/tex]

Finally, substitute the found values of a and b into the equation for c and solve for c:

[tex]\begin{aligned}c&=-a-b-1\\&=-3-(-3)-1\\&=-3+3-1\\&=-1\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\boxed{T_n=3n^2-3n-1}[/tex]

The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:

[tex]\begin{aligned}T_3&=3(3)^2-3(3)-1\\&=3(9)-3(3)-1\\&=27-9-1\\&=18-1\\&=17\end{aligned}[/tex]

Therefore, the value of x is 17.

[tex]\hrulefill[/tex]

Given quadratic number pattern:

To find the equation for the nth term, we can use the general form of a quadratic equation:

[tex]\boxed{T_n=an^2 + bn + c}[/tex]

where n is the position of the term.

Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:

[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=4\\a+b+c&=4\end{aligned}[/tex]

[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=9\\4a+2b+c&=9\end{aligned}[/tex]

[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=37\\16a+4b+c&=37\end{aligned}[/tex]

Rearrange the first equation to isolate c:

[tex]c=-a-b+4[/tex]

Substitute this into the second and third equations:

[tex]\begin{aligned}4a+2b+(-a-b+4)&=9\\3a+b&=5\end{ailgned}[/tex]

[tex]\begin{aligned}16a+4b+(-a-b+4)&=37\\15a+3b&=33\end{ailgned}[/tex]

Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:

[tex]b=-3a+5[/tex]

[tex]\begin{aligned}15a+3(-3a+5)&=33 \\15a-9a+15&=33\\6a&=18\\a&=3 \end{aligned}[/tex]

Substitute the found value of a into the equation for b and solve for b:

[tex]\begin{aligned}b&=-3a+5\\&=-3(3)+5\\&=-9+5\\&=-4\end{aligned}[/tex]

Finally, substitute the found values of a and b into the equation for c and solve for c:

[tex]\begin{aligned}c&=-a-b+4\\&=-3-(-4)+4\\&=-3+4+4\\&=5\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\boxed{T_n=3n^2-4n+5}[/tex]

The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:

[tex]\begin{aligned}T_3&=3(3)^2-4(3)+5\\&=3(9)-4(3)+5\\&=27-12+5\\&=15+5\\&=20\end{aligned}[/tex]

Therefore, the value of x is 20.

Answer: the question doesn't give that much information but you would have 7/4 or 1.75 green counters.

Step-by-step explanation: 7/4 as a decimal is 1.75

Answer:

Each person will get 2 pounds of candy

Step-by-step explanation:

Nicole + 3 friends = 4 total

8 pounds of candy = total

total candy / total people

8/4 = 2

The maximum number of CYN Dewi can buy is 4268.8 CYN and cost in pounds is  £453.20.

Maximum number of CYN Dewi can buy:

Since £1 buys 9.28 CYN, Dewi's £460 can be converted to Chinese yuan by multiplying it by the exchange rate:

Maximum CYN = £460 × 9.28 CYN/£1

To calculate this, we multiply the pound amount by the exchange rate:

Maximum CYN = £460 × 9.28 CYN/£1 ≈ 4268.8 CYN

Cost in pounds to the nearest penny:

To calculate the cost in pounds, we divide the desired amount of Chinese yuan by the exchange rate:

Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1

To calculate this, we divide the Chinese yuan amount by the exchange rate:

Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1

= £453.20

Therefore, the cost in pounds, to the nearest penny, will be £453.20.

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Complete question

Buying chinese yuan (CYN)             £1 buys 9.28 CYN

Selling chinese yuan (CYN)           9.42 CYN buys  £1

(a) Dewi has £460 to buy Chinese yuan.

Calculate the maximum number of CYN Dewi can buy, and

how much, to the nearest penny, this will cost him.

Answer:

32 inches Aprox

Step-by-step explanation:

To find the size of a rectangular television screen given its height and width, we can use the Pythagorean theorem. The diagonal measurement (size) is the hypotenuse of a right triangle formed by the height and width.

Given:

Height of the television screen (h) = 20 inches

Width of the television screen (w) = 25 inches

Using the Pythagorean theorem:

diagonal² = height² + width²

diagonal² = 20² + 25²

diagonal² = 400 + 625

diagonal² = 1025

Taking the square root of both sides:

diagonal ≈ √1025

diagonal ≈ 32.02

Rounding to the nearest inch, the size of the television screen is approximately 32 inches.

Therefore, the size of the rectangular television screen, rounded to the nearest inch, is 32 inches.

The solution is the multiplication is: 5x × (3x-2)  = 15x² - 10x.

Here, we have,

given that,

the expression is:

5x(3x-2)

now, we have to Multiply out

so, we have,

5x × (3x-2)

= 5x×3x - 5x×2

=15x² - 10x

Hence, The solution is the multiplication is: 5x × (3x-2)  = 15x² - 10x.

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By using the table of values, a graph of the exponential function is shown in the image below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided above, we can logically deduce the following exponential function;

[tex]y = 2^x[/tex]

Next, we would create a table of values based on the exponential function;

when x = 0, the y-value is given by;

y = 2⁰

y = 1

when x = 1, the y-value is given by;

y = 2¹

y = 2

x                     y____

-2                 0.25

-1                  0.5

0                   1

1                    2

2                   4

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Answer:

150

Step-by-step explanation:

The measure of unknown angles,

∠1  = ∠4 = 110 degree

∠2 = ∠3 = 70 degree

Labeling the figure,

Then from figure we have,

⇒ x + 40 + x = 180

⇒     2x + 40 = 180

Subtract 40 both sides,

⇒            2x  = 140

Divide both sides by 2

⇒              x  = 70

From figure,

⇒ ∠1 + 70 = 180

⇒         ∠1 = 180 - 70

⇒         ∠1 = 110 degree

And from figure,

⇒ ∠1 + ∠2 = 180

⇒ 110 + ∠2 = 180

⇒          ∠2 =  70 degree

Since,

∠2 = ∠3 = 70 degree

And  ∠1  = ∠4 = 110 degree

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