Is this correct? (The question with the star on it)

The area for the shaded region is obtained as 2 units.

In order to find the area, first find the intersection points of the two curves. Then, the area of the region can be found by taking the integration from the intersection point.

The curves in the graph in the form of equation are as follows,

y = x² + 3                     (1)

x = (y - 5)² - 2

=> y = √(x+ 2) + 5       (2)  

Part A :

The intersection points of the two curves are (-1.5, 5.5), (-1, 4) and (0.5, 3.5).

Thus, to calculate the area the limit is from x = -1.5 to x = 0.5.

Part B :

The expression of the integral is given as,

[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]

Part C :

The area is found by evaluating the integral as follows,

[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]

= [-1/3 + 3.375/3 + 3(-1 - (-1.5))] - [5(-1 - (-1.5)) + 2/3([tex]1^{3/2} - 0.5^{3/2}[/tex])] + [5(0.5 - (-1)) -(0.125/3 + 1/3 + 3(0.5 - (-1))]

= 2.291 - [2.5 + 2/3 × 0.647] + [5 × 1.5 - 4.8716]

= 2.291 - 2.927 + 2.6284

= 1.9924

Which is approximately 2.

Hence, the area between the curves is given as 2 units.

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Answer:

15

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

So we have f(x) = x + 1 and g(x) = 5x. We need to find f(g(x))(-1). So let's put g(x) into f(x): f(g(x)) = f(5x) = 5x + 1. Now we have x = -1. Let's substitute this into 5x + 1 = -5 + 1 = -4.

The  equation that correctly solves for x in △RST is; x² + 11x - 42 = 0

We are given that ΔDEF ∼ △RST.

This means that ΔDEF is similar to △RST.

From the concept of similar triangles, all corresponding sides are usually in the same ratio. Thus, applying this to our given triangles, we have;

DE/RS = EF/ST = DF/RT

This means when we plug in the relevant values, we will get;

(x + 5)/12 = (x + 7)/(x + 12) = 6/(x + 6)

Thus, we can say that;

(x + 5)/12 = 6/(x + 6)

Cross multiply to get;

(x + 5)(x + 6) = 72

x² + 11x + 30 - 72 = 0

x² + 11x - 42 = 0

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Complete question is;

In the figure shown, ΔDEF ∼ △RST . Which equation can be used to find the value of x?

The difference between fundamental theorem of calculus part 1 and 2 is explained below:

The basic theorem of calculus is a theorem that connects the ideas of differentiating and integrating functions. A constant value that relies on where one begins to compute area makes the two procedures the inverses of one another. The relationship between the integral and derivative is established by the calculus fundamental theorem. Simply put, it says that the height of the area at a point x equals the rate of change of the area under the curve up to that point. We can find definite integrals with the aid of this theorem.

The connection between the integral and the derivative is demonstrated in The Fundamental Theorem of Calculus, Part 1. Take note. A definite integral can be assessed in terms of an antiderivative of its integrand using the Fundamental Theorem of Calculus, Part 2. This formula will calculate the total area under a curve.

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Answer:

148 cm²

Step-by-step explanation:

Using the formula for the total surface area of a cuboid,

[tex]2(6 \times 4+6 \times 5+4 \times 5)=148[/tex]

Adding the times on A and B gets you 16 minutes and 3 seconds. 20 minutes minus 16 minutes and 3 seconds will leave you with

3 minutes, 57 seconds

to solve for m

distribute into parentheses

176 = -16 - 24m

get m on one side

176 + 16 = -24m

192 = -24m

divide by -24

-8 = m

m = -8

Answer:

Step-by-step explanation: Can u show the picture of the table so i can understand this better

The required expected number of women on the committee is 1/2 or 0.5.

The expected number of women on the committee can be found by calculating the probability that a woman is selected for the committee and then multiplying that probability by the number of people on the committee.

There are a total of 6 + 2 = 8 people in the club, and the committee has 2 people.

Given the committee is selected randomly, the probability that a particular person is selected for the committee is 2/8 = 1/4.

There are 2 women in the club, so the probability that a woman is selected for the committee is 2/8 = 1/4.

The expected number of women on the committee is the probability that a woman is selected for the committee multiplied by the number of people on the committee, which is (1/4) * 2 = 1/2.

Thus, the expected number of women on the committee is 1/2 or 0.5.

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Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to complex numbers (1∕2 + 4i)².

Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the case of quadratic equations, the unknown roots are simplified using complex numbers if the roots are not real. In computer science and engineering, complex numbers are used. Both mechanical and civil engineering use complex numbers. Control systems employ complex numbers.

Given,

Complex numbers:;

(1/2 + 4i)²

(a +b )² = a² + b² + 2ab

Multiplying,

(1/2)² + (4i)² + 2(1/2)(4i)

1/4 + 16i² + 4i

i² = -1

1 - 64/4 + 4i

-63/4 + 4i

Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to (1∕2 + 4i)².

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The z score that has 70.54% of the distribution area is 9.92

The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.

For the random variable x, the z-score is;

z = (x - 11)/2

therefore, 70.54% of the area under the curve lies to the right of x,

then the area to the left of x is;

100 - 70.54 = 29.46%

From the standard table, a z-score of -0.54 will yield an area of 29.46% to the left of x.

Therefore, we get;

(x - 11)/2 = -0.54

x - 11 = -0.54(2)

x = 9.92

The z score  is 9.92

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Answer:

3 / 5

Step-by-step explanation:

TOA-CAH-SOH are 3 trigonometry ratios. They are:

TOA - tan(theta) = Opposite ÷ Adjacent

CAH - cos(theta) = Adjacent ÷ Hypotenuse

SOH - sin(theta) = Opposite ÷ Hypotenuse

We are finding Cos(A)

Cos(A) = Adjacent ÷ Hypotenuse

= AB ÷ AC

=

[tex] \frac{30}{50} \\ = \frac{3}{5} [/tex]

Therefore Cos(A) = 3 / 5.

The situation that is best described by the situation is that D. The temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is given as:

y = 2x - 2.

This illustrates that the temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.

In conclusion, the correct option is D.

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Answer: (-3,-3)

Step-by-step explanation:

Sub in the numbers

3(0)-4(-4)<16

16<16 wrong

3(-3)-4(-3)<16

-9+12<16

3<16 Correct

(-3,-3)

Answer:

A. true

Step-by-step explanation:

I believe you pay most of your interest when you first receive the loan.

Answer:

-13

Step-by-step explanation:

The ys can combine and so can the numbers so if you take -5y + 5y you get 0. so those completely cancel out, so then you would add -12 + -1 which is -13.

The strategic decision based on the p-value is given as follows:

Allow the machine to continue operating as it is.

The decision depends if we reject or do not reject the null hypothesis in this problem, as follows:

The decision rule to accept or reject the null hypothesis is given as follows:

The p-value in this problem is given as follows:

0.06811.

Which is greater than the significance level, hence the null hypothesis is not rejected and the first option is correct, as the machine should be allowed to continue operating as it is.

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Answer:

n = -1

Subtract and isolate

To solve this problem, the first thing we have to do is regroup the terms so that we can then subtract, simplify, subtract, and finally simplify again.

But first we must know.

Equations are those mathematical equalities divided between two expressions which are called members and separated by their equal sign, in which known elements and unknown or unknown data appear, related by mathematical operations.

Now we must check our results.

8n -7 = -12 + 3n

8 × - 1 - 7 = -12 + 3 × - 1

- 8 - 7 = - 12 - 3

- 15 = - 12 - 3

- 15 = - 15

So, our results are correct, the answer is n = - 1

¡Hope this helped!

Answer:

6x-3=15

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

5 x 4 = 20

Answer: 2nd first 1st second third 4th fourth 3rd and 5th in 5th

Step-by-step explanation:

Answer:

[tex]h=\pm 21[/tex]

Step-by-step explanation:

[tex]h^2=441 \implies h=\pm \sqrt{441}=\pm 21[/tex]

Answer:

To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 68, as it is the middle value when the data is arranged in ascending order.

Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {56, 58, 64}, and the upper half of the data is {72, 75, 78}. The median of the lower half is 58, and the median of the upper half is 75.

Therefore, the value of the quartiles is Q1 = 58, Q2 = 68, and Q3 = 75.

Option D, Q1 = 58; Q2 = 68; Q3 = 75, is the correct answer.

Step-by-step explanation:

Answer: 2/1

Step-by-step explanation:

You can decide this by looking at the rise over the run.

Answer:

12 Pieces left!

Step-by-step explanation:

Because, Look. 6 is 1 quarter, He gave some of his other friends less.

If you add 2 + 4, thats 6! 6 is 1 quarter. There is 4 quarters in a cake. SO 6 + 6 12, thats half of a quarter. And then he gets the other half! Good luck!

(24 pieces in his cake)

Answer:

120

Step-by-step explanation:

Using the theorems of geometry, you know that all angles of a triangle add up to 180º. We can use an equation after looking at both angles, and the total:

30 + 30 + x = 180

60 + x = 180

x = 180 - 60

x = 120

Answer:216

Step-by-step explanation: