Sketch a figure that is similar to this figure. Label side and angle measures.

Use the fact that -1 ≤ sin(x) ≤ 1.

Then

20 ≥ -20 sin(x) ≥ -20 … … … (multiply each side by -20)

-20 ≤ -20 sin(x) ≤ 20 … … … (swap the endpoints)

10x - 20 ≤ 10x - 20 sin(x) ≤ 10x + 20 … … … (add 10x to each side)

and over the interval [7, 8], we have

7 ≤ x ≤ 8

70 ≤ 10x ≤ 80 … … … (multiply each side by 10)

so that the whole integrand is bounded by

70 - 20 ≤ 10x - 20 sin(x) ≤ 80 + 20

50 ≤ 10x - 20 sin(x) ≤ 100

Take m = 50 and M = 100. It follows that

[tex]50(8-7) \le \displaystyle \int_7^8 (10x-20\sin(x)) \, dx \le 100(8-7)[/tex]

which places the value of the integral between 50 and 100.

Answer:

WHEN THE BIRDS FLYING IN THE FIRE COZ THE MOON IS RECTANGLE I LIKE COLOR YELLOW COZ MY POP IS CIRCLE

Answer:

y = -2/3x - 13

Step-by-step explanation:

The slope remains the same, but the y-intercept changes to -13

Answer:

x^3 - 4x^2 - 6x + 3

Step-by-step explanation:

Divide using polynomial division.

Answer:

817.51

Step-by-step explanation:

The n-th term of an arithmetic sequence with first term a and common difference d is

a + (n - 1) d

So, the 51st term of A is

30 + 9 (51 - 1) = 480

while the 51st term of B is

30 + 4 (51 - 1) = 230

The difference between them 480 - 230 = 250.

Answer: 6

Step-by-step explanation:if you add -5 1/3 plus (-2/3) that equals to -6 and if you are adding you gotta add a positive 6 to the negative 6 and that makes 0

[tex] - 5 \frac{1}{3} + ( - \frac{ 2}{3} ) + ? = 0[/tex]

The missing term

Taking the missing term as "x"

[tex] - 5 \frac{1}{3} + ( - \frac{ 2}{3} ) + ? = 0 \\ \\ \implies - \frac{ 16}{3} - \frac{2}{3} + x = 0 \\ \\ \implies \frac{ - 16 - 2}{3} + x = 0 \\ \\ \implies \frac{ - 18}{3} + x = 0 \\ \\ \implies \cancel \frac{ - 18}{3} + x = 0 \\ \\ \implies - 6 + x = 0 \\ \\ \implies x = 0 + 6 \\ \\ \implies x = \red6[/tex]

[tex] \therefore \tt{The \: \: missing \: \: term= 6}[/tex]

= 8

step-by-step explanation:

evaluate

-8c⁴ d +4c² d² + 16c - 2d

when c =-1 ,d=4

=8

#carry on learning

Sorry if I am incorrect.....

Answer:

6 miles per hour

does this help??

Step-by-step explanation:

Average speed = distance/time = 30/5 = 6 miles/hour

Answer:

410 i think

Step-by-step explanation:

Answer:

D.  none of the above

Step-by-step explanation:

no side lengths given

no angles are the same in both triangles

Answer: I think its d

Step-by-step explanation:

Answer:

y=-6x+5

Step-by-step explanation:

Answer:

4 dollars in total

Step-by-step explanation:

its 75 after the spend

Answer: R = 2.38732415 D = 4.7746482927568605

Answer:

64874577837

Step-by-step explanation:

you simply add the numbers

45292062 + 64829162629 + 123146 =

64874454691 +123146

Answer:

100

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer:

Lol

Step-by-step explanation:

The coworkers meet each day after the official work hours, then they are an example of an informal group. An informal group is a group made up of people to discuss non-official matters.

The two major types of groups relating to official function are formal and informal. Formal groups are groups formed by the management for a specific or official purpose. This type of groups discuss official matters and issues, and probably are dissolved after achieving the purpose of forming the group.

Informal groups are groups formed by a set of workers( which may sometimes include an external person) formed to discuss non-official maters. The members meet at the non-official hours to deliberate, gist or discuss personal and other relating issues.

Therefore, the four coworkers mentioned in the given question are an example of an informal group.

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Answer:

c maybe

Step-by-step explanation:

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The slope of the given line is Undefined because it is parallel to y - axis ~

Answer:

zero

Step-by-step explanation:

Answer:

Function; Not a function

Step-by-step explanation:

Write the ordered pair in the first set (x, y):     (1, 11), (2, 7) , (3, 2)

Write the ordered pair in the second set (x, y):     (1, 3), (1, 4),  (2, 4) , (3, 2)

The first set in a function because no ordered pair has the same x value.

The second set in not a function because the x value is the same in two of the ordered pairs.

Answer:

Step-by-step explanation:

The first choice is 1 out of 52

The second choice is 1 out of 51 because 1 card went with the first choice

The third is 1 out of 50

The fourth is 1 out of 49

Number of hands = 52*51*50*49

Number of hands = 6497400

Answer:

x³+y³+z³=k

Explanation:

I talk, he talk, why you middle talk? You rotate the ground 4 times. You go and understand the tree.  I'll give you clap on your cheeks. Bring your parents and your mother and especially your father.  Close the window airforce is coming. I have two daughters and both are girls. Stand in a straight circle. Don't stand in front of my back

1. The order of the angles from smallest to greatest is PQR, QRP, PRQ.

2. The value of x + y is (2x + 179)/7.

3. Triangle GHK is isosceles because angles H and K are congruent.

4. The hypotenuse is always the longest side of a right triangle.

1. To determine the order of the angles in the given triangle, we can use the fact that the largest angle will be opposite the longest side. Let's compare the lengths of the sides:

- PQ = 5.6

- PR = 6.1

- QR = 5.2

From the given lengths, we can see that PR is the longest side. Therefore, angle PRQ will be the largest angle. Now we need to compare the remaining two angles, PQR and QRP. Since QR is the shortest side, angle PQR will be the smallest angle. This means that the order of the angles from smallest to greatest is: PQR, QRP, PRQ.

2. In a triangle, the sum of the interior angles is always 180 degrees. Given the angles in terms of y and x, we can set up an equation:

(4y - 8) + (3y + 9) + 5x = 180

Combining like terms:

7y + 5x + 1 = 180

To find the value of x + y, we need to solve for y in terms of x first. Let's isolate y:

7y = 180 - 5x - 1

7y = 179 - 5x

y = (179 - 5x)/7

Now, we can substitute this expression for y into the equation x + y:

x + y = x + (179 - 5x)/7

To simplify further, we can distribute the division:

x + y = (7x + 179 - 5x)/7

x + y = (2x + 179)/7

Therefore, the value of x + y is (2x + 179)/7.

3. To prove that triangle GHK is isosceles, we need to show that two of its sides are congruent. Given that angle H is 56 degrees, and angles IKJ and H are alternate interior angles, we know that angle IKJ is also 56 degrees. Since angle IKJ is 68 degrees, this implies that angle KJI is 112 degrees (180 - 68 = 112).

Now, considering triangle GHK, we have:

- Angle G = 180 - (angle H + angle K) = 180 - (56 + 112) = 180 - 168 = 12 degrees

Since angle G is 12 degrees, and angles G and H are alternate interior angles, we know that angle H is also 12 degrees.

Therefore, we have two angles in triangle GHK that are congruent, namely angle H and angle K, making it an isosceles triangle.

4. Proof that the hypotenuse is always the longest side of a right triangle:

Let's consider a right triangle with sides a, b, and c, where c is the hypotenuse.

According to the Pythagorean theorem, which is a fundamental property of right triangles, we have:

[tex]c^2 = a^2 + b^2[/tex]

To compare the lengths of a, b, and c, let's square all the sides:

[tex]a^2, b^2, and c^2[/tex] are all positive since they are the squares of real numbers.

Now, if we examine the inequality [tex]a^2 + b^2 < c^2[/tex], we can see that the sum of the squares of the shorter sides is less than the square of the hypotenuse.

Since [tex]c^2 = a^2 + b^2[/tex], the inequality becomes [tex]a^2 + b^2 < a^2 + b^2[/tex], which is not possible.

Therefore, we can conclude that in a right triangle, the hypotenuse (side c) is always the longest side.

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