27
The diagram shows a right-angled triangle and a quarter circle.
D
9 m
А
6 m
B.
The right-angled triangle ABC has angle ABC = 90°
The quarter circle has centre C and radius CB.
Work out the area of the quarter circle.
Give your answer correct to 3 significant figures.
You must show all your working.

Answer:

x = -9

Step-by-step explanation:

Given:

BC = x + 19

ST = x + 29

Required:

Value of x

Solution:

Midsegment theorem states that the midsegment of a triangle = ½ of the length of its third side

Thus:

BC = ½(ST)

Substitute

x + 19 = ½(x + 29)

Multiply both sides by 2

2(x + 19) = x + 29

2x + 38 = x + 29

Collect like terms

2x - x = -38 + 29

x = -9

Answer:

6

i think the - was meant to be an = instead of -

Step-by-step explanation:

rate of change is the same as slope

that is slope-intercept form.

y=mx+b

m is slope

slope= 6

Answer:

The rate of change is 6

Step-by-step explanation:

Set the equation equal to 0:

y-6x+3=0

Now solve for y because we want the equation in y=mx+b form where m is the rate

Subtract 3:

y-6x=-3

add 6x

y=6x-3

Now in y=mx+b form

m would equal 6

Answer:

-4x, 1y, -14

Step-by-step explanation:

Hope this helps :)

Answer:

C. 140, 40

Step-by-step explanation:

Supplementary angles are two angles that add up to a sum of 180°.

140+40 = 180

Answer:

Hello!

Distributive property: a(b+c)=ab+ac

Minus and plus sign.

Then multiply by the numbers.

Hope this helps!

Thanks!

Have a great day!

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The approximate rate of change of this function on the interval [-2, 2] is Option A; -9/8.

Suppose that we have to measure the rate of change of y as x changes, then we have:

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where we have

[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]

Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

The interval given as:  -2 ≤ x ≤ 2

Let (x_1,y_1) = (-2, 2)  and  (x_2,y_2) = (2, -2.5)

The rate of change

[tex]\dfrac{y_2-y_1}{x_2-x_1}\\\\\\=\dfrac{-2.5-2}{2+2} \\\\=\dfrac{-4.5}{4}\\\\=-\dfrac{9}{8}[/tex]

Therefore, the approximate rate of change of this function on the interval [-2, 2] is Option A; -9/8.

Learn more about rate of change here:

https://brainly.com/question/19167959

#SPJ2

The plane was flying long so it's true!

Answer:

Step-by-step explanation:

6

Answer:

11 Doesn't belong because there are a 3 and 33, 6 and 66, but no 1 before 11.

Answer:

Okay

Step-by-step explanation:

I'll see if I know the answer

Answer:

16

Step-by-step explanation:

Answer:

16 feet is the length.

Step-by-step explanation:

The area of a rectangle is A = L x W

If we know the area then:

208 = L x 13

208/13 = L

L= 16 feet

Answer:

$19,500 - $1000

Step-by-step explanation:

the amount Brianna earns in excess of the amount Lisa earns can be determined by subtracting the amount Brianna earns from that Lisa earns

$19,500 - $1000 = $18,500

Answer:

Don't click the site its a scam and will give your phone a virus

Answer:

x=70

Step-by-step explanation:

To solve this problem, you set up the equation 45+(2x-5)=180

Next, subtract 45 from 180 to get the equation 2x-5=135

After that, add 5 to 135 to get 2x=140

Divide 140 by 2 to get X=70

Answer:

18x+15

Step-by-step explanation:

This is basically asking you to simplify the expression.

5(4x+3)-2x

Distribute the 5

20x+15-2x

Combine like terms (x values)

18x+15

Answer:

The null hypothesis is: [tex]H_{0}: \mu = 100[/tex]

The alternative hypothesis is: [tex]H_{a}: \mu > 100[/tex]

Step-by-step explanation:

At the null hypothesis, we test if the mean is equal to a certain value.

At the alternate hypothesis, we test if the mean is less than, more than, or different from the value tested at the null hypothesis.

The tuft bind strength of a synthetic material used to make carpets is known to have a mean of 100 lb and standard deviation of 20 lb.

This means that the null hypothesis is: [tex]H_{0}: \mu = 100[/tex]

Could it be that the average tuft strength is above 100 lb?

The world above means that the appropriate alternative hypothesis is: [tex]H_{a}: \mu > 100[/tex]

Most of the numbers are in the 50’s and 60’s so the outlier would be 98

Answer:

[tex] {x}^{2} - 36 [/tex]

Step-by-step explanation:

[tex] {x}^{2} - 36 \\ \\ = {x}^{2} - {6}^{2} [/tex]

Answer:

B

Step-by-step explanation:

Anything to the 0 power is 1

Answer:

It’s C

Step-by-step explanation:

Why because it’s is

Dream should do a facial revile

Answer: B

Step-by-step explanation:

negative correlation so as x increases y decreases,

as population rises houses should rise, not A

as buildings rise, need more space and less trees, B is the answer

as cars rise population should rise, not C

no correlation, not D

Answer:

4/52 or 1/13 (simplified)

Step-by-step explanation:

There are 4 "10's" in a pack.

This means you have the chance to pick 4 10's.

So out of 52 cards, you can get 4.

4/52 -> Which can be simplified to 1/13.

This is the probability of getting a 10 (once) in a standard deck of cards.

The probability of drawing a 10 from a standard deck of 52 cards is 1/13.

Number of 10's in a standard deck of 52 cards  =4

Total cards =52

Probability is the measurement of the possibilities of events.

P(event) =Favorable outcomes/ Total possible outcomes

Here, Favorable outcomes =4

Total possible outcomes =52

P(10) =4/52

P(10) =1/13

So, the probability of drawing a 10 from a standard deck of 52 cards =1/13

Thus, the probability of drawing a 10 from a standard deck of 52 cards is 1/13

To get more about probability visit:

https://brainly.com/question/24756209

Answer:

3.79 centimetres

Step-by-step explanation:

1 day = 24 hours

91 ÷ 24 = 3.79 centimetres

Answer:

if the question you're asking is how many cm does bamboo grow per hour, then around 3.81 cm per hour.

Answer:

3

Step-by-step explanation:

Given that,

[tex]f(x) =-x^3-8x^2-15x+3[/tex]

We need to find the value of  f(x) when k = -5

Put x = -5 in th  given function.

So,

[tex]f(-5) =-(-5)^3-8(-5)^2-15(-5)+3\\\\=3[/tex]

Hence, the value of the given function is equal to 3.

Answer:

-3

Step-by-step explanation:

The slope should be -3 since the rise is -3 and the run is 1 it would be -3/1.

Answer:

d

Step-by-step explanation:

Answer: D

Step-by-step explanation:

The probability of picking a brown pencil greater than the probability as NOT picking a brown pencil because there more brown pencils than purple so there is a higher chance you will get a brown than NOT get a brown.

Answer:

$1125000

Step-by-step explanation:

45,000 x 25 = 1125000

Since the question didn't specify what values to calculate, I will assume that it is how much money was issued in total.

Answer:

a,d,e

Step-by-step explanation:

In this question, we apply limit concepts to get the desired limit, finding that the correct options are: A, D and E, leading to the result of the limit being [tex]\frac{1}{6}[/tex].

Limit:

The limit given is:

[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7}[/tex]

If we apply the usual thing, of just replacing x by 7, the denominator will be 0, so this is not possible.

When we have a term with roots, we rationalize it, multiplying both the denominator and the denominator by the conjugate.

Multiplication by the conjugate:

The term with the root is:

[tex]\sqrt{x+2} - 3[/tex]

It's conjugate is:

[tex]\sqrt{x+2}+3[/tex]

Multiplying numerator and denominator by the conjugate, meaning option A is correct:

[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3}[/tex]

We do this because at the numerator we can apply:

[tex](a+b)(a-b) = a^2 - b^2[/tex]

Thus

[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3} = \lim_{x \rightarrow 7} \frac{(\sqrt{x+2})^2 - 3^2}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x+2-9}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x-7}{(x-7)(\sqrt{x+2}+3)}[/tex]

Thus, we can simplify the factors of x - 7, meaning that option D is correct, and we get:

[tex]\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3}[/tex]

Now, we just calculate the limit:

[tex]\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3} = \frac{1}{\sqrt{7+2}+3} = \frac{1}{3+3} = \frac{1}{6}[/tex]

Thus, option E is also correct.

Using a limit calculator, as given by the image below, we have that 1/6 is the correct answer.

For more on limits, you can check https://brainly.com/question/12207599