find the area bounded by the Curves y=4-x² and y

Answers

Answer 1

The area bounded by the Curves y=4-x² and y = 2x + 1 is 10 1/3 units.

What is area?

Area is the amount of space occupied by a two dimensional shape or object.

y = 4 - x² and y = 2x + 1

4 - x² = 2x + 1

x² + 2x - 3 = 0

(x + 3)(x - 1) = 0

x = -3; or x = 1

The area (A) is given by:

[tex]A=\int\limits^1_{-3} {x^2+2x-3} \, dx \\\\A=10\frac{1}{3}[/tex]

The area bounded by the Curves y=4-x² and y = 2x + 1 is 10 1/3 units.

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Related Questions

Although the numbers are not included on either axis, it is possible to determine from shape and location that the equation y = -1.2x+4 corresponds to graph​

Answers

It looks like your question is incomplete. I believe you also have options to pick which graph is correct. However, I can still give you the information you are looking for.

The slope of the line is -1.2

The Y-intersect is (0, 4)

I have also attached an image of what the graph would look like.

Hope this helps.

Probability and statistics

Answers

Probability and statistics are two branches of mathematics that are used to calculate the possibility of occurrence of an event or trend of data.

What is probability?

Probability is a term to refer to the science that studies the measurement of the certainty of occurrence of an event. Generally, the probability of occurrence is associated with a value between 0 and 1, where an impossible event corresponds to zero and a certain event corresponds to one.

What is statistics?

Statistics is a term to refer to a branch of mathematics that studies different phenomena related to data such as:

VariabilityCollectionOrganizationAnalysisInterpretationPresentation

Another outstanding aspect of statistics is that it is a formal deductive science framed in the formal scientific method.

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Which function is best represented by this graph? Brainliest

Answers

Answer:B

Step-by-step explanation:the slope is 1/4, and it crosses the y axis at -2.

Riley tried the following homework question:
On July 1st, the billing date, Jenson's American Express credit card account had a balance of $375.80. The transactions during the
month of July were:
July 5 Payment made $150.00
July 10 Dinning
$74.35
July 18 Car repair
$123.50
July 28 Groceries
$142.50
The card has a low-interest rate of 1.3% per month. What is the balance due on August 1st?
The instruction hinted that "to find the balance due, you need to calculate the Average Daily Balance (ADB)."
So Riley made a running balance table and got ADB = 372.08, finance charge = 4.84, and Riley wasn't sure what to do next to answer
the final question "balance due on August 1st"? Please make a running balance table to show the ADB Riley got, and further explain
how to find the final balance on August 1st. What is the balance due on August 1st? Be specific with your answer.

Answers

Answer:

her balance aka ADB would be 372.08

this urgent pls
thank you ​

Answers

Answer:

x is less or equal to 30

the last Choice is correct.

Answer:

Last option D.

Step-by-step explanation:

IF it can be no more than 30, the 4th one says it can be equal to 30 or less than thirty.

solve this sum. ....​

Answers

Z = -5 , O = 0 , P = 3

Given that points Q, R, S lies between O and P meaning that the points are between 0 and 3

OQ = QR = RS = SP

Draw a number line and find three equal points

so points:

Q = 0.75R = 1.5S = 2.25

Answer:

[tex]\sf Q=\dfrac34, \ R=\dfrac32, \ S=\dfrac94[/tex]

Step-by-step explanation:

Given information:

O = 0P = 3Points Q, R and S are between O and POQ = QR = RS = SP

Therefore, there are 4 segments of equal distance between points O and P.    

Length of OP = 3 - 0 = 3

⇒ Length of each segment = 3/4

To find the point of Q, R and S, add 3/4 to each point:

   Point O = 0

⇒ Point Q = 0 + 3/4 = 3/4

⇒ Point R = 3/4 + 3/4 = 3/2

⇒ Point S = 3/2 + 3/4 = 9/4

   Point P = 9/4 + 3/4 = 3

Therefore,

[tex]\sf Q=\dfrac34, \ R=\dfrac32, \ S=\dfrac94[/tex]

I need help for this one.

Answers

Answer:

D. 48 feet

Step-by-step explanation:

Ladder (50 ft) = hypotenuse

Floor distance (14 ft) = b

Wall (unknown) = a

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

[tex]a^2+14^2=50^2[/tex]

[tex]a^2+196=2500[/tex]

[tex]a^2=2500-196[/tex]

[tex]a=\sqrt{2304}[/tex]

[tex]a=48[/tex]

Hope this helps!

Answer:

48 feet

Step-by-step explanation:

Here,

c = 50 ft

b = 14 ft

To find : the height of the wall that the ladder reaches ( a ) = ?

Formula : -

a² + b² = c²

a² = c² - b²

= 50² - 14²

= ( 50 x 50 ) - ( 14 x 14 )

= 2500 - 196

= 2304

= 48 x 48

a² = 48²

a = 48 feet

Solve the equation Enter your answer as an equation that shows the value of
the variable (like s = 2/3, or 4 = w).
8x - 2 = 70

Answers

Algebra 1 Answer Key. ITEM 98. Find the equation that is equivalent to the quadratic equation shown. x2 – 8x – 8 = 0. A. x(x – 4) = 32. B. (x – 8)2 = 64.

There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?

Answers

Answer:

85 dogs have signed up to compete

Step-by-step explanation:

its 85 small dogs because 49+36=85

The daily sleep duration among college students is normally distributed with a mean of 8.13 and standard deviation of 1.87. You want to use a sample size such that 95% of the averages fall within +/- 15 minutes (.25 of an hour) of the true mean of 8.13. Determine the smallest number of students you need to sample.

Answers

Using the z-distribution, as we have the standard deviation for the population, it is found that 215 students must be sampled.

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is of M = 0.25, with a population standard deviation of [tex]\sigma = 1.87[/tex], hence we solve for n to find the minimum sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.25 = 1.96\frac{1.87}{\sqrt{n}}[/tex]

[tex]0.25\sqrt{n} = 1.96(1.87)[/tex]

[tex]\sqrt{n} = \frac{1.96(1.87)}{0.25}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96(1.87)}{0.25}\right)^2[/tex]

[tex]n = 214.9[/tex]

Rounding up, 215 students must be sampled.

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PLEASEEE HELP QUICK :D

Answers

Answer:

Option a!

Step-by-step explanation:

inverse means opposite:

First part of the statement:

If I studied for it

(opposite)

If I did not study for it

Second:

I did well on the exam

(opposite)

I did not do well on the exam

Hope this makes sense.

- profparis

Elise is in a challenge with her gym class to run a total of 200 miles in one
school year. In the first month she ran 18 miles. If she wants to split the
remaining amount of miles over the
next seven months, how many miles will
she run each month?
Show your work.

Answers

Total : 200 miles
1 month ran : 18 miles
Raking miles left :182
Remaining months :7
182/7 = 26
So she should run a total of 26 miles per month

The average transaction at an automatic teller can be completed in six minutes and customers arrive at the average rate of one every ten minutes. On average, how many customers are there in the queue? a. 0.375 Customers b. 0.900 Customers c. 1.160 Customers d. 4.000 Customers

Answers

Answer:

Zero, based on the information provided.

Step-by-step explanation:

The output rate of the teller machine is (1 transaction/6 minutes).  The input rate is (1 customer/10 minutes).  This means that the machine completes a cycle faster than the customers arrive, on the average.  I don't know how an average can be calculated without more information.  If we assume customers arrive every 10 minutes, and no one screws up the machine, that there should be no waiting line.   Is there more information about when the customers arrive?  E.g., 50 arrive in the first hour the machine is open.

If the average transaction at an automatic teller can be completed in six minutes and customers arrive at the average rate of one every ten minutes. The average number of customers in the queue is: B. 0.900 customers.

What is the average number?

M represent Markovian (memoryless) arrivals and service times

1 represents a single server.

Arrival rate (λ) is 1 customer every 10 minutes and the service rate (μ) is 1 customer every 6 minutes.

The formula to determine the average number of customers in the queue (Lq) is:

Lq = (λ^2) / (μ * (μ - λ))

Plugging in the values:

λ = 1/10

μ = 1/6

Lq = ((1/10)^2) / ((1/6) * ((1/6) - (1/10)))

Lq = (1/100) / ((1/6) * (10 - 6)/60))

Lq = (1/100) / ((1/6) * (4/60))

Lq = (1/100) / ((1/6) * (1/15))

Lq = (1/100) / (1/90)

Lq = (1/100) * (90/1)

Lq = 90/100

Lq = 0.9

Therefore, the correct option is B.

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#SPJ3

Find the sum of 458 and 342

Answers

Answer: 800

Step-by-step explanation:

A line passes through the point (3,-6) and has a slope of -4

Write an equation in point-slope form for this line

Answers

Answer:

step by step explanation

please see photo

Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.

Answers

The answers is X = 23

Answer:

x=23

Step-by-step explanation:

2x-6/4 = 10

2x-6 = 10(4)

2x-6 = 40

2x = 40+6

2x = 46

x = 46/2

x = 23

Write an equation that best describes the pattern in the table
а
a
1
0 1
2
1
1
24-
58
2
2
b
0
3
4.
9
10 17

Answers

Answer:

not sure about the equation or answer

10 1/5 • 4 1/4 • 2 not simplified please

Answers

51/5 × 17/4 ×2

=51/5 ×17/2

= 867/10

Which point on the number line best represents √10

Answers

Answer:

So it would be around 3.

Step-by-step explanation:

[tex]\sqrt{10}[/tex]= 3.16227766017

Guys please help! i will mark brainliest to the right answers

Note: in order for me to mark a brainliest 2 people need to answer

Answers

Answer:

look at the picture i have attached and tell me what you think???

Step-by-step explanation:

parallel is two lines that go like this \\ or like this =

perpendicular is two lines that go like this +

which is it?

Answer:

they are parallel as gradient is the same because in first equation coefficient of x is -2 and in second equation after rearranging equation in form of y= mx + c, m is -2

WHEN THE WHOLE IS THE SAME, HOW MANY 8THS DOES IT TAKE TO EQUAL 1\4. DRAW A MODEL TO SHOW YOUR ANSWER.

Answers

Answer: 4

Step-by-step explanation:

4 times 2 is 8 if you make 4 eighths you will get 1/4 a

It takes 2 eighths to equal 1/4
This is why:

Zoe planted a walnut tree. Every week, she measures the tree and records its
growth. On the first week, the tree was 27 1/2 inches tall. On the second week, it was
29 1/4 inches tall. On the third week, it was 31 1/3 inches tall. How much did the tree
grow from the first week until it was measured on the third week? Show your work.

Answers

The tree grew about 3.83 inches between the first and third week.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

On the first week, the tree was 27 1/2 inches (27.5) tall. On the second week, it was 29 1/4 inches (29.25) tall. On the third week, it was 31 1/3 inches (31.33) tall.

The length grown = 31.33 - 17.5 = 3.83 inches

The tree grew about 3.83 inches between the first and third week.

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Find LCD in number 16 and multiply all numerators by it to clear the fractions

Answers

The LCD of the given terms of expression will be x² - 4 since others can divide it.

How to find the LCD

The least common denominator is the smallest number or expression of all the common multiples of the denominators when 2 or more fractions or expressions are given.

Given the terms of the expressions

(x+2)(x-2) and (x^2 - 4)

Expand (x^2 - 4) using the difference of two square:

x² - 4 = x² - 2²

x² - 4 = (x+2)(x-2)

Based on the expansion, we can conclude that the LCD of the given terms of expression will be x² - 4

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A shop sells pairs of trainers for £68 each. They make a percentage profit of 70% on each pair.
What was the cost of each pair of trainers to the shop?

Answers

Answer:

47.6 euros

Step-by-step explanation:

68 x .70 = 47.6

.70 = 70%

70% of 68

of means multiply

You turn the percent into a decimal and multiply

Jessica sells 50.5 ounces of lemonade for a total of 20.20.
Find the unit price in dollars per ounce.
If necessary, round your answer to the nearest cent.

Answers

Answer:

2.5

Step-by-step explanation:

Answer: 2.5

Step-by-step explanation: do it yourself jk lol first you add then divide by 6.5

What is the balance point for the following data set? 19 80 15 20​

Answers

The balance point of the dataset is the mean of the dataset

The balance point of the dataset is 20

How to determine the balance point?

From the dataset, we have the following frequency table

Data (x)     Frequency (f)

15                    2

24                   1

26                  1

The balance point of the dataset is the mean value of the dataset, and the mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

This gives

[tex]\bar x = \frac{15 * 2 + 24 * 1 + 26 *1}{2 +1+1}[/tex]

Evaluate the sum

[tex]\bar x = \frac{80}{4}[/tex]

Evaluate the quotient

[tex]\bar x = 20[/tex]

Hence, the balance point of the dataset is 20

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2 pounds of zucchini for 4 servings

Answers

Answer:

One pound of zucchini equals about 4 cups grated zucchini;

Step-by-step explanation:

2 cups of salted and squeezed zucchini; about 1 cup mashed zucchini; and 3 cups chunked zucchini.

Help with this question pls

Answers

Answer:

Exact: [tex]4\sqrt{55}[/tex] m

Approximate: 29.7 m

Step-by-step explanation:

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

[tex]9^2+b^2=(31\sqrt{5} )^2[/tex]

[tex]81+b^2=31^2(5)[/tex]

[tex]b^2=961-81[/tex]

[tex]b=\sqrt{880} =4\sqrt{55}[/tex]

[tex]4\sqrt{55}[/tex] ≈ 29.7 m

Hope this helps!

Graph y = 0.5|x|
The graph of the function f(x) = 0.5|x| is than its parent graph, f(x) = |x|.
The Domain and Range?

Thanks!

Answers

Domain: x is all reals
Range: y ≥ 0

Find the area of the trapezoid

Answers

It is 60. sans as a s abs
The area of a trapezoid is 60
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