Find the inverse for: f(x) = 2x^2-3

Given the system of equations:

-10x-15y=25...................................equation 1

x - 5y = -9.....................................equation 2

Let's solve using substitution method.

From equation 2, make x the subject:

x = -9 + 5y

Substitute (-9 + 5y) for x in equation 1:

-10(-9 + 5y) - 15y = 25

-10(-9) - 10(5y) - 15y = 25

90 - 50y - 15y = 25

90 - 65y = 25

Subtract 90 from both sides:

90 - 90 - 65y = 25 - 90

-65y = -65

Divide both sides by -66



Answer:

Point A is at (0, –4).

Point B is at (–8, –7).

Step-by-step explanation:

point A is 4 units down : y = –4

Point B is 8 units to the left : x = –8

and 7 units down: y = –7

A : (0, –4)

B : ( –8, –7)

Answer:

9

Step-by-step explanation:

2x + 3y - 2 =9

(2) + (9) -2 =9

The dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

A box plot, sometimes called a box whisker plot, shows the distribution of a dataset graphically. The minimum value, the first quartile (25th percentile), the median (50th percentile), the third quartile (75th percentile), and the maximum value are the five main values used to standardise this method of displaying the distribution of data.

Two whiskers that extend from a rectangular box make up a box plot. The range of values between the first and third quartiles is represented by the box, which is known as the interquartile range (IQR).

From the given box plot we observe that the minimum value is 12 and the maximum value is 24.

Here, the median is 19.

From the information the two data set that have the corresponding values are:

12, 15, 15, 17, 19, 19, 20, 22, 24

12, 15, 17, 17, 19, 19, 22, 22, 24

The lower quartile is 15.

The upper quartile is 21.

Calculating the lower quartile for the data sets:

12, 15, 15, 17, 19, 19, 20, 22, 24

Lower quartile = 15

Hence, the dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

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The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

The quartiles of the distribution are given as follows:

The sample size of the distribution is of:

n = 40.

The first quartile is the value that is greater than 25% of the distribution, hence it is the value at the position which is 25% of the sample size, hence:

The second quartile is the value that is greater than 50% of the  distribution, hence it is the value at the position which is 50% of the sample size, hence:

The third quartile is the value that is greater than 75% of the  distribution, hence it is the value at the position which is 75% of the sample size, hence:

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Answer

the answer is 90 (C)

Step-by-step explanation:

Beth = x

Caroline = 60 + x (because if Beth has 60 less than Caroline then Caroline has 60 more than Beth)

Since the ratio = 1/3 ( another way of writing 1:3) then x/60+x = 1/3

3x = 60 + x

3x - x = 60

2x = 60

x = 60/2

x = 30 (Beth has 30 stickers)

Caroline has 60 + x stickers = 60 + 30 = 90

Answer: Lee would make $25 on commission.

Step-by-step explanation: I found this by multiplying 500 by .05 or 5%. Lastly you can check this by taking 25 times 20, because 5% x 20 = 100%, so if 25 was really equal to 5% then it would equal the whole, or 500.

Hope this helps.

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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Answer:

c

Step-by-step explanation:

12 times 1.5 times 3.8

\(p(t)=1650e^{0.11t}\implies \stackrel{p(t)}{2479}=1650e^{0.11t}\implies \cfrac{2479}{1650}=e^{0.11t} \\\\\\ \log_e\left( \cfrac{2479}{1650} \right)=\log_e\left( e^{0.11t} \right)\implies \log_e\left( \cfrac{2479}{1650} \right)=0.11t \\\\\\ \ln\left( \cfrac{2479}{1650} \right)=0.11t\implies \cfrac{ ~~ \ln\left( \frac{2479}{1650} \right) ~~ }{0.11}=t\implies 3.7\approx t\)

at that moment, the population will reach 2479, and right after that, it'll exceed it.

The expected number of pizzas to be stuffed crust is given as follows:

500.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The sample size is given as follows:

408 + 224 + 208 + 200 = 1040.

Out of these, 208 are stuffed crust, hence the probability is given as follows:

p = 208/1040.

Out of 2500 pizzas, the expected number is then given as follows:

E(X) = 2500 x 208/1040

E(X) = 500.

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Answer:

i believe its C

Step-by-step explanation:

Answer:

52 degree angle

A company's income tax liability is referred to as "deferred tax liability" when it is not paid in full during the fiscal year. This record is accounted for on the accounting report of the organization as an obligation.

Taxable income is the sum of the following: pre-tax financial income, insurance costs, depreciation, and 154,000 dollars. Taxable income is $148,000.

A listing on a company's balance sheet known as a "deferred tax liability" records taxes that are owed but will not be paid until a later date.

It varies. There are two kinds of deferred tax items: a liability and an asset. The first one is the money that the company owes (the deferred tax liability), and the second one is the money that the company is owed (the deferred tax asset).

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Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

170,070 residents

Step-by-step explanation:

Original population = 1500 residents

Total population after 6 years is calculated using the formula

A = P(1+r)^t

r is the rate = 120% = 1.2

t is the time = 6 years

P is the original population

A = 1500(1+1.2)^6

A = 1500(2.2)^6

A = 1500(113.379904)

A = 170,069.856

Hence the total people using the recycling program after 6 years is approximately 170,070 residents

Answer:

No

Step-by-step explanation:

the graph fails the vertical line test

False. The value of 5(1 + 3) ^2 is 80.

If I'm wrong, I apologize.

Answer:

The answer is false

Step-by-step explanation:

\( {5}^{2} + {15}^{2} = 250\)

The velocity at pART a =  584

The velocity in answer B = 576

The change in time = 4

distance traveled using the 20 second interbval is

4[ 31 + 31 + 33 + 28 + 23 ]

= 4 * 146

= 584

At the end of the time periods the velocities would be:

4[31 + 33 + 28 + 23 + 29]

= 4 x 144

= 576

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An inequality to represent the cost of Jason’s food for the party is

An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is

The two options for buying wings and hot dogs include the following:

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:

Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;

7x + 5y ≤ 40

Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;

y ≥ 5

Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.

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Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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The height of the person that cast a shadow of 1.5 foot is 6 foot.

When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow. A person cast a shadow of 1.5 foot at the same time.

Therefore, the height of the person can be found by setting up a proportional relationship between the length of shadow and the actual height of the building and person.

Hence,

let

x = height of the person

Therefore,

100 / 25 = x / 1.5

cross multiply

25x = 100 × 1.5

25x = 150

divide both sides of the equation by 25

x = 150 / 25

x = 6

Therefore,

height of the person  = 6 foot.

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The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Answer: To compare −7/8 and −5/6, we can convert them to a common denominator.

Multiplying the denominator and numerator of −7/8 by 6, we get:

−7/8 = −(7/8) × (6/6) = −42/48

Multiplying the denominator and numerator of −5/6 by 8, we get:

−5/6 = −(5/6) × (8/8) = −40/48

Now we can compare the two rational numbers:

−42/48 is less than −40/48, since negative numbers get larger as their value gets closer to zero.

Therefore, we have:

−7/8 < −5/6.

The correct sign to compare the two rational numbers is "<".

Step-by-step explanation:

Answer:

Nut

Step-by-step explanation:

The length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm² respectively.

A rectangle is a polygon in two dimension with four sides with opposide sides are equal and all the angles are right angles.

Given smaller rectangle is 1/2 scale drawing of the original figure. So the dimensions of the smaller rectangle will be half of the dimensions of the bigger rectangle.

For bigger rectangle,

Length = 36 cm

Width = 28 cm

Area = 1,008 cm²

So for smaller rectangle,

Length = 36/2 = 18 cm

Width = 28/2 = 14 cm

Area = 18 × 14 = 252 cm²

Hence the length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm².

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Answer:

your answer will be option 2

None of the choices are correct.

Step-by-step explanation:

have a nice day and good luck!!!

Answer

Step-by-step explanation:

so, this triangle is an "impossible' triangle, b/c  even when the 5 and 4 sides are laid out, in opposite directions, they only make a distance of 9. so the side of 12 is not ever going to work in this triangle, it's just too long.  so the answer is none of the choices are correct.  To be fair, this question is incorrect.  The picture that is drawn, makes it look like the triangle could be real. when it's not.  like an Escher drawing. if  you don't know Escher drawings look  them up