Solve the equation for y in terms of x, and replace y with function notation f(x). Then find f(2).
y+3x^2=5
f(x)=?
f(2)=?

The final answer is:

-1/7 < 5 < 2

Or, in interval notation:

(−1/7, 2)

What is interval?

In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded. For example:

First, let's simplify the expression inside the parentheses:

3 + 2 = 5

Now we can substitute this value into the expression and simplify further:

-14 < -7(5) < 1

-14 < -35 < 1

To solve this compound inequality, we need to isolate the variable (in this case, there is no variable) to find the range of values that satisfy the inequality. We can do this by dividing all three parts of the inequality by -7. However, we need to reverse the direction of the inequality signs since we are dividing by a negative number:

-14/-7 > -35/-7 > 1/-7

2 > 5 > -1/7

Therefore, the solution to the inequality is:

-1/7 < 5 < 2

In interval notation, this can be written as:

(−1/7, 2)

To sketch the solution, we can plot the interval on a number line. The interval does not include the endpoints, so we use open circles to indicate this:

<-------------(○======○)------------->

             -1/7    5     2

The open circle at -1/7 indicates that -1/7 is not included in the interval, and the open circle at 2 indicates that 2 is also not included in the interval. The line segment between the circles represents the range of values that satisfy the inequality.

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According to the given information, f(125) is equal to 48479.

What is function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

To find f(125), we need to apply the recursive formula for f(n) when n is a positive integer divisible by 5. Since 125 is divisible by 5, we can use the formula:

f(125) = f(125/5) + 3(125)²

f(125/5) = f(25) = f(25/5) + 3(25)²

f(25/5) = f(5) = f(5/5) + 3(5)²

f(5/5) = f(1) = 4

Now we can substitute the values back into the formula and simplify:

f(5) = f(5/5) + 3(5)² = 4 + 75 = 79

f(25) = f(25/5) + 3(25)² = 79 + 3(625) = 2054

f(125) = f(125/5) + 3(125)² = 2054 + 3(15625) = 48479

Therefore, f(125) is equal to 48479.

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The area of the purse can be calculated using the formula for the area of a trapezoid. The purse (not including the handle) takes up 34 cm² in the magazine layout.

The formula states that the area of a trapezoid is equal to one half of the product of the length of the two parallel sides, multiplied by the height. Thus, the area of the purse can be calculated as:

Area = (1/2) x (11cm + 6cm) x 4cm

Area = (1/2) x (17cm) x 4cm

Area = 34 cm²

Therefore, the purse (not including the handle) takes up 34 cm² in the magazine layout.

It is important to note that the formula for the area of a trapezoid can be used in this instance because the purse has a shape of a trapezoid.

This is due to the fact that the line parallel to the 11cm base has a length of 6cm. The line is not parallel to the 4cm height and thus, the shape of the purse is a trapezoid and not a rectangle.

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Step-by-step explanation:

I = E/R    multiply both sides of the equation by R

I R = E / R  * R

I R = E     Now divide both sides by I

R  = E/ I

Answer:

2x + 3y

Step-by-step explanation:

= 3x + 2y - x + y

= 2x + 2y + y

= 2x + 3y

hope this helps

Answer:

The answer is A. Depreciation.

A cash budget is a financial statement that projects a company's future cash inflows and outflows. It is used to help the company manage its cash flow and avoid running out of money. The cash budget includes all of the company's expected cash receipts and payments, including sales, purchases, expenses, and taxes. Depreciation is not a cash flow, so it does not appear on a cash budget.

Depreciation is an accounting concept that allows companies to spread the cost of an asset over its useful life. It is not a cash expense, because the company does not actually pay out any money when it depreciates an asset. Instead, the company reduces the value of the asset on its balance sheet.

The cash budget is a valuable tool for businesses of all sizes. It can help businesses to plan for future cash needs, avoid running out of money, and make sound financial decisions.

Step-by-step explanation:

Hence, by multiplying the number of airports in California by a factor of three-quarters, we may get the number of airports in Georgia.

To find how many airports Georgia has, we need to use division. We can divide the total number of airports in California by 3 to find the number of airports in Georgia.

The key math word in the problem is "three times."

Let's say the number of airports in California is "C". Then, we can represent the number of airports in Georgia as "G," and we know that:

C = 3G

To solve for G, we can divide both sides of the equation by 3:

C/3 = G

Therefore, the number of airports in Georgia is equal to one-third of the number of airports in California.

The key math word in the problem is "three times."

We need to divide in order to determine the number of airports in Georgia. The number of airports in Georgia can be calculated by dividing the total number of airports in California by 3.

Let's say the number of airports in California is "C". Then, we can represent the number of airports in Georgia as "G," and we know that:

C = 3G

To solve for G, we can divide both sides of the equation by 3:

C/3 = G

Therefore, the number of airports in Georgia is equal to one-third of the number of airports in California.

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Step-by-step explanation:

pls send a picture for better clarification of the questions

Answer:

x = 4,5

Step-by-step explanation:

These two triangles are similar (according to 3 sides):

The three sides of one triangle are proportional to the three sides of the other triangle:

[tex] \frac{7.5}{5} = \frac{6}{4} = \frac{x}{3} [/tex]

[tex] \frac{6}{4} = \frac{x}{3} [/tex]

Use the property of proportion to find x (cross-multiply):

[tex]4x = 6 \times 3[/tex]

[tex]4x = 18[/tex]

Divide both sides by 4 to make x the subject:

[tex]x = 4.5[/tex]

Answer:

it is better to buy brand B for both dish washing liquid and shoe polish.

Step-by-step explanation:

D. Reflection across the y-axis, translation 4 units to the right. sequence of transformation is most likely applied to figure QRSTU to form Q'R'S'T'U'.

What is transformation?

To determine the sequence of transformations applied to figure QRSTU to form Q'R'S'T'U', we can compare the corresponding vertices of the two pentagons:

Q and Q': Q' is to the right of Q and has a positive x-coordinate.

R and R': R' is to the left of R and has a negative x-coordinate.

S and S': S' is above S and has a positive y-coordinate.

T and T': T' is above T and has a positive y-coordinate.

U and U': U' is to the right of U and has a positive x-coordinate.

Based on these comparisons, it appears that the figure has been reflected across the y-axis and then translated 4 units to the right. Therefore, the most likely sequence of transformations applied to QRSTU to form Q'R'S'T'U' is:

D. Reflection across the y-axis, translation 4 units to the right.

What are vertices?

A vertex (plural: vertices) is a point where two or more line segments or curves meet. Vertices are the corner points of a polygon or the endpoints of a line segment or ray. In three-dimensional geometry, vertices are the corner points of a polyhedron or the endpoints of an edge.

Vertices are important in defining the properties of a shape, such as its angles, sides, and symmetry. They are also used in graph theory to represent points in a graph or network.

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Complete question is: D. Reflection across the y-axis, translation 4 units to the right. sequence of transformation is most likely applied to figure QRSTU to form Q'R'S'T'U'.

Answer:

I CANT SEE WHAT IT SAYS

Step-by-step explanation:

The functiοn is increasing and has a dοmain οf (1, ∞) is οptiοn D f(x) = lοg (x - 1) + 1.

Every equatiοn with οne οr mοre ratiοnal expressiοns is said tο be ratiοnal. A fractiοn whοse numeratοr and denοminatοr are pοlynοmials is knοwn as a ratiοnal expressiοn. A ratiο οf twο pοlynοmials is, in οther wοrds, a ratiοnal expressiοn.

The LCD (Least Cοmmοn Denοminatοr) οf the fractiοns, eliminatiοn οf the denοminatοrs, and simplificatiοn οf the resultant equatiοn are methοds fοr sοlving ratiοnal equatiοns. Sοlving the resultant equatiοn—which can require factοring, simplificatiοn, οr the use οf οther algebraic strategies—will prοvide the answers tο a ratiοnal equatiοn.

Fοr the given functiοn:

Optiοn A:

f(x) = -lοg(x - 1) + 2

Here, lοg is negative, hence fοr increasing value οf x f(x) will decrease.

Optiοn B:

f(x) = -lοg(x - 2) + 1

Here, lοg is negative, hence fοr increasing value οf x f(x) will decrease.

Optiοn C:

f(x) = lοg(x - 2) + 1

Here, (x - 2) > =

x > 2

The dοmain dοes nοt satisfy.

Optiοn D:

f(x) = lοg (x - 1) + 1

Here, (x - 1) > 0

x > 1 tο infinity.

Hence, the functiοn is increasing and has a dοmain οf (1, ∞) is οptiοn D f(x) = lοg (x - 1) + 1.

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The complete function is:

Using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.

A prism with oblique bases is one in which the bases are not parallel to one another.

An oblique rectangular prism is a rectangular prism with bases that are not arranged one over the other.

The following qualities describe an oblique prism: It seems to be slanted or skewed. Parallelograms make up an oblique prism's faces.

The height is gauged from the outside.

The two bases are not positioned next to one another exactly.

So, the volume formula for the oblique rectangular prism:

V=l⋅w⋅h

Now, insert values:
V=l⋅w⋅h

V=15*10*8

V=1,200 units ³

Therefore, using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.

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Answer:

Question 1 C. 25 1/3

Question 2 C. 19

Step-by-step explanation:

brief :

1. 6 1/3 = 19/3

19/3 * 4 = 76/3

76/3 = 25 1/3

To solve this problem, we need to use the information provided and do some simple arithmetic.

Question 1:

The candy store sold 6 1/3 pounds of white chocolate. Since it sold 4 times as much milk chocolate as white chocolate, we can find the amount of milk chocolate sold by multiplying 6 1/3 by 4:

6 1/3 * 4 = 25 1/3

Therefore, the candy store sold 25 1/3 pounds of milk chocolate last week.

Answer: C. 25 1/3

Question 2:

To find the difference between the amount of milk chocolate and white chocolate sold, we can subtract the amount of white chocolate from the amount of milk chocolate:

25 1/3 - 6 1/3 = 19

Therefore, the candy store sold 19 more pounds of milk chocolate than white chocolate.

Answer: C. 19

chatgpt

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 9000[1+(0.04)(1)] \implies A = 9360[/tex]

The value of z that lies in a given area through which the given complex number expression is satisfied is z = 1.6

What about complex number?

A complex number is a number that can be expressed in the form a + bi, where "a" and "b" are real numbers and "i" is the imaginary unit, which is defined as the square root of -1. The real part of a complex number is "a" and the imaginary part is "b".

Complex numbers are important in many areas of mathematics, science, and engineering. They are used to represent and manipulate quantities that involve both real and imaginary components, such as alternating currents in electrical engineering and wave functions in quantum mechanics. Complex numbers also have a geometric interpretation, where they can be represented as points in the complex plane, which is a two-dimensional coordinate system where the horizontal axis represents the real part and the vertical axis represents the imaginary part.

Define area:

Area is a measure of the size of a two-dimensional region or surface. It is usually measured in square units, such as square meters, square centimeters, or square feet.

The area of a shape can be calculated using different formulas depending on the shape's characteristics.

According to the given information:

⇒ Here,  the z scores be z1 and z2

⇒ In which Z1 = 0.5 - 0.8904/2 = 0.0548

⇒ And,       Z2 = 0.5 + 0.8904/2 = 0.9452

⇒ Using standard normal distribution table,

⇒ We, have that, Z1 = -1.6

⇒ Z2 = 1.6

⇒ So, the value of Z = 1.6

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Triangle 1:
A = 45 degrees, C = 40 degrees, c = 4.2
First, we need to find angle B.
B =[tex] 180 - (A + C) = 180 - (45 + 40) = 95[/tex] degrees

Now, we can use the Law of Sines to find side b.
[tex]b/sin(B) = c/sin(C)[/tex]
b =[tex] (c * sin(B)) / sin(C)[/tex]
b =[tex] (4.2 * sin(95)) / sin(40)[/tex]
b ≈ [tex]5.6[/tex]

Triangle 2:
N = 45 degrees, M = 180 - N = 135 degrees, m = 2
To find side n, we can use the Law of Sines again.
[tex]n/sin(N) = m/sin(M)[/tex]
n =[tex] (m * sin(N)) / sin(M)[/tex]
n =[tex] (2 * sin(45)) / sin(135)[/tex]
n ≈ [tex]1.4[/tex]

So, the solutions for the two triangles are:
Triangle 1: A = 45 degrees, B = 95 degrees, C = 40 degrees, b ≈ 5.6, c = 4.2
Triangle 2: N = 45 degrees, M = 135 degrees, n ≈ 1.4, m = 2

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1.3.1 There are 380 pieces of 50 cents coins.

1.3.2 The total amount of cents in the money box are 23,400.

1.3.3 The amount in rands is 234.

The solution has been obtained by using unit conversion.

What is unit conversion?

Unit conversion is a multi-step procedure that requires multiplying or dividing by a numerical factor, or more specifically, a conversion factor. Furthermore, rounding and choosing the right number of significant digits may be required. Various metrics are measured using various conversion units.

1.3.1 Let the number of 50 cents coin be x.

We are given that total number of coins are 600.

This gives us an equation as x + 220 = 600.

So,

x = 600 - 220

x = 380

1.3.2 The total cents is given by the following expression

⇒ (20 * 220) + 50x

⇒ 4400 + (50 * 380)

⇒ 4400 + 19000

⇒ 23,400 cents

1.3.3 We know that 100 cents = 1 rand.

So, using unit conversion, we get

⇒ 1 cent = [tex]\frac{1}{100}[/tex] rands

⇒ 23400 cents =  [tex]\frac{1}{100}[/tex] * 23400 rands

⇒ 23400 cents = 234 rands

Hence, the required solutions have been obtained.

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The complete question has been attached below.

1)The number of milk chocolate that sold last week is = [tex]25\frac{2}{3}[/tex] B is correct

2)white chocolate at the candy store last week is 19.

Last week, a candy store sold [tex]5\frac{1}{3}=\frac{16}{3}[/tex] pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate.

The number of milk chocolate did the candy store sell last week.

Since the candy store sold 4 times as much milk chocolate as white chocolate, it sold:

[tex]4 *\frac{ 19}{3 } =\frac{ 76}{3}\\ pounds\ of\ milk\ chocolate.= 25 \frac{2}{3}[/tex]

option B is correct.

2)

To find out how many more pounds of milk chocolate were sold than white chocolate at the candy store last week, we can subtract the amount of white chocolate sold from the amount of milk chocolate sold:

[tex]\frac{76}{3} - \frac{19}{3} \\= \frac{57}{3}\\ = 19\ pounds.[/tex]

option C is correct

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The test statistic is less than the critical value, so, we reject the null hypothesis and conclude that there is a statistically significant difference between the population means.

A two-sample t-test is used to compare the means of two samples to determine if there is a statistically significant difference between them.

To answer this question, we must conduct a two-sample t-test.

In this case, the null hypothesis is that there is no difference between the population means, and the alternative hypothesis is that there is a difference between the population means.

The test statistic is calculated using the following formula:

t = (x₁ - x₂) / (√((s₁²/n₁) + (s₂²/n₂)))

Where x₁ and x₂ are the sample means of the two samples, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.

Plugging in the sample data, we get:

t = (22 - 26) / (√((4.3²/11) + (4.4²/8)))

= -1.98

The critical value of t for a two-tailed test at the 0.01 significance level is 2.58.

Since the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference between the population means.

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Question:

A random sample of 11 observations from one population revealed a sample mean of 22 and a sample standard deviation of 4.3. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 4.4. At the 0.01 significance level, is there a difference between the population means?

The equation of the line passing through points [tex]A(a,b)[/tex] and [tex]B(b,a)[/tex] is [tex]x + y = a + b[/tex]  , and the length of   [tex]AB[/tex] is  [tex]\sqrt(2(a - b)^2).[/tex]

To find the equation of the line passing through points A(a,b) and B(b,a), we can first find the slope of the line. using the two given points, and then use the point-slope form of a line equation.

The slope of a line passing through two points ([tex]x_{1} , y_{1}[/tex]) and ([tex]x_{2}, y_{2}[/tex]) is given by:

[tex]m = (y_{2} - y_{1} ) / (x_{2} - x_{1} )[/tex]

Applying this formula, we can find the slope of the line passing through points A(a,b) and B(b,a):

Slope [tex](m) = (a - b) / (b - a)[/tex]

Since a and b can take any real values, we can see that the slope of the line passing through points A and B is -1.

Now, let's find the equation of the line passing through points A and B using the point-slope form of a line equation:

Point-slope form: [tex]y - y_{1} = m(x - x_{1} )[/tex]

Substituting the slope (-1) and the coordinates of point A(a,b) into the point-slope form, we get:

[tex]y - b = -1(x - a)[/tex]

Expanding the equation, we get:

[tex]y - b = -x + a[/tex]

Rearranging the terms, we get the equation of the line passing through points A(a,b) and B(b,a):

[tex]x + y = a + b[/tex]

Now, let's find the length of AB using the distance formula:

The distance between two points [tex](x_{1} , y_{1} )[/tex] and  [tex](x_{2} , y_{2} )[/tex] is given by:

[tex]d = \sqrt((x_{2} - x_{1} )^2 + (y_{2} - y_{1} )^2)[/tex]

Applying this formula, we can find the length of AB using the coordinates of points A(a,b) and B(b,a):

Length of  [tex]AB (d) = \sqrt((b - a)^2 + (a - b)^2)[/tex]

Simplifying the expression, we get:

Length of [tex]AB (d) = \sqrt(2(a - b)^2)[/tex]

Therefore, The equation of the line passing through points [tex]A(a,b)[/tex] and [tex]B(b,a)[/tex] is [tex]x + y = a + b[/tex]  , and the length of   [tex]AB[/tex] is  [tex]\sqrt(2(a - b)^2).[/tex]

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To find the total units of water collected for day 3, we can simply add up the units of water collected on each day, starting with the 1 unit of water we already have:

Day 1: 1 unit of water

Day 2: 1 unit of water

Day 3: 1 unit of water

1. Total units of water collected for day 3 = 1 + 1 + 1 = 3 units of water

2. Since we only need to consume 1 unit of water per day to survive, we would have consumed a total of 3 units of water in 3 days.

3. To find the amount of water leftover, we can subtract the units of water consumed from the total units of water collected:

Total units of water collected = 3 units

Units of water consumed = 3 units

Water leftover = Total units of water collected - Units of water consumed

= 3 - 3

= 0 units of water leftover

4. We could collect water in a number of ways, depending on what resources were available on the island. We could collect rainwater using containers, or we could find a freshwater stream or well and collect water from there. We could also try to collect dew or moisture using a cloth or other absorbent material.

5. The tools we would use to collect water would depend on the method we chose. For example, if we were collecting rainwater, we would need containers to catch the water, such as buckets or barrels. If we were collecting water from a stream or well, we would need a way to transport the water back to our shelter, such as a jug or canteen. If we were collecting moisture, we would need a cloth or other absorbent material to collect the water.

Answer: 222

Step-by-step explanation:

So you know 40% of x is 111

and we need to find 80%

80% is twice of 40%

so we multiply 111  by 2 and get 222

x=222

The probability that the contestant wins at least one car is 13/35.

A television game show has 15 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive cars, and behind the other 12 doors are consolation prizes

probability of an event =total favorable outcome for event/total possible outcomes

P(contestant wins at least one car) will be:

= 1 - 12/15 × 11/14

=13/35

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The number of inches the plant grew this week would be 8-x. As the length increased this week the length is substracted from this week to last week.

Subtraction (which is signified by the minus sign −) is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches.

Therefore, the difference of 5 and 2 is 3; that is, 5 − 2 = 3. While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.

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Answer:

Step-by-step explanation:

B. Government support for education decreasing by​ 1% per year is an example of exponential decay because the support decreases by the same percentage each year.

Exponential decay is a mathematical concept that describes the decrease of a quantity over time at a rate proportional to its current value. In other words, the amount by which the quantity decreases over a certain period of time is proportional to the current value of the quantity. This is often represented by an exponential function with a negative exponent, where the exponent is a function of time. The concept of exponential decay is used in many fields, including physics, chemistry, biology, and finance, among others.

Reasoning: It is because the support decreases by the same percentage each year. Exponential decay refers to a process in which a quantity decreases over time at a rate proportional to its current value. In this case, the government support is decreasing by a constant percentage each year, which is a characteristic of exponential decay.

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