LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)

Answer:

I have attached the answers

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Answer: Choice C) \(\frac{8}{9}n - 1\frac{1}{3}\)

====================================================

Explanation:

We multiply the outer term 4/9 with each term inside

The improper fraction 4/3 converts to the mixed number 1 & 1/3

4/3 = (3+1)/3 = 3/3 + 1/3 = 1 + 1/3 = 1 & 1/3

So overall, we can say \(\frac{4}{9}(2n-3) = \frac{8}{9}n - 1\frac{1}{3}\)

This is equivalent to saying \(\frac{4}{9}(2n-3) = \frac{8}{9}n - \frac{4}{3}\)

Answer:

(a)  t = 2, N = 204

     t = 14, N = 603

     t = 24, N = 786

(b)  1500 deer

Step-by-step explanation:

Given function:

\(N=\dfrac{20(5+3t)}{1+0.04t}, \quad t \geq 0\)

\(\boxed{\begin{aligned}t = 2 \implies N&=\dfrac{20(5+3(2))}{1+0.04(2)}\\\\&=\dfrac{20(5+6)}{1+0.08}\\\\&=\dfrac{20(11)}{1.08}\\\\&=\dfrac{220}{1.08}\\\\&=203.703703...\\\\&=204\end{aligned}}\)

\(\boxed{\begin{aligned}t = 14 \implies N&=\dfrac{20(5+3(14))}{1+0.04(14)}\\\\&=\dfrac{20(5+42)}{1+0.56}\\\\&=\dfrac{20(47)}{1.56}\\\\&=\dfrac{940}{1.56}\\\\&=602.56410...\\\\&=603\end{aligned}}\)

\(\boxed{\begin{aligned}t = 24 \implies N&=\dfrac{20(5+3(24))}{1+0.04(24)}\\\\&=\dfrac{20(5+72)}{1+0.96}\\\\&=\dfrac{20(77)}{1.96}\\\\&=\dfrac{1540}{1.96}\\\\&=785.71428...\\\\&=786\end{aligned}}\)

To find the limiting size of the herd, find the horizontal asymptote of the function.

As the degree of the numerator is equal to the degree of the denominator, the asymptote is the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.

Expand the numerator of the function:

\(N=\dfrac{20(5+3t)}{1+0.04t}=\dfrac{100+60t}{1+0.04t}\)

Divide 60t by 0.04t:

\(\textsf{Horizontal asymptote}:\;y=\dfrac{60t}{0.04t}=1500\)

Therefore, the limiting size of the herd as time increases is 1500.

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

Step 1

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. This means that you cannot draw a triangle that has side lengths 2, 7 and 12, for instance, since 2 + 7 is less than 12.

Step 2

For sides 29 , 40 and x

x must be less than 29 + 40 = 69. x must be less than 69.

x must also be greater than 11

Final answer

11 < x < 69

Option C

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"p" varies directly as "q"}}{p~~ = ~~kq}\qquad \textit{we also know that} \begin{cases} q=70\\ p=10 \end{cases}\implies 10=k70 \\\\\\ \cfrac{10}{70}=k\implies \cfrac{1}{7}=k\hspace{15em}\boxed{p=\cfrac{1}{7}k} \\\\\\ \textit{when p = 12, what is "q"?}\qquad 12=\cfrac{1}{7}q\implies 12=\cfrac{q}{7}\implies 84=q\)

Answer:

5

Step-by-step explanation:

The mean represents an average of all the numbers, so we have \(\frac{sum-of-all-numbers}{total-amount-of-numbers}\). Although that may seem confusing, it's actually pretty easy.

We have a total of five numbers, which are 1, 6, 2, 7, and 9.

We add these numbers up to find the sum, so 1 + 6 + 2 + 7 + 9 = 25

So our final answer will be \(\frac{25}{5}\) which can be simplified to 5.

The equation C(t) = 2 tells us that at a moment of t, the numeric value of the variable C is of 2 units.

The general format of an ordered pair is given as follows:

(x,y).

The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.

The ordered pair for this problem is given as follows:

(t, C(t)) = (t,2).

Meaning that at a moment of t, the numeric value of the variable C is of 2 units.

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Answer: you need to add

Step-by-step explanation: I would ask your teacher to help you understand the lesson.  

The expected cost of a can of Coca-Cola in 1970 is 0.22 (rounded to the nearest cent).

The expected cost of a can of Coca-Cola in 2005 is 2.09 (rounded to the nearest cent).

The expected cost of a can of Coca-Cola in 2015 is 7.49 (rounded to the nearest cent).

The expected cost of a can of Coca-Cola in 2040 is 76.92 (rounded to the nearest cent).

Using the exponential function \(C(t)=0.10e^0.0576t\), given below,

where t is the number of years since 1960, the expected cost of a can of Coca-Cola can be calculated for different years, as follows:

For 1970: \(t = 10 (1970 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(10) = 0.10e^0.576≈0.22\)

Therefore, the expected cost of a can of Coca-Cola in 1970 is 0.22

For 2005: \(t = 45 (2005 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(45) = 0.10e^2.592≈2.09\)

Therefore, the expected cost of a can of Coca-Cola in 2005 is 2.09

For 2015: \(t = 55 (2015 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(55) = 0.10e^3.168≈7.49\)

Therefore, the expected cost of a can of Coca-Cola in 2015 is 7.49

For 2040: \(t = 80 (2040 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(80) = 0.10e^4.608≈76.92\)

Therefore, the expected cost of a can of Coca-Cola in 2040 is 76.92

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Answer:

z ≤ 6

Explanation:

z is less than or equal to: z ≤

z is less than or equal to six: z ≤ 6

The lateral area and the surface area of the right prism are 540 square yards and 1152 square yards, respectively.

Herein we find the case of a right prism with a triangular base, whose lateral area (A) and surface area (A'), both in square yards, must be determined.

The lateral area is the sum of the areas of three rectangular faces and the surface area is the sum of the lateral area and the area of the two triangles. Area formulas for rectangles and triangles are shown below:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Where:

Now we determine the lateral area and the surface area of the prism:

Lateral area

A = (37 yd) · (5 yd) + (20 yd) · (5 yd) + (51 yd) · (5 yd)

A = 540 yd²

Surface area

A' = 540 yd² + 2 · 0.5 · (51 yd) · (12 yd)

A' = 1152 yd²

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The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

the right answer is the constant of proportionality

Step-by-step explanation:

The unchanging value of the ratio between two proportional quantities is the constant of proportionality.

INTERPRETATION----

Lets say a is directly proportional to b and k is a constant.

                                         OR

If two variables are related and this relationship is that there is a constant ratio between them, then we are talking about proportionality. There are two types of proportionality.

In a mathematical language this is given by this equation:

\(y = kx\)

where k is in fact this constant of proportionality. If x increases, y also increases at the same rate.

On the other hand,  If x decreases, y also decreases at the same rate.

In a mathematical language this is given by this equation:

\(y=\frac{k}{x}\)

where k is also called the constant of proportionality. If x increases, y decreases at the same rate. On the other hand,  If x decreases, y increases at the same rate.

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Answer:

Option 2: (1,0) is the correct answer

Step-by-step explanation:

Given inequality is:

y>-5x+3

In order to find which point is solution to the given inequality we'll put the point one by one in the inequality. If the point satisfies the inequality, then the point is the solution of the inequality.

Putting (0,3) in inequality

\(3 > -5(0)+3\\3>0+3\\3>3\)

Putting (1,0) in inequality

\(0>-5(1)+3\\0>-5+3\\0>-2\)

Putting (-3,1) in inequality

\(1 > -5(-3)+1\\1> 15+1\\1>16\)

Putting (-1,-2) in inequality

\(-2>-5(-1)+3\\-2>5+3\\-2>8\)

The inequality is true for (1,0)

Hence,

Option 2: (1,0) is the correct answer

Answer:

\(\frac{1}{12}\)

Step-by-step explanation:

1) Construct a probability tree (check the attachment).

1.1) Change the given items/values into fractions. In this case, there are 3 entrees, each with a probability of \(\frac{1}{3}\) because the probability of selecting a hamburger (an example that could be applied to other options too) is 1 out of the 3 options. Likewise is the case with sides and drinks; the probability of selecting fries (or vegetable) out of the two options is \(\frac{1}{2}\), and the probability of selecting milk (or juice) out of the two options is \(\frac{1}{2}\).

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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The value of the side y is 3√3. Option C

It is crucial to note the different types of trigonometric identities.

They are;

From the diagram shown, we have that;

The angle θ = 60 degrees

The opposite side = y

The adjacent side = 3

Let's use the tangent identity

tan 60 = y/3

Find the value

√3 = y/3

cross multiply

y = 3√3

Hence, the value is 3√3

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Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

Answer:

answer choice c

Step-by-step explanation:

To find the percentage increase, first find the difference between the two prices:

$9.62 - $9.53 = $0.09

Then, divide the difference by the original price:

$0.09 ÷ $9.53 = 0.0094

Finally, multiply by 100 to convert to a percentage and round to the nearest tenth of a percent:

0.0094 × 100 ≈ 0.9%

Therefore, the percentage increase is approximately 0.9%.

On the vertical number line, negative numbers are to the bottom of 0. Therefore, -1/4 will go one unit down from 0.

On the horizontal number line, negative numbers are to the left of 0. Therefore, -1/4 will go to the left one unit.

Best of Luck!

Answer:

-15

Step-by-step explanation:

common difference = -2

next term is -13-2= -15

Answer:

\(274\,\text{in}^3\)

Step-by-step explanation:

\(V=\pi r^2h=\pi(3.75)^2(6.21)\approx274\,\text{in}^3\)

When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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Answer:

\(d =\frac{10}{3}t + 11\)

Step-by-step explanation:

Given

Represent time with t and distance with d

The time at which he sets his timer is 0.

So:

\((t_1,d_1) = (0,11)\)

After 3 seconds:

\((d_2,d_2) = (3,21)\)

Required

Determine the linear equation

First, we need to determine the slope (m):

\(m = \frac{d_2 - d_1}{t_2 - t_1}\)

Substitute in, values

\(m = \frac{21 - 11}{3 - 0}\)

\(m = \frac{10}{3}\)

Next, we determine the equation sing

\(d - d_1 = m(t - t_1)\)

Where

\((t_1,d_1) = (0,11)\)

\(m = \frac{10}{3}\)

\(d - 11 =\frac{10}{3}(t - 0)\)

\(d - 11 =\frac{10}{3}t - 0\)

\(d - 11 =\frac{10}{3}t\)

Add 11 to both sides

\(d - 11+11 =\frac{10}{3}t + 11\)

\(d =\frac{10}{3}t + 11\)

Hence, the linear equation is: \(d =\frac{10}{3}t + 11\)

The linear equation used to represent Carlos distance (d) from his starting position after t seconds is d = 3t + 12

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

Let d represent Carlos distance from his starting position after t seconds.

Given that He starts a timer when he is  12 feet from his starting position, hence b = 12 feet. After 3 seconds, Carlos is 21 feet from his starting position. Therefore:

21 = 3m + 12

3m = 9

m = 3 ft per second

The linear equation used to represent Carlos distance (d) from his starting position after t seconds is d = 3t + 12

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A.

Overall it has a relation that there are more sold cups when the temperature is lower. On the other hand, based on the 40 degrees part, that have to different values of two different days, we can say is not the only factor.

B.

The best lineal approach is the line created with the points at 20 and 80 degrees. First the slope:

Now the intercept with y axis, b:

The final line formula is:

Answer:

(0,5)

Step-by-step explanation:

f(x) = x^2 + 3x + 5

The y intercept is when x =0

f(0) = 0 + 3*0 + 5

f(0) = 5

(0,5)