Factor this equation using the Zero product property , What are the x-intercepts?: f(x)=2x^2+5x-3

A'B'C' is the image of triangle ABC under rotation about 120° CCW about point Q. This is true.

It should be noted that triangle A'B'C' appears to be congruent to triangle ABC and about the same distance from point Q.

Here, the angle of rotation from ABC to A'B'C' appears to be about 120° counterclockwise when measured using a geometry program.

Therefore, triangle A'B'C' is the image of triangle ABC under rotation about 120° CCW about point Q.

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The proof of the congruent sides RU and TS is given below.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given figure is a rectangle RSTU.

Since the all four angles of rectangle are of 90 degree.

So, each angle of rectangle RSTU is 90 degree.

Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.

Both the triangles having same measure of angles and sides.

⇒  ΔSRU ≅ ΔSTU

As the triangles are congruent so their sides are congruent.

Hence, RU is congruent to TS.

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Multiple regression offers a more comprehensive and nuanced analysis by considering the influence of multiple predictors, capturing complex relationships, controlling for confounding variables, and enhancing predictive capabilities.

A study using multiple regression has several advantages over a study using bivariate correlation:

Multivariate analysis: Multiple regression allows for the inclusion of multiple predictor variables, which enables the examination of their individual contributions while controlling for the effects of other variables. This helps to identify the unique influence of each predictor on the outcome variable, considering their interrelationships.

Complex relationships: Multiple regression can capture complex relationships between variables by accounting for their combined effects. Bivariate correlation can only assess the linear relationship between two variables, whereas multiple regression can handle non-linear relationships and interactions between predictors.

Control of confounding variables: Multiple regression enables the control of confounding variables by including them as predictors in the model. By controlling for potential confounders, the relationship between the predictor and outcome variables can be more accurately assessed, reducing the likelihood of spurious associations.

Increased predictive power: Multiple regression can improve the predictive power of the model by incorporating multiple predictors. By considering multiple factors simultaneously, it can provide a more comprehensive understanding of the factors influencing the outcome variable and better predict its values.

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The lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given is prism, we need to find the lateral surface and the total surface areas,

Lateral surface area = (perimeter of base) × length

Perimeter of base = 3 × 4 = 12 in

length = 8 in

The lateral surface area = 12 × 8 = 96 in²

Total surface area = (perimeter of base) × length × 2(base area)

= 96 × 2(3×4)

= 96 × 24

= 2304 in²

Hence, the lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

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Answer:

d

Step-by-step explanation:

hiiiiiiii

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer:

Growth rate is 17%

2025 value is $76

Step-by-step explanation:

Here, we want to determine the annual growth rate

The general equation form is;

F = l( 1 + r)^n

where F is the future value

I is the initial value

r is the growth rate

n is the numbering years

To get the growth rate, we simply equate what we have in the bracket to 1 + r

Thus;

1 + r = 1.17

r = 1.17-1

r = 0.17

0.17 is same as 17/100 which is same as 17%

Secondly, we want to get the value of the book in 2025

What we have to do here is to substitute (2025-2000) for t which is 25

We have;

V(t) = 1.50(1.17)^25

V(25) = 75.986 which is approximately 76

We will see that the annual growth rate is of 17%, and in the year 2025, the value will be $75.99.

Exponential growth functions:

A general exponential growth can be written as:

f(x) = A*(1 + r)^x

Where A is the initial value and r is the growth rate. Now we can rewrite our function to get:

V(t) = 1.50*(1 + 0.17)^t

Then you can see that the growth rate is 0.17, or 17% in percentage form (to get it just multiply it bt 100%).

To get the value of the comic book in 2025 you just need to evaluate the function in t = 25 (25 years after the 2000).

V(25) = 1.50*(1 + 0.17)^25 = 75.99

So the value in 2025 is $75.99

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Answer:

−7<x<7

Step-by-step explanation:

Let's find the critical points of the inequality:

x2=49

x=±√49(Take square root)

x=7 or x=−7

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<−7(Doesn't work in original inequality)

−7<x<7(Works in original inequality)

x>7(Doesn't work in original inequality)

Hope this helped :)

Answer:

11) 20%

12)40

13)19

14)216

15)25%

16) 50

17) 986

18)220%

19)40

20)100%

Step-by-step explanation:

with percentages it is part divided by the whole times 100 so an example would be 73 divided by 365 times 100

Answer:

11) 20%

12) 40

13) 19

14) 216

15) 25%

16) 50

17) 986

18) 220%

19) 40

20) 100%

Here's a fat rat in a hat

Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

Répondre:

Explication étape par étape:

Vitesse = Distance / Temps

Distance donnée = 200 km

Durée = 2 h 30

Convertir le temps en heures

Depuis 60 minutes = 1h

2 heures 30 minutes = 2+ (30/60)

2h30 = 2 + 1/2 hors

2 heures 30 minutes = 2,5 heures

Vitesse en km / h = 200 km / 2,5 h

Vitesse en km / h = 80 km / h

D'où sa vitesse moyenne en km / h est de 80 km / h

a) Distance = Vitesse * Temps

Vitesse donnée = 80 km / h

Durée = 3h15

Temps = 3 15/60 h

Durée = 3,25 h

Distance = 80 * 3,25

Distance parcourue en 3h15 = 260 km

b) Distance = Vitesse * Temps

Vitesse donnée = 80 km / h

Durée = 42 minutes

Durée = 42/60 h

Distance = 80 * 42/60

Distance = 3360/60

Distance = 56 km

Distance parcourue en 42 minutes = 56 km

c) Distance = Vitesse * Temps

Vitesse donnée = 80 km / h

Durée = 3 h 36 minutes

Temps = 3 36/60 h

Durée = 3,6 h

Distance = 80 * 3,6

Distance = 288 km

Distance parcourue en 3 h 36 min = 288 km

d) Distance donnée = 540 km

Vitesse = 80 km / h

Temps = Distance / Vitesse

Heure = 540/80

Temps = 6,75 heures

Par conséquent, le temps nécessaire pour parcourir 540 km est de 6,75 heures

You have

  y = - x^2 + 2

  y = x

Since, y=x, we can say

 x = -x^2 +2

 x^2 + x - 2 = 0

 (x+2)(x-1) = 0

 x = -2 or x = 1

Since y = x, then we have either the solutions:

  (-2,-2)  and  (1,1)

Answer:

(2x-3)(2x+3)

Step-by-step explanation:

4x^2-0x-9

(4x^2-9)

(2x)^2 - (3)^2

We recognize that this is the difference of squares a^2 - b^2 = (a-b)(a+b)

(2x-3)(2x+3)

A positive value c, for x, that satisfies the conclusion of the Mean Value Theorem for Derivatives for f(x) = 3x² - 5x + 1 on the interval [2, 5] is 23/6. The correct answer is C.

The Mean Value Theorem for Derivatives states that there exists a value c in the open interval (a, b) such that:

f'(c) = (f(b) - f(a))/(b - a)

Here, f(x) = 3x² - 5x + 1 and the interval is [2, 5]. Therefore, a = 2 and b = 5.

First, we find f'(x) by differentiating f(x) with respect to x:

f'(x) = 6x - 5

Then, we find f(b) and f(a):

f(b) = 3(5)² - 5(5) + 1 = 61

f(a) = 3(2)² - 5(2) + 1 = 7

Now we can plug in these values to the Mean Value Theorem:

f'(c) = (f(b) - f(a))/(b - a)

6c - 5 = (61 - 7)/(5 - 2)

6c - 5 = 18

6c = 23

c = 23/6

Therefore, the value of c that satisfies the conclusion of the Mean Value Theorem for Derivatives for f(x) = 3x² - 5x + 1 on the interval [2, 5] is 23/6. The correct answer is C.

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Answer: 7 - 2n

Step-by-step explanation:

a1 = 5

a6 = -5 = a + (n - 1)d = a + (6 - 1)d

a + 5d = -5

Since a1 = 5

5 + 5d = -5

5d = -5 - 5

5d = -10

d = -10/5

d = -2

Therefore, the equation to calculate the nth term of this sequence will be:

= a + (n-1)d

= a + (n - 1)-2

= 5 -2n +2

= 7 - 2n

Answer:

Hey there!

A line parallel to y=-4x+3 would have a slope of -4.

Point slope form: y-2=-4(x+3)

Simplify: y=-4x-10

Let me know if this helps :)

Answer:

A

Step-by-step explanation:

So we want an equation that is parallel to:

\(y=-4x+3\)

And passes through:

\((-3,2)\)

First, since we want the equation to be parallel to the first, the slope must be -4. This is because parallel lines have the same slope.

Now that we know the slope of our equation is -4, we can use the point-slope form to figure out the rest.

The point-slope form is:

\(y-y_1=m(x-x_1)\)

m is -4. Let (-3,2) be x₁ and y₁. Thus:

\(y-2=-4(x--3)\)

Simplify:

\(y-2=-4(x+3)\)

Distribute:

\(y-2=-4x-12\)

Add 2 to both sides:

\(y=-4x-10\)

So our answer is A :)

Answer:

6

Step-by-step explanation:

Corresponding sides of similar triangles have proportional side lengths.

\(\frac{x}{4.5}=\frac{4}{3} \\ \\ x=\frac{4.5(4)}{3} \\ \\ x=6\)

Answer:

A

Step-by-step explanation:

also, (the image) is a great friend :)) it   it wouldn't let me say it

Answer:

Voluntary Sample A voluntary sample is one of the main types of non-probability sampling methods. A voluntary sample is made up of people who self-select into the survey. Often, these folks have a strong interest in the main topic of the survey.

a. The critical numbers are -7, -4.04, 4.04, and 7.

b.  F(x) is decreasing on the intervals (-∞, -4.04) and (4.04, ∞)

c.  There are no local maxima.

d. The local minima occur at x = -4.04 and x = 4.04.

e. The inflection points are x = -√21, 0, and √21.

f. F(x) is concave up on the intervals (-∞, -√21) and (√21, ∞).

g. F(x) is concave down on the intervals (-√21, 0) and (0, √21).

h. The horizontal asymptote is y = 0.

I.  There are vertical asymptotes at x = -7 and x = 7.

A. To find the critical numbers, we need to find where the derivative of f(x) is equal to zero or undefined.

f(x) = (3x)/(x^2-49)

f'(x) = [3(x^2 - 49) - 6x^2] / (x^2 - 49)^2

f'(x) = (9x^2 - 147) / (x^2 - 49)^2

The derivative is undefined when the denominator is zero, i.e. when x = ±7. The numerator is equal to zero when x = ±√(147/9) ≈ ±4.04. Therefore, the critical numbers are x = -7, -4.04, 4.04, and 7.

B. f(x) is decreasing on the intervals (-∞, -4.04) and (4.04, ∞), since the derivative is negative on these intervals.

C. . The x-values of all local maxima of f: Local maxima occur at points where the function increases up to that point and then decreases after. To find local maxima, you can take the derivative of f and solve for when it equals zero or does not exist, and then check the sign of the second derivative at those points to ensure they are indeed local maxima. There are no local maxima.

D.  The x-values of all local minima of f: Local minima occur at points where the function decreases up to that point and then increases after. To find local minima, you can take the derivative of f and solve for when it equals zero or does not exist, and then check the sign of the second derivative at those points to ensure they are indeed local minima. The local minima occur at x = -4.04 and x = 4.04.

E. To find the inflection points, we need to find where the second derivative of f(x) changes sign.

f''(x) = (18x(x^2 - 21)) / (x^2 - 49)^3

The second derivative is equal to zero when x = 0 or ±√21. The second derivative is positive when x < -√21 or x > √21, so f(x) is concave up on these intervals. The second derivative is negative when -√21 < x < 0 or 0 < x < √21, so f(x) is concave down on these intervals. Therefore, the inflection points are x = -√21, 0, and √21.

F. Interval notation where f(x) is concave up: A function is concave up on an interval if its second derivative is positive on that interval. You can find the intervals where the second derivative is positive by taking the derivative of f twice and solving for when it is greater than zero. f(x) is concave up on the intervals (-∞, -√21) and (√21, ∞).

G. Interval notation where f(x) is concave down: A function is concave down on an interval if its second derivative is negative on that interval. You can find the intervals where the second derivative is negative by taking the derivative of f twice and solving for when it is less than zero. f(x) is concave down on the intervals (-√21, 0) and (0, √21).

H. Since the degree of the numerator is less than or equal to the degree of the denominator, the horizontal asymptote is y = 0.

I. All vertical asymptotes of f: A function has a vertical asymptote at a point x=a if the denominator of the function approaches zero as x approaches a and the numerator does not. To find vertical asymptotes, you can set the denominator of f equal to zero and solve for x. The resulting values of x are the locations of the vertical asymptotes. There are vertical asymptotes at x = -7 and x = 7.

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At the 0.10 level of significance, the evidence is insufficient to disprove the assertion that the proportion is 48%.

Based on the given conditions,

The analyst or researcher establishes a null hypothesis based on the research question or problem that they are trying to answer. Depending on the question, the null may be identified differently. For example, if the question is simply whether an effect exists (e.g., does X influence Y?) the null hypothesis could be H0: X = 0. If the question is instead, is X the same as Y, the H0 would be X = Y. If it is that the effect of X on Y is positive, H0 would be X > 0. If the resulting analysis shows an effect that is statistically significantly different from zero, the null can be rejected.

Let's start by outlining the research's null and alternate hypotheses;

A newsletter publisher believes that 60`% of their readers own a Rolls Royce.

This means that the null hypothesis is:

H0: p = 0.48

That is, that the proportion of their readers who own a Rolls Royce is of 0.48.

A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim.

The alternate hypothesis is:

Ha: p ≠ 0.48

Now that he fails to disprove the null hypothesis based on the evidence, we will draw the following conclusion:

Therefore,

At the 0.10 level of significance, the evidence is insufficient to disprove the assertion that the proportion is 48%.

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Answer:

1/8th

Step-by-step explanation:

since there are 24 hours in a day

Answer: 1/8

Step-by-step explanation:

a day is 24 hours long. If you spend 3 hours out of 24 hours a day to practice piano it would be 3/24. Then to get it in simpilest  form, you divide 3 by 3 and 24 by 3 which would get you the answer 1/8.

Hope i helped have a good rest of your day!!

1. $7,560 is left to pay creditor claims.

2. Beamis Supply Company was paid $480.06 which represents 6.35% of their claim.

The amount left to pay creditor claims:

= $16,760 - $9,200

= $7,560

Therefore, $7,560 is left to pay creditor claims.

The percent of claims that each creditor gets is computed as:

Data:

Total creditor claims = $50,400

Amount available for creditors = $7,560

The percent of each claim paid:

= (Creditor's claim / Total creditor claims) x 100%

= ($3,200 / $50,400) x 100%

= 6.35%

The amount that Beamis Supply Company was paid is:

= Percent of claim paid x Total available funds

= 6.35% x $7,560

= $480.06.

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The probability that all of the next ten customers who want this racket can get the version they want from current stock is 0.821

Given: currently has seven rackets of each version.

Then the probability that the next ten customers get the racket they want is P(3≤X≤7)

Note that If less than 3 customers want the oversize, then more than 7 want the midsize and someone's going to miss out.

X ~ Binomial (n = 10, p = 0.6)

P(3≤X≤7)  = P(X≤7) - P(X≤2)

From Binomial Table:

               = 0.8333 - 0.012

               = 0.821

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To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator. To find the conjugate, just change the sign in the denominator.

Now, According to the question:

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.

Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator. To find the conjugate, just change the sign in the denominator.

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Answer:

\(1 \dfrac{11}{12} \text{ yd}\)

Step-by-step explanation:

We know that there are 36 inches in 1 yard. Using this information, we can construct the conversion rate:

1 yd : 36 in

To convert 69 in to yards, we simply have to multiply it by the above conversion rate.

\(69 \text{ in} \cdot \dfrac{1 \text{ yd}}{36\text{ in}}\)

↓ multiply the numerators

\(\dfrac{69 \not\text{in} \cdot \text{ yd}}{36 \not \text{in}}\)

↓ cancel inches

\(\dfrac{69}{36}\text{ yd}\)

↓ rewrite as a mixed number

\(1 \dfrac{33}{36} \text{ yd}\)

↓ simplify

\(\boxed{1 \dfrac{11}{12} \text{ yd}}\)

Answer:8.44

Step-by-step explanation:

Area of the circle is 56.

Divide 56 by 3.14(Pi)

56/3.14=17.8343949

Square root it

Square root of 17.8343949=4.223078841

4.22 is the radius so to find the diameter you just multiple by 2.

4.223078841x2=8.446157683

Answer:

I think its a trapezium

area of trapezium= 1/2×(sum of parallel sides) ×height

1×(28+26)×18

2

1/2×54×18

54×9

= 586 km²

hope it helps

Answer:

-32.25 + 10.75 = -21.5

Step-by-step explanation:

-10.75 + -10.75  = -21.5

-32.25 + 10.75 = -21.5

Answer:

4.3+4.3+4.3+4.3+4.3 equals 21.5

Jo has read 14% of the book if she has read 35 pages of a 250 pages book.

If Jo has read 35 pages out of a 250-page book, we can calculate what percentage of the book she has read by dividing the number of pages she has read by the total number of pages and multiplying by 100:

Percentage of book read = (35 / 250) x 100%

Percentage of book read = 0.14 x 100%

Percentage of book read = 14%

Therefore, Jo has read 14% of the book. Percentage is a way of expressing a number as a fraction of 100. It is often used to describe the relationship between a part and a whole, where the part represents a portion of the whole. Percentages are commonly used in various fields, including mathematics, finance, and statistics, to measure changes or represent data in a more accessible format.

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