You rotate triangle ABC, with vertices A(-3, 1), B(-2, 2), and C(-3, 4), 90° counterclockwise about the origin to form triangle A′B′C′. Match each vertex of triangle A′B′C′ to its coordinates.

We're given [tex]f(x) = 0[/tex] when [tex]x=-2[/tex] and [tex]x=3[/tex], so both [tex]x+2[/tex] and [tex]x-3[/tex] divide [tex]f(x)[/tex]

We're also told [tex]2x^2+3x+2[/tex] divides [tex]f(x)[/tex]. This quadratic does not have roots at -2 or 3, so we can factorize [tex]f(x)[/tex] as

[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]

where the leading coefficient is 2 because the full expansion should have a leading term of [tex]4x^4[/tex].

Now just expand [tex]f(x)[/tex] :

[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]

[tex]f(x) = 2 (x^2 - x - 6) (2x^2 + 3x + 2)[/tex]

[tex]f(x) = 2 (2x^4 + x^3 - 13x^2 - 20x - 12)[/tex]

[tex]f(x) = \boxed{4x^4 + 2x^3 - 26x^2 - 40x - 24}[/tex]

Answer:

Step-by-step explanation:

2,816 lol

Answer:

It is not arithmetic, so therefore there is no common difference

Step-by-step explanation:

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. There is no constant term in the above pattern.

Answer:

  not an arithmetic sequence

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers that have a common difference. That is, the difference between any term and the previous term is constant for the sequence. Other kinds of sequences have other relationships between the differences.

The "first" differences of this sequence are ...

The first differences are not constant. However, we notice the "second" differences are constant. These are the differences of successive first differences.

The first differences are not constant, so this sequence is not an arithmetic sequence.

For polynomial sequences, the level of constant difference tell you the degree of the polynomial describing the sequence. This sequence has constant 2nd-level differences, so can be described by a 2nd degree (quadratic) polynomial:

  f(n) = 1.5n² +1.5n +1 . . . . . a quadratic sequence

__

Additional comment

Sequences that are exponential have differences that have a common ratio. That ratio is the same at every level. It is the base of the exponential function.

Answer:

2 times a number more than 4

Answer:B

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

x to the zeroth power is always 1

Answer:

Step-by-step explanation:

90 - 20 = 70

So now do 5 times x and that's also equal to 70

70.x =11

The fraction of players who don't stretch and get injured = 4/9.

The frequency tree is shown in the image attached.

The total number of footballers = 45.

The total number of footballers who stretch = 36.

Therefore, the number of footballers who don't stretch = 45 - 36 = 9.

The total number of injured footballers = 10.

The number of injured footballers from the players who stretch = 6.

Therefore, the number of injured footballers from the footballers who don't stretch = 10 - 6 = 4.

The total number of footballers who don't get injured = 45 - 10 = 35.

The number of footballers who stretch and don't get injured = 36 - 6 = 30.

The number of footballers who don't stretch and don't get injured = 9 - 4 = 5.

Therefore, the frequency tree can be shown in the image attached.

The fraction of players who don't stretch and get injured = 4/9.

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Answer:

y-2=1/3(x-3)

Step-by-step explanation:

Point slope formula: y-y1=m(x-x1)

m is slope.

y-2=1/3(x-3)

Hope this helps!

If not, I am sorry.

Step-by-step explanation:

please mark me as brainlest

Answer:

It is an obtuse triangle I think because

Answer: 68.852459016393 or 68.9 if you round up

Step-by-step explanation:

If you add all the students subjects together you get a total of 41. Then if you add up the total of students who study physics, chemistry, and both you get 20. Then I put those numbers is a percentage calculator then boom you got your answer.

Step-by-step explanation:

Let u=x^2.

Notice that

[tex] {x}^{4} - 9 {x}^{2} + 8 = 0[/tex]

[tex]( {x}^{2} ) {}^{2} - 9( {x}^{2} ) + 8 = 0[/tex]

[tex]u {}^{2} - 9u + 8 = 0[/tex]

[tex](u - 8)(u - 1) = 0[/tex]

[tex]u = 8[/tex]

[tex]u = 1[/tex]

Replace x^2= u

[tex] {x}^{2} = 8[/tex]

[tex]x = ±2 \sqrt{2} [/tex]

[tex] {x}^{2} = 1[/tex]

[tex]x = ±1[/tex]

So our answer is

[tex]±1 \: [/tex]

and

[tex]±2 \sqrt{2} [/tex]

Answer:

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.

No we cannot conclude that there is a difference between the population proportion of adults between the ages of 27 and 35 in the two cities.

For Seattle

66/200 = 0.33

For Minneapolis

63/180

= 0.35

We have to form our hypothesis

H0: p1 = p2

H1: p1 ≠ p2

We solve for the test statistic

z = (p1-p2)/√(p1*(1-p1)/n1+p2x(1-p2)/n2)

The calculation is given as -0.41

The excel output is given in the attachment

=-0.41

At a significance level of 0.1, the level of acceptance is at -1.645 and 1.645. The value of the test stat can be found here.

Since Z=-0.41 is between -2.58 and 2.58, we do not reject H0.

Hence we fail to reject the null hypothesis.

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Answer:

-1

Step-by-step explanation:

the answer snis negative One

1) Given

2) Segment addition postulate

3) Substitution property

4) Segment addition postulate

5) Transitive property of equality

Answer:

Formula for a linear sequence is

Tn=a+(n-1)d

where Tn is the nth term

a is the first term

n is the number of term

d is common difference

Answer:

6

Step-by-step explanation:

f(6) is the y-value when x = 6

From inspection of the graph, f(6) = -6

g(5) is the y-value when x = 5

From inspection of the graph, g(5) = -5

Substitute the found values into the given equation:

  4 · f(6) - 6 · g(5)

= 4 · (-6) - 6 · (-5)

= -24 - (-30)

= -24 + 30

= 6

Answer:

m∠1 = 50°

m∠2 = 130°

Step-by-step explanation:

There is a formula:

[tex]\text{angle} = \frac{1}{2} (\text{intercepted arc}_1 + \text{intercepted arc}_2)[/tex]

[tex]\text{m} \angle 1 = \frac{1}{2} (53^\circ + 47^\circ)[/tex]

[tex]\text{m} \angle 1 = \frac{1}{2} (100^\circ)[/tex]

[tex]\text{m} \angle 1 = 50^\circ[/tex]

Angle 1 and angle 2 together form a straight angle, which measures 180°. Angle 1 and angle 2 are suplementary angles.

[tex]\text{m} \angle 1 + \text{m} \angle 2 = 180^\circ[/tex]

[tex]50^\circ + \text{m} \angle 2 = 180^\circ[/tex]

[tex]\text{m} \angle 2 = 180^\circ - 50^\circ[/tex]

[tex]\text{m} \angle 2 = 130^\circ[/tex]

Answer:

$989

Step-by-step explanation:

860*0.15 is = 129

129 + 860 is 989

Answer:

[tex]\sqrt{69}[/tex]

Step-by-step explanation:

from the pythagorean theorem:

[tex]a^2 + b^2 = c^2\\10^2 + b^2 = 13^2\\100 + b^2 = 169\\b^2 = 69\\b = \sqrt{69}[/tex]

The arc length of the semicircle is 5π units

From the question, we are to calculate the arc length of the semicircle

Arc length of a semicircle = 1/2 the circumference of the circle

∴ Arc length of a semicircle = 1/2 × 2πr

Arc length of a semicircle = πr

Where r is the radius

From the given information,

r = 5

∴ Arc length of the semicircle = 5 × π

Arc length of the semicircle = 5π units

Hence, the arc length of the semicircle is 5π units

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The error that Maria made is that she did not divide correctly.

The simple interest that is paid on an amount of money is a function of the amount deposited, time and interest rate.

Simple interest = principal x time x interest rate

2666 = 4300 x 0.062 x t

2666 = 266.60t

t = 2666 /  266.60

t = 10 years

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The simple interest earned in year 1 is 7.5. The simple interest earned in year 1 is $7.50. The total interest earned at the end of year 4 is $30.00

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, it is left for T years for that simple interest.

3% simple annual interest paid on $250

A 2-column table with 4 rows.

Column 1 is labeled Year with entries 1, 2, 3, 4.

Column 2 is labeled Total Interest Paid with an entries question mark, 15 dollars, 22 dollars, and 50 cents,

The simple interest earned in year 1 is calculated as

The first one is (0.03)(250) = 7.5

The simple interest earned in year 1 is

The second one is $7.50

The total interest earned at the end of year 4 is

The third one is $30.00

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First we must solve the bottom situations.

___________________________________________ (2A and 2B)

First expression (2A): 2v+8.3+2v-6.1

⇒  Collect like terms

(2v + 2v)  + (8.3 - 6.1)

⇒ Simplify

4b + 2.2

Second expression (2B): 3v+14.4-v

⇒ Collect like terms

(3v - v) + 14.4

⇒ Simplify

2v + 14.4

They are not equivalent because when simplified they both have different coefficients and constants each of different values.

_____________________________________________ (4A and 4B)

First expression (4A): 10 + 3 (1/3x + 2)

⇒ Simplify 1/3x to x/3.

10 + 3(x/3 + 2)

⇒  Expand by distributing terms.

10 + x + 6

⇒ Collect like terms.

x + (10 + 6)

⇒ Simplify.

x + 16

Second expression: x + 16

This expression can not be simplified any further. This is because it is a simplified version of another expression.

These expressions are equivalent because expression 4B is the simplified version of expression 4A.

______________________________________

Level: 7th Grade

Unit: Distributing and Combing Like Terms

The missing words to complete the proof are respectively; Vertical Angles; Corresponding angles; Transitive Property

The image of the transversal line is attached.

1) We know that lines a and b are parallel and that line c is a transversal because that is given.

2) We can tell that angles 2 and 5 are congruent because vertical angles are congruent.

3) Angles 5 and 7 are congruent because corresponding angles by parallel lines cut by a transversal are congruent.

4) Therefore, angles 2 and 7 are congruent based on the transitive property.

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Answer: vertical, corresponding, and transitive property

Step-by-step explanation: I got the correct answer on Edge 2022. The answer is correct trust me! Proof is shown down below.

7978978

Step-by-step explanation:

Step-by-step explanation:

Part A:

4x² - 7x - 15

a, b, c = 4, -7, -15

ac = -60

factors that add up to -7 and multiply to -60 are (-12, 5)

rewrite equation

(4x² - 12x) + (5x - 15)

factor out GCF from both groups

4x(x - 3) + 5(x - 3)

(4x+5)(x-3)

Part B:

Using the factored form from the previous part we can set both factors equal to 0 to solve for x.

4x+5 = 0

4x = -5

x = -5/4

x-3 = 0

x = 3

the two x-intercepts are -5/4 and 3

Part C:

Since the leading coefficient is positive, the right side of the function will be going up or to positive infinity as x goes towards positive infinity. Since the degree is even both sides go in the same direction so on the left side it also goes towards positive infinity as x goes towards negative infinity.

Answer: (3,6)

Rewrite in vertex form and use this form to find the vertex (h,k)

Answer:

(3,6)

Step-by-step explanation:

f(x) = |x| is a V-shaped graph with the vertex at (0,0). It is called a parent graph, because its super basic.

f(x) = |x - 3| + 6

has had two changes made to it. The "- 3" that's in there close to the x slides the graph over to the right 3 units. This is kind of the opposite of what you might think. Minus3 shifts right. (Plus3 would shift left)

The +6 tacked on to the end shifts the whole graph UP 6.

That slides the graph RIGHT3 and UP6. So the vertex lands at (3,6). See image.

The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.

A function is a law that relates a dependent variable and an independent variable with each other

It is given that

y = 2tan (x - π/2) +3

To find the zeroes of a function that function has to be equated to zero.

2tan (x - π/2) +3 = 0

2tan (x - π/2)  = -3

tan (x - π/2)  = -3/2

x - 90 = -56.31

x = 33.69 degree

The zero of the function is at 33.69 degree

For finding the maxima /minima

the derivative is

dy/dx = 2 sec² (x - π/2)

the point at which the slope is zero is substituted in the second derivative to find maxima/minima

d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)

if the value is negative then it is a maxima and if it is positive it is a minima.

The vertical asymptote is found by finding the values that make the function undefined

x = 0+ πn

No horizontal or oblique asymptote

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