A function is shown.
f(x)=x2+2x−1


Which graph represents the function?

The values of x and y have been calculated as [tex]15[/tex] and [tex]12[/tex] respectively making option A the appropriate choice.

In the given question we can see that the angles [tex]62[/tex] degrees and [tex]4x + 2[/tex] degrees are alternate interior angles because they are alternately on the interior side of two parallel lines and transversal. hence, we can calculate x as:
[tex]62 = 4x + 2\\4x = 60\\x = 60/4 = 15[/tex]
Similarly, we can find the value of y as the angles [tex]12y[/tex] degrees and [tex]144[/tex] degrees are alternate interior angles.
[tex]12y = 144\\y = 144/12\\y = 12[/tex]

The values of x and y are [tex]15[/tex] and [tex]12[/tex] respectively.
Therefore, option A is the correct answer.

To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can use the expression 9(8 - x), where x represents 'a number'.

To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can start by assigning the letter x to represent a number. Then, we can write the expression as 9(8 - x), where 8 - x represents the difference of 8 and the number x.

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The given sentence 'Nine times the difference of 8 and a number' can be translated into the algebraic expression 9(8 - x).

The given sentence, 'Nine times the difference of 8 and a number' can be represented as an algebraic expression as follows: First, identify the operation for 'difference' which is subtraction. Then, identify the 'number', which is given as x. So, 'the difference of 8 and a number' would be 8 - x. 'Nine times the difference' implies multiplication, so the entire expression would be 9(8 - x). Therefore, the algebraic expression to represent the sentence in question is 9(8 - x).

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ANSWER

[tex]S_5=91\frac{10}{81}[/tex]

EXPLANATION

The sum of the first [tex]n[/tex] terms of a geometric sequence is given by;

[tex]S_n=\frac{a_1(1-r^n)}{1-r} ,-1<\:r<\:1[/tex]

Where [tex]n[/tex], is the number of terms and [tex]a_1[/tex] is the first term.

When [tex]n=5[/tex], we have [tex]a_1=81[/tex], we get;

[tex]S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}[/tex]

[tex]S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}[/tex]

[tex]S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}[/tex]

[tex]S_5=\frac{7381}{81}[/tex]

[tex]S_5=91\frac{10}{81}[/tex]

To find the length of the hypotenuse in a right-angled triangle with sides measuring 7ft and 4ft, use the Pythagorean Theorem: 7² + 4²= c², which gives us the hypotenuse length of approximately 8.06 feet.

The question is asking for the length of the hypotenuse of a right-angled triangle when the lengths of the other two sides are known (7ft and 4ft).

To find the hypotenuse, we use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as a² + b² = c².

By applying the Pythagorean Theorem:

72 + 42 = c²
49 + 16 = c²
65 = c²
c = √65 ≈ 8.06 ft

Therefore, the length of the hypotenuse is approximately 8.06 feet.

Using the exponential decay formula, the resale value of a car initially purchased at $29,500 and depreciating at 35% per year will be approximately $5,266.08 after 4 years.

To calculate the resale value of a car after depreciation, we can use the formula for exponential decay, which is [tex]V = P (1 - r)^t[/tex], where V is the future value of the car, P is the initial purchase price, r is the rate of depreciation, and t is the time in years. In this case, P = $29,500, r = 35% or 0.35, and t = 4 years.

Following the formula, the resale value after 4 years would be:

V = $29,500 (1 - 0.35)⁴

V = $29,500 (0.65)⁴

V = $29,500 (0.17850625)

V = $5,266.08 approximately

Therefore, the resale value of the car after 4 years will be around $5,266.08.

Final answer:

The margin of error for the poll, given a range of 33-37%, is ±2%. This means the actual percentage of the town's population that visits the library at least once a year could reasonably be expected to fall within 2% of the poll's reported value, which is 35%.

Explanation:

The margin of error in a poll is a statistic that reflects the degree of accuracy of the poll's results. It indicates how much the actual percentage could differ from the reported percentage in either direction. In this case, the poll indicates a visitation range between 33% and 37%. To calculate the margin of error, you find the difference between the highest value and the mean or the difference between the mean and the lowest value of the range.

In this instance, (37% + 33%) / 2 = 35%, which is the mean. The margin of error is then calculated as either 37% - 35% or 35% - 33%, both resulting in a 2%. Therefore, the poll's margin of error is ±2%.

Answer:

3 × ( p + 4m ) + 8 and 3p + 4 × ( 3m + 2 ) are the equivalent expressions.

Step-by-step explanation:

Given: Expression = 3p + 12m + 8

To find:  Equivalent Expression.

Equivalent Expression means the expression which repesent original expression .i.e., on simplifying we get back original expression.

Consider,

3p + 12m + 8

Ist Equivalent expression we get by taking 3 common from first two terms,

⇒ 3 × ( p + 4m ) + 8

Another Equivalent Expression we get by taking 4 common from last two terms.

⇒ 3p + 4 × ( 3m + 2 )

The equivalent expression of 3p+12m+8 are 3(p+4)+8 and 3p+4(3m+2).

Expression in mathematics consist of terms separated by operations like + and -.

Given expression is 3p+12m+8,

To find the equivalent expression of the given expression:

3p+12m+8

Taking 3 common from first and second term as follows:

3(p+4)+8

one more possible equivalent expression of the given expression:

Taking 3 common from first and second term as follows:

3p+4(3m+2)

Thus, 3(p+4)+8 and 3p+4(3m+2) are  the equivalent expression of 3p+12m+8.

Learn more about expression, here:

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The next number would be 6.

The pattern is add 3, then subtract two.

The next number in the series 3 6 4 7 5 8 is 6.

The next number in the series 3 6 4 7 5 8 is 6.

This is an alternating pattern where the first number increases by 1, the second number stays the same, and the third number increases by 1. So, starting with 3, the next number after 8 should be 9. However, since 9 is not given in the options, we can look for the closest number that follows the pattern, which is 6.

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Answer:

The width of the room is 20 feet.

The Length of the room is  [tex]46[/tex] feet.

Step-by-step explanation:

Lets take the width of the room as [tex]x[/tex] feet

Then the length of the room will be [tex]2x+6[/tex] feet

Perimeter of a room is the addition of all the walls making the boundary of the room.

Perimeter of the rectangular room = 2 * Width + 2 * Length

⇒[tex]132=2*x+2*(2x+6)[/tex]

⇒[tex]132=2x+4x+12[/tex]

⇒[tex]132=6x+12[/tex]

⇒[tex]132-12=6x[/tex]

⇒[tex]120=6x[/tex]

⇒[tex]20=x[/tex]

Therefore,

The width of the room is 20 feet.

The Length of the room is,

[tex]2x+6[/tex] = [tex]2*20+6[/tex] = [tex]46[/tex] feet

Go to a website called desmos graphing calculator and it will help you out but I put a image of the graphed equation as well.

Answer:

The required graph is shown below.

Step-by-step explanation:

Consider the provided function.

[tex]y=-\frac{4}{7}x+1[/tex]

The above function is a linear function.

We can draw the graph of the function with the help of 2 points.

Substitute x = 0 in the above function.

[tex]y=-\frac{4}{7}(0)+1[/tex]

[tex]y=1[/tex]

Substitute y = 0 in the above function.

[tex]0=-\frac{4}{7}x+1[/tex]

[tex]\frac{4}{7}x=1[/tex]

[tex]x=\frac{7}{4}[/tex]

Now plot the points.

Draw a straight line passing through (0,1) and (7/4,0)

The required graph is shown below.

Binomial: A polynomial that is the sum of two terms, each of which are monomials. The answer here would be A. b² - 14, because it is comprised of two terms. Answer B is a monomial because it only has ONE term, C is a trinomial because it has three terms, and D. is a multinomial, or a polynomial because it has more than three terms. Hope that helps!

The division between two numbers is positive if and only if they have the same sign. So, this fraction is positive if numerator and denominator are either both positive or both negative.

For this reason, you want to study the sign of numerator and denominator separately first.

As for the numerator, you have

[tex] 3x+8 \geq 0 \iff 3x \geq -8 \iff x \geq -\dfrac{8}{3} [/tex]

Similarly, for the denominator you have

[tex] x-4 > 0 \iff x > 4 [/tex]

(note that we used strict inequality for the denominator, since it can't be zero).

So, the sign of the fraction works like this:

Answer:

A. x ≤ −8/3 or x>4

Step-by-step explanation:

Edge 2020 answer is A

Answer:

Always

Step-by-step explanation:

A mononomial's variable can only have exponents 0,1,2,3 etc  so the product will also be a mononomial.

Answer:

the answer is -always

Step-by-step explanation:

Answer:

Independent.

Step-by-step explanation:

Answer: Picture

Step-by-step explanation:

f(x)=-3x^2-1

f(-2)= -3(-2)²-1=-3·4-1= - 13

The answer is (-3,0) if you plug the coordinates into the equation you will find that it satisfies it and indicates that you should shade below the line

:)

First we have to change 7 1/5 into an improper fraction. 7 1/5 converted to an improper fraction is 36/5. Now, to divide this by 1/8, we need to multiply it by 8 (multiplying by the reciprocal). 36/5 * 8/1 = 288/5. In simplest form, this is 57 3/5.

The division problem 7 1/5 divided by 1/8 is solved by converting the mixed number to an improper fraction, converting the division problem to a multiplication problem by multiplying by the reciprocal, and then simplifying the resulting fraction. The final answer is 57.6.

To solve the problem 7 1/5 divided by 1/8, we first need to convert the mixed number 7 1/5 into an improper fraction. We do this by multiplying the whole number 7 by the denominator of the fraction 5 and then adding the numerator 1. So, 7 * 5 + 1 = 36.

So, 7 1/5 becomes 36/5. Now, we have 36/5 divided by 1/8.

When we are dividing by a fraction, we need to multiply by its reciprocal. The reciprocal of 1/8 is 8/1. So the problem becomes 36/5 multiplied by 8/1.

When multiplying fractions, we simply multiply the numerators and the denominators together. So, 36 * 8 = 288 and

5 * 1 = 5. Therefore, our answer is 288/5. Lastly, when we simplify this, it becomes 57.6.

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To factor 9x^4 - 64y^2, use the difference of squares formula. The factored form is (3x^2 + 8y)(3x^2 - 8y).

To factor 9x^4 - 64y^2, we can use the difference of squares formula: a^2 - b^2 = (a + b)(a - b). Applying this, we get: 9x^4 - 64y^2 = (3x^2 + 8y)(3x^2 - 8y)

Therefore, the factored form of 9x^4 - 64y^2 is (3x^2 + 8y)(3x^2 - 8y).

The formula of a midpoint SR:

[tex]M\left(\dfrac{x_S+x_R}{2},\ \dfrac{y_S+y_R}{2}\right)[/tex]

We have

S(4, 1) and M(7, -5)

Substitute:

[tex]\dfrac{4+x_R}{2}=7\qquad|\cdot2\\\\4+x_R=14\qquad|-4\\\\x_R=10\\\\\dfrac{1+y_R}{2}=-5\qquad|\cdot2\\\\1+y_R=-10\qquad|-1\\\\y_R=-11[/tex]

Direct variation

The equation is written as y=mx+b

The  variation f(x) = 3x is A. Direct variation.

The function f(x) = 3x represents a type of relationship called a direct variation. In mathematics, a direct variation can be expressed in the form y = kx, where k is a constant. Here, k is 3. This means that as x increases or decreases, f(x) = 3x changes proportionally. The correct answer is therefore:

To further illustrate, consider two pairs of values for x and f(x):

if x = 2, then f(x) = 3(2) = 6,

And if x = 4, then f(x) = 3(4) = 12.

Notice that the ratio f(x)/x = 3 is constant.

Answer: [tex]\frac{16}{21}[/tex]

Step-by-Step Explanation:

KCFmeans: Keep, Change, Flip

  [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{7}{8}[/tex]

= [tex]\frac{2}{3} * \frac{8}{7}[/tex]   KCF is applied here!

= [tex]\frac{2(8)}{3(7)}[/tex]

= [tex]\frac{16}{21}[/tex]

ASNSWER

[tex]Perimeter=\frac{5x-16}{2}[/tex]

EXPLANATION

Let [tex]w=x[/tex] represent the width of the rectangle.

One-fourth of the width will be,

[tex]\frac{1}{4}x[/tex]

Let [tex]l[/tex] represent the length of the rectangle.

Then, subtracting 4 units from one-fourth the width gives us the length

[tex]\Rightarrow l=\frac{1}{4}x-4[/tex]

Perimeter[tex]=2x+2l[/tex]

[tex]\Rightarrow Perimeter=2x+2(\frac{1}{4}x-4)[/tex]

We expand to obtain;

[tex]Perimeter=2x+\frac{x}{2}-8[/tex]

[tex]Perimeter=\frac{x+4x-16}{2}[/tex]

[tex]Perimeter=\frac{5x-16}{2}[/tex]

1. Part A

C

Part B

A

2a

4c

srry all i can do

Answers:

1.

Part A. Option a) vertical angles theorem and triangle angle-sum theorem

Part B. Option b) x=80, y=80

2. Option d) 123

3. Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Option c) x=37

Solution:

1. Part A

First, you can find x using the triangle angle-sum theorem: The sum of the interior angles of any triangle must be equal to 180°.

Second, you can apply the vertical angles theorem to find y: the angles opposite by the vertex must be congruent.

Then, the answer is option a) vertical angles theorem and triangle angle-sum theorem.

1. Part B.

First: Triangle angle-sum theorem

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are x°, 30°, and 70°, then:

x°+30°+70°=180°

(x+30+70)°=180°

(x+100)°=180°

x+100=180

Solving for x: Subtracting 100 both sides of the equation:

x+100-100=180-100

x=80

Second: Vertical angles theorem: The angles opposite by the vertex must be congruent:

In the figure, the angles x° and y° are opposite by the vertex, then they must be congruent:

y°=x°

y=x

and x=80, then:

y=80

Answer: Option b) x=80, y=80

2. The <1 is an exterior angle of the triangle in the figure, and according with the Triangle Exterior Angle Theorem, an exterior angle of a triangle must be equal to the sum of the interior angles no adjacents to it:

<1=60°+63°

<1=123°

Answer: Option d) 123

3.

You can apply the Triangle Angle-Sum Theorem, to find the third interior angle of the triangle. With this angle you can find the exterior <1.

You can apply the Triangle Exterior Angle Theorem to find the exterior <1.

Answer: Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Using the Triangle angle-sum theorem:

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are (2x-9)°, x°, and (2x+4)°, then:

(2x-9)°+x°+(2x+4)°=180°

(2x-9+x+2x+4)°=180°

Adding similar terms:

(5x-5)°=180°

5x-5=180

Solving for x: Adding 5 both sides of the equation:

5x-5+5=180+5

Adding:

5x=185

Dividing both sides of the equation by 5:

(5x)/5=185/5

x=37

Answer: Option c) x=37

Complimentary angles equal 90 degrees.  So the answer would be C because  77+13= 90.

Answer: Two angles are complementary when they add up to 90°

then, doing all the options:

A) 50° + 41° = 91°, so this angles are non complementary.

B) 100° + 80° = 180°, so this aren't complementary, but they are Supplementary (because their addition is 180°) angles.

C) 77° + 13° = 90°, si this angles are complementary

D) 35° + 10° = 45°, this pair is not complementary.

So the only correct answer is C.

Answer:

y = 3x - 17

Step-by-step explanation:

Here is the point-slope form of the equation of a line.

[tex] y - y_1 = m(x - x_1) [/tex]

If you are given a slope, m, and a point on the line, (x1, y1), you just plug in the values into the equation above, and you get the equation of the line.

In your problem, you are given a point on the line, (5, -2). Now you need the slope of the line. Your line is perpendicular to the given line. The slopes of perpendicular lines are negative reciprocals. If you know the slope of a line, the slope of its perpendicular is found by flipping the fraction and changing the sign.

The given line has slope -1/3.

Flip -1/3 to get -3.

Now change the sign to get 3.

The slope of the line you need is 3. The line passes through point (5, -2).

Now we use the point-slope equation and we plug in the values we have.

[tex] y - y_1 = m(x - x_1) [/tex]

[tex] y - (-2) = 3(x - 5) [/tex]

[tex] y + 2 = 3x - 15 [/tex]

[tex] y = 3x - 17 [/tex]