Evaluate................

Answer:

A

Step-by-step explanation:

y = 2x² + 8x + 3

Complete the square:

y = 2(x² + 4x) + 3

y = 2(x² + 4x + 4) + 3 - 2(4)

y = 2(x + 2)² - 5

So the vertex is at (-2, -5).  The graph must be Graph A.

Graph A has its vertex at (-4, -5). Then the correct option is A.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The parabolic expression is given below.

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

y = 2(x² + 4x + 4) - 8 + 3

y = 2(x + 4)² -5

The vertex of the parabola is at (-4, -5).

Graph A has its vertex at (-4, -5). Then the correct option is A.

Then the graph of the parabola is given below.

More about the parabola link is given below.

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Answer:

720

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

We are given the following permutation problem to solve:

[tex] _ 6 P _ 6 [/tex]

We know that the number of possibilities to choose an ordered set of [tex] r [/tex] objects from a total of [tex]n[/tex] objects is given by:

[tex] _ n P _ r = \frac { n ! } { ( n - r ) ! } [/tex]

Substituting the given values, n = 6, r = 6:

[tex] _ 6 P _ 6 = \frac { 6 ! } { ( 6 - 6 ) ! } [/tex] = 720

Final answer:

Using the Rational Root Theorem, the polynomial equation 2x⁴+ 4x³-6x²+15x-12=0 has 12 distinct possible rational roots, where factors of the constant term are divided by factors of the leading coefficient.

Explanation:

To determine the number of possible rational roots for the polynomial equation 2x⁴+4x³−6x²+15x−12=0, we can use the Rational Root Theorem. This theorem states that if the polynomial has any rational roots, they must be of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The constant term in this case is -12, and its factors are ±1, ±2, ±3, ±4, ±6, and ±12. The leading coefficient is 2, and its factors are ±1 and ±2.

Thus, the possible rational roots are combinations of the factors of -12 divided by the factors of 2, giving us ±1, ±2, ±3, ±4, ±6, and ±12 combined with ±1 and ±2. So, our possible rational roots are: ±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±12/1, ±1/2, ±2/2, ±3/2, ±4/2, ±6/2, and ±12/2 which simplifies to ±1/1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, and ±6/2.

After simplification, there is a total of 12 distinct possible rational roots, corresponding to option D.

Answer:

a = -4

b = 6

Step-by-step explanation:

See attached

Answer:

a=-4 and b=6

Step-by-step explanation:

[tex]\frac{a}{x-8} +\frac{b}{x+4} =\frac{2x-64}{(x-8)(x+4)}[/tex]

First, add the fractions by finding the common denominator.

In this case, (x-8)(x+4).

[tex]\frac{a(x+4) + b(x-8)}{(x-8)(x+4)} =\frac{2x-64}{(x-8)(x+4)}[/tex]

Therefore, the numerators are equal:

[tex]a(x+4) + b(x-8) =2x-64[/tex]

Simplify:

[tex]ax+4a + bx-8b =2x-64\\(a+b)x+4a-8b=2x-64[/tex]

Now match the coefficients.

[tex]a+b=2, 4a-8b=-64[/tex]

Solve the system of equations.  I'll use substitution, but you can also use elimination if you prefer.

[tex]4a-8b=-64\\a-2b=-16\\(2-b)-2b=-16\\2-3b=-16\\-3b=-18\\b=6\\a=-4[/tex]

Therefore, a=-4 and b=6.

Answer:  101 revolutions

Step-by-step explanation:

Answer:  The total number of revolutions is 101.

Step-by-step explanation:  Given that the wheels on Jason's dirt bike measure 19 inches in diameter.

We are to find the number of revolutions that the wheels make when Jason rides for 500 feet.

We know

1 foot = 12 inches.

So, 500 feet = 12 × 500 = 6000 inches.

Now, diameter of the wheels is given by

d = 19 inches.

So, the circumference of the wheels will be

[tex]C=\pi d=3.14\times19=59.66~\textup{inches}.[/tex]

Therefore, to ride 500 feet, The number of revolutions that the wheels make is given by

[tex]n=\dfrac{6000}{59.66}=100.56989...[/tex]

Rounding to the nearest whole number, the required number of revolutions will be 101.

Thus, the total number of revolutions is 101.

Answer:

B).  (2, –23)

Well this person made it easy by literally saying the answer...

Step-by-step explanation:

Hope this helps!!  Also heart and rate if you found this answer helpful!!

The correct option is, (B) (2, –23).

Learn more about  coordinates here:

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Answer:

Part 1) The  lateral area of the cone is [tex]LA=2\pi\ cm^{2}[/tex]

Part 2) The lateral surface area of the cylinder is [tex]LA=36\pi\ cm^{2}[/tex]

Part 3) The surface area of the crayon is [tex]SA=41.50\pi\ cm^{2}[/tex]

Step-by-step explanation:

Part 1) Find the  lateral area of the cone  

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

we have

[tex]r=1\ cm[/tex]

[tex]l=2\ cm[/tex]

substitute

[tex]LA=\pi (1)(2)[/tex]

[tex]LA=2\pi\ cm^{2}[/tex]

Part 2) Find the lateral surface area of the cylinder

The lateral area of the cylinder is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=1.5\ cm[/tex]

[tex]h=12\ cm[/tex]

substitute

[tex]LA=2\pi (1.5)(12)[/tex]

[tex]LA=36\pi\ cm^{2}[/tex]

Part 3) Find the surface area of the crayon

The surface area of the crayon is equal to the lateral area of the cone, plus the lateral area of the cylinder, plus the top area of the cylinder plus the bottom base of the crayon

Find the area of the bottom base of the crayon

[tex]A=\pi[r2^{2}-r1^{2}][/tex]

where

r2 is the radius of the cylinder

r1 is the radius of the cone

substitute

[tex]A=\pi[1.5^{2}-1^{2}][/tex]

[tex]A=1.25\pi\ cm^{2}[/tex]

Find the area of the top base of the cylinder

[tex]A=\pi(1.5)^{2}=2.25\pi\ cm^{2}[/tex]

Find the surface area

[tex]SA=2\pi+36\pi+2.25\pi+1.25\pi=41.50\pi\ cm^{2}[/tex]

Answer:

2

36

41.5

Step-by-step explanation:

just got it all right even though I guessed soooo, yay

Step-by-step explanation:

Answer:

(5sqrt(2), 45 deg)

(-5sqrt(2), 225 deg)

Step-by-step explanation:

(x,y)=(5,5)

So theta=arctan(5/5)=arctan(1)=45 degrees

Now r! r=sqrt(x^2+y^2)=sqrt(5^2+5^2)=sqrt(50)=sqrt(25)sqrt(2)=5sqrt(2)

So one polar point is (5sqrt(2) , 45 degrees)

Now if we do 180+45=225 degrees... this puts us in the 3rd quadrant... to get back to quadrant 1 we just take the opposite of our r

so another point is (-5sqrt(2) , 225 degrees)

Answer: both are 21/29

Step-by-step explanation:

Use SOHCAHTOA so the opposite/hypotenuse for P is 21/29 and the adjacent/hypotenuse for Q is also 21/29

Answer:

| x - 0 | ≤ 2

Step-by-step explanation:

Given,

The ideal temperature of the freezer = 0° F,

Also, it can fluctuate by 2° F,

Thus, if x represents the temperature of the freezer,

Then, there can be two cases,

Case 1 : x > 0,

⇒ x - 0 ≤ 2

Case 2 : If x < 0,

⇒ 0 - x ≤ 2,

⇒ -( x - 0 ) ≤ 2,

By combining the inequalities,

We get,

| x - 0 | ≤ 2,

Which is the required inequality.

Answer: [tex]7m^5-3m^3-3[/tex]

Step-by-step explanation:

You can observe that you need to subtract the polynomial [tex](6m^5 + 3 - m^3 -4m)[/tex] and the polynomial [tex](-m^5 + 2m^3- 4m + 6)[/tex].

It is important the remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]

Then, the first step is to distribute the negative sign:

[tex](6m^5 + 3 - m^3 -4m)-(-m^5 + 2m^3- 4m + 6)=\\=6m^5 + 3 - m^3 -4m+m^5-2m^3+ 4m- 6[/tex]

And finally you must add the like terms. Then:

[tex]=7m^5-3m^3-3[/tex]

Answer:

  183.7 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation between the hypotenuse and opposite side in a right triangle is ...

  Sin = Opposite/Hypotenuse

For the first observation, the angle is 45° and the length of the hypotenuse of the triangle is given as x. For the second observation, the opposite side (building height) is the same, the angle is 60°, and the hypotenuse is 150 ft.

We can multiply the above equation by "Hypotenuse" to get an expression for "Opposite".

  Opposite = Sin×Hypotenuse

For our two observations, this becomes ...

  sin(45°)·x = (building height) = sin(60°)·(150 ft)

Dividing by the coefficient of x, we have ...

  x = (150 ft)·sin(60°)/sin(45°) ≈ 183.7 ft

Answer:

B: 183.7

Step-by-step explanation:

First we need to find our values

A = 45°

B = 180 - 60 = 120

a = 150

Then we can solve for x using this formula x = a * sin(B)/sin(A).

x = 150 * sin(120)/sin(45)

x = 150 * √6/2

x = 75√6

x = 183.71173

Answer: C (600 - 28w < 300)

I know this because: I took the E2020 test

Answer:

Answer: C (600 - 28w < 300)

Step-by-step explanation:

So the series looks something like this:

[tex]\Sigma_{n=4}^{\infty}\frac{n-1}{16} \\

\frac{1}{16}\Sigma_{n=4}^{\infty}n-1[/tex]

If [tex]\lim_{n\rightarrow\infty}\neq[/tex] than [tex]\Sigma{a_n}[/tex] diverges. So we must apply limit infinity property:

[tex]\lim_{n\rightarrow\infty}(ax^n+\dots+bx+c)=\infty, a>0[/tex] and n is odd.

So...

[tex]\lim_{n\rightarrow\infty}n-1=\infty[/tex]

The series diverges.

Hope this helps.

r3t40

Answer:

  -8, 0

Step-by-step explanation:

The floor and ceiling functions have equal values for any integer argument. Their value is that integer.

Among your answer choices, the integers are -8 and 0.

Answer:

-8 and 0 or A and D

Step-by-step explanation:

Just took it on Edge 2020

Answer:

x =23/14

If we want to change it to a mixed number

x = 1 9/14

Step-by-step explanation:

42x – 5 = 64

Add 5 to each side

42x – 5+5 = 64+5

42x = 69

Divide each side by 42

42x/42 = 69/42

x = 69/42

Divide the top and bottom by 3

x =23/14

If we want to change it to a mixed number

x = 1 9/14

Answer:

d)4

Step-by-step explanation:

Answer:

A glide reflection is a composition of transformations.In a glide reflection, a translation is first performed on the figure, then it is reflected over a line. Therefore, the only required information is the translation rule and a line to reflect over. ... The first one is a translation rule.

Final answer:

In a glide reflection, the translation occurs first, moving the figure along a straight line, followed by a reflection over a line parallel to the translation vector, resulting in a figure that has been moved and potentially reoriented.

Explanation:

In a glide reflection, a transformation that combines a translation with a reflection, the proper sequence is important. The translation part comes first, where the figure is slid along a straight line called the translation vector. After the figure has been moved, the second step is the reflection over a line parallel to the vector of the translation. This two-step process results in a final image that has the same size and shape as the original figure but is in a different position and may have a different orientation.

Imagine a point undergoing a glide reflection. Initially, it is translated along a vector, and then it is reflected across a line that is parallel to the direction of translation. The end result is that the point has 'glided' to a new location, as if it had slid across a mirror placed at an angle to its original path.

The z-score for a student who scored 75 on the test with an average of 80 and a standard deviation of 6 is approximately -0.833, indicating the score is 0.833 standard deviations below the mean.

To calculate the z-score for a student who scored 75 on a history test, we can use the z-score formula:

[tex]Z = \( \frac{X - \mu}{\sigma} \)[/tex]

Where:

X is the raw score (75 in this case)

[tex]\( \mu \)[/tex] is the mean score (80)

[tex]\( \sigma \)[/tex] is the standard deviation (6)

Inserting the values, we get:

[tex]Z = \( \frac{75 - 80}{6} \) = \( \frac{-5}{6} \) = -0.833\[/tex]

The z-score for a student who earned 75 on the test is approximately -0.833, rounded to the nearest thousandth. This z-score indicates that the student's score is about 0.833 standard deviations below the mean

Answer:

i believe the answer is 9/18

Final answer:

The angle 237° is located in the third quadrant since it is between 180° and 270°.Therefore, the correct answer to the question is:

D. III

Explanation:

The question asks in which quadrant the angle 237° is located. To determine the quadrant of an angle in standard position (angle measured from the positive x-axis), we use the following information:

Angles from 0° to 90° are in the first quadrant.

Angles from 90° to 180° are in the second quadrant.

Angles from 180° to 270° are in the third quadrant.

Angles from 270° to 360° are in the fourth quadrant.

Since 237° is between 180° and 270°, it is located in the third quadrant. Therefore, the correct answer to the question is:

D. III

Answer:

  see below

Step-by-step explanation:

A proportional relationship has a graph that always goes through the origin. This fact by itself eliminates all the wrong answers.

A slope of 2/3 means the rise is 2 for each horizontal run to the right of 3. The two given points are 2 vertical units and 3 horizontal units apart, demonstrating a slope of 2/3.

Answer:

b

Step-by-step explanation:

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)

d = [tex]\sqrt{(4+1)^2+(1-4)^2}[/tex]

  = [tex]\sqrt{5^2+(-3)^2}[/tex]

  = [tex]\sqrt{25+9}[/tex] = [tex]\sqrt{34}[/tex] → b

ANSWER

Point-slope form:

[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]

Slope-intercept form:

[tex]y= -\frac{3}{5} x + \frac{9}{5}[/tex]

EXPLANATION

The graphed line passes through

[tex](-2,3) \: \: and \: \: (3,0)[/tex]

The slope of this line is determined using

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

We substitute the points to get;

[tex]m = \frac{0 - 3}{3 - - 2} [/tex]

[tex]m = -\frac{3}{5} [/tex]

The point-slope formula is:

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

Substitute the first point and slope to get:

[tex]y - 3 = -\frac{3}{5} (x - - 2)[/tex]

[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]

To find the slope-intercept form, we expand to get:

[tex]y= -\frac{3}{5} x - \frac{6}{5} + 3[/tex]

[tex]y= -\frac{3}{5} x + \frac{9}{5} [/tex]

Answer:

Slope

[tex]m=-\frac{3}{5}[/tex]

point-slope form

[tex]y=-\frac{3}{5}(x-3)[/tex]

slope-intersection form

[tex]y=-\frac{3}{5}x+1.8[/tex]

Step-by-step explanation:

The equation of a line in the point-slope form has the following formula:

[tex]y-y_0 = m (x-x_0)[/tex]

Where m is the slope and [tex](x_0, y_0)[/tex] is a point belonging to the line.

The equation of a line in the slope-intersection form has the following formula:

[tex]y = mx + b[/tex]

Where b is the intersection of the line with the y axis.

To calculate the slope of the line knowing 2 points we use the following formula:

[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]

In this case:

[tex]x_0 =3\\y_0=0\\x_1=-2\\y_1=3[/tex]

So

[tex]m=\frac{3-0}{-2-3}[/tex]

[tex]m=-\frac{3}{5}[/tex]

So the equation of a line in the point-slope form

[tex]y-0 =-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}(x-3)[/tex]

The equation of a line in the slope-intersection form is:

[tex]y-0=-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}x+\frac{9}{5}[/tex]

[tex]y=-\frac{3}{5}x+1.8[/tex]

with [tex]b=1.8[/tex]

Answer:

sqrt(5)

Step-by-step explanation:

Honestly think this person means to find the magnitude of the vector.  You can use dot product here, the vector with itself... But that isn't the last step.

v dot v=4+1=5

and so |v|=sqrt(5)

Answer:

It doesn't. x = 22 271 201

Step-by-step explanation:

You are going to need a calculator no matter how you do it.

[tex]x =19 169 000 \times e^{0.15}[/tex]

(a) The direct method

[tex]x = 19 169 000\times 2.718 281 828^{0.15} = 19 169 000 \times 1.161 834 243 = 22 271 201[/tex]

(b) The indirect method

[tex]\ln \left (19 169 000\times 2.718 281 828^{0.15} \right ) = \ln(19 169 000) + 0.15 = 16.768 805 + 0.15 = 16.918 804\\\\e^{16.918 804} = 22 271 201[/tex]

Answer:

The missing coefficient of the x-term of the product (-x-5)2 is 10.

Step-by-step explanation:

Through whole square formula.

(-x-5)2 = (-x)^2 -2(-x)(5)+(5)^2

=x^2+10x+25

Therefore, the missing coefficient of the x-term of the product is 10

Answer:

10

Step-by-step explanation:

The given expression is

[tex](-x-5)^2[/tex]

We need to find the coefficient of x.

According to the property of algebra.

[tex](a-b)^2=a^2-2ab+b^2[/tex]

In the given expression a=-x and b=5.

Substitute a=-x and b=5 in the above formula.

[tex](-x-5)^2=(-x)^2-2(-x)(5)+(5)^2[/tex]

On further simplification we get

[tex](-x-5)^2=x^2+10x+25[/tex]

Coefficient of x is a multiplicative factor of x.

Therefore, the coefficient of x is 10.

ANSWER

The correct answer is C

EXPLANATION

We want to find the value of

[tex] - \frac{3}{8} \times \frac{8}{15} [/tex]

This is the same as:

[tex] - \frac{3}{8} \times \frac{8}{3 \times 5} [/tex]

We cancel out the common factors to get:

[tex]- \frac{1}{1} \times \frac{1}{1 \times 5} [/tex]

We simplify to get:

[tex] - \frac{1}{5} [/tex]

The correct answer is C

Answer:

276.75

Step-by-step explanation:

Deposit 1230. paying 2.25 % 10 yrs.

the interest is 276.75 and the amount is 1506.75

Answer:

The answer to the first question is $276.75     and the answer to the second question is $4882.50

Step-by-step explanation:

Johnny deposited $1230 in a savings account at 2.25 percent interest. How much interest will the account earn in 10 years?

To solve this, we simply use the simple interest formula;

Simple Interest = PRT / 100

where p is the principal, R is the rate and T is the time (in years)

In this question principal = $1230  rate = 2.25   and time = 10

We can now plug the variables into the formula;

Simple Interest = PRT / 100

                           =$1230  × 2.25× 10    /     100

                             = $27675  / 100

                              = $276.75

Therefore, the amount of interest earn in 10 years is  $276.75

Will got an insurance check of $4500 after a car accident. He deposited it into a savings  account at 1.7 percent interest for five years. What was the total amount of money in the  account after five years?

We can also solve this second part of the question using the simple interest formula, here;

principal = $4500

Rate =1.7

Time =5

We will now insert our values into the simple interest formula, thus;

Simple Interest = PRT / 100

                          =$4500 × 1.7 × 5   / 100

                          =$38250 / 100

                          =$382.50

Simple interest =$382.50

Total amount = $4500 + $382.50

                      =$4882.50

Therefore, the total amount in the account after five years is $4882.50

Answer:

B

Step-by-step explanation:

We will use substitution method after writing 2 equations to solve for number of glass items.

Let number of glass items be g and number of plastic items be p

"The number of plastic items is 30 less than nine times the number of glass items":

We can write the equation as  [tex]p=9g-30[/tex]

"The recyclables are 85% plastic":

This means that plastic (p) is 0.85 of  the total (p+g). Thus we can write equation as  [tex]p=0.85(p+g)[/tex]

We can substitute the expression for p in first equation into 2nd and solve for g:

[tex]p=0.85(p+g)\\(9g-30)=0.85((9g-30)+g)\\9g-30=0.85(10g-30)\\9g-30=8.5g-25.5\\0.5g=-25.5+30\\0.5g=4.5\\g=\frac{4.5}{0.5}\\g=9[/tex]

The number of glass items is 9

Answer:

b. 9

Step-by-step explanation:

x : glass items

9x - 30 : plastic items

(the equation will be set equal to [tex]\frac{15}{85}[/tex] because 85% of the recyclables are plastic, so that means 15% must be glass.)

[tex]\frac{x}{9x-30} =\frac{15}{85}[/tex]

[tex]85x=135x-450[/tex]  (now subtract 135x from each side to isolate x to one side of the equation)

[tex]-50x=-450[/tex] (divide each side of the equation by -50 to isolate x)

[tex]x=9[/tex]