Which term refers to a pictorial representation of given set of data involving two variables?
A- graph
B- decimal
C- formula
D- axis

Answer:

Axis of symmetry is [tex]x=1.5[/tex].

Step-by-step explanation:

Given equation is [tex]y=2x^2-6x+2[/tex].

Now we need to find about what is the axis of symmetry of the given function.

So compare it with [tex]y=ax^2+bx+c[/tex], we get:

a=2, b=-6, c=2

Axis of symmetry is given by the formula

[tex]x=-\frac{b}{2a}[/tex]

[tex]x=-\frac{-6}{2(2)}[/tex]

[tex]x=\frac{3}{2}[/tex]

[tex]x=1.5[/tex]

Hence final answer is given by:

Axis of symmetry is [tex]x=1.5[/tex].

Answer:

C

Step-by-step explanation:

The angle 160° and the interior angle of the triangle form a straight angle

interior angle = 180° - 160° = 20°

Similarly with angle 131° and the interior angle at the top of the triangle

interior angle = 180° - 131° = 49°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

n is an exterior angle, hence

n = 20° + 49° = 69° → C

Your answer is 8

Hope I helped

Answer:

32

Step-by-step explanation:

The answer is:

The second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.

Since we are given two forces acting at distance, torque will be created. We are given two forces and one distance, so, to calculate the other distance required to balance the system (solve this fulcrum problem), we need to write the following equation:

[tex]Torque_{1}=Torque_{2}[/tex]

Where,

[tex]Torque=F*Distance[/tex]

We are given,

[tex]Force_{1}=Weight_{1}=150lb\\Force_{2}=Weight_{2}=30lb\\distance_{1}=15ft\\[/tex]

So, substituting and calculating, we have:

[tex]Torque_{1}=Torque_{2}[/tex]

[tex]Weight_{1}*distance_{1}=Weight_{2}*distance_{2}[/tex]

[tex]150lb*15ft=300lb*distance_{2}[/tex]

[tex]distance_{2}=\frac{150lb*15ft}{300lb}=7.5ft[/tex]

Hence, the second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.

It's a logical solution since the second force is twice the first force and it means that the second distance must be equal to half the first distance in order to maintain the equilibrium condition.

Have a nice day!

Answer:

Option A

Step-by-step explanation:

Easy-Peasy!

The function is f(x) = z^2 + c, where c=1-3i and z0 = i.

So what you have to do, is to substitute the given values of Z and C into the function:

f(x) = z^2 + c

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

f(x) =  -1 + 1 - 3i = -3i.

Then the first value is z1 = -3i.

Then we substitute new value z1 = -3i into the fuction:

f2(x) = (-3i)^2 + 1 - 3i

f2(x) = -9 + 1 - 3i = -8 - 3i

Then the second value is: z2 = -8 - 3i

Again, we substitute the value z2 = -8 - 3i into the function:

f3(x) = (-8 - 3i)^2 + 1 -3i

f3(x) = 64 + 48i -9 + 1 - 3i = 56 + 45i

Z3 = 56+45i

So, the correct option is: Option A.

Answer:

B)3

Step-by-step explanation:

to find "x" intercept substitute 0 for y and solve

4x+3(0)=12

4x+0=12

divide by "4" on both sides:

4x/4=12/4

x=3

hope this helps!

Answer: B

Step-by-step explanation: I put it in a website and the answer is b

(n-2)*180 divided by n

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5, hence

sum of interior angles = 180° × 3 = 540°

14$ because you subtract 8 - 36 = 28 then divide 28 by 2 and get 14

36 - 8 = 28 divided by 2 equals 14

Answer:

9/2

Step-by-step explanation:

4* 3/8+6*1/8 divided by 1/4

first dividing a fraction is the same as mutiplying by the recirpocal so you can take 1/4 as times it by 4/1 which equals 4

leaving you with 4* 3/8+6*1/8*4

then you can reduze 4* 3/8 by finign the greatest common factor which is four

so you get 3/2+6*1/8*4

reduce 1/8 * 4 into 1/2

so you get 3/2+6*1/2

then rudce 6* 1/2 and get 3

then add whats left which is 3/2+3

you get 9/2

Answer:

4.575% APEX

Step-by-step explanation:

The new rate would be 3.75% when Peter's bank offered him a 4.95% interest rate for his mortgage. If he purchases 3 points.

A mortgage exists as an arrangement between you and a lender that provides the lender the right to consider your property if you forget to repay the money you've borrowed plus interest.

Mortgage loans exists utilized to buy a home or to borrow money against the significance of a home you already possess.

Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of a 1% interest reduction.

A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)

New interest rate = 4.5% - 0.75% = 3.75%

Therefore, the correct answer is option C. 4.575

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Answer:

Step-by-step explanation:

-12n - 20

-12n = (-2)(6n)

-20 = (-2)(10)

-12n - 20 = (-2)(6n+10)

Answer:

1L

Explanation:

Millimeter is a metric measurement for distance/length, while Liter is a metric measurement for volume/capacity.

Hope this helps! :)

Answer:

Step-by-step explanation:

The answer is acd

Answer: A, C, D,

A: 6 (x+7) -2

C: 4f - 2g

D: 3 xyz=-10

Step-by-step explanation:

A difference is the result of a sustraction problem.

In the expression 6( x-7 ) -2, the expressions 6( x-7 ) and 2 are being substracted.

In the expression 4f - 2g. The expresions of 4f and 2g are being substracted.

in the expression 3xyz-10, the expressions 3xyz and 10 are being subtracted.

The following expressions represent the difference of exactly 2 expressions:

6 (x+7) -2

4f - 2g

3 xyz=-10

Answer:

A

Step-by-step explanation:

An excluded value is any value of x that makes the denominator of the rational expression zero as this would make the expression undefined.

For expression A

[tex]\frac{x-3}{x^2-4}[/tex]

The denominator will be zero when x² - 4 = 0

x² - 4 is a difference of squares, thus

(x - 2)(x + 2) = 0

x - 2 = 0 ⇒ x = 2

x + 2 = 0 ⇒ x = - 2

The excluded values of x are x = ± 2 ⇒ A

Option A) is the answer

Answer:

[tex]\large\boxed{S.A.=4500\pi\ in^2\approx14130\ in^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a ball (sphere):

[tex]S.A.=\dfrac{4}{3}\pi R^3[/tex]

R - radius

We have R = 15in. Substitute:

[tex]S.A.=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3375)=4500\pi\ in^2[/tex]

If you want to get an approximation, then:

[tex]\pi\approx3.14\\\\S.A.\approx(4500)(3.14)=14130\ in^2[/tex]

Answer:

SA=(4⋅3.14⋅225) square inches

Step-by-step explanation:

TTM

Final answer:

The volume of a rectangular pyramid with a base of 13 inches by 12 inches and a height of 8 inches is 416 inches³, calculated using the formula V = (1/3) × base area × height.

Explanation:

To calculate the volume of a rectangular pyramid, the formula is V = (1/3) × base area × height. The base area is the length times the width of the pyramid's base, while the height is the perpendicular distance from the base to the apex. Given the dimensions of the pyramid as a base of 13 inches by 12 inches and a height of 8 inches:

Final answer:

The volume of the rectangular pyramid with a base of 13 inches by 12 inches and a height of 8 inches is 416 cubic inches, calculated using the formula V = ¼Bh.

Explanation:

To find the volume of a rectangular pyramid, you can use the formula for the volume of any pyramid, which is ¼ the base area multiplied by the height (V = ¼Bh). In this case, the base area (B) can be calculated by multiplying the length and width of the base of the pyramid. Therefore, the base area B is 13 inches * 12 inches, which equals 156 square inches. The height (h) of the pyramid is given as 8 inches.

Using the volume formula:

Base area (B) = 13 in * 12 in = 156 in²

Height (h) = 8 in

Volume (V) = ¼ * B * h = ¼ * 156 in² * 8 in

Calculation:

V = ¼ * 156 in² * 8 in

V = 1,248 in³ ´  3

V = 416 in³

Therefore, the volume of the pyramid is 416 cubic inches.

Answer:

1,206

Step-by-step explanation:

Since we'll have to deal with cubic inches (with the ball volume), we should also calculate the volume of the car in cubic inches.

We are told the car is a rectangular prism measuring 10ft x 5 ft x 3 ft.

So, in inches (12 inches/foot), we have: 120 in x 60 in x 36 in = 259,200 cu inches.

The ball is a sphere with a radius of 3 inches.

Real volume of the ball: V = (4/3) π r³

V = (4/3) π 3³ = 36 π = 113.1 cu inches

But of course, balls don't fit perfectly one next to another, like cubes, so we have to take into account the loss... the question tells us to use a factor of 190%.

So, the packing volume of a ball is 190% its real volume:

PV = 190% * 113.1 = 214.9 cu inches

Now, how many times does that fit inside the car?

259,200 / 214.9 = 1,206.14

Let's round it to 1,206, which is a possible answer.

Answer:

The triangles abc and dbe show that the consistent cost of the pens is 2 dollars for each individual pen

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The cube root is the number which multiplied by itself 3 times results in 125

Note that 5 × 5 × 5 = 25 × 5 = 125

Thus the cube root of 125 is 5

To find another angle in an acute triangle with one angle measuring 38 degrees, any value less than 90 degrees is possible for the second angle, provided that the third angle remains acute as well.

One angle measure in an acute triangle is 38°, and to determine the measure of one of the other angles, we must consider the geometric principle stating that the sum of angles in a triangle is 180°. Since we have one angle measuring 38°, the sum of the remaining two angles must be 180° - 38° = 142°. Given that an acute triangle has all angles measuring less than 90°, one of the other angles could be any value less than 90° but also must leave enough degrees so that the third angle is also acute (less than 90°). For example, if the second angle were 52°, the third angle would be 142° - 52° = 90°, which is the highest possible value without losing the acute property of the triangle.

Answer:

a=2

h=8

k=-72

Step-by-step explanation:

[tex]y = 2 {x}^{2} - 32x + 56 \\ = 2( {x}^{2} - 16x + 28) \\ = 2( {x}^{2} - 2 \times 8 x + 64 - 36) \\ = 2 {(x - 8)}^{2} - 72 \\ then \: the \: minimum \: is \: - 72 \: and \\ \: the \: x - coordinate \: of \: minimum \: is \: 8.[/tex]

The rewritten equation is 2(x-8)^2 - 100, and the x-coordinate of the minimum is 8.

A quadratic equation is a second-degree algebraic equation in x. The conventional form of the quadratic equation is ax^2 + bx + c = 0, with a and b as coefficients, x as the variable, and c as the constant component.

y = 2x^2 - 32x + 56

y = 2(x^2 - 16x + 28)

y = 2((x^2 - 16x + 64) - 36)

y = 2((x - 8)^2 - 36)

y = 2(x - 8)^2 - 72

The equation when converted in the form  y = a(x - h)^2 + k will look like  y = 2(x - 8)^2 - 72.

The minimum value of this function is y = -72 and the x-coordinate of the minimum is x = 8.

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Answer:

2 points

Step-by-step explanation:

A quadratic equation is in the form of ax²+bx+c. The points at which the graph of the function y = 4x² - 6x + 1 intersects the x-axis is 0.191 and 1.309.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The points at which the graph of the function y = 4x² - 6x + 1 intersects the x-axis can be found by substituting the value of y as 0 in the equation and then solving the equation.

0 = 4x² - 6x + 1

Since the equation is in the quadratic form, the roots of the equation are,

[tex]x = \dfrac{-(-6)\pm\sqrt{(-6)^2-4(4)(1)}}{2(4)}\\\\x = \dfrac{6\pm\sqrt{36-16}}{8}\\\\x = \dfrac{6\pm\sqrt{20}}{8}\\\\x = \dfrac{6\pm2\sqrt{5}}{8}[/tex]

x = 0.191, 1.309

Hence, The points at which the graph of the function y = 4x² - 6x + 1 intersects the x-axis is 0.191 and 1.309.

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Final answer:

The value of 12 + 6/n when N=2 is 15.

Explanation:

The value of 12+6/n when N=2 is found by substituting N=2 into the expression:

12 + 6/2 = 12 + 3 = 15

Therefore, the value of 12 + 6/n when N=2 is 15.

Answer:

what are the answer options?

Step-by-step explanation:

ANSWER

[tex] 10C_5(2)^{5}( - 3)^5[/tex]

EXPLANATION

The given binomial expression is

[tex](2x-3y)^{10} [/tex]

The nth term in this expansion is calculated using the formula,

[tex]T_{r+1} = nC_ra^{n-r}b^r[/tex]

To find the term with coefficient

[tex] {x}^{5} {y}^{5} [/tex]

we substitute r=5, n=10, a=2x, and b=-3y

[tex]T_{6} = 10C_5(2x)^{10-5}( - 3y)^5[/tex]

[tex]T_{6} = 10C_5(2x)^{5}( - 3y)^5[/tex]

[tex]T_{6} = 10C_5(2)^{5}( - 3)^5 {x}^{5} {y}^{5} [/tex]

The coefficient is

[tex] 10C_5(2)^{5}( - 3)^5[/tex]

The second choice is correct.

Answer:

second one

Step-by-step explanation:

ANSWER

The value of x is 18.

EXPLANATION

The given expression is

[tex]2x + 3y = 36[/tex]

when y=6, we substitute y=6 into the expression to get:

[tex]2x + 3(6) = 36[/tex]

This gives us:

[tex]2x + 18= 36[/tex]

We group similar terms to obtain:

[tex]2x = 36 - 18[/tex]

We simplify the RHS to get

[tex]2x =18[/tex]

We divide both sides with 2 to get,

[tex]x = \frac{18}{2} [/tex]

x=9

Answer:

The value of x = 9

Step-by-step explanation:

It is given an expression in variables x and y

2x + 3y = 36

To find the value of x

Let 2x + 3y = 36

When y = 6, the expression becomes

2x + (3 * 6) = 36

2x + 18 = 36

2x = 36 - 18  = 18

2x = 18

x = 18/2 = 9

x = 9

Therefore the value of x = 9

The domain is all real numbers and the range is all the reals at or above the vertex y coordinate (if the coefficient on the squared term is positive) or all the reals at or below the vertex (if said coefficient is negative).

Answer:

The domain is all real numbers, and the range is nonnegative real numbers (y > 0)
-

Step-by-step explanation:

tha pex

Final answer:

A 52% chance indicates that it is more likely than not for a player to win a carnival game, expecting roughly 52 wins out of 100 plays.

Explanation:

The likelihood that a player will win a certain carnival game, with a 52% chance, suggests that it is more likely than not that the player will win. This percentage can be interpreted as a probability of 0.52 (where 0 represents an impossible event and 1 represents a certainty). To describe this likelihood in terms of probability theory, if the game were played 100 times, we would expect the player to win approximately 52 times, although the actual outcome could vary due to randomness.

When comparing to other probabilities, such as a child winning one out of five times (20% chance) or the very low probability of winning the grand prize in another carnival game (0.005 or 0.5%), a 52% chance is relatively high, indicating that winning the game is a probable outcome.

The statement that describes the likelihood that a player will win the game is the fourth option

The likelihood of the player winning can be described as follows;

The probability that a player will win the carnival = 52%

The chance of a player winning the carnival is approximately 50%, which indicates that it almost equally likely or unlikely that a player may win the game

The above statement indicates that out of two plays, the player will likely win one and out of 10 palys, the player will likely win five

Therefore, the statement that describes the likelihood of a player will the game is the fourth statement

It is neither likely or unlikely that the player will win the game

Answer:

0.68

Step-by-step explanation:

$17 out of $25 comes to 17/25, or 0.68.  This is the desired decimal equivalent.

She spent 17/25, and the decimal equivalent is .68

Answer:

1. c

Step-by-step explanation:

2. A

Answer:

C and A

Hope This Helps!    Have A Nice Day!!