Choose the equation that represents the line that passes through the point (6, -3) and has a slope of
1/2
y=-x+6
y=2x-6
y=2x+3

Answer:

a. {(1,3), (1,4) ,(2,3), (2,4) }

b. {(1,4), (1,5), (2,4), (2,5)}

Answer:

PxR={(1,4)(1,5)(2,4)(2,5)}

PxQ={(1,3)(1,4)(2,3)(2,4)}

Step-by-step explanation:

Each of the members of set P is multiplying by each member of set Q or R,

so, 1 in set P has to multiply by 3 and 4 in set Q or 4 and 5 in set R. (We do the same for 2)

When a member of a set multiplies with another, we put the two members of two sets we are multiplying in parentheses.

Answer: x=3

Step-by-step explanation:

First we're going to get rid of the fraction by multiplying both sides by the square root of x-2

Now square both sides

[tex](\sqrt{3x })^2=3^2(\sqrt{x-2 })^2\\3x=9(x-2)[/tex]

Next use the distributive property

[tex]3x=(9)(x)-(9)(2)\\3x=9x-18[/tex]

Now subtract 9x from both sides

[tex]3x-9x=9x-18-9x\\-6x=-18[/tex]

Finally divide -6 on both sides

[tex]\frac{-6x}{-6} =\frac{-18}{-6} \\x=3[/tex]

Answer:

[tex]\displaystyle -x^3+10x^2-48x+64[/tex]

Step-by-step explanation:

We want to find the minimum-degree polynomial with real coefficients and zeros at:

[tex]x= 4+4i\text{ and } x = 2[/tex]

As well as a y-intercept of 64.

By the Complex Root Theorem, if a + bi is a root, then a - bi is also a root.

So, a third root will be 4 - 4i.

The factored form of a polynomial is given by:

[tex]P(x)=a(x-p)(x-q)...[/tex]

Where a is the leading coefficient and p and q are the zeros. More factors can be added if necessary.

Substitute:

[tex]P(x)=a(x-(2))(x-(4+4i))(x-(4-4i))[/tex]

Since we want the minimum degree, we won't need to add any exponents.

Expand the second and third factors:

[tex]\displaystyle \begin{aligned} (x-(4+4i))(x-(4-4i))&=(x-4-4i)(x-4+4i) \\ &= x(x-4-4i)-4(x-4-4i)+4i(x-4-4i)\\ &=x^2-4x-4ix-4x+16+16i+4ix-16i-16i^2\\ &= x^2-8x+32\end{aligned}[/tex]

Hence:

[tex]P(x)=a(x-2)(x^2-8x+32)[/tex]

Lastly, we need to determine a. Since the y-intercept is y = 64, this means that when x = 0, y = 64. Thus:

[tex]64=a(0-2)(0^2-8(0)+32)[/tex]

Solve for a:

[tex]-64a=64\Rightarrow a=-1[/tex]

Our factored polynomial is:

[tex]P(x)=-(x-2)(x^2-8x+32)[/tex]

Finally, expand:

[tex]\displaystyle \begin{aligned} P(x) &=-(x^2(x-2)-8x(x-2)+32(x-2)) \\&=-(x^3-2x^2-8x^2+16x+32x-64)\\&=-(x^3-10x^2+48x-64)\\&= -x^3+10x^2-48x+64\end{aligned}[/tex]

Answer:

The answer is 0.5

Answer:

rhe answer is r= .50

Step-by-step explanation:

125-75=50

Answer:

Hence when the radius is halved the area is divided by 4

2.5 inches^2

Step-by-step explanation:

Given data

Area= 10inches^2

We know that the expression for the area of  a circle is given as

Area= πr^2

10= 3.142*r^2

10/3.142= r^2

r^2= 3.18

Square both sides

r= √3.18

r= 1.78 inches

Now let us half the radius and find the area of the new circle

r/2= 1.78/2

r= 0.89

Area of the new circle is

Area= 3.142*0.89^2

Area= 3.142*0.7921

Area= 2.5 inches^2

Answer:

Step-by-step explanation:

7x + 2x =90 (being perpendicular)

9x =90

x =90/9

x =10

substiute the value of x

7x

=7*10

=70

2x

=2*10

=20

Answer:

x = 10

Step-by-step explanation:

See image. Due to the logic of vertically opposite angles (when one angle is equal to the other that is "vertically opposite" to it), the two angles that I have marked in the diagram are going to equal.

Therefore, if we were to write it out:

2x + 7x = 90

(vertically opposite angles)

       9x = 90

     ∴  x = 10

Answer:

angle B is 45 degree.

Step-by-step explanation:

since both radius are equal in a circle the triangle formed is ann isosceles triangle.

base angle of an isosceles triangle are equal

angle B be x

angle A = angle B (being base angles of a triangle)

then angle A is also x

angle A + angle B + angle C =180 degree (sum of interior angles of a triangle)

x + x + 90=180

2x =180-90

x=90/2

x=45 degree

Answer:

Yes, this graph represents a function

Step-by-step explanation:

The function passes the vertical line test, which tests for if any input has more than one unique output by moving a vertical line from left to right. If the vertical line doesn't pass 2 or more points at a time, then the function is indeed a function.

Answer:

The graph does represent a function

Step-by-step explanation:

The function is at about 30y = x^3

Answer:

The amount of interest he paid at the end of the loan is $ 311.85.

Step-by-step explanation:

Given that Juan borrowed $ 1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%, to determine what is the amount of interest he paid at the end of the loan, the following calculation must be performed:

(1500 x 0.0297) x 7 = X

44.55 x 7 = X

311.85 = X

Therefore, the amount of interest he paid at the end of the loan is $ 311.85.

Answer:

16 3/2

Step-by-step explanation:

So lets go thru each one.

16 3/2 is just 17.5

A square root cancels out a square.

A cubed root cancels out a cube.

So, in the next answer:

16 squared, to the square root is just 16, since the squaring and root cancels out.

64 sqaured to the cube root must be 16. Lets break it all down:

2^6=64.  We need to square this, so we can rewrite it as:

64^2 = [tex](2^6)^2[/tex]

Normally we add/subtract exponents, but since the 6 exponent is in parethesese, it is multiplied by the 2 exponent. This makes it 2^12. So we can rewrite [tex]\sqrt[3]{64^2}[/tex] as:

[tex]\sqrt[3]{2^1^2}[/tex]

Now, when we divide a exponent by a exponent, we subtract.

However, when we root a exponent, it is division.

So it is the 2 [tex]\frac{^1^2}{^3}[/tex]

=

[tex]2^4[/tex]

Or

16

Finally we have the cubed root of 8^4.

using the same steps as above, 8^4 = [tex](2^3)^4[/tex]. This equals [tex]2^1^2[/tex]

Then again, we cube root it.

This is division of the 12 exponent by the 3 root, so we get:

[tex]2^4[/tex]

=

16

So in the end:

A - 17.5

B - 16

C - 16

D - 16

So a is the largest number

Hope this helps!

Answer:

She is born with it. So be nice to here and don't talk about here lisp. If you do you would become here favorit. Don't talk bad about here behind here back.

Step-by-step explanation:

Lisp is a family of programming languages with a long history and a distinctive, fully parenthesized prefix notation. Originally specified in 1958, Lisp is the second-oldest high-level programming language in widespread use today. Only Fortran is older, by one year.

Answer:

The answer is C

Step-by-step explanation:

3    :    4

^          ^

II          II

red    blue

Answer:

(a) The mean is 0

(b) The median is -30

(c) The mode is unimodal

Step-by-step explanation:

Given

[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]

Solving (a): The mean.

This is calculated using:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]

[tex]\bar x =\frac{0}{8}[/tex]

[tex]\bar x =0[/tex]

Solving (b): The median

First, arrange the data

[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]

There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.

[tex]Median = \frac{-4-2}{2}[/tex]

[tex]Median = \frac{-6}{2}[/tex]

[tex]Median = -3[/tex]

Solving (c): The mode

The item that has occurs most is -10.

Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).

Answer:

55

Step-by-step explanation:

It is 55 minutes more because 1 1/2 hrs = 90 minutes and when you add 20 plus quarter of an hour it equal to 35. SO than you subtract 35 from 90 and you get 55 which is the more minutes .

Answer:

40.2667

Step-by-step explanation:

P(X=36)= 36/120

P(X=40)= 40/120

P(X=44)=44/120

E(X) = 36(36/120)+40(40/120)+44(44/120)=1208/30=40.2667

hope this helps

If a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A school class of 120 students is driven in 3 buses to a symphonic performance.

There are 36 students on one of the buses, 40 on another, and 44 on the third bus.

From the data given:

Let X be the total number of passengers on the bus carrying that randomly selected student,

Total number of students = 120

Let:

Probability:

P(X = 36) = 36/120

Probability:

P(X = 40)= 40/120

Probability:

P(X = 44)=44/120

E(X) = 36(36/120) + 40(40/120) + 44(44/120)

E(X) = 1208/30

E(X) = 40.26

Therefore, if a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.

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Answer:

3 miles

Step-by-step explanation:

5-1+2=3

From the calculation done using the pythagoras theorem, the distance from Sarah's apartment is 12m

This theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Using the pythagoras theorem

BC² = AB² + AC²

The sides of the triangle are x, x - 1 and 5

x² = (x-1)² + 5²

x² = (x-1)(x-1) +25

x² = x²-x-x -1 + 25

collect like terms

2x = 24

divide through the equation by 2

x = 24/2

= 12m

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Answer:

See image below for answer:)

Step-by-step explanation:

The inequality b < - 1.4 written as interval notation is b ∈ (- ∞, - 1.4).

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality b < - 1.4.

We know in interval notation if x is greater than a and less than b we write

a < x < b.

Therefore, The inequality b < - 1.4 can be written as,

- ∞ < b < - 1.4 Or b ∈ (- ∞, - 1.4).

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Answer:

20x² + 40y²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4x(2x + 3x) + 5y(5y + 3y)

Step 2: Simplify

Answer:

20 x ² + 40 y ²

Step-by-step explanation:

4 x ( 2 x + 3 x ) + 5 y ( 5 y + 3 y )

Combine likes term

4 x ( 5 x ) + 5 y ( 8 y )

multiply, we get

20 x ² + 40 y ²

Answer:

The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

Step-by-step explanation:

9514 1404 393

Answer:

  the correct choice is marked: x = 11; Q = 55°

Step-by-step explanation:

If P and Q are supplementary, then ...

  Q = 180° -P

  Q = 180° -125°

  Q = 55°

Then we have ...

  5x = 55°

  x = 11°

Answer:

P = 7.7 C + 1.1 XC

Step-by-step explanation:

From the question, it is noted that the price of helium required to fill each of the balloons would increase by 10%. Let the current price of helium be C, so that;

10% of C = 0.1 C

The price of helium next year = C + 0.1 C

                        = 1.1 C

Cost of 7 small balloons = 1.1 C * 7

                         = 7.7 C

Cost of X large balloons = 1.1 C * X

                         = 1.1 XC

The total price, P for helium next year = 7.7 C + 1.1 XC

Thus, the equation to find the total price of helium that would fill the balloons next year is;

P = 7.7 C + 1.1 XC

Answer:

AB ≈ 11.17 m

Step-by-step explanation:

The arc AB is calculated as

AB = circumference of circle × fraction of circle

    = 2πr × [tex]\frac{80}{360}[/tex]

    = 2π × 8 × [tex]\frac{8}{36}[/tex]

    = 16π × [tex]\frac{2}{9}[/tex]

    = [tex]\frac{32\pi }{9}[/tex] ≈ 11.17 m ( to the nearest hundredth )

Answer:

A. Acute

B. 80 degrees

Step-by-step explanation:

Answer:

165°

Step-by-step explanation:

Find the interior angle measure by using the formula, ((n - 2) x 180°) / n

Plug in 24 as n:

((n - 2) x 180°) / n

((24 - 2) x 180°) / 24

(22 x 180°) / 24

3960 / 24

= 165

So, the measure of each angle is 165°

Answer:

163.6

Step-by-step explanation:

180•(22-2)=180•20 =3600

3600/22= 163.636363…

Answer:

The distance between A(-8, 4) and B(4, -1) is 13 units.

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula given by:

[tex]\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

We have the two points A(-8, 4) and B(4, -1). Let A(-8, 4) be (x₁, y₁) and let B(4, -1) be (x₂, y₂). Substitute:

[tex]d=\sqrt{(4-(-8))^2+(-1-4)^2}[/tex]

Evaluate:

[tex]d=\sqrt{(12)^2+(-5)^2}[/tex]

So:

[tex]d=\sqrt{144+25}=\sqrt{169}=13\text{ units}[/tex]

The distance between A(-8, 4) and B(4, -1) is 13 units.

___________________________________

[tex]\quad\quad\quad\quad\tt{A.) x\tiny{1}\small{=-8}, y\tiny{1}\small{=4}}[/tex]

[tex]\quad\quad\quad\quad\tt{B.) x\tiny{2}\small{=4}, y\tiny{2}\small{=-1}}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{(x \tiny{2} \small{ - x \tiny{1} \small {)}^{2} + (y \tiny{2} \small{ - y \tiny{1} \small{)}^{2} } }}} [/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{(4 - \small{ (- 8}{))}^{2} + ( \small{- 1)}\small{ - {4)}}^{2} }}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{ ( {12)}^{2} + {( -5)}^{2} }}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{ {144} + {25}}}[/tex]

[tex]\quad\quad\quad\quad\tt{d = \sqrt{ 169}}[/tex]

[tex]\quad\quad\quad\quad\tt{d = 13}[/tex]

[tex]\quad\quad\quad\quad\boxed{\boxed{\tt{\color{magenta}d = 13}}}[/tex]

___________________________________

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✍︎ C.Rose❀

Answer:

158

Step-by-step explanation:

The cost of the minimum spanning tree to connect all four landmarks will be $158.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The cost to make a path connecting all four landmarks is based on the proposal shown.

The cost of path A is $29.

The cost of path B is $59.

The cost of path C is $32.

The cost of path D is $38.

Then the cost of the minimum spanning tree to connect all four landmarks will be

Total cost = cost of path A + cost of path B + cost of path C + cost of path D

Total cost = $29 + $59 + $32 + $38

Simplify the expression, then we have

Total cost = $29 + $59 + $32 + $38

Total cost = $158

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Answer:

This identity holds as long as [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].

For the proof, make use of the fact that:

[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] (definition of tangents,) and

[tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] (Pythagorean identity,) which is equivalent to [tex]1 - \cos^{2}(\theta) = \sin^{2}(\theta)[/tex].

Step-by-step explanation:

Assume that [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex]. This requirement ensures that the [tex]\tan(\theta)[/tex] on the left-hand side takes a finite value. Doing so also ensures that the denominator [tex]\sqrt{1 - \sin^2(\theta)}[/tex] on the right-hand side is non-zero.

Make use of the fact that [tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] to rewrite the left-hand side:

[tex]\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}[/tex].

Apply the Pythagorean identity [tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex] and [tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] to rewrite this fraction:

[tex]\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}[/tex].

Hence, [tex]\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}[/tex].

Answer:

1,736 chocolate cover peanuts

Step-by-step explanation:

do 28×62 hope this helps

Answer:

1736 chocolate-covered peanuts

Step-by-step explanation:

[tex]\frac{1}{62} :\frac{28}{y}[/tex]

1 · y = 62 · 28

y = 1736