A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
A. −3x + 5y = 13
B. −3x + y = −7
C. −3x + y = 17
D. −3x + 5y = −13
Which answer is an equation in point-slope form for the given point and slope?
Point: (1, 9); Slope: 5
A. y − 1 = 5 (x + 9)
B. y − 9 = 5 (x − 1)
C. y + 9 = 5 (x−1)
D. y − 9 = 5 (x+1)

[tex]e^y +19-e^2 = 3x^2 +4y^2\\\\\implies \dfrac{d}{dx}(e^y +19-e^2) = \dfrac{d}{dx}(3x^2 +4y^2)\\\\\implies e^y \dfrac{dy}{dx}+0 = 3\dfrac{d}{dx} x^2 +4\dfrac{d}{dx} y^2\\\\\implies e^y y' = 6x + 8y y'\\\\\implies e^y y' -8yy' = 6x\\\\\implies y'(e^y -8y) = 6x\\\\\implies y' = \dfrac{6x}{e^y -8y}\\\\\text{At point (-1,2)}\\\\y' = \dfrac{6(-1)}{e^2 -8(2)} = - \left(\dfrac{6}{e^2 -16}\right) =-0.25[/tex]

Answer:

9

Step-by-step explanation:

Each side is being multiplied by 1.5.

3 times 1.5 is 4.5.

7 times 1.5 is 10.5.

6 times 1.5 is 9.

Answer:

Step-by-step explanation:

(x + 2y²)(2x - 2y²)

FOIL

First

x(2x) = 2x²

Outside

x(-2y²) = - 2xy²

Inside

2y²(2x) = 4xy²

Last

2y²(-2y²) = - 4y⁴

combine like terms

2x² + 2xy² - 4y⁴

Answer:

-4y^4 + 2xy^2 + 2x^2

Step-by-step explanation:

(x + 2y^2) (2x - 2y^2)

x(2x) + x(-2y^2) = 2x^2 - 2xy^2

2y^2(2x) + 2y^2(2y^2) = 2xy^2 + 4y^4

2x^2 - 2xy^2 + 4xy^2 - 4y^4

2x^2 + 2xy^2 - 4y^2

or

-4y^4 + 2xy^2 + 2x^2

Answer:

14%

Step-by-step explanation:

Find the quotient of 29 and 200.

[tex]\frac{28}{200}=0.14[/tex]

Therefore, 28 is 14% of 200.

The number 28 is 14% of the number 200.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the number is 200 and 28 is what percent of 200 will be calculated as:-

The percentage will be calculated as:-

200 x (X)% = 28

X% = ( 28 x 100) / 200

X% = 14%

Therefore, the number 28 is 14% of the number 200.

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Answer:

Second and fourth

Step-by-step explanation:

A line is in point-slope form when you write down as [tex]y-y_0=m(x-x_0)[/tex] - do not be distracted by the signs, +1 and +5 can both be written as -(-1) or -(-5) rispectively.

11 miles far does the boat travel

Step-by-step explanation:

hope it helps

The total distance travelled will be 22 miles and the bearing will be 60.89° .

It is given that a boat travels from port town to north for 7.4 miles and then east for 3.6 miles and stops at destination.

We have to find out the total distance travelled and bearing from stopped position.

What are bearings ?

A bearing is the angle in degrees measured clockwise from north i.e., 30° from north.

As per the question ;

Boat travels from port town to north for 7.4 miles and then east for 3.6 miles and it then stops at destination.

So ;

a)

Total distance travelled from port town to destination is ;

= 7.4 miles + 3.6 miles

= 11 miles

And

If boat's captain turns back to town , then total distance will be ;

= 11 + 11

= 22 miles

b)

We know that ;

cos θ = B/H

The bearing would be ;

cos θ = [tex]\frac{3.6}{7.4}[/tex]

cos θ = 0.486

θ = [tex]cos^{-1}[/tex] (0.486)

θ = 60.89°

Thus , the total distance travelled will be 22 miles and the bearing will be 60.89° .

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Explanation:

Start by calculating the first derivative of f(x) - use the quotient rule

ddx(f(x))=[ddx(x2)]⋅(x2+3)−x2⋅ddx(x2+3)(x2+3)2

f′=2x⋅(x2+3)−x2⋅2x(x2+3)2

f′=2x3+6x−2x3(x2+3)2=6x(x2+3)2❤

Answer:

I believe that it would take 5 hours for 8 people to paint 8 fences.

Step-by-step explanation:

If 2 people are painting 2 fences in 5 hours, then 8 people can also paint 8 fences in the same time because each person is painting one fence. It take 5 hours to paint 1 fence if 1 person is painting it. The same goes for 2 or 8 people painting the same amount of fences as there are people. Im not 100% sure if this is accurate but I hope it helps.

1. Assuming OP || NM, considering the triangle proportionality theorem possible measurements for the segments are: ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units

2. The possible values are decided by assuming  [tex]\frac{ON}{LO} = \frac{PM}{LP} = 3[/tex] using the triangle proportionality theorem.

3. Another method is applying the AA Similarity Theorem to compare corresponding side lengths of the triangles that are proportional to each other.

Triangle proportionality theorem states that if a line is parallel to one of the sides of a triangle intersects two of the other two sides, it divides the two sides into proportional corresponding segments.

1. Assuming that OP || NM, we would apply the triangle proportionality theorem to have the following ratio:

[tex]\frac{ON}{LO} = \frac{PM}{LP}[/tex]

Using the above ratio, we can choose the following possible lengths for the segments:

ON = 3 units

LO = 1 unit

PM = 6 units

LP = 2 units

2. The values are decided assuming that the ratio, [tex]\frac{ON}{LO} = \frac{PM}{LP} = 3[/tex]

This means that the ratio of the proportional segments, irrespective of the their measurement should give you an assumed equal ratio of 3:1.

Therefore, since:

[tex]\frac{3}{1} = 3\\\\\frac{6}{2} = 3[/tex]

The measurements, ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units are therefore possible measurements.

3. Using the AA Similarity Theorem to prove that ΔLPO ≅ ΔLMN, the corresponding sides of both triangles will be proportional.

LP/LM = LO/LN = PO/MN

We can use this to choose possible measurements while assuming a ratio between the proportional sides of both triangles.

Let's assume that: LP/LM = LO/LN = PO/MN = 1/4

Let,

LO = 1 unit

LN = 4 units

Therefore, ON = LN - LO = 4 - 1 = 3 units.

Same way the other possible measures can be gotten provided a ratio is assumed.

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Answer: your answer is A) & D)

Step-by-step explanation:     Hope this helps :)

Answer:

A) (-5,10), (0,15), (5,10)

Step-by-step explanation:

In order for an ordered pair to be a function, no pair of coordinates can have the same x variable.

Answer: 23,364

Step-by-step explanation:6 x 3000 + 6 x 800 + 6 x 90 + 6 x 4

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

A plane that travels a distance [tex]r[/tex], in kilometers, with a bearing of [tex]\theta[/tex] sexagesimal degrees can be represented in standard position by means of the following expression:

[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)

We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:

[tex]\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})][/tex] (2)

If we know that [tex]r_{1} = 5\,km[/tex], [tex]\theta_{1} = 0^{\circ}[/tex], [tex]r_{2} = 6\,km[/tex], [tex]\theta_{2} = 60^{\circ}[/tex], [tex]r_{3} = 4\,km[/tex] and [tex]\theta_{3} = 120^{\circ}[/tex], then the resulting vector is:

[tex]\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})[/tex]

[tex]\vec R = (5\sqrt{3}, 6) \,[km][/tex]

The magnitude of the resultant is found by Pythagorean theorem:

[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]

And the bearing is determined by the following inverse trigonometric relationship:

[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)

If we know that [tex]R_{x} = 5\sqrt{3}\,km[/tex] and [tex]R_{y} = 6\,km[/tex], then the magnitude and the bearing of the resultant is:

[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]

[tex]\|\vec R\| \approx 10.536\,km[/tex]

[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]

[tex]\theta_{R} \approx 34.715^{\circ}[/tex]

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

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Answer: 471 years old

Step-by-step explanation:

1946-1475= 471

[tex]\text{Given that,}\\\\(x+2y)^2 - (x-2y)^2\\\\=(x+2y +x -2y)(x+2y -x+2y)~~~~;[a^2 - b^2 = (a+b)(a-b)]\\\\=(2x)(4y)\\\\=8xy[/tex]

Answer: -30

Step-by-step explanation:

-2 X -5 = 10

10 X -3 = -30

Therefore, -2(-5)(-3) = -30

The multiplication of −2(−5)(−3) is -30

The multiplication of numbers in brackets with negative signs takes a method whereby the signs are taken into account when performing the arithmetic operation.

From the given question, we are to multiply:

= - 2 × (-5) × (-3)

= +10 × (-3)

= -30

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Answer:

$88

Step-by-step explanation:

442.70 rounded to the nearest 10 dollars is 440.

20%= .2.

440 times .2 =

88

Answer:

m=-7/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/15

Answer:

See below

Step-by-step explanation:

(-4,0) is the solution to x+4=0

(0,0) is the solution to x=0

(2,0) is the solution to x-2=0

Therefore, (x+4)(x-2)(x) = (x²-2x+4x-8)(x) = (x²+2x-8)(x) = x³+2x²-8x is the function that has the given zeroes

Answer:

$0.44

Step-by-step explanation:

lmk if you want an explanation

Part 1) Computing (p °q) (5)

[tex]p(x) = x-3\\\\p(q(x)) = q(x)-3\\\\(p \circ q)(x) = 2x-5-3\\\\(p \circ q)(x) = 2x-8\\\\(p \circ q)(5) = 2(5)-8\\\\(p \circ q)(5) = 2\\\\[/tex]

===========================================================

Part 2) Computing   (q °p) (5)

[tex]q(x) = 2x-5\\\\q(p(x)) = 2(p(x))-5\\\\q(p(x)) = 2(x-3)-5\\\\(q \circ p)(x) = 2x-6-5\\\\(q \circ p)(x) = 2x-11\\\\(q \circ p)(5) = 2(5)-11\\\\(q \circ p)(5) = -1\\\\[/tex]

Answer:

6/8 and 12/16

Step-by-step explanation:

Important: 3/4 looks like a fraction, but it is actually an improper fraction.

There is an infinity number of equivalent fractions to 3/4. To find an equivalent fraction to 3/4 , or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By multiplying the original fraction by 2, we get:

3x2/3x2=6/8

List of Equivalent Fractions of 3/4:

3/4, 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36, 30/40, 33/44, 36/48, 39/52, 42/56, 45/60, 48/64, 51/68, 54/72, 57/76, 60/80 ...

Equaling both equations, it is found that the correct option that states the number of solutions you will have for the system is:

The equations are:

[tex]4y + x = 16 \rightarrow x = 16 - 4y[/tex]

[tex]y = 4 - x \rightarrow x = 4 - y[/tex]

Equaling both equations for x, we have that:

[tex]16 - 4y = 4 - y[/tex]

[tex]3y = 12[/tex]

[tex]y = \frac{12}{3}[/tex]

[tex]y = 4[/tex]

[tex]x = 4 - y = 4 - y = 0[/tex]

Hence, the system has one solution, which is (0,4), and option d is correct.

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Answer:

what are your options ??

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

72 + 76 = 148

180 - 148 = 32

I hope this helps!!

The store  Grand Rapids in Michigan placed and advert for a refrigerator for $1,699.99, also the tax rate is 6%.

Total cost = Tax + cost of refrigerator

$2719.984

Solution

let us find 6% of $1,699.99, this will be the amount paid as tax

Tax = 6/100*$1,699.99

Tax = 0.6*1,699.99

Tax = $1019.994

Now let us find the total amount paid for the refrigerator

This will be the cost of the refrigerator plus the Tax paid

Total = 1,699.99+1019.994

Total = $2719.984

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