Mia removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 10x2 −19x + 6, where x is time in minutes. Choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty. 10(0)2 − 19(0) + 6 10(x − 6)2 − 1 10(x − 1)2 − 6 (5x − 2)(2x − 3)

Answer:

A.

Step-by-step explanation:

NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

[tex]y=2(x+3)[/tex]

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

[tex]y=3x+5[/tex]

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

[tex]y=2(x+3)\\y=2x+6\\-2x+y=6[/tex]

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

[tex]-2x+y=6\\2x-y=-6[/tex]

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

[tex]y=3x+5\\-3x+y=5\\3x-y=-5[/tex]

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.

Answer:

It is F

Step-by-step explanation:

if you plug in the y and x values that should get you the answer

Answer:

F.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\==============================[/tex]

[tex]\text{We have the equation:}\ y=5x-4\to m_1=5.\\\\\text{Therefore}\ m_2=5.\\\\\text{We have the equation:}\ y=5x+b.\\\\\text{Put the coordinates of the given point (3, 4) to the equation:}\\\\4=5(3)+b\\\\4=15+b\qquad\text{subtract 15 from both sides}\\\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=5x-11[/tex]

Answer: x = 10  y = 6

Step-by-step explanation:

0.1X + 5 = y

0.2X + 4 = y

0.1X + 5 = 0.2X  + 4

-0.1X - 4 = -0.1X - 4

1 = .1X

x = 10

0.1(10) + 5 = y

1 +5 = y

6 = y

Question 7

Answers:

Jane's Uber business has the function f(x) = 0.10x+5

Joe's Uber business has the function f(x) = 0.20x+4

x is the number of miles, f(x) is the total cost for the customer

-------------------------

Explanation:

Jane charges $5 no matter how many miles are driven. This is the base fee. On top of this base fee, an additional price is charged based on the number of miles driven. If Jane drives 1 mile, then an additional 0.10*1 = 0.10 dollars is added on. If 2 miles are driven, then 0.10*2 = 0.20 dollars is added on. And so on.

In general, an additional 0.10*x dollars is added on the base fee to get the total cost to be 5 + 0.10x which rearranges to 0.10x + 5. That's how I ended up with f(x) = 0.10x + 5

Joe's equation will be constructed in a similar way. His base fee is $4 and you add on 0.20x dollars (since it costs $0.20 per mile for Joe's company). Overall, we get f(x) = 0.20x + 4 for Joe's company.

Note how your teacher is not asking you to solve for x or f(x). If you want, you can replace f(x) with y; however, this isn't in function notation.

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

Question 8

Answers:

Function for Joseph's plan is: f(x) = 0.10x + 20

Function for Micki's plan is: f(x) = 0.15x + 10

The plans cost the same when 200 text messages are sent

-------------------------

Explanation:

We'll set up the equations in a similar way done in problem 7. We start with $20 as the base fee for Joseph's plan and then add on 0.10x dollars because $0.10 is charged per text message. We have x represent the number of text messages. Joseph's function is therefore f(x) = 0.10x + 20. Similarly, Micki's function is f(x) = 0.15x + 10

Let's replace f(x) with y and we have these two equations: y = 0.10x + 20 and y = 0.15x + 10

Now use substitution to solve for x and y

y = 0.10x + 20

0.15x + 10 = 0.10x + 20 ... y replaced with 0.15x+10

0.15x-0.10x = 20-10

0.05x = 10

x = 10/0.05

x = 200

This means that the two plans cost the same when 200 messages are sent.

Note plugging x = 200 into each f(x) function leads to

f(x) = 0.10x + 20

f(200) = 0.10*200 + 20

f(200) = 20 + 20

f(200) = 40 <<--- it costs Joseph $40 to send 200 messages

and

f(x) = 0.15x + 10

f(200) = 0.15*200 + 10

f(200) = 30 + 10

f(200) = 40 <<--- it costs Micki $40 to send 200 messages

Answer:

x^2+7x if you are asked to find the difference of a function f and function g

Step-by-step explanation:

We are asked to A-B or f(x)-g(x).

(4x^2+6x)-(3x^2-x)

4x^2+6x-3x^2+x

The like terms I'm going to pair up.

4x^2-3x^2+6x+x

1x^2          +7x

x^2            +7x

The answer is x^2+7x

Answer:

OPTION D: [tex]h(x)=x^2+7x[/tex]

Step-by-step explanation:

You know that the area of Rectangle A is given by :

[tex]f(x)= 4x^2+6x[/tex]

And the area of Rectangle B is given by:

[tex]g(x)=3x^2-x[/tex]

Therefore, in otder to find the function that represents the difference, you need to subtract the functions f(x) and g(x).

Then, you get this function h(x):

 [tex]h(x)=f(x)-g(x)\\\\h(x)= (4x^2+6x)-(3x^2-x)\\\\h(x)=4x^2+6x-3x^2+x\\\\h(x)=x^2+7x[/tex]

Answer:

[tex]\large\boxed{C.\ y=\dfrac{1}{2}x-5}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept

[tex]\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff\ m_1m_2=-1\to m_2=\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]

Parallel line have the same slope.

Therefore a line parallel to the line [tex]y=\dfrac{1}{2}x+1[/tex] has equation

[tex]y=\dfrac{1}{2}x+b[/tex]

Answer:

x = 8

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Sum the exterior angles and equate to 360

62 + 66 + 77 + 59 + 12x = 360, that is

264 + 12x = 360 ( subtract 264 from both sides )

12x = 96 ( divide both sides by 12 )

x = 8

Answer:

So any number in the following set is a solution:

[tex](-\infty,-4) \cup (1,\infty)[/tex]

given the inequality to solve was:

[tex]x^2+3x-4>0[/tex]

Step-by-step explanation:

The left hand side is a quadratic while the right hand side is 0.

Since this is a quadratic>0, I'm going to factor the quadratic if possible and then solve that quadratic=0 for x.

That is I'm going to solve:

[tex]x^2+3x-4=0[/tex]

Since a=1, I get to ask what multiplies to be c (-4) and add up to be b(3).

Those numbers are 4 and -1.

So the factored form for the equation is:

[tex](x+4)(x-1)=0[/tex]

Setting both factors equal to 0 since 0*anything=0:

x+4=0            and              x-1=0

 -4   -4                                 +1   +1

---------------------------------------------------

x=-4              and                   x=1

Ok so if this wasn't a quadratic I would make a number line and choose numbers to plug into the quadratic to see which intervals would give me positive results.  I say positive due to the >0 part.

However since I know about the shapes of quadratics, I'm going to use that.

The quadratic function [tex]f(x)=x^2+3x-4[/tex] has x-intercepts (-4,0) and (1,0) and is open up.

I determine that it was opened up because the leading coefficient is 1 which is positive.

Now the left tail and right tail is what is above the x-axis so the solution set is:

[tex](-\infty,-4) \cup (1,\infty)[/tex]

Answer:

-6 and 5

Step-by-step explanation:

Answer:

A= 706.85m^2

Step-by-step explanation:

A= 4• Pi•r^2

= 4•Pi•15^2

=2827.43/4

=706.8575m^2

For this case we have that by definition, the area of a circular sector is given by:

[tex]A = \frac {a * r ^ 2} {2}[/tex]

Where:

r: It's the radio

a: It is the angle of the sector

We have to:

a = 90 degrees

[tex]90\ degrees = \frac {\pi} {2}[/tex]

Then, replacing:

[tex]A = \frac {\frac {\pi} {2} * 15 ^ 2} {2} = \frac {225 \pi} {4}[/tex]

Answer:

Option A

Answer:

A) the longest side

B) the smallest angle

Step-by-step explanation:

Relationship of sides to interior angles in a triangle

In a triangle:    

Recall that in a scalene triangle, all the sides have different lengths and all the interior angles have different measures. In such a triangle, the shortest side is always opposite the smallest angle. Similarly, the longest side is opposite the largest angle.

So,

A) the longest side

B) the smallest angle

Answer:  the longest side

the smallest angle

Step-by-step explanation: the largest is longest

the smallest is shortest

Answer:

24.4444

Step-by-step explanation:

76 degrees faherheit = 24.4444 degrees Celsius

(76°F − 32) × 5/9 = 24.444°C

Answer:

rjjj3krktkkrkrkektk4kgk4mgk3mrl3lfkwjkeoc

Answer:

I'm pretty sure its A

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

Option: A is the correct answer:

                     [tex]A.\ y=-3x[/tex]

The equation of a line passing through two points (a,b) and (c,d) is calculated with the help of a two-point formula:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Based on the graph we observe that the line passes through:

(0,0) and (3,-9)

i.e. we have: (a,b)=(0,0) and (c,d)=(3,-9)

i.e. the equation of line is given by:

[tex]y-0=\dfrac{-9-0}{3-0}\times (x-0)\\\\i.e.\\\\y=\dfrac{-9}{3}\times x\\\\i.e.\\\\y=-3x[/tex]

          The answer is: Option: A

Answer:

1/110

Step-by-step explanation:

Her chance of originally grabbing a pink marker is 1/11. Her chance of grabbing a blue marker after the pink marker is taken out is 1/10. When you multiply 1/11 by 1/10, you get a 1/110 chance of getting the colored markers in this series

Answer:

The probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]

Step-by-step explanation:

Hello, this is a great question and one that many people struggle with in school. Hopefully I can help you understand it more clearly. Kelly has 11 markers in total within her backpack and needs to randomly pick out the pink marker. since there is only 1 that would mean her probability of picking out the pink marker is 1/11 .

Now there are 10 markers inside the backpack and she needs to randomly pick out the blue marker. since there is only 1 blue marker that would mean her probability of picking that one out is 1/10.

So now we have the following probabilities

Now if we want to find the probability of her getting the pink marker and the blue marker one after another we would need to multiply both fractions together

[tex]\frac{1}{11} * \frac{1}{10} = \frac{1}{110}[/tex]

So the probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]

Answer:

41 units

Step-by-step explanation:

In this question, you should remember that the diagonal  drawn will represent the longest side of the triangle that will be formed .This is to say the triangle will have the two shorter sides (the length and width) and the longest side (diagonal).

Apply the Pythagorean relationship where

The formula to apply here will be

[tex]a^2+b^2=c^2\\\\\\a=9,b=40,c=?\\\\\\9^2+40^2=c^2\\\\\\81+1600=c^2\\\\\\c^2=1681\\\\\\c=\sqrt{1681} =41units[/tex]

Answer:

Diagonal = 41 units

Step-by-step explanation:

It is given that,a rectangle has a width of 9 units and a length of 40 units.

To find the diagonal of rectangle

We know that rectangle can be considered as combination of two right triangles.

Here length of right triangle = 40 units and height = 9 units

Hypotenuse = diagonal of rectangle.

Hypotenuse² = Length² + height

 = 40² + 9²

 = 1600 + 81

 = 1681

Hypotenuse = √1681 = 41

Therefore diagonal of rectangle = 41 units

Answer:

9/10p

Step-by-step explanation:

1/2p+ 2/5 p

Get a common denominator of 10

1/2 p *5/5 = 5/10 p

2/5p *2/2 = 4/10 p

1/2p * 2/5 p

5/10p * 4/10 p

9/10p

Answer:

LARGEST ANGLE= 96 DEGREES

Step-by-step explanation:

MEASURE OF LARGEST ANGLE= 3A

SMALLEST ANGLE= A

THIRD ANGLE= 20+A

3A+A+20+A=180(SUM OF INTERIOR ANGLES OF TRAINGLE IS 180 DEGREES)

TRANSPOSE 20 TO RHS.

5A=180-20=160

A=160/5

=32

MEASURE OF SMALLEST ANGLE=32

LARGEST ANGLE=3A=3*32=96 DEGREES

THIRD ANGLE=32+20=52 DEGREES

Answer:

The largest angle has a measure of 96 degrees.

Step-by-step explanation:

In order to solve this problem, we have to know the fact that the sumatory of the internal angles of any triangle is 180 degrees.

With this statement in mind, and looking at the image, we can say:

180 = A + B + C (eq. 1)

Before continue any further, let's affirmt that B is the smallest angle.

Now the enunciate says "One angle in a triangle has a measure that is three times as large as the smallest angle"; This can be express as:

A = 3B (eq. 2)

The other enunciate is "The measure of the third angle is 20 degrees more than that of the smallest angle" This can be express as:

C = B + 20 (eq. 3)

Now, replacing equations 2 and 3 into 1:

(eq. 1) 180 = 3B + B + B + 20

And clearing B:

B = 32.

By knowing B, we can clear A and C from equations 2 and 3 respectively:

(eq. 2) A = 3B,  so A= 96

(eq. 3) C = B + 20, so C =52

c.10/18 and 45/81

10/18=.5555555555555555555555

45/81=.5555555555555555555555

Answer:

D 5/6 and 5/24

step by step explanation  :

when you multiply 6 times 4 it equals 24

Answer:

6

Step-by-step explanation:

The interquartile range is a measure of the difference between the upper quartile and the lower quartile.

The first step is to organise the data in ascending order, that is

10, 12, 13, 15, 17, 18, 21

Next find the median which is the middle value of the data.

10, 12, 13, 15, 17, 18, 21

                 ↑ ← the median = 15

Now find the upper and lower quartiles which are the middle values of the data to the right and left of the median.

10, 12, 13, 15, 17, 18, 21

      ↑                    ↑

upper quartile = 18 and lower quartile = 12

interquartile range = 18 - 12 = 6

Interquartile range of the given data set is 6.

Interquartile is the difference between upper quartile and lower quartile

Lower quartile is the median of the lower half of the data set.

Upper quartile is the median of the upper half of the data set.

Given data set 13, 17, 18, 15, 12, 21, 10

Arranging the data set in ascending order we get 10, 12, 13, 15, 17, 18, 21

Number of values in the data set is n = 7

Lower quartile is given by [tex]Q_{1} =\frac{n+1}{4} =\frac{7+1}{4} =\frac{8}{2} =2^{nd} \ value[/tex]

Therefore, the lower quartile is [tex]Q_{1} =12[/tex]

Upper quartile is given by [tex]Q_{3}=\frac{3}{4} (n+1)=\frac{3}{4} (7+1)=\frac{3}{4}(8)=6^{th} \ value[/tex]

Therefore, the upper quartile is [tex]Q_{1} =18[/tex]

Therefore, the inter quartile is given by [tex]Q_{3}-Q_{1} =18-12=6[/tex]

Interquartile range of the given data set is 6.

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Answer:

x  , reciprocal= 1/x  

x+2(1/x)=27/5  

x+2/x=27/5  

x^2+2=27/5*x  

x^2-27/5*x+2=0  

(x-5)(x-2/5)=0  

x=5, 2/5

Answer:

80

Explanation:

46 + 37 = 83 so 83 rounded to the nearest 10 is 80

Answer:

80

Step-by-step explanation:

46+37 = 83

Rounding to the nearest ten

80

[tex]

f(x)=-x^2+6x-1 \\

g(x)=3x^2-4x-1 \\

f(x)+g(x)=-x^2+6x-1+3x^2-4x-1=\boxed{2x^2+2x-2}

[/tex]

The answer is A.

Hope this helps.

r3t40

Midpoint has form of,

[tex]M(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

We can insert the data,

[tex]M(\dfrac{4+3}{2},\dfrac{-1+2}{2})[/tex]

Which simplifies to,

[tex]\boxed{M(3.5, 0.5)}[/tex]

Hope this helps.

r3t40

B, because every prime number greater than 2 is odd, and the product of two odd numbers is odd.

Answer: I'm pretty sure its B

Step-by-step explanation:

..

Answer:

The true statements are:

m∠ 3 + m∠ 4 = 180° ⇒ 1st

m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd

m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd

Step-by-step explanation:

* Look to the attached diagram to answer the question

# m∠ 3 + m∠ 4 = 180°

∵ ∠ 3 and ∠ 4 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠ 3 + m∠ 4 = 180° ⇒ true

# m∠ 2 + m∠ 4 + m∠ 6 = 180°

∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle

∵ The sum of the measures of interior angles of any Δ is 180°

∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ true

# m∠ 2 + m∠ 4 = m∠ 5

∵ In any Δ, the measure of the exterior angle at one vertex of the

  triangle equals the sum of the measures of the opposite interior

  angles of this vertex

∵ ∠ 5 is the exterior angle of the vertex of ∠ 6

∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6

∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ true

# m∠1 + m∠2 = 90°

∵ ∠ 1 and ∠ 2 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠1 + m∠2 = 90° ⇒ Not true

# m∠4 + m∠6 = m∠2

∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle

∵ There is no given about their measures

∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is

  equal to the measure of ∠ 2

∴ m∠4 + m∠6 = m∠2 ⇒ Not true

# m∠2 + m∠6 = m∠5

∵ ∠ 5 is the exterior angle at the vertex of ∠ 6

∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ Not true

Answer: A,B,C. OR 1,2,3

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

1. [tex]JK\cong LM[/tex] - given

2.  [tex]JL\cong LN[/tex] - definition of midpoint (the midpoint of the segment divides the segment into two congruent segments)

3. [tex]\angle LJK\cong \angle NLM[/tex] - corresponding angles theorem (corresponding angles theorem states: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.)

4. [tex]\triangle JLK\cong \triangle LNM[/tex] - SAS (SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent).

Answer:

A 40, 80, 160

Step-by-step explanation:

Given:

2.5, 5, 10, 20, ...

geometric sequence has a constant ratio r and is given by

an=a1r(r)^(n-1)

where

an=nth term

r=common ratio

n=number of term

a1=first term

In given series:

a1=2.5

r= a(n+1)/an

r=5/2.5

r=2

Now computing next term a5

a5=a1(r)^(n-1)

   = 2.5(2)^(4)

   = 40

a6=a1(r)^(n-1)

   = 2.5(2)^(5)

   =80

a7=a1(r)^(n-1)

   = 2.5(2)^(6)

   =160

So the sequence now is 2.5, 5, 10, 20,40, 80, 160!

Answer:

its B and the next one is C

Step-by-step explanation:

Formula for the sequence based on term number is

[tex]a_{n} =(4)(2)^{n-1}[/tex].

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given

First term [tex]a[/tex] = 4

Common ratio r = -2

It is a geometric sequence because we have common ratio

Formula for the sequence based on term number is

[tex]a_{n} =ar^{n-1}[/tex]

[tex]a_{n} =(4)(2)^{n-1}[/tex]

Hence, Formula for the sequence based on term number is

[tex]a_{n} =(4)(2)^{n-1}[/tex].

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Answer:

3q = 36

q = 12

Step-by-step explanation:

Just work out the steps and compare to the choices

√(3q) = 6

[√(3q)]² = 6²

3q = 36  (Answer)

q = 36/3 = 12 (Answer)

A=36 and B=12 is the required steps for the equation √3q=6 given that 3q=A and q=B. This can be obtained by finding the remaining steps for finding q.

Given that √3q=6

              (√3q)²=6²

                   3q = 6×6 = 36 ⇒ A = 36 (squaring both sides)

                     q = 36/3 = 12 ⇒ B = 12 (divide both sides by 3)

Hence A=36 and B=12 is the required steps for the equation √3q=6 given that 3q=A and q=B.

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