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)

Answer:

"D"

if you multiply by Conjugate

the denominator would end up A^2 - b^2

the answer has 25 - 10x

that is D

Step-by-step explanation:

Answer:

2500 mg

Step-by-step explanation:

Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.

Since r(t) =  50 (e^-01t - e^-0.20t)

m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)

= 50∫₀⁰⁰(e^-01t - e^-0.20t)

= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]

= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)

= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})

= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})

= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})

= 50(1/-0.01[- 1] - {1/-0.02[- 1]})

= 50(1/0.01 - 1/0.02)

= 50(100 - 50)

= 50(50)

= 2500 mg

It seems like you want to find the sum of 38 to 115:

[tex] \displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}[/tex]

If we notice, this is arithmetic series or the sum of arithmetic sequences.

To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.

[tex] \displaystyle \large{S_n = \frac{n(a_1+a_n) }{2} }[/tex]

This formula only applies to the sequences that have the common difference = 1.

Given that a1 = first term of sequence/series, n = number of terms and a_n = last term

We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.

To find the n, you can use the following formula.

[tex] \displaystyle \large{n = (a_n - a_1) + 1}[/tex]

Substitute an = 115 and a1 = 38 in the formula of finding n.

[tex] \displaystyle \large{n = (115 - 38) + 1} \\ \displaystyle \large{n = (77) + 1} \\ \displaystyle \large{n = 78}[/tex]

Therefore the number of sequences is 78.

Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.

[tex] \displaystyle \large{S_{78} = \frac{78(38+115) }{2} } \\ \displaystyle \large{S_{78} = \frac{39(38+115) }{1} } \\ \displaystyle \large{S_{78} = 39(153) } \\ \displaystyle \large \boxed{S_{78} = 5967}[/tex]

Hence, the sum is 5967.

Answer:

answers in the explanation cz I'm too lazy to type :(

not entirely sure tho

Step-by-step explanation:

w²+2w-42=0

*quadratic formula*

w= -1+ square root 43 m

or w= -1- square root 43 m

then since the length is 2m more than w

add 2 to both answers

l= 1+ square root 43 m

l=1- square root 43 m

9514 1404 393

Answer:

Step-by-step explanation:

Given:

  a rectangular patio of width w meters, length w+2 meters, and area 42 m²

Find:

  width and length

Solution:

The area is ...

  A = LW

  42 = w(w +2)

  43 = w² +2w +1 . . . . . . add 1 to complete the square

  √43 = w+1

  w = √43 -1 ≈ 5.557 . . . meters

  l = w+2 = √43 +1 ≈ 7.557 . . . meters

The width and length of the patio are 5.557 m and 7.557 m, respectively.

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

A (- 1, - 17 ) → A' (- 1, 17 )

B (0, - 12 ) → B' (0, 12 )

C (- 5, - 11 ) → C' (- 5, 11 )

D (- 6, - 16 ) → D' (- 6, 16 )

Answer:

150°

Step-by-step explanation:

Sum of all angles in a hexagon = 720°

90° + 120° + 150° + 145° + 65 ° = 670°

720° - 570° = t

t = 150°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

50,000

Step-by-step explanation:

3 is in the ones place so 3

9 is in the tens place (90)

1 is in the hundreds place (100)

3is in the thousands place (3,000

Answer:

Step-by-step explanation:

P = 2(3x-20) + 2(2x+4) = (6x-40) + (4x+8) = 10x-32

The required perimeter of the playground is 10x-32.

The length of the playground measures (3x-20) metres.
The width of the playground measures (2x+4) metres.

Perimeter, is the measure of the figure on its circumference.

The Required perimeter is for the playground is given by
= 2(3x-20) + 2(2x+4)

= 10x-32

Thus the required perimeter of the playground is 10x-32.

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Answer:

Step-by-step explanation:

Let the quadratic function be

y=a(x+4)²-1

∵(-7,8) lies on it.

8=a(-7+4)²-1

8+1=a(-3)²

9a=9

a=9/9=1

so quadratic function  is

f(x)=1(x+4)²-1

or

f(x)=x²+8x+16-1

so quadratic function is

f(x)=x²+8x+15

Answer:

Step-by-step explanation:

(D+R) = 80:2 = 40

D = 40-R

(D+8) * R = 72X

Thay D=40-R

(40-R+8)*R = 72X

R=1.55, D=38.45

Answer:

x = 8

Step-by-step explanation:

undefined slope => m = oo

passes (8, -3) => (x1, y1)

the equation is : y-y1 =m(x-x1)

y+3 = oo(x-8)

=> x -8 = (y+3)/oo

x -8 = 0

x = 8

so, the equation is: x = 8

Answer:

-1/3x+3 = x-1

Step-by-step explanation:

The solution is (3,-2)

Check and see if the point solves the equation

-1/3x+3 = x-1

-1/3(3) +3 = 3-1

-1+3 = 3-1

2=2 yes

Answer:

C

Step-by-step explanation:

Answer:

This number line show the inequality x > 2

Step-by-step explanation:

| - 5 | + | - 4 |

5 + 4

= 9

| - 6| - 4

6 - 4

2

I hope this answers your question.

Answer: Because [tex]\frac{\pi }{3} =\frac{180\°}{3} =60\°[/tex], therefore [tex]\frac{\pi }{3} =60\°[/tex].

9514 1404 393

Answer:

  6

Step-by-step explanation:

The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...

  A = P(1 +r/n)^(nt)

Solving for t, we get ...

  t = log(A/P)/(n·log(1 +r/n))

Using the given values, we find t to be ...

  t = log(38302/32000)/(12·log(1 +0.03/12)) ≈ 5.9997

The investment was for 6 years.

Answer:

D

Step-by-step explanation:

The answer is D.

Answer:

Option D is the correct answer.

Step-by-step explanation:

The equation of the function is in vertex form. Thus, we can analyze the equation to determine the x and y values of the vertex. We know that the template format of a vertex form equation is as follows:

f(x) = a(x – h)2 + k . The only constants we need are h and k, where 'h' is the x-value of our vertex and 'k' is the y-value of our vertex.

The value of 'k' can be found quite simply by looking at the equation: -9.

The value of 'h' is a little trickier, as we must take into account the 'subtract' sign of the template equation, meaning that the '+7' in the given equation actually means that we are subtracting negative seven. Thus, the value of 'h' is -7.

Thus, the vertex of this graph is (-7,-9).

This means that option D is correct.

Answer:

The vertex is at ( -7, -9)

Step-by-step explanation:

y = (x+7)^2 -9

This is written in vertex form

y = a( x-h)^2 +k where ( h,k) is the vertex

y = ( x - -7)^2 + -9

The vertex is at ( -7, -9)

Answer:

The guy above me is correct

Step-by-step explanation:

2022

Answer:

number of seeds planted per square foot

Step-by-step explanation:

response is the yield explained by how many seeds are planted

Answer:

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

Step-by-step explanation:

x^3 + 3x^2 - 6x – 18

Factor by grouping

x^3 + 3x^2    - 6x – 18

Factor x^2 out of the first group and -6 out of the second group

x^2( x+3)  -6(x+3)

Factor out x+3

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

Answer:

Step-by-step explanation:

From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.

In first place, you must know that the roots or solutions of a quadratic function are those values ​​of x for which the expression is 0. This is the values ​​of x such that y = 0. That is, f (x) = 0.

Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c

The solutions of a quadratic equation can be calculated with the quadratic formula:

[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]

The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c

The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.

If the discriminant:

In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:

discriminant= 10² -4*(-40)*(-1)

Solving:

discriminant= 100 - 160

discriminant= -60

The discriminant is negative, so the quadratic function has no real solutions.

Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25

Answer:

5/9

Step-by-step explanation:

In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:

Negative -> Positive

Positive -> Positive

Since we are working with a negative value, it will turn positive.

Best of Luck!

Answer:

y=6x-8

Step-by-step explanation:

y=2(x-8)+4x

y=2x+4x-8, y=6x-8

Answer:

13.5 %

Step-by-step explanation:

For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)

To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean

= 95-68 = 27 %

Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5

The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

Given that, average age managers = 52 years standard deviation = 2.5 years.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Considering the equation Z =  (X−μ)/σ

Where, X is the lower or higher value, as the case may be μ  is the average σ  is standard deviation

Now, z1= (54.5 - 52)/2.5

= 1

z2= (57 - 52)/2.5

= 2

Now, z2-z1= 2-1

= 1

P(54.5>Z<57)= 0.8413

Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

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Answer:

C

Step-by-step explanation:

The expression is x>55 and 55 isn't included

Answer:

c

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

a) 1/4 of 28 = 28/4 = 7 coins are quarters.

  2/3 of (28 -7) = (2/3)(21) = 14 coins are dimes

The remaining 28 -7 -14 = 7 coins are nickels

__

b) The amount of money in coins is ...

  7×$0.25 +14×$0.10 +7×$0.05 = $3.50 . . . in coins

__

c) 2 packs of cards at $1.35 each will cost 2×$1.35 = $2.70. After the purchase, the remaining money would be ...

  $3.50 -2.70 = $0.80 . . . remaining