Write the equation of the line that passes through
the points (-1, 2) and (6, 3) in slope-intercept form.

Answer:

Sean's rocket lands 3 seconds after Kiara's rocket.

Step-by-step explanation:

Kiara:  f(t)= -16t² + 80t

Sean:  h(t) = -16t² + 120t + 64

Assume that both rockets launch at the same time.  We need to be suspicious of Sean's rocket launch.  His equation for height has "+64" at the end, whereas Kiara's has no such term.  The +64 is the starting height iof Sean's rocket.  So Kiara has a 64 foot disadvantage from the start.  But if it is a race to the ground, then the 64 feet may be a disadvantage.  [Turn the rocket upside down, in that case.  :) ]

We want the time, t, at which f(t) and h(t) are both equal to 0 (ground).  So we can set both equation to 0 and calculate t:

Kiara:  f(t)= -16t² + 80t

0 = -16t² + 80t

Use the quadratic equation or solve by factoring.  I'll factor:

0 = -16t(t - 5)

T can either be 0 or 5

We'll choose 5.  Kiara's rocket lands in 5 seconds.

Sean:  h(t) = -16t² + 120t + 64

0= -16t² + 120t + 64

We can also factor this equation (or solve with the quadratic equation):

0 = -8(t-8)(2t+1)

T can be 8 or -(1/2) seconds. We'll use 8 seconds.  Sean's rocket lands in 8 seconds.

Sean's rocket lands 3 seconds after Kiara's rocket.

Answer:

45

Step-by-step explanation:

Simply start by listing out the numbers from smallest to largest.

We start out with the smallest number following this information being the number 10. The next are 21 and 20. The next are 32, 31, and 30. We can start to see a pattern. If the ten's digit is n, then there are n numbers within that ten-group that have a greater 10's digit than unit's digit. The largest ten-group (90 to 98) has 9 integers following the rules established. Thus, the number of 2-digit integers that have ten's digits greater than units digit is 1+2+3+...+9=45

The profit is Rs.4800.

When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. It is calculated with the help of the formula: Profit = Selling price - Cost price.

Given that,

S.P =$6000

C.P = $6000

If, 1$ = Rs.115.4 (in cost price)

  1$ = Rs.116.20 (in selling price)

Then,

C.P =  Rs. 115.40×6000

S.P = Rs.  116.20×6000

Then,

Profit = S.P-C.P

         =  116.20×6000 -115.40×6000

         =  (116.20-115.40)×6000

         = 0.80×6000

         =  Rs.4800

Hence, The profit is Rs.4800.

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Answer:

The total selling price for the parcel is 1,524,600 dollars.

Step-by-step explanation:

We are given that 10 acre parcel was sold for $3.50.

First we need to figure out how many square foot is in 10 acres.

when we convert 10 acres we get 435600 square feet.

Since we know that parcel was sold for $3.50 per square foot we simply multiply 435600 by 3.5 = 1,524,600

The system of linear equations has at least one solution is consistent , whereas a system of linear equations that has no solution is inconsistent

What is a system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system (see linearization).

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Using a calculator, the exponential regression equation for the data is:

y = 16615.21e^(-0.14x)

Using it, the estimate for the value of car after 11 years is $3,561.99.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points are given as follows:

(0, 16700), (1, 14370), (2, 12520), (3, 10301), (4, 9871), (5, 7982), (6, 6984).

Inserting these points in the calculator, the equation is:

y = 16615.21e^(-0.14x)

Hence the value of the car after 11 years is given by:

y = 16615.21e^(-0.14 x 11) = $3,561.99.

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The value of the missing probability is:

P(A) = 1/5

So the correct option is D.

First, we know that:

P(A∩B) = probability that events A and B are true = 3/100

And we also know that:

P(B|A) = probability that event B is true given that event A is true = 3/20

Here we have the rule:

P(A∩B) = P(B|A)*P(A)

Replacing the first two:

3/100 = (3/20)*P(A)

Solving for P(A), we get:

(3/100)*(20/3) = 1/5 = P(A).

So we conclude that the correct option for the missing probability is the one in option D.

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The area of the shaded region is 3.125π - 6. The correct option is E. 3.125π - 6

From the question, we are to determine the area of the shaded region

The area of the shaded region = Area of the semicircle - Area of the triangle

First, we will determine the diameter, d, of the semicircle

d² = 3² + 4² (Pythagorean theorem)

d² = 9 + 16

d² = 25

d = √25

d = 5

∴ Diameter of the semicircle is 5

Thus,

Radius, r = 5/2 = 2.5

Now,

Area of the shaded region = 1/2(π×2.5²) - 1/2(3×4)

Area of the shaded region = 1/2(π×6.25) - 1/2(12)

Area of the shaded region = 3.125π - 6

Hence, the area of the shaded region is 3.125π - 6. The correct option is E. 3.125π - 6

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All the x-values in the interval for which the function is equal to its average value [tex]5-\sqrt{5}[/tex] .

An interval program language period accommodates the numbers mendacity between specific given numbers. for instance, the set of numbers x gratifying 0 ≤ x ≤ five is a c programming language that contains zero, five, and all numbers among 0 and five.

The interval program language period is the distinction between the higher class restriction and the lower magnificence restriction. As an example, the dimensions of the class c program language period for the first class is 30 – 21 = 9. further, the size of the class c programming language for the second magnificence is forty – 31 = nine.

In arithmetic, an interval language is fixed of actual numbers that carry all actual numbers mendacity among any numbers of the set. For example, the set of numbers x pleasurable zero ≤ x ≤ 1 is a  language that includes zero, 1, and all numbers in between.

f(x)=(91-55 [0,1]

value of the function on the interval [0,1] is (9-0)

Let x-5=3

now, find the value of x, for which

f(x) =(2x-5) 2 =

5/X-5 =√5

24 X = 54√5 and 5. √5

Strs [ay] and 5- 5-√5 €0.4]

value of x is 5- sqrt15

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Answer:

-1/3

Step-by-step explanation:

Slope is rise over run. Every 3 units to the left, it rises 1 unit, so the slope is -1/3.

Answer:

61

Step-by-step explanation:

You can see that the sides are both 6. That means that this triangle is an isosceles triangle.

Therefore do this:

180-58=122

122/2= 61

So x= 61 Degrees

Hope This helps! :)

Answer:

x = 61

Step-by-step explanation:

This triangle is an isosceles triangle which means 2 sides are congruent. This also means the 2 angles across from the congruent sides are congruent. So, you would subtract 58 from 180 which equals 122. Then you would divide that in half, which gets you 61. (The angle 58 is the one across from the side that is not congruent to the others. That is why I used it)

The time spent practicing and the number of free throws made has a positive correlation. The number of items bought and the checking account balance has a negative correlation. The height of baseball player and the

number of hits made has no correlation.

About positive correlation:

Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation.

About negative correlation:

A negative or inverse relationship between two variables in statistics exists when higher values of one variable tend to be correlated with lower values of the other. Such scenarios have negative correlation.

About no correlation:

When two events or variables are unaffected by each other or are not inter-related, they are said to possess no correlation.

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Answer:

option 1 is positive option 2 is negative option 3 is none

Step-by-step explanation:

Enginuity said so

The required answers are:

1) The center of the circle = (4, 8)

2) The radius of the circle = 2.5 units

3) The equation of the circle = (x - 4)² + (y - 8)² = 6.25

The equation of the circle which has a center at (h, k) and a radius of 'r' units is (x - h)² + (y - k)² = r²

To calculate radius 'r', we have r = sqrt( (x1 - h)² + (y1 - k)²)

Where (x1, y1) is the point that lies on the circle.

Given that,

The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)

We know that the longest chord on a circle is nothing but the diameter of the circle.

So, the center is the midpoint of the diameter. I.e.,

(h, k) = ([tex]\frac{4+4}{2}[/tex], [tex]\frac{5.5+10.5}{2}[/tex])

⇒ (h, k) = (4, 8)

Therefore, the center of the circle is (4, 8)

Then, the radius is calculated by

r = sqrt( (x1 - h)² + (y1 - k)²)

⇒ r = [tex]\sqrt{(4-4)^2+(5.5-8)^2}[/tex]

⇒ r = 2.5 units

Thus, the radius of the circle is 2.5 units.

So, the equation of the circle with center (4, 8) and radius of 2.5 units is,

(x - h)² + (y - k)² = r²

⇒ (x - 4)² + (y - 8)² = 2.5²

⇒ (x - 4)² + (y - 8)² = 6.25

Thus, the equation of the circle is x - 4)² + (y - 8)² = 6.25.

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The sum of the equation is  = 5494000.

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

Distribute 2j to (j+3).

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used.

The sum is 5,494,000.

[tex]\sum_{j=1}^{200} 2 j(j+3)[/tex]

simplifying them we get:

[tex]\sum_{j=1}^{200} 2 j^{2}+6 j[/tex]

Split the summation into smaller summations that fit the summation rules.

[tex]\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j[/tex]

[tex]\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}[/tex]

The formula for the summation of a polynomial with degree 2

is:

[tex]\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}[/tex]

Substitute the values into the formula and make sure to multiply by the front term.

[tex](2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$[/tex]

we get: 5373400

Evaluating same as above : [tex]6 \sum_{j=1}^{200} j[/tex]

we get: 120600

Add the results of the summations.

5373400 + 120600

= 5494000

The sum of the equation is  = 5494000.

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Answer:

x = 8

Step-by-step explanation:

→ Add 16 to both sides

x = 8

The correct solution for the given expression [tex]-16+x = -8 \\[/tex]  is [tex]x[/tex] is equal to [tex]8[/tex].

Given expression:

[tex]-16+x =- 8 \\[/tex]

To solve for [tex]x[/tex], Rearrange the equation or isolate [tex]x[/tex] terms on one side of the expression.

Add [tex]8[/tex] on both side of the equation:

[tex]-16+x+8=-8+8[/tex]

Simplify:

[tex]x-8 = 0[/tex]

Isolate [tex]x[/tex] on one side:

[tex]x= 8[/tex]

The correct value of [tex]x[/tex] is [tex]8[/tex].

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To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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The system of equations when been placed in a matrix yields

[tex]\left[\begin{array}{ccc}650&-1\\120&1\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}-175\\25080\end{array}\right][/tex]

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

y = 650x + 175 and;

y = 25080 - 120x

Rearranging the equations gives:

650x - y = -175 and;

120x + y = 25080

Placing the equations in a matrix gives:

[tex]\left[\begin{array}{ccc}650&-1\\120&1\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}-175\\25080\end{array}\right][/tex]

The system of equations when been placed in a matrix yields

[tex]\left[\begin{array}{ccc}650&-1\\120&1\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}-175\\25080\end{array}\right][/tex]

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Using the normal distribution, we have that the desired information is given as follows:

a) X ~ N(3,1.8).

b) 3 days.

c) Z = 0.5556.

d) 0.33 = 33%.

e) 0.2048 = 20.48%.

f) 5.3 days.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 3, \sigma = 1.8[/tex]

Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.

The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:

Z = (4 - 3)/1.8 = 0.5556.

The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:

Z = (3.8 - 3)/1.8 = 0.44.

Z = 0.44 has a p-value of 0.67.

1 - 0.67 = 0.33.

The probability is of 0.33 = 33%.

The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:

X = 4.2:

Z = (4.2 - 3)/1.8

Z = 0.67.

Z = 0.67 has a p-value of 0.7486.

X = 3.2:

Z = (3.2 - 3)/1.8

Z = 0.11.

Z = 0.11 has a p-value of 0.5438.

0.7486 - 0.5438 = 0.2048 = 20.48%.

The 90th percentile is X when Z = 1.28, hence:

1.28 = (X - 3)/1.8

X - 3 = 1.8 x 1.28

X = 5.3 days.

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The statement that the equation has no solutions because the constant is the same is true

The equation is given as:

3x - 8 = 7x- 8

Add 8 to both sides

3x - 8 + 8= 7x-  8 + 8

Evaluate the like terms

3x = 7x

Divide both sides by x

3 = 7

The above equation is false, because 3 and 7 are not equal

This means that the statement that the equation has no solutions because the constant is the same is true

Hence, I agree with Kiran

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Answer:

Step-by-step explanation:

D, -9, 62.85, 6.28x100(628)

Answer:

Step-by-step explanation:

The answer would be C

Since of course negative 5 is a negative and any negative number plus a positive number would end up being a negative number and that means that that would be the least since no other number is a negative. The square root of 132.... Can it be bigger than 7  5/16? Yeah. Because the Square root of 132, if rounded, it would be 11 which 11 is greater than 7 which would mean the correct order would be -5 x 10^2,   7  5/16,  and the square root of 132.

give me brainlyest

Answer:

  (B)  1

Step-by-step explanation:

The number of such integers will be the number of places where the functions f(x) = x² and g(x) = √x intersect.

The attachment shows the graphical solution to f(x) = g(x) for x > 0. There is exactly one point of intersection at x=1.

There is one such number.

Answer:x=5

Step-by-step explanation: 73+73+6x+4=180

150+6x=180

6x=30

x=5

Answer:

y = - 2x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - 2x - 1 ← equation of line

6) The solution of the system of linear equations is (x, y, z) = (2, 5, 3).

11) The average depth of the water is 0.35 kilometers.

12) The dollar value of the deposit after 10 years is $ 1205.85.

13) Three horses need a consumption of 930 pounds of hay for the month of July.

14) The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.

15) Anna has a mean time of 7.39 minutes.

In this question we must analyze and resolve on algebraic equations such as linear equations or conic sections. 6) We must use algebra properties to solve on the system of linear equations. First, we clear x in the first equation:

x = y - z

Then, we apply it in the two remaining equations:

- 5 · (y - z) + 3 · y - 2 · z = - 1

2 · (y - z) - y + 4 · z = 11

- 2 · y + 3 · z = - 1

y + 2 · z = 11

Second, we clear y in the second expression and we substitute into the first expression:

y = 11 - 2 · z

- 2 · (11 - 2 · z) + 3 · z = -1

- 22 + 7 · z = - 1

z = 3

y = 5

x = 2

The solution of the system of linear equations is (x, y, z) = (2, 5, 3).

11) There is a function of the speed of a tsunami in terms of the average depth of the water. The former variable is known and we need to clear d in the formula to find the missing value:

145 = 356 · √d

d = (145 / 356)²

d = 0.345 km

The average depth of the water is 0.35 kilometers.

12) The compound interest model is shown below:

C' = C · (1 + r / 100)ˣ      (1)

Where:

If we know that C = 500, r = 4.5 and x = 20, then the resulting capital after 10 years is:

C' = 500 · (1 + 4.5 / 100)²⁰

C' = 1205.85

The dollar value of the deposit after 10 years is $ 1205.85.

13) The situations indicates a direct variation as the amount of hay is directly proportional to the number of days. Hence, we have the following linear model for the hay consumption of one horse:

y = m · x        (2)

y = 10 · x

Where:

The total consumption of three horses during July is equal to the product of the number of horses and consumed hay by one horse during one month:

y' = 3 · [10 · (31)]

y' = 930

Three horses need a consumption of 930 pounds of hay for the month of July.

14) There is the general equation of the circumference and we must transform it into its vertex form to find information about the radius. This can done by algebraic procedures:

x² + y² + 8 · y + 8 · y + 28 = 0

(x² + 8 · y) + (y² + 8 · y) = - 28

(x² + 8 · y + 16) + (y² + 8 · y + 16) = 4

(x + 4)² + (y + 4)² = 2²

The circle with equation x² + y² + 8 · y + 8 · y + 28 = 0 has a radius of 2.

15) We need to sum all the times described in the table and divide it by the number of data to find the mean time for a 1-kilometer race:

x = (7.25 + 7.40 + 7.20 + 7.10 + 8.00 + 8.10 + 6.75 + 7.35 + 7.25 + 7.45) / 10

x = 7.39

Anna has a mean time of 7.39 minutes.

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Answer:

the answer is 1.5/10 cause the 5000 is added to 30000

TheThe number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.

A. Let assume the two are linear relationship

Let y represent juice made

Let x represent the concentrate remaining

Hence:

Slope=600-200/200-280

Slope=400/-80

Slope=-5

y=-5x+b

Where:

x=200

y=-5(200)+b=600

y=-1000+b=600

b=1600

Thus,

y=-5x+1600

y=0.  -5x+1600=0

        -5x=-1600

divide both side by 5x

x=-1600/-5

x=320 ounces

B. x=0

y=1600 ounces

Therefore the number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.

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Your net worth change by zero dollars.

Net worth is the difference between asset and liability.  

In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.

Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.

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The speed of private jet is = 252 mph

The speed of commercial jet is =  360 mph

What is speed ?

Let the speed of private jet be x mph.

Then the speed of commercial jet will be = 2x - 144

Equation forms:

10x = 7 ( 2x - 144 )

Solving for x

10x = 14x - 1008

⇒ 10x - 14x =  - 1008

⇒ - 4x = - 1008

⇒ x = 252

So, x = 252

Hence, the speed of private jet is = 252 mph

The speed of commercial jet is =  = 2(252) - 144 = 360 mph

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Answer:

2x+6-(x^2+6x+9)*pi

Step-by-step explanation:

2*(x+3) - (x+3)^2*pi

2x+6-(x^2+6x+9)*pi

um I think there are answer choices so I don't know if I have to keep going but that should be right