What is an equation of the line that passes through the points (0, 5)(0,5) and (-5, 1)(−5,1)? Put your answer in fully reduced form.

Answer:

Slope = -2/5 new points (5/2,1) and (5,0)

Step-by-step explanation:

Standard point slope equation:

y = mx + b   where m is the slope and b is the y-intercept.

First find the slope between the given points.

Slope = rise/run

m = (y1 - y2) / (x1 - x2)

   = (4 - 0)/(-5 - 5)

   = 4/-10 = -2/5 then

y = (-2/5)x + b then one point (I picked (-5,4) to find b

4 = (-2/5)(-5) + b

4 = 2 + b

b = 2

y = (-2/5)x + 2 then pick an x and find y for additional points.

x = 5/2

y = (-2/5)(5/2) + 2

y = -1 + 2

y = 1 so the point is (5/2,1) and let x = 5

y = (-2/5)(5) + 2

y = -2 + 2

y = 0 so the point is (5,0)

Suppose that :

A = ( 5 , 0 )

B = ( - 5 , 4 )

Then we have :

Slope = [ y(B) - y(A) ] ÷ [ x(B) - x(A) ]

Slope = [ 4 - 0 ] ÷ [ -5 - 5 ]

Slope = 4 ÷ ( - 10 )

Slope = - 4/10

Slope = - 2/5

________________________________

It's time to find the formula of this linear function using following formula :

y - y ( A or B ) = Slope × ( x - x ( A or B ) )

I'm gonna using point A but u can do it with point B which will gave the same answer :

y - 0 = - 2/5 × ( x - 5 )

y = - 2/5 x + 2

_______________________________

We have the formula of the function now thus it's time to find two more points that line passe through ;

To do that we just have to put two desired values of x instead of it and find the y to have the coordinate of those points that line passes through :

I'm gonna use x = - 10 and x = 15 :

x = - 10 x = 15

y = - 2/5 × ( -10 ) + 2 y = -2/5 × ( 15 ) + 2

y = 4 + 2 y = - 6 + 2

y = 6 y = - 4

________________________________

Thus ( -10 , 6 ) & ( 15 , - 4 ) are two other points that line passes through.

The values from the given replacement set make up the solution set of the inequality is {8, 9, 10]

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Let's solve the inequality to find the replacement set that make up the solution set of the inequality as follows:

m + 7 < 18

subtract 7 from both sides of the inequality

m + 7 < 18

m + 7 - 7 < 18 - 7

m < 11

Therefore, the set of value of m is less that 11.

The solution sets are {8, 9, 10}

learn more on inequality here:https://brainly.com/question/8035078

#SPJ1

Step-by-step explanation:

Marie has decided to start saving for a down payment on her home. If she puts $1,000 every quarter for five years into a GIC earning 6% compounded monthly she will have $20,979.12. She will make her first deposit three months from now.

Laroquette Holdings needs a new $10 million warehouse. Starting today the company will put aside $139,239.72 every month for five years into an annuity earning 7% compounded semi-annually.

Brenda will lease a $25,000 car at 3.9%

The required amount that is paid on hire price is $190.

Given that,
A stereo has a cash price of $850. It can be bought for a deposit of $200 and 12 monthly installments of $70.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Total price = $850
Total paid = 200 + 70×12
Total paid = $1040
Total extra pay = 1040 - 850 = $190.

Thus, the required amount that is paid on hire price is $190.

Learn more about arithmetic here:

https://brainly.com/question/11559160

#SPJ2

The units of weight of watermelon on the digital scale could be kilogram, gram and pounds.

According to the question,

We have the following information:

A watermelon is placed on a digital scale. The scale reads 10.5.

We know that there are several units of measurements for every physical quantity. For example, the units for measuring length are kilometers, meters, centimeters, feet, inches and many more.

In the same way, there are many units for measurements of weight. However, in most of the cases for the weight on a digital scale, it can be kilogram, gram or pound.

So, it could 10.5 kg or 10.5 g or 10.5 pounds.

Hence, the units of the weight of watermelon on the digital scale could be kilogram, gram and pounds.

To know more about units of weight here

https://brainly.com/question/15908885

#SPJ1

The equation for a hydraulic lift can be used to calculate the force on each mass.  F1 = F2

m2 = 210 kg

Using the equation for a hydraulic lift, the force on each mass can be calculated.

F1 = F2

(m1 x g) x (d1/d2) = (m2 x g)

(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)

210 kg = m2 x 9.8 m/s2

m2 = 210 kg/9.8 m/s2

m2 = 21.43 kg

m2 = 210 kg (rounded up)

The equation for a hydraulic lift can be used to calculate the force on each mass.  F1 = F2

(m1 x g) x (d1/d2) = (m2 x g)

Plug in the given values:

(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)

Solve for m2:

m2 = 210 kg/9.8 m/s2

m2 = 21.43 kg

m2 = 210 kg (rounded up)

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer:3.52x10^-3

Step-by-step explanation:

Answer:

3.52*10^-3

Step-by-step explanation:

The approximate values of the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values represent the values at which the polynomial equation evaluates to zero, indicating the roots of the equation.

To find the roots of a polynomial equation, we set the equation equal to zero and solve for the unknown variable. In this case, we have a polynomial equation with non-integral roots.

To obtain the approximate values of these roots, numerical methods such as iterative methods or numerical approximation techniques can be used. These methods involve making educated guesses and refining the guesses until the equation evaluates to zero.

The resulting approximate values for the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values are not exact, but they are close approximations to the actual roots of the equation.

Learn more about Polynomial equation here :

brainly.com/question/28947270

#SPJ11

Answer:

D

Step-by-step explanation:

4x + 7

this is exactly, 1:1, what the sentence said.

the product of 4 and a number = 4x

is increased by 7 = 4x + 7

The values of the missing angles and sides after dilation are:

m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

Thus, by way of scale factor we can say that:

BC/B'C' = BD/B'D' = 36/18 = 2

B'D' = ¹/₂BD = ¹/₂ * 22 = 11

ΔC'P'Q ∼ ΔCPQ

Thus:

C'Q'/CQ = C'D'/CD = D'Q'/DQ

CQ = 2C'Q' = 2 * 3 = 6

Therefore, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

Read more about transformation at: https://brainly.com/question/4289712

#SPJ1

Radius of the semicircle is 8 km and diameter is 16 km.

What is area of the semicircle?

The area of the semicircle can be determined using the formula,\(A = 1/2 * \pi * r^2\)

The area of a semicircle is given by the formula:

\(A = 1/2 * \pi * r^2\)

where A is the area and r is the radius.

We are given that the area of the semicircle is 32π km². So, we can set up the equation:

\(32\pi = 1/2 * \pi * r^2\)

Simplifying this equation, we get:

r² = (2 × 32π) / π = 64

Taking the square root of both sides, we get:

r = 8 km

So, the radius of the semicircle is 8 km.

The diameter of the semicircle is twice the radius, so:

d = 2r = 2 × 8 km = 16 km

Therefore, the diameter of the semicircle is 16 km.

To know more about area of the semicircle visit,

https://brainly.com/question/15822332

#SPJ1

The numerical value of a dependent variable is dependent on the value of the independent variable. In other words, the numerical value of the dependent variable changes based on the value of the independent variable. For example, in the equation y = 2x + 3, the numerical value of y (the dependent variable) is dependent on the value of x (the independent variable). If x is 1, then the numerical value of y is 5 (2*1 + 3). If x is 2, then the numerical value of y is 7 (2*2 + 3). So, the numerical value of the dependent variable is dependent on the value of the independent variable.

Read more about  dependent variable here:https://brainly.in/question/24870802

#SPJ11

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

To know more about sum visit:

https://brainly.com/question/31538098

#SPJ11

This is because the values of f(x) in the table match the corresponding values obtained by evaluating the polynomial function for the given input values of the function represented by the data a polynomial function is represented by the data is f(x) = x^3 - x^2 - 24.

A polynomial is an expression with more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable. A polynomial function is a function that includes a polynomial expression with an independent variable (x) that can only take on integer values because of its discrete nature.

Choose the function represented by the data: The polynomial function represented by the data is f(x) = x^3 - x^2 - 24.

A table representing the function f(x) = x^3 - x^2 - 24 is shown below:

x | f(x)

0 | -24

1 | -14

2 | 0

4 | 40

Therefore, the function represented by the data is f(x) = x^3 - x^2 - 24.

The provided table displays the values of the function f(x) for different input values of x. By substituting the corresponding values of x into the function, we can observe the corresponding output values. This allows us to identify the pattern and equation that represents the function.

In this case, the table shows that when x is 0, the value of f(x) is -24. When x is 1, f(x) is -14. When x is 2, f(x) is 0. And when x is 4, f(x) is 40.

Based on these data points, we can conclude that the function represented by the data is f(x) = x^3 - x^2 - 24.

Learn more about polynomial function :

brainly.com/question/30474881

#SPJ11

We find that Option 2, f(x) = \((x^3)/4 + 2x^2 - 24\), matches the data given in the table.

Based on the data given in the table, we need to determine the polynomial function that represents the data.
To do this, we can compare the values of f(x) in the table with the given options for the polynomial functions. We are looking for a function that matches the given data points.

Let's evaluate each option using the x-values from the table:
Option 1: f(x) = \(x^3 - x^2 - 24\)
For x = 0,\(f(0) = 0^3 - 0^2 - 24 = -24\) (matches the data)
For x = 1, \(f(1) = 1^3 - 1^2 - 24 = -24 - 1 - 24 = -49\) (does not match the data)
For x = 2,\(f(2) = 2^3 - 2^2 - 24 = 8 - 4 - 24 = -20\) (does not match the data)
Option 2: \(f(x) = (x^3)/4 + 2x^2 - 24\)
For x = 0,\(f(0) = (0^3)/4 + 2(0^2) - 24 = 0 - 0 - 24 = -24\) (matches the data)
For x = 1,\(f(1) = (1^3)/4 + 2(1^2) - 24 = 1/4 + 2 - 24 = -20.75\)(does not match the data)
For x = 2, \(f(2) = (2^3)/4 + 2(2^2) - 24 = 8/4 + 8 - 24 = -14\)(matches the data)
Option 3: f(x) = -24 - 14(3/3)(3/4)
Simplifying, f(x) = -24 - 14(1)(3/4) = -24 - 14(3/4) = -24 - 10.5 = -34.5 (does not match the data)
Option 4: \(f(x) = -2 1/4 * x^2 + 24\)
For x = 0, \(f(0) = -2 1/4 * 0^2 + 24 = 24\) (does not match the data)
For x = 1,\(f(1) = -2 1/4 * 1^2 + 24 = -2 1/4 + 24 = 21.75\) (does not match the data)
For x = 2,\(f(2) = -2 1/4 * 2^2 + 24 = -2 1/4 * 4 + 24 = -9 + 24 = 15\) (does not match the data)
Option 5: \(f(x) = 3/4 * x^2 - 3x + 24\)
For x = 0, \(f(0) = 3/4 * 0^2 - 3(0) + 24 = 24\) (does not match the data)
For x = 1, \(f(1) = 3/4 * 1^2 - 3(1) + 24 = 3/4 - 3 + 24 = 21.75\) (does not match the data)
For x = 2,\(f(2) = 3/4 * 2^2 - 3(2) + 24 = 3/4 * 4 - 6 + 24 = 3 - 6 + 24 = 21\)(matches the data)

Learn more about polynomial function  from the given link:

https://brainly.com/question/1496352

#SPJ11

Answer:

The answer is B.

Step-by-step explanation:

3 times 3 is 9. 2 times -6 is -12. 9 + -12 is -3.

9 times 3 is 27. 4 times -6 is -24. 27 + -24 is 3.

Answer:

Step-by-step explanation:

Factor 49p+42

49p+42

=7(7p+6)

Answer:

7(7p+6)

Answer:

X = 4, x = -7

Step-by-step explanation:

You can set each equation in the parenthesis Equal to 0.

x - 4 = 0 and x + 7 = 0

start with x - 4 =0

add 4 to both sides

x = 4.

then do x +7 =0. subtract 7 from both sides.

x = -7

so x =4, and x = -7

Answer: "x" is 4.5

Step-by-step explanation:

first lets find the leg of the first right triangle using the given leg of 6 and the hypoteneuse of 9 using Pythagorean theorem a^2 + b^2 = c^2.

6^2 + b^2 = 9^2

36 + b^2 = 81

subtract 36 from both sides to isolate b

36 - 36 + b^2 = 81 - 36

simplify

b^2 = 45

take square root of both sides

\(\sqrt{b^{2} }\) = \(\sqrt{45}\)

b = 6.7

Now we can find x of the 2nd right triangle using the know hypoteneuse of 6.7 and the known leg of 5

a^2 + b^2 = c^2

5^2 = b^2 = 6.7^2

25 + b^2 = 44.9

subtract 25 from both sides to isolate b

25 - 25 + b^2 = 44.9 - 25

b^2 = 19.9

take square root of both sides

\(\sqrt{b^2}\) = \(\sqrt{19.9}\)

b= 4.5

so your answer to what is "x" is 4.5

The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

Learn more about circles and circumferences here:

https://brainly.com/question/17130827

#SPJ11

Step-by-step explanation:

Paul behavior is not unethical is that the information is firsthand hand factual and

The graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1

The equation is given as:

y = - 3x + 1

The above equation is a linear function

A linear function is represented as:

y = mx + c

Where m represents the slope and c represents the y-intercept

This means that the graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1

Read more about linear equations at:

https://brainly.com/question/4025726

The null hypothesis will be same as the claim value which is 75%.

What is null hypothesis?

The null hypothesis is a statistical claim that no statistical significance can be found in a set of given observations. To determine the validity of a theory, hypothesis testing is carried out using sample data. Its symbol is H₀, and it is occasionally referred to as simply "the null".

We are given that the claim is that the proportion is less than 75%.

So, the statement of the null hypothesis states that the population value is the same as the claim value.

So,

H₀ : p = 75% = 0.75

If this null hypothesis is correct, then 75% of all students at the researcher's school finished their homework assignments last night.

Hence, this will mean that the null hypothesis is true.

Learn more about null hypothesis from the given link

https://brainly.com/question/15980493

#SPJ1

Question: No homework? Refer to Exercise 1. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265.

Explain what it would mean for the null hypothesis to be true in this setting.

Answer:

q<-56

Step-by-step explanation:

explanation is in the image above

Answer:

We need to know how many students are in sixth grade and compare the real number with the 84 sixth graders that Jasmine claims to be.

Step-by-step explanation:

We would need to know how many students are in sixth grade to determine who is right. If two students out of seven have an overdue library book and grace claims that 24 of them are overdue by that means, what we would need to do is divide the allegedly 24 students between 2. Now we have 12 pairs of students that have overdue books. For every pair of students in sixth grade that have overdue books, seven students don’t have overdue books, so now we multiply 12 pairs of students with overdue books times 7 students who don’t have overdue books. By Jasmine calculation then, sixth grade have 84 students.  

If sixth grade have indeed 84 students, Jasmine is right. If there are not 84 students in sixth grade, she is wrong. Grace is right if there are fewer students than 84 in sixth grade.

Answer:

H = 3.5m + 90

m = 12 months

Step-by-step explanation:

We can use a linear equation (H = 3.5m + 90), where H is the height in centimeters and m is month.

We can let H = 132 to solve for m:

\(132=3.5m+90\\42=3.5m\\12=m\)

Thus, it will take the boy 12 months to reach 132 cm.

On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts

data across time numbers about the population

The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.

Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

To know more about statistical data visit:

https://brainly.com/question/14893265

#SPJ4

The athlete that has the shortest training ride is athlete A.

The athlete that has the shorter range is Athlete B.

The athlete that has the greater median is Athlete B.

The athlete that has the greater IQR is  athlete A.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.

Range of Athlete A = 36 - 13 = 13

Range of Athlete B = 30 - 19 = 11

Training ride of  Athlete A = 16

Training ride of  Athlete B = 21

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median of  Athlete A = 20

Median of  Athlete B = 25

IQR of  Athlete A = 30 - 16 = 14

IQR of  Athlete B = 28 - 21 = 7

To learn more about box plots, please check: https://brainly.com/question/27215146

#SPJ1

A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.

The problem can be solved using the average value approach.

Average value = total amount or sum of data / number of data

In the given problem,

total amount = total coffee served last year

total amount = 40,000

number of data = number of hours in a year

number of data = 365 day/year x 24 hours/day = 8760 hours

Hence,

Average value = total amount or sum of data / number of data

                         = 40000 / 8760

                         = 4,6 ≈ 5 (round to the nearest whole cup)

Hence, the average coffee served is 5 cups per hour.

Learn more about average here:

https://brainly.com/question/28254231

#SPJ4