The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y plus 7 equals negative StartFraction 2 over 5 EndFraction left-parenthesis x minus 10 right-parenthesis.. What is the standard form of the equation for this line?

Answer:

10

Step-by-step explanation:

multiply both numbers by same number

Answer:

-51

Step-by-step explanation:

Let's do order of operations.

10+8-70-(-1)     <- We did negative 7 times 10.

18-70-(-1)    <- We did 10 plus 18.

-52-(-1)     <- We did 18 minus 70

When you open the () we get:

-52--1

Negative minus a negative equals a positive.

-52+1=

-51

Answer:

If im correct it actually equals 18x because you add the like terms.

Step-by-step explanation:

it equals 18x because you add the like terms.

Step-by-step explanation:

. .                 . .               . .                . .

Answer:

Yes

Step-by-step explanation:

Roberto 4:6 = 2:3

divisor 2. 4/2=2  6/2=3

Casey 6:9 = 2:3

divisor 3

6/3=2   9/3=3

Final answer:

The inverse of the function f(x) = 3x^8 + 1 is found by reversing the operations: subtract 1, divide by 3, and take the eighth root. The correct equation for the inverse is f⁻¹(x) = ⁸√((x - 1) / 3), which simplifies to f⁻¹(x) = ((x - 1) / 3)^(1/8). The options provided do not match this result.

Explanation:

The question asks for the equation of the inverse of the given function f(x) = 3x^8 + 1. To find the inverse function, f⁻¹(x), we must reverse the operations of the original function on x. First, you would subtract 1 from both sides to undo the addition, and then divide by 3 to undo the multiplication, followed by taking the eighth root to reverse the exponentiation. The correct inverse function will therefore reverse all these operations in that order.

Here's the step-by-step solution:

Start with y = 3x^8 + 1

Subtract 1 from both sides: y - 1 = 3x^8

Divide both sides by 3: (y - 1) / 3 = x^8

Take the eighth root of both sides: x = ⁸√((y - 1) / 3)

Therefore, the inverse function is f⁻¹(x) = ⁸√((x - 1) / 3), which simplifies to f⁻¹(x) = ((x - 1) / 3)^(1/8). However, none of the options provided fully match this result, implying there might be a typo or mistake in the question or options provided.

Answer:

Step-by-step explanation:

first question:

angles opposite to equal sides are equal

angle a + angle b + angle c =180

angle a = angle b

2 * angle B + angle c = 180

2* angle B = 128

angle B = 44

Answer:

He lost 7 dollars

Step-by-step explanation:

In Luke’s business, total loss in business during three days = $7

The profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.

The amount the seller incurs after selling the product less than its cost price is mentioned as a loss.

Given,

Loss on Monday = $15

Profit on Tuesday = $8

On Wednesday, no profit or loss

Total profit or loss = Profit + ( - loss)

=$8+(-$15)

= -$7

Hence, there was total loss of $7 during three days in Luke’s business.

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Answer:

[tex]Distance\ cover\ by\ Rosa = 141.3\ m[/tex]

Step-by-step explanation:

Given:

Rosa has to skate around a face off circle five times.

[tex]Distance = 5\times circumfrance\ of\ circle[/tex]

Diameter of a circle = 9.0 m

Radius of a circle = [tex]\frac{d}{2} =\frac{9}{2}=4.5\ m[/tex]

Solution:

We know that the circumference of a circle.

[tex]C = 2\pi r[/tex]

Where;

r = Radius of a circle

Substitute [tex]\pi =3.14\ and\ r = 4.5[/tex] in above equation.

[tex]C = 2\times 3.14\times 4.5[/tex]

[tex]C = 28.26\ m[/tex]

So, the circumference of the circle is 28.26 m.

Rosa has to skate around a face off circle five times, so Rosa cover 28.26 m 5 times.

[tex]Distance\ cover\ by\ Rosa = 5\times 28.26[/tex]

[tex]Distance\ cover\ by\ Rosa = 141.3\ m[/tex]

Therefore, the distance cover by Rosa to skate 141.3 m.

Rosa has to skate approximately 141.35 meters to go around the face off circle with a diameter of 9.0m five times.

To calculate how far Rosa has to skate, we need to determine the circumference of the face off circle, which can be calculated using the formula C = pi × d, where C is the circumference and d is the diameter of the circle. Since Rosa skates around the circle five times, we will multiply the circumference by five.

Given that the diameter (d) of the face off circle is 9.0 meters, the circumference is:

Now, we calculate the total distance Rosa skates by going around the circle five times.

Total distance = Circumference × Number of laps

Total distance = 28.27m × 5 = 141.35m

Therefore, Rosa has to skate approximately 141.35 meters around the face off circle.

Answer : $8

Step-by-step explanation:

24 divided by 3 equals 8

Answer:

Step-by-step explanation:

Final answer:

The shortest distance from the park to the library, forming a right-angled triangle with sides of 6 miles and 11 miles, can be found using the Pythagorean theorem, and it is approximately 12.5 miles when rounded to the nearest half mile.

Explanation:

The question involves finding the shortest distance from the park to the library. This is a basic problem of geometry that can be solved using the Pythagorean theorem. Since the park is 6 miles due west of your house and the library is 11 miles north, we can form a right-angled triangle with one side as 6 miles and the other side as 11 miles.

We find the shortest distance by calculating the hypotenuse of the right-angled triangle:

Represent the distances as sides of a triangle: one leg is 6 miles (west) and the other is 11 miles (north).

Apply the Pythagorean theorem: hypotenuse2 = 62 + 112

Calculate the hypotenuse: hypotenuse = √(62 + 112) = √(36 + 121) = √157

Find the nearest half mile: √157 is approximately 12.53. So rounded to the nearest half mile, the distance is 12.5 miles.

Therefore, the shortest distance from the park to the library is about 12.5 miles.

Answer:

20,602 feet is the difference in height between the top of Mt. McKinley and the bottom of the Death Valley.

Step-by-step explanation:

Given:

Mt. McKinley, which is the highest elevation in North America, is 20,320 feet above sea level.

Death Valley, which is the lowest elevation in North America, is 282 feet below sea level.

Now, to find the difference in height between the top of Mt. McKinley and the bottom of the death valley.

Height of Mt. McKinley above sea level = 20,320 feet.

Height of Death Valley below sea level = 282 feet.

Now, to get the difference in height between the top of Mt. McKinley and the bottom of the Death Valley by adding both the heights:

[tex]20320+282[/tex]

[tex]=20602\ feet.[/tex]

Therefore, 20,602 feet is the difference in height between the top of Mt. McKinley and the bottom of the Death Valley.

Answer:

20,602 feet.

Step-by-step explanation:

Answer:

1/1 9

Step-by-step explanation:

ok

The equation that represents the relationship between Anne's age and Betty's age is a = 2b - 3. The equation indicates that Anne's age is 3 years less than twice Betty's age.

The relationship between Anne's age and Betty's age is expressed through the given information: 'Anne is 3 years younger than twice Betty's age'. This can be translated into an equation using 'a' to represent Anne's age and 'b' to represent Betty's age. Accordingly, the equation becomes a = 2b - 3.

The equation shows that to get Anne's age, you have to double the age of Betty and then subtract 3 years. For example, if Betty was 10 years old, Anne would be 2*10 - 3 = 17 years old.

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The amount of money in account after 8 years is $ 111569.36

Solution:

Given that, Suppose that 70,000 is invested at 6% interest

We have to find the amount of money in the account after 8 years if the interest is compounded annually

Formula for Amount compounded annually is as follows:

[tex]\mathrm{A}=P\left(1+\frac{r}{100}\right)^{n}[/tex]

Where,

"A" is the total amount after "n" years

"P" is the principal

"r" is the rate of interest

"n" is the number of years

Here in this sum,

P = 70000

r = 6 %

n = 8 years

Substituting the values in formula,

[tex]A = 70000(1+\frac{6}{100})^8\\\\A = 70000(1+0.06)^8\\\\A =70000 \times 1.06^8\\\\A = 70000 \times 1.59384\\\\A = 111569.36[/tex]

Therefore, the amount of money in account after 8 years is $ 111569.36

When $70,000 is invested at an annual interest rate of 6%, compounded annually for 8 years, the amount in the account will grow to approximately $104,613.78.

This question asks you to calculate future investment value when $70,000 is invested at 6% interest, compounded annually for 8 years. The formula we use for compound interest is A = P(1 + r/n)^(nt), where 'A' is the amount of money accumulated after n years, 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal), 'n' is the number of times that interest is compounded per year, and 't' is the time the money is invested for in years.

Since it's compounded annually, n equals to 1. So the formula now becomes A = P(1 + r)^(t). Plug in the given amounts into the formula: A = 70000(1 + 0.06)^(8). Solving this equation, we find that the amount of money in the account after 8 years will be approximately $104,613.78.

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Answer:

n = 0

Step-by-step explanation:

Answer:

the required ans is 48

Step-by-step explanation:

given,

15-n/6 =n/6-1

or,15-n/6-n/6=-1

or,15-2n/6=-1

or,-2n/6=-1-15

or,-2n/6=-16

or,-2n=-96

or,n= -96/-2

therefore,n=48.

henece the required value of n is 48.

explanation in word.

firstly we write the question.

n/6 of right side bring ti the left side and being negative.

we solve -n/6-n/6 by sing LCM method.

again, we bring 15 to the right side of tge queation and being negative

in 6 step there is in multiply so when we bring that multiply in left side it become in divide. we can find the answer this way

Answer:

He needs to pay back $64

Step-by-step explanation:

He has already paid $4802, and according to the chart that goes with this question, he owed $4866.

What he owes: $4866

subtract what he has paid: $4802

4866-4802=64

So he needs to pay the IRS $64

You can use subtraction here to get to the correct option.

The correct option for the given condition is

Option A: He will pay $64

Since the chart that goes along with the given question says that  Yung had to give $4866 for the taxes, and since it is given that Yung already paid $4802, we see that he didn't paid full tax yet since 4802 < 4866.

So he has to pay the remaining amount of the tax.

To get the remaining amount he has to pay, we will use subtraction.

Thus:

Remaining amount = Total amount to pay - amount already paid

Remaining amount = $4866 - $4802 = $64

Thus,

The correct option for the given condition is

Option A: He will pay $64

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Answer:

Step-by-step explanation:

39 = x - 12

Adding 12 to both side

39 + 12 = x - 12 + 12

51 = x

X = 51

Answer:

Zora should have added 12 to both sides of the equation instead of subtracting.

Step-by-step explanation:

          シ︎

Answer:

[tex]New\ level\ of\ cholesterol = 192[/tex]

Step-by-step explanation:

Given:

Reduced level of cholesterol = 20%

Original level of cholesterol = 240

We need to find cholesterol level now

Solution:

First we find reduced level of cholesterol using percentage formula.

[tex]Percentage = \frac{Value}{Toatl\ value}\times 100[/tex]

Substitute all known value in above formula.

[tex]20 = \frac{Value}{240}\times 100[/tex]

[tex]Value = \frac{20\times 240}{100}[/tex]

[tex]Value = \frac{4800}{100}[/tex]

[tex]value = 48[/tex]

So reduced level of cholesterol = 48

But we need to find cholesterol level now, so we subtract reduced level from original level of cholesterol.

[tex]New\ level = original\ level - reduced\ level[/tex]

[tex]New\ level = 240 -48[/tex]

[tex]New\ level = 192[/tex]

Therefore, Cholesterol level at present = 192

Answer:

see attached picture please

Answer:

slope = dY/dX

Step-by-step explanation:

dY/dX = (-2 - 6 ) / (4 - 0)

dY/dX = -2

Answer:

see the attached picture please

Answer:

The y-intercept represent Height

Step-by-step explanation:

In a graph the independent variable is plotted on the  X axis and attain only certain discrete values. The Dependent variable is plotted against the Y axis and may be discrete or continuous.

Here in the given question

Days:    2,5,8,12,18,22,25,30,32,35

Height: 3,4,6,9,13,15,16,20,21,24

The height is a dependant variable because we are trying to determine a relationship between the Days and the height. In particular, we are trying to see how the height depends upon what day it is or what is the height of the pant on the particular day.

The day can be only discrete values where height can be both discrete and continuous.

So height can be represented along Y axis

Answer:

Step-by-step explanation:

The relation that the problem shows is between Days (x) and Height (y).

Remember that a y-incercept is a point with the form (0, k), where k is a real number.

In this case, the y-intercept represents the height of a tomato plant at day zero. In other words, it represents the initial condition, the height at the beginning of the experiment.

To find the number of robberies this year, we need to calculate 14% of last year's total and subtract it from that total. This results in an estimated 286 robberies this year.

The question asks for the number of robberies this year given a 14% decrease from the prior year's total of 332 robberies. To calculate this, you would multiply last year's number of robberies by 14% (or 0.14) to find the decrease in robberies. Then, subtract this decrease from the original number of robberies.

First, calculate the decrease: 332 * 0.14 = 46.48. This rounds down to 46 robberies, as it would be unlikely to have a fraction of a robbery.

Next, subtract this from the original amount: 332 - 46 = 286. There were approximately 286 robberies this year, rounded to the nearest whole number, assuming a 14% decrease from 332.

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Answer:

1) The slope of the function [tex]g(x)[/tex] is [tex]0[/tex] and the slope of the function [tex]f(x)[/tex] is [tex]-1[/tex].

2) The negative slope of the function [tex]f(x)[/tex] shows that it is the line is increasing and the slope [tex]0[/tex]  of the function  [tex]g(x)[/tex]  shows that the line will always have the same y-coordinate.

3) The slope of the function is [tex]f(x)[/tex] is greater than the slope of the function  [tex]g(x)[/tex].

Step-by-step explanation:

 For this exercise you need to know that the slope of any horizontal line is zero ([tex]m=0[/tex])

The slope of a line can be found with the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

You can observe in the graph of the function  [tex]g(x)[/tex]  given in the exercise, that this is an horizontal line.  Then,  you can conclude that its slope is:

[tex]m=0[/tex]

The steps to find the slope of the function [tex]f(x)[/tex] shown in the table attached, are the following:

- Choose two points, from the table:

[tex](0,3)[/tex] and [tex](4,-1)[/tex]

- You can say that:

[tex]y_2=-1\\y_1=3\\\\x_2=4\\x_1=0[/tex]

- Substitute values into the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]:

[tex]m=\frac{-1-3}{4-0}[/tex]

- Finally, evaluating, you get:

[tex]m=\frac{-4}{4}\\\\m=-1[/tex]

Therefore:

1) The slope of the function [tex]g(x)[/tex] is [tex]0[/tex] and the slope of the function [tex]f(x)[/tex] is [tex]-1[/tex].

2) The negative slope of the function [tex]f(x)[/tex] shows that it is the line is increasing and the slope [tex]0[/tex]  of the function  [tex]g(x)[/tex]  shows that the line will always have the same y-coordinate.

3) The slope of the function is [tex]f(x)[/tex] is greater than the slope of the function  [tex]g(x)[/tex].

Answer:

It D

Step-by-step explanation:

Answer:

It's D

Step-by-step explanation:

I did it on UsaTestPrep

Answer:

Thus, the equivalent expression in standard form is:

⇒ [tex]-23.9m+121.1n[/tex]

Step-by-step explanation:

Given expression:

[tex](-87.9m+35.1n)+(64m+86n)[/tex]

To give the equivalent expression in standard form.

Solution:

In order to find the equivalent expression in standard form we will simplify the expression.

We have:

[tex](-87.9m+35.1n)+(64m+86n)[/tex]

Simplifying by removing parenthesis.

⇒ [tex]-87.9m + 35.1n+ 64m + 86n[/tex]

Combining like terms.

⇒ [tex]-87.9m+64m + 35.1n + 86n[/tex]

⇒ [tex]-23.9m+121.1n[/tex]

Thus, the equivalent expression in standard form is:

⇒ [tex]-23.9m+121.1n[/tex]

Answer:

k=-5

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]6x^{2} +7x+k=0[/tex]  

so

[tex]a=6\\b=7\\c=k[/tex]

substitute in the formula

[tex]x=\frac{-7\pm\sqrt{7^{2}-4(6)(k)}} {2(6)}[/tex]

[tex]x=\frac{-7\pm\sqrt{49-24k}} {12}[/tex]

so

[tex]x_1=\frac{-7+\sqrt{49-24k}} {12}[/tex]

[tex]x_2=\frac{-7-\sqrt{49-24k}} {12}[/tex]

Remember that

[tex]2x_1+3x_2=-4[/tex]

substitute

[tex]2(\frac{-7+\sqrt{49-24k}} {12})+3(\frac{-7-\sqrt{49-24k}} {12})=-4[/tex]

[tex](\frac{-14+2\sqrt{49-24k}} {12})+(\frac{-21-3\sqrt{49-24k}} {12})=-4[/tex]

Multiply by 12 both sides

[tex](-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48[/tex]

[tex]-35-\sqrt{49-24k}=-48[/tex]

[tex]\sqrt{49-24k}=48-35[/tex]

[tex]\sqrt{49-24k}=13[/tex]

squared both sides

[tex]49-24k=169\\24k=49-169\\24k=-120\\k=-5[/tex]

therefore

The equation is

[tex]6x^{2} +7x-5=0[/tex]  

The roots are

[tex]x=\frac{-7\pm\sqrt{49-24(-5)}} {12}[/tex]

[tex]x=\frac{-7\pm\sqrt{169}} {12}[/tex]

[tex]x=\frac{-7\pm13} {12}[/tex]

[tex]x_1=\frac{-7+13} {12}=\frac{1} {2}[/tex]

[tex]x_2=\frac{-7-13} {12}=-\frac{5} {3}[/tex]

Final answer:

To find the constant k, use Vieta's formulas to express x_1 and x_2 in terms of the equation coefficients, then solve the given equation 2x_1+3x_2=−4 to find individual values for x_1 and x_2, and use these values to determine k through the product of the roots.

Explanation:

The student needs to find the constant k in the equation 6x^2+7x+k=0, given that x_1 and x_2 are roots of this equation, and that 2x_1+3x_2=−4. According to Vieta's formulas, which relate the roots of a polynomial to its coefficients, the sum of the roots is −(b/a) and the product of the roots is (c/a). Since the coefficient of x^2 (a) is 6 and the coefficient of x (b) is 7, we can state that x_1 + x_2= −7/6 and x_1x_2 = k/6.

Using the second given condition, 2x_1+3x_2=−4, we can substitute x_2 from the first Vieta's formula: x_2= −(7/6)−x_1, and plug this into the second condition to get 2x_1+3(−(7/6)−x_1)=−4. Simplifying, we find a value for x_1. We then substitute this x1 back into the expression for x_2 to find its value. With both x_1 and x_2 found, we use the product of the roots to find k: k = 6(x_1x_2).

The percentage of the students that like country and also in grades 9-10 is 61%

Step-by-step explanation:

                          Rap    Rock   Country   Total

Grades 9-10       40        30          55          125

Grades 11-12     60        25          35          120

Total                  100       55          90          245

Percentage= (Number of students in both country and grades/ Total students in country)*100

Total students in country= 90

Number of students in both country and grades 9-10= 55

Percentage= (55/90)*100

                   = 61.11%= 61%(rounded to the nearest whole %)

Answer:

D 61%

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

slope = difference of y/ difference of x

m = (9-5) / (4-2) = 4/2 = 2

Answer:

The common difference (or common ratio) = 0.75

Step-by-step explanation:

i) let the first term be [tex]a_{1}[/tex] = 80

ii) let the second term be [tex]a_{2}[/tex]  = [tex]a_{1}[/tex] . r = 80 × r = 60      ∴  r = [tex]\frac{60}{80}[/tex] = 0.75

iii) let the third term be     [tex]a_{3}[/tex]  = [tex]a_{2}[/tex] . r = 60 × r = 45      ∴  r = [tex]\frac{45}{60}[/tex] = 0.75

iv) let the fourth term be   [tex]a_{4}[/tex] = [tex]a_{3}[/tex] . r = 45 × r = 33.75   ∴ r = [tex]\frac{33.75}{45}[/tex] = 0.75

Therefore we can see that the series of numbers are part of a geometric progression and the first term is 80 and the common ratio = 0.75.

Answer:

$95.38

Step-by-step explanation:

step 1

Find the area of one button

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=9/2=4.5\ cm[/tex] ---> the radius is half the diameter

Convert to meters

[tex]r=4.5\ cm=4.5/100=0.045\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(0.045)^{2}\\A=0.0063585\ m^2[/tex]

step 2

Find the area of 1,00 buttons

Multiply by 1,000

[tex]A=0.0063585(1,000)=6.3585\ m^2[/tex]

step 3

Find the cost

Multiply $15 per square meter by the total area of 1,000 buttons

[tex](15)6.3585=\$95.38[/tex]