Write a linear equation that passes through the points (-3,3) and (9,-13)

please help!

Answers

Answer 1

The equation of the line that passes through the given points is 3y + 4x = -3

From the question,

We are to determine the equation of the line that passes through the points (-3,3) and (9,-13)

The equation can be determined by using the formula for calculating the equation of a line with two given points.

The formula for determining the equation of a straight line with two given points (x₁, y₁) and (x₂, y₂) is

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

From the question,

x₁ = -3

y₁ = 3

x₂ = 9

y₂ = -13

Putting the parameters into the formula, we get

[tex]\frac{y-3}{x--3}= \frac{-13-3}{9--3}[/tex]

This becomes

[tex]\frac{y-3}{x+3} = \frac{-16}{12}\\[/tex]

Then,

[tex]\frac{y-3}{x+3}=\frac{-4}{3}[/tex]

This becomes

[tex]3(y-3) = -4(x+3)[/tex]

Clearing the brackets, we get

[tex]3y -9 = -4x -12[/tex]

[tex]3y+4x= -12 +9[/tex]

[tex]3y +4x =-3[/tex]

Hence, the equation of the line that passes through the given points is 3y + 4x = -3

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Answer 2
Final answer:

The linear equation that passes through the points (-3,3) and (9,-13) can be found by first calculating the slope (m) using the formula (y2 - y1) / (x2 - x1), giving m = -4/3. Next, substitute one of the points and the slope into the slope-intercept form of a linear equation, y = mx + b, to solve for the y-intercept (b), resulting in b = -1. Thus, the desired linear equation is y = -4/3x - 1.

Explanation:

To write a linear equation that passes through two points (-3,3) and (9,-13), we first need to find the slope (m) of the line. The formula to find the slope is (y2 - y1) / (x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Therefore, m = (-13 - 3) / (9 - (-3)) = -16/12 = -4/3.

Next, we use the slope-intercept form of a linear equation, y = mx + b where 'm' is the slope, and 'b' is the y-intercept. We can substitute one of our points and the slope into this equation to solve for b. Let's use the point (-3,3). So, 3 = (-4/3)*(-3) + b. This simplifies to 3 = 4 + b. Solving for b gives b = 3 -4 = -1.

Therefore, the linear equation that passes through the points (-3,3) and (9,-13) is y = -4/3x - 1.

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Related Questions

Please please help me out!!!

Answers

Answer: 8.50 dollars

The result is positive, so this is a gain (instead of a loss)

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

Explanation:

Focus on the "stock JKL" row only when it comes to the percentages we'll use. We need to convert them to decimal form

15% ---> 0.15

65% ---> 0.65

20% ---> 0.20

I just moved the decimal point over 2 spots, or you can divide by 100 (eg: 15% = 15/100 = 0.15)

Multiply each of these values by their corresponding loss or gain. Use negative numbers for losses

15% chance of losing $25 ---> 0.15*(-25) = -3.75

65% chance of winning $5 ---> 0.65*(5) = 3.25

20% chance of winning $45 ---> 0.20*(45) = 9

Now add up those results: -3.75+3.25+9 = 8.50

When the lights go out at the store at night there's a 15% off sign hanging out by the make up counter what is a number as a decimal and a fraction in simplest form

Answers

Answer:

As per the given statement: when the lights go out at the store at night there's a 15% off sign hanging out by the make up counter.

To find the number as a decimal and a fraction in simplest form.

Given the Number = 15%.

If we convert any number from percent to decimal divide by 100 and remove the % sign.

[tex]\frac{15}{100} = 0.15[/tex]

Then the given number in decimal is, 0.15

Now, to convert this percent into fraction;

[tex]\frac{15}{100}[/tex]

Divide both numerator and denominator by 5 to get;

[tex]\frac{\frac{15}{5} }{\frac{100}{5} } = \frac{3}{20}[/tex]

Therefore, the given number in fraction is; [tex]\frac{3}{20}[/tex]



help please
I WILL MARK YOU BRAINLYEST if you answer all of my problems !!!!!!!!!!!


Solve the system of linear equations by substituting. Check your solution


4# y=5x-7

-3x-2y=-12


5# -4x+y=6

-5x-y=21


6# -7x-2y=-13

x-2y=-13

Answers

Answer:

4. x=2 y=3

5. x=-3, y=-6

6. x=0, y=6.5

Step-by-step explanation:

A system of equations is 2 or more equations for which the same x,y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. To use substitution, we substitute a equivalent expression in for a variable and solve for the remaining variable. We then substitute again to find the other variable.

y=5x-7  & -3x-2y=-12

We will input for y, the expression 5x-7 into -3x-2y=-12. We will then isolate x to solve for it using inverse operations.

-3x-2(5x-7)=-12

-3x-10x+14=-12

-13x+14=-12

-13x+14-14=-12-14

-13x=-26

x=2

We substitute back in now to solve for y. y=5(x)-7=5(2)-7=10=7=3

-4x+y=6  & -5x-y=21

We will input for y, the expression 6+4x into -5x-y=21. We will then isolate x to solve for it using inverse operations.

-5x-(4x+6)=21

-5x-4x-6=21

-9x-6=21

-9x-6+6=21+6

-9x=27

x=-3

We substitute back in now to solve for y. y=4(x)+6=4(-3)+6=-12+6=-6

-7x-2y=-13  & x-2y=-13

We will input for x, the expression 2y-13 into -7x-2y=-13. We will then isolate y to solve for it using inverse operations.

-7(2y-13)-2y=-13

-7(2y)+-7(-13)-2y=-13

-14y+91-2y=-13

-16y+91=-13

-16y+91-91=-13-91

-16y=-104

y=6.5

We substitute back in now to solve for x. x=2y-13=2(6.5)-13=13-13=0.

700,000,000 + 10,000,000 + 1,000,000 + 40,000 + 2,000 + 200 + 7 in standared form

Answers

Answer:

711,042,207 is the standard form.

Step-by-step explanation:

The expanded form can be compressed by simply adding the numbers together. When you add each of these together, you get the number above.

Can someone explain how to get to answer B?

Answers

Yo have to find the distance between point L and point M. First, you have to do the x values. 1 - -3 = 4. Then, you subtract the y values. -2 - 4 = -6. Next, you add the found numbers to the x and y of the midpoint (m). Leaving 1 +4=5 and -2 + -6 = -8.

(5,-8)

Marta put $4.87 in her coin bank. Each day she added 1 quarter, 1 nickel, and 3 pennies. How much money was in her coin bank after 6 days? Describe the partten you used to solve

Answers

Answer:

$0.25+$0.05+$0.03=$0.33

$0.33•6=$1.98

$1.98+$4.87=$6.85

Step-by-step explanation:


I really need help with the questions following this one.

Answers

9.

[tex]\begin{array}{c|c}\underline{Statement}&\underline{Reason}\\1. SJ=FJ&\text{1. Given}\\2.KS=3, KF=3&\text{2. Given}\\3.KS=KF&\text{3. Transitive Property}\\4.\angle SJK = \angle FJK&\text{4. Congruent sides }\\5.JK=JK&\text{5. Reflexive Property}\\6. \triangle SJK \cong \triangle FJK&\text{6. Side-Angle-Side Theorem}\\\end{array}[/tex]


10.

[tex]\begin{array}{c|c}\underline{Statement}&\underline{Reason}\\1.MA || TH&\text{1. Given}\\2. \angle MAX \cong \angle THX&\text{2. Alternate Interior Angles}\\ \text{3. x is midpoint of AH}&\text{3. Given}\\4.AX \cong HX&\text{4. Deefinition of midpoint}\\5. \angle AXM \cong \angle HXT&\text{5. Vertical angles}\\6. \triangle MAX \cong \triangle THX&\text{Angle-Side-Angle Theorem}\\\end{array}[/tex]

help? anyone please thank youuuuuuuuu

Answers

Is it asking about the slope of this vertical line? if so, then the answer is "undefined". The rise is any number you want, let's say 1, and the run is 0

slope = rise/run = 1/0 = undefined

you cannot divide by zero

A theme park has a tram that goes around the 2.5-mile perimeter of the park in 10 minutes. The equation s • (16) = 2.5 gives the speed of the tram. What exactly does s represent?

Answers

s in the expression s • (16) = 2.5  represents the speed in miles per hour.

What is speed?

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
A theme park has a tram that goes around the 2.5-mile perimeter of the park in 10 minutes.
So,
Speed = 2.5 miles / 10 minutes

Since, 1 hour = 60 minutes,
And 1 minute = 1/60 hours,

Now, converting the unit of speed of tram from miles per minute to miles per hour where,
Speed = 2.5 miles / 10 (1/60 hours)
Speed = s (say)

s = 2.5/ (1/6)
s (1/6) = 2.5

hence, s in the above expression represents the speed.

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Final answer:

The symbol 's' in the equation represents the speed of the tram in miles per minute

Explanation:

The student's question involves solving for the speed s of a tram that goes around the perimeter of a theme park. The equation provided is s (16) = 2.5, where s represents the speed of the tram in miles per minute. To find the value of s, we need to divide both sides of the equation by 16, which yields:

s = 2.5 / 16

Now, performing the division gives us:

s = 0.15625

Therefore, the speed of the tram is 0.15625 miles per minute.

PLS HELP ASAP!! Which value of x makes 7 + 5(x - 3) = 22 a true statement? khan academy

A) x = 4
B) x = 5
C) x = 6
D) x = 7

Answers

Answer:

The Answer is c) 6

Step-by-step explanation:

Solve for x:

5 (x - 3) + 7 = 22

5 (x - 3) = 5 x - 15:

5 x - 15 + 7 = 22

Grouping like terms, 5 x - 15 + 7 = 5 x + (7 - 15):

5 x + (7 - 15) = 22

7 - 15 = -8:

5 x + -8 = 22

Add 8 to both sides:

5 x + (8 - 8) = 8 + 22

8 - 8 = 0:

5 x = 22 + 8

22 + 8 = 30:

5 x = 30

Divide both sides of 5 x = 30 by 5:

(5 x)/5 = 30/5

5/5 = 1:

x = 30/5

The gcd of 30 and 5 is 5, so 30/5 = (5×6)/(5×1) = 5/5×6 = 6:

Answer:  x = 6

Answer:

x=6

Step-by-step explanation:

7 + 5(x - 3) = 22

The first step is to distribute the 5

7+ 5x-5*3 =22

7+ 5x-15 =22

Combine like terms

5x-8 =22

Add 8 to each side

5x-8+8 =22+8

5x = 30

5x/5 = 30/5

x=6


Keith and jolene raised 152.75 to buy shirts for new players on their softball teams. Jolene needs to buy four shirts for her team. Each shirt will cost 11.75. Write an equation that can be used to determine the maximum number of shirts Keith can buy for his team in addition to the four shirts jolene needs to buy. What is the maximum number of shirts keith can buy for his team in addition to the four shirts jolene needs to buy>

Answers

First, you should multiply 11.75 by 4 to include the shirts that Jolene needs to buy. then, add 11.75x to the equation and it should look like this:
[tex]47 + 11.75x = 152.75[/tex]
Next, subtract 47 on each side of the equation.
[tex]11.75x = 105.75[/tex]
Finally, divide each side by 11.75. Keep in mind that x isn't the only variable you can use.

You should get x=9, which is the number of shirts Keith can buy.

Answer: x=9

Step-by-step explanation:

First, you should multiply 11.75 by 4 to include the shirts that Jolene needs to buy. then, add 11.75x to the equation and it should look like this:

Next, subtract 47 on each side of the equation.

Finally, divide each side by 11.75. Keep in mind that x isn't the only variable you can use.

You should get x=9, which is the number of shirts Keith can buy.

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Gloria has a job of clearing a vacant lot that is 40 yards long and 25 yards wide. She can clear 12 square yards a day. Gloria wants to know how long it will take to clear the entire lot. Which formula would most help you solve this problem?

Answers

Answer: [tex]83\dfrac{1}{3}\ \text{days}[/tex]

Step-by-step explanation:

[tex]\dfrac{40\ \text{yards} \cdot \ 25\ \text{yards} }{12\ \text{yards}^2} = \dfrac{1000\ \text{yards}^2}{12\ \text{yards}^2}=\dfrac{1000}{12}=\dfrac{250}{3}=83\dfrac{1}{3}[/tex]

Answer:

Formula for the area of a rectangle

Your welcome:) TTM

You buy clothing at a sale.You buy sneakers at 2/3 of their original price of $60, a sweater at 7/10 of it original price of $35, and a jacket at 5/6 of its original price of $45.

a. How much money did you spend?

b. How much money did you save?

c. What fraction of the total original price did you save?

Answers

Answer:

a. $102  b. $38  c. 19/70.

Step-by-step explanation:

a. You spent  2/3 * 60 + 7/10 * 35 + 5/6 * 45

= $102.

b. Cost before the sale discount = 60 + 35 + 45 = $140 , so the amount you saved = 140 - 102 = $38.

c.  Fraction on original price saved = 38/140 = 19/70.

Money spent is $102. Money saved is $38. The fraction of the total original price saved is 19/70.

a. How much money did you spend?

Sneakers: 2/3 of $60 = $40

Sweater: 7/10 of $35 = $24.50

Jacket: 5/6 of $45 = $37.50

Total spent = $40 + $24.50 + $37.50 = $102

b. How much money did you save?

Original total price = $60 + $35 + $45 = $140

Amount saved = $140 - $102 = $38

c. What fraction of the total original price did you save?

Fraction saved = Amount saved / Total original price = $38 / $140 = 19/70

When tyrell buys the regular school lunch he spends $2.75. On some days he buys ala carte he spends $4.85. How much dose tyrell spend if he buys the regular school lunch 9 days and buys ala carte 4 days

Answers

Answer:

$44.15 spend by tyrell if he buys the regular school lunch 9 days and buys ala carte 4 days .

Step-by-step explanation:

As given

When Tyrell buys the regular school lunch he spends $2.75.

On some days he buys ala carte he spends $4.85.

Tyrell buys the regular school lunch 9 days and buys ala carte 4 days.

Than

Tyrells spends money when he buys regular school lunch 9 days and ala carte 4 days = 9 × 2.75 + 4 × 4.85

                    = 24.75 + 19.4

                    = $44.15

Therefore $44.15 spend by tyrell if he buys the regular school lunch 9 days and buys ala carte 4 days .

A tiger can eat food that weighs up to 15% of its body weight.If a tiger can eat 75 pounds of food, how much does a tiger weigh?

Answers

Answer:

500 pounds

Step-by-step explanation:

By proportion :-

15% of the tigers weight   = 75 pounds

1%    ....................................   = 75/15 pounds

100% ..................................   = 75*100 / 15 pounds

= 7500 / 15

= 500 pounds


Write an equation for the line that has a y-intercept of 2 and is perpendicular to the line 3x + y = 6.

Answers

Answer:

The equation of the line would be y = 1/3x + 2

Step-by-step explanation:

To find this, we must first solve the original equation for y.

3x + y = 6

y = -3x + 6

This means the original slope is -3. Since the original slope is -3, we know that the perpendicular slope is 1/3. This is because perpendicular slopes are opposite and reciprocal.

Now we use the slope and the intercept in slope-intercept form to get the equation.

y = mx + b

y = 1/3x + 2

Final answer:

The equation of a line perpendicular to the line 3x + y = 6 and passing through the y-intercept of 2 is y = 1/3x + 2.

Explanation:

To find the equation of a line that is perpendicular to a given line and passes through a certain y-intercept, we first find the slope of the given line, and then use the negative reciprocal of that slope as the slope of the new line.

The given line is in standard form 3x + y = 6. To convert it to slope-intercept form, we isolate y: y = -3x + 6. Therefore, the slope of the given line is -3. The slope of any line perpendicular to this line is the negative reciprocal of this slope, or 1/3.

The new line must pass through the point where y = 2. So, we plug this value into the slope-intercept form of the equation: y = mx + b, where m is the slope and b is the y-intercept. As a result, the new equation is: y = 1/3x + 2.

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The lengths of two sides of a triangle are 3 inches in 8 inches find the range of possible links for the third side S

Answers

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

1. a ≤ 3 ≤ 8 then a + 3 > 8 → a > 8 - 3 → a > 5 FALSE, because a ≤ 3.

2. 3 ≤ a ≤ 8 then 3 + a > 8 → a > 5 therefore  5 < a ≤ 8

3. 3 ≤ 8 ≤ a then 3 + 8 > a → 11 > a → a < 11 therefore 8 ≤ a < 11.

Answer: 5 < a < 11 → S = (5, 11)

The range of possible links for the third side s is 5 < s < 11

What is a triangle ?

A triangle is a polygon with three sides , three vertices and three angles.

It is known that if a, b and c are the lengths of the sides of a triangle and

then

a + b > c  

b+c > a  

c+a > b

Then the length of the third side lies between

8-3 < s < 8+3

5 < s < 11

Therefore the range of possible links for the third side s is 5 < s < 11

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Matt has a full jar of marbles he gave Kayla 3/4 and Marbles and Kayla return 1/3 of the jars worth of Marvel's to the jar how much are the jars now full marbles

Answers

Answer:

Matt has 7/12 of the jar of marbles left.

Step-by-step explanation:

In order to find this, simply subtract the 3/4 from the full jar (1) and then add 1/3. They will need common denominators to complete this operation.

1 - 3/4 + 1/3 = Amount

12/12 - 9/12 + 4/12 = Amount

7/12 = Amount

An evil supervillian has launched a drone from his/her submarine. The drone's height, in meters above sea level, as a function of time, t , in seconds, is given by h ( t ) = − 4.9t^2 + 133t + 152

What is the maximum height? Round your answer to three decimal places.

Answers

Answer:

the maximum height is 1054.500 meters

Step-by-step explanation:

h ( t ) = − 4.9t^2 + 133t + 152

a= -4.9 , b= 133  and c= 152

To find maximum height , we find vertex

[tex]x= \frac{-b}{2a}=\frac{-133}{2(-4.9)}= 13.5714 [/tex]

Now plug in 13.5714 for 't' in h(t)

[tex]h(t) =-4.9t^2 + 133t + 152[/tex]

[tex]h(t)=-4.9( 13.5714)^2 + 133( 13.5714)+ 152=1054.500[/tex]

the maximum height = 1054.500 meters

The maximum height of the drone is approximately 1347.174 meters.

To find the maximum height of the drone, we need to find the vertex of the quadratic function h(t) = -4.9t^2 + 133t + 152. The vertex of a quadratic function in the form f(t) = at^2 + bt + c is given by the coordinates (t, f(t)) where t = -b/2a and f(t) is the maximum value.

Plugging in the values from our function, we have t = -133/(2*(-4.9)) = 13.67347. Substituting this value of t back into the function, we get h(13.67347) = -4.9*(13.67347)^2 + 133*(13.67347) + 152 = 1347.174 meters. Therefore, the maximum height of the drone is approximately 1347.174 meters.

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plss help look at all three pic i need 3 answers!!!!!

Answers

Answer:

The measure of <Q is 44.4 degrees. The measure of <T is 44.4 degrees These both mean that they are congruent. I hope this helps

Step-by-step explanation:

180-(98+37.6)=44.4

Find the coordinates of the midpoint of the segment. MN with endpoints M (6, 14) and N( −4, −4)

Answers

Final answer:

The midpoint of line segment MN with endpoints M (6, 14) and N (-4, -4) can be calculated using the formula: ( (x1 + x2) / 2, (y1 + y2) / 2 ) which gives the midpoint coordinates as (1, 5).

Explanation:

In order to find the midpoint of a line segment in a 2-dimensional space, you can use the midpoint formula: ( (x1 + x2) / 2, (y1 + y2) / 2 ). For the given endpoints M (6, 14) and N(-4, -4), substitute the respective values into the formula:

X-Midpoint = (6 + -4) / 2 = 1

Y-Midpoint = (14 + -4) / 2 = 5

Thus, the coordinates of the midpoint of segment MN are (1, 5).

Note: The reference information provided does not apply to this question as it seems to be talking about different points and using the slope matrix, not the midpoint formula.

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Calculate the area of trapezium CDEF.
You must show all your working.

Answers

Brainly keeps saying that my answer contains inappropriate words.

It doesn't!!!

I'll try again.


A convex polyhedron has 6 vertices and 12 faces. How many edges does it have?
Please help me and I will give you the Brainliest answer

Answers

Answer:

16 edges.

Step-by-step explanation:

We will use Euler's polyhedron formula to solve for the edges of our convex polyhedron.

Euler's polyhedron formula is: [tex]V+F-E=2[/tex], where,

V= Vertices of polyhedron,

F= Faces of polyhedron,

E= Edges of polyhedron.

Let us substitute V=6 and F=12 in Euler's formula to find number of edges of our polyhedron.

[tex]6+12-E=2[/tex]

[tex]18-E=2[/tex]

Let us subtract 18 from both sides of our equation.

[tex]18-E-18=2-18[/tex]

[tex]-E=2-18[/tex]

[tex]-E=-16[/tex]

[tex]E=16[/tex]

Therefore, our convex polyhedron will have 16 edges.

please help on this one?

Answers

A, since the graph is not in a "U" shape aka parabola the degree cant be 2 so C is wrong and B and D are negative fuctions while the graph is showing one that is positive.

Answer:

A. [tex]F(x)=2x^{9} -4x^{2} +4[/tex]

Step-by-step explanation:

First of all, par and odd functions have their graphic particularities.

Specificially, if the grade of the polynomial is pair, then the function has a symmetric graph, the curve will have a returning point, like the parabola. On the other and, if the grade of the polynomial is odd, then the graph of the function won't have an symmetry like pair ones, and it won't have a returning points like parabolas

So, in this case, the raph doesn't have a returning point like a parabola or an U movement, that means possible answers are A and B.

Choice B cannot be the answer because the negative sign in the first term indicates a reflection accros the vertical axis, and the graph is showing an original function.

Therefore, the right answer is A. [tex]F(x)=2x^{9} -4x^{2} +4[/tex]

Your gym teacher needs to put 96 students into 12 equal groups. Complete the equation to show which operation to use and how many students will be in each group. Then complete the sentence to explain your reasoning.

Answers

Answer:

8

Step-by-step explanation:

We will use the math operation division to find the answer. Division takes a total and divides it into equal amounts. We have a total of 96 and need equal amounts in to each of the 12 groups.

96/12=8 students per group


To divide 96 students into 12 equal groups, you perform a division operation. Using 96 / 12, we find that there are eight students per group.

To determine how many students will be in each of the 12 equal groups, you use division. The total number of students which is 96 will be divided by the number of groups which is 12. Therefore, the equation you need is 96 / 12 = eight students per group.

This division operation is similar to when five students working on a group assignment divide it into five equal parts. Each of the students completes one part. In our scenario, instead of five parts, we are dividing 96 students into 12 parts, hence creating equal groups for the gym class activity.

Write a linear equation in slope intercept form to model the situation and internet company charges $4.95 per month plus $2.50 for each hour of use how much would it cost in a month when you use the internet for 14 hours

Answers

Answer:

it cost $39.95 in a month when you use the internet for 14 hours

Step-by-step explanation:

internet company charges $4.95 per month plus $2.50 for each hour

Let x be the amount of hours internet used

for 1 hour, charge is 2.50

for x hours , charge is 2.50x

To get linear equation we use y=mx+b

m is the slope and b is the fixed cost

fixed cost b= 4.95 and slope m = 2.50

So equation becomes y = 2.50x + 4.95

we need to find the cost y for 14 hours

So we plug in 14 for x  and find out y

y = 2.50(14) + 4.95= 39.95


Final answer:

The linear equation to model the monthly cost of internet use is y = 4.95 + 2.50x. For using the internet for 14 hours, the total cost would be $39.95.

Explanation:

The student is asking for a linear equation in slope-intercept form to model the monthly cost of internet usage based on the number of hours used. The internet company charges a monthly subscription fee plus an additional fee per hour of use. The equation to represent this situation is y = 4.95 + 2.50x, where y represents the total monthly cost in dollars and x represents the number of hours the internet is used. To calculate the cost for 14 hours of use in a month, we substitute x with 14: y = 4.95 + 2.50(14), which equals $39.95 for the month.

(-19+7i)-(29+32i)=

in the form (a+bi)

Answers

ANSWER

[tex]-48-25i[/tex]

EXPLANATION

We want to simplify the expression,

[tex](-19+7i) - (29+32i)[/tex]

Let us expand the bracket to obtain,

[tex]-19+7i-29-32i[/tex]

We now group the complex number parts and real number parts.

[tex]-19 -29+7i-32i[/tex]


We simplify further to obtain,

[tex]- 48-25i[/tex]


This is in the form,

[tex]a+bi[/tex]

where

[tex]a=-48[/tex]

and

[tex]b=-25[/tex]

Find the coordinates of the center of the given circle. (x - 5)2 + (y + 3)2 = 25

Answers

Answer:

The center is at (5, -3) and the radius is 5

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center of the circle and r is the radius of the circle.

(x - 5)2 + (y + 3)2 = 25

Rewriting the equation

(x - 5)2 + (y -  -3)2 = 5^2

The center is at (5, -3) and the radius is 5

The center is (5,-3) the radius of 25 is 5

Which point on the unit circle corresponds to −4π/3 ?

(1/2, −3√/2)
(-3√/2, 1/2)
(-1/2, 3√/2)
(3√/2, −1/2)

Answers

Answer:

[tex]\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]

Step-by-step explanation:

We know that coordinate of any point on unit circle is given by

[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]

Given that [tex]\theta=-\frac{4\pi}{3}[/tex]

So we just need to plug the value of given angle [tex]\theta=-\frac{4\pi}{3}[/tex] into above formula:

[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]

[tex]=\left(\cos\left(-\frac{4\pi}{3}\right),\sin\left(-\frac{4\pi}{3}\right)\right)[/tex]

[tex]=\left(\cos\left(2\pi-\frac{4\pi}{3}\right),\sin\left(2\pi-\frac{4\pi}{3}\right)\right)[/tex]

[tex]=\left(\cos\left(\frac{2\pi}{3}\right),\sin\left(\frac{2\pi}{3}\right)\right)[/tex]

[tex]=\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]

Hence choice (3) is correct.

Answer:

-1/2, √3/2

Step-by-step explanation:

A collection of nickels and quarters is worth 2.85 . Thereare 3 more nickels than quarters . How many nickels and quarters are there

Answers

Answer:

9 quarters and 12 nickles

Step-by-step explanation:

9 quarters = $2.25

12 nickles = .60

$2.25 + .60 = 2.85

12 is 3 more than 9

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