Write the equation of a line that passes through the two points (3, 5) and (3,8).​

The equation of the perpendicular bisector of the line segment whose endpoints are (-7 , -2) and (5 , 4) is y = -2x - 1

Step-by-step explanation:

Let us revise some rules

∵ A line has endpoints (-7 , -2) and (5 , 4)

∴ [tex]x_{1}[/tex] = -7 and [tex]x_{2}[/tex] = 5

∴ [tex]y_{1}[/tex] = -2 and [tex]y_{2}[/tex] = 4

- Use the formula of the slope up to find the slope of the line

∴ [tex]m=\frac{4-(-2)}{5-(-7)}=\frac{4+2}{5+7}=\frac{6}{12}=\frac{1}{2}[/tex]

To find the slope of the perpendicular line to the given line reciprocal it and change its sign

∵ The slope of the given line = [tex]\frac{1}{2}[/tex]

∴ The slope of the perpendicular line = -2

∵ The perpendicular line is a bisector of the given line

- That means the perpendicular line intersect the given line

   at its midpoint

∵ The mid point of the given line = [tex](\frac{-7+5}{2},\frac{-2+4}{2})[/tex]

∴ The mid point of the given line = [tex](\frac{-2}{2},\frac{2}{2})[/tex]

∴ The mid point of the given line = (-1 , 1)

Now we wand to find the equation of the line whose slope is -2 and passes through point (-1 , 1)

∵ The form of the equation is y = mx + b, where m is the slope

   and b is the y-intercept

∵ m = -2

- Substitute the value of m in the form of the equation

∴ y = -2x + b

- To find b substitute x and y in the equation by the coordinates

   of a point on the line

∵ Point (-1 , 1) lies on the line

∴ x = -1 and y = 1

∵ 1 = -2(-1) + b

∴ 1 = 2 + b

- Subtract 2 from both sides

∴ -1 = b

- Substitute the value of b in the equation

∴ y = -2x + (-1)

∴ y = -2x - 1

The equation of the perpendicular bisector of the line segment whose endpoints are (-7 , -2) and (5 , 4) is y = -2x - 1

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Paulo's family has 1 hour 45 minutes before the trip to Scenic Lake Park.

To find out how long Paulo's family has before the trip to Scenic Lake Park, we will determine the amount of time between their arrival and the start of the trip.

Paulo's family arrived at the reunion at 8:30 A.M. The trip to Scenic Lake Park starts at 10:15 A.M.

Here's how to calculate the difference between these two times manually:

1. Convert both times to a 24-hour format (if needed):
  - Paulo's family arrival time: 8:30 A.M. is already in the morning, so it stays the same.
  - Trip start time: 10:15 A.M. is also in the morning, so it stays the same.

2. Calculate the hours remaining:
  - From 8 A.M. to 9 A.M. is 1 hour.
  - From 9 A.M. to 10 A.M. is another hour.
  - From 8:30 A.M. to 10 A.M., they have a total of 1 hour and 30 minutes.

3. Calculate the additional minutes remaining:
  - From 10:00 A.M. to 10:15 A.M. is an additional 15 minutes.

4. Add the additional minutes to the total time calculated:
  - They already have 1 hour and 30 minutes, and we add another 15 minutes to this.
  - So, the total time they have before the trip is 1 hour and 45 minutes.

Therefore, Paulo's family has 1 hour and 45 minutes of free time before the trip to Scenic Lake Park starts.

Answer:

123 coupons.

Step-by-step explanation:

Divide the total of 164 coupons by 4. 164/4 = 41

Find the amount of coupons sent by multiplying 41 by 3. 41 x 3 = 123

The answer is 123 coupons. (123/164 = 3/4)

Answer: A the bank building is 150 feet tall.

Step-by-step explanation:

If you subtract 20 from 320 then you get 300 then divide that by 2 you get 150.

Answer:

On Saturday night it had sold 35 numbers of cups.

Step-by-step explanation:

On the Saturday night the ratio of the number of cones to the number of cups sold is 6 : 5 in Freshly frozen yogurt however on Sunday night the ratio of the number of cones to the number of cups is 4 : 1.

Now, if the Freshly frozen yogurt sold 42 cones on Saturday night then in the ratio of 6 : 5, it sold cups [tex]\frac{5}{6}[/tex] times the number of cones.

Therefore, on Saturday night it had sold [tex]42 \times \frac{5}{6} = 35[/tex] numbers of cups. (Answer)

In the multiplication operation of numbers 435 and 173, the regrouped or carried over amounts are 10 (in units place calculation) and 30 (in tens place calculation). Therefore, the answer corresponds to option B: 20 and 3.

In multiplicaton problems, we often need to 'regroup' or carry values. In the multiplication of 435 and 173, regrouping is necessary. Here's how it's done:

We start by multiplying 5 from 435 with 3 from 173, to get 15. We write down 5 and carry over the 1 (or 10 from 15).

Next, we multiply the 5 in 435 with 7 (the tens-place in 173), which equals 35. We add the carry-over 1 to get 36. We write down the 6 and carry over the 3 (or 30).

Finally, we multiply the 5 in 435 with 1 (the hundreds-place in 173). Then add the carried over 3, resulting in 8.

The process is repeated with the remaining numbers in 435.

So for the multiplication above, the regrouped amounts are 10 and 30, corresponding to option B: 20 and 3.

For more such question on multiplication operation visit:

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Answer:

D

Step-by-step explanation:

1 1/4 + 3/4 + 2/4 + 1/4

1+1+ 3/4

2  3/4

Answer:

1 hour with 21 pages completed for each.

Step-by-step explanation:

First you need to list out what you know.

Tori:

Finished: 16 pgs

Rate: 5 pgs per hr

Cora:

Finished: 13 pgs

Rate: 8 pgs per hr

Now we compose Equations. In an equation we put the rate with the "X" because it is a constant rate of change. The finished amount of pages is our starting point or our y intercept we write it in this format:

y=mx+b

m being the rate of change

b being the initial amount or the starting point

For Tori the equation would be 5x+16 because 5 is our rate of change since she completes 5 pages per hour and 16 is our initial amount since she already completed them.

For Cora the equation would be 8x+13 because 8 is our rate of change since she completes 8 pages per hour and 13 is our initial amount since she already completed them.

we set these equation equal to each other:

5x+16=8x+13

eliminate the 5x on one side to leave the 16 by its self which in this case we subtract 5x to each side and get :

16=3x+13

the we subtract the 13 to leave 3x by its self and subtract 13 on both sides and get :

3=3x

lastly we divide 3 on both sides to isolate x and this would be our hours until they are both working on the same page:

1=x

this gives us 1 which means in 1 hour of working, both Cora and Tori will be working on the same page.

Substitute the 1 for each equation to get the total amount of pages completed in 1 hour:

5(1)+16

5+16

21 pages for Tori

8(1)+13

8+13

21  pages for Cora

Done

In one hour both Tori and Cora will have done 21 pages

Answer:

If (3, 4) is reflected over the x-axis, the new coordinates are (3, -4).

The correct answer is B.

Answer:

Step-by-step explanation:

My frist store wen you I was a little kid and the most main street from this is

Answer:

Answers are in picture, if you want an explanation for anything, just ask.

Step-by-step explanation:

Answer:

He missed 14 questions

Step-by-step explanation:

Total = Right + Miss ⇒ t = r + m

Right = Miss + 12 ⇒ r = m + 12

t = 40

Since t = r + m and r = m + 12 then:

t = m + 12 + m

t = 2m + 12

40 = 2m + 12

28 = 2m

m = 14

Final answer:

Ben missed 14 questions.

Explanation:

To find the number of questions Ben missed, we can create an equation using the information given.

Let x represent the number of questions Ben missed.

We know that Ben correctly answered 12 more than he missed, so the number of questions he answered correctly can be represented as

x + 12.

Since the test had 40 questions, we can set up the equation:

x + (x + 12) = 40.

Simplifying this equation, we get

2x + 12 = 40.

Solving for x, we subtract 12 from both sides to get

2x = 28,

and then divide both sides by 2 to get

x = 14.

Therefore, Ben missed 14 questions.

Answer:

The GCF of 7 and 12 is 1.

Answer:

Step-by-step explanation:

GCF of 12 and 7 = 1

If there is no common factor then , GCF will be 1

Answer:

perpendicular bisector

Answer:

(-20,20)

Step-by-step explanation:

Given coordinates are (-4,4).

Also, we need to dilate by a scale factor of 5.

The term dilation refers to changing the value of coordinate by a scale factor.

If the coordinate is said [tex](x,y)[/tex] and it is going to be dilated by a scale factor [tex]'k'[/tex].

Then the new coordinate will be (kx, ky).

So,

[tex](-4,4)\\\\k=5\\\\(-4\times5,4\times5)=(-20,20)[/tex]

The coordinate [tex](-4,4)[/tex] after dilated by a scale factor [tex]5[/tex] will be [tex](-20,20)[/tex]

Lydia invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %

Solution:

Given that on two investment totaling $ 7500

Lydia lost 2% on one and earned 5% on the other

Her net annual receipts were $158

To find: amount invested in both investments

Let Lydia invest $ x in first investment where she lost 2 %

Let Lydia invest $ y in second investment where she earned 5 %

Total investment given = 7500

x + y = 7500 ---- eqn 1

Net annual receipt = 158

5 % y- 2 % x = 158

[tex]\frac{5}{100}y - \frac{2}{100}x = 158[/tex]

0.05y - 0.02x = 158 ------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 7500 - y

Substitute x = 7500 - y in eqn 2

0.05y - 0.02(7500-y) = 158

0.05y -150 + 0.02y = 158

0.07y = 158 + 150

0.07y = 308

y = 4400

Thus,

x = 7500 - y

x = 7500 - 4400

x = 3100

Thus she invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %

Final answer:

Lydia invested $3,100 at a 2% loss and $4,400 at a 5% gain. A system of equations is set up and solved using substitution to determine the amount invested in each scenario.

Explanation:

To solve Lydia's investment problem, we need to set up a system of equations based on the given information

Total investment is $7,500.

She lost 2% on one investment and earned 5% on the other.

Her net annual receipts were $158.

Let's define:
x = the amount of money invested at a 2% loss
y = the amount of money invested at a 5% gain

The system of equations can be written as:

x + y = 7500 (the total amount invested)

-0.02x + 0.05y = 158 (the net receipts from the investments)

Multiplying the second equation by 100 to simplify the decimals:

-2x + 5y = 15800

Now we can use the method of substitution or elimination to solve for x and y. For this example, we'll use the substitution method:

Solve for y in the first equation: y = 7500 - x

Substitute y into the second equation: -2x + 5(7500 - x) = 15800

Now solve for x: -2x + 37500 - 5x = 15800

Combine like terms: -7x = 15800 - 37500

-7x = -21700

Divide by -7: x = 3100

Substitute x into y = 7500 - x: y = 7500 - 3100 = 4400

So Lydia invested $3,100 at a 2% loss and $4,400 at a 5% gain.

Answer:

8/14 and 12/21

Step-by-step explanation:

Just multiply numerator and denominator by the same number, e.g., 2 and 3 to get above.

Answer:

8/14 and 12/21

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

4x-1=2x+11

4x-2x-1=11

2x-1=11

2x=11+1

2x=12

x=12/2

x=6

Answer: 10%

50 is half of 100, so if it decreases 5 dollars from 50, then it has to be 10% of a decrease, or discount.

Hope this helps!

Answer:

10%

Step-by-step explanation:

50-45=5

5/50=1/10=10%

Answer:

[tex]3\frac{3}{4}[/tex] hours.

Step-by-step explanation:

Sean read [tex]\frac{1}{5}[/tex] of a book in [tex]1\frac{1}{2}[/tex] hours.

We are asked to determine the time that Sean requires to read [tex]\frac{1}{2}[/tex] of this book.

If the rate of reading the book is assumed to be constant, then we can use the unitary method to find the answer.

Now, Sean reads [tex]\frac{1}{5}[/tex] of a book in [tex]\frac{3}{2}[/tex] hours.

So, Sean reads the total of the book in [tex]\frac{3}{2} \div \frac{1}{5} = \frac{15}{2}[/tex] hours.  

Hence, Sean reads  [tex]\frac{1}{2}[/tex] of this book in [tex]\frac{15}{2} \times \frac{1}{2} = \frac{15}{4} = 3\frac{3}{4}[/tex] hours. (Answer)

Answer:

HI hydrogen iodide

Step-by-step explanation:

H2(gas)+I2(gas)---------->2HI(gas)

Answer:

I don't really know what you were asking; would you mind please clarifying? :)

Step-by-step explanation:

From what I'm guessing from the question is, "Iodine, and hydrogen combine to form hydrogen iodide. In the reverse reaction, hydrogen iodide decomposes back into hydrogen and iodine."

Did that help?

Answer:

Therefore 12.5 centimeters on the map represents an actual distance of 5 kilometers.

Step-by-step explanation:

Given:

The scale map shows that

5 centimeters =2 kilometers.

To Find:

What number of centimeters on the map represents an actual distance of 5 kilometers?

Solution:

Let 'x' cm be on the map to represent 5 kilometer.

Given:

5 centimeters = 2 kilometers.

Therefore,

x cm = 5 kilometer

Soon Equality of proportion we get

[tex]\dfrac{5}{x}= \dfrac{2}{5}\\ \\x=\dfrac{5\times 5}{2}=\dfrac{25}{2}=12.5\ cm\\\\\therefore x = 12.5\ cm[/tex]

Therefore 12.5 centimeters on the map represents an actual distance of 5 kilometers.

Answer:

.875 = 875/1,000 = 7/8

The correct answer is D.

Answer:

This is simple. And, you best not be cheating either.

15 - 1 x 18 / 6

1x18 = 18

18/6 is 3.

15 - 3 = 12

12 is the answer.

Step-by-step explanation:

The sign of cos pi divided by seven is positive

Solution:

Given that we have to determine the sign of cos pi divided by seven

Let us first understand the signs of sine, cosine and tangent by quadrants

In the first quadrant, the values for sin, cos and tan are positive.

In the second quadrant, the values for sin are positive only.

In the third quadrant, the values for tan are positive only.

In the fourth quadrant, the values for cos are positive only.

Determine the sign of cos pi divided by seven

cos pi divided by seven ⇒ [tex]cos \frac{\pi}{7}[/tex]

The angle [tex]\cos \frac{\pi}{7}[/tex] lies in quadrant 1, Where angles are zero (0) to [tex]\frac{\pi}{2}[/tex]

In first quadrant, all trignometric functions are positive

so, [tex]\cos \frac{\pi}{7}[/tex] has positive sign.

Answer:

20 units

Step-by-step explanation:

Consider right triangle ABD. In this triangle,

[tex]BD=37\ un.\\ \\AD=19+16=35\ un.[/tex]

By the Pythagorean theorem,

[tex]BD^2=AD^2+AB^2\\ \\37^2=35^2+AB^2\\ \\AB^2=37^2-35^2=(37-35)(37+35)=2\cdot 72=144\\ \\AB=12\ un.[/tex]

Consider right triangle ABC. In this triangle,

[tex]AC=16\ un.\\ \\AB=12\ un.[/tex]

By the Pythagorean theorem,

[tex]BC^2=AB^2+AC^2\\ \\BC^2=16^2+12^2\\ \\BC^2=256+144=400\\ \\BC=20\ un.[/tex]

Answer:

V=20

Step-by-step explanation:

Simplify both sides of the equation.

4−2(v+9)=26

4+(−2)(v)+(−2)(9)=26(Distribute)

4+−2v+−18=26

(−2v)+(4+−18)=26(Combine Like Terms)

−2v+−14=26

−2v−14=26

Step 2: Add 14 to both sides.

−2v−14+14=26+14

−2v=40

Step 3: Divide both sides by -2.

−2v

−2

=

40

−2

v=−20

Answer:

see explanation

Step-by-step explanation:

The equation of proportionality is

y = kx ← k is the constant of proportionality

k = y ÷ x, thus

k = 160 ÷ 25 = 320 ÷ 50 = 480 ÷ 75 = 640 ÷ 100 = 6.4

and

y = 6.4x ← equation of proportionality

Answer:

Step-by-step explanation:

Every next number is incremented by 8 from the previous number hence the sequence is arithmetic and the common difference is 8.

Hope this helps.

Answer:

The given sequence is arithmetic and common difference is 8.

Step-by-step explanation:

Given that :

            - 19, - 11, - 3, 5......

Here, a = - 19 ;  a is the first term of the series.

Now, For common difference-

d = [tex]t_{2} - t_{1}[/tex] = [tex]t_{3} - t_{2}[/tex] = [tex]t_{4} - t_{3}[/tex]

Let [tex]t_{1} = - 19,  t_{2} = - 11[/tex]

 d = - 11 - (-19)

 =  -11 + 19

  = 8

Let [tex]t_{3} = - 3,  t_{2} = - 11[/tex]

d = - 3 -(-11)

  = - 3 + 11

   = 8

Let [tex]t_{4} = 5,  t_{3} = - 3[/tex]

d = 5 - (-3)

  = 8

In each condition common difference d is same therefore the given sequence is arithmetic and common difference d = 8.

Answer:

C

Step-by-step explanation:

Answer:

B) x = -6  and  x = 2

Step-by-step explanation:

[tex]\frac{3x+9}{x^{2}+4x-12}[/tex]

can be rewritten as

[tex]\frac{3x+9}{(x+6)(x-2)}[/tex]

because

-2 · 6 = -12

-2 + 6 = -4

so thats why the denominator is (x+6)(x-2)

A vertical asymptote is where the denominator equals 0, so,

-6 + 6 = 0

2 + -2 = 0

So the Answer is:

B) x = -6  and  x = 2