Mathematics High School

What is the equation of a vertical line passing through (−5, −2)?
x = −5
y = −2
x = −7
y = −3

Answers

Answer 1
A vertical line will pass through  one value of x  
here the equation is x = -5   ( the x coordinate of (-5,-2)
Answer 2

Answer:

x = -5

First option is correct.

Step-by-step explanation:

The vertical line is passing through the point (−5, −2).

The equation of a vertical line is in the form x = k

For vertical line, the x-coordinate of each point that lie on the line remains same. Only the y-coordinate is different

For the given point, the x-coordinate = -5

Hence, k = -5

Therefore, the equation of line is x = -5

First option is correct.

Related Questions

Janey bought a used bicycle for $640. the bike was 3 years old when she bought it, and cost $850 new. assuming it decreases in value by the same amount each year, write a linear equation for the value of the bicycle, v, when it is t years old (so t = 0 was when it was new).

Answers

The first thing we must do in this case is to define the variables.
 We have then:
 v: the value of the bicycle
 t: years
 The standard equation of the line is:
 v-vo = m (t-to)
 The slope is:
 m = (v2-v1) / (t2-t1)
 Substituting values:
 m = (640-850) / (3-0)
 m = -70
 We choose an ordered pair:
 (to, vo) = (0, 850)
 Substituting values:
 v-850 = -70 (t-0)
 Rewriting:
 v = -70t + 850
 Answer:
 assuming it decreases in value by the same amount each year, a linear equation for the value of the bicycle, v, when it is t years old is:
 v = -70t + 850

1. Your total restaurant bill is _____. (1 point)
Captionless Image
*

the items purchased minus sales tax, and plus tip.
the items purchased plus sales tax and tip.
the items purchased minus sales tax, and plus tip.

2. A check is _____. (1 point)
Captionless Image
*

required to be paid by your bank when presented
a promissory note (I.O.U.)
not able to be forged

3. There are several different ways to pay for items. In most modern economies, which is not a way to pay? (1 point)
Captionless Image
*

credit cards
bartering
cash

Answers

First question:

Your total restaurant bill is the items you have purchased plus the sales tax and plus the tip (if there’s any). Sales tax is added to your purchase because this is tax imposed to the consumer and not to the buyer. The buyer is only required to collect this tax from the buyer.

Second question:

A check is a financial instrument wherein the bank is required to pay when presented or encashed to them. You just have to make sure that you have account balance to that certain bank.

Third question:

The way of payment not any more common in the most modern economies is the bartering. Both credit cards and cash are the most common way of paying for your purchases.

Answer:

1. the items purchased plus sales tax and tip.

2. a promissory note (I.O.U.)

3. bartering


4.Krissa drew a circle with a radius of 4 inches.

Fill in the blanks.

The area of the circle is _______ square inches and the circumference is _______ inches.



64π, 16π


16π, 8π


16π, 64π


8π, 16π

Answers

Answer: second option: 16π, 8π

Explanation:

1) To calculate the area use the formula:

Area = π (radius)^2

radius = 4 in => area = π (4 in)^2 = 16π in^2

2) To compute the circumference use the formula:

Circumference = 2π(radius)

=> Circumference = 2π (4 in) = 8π in.

To calculate the area of a circle, use the formula A = πr², where r is the radius. For this specific circle with a radius of 4 inches, the area is 16π square inches, and the circumference formula is C = 2πr, resulting in a circumference of 8π inches.

To find the area of a circle: A = πr². Substituting the given radius of 4 inches, we get Area = π(4)² = 16π square inches. The circumference of a circle is C = 2πr. Substituting the radius, we get C = 2π(4) = 8π inches.

The owner of a garden center delivers bags of mulch. Each bag is sold for $6. The owner spends $16 for transportation to deliver the bags. Which of the following is the slope of the profit function for the garden center owner per delivery? Answer Choices m=6 m=−6 m=16 m=−16

Answers

m=6  
The profit function for this would be  P=6s-16 where P is profit, s is bags sold and -16 is the cost of transportation. the 6 represents how much each bag sells for. it is a linear equation that can be represented as y=mx+b where m is the slope or 6 in this case. 

14. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5). Show your work.

Answers

The circumcenter has equal distance to each of the three vertices. Suppose the coordinates of the circumcenter O are (a,b). Then OD=\sqrt((a-1)^2+(b-3)^2), OE=\sqrt(a-8)^2+(b-3)^2), OF=\sqrt((a-1)^2+(b+5)^2). Let OD=OE=OF, solve the equation. x=9/2, y=-1. O(9/2, -1).

Jacob drew the similar triangles below to represent the sides of two bicycle stunt jumps. The area of the smaller triangle is 36 square inches. what is the area of the larger triangle?

A. 54
B.108
C. 324
D. 432

Answers

The answer is D. 432.
Solution to this is,
36 x 12= 432
If the area of the smaller triangle is 36, then the answer to the area of the larger triangle is 432 inches square.

If the height of Mount Everest is about 8.8×103 meters, and the height of the Empire State Building is about 3.8×102 meters, which of these statements is true?

Answers

Mount Everest is about 23 times as tall as the Empire State Building. Hope that helps!

Answer:

option C is correct, i.e. Mount Everest is about 23 times as tall as the Empire State Building .

Step-by-step explanation:

Given options are:-

A. There is no way to compare these heights .

B. Mount Everest is about 40 times as tall as the Empire State Building .

C. Mount Everest is about 23 times as tall as the Empire State Building .

D. The Empire State Building is about 23 times as tall as Mount Everest.

Given the height of Mount Everest is about 8.8×10^3 meters, and the height of the Empire State Building is about 3.8×10^2 meters.

Finding ratios of given heights:-

[tex]\frac{Mount\;\;Everest}{Empire\;\;State\;\;Building} =\frac{8.8*10^3m}{3.8*10^2m} \\\\\frac{Mount\;\;Everest}{Empire\;\;State\;\;Building} =23.15789474 \approx 23 \\\\Mount\;\;Everest=23*(Empire\;\;State\;\;Building)[/tex]

Hence, option C is correct, i.e. Mount Everest is about 23 times as tall as the Empire State Building .

Anyone have the proper answer to this?

Answers

The translation rule used here is (x+2 , y+4).

So the image of (-7,3) will be:

(-7+2 , 3+4)
(-5 , 7)

So the answer is (-5,7).

Hope this helps :)


A playground is being designed where children can interact with their friends in certain combinations.

If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 3 interactions.
If there are 3 children, there can be 12 interactions.
If there are 4 children, there can be 39 interactions.

Which recursive equation represents the pattern?

an = an – 1 + 3(n – 1)

an = an – 1 + 3(n – 1)

an = an – 1 + (3n – 1)

an = an – 1 + (n – 1)3

Answers

From your situations given:
If there is 1 child, there can be 0 interactions. 
If there are 2 children, there can be 3 interactions. 
If there are 3 children, there can be 12 interactions. 
If there are 4 children, there can be 39 interactions. 

The equation would be an = an – 1 + 3(n – 1)

Answer:

[tex]a_n=a_{n-1}+3^{n-1}[/tex]

Step-by-step explanation:

It is given that

If there is 1 child, there can be 0 interactions.

If there are 2 children, there can be 3 interactions.

If there are 3 children, there can be 12 interactions.

If there are 4 children, there can be 39 interactions.

It means we have,

[tex]a_1=0, a_2=3, a_3=12, a_4=39[/tex]

We need to find the recursive equation that represents the pattern.

[tex]a_2=3\Rightarrow 0+3=a_1+3[/tex]

[tex]a_3=12\Rightarrow 3+9=a_2+3^2[/tex]

[tex]a_4=39\Rightarrow 12+27=a_3+3^3[/tex]

Similarly,

[tex]a_n=a_{n-1}+3^{n-1}[/tex]

Therefore, the required recursive formula is [tex]a_n=a_{n-1}+3^{n-1}[/tex].

What is the equation of the midline for the function y = 2sin(x - π) + 3

Answers

the maximum value of sin(x-π) is 1, the minimum is -1, so the maximum value for the function y = 2sin(x - π) + 3 is 2*1+3=5, the minimum is -2+3=1, half way between 5 and 1 is 3, so y=3 is the midline. 

The equation of the midline for the function 2sin (x - π) + 3 is y = 3.

What is the Midline of a Function?

The midline of a function is the line horizontal to the minimum value and maximum value of the function.

Given function is 2sin (x - π) + 3.

We know the trigonometric formula,

sin (A - B) = sin A cos B - cos A sin B

sin (x - π) = sin x cos π - cos x sin π

               = (sin x × -1) - (cos x × 0)          [Since cos π = -1 and sin π = 0]

               = -sin x

So, 2sin (x - π) + 3 = -2sinx + 3

Now, we know that,

-1 ≤ sin x ≤ 1

Multiplying whole sides by -2,

2 ≥ -2sin x ≥ -2

[since the inequality sign changes when negative is multiplied or divided]

Adding 3 throughout,

5 ≥ -2sin x + 3 ≥ 1

Maximum value is 5 and minimum value is 1.

Midline value = (5 + 1) / 2 = 3

So the equation of the midline is y = 3.

Hence the equation of midline is y = 3.

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The opening of the tunnel can be modeled by the graph of the equation y=-0.18x^2+4.4x-12 where x and y are measured in feet. Find the maximum height of the tunnel.

Answers

1. To find the vertex of a parabolla whose equation is written in the standard form, you must apply the following proccedure:
 
 2. You have:
 
 y=-0.18x²+4.4x-12 
 
 a=-0.18
 b=4.4
 
 3. You must apply the following formula:
 
 x=-b/2a
 x=-4.4/2(-0.18)
 x=-4.4/-0.36
 x=12.22
 
 4. When you susbtitute x=12.22 into the equation y=-0.18x²+4.4x-12, you obtain:
 
 y=-0.18x²+4.4x-12
 y=-0.18(12.22)²+4.4(12.22)-12
 y=14.88 feet
 
 5. The answer is: The maximum height of the tunnel is 14.88 feet

Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of
12 inches. He will make the "X" by stretching red ribbon diagonally from corner to corner. How many inches of ribbon will Peter need to make the "X"? Round your answer to the nearest inch.

Answers

To answer this question you can use the Pythagorean Theorem Which states that a squared plus b squared equals c squared. C is the hypotenuse of a triangle (one of the diagonals forming the X). The hypotenuse is the side directly across from the right angle. A and b are both 12, so 12 squared plus 12 squared is 288. To solve for c, find the square root of 288, which is approximately 17 inches. Double this (one for each line in the X and you need approximately 34 inches of ribbon. Always label your answers!
the answer would be 34

The square of the sum of 7 times x and 3 divided by 4 times the difference of x and 1

Answers

I believe the 3rd answer down if the information you provided is correct

Squaring the sum on the top, rules out 1 and 2 (not squaring the 7 only)
then 4 times the difference.  so I believe 4 (x-1) on the bottom.

Answer:  Third option is correct.

Step-by-step explanation:

Since we have given that

The square of the sum of 7 times x and 3 divided by 4 times the difference of x and 1.

The square of the sum of 7 times x and 3 would be written as

[tex](7x+3)^2[/tex]

and 4 times the difference of x and 1 is written as

[tex]4(x-1)[/tex]

Mathematically, it is expressed as

[tex]\dfrac{(7x+3)^2}{4(x-1)}[/tex]

Hence, Third option is correct.

Which expression is equivalent to 3^12 • 7^9

Answers

The answers are...

B. (3 ^3) ^9 * (7 ^3) ^6
D. (3 ^3 + 3 ^9) * (7 ^6 + 7 ^3)

i need help PLEASEEEEEEEEEE!:P Susan is paying $0.30 per $100 on her $483,000 home in homeowners insurance annually. If her annual homeowners insurance premium is divided into twelve equal monthly installments to be included on each of her monthly mortgage payments of $2128.00, what is her total monthly payment?
a.
$2,248.75
b.
$2,409.75
c.
$3,381.00
d.
$3,577.00

Answers

We first need to figure out how much insurance Susan pays annually. For every $100, she pays 30 cents. Well, let's pretend that we have her entire home's value in 100 dollar bills. There will be 4830 bills. On each of those bills, she will pay 30 cents. If we multiply .30 x 4830 we get $1449. This is how much she pays all year- to find out how much she pays each month, we divide by 12. This gives us 120. 75. We include this on her monthly mortgage payment: 120.75 + 2128 and we get A) 2248.75.

6.2 practice a 6th grade

Answers

U need to practice what you have trouble with

PLEASE HELP ME ON THIS!!!!

Answers

The last two choices are appropriate.

Both give you f(1) = 7, f(2) = 9.50, f(3) = 12.00, ... as they should.

Please help me. Thank you.

Answers

The equation for Circumference is: 2πr

The diameter is 8.4 cm

to find radius (r), divide 8.4 by 2

8.4/2 = 4.2

plug in 4.2 for "r"

2π(4.2)

8.4π cm is your answer

hope this helps

Question 4 find the indicated probability or percentage for the normally distributed variable. the volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. what is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

Answers

Answer: 40.13% of the soda bottles will have a volume less than 32 oz.

First, we need to find the z-score. That is the number of standard deviations below the mean.

(32 - 32.3) / 1.2 = -0.25

A bottle of 32 oz is -0.25 standard deviations below the mean. Use a standard normal distribution probability table and you will find the 40.13% of the scores are below a z-score of -0.25.

one light year is 5.88 x 10^12 miles. suppose a star is 2.23 x 10^2 light years away from earth. In scientific notation how many miles is it?

Answers

we have that

applying a rule of three

if 1 light year is ----------------> 5.88 x 10^12 miles
2.23 x 10^2 light years-----------> X
X=2.23 x 10^2*(5.88 x 10^12 miles)---------> 1.31 x 10^15 miles

the answer is 1.31 x 10^15 miles

PLEASE HELP 20 POINTS!!!!!!!!! The graph below shows a system of equations: Draw a line labeled y equals x plus 4 by joining the ordered pairs negative 4, 0 and 1, 5. Draw a line labeled 3 times y equals minus 2 x plus 2 by joining the ordered pairs negative 2, 2 and 4, negative 2 The x-coordinate of the solution to the system of equations is__________

Answers

2 y = - x - 12 y = x + 5

- x - 1 = x + 5- 2 x = 5 + 1- 2 x = 6x = - 6 : 2x = - 32 y = - 3 + 52 y = 2y = 1The solution is ( - 3 , 1 ).Answer: x = - 3.
this was easy it is -3

Help! Please. I don't get this.

Answers

a) ∠SQR and ∠2
b) Q
c) QR and QT

Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(1.25, 0.75) , B′(0.75, 1.75) , and C′(0.25, 1) . The center of dilation is the origin. What is the scale factor of the dilation? 0.25 0.5 2 4

Answers

fFirst, we have the following points:
 A (5, 3) 
 B (3, 7) 
 C (1, 4) 
 We multiply these vertices by a factor k to obtain the new vertices: 
 A '(k * 5, k * 3) = (1.25, 0.75) 
 B '(k * 3, k * 7) = (0.75, 1.75) 
 C '(k * 1, k * 4) = (0.25, 1)
 We note that the value of k is: k = 1/4
 Answer:
 the scale factor of the dilation is:
 0.25

This is the answer the other is right

Can someone do question 3 by showing step by step solutions

Answers

The question is asking for the largest possible area

BUT it only gives you details on the perimeter of the fence. One of the sides of the area enclosure will be used from his fence and he has a maximum of 1,000 meters available for a perimeter... So the first step is to set up a perimeter equation and solve for the dimensions, before solving the max area problem

The equation for the perimeter will be:
2 (Width) + 1 (Length) =  1,000 m
Theres only 1 length being included in the equation because the fence the farmer has will be used instead of the building materials.

Solving for Length =
L = 1,000 m - 2 Width

Now using this equation (and replacing the L) into Area of a rectangle:
Length * Width = (1,000 m - 2 W) * W =

Area = - 2(W^2) + 1,000 W 

Now that we have the area, there are a few methods to find the maximum amount. Using calculus we can find the derivative of the function and solve for critical points to find extrema points and find the absolute maximum area.

You can also solve this using algebra by factoring this function because its a quadratic and then you can solve for the highest values.   y = -2x^2 +1000x 
=  -2x(x + 500)  where x = 0 and -500

Checking at x = -1,  y(-1) = 998

***** EDIT *****

Sorry, the question is only asking for the dimensions of the fence. Its not asking for you to solve the actual maximum size.

The dimensions would be 2 Width x Length

The angle between 0 and 2 π in radians that is coterminal with the angle 62 9 π in radians is

Answers

ill  recomment on my thing right now with the answer let me just go read up on how to do this 

8π/9 is coterminal with 62π/9 and lies between 0 and 2π.

Given that, the angle between 0 and 2 π in radians that is coterminal with the angle 62π/9 in radians.

What is the coterminal with the angle?

The coterminal angles are the angles that have the same initial side and the same terminal sides. We determine the coterminal angle of a given angle by adding or subtracting 360° or 2π to it.

To find a coterminal angle, add or subtract any multiple of 2π, that is

62π/9 - 2π = (62π-18π)/9

44π/9 - 2π = 26π/9

26π/9 - 2π = 8π/9

Therefore, 8π/9 is coterminal with 62π/9 and lies between 0 and 2π.

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MATH HELP PLEASE UGRGENT WILL GIVE BRAINIEST!!
In the figure, YX−→− and YZ−→− are tangents to circle A at points X and Z, respectively.

mXZ=140∘
mXSZ=220∘



What is the measure of ∠XYZ ?

Answers

The measure of an angle formed by two tangent lines intersecting at a point outside the circle is equal to one-half their intercepted arcs.
XYZ = 1/2(XSZ - XZ)
XYZ = 1/2 (220 - 140)
XYZ = 1/2 (80)
XYZ = 40

The measure of angle XYZ is 40 degrees.

Hope this helps =)

Answer:

40

Step-by-step explanation:

What is the answer to this question please explain...

Answers

Do what it says.

F = (9*30)/5 +32 . . . . . replace the variable C with the value 30
F = 270/5 +32 . . . . . . . order of operations says do multiplication and division in the order in which they appear. We have multiplied 9*30
F = 54 +32 . . . . . . . . . . division appears next. We have divided 270 by 5
F = 86 . . . . . . . . . . . . . . after multiplications and divisions are done, we add in the order of appearance. There is only one addition to perform.

F = 86 . . . . . . . . we suppose only the numerical value 86 should be entered

Hey there

Could you plz help me id appreciate it so much: )
LIMITED TIME

Answers

The independent variable is known as 'x', and the dependent variable is known as 'y'. They just changed the variables here 'f(t)' or 'f(x)' is the same thing as 'y', and 't' is the same thing as 'x'.

So 't' is the independent variable, and 'f(t)' is the dependent variable.

The wording of the second option, the second to last, and the last is all correct. The questions says "let 't' be the time in years after 2000", so if 't' were say 5, this would mean 5 years after 2000 or 2005.  The question also states "let f(t) be the amount of garbage", so the result must be the amount of garbage.

So now we just need to confirm if the calculations were done correctly.

Option 2:

[tex]\sf f(2)=1233[/tex]

This is the same thing as saying if you plug in 2 for 't', you will get 1233, let's try it:

[tex]\sf f(t)=1200\cdot (1.05)^t[/tex]

Plug in 2 for 't':

[tex]\sf f(2)=1200\cdot (1.05)^2[/tex]

Simplify the exponent:

[tex]\sf f(2)=1200\cdot (1.1025)[/tex]

Multiply:

[tex]\sf f(2)=1323[/tex]

So option 2 is incorrect, and we see also that option 6 is correct. Now for the last one:

Option 7:

[tex]\sf f(4)=1458.6[/tex]

This is the same thing as saying if you plug in 4 for 't', you will get 1458.6, let's try it:

[tex]\sf f(t)=1200\cdot (1.05)^t[/tex]

Plug in 4 for 't':

[tex]\sf f(4)=1200\cdot (1.05)^4[/tex]

Simplify the exponent:

[tex]\sf f(4)=1200\cdot (1.21550625)[/tex]

Multiply:

[tex]\sf f(4)\approx 1458.6[/tex]

So the last option is also correct.

So your answers are options 3, 4, 6 and 7.

A product transformation _____.
multiplies coordinates to transform the image
combines the coordinates of multiple transformations
finds the result of combining multiple transformations
uses a scale factor to multiply coordinates of the image

Answers

The answer is 'D' because a transformation needs to have a pattern. Only A and D have a pattern to them and B and C don't because they are random every time. It's not A because it doesn't specify what you multiply the coordinates by.

Answer:

The answer is C

Step-by-step explanation:

The distance from the origin to the point ​(-24​, 32​) is

Answers

The Pythagorean theorem tells you that distance is
.. √((-24)^2 +32^2)) = √(576 +1024) = √1600 = 40
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