the equation of the line that is perpendicular to the line with equation y=-2x-1 and passes through the point (1, -2) is?

Answers

Answer 1

Answer:

[tex]y=\frac{1}{2} x-\frac{5}{2}[/tex]

Step-by-step explanation:

Hi there!

Note that:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals of each other (ex. 3 and -1/3, 5/6 and -6/5, etc.)

1) Determine the slope (m)

When we look at the given line, [tex]y=-2x-1[/tex], we can identify that -2 is in the place of m, the slope of the line. Because perpendicular lines are negative reciprocals of each other, we know that a line perpendicular to this would have a slope of [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{1}{2} x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{2} x+b[/tex]

Plug in the given point (1,-2)

[tex]-2=\frac{1}{2}(1)+b\\-2=\frac{1}{2}+b[/tex]

Subtract 1/2 from both sides

[tex]-2-\frac{1}{2}=\frac{1}{2}+b-\frac{1}{2}\\-\frac{5}{2} = b[/tex]

Therefore, the y-intercept of the line is [tex]-\frac{5}{2}[/tex]. Plug this back into [tex]y=\frac{1}{2} x+b[/tex]

[tex]y=\frac{1}{2} x-\frac{5}{2}[/tex]

I hope this helps!


Related Questions

The owner of a flower shop on H street sells 28 roses for $140. What is the cost in dollars per rose?

Answers

Answer:

$5 ( sorry if it is incorrect)

Step-by-step explanation:

the answer is 5. 140 divided 28 equals 5

What is m∠BAC.

............

Answers

Answer:

37 degrees

Step-by-step explanation:

1. m∠CBA = 71+45 = 116 degrees

2. m∠CBA = m∠CDA because of the quadrilateral property of opposite sides.

3. m∠CBA + m∠CDA = 2*116 = 232.

4. Total angle measure of a quadrilateral is 360 degrees, so m∠BAD + m∠BCD = 360-232 = 128 degrees.

5. m∠BAD = m∠BCD = 128/2 = 64 degrees

6. m∠BAC = m∠BAD - m∠CAD = 64 - 27 = 37 degrees

Please help me with this. And my teacher said to show your work so what do I have to do and she said on paper please help thank you!

Answers

Answer:

Step-by-step explanation:

V=H x W x  L  so 11.25= H (1.5) (2);  3H=11.25 so the height of one box is 3.75’

To find the volume of 5 stacked boxes multiply the volume of one box by 5.

5(3.75 x 1.5 x 2) which is 20.25 cubic feet.

Im being asked to put this in simplest form can anyone help me?
What is 0.57 (7 repeating) expressed as a fraction in simplest form?

Answers

Answer:

57/100

Step-by-step explanation:

look it up

Solve for m.
3m = 15

A. m = 45
B. m = 35
C. m = 12
D. m = 5​

Answers

Answer:

D.

Step-by-step explanation:

Have a Nice Day

Answer:

it's D.

Step-by-step explanation:

. Which of the following is the correct algebraic representation of the translation below?


a. (x – 6, y – 5)
b. (x – 5, y – 6)
c. (x + 5, y + 6)
d. (x + 6, y + 5)

Answers

Answer:

D) (x+6, y+5)

Step-by-step explanation:

You can start with the top corner of triangle A

Then count up 5 units and right 6 units

Because you count vertically 5 units that means you're using the y-axis, And because you're counting up, than means the values are positive.

And because you count horizontally 6 units you're using the x-axis, And you are counting to the right so the values are positive.

Down vertically=Negative Y-axis Values. Up vertically=Positive Y-axis Values

Right horizontally=Positive X-axis values. Left horizontally=Negative X-axis Values

Emma bought a pair of earrings, a dress and a coat. The dress cost 6 times as much as the earrings, and the coat cost 13 times as much as the earrings. If the three items cost a total of $3200, how much did each of them cost?

Answers

Answer:cost of earring=$160

cost of dress=  $960

cost of coat =$2,080

Step-by-step explanation:

Let cost of earring be represented as x

so that the cost of dress =6x

And the cost of coat =13x

Since the  three items cost a total of $3200, we can develop an equation which can be represented as

cost of earring+cost of dress +cost of coat =3200

x +6x+13x=3200

20x =3200

x=3200/20=160

THerefore cost of earring=$160

cost of dress=  6x =$160 x 6=$960

cost of coat = 13x = $160 x 13=$2,080

Based on equation of the line of best fit how much money should Millie expect to earn if he works a five hour shift?

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]x = 5[/tex] ---- 5-hour shift

Required

The expected earnings

The question is incomplete, as the equation is not given. A general way to solve this, is to substitute the value of x in the equation, then solve for the y variable.

Take for instance, the equation is:

[tex]y = 10x + 2[/tex]

The expected earnings will be:

[tex]y = 10*5 + 2[/tex]

[tex]y = 50 + 2[/tex]

[tex]y = 52[/tex]

Expected Earnings = $52

An investment of $100 is now valued at $149.18 the interest rate is 8% compounded continuously about how long has the money been invested

Answers

question: An investment of $100 is now valued at $149.18 the interest rate is 8% per year, compounded continuously about how long has the money been invested

Answer:

5.2 years

Step-by-step explanation:

Applying

A = P(1+R/100)ⁿ.......................... Equation 1

Where A = amount, P = principle, R = rate, n = time.

From the question,

Given: A = $149.18, P = $100, R = 8%

Substitute these values into equation 1 and solve for n

149.18 = 100(1+8/100)ⁿ

149.18/100 = (1+8/100)ⁿ

1.4918 = (1+0.08)ⁿ

1.4918 = (1.08)ⁿ

Taking the Logarithm of both side

Log(1.4918) = Log(1.08)ⁿ

Log(1.4918) = nLog(1.08)

n = Log(1.4918)/Log(1.08)

n = 0.1737/0.0334

n = 5.2 years.

A car lot has both used and new cars. If 86% of the cars on the lot are new and 45% of the cars are new and have a sunroof, find the probability of randomly choosing a car with a sunroof, given that it is a new car

Answers

Answer:

0.523

Step-by-step explanation:

Let :

New car = N

Sunroof = S

P(N) = 0.86

P(N n S) = 0.45

Recall :

P(A|B) = p(AnB) / p(B)

Therefore ;

P(S|N) = P(SnN) / p(N)

P(S|N) = 0.45 / 0.86

P(S|N) = 0.523

i really need help on this i’m confused

Answers

Ummm what u want me to do

What is the distance between the two points? (Round to the nearest tenth)

8.6 units

6.1 Units

2.8 units

9.2 units

Answers

6.1 units you count how many number are far away from each other

Solve for b.
-7b – 12 = -61

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-7b - 12 = -61}[/tex]

[tex]\large\textsf{ADD 12 to BOTH SIDES}[/tex]

[tex]\mathsf{-7b - 12 + 12 = -61 + 12}[/tex]

[tex]\large\textsf{CANCEL out: -12 + 12 because that gives you 0}[/tex]

[tex]\large\textsf{KEEP: -61 + 12 because it helps solve for your b-value}[/tex]

[tex]\mathsf{-61+12=\bf -49}[/tex]

[tex]\large\text{NEW EQUATION: \textsf{-7b = -49}}[/tex]

[tex]\large\textsf{DIVIDE -7 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{-7b}{-7}=\dfrac{-49}{-7}}[/tex]

[tex]\large\textsf{CANCEL out: }\mathsf{\dfrac{-7}{7}}\large\textsf{ because that gives you 1}[/tex]

[tex]\large\textsf{KEEP: }\mathsf{\dfrac{-49}{-7}}\large\textsf{ because that gives you your b-value}[/tex]

[tex]\mathsf{\dfrac{-49}{-7}= \bf b}[/tex]

[tex]\uparrow\large\text{SIMPLIFY ABOVE \& YOU HAVE YOUR ANSWER}\uparrow[/tex]

[tex]\mathsf{-49\div -7= \bf 7}[/tex]

[tex]\boxed{\boxed{\large\text{Answer: \huge \bf b = 7}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

FREEEE POINTS REALLY

Answers

Answer:

x is less than 46

x<46°

Step-by-step explanation:

............

anybody know the answer? please help

Answers

Answer:

the first one. slope is 1/2 and y intercebt (b value) is positive 2.

Step-by-step explanation:

Answer:

y=1/2x+2

Step-by-step explanation:

This equation is linear because the graph is a straight line. Therefore, use the slope-intercept form y=mx+b to create the equation.

To find m (the slope), pick two points like (0,2) and (2,3). Find the change in y over the change in x: (y2-y1)/(x2-x1).

y2=3, y1=2, x2=2, x1=0

(3-2)/(2-0)= 1/2

This is the slope which means the equation is one of the first 2 options.

Next find b (the y-intercept) by finding the y value on the graph when x=0. When x=0, y=2. Therefore, b=2 and the final equation is y=1/2x+2

Tell if the number is rational or irrational. 3.65028​

Answers

Answer:

Irrational

Step-by-step explanation:

Answer: YES

Explanation: 3.65028 is a terminating decimal, or decimal that ends, and all terminating decimals are rational numbers.

Can someone please show me how to do this, I know the answer is 125 a^3 b^2.
The question is shown below in a picture I’m not sure how to do it please explain!

Answers

Answer:

Step-by-step explanation:

5^4 = 625. I hope your calculator will do this.

625 / 5 = 125

There is a more general way to do this which will be in harmony with the rest of the question.

5^4 / 5^1 = 5^(4 - 1) = 5^3 = 125

b^4 / b2 = b^(4 - 2) = b^2

a remains as it is at a^3

So the answer is 125 a^3 b^2

In a high school high jump contest, the height of clearing the bar ranged from 71 inches to 84 inches. The mean height was 76 inches and the standard deviation was 3.5 inches. What percent of the jumpers were in the group jumping below 79.5 inches

Answers

Step-by-step explanation:

Given data:

Range of jumps  = 71 to 84 inches

Mean of jumps = 76 inches

standard deviation = 3.5

To calculate the percent of jumpers in the group jumping below 79.5 inches

Let us calculate the number of standard deviation in 79.5 inches

= 79.5/3.5

= 22.71 times

Answer:

84.1%

Step-by-step explanation:

the sum of two numbers is 19 and their diffrence is 3

Answers

Answer:

8 and 11

Step-by-step explanation:

A frosting is made of cream cheese and powdered sugar in the ratio 3:2. If you use 120g or cream cheese, how much powdered sugar should you use

Answers

Answer: 80 g

Step-by-step explanation:

Given

The frosting is made of cream cheese and Powdered sugar in the ratio of 3:2.

If 120 g of cheese is used

Assume the quantity of powdered sugar is x

So, we can write the ratio as

[tex]\Rightarrow \dfrac{3}{2}=\dfrac{120}{x}\\\\\Rightarrow x=\dfrac{2}{3}\times 120\\\\\Rightarrow x=\dfrac{2}{3}\times 3\times 40\\\\\Rightarrow x=80\ g[/tex]

So, 80 g of powdered sugar is used.

Answer: 80grams

Step-by-step explanation: pretty simple 120/3=40. 40x2=80 grams. Sorry for explanation not being really clear.

NEED HELPPPPP LOL XDDDDD OH MY GODDD

Answers

Answer:

yo w t f is thisssssss

Step-by-step explanation:

b  c  idek im so cluless rn im in 7th grade XD

Complete the following sentence. x = x' cos⁡θ - y'sin⁡θ where x’ and y’ are _____.

rotated points
original points
translated points
vertex points

Answers

Answer:

ROTATED POINTS

Step-by-step explanation:

HOPE IT HELP MHUW

Help me with my ixl please?!?

Answers

Answer:

funding a stuggling

Step-by-step explanation:

Find the mode, median, mean and range for this set of data.
Number of Hours Slept: 8.5, 7,6.75,5.75, 8.75,6.25,7,7.5, 4.25

Answers

The Mode of the set of data is 8.75The Median for the set of data is 7The Mean for the set of data is 6.86The Range of the set is 4.5

What is Central Tendency?

Central Tendency is the statistical measure that can be used to represent all the distribution or a dataset using a single value. The most common measures of central tendency are the mode, median, and mean.

How to determine this

Mode is the value that has the highest frequency in a given data set.

So,

8.75 the highest frequency in the data set

Mode = 8.75

Median is the middle of a sorted list of numbers when arranged in ascending order.

So,

4.25, 5.75, 6.25, 6.75, 7, 7, 7.5, 8.5, 8.75 in ascending order

Median = 7

Mean is the average or the most common value in a given set of values.

Mean = 8.5 + 7 + 6.75 + 5.75 + 8.75 + 6.25 + 7 + 7.5 + 4.25/9

Mean = 61.75/9

Mean = 6.8611

Mean = 6.86 to 2 decimal place

Range is the difference between the highest value and lowest values.

Range = Maximum value - Minimum value

Range = 8.75 - 4.25

Range = 4.5

Read more about Central Tendency

https://brainly.com/question/542771

#SPJ1

Please help me with this homework

Answers

Answer:

C.

Step-by-step explanation:

The pythagorean theorem shows a^2+b^2=c^2.

a=8, b=15, c= the unknown distance

8^2+15^2=c^2

Suppose that there were a strong correlation between the variables n and a
Which of these is a true statement?
A. n must cause p.
B. n must not cause p.
C. p must cause n.
D. n may cause p.

Answers

Answer:

D

Step-by-step explanation:

correlation does not= causation

I just need help with this

Answers

Answer:

z = 4.5

Step-by-step explanation:

∠B = ∠B      ∠BAD = 90° - ∠B = ∠C

ΔBAD ~ ΔBCA

AB / z = BD / AB

z = AB * AB / BD = 3*3 / 2 = 4.5

Please help me with full calculations

Answers

Answer:

use formula,

P(x,y)=P'(-y,x)

so.

R(-2,-2)=R'=(2,-2)

S(1,1)=S'(-1,1)

T(-1,-3)=T'(3,-1)

Step-by-step explanation:

plot R,S,T and R',S',T' in the graph

Amy is baking her famous pies to sell at the Town Fall Festival. She 1 point
uses 32 /4 cups of flour for every 1/2 batches of pie that she makes. How
many cups of flour would Amy use for 7 batches of pie?
A. 21 1/2 cups
B. 112 7/8 cups
C. 150 72 cups
D. 225 34 cups

Answers

Answer:

Step-by-step explanation:

A

NO LINKS The circumference of a circle is 36 feet. What is the length of the radius of this circler
O 9 ft
18 ft
36 ft
O 72 ft

Thank you so much for your help! :)

Answers

18ft ..................

Answer:

18ft

Step-by-step explanation:

Formula of circumference * r x r x 3.14* or d x 3.14*

:DDD And ye glad I could help!

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