Which line is perpedicular to a line that has a slope of 1/2?

Answers

Answer 1
A line with gradient is perpendicular to a line with gradient -1/m.
The gradient perpendicular to 1/2 is -1/0.5 = -2

Related Questions


Find the equation for the line that passes through the point (2, -3), and that is parallel to the line with the equation x - 3y = 3

Answers

Step-by-step explanation:

the slope of a line is the factor of x, when the equating looks like

y = ...

so,

x - 3y = 3

x = 3y + 3

3y = x - 3

y = 1/3 x - 1

so, the original slope is 1/3.

a parallel line has the same slope.

having a specific point we can use the point-slope form as equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

y - -3 = 1/3(x - 2)

y + 3 = 1/3(x - 2)

simplified that is

y + 3 = 1/3 x - 2/3

y = 1/3 x - 2/3 - 3 = 1/3 x - 2/3 - 9/3 = 1/3 x - 11/3 =

= 1/3 × (x - 11)

Answer:

[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]

Step-by-step explanation:

We are given the line x-3y=3.

We want to write the equation of the line that is parallel to this line, and that passes through (2, -3).

Parallel lines have the same slope.

Therefore, let's find the slope of x-3y=3.

The line is currently written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients.

In order to find the slope of this line, we can convert it into slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

To do that, we need to isolate y on one side; this is the same as solving the equation for y.

x - 3y = 3

Start by subtracting x from both sides

-3y = -x + 3

Now divide both sides by -3

[tex]y = \frac{1}{3} x - 1[/tex]

The slope of the line is 1/3, as 1/3 is the coefficient in front of x.

It is also the slope of our new line.

Since the question doesn't specify which format for the equation of the line, we can use any form. However, let's put the equation of the new line into slope-intercept form.

So, substitute 1/3 as m in y=mx+b.

[tex]y = \frac{1}{3} x + b[/tex]

Now we need to find b.

As the equation passes through the point (2, -3), we can use its values to help solve for b.

Substitute 2 as x and -3 as y.

[tex]-3 = \frac{1}{3} (2) + b[/tex]

Multiply.

[tex]-3 = \frac{2}{3} + b[/tex]

Subtract 2/3 from both sides (we can write this as an improper fraction).

[tex]-\frac{11}{3} = b[/tex]

Substitute -11/3 as b in the equation.

[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]

HELP
Often times you can use similar triangles in the real world. Sarah is attempting to find the height of a tree by using a mirror. By the laws of physics she knows that the angle of incidence is congruent to the angle of reflection (these are marked in red on the diagram). Explain why the two triangles are similar and if she knows her height and the distance from the mirror to her feet and also the distance from the mirror to the tree how could she calculate the height of the tree?

Answers

The two triangles are similar by the AA Similarity theorem.

The height of the tree can be calculated by figuring out the ratio between the distance between the mirror to her feet and the distance from the mirror to the tree

How to use the concept of similar Triangles?

From Law of Reflection, we know that the angle of incidence and the angle of reflection are equal to each other.

Now, triangles can be proved similar by the AA, SAS, or SSS theorems. However, in this question, the triangles as seen in the attached image can be proved similar by the AA similarity theorem.

This is because both triangles have one congruent angle in common.

Sarah and the tree are standing straight and perpendicular to the ground and as such, the angles formed by Sarah and the tree are right angles.

The above tells us that the two triangles have two angles in common, making them similar triangles by the AA (Angle Angle) similarity theorem.

Since the triangles are similar, it means that the ratios of the sides of the triangles will be the same. Thus,  if Sarah knows the distance from the mirror to her feet and the distance from the mirror to the tree, she can create the ratio between the two triangles.

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What is the slope of the linear function represented in
the table?

Answers

Slope formula: [tex]\frac{y1-y2}{x1-x2}[/tex]

To find the slope:

[tex]\frac{1-0}{0-(-7)} =\frac{1}{7}[/tex]

Hope it helps!

Answer:

Step-by-step explanation:

Good morning/evening!

The table we have is,

[tex]\Large\boxed{\begin{tabular}{c | 1} x & y \\ \cline {1-2} -7 & 0 \\ 0 & 1 \end{tabular}}}[/tex]

This is enough information. Using this we CAN find the slope of the line.

We will utilise the formula,

[tex]\Large\boldsymbol{\sf{m=\dfrac{\triangle y}{\triangle x}}}[/tex]

Slope = Change in y divided by the change in x

The change in y is 1, and the change in x is 7.

∵, the slope is [tex]\boxed{\rm{1/7}}[/tex]

done !!

[tex]\orange\hspace{300pt}\above3[/tex]

How many yards are in 1 mile 300 feet?

Answers

there are 1,860 yards in a mile & 300 ft

Answer:

1860 yards

Step-by-step explanation:

17.3152 to the nearest hundredth=

Answers

Answer:

17.32

Step-by-step explanation:

since there is a 5 in the thousandths, we round the 1 in the hundredths up and get 17.32

A polygon has the following interior angle , (y+10); (y+20); (y+30); (y+40); (y+50);

Answers

Y=78
A polygon has a total of 5 interior angles
In order to find the total amount of angles in a shape you do (the amount of angles - 2)x180 degrees
(5-2(3))180
3x180=540
Add the numbers you know (10+20+30+40+50=150)
540-150=390 and there are 5y altogether so divide 390 by 5 which is 78

8/11 minus negative 1/3

Answers

Answer:

[tex] \frac{35}{33} [/tex]

Step-by-step explanation:

[tex] \frac{8}{11} - ( - \frac{1}{3} ) \\ = \frac{8}{11} + \frac{1}{3} \\ = \frac{8 \times 3}{11 \times 3} + \frac{1 \times 11}{3 \times 11} \\ = \frac{24}{33} + \frac{11}{33} \\ = \frac{35}{33} [/tex]

Things to note :

Subtracting a negative value will be equals to adding.

To add/subtract 2 fractions together, the denominator must be the same.

describe how you can use similar triangles to explain that the slope

Answers

Similar triangles can be used to explain the slope through the right angle.

What is a triangle?

It should be noted that a triangle refers to a shape that has three sides and angles.

In this case, similar triangles can be used to explain the slope through the right angle. The slope of the hypotenuse is what we are concerned about.

The legs of the triangle will be the horizontal change and the vertical change of the endpoints.

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Suppose y varies directly with x. If x is 15 when yis 25, what is x when y is 10?

Answers

Answer:

the value of x will be

x= (10x15)/25=6

Which linear inequality is represented by the graph?
O y > ²/ ²x-3/1/2 -X 5
O y²³x+²/ 1
O y ≤ ² x + 1/1/0
O y< ²/x - / / -X 5​

Answers

The linear inequality depicted by the graph is: [tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this line, when x = 0, y = 0.2, hence the y-intercept is of b = 0.2. When x = 3, y = 2.2, hence the slope is given as follows:

[tex]m = \frac{2.2 - 0.2}{3 - 0} = \frac{2}{3}[/tex]

Hence the equation of the line is:

[tex]y = \frac{2}{3}x + 0.2[/tex]

[tex]y = \frac{2}{3}x + \frac{1}{5}[/tex]

The inequality is the values below(less) than the line, also including it, as it is not dashed, hence:

[tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

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Which list shows all the factors of 16?
A. 1, 2, 4, 8
B. 1, 2, 3, 8, 16
C. 1, 2, 4, 8, 16
D. 16, 32, 48, 64

Answers

Answer:

C

Step-by-step explanation:

To be a factor of 16 they need to be numbers that divide into it without remainders.

Answer:

Step-by-step explanation:

its C

You are working out a budget for your holiday. Here is your list: Food $594.09 Clothes $204.33 Trips $100.40 Transport $310.05 Extras $189.74 Estimate how much you will spend altogether $ (Round each price to a hundred dollars before estimating)

Answers

We will spend altogether $1400.

We know that the process of combining two or more items is known as an addition. Addends are the sums of the numbers that are added. The addition sign (+), which is positioned in between the addends, is present. The outcome of adding the addends is referred to as the sum.

Given that

Food = $594.09

Clothes = $204.33

Trips = $100.40

Transport = $310.05

Extras = $189.74

Now we have to round each price to a hundred dollars.

Food = $600

Clothes = $200

Trips = $100

Transport = $300

Extras = $200

Now the sum = 600 + 200 + 100 + 300 + 200 = 1400

Therefore, we will spend altogether $1400.

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Lila’s dog Mollie had 8 puppies. 6 of them were male and 2 were female. What percent of Mollie’s puppies were female?

Answers

25% of mollies puppies were female

You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.

All the roles have now been cast, and the lead actors playing the following parts are gathered around a large circular table for their first read: Jean Valjean, Inspector Javert, Thénardier, Enjolras, Marius, Fantine, adult Cosette, adult Éponine, and Madame Thénardier. It is your job to seat these 9 actors, the 3 producers, and the director around the table.


In Les Misérables, Monsieur Thénardier and Madame Thénardier are married, and during Act 2, Cosette and Marius become married. If the Thénardiers must next to one another, and Cosette and Marius must sit next to one another, but there are no restrictions on how the others can sit, how many different ways can you seat the 13 people around the circular table?



4
17,160
14,515,200
6,227,020,800

Answers

There are 14,515,200 ways to arrange the people around the table

How to determine the number of ways?

The given parameters are:

People = 13

Thénardiers = 2 actors

Cosette and Marius = 2 actors

If the married actors must seat together, then the actors must be grouped as 1.

The 2 actors can be arranged in 2! ways each

Now, there are 9 individuals remaining

The 9 people can be arranged in 9! ways

So, the number of ways is

Ways= 2! * 2!* 9!

Evaluate

Ways =14,515,200

Hence, there are 14,515,200 ways to arrange the people around the table

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jake has 32 quarters on his desk, and molly has q qaurters in her purse. Which algebraic expression represents the total numbers of quarters that jake and molly have.

Answers

Answer:

32+q=x

Step-by-step explanation:

32(jakes) + q (molly) = x(total)

Answer:

32+Q= total number of quarters.

Step-by-step explanation:

Find the critical value z alpha/2 that corresponds to the given confidence level. ​81%

Answers

Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie. The required critical value is 1.31.

What are critical Values?

Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie; for example, if the null hypothesis is true, the critical value is surpassed with probability alpha.

The value of α can be written as,

α = 1 - 0.81 = 0.19

[tex]z_{\frac{\alpha}{2}} = \dfrac{0.19}{2}= 0.095[/tex]

Now, using the z-table the value of z will be,

z = 1.31

Hence, the required critical value is 1.31.

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Which of the following number lines represents the solution set of > -6?

Answers

The number line first represents the solution to the inequality x/-1 > -6 option first is correct.

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The complete question is:

Which of the following number lines represents the solution set of x/-1 > -6?

For the number lines shown in the attached picture, please refer to the picture.

We have an inequality:

x/-1 > -6

x < 6  

x ∈ (-∞, 6)

Thus, the number line first represents the solution to the inequality x/-1 > -6 option first is correct.

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Please help! Need to pass!

Answers

The height of the ramp of Raúl is calculated as; 8ft

How to use the principle of similar triangles?

Both big and small triangles are similar triangles because all three of their corresponding angles are congruent.

Now, to get the height we will use the concept of similar triangles to get;

h/2 = 12/3

Cross multiply to get;

h = 24/3

h = 8 ft

Thus, the height of the ramp of Raúl is 8ft.

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twelve bottles of water cost $9. How many bottles can you buy for $3?
What is the cost per bottle of water? How much would 7 bottles of water cost?

Answers

That is the answer for the 3 questions

12 bottles cost 9
And 3 dollars goes into 9 dollars three times, so to figure out how many u must do 12/3 = 4
So he can buy 4 bottles for three dollars
What is the cost per bottle?
Let x be cost of one bottle
12x=9
So x = 9/12 =3/4 = 0.75 cent
We know that if one bottle is 0.75 cent, then 7 bottles must be 0.75 x7= $5.25

Suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.
Determine the iterative rule for each sequence. Show your work.

Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.

my table is below (it is correct, I checked with my math teacher, it is ten percent added to the previous week for all you doubters)

Answers

The iterative rule for each sequence in the table will be to use the slope-intercept form of the equation of a line y=mx+b.

How to depict the information?

In this situation, x is the week, and y is the amount paid. Basically, you need to find the slope, represented by m, which is the amount the amount paid increases by each week, and the y-intercept, b, which is the "amount paid" at week 0.

The x-coordinate is the week, and the y coordinate is the amount paid. Because the weeks are incrementing by 1, x2-x1=1.

After that, to complete the rule, you need to find the y-intercept. If the amount paid is 200 on week 1, and the amount paid increases by 50 each week.

Another way to think about it is by plugging your points into the incomplete rule. Let b represent the y-intercept. Plug in the values for week 1 and solve for b.

The calculations to convince your friend that both your rules work are:

m=(y2-y1)/(x2-x1)

(x1,y1)=(1,200)

(x2,y2)=(2,250)

m=(250-200)/(2-1)

=50/1 =50

y=50x+b

200=50(1)+b

200=50+b

b=200-50

b=150

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For 2018, XYZ Co. uses machine-hours as the only overhead cost-allocation base. The direct cost rate is $8.00 per unit. The selling price of the product is $25.00. The estimated manufacturing overhead costs are $320,000 and estimated 50,000 machine hours. The actual manufacturing overhead costs are $360,000 and actual machine hours are 55,000. Using job costing, the 2018 actual (not predetermined) overhead cost rate is ________.

Answers

The 2018 actual overhead cost rate is $6.55

Compute the actual overhead cost rate for 2018?

Note that the requirement is to determine the actual overhead cost rate per machine hour in the year 2018, which considers the actual manufacturing overhead incurred and the actual machine hours used.

In essence, the actual overhead cost rate is the actual manufacturing overhead cost divided by the actual machine hours

actual overhead cost rate=$360,000/55,000

actual overhead cost rate=$6.55

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Write the equation of the line with slope -5 and y-intercept 300.

Answers

The slope-intercept form is y=mx+b

m=slope=-5

y-int/b = 300

so, y = -5x+300 is the equation of the line

Graph the image of the figure given the transformation

Answers

This transformation requires us to shift 1 unit left and 4 units down.

A whale swimming against an ocean current traveled 140 mi in 7 h. Swimming in the opposite direction, with the current, the whale was able to travel the same distance in 3.5 h. Find the speed of the whale in calm water and the rate of the ocean current.

Answers

The whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

How to estimate the speed of the whale in calm water and the rate of the ocean current?

Let x be the speed of a whale in calm water

and y be the speed of the current

In 7 hours the whale swims against the current and travels 140 miles:

7(x - y) = 140

x - y = 140/7

x - y = 20 ...........(1)

In 3.5 hours the whale swims the same distance with the current:

3.5(x + y) = 140

x + y = 140/3.5

x + y = 40 ...........(2)

Adding (1) and (2), we get the value of x:

x - y = 20  + ...........(1)

x + y = 40 ...........(2)

-----------------

2x = 60

x = 60/2

x = 30

Using this value for "x" in either (1) or (2) we can solve for "y":

x - y = 20 ...........(1)

substitute for "x"

30 - y = 20

10 = y

Therefore, the whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

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How to Answer this i dont know please like it was not in the book im so confused

3y−13≥−9 and 3y−13≤−1

Answers

The solution to the system of inequalities given is: [tex]\frac{4}{3} \leq y \leq 4[/tex]

What is the solutions to a system of inequalities?

The solution is the set of values that respect all conditions of the system.

The first condition is:

[tex]3y - 13 \geq -9[/tex]

[tex]3y \geq 4[/tex]

[tex]y \geq \frac{4}{3}[/tex]

The second condition is:

[tex]3y - 13 \leq -1[/tex]

[tex]3y \leq 12[/tex]

[tex]y \leq \frac{12}{3}[/tex]

[tex]y \leq 4[/tex]

The intersection of the conditions, which is the solution to the inequality, is:

[tex]\frac{4}{3} \leq y \leq 4[/tex]

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A grain silo has a cylindrical shape. Its diameter is 19ft, and its height is 40ft. What is the volume of the silo? Use the value 3.14 for π, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.

Answers

Step-by-step explanation:

formula to get the volume of a cylindrical shape =πr²h

π=3.14 , r=diameter /2=19/2= 9.5, h= 40

: πr²h= 3.14 ×9.5²×40

3.14×90.25×40

=11,335.4

=11,335

Dalvin drove 190 miles in 5 hours. If he continued at the same rate, how far would he travel in 8 hours?

Answers

Calvin would travel 304 miles in 8 hours.
Answer:  304 miles

Explanation:

Dalvin drives 190 miles in 5 hours. His speed is 190/5 = 38 mph.

From here we would say the following

distance = rate*time

distance = (38 mph)*(8 hrs)

distance = 304 miles

If the coordinates of one endpoint of a
line segment are (2, 3) and the midpoint
of the segment is (5,3), what are the
coordinates of the other endpoint of the
segment?

Answers

Answer: (8,3)

Step-by-step explanation:

The distance from (2,3) to (5,3) is 3. The only other point that is 3 units away from (5,3) where y=3 is (8,3).

The difference of a number and its reciprocal is 35/6 Find the number.

Answers

Answer:

[tex]\huge\boxed{\sf x = 6 \ \ \ OR \ \ \ x = -1/6}[/tex]

Step-by-step explanation:

Let the number be x

Given condition:

[tex]\displaystyle x - \frac{1}{x} =\frac{35}{6} \\\\Subtract \frac{35}{6} \ to \ both \ sides\\\\x - \frac{1}{x} -\frac{35}{6} = 0\\\\Multiply \ 6x \ to \ both \ sides\\\\x \times 6x - \frac{1}{x} \times 6x -\frac{35}{6} \times 6x = 0 \times 6x\\\\6x^2-6-35x=0\\\\6x^2-35x - 6 = 0[/tex]

Applying mid term break formula

We can use the factor -36 and +1 to break the mid term (-35x) because multiplying -36 and +1 gives -36 which is the product of side terms (-6 * +6 = -36)

[tex]6x^2-36x+x-6=0\\\\Take \ common\\\\6x(x-6)+1(x-6)=0\\\\Take \ (x-6) \ common\\\\(x-6)(6x+1)=0[/tex]

Either:

x - 6 = 0     OR    6x + 1 = 0

x = 6          OR      6x = -1

x = 6          OR       x = -1/6

a wholesaler allows a discount of 25kobo for every 25 naira goods purchased . find the percentage discount allowed.

Answers

The percentage discount allowed by the wholesaler is 1%

Percentage

1 naira = 100 Kobo

25 naira = 25 × 100

= 2500 Kobo

Percentage discount allowed = 25 / 2500 × 100

= 0.01 × 100

= 1%

Therefore, the percentage discount allowed is 1%

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