Mathematics High School

subtract 13 5/8 - 3 2/3

Answers

Answer 1

Answer:

9 23/24

Step-by-step explanation:

Change both mixed fractions to improper fractions

13 5/8=109/8

3 2/3=8

Now substract: 109/8 - 8/3= 10 23/24.

Hope this helps!!

Related Questions

suppose the data on natural birth weights (collected by the world health organization (who)) is normally distributed with the mean equal to 7.25 pound for a full-term birth and standard deviation of 1.0 pounds. what is the probability that a randomly selected baby will weigh more than 9.75 pounds at birth? 0.0062

Answers

The probability that a randomly selected baby will weigh more than 9.75 pounds at birth is 0.0062, or about 0.62%. This means that the vast majority of babies will weigh less than 9.75 pounds at birth, as this value is more than two standard deviations above the mean.

We can use the standard normal distribution to solve this problem by first standardizing the value of 9.75 pounds using the formula:

z = (x - mu) / sigma

where x is the value of 9.75 pounds, mu is the mean of 7.25 pounds, and sigma is the standard deviation of 1.0 pound.

Substituting the values, we get:

z = (9.75 - 7.25) / 1.0 = 2.5

We can then use a standard normal distribution table or calculator to find the probability of a z-score greater than 2.5. From the table or calculator, we find that this probability is approximately 0.0062.

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Algebraic Inequalities
Help pls need assistance
DUE today in

Answers

Answer:

8, 8.001, 8.01, 8.1, 9, 11, 13, 16

Step-by-step explanation:

From the instructions given, we know that variable u [tex]\geq[/tex] 8. the [tex]\geq[/tex] sign means that the number is greater than or is equal to the number, which is in this case, 8. In the numbers given, (0, 7, 7.999, 8.01, 11, 3, 7.9, 8, 8.1, 13, 5, 7.99, 8.001, 9, 16) we name the numbers greater than or equal to 8 that are stated in the list.

draw a quadratic function that only has one root at 3

Answers

The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2

What is quadratic equation?

A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:

ax^2 + bx + c = 0

If a quadratic function has only one root at 3, then it must be of the form:

f(x) = a(x - 3)^2

where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.

To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:

4 = a(0 - 3)^2

4 = 9a

a = 4/9

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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]

Why is it called a quadratic equation?

A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.

A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:

[tex]ax^2+bx+c=0[/tex]

If the quadratic function has only one root at 3, it must have the following form:

[tex]f(x)=a(x-3)^2[/tex]

This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.

We know that f(0) = 4, so we can plug these numbers into the equation to get:

[tex]4=a(0-3)^2[/tex]

simplify the above equation

4 = 9a

The value is,

a = 4/9

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A random survey of enrollment at 35 community colleges across the United States yielded the following figures:
6,414; 1,550; 2,109; 9,350; 21,828; 4,300; 5,944; 5,722; 2,825; 2,044; 5,481; 5,200; 5,853; 2,750; 10,012; 6,357; 27,000; 9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080; 11,622.
Assume the underlying population is normal.
a.
i. = __________
ii. sx = __________
iii. n = __________
iv. n – 1 = __________
b. Define the random variables X and in words.
c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United States.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
e. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?

Answers

The larger sample size also reduces the impact of individual outliers, which could potentially skew the results. Therefore, increasing the sample size will result in more reliable results, and a smaller error bound and confidence interval.

The error bound (E) for the sample size of 35 community colleges is calculated using the formula: E =[tex]1.96 * √[p*(1-p)/n].[/tex]

With n = 35, p = 0.5 (assuming the mean of the enrollment figures is 0.5), the error bound is calculated to be E = 0.823.

If the sample size is increased to 500 community colleges, the error bound would be reduced to 0.338. This is because the larger the sample size, the smaller the error bound. The confidence interval would also be reduced, since it is directly proportional to the error bound.

In practical terms, a larger sample size means more reliable results. This is because when the sample size is increased, the results tend to be more representative of the entire population, leading to more accurate conclusions.

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1. Representar en GeoGebra las funciones dadas y determinar comprobando analíticamente: a. Tipo de función b. Dominio y rango c. Asíntotas, tanto vertical y horizontal, si las tiene: [tex]f(x)=\frac{2x^{2}-4}{x^{2}-4 }[/tex]

Answers

The given functions in GeoGebra and determine by analytically checking:

a. function type is [tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

b. Domain and range Range (-2, +2).

c. Asymptotes is HA = 2 and VA = ±2

The function y = f( x) is classified into different types of functions, grounded on factors similar as the sphere and range of a function, and the function expression. The functions have a sphere x value that's appertained as input. The sphere value can be a number, angle, numeric, bit.

[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

Functions in mathematics can be compared to the operations of a dealing (soda pop) machine. When you put in a certain quantum of plutocrat, you can elect different types of tonics. also, for functions, we input different figures and we get new figures as the result. sphere and range are the main aspects of functions.

[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

x² = 4

x = ± 2

Range (-2, +2).

An asymptote is a line being approached by a wind but noway touching the wind. i.e., an asymptote is a line to which the graph of a function converges. We generally don't need to draw asymptotes while graphing functions. But graphing them using dotted lines( imaginary lines) makes us take care of the wind not touching the asymptote. Hence, the asymptotes are just imaginary lines.

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Complete question:

Represent the given functions in GeoGebra and determine by analytically checking: a. function type b. Domain and range c. Asymptotes, both vertical and horizontal, if it has them:

which formula would you use to calculate the total enclosed space of firms 2’s structure?

Answers

Answer:

Firm 2's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,

Volume = πr²h

where r = radius of the structure

h = height of the Firm

By substituting the values of 'r' and 'h' in the given formula,

V =

�

(

)

(

)

π(

)

(60)

�

(

)

π(35)×60

= 6597.345

≈ 6597.35 cubic feet

Total enclosed space of Firm 2 is 6597.35 cubic feet.

if only the upper 35% of a normally distributed class passed a quiz for which the mean was 70 and the standard deviation was 10, what was the lowest score a student could have received and still have passed? g

Answers

The lowest score a student could have received and still have passed the quiz with a normally distributed class is 55.

This is because the upper 35% of a normally distributed class corresponds to a score of 1.5 standard deviations above the mean. Since the mean was 70 and the standard deviation was 10, that would mean the lowest score a student could have received and still have passed the quiz is 70 + (1.5 * 10) = 70 + 15 = 55.

In summary,
1. Start with the mean of the quiz which is 70.
2. Add 1.5 standard deviations which is 1.5 * 10 = 15.
3. The result is the lowest score a student could have received and still have passed the quiz which is 70 + 15 = 55.

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Helen flips a coin and rolls a dice calculate the probability of getting 4 and tails

Answers

Answer:

1/12 or 0.0833

Step-by-step explanation:

P(Coin) = 1/2

P(Dice) = 1/6

1/2 × 1/6 = 1/12

noah sold 30 avocados that were small and large. he sold the small avocados for 35 cents and the large ones for 50 cents. if noah made $13.50, how many of each kind did he sell?

Answers

Noah sold 10 small avocados and 20 large avocados.

Let's assume that Noah sold "x" small avocados and "y" large avocados.

From the given information, we can write two equations:

x + y = 30 (since Noah sold a total of 30 avocados)

0.35x + 0.50y = 13.50 (since Noah made $13.50)

Now, we can use any method to solve these equations, such as substitution or elimination. Here, we will use the substitution method:

From the first equation, we can write:

x = 30 - y

Substituting this value of x in the second equation, we get:

0.35(30 - y) + 0.50y = 13.50

Simplifying this equation, we get:

10.50 - 0.35y + 0.50y = 13.50

0.15y = 3

y = 20

Substituting this value of y in the equation x = 30 - y, we get:

x = 30 - 20 = 10

Therefore, Noah sold 10 small avocados and 20 large avocados.

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to secure a 500 meter radio tower against high winds, guy wires are attached to a ring 5 meters from the top of the tower. the wires for a 15 degree angle with the tower. find the distance from the tower to the guy wire anchor in the ground

Answers

The distance from the tower to the ground anchor is approximately 2091.36 meters.

We can use trigonometry to solve this problem. Let's call the distance from the tower to the ground anchor "x". We can draw a right triangle with the tower as the vertical side, the guy wire as the hypotenuse, and the distance we're trying to find as the horizontal side.

The angle between the tower and the guy wire is 15 degrees, so the angle between the guy wire and the horizontal is 90 - 15 = 75 degrees.

Using the trigonometric function tangent, we can set up the following equation

tan(75) = x / 500

We can solve for x by multiplying both sides by 500 and taking the tangent of 75 degrees

x = 500 × tan(75)

x ≈ 2091.36 meters

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1. use the quadratic equation to find the exact solutions to this equation, and simplify your answer: 2x^2 6x 12

Answers

As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].

To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.

Substituting these values in the quadratic formula, we get

[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]

Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]

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Please help :( I don't quite understand...

Answers

Step-by-step explanation:

For Part A, use the function f(x) to find the average of tests taken.

X is number of test taken

f(x) is the average score given said num of tests taken,x,

We want after test number 3 so using the function,

[tex]f(x) = 0.2x + 79[/tex]

Plug in. 3 for x, and we will get our answer.

[tex]f(3) = 0.2(3) + 79 = 79.6[/tex]

Part B: Use the table for the answer.

When 2 test are taken, the average test score is

So part B is 84.

Part C:

[tex]f(2) = 0.2(2) + 79 = 79.4[/tex]

[tex]g(2) = 84[/tex]

Since

[tex]g(2) > f(2)[/tex]

The science class had a higher average after 2 tests

Answer:

you shoulda payed attention in class

Step-by-step explanation:

also u know it's bad when the test is so hard you can't even cheat on it

antonio rolls the 10-sided die from the example. what is the probabilty of rolling a number 10 or less? a number greater than 10

Answers

The probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

The 10-sided die has 10 faces, each marked with a unique number from 1 to 10. When we talk about the probability of rolling a particular number, we're asking what the chances are of that number coming up when the die is rolled.

In this case, the question asks for the probability of rolling a number 10 or less, which means we're interested in the probability of rolling any number from 1 to 10. Since all the possible outcomes are numbers from 1 to 10, the probability of rolling a number 10 or less is certain, or 1.

This is because the sum of probabilities of all possible outcomes of an experiment is always 1.

Similarly, the probability of rolling a number greater than 10 is impossible, or 0. This is because there are no possible outcomes greater than 10 on the 10-sided die. In general, the probability of an event that cannot occur is always 0.

So, the probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

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there are 3 soccer games in a month, and 8 are played at night. the season is 4 months. how many games are the season?

Answers

There are a total of 48 soccer games in the season.

Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:

Number of day games = Total number of games - Number of night games

= 12 games/month x 4 months - 8 night games/month x 4 months

= 48 games - 32 games

= 16 games

Therefore, the total number of games in the season is:

Total number of games = Number of day games + Number of night games

= 16 games + 32 games

= 48 games

So, there are 48 soccer games in the season.

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Find the value of x.

Answers

The value of x is 5

What is a chord?

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. All diameters are chord and but all chords are not diameter.

Since the value of the chords are thesame, the arc length RS and PQ are thesame.

Therefore ;

x+17 = 4x+2

collect like terms

4x -x = 17-2

3x = 15

divide both sides by 3

x = 15/3

x = 5

therefore the value of x is 5

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1. A rain barrel collects water off the roof of a house during three hours of heavy rainfall. The height of the water in the barrel increases at the rate of r(t) = 47-15 feet per hour, where is the time in hours since the rain began. At time t = 1 hour, the height of the water is 0. 75 foot. What is the height of the water in the barrel at time = 2 hours? (A) 1. 361 ft (B) 1. 500 ft (C) 1. 672 (D) 2. 111

Answers

As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).

The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.

In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.

∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922

So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:

0.75 + 0.922 = 1.672 feet

Therefore, the correct option is (C).

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g calculate the labor force participation rate if you know that the adult working-age population is 320 million, 114 million of which are not in the labor force. what is the labor force participation rate? (round your answer to the nearest tenth.)

Answers

The labor force participation rate is 64.4%.

To calculate the labor force participation rate, we need to know the number of people who are either employed or actively seeking employment. We can calculate this as follows:

Labor force = adult working-age population - not in labor force

Labor force = 320 million - 114 million

Subtract the numbers

Labor force = 206 million

So the labor force participation rate is

Labor force participation rate = (labor force / adult working-age population) x 100%

Substitute the values in the equation

Labor force participation rate = (206 million / 320 million) x 100%

Labor force participation rate = 64.4%

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I ask you, to solve the system.
y=x2+2x-2
y=x+10

Answers

Answer:

y = 22 - x2 or x = 12 - x2

Step-by-step explanation:

Suppose that the next day there were sales of $7,100. What measure of center would you use to summarize the typical daily revenue of the food truck now?

Answers

Answer:

To summarize the typical daily revenue of the food truck now, we would use the new mean of the daily revenue, which takes into account the new sale of $7,100. We can add this new value to the previous sum of daily revenues and divide the total by the number of days to find the new mean:

New mean = (total sum of daily revenues + $7,100) / (number of days + 1)

This would give us the updated measure of center that reflects the new data point.

The mean daily revenue of the food truck now is $6,550.

What is average?

The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.

To summarize the typical daily revenue of the food truck now, we would use the mean as the measure of the center.

We can calculate the mean daily revenue by adding the daily revenues from the two days ($6,000 + $7,100 = $13,100) and dividing by the number of days (2).

Mean daily revenue = (Total revenue) / (Number of days) = $13,100 / 2 = $6,550

Therefore, the mean daily revenue of the food truck now is $6,550.

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hills vanessa is walking up a hill. after walking 40 feet, she has climbed a total of 8 feet vertically. if she walks an additional 25 feet up the hill, how many feet will she have climbed vertically in total?

Answers

Vanessa's vertical climb rate is 0.2 feet per foot of horizontal distance. When she walks 65 feet horizontally up the hill and climbs an additional 25 feet, her total vertical climb will be 21 feet.

For every 40 feet of horizontal distance Vanessa walks, she climbs 8 feet vertically. So her vertical climb rate is 8/40 = 0.2 feet per foot of horizontal distance.

If she walks an additional 25 feet up the hill, her total horizontal distance traveled will be 40 + 25 = 65 feet.

Therefore, her total vertical climb will be 0.2 times her total horizontal distance:

8 + (0.2 * 65) = 8 + 13 = 21 feet

So, Vanessa will have climbed a total of 21 feet vertically after walking 65 feet horizontally up the hill.

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Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content

Answers

The expression represents the constraint that the amount of fat in the cookie should not deviate from the target fat content by more than 1.8 grams per cookie is |f - 5| ≤ 1.8

To express the difference between the fat in a cookie from the new recipe and the target fat content, we can use an expression. Let's represent the amount of fat in a cookie from the new recipe as f. Then, the difference between the fat in the cookie and the target fat content of 5 grams per cookie can be expressed as:

|f - 5|

The vertical bars around the expression indicate the absolute value, which means that we want the difference to be positive, regardless of whether f is greater or less than 5.

Now, we also know that the company will accept a difference of up to 1.8 grams per cookie. This means that the expression above should be less than or equal to 1.8:

|f - 5| ≤ 1.8

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Complete Question:

The Billing sly Cookie Company is experimenting with a new low-fat cookie recipe. The management wants the bakers to come up with a cookie that is low in fat but still has good taste. The company decides on a target fat content of 5 grams per cookie. In order to be labeled low-fat, a difference of 1.8 grams per cookie is acceptable. This means the amount of fat should be no more than 1.8 grams above 5 or no more than 1.8 grams below 5.

Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content. Use f to represent the amount of fat in a cookie from the new recipe.

1. Compare the two box plots.
Looking at the majority, which group is taller?
Circle.
●
Boys
●
Girls
Which group has a smaller center of data? By how much?
Circle: Boys Girls
by
inches.
Which group has a larger range? Circle.
2. Compare the two dot plots.
● Are the graphs symmetrical or skewed?
Which dot plot has a larger center of data?
Which dot plot has a larger range?
Boys
Girls
Boys
+ + +
60 61
Girls
Height (inches) of Girls and Boys
.
62 63
+
64 65 66 67
+
69
68
+
70
+
71
Number of Fruit Smoothies Sold
+
72
Smoothies
Galore
50 55 60 65 70 75 80 85 90 95 100
Sunshine
Smoothies

Answers

Boys are taller than girls on average, with a larger center of data and larger range in height;

the dot plots are not shown.

This rich aunt invests $37000 in a savings bond for the baby which earns 1.125% interest every quarter. How much total interest has this savings bond earned 24 quarters after the rich aunt invested? [Include a dollar sign in your answer and round to the nearest penny.]

Answers

The total interest earned on a savings bond over 24 quarters with a principal investment of $37,000 and an interest rate of 1.125% per quarter, the savings bond has earned a total interest of $9,990.

The savings bond earns 1.125%/quarter, so its quarterly interest rate is 0.01125. The amount of interest earned in one quarter is the product of the interest rate and the principal amount, which is:

To calculate the interest earned in one quarter, we multiply the principal amount by the interest rate expressed as a decimal.

Interest earned in one quarter = 0.01125 x $37,000 = $416.25

In this case, the interest earned in one quarter is $416.25.

To find the total interest earned over 24 quarters, we multiply the interest earned in one quarter by the number of quarters, which is 24.

After 24 quarters, the total interest earned is:

Total interest earned = 24 x $416.25 = $9,990

Therefore, the savings bond has earned a total interest of $9,990 after 24 quarters.

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5x+2y=10
Find the Y intercept and gradient

Answers

1. Rearrange the equation into y=mx+b

- Subtract 5x on both sides

2y = -5x + 10

2. Divide both sides by 2 to get y by itself.

y = -5/2x + 10/2

y= -5/2x + 5

Answer: y-intercept > 5 gradient > -5/2

what is $510,451 rounded to the nearest 1,000 dolllars?

Answers

Answer:

$510,000

Step-by-step explanation:

Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.

Remember, 4 or less, round down. 5 or more, round up.

Since the hundreds digit is 4, we do not need to round.

We only need to change the rest of the digits to 0.

So, our answer would be $510,000.

Kim's hourly wage is $14. She works 37 hours per week. What is her monthly income?

Answers

Answer:

2072

Step-by-step explanation:

Multiply 14 x 37

518 x 4

2072

Answer: $2,072 a month

Step-by-step explanation:

multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply 518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072

Geometry, and Slope. Worth 15 Points
Please Explain

Answers

The equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

Given,

x+2y=2

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

Slope = -1/2 = [tex]m_{1}[/tex]

Let Slope of line perpendicular to line x+2y=2 is [tex]m_{2}[/tex]

⇒ [tex]m_{1}[/tex] * [tex]m_{2}[/tex] = -1

Then [tex]m_{2}[/tex] = 1/2

Equation of line perpendicular is given by

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

Since it contains point (5,6)

6 = [tex]\frac{1}{2} (5) + c[/tex]

c= [tex]\frac{7}{2}[/tex]

Then the equation of line is:

[tex]y = \frac{1}{2}x+ \frac{7}{2}[/tex].

Therefore, the equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

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The graphs of line a and b are shown in this coordinate grid
Match each line with it's equation. Drag each equation to the corresponding box for each line

Answers

The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)