Answers
Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]
Option A is correct
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here, the given line is
2x + 5y = 10
5y = -2x + 10
[tex]y = -\frac{2}{5}x + \frac{10}{5}\\y = -\frac{2}{5}x + 2[/tex]
Slope of the given line is [tex]-\frac{2}{5}[/tex]
Slope of the line perpendicular to this given line is [tex]\frac{5}{2}[/tex]
The line passes through (-2, -3)
Equation of the required line
[tex]y - (-3) = \frac{5}{2}(x - (-2))\\y + 3 = \frac{5}{2}(x + 2)\\2y + 6 = 5x + 10\\2y = 5x + 10 - 6\\2y = 5x + 4\\y = \frac{5}{2}x + \frac{4}{2}\\y = \frac{5}{2}x + 2[/tex]
Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]
Option A is correct
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Related Questions
Can someone help pls
Answers
Answer:
99
Step-by-step explanation: 99
40
100%
Complete the table to show different percentages of the steaming time.
Time (min)
Percentage
100% of 40 min
50% of 40 min
250% of 40 min
Answers
The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively
How to complete the table to show different percentages of the steaming time?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min
100% of 40 min:
100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min
50% of 40 min:
50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min
250% of 40 min:
250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min
Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.
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what are her monthly payments
Answers
The interest she is pay total is $2340.822 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
Given that,
For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
We have to find will she pay interest at all.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $6490
r is 7.26%
t is 5 years
So,
i= 6490×0.0726×5
i= $2355.87
Therefore, the interest she is pay total is $2355.87 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
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HELP PLEASE!!
Are these expressions equivalent?
Drag and drop a symbol to correctly complete the comparison.
5+9-2^3___4^2-6
A. =
B.≠
Answers
The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expressions are given below.
(5 + 9 - 2³) and (4² - 6)
Simplify the expression, then we have
(5 + 9 - 2³) = 5 + 9 - 8 = 6
(4² - 6) = 16 - 6 = 10
The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.
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How many legs do 40 cows have if 3 cows only have 2
Answers
Answer:
154 legs
Step-by-step explanation:
40-3=37
37 times 4 = 148
3 times 2 ° 6
148+6= 154
Answer: 154 legs
Step-by-step explanation: First, multiply 37×4 because there are 37 cows with 4 legs, which gets you 148. Since there are 3 cows with only 2 legs, do 3×2=6. Finally, add 148 and 6 to get 154 legs.
please give brainliest!
Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72. Which of the following are still outstanding?
I. A $44.09 check to the electronics store
II. A $73.98 check to the mechanic
III. A $49.96 paycheck deposit
IV. A $64.79 check deposit from Brett’s cousin
Answers
Is there a proportional relationship between the area and radius of a circle? Explain.
Answers
The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
The area of a circle with radius "r" is given as,
A = πr²
Since,π = constant.
Removing constant by proportionality.
A ∝ r²
Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".
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reduce 12/16 to simplest terms
Answers
Answer: 3/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 12 and 16 is 4
Divide both the numerator and denominator by the GCD
12 ÷ 4
16 ÷ 4
Reduced fraction: 3/4
Therefore, 12/16 simplified to lowest terms is 3/4.
Answer:.
Step-by-step explanation:
Using the graph below, determine the employee's hourly wage.
Answers
Using the graph, the hourly wage of the employees is: $8 per hour.
How to Determine Hourly Wage From a Graph?Slope of a proportional graph is the unit rate between two variables, x and y, and it is calculated as: k = y/x.
To find the unit rate or slope of the graph, use any point on the graph (x, y).
The unit rate of the graph in the image above is the hourly wage of the employees.
Using any point on the line, say, (13, 104), we can find the slope/unit rate. Therefore:
Unit rate/slope, k = 104/13
Unit rate/slope, k = 8
Therefore, the hourly wage is: $8 per hour.
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What are two other names for AB?
Will give Brainliest, answer quick please.
Answers
The other names of AB in the given figure are
collinear pointsline segmentWhat are collinear points?Collinear points refers to points that lies on the same plane and on the same straight line.
The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear
Points A, B and C are non colinear to points Q and R
Points AB are still part of line AC hence can be noted as part of line segment BC.
The line has arrow head and may also be called rays. In this case the are part of an arrow
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My friend is hoping to move to your town but is concerned because she doesn’t have a car. Do you think this will present a big problem for her? Use the distance formula in some way to justify your response.
Answers
There are many things obstructing the route so yes. I cannot give a detailed answer as I have not been given the "distance formula" sorry
Pls help need by today
Answers
Answer:
use AAA congurency rule
Step-by-step explanation:
angle a=angle f
angle b=angle e
angle c= angle d(a+b+c=180 when the triangle 2 sides are equal that means 3 is also equal)
5. Point A is 3 units directly below (2, 2). What are the coordinates of point A? Answer: Point A (___)
Answers
The X axis will not change since A is not going left or right of (2,2). You would count down 3 spaces for the y-axis and that would land you at -1 or you could solve by subtraction.
2-3= -1
There was 3/5 of a gallon of paint in the bucket. Dr. Wu used 2/5 of that. How much paint was left?
Answers
Answer:
1/5
Step-by-step explanation:
equation: 3/5-2/5=x
we can multiply the whole equation by 5 so that we can easily subtract the numbers
3-2=1
now we divide it by 5 so that we get our number in a fraction
after we divide we get 1/5
Ms. Jones is comparing two sets of scores. For Test A, the standard deviation is 7, and for Test B, the standard deviation is 12. This means that
Answers
The comparison done by Mr Jones means that Test A of standard deviation 7 is closer to the mean scores and Test B of standard deviation 12 is further apart from the mean score
What is standard deviation?The standard deviation is a statistic measure that expresses how much variance or dispersion there is in a group of numbers.
A high standard deviation suggests that the values are dispersed throughout a wider range,
A low standard deviation suggests that the values tend to be close to the established mean.
A positive value means the standard deviation is above the mean while a negative value means the standard deviation is below the mean
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rita class has 14 girls and 16 boys how does the ratio 14:30 describe ritas class
Answers
Answer:
The ratio shows that there are 14 girls to 30 students in total
Step-by-step explanation:
14 + 16 = 30 that mean that there are 30 students in total, therefore, the ratio shows 14 girls : 30 students
Solve-ns16 Which of the following must be true about the inequality and the resulting graph? Select three
options.
ns<-24
n>-24
The circle is open.
The circle is closed.
The arrow points right.
Answers
By using the concept of inequality, the correct options are
2nd, 4th and 5th option
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here,
The given inequation is
[tex]\frac{-2}{3}n \leq 16[/tex]
Now,
[tex]\frac{-2}{3}n \leq 16\\n \geq -16 \times \frac{3}{2}\\n \geq -24\\[/tex]
Since n is greater than or equal to 24, the arrow will point towards right
The circle will be closed as there is an equality
So the correct options are 2nd, 4th and 5th option
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Complete Question
The complete question has been attached here
If A = (1 , 4) and B = ( 7 , 6), then coordinates of the midpoint of AB are
Answers
Answer:
(4 , 5)
Step-by-step explanation:
midpoint formula: (x1+x2/2 , y1+y2/2)
so
(1+7/2 , 4+6/2)
(8/2 , 10/2)
4 , 5
Graph the solution set to the inequality: 8x - 7y ≥ 42
Answers
Answer:
How do I show you the graph because I have it
Step-by-step explanation:
NO LINKS!! Please help me with this probability question Part 1j
Answers
Answer:
[tex]\textsf{b)} \quad \text{P}(A\;\text{and}\;B)=\dfrac{1}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\text{P}(A)=\dfrac{1}{4}[/tex]
[tex]\text{P}(B)=\dfrac{1}{4}[/tex]
[tex]\text{P}(A|B)=\dfrac{4}{5}[/tex]
Conditional Probability Formula
[tex]\text{P}(A \cap B)=\text{P}(B)\;\text{P}(A|B)[/tex]
Substitute the given values into the formula:
[tex]\begin{aligned}\implies \text{P}(A \cap B)&=\dfrac{1}{4} \cdot \dfrac{4}{5}\\\\&=\dfrac{4}{20}\\\\&=\dfrac{1}{5}\end{aligned}[/tex]
A researcher believes that 8% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3%? Round your answer to four decimal places.
Answers
The probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3% is 0.9964
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 8% = 0.08
sample size, n = 694
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.08(1 - 0.08)) / 694}
= √{(0.08 * 0.98) / 694}
= 0.0103
The probability
differ from the population proportion by less than 3%
|X - 0.08| < 0.03
X < 0.11 OR X > 0.05
0.05 < X < 0.11
P(z < 0.11) - P(z < 0.05 )
z score for z < 0.05
z = (0.05 - 0.08) / 0.0103
= -2.9126
p value for z < -2.9126 = 0.001792
z score for z < 0.12
z = (0.12 - 0.09) / 0.0102
= 2.9412
p value for z < 2.9412 = 0.9982
The probability required = 0.9982 - 0.0016 = 0.9964 or 99.64%
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Solve the inequality.
3-x≤-19 or -x ≥ 24
x> [?] or x ≤
x≤[
Enter
Answers
The solution to the given inequality 3 - x ≤ 19
or - x ≥ 24 is x ≥ -16 or x ≤ -24
What is the solution of the inequality?An inequality is a statement that is of two quantities; one is specifically less than or greater than another. Inequality symbols are:
Less than < Less than or equal to ≤ Greater than > Greater than or equal to ≥ equal to =3 - x ≤ 19
or
- x ≥ 24
3 - x ≤ 19
substract 3 from both sides-x ≤ 19 - 3
- x ≤ 16
divide both sides by -1
x ≤ 16/-1
x ≥ -16
or
- x ≥ 24
divide both sides by -1x ≥ 24/-1
x ≤ -24
In conclusion, the solution to the inequality is given by x ≥ -16 or x ≤ -24
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Adam has a goal to hike
70 miles. If he hikes 8
miles per day, how
long will it take him to
hike all 70 miles?
Answers
Answer:
9 days (round up)
Step-by-step explanation:
70 ÷ 8 = 8.75
≈ 9 (round up)
Right now you have 8 times X = 70.
To solve this, you’re going to divide both sides by 8.
So you have X = 70/8
Now, assuming you’re not wanting that big of a fraction, we can simplify to 35/4 or put it in decimal format with 8.75.
Then your answers is 8.75!
Which animals will live in a building that is similar to the chimpanzee's house?
A. gorillas
B. Main Primate House
C. gibbons
D. orangutans
Answers
We can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.
What is a rectangle?In the Euclidean plane, a rectangle is a quadrilateral with four right angles. As an equiangular quadrilateral, which means that all of its angles are equal, it can also be referred to as a parallelogram with a right angle. A rectangle with four equal-length sides is a square.So, observe the given shapes on the graph:
The chimpanzee house is a rectangle with 8units×2units.If we take dimensions 8units×2units into consideration, then we notice that:Gibbons also has a house with identical dimensions as 8units×2units.
Therefore, we can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.
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Find the slope of the line that contains the points named.
P(1, 2), Q(3, 4)
0-1
01
02
Answers
Answer:
If the coordinates of at least two points in the line are given, the slope (m) may be calculated by, m = (y2 - y1) / (x2 - x1
Please help I need to find X
Answers
Answer:
x=17
Step-by-step explanation:
8x+20 is equal to 11x-31 because l parallel to m.
8x+20=11x-31
3x=51
x=17
Answer:
[tex]\sf x=17^o[/tex]Step-by-step explanation:
L || m
[tex]\sf (8x+20)^o=(11x-31)^o[/tex]
[ Corresponding angles]
[tex]\sf 8x+20=11x-31[/tex]
[tex]\sf 8x-11x=-31-20[/tex]
[tex]\sf -3x=-51[/tex]
[tex]\sf \cfrac{-3x}{-3}=\cfrac{-51}{-3}[/tex]
[tex]\sf x=17^o[/tex]
__________________
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Have a great day!
What expression has the same value as 2(5x + 2) - (3y)2x – 4x
Answers
Answer:
10x+6xy+4
Step-by-step explanation:
2(5x+2)-(3y) 2x-4x
By removing the bracket
10x+4-6xy+12xy
10x+4+6xy
10x+6xy+4
please help 25 points
Answers
⇒ ∠AEC is the angle vertical opposite to ∠BEC
You can add and subtract fractions with different denominators. trite or false
Answers
Answer:
False
Step-by-step explanation:
The denominators have to be the same for you to be able to add or subtract a fraction.
Can someone help me with this
Answers
Using the information from the given diagram, the measure of angle x (m ∠x) is 52°
Calculating the measures of anglesFrom the question, we are to determine the measure of angle x.
From the given diagram, we can write that
m ∠A + m ∠H + m ∠I = 180° (Sum of angle in a triangle)
Also,
m ∠K = m ∠I (Corresponding angles theorem)
∴ m ∠I = 62°
Thus,
x° + 66° + 62° = 180°
x° + 128° = 180°
x° = 180° - 128°
x° = 52°
Hence, the measure of ∠x 52°
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