To find: Equation of line parallel to 5x + 3y = -21 and passes through the point (-9, -3)
Solving the given 5x + 3y = -21 for 3y yields 3y = -5x - 21.
Dividing all three terms by 3, we get:
y = (-5/3)x - 7, indicating that the given line has slope -5/3.
The slope of a line perpendicular to this y = (-5/3)x - 7 is 3/5, the negative reciprocal of -5/3.
Start with y = mx + b
Substitute -3 for y, -9 for x, and 3/5 for m
We get,
-3 = (3/5) (-9) + b
∴ b = 5/9
Thus, the equation is y = (3/5)x + 5/9 is the required equation of a line parallel to 5x+3y=−21 that passes through the point (-9,-3)
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An ice skater is penalized 1.2 points for a fall. Write an expression for the ice skater’s final score.
The expression for the given case can be written as F = P - 1.2n.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The addition and subtraction can only take place between like terms.
Given that,
The penalty for an ice skater for a fall is 1.2 points.
Suppose the total points of ice skater be P, the number of falls be n and the final score be F.
Then following expression can be written for final score,
F = P - 1.2n
Hence, the expression for ice skater's final score is F = P - 1.2n.
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1/x-2 identify the asymptotes
The vertical asymptote is x=2 and horizontal asymptote is y = 0
What are asymptotes?An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.
There are three types is asymptotes:
Horizontal asymptote , Vertical asymptote and oblique asymptote.
in the expression 1/x-2, the horizontal asymptote is y=0 since the power of x in the numerator is less than that of denominator.
And the vertical asymptote is found by equation the denominator to zero
therefore x-2= 0
x= 2
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Toby submitted the following work when asked to convert 12 2/3 to an improper fraction
Answer:
a) He didn't add 2.
b) 38/3
In ΔTUV, m∠T = 58° and m∠U = 97°. Which list has the sides of ΔTUV in order from longest to shortest?
The angle ∠U is the largest in triangle ΔTUV. Then the largest side will be TV.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In ΔTUV, m∠T = 58° and m∠U = 97°.
Then the third angle of the triangle will be given as,
∠T + ∠U + ∠V = 180°
58° + 97° + ∠V = 180°
155° + ∠V = 180°
∠V = 180° - 155°
∠V = 25°
In a triangle, the opposite angle of the largest side will be the largest one.
The angle ∠U is the largest in triangle ΔTUV. Then the largest side will be TV.
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¯2(*3+¯4+¯8+*7).
Please help asap
Answer:-2(3+(-4)+(-8)*7)=114
Step-by-step explanation: You wrote the equation wrong, but if you use PEMDAS that's the answer you'll get.
Given: 2x+3=4x-5
Prove: x=4
Answer:
Step-by-step explanation:
2x + 3 = 4x - 5
4x - 5 = 2x + 3
Step 1 : Add 5 on both sides.
4x = 2x + 3 + 5
4x = 2x + 8
Step 2 : Subtract 2x on both sides.
4x - 2x = 8
2x = 8
Step 3 : Divide 2 on both sides.
x = 8/2
x = 4
Hence proved.
Answer:
Collect like terms
3+5=4x-2x
(note that when - crosses a line it turns to +
8=2x
8/2=2x/2
x=4
A: 10:00 am a truck started traveling from point A with a speed of 40mph. 3 hours
and 10 minutes later a car started to drive from point A in the same direction
with an
average speed of 60mph. At what time will the car catch up with
the truck?
Answer:h
Step-by-step explanation:
ihlug
A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
The smaller number is 9 and the larger number is 18.
According to the question,
We have the following information:
A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
Now, let's take the larger number to be x and the smaller number to be y.
So, we have the following expressions:
x = 2y ...(1)
x+14 = 4y-4
Putting the values of x from the equation 1:
2y+14 = 4y-4
Adding 4 to both sides of the equation:
2y+14+4 = 4y
2y+18 = 4y
Subtracting 2y from both sides of the equation:
18 = 4y-2y
18 = 2y
Dividing by 2 on both sides:
y = 18/2
y = 9
Now, putting this value in equation 1:
x = 2y
x = 2*9
x = 18
Hence, the smaller number is 9 and the larger number is 18.
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snoopy brown is interested in the number of businesses that do not allow dogs in st. paul, mn. to conduct his study, he randomly selects 100 businesses listed in the st. paul phone book, calls them and asks their policy. what is the sample of this study?
The sample of study is 100 business.
Define sample.An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values. A sample is that precise value. The probability distribution of the random variable determines the possible values and the likelihood of each. A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.
Given,
Snoopy brown is interested in the number of businesses that do not allow dogs in st. paul, mn. to conduct his study, he randomly selects 100 businesses listed in the st. paul phone book, calls them and asks their policy.
The sample of study is 100 business.
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to test whether the overall regression equation is statistically significant one uses a. the r2-statistic. b. the standard error statistic. c. the f-statistic. d. the t-statistic.
One can use the f-statistic to test whether the overall regression equation is statistically significant, one uses the f-statistic.
A reasonably high R-squared score makes sense if your regression model includes independent variables that are statistically significant. According to the statistical significance, shifts in the dependent variable are correlated with changes in the independent variables.
The ratio of two variances is known as an F-statistic, and it bears Sir Ronald Fisher's name. Variances gauge how widely apart the data points are from the mean. When the individual data points tend to deviate further from the mean, there are more variances.
The F-test determines that it is unlikely that all of the coefficients will equal zero by adding the predictive power of all independent variables. But it's likely that none of the variables are individually important enough to be statistically significant.
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Between his 9th and 10th birthdays jimmy read one book each week there are 52 weeks in a year if each book at about 95 pages about how many pages did he read during the year?
Answer:
he read 4940 pages in a year
Step-by-step explanation:
Given data:
1 year= 52 weeks
1 book= 95pages (takes 1 week to complete)
for 1 year = 52x95
=4940
If tan(A+B) = -4 and tan B=5/3, find tan A.
The value of tan A = 1
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The six trigonometric ratios of a right angle triangle are Sin, Cos, Tan, Cosec, sec and cot.
The trigonometric ratios relate the sides of the triangle with the angles of the triangle.
tan(A+B) = -4, tan B = 5/3
But tan(A + B) = [tex]\frac{tan A + tanB}{1-tanAtanB}[/tex]
Substituting the values of tan(A +B) tan B
-4 = [tex]\frac{tan A + 5/3}{1 - 5/3tanA}[/tex]
multiply numerator and denominator by 3, you have
-4 = [tex]\frac{3tanA + 5}{3 -5tanA}[/tex]
-4(3-5tanA) = 3tanA +5
-12 +20tanA = 3tanA +5
collect like terms
20tanA - 3tanA = 5 +12
17tanA = 17
tan A = 17/17
tanA = 1
In conclusion, the value of tanA = 1
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help meeeeee pls bro
in order to estimate the proportion of all credit card holders who pay their credit card bills in full each month a credit counseling bureau took a random sample of 450 credit card holders and found that 127 pay all their credit card bills in full each month. a 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is:
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
Define confidence interval.Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications. The sample is used to calculate the confidence interval, which represents the range of likely population parameters. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Given,
Number of credit card holders
n = 450
x = 127
p = 127/450
Proportion:
p = 0.2822
99% confidence interval:
C I = 0.2822 ± 2.576 × 0.2122
CI = 0.2822 ± 0.05465
CI = 0.282 + 0.055
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
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Graph this line using the slope and y-intercept: y= 1/5x + 8
The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
According to the given information line using the slope and y-intercept is; y= 1/5x + 8
thus, the slope of this line is:
m = 1/5
And its y-intercept is: c= 8
The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.
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EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the point slope form of the equation of the line through the given point with the given slope
through: (-1, -2) slope =3
Answer:
y=3x+1
Step-by-step explanation:
we know slope so just fill in the rest
y=3x
-2=3(-1)
-2=-3
We add 1 to make the equation true so the y intercept is 1
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The measure of an angle is 161.4°. What is the measure of its supplementary angle?
Answer:
The measure of its supplementary angle is 18.6 degrees
Step-by-step explanation:
A Supplementary angle is any two angles that sum up to 180 degrees
With this in mind we can subtract 180 - 161.4 to get the measure of the other angle.
Since 161.4 + 18.6 = 180 this is correct
Answer: The supplementary angle to 161.4 degrees is 18.6 degrees.
Step-by-step explanation: the sum of two supplementary angles is always 180 degrees.
180-161.4 is equal to 18.6 degrees.
An isosceles right triangle has a hypotenuse length that can be modeled with the function . the combined length of the legs can be modeled with the function l(x) = 2x. which function, p(x), can be used to find the perimeter of the triangle?
The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.
A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be L(x) = 2x. Using this information the perimeter of the triangle comes out to be,
P(x) = h(x) + L(x).
P(x) = x√2 + 2x
Hence the perimeter of the triangle comes out to be P(x) = x√2 + 2x
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the price of a 2 liter bottle of sprite holds 67.6 oz and costs $3.38. what is the unit price per oz
The unit of price per oz = 114.2
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.We are aware of the quantity of apples and the amount of money in the aforesaid problem.According to our question-
the price of a 2 liter bottle of sprite holds 67.6 oz
and costs $3.38.
2 = 67.6
67.6/2= 33.8
33.8*3.38= 114.24
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Sasha sells t-shirts. Each day she earns a set amount, plus a commission. What kinds of numbers make sense for the domain of this function? Explain your reasoning.
The domain of the given function is {1, 2, 3, 4, 5} which represents she sells t-shirts.
What are the domain and the range of a set of ordered pairs?The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.
We have been given that Sasha sells t-shirts. Each day she earns a set amount, plus a commission.
The domain of the given function represents she sells t-shirts.
According to the given table, the required domain will be as:
The domain of the given function = {1, 2, 3, 4, 5}.
Therefore, the domain of the given function is {1, 2, 3, 4, 5}.
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An elevator ascends at a rate of 29.6 feet per second. If a building is 1,450 feet tall, about how long would it take for the elevator to travel from the ground floor to the roof?
A. 0.49 minutes
B. 0.82 minutes
C. 4.9 minutes
D. 8.2 minutes
Find g(x) if g(x) is the resulting function from moving f(x) = (x + 2) right 1 unit and up 6 units.
g(x) = (x+2-3) + 4 = (x-1)+4
Complete the statement. Round to the nearest hundredth if necessary.
64 lb kg
Answer: you are dummy
Step-by-step explanation:dummy
Sweet Lucy’s ice cream shop offers customers 2 different types of cones, 5 different flavors of ice cream, and 6 different toppings. Assuming a customer picks one type of cone, one flavor of ice cream, and one topping only, how many different combinations of cone, ice cream, and topping are possible?
60 different combinations of cone, ice cream, and topping are possible.
What is combination?The combination is defined as an arrangement of objects where the order in which the objects are selected does not matter.
Given that, an ice cream shop offers customers 2 different types of cones, 5 different flavours of ice cream, and 6 different toppings
Total combination = 2*5*6 = 60
Hence, there are 60 different combinations of cone, ice cream, and topping are possible.
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How long is long? Please help I need to know
Answer:
it depends on how long long is
help me please ! correct answer gets brainliest
The expressions that show the distance between P and Q are option (d) |-6| + (-2) and option (e) 6 - 2
From the given number line
The distance between P and Q = 4 units
Now we have to solve each expression
Expression 1
|-6| + |-2| = 6 +2
Add the terms
= 8
Expression 2
|2-(-6)| = | 2 + 6|
= |8|
= 8
Expression 3
|-2| - (-6) = 2 + 6
Add the terms
= 8
Expression 4
|-6| + (-2) = 6 - 2
Subtract the term
= 4
Expression 5
6 - 2 = 4
Hence, the expressions that show the distance between -6 and -2 are option (d) |-6| + (-2) and option (e) 6 - 2
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Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
The scale that Wyatt has made use of based on the figures in the question is 1 inch to 0.36 yards.
What is a scale in mathematics?Building construction would be extremely challenging without a blueprint. You'd be lost without a map! Large objects, such as roads and buildings, can be easily visualized on paper using scale drawings. Scale drawings are even used by a GPS
The scale that Wyatt has used for this drawing is given as:
84 / 231 = 0.36
We would say that for every 1 inch, Wyatt made use of 0.36yards.
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A trapezoid has an area of 139.8 square yards. One base is 7 yards long. The height measures 12 yards. What is the length of the other base? PLS ASAP
Answer:
b)1.39
Step-by-step explanation:
i got it right on test
Answer:
other base = 16.3 yds
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the parallel bases b₁ and b₂
given b₁ = 7 , h = 12 and A = 139.8 , then
[tex]\frac{1}{2}[/tex] × 12 × (7 + b₂ ) = 139.8
6(7 + b₂ ) = 139.8 ( divide both sides by 6 )
7 + b₂ = 23.3 ( subtract 7 from both sides )
b₂ = 16.3
the length of the other base is 16.3 yards
Melissa's monthly budget is shown in
the table
Melissa's Budget
Category
Housing
Transportation
Clothing
Savings
Other
Amount
$1,200
$600
$250
$250
$825
What percentage of her total monthly
budget does she plan for savings?
8 percentage of her total monthly budget does she plan for savings.
Define percentage.The proportion of value in relation to the original value is measured using the percentage concept. In business, percentages are frequently employed to calculate a company's profit or loss percentage. Additionally, it is used in schools and colleges to show the grades that pupils have earned. A percentage formula can be used to assess the pupils' grades. In general, the definition of a percentage is any ratio of a value to the total value multiplied by 100. The percentage is denoted by the sign %.
Given,
Melissa's monthly budget is shown in the table,
Melissa' s saving = $250
Total amount = 3125
Percentage = Value/ Total × 100
Percentage = 250/3125 × 100
Percentage = 0.08 × 100
Percentage = 8%
8 percentage of her total monthly budget does she plan for savings.
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2.8x + 10 + 5.7x = 70+x
Answer:
Step-by-step explanation a=0.32
The required simplified value of x in the given expression is 8.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
2.8x + 10 + 5.7x = 70+x
Simplifying,
8.5x + 10 = 70 + x
8.5x - x = 70 - 10
7.5x = 60
x = 60 / 7.5
x = 8
Thus, the required simplified value of x in the given expression is 8.
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