Write the equation of the line that is parallel to 5x - 2y =16 and passes through (10,5).
Group of answer choices
A. y =5/2x -30
B. y = 5/2x -20
C. y = -2/5x -15
D.y = -2/5x +30
Answers
Answer:
B
Step-by-step explanation:
Parallel lines have same slope. Parallel means to never intersect. So if something has to not intersect, they must have similar slopes but from a different starting position.
So Parallel Lines have similar slopes.
So using the given equation let manipulate this expression to find our a slope. This looks like a linear equation in the form of Ax+By=C (standard form). So let isolate this to y=mx+b because the latter is slope intercept form, which gives us our slope which is m.
\(5x - 2y = 16\)
We need to get it to look like
\(y = mx + b\)
So we need to isolate our y value.
In order to do this, we do basics of Algebra
\( - 2y = 16 - 5x\)
\(y = \frac{16 - 5x}{ - 2} \)
\(y = - 8 + \frac{5}{2} x\)
So our slope of the original line is 5/2. So our new Parallel lines must have this slope as well. Our new line also passes through 10,5 so since we have a point and a slope we use point slope form
\(y - {y} _{1} = m( x - x _{1})\)
where m is our slope and (x1,y1) is our given point.
Subsitue
\(y - 5 = \frac{5}{2} (x - 10)\)
\(y - 5 = \frac{5}{2} x - 25\)
Add 5 to both sides
\(y = \frac{5}{2} x - 20\)
Related Questions
Lilliana is training for a marathon. She runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 3 laps on a running trail and then runs 8 more miles. On Tuesday and Sunday, she runs 5 laps on the trail and then runs 4 more miles. On Saturday, she just runs laps. How many laps does Lilliana run on Saturday?
Answers
Answer:
Letting L = distance per lap
4L + 8 = 6L + 4
2L = 4
L = 2 miles
She runs 16 miles each day
2 miles per Lap = 8 Laps on Saturday
Step-by-step explanation:
what is inequalities
Answers
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.
The most common symbols used in inequalities are:
">" (greater than): indicates that the value on the left side is larger than the value on the right side.
"<" (less than): indicates that the value on the left side is smaller than the value on the right side.
"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.
"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.
"≠" (not equal to): indicates that the values on both sides are not equal.
Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
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jack popped some popcorn, but 3 of the 150 kernels did not pop
Answers
A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3?
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/2
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3
For three rolls of the die, a number less than 3 will land face up one time.
It will take three rolls of the die before a number less than 3 lands face up for the first time.
Answers
The best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\).
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is \(\frac{1}{3}\).
As per the given question a fair die with its faces numbered from 1 to 6 will be rolled.
Here we have to calculate the probability that the number landing face up will be less than 3.
The event of the number landing face up will be less than 3 is exhaustive, mutually exclusive, and independent face of a die = 6
(1, 2, 3, 4, 5, 6)
Favorable number of faces of a die = 2
(1, 2)
Since the number landing faces up will be less than 3.
Therefore the probability that the number landing face up will be less than 3
\(=\frac{\text { Favourable Number }}{\text { Total Number }}$\)
\(& =\frac{2}{6} \\\)
\(& =\frac{1}{3}\)
Therefore the best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\)
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The long-run relative frequency of a number less than 3 landing face up is 2/3.
The best interpretation of the probability that the number landing face up will be less than 3 is that for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3. This can be expressed mathematically as P(x<3) = 2/3, where P(x) is the probability of the number landing face up being less than 3.
For a single roll of the die, the probability of a number less than 3 landing face up is 1/2. This is because there are three numbers (1,2,3) which are less than 3, and 6 possible outcomes. Therefore, the probability of any one of those three numbers landing face up is 3/6, or 1/2.
For multiple rolls of the die, the probability of a number less than 3 landing face up is the sum of the probabilities of each of those three numbers landing face up. This can be expressed mathematically as P(x<3) = (1/2) + (1/2) + (1/2), or 2/3.
Therefore, for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3.
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There are 8 midsize cars and 15 compact cars and 6 will be selected. What is the probability of selecting all midsize cars?
Answers
Answer:
Assuming order does not matter, the probability of selecting all midsize cars is 0.000277373, or \(\frac{4}{14421}\).
Step-by-step explanation:
First, we must find the n(Total arrangements of selections)=(8+15)C6
n(Total arrangements of selections)=23C6
n(Total arrangements of selections)=100,947
Second, we must find the n(Arrangements where all are midsize cars)=8C6
n(Arrangements where all are midsize cars)=28
To find the probability of selecting all midsize cars, we divide the n(Arrangements where all are midsize cars) by the n(Total arrangements of selections):
P(All midsize cars)= \(\frac{28}{100,947}\)
P(All midsize cars)= \(\frac{4}{14421}\)=0.000277373.
A square on a coordinate plane has one vortex at (-0.5, -2) and a perimeter of 10 units. If all the vertices are located in quadrant III, what are the coordinates of the other three vertices
Answers
Answer:
Step-by-step explanation:
each side of square=10/4=2.5
because all the vertices are in quarter |||
so all the coordinates are negative.
x coordinate=-0.5-2.5=-3
y coordinate=-2-2.5=-4.5
all the coordinates are (-3,-2) ,(-0.5,-2)
and (-3,-4.5),(-0.5,-4.5)
To express the polynomial 4a^3 + a^2 - 6a^5 + 2a^3 - 4a + 1 in standard form, which terms should be combined?
Answers
Answer:
Step-by-step explanation:
-6a^5+6a^3+a^2-4a+1
Answer:
4a^3 and 2a^3
Step-by-step explanation:
you always start by combining like terms
When dots are printed from a laser printer to form letters, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh's criterion of your eye at distances typical for reading Randomized Variables D 2.5 mm d-38 cm Take the pupil of the eye to be 2.5 mm in diameter and the distance from the paper to the eye as 38 cm. Find the minimum separation of two dots such that they cannot be resolved in cm. Assume a wavelength of 555 nm for visible light.
Answers
Answer:
The minimum separation is \(z = 1.0292 *10^{-4} \ m\)
Step-by-step explanation:
From the question we are told that
The reading randomized variable are \(D= 2.5 \ mm\) and \(d = 38 \ cm\)
The diameter of the pupil is \(d = 2.5 \ mm = \frac{2.5}{1000} = 0.0025 \ m\)
The distance from the paper is \(D = 38 \ cm = 0.38 \ m\)
The wavelength is \(\lambda = 555 \ nm = 555 * 10 ^{-9} m\)
Generally the Raleigh's equation for resolution is
\(\theta = 1.22 [\frac{\lambda}{D} ]\)
substituting values
\(\theta = 1.22 * \frac{555*10^{-9}}{0.0025}\)
\(\theta = 2.7084*10^{-4} \ rad\)
The minimum separation of two dots is mathematically represented as
\(z = \theta d\)
substituting values
\(z = 2.7084*10^{-4} * 0.38\)
\(z = 1.0292 *10^{-4} \ m\)
These shapes are similar.
Find X.
5
5
30
24
30
Answers
Answer: 4
Step-by-step explanation:
Find the value of y.
Answers
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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7).
2. Hot Text: For each graph, choose the correct sentence to describe the graph.
The graph represents a proportional relationship.
The graph does not represent a proportional relationship.
Answers
a. The graph represents a proportional relationship.
b. The graph does not represent a proportional relationship.
c. The graph does not represent a proportional relationship.
d. The graph represents a proportional relationship.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:
y = kx.
Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.
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Help help help math math
Answers
Answer:
(2,7)
Step-by-step explanation:
Select all equivalent options
A. 6
B. 3^2
C. 9
D. 33
Answers
Question 4Fill out the boxes to demonstrate your understanding of estimating a non perfect square?Estimate V388 to the nearest whole number?V388АBCDEFFinal Estimate
Answers
For this problem we want to estimate:
\(\sqrt{388}\)We need to take in count that this number is not a perfect square. And we can use the following definition:
\(\sqrt{x}=\sqrt{nearestp\operatorname{erf}ectsquare}\text{ + }\frac{x-p\operatorname{erf}ectsquare}{2\sqrt{p\operatorname{erf}ectsquare}}\)The nearest perfect square to 388 is 361 because:
\(\sqrt{361}=\text{ }\sqrt{19\cdot19}=19\)And replacing we have:
\(\sqrt{388}=\sqrt{361}+\frac{388-361}{2\sqrt{361}}=19+\frac{27}{2\cdot19}=19+\frac{27}{38}\text{ }\)\(A=361,B=19,C=400,D=20,E=19,F=20\)NEED HELP ASAP
The formula for the simple interest, I, is I=prt where p is principal, r is the annual interest rate, and t is the time elapsed in years.
A) solve the formula for r.
B) use the equation you just found to determine the annual interest rate on an account that earned $125.00 in simple interest after 6 months with principal deposit of $5.000.00.
Answers
A) Formula for r is r = I/p*t
B) The annual interest rate on the account is 0.05%
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal and by the number of days that elapse between payments.
For part A of the question, I=p*r*t
Therefore, r = I/p*t ( by taking interest rate on one side and moving rest of the terms on the other side of the 'equals to'. As we know that when we move a term which is being multiplied on one side to the other side, it is then used as a divisor.)
For part B of the question, put values in the above formula
simple interest earned = $125,00
principal deposit = $5,000,00
time period in years = 6 months that is 1/2 years
r = I/p*t
r = 125,00/5,000,00*1/2
r = 0.05%
Therefore, The formula solved for r is r = I/p*t and the annual interest rate on the account that earned $125,00 in simple interest after 6 months with principal deposit of $5,000,00 is 0.05%.
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Can Someone explain why this is wrong please?
Answers
You have taken unit for mass as grams.
Converted mass:-
\(\\ \sf\longmapsto 2752.512g\)
1kg=1000gHence our and should be
\(\\ \sf\longmapsto 2.752kg\)
Answer:
Your answer is correctStep-by-step explanation:
Volume of the cube:
(0.64m)³= (64 cm)³ = 262144 cm³Mass:
262144 cm³ * 10.5 g/cm³ =2752512 g =2752.512 kgYour answer is correct
Question explains itself in the picture.
Answers
Answer:
30 cm
Step-by-step explanation:
Area of a triangle formula:
A = 0.5bh
Given:
b = 12
c = 5
Work:
A = 0.5bh
A = 0.5(12)(5)
A = 6(5)
A = 30
Water is boiled at sea level in a coffee maker equipped with an immersion-type electric heating element. The coffee maker contains 1 L of water when full. Once boiling starts, it is observed that half of the water in the coffee maker evaporates in 25 min. Determine the power rating of the electric heating element immersed in water. Also, determine how long it will take for this heater to raise the temperature of of cold water from to the boiling temperature.
Answers
It will take 2.96 minutes for the electric heating element to raise the temperature of cold water from to the boiling temperature.
The power rating of the electric heating element can be determined by using the equation:
Power = (Mass of water × Specific heat capacity × Change in Temperature)/Time taken
For the given case, the power rating of the electric heating element = (1 L × 4.18 kJ/kgK × 100°C)/25 min = 16.7 kW
To determine how long it will take for this heater to raise the temperature of cold water from to the boiling temperature, we can use the equation:
Time taken = (Mass of water × Specific heat capacity × Change in Temperature)/Power
For the given case, the time taken = (1 L × 4.18 kJ/kgK × 100°C)/16.7 kW = 2.96 min.
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Select the correct answer.
Right triangle DEF has two 45° angles with the hypotenuse, DF, having a length of 8. What is DE?
A.
8v2
B.
4v2
C.
4
D.
8
Answers
The length of DE is 4√2, the correct option is B.
What is an Isosceles Triangle?An Isosceles triangle is a triangle whose two sides are equal in length, and so two angles are also equal in measure.
DEF is a right angled triangle has two angles as 45 degree,
The triangle is therefore an Isosceles Triangle as the two angles are equal, so the side lengths corresponding to it will be equal,
The hypotenuse DF = 8
The length of DE can be determined by Pythagoras Theorem.
Let the side length be x units then,
8² = x² + x²
64 = 2x²
32 = x
x = 4√2
DE = 4√2
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15) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the
rope is taut while the balloon is directly above a flag pole that is 40 feet from where the rope is
staked down. Find the altitude of the balloon if the rope is 80 feet long. HINT: Use the
Pythagorean Theorem., label the drawing.
A) 2√10 ft
B) 40-√√5 ft
C) 40-√√3 ft
D) 4√ √/30 ft
Answers
The altitude of the balloon found using Pythagorean Theorem is 40·√3 feet, the best correct option is option C)
C) 40·√3 ft
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is the same as the sum of the square of each of the two legs of the right triangle.
15) The parameters in the question includes;
Horizontal distance of the flag pole from the point the rope is staked down = 40 feet
Length of the rope to which the balloon is secured = 80 feet
Location of the balloon = directly above the flag pole
Therefore, the altitude of the balloon, the length of the rope, and the horizontal distance from the flag pole from the point the rope is staked form a right triangle, with the length of the rope representing the hypotenuse side.
Let h represent the altitude of the flag pole, using Pythagorean Theorem, we get;
80² = 40² + h²
Therefore; h² = 80² - 40² = 4800
The altitude of the balloon, h = √(4800) = 40·√3
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hi..
Answers
Round to the nearest hundredth (2 decimal places) when necessary
Answers
Answer:
do you need to find the area of it or something
Step-by-step explanation:
Can someone help me please?!
Answers
Answer:
(4,2)
Step-by-step explanation:
x=4,y=2
Read and write the number in two other forms.
314,207
Answers
Answer:
The required forms of 314, 207
1. 3 lakh fourteen thousand two hundred seven. (word form)
2. 300000 + 10000 + 4000 + 200 + 7 (expanded form)
What are the solutions of the equation 9x4 - 2x2 - 7 = 0? Use u substitution to solve.
Answers
Answer: this is what i got hope this helped i took a sceernshot of it
Step-by-step explanation:
ples make brainly
Evaluate the expression for the given variable values. - x² + 3x -2 if x = -4-1218-6-30
Answers
We need to substitute the given value into the expression, that is,
\(-(-4)^2+3(-4)-2\)which gives
\(-16-12-2\)By adding these values, the answer is -30
What is the factored form of the expression 9x2 + 6x + 1?
Answers
Answer:
(3x+1)^2
Step-by-step explanation:
LOOK AT THE BOTTOM PLEASE BE RIGHT
Answers
Answer:
236i217621
Step-by-step explanation:i didi it
turunan dari f(x) = 9132x^31 + x + x + x + x + x + x
Answers
The derivative of the expression is: f'(x) = 9132(31x^30) + 6.
How to obtain the derivativeThe derivative of this function can be obtained by applying the constant multiple rule in which the constant is multiplied by the derivative of the function. Next, we will apply the power rule of differentiation in which the power rule of differentiation. When these are applied, we will have the following:
First, the principle of linear differentiation is applied to all the values on the right as follows:
f'(x) = d/dx [9132x^31 + x + x + x + x + x + x]
= d/dx [9132x^31] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x]
When we apply the constant multiple rule, this then equals:
9132 d/dx [x^31] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x]
Finally, we apply the power rule of differentiation to obtain:
= 9132 (31x^30) + 1 + 1 + 1 + 1 + 1
= 9132 (31x^30) + 6
So, the derivative of the function is f'(x) = 9132(31x^30) + 6.
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If A={A,15,E,17,18, B,20} and B={ X,22, F,42, Y,62,72}, then what is n(A∪B)?
Answers
Answer:
14
Step-by-step explanation:
There are 7 elements in each set, and no elements are shared. The number of elements in the union of the sets is then ...
n(A∪B) = 7+7 = 14