Answer:
[tex]y=3x-7[/tex]
Step-by-step explanation:
Parallel Lines:Parallel lines, by definition, never intersect. They have the same slope but different y-intercepts (otherwise they would be the same line) on a graph.
Slope-Intercept Form:
Slope-Intercept form is expressed as: [tex]y=mx+b[/tex], where
[tex]m = \text{slope}[/tex][tex]b = \text{y-intercept}[/tex]This form is super useful for linear equations as it gives us the two key features of a linear equation. It's how each of the options are formatted, so we know we'll have to use this form.
Generally Finding a Parallel Line:The line is parallel to [tex]y=3x-4[/tex], meaning it has a slope of 3, but also a y-intercept other than -4 (otherwise they would be the same equation).
So we can generally form an equation: [tex]y=3x+b\text{, }b\ne-4[/tex], so we can plug any value for "b" here (except -4) and have a parallel line
Finding a line passing through a point:Since we not only want to find a parallel line, but also one that passes through a specific point, we can use our general parallel equation: [tex]y=3x+b\text{, }b\ne-4[/tex], and plug in known values. We of course already have the slope plugged in, but now we have a (x, y) coordinate, which we can plug in for x and y in the equation.
Original Equation:
[tex]y=3x+b[/tex]
Point given: (3, 2), substitute in x=3 and y=2:
[tex]2=3(3)+b[/tex]
Simplify:
[tex]2=9+b[/tex]
Subtract 9 from both sides:
[tex]-7=b[/tex]
Now we can take this value. and plug it back into the general equation:
[tex]y=3x+(-7)\implies y=3x-7[/tex]
Now we have our answer!
Complete the two-way frequency table below, which shows the relationship between adults' gender and whether these adults buy a truck or a car for their first new vehicle. From a sample of 88 adults, the following data are collected:
Truck Car Total
Female 5 35
Male 27 21
Total 88
What is the probability (rounded to the nearest whole percent) that an adult will buy a car, given that she is a female? Are the events being female and buying a car independent?
Answer:
Truck Car Total
Female 5 35 40
Male 27 21 48
Total 32 56 88
P(buying a car given a male ) = 21/88 = .238 ≈ 24%
Step-by-step explanation:
Let B = Probability of buying a car and being male 21/88
Let M = Probability of being a male = 48/88
P(B l M) = P(B and M) / P(M) = (21/88) / (48/88) = 21/48 = .4375 = 44%
Happy To Help!!!PLEASE HELP FRACTION S EASY!! A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses pounds of gravel. For each pound of gravel, he uses pound of cement. He is making enough concrete that he needs to use 3 pounds of sand.
How many pounds of cement does he use?
The pound of cement used based on the information will be C. 2 pounds.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.
The pound of cement used will be:
Gravel = 1 2/3 × 3
= 5 pounds
Cement used will be:
= 2/5 × 5.
= 2 pounds.
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Instructions: Find the missing segment in the image below.
Help please
Answer:
9
Step-by-step explanation:
It’s a ratio.
5/30=x/54
reduce
1/6=x/54
cross multiply
54=6x
x=9
ASAP PLZ HELP I WILL GIVE BRAINLIEST ALL QUESTIONS NO LINKS PLZZ
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Answer:
53
Step-by-step explanation:
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The amount Y (in dollars) Of money in your savings account after X months is represented by the equation Y equals 12.5 X +100 a. graph the linear equation b. how many months will it take for you to save a total of $237.50[QUICK ITS HOMEWORK AND ITS LATE]
The graph of the linear equation is attached below. After 11 months, the total savings will be $237.50.
What is a saving account?
An account in a retail bank is a savings account. Common characteristics include having a finite number of withdrawals allowed, not having check or connected debit card facilities, having few transfer choices, and not being able to become overdrawn.
Given equation is
y = 12.5x + 100
To find points on the linear equation, putting x = 0, 1 and 2 in the given equation:
y(0) = (12.5 × 0) + 100
y(0) = 100
y(1) = (12.5 × (1)) + 100
y(1) = 12.5 + 100
y(1) = 112.5
y(2) = (12.5 × 2) + 100
y(2) = 25 + 100
y(2) = 125.
The points on the linear equation are (0,100), (1, 112.5), (2,125).
Plot the points and join the points to draw the line to get graph the linear equation.
Putting y = 237.50 in the given equation y = 12.5x + 100:
237.50 = 12.5x + 100
Subtract 100 from both sides:
237.50 - 100 = 12.5x + 100 - 100
137.50 = 12.5x
Divide both sides by 12.5:
x = 137.50/12.5
x = 11
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Jordan is 12 years older than Anna. The
sum of their ages is 50. Find the age of
each person.
First complete the equations below, where I stands for
Jordan's age and A stands for Anna's age.
J = [?] + A; J + A = []
Help
9514 1404 393
Answer:
J = [12] +AJ + A = [50]Step-by-step explanation:
If Anna's age is represented by A, then 12 more than Anna's age will be ...
12 + A
Jason's age is said to be 12 more than Anna's age, so ...
J = 12 + A
__
The sum of their ages will be J + A. That is said to be 50, so ...
J + A = 50
_____
These equations can be solved by using the first to substitute for J in the second.
(12 +A) +A = 50
2A = 38 . . . . . . . . subtract 12
A = 19 . . . . . . . . . . divide by 2
J = 12 +19 = 31 . . . find Jason's age
Jason is 31; Anna is 19.
1 18. You have a --cup 4 1 measuring cup and a --cup measuring 2 cup. What are two ways you can 3 measure 2 cups of water? - 4
if the parent function is y=3×,which is the dunction of the graph?
On solving the provided question, we can say that - the linear equations, is [tex]x =10 / 5 = 2 = > x=2[/tex]
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
Here,
to solve the system of equations given. .
[tex]2x + y = 4 \\+\\3x - y = 6\\= > 5x =10[/tex]
system of equations 2x + y = 4 ,
6=3x-y is 5x =10
The value of x :
[tex]x =10 / 5 = 2\\ x=2[/tex]
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A __________ is a promise by a borrower to repay a loan at a specified rate of interest.
Select one:
a. Bond
b. Premium
c. Quoted Price
Solve the expression 8 + (9 x one third ) ÷ 3 using PEMDAS. (4 points)
Group of answer choices
4
7
8
9
Answer:
the answer is 9 hope this helps
Step-by-step explanation:
A rhombus has a side length equal to one of the diagonals. The other diagonal is 4cm longer. Find the area of the rhombus.
Answer:
The area of the rhombus is 25.83 cm².
Step-by-step explanation:
The area of a rhombus is given by:
[tex] A = \frac{d_{1} \times d_{2}}{2} [/tex]
Where:
d₁: is one diagonal
d₂: is the other diagonal = d₁ + 4 cm
We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:
h: hypotenuse of the right triangle
a: one side of the right triangle
b: is the other side of the right triangle
From the above we know that:
h = d₁
[tex] a = \frac{d_{2}}{2} = \frac{d_{1} + 4}{2} [/tex]
[tex] b = \frac{d_{1}}{2} [/tex]
We can find d₁ with Pitagoras:
[tex] h^{2} = a^{2} + b^{2} [/tex]
[tex] d_{1}^{2} = (\frac{d_{1} + 4}{2})^{2} + (\frac{d_{1}}{2})^{2} [/tex]
[tex] d_{1}^{2} = \frac{1}{4}(d_{1}^{2} + 8d_{1} + 16 + d_{1}^{2}) [/tex]
By solving the above quadratic equation for d₁ and taking the positive solution we have:
[tex] d_{1} = 5.46 cm [/tex]
So, d₂ is:
[tex] d_{2} = d_{1} + 4 = 5.46 cm + 4 cm = 9.46 cm [/tex]
Now, we can find the area:
[tex] A = \frac{d_{1} \times d_{2}}{2} = \frac{5.46 cm \times 9.46 cm}{2} = 25.83 cm^{2} [/tex]
Therefore, the area of the rhombus is 25.83 cm².
I hope it helps you!
Find the value of x
Answer:
x = 30
Step-by-step explanation:
24(24 + x) = 36² => tangent-secant theorem
Open the bracket
24*24 + 24*x = 36²
576 + 24x = 1,296
24x = 1,296 - 576
24x = 720
Divide both sides by 24
24x/24 = 720/24
x = 30
MAth question:
A square pyramid has a height of 9 cm and a base length of 4 cm. Find the volume
Answer: 48
Step-by-step explanation:
If the HCF is 5 and the product of the two numbers is 70, find the value of LCM.
If the HCF is 5 and the product of the two numbers is 70, then the value of LCM is 14.
Do two numbers make a product when they are the LCM of two numbers?The smallest number that can be divided by both numbers is known as the least common multiple, or LCM, of two numbers. The product of the two numbers is the LCM if their greatest common divisor is 1, in which case their product is 1.
Using the fundamental theorem of mathematics, how do you find the HCF and LCM?First, multiply both numbers by their prime factors to express them. Then, multiply the common factor with the highest power by the remaining factors to obtain the LCM. Take the common factors with the lowest power and multiply them to determine HCF.
To find the LCM of two numbers, you can use the formula: LCM = (a * b) / HCF.
In this case, we know that the HCF is 5, and the product of the two numbers is 70. Therefore, we can substitute these values into the formula:
LCM = (70) / 5 = 14.
So the LCM of the two numbers is 14.
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Please help will mark Brainly
Answer:
which of the following is not a true statement 4/6 equals 8/12 2/3 equals 10/15 2/10 equals 3/15 3/4 equal 6/9
Step-by-step explanation:
Based on the Theoretical Probability of rolling a 1, what is the expected number of times a 1should have been rolled out of the 15 times in the experiment? How does this compare to the Experimental Probability?
Answer:
420 69
Step-by-step explanation:
420 420
Which of the binomials below is a factor of this trinomial? X^2 - 14x + 24
Answer:
(x - 12)(x - 2)
Step-by-step explanation:
[tex] {x}^{2} - 14x + 24 \\ \\ = {x}^{2} - 12x - 2x + 24 \\ \\ = x(x - 12) - 2(x - 12) \\ \\ = (x - 12)(x - 2)[/tex]
ABC is an equilateral triangle. A circle with radius 1 is tangent to the line
AB at the point B and to the line AC at point C. What is the side length of
ABC? Show your work?
The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.
How to evaluate for the side length of the triangleAn equilateral triangle have all its side lengths equal so;
line AB = line BC = line AC
At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle
Line BC form the diameter of the circle which is 2 radius of the circle so;
line BC = 2 × radius of the circle
line BC = 2 × 1
line BC = 2
Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.
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The saucer for Aisha's teacup has a diameter of 6 inches. What is the saucer's radius?
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Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Train A and Train B both leave the station at 9am. Train A stops every 15 minutes. Train B stops every 24 minutes. At what time do both Trains stop at the same time again?
Answer:
here
Step-by-step explanation:
180 minutes
please answer the following question, if you send me a link then you will be reported
Find the surface area of the triangular prism.
Answer:
16 x 12 = 192
192 x 2 = 384
10 x 8 = 80, 80 divided by 2 = 40
40 x 2 = 80
10 x 16 = 160
Add all given areas:
384 + 80 + 160 = 624 cm2 is your answer.
Convert:
25 decimeters
=
Round to the tenths.
meters
Answer:
2.5
Step-by-step explanation:
Decimeter is 0.1 meter (10 centimeters). That means 25 decimeters is 2.5 meters.
Divide. Round to the nearest tenth.
3.5/2.29
Answer:
The answer will be 1.53 after dividing and rounding to the nearest tenth 3.5 divided by 2.29.
What value for the
constant, h, in the equation
shown below will result in an infinite number of
solutions?
6t + 18 = h(3x + 9)
Therefore , As a result, h = 2 is the answer to the equation in the given question.
Explain equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra is the fundamental foundation of mathematics.
Here,
The formula is as follows: 6x + 18 = h(3x + 9)
To ensure that the expression has an unlimited number of answers, h's value must be determined.
Take the expression now and continue solving it.
=> 6x + 18 = h(3x + 9)
=>3hx + 9h= 6x +8
The expression will have an endless number of solutions if the coefficients of the left-hand side and the right-hand side are equal.
Therefore, 3h = 6 and h = 2
As a result, h = 2 is the answer to the equation in the given question.
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if a borrowed car averges 38 miles per gallon how many miles can u travel with 12 gallons of gas
What is the meaning of panchtantra???
Answer:
✍ PANCHTANTRA :⎆ The word “Panch.atantra” is a combination of the words Pancha – meaning five in Sanskrit, and Tantra – meaning weave. It's an ancient Indian inter-related collection of animal fables in verse and prose, in a frame story format.
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Answer:
Five treatises or five chapters
In circle J with m
a. 46.5'
b.73'
c.292'
d.214'
Answer:
B. 73°
Step-by-step explanation:
mL HLK = ½ × mL HJK = ½×146=73°
Select all the polygons that would be used in a net of the solid figure shown.
A triangular pyramid. The base has all three sides equal in length. The pyramid is taller than the width of the base.
right triangle
equilateral triangle
isosceles triangle
rectangle
square
Answer:
C, definitely two sides are different in the triangle.
A, it looks as if the bottom is a right triangle if you look at it in a different way.
The polygons that would be used in a net isosceles triangle & right triangle
What is Pyramid?A pyramid is a structure whose outer surfaces are triangular and converge to a single step at the top,
As, we need a triangular pyramid whose base has all the three sides equal in length.
We can have a net in the form of isosceles triangle whose two are equal
i.e., two sides are different in the triangle.
and also, bottom with the right angle
i.e., the bottom is a right triangle if you look at it in a different way.
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