In order to solve this problem, we need a few formulas to help us get to the answer:
The first formula we need is the Slope Formula:
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are two different points.
The second formula we need is Point-Slope Form:
[tex]\displaystyle y - y_0 = m(x - x_0)[/tex]
where (x₀, y₀) is a given point on the line and m is the slope.
DefiningNow, we can organize and define what the problem has given us:
We are first given information that a line passes through the points (6, 2) and (2, 4).
We are also given that the parallel line passes through (-1, 6).
WorkLet's first find the slope of the line that passes through two points:
[tex]\displaystyle\begin{aligned}m & = \frac{4 - 2}{2 - 6} \\& = \frac{2}{-4} \\& = \boxed{ - \frac{1}{2} } \\\end{aligned}[/tex]
∴ we know that the slope is equal to negative one-half.
Let's substitute in our slope into Point-Slope Form since parallel lines have the same slope:
[tex]\displaystyle y - y_0 = m(x - x_0) \Rightarrow y - y_0 = - \frac{1}{2} (x - x_0)[/tex]
Recall that we were given the initial point (-1, 6). Let's also substitute this into Point-Slope Form:
[tex]\displaystyle \begin{aligned}y - y_0 = m(x - x_0) & \Rightarrow y - y_0 = - \frac{1}{2} (x - x_0) \\& \Rightarrow y - 6 = - \frac{1}{2} (x - -1) \\& \Rightarrow \boxed{ y - 6 = -\frac{1}{2}(x + 1) } \\\end{aligned}[/tex]
Answer∴ we have found that the point-slope form of the equation of a line that passes through the point (-1, 6) and is parallel to the line that passes through the points (6, 2) and (2, 4) is equal to:
[tex]\displaystyle \boxed{ y - 6 = -\frac{1}{2}(x + 1) }[/tex]
Hope this helps!
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Determine if the table shows a proportional relationship.
x 25.6 72.8 77.2
y 6.4 18.2 19.3
--------------------------------
Explanation:
25.6/6.4=472.8/18.2=477.2/19.3=4The formula for finding the volume of a cube is V = s to the power of 3, where s is the length of the side of the cube. Terrance has a cube that measures 3 inches long along each side. What is the volume of the cube? _______________inches3 ( just write the number)
Thx!
Answer: 27
Step-by-step explanation:
formula: v=[tex]s^{3}[/tex]
v=[tex]3^{3}[/tex]
[tex]3^{3}[/tex]=3*3*3
3*3=9
3*9=27
Answer: the correct answer is 27 I believe
Step-by-step explanation:
A movie theater has 940 seats. Tickets were sold for 846 of the seats. For what percent of the seats were tickets sold?
(Please show work)
Answer:
90%
Step-by-step explanation:
trust me i used a calculator
Need Answered ASAP. Find the difference between (1.4 × 10^8) and (5.7 × 10^7). Write the final answer in scientific notation.
−4.3 × 10^1
4.3 × 10^−1
8.3 × 10^8
8.3 × 1067
Answer:
-4.3 x10-1
Step-by-step explanation:
answer.,...............
A circle has a radius of 7 centimeters (cm).
What is the approximate area of the circle?
Use the approximation of 22/7 for π in your calculations.
Answer:
154 cm
Step-by-step explanation:
the formula for the area of a circle is: [tex]\pi r^{2}[/tex]
Instead of [tex]\pi[/tex] we will use [tex]\frac{22}{7}[/tex]
[tex]\frac{22}{7} . (7)^2\\\\\frac{22}{7} . 49\\\\22 . 7 = 154\\[/tex]
what is the transformation of f(x)=|x| to g(x)=-4|x-2|-1
Answer:
Step-by-step explanation:
Kayleen buys one 3 -pound bag of cat food. Her cat eats about 34 of a pound every week. How many weeks does one bag last?
7.67 is what fraction of 23
Answer:
2.99869621904
Step-by-step explanation:
23/7.67=2.99869621904.
23/2.99869621904=7.67
I hope this helped!
Answer:
7.67 = 767
100
= 767
100
as a fraction
Step-by-step explanation:
In which expression is the number 3 expressed as a coefficient of a variable?
Group of answer choices
3 - y
3 + y
7y + 3
3y + 1
Thx!
Answer: 3y+1
Step-by-step explanation:
Answer: The correct answer is d 3y+1
Step-by-step explanation:
A builder buys 29.5 acres of land to develop a new community of homes and parks.
The builder plans to use 0.75 of the land for a park. How many acres will he use for the park?
Find the y-intercept of the line that passes through the point (6, –1) with a rate of change of −3/5
Answer:
the y-int is 2.6 or 13/5
Step-by-step explanation:
y=mx+b
-1=-3/5(6)+b
-1=-18/5+b
b=2.6 or b=13/5
If x and y are in direct proportion and y is 45 when xx is 15, find y when x is 4.
Answer:
y = 12
Step-by-step explanation:
the equation is
y = 3x
You find the constant or proportionality by put y/x
(15,45) is in the form (x,y) The x is 15 and the y is 45. Put this in the form y/x and you get 45/15 or 3. 3 is the constant of proportionality.
y = 3x
y = 3(4)
y = 12
please help!!!!!!!!!!!!!
Identify all of the expressions that can be used to find the slope of a linear function.
Answer:
Step-by-step explanation:
it will be AB
please help!!!!!!!!!!!!!!!!1
Answer: 29
Step-by-step explanation: We first replace the variables with the numbers so it turns into 5 + 6 x 4 and according to the order of operations we do 6 x 4 first which is 24 and then we do 5 + 24 which is 29.
Kayleen buys one 3 -pound bag of cat food. Her cat eats about 3/4 of a pound every week. How many weeks does one bag last?
Answer: 4 weeks
Step-by-step explanation:
To find the answer to this question, we will divide 3 by 3/4 to find the number of weeks one bag will last.
3 / (3/4) = 3 * (4/3) = 12/3 = 4 weeks
One 3 -pound bag will last the cat 4 weeks.
Need answer by today
Answer:
980 feet per minute
Step-by-step explanation:
I'LL GIVE BRAINLIEST!!
( True / False ) Force is used in aristocracy.
If true how?
If false why?
Answer:
true
Aristocracy is a form of government in which political power is held by a select few privileged people called aristocrats or nobles. Coming from a Greek word meaning “rule by the best,” aristocrats are considered the most qualified to rule because of their moral and intellectual superiority.
6/7 equals 18 over Y +15
Y= 3
Y=13
Y= 6
Y= 3.2
Answer:
[tex]y = 6[/tex]
Step-by-step explanation:
[tex]6(y + 15) = 126 \\ y + 15 = 21 \\ y = 21 - 15 \\ y = 6[/tex]
Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.
A= $8
B= $10
C= $100
Length: 2 and 1 over 4 feet
Width: 1 foot
Height: 1 and 1 over 4 feet
The lengths of the sides of a small cube are 1 over 4 foot each.
Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points)
Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (10 points)
Answer: 84 cubes
Step-by-step explanation: Given, The dimension of the rectangular prism are, 1 1/3 ft. * 1 * 2 1/3 = 4/3 * 7/3 = 28/9 cube ft.
Now, the volume of a cube = side³, if side = 1/3 ft., Then the volume of each cube, V = (1/3)³ = 1/27 cube ft.
Hence, the number of cubes that can be packet in the prism = V/V1 = 28/9 / 1/27 = 27*28/9 = 3 * 28 = 84
A) The number of small cubes which can be packed in the rectangular prism are 180.
B) The volume of the rectangular prism in terms of the small cube and a unit cube will be 180 units³
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
Length = 2 1/4 feet
Width = 1 feet
Height = 1 1/4 feet
And, The lengths of the sides of a small cube are 1 /4 foot each.
Now,
Since, The volume of rectangular prism = Length x width x height
Substitute all the values, we get;
⇒ The volume of rectangular prism = 2 1/4 × 1 × 1 1/4
= 9/4 × 1 × 5/4
= 45/16 ft³
= 2.81 ft³
And, The Volume of one cube = Side³
Here, The length of side of cube = 1/4 feet = 0.25 feet
Hence, The Volume of one cube = Side³
The Volume of one cube = 0.25³
The Volume of one cube = 0.015625 ft³
So, The number of small cubes that can be packed in the rectangular prism = Volume of rectangular prism / Volume of cube
= 2.81 /0.015625
= 180
B) The length, the width and the height of the rectangular prism in term of units cubes is:
Length = 2 1/4 feet / 0.25 feet = 2.25 / 0.25 = 9 units
Width = 1 feet / 0.25 feet = 4 units
Height = 1 1/4 feet / 0.25 feet = 1.25 / 0.25 = 5 units
So, The volume of the rectangular prism in terms of the small cube and a unit cube is,
Volume = 9 x 4 x 5
= 180 units³
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In the triangle ABC, AB = 13cm, BC =10cm and angle BAC = 30degrees
Find the two possible sizes of angle ABC, giving your answers to two decimal places.
Answer:
109.46° and 10.54°
Step-by-step explanation:
Attached in the image.
Hope it helps :)
Which equation is equivalent to this proportion? Select all that apply.
Answer:
250y = 800
Step-by-step explanation:
[tex]\frac{8}{250}[/tex] = [tex]\frac{y}{100}[/tex] Cross multiply
250y = 800
Answer:
A) 250y = 800
Step-by-step explanation:
Given equation:
[tex]\dfrac{8}{250}=\dfrac{y}{100}[/tex]
Cross multiply by multiplying the numerator and denominator of the first fraction by the denominator of the second fraction, and multiplying the numerator and denominator of the second fraction by the denominator of the first fraction:
[tex]\implies \dfrac{8 \times 100}{250\times 100}=\dfrac{y \times 250}{100 \times 250}[/tex]
Simplify:
[tex]\implies 8 \times 100 = y \times 250[/tex]
[tex]\implies 800=250y[/tex]
[tex]\implies 250y=800[/tex]
I NEED THIS ANSWER ASAP PLEASE <33
What is the value of the expression below when
x = 3 and y = 5?
x = 9y ?
Answer:
x = 9y
3 = 9 × 5
3 = 45
0 = 45 - 3
0 = 42
Step-by-step explanation:
First of all, write the values of x and y respectively. Then do the DMAS. When there is equal to sign between two numbers then you can bring on number to the other side of equal to sign with the sign changed. Then you get your answer
Answer:
When x= 3, then y= 1/3 and When y= 5, then x= 45
Step-by-step explanation:
3 = 9y
3/9 = y
1/3 = y
and
x = 9 * 5
x = 45
What does the expression opposite of yi ÷m help you find? select all that apply.
Responses
Answer:
The correct answer for this is:
a zero
Pls help like asap this is due be4 after break!
Answer:
Step-by-step explanation:
order of operations parentheses first!
so 4(6k+4) = (4x6)k + (4x4)
which gets you to
5k + 24k + 16 - 29k = 16
simplified down to
29k + 16 -29k = 16
the answer is 16 = 16 the 29k’s cancel out
hope that helped
The data shows how many videos were rented for a forty-day period. Which table matches the information data that was collected?
Find the slope (in reduced form) between the points (4, –6) and ( –2, 8).
pls help me, this is due tomorrow and i need to show my work but i don’t know how
Evaluate the following numerical expression:
(15 ÷ 3)to the power of 2 + 9 ÷ 3
Group of answer choices
-5
-13
-11.3
-28
Thank u I appreciate it!
Answer: 13
Step-by-step explanation:
use PEMDAS
(15 ÷ 3)2 + 9 ÷ 3=
(5)2+9/3
10+3
13