Answer:
The value of k is:
[tex]k=-\frac{31}{4}[/tex]
Step-by-step explanation:
Given
The line containing the points (-3,k) and (4,8) is parallel to the line containing the points (5,3) and (1,-6).
To determine
what is the value of k?
To determine the value of k, the first step we need to do is to find the slope of the line containing the points (5,3) and (1,-6) using the formula
[tex]\mathrm{Slope}=m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
[tex]\left(x_1,\:y_1\right)=\left(5,\:3\right)[/tex][tex]\left(x_2,\:y_2\right)=\left(1,\:-6\right)[/tex]now substituting (x₁, y₁) = (5, 3) and (x₂, y₂) = (1, -6) in the formula
[tex]m=\frac{-6-3}{1-5}[/tex]
[tex]m=\frac{-9}{-4}[/tex]
Apply the fraction rule: [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]
[tex]m=\frac{9}{4}[/tex]
Thus, we conclude that the slope of the line containing the points (5,3) and (1,-6) will be:
[tex]m=\frac{9}{4}[/tex]
Importing Tip:
We know that the parallel lines have the same slopes, so the slope of the line containing the points (-3,k) and (4,8) will also be 9/4.Thus, using the slope formula for the line containing the points (-3,k) and (4,8).
[tex]\mathrm{Slope}=m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
[tex]\left(x_1,\:y_1\right)=\left(-3,\:k\right)[/tex][tex]\left(x_2,\:y_2\right)=\left(4,\:8\right)[/tex]As we know that the parallel lines have the same slopes.
Thus, the second step we need to do is to substitute m = 9/4 in the slope formula
[tex]\frac{9}{4}=\frac{y_2-y_1}{x_2-x_1}[/tex]
now substituting (x₁, y₁) = (-3, k) and (x₂, y₂) = (4, 8) in the formula
[tex]\:\:\:\frac{9}{4}=\:\frac{8-k}{4-\left(-3\right)}[/tex]
switch sides
[tex]\frac{8-k}{4-\left(-3\right)}=\frac{9}{4}[/tex]
Multiply both sides by 7
[tex]\frac{7\left(8-k\right)}{4-\left(-3\right)}=\frac{9\cdot \:7}{4}[/tex]
Simplify
[tex]8-k=\frac{63}{4}[/tex]
Subtract 8 from both sides
[tex]8-k-8=\frac{63}{4}-8[/tex]
Simplify
[tex]-k=\frac{31}{4}[/tex]
Divide both sides by -1
[tex]\frac{-k}{-1}=\frac{\frac{31}{4}}{-1}[/tex]
Simplify
[tex]k=-\frac{31}{4}[/tex]
Therefore, the value of k is:
[tex]k=-\frac{31}{4}[/tex]
VERIFICATION:
As the value of k = -31/4.
So the first line will contain the points:
(-3, -31/4)(4, 8)Finding the slope between (-3, -31/4) and (4, 8) using the slope formula
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
[tex]\left(x_1,\:y_1\right)=\left(-3,\:-\frac{31}{4}\right)[/tex][tex]\left(x_2,\:y_2\right)=\left(4,\:8\right)[/tex]so substituting (x₁, y₁) = (-3, -31/4) and (x₂, y₂) = (4, 8) in the formula
[tex]m=\frac{8-\left(-\frac{31}{4}\right)}{4-\left(-3\right)}[/tex]
Apply rule: [tex]-\left(-a\right)=a[/tex]
[tex]m=\frac{8+\frac{31}{4}}{4+3}[/tex]
Add the numbers: [tex]4+3=7[/tex]
[tex]m=\frac{8+\frac{31}{4}}{7}[/tex]
[tex]m=\frac{\frac{63}{4}}{7}[/tex] ∵ [tex]8+\frac{31}{4}=\frac{63}{4}[/tex]
Apply fraction rule: [tex]\frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}[/tex]
[tex]m=\frac{63}{4\cdot \:7}[/tex]
[tex]m=\frac{63}{28}[/tex]
Cancel the common factor: 7
[tex]m=\frac{9}{4}[/tex]
So, the slope of the line containing the points (-3,k) and (4,8) is m = 9/4. It means both lines have the same slopes. Hence, they are parallel.
Therefore, we conclude that the value of k = -31/4 is true.
help and get brainliest!!!
Answer:
a
Step-by-step explanation:
need help very fast pls
Answer:
Step-by-step explanation:
(0, -5) (5, 0)
(0 + 5)/(5 - 0)
5/5= 1
y + 5 = x - 0
y = x - 5
A shop has 400 bulbs
out of which 24 are defective What percent are good bulb?
Answer:
look at the picture i sent plz......
Answer:
Number of non defective bulbs-
400-24
376
Our fraction would be-
376/400
To make it into percentage we need to always multiply it by 100
376/400 x 100
=94%
Thus 94% of the bulbs are non defective
Can someone help me find this answer: tan12=22/x Please explain the steps
Answer:
Solve the rational equation by combining expressions and isolating the variable.
x=47.04630109.
Step-by-step explanation:
Please help me :( I really need it.
Answer:
6
Step-by-step explanation:
since it's a right triangle you can use the Pythagorean Theorem
2.7² + b² = 6.5²
7.29 + b² = 42.25
b² = 34.96
b = [tex]\sqrt{34.96}[/tex] which equals 6 when rounded to the nearest tenth
The Marked Price of an article is 25% above the Selling Price and Cost price is 40% below Selling Price. Find the percentage of discount and profit.
Answer:
65% profit
-25% discount
Step-by-step explanation:
cost price = 40+25 = 65% higher than marked price
discount = -25%
PLEASE ANSWER ASAP !!!!
Answer:
probaly 2
Step-by-step explanation:
you have to figure out the slope.
y1 - y2/x1-x2
Help please, please
Answer:
x = 17
Step-by-step explanation:
Assuming you require to find x
4x - 3 and 115 are same- side interior angles and supplementary, sum to 180°
4x - 3 + 115 = 180
4x + 112 = 180 ( subtract 112 from both sides )
4x = 68 ( divide both sides by 4 )
x = 17
PLEASE HURRY!!!!!!!
What is the scale factor of this dilation?
Mark this and return
Save and Exit
Next
Submit
Answer:
3
Step-by-step explanation:
The scale factor of the dilation is 3
A tree 16 feet tall casts a shadow which forms an angle of 40° with the ground. How long is the shadow to the nearest hundredth of a foot?
Answer:
x = 19.06 feet
Step-by-step explanation:
Given that,
The length of a tree, h = 16 feet
It casts a shadow which forms an angle of 40° with the ground.
We need to find the length of the shadow. We can find it using trigonometry such that x be the length of the shadow. So,
[tex]\tan\theta=\dfrac{h}{x}\\\\x=\dfrac{h}{\tan\theta}\\\\x=\dfrac{16}{\tan(40)}\\\\x=19.06\ \text{feet}[/tex]
So, the length of the shadow is 19.06 feet.
could someone help me out for number 5 please?
Answer:
she didnt multiply 5 times 12
The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers.
Answer:
11.14
Step-by-step explanation:
Mean = sum of numbers / total numbers
the mean of the 7 numbers = sum of the numbers / 7
sum of numbers for the 3 numbers = 10 x 3 = 30
Sum of numbers for the other 4 numbers = 12 x 4 = 48
Sum of the 7 numbers = 48 + 30 = 78
Mean of the 7 numbers = 78 / 7 = 11.14
Which can be used to expand the expression below?
Answer:
Distributive Property
Step-by-step explanation:
We have
5(3x - 6/7)
Distributive Property would work because 5 has to be mutliplied by 3x and -6/7 to rid the parenthesis and also give a final answer for the equation. Any others will lead to a wrong answer.
The legs of a right triangle measure 10 m and 24 m. What is the length of
the third side of the right triangle?
Answer:
26
Step-by-step explanation:
100 +(24^2) = 676
square root of 676 = 26
Answer:
either 26 m or 21.8174 m
Step-by-step explanation:
If 24 is the hypotenuse, then 24^2-10^2=x^2
x^2=576-100=476
x=21.8174 m
if x=hypotenuse, then 24^2+10^2=x^2
x^2=576+100=676
x=26 m
What is the slope of the line shown above? Just tap on the picture. Yes I’m watching Daniel tiger’s neighborhood. I’m babysitting while doing school work.
Answer:
The slope is 1/3
Step-by-step explanation:
Equation for slope is rise over run or y2-y1/x2-x1
-5,1 -2,2 these are the 2 points, so it could be 2-1/-2--5 which is equal to 1/3.
please helpppppp!!!!!
9514 1404 393
Answer:
A + 2×BD - 2×CStep-by-step explanation:
The shaded area contains area A and two of area B. The expression for that area can be written ...
Area of trapezoid = A + 2×B
__
The overall rectangle has an area of D. The areas labeled C can be subtracted from that to leave the shaded area. The expression for that is ...
Area of trapezoid = D - 2×C
please help if your able to (:
Answer:
4/9
Step-by-step explanation:
(2/3)^2 is another way of writing:
2/3*2/3
Which is 4/9
Hope this helps
Answer:
2/3*2/3 4/3
Step-by-step explanation:
Brainliest to anyone who can answer and show working out :)
Answer:
d = 9
Step-by-step explanation:
solving for d
let's get ride of the fraction first so multiple the whole thing by 3
3= 1d - 6
add 6 to both sides
9 = d
easy peasy.
Suppose point A is located at (1, 3) on a coordinate plane. If AB is 10 and the x-coordinate of point B is 9, explain how to use the Distance Formula to find the y-coordinate of point B.
Answer:
y =9
Step-by-step explanation:
you know the distance is 10 and some of the x,y points. so start filling what you know into the distance formula
10= √((9-1)^2 + (y-3)^2 )
square both sides to get ride of the square root
100 = 64 + (y-3)^2
36 = (y-3)^2
6 = y-3
y = 9
double check by using 9 for Y and you'll see it works.
help mee pleaseeeeeeas
Answer:
Step-by-step explanation:
Volume = 1/2 a * b*h
So
V= 1/2 (9)(6)(21)= 567 us ^3
Can y’all please answer this?
Answer:
Look at the description:
Step-by-step explanation:
The mistake is that they did not need to divide the radius by two since the radius is already half of the diameter. The area of a circle is pi*r^2. The second mistake they made was that they assigned pi the value of 3 which is wrong. After calculating, the area of the circle is 53^2pi = 8824.73mm^2
45-45-90...find the value of x?
Answer:
x = 19Step-by-step explanation:
If the angles of a triangle are 45°, 45° and 90°, the the sides of the triangle are x. x and x√2
x√2 = 19√2 ⇔ x = 19
Subtract (-x-3) - (5x + 2).
Answer:
-1.2 or -5/6
Step-by-step explanation:
thats all I can say pls
Luke, Kira and Ali each served 2/3 of their own cake. Each cake was the same size, but luke served 4 slices, Kira served 6 slices and Ali served 8 slices. How is this possible?
Answer:
The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.
Step-by-step explanation:
It's possible because they cut cakes into different number of slices.
You know that Luke, Kira and Ali each served [tex]\frac{2}{3}[/tex] of their own cake and Luke served 4 slices, Kira served 6 slices and Ali served 8 slices.
Being x the whole slices of cake, and if Luke served [tex]\frac{2}{3}[/tex] of his cake, which are 4 slices, the whole slices of cake of Luke is:
[tex]\frac{2}{3}*x=4 slices[/tex]
Solving:
x= 4 ÷[tex]\frac{2}{3}[/tex]
x= 6
Then, whole slices of Luke's cake is 6.
Performing the same approach for Kira you get:
[tex]\frac{2}{3}*x=6 slices[/tex]
x= 6 ÷[tex]\frac{2}{3}[/tex]
x= 9
Then, whole slices of Kira's cake is 9.
Finally, performing the same approach for Ali you get:
[tex]\frac{2}{3}*x=8 slices[/tex]
x= 8 ÷[tex]\frac{2}{3}[/tex]
x= 12
Then, whole slices of Ali's cake is 12.
The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.
james and elaine share a box of sweet in the ratio 2:3 what fraction of sweets does james receive and elaine receive
Answer:
james get 2 thirds
Step-by-step explanation:
Sally used 8 cubes to make this square frame that has 3 cubes on each side. If she uses 20 cubes to make a square frame, how many cubes will be on each side of the frame? Think of using objects to help you solve this problem.
Answer:
5
Step-by-step explanation:
The number of cubes that should be on each side of the frame should be considered as the 5.
Calculation of the number of cube:Since Sally used 8 cubes to make this square frame that has 3 cubes on each side.
So here the no of the cube be like
= 8 - 3
= 5
hence, The number of cubes that should be on each side of the frame should be considered as the 5.
Learn more about cube here: https://brainly.com/question/3510925
Linear system
x-y=9
X+2y=27
find the slope of the line (17,-12) and (17,8)
Will mark brainliest if ur right! if not, u wont get it.
Answer:
(-4,4)
Step-by-step explanation:
I believe that's it
Helpp! Will give brainliest
Answer:
all of them are correct
Step-by-step explanation: