Given:
The equation of a line is
[tex]y=-\dfrac{2}{3}x+2[/tex] ...(i)
The perpendicular line passes through the point (-1,4).
To find:
The equation of the perpendicular line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
[tex]m=-\dfrac{2}{3}[/tex]
Product of slopes of two perpendicular lines is -1.
Let the slope of perpendicular line is [tex]m_1[/tex].
[tex]m\times m_1=-1[/tex]
[tex]-\dfrac{2}{3}\times m_1=-1[/tex]
[tex]m_1=\dfrac{3}{2}[/tex]
The slope of the perpendicular line is [tex]m_1=\dfrac{3}{2}[/tex] and it passes through the point (-1,4). So, the equation of the line is:
[tex]y-y_1=m_1(x-x_1)[/tex]
[tex]y-4=\dfrac{3}{2}(x-(-1))[/tex]
[tex]y-4=\dfrac{3}{2}(x+1)[/tex]
[tex]y-4=\dfrac{3}{2}x+\dfrac{3}{2}[/tex]
Add 4 on both sides.
[tex]y-4+4=\dfrac{3}{2}x+\dfrac{3}{2}+4[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{3+8}{2}[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex]
Therefore, the equation of required line is [tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex].
A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of the crop. Which of the following correctly labels the population?
00–99
01–99
0–99
1–100
Answer:
00–99
Step-by-step explanation:
I got it Correct
The correct label for the population would be: 1-100 as per the given scenario.
What is population?In statistics, a population refers to the entire group of individuals, objects, or measurements that the researcher is interested in studying.
In this scenario, the population refers to the entire group of items or people that the farmer is interested in studying.
In this case, the population is the total number of ears of corn produced by all 100 seeds sown by the farmer.
As a result, the population's correct label would be: 1-100. Because the farmer is interested in the yield of all 100 seeds, the population includes all possible outcomes of the experiment, ranging from one to one hundred ears of corn.
Option A, B, and C do not include all possible outcomes, whereas option D includes the number 0, which is not an option in this scenario.
Thus, the answer is 1-100.
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PLEASE HELP:,). The difference between the two numbers is 12. If you increase the first number by 2 and decrease the second number by 10, the first number is 9 times larger than the second. Find these numbers.
Answer:
25 and 13
Step-by-step explanation:
25 - 13 = 12
25 + 2 = 27
13 -10 =3
27 is 9 times larger than 3
i need help plz answer correctly, im giving brainliest and extra points for the 1st person so you better hurry.
Answer:
jsjzjdjdjdkthtabzgbgzbtzngzngzngsnysngsngdjysjysj
STION 1
Michael Smith buys and sells lovebirds. He currently has 80 yellow birds and
120 green birds. The birds are equally divided into five cages.
1.1.1
How many lovebirds does Michael have in total?
1.1.2
How many birds are in each cage?
1.1.3
Write the ratio of yellow birds to green birds that Michael has.
Give your answer in simplest form.
Answer:
1.1.1- Michael has 200 lovebirds in total
1.1.2- There are 40 birds in each cage
1.1.3- 120/80 = 3/2
Step-by-step explanation:
120+80=200
200÷5=40
120÷40=3, 80÷40=2
Step-by-step explanation:
The picture below shows the food that Michael gives to his lovebirds. He gives Each cage every morning
What are the coordinates of the vertex
PLZ HELP me with this and i will elect brainliest winne i promise just look at the photo and tell me what to do plz.
A clothing store sells all of their jeans for one price and all of their t-shirts for another price. Marisol purchased 2 pairs of jeans and 6 t-shirts for $60. Ernestine purchased 4 pairs of jeans and 3 t-shirts for $75. What is the cost of one pair of jeans and one t-shirt?
Answer:
j = $15
t = $5
Step-by-step explanation:
This question can be solved using simultaneous equation
let the price of t-shirt be represented with t
let the price of jeans be represented with j
From the question, these two equations can be derived
2j + 6t = 60 eqn 1
4j + 3t = 75 eqn 2
multiply eqn 1 by 2
4j + 12t = 120 eqn 3
Subtract eqn 2 from 3
9t = 45
divide both sides by 5
t = 5
Substitute for t in eqn 1
2j + 6(5) = 60
2j = 30
j = 15
Please hurry this is 7th grade hon
Answer:
1. place the circle on -1
2. open circle
3. Left
Step-by-step explanation:
help please
Find the hypotenuse of the triangle, the
distance between points (4, 4) and (-2,-2).
[?]
Enter the number that
16 goes beneath the radical
symbol
(
Combine like terms to create an equivalent expression.
Make sure to simplify coefficients and constants as well.
-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v−
5
6
−
3
2
v+
15
4
+
3
1
v
Answer is in the file below
tinyurl.com/wpazsebu
Your Welcome!!!!
The answer is in the picture!!!! :3
Find the equation of the line through point (4,−1) and perpendicular to y=x+2. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
simplify by pulling out the GCF from the numerator and the dominator? 6/8
Answer:
3/4
Step-by-step explanation:
The greatest common factor is 2 since 2 divides both into 6 and 8 so 3/4 is the answer since 3x2/4x2
The value of
(4-1)+a? --- 2 2(0,0)
when a = 2 and b= -1 is
Answer:
it's probably really hard to read and out of order but the answer is 1/3
one third
Question 1: To enter their home, the Cepeda family types in a 4 digit
code. How many codes are possible? *
40
10
1,000
10,000
So the first digit could be 0-9.
second is the same 0-9
And the 3rd 0-9 and lastly the 4th 0-9
There is a [tex]\frac{1}{10} *\frac{1}{10} *\frac{1}{10}* \frac{1}{10}[/tex] chance that they will get it right by guessing.
So that means a [tex]\frac{1}{10000}[/tex] chance that they will get it right.
So their are 10000 possible codes.
Identify the a, b and c terms from the equation 3x^2+5x-2.
Answer:
a - 3
b - 5
c - -2
Step-by-step explanation:
The quadradic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
When:
[tex]ax^2+bx+c[/tex]
This is the standard form of a quadradic equation.
We have the equation:
[tex]3x^2+5x-2\\\\[/tex]
Recall the standard form.
'3' is in a's place, '5' is in b's place, and '-2' is in c's place.
Hope this helps you.
8 folders cost $25.20. Write an equation to determine the cost of 3 folders.
Answer:
9 dollars and 45 cents
Step-by-step explanation:
First find the price of one folder.
$25.20 divided by 8 = $3.15
Then, multiply by 3.
$3.15 x 3 = $9.45
(I accidentally used 3.18 instead of 3.15. Someone corrected me.)
Answer:
25.20 divided by 8 = $3.15 x 3 = 9.45
Step-by-step explanation:
used a calculator, Hope this helps!
What is 300% of 15? Please show your work
Answer:
300/100*15=45 plz mark me branliest
identify the graph of 2x^2 + 4xy + 4y^2 = 0 then find theta to the nearest degree.
Answer: 2x2 + 4xy + 4y2 = 0
2 xx + 4xy + 4yy = 0
...xx + 2xy + y*y + yy = 0
(x + y)^2 + yy = 0
if x is a constant
... 2yy + 4xy - 2xy + xx = 0
(2yy + 4xy + 2xx -2xx) - 2xy + xx = 0
2(y + x)^2 - 2xx - 2xy + xx = 0
2(y + x)^2 - xx - 2xy = 0
2(y + x)^2 - xx - 2xy +yy - yy = 0
(x + y)^2 + yy = 0
x = i*y - y
if x = r cos a
y = r sin a
cos a )^2 + cos a sina + sin a)^2 + sin a)^2 = 0
cos a sin a + sin a)^2 = -1
Step-by-step explanation:
Answer:
Ellipse; -32deg
Step-by-step explanation:
Got it right on Edge
x + y = 16
5x - 4y = 12
Answer:
x = 8.44, y = 7.56
Step-by-step explanation:
x + y = 16 (equation 1)
5x - 4y = 12 (equation 2)
(x + y = 16)× 5
(5x - 4y = 12) × 1
9y/9 = 68/9
y = 7.56
Substitute the value of x in equation 1
x + 7.56 = 16
x = 16 - 7.56
x = 8.44
Therefore, x = 8.44, y = 7.56
Answer:
x = 76 / 9 [ 8 (4 / 9) = [tex]8.\bar{4}[/tex] ]
y = 68 / 9 [ 7 (5 / 9) = [tex]7.\bar{5}[/tex] ]
__________________
Step-by-step explanation:
There are several methods that can be used to solve systems but in this situation, it is generally easier to cancel out a variable by adding the system of equations together.
This is how it's done:
x + y = 16
5x – 4y = 12
__________
4 ( x + y = 16 )
+ 5x – 4y = 12
[Multiplying the entire equation by 4 to cancel out the y because 4y – 4y = 0]
___________
4x + 4y = 64
+ 5x – 4y = 12
__________
9x = 76
÷9 ÷9
[Dividing by the coefficient of 9x in x to get x]
______
x = 76 / 9.
_______
Now that we have the x variable, you can simply substitute that quantity into x + y = 16 to solve for y.
So:
x + y = 16
[substituting the value of x into the equation]
(76 / 9) + y = 16
[Creating a common denominator that
can be canceled out]
(76 / 9) + (9y / 9) = (144 / 9)
76 + 9y = 144
[Subtracting 76 from both sides to isolate 9y]
–76 –76
__________
9y = 68
÷9 ÷9
[Dividing both sides by the coefficient of 9y in y to get y]
_________
y = 68 / 9
_________
We can also verify that these variables have the correct value because:
x + y = 16
5x – 4y = 12
→
(76 / 9) + (68 / 9) = 16
5(76 / 9) – 4(68 / 9) = 12
__________________
(76 + 68 / 9) = 16
(380 / 9) – (272 / 9) = 12
___________________
144 / 9 = 16
(380 – 272 / 9) = 12
__________________
144 / 9 × 9 = 16 × 9
108 / 9 = 12
__________________
144 = 144 ✓
108 / 9 × 9 = 12 × 9
_________________
144 = 144 ✓
108 = 108 ✓
in the first quadrant you start at 4,6 then u move 6 units right and 5 units up
Answer:
10, 11
Step-by-step explanation:
4 plus 6 = 10
6 plus 5 = 11
Please help me with the correct answers!!
Answer:
circle
rectangle, or possibly a square
triangle
square
Step-by-step explanation:
Y is inversely proportional to cube root of x. what x= 1/8y=2 find the constant of proportional
Answer:
1/2
Step-by-step explanation:
[tex]y = \sqrt[3]{\frac{1}{8x}}\\\\=\sqrt[3]{\frac{1}{2*2*2*x}}\\\\=\frac{1}{2}\sqrt[3]{\frac{1}{x}}[/tex]
Constant of proportional= 1/2
Can someone help me please
Answer:
the answer is yes.
Step-by-step explanation:
Answer:
It is a which is (-2,2).............
A cube has a surface area of 126 feet. What is the area of one face?
Answer:
21 square feet
Step-by-step explanation:
A cube has 6 faces, therefore 126/6 = 21 sq/ft the area of 1 face
The area of one face of a cube is 21 feet.
What is the surface area of cube?Surface area of cube is the sum of areas of all the faces of cube, that covers it.
The formula for surface area is equal to six times of square of length of the sides of cube.
A cube has a surface area of 126 feet.
The area of one face is given by;
[tex]\rm Area \ of \ one \ face=\dfrac{Surface \ area}{Total \ number \ of \ faces}\\\\ Area \ of \ one \ face=\dfrac{126}{6}\\\\ Area \ of \ one \ face=21[/tex]
Hence, the area of one face of a cube is 21 feet.
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There are 4 red golf balls and 2 green golf balls in a bucket. You select a ball at random, keep it, and select again. Find the probability.
P(both green) HELP I NEED ANSWERS
Answer:
4/2
Step-by-step explanation:
$834 at 7.25% for 1 1/2years
Which of these shapes are rectangles? Choose ALL the correct answers
Answer:
Bottom two
Step-by-step explanation:
The shapes that are rectangles are the two blue shapes on the right-hand side in the image attached.
What are rectangles?A rectangle is a plane figure that comprises four side sides and it also has four right angles. The opposite sides of a rectangular shape are usually equal.
From the given image, the shapes that exhibit the rectangular shapes are the second and the fourth blue shapes which can be seen on the right-hand side in the image attached.
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Which expression and value represents 100 less than 3 times the sum of 18 and 2?
O 3 (18+ 2) - 100; -44
O 3 % (18 + 2) - 100; -40
O 100 - 3* (18 + 2); 40
O 100 - 3x (18+ 2): 48
Answer:
3 times (18+ 2) - 100
3 (18+2) - 100 = -40
first come first served brainiest
Answer:
5 yard
Step-by-step explanation:
It is estimated that 78% of drivers use their turn signal. Part A: What is the probability that exactly 3 drivers use their turn signal if a police officer pulls over five drivers? (5 points) Part B: What is the probability the next driver using their turn signal that the police officer pulls over if the fifth driver? (5 points) (10 points)
Answer:
0.2297 ;
78% of drivers use their turn signal. Part A: What is the probability that exactly 3 drivers use their turn signal if a police officer pulls over five drivers? (5 points) Part B: What is the probability the next driver using their turn signal that the police officer pulls over if the fifth driver? (5 points) (10 points)
Step-by-step explanation:
p = 0.78
1 - p = 0.22
P(x = 3)
Using the binomial distribution formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 3) = 5C3 * 0.78^3 * 0.22^2
P(x = 3) = 10 * 0.78^3 * 0.22^2
P(x = 3) = 0.2297