Answer:
y=-[tex]\frac{1}{2}[/tex]x+[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
First, calculate the slope of the line that is perpendicular to the equation of line we are asked to find
m=(y2-y1)/(x2-x1)
=(2-(-4))/(-2-1)
=6/-3
=-2
in this equation the slope is 2, and to find the first equation, use y=mx+b
use the point (1, -4) to find b
-4=(2)(1)+b
-4=2+b
b=-6
the first equation of the line is y=2x-6
to find the x intercept of that line substitute 0 for y
0=2x-6
2x=6
x=3
the slope of a line perpendicular to this would be the opposite reciprocal of the slope which would be equal to -1/2
for the second equation of the line to pass thorugh the x-intercept of the first line, it must pass through (3, 0), so substitute and solve for b
y=mx+b
0=(-1/2)(3)+b
b=3/2
thus the equation of the line that is perpendicular to the line through (1,-4) and (-2, 2) and passes through the x intercept of that line is y=-[tex]\frac{1}{2}[/tex]x+3/2
The equation of the line that is perpendicular to the line through (1,-4) and (-2,2) is [tex]y= \frac{1}{2}x+3[/tex]
The equation of the line perpendicular to the line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
[tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]
The slope m is calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{2-(-4)}{-2-1} \\\\m=\frac{6}{-3} \\\\m=-2[/tex]
For the line passing through the points (1,-4) and (-2,2), substitute m = -2, x₁ = 1, and y₁ = -4 into the equation [tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]
[tex]y-1=\frac{-1}{-2} (x-(-4))\\\\y-1=\frac{1}{2}(x+4)\\\\y=\frac{1}{2}x+2+1\\\\y= \frac{1}{2}x+3[/tex]
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If the following figure is a rectangle, find wz.
Answer:
Step-by-step explanation:
as both sides are equal so
7x-6 = 3x+14
7x-3x = 14+6
4x = 20
x= 5
Now, put x in 7x-6 to find WZ
7(5)-6 = 29
Also, 3(5)+14 = 29
The measurement of the side WZ of rectangle WXYZ is 29.
What are rectangles?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.
Given that, WXYZ is a rectangle, we need to find WZ,
As we know that, a rectangle is a type of parallelogram and opposite sides of a parallelogram are equal and parallel,
WZ and XY are opposite sides of the rectangle, therefore, are equal.
Thus,
WZ = XY
7x - 6 = 3x + 14
4x = 20
x = 5
Put x =5 in 7x - 6
WZ = 7(5) - 6
WZ = 29
Hence, the measurement of the side WZ of rectangle WXYZ is 29.
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Subtract 4/15 - 1/6. Simplify the answer.
Answer:
Find the smallest multiple the denominators have in common
30
Expand each fraction so that the denominators are 30
[tex]\frac{8}{30} + \frac{- 5}{30}[/tex]
Add or subtract the numerators and keep the same denominator
[tex]\frac{8- 5}{30}[/tex]
Simplify
[tex]\frac{1}{10}[/tex]
Find the value of x and y
Answer:
Step-by-step explanation:
Step One: We need to find a way to equate either the x terms of the y terms in each equation. ...
Step Two: Take equation b) from equation a) to eliminate the x component. ...
Step Three: substitute the value of y into either equation to find the value of x.
hope this helps!
Someone pls help! X*2(4x+3^2%)/23/21^2
Answer:
x+2^23(45*21)
Step-by-step explanation:
Plz help me I am timed plz don’t guess
DeArah made 88, 90, and 92 on her math tests this grading
period. What is the mean of her math test scores?
OA) 89
OB) 90
OC) 91
OD) 92
Answer:
B. 90
Step-by-step explanation:
Add them all, divide by 3.
88 + 90 + 92 = ?
270 = 270
270/3 = 90
Answer: 90
Step-by-step explanation:
You just add up all the numbers then divide by how many numbers there are.
( 88 + 90 + 92 = 270 ) There are 3 numbers so take 270 / 3 = 90.
You have a globe that has a radius of 11 inches. Find the volume of your globe
Answer:5,575.3in cubed
Step-by-step explanation:
The volume of a globe that has a radius of 11 inches would be equal to 5,575.3 cubic inches.
What is the volume of a sphere?A sphere is a three-dimensional shape analouge of a circle.
The volume of a sphere = 4/3πr^3
The radius of the sphere is 11 inches.
The volume of a sphere = 4/3πr^3
= 4/3 x 11 x 11 x 11 x π
= 4/3 x 11 x 11 x 11 x 3.14
= 5,575.3
Thus, The volume of a globe that has a radius of 11 inches would be equal to 5,575.3 cubic inches.
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What is 4/5 divided by 1/2
Answer:
4/5 / 1/2=1 3/5
Step-by-step explanation:
Calculating Percents 2
You may use a calculator for all calculations
Part 1 - Write each percent as a decimal equivalent
120%
2 15%
3 45%
4 50%
51%
63%
75%
8 6%
Answer: 120% is 1.2 in decimal form.
215% 2.15
345% 345
450% 4.50
51% 0.51
63% 0.63
75% 0.75
86$ 0.86
Step-by-step explanation:
A circular mirror has a diameter of 22 inches. Which measurement is closest to the area of the mirror in square inches
Answer:
379.94 square inches, or 379.94 in².
Step-by-step explanation:
The area of a circle is π r². The diameter of the circle is listed as 22 inches, and the radius, or "r", is equal to half of the diameter. So, half of 22 is 11.
Since the formula says r², 11 needs to be squared, or multiplied once by itself. 11 x 11 = 121, so the last part of the equation is to multiply 121 by π. Because pi is an irrational number that never ends, it is commonly accepted to use 3.14, or the first three digits of pi, as the value of pi in an equation.
With that, 121 x 3.14 = 379.94, giving a final answer of 379.94 in².
Let me know if I need to change or clarify anything. I hope this helps! :D
Answer:
19.6ft2
Step-by-step explanation:
a small refrigerator is a cube with a side length of 12 inches use the formula S= 6s2 to find the surface area of the cube
can someone please help me with this it's the last problem on my exam
Answer:
Surface area of the refrigerator is 864 in².
Step-by-step explanation:
Formula to calculate the surface area of a cube is,
Surface area = 6s²
Here, s = length of a side of the cube
If side length 's' = 12 inches
By substituting this value in the formula,
Surface area = 6(12)²
= 6 × 144
= 864 inch²
Therefore, surface area of the refrigerator is 864 in².
Can someone help me with this question?
Answer:it is A
Step-by-step explanation:
What is the value of x?
O 100°
140°
O 120°
O 130°
O 150°
56°
34°
Mark this and retum
Save and Exit
Next
Submit
Answer:
ans will option 130 degree
The value of x in the given figure is 130 degrees.
What is the value of x?The first step is to determine the value of all of the angles in the quadrilateral.
First angle = 180 - 140 = 40 Second angle = 180 - 34 = 146Third angle = 180 - 56 = 124Fourth angle = 360 - (40 + 146 + 124) = 50Angle x = 180 - 50 = 130
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Simplify by combining like terms.
4 1/3 B + 2 3/4 B + 1
Remember to simplify the mixed number!
Enter the number that goes in the green box.
What are the steps to solving this equation? 4x+20x-8=-2(-12x+8)
Answer: See explanation
Step-by-step explanation:
4x + 20x - 8 = -2 (-12x + 8)
Step 1
Distribute -2 to (-12x + 8)
4x + 20x - 8 = 24x - 16
Step 2
Combine 4x and 20x together
24x - 8 = 24x - 16
Step 3
Add 8 to both sides
24x = 24x - 8
Step 4
Subtract 24x from both sides
0 ≠ -8
That is incorrect so it's not a solution
Hope I helped!
HELP!!! WILL GIVE BRAINLIEST!!!
If a line passes through the points (3,5) and (1, 2), its slope is_______.If
necessary, use the slash (/) to indicate a fraction.
Answer:
answer: The formula is
(Y2-y1) /(x2-x1)
(3-1)/(5-2)
2/3
Step-by-step explanation:
Have a good day;-)
Helppppp Me!!!!!!!!!
Answer:
Top right
Step-by-step explanation:
Answer:
The bottom right triangle is both acute and scalene.
Explanation:
A scalene triangle is a triangle in which all 3 sides have different lengths. An acute triangle has 3 different angles under 90º. This triangle has 3 different lengths (8.3ft, 9ft, and 10 ft) and angles less than 90º (51º, 58º, and 71º); therefore, it's both acute and scalene.
if there is a trophy that is 13 inches tall and it's shadow is 26 inches and there's another trophy that's 7 inches tall, whats is it's height?
The sales tax of 8% on a purchase of $12 is
A. $0.86
B. $0.96
C. $1.06
D. $1.60
x times x times x times y times y
Answer:
3x × 2y
Step-by-step explanation:
x*x*x= 3x
y*y= 2y
3x*2y
solve the equation. 7+3lnx=20
Answer:
Simplifying
7 + 3lnx = 15
Solving
7 + 3lnx = 15
Solving for variable 'l'.
Move all terms containing l to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 3lnx = 15 + -7
Combine like terms: 7 + -7 = 0
0 + 3lnx = 15 + -7
3lnx = 15 + -7
Combine like terms: 15 + -7 = 8
3lnx = 8
Divide each side by '3nx'.
l = 2.666666667n-1x-1
Simplifying
l = 2.666666667n-1x-1
Answer:
The answer for " X" would be,
[tex]x = \frac{13}{3in} [/tex]
The answer for "N" would be,
[tex]n = \frac{13}{3ix} [/tex]
What is the solution to 3(4x - 8) = 4(6 - 3x)?
A)
-4
B)
2
C)
-10
D)
7
B is the correct answer
hope this can help :)
Given that f(x)=x^2-1
A) find f(5)
B) find f^-1(x)
C)f^-1(8)
Answer:
a) f(5) = 24
b) The inverse of given function
f⁻¹ ( x ) = √x+1
c) f⁻¹ ( 8 ) = √9 =3
Step-by-step explanation:
Explanation:-
Given f(x) = x² - 1
a)
f(5) = 5² -1 = 25-1 =24
b)
put y = f(x) = x² - 1
⇒ y = x² - 1
⇒ x² = y + 1
⇒ x = √y+1
⇒ f⁻¹ ( y ) = √y+1 ( ∵ f⁻¹ ( y) =x)
The inverse of given function
f⁻¹ ( x ) = √x+1
c) put x=8
f⁻¹ ( 8 ) = √8+1 = √9 =3
anna has 300naira and ojo has 1860naira.if anna saves 50 naira a day and ojo spends 70 a day, after how many days will they have equal amounts?
Answer:
Anna and Ojo will have same amount after 13 days.
Step-by-step explanation:
Given that:
Anna has 300 naira
She saves 50 naira per day.
Let,
x be the number of days.
y be the amount saved
y = 50x + 300
Ojo has 1860 naira
He spends 70 naira per day.
Let,
x be the number of days
y be the amount left
y = 1860 - 70x
For equal amount, the equations will be equal
50x +300 = 1860 - 70x
50x + 70x = 1860 - 300
120x = 1560
Dividing both sides by 120
[tex]\frac{120x}{120}=\frac{1560}{120}\\x=13[/tex]
Hence,
Anna and Ojo will have same amount after 13 days.
Members of the robotics club are ordering shirts with the club logo on the front. They can choose from a T-shirt, a sweatshirt, or a collared shirt
Each type of shirt comes in either red, blue, green, or purple. What is the probability that a club member will order a sweatshirt that is neither
red nor blue?
Answer:33
Step-by-step explanation: because they all have a chance so if you split 100 by three you get the product with a remainder of one that cant be split with out going into decimals
Hope this helps
The work of a student to solve the equation 2(3x − 4) = 8 + 2x + 4 is shown below:
Step 1: 2(3x − 4) = 8 + 2x + 4
Step 2: 5x − 6 = 12 + 2x
Step 3: 5x − 2x = 12 + 6
Step 4: 3x = 18
Step 5: x = 6
In which step did the student first make an error and what is the correct step? (5 points)
A. Step 2; 6x − 6 = 2(6 + x + 2)
B. Step 2; 6x − 8 = 12 + 2x
C. Step 3; 5x − 2x = 12 − 6
D. Step 3; 5x + 2x = 12 + 6
Answer:
B. Step 2; 6x - 8 = 12x + 2x
Step-by-step explanation:
Option B is correct, the student first make an error in step 2 and the correct step is 6x − 8 = 12 + 2x.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 2(3x − 4) = 8 + 2x + 4
Two times of three x minus four equal to eight plus two times of x plus four.
The work of student
Step 1: 2(3x − 4) = 8 + 2x + 4
Step 2: 5x − 6 = 12 + 2x
Step 3: 5x − 2x = 12 + 6
Step 4: 3x = 18
Step 5: x = 6
The student made a error in step 2.
After applying to the distributive property to the equation
6x-8=8+2x+4
The correct step is 6x-8=2x+12
Hence, Option B is correct, the student first make an error in step 2 and the correct step is 6x − 8 = 12 + 2x.
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What is the slope of the line which passes through (1, 4) and (0, 1)?
(Worth 50 points. Don't post your answer unless you have good ideas) Solve the following problem:
Which triangles are similar ?
Answer: ΔABC ≅ ΔADB
Step-by-step explanation:
In order to be similar, they must have the same angles.
ΔABC ΔADB ΔDBC
∠A = 180 - (2a + b) ∠A = 180 - (2a + b) ∠D = 180 - (a + b)
∠B = a + b ∠D = a + b ∠B = b
∠C = a ∠B = a ∠C = a
ΔABC and ΔADB have the same angles so they are similar.
Plot the points (0, −5) and (2, 4) on the coordinate plane.
Answer:
Hope i helped
Step-by-step explanation:
The answer is in the picture.
If the relationship is proportional, what is the missing value from the table?
Alia has a AED 20 gift card for an online music store. All songs at the store have the same price. After Alia buys 3 songs, the balance on the card is AED 16.25. What will be the remaining balance on the card after he buys 5 more songs
Answer:
Remaining balance = AED 13.75
Step-by-step explanation:
Given that:
Amount of gift card = AED 20
Amount left after buying 3 songs = AED 16.25
Cost of 3 songs = 20 - 16.25 = AED 3.75
Cost per song = [tex]\frac{3.75}{3}[/tex]
Cost per song = AED 1.25
Cost of 5 songs = 5(1.25) = AED 6.25
Remaining balance = 20 - 6.25 = AED 13.75
Hence,
Remaining balance = AED 13.75