Answer:
[tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
-6x +7y= -62
Rewriting this equation into the slope-intercept form:
7y= 6x -62
[tex]y = \frac{6}{7} x - \frac{62}{7} [/tex]
The product of the slope of 2 perpendicular lines is -1.
Let the slope of the unknown line be m.
[tex]m( \frac{6}{7} ) = - 1[/tex]
[tex]m = - 1 \div \frac{6}{7} [/tex]
[tex]m = - \frac{7}{6} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{7}{6} x + c[/tex]
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= -3,
[tex] - 3 = - \frac{ 7}{6} (8) + c[/tex]
[tex] - 3 = - \frac{28}{3} + c[/tex]
[tex]c = \frac{28}{3} - 3[/tex]
[tex]c = \frac{19}{3} [/tex]
[tex]c = 6 \frac{1}{3} [/tex]
Thus, the equation of the line is [tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex].
Caleb sketched the following diagram on graph paper. He dilated points B and C from center o. B a. What is the scale factor r? Show your work. b. Verify the scale factor with a different set of segments. C.) Which segments are parallel? How do you know? d. Which angles are equal in measure? How do you know?
Chris is standing on a cliff that is 3 feet above sea level. He dives into the water and descends to a depth 10 feet below the surface of the sea. On a number line, what is the distance between the two elevations?
7
8
13
14
Answer:
C
Step-by-step explanation:
Cumulative Exam 2021
Merry Christmas <3
P.S. Have a good winter break :)
Pls help I’ll brainlest ASAP I’ll add extra points
Answer:
I think the slope is -1/-4 or - 1/4
The gas tank in dads car holds 5 gallons. The gas tank in moms truck holds 50% more than that. How much gas does the truck's tank hold.
Answer:
7.5 gallons
Step-by-step explanation:
the 50% of 5 gallons is 2.5 then add up 5 gallons so the answer is 7.5 gallons of gas
Tressa’s home is 45 mile from school. Anton’s home is 35 mile from school. How many times the distance from Anton’s home to school is the distance from Tressa’s home to school?
Answer:
1.3
Step-by-step explanation:
y’’’’ - y = 0
y(0) = 0
y’(0) = 1
y’’(0) = 0
y’’’(0) = 0
Answer:
bick in my vaogina toes Step-by-step explanation:
A paper company ships notepads in rectangular boxes that have dimensions measuring 9 inches long, 9 inches wide, and 10 inches tall. Show work. Complete sentences.
V = LWH The volume of a rectangular prism / cube is equal to the length times the width times the height.
a. What is the volume of the box?
b. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the volume of each notepad?
c. What is the maximum number of notepads that will fit in 1 closed box
i will give brainliest :)
Answer:
a. 810
b. 27
c. 30
Step-by-step explanation:
Part a.
The volume is 9 * 9 * 10.
9 * 9 = 81, and 81 * 10 = 810.
Part b.
The volume of a cube is x^3, where x is the side length of the cube.
If x = 3, then 3^3 = 27.
Part c.
If each notebook has a volume of 27, then the maximum amount of notebooks that will fit in a box with volume 810 is 810/27 = 30 notebooks
a. The volume of the rectangular box is 810 inch³.
b. The volume of the notepad is 243 inch³.
c. The maximum number of notepads that will fit inside the box is 3.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, A paper company ships notepads in rectangular boxes that have dimensions measuring 9 inches long, 9 inches wide, and 10 inches tall.
Therefore, The volume of the box is, = (9×9×10) inch³.
= 810 inch³.
The dimensions of the notepad are 9 inches by 9 inches with an height of 3 inches.
Therefore, The volume of the notepad is = (9×9×3) = 243³ inches.
The maximum number of notepads that will fit inside thebox is,
= (810/243).
= 3.33 but it sholud only be 3 notepads.
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Simplify the square root of 5 times the cube root of 5.
I know the answer is, five to the five sixths power but I would like to know the steps to solve it.
Please help me with it, I'm not doing so well right now, and I need help.
Answer:
Step-by-step explanation:
Which statement is true regarding the functions on the
graph?
Answer:
f(3) = g(6)
Step-by-step explanation:
Differentiate y = sin^2x - cos^2x
Using the power and chain rules, the derivative of
y = sin²(x) - cos²(x)
is
dy/dx = 2 sin(x) cos(x) - 2 cos(x) (-sin(x))
dy/dx = 2 sin(x) cos(x) + 2 sin(x) cos(x)
dy/dx = 4 sin(x) cos(x)
and using the double angle identity for sine, this is equivalent to
dy/dx = 2 sin(2x)
Alternatively, we can first simplify y using the double angle identity for cosine:
cos(2x)= cos²(x) - sin²(x)
so that
y = -cos(2x)
and the derivative is
dy/dx = sin(2x) • 2
dy/dx = 2 sin(2x)
A small tree was planted at a height of 5 feet. The tree has been planted for 16 months, and is now 48.2 feet tall. Which equation
could be used to find x, the average number of feet the tree grew each month?
Answer:
Use the equation for Average Rate of Change which will give you 2.7 feet per month
Step-by-step explanation:
The equation is:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now insert your values:
[tex]\frac{48.2-5}{16-0}[/tex]
The answer is: 2.7 feet per month
Step-by-step explanation:
how much did it grow per month ?
well, it grew from 5 to 48.2 ft in 16 months.
that means it grew 48.2 - 5 = 43.2 ft.
per month that is 43.2/16 = 2.6875 ft per month.
so, the equation would look like
x = (48.2 - 5)/16
PLS HELP i will mark brainliest
Classify the following polynomial by its degree value. -x + x26 - 104
[tex] \: \: \: \: \: \: [/tex]
[tex] = 25x - 104[/tex]
Step-by-step explanation:
[tex] - x + x26 - 104[/tex]
use the commutative property to reorder the terms[tex] - x + 26x - 104[/tex]
collect like terms[tex] = 25x - 104[/tex]
hope it helps3] What is - 2y + 10 + 2y - 8 simplified?
a) – 4y + 18
C) 18
b) 4y + 2
d) 2
Expressions
Answer:
d. 2
Step-by-step explanation:
-2y +10+2y-8
10-8. ( -2y+2y = 0)
2
Answer:
d) 2
Step-by-step explanation:
We can first combine like terms
-2y + 2y = 0
Now, our expression is simply 10 - 8, which is 2
So, the answer is
d) 2
Find the quotient. 9,270,000 100
Answer: 92,700
Step-by-step explanation:
9,270,000 / 100 = 92,700
Solve the exponential equation: 2^3x+1 = 128
Answer:
So x=2.32956156226
Step-by-step explanation:
First subtract 1 on both sides
2^3x=127
Now you can rewrite this as
(2^3)^x
As it still equals the same thing
Now 2^3 is 8
So the equation is now
8^x=127
So we use log formula
log8 127=x
So how many times do we have to multiply 8 by itself to get 127?
The answer is: 2.32956156226
Hope this helps!
Assume that the demand curve D(p) given below is the market demand for widgets:
Q=D(p)=1204−11p, p > 0
Let the market supply of widgets be given by:
Q=S(p)=−3+6p, p > 0
where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price.
What is the equilibrium price?
Please round your answer to the nearest hundredth.
What is the equilibrium quantity?
Please round your answer to the nearest integer.
What is the consumer surplus at equilibrium?
Please round the intercept to the nearest tenth and round your answer to the nearest integer
What is the producer surplus at equilibrium?
Please round the intercept to the nearest tenth and round your answer to the nearest integer.
What is the unmet demand at equilibrium?
Please round your answer to the nearest integer.
Answer:
Step-by-step explanation:
I'll use y for quantity and x for price [love my x and y] and rewrite the demand and supply functions:
Demand: y=1204−11x
Supply: y = -3 + 6x
==
We want to know the equilibrium price and quantity. The quantities purchased and sold would be equal to the quantities supplied:
1204−11x = -3 + 6x
-17x = - 1207
x = 71 The price of a widget is 71 units ($, €,£,¥, etc.) at equilibrium
A price of 71 would lead to a demand and supply of:
y = 1204−11x
y = 1204−11(71)
y = 423 Widgets
We can also plot this to find the point (71,423). See the attachment.
At this point, I'm uncertain how to answer the "producer surplus" and "unmet demand" at equilibrium. This is what I did, so please judge if it is correct.
The demand line, y=1204−11x, tells us that if the price were 0, the demand would be 1204, which I'll assume in the maximum, since it is stipulated that x > 0 (I imagine it may no longer be a straight line when the price goes into negative territory. I'd be the first in line to accept a widget and $5 if they were priced at -$5).
At equilibrium, therefore, we would still have an unmet demand of (1204 - 423) or 781 widgets that customers wanted, but wouldn't pay the price.
It seems to me that this would also be the unmet demand: Product that could have been sold, but wasn't, due to the price. I'm unsure, however.
ILL GIVE BRAINLIEST TO THE RIGHT ANSWER!!!!!
Write an equation involving absolute value for the graph.
Answer:
-3<lxl<5
Step-by-step explanation:
take least number than use x in absolute value bars than take highest number sorry if this is wrong I'm just a kid
need help with math probelm
[tex]28+24=4(7)+4(6)=4(7+6)[=4(13)=52][/tex]
The answer: 4(7+6)
ok done. Thank to me :>
Work out the area of the shaded shape 4m 9m 14m 8m
Answer:
76 m^2
Step-by-step explanation:
To find the area of the figure, you must divide the figure into multiple shapes. By dividing the figure into a 4 x 9 rectangle and a 5 x 8 rectangle, you can calculate the area of these two figures and add them together. After doing this, your answer should be 76 m^2.
what are the subsets of set B =(a. b. c. d)?
Answer:
{},{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}
Step-by-step explanation:
Which expression is equivalent to 5(x + 7)?
Answer:
5x+35
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
Which variable expression represent the word phrase? The sum of 10 and the product of 7 and a number
Answer:
Step-by-step explanation:
y = 7x + 10
slope-intercept form of a linear equation
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
a
Only A
b
Only B
c
Both A and B
d
Neither A nor B
Answer: D, neither A nor B
Step-by-step explanation: In a function, the x (the input) cannot repeat in the given set of ordered pairs. In Set A, 2 repeats in the third and fourth ordered pairs. In Set B, 9 repeats in the third and fourth ordered pairs as well.
Answer: B
Step-by-step explanation:
Functions and Relations
A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values.
What is the opposite of 3.5? Write your answer as a decimal
PLSS Someone plss help plss helppp plllsss Will mark brainliest!!!
Answer:
( 6 , 8 )
Step-by-step explanation:
y = kx
k = [tex]\frac{y}{x}[/tex]
( 3 , 4 )
k = [tex]\frac{4}{3}[/tex]
[tex]\frac{4}{3}[/tex] = [tex]\frac{8}{6}[/tex] = [tex]\frac{12}{9}[/tex] = ....
( 6 , 8 )
X^3+3x^2-19/x-2
Find the quotient and remainder using synthetic division:
The quotient is
The remainder is
Submit Question
Step-by-step explanation:
x³ + 3x² - 19 ÷ x - 2 = x² + 5x + 10 rem 1
x³ - 2x²
5x² - 19
5x² - 10x
10x - 19
10x - 20
1
The quotient is ⇒ x² + 5x + 10 The remainder is ⇒ 1Answer:
quickly:
x-2=0 x^3+3x^2-19
x=0+2 = 2^3+3(2)^2-19
x=2 = 8+6^2-19
=8+36-19
=42-19
=23
The remainder is 23
HELP ME PLEASEEEE I WILL GIVE BRAINLIEST
Answer: DE, EW WD
Step-by-step explanation:
It looks shortest to longest...i think its the best answer. good luck :>
How much would you make for the YEAR at $25.02 per hour,
worked 51 hours and do get paid overtime? Round to the nearest
cent.
Answer:
1276.02
Step-by-step explanation:
25.02*51=(25*51)+(.02*51)=1275+1.02=1276.02
Melanie is making a piece of jewelry that is in the shape of a right triangle. The two shorter sides of the piece of jewelry are 5 mm and 12 mm. Find the perimeter of the piece of jewelry.
Answer:
30 mm.
Step-by-step explanation:
The longest side = sqrt(5^2 + 12^2)
= sqrt169
= 13. (Using Pythagoras).
So the perimeter = 5+12+13
= 30 mm.
Perimeter of the piece of jewelry = 30mm
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".
Given,
Shape of jewelry is right angle triangle ABC
length of shorter sides,
AB = 5mm
BC = 12mm
By Pythagoras theorem,
AC² = AB²+BC²
AC = √(5² + 12²)
AC = √169
AC = 13 mm
Perimeter of Triangle = AB + BC + AC
= 5 + 12 + 13
Perimeter of Triangle = 30
Hence, 30 mm is the perimeter of jewelry.
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