Answers
Answer:
See Explanation
Step-by-step explanation:
We will make use of the following rules in solving these questions:
Inverse Variation: [tex]a\ \alpha\ \frac{1}{b}[/tex] ==> [tex]a = k/b[/tex]
Direct Variation: [tex]a\ \alpha\ b[/tex] => [tex]a = kb[/tex]
Direct, then inverse variation: [tex]a\ \alpha\ b\ \alpha\ \frac{1}{c}[/tex] ==> [tex]a= kb/c[/tex]
Joint Variation: [tex]a\ \alpha\ bc[/tex] ==> [tex]a= kbc[/tex]
The solution goes thus:
1. m varies directly to a
[tex]m\ \alpha\ a[/tex]
[tex]m =ka[/tex]
2. p varies inversely as q.
[tex]p\ \alpha\ \frac{1}{q}[/tex]
[tex]p\ = k\frac{1}{q}[/tex]
3. [tex]r\ varies[/tex] directly as s and inversely as t.
[tex]r\ \alpha\ s\ \alpha\ \frac{1}{t}[/tex]
[tex]r = k\frac{s}{t}[/tex]
4. z varies jointly as [tex]e\ and\ f.[/tex]
[tex]z\ \alpha \ ef[/tex]
[tex]z = kef[/tex]
5. F varies directly as the [tex]square\ of\ t.[/tex]
[tex]F\ \alpha\ t^2[/tex]
[tex]F = kt^2[/tex]
6. d varies jointly r and t
[tex]d\ \alpha\ rt[/tex]
[tex]d = krt[/tex]
7. P is inversely proportional to h.
[tex]P\ \alpha\ \frac{1}{h}[/tex]
[tex]P= \frac{k}{h}[/tex]
8. P varies directly as V
[tex]P\ \alpha\ V[/tex]
[tex]P=kV[/tex]
9. d varies directly as the square of t
[tex]d\ \alpha\ t^2[/tex]
[tex]d = kt^2[/tex]
10. s varies jointly as b and d and inversely as the square L
[tex]s\ \alpha\ bd\ \alpha\ \frac{1}{L^2}[/tex]
[tex]s = k\frac{bd}{L^2}[/tex]
Related Questions
Find GK pls help with this problem
Answers
Answer:
Step-by-step explanation:
IH:GH = 45:30 = 3:2
JK:GK = 36:GK = 3:2
GK = 24
describe how to obtain the graph of g from the graph of f(x) =
[tex] \sqrt{x} [/tex]
Answers
Problem 7
Consider the general template
g(x) = a*sqrt(x-h) + k
and compare it to the general parent function
f(x) = sqrt(x)
We have the following variables: a, h and k
They are defined as such:
a = handles the vertical stretch and if any reflections occur. If a > 0, then the curve goes upward; if a < 0, then the curve goes downward. Going from positive to negative, or vice versa, is a reflection over the x axis.h = handles the left and right shift. If h > 0, then you shift right. If h < 0, then you shift left.k = handles the up and down shifting. If k > 0, then you shift up. If k < 0, then you shift down.For this problem, we have
a = 1h = -4k = 3Since g(x) = sqrt(x+4)+3 is the same as g(x) = 1*sqrt(x - (-4)) + 3
With a = 1, we know that the curve moves upward. Compared to the parent graph y = sqrt(x), which also goes upward, no reflection has been done over the x axis.
The h = -4 means we shift 4 units to the left
The k = 3 means we shift 3 units up
Answer: Shift the parent function 4 units to the left and 3 units up=====================================================
Problem 8
We'll use the ideas mentioned in problem 7. They'll also be used for problems 9 and 10 as well.
For problem 8, we have
a = 1h = -4 = shift 4 units to the leftk = -2 = shift 2 units downAnswer: Shift the parent function 4 units to the left and 2 units down.=====================================================
Problem 9
This time we have
a = 1h = 4k = -3Answer: Shift the parent function 4 units to the right and 3 units down=====================================================
Problem 10
So far, all of the 'a' values have been positive 1. This means that there hasn't been any reflection or vertical stretching going on.
This time we have a = -1 instead of a = 1.
So we will reflect over the x axis along with the shiftings similar to the ones that occurred with the previous problems.
Answer: Reflect the parent function over the x axis, shift 4 units to the right, and shift 2 units upJackie decorated 4 posters in 24 minutes. At that rate, how many minutes would it take to decorate 12 posters?
Answers
Answer:
72 mins
Step-by-step explanation:
24/4 = 6
So each poster take 6 mins to decorate
12 x 6 = 72
I need help fast, timed assignment
Answers
Answer:
C
Step-by-step explanation:
the line seems to either separate or have multiple y places for 1 x place, making it not continuous at x=0 where this happens
465.00 base
24.0%
What is the percentage
Answers
Answer:
111.6
Step-by-step explanation:
A JET PLANE CARRY UP TO 200,000 LITTERS OF FUOL IT USED 130, OOO LITTERS OF FUEL DURING A FLIGHT WHAT PERCENTAGE OF THE FUOL CAPACITY DID IT USE ON THIS FLIGHT
Answers
Answer:
Step-by-step explanation:
100(13/20)=65%
What are the coordinates of the point on the directed line segment from (-8, -2) to
(6,2) that partitions the segment into a ratio of 1 to 3?
Answers
Answer:
The coordinates of the point are (-4.5,-1).
Step-by-step explanation:
We want to find point T(x,y).
I am going to say that out points are A(-8,-2) and B(6,2)
Since it partitions the segment in a 1:3 ratio, we have that:.
[tex]T - A = \frac{1}{1+3}(B-A)[/tex]
[tex]T - A = \frac{1}{4}(B-A)[/tex]
We apply this to both the x-coordinate and y-coordinate of T.
x-coordinate:
x-coordinate of A: -8
x-coordinate of B: 6
x-coordinate of T: x.
So
[tex]T - A = \frac{1}{4}(B-A)[/tex]
[tex]x - (-8) = \frac{1}{4}(6-(-8))[/tex]
[tex]x + 8 = \frac{14}{4}[/tex]
[tex]x = \frac{14}{4} - 8[/tex]
[tex]x = \frac{14}{4} - \frac{32}{4}[/tex]
[tex]x = -\frac{18}{4}[/tex]
[tex]x = -4.5[/tex]
y-coordinate:
y-coordinate of A: -2
y-coordinate of B: 2
y-coordinate of T: y.
[tex]T - A = \frac{1}{4}(B-A)[/tex]
[tex]y - (-2) = \frac{1}{4}(2-(-2))[/tex]
[tex]y + 2 = 1[/tex]
[tex]y = -1[/tex]
The coordinates of the point are (-4.5,-1).
Y / -7 = -3
What does the Y equal
Answers
Answer:
y=21
Step-by-step explanation:
-3 * -7 = 21
Answer:
21
Step-by-step explanation:
For this question multiply 7 to 3
Pls help ASAP I’ll brainlest
Answers
Answer:
b) x= -13
Step-by-step explanation:
Answer:
it's answer is= - 13.175
but it is not in option
so B) - 13
is right
Find mZBCD
А
65°
(4x + 5)
B
C с
(9x - 5)°
D
m BCD
Answers
Answer:
I don't know
Step-by-step explanation:
I really don't know I just tried but don't know sorry
factorise 3a-6b+ax-2bx
Answers
Answer:
(a-2b) ×(3+x)
Step-by-step explanation:
plz mark as brainliest
Complete the statement using <> or = -8/15 10/18
Answers
Answer:
-8/15 is less than 10/18 so <
Step-by-step explanation:
the product of four numbers is 540 three of the numbers are 2, 5 and 9. what is the other number
Answers
Answer:
Step-by-step explanation:
abcd=540
2(5)9a=540
90a=540
a=540/90
a=6
Simply the expression by combining like terms 6x+9+2x+4
Answers
One-seventh of a number, increased by twelve
Answers
Answer:
one seventh of 14 increased by 12 is 14
Step-by-step explanation:
so my example will use 14, so one seventh of 14 is 14 divided by 7 which is 2 then you just add 12 to 2 which gets you 14
An expression is defined as a set of numbers, variables, and mathematical operations. The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given statement "One-seventh of a number, increased by twelve" can be written in the form of an expression as shown below.
One-seventh of a number → x × (1/7) = x/7One-seventh of a number, increased by twelve→ x/7 + 12Hence, The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.
Learn more about Expression here:
https://brainly.com/question/13947055
#SPJ2
How many nineths does it take to make the same as 1/3
Answers
Answer:
3
Step-by-step explanation:
Answer:
3/9ths
Step-by-step explanation:
The diagram below is a scale drawing of a former's vegetable garden, where the length is 12 inches and the width is inches. The actual garden has a scale of 1 in 16 foot Select the following statements below the accurately represent the
cual garden.
Answers
Find c. Round to the nearest tenth.
Answers
Answer:
Here,
150+10=180
162-180=18
Answer is 18°
Step-by-step explanation:
So the round of nearest tenth is 18°
Hope it will help have a great day at school. ^_^
Each month the Dover family purchases 16 gallons of
milk. How many gallons of milk does the family
purchase in 12 weeks?
Answers
16*12=192
at a party 136 handshakes took place. each person shook hands exactly once with each of the others present. how many people were at the party?
Answers
9514 1404 393
Answer:
17
Step-by-step explanation:
The number of handshakes among n people is n(n -1)/2. Then ...
n(n -1)/2 = 136
n(n -1) = 272 = 17×16*
n = 17
There were 17 people at the party.
_____
* This factoring can be facilitated by recognition that √272 ≈ 16.5, the number midway between the consecutive factors.
ASAP please i need help on this also ill give brainlist and please explain how you go the answer
Answers
9514 1404 393
Answer:
110 square inches
Step-by-step explanation:
First, recall the formula for the area of a trapezoid:
A = (1/2)(b1 +b2)h
Next, identify the base and height dimensions on the figure.
b1 = 13 in; b2 = 9 in; h = 10 in
Next, fill the numbers into the formula and do the arithmetic.
A = (1/2)(13 in + 9 in)(10 in) = (1/2)(22 in)(10 in) = 110 in^2
Last, answer the question asked.
The area of the trapezoid is 110 square inches.
Write the simplest polynomial function with the zeros..?
Answers
Hannah and Anthony are siblings who have ages that are consecutive odd integers. The sum of their
ages is 92. Which equations could be used to find Hannah's age, h, if she is the older sibling?
Answers
Answer:
2h-2=92 and h-2=92-h.
Step-by-step explanation:
Hannah, h, is the older sibling and their ages are consecutive odd integers. This means that Anthony's age will be 2 less than Hannah's, or h-2.
The sum of these would be h+(h-2), giving us the equation h+(h-2)=92.
Combining like terms we would have the first correct choice, 2h-2=92.
Our first equation can be transformed, however, to have (h-2) by itself. To do this, we would subtract h from both sides, giving us h-2=92-h.
The equation that will represent the sum of the age of Hannah and Anthony will be 2x+2=92.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the age of Hannah be x. and Since the age of Hannah and Anthony are two consecutive odd integers, therefore, the age of Anthony will be (x+2).
As it is given that the sum of the ages of the two other person is 92, therefore, the equation that will represent the sum of the age of the two persons can be written as,
[tex]x+(x+2)=92\\\\x+x+2=92\\\\2x+2=92[/tex]
Thus, the equation that will represent the sum of the age of Hannah and Anthony will be 2x+2=92.
Learn more about Equation:
https://brainly.com/question/2263981
Can someone solve all this as soon as possible please please
Answers
Answer:
x=405
28.7
x=450
Step-by-step explanation:
Plot the points A(9, 11) and B(–3, –5). Find midpoint M of AB. Then show that AM = MB and AM + MB =AB
Answers
Answer:
The midpoint is (3, 3).
Step-by-step explanation:
We are given the two points A(9, 11) and B(-3, -5).
The midpoint is given by:
[tex]\displaystyle M=\Big(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\Big)[/tex]
So:
[tex]\displaystyle M = \Big( \frac{9+(-3) }{2}, \frac{ 11+(-5) }{2} \Big) = (3,3)[/tex]
The midpoint is (3, 3).
We want to show that AM = MB.
We can use the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
The distance between A(9, 11) and M(3, 3) will then be:
[tex]AM=\sqrt{(9-3)^2+(11-3)^2}=\sqrt{6^2+8^2}=\sqrt{100}=10[/tex]
And the distance between B(-3, -5) and M(3, 3) will be:
[tex]MB = \sqrt{ (3-(-3))^2 + (3-(-5))^2 } = \sqrt{(6)^2+(8)^2} = \sqrt{ 100 } = 10[/tex]
So, AM = MB = 10.
Since AM = MB = 10, AM + MB = 10 + 10 = 20.
So, we want to prove that AB = 20.
By the distance formula:
[tex]AB=\sqrt{(9-(-3))^2+(11-(-5))^2}=\sqrt{12^2+16^2}}=\sqrt{400}=20\stackrel{\checkmark}{=}20[/tex]
in a lottery, players must match five numbers plus a bonus number. five white balls are chosen from 59 white balls numbered from 1 to 59, and one red ball (the bonus number) is chosen from 35 red balls numbered 1 to 5. how many different results are possible?
Answers
The tape diagram a way to model 5/8x11 what fraction
Answers
Answer:
its 6 7/8
Step-by-step explanation:
Shawn is buying his first home. At closing he brought a check for $7570. The
closing costs were as follows:
Title Fee
Processing Fee
Appraisal
No. of Points
$545
$2100
$695
2
Based on this information, how much did the house cost?
A. $211,500
B. $141,000
C. $159,000
D. $175,000
Answers
Answer: 211,500
Step-by-step explanation:
Just took the quiz
Jason had 141 dollars to spend on 8 books. After buying them he had 13 dollars. How much did each book cost ?
Answers
Answer:
Each book cost $16
Step-by-step explanation:
Step 1: Subtract $13 from 141 to get 128
Step 2: Divide 8 by 128 to get 16
Each book cost $16
Hope this helps
pls mark brainliest!
I need help with this question
Answers
Answer:
[tex]Tax~required~to~be~paid = 5.4% (5) = \frac{5.4}{100}(5) = \frac{27}{100}[/tex][tex]~of~(5) = \frac{5.4}{100}(5) = \frac{27}{100} = 0.27~dollars[/tex]