Answer:
exactly one of the four are white
Given that (7x-8)/(2x-1)(x-2)
Use Partial Fraction Decomposition to Find A and B.
We look for constants a and b such that
[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac a{2x-1} + \frac b{x-2}[/tex]
Rewrite all terms with a common denominator and set the numerators equal:
[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac{a(x-2)}{(2x-1)(x-2)} + \frac{b(2x-1)}{(x-2)(2x-1)} \\\\ \frac{7x-8}{(2x-1)(x-2)} = \frac{a(x-2)+b(2x-1)}{(2x-1)(x-2)} \\\\ \implies 7x-8 = a(x-2) + b(2x-1) = (a+2b)x - 2a - b[/tex]
Then
a + 2b = 7
-2a - b = -8
Solve for a and b. Using elimination: multiply the first equation by 2 and add it to the second equation:
2 (a + 2b) + (-2a - b) = 2(7) + (-8)
2a + 4b - 2a - b = 14 - 8
3b = 6
b = 2
Then
a + 2(2) = 7 ==> a = 3
and so
[tex]\displaystyle \frac{7x-8}{(2x-1)(x-2)} = \frac 3{2x-1} + \frac 2{x-2}[/tex]
Answer:
a=3
b=2
Do whatever you want with that information^^
Calculate area and round to nearest tenth.
Johan leased a car for three years. He
paid a one-time fee of $1,000, and an
additional $300 per month for the full
three years. At the end of the three years,
what is the total amount Johan paid for
leasing this car?
Answer:
Step-by-step explanation:
A year has 12 months. 3 years have 36 months.
Total amount = 36 * 300 + 1000
Total amount = 10800 + 1000
Total amount = 11800
Which of the following values are solutions to the inequality 3x+10\ge 2?3x+10≥2?
\text{I.}\hspace{2px}-1\hspace{20px}\text{II.}\hspace{2px}3\hspace{20px}\text{III.}\hspace{2px}-11
I.−1II.3III.−11
\text{None}None
\text{I only}I only
\text{II only}II only
\text{III only}III only
\text{I and II}I and II
\text{I and III}I and III
\text{II and III}II and III
\text{I, II and III}I, II and III
9514 1404 393
Answer:
I and II
Step-by-step explanation:
The inequality ...
3x +10 ≥ 2
has solutions ...
3x ≥ -8 . . . . . . . . subtract10
x ≥ -2 2/3 . . . . . divide by 3
Of the answer choices {-1, 3, -11}, the ones that are greater than -2 2/3 are ...
-1, 3 . . . . . . I and II only
find the distance between the two points rounding to the nearest tenth (if necessary) (6, 5) and (-3, -7)
Answer:
15 units
Step-by-step explanation:
that is the answer yep
Answer:
9.2
Step-by-step explanation:
it said it
What is the measurement??
Answer:
83°
.......................
Answer:
83
Step-by-step explanation:
Select the following statement that describes overlapping events.
A. Receiving a Jack of diamonds meets the requirement of getting both a Jack and a diamond
B. Amanda rolls a three when she needed to roll an even number
C. Amanda understands that she cannot get a black diamond when playing poker
D. Amanda wants a black card so she can have a winning hand, and she receive the two of hearts
Answer:
Step-by-step explanation:
Having a jack and also having a diamond, satisfies two sets in a Venn diagram. An overlapping set is the intersection of the two. So A is the only one that can be in an intersection of these two sets.
The statement from the given choices that describes an overlapping event is A. Receiving a Jack of diamonds meets the requirement of getting both a Jack and a diamond.
What are overlapping events in probability?Events that share one or more outcomes are said to be overlapping events.
How to solve the question?In the question, we are asked for the statements from the given options that describe overlapping events.
To check for overlapping events, we analyze each option as follows:-
A. Receiving a Jack of diamonds meets the requirement of getting both a Jack and a diamond. The receiving of a jack of diamond shows an overlapping event, with the overlapping of the events of getting a jack and getting a diamond.B. Amanda rolls a three when she needed to roll an even number. The rolling of a three when the requirement was to roll an even number doesn't show an overlapping event as three doesn't fall in even numbers.C. Amanda understands that she cannot get a black diamond when playing poker. The event of getting a black diamond is not overlapping as black cards are spades and clubs, and not diamonds.D. Amanda wants a black card so she can have a winning hand, and she receives the two of hearts. The event of receiving two of hearts when the requirement was of a black card is not an overlapping event as two of hearts is not a black card.Thus, the statement from the given choices that describes an overlapping event is A. Receiving a Jack of diamonds meets the requirement of getting both a Jack and a diamond.
Learn more about overlapping events at
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calculate the highest common fac for it to the following 4 45, 6 o and is
Answer:
The greatest common factor is 1
Step-by-step explanation:
The factors of 4 are: 1, 2, 4
The factors of 6 are: 1, 2, 3, 6
The factors of 45 are: 1, 3, 5, 9, 15, 45
Then the greatest common factor is 1.
What makes composing functions different from doing an arithmetic operation of two functions such as adding or dividing them?
(50 points) please i beg xoxoxo
Answer:
the answer is that one tells about nomadic responses
while the other talks about seramic responses
The graph of a square root function has a domain of (0, ∞) and range of [1,∞). In two or more complete sentences, explain how the given range of the function can help you to the maximum or minimum y-value of the function.
Answer:
As per given domain and range we can conclude that:
The function has positive domain only, since x = (0, ∞).The function has minimum value of 1 and no maximum value, since y = [1, ∞)Here
[tex]\\ \sf\longmapsto Domain=(0,\infty)[/tex]
[tex]\\ \sf\longmapsto Range=(1,\infty)[/tex]
The function has positive integral values as it lies in 1st Quadrant
[tex]\\ \sf\longmapsto (x,y)=(1,\infty)[/tex]
It has minimum value 1It has infinite or no maximum valuesSolve the system of equations by substitution
5x +y = 36
y = 4x
Step-by-step explanation:
The answer is mentioned above.
58 round of to the nearest 10
Answer:
58 to the nearest ten is = 60
Answer:
Here is your answer ⤵️
58 rounded to the nearest tens is 60.
The graph of the invertible function h is shown on the grid below.
What is the value of h^-1 (-1)?
Answer:
1
Step-by-step explanation:
[tex]h {}^{ - 1} ( - 1)[/tex]
means that what is the value of the inverse function of h(x) when x=-1. The inverse function x and y values swap with original functions. When x=1, y=-1 so the inverse of that will be when x=-1, y=1.
Applying the inverse function concept, it is found that [tex]h^{-1}(-1) = 1[/tex]
The inverse function [tex]f^{-1}(x) = a[/tex] means that [tex]f(a) = x[/tex].
In this problem, it is asked [tex]h^{-1}(-1)[/tex].
From the graph, it is taken that at the original function, when [tex]x = 1, y = -1[/tex], hence [tex]h(1) = -1[/tex].Then, applying the inverse function, we have that [tex]h^{-1}(-1) = 1[/tex], and thus 1 is the value of the inverse function.A similar problem, also involving inverse functions, is given at https://brainly.com/question/23950969
Determine whether each is rational or not rational.
pi is not a rational number.
decimals is also not a rational number.
whole number is rational number.
Can someone please explain
Answer:
r = 5
Step-by-step explanation:
the sine rules formula :
sin Q/q = sin R/r
=> r = q× sin R / sin Q
= 6× ⅓ / (2/5)
= 2 /(2/5)
= 2× 5/2
= 5
Answer:
r = 5
Step-by-step explanation:
Sine trigonometric ratio
[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse (the side opposite the right angle)The sides of a triangle are opposite their angles. Therefore, in ΔPQR:
⇒ side r is opposite angle R
⇒ side p is opposite angle P
⇒ side q is opposite angle Q
Using the given ratio of sin Q:
[tex]\sf \implies \sin Q=\dfrac{q}{H}=\dfrac{2}{5}[/tex]
Substitute the given value of q = 6 and solve for H:
[tex]\sf \implies \dfrac{6}{H}=\dfrac{2}{5}[/tex]
[tex]\sf \implies H=6 \cdot\dfrac{5}{2}[/tex]
[tex]\sf \implies H=15[/tex]
Using the given ratio of sin R:
[tex]\implies \sf \sin R=\dfrac{r}{H}=\dfrac{1}{3}[/tex]
Substitute the found value of H and solve for r:
[tex]\implies \sf \dfrac{r}{15}=\dfrac{1}{3}[/tex]
[tex]\implies \sf r=15 \cdot\dfrac{1}{3}[/tex]
[tex]\implies \sf r=5[/tex]
Learn more about trigonometric ratios here:
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https://brainly.com/question/27938163
Sam is saving digital copies of his movies on his computer. Right now, 270 movies take up 486,270 kilobytes. If each movie takes up the same amount of kilobytes, how many kilobytes does each movie take up?
A.
3,602
B.
1,531
C.
2,071
D.
1,801
Multiply v (5,-4) by u (-8,7)=
multiply x with x:
5×-8= -40
multiply y with y:
-4×7=-28
Answer:
(-40,-28)
A scientist removed a sample of 39.1 grams of a chemical from a container. The sample was 5 3/4 grams less than 3/10 of the total mass of the chemical in the container. What was the total mass in grams of the chemical in the container before the scientist removed the sample of 39.1 grams. show work please.
The first thing we must do for this case is to define variables:
x: the total mass of the chemical in the container
y: a sample of a chemical from a container
We have the following equation:
y = (3/10) x - 5 3/4
Then, for y = 39.1 we have:
39.1 = (3/10) x - 5 3/4
Clearing x:
(3/10) x = 39.1 + 5 3/4
(3/10) x = 44.85
x = (10/3) * (44.85)
x = 149.5 grams
Answer:
the total mass in grams of the chemical in the container before the scientist removed the sample of 39.1 grams was:
x = 149.5 grams.
help please someone
Answer:
(fog)(x) =x –14
(gof)(x) =x
Step-by-step explanation:
[tex](fog)(x) = f(g(x)) \\ = 8( \frac{x - 7}{8} ) - 7 \\ = x - 7 - 7 \\ = x - 14[/tex]
[tex](gof)(x) = g(f(x)) \\ = \frac{(8x - 7) + 7}{8} \\ \\ = \frac{8x}{8} \\ \\ = x[/tex]
In ΔPQR, sin P = 0.2, sin R = 0.2 and r = 12. Find the length of p.
9514 1404 393
Answer:
p = 12
Step-by-step explanation:
The sines of the opposite angles are the same, so the lengths of the sides are the same.
p = 12
_____
The law of sines tells you ...
p/sin(P) = r/sin(R)
p/0.2 = 12/0.2 . . . . . . substitute given values
Multiply by 0.2 to get ...
p(0.2/0.2) = 12(0.2/0.2)
p = 12
linear equation 5+3x=17
Answer:
x=4
Step-by-step explanation:
5+3x=17
-5 -5
3x=12
3 3
x=4
Answer:
x = 4
Step-by-step explanation:
[tex]5+3x=17\\\\3x=12\\\\x=4[/tex]
Calculus please help
Answer:
The balloon is rising at a rate of 50π/3 feet per minute.
Step-by-step explanation:
A weather balloon is rising vertically while being observed from a point who is exactly 300 feet away from the spot directly beneath the ground.
This is represented in the diagram below.
We want to find the rate at which the balloon is rising (i.e. find dh/dt) when the angle between the ground and the observer is π/6 (i.e. when θ = π/6), and is increasing at a rate of π/24 radians per minute (i.e. when dθ/dt = π/24).
Write a ratio relating the variables:
[tex]\displaystyle \tan \theta = \frac{h}{300}[/tex]
Take the derivative of both sides with respect to t:
[tex]\displaystyle \frac{d}{dt}\left[ \tan\theta\right] = \frac{d}{dt}\left[ \frac{h}{300}\right][/tex]
Implicitly Differentiate:
[tex]\displaystyle \sec^2\theta \cdot \frac{d\theta}{dt} = \frac{1}{300} \frac{dh}{dt}[/tex]
Substitute in known values:
[tex]\displaystyle \sec^2 \left(\frac{\pi}{6}\right) \left(\frac{\pi}{24}\right) = \frac{1}{300} \frac{dh}{dt}[/tex]
Solve for dh/dt:
[tex]\displaystyle \begin{aligned} \frac{dh}{dt} &= 300\left(\sec^2\left(\frac{\pi}{6}\right)\left(\frac{\pi}{24}\right)\right) \\ \\ &= 300\left(\frac{4}{3}\right)\left(\frac{\pi}{24}\right) \\ \\ &= \frac{50\pi}{3} \text{ feet per minute}\end{aligned}[/tex]
In conclusion, the balloon is rising at a rate of 50π/3 feet per minute.
I need a answer ASAP what is 1/7 equal to?
Answer:
1/7 = 2/14 = 3/21 = 4/28 = 5/35 = 6/42 = 7/49 = 8/56 = 9/63 = 7/10
Step-by-step explanation:
Write an
equation in slope intercept form y = mx +b.
6) slope = 4, y-intercept = -3
Answer:
y = 4x - 3
Step-by-step explanation:
Slope intercept form is made up of these components:
y = outputm = slopex = inputb = y-interceptThe question gives you the slope and the y-intercept. Now all you need to do is substitute the values for the variables. Therefore, the equation is y = 4x - 3.
What is the range of (-1,7)(6,2)(0,4)(5,2)(-3,1)
Answer:
range =(7,2,4,2,1)
if my answer helps you than mark me as brainliest.
Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the age of each. Jane is years old. Harvey is years old.
Answer:
Jane is 12 years old.
Harvey is 36 years old.
Step-by-step explanation:
The explanation is attached.
hiiiiiiiiiiiiiiiiiiii my frndz give me the answer3x/4-2y/3=5
2x/5+3y/5=17
Answer:
[tex]thank \: you[/tex]
distinguish between the constant difference and constant ratio :use examples for each co concept
Constant difference ..refers to the idea that the difference between two numbers does not change after adding or subtracting the same quantity to both numbers..
connstant rario .means that youe ratio is the same all points
Step-by-step explanation:
When you have points with a constant ratio, it means that your y:x or x:y ratio is the same for all points. .
Constant difference could have been thought of as 52-19 = 53-20 or as 52-19 = 50-17, a similar problem that maintains the same difference between the larger and smaller values.
Pls help A card is drawn from a standard deck of 52 cards. What is the probability of drawing a face card (jack, king, or queen) or a black card?
Answer:
probability is 32/52 or about 0.615
Step-by-step explanation:
There are 12 face cards
of the remaining 52 - 12 = 40 cards, half of them are black
so 12 + 40/2 = 32 cards would be considered successful
PLEASE HELP
write and solve an equation to find the value of X. please explain in details and show your work!
Answer:66.5 degrees
Step-by-step explanation: