Step-by-step explanation:
In the rational fraction (x - 4)/(x² + 2x - 24),
x² + 2x - 24 is the denominator.
When x² + 2x - 24 = 0, (x + 6)(x - 4) = 0.
=> x = -6 or x = 4.
The excluded values for x are -6 and 4.
When P(x) is divided by x-2 the quotient is Q(x) and the remainder is 5.When Q(x) is divided by x^2+2x+4 the remainder is 2x-3.What is remainder when P(x) is divided by x^3-8
Step-by-step explanation:
P(x)
= (x - 2)Q¹(x) + 5
= (x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5.
Since x³ - 8 = (x - 2)(x² + 2x + 4),
(x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5
= (x - 2)(x² + 2x + 4)Q²(x) + (x - 2)(2x - 3) + 5
= (x³ - 8)Q²(x) + (2x² - 7x + 11).
Hence when P(x) is divided by (x³ - 8),
the remainder is 2x² - 7x + 11.
Find the slope of the line.
a. Undefined
b. 0
c. 3/2
d. -1
Answer:
Haven't found the answer but in the comments above me someone said it was D and it was def not D so try anything other than that, I just took the test on Edg2020
Step-by-step explanation:
In 2017, the population of a city is 11500, and is increasing exponentially at a rate of 3.1% per year (a) What will the population be in the year 2033? Population size = (b) In what year will the population have tripled? Year = Note You can earn partial credit on this problem
Answer:
(a) The population in the year 2033 is 18630.
(b) After nearly 36years from the starting population of 11500 we will get our population tripled.
Step-by-step explanation:
In 2017, the population of a city is 11500, and is increasing exponentially at a rate of 3.1% per year
This can be formulated with the compound interest formula, also we can think the given situation as we have 11500 rupees which increases at the rate of 3.1% per year.
we can formulate the given situation using the compound interest formula.
A = P(1 + [tex]\frac{r}{n}[/tex])^n*t
A is the final population
P is the initial population = 11500
r is the rate at which the population increases = 3.1A =% = 0.031
n denotes the number of times the population increases per year = 1
t is the time or year = 1
A = [tex]11500( 1 + 0.031)[/tex]^1*t
(a) The number of years to reach the year 2033 from 2017 is 16years.
so we have the value of t = 16
so the final population in the year 2033 will be
A = 11500(1+0.031)^1*16
= 11500(1.031)^16
= 11500*1.63
A = 18630
Therefore the population size in the year 2033 will be 18630.
(b) We need to find the year in which the population gets tripled. we will triple our population from the population which was in 2017
so the our equation will be
11500*3 = 11500(1+0.031)^1*t
3 = (1.031)^t
upon taking logarithm both sides we get
log(3) = t*log(1.031) ( using the property log(a^b) = blog(a)
0.477 = t*0.133
t = 0.477/0.0133
t = 35.86years
upon taking approximation we will get 36 years.
Therefore after nearly 36years from the starting population of 11500 we will get our population tripled.
Select Is a Function or Is not a Function to correctly classify each relation.
{(3, 2),(6, 4),(9, 6),(12, 8)}
{(2, 3),(2, 5),(3, 6),(9, 4)}
{(2, 4),(6, 3),(4, 8),(6, 6)}
{(3, 4),(5, 2),(6, 8),(6, 4)}
Which ones are functions and which ones aren't?
Answer:
first is a function second third ad fourth arent function
Step-by-step explanation:
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.
Given:
As, we know the relation is said to be a function if we have distinct inputs.
If the inputs are repeated then it is not a function.
So, {(3, 2),(6, 4),(9, 6),(12, 8)} is a function.
Also, {(2, 3),(2, 5),(3, 6),(9, 4)} is not a function.
{(2, 4),(6, 3),(4, 8),(6, 6)} is not a function.
{(3, 4),(5, 2),(6, 8),(6, 4)} is not a function.
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Jason buys 8 colored markers at the art store. He handed the cashier $15. The cashier gave him back $1. How much did each marker cost?
Answer:
2.25
Step-by-step explanation:
i think though
Each colored marker costs $1.75.
What is Unit Rate?The amount of one quantity in another single quantity is termed as the unit rate of that quantity.
For example, speed is a unit rate in terms of distance and speed.
Number of colored markers Jason bought = 8
Cash that Jason gives the cashier = $15
Cash that cashier gives back = $1
Price of 8 colored markers = 15 - 1
= $14
We have to find the unit rate of the colored marker, that is the price of one colored marker.
Let x be the cost of the one colored marker.
Using proportion,
8 : 14 = 1 : x
8/14 = 1/x
Doing cross multiplication,
8x = 14
x = 14/8
x = 1.75
Hence the unit rate of the colored marker or the cost of one colored marker is $1.75.
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help please will give brainliest
Answer:
B. the slope is 1/4
the y-intercept is (0,3)
Step-by-step explanation:
(-8,1)(0,3)
rise/run
find the missing value of the direct variation (2,5) (5,y)
Answer:
The missing value y=12.5 and we have (5,12.5)
Step-by-step explanation:
The formula used for direct variation is:
[tex]y\: \alpha \:x\\y=kx[/tex]
We need to find missing value (2,5)(5,y)
First we will find k, and then y
We have x=2, y=5
Find k:
[tex]y=kx\\5=k(2)\\k=\frac{5}{2}\\k=2.5[/tex]
Now, we cam find missing value in (5,y)
We have x=5, k=2.5 and y=?
[tex]y=kx\\y=2.5(5)\\y=12.5[/tex]
So, the missing value y=12.5 and we have (5,12.5)
What is an equation of the line that passes through the points (4, -2) and (8, – 7)?
Answer:
y = -1.25x + 3
Step-by-step explanation:
To see if the coordinate pairs are on this line, plug x into the equation above.
y = -5 + 3
y = -2, so (4, -2) is on that line.
y = -1.25(8) + 3
y = -10 + 3
y = -7, so (8, -7) is also on that line.
Answer:
y = -1.25x + 3
Step-by-step explanation:
i got it right
Which value, when placed in the box, would result ina system of equations with infinitely many solutions?
y=-2x + 4
6x + 3y = O
-12
-4
4
12
Answer:
-4
Step-by-step explanation:
Alice had x dollars in her account. She spends $35.31 to buy Medicines for her grandmother. If the balance in her account is $161.23, what was the amount in her account before purchase.?
Answer:
Alice started with $196.54 in her account.
Step-by-step explanation:
161.23 + 35.31 = 196.54
You draw a 52-card deck. Then the card is replaced in the deck, the deck ls shuffled and you draw again. Find the probability of drawing a red card each time
Answer:
we know that the probability of drawing black card is 26/52. Probability of drawing a king is 4/52
Step-by-step explanation:
Of the 200 students in school 90 volunteered to work the book sale. what percent of students volunteered?
Answer:
45%
Step-by-step explanation:
90/200 = 0.45
0.45 = 45%
noob
2/3 (a-18)=-6
What is a?
Answer:
a=9
Step-by-step explanation:
2/3 (a-18)=-6
a−18=−6×( 3/2)
a−18=−6×3/2
a−18= −18/2
a−18=−9
a=−9+18
a=9
Answer:
A=9
Step-by-step explanation:
Simplify both sides of the equation.
2/3(a−18)=−6
(2/3)(a)+(2/3)(−18)=−6(Distribute)
2/3a+-12=-6
2/3a-12=-6
Add 12 to both sides.
2/3a−12+12=−6+12
2/3a=6
Multiply both sides by 3/2
(3/2)* (2/3a)= (3/2)* (6)
A=9
Use the graph to find the solution y=x+4 y=-2x-2
Answer:
(-2 , 2)
Step-by-step explanation:
y=x+4
y=-2x-2
x+4=-2x-2
3x=-6
x=-2
y=2
graph attached
[tex]\large\boxed{\boxed{\pink{\bf \leadsto (-2,2) \ is \ the \ solution \ of \ the \ given \ linear \ equations .}}}[/tex]
Step-by-step explanation:Given to equations to us are ,
[tex]\qquad \red{\bullet} \: y = x + 4 \\\\\qquad \red{\bullet} \: y = -2x - 2 [/tex]
And we need to find the solution using graphical method.
So , after plotting the graph of both equations the point where both lines intersect will be the solution of the graph.
And , for plotting we need at least two points .
For equation (1) :-
[tex]\implies y = x + 4 [/tex]
When x = (-4) .
[tex]\implies y = -4+4\\\\\bf\implies y = 0 [/tex]
When x = (-3)
[tex]\implies y = -3+4\\\\\bf\implies y = -1 [/tex]
[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-4) & (-3) \\\cline{1-3} \bf y & 0 & 1 \\\cline{1-3}\end{tabular}}[/tex]
For equation 2 :-
[tex]\implies y = -2x - 2 [/tex]
When x = (-1) .
[tex]\implies y = -2(-1)-2\\\\\bf\implies y = 0 [/tex]
When x = (0)
[tex]\implies y = 0-2\\\\\bf\implies y = -2 [/tex]
[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-1) & 0 \\\cline{1-3} \bf y & 0 & -2 \\\cline{1-3}\end{tabular}}[/tex]
Now , let's plot their graphs. Graph is in attachment. Hence on plotting the graph we see that both the lines Intersect on (-2,2) . Hence x = -2 and y = 2 is the solution of the given linear equation.
Hence (-2,2) is the solution of the given pair of linear equations in two variables.HELP Find the value of x
Answer:
90
Step-by-step explanation:
Any two lines coming from the two edges of a diameter when they meet it gives 90
geometry help please !
Answer:
5 is the correct answer.............
A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans.
Answer:
[0.184, 0.266]
Step-by-step explanation:
Given:
Number of survey n =280
Number of veterans = 63
Confidence interval = 90%
Computation:
Probability of veterans = 63/280
Probability of veterans =0.225
a=0.1
Z(0.05) = 1.645 (from distribution table)
Confidence interval = 90%
So,
p ± Z*√[p(1-p)/n]
0.225 ± 1.645√(0.225(1-0.225)/280)
[0.184, 0.266]
Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.
What is the total running distance of the four runners?
X-3y=-12 and 4x+6y=-12 substitution
Answer:
x = -6
y = 2
Step-by-step explanation:
1. Approach
x - 3y = -12
4x + 6y = -12
In this problem, it would likely be easier to use elimination, but since the problem specifically says that one must use substitution, substitution will be used. Substitution is when one solves one of the equations for a variable, similar to solving a literal equation. The one will substitute in the value of the variable into the other equation and solve for the other varibale. Then one will finally back substitute in that value of the other variable to find the value of the first variable, hence solving the equation.
2. Solve equation 1
x - 3y = -12
Solve the literal equation with inverse operations;
x - 3y = -12
+3y + 3y
x = 3y - 12
3. Substitute the answer into the second equation
4x + 6y = -12
x = 3y - 12
4 ( 3y - 12 ) + 6y = -12
Distribute;
12y - 48 + 6y = -12
Simplify;
12y - 48 + 6y = -12
18y - 48 = -12
Inverse operations;
18y - 48 = -12
+48 +48
18y = 36
/18 /18
y = 2
4. Backsolve for x
Substitute the value for y back into the equation for x and solve
x = 3y - 12
y = 2
x = 3(2) - 12
x = 6 - 12
x = -6
Sabrina has 54 ballon to arrange in bunches. She want to put the same numberof ballon on each bunch .list all the different ways can sabrina arrange the ballon
Answer:
54 groups of 1, 27 groups of 2, 18 groups of 3, 9 groups of 6, and repeat vice versa (6 groups of 9, etc).
Step-by-step explanation:
Total number of ways are 8 to arrange the balloon,
What is permutation and combination?Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,
Given that,
Total number of balloon Sabrina has = 54,
The number of ways Sabrina can arrange the balloon are:
1 group of 54 balloons,
2 groups of 27 balloons,
3 groups of 18 balloons,
6 groups of 9 balloons,
9 groups of 6 balloons,
18 groups of 3 balloons,
27 groups of 2 balloons,
54 groups of 1 balloon,
There are total 8 different ways Sabrina can arrange the balloons.
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A rectangle piece of land is 400m*150m.Find the cost of the piece of land if one square meter of land costs ₹15,000.
Answer:
900000000
Step-by-step explanation:
Area=400×500
=60000m²
Since
1m² = 15000
60000m² = x
x = 60000×15000
x = 900000000
Which of the following are true statements?
Check all that apply
Answer:
a and d
Step-by-step explanation:
Imma try again
Can someone link me a website or pdf explaining how to solve this?
I'm sure it is easy but I just haven't been taught this
hi can you send me the formula...let me teach you
Answer:
B. BD = 67Step-by-step explanation:
ABCD is a square.
BD and AC are diagonals and they have equal length.
We have AC = 7x + 18 and BD = 10x - 3
Since AC = BD, we substitute their values and solve for x:
7x + 18 = 10x - 310x - 7x = 18 + 33x = 21x = 21/3x = 7Then find the length of BD:
BD = 7x + 18 = 7*7 + 18 = 49 + 18 = 67Correct option is B. BD = 67
Two families buy large sandwiches of the same size. Family A shares one sandwich equally among 4 people. family B shares one sandwich equally among 2 people. Will a person from Family A get the same amount or a different amount of a sandwich as a person from family B?
there's a drawing of 4 squares to represent the 4 ppl
Answer:
Different Amount
Step-by-step explanation:
4 is more than 2 and there would need to be 2 sandwiches in family a in order for them to be equal
How do I Solve 2-V=17
Answer:
solution
-V=17-2
-V=15
Last year Hank cashed out his investment account that earned 4.5% simple interest after 10 years
of investing. He ended up with $350 in interest on the account. How much was his initial investment?
Show your work
I=
P=
R=
T=
Answer:
Initial investment= $777.78
Step-by-step explanation:
Giving the following information:
Last year Hank cashed out his investment account that earned 4.5% simple interest after 10 years of investing. He ended up with $350 in interest on the account.
To calculate the principal (initial investment), we need to use the following formula:
I= P*r*t
I= $350
r= 0.045
t= 10
P= ?
350= P*0.045*10
350/0.45 = P
$777.78= P
Solve for X
5(3X-2)=5
Using the inverse trig functions, find the measure of angle A to the nearest degree.
1. 43 degrees
2. 37 degrees
3. 90 degrees
4. 53 degrees
Answer correct plz if u steal points ill report
Answer:
I think it might be y= x+2
Step-by-step explanation: because it is going up times 2 every time
OWO
Moving the decimal point to the right 4 places in a number is the same as?
Answer:
0^4
Step-by-step explanation:
lets say the number is 1.0 if you where to move the decimal to the right 4 place the number would then be 10,000.0. basically if it says 10^4 add 4 0's
Answer:
it is 10^4
Step-by-step explanation: