Answer:
π = 2A/ r²
Step-by-step explanation:
[tex]\pi = \frac{2a}{ {r}^{2} } [/tex]
A man is paid $1500 salary. He spends 20% of the salary for his kids education, 35% for food, 15% for miscellaneous and he saves the rest. How much money does he save?
Answer:
450
Step-by-step explanation:
The total is 100 %
20% + 35% +15% = 70%
100-70 = 30
He saves 30%
1500 * 30%
1500 *.30
450
A man is paid $1500 salary. He spends 20% of the salary for his kids education, 35% for food, 15% for miscellaneous and he saves the rest. How much money does he save?
S O L U T I O N :Total Income = $ 1500
According to the question,
He spends 20% to his kids education
He spends 35% for food
He spends 15% for miscellaneous
Out of total income he spends 20% on kids education
So, amount spent on kids education = 20% of $1500
Amount = 20/100 × $1500
Amount = $300
Hence, money spent on his kids education is $300
35% is spent on food
Money spent on food = 35% of $1500
Money spent = 35/100 × $1500
Money spent = $525
Hence, money spent on food is $525
15% is spent on miscellaneous
Money spent on miscellaneous = 15% of $1500
Money spent = 15/100 × $1500
Money spent = $225
Hence, money spent on miscellaneous is $225
Now, adding all the three we get
$300 + $525 + $225
$825 + $225
$1050
Total money spent = $1050
Remaining money = $1500 - $1050 = $450
Remaining amount left with him is $450Solve for p.
8 − 4(2p − 2) = 7 + p + 9
p =
p = 0
Step-by-step explanation:[tex]8 - 4(2p - 2) = 7 + p + 9[/tex]
➡️ [tex]8 - 8p + 8 = 16 + p[/tex]
➡️ [tex]16 - 8p = 16 + p[/tex]
➡️ [tex] - 8p = p[/tex]
➡️ [tex] - 8p - p = 0[/tex]
➡️ [tex] - 9p = 0[/tex]
➡️ [tex]p = 0[/tex]
Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet$ $f(x) 2$ is divisible by $(x 1)^3$. Write your answer in expanded form (that is, do not factor $f(x)$).
There seems to be one character missing. But I gather that f(x) needs to satisfy
• [tex]x^3[/tex] divides [tex]f(x)[/tex]
• [tex](x-1)^3[/tex] divides [tex]f(x)^2[/tex]
I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or
[tex]f(x) = x^5 + \cdots[/tex]
Since [tex]x^3[/tex] divides [tex]f(x)[/tex], and
[tex]f(x) = x^3 p(x)[/tex]
where [tex]p(x)[/tex] is degree-2, and we can write it as
[tex]f(x)=x^3 (x^2+ax+b)[/tex]
Now, we have
[tex]f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2[/tex]
so if [tex](x - 1)^3[/tex] divides [tex]f(x)^2[/tex], then [tex]p(x)[/tex] is degree-2, so [tex]p(x)^2[/tex] is degree-4, and we can write
[tex]p(x)^2 = (x-1)^3 q(x)[/tex]
where [tex]q(x)[/tex] is degree-1.
Expanding the left side gives
[tex]p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2[/tex]
and dividing by [tex](x-1)^3[/tex] leaves no remainder. If we actually compute the quotient, we wind up with
[tex]\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}[/tex]
If the remainder is supposed to be zero, then
[tex]\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}[/tex]
Adding these equations together and grouping terms, we get
[tex](a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1[/tex]
Then [tex]b=-1-a[/tex], and you can solve for a and b by substituting this into any of the three equations above. For instance,
[tex]2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1[/tex]
So, we end up with
[tex]p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}[/tex]
“Angle 7 and angle 8 are complementary. Angle 5 ≅ angle 8 and the measure of angle 6 = 29. Show your work to find the measure of angle 7 and 5.”
Based on the definition of complementary angles:
Measure of angle 7 = 29°
Measure of angle 5 = 61°
What are Complementary Angles?Complementary angles have a sum that is equal to 90 degrees. If two angles are complementary, then their sum = 90 degrees.
Angle 7 and angle 8 are complementary [given]
Angle 5 and angle 6 will also be complementary
Angle 5 ≅ angle 8 [given]
Angle 7 will also be congruent to angle 6
Measure of angle 6 = 29° [given]
Measure of angle 7 = 29°
Measure of angle 5 + measure of angle 6 = 90 degrees
Substitute
Measure of angle 5 + 29° = 90°
Measure of angle 5 = 90° - 29°
Measure of angle 5 = 61°
Therefore, based on the definition of complementary angles:
Measure of angle 7 = 29°
Measure of angle 5 = 61°
Learn more about complementary angles on:
https://brainly.com/question/16281260
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Find a polynomial f(x) of degree 4 that has the following zeros. 2, 5, 0, -7
Answer:
Step-by-step explanation:
f(x) = (x - 2)(x - 5)x(x+ 7)
f(x) = (x^2 - 7x + 10)*x * (x + 7)
f(x) = x(x^3 - 39x + 70)
f(x) = x^4 - 39x^2 + 70x
To show that this is correct, I've made a graph with these points labeled. The graph is just around the x axis. The local maximums and minimums are just too large a value.
6.55743... is an irrational number because it is an
a terminating decimal
a repeating decimal
a non-terminating and non-repeating decimal
a non-repeating decimal
a non-terminating decimal
Answer:
#3. a non-terminating and non-repeating
Step-by-step explanation:
6.55743... never ends and it never repeats either
Answer:
Not terminating but doesn't repeat either
Step-by-step explanation:
simplify each expression
Answer:
[tex] {x}^{ \frac{1}{2} } \times {x}^{ \frac{2}{3} } [/tex]
[tex] {x}^{ \frac{3 + 4}{6} } [/tex]
[tex] {x}^{ \frac{7}{6} } [/tex]
The fifty people at a library are only allowed to sit in groups of 3,4, or 5 people. If all 50 people are seated, the greatest possible number of groups is
Answer:
16
Step-by-step explanation:
50÷3=16R2
Second largest multiple of 3 that is smaller than 50=45
45÷3=15 groups of 3 people each
50-45=5
=1 group of 5 people
Greatest possible number of groups=15+1
=16
In 2004 a certain oil company spent sh 1740000 on crude oil import .This was a 20%increase 0ver the money on crude oil import in 2003.
a) How much did the company spend on crude oil import in 2003.
b)What was the difference in the money spent on crude oil import in the two years?
Answer:
a = 1,450,000
b = 290,000
Step-by-step explanation:
A: 1,740,000 = x*1.20
1,740,000/1.2 = x1.20/1.20
1,450,000 = x
B: 1,740,000 - 1,450,000 = 290,000
janessa is playing a board game with two friends. using a single die, one friend rolled a four, and the other friend rolled a three. janessa needs to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning. Is the probability of Janessa winning an independent event or dependent event
Answer:
It is a dependent event, because it depends of the number she'll get rolling the die
help!! this is math.
Answer:
2,78,31,64,4-2,10-6,54,-97,-38,-8-7,-4-5,-11-1,-16(b) Eric removed 72 fish from his pond over a period of 9 days. He removed the same number of
fish each day, What was the change in the number of fish in the pond each day?
fish
FASTEST WIL BE THE BRAINLIEST
Answer:
-8
Step-by-step explanation:
72 ÷ 9 = 8
The fish are being taken out, so negative.
I hope this helps!
pls ❤ and mark brainliest pls!
Which of the following is the inverse of f (x) = 3 - 14x
(03.03)
How does the graph of f(x) = (x – 9)^4-3 compare to the parent function g(x) =x^4?
Answer:
Step-by-step explanation:
The child graph is shifted 9 units to the right. That's what the nine does. The graph also shifts 3 units down when compared to g(x).
I have put a graph in so that you can see the shifts for yourself.
The red line is g(x) = x^4
The blue line is f(x) = (x - 9)^4 - 3
The quotient of 31 and the product of a number and - 8?
Answer:
[tex]\frac{31}{-8n}[/tex]
Step-by-step explanation:
Overall, the expression is a quotient, and you're dividing 31 by whatever the product is of -8 and an unknown number (a variable). The product of -8 and a number means you multiply them together
why are there three zeros in the product of 6 times 103
Answer:
There’s not
Step-by-step explanation:
It’s 618
HELP ASAP!! THIS IS SLOPE INTERCEPT FORM AND I HAVE NO IDEA HOW TO TO DO PLEASE EXPLAIN
Write a function C(t) to represent the cost of
renting a canoe for t hours. The rental charge
is $25 plus $2 for every 20 minutes of rental.
Find C(1.5) and describe its meaning.
Answer:
C(t)=25+2t
C(1.5)=25+2(1.5)=28
$28 for 1.5 minutes rent
A function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t and the cost for 1.5 minutes will be $28.
What is a function?
A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given that the rental charge is $25 plus $2 for every 20 minutes of rental.
The function formed for the given data will be:-
C(t)=25+2t
At 1.5 minutes the rent will be calculated as below:-
C(1.5)=25+2(1.5)=28
Therefore, the function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t, and the cost for 1.5 minutes will be $28.
To know more about the function follow
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Part A Which features describe the graph? Select all that apply. A domain: (-3, 4] B. range: (-3, 3] o C. increasing: (-3. -1) D. decreasing: (-1, 4) E positive: (-2, 2) F. negative: (-3.-2). (2, 4] Part B What is the average rate of change over the interval [-2. O for the graph in Part A? average rate of change =
Answer:
C, F
Step-by-step explanation:
1/2-(-1/3)
Does anyone know the answer to this question?
Answer:
5/6
.......................
Answer: 0.83
Step-by-step explanation: 1/2-(-1/3)= 5/6: Decimal form is 0.83
m−4=2m what does m= Please help
Answer:
-4
Step-by-step explanation:
you would subtract m from both sides to get -4=m
What was Veronica's speed if she drove 475 miles in 6 1/4 hours?
Answer: 76 mph
Step-by-step explanation: speed is distance divided by time so 475 : 6.25 = 76 (mph)
Answer:
76 mph
Step-by-step explanation:
To find the answer, you would divide the miles she drove: 475 by the amount of time it took to get there: 6 1/4 hours. Convert the fraction to a decimal: 1/4= .25 so your problem would look like this...
475 / 6.25 = 76
Emma jogs 2 miles along the beach in 1/3 of an hour. If she travels at a constant rate, how far will she jog in an hour?
Answer:
6
Step-by-step explanation:
you do 2 times 3 because you 2 miles is only 1/3 and you want do get the answer for an hour so 2/3 is 6
Answer:
6 miles
Step-by-step explanation:
If emma jogs at a constant rate she will travel 6 miles in 1 hour.
1/3 of an hour times 3 equals 1 hour and the 2 miles every 1/3 times 3 will be 6
hope it helps
WILL GIVE BRAINLIEST TO WHOEVER CAN EXPLAIN:
True or False-in scientific notation when you move the decimal point left is it positive.
Answer:
false.
Step-by-step explanation:
just cause you move a decimal point to the left dosent mean its positive.
What does x equal?
2x + 5x – 4= 17
Answer:
x = 3
Step-by-step explanation:
2x + 5x - 4 = 17 (Given)
7x - 4 = 17 (Simplify)
7x - 4 + 4 = 17 + 4 (Add 4 on both sides)
7x = 21 (Simplify)
7x/7 = 21/7 (Divide 7 on both sides)
x = 3 (Simplify)
work out the value of v°
Answer:
v+91=180(being co-interior angle)
v=180-91
v=89,
Answer:
Step-by-step explanation:
v°+120°+91°+(180°-155°)=360°
v°+236°=360°
v°=360°-236°
v°=124°
What is the slope of the line represented by the equation y = -1/2x+ 1/4
Answer:
y = mx+ b
m=slope
-1/2
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slopeb = y-interceptBy comparing the formula to the equation given, it is clear the slope of the line is -1/2.
3/5 of the T-shirts and a T-shirt shop are blue 5/8 of those T-shirts are on sale 1/3 of the blue T-shirts that are on sale or size medium what fraction of the shops T-shirts are blue T-shirts that are on sale and are size medium
Answer:
yes their size is medium
A company that makes barber scissors has found that the sales volume for barber scissors is directly proportional to the size of the sales force and inversely proportional to the price of the scissors. If 19440 pairs were sold in 2003, when there were 54 salespeople and the price was $20 a pair, what is the sales forecast for the upcoming year with 50 salespeople and a price of $18 a pair?
Answer:
20,000 pairs of barber scissors.
Step-by-step explanation:
The sales volume V for barber scissors is directly proportional to the size S of the sales force and inversely proportional to the price P of the scissors.
In other words, we can write that:
[tex]\displaystyle V = \frac{kS}{P}[/tex]
Where k is the constant of proportionality.
19,440 pairs were sold in 2013, when there was 54 salespeople and the price was $20 a pair. Hence, V = 19440 when S = 54 and P = 20. Substitute and determine the value of k:
[tex]\displaystyle \begin{aligned} (19440) &= \frac{k(54)}{(20)} \\ \\ 19440 &= \frac{27}{10}k \\ \\ k &=\frac{10}{27}(19440) = 7200 \end{aligned}[/tex]
Hence, our equation is:
[tex]\displaystyle V = \frac{7200S}{P}[/tex]
We want to determine the sales forecast with 50 salespeople and a price of $18 a pair. Hence, S = 50 and P = 18:
[tex]\displaystyle \begin{aligned} V&= \frac{7200(50)}{(18)} \\ \\ &= 20000\end{aligned}[/tex]
In conclusion, 20,000 pairs of barber scissors can be expected to be sold.
8w-2=12w+6 both answers
Answer:
your answer is -2
I hope it's helps you
Answer:
[tex]8w - 2 = 12w + 6 \\ 8w - 12w = 6 + 2 \\ - 4w = 8 \\ w = \frac{8}{ - 4} \\ w = - 2[/tex]
I hope it helped U
stay safe stay happy
