Answers
Option A:
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
Solution:
Given expression [tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)[/tex].
To find the product of the above expression:
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)[/tex]
First multiply first two factors with each term.
[tex]=(x^{4} \times 3 x^{3}- x^{4} \times 2 ) \left(4 x^{2}+5 x\right)[/tex]
Using exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]=(3 x^{7}- 2x^{4} ) \left(4 x^{2}+5 x\right)[/tex]
Now multiply these two factors with each term.
[tex]=3 x^{7} (4 x^{2}+5 x)- 2x^{4} \left(4 x^{2}+5 x\right)[/tex]
[tex]=(4 x^{2} \times 3 x^{7} +5 x \times 3 x^{7} )- \left(4 x^{2} \times 2x^{4}+5 x \times 2x^{4}\right)[/tex]
Using exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]=(12 x^{9} +15 x^{8} )- (8 x^{6}+10 x^{5})[/tex]
[tex]=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
Hence option A is the correct answer.
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Karen buys a water heater during the sale.
If Karen pays $350 , what was the original price?
Answers
Answer:
350 *100 /50 = 700
Step-by-step explanation:
Basically 350 is 50 percent of the total. What u need to do is find the 100 percent. Just use this formula
Discounted price *100 / (what was the discount percentage when it was bought)
Answer:
original price is $525
Step-by-step explanation:
Melissa's family is on vacation.they spend $125 per day on food and entertainment.they have a budgeted only up to $750 for food and entertainment.how many days of vacation can they afford
Answers
Melissa's family can afford 6 days of vacation.
Reason:
You need to divide the budget by the money they spend everyday.
$750 ÷ $125 = 6 days that the family can afford to pay for vacation.
Hope this helps you!
ƒ(x) = -2x + 3?
(-1, ___)
Answers
Answer:
(-1, 5)
Step-by-step explanation:
When f(x) = f(-1)
f(-1) = -2(-1) + 3
f(-1) = 2 + 3
f(-1) = 5
-1 is x
5 is y
(-1, 5)
Answer: (-1, 5)
Answer:
(-1,5)
Step-by-step explanation:
x=-1 then
f(-1)=-2*(-1)+3=2+3=5
How do I find side length x and would I use sin cos or tan
Answers
Check the picture below.
Make sure your calculator is in Degree mode.
Convert the mass 21mg=___g
Answers
Answer:
0.021g
Step-by-step explanation:
Select all the statements that correctly describe the solutions to this system of equations?
2x-y= 0
x+y=9
Answers
x + y = 9
x = 9 - y
2x - y = 0
2(9 - y) - y = 0
18 - 2y - y = 0
-3y = -18
y = 6
x = 9 - y
x = 9 - 6
x = 3
The value of x and y are 3 and 3 respectively in the given system of equations.
A system of equations is a set of two or further equations that own an identical set of unknowns. The thing of solving a system of equations is to determine the values for the unknowns that quench all of the equations in the system.
It is given that the system of equations is,
2x - y = 0
x + y = 9
Now, from the first equation, we get
y = 2x
On putting the above value of y in the second equation, we get
x + 2x = 9,
3x = 9,
x = [tex]\frac{9}{3}[/tex]
x = 3.
Now putting this value of x in the first equation, we get
2 [tex]\times[/tex] 3 + y = 9
6 + y = 9
y = 9 - 6
y = 3.
So, x = 3 and y = 3 in the above system of equations.
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Giselle is building a small baseball infield for her brother. The infield should be in the shape of a square. Each side of the infield,
between bases, measures 30 feet. The distance between home plate and second base, as shown in the picture, is 45 feet.
Which best describes the shape of the baseball field?
Answers
Answer:
Step-by-step explanation:
B
for a square diagonal is found by using pythagoras theorem.
(30)²+30²=900+900=1800≠45²
The best describes the shape of the baseball field would be; B Not square (30)² + 30² ≠45².
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Giselle is building a small baseball infield for her brother.
The infield should be in the shape of a square.
Each side of the infield, between bases, measures 30 feet.
The distance between home plate and second base, as shown in the picture, is 45 feet.
A square diagonal can be calculated by using the Pythagoras theorem.
|AC|^2 = |AB|^2 + |BC|^2
= (30)² + 30²
= 900 + 900
= 1800
≠45²
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Ivanna is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of History is Fun she sells. Suppose that x and
y are related by the equation 2400+120x = y.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Ivanna's total pay for each copy of History is Fun she sells?
$
What is Ivanna's total pay if she doesn't sell any copies of History is Fun?
Answers
1. For every extra copy, Ivanna sells she gets an additional 120 dollars (+$120) and for every less copy she loses $120 dollars (-$120).
2. Ivanna's total pay is $2,400 if she doesn't sell any copies of History is Fun.
Step-by-step explanation:
Step 1:
y = 2,400 + 120x, where y is Ivanna's total pay and x is the number of copies of history is fun she sells.
To calculate the change is Ivanna's pay we find the difference in pay for two consecutive values of y.
We must calculate y when x is of consecutive values i.e. 1, 2, 3, 4 ...
Step 2:
We calculate the value of y when x = 1, 2 and 3.
When x = 1, y = 2,400 + 120 (1) = 2,400 + 120 = $2,520.
When x = 2, y = 2,400 + 120 (2) = 2,400 + 240 = $2,640.
When x = 3, y = 2,400 + 120 (3) = 2,400 + 360 = $2,760.
Step 3:
To calculate the increase in her pay for a copy, we subtract y when x = 2 from y when x = 3.
(y when x = 3) - (y when x = 2) = $2,760 - $2,640 = $120.
So for every extra copy, Ivanna gets an extra $120.
To calculate the decrease in her pay for a copy, we subtract y when x = 3 from y when x = 2.
(y when x = 2) - (y when x = 3) = $2,640 - $2,760 = -$120.
So for every less copy, Ivanna loses $120.
Step 4:
To calculate her pay when she doesn't sell any copies of history is fun, we substitute the value of x as 0 in y.
When x = 0, y = 2,400 + 120 (0) = $2,400.
So Ivanna earns $2,400 if she doesn't sell any copies of history is fun.
A cone has a radius of 7 in and a volume of 512.87 in3.what is the height?
Answers
Height of the cone is 9.99 in
Step-by-step explanation:
Step 1: Volume of a cone = 1/3 πr²h. Given volume of the cone = 512.87 in³ and r = 7 in. Find height, h.512.87 = 1/3 × 22/7 × 7² × h
512.87 × 3 = 22 × 7 × h
1538.61 = 154h
∴ h = 1538.61/154 = 9.99 in
A community garden center hosts a plant giveaway every spring to help community members start their gardens. Last year, the giveaway
supported 50 families by giving away 150 plants. Based on this ratio, how
many plants will the center give away this year in order to support 65 families?
Answers
Answer:
195?
Step-by-step explanation:
One cubic foot of sand weighs about 90 pounds. Approximate the weight of the cone-shaped pile of sand. Round your answer to the nearest hundred pounds. Please show your work too, thank you. :)
Answers
Answer:
3485.63 pounds
Step-by-step explanation:
For cone shaped sand:
Height (h) = 3.5 ft
Diameter (d) = 6.5 ft
Therefore, radius (r) = 6.5/2= 3.25 ft
[tex]volume \: of \: sand \\ = \frac{1}{3} \pi {r}^{2} h \\ \\ = \frac{1}{3} \times \frac{22}{7} \times {(3.25)}^{2} \times 3.5\\ \\ = \frac{1}{3} \times 22 \times 10.5625 \times 0.5\\ \\ = \frac{1}{3} \times 11 \times 10.5625 \\ \\ = \frac{1}{3} \times 116.1875 \\ \\ = 38.7291667 \: {ft}^{3} \\ \\ \because \: 1 \: {ft}^{3} = 90 \: pounds \\ \\ \therefore \: 38.7291667 \: {ft}^{3} \\ = 38.7291667 \times 90 \ \\ = 3,485.625 \: pound \\ \approx \: 3485.63 \: pounds[/tex]
Hence, weight of sand is 3485.63 pounds.
Find the distance between (1,0) and (9, 15).
Distance =
Answers
Answer:
d = 17
Step-by-step explanation:
d = √ (9 − 1) 2 + (15− 0)^2
d = √ (8) ^2 + (15) ^2
d = √ 64 + 225
d = √289
d = 17
Answer:
17
Step-by-step explanation:
i got it right on a quiz
Lee got 77,67,99,79,100,65,79,89,58 and 67 on his English tests
What is the mean of Lee’s English tests
Answers
Answer:78
Step-by-step explanation:
77+67+99+79+100+65+79+89+58+67 = 780
Divide this number by the toal number of factor,which here is 10:
780/10 = 78
A group of construction workers were able to lay 27 bricks in an hour on a new house. This was 30% of the total number of bricks laid that day. What was the total number of bricks laid that day?
Answers
A total of 90 bricks were laid that day.
Step-by-step explanation:
Given,
Number of bricks laid in one hour = 27
This represents 30% of total bricks laid that day.
Let,
x be the total number of bricks laid that day.
30% of x = 27
[tex]\frac{30}{100}*x=27\\0.3x=27[/tex]
Dividing both sides by 0.3
[tex]\frac{0.3x}{0.3}=\frac{27}{0.3}\\x=90[/tex]
A total of 90 bricks were laid that day.
claire spends 1/2 of her monthly salary on food, 1/4 on rent and 1/3 on power bills, she saves rest. what fraction of her monthly salary does she have?
Answers
1/2=6/12
1/4=3/12
1/3=4/12
Then we add of these fractions together:
6/12+3/12+4/12=13/12
It looks like Claire is over-budget with her purchases.
(I’m not really sure if that is the problem)
Maybe it’s 1/2+1/8+1/24=12/24+3/24+1/24=16/24
This simplifies to 2/3 (dividing by 8).
So if Claire spends 1/2 on food, 1/4 of what’s left on rent, and 1/3 of that on power bills, then she will have 1/3 (1-2/3) left of her monthly salary.
I resaltó hope this helps!
What is the midpoint of EC?
Answers
Answer:
The correct answer is first option
(t + p, r)
Step-by-step explanation:
Points to remember
midpoint formula
Length of a line segment with endpoints (x1, y1) and (x2, y2) is given by,
Midpoint= [(x2 + x1)/2 , (y2 + y1)/2]
To find the midpoint of EC
Let (x1, y1) = E(2t, 0) and (x2, y2) = C(2p, 2r)
Midpoint = [(2t + 2p)/2 , (0 + 2r)/2]
= (2(t + p)/2 , 2r/2)
= (t + p, r)
Therefore midpoint of EC = (t + p, r)
The correct answer is first option
If one measurement of a golden rectangle is 5.7 inches, what is the other measurement?
Answers
The other measurement of the golden rectangle is approximately 9.1 inches.
A golden rectangle is defined by the property that the ratio of its length to its width is equal to the golden ratio, which is approximately 1.61803398875. This ratio is often denoted by the Greek letter phi (φ).
Given that one measurement of the golden rectangle is 5.7 inches, we can denote this as the width, w. To find the length, l, we use the golden ratio formula:
[tex]\[ l = w \times \phi \][/tex]
Substituting the given width and the value of φ:
[tex]\[ l = 5.7 \text{ inches} \times 1.61803398875 \][/tex]
[tex]\[ l \approx 9.1 \text{ inches} \][/tex]
Therefore, the other measurement of the golden rectangle, which is the length, is approximately 9.1 inches.
41% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
Answers
Answer:
Step-by-step explanation:
41%
(a) P(X = 3) ≈ 0.2687
(b) P(X ≥ 4) ≈ 0.9852
(c) P(X < 8) ≈ 0.9998
These probabilities were calculated using the binomial probability formula for a 41% favorability rate and 12 trials.
To find the probability in this scenario, we can use the binomial probability formula. Let's break down each part of the question:
(a) To find the probability that exactly three out of twelve U.S. adults favor the use of unmanned drones, we can use the binomial probability formula:
P(X = k) = (n choose k) ×[tex]p^k[/tex] ×[tex](1-p)^(n-k)[/tex]
Where:
n is the number of trials (12 in this case).
k is the specific number of successes we're interested in (3 in this case).
p is the probability of success (41% or 0.41 in decimal form).
P(X = 3) = (12 choose 3) × [tex](0.41^3)[/tex] × [tex](0.59^9)[/tex]
Calculate this using a binomial calculator or software to find the exact probability.
(b) To find the probability that at least four out of twelve U.S. adults favor the use of drones, we need to calculate the complementary probability of having fewer than four favoring drones and subtract it from 1:
P(X ≥ 4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]
(c) To find the probability that less than eight out of twelve U.S. adults favor the use of drones, calculate:
P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)
You can compute these probabilities using a binomial calculator or statistical software to get the precise answers.
For more such questions on probability
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The two pentagons are similar. Find the value of x. Enter your answer in the box.
Answers
6/2 simplifies to 3, so 15/x, x must make the fraction equal to 3 as well.
So x=5. This is because 15/5=3
The scale factor is 2 1/2 if you need that.
Hope this helps!
what is the distance between ( 1,0) and ( 9,15)
Answers
Answer:
(8,15)
Step-by-step explanation:
please help me again
Answers
Answer:
AC=96 units
Step-by-step explanation:
x^2 - 16 = 6x
x^2 - 6x - 16 = 0
(x - 8)(x + 2) = 0
x - 8 + 8 = 0 + 8
x = 8 WORKS
x + 2 - 2 = 0 - 2
x = -2 CANT WORK BECAUSE IS NEG
CE = 6(8)
48
AC = AE + CE
AC = 48 + 48
AC = 96
Answer: AC = 96
Please help I don't understand this problem. I need to get this done by tonight.
Answers
Answer:
Step-by-step explanation:
24
(4x^-3 y^5 z^-2)(2^-1 x^-1 y^-2)
Answers
Answer:
[tex]\frac{2y^{3} }{x^{4}z^{2} }[/tex]
Step-by-step explanation:
Simplify the expression until you get the given answer.
Hopefully this helps you out~
-(v + 7) -3 = -26 + v
Answers
Answer:
v = 8
Step-by-step explanation:
-v -7-3 = -26+v
2v = -10+26
2v = 16
v = 8
There are 5,280 feet in one mile. How many feet are in 6 miles?
Answers
Answer:
31,680 feet
Step-by-step explanation
5280*6
Answer: 31, 680 feet
Step-by-step explanation:
If 5280 feet = 1mile
x = 6 miles
Step 1: cross multiply the equation to the the value of x
x= 5280 × 6
=31,680 feet
3.
Fred is making a fruit salad. The ratio
of cups of peaches to cups of cherries
is 2 to 3. How many cups of peaches
will Fred need to make 60 cups of
fruit salad?
Answers
Answer:
24 cups
Step-by-step explanation:
Peaches to Cherries is given as 2 to 3
We can think of this as "parts". So total parts in the salad would be:
Total Part = 2 + 3 = 5 parts
So, now we need cups of peaches to cups of TOTAL
The ratio would be:
2 : 5
The total would be 60 cups
We let total cup of peaches be x
So we can write the ratio:
[tex]\frac{2}{5}=\frac{x}{60}[/tex]
Now, we cross multiply and solve for x:
[tex]\frac{2}{5}=\frac{x}{60}\\5x=2*60\\5x=120\\x=24[/tex]
Fred will need 24 cups of peaches
You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?
Answers
Answer:
$361,223
Step-by-step explanation:
Each year, the value is multiplied by 1+5% = 1.05. After 51 years, it has been multiplied by that factor 51 times, so is now ...
$30,000×1.05^51 ≈ $361,223
Final answer:
To find the approximate value of land purchased for $30,000 in 1960 with a 5% annual increase by 2011, we use the compound interest formula which results in an approximate value of $447,187.25.
Explanation:
To determine the approximate value of land in the year 2011, which was purchased for $30,000 in 1960 with an average annual increase of 5%, we will use the formula for compound interest. This situation can be treated as a compound interest problem where the initial principal is the initial land value, the rate is the annual increase, and the time is the number of years the land has appreciated.
The compound interest formula is [tex]A = P(1 + r/n)^(nt),[/tex] where A is the future value of the investment/loan, including interest, P is the principal investment amount (initial value of land), r is the annual interest rate (annual increase in value), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.
In this scenario, P is $30,000, r is 0.05 (5% expressed as a decimal), n is 1 since we are compounding annually, and t is 51 (2011 - 1960).
Therefore,
[tex]A = 30,000(1 + 0.05/1)^(1*51).[/tex]
Carrying out the calculation gives us the approximate value of the land in 2011.
[tex]A = 30,000(1.05)^51[/tex]
Approximate value of the land in 2011 = $447,187.25
Can someone please help me? Pics included!!!
Answers
Answer:
I think the answer would be C.
Step-by-step explanation:
What is 40% of 35 I NEEEED TO NOOOO
Answers
Answer:
14
Step-by-step explanation:
%40 * 35 is same as 0.4 * 35
14
Answer: 14
Answer:
14
Step-by-step explanation:
on a map, 1 inch equals 5 miles. Two cities are 5 inches apart on the map. What is the actual distance between the cites?
Answers
Answer:
25 in
Step-by-step explanation:
Answer:
25 miles
Step-by-step explanation:
If 1 inch equals 5 miles, which I wrote like 1in/5mi = 5in/x.
To find our answer we just multiply 5 miles by 5 inches to get 25 miles.