The correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].
The correct option is (a).
To use the distributive property to simplify the expression (9(x+3) + 15x), we need to distribute the terms outside the parentheses to each term inside the parentheses.
The given expression is [tex]\(9(x+3) + 15x\)[/tex].
1. Distribute 9 to (x) and (3):
[tex]\[ 9(x+3) = 9 \times x + 9 \times 3 \][/tex]
2. Distribute 15 to (x):
[tex]\[ 15x \][/tex]
So, after using the distributive property, the expression becomes:
[tex]\[ 9 \cdot x + 9 \cdot 3 + 15x \][/tex]
Now, let's compare this with the options:
a. [tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex] - This matches our result.
b. [tex]\(9(x+3+15)x\)[/tex] - This option seems incorrect as it doesn't distribute 9 to each term inside the parentheses correctly.
c. [tex]\(9:x+3+15x\)[/tex] - This option doesn't seem to use the distributive property correctly.
d. [tex]\(9x+9 \cdot 3+9 \cdot 15x\)[/tex] - This option distributes 9 correctly but includes an extra term (9x) that doesn't appear in the original expression.
Therefore, the correct answer is option a.[tex]\(9 \cdot x + 9 \cdot 3 + 15x\)[/tex].
Which expression is equivalent to the given expression after using the distributive property? 9(x+3)+15x
a.9· x+9· 3+15x
b.9(x+3+15)x
c.9: x+3+15x
d.9 x+9· 3+9· 15x
Answer:
24x + 15
Step-by-step explanation:
9(x+3)+15x
Use the distributive property.
9*x +9*3 + 15x
9x + 15 + 15x
Combine the like terms.
24x + 15
Is the triangle with side lengths of 18cm, 24cm and 30 cm a right triangle ?
If a, b and c are the lengths of a right triangle and c is the longest side, then:
[tex]a^2+b^2=c^2[/tex]
We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:
[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]
Answer: It's the right triangle.The triangle with side lengths of 18cm, 24cm, and 30cm is a right triangle and this can be determined by using the Pythagorean theorem.
Given :
The triangle with side lengths of 18cm, 24cm, and 30 cm.
The following steps can be used to determine the given triangle is a right triangle or not:
Step 1 - The Pythagorean theorem can be used to determine whether the given triangle is a right triangle or not.
Step 2 - According to the Pythagorean theorem, the sum of the square of the two shorter sides of the triangle is equal to the square of the larger side of the triangle that is:
[tex]\rm H^2 = P^2+B^2[/tex]
where H is the hypotenuse, P is the perpendicular, and B is the base of the right angle triangle.
Step 3 - To determine the given triangle is a right angle triangle, the Pythagorean theorem must be satisfied.
[tex]24^2 + 18^2 = 30^2[/tex]
LHS = [tex]24^2+18^2[/tex]
= 576 + 324
= 900
RHS = [tex]30^2[/tex]
= 900
So, LHS is equal to RHS. Therefore, the given triangle is a right angle triangle.
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The letters in the word MISSISSIPPI are put into a bag. What is the probability of randomly selecting the letter S from the bag?
What is the value of a
A. 27.5
B. 45
C. 50
D. 90
Answer:
90 degrees
Step-by-step explanation:
Which functions are continuous at x= -2? Select all that apply.
Answer:
(i) and (iii)
Step-by-step explanation:
for i)
f(x) = [tex]\frac{x^{2}-4}{x+2}[/tex]
=[tex]\frac{(x+2)(x-2)}{x+2}[/tex]
=(x-2)
As x =-2
f(x)=-2-2
f(x)=-4
so it is a continuous function
for ii)
from the result of (i) we can deduce the result of second and we see that it is not equal to zero so it is not a continuous function
iii)
f(x)=[tex]\frac{x^{2}+4x+4}{x+2}[/tex]
f(x)=[tex]\frac{(x+2)^{2}}{x+2}[/tex]
f(x)=[tex]\frac{(x+2)(x+2)}{x+2}[/tex]
f(x)=x+2
as x= -2
f(x)=-2+2
f(x)=0
so it is a continuous function
iv) From the result of iii we can deduct that
f(x)=0 because it have the same equation so it is not a continuous function
Answer:
The first and third functions are continuous at x=-2
Step-by-step explanation:
Please, see the attached files.
Thanks.
Calculate the shaded area of the figure.
Answer:
36.5cm²
Step-by-step explanation:
Area of quarter circle=8²[tex]\pi[/tex]/4=64[tex]\pi[/tex]/4=16[tex]\pi[/tex]cm²
Area of square+Area of shaded region =2(16[tex]\pi[/tex])=32[tex]\pi[/tex]=100.5cm²
Area of square=8²=64cm²
Area of shaded region=100.5cm²-64cm²=36.5cm²
Therefore, the area of the shaded region is 36.5cm².
Answer:
Area shaded area = 36.48
Step-by-step explanation:
Preliminary
Draw a line from D to BAssume that the quarter circle has its center at C. Find the area of the quarter circle. [Arc DBC]Subtract the area of TriangleDBCThat gives 1/2 the shaded area. Double the 1/2 of the shaded areaGiven
ABCD is a square. It better be or we can't do this.One side of the square = 8 cm4 sides of the square = 32 cmThe center of the quarter circle is at CSolution
Quarter Circle Area
Formula
Area = 1/4 * pi * r^2
Solution
r = 8 cmpi = 3.14Area = 1/4 * 3.14 * 8^2Area = 50.24 cm^2Triangle Area
Formula
Area = 1/2 r^2
Given
r = 8
Solution
Area = 1/2 8^2Area = 32 cm^2Area of 1/2 the Shaded area
Formula
Area of 1/2 shaded area = Area of 1/4 circle - Area of Triangle
Givens
Area of 1/4 circle = 50.24Area of triangle= 32Solution
Area of 1/2 shaded area = 50.24 - 32Area of 1/2 shaded area = 18.24Answer= 2* 18.24Area Shaded area = 36.48
1. Tom distributed chocolates among his friends Alex and Kevin in the ratio 2: 1. If he had 12chocolates, how many did Kevin get?
Kevin:
[tex]\frac{2}{2+1}\cdot12=\frac{2}{3}\cdot12=8[/tex]
What expression can be used to determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound?
The expression for determining the total cost of buying granola and flour is (3.25/g) * g + (0.74/f) * f. The values of g and f represent the number of pounds of each item. To find the total cost, substitute the values into the expression.
Explanation:The expression that can be used to determine the total cost is:
Total cost = ($3.25/g) * g + ($0.74/f) * f
where 'g' represents the number of pounds of granola and 'f' represents the number of pounds of flour.
For example, if you wanted to find the total cost of buying 5 pounds of granola and 2 pounds of flour, you would substitute g = 5 and f = 2 into the expression to get:
Total cost = ($3.25/5) * 5 + ($0.74/2) * 2 = $16.25 + $1.48 = $17.73
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The total cost of buying g pounds of granola at $3.25 per pound and f pounds of flour at $0.74 per pound can be determined using the expression 3.25g + 0.74f.
To determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound, you can use the following expression:
3.25g + 0.74f
Here's a step-by-step explanation:
For granola, the cost per pound is $3.25. Therefore, for g pounds, the total cost is 3.25g.For flour, the cost per pound is $0.74. Therefore, for f pounds, the total cost is 0.74f.Add the costs together to get the total cost: 3.25g + 0.74f.This expression gives you the total cost based on the quantities of granola and flour you wish to purchase.
Which binomial expressions are factors of 5x^3+8x^2-7x-6
Answer:
x - 1 and x + 2
Step-by-step explanation:
By the factor theorem if (x - a) is a factor then f(a) = 0.
Try x - 1:_
f(1) = 5(1)^3 + 8(1)^2 - 7 - 6
= 5 + 8 - 7 - 7
= 0 so x - 1 is a factor
We can find the other factors by long division:-
5x^2 + 13x + 6
-----------------------------------
x - 1 ) 5x^3 + 8x^2 - 7x - 6
5x^3 - 5x^2
--------------------
13x^2 - 7x
13x^2 - 13x
------------------
6x - 6
6x - 6
-----------------
5x^2 + 13x + 6 = (5x + 3)(x + 2)
You invest $4000 in an account at 6.5% per year simple interest. How much will you have in the account at the beginning of the 9th year.
Answer:
$6340
Step-by-step explanation:
First figure out what 6.5% of 4000 is by multiplying not dividing because dividing will give you a way bigger number.
4000 x 6.5%=260
260 x 9=2340
2340+4000=6340
This table shows the input and output values for an exponential function f(x) .
What is the ratio of outputs for any two inputs that are three values apart?
x −3 −2 −1 0 1 2 3
f(x) 8/27 8/9 8/3 8 24 72 216
Enter your answer, as a simplified fraction
Answer:
Given the table as shown below:
x y
-3 8/27
-2 8/9
-1 8/3
0 8
1 24
2 72
3 216
Taking any input variable x that are three apart:
i,e x = 0 and x = 3
The output values at x =0 and x = 3 are:
f(0) = 8 and f(3) = 216
Then;
The ratio of outputs is:
[tex]\frac{f(3)}{f(0)} = \frac{216}{8}= \frac{27}{1}[/tex] or 27 : 1
Therefore, the ratio outputs for any two inputs that are three values apart is: [tex]27: 1[/tex]
Answer:
0.5
Step-by-step explanation:
Lily swims a 100-meter race. She swims the first half in 27.8 seconds. She swims the second half in 30.12 seconds. About how much longer does it take her to swim the second half of the race than the first half? Choose the best estimate.
Lily swam a 100-meter race, completing the first half in 27.8 seconds and the second half in 30.12 seconds. The difference between these times reveals that it took Lily about 2.32 seconds longer to swim the second half of the race compared to the first half.
Explanation:The student, Lily, swam a 100-meter race with the first and second halves timed separately. She completed the first half in 27.8 seconds and the second half in 30.12 seconds. To find out how much longer it took her to swim the second half than the first, we need to subtract the first time from the second.
So, the calculation would be: 30.12 seconds (second half) - 27.8 seconds (first half) = 2.32 seconds. Therefore, it took Lily about 2.32 seconds longer to swim the second half of the race compared to the first half.
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Joe ate 7 pies on wednesday. If that is only 1/4 of the world record for pie eating what is the pie record
Answer:
7 pie is the world record. That is 1/4 under the record and your Answer.
Step-by-step explanation:
Who come up with these dump questions??
Stu takes a job with a starting salary of $65,000 for the first year. He earns a 2% increase each year. How much does Stu make over five years?
$325,000
$331,500
$338,263
$358,826
Answer:
Stu makes $338,263 over five years.
Step-by-step explanation:
In order to find the total amount Stu would make after five years, you need to find out how much he will make each year based on the 2% increase. Starting with year 1 at $65,000, we need to take his total salary and multiply by 1.02 (or the whole salary plus an increase of 2%). So, in year 2, he would make $66,300. Again, we would take his year 2 total salary and multiply by 1.02 to get $67,626 for year 3. We apply these same steps to years four ($68,978.52) and five ($70,358.10). To find his income over the five years, we need to add his salary from all five years together to get a total of $338,263.
Answer:
Option C which is $ 338,263
Step-by-step explanation:
The salary for the first year = $65,000
Increase per year= 2 %
To find total money made in five years = ?
total earned in first year = $65,000
Total increase in money after first year = 2 % of 65,000
= [tex]\frac{2*65000}{100}[/tex]
=$ 1300
Total earned in second year = 65,000 + 1300
= $ 66,300
Total increase in money after second year = 2 % of 66,300
= [tex]\frac{2*66300}{100}[/tex]
=$ 1326
Total earned in third year = 66300 + 1326
= $ 67,626
Total increase in money after third year = 2 % of 67,626
= [tex]\frac{2*67626}{100}[/tex]
=$ 1352.52
Total earned in fourth year = 67626 + 1352.52
= $ 68978.52
Total increase in money after fourth year = 2 % of 68978.52
= [tex]\frac{2*68978.52}{100}[/tex]
=$ 1379.58
Total earned in fifth year = 68978.52 + 1379.58
= $ 70358.1
Total Made in all five years = 65000+66300+67626+68978.52+70358.1
= $ 338262.62
≅$ 338,263
PLEASE HELP 20pts
what is the number ? fifty
-three more then 3 times that number
-35 less than seven times a certain number is
what is the number? is twenty
-nine more than 12 times that number 21 less than fourteen times a certain number
Answer:
53+3=56
56 times -35
-1960-7
-1967
i think this is how you do it.
Step-by-step explanation:
A rectangular garden is 17 feet wide. Its length is 3 feet more than twice the width. What is the area of the garden?
Answer:
a = 629
Step-by-step explanation:
a = w * L
w = 17
L = 2w + 3
a = (17) * (2w + 3)
a = (17) * (2(17) + 3)
a = 17 * (34 + 3)
a = 17 * (37)
a = 629
A line contains the points S (4, -10) and B (10, -16). Find the slope of ̅̅̅̅SB. Must show your work to receive full credit.
Answer:
The slope is -1
Step-by-step explanation:
To find the slope when we have 2 points, we can use the formula
m = (y2-y1)/(x2-x1)
= (-16--10)/(10-4)
= (-16+10)/(10-4)
= -6/6
= -1
The slope is -1
1. What is the smallest whole number greater than √30 + √50 + √110?
2. For how many single-digit positive integers d are there an integer n for which the units digit of [tex]d^{n}[/tex] is 6?
3. A rectangular prism with whole number dimensions has faces with areas 54, 72, and 108 square inches. How many cubic inches are there in its volume?
60 points! Partial answers accepted as well.
In 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars. Which of the following represents the national debt in scientific notation?
Answer: [tex]1.3 \times 10^{13}[/tex]
Explanation:
We are given, that in 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars.
We are required to find the national debt in scientific notation. The scientific notation is used to represent either very small number or very large number.
The scientific form of the given number is:
[tex]1.3 \times 10^{13}[/tex]
In the diagram below, what needs to be labeled in order to prove triangle AHL and triangle EML are congruent by the SSS postulate
Answer:
HL = LM
Step-by-step explanation:
We have been given a diagram in which sides AH= EM and AL=EL.
Now we need to find which statement is missing to prove that triangles AHL and EML are congruent using SSS.
SSS means (side - side - side)
Two pair of equal sides are already given so we have completed SS of SSS.
Last "S" means we need one more pair of equal sides so that must be using remaining sides HL and LM
Hence final answer is HL = LM.
Each group member is permitted to consume one-third of a pizza. If there are twenty-four members in the group, how many pizzas should be ordered?
Answer:
8
Step-by-step explanation:
so they are one third of a pizza so thats 1/3 and 24 memebers so basically you just have to multiply 1/3 x 24 = 24/3 which is 8.
Answer:
8 pizzas should be ordered.
Step-by-step explanation:
To get the number of pizzas to be ordered, all we simple need to do is to multiply the numbers of the group members by the amount to be consume by each group member. That is;
Number of pizzas to be ordered = amount to be consume by each group member × number of group members.
amount to be consume by each group member = [tex]\frac{1}{3}[/tex]
Number of group members = 24
We can now proceed to insert our values into the formula
Number of pizzas to be ordered = amount to be consume by each group member × number of group members.
Number of pizzas to be ordered = [tex]\frac{1}{3}[/tex] × 24
= [tex]\frac{24}{3}[/tex]
= 8
Number of pizzas to be ordered = 8
Therefore, 8 pizzas should be ordered.
Anumeha is mowing the lawns for a summer job. For every mowing job, she charges and initial fee of $10 plus a constant fee for each hour of work. Her fee for a 5-hour job, for instance is $35. Let F(t) denote Anumeha's for a single job F (measured in dollars) as a function of the number of hours t it took her to complete it. Write the functions formula
Answer:
F(t) = 10 +5t
Step-by-step explanation:
Income equals the initial fee plus the hours worked times the hourly rate
We know the initial fee = 10
hours = t
hourly rate =r
F(t) = 10 + r*t
We know a 5 hour job is 35 dollars
35 = 10 + r*5
Subtract 10 from each side
35-10 = 10-10 +5r
25 = 5r
Divide by 5
25/5 = 5r/5
5 =r
The hourly rate is 5
F(t) = 10 +5t
math help will mark brainliest please give an explanation on how you got the answer
Answer:
It would be 2/13 because imagine being given 4 decks of 13 cards and you have. Higher chance of having one to two of an ace or king in the deck compared to pulling none to all four. So 2/13 due to the ratio of 13
If the smallest angle of rotation fir a regular polygon is 18 how many sides does the polygon have
He orders 5 veggie pizzas he orders enough for everybody to 5/6 of a pizzas.How many people can he feed
Answer: 25 people
Step-by-step explanation: 6 x 5 = 30 30-5 = 25
graft the solution to the inequality on the number line.
m>2.8
Answer:
See the graph of the given inequality in the attachment as shown below:
Step-by-step explanation:
Given the inequality: [tex]m > 2.8[/tex]
To graph this inequality on the number line.
Remember:
If the symbol is [tex](\geq or \leq)[/tex] then you fill in the dotIf the symbol is [tex](> or <)[/tex] then you do not fill in the dot.Since, in the given inequality the symbol is '>'
Now, sketch a number line and draw an open circle around the number 2.8.
You can see the number line as shown below in the attachment.
Find the least common multiple. 30, 25, and 4 a. 60 b. 3,000 c. 300 d. 150
Answer:
The least common multiple is 4.
Step-by-step explanation:
The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
the equation given to solve this is v=4/3 pi radius by the power of 3
The given radius is = 60 feet
The volume of the sphere is given by = [tex]\frac{4}{3} \pi r^{3}[/tex]
So we will find the volume of the sphere using radius as 60 and pi as 3.14
Volume = [tex]\frac{4}{3}*3.14*60*60*60[/tex] = 902059.20 cubic feet
As quarter of anything is defined as its one-fourth part, so here the volume of the quarter of sphere can be calculated by finding one fourth of the calculated volume.
So volume of quarter sphere = [tex]\frac{902059.20}{4}[/tex]
= 225514.80 cubic feet
And rounding this to nearest whole number we get 225515 cubic feet as the answer.
A 24000 gallon of pool is being filled at the rate of 40 gallons per minute at this rate how many minutes will it take to fill up this pool A.450 B.560 C.600 D.150
Answer:
Option no C 600 minutes
Step-by-step explanation:
Given:
gallons of pool = 24000 gallon
Rate at which it is filled = 40 gallons per minute
To find :
Time taken to fill the pool=?
Solution:
We know that rate is the time in which a thing is being done at per minute or per hour or per second. In our question it is given that the rate is 40 gallons per minute which means that 40 gallons are filled in one minute
Now
In one minute = 40 gallons filled
Total pool size = 24000 gallons
Total time taken = [tex]\frac{Total pool size}{gallon filled in one minute}[/tex]
Putting in the values
Total time taken = [tex]\frac{24000}{40}[/tex]
Total time taken = 600 minutes
So the answer is option c which is 600 minutes
Which property is illustrated by the following statement statement
Answer:
C) Symmetric
Step-by-step explanation:
The symmetric property is the idea that if A = B, then B = A. Flipping the equation around doesn't matter.
It's like saying 2+3 = 5 is the same as 5 = 2+3. We can extend the symmetric property to not only deal with equations, but include congruence statements as well.
Answer:symmetric
Step-by-step explanation: a p e x
1. Which of the following is not equivalent to the formula for angular velocity, v = wr?
vw = r
v/w = r
v/wr = 1
v/r= w
2. Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories (c) she actually burns in one hour varies no more than 45 calories. Which inequality below represents this scenario?
|c − 450| ≤ 45
|c + 450| ≥ 45
|c − 45| ≤ 450
|c − 45| ≥ 450
Answer:
vw = r This is not correct
abs ( c - 450) <= 45
Step-by-step explanation:
1. v = wr
Divide by w Divide by wr Divide by r
v/w = wr/w =r v/wr = wr/wr =1 v/r = wr/r =w
vw = r This is not correct
v/w = r This one is good
v/wr = 1 This one is good
v/r= w This one is good
2. When working with absolute values, the amount that can vary is on the other side from the absolute value.
abs( value - target) inequality amount that it varies by
the target is 450
no more than is less than or equal to
the amount we can vary by is 45
abs ( c - 450) <= 45
1. The first offered choice is equivalent to ...
... v = r/w . . . . . divide both sides by w
which is not the same as v = wr.
___
2. The wording "no more than 45" means ≤ 45. There's only one formula with such a relationship—the first one.
Comment on "this scenario"
The problem statement describes several relationships, and never tells us whether Lucy's goal is met. The precise "scenario" that is intended to be modeled is not clear. The first inequality has a solution that is the range of calories Lucy might have burned had she reached her goal.
The other inequalities describe other "scenarios," some of which are harder to describe.