Answer:
6x^2
Step-by-step explanation:
Because we are multiplying 6 and a number x squared, we know that x will have an exponent of 2. Then, multiplying that by 6 and using conventional algebraic techniques, we can combine the two terms together.
6 * x^2
6x^2
Answer:
[tex]\displaystyle \rm \longmapsto 6 \times x {}^{2} [/tex]
[tex]\displaystyle \rm \longmapsto {6x}^{2} [/tex]
Dan is 5 years older than David. Bridget is 8 years younger than David. If the total of their ages is 57, how old is the eldest of them
Answer:
The oldest person is 25 years old
Step-by-step explanation:
Represent David's age by d.
Then Dan's age is d + 5, and Bridget's is d - 8.
The sum of these three ages is 57:
d + (d + 5) + (d - 8) = 57
This simplifies to
3d - 3 = 57, or 3d = 60. Then d must be 20.
David is 20, Dan is 25 (5 years older than David), and Bridget is 12 (8 years younger than David).
Check: Do these three ages add up to 57?
20 + 25 + 12 = 57 YES\
The oldest person is 25 years old. That's Dan's age.
6. Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges? F. H. G. J. CARDS, c 2 9 11 15 DOLLARS, d 9 40.5 50.5 67.5 CARDS, c 9 18 27 36 DOLLARS, d 2 4 6 8 CARDS, c 2 4 7 10 DOLLARS, d 9 18 31.5 45 CARDS, c 2 3 4 5 DOLLARS, d 9 10 11 12
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
Hector works in a gas station and earns $15.50 per hour. Last week he worked 29 hours. What was his gross pay?
Answer:
449.50
Step-by-step explanation:
because gross pay is before taxes and everything else and he worked 29 hours so 15.50 × 29 = $449.50
The amount of money that Hector works in a gas station will be $449.50.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Hector works in a service station and procures $15.50 each hour. Last week he worked 29 hours.
The total cost that Hector can earn will be given as,
⇒ $15.50 x 29
⇒ $449.5
The gross pay that Hector works in a corner store will be $449.50.
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Brand on has 25 buttons.Mason has 6 times as many buttons.How many buttons does Mason have?
Answer: Mason has 150 buttons.
Step-by-step explanation: Brandon has 25 buttons. If Mason has 6 times as many, all you have to do is multiply 25 times 6. You end up with 150 buttons.
Fifty part-time students were asked how many courses they were taking this term. The incomplete) results are shown below.
Part (b)
What percent of students take exactly two courses?
Part (c)
What percent of students take one or two courses?
%
Answer:
There are 50 part-time students:
15 of them, take only one course.
10 of them, take only two courses.
then the rest, this is:
50 - 10 - 15 = 25
25 students take 3 courses.
b) What percent of students take exactly two courses?
15 out of 50 take exactly two courses, the percentage is:
p = (10/50)*100% = 20%.
c) What percent of students take one or two courses?
This will be the percentage of students that take only one course plus the percentage of students that take two courses:
The percentage of students that take two courses is already known: 20%.
Now, for 1 course we have 15 students out of 50, the percentage is:
p = (15/50)*100% = 30%.
Then the percentage that take 1 or 2 courses is:
P = 30% + 20% = 50%
20% of students take exactly two courses, and 50% of students take one or two courses.
Given that fifty part-time students were asked how many courses they were taking this term, of which 15 take only 1 course, while 10 take 2 courses, to determine what percent of students take exactly two courses, and what percent of students take one or two courses, the following calculation must be performed:
(10/50) x 100 = X 0.2 x 100 = X 20 = X
(25/50) x 100 = X 0.5 x 100 = X 50 =X
Therefore, 20% of students take exactly two courses, and 50% of students take one or two courses.
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Find the equation for the set of points whose distance from the y-axis equals the distance from the xz-plane.
Answer:
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
Step-by-step explanation:
Let [tex]$ p(x_1, y_1, z_1)$[/tex] be the point.
Any point on y-axis is (0, y, 0)
So, distance is
= [tex]$ \sqrt{x_1^2+0 + z_1^2} $[/tex]
= [tex]$ \sqrt{x_1^2 + z_1^2} $[/tex] ......(1)
Now any point on x-z plane is [tex]$ ( x_1, 0, z_1 ) $[/tex]
Distance from p to this point is
= [tex]$ \sqrt{0+y_1^2 + 0} $[/tex]
= [tex]$\sqrt{y_1^2}$[/tex] .........(2)
Equating (1) and (2), we get
[tex]$ \sqrt{x_1^2 + z_1^2} = \sqrt{y_1^2}$[/tex]
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
This is the required equation.
Bodie Raptor's Iphone 11 has 4/5 of the battery still remaining. His phone battery drains at a rate of 1/3 every hour. If he uses his phone continuously, how many more hours will his phone last. Please give your answer as a mixed number in simplest form in the form of A . b/c
Answer:
[tex]2\frac{2}{5}[/tex] hours, or 1 hours and 24 minutes
Step-by-step explanation:
4/5 battery remaining
drains at rate of 1/3 per hour
[tex]\frac{1}{3}h=\frac{4}{5}\\\frac{3}{1}(\frac{1}{3}h)=\frac{3}{1}*\frac{4}{5}\\h=\frac{3*4}{1*5}=\frac{12}{5}=2\frac{2}{5}[/tex]
He has 2 2/5 hours or 2 hours and 24 minutes left until his phone dies. (A fifth of an hour is 12 minutes and we have 2/5 to deal with, so 12 times 2 is 24 mins.)
Solve the following inequality. Write the answer in interval notation. 3×+13≤8×+2
Answer:
[ 11/ 5 , ∞ )
Step-by-step explanation:
Please help me ! So lost rn
Answer:
2.7 meters
Step-by-step explanation:
So, we know that 1 foot is about 0.305 meters.
To find how many meters are in 9 feet, multiply 0.305 by 9.
Therefore:
[tex]9(1\text{ foot})=9(0.305\text{ meters})[/tex]
Multiply:
[tex]9\text{ feet}=2.745\text{ meters}[/tex]
To the nearest, tenth this would be 2.7 meters.
And we're done!
In a poll, 22% of 714 surveyed adults said that . What is the actual number of adults who said that
Answer:
157 surveyed adultStep-by-step explanation:
IF 22% of 714 surveyed adult made a statement, the actual number of those that made the statement can be gotten by simply evaluating 22% of 714 as shown below;
= 22% of 714
= 22/100 * 714
= (22*714)/100
= 15708/100
= 157.08
≈ 157 surveyed adult
This means that about 157 surveyed adults made the statement.
How many quarts of pure antifreeze must be added to 5 quarts of a 10 % antifreeze solution to obtain a 20 % antifreeze solution?
the domain for f(x) is all real numbers. (Blank) than or equal to 3
Answer:
greater
Step-by-step explanation:
The domain is the number that x can be
sqrt(x-3) must be greater than or equal to zero
x-3 must be greater than or equal to zero
x must be greater than or equal to three
The other restriction is x+2 cannot equal zero
x cannot equal -2
The first restriction is more restrictive so that is the one we go with
What is the value of the underline digit?
14.097
Answer:14.097
Step-by-step explanation:
Three-fifths of the students on a school trip are boys. There are 33 boys on the trip. How many students are on the trip?
Answer:
55 students
Step-by-step explanation:
Write an equation.
3/5 = 33
Divide by 3 to get a unit fraction.
3/5 / 3 = 1/5
33 / 3 = 11
1/5 = 11
Multiply by 5
1/5 x 5 = 1
11 x 5 = 55
1 = 55
So, there are 55 students on the school trip.
give an example of a set of five different numbers whose mean is 290
Answer:
200,300,290,320,340
Step-by-step explanation:
If the mean of five numbers = 290
Then the total sum of the five numbers should be= 290*5
= 1450
an example of a set of five different numbers whose mean is 290
= 200,300,290,320,340
Summation of the above
=( 200+300+290+320+340)
= 1450
So the above set of numbers is a good example of a set of five different numbers whose mean is 290
G(x)= -x^2 + 9 find: g(-4)
Answer:
G(-4) = -7
Step-by-step explanation:
G(x)= -x^2 + 9
x= -4
G(-4)= - (-4)^2 + 9
= -16 +9
= -7
I NEED HELP...finding the slope-intercept form equation
of the line passing through this points
(-12, 6) and (-36, 32)
Answer: y=-13/12x-7
Step-by-step explanation:
To find the slope-intercept form, we first need to find the slope. To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We use the two given points to find the slope.
[tex]m=\frac{32-6}{-36-(-12)} =\frac{26}{-24} =-\frac{13}{12}[/tex]
Now that we have our slope, we can start filling out the slope-intercept form equation.
y=mx+b
y=-13/12x+b
Since we don't know the y-intercept, we can use one of the given points and solve for b.
6=(-13/12)(-12)+b [multiply (-13/12) and -12]
6=13+b [subtract both sides by 13]
b=-7
With the y-intercept, we can complete our equation.
y=-13/12x-7
Find the indicated side of the
triangle.
Answer:
8
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
21 2/3 Divided by 3 1/4
Answer:
the answer is 20/3 or 6 2/3
Step-by-step explanation:
Determine algebraically whether f(x)=3x-2 and g(x)=(x+2)/3 are inverse functions. Show all work.
Answer:
Yes
Step-by-step explanation:
f(x)=3 x-2
y= 3 x-2
x= 3y - 2
3 y -2 = x
3 y -2 + 2 = x + 2
3 y = x + 2
3 3 3
3 y = x + 2
3 3 3
y = x + 2 replace y with f ^ -1(x)
3 3
f ^-1 (x) = x + 2
3 3
Find the pattern and use inductive reasoning to predict the next number in the sequence 100,50,80,40,70,35,…
Answer:
65
Step-by-step explanation:
100, 50, 80, 40, 70, 35, 65.
|____|__|___|___|__|__|
÷2. +30. ÷2. +30 ÷2. +30
A pattern is a recurring arrangement of numbers, forms, colors, and so on. The next number in the given pattern will be 65.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colors, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
If the given pattern is observed closely then it can be observed that the second number is decreased by half the previous one, while the next number is formed by adding 30, therefore,
The First Number = 100The second number, half of the previous = 50For the third number, add 30 = 80The fourth number, half of the previous = 40For the fifth number, add 30 = 70The sixth number, half of the previous = 35For the seventh number, add 30 = 65Hence, the next number in the given pattern will be 65.
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x+z-w/r=1 solve for z
Answer: z=1−x+w/r
Step-by-step explanation:
Subtract x from both sides.
z-w/r=1-x
Add w/r to both sides.
z=1−x+w/r
hope i helped
-lvr
When you multiply numbers, the answer is the product of those numbers. Name two different pairs of whole numbers whose product is 12.
Answer: 4 x 3 = 12
6 x 2 = 12
Step-by-step explanation:
How many ounces of a 30% alcohol solution must be mixed with 18ounces if a 35% alcohol solution to make a 33% alcohol solution
Answer:
12 ounces
Step-by-step explanation:
0.30 x + 0.35 (18) = 0.33 (x + 18)
0.30 x + 6.3 = 0.33 x + 5.94
0.36 = 0.03 x
x = 12
Which sum or difference identity would you use to verify that cos (180° - q) = -cos q?
a.
sin (a -b) = sin a cos b – cos a sin b
b.
cos (a -b) = cos a cos b – sin a sin b
c.
cos (a -b) = cos a cosb + sin a sin b
d.
sin (a + b) = sin a cos b + cos a sin b
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
In this case, we'd have a = 180 and b = q, so,
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
cos(180 - q) = cos(180)cos(q) + sin(180)sin(q)
cos(180 - q) = -1*cos(q) + 0*sin(q)
cos(180 - q) = -cos(q) + 0
cos(180 - q) = -cos(q)
Find three positive integers x, y, and z that satisfy the given conditions. The product is 125, and the sum is a minimum.
Answer:
Step-by-step explanation:
Given 3 positive integers x, y and z, if their product is 125, then;
xyz = 125 .......... 1
Sum of the integers S(x, y, z) = x+y+z ........... 2
From equation 1; x = 125/yz ........3
Substitute equation 3 into 2
S(x, y, z) = 125/yz+y+z
Sy = -125/y²z + 1
Sz = -125/z²y + 1
For the sum to be minimum, Sy = Sz = 0
-125/y²z + 1 = 0
-125/y²z = -1
-125 = -y²z
125 = y²z
Also; is Sz = 0
-125/z²y + 1 = 0
-125/z²y = -1
-125 = -z²y
125 = z²y
Hence y²z = z²y = 125
From y²z = 125, z = 125/y²
Substitute z = 125/y² into the equation 125 = z²y
125 = (125/y²)²× y
125 = 125²/y⁴ × y
125 = 125²/y³
1 = 125/y³
y³ = 125.
y = 5
Since 125 = y²z
5²z = 125
25z = 125
z = 5
From the product xyz = 125
x(5)(5) = 125
25x = 125.
x = 5
Hence x = y = z = 5
Which of the following are solutions to the equation below?
Check all that apply.
9x^2- 6x + 1 = 7
The answer is C and D
First we must make one side of the equation zero, so we subtract 7 on both sides of the equation, making the equation 9x^2 - 6x - 6 = 0
Then we will use the quadratic formula to find the answers.
using the Quadratic Formula where:
a = 9, b = -6, and c = -6
and the formula is 6 +- [tex]\sqrt{6^{2} } -4 (9)(6) /2 (9)[/tex]
9. An air conditioning system can circulate 350 cubic feet of air
per minute. How many cubic yards of air can it circulate per
minute?
An air conditioning system can circulate 350 cubic feet of air
per minute. How many cubic yards of air can it circulate per
minute?
About 13.0 cubic yards
The amount of air in cubic yards per minute will be 12.96 cubic yards per minute.
What is conversion?Conversion means to convert the same thing into different units.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
An air conditioning system can circulate 350 cubic feet of air per minute.
We know that 1 foot = (1/3) yards, then the 1 cubic foot = (1/27) cubic yards.
350 cubic feet / minute = (1/27) x 350 cubic yards / minute
350 cubic feet / minute = 12.96 cubic yards / minute
The amount of air in cubic yards per minute will be 12.96 cubic yards per minute.
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Find A∩B, given A={−6,−2,0,2,6} and B={−4,0,1,2,5,6}.
Answer:
Step-by-step explanation:
A ∩ B = {0, 2, 6}
PLEASE HELP!! ALGEBRA! For a movie theater 4,000 tickets were sold, and the proceeds were $37,000. Tickets for children 16 and younger, were $10, adults were $12, and seniors 60 and older were $8. There were 4 times more seniors than adults at the movie theater. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the movie theater?
Answer: Fourth answer choice
c+a+s = 4000
10c+12a+8s = 37000
4a = s
==========================================
Explanation:
The first equation
c+a+s = 4000
is fairly straightforward. We add the individual counts of children (c), adults (a) and seniors (s) to get the total number of people (4000) who attended
-------------
If 1 child ticket costs $10, then 2 of them cost 20, and so on. If we don't know how many children there are, then we say 10c is the total cost for just the children alone. The c is a placeholder for some number.
Similarly, 12a represents the total cost for just the adults since 1 adult pays $12
8s is the total cost for all the seniors only
10c+12a+8s is the total cost of everyone and this total cost is 37000 dollars
The second equation is therefore
10c+12a+8s = 37000
----------------
We're told that "There were 4 times more seniors than adults at the movie theater" meaning
number of seniors = 4*(number of adults)
s = 4a
which is the same as 4a = s since we can flip both sides. So this is the third equation of our system.
------------------
We found these three equations
c+a+s = 4000
10c+12a+8s = 37000
4a = s