Answer:
33, 72, and 24
Step-by-step explanation:
Let's the three numbers are x, y, and z.
x + y + z = 129
z = x − 9
y = 3z
Solve the system of equations. Using substitution:
y = 3(x − 9)
y = 3x −27
x + (3x − 27) + (x − 9) = 129
5x − 36 = 129
5x = 165
x = 33
y = 3x − 27
y = 72
z = x −9
z = 24
7 more than a number is -3
Answer:
4
Step-by-step explanation:
7-3 pretty much
Answer: x=-10
Step-by-step explanation:
let x be that number
so, 7+x=-3
subtract 7 on both sides and...
x=-10
Sal is saving for a new bike that will cost him $150. He currently has $35 and can save $23 per week. How many weeks will it take him to earn enough money for the bike?
Let w equal the number of weeks that Sal saves his money. Select an equation and solution that matches this situation.
23w+35=150; Sal will have enough money in 5 weeks.
23w+35=150; Sal will have enough money in about 8 weeks.
150−23w=w; Sal will have enough money in 24 weeks.
35w+23=150; Sal will have enough money in about 5 weeks.
35w+23=150; Sal will have enough money in about 138 weeks.
[A] 23w + 35 = 150 ; Sal will have enough money in 5 weeks.
We can see 35 as the starting value since he already has that amount when he started saving up money. We can subtract it (150 - 35 = 115). Then we can divide (115 / 23 = 5). It took Sal 5 weeks to save enough money for the bike. The first option makes the most sense because the expression can be solve to find how many weeks he save up his money.
_______
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5/6 is equivalent to a percent that is larger than 100%.
True or False
13 pts.
I think it's false.... 5/6 is 83.33% as a percent so I don't think it's true.
6/6 ......... 100%
5/6 ..............x%
x = 5/6*100/6/6 = 500/6 = 83,(3)%
Which does not show a direct variation between x and y ?
A) y = 5x
B) y = 6/x
C) y - 0.7x
D) y = x/9
Answer:
B
Step-by-step explanation:
in B, the expression can be writting in variation form as
y∝1/x
this indicate an inverse variation
Answer:
B) y=6/x
Step-by-step explanation:
I took the test.
what is the greatest common factor of 12, 40 and 68
Answer:
4 is the greatest
Step-by-step explanation:
8. You are a computer technician for Data Control. You earn a regular hourly
rate of $15.40. You earn time and a half for overtime work on Saturdays and
double time on Sundays. This week you worked 38 hours from Monday
through Friday, 8 hours on Saturday, and 5 hours on Sunday. What is your
total pay for the week?
Answer:
Total pay for the week is $924.
Step-by-step explanation:
The per hour rate of weekdays from Monday to Friday = $15.40
The rate for Saturday = One and Half ( $15.40)
Now, [tex]1\frac{1}{2} \times (15.40) = \frac{3}{2} (15.40) = 23.1[/tex]
So, the per hourly rate for work on Saturday = $23.1
The rate for Sunday = 2 x ( $15.40) = $30.80
So, the per hourly rate for work on Sunday = $30.80
Now, total hours worked in weekday = 38
So, the rate of 38 hours = 38 x ( Per hour rate) = 38 x ($15.40)
= $585.2
Now, total hours worked on Saturday = 8
So, the rate of 8 hours = 8 x ( Per hour rate) = 8 x ($23.1) = $184.8
Now, total hours worked on Sunday = 5
So, the rate of 5 hours = 5 x ( Per hour rate) = 5 x ($30.80) = $154
Hence the total pay = Payment of ( weekday + Saturday +Sunday)
= $585.2 + $184.8 + $154 = $924
Hence, total pay for the week is $924.
Alex buys 5 DVDs. Each DVD costs $9. If Alex receives a $2 discount on each DVD, what is the total amount of money alex apends? Write an expression that matches the words
Answer:
The total amount of money Alex spends on 5 DVD = $ 35.
Step-by-step explanation:
Total number of DVD purchased by Alex = 5
The cost of each DVD = $9
So, the total cost of purchasing 5 DVD = 5 x ( csot of 1 DVD)
= 5 x ( $ 9) = $ 45
Now , the discount if 1 DVD = $ 2
So, the total discount of 5 DVD = 5 x ( Discount on1 DVD)
= 5 x ($ 2) = $ 10
⇒ The total amount Alex spends
= Total cost of 5 DVD - Discount on 5 DVD
= $ 45 - $ 10 = $ 35
Hence, the total amount of money Alex spends on 5 DVD = $ 35.
It takes 60 minutes to make 2000 copies on an old copy machine. The newer copier works with the old copier to create 2000 sheets and it only takes 15 minutes. How many minutes would the new copier need to create the 2000 copies on its own?
The new copier can create 2000 copies in 20 minutes.
Step-by-step explanation:
Given,
It takes 60 minutes to make 2000 copies by old printer and 15 minutes to made x number of copies, therefore, using proportion
[tex]60:2000::15:x[/tex]
Product of mean = Product of extreme
[tex]2000*15=60*x\\30000=60x\\60x=30000[/tex]
Dividing both sides by 60
[tex]\frac{60x}{60}=\frac{30000}{60}\\x=500[/tex]
As the new copier is working with old copier, therefore,
Copies made by new printer = 2000 - 500 = 1500
New copier can make 1500 copies in 15 minutes and 2000 copies in x minutes, using proportion
[tex]1500:15::2000:x\\1500*x=15*2000\\1500x=30000[/tex]
Dividing both sides by 1500;
[tex]\frac{1500x}{1500}=\frac{30000}{1500}\\x=20[/tex]
The new copier can create 2000 copies in 20 minutes.
Keywords: ratio, proportion
Learn more about proportions at:
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if the area of a parallelogram is 86cm and the height is 12cm write an equation that relates the height,base and area of the parallelogram
Answer:
The relation to find base is, [tex]base=\frac{area\ of\ the \ parallelogram}{height}=\frac{86}{12}=7.16\ cm[/tex]
Step-by-step explanation:
Given
Area of the parallelogram [tex]=86\ cm^2[/tex]
Height of the parallelogram [tex]=12\ cm[/tex]
We know that the area of the parallelogram [tex]=base\times height[/tex]
So
To find base we have to divide the height on both sides of the equation.
[tex]base=\frac{area\ of\ the \ parallelogram}{height}[/tex]
Plugging the values.
[tex]base=\frac{86}{12} =7.1\ cm[/tex]
So the base in terms of area of the parallelogram and its height is [tex]b=\frac{area}{height} =\frac{86}{12}=7.16\ cm[/tex]
What is the expression for add g to 4, then subtract 5 from the result?
Answer:
g+4-5
Step-by-step explanation:
because the plus would go first anyways.
√6(7+√2)
Please solve and list steps
√6(7+√2)
Use the distributive property:
√6 * 7 + √6 * √2
Move the 7 to the left:
7 * √6 + √6 * √2
Use the product rule for radicals on √6 * √2
7 * √6 + √(6*2)
Simplify:
7√6 + √12
Rewrite 12 as 2^2*3
7√6 + √(2^2*3)
Pull terms out from under the radical for final answer:
7√6 + 2√3
help ASAP!
The dinner check was $85.00. If Tyler gave the waiter a 20% tip, how much was the tip?
The dinner check was $85.00. If Tyler gave the waiter a 20% tip, how much did Tyler spend in total?
Answer: The tip is $17. The total amount he paid is $102.
Step-by-step explanation: 85 times .2 gets the tip, then you add that sum to the subtotal.
write the solution in set builder notation
-2(2x+8)>-16-4x
Good evening ,
Answer:
The set of solutions is IR
Step-by-step explanation:
-2(2x+8)>-16-4x ⇌ -4x-16>-16-4x
Any x∈IR verify the inequality
then The set of solutions is IR.
:)
6 people voted, and it ended up 84% to 16%. How many people voted for each option?
Answer:
see the explanation
Step-by-step explanation:
we know that
To find out how many people voted for each option multiply the percentage in decimal form of each option by the total number of people
so
[tex]84\%=84/100=0.84[/tex] ---> [tex]0.84(6)=5.04=5\ people[/tex]
[tex]16\%=16/100=0.16[/tex] ---> [tex]0.16(6)=0.96=1\ people[/tex]
What is the equation of the line that all inverses reflect across?
So if you're asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Just look at all those values switching places from the f(x) function to its inverse g(x) (and back again), reflected over the line y = x.
The equation of the line across which all inverses reflect is y = x. This reflection principle applies to linear functions, hyperbolas, and other mathematical relations where inverses can be found by interchanging the roles of x and y.
The equation of the line that all inverses reflect across is y = x. This is because when you are finding the inverse of a function, you swap the x and y variables, thus mirroring the original function across the line y = x. If you have a linear function in the slope-intercept form (y = mx + b), and you find its inverse, assuming the function is one-to-one and therefore has an inverse, you would essentially swap the x and y coordinates, resulting in the equation of its inverse. This process reflects each point of the original function across the line y = x.
As an example, for a line with an equation y = -x + 1, the inverse when reflected across the line y = x would result in swapping x and y to get x = -y + 1, which when solved for y, gives the inverse function's equation. Conversely, for a function expressed in another form, such as a hyperbola or a set of simultaneous linear equations, the principle is the same: to find the inverse, interchange the roles of the dependent and independent variables. For instance, a hyperbola described by y = a - b/x could have its inverse derived by interchanging x and y, leading to the inverse relation x = a - b/y.
If 4x < 24, then x < 6
Answer:
x is less than 6 so that is correct because 24 divided by 4 is 6
Describe the pattern 0.13, 0.65, 3.25, 16.25
Answer:
multiply by 5
Step-by-step explanation:
Note the ratio between consecutive terms is constant, that is
[tex]\frac{0.65}{0.13}[/tex] = [tex]\frac{3.25}{0.65}[/tex] = [tex]\frac{16.25}{3.25}[/tex] = 5
Thus the pattern is multiply by 5
Answer:Multiply by 5
Step-by-step explanation:
Kiera is buying the items shown at the right
for her kitchen. Will $35 be enough to purchase all three items?
Explain your reasoning.
mixing bowl
14.95
spatula
8.49
measuring cups
10.75
Answer:
Yes
Step-by-step explanation:
Total Price of all 3 items - $34.19
35 > 34.19
Yes, Kiera will have enough to purchase all three items.
No, $35 will not be enough to purchase all three items.
To determine if $35 is enough to purchase all three items, we need to calculate the total cost of the items and compare it to the amount of money Kiera has.
The cost of each item is as follows:
- Mixing bowl: $14.95
- Spatula: $8.49
- Measuring cups: $10.75
Now, let's add up the costs of these items to find the total cost:
Total cost = Cost of mixing bowl + Cost of spatula + Cost of measuring cups
Total cost = $14.95 + $8.49 + $10.75
To make the calculation easier, we can round each price to the nearest whole number:
- Mixing bowl: $14.95 ≈ $15.00
- Spatula: $8.49 ≈ $8.50
- Measuring cups: $10.75 ≈ $10.75 (already a whole number)
Now, let's calculate the total cost with these rounded numbers:
Total cost ≈ $15.00 + $8.50 + $10.75
Total cost ≈ $34.25
However, even with rounding, the total cost is $34.25, which is still less than $35. Therefore, we need to calculate the exact total cost without rounding:
Total cost = $14.95 + $8.49 + $10.75
Total cost = $34.19
Since the total cost of $34.19 is less than $35, it appears that Kiera has enough money to purchase all three items. However, we must also consider sales tax, which is not included in the given prices. Sales tax rates vary by location, but let's assume a standard rate of 7%.
To calculate the total cost including sales tax:
Total cost with tax = Total cost before tax + (Total cost before tax × Sales tax rate)
Total cost with tax = $34.19 + ($34.19 × 0.07)
Total cost with tax = $34.19 + $2.3933
Total cost with tax ≈ $34.19 + $2.40 (rounded to the nearest cent)
Total cost with tax ≈ $36.59
After including the sales tax, the total cost is approximately $36.59, which is more than the $35 Kiera has. Therefore, $35 will not be enough to purchase all three items once sales tax is included.
Through: (-1,-5), slope=3
Answer:
y + 5 = 3(x + 1) → point-slope form
y = 3x - 2 → slope-intercept form
3x - y = 2 → standard form
Step-by-step explanation:
The point-slope form of an equation of a line:
y - y₁ = m(x - x₁)
m - a slope
(x₁, y₁) - a point on a line
We have
m = 3, (-1, -5) → x₁ = -1, y₁ = -5
Substitute:
y - (-5) = 3(x - (-1))
y + 5 = 3(x + 1) → point-slope form
convert to the slope-intercept form y = mx + b:
y + 5 = 3(x + 1) use the distributive property: a(b + c) = ab + ac
y + 5 = 3x + 3 subtract 5 from both sides
y = 3x - 2 → slope-intercept form
convert to the standard form Ax + By = C:
y = 3x - 2 subtract 3x from both sides
-3x + y = -2 change the signs
3x - y = 2 → standard form
Write an explicit furmula for the question below
40 points!!!!!!!!!!!!!
Answer:
aₙ = a₁ . 5⁽ⁿ⁻¹⁾
Step-by-step explanation:
The first term in the sequence is a₁ = 6.
a₂ = 30. a₃ = 150.
We see that each consecutive term is multiplies by 5 to arrive at the next term.
That is: a₂ = 30 = a₁ . [tex]$ 5^{2 - 1} = 5 $[/tex] = 6.5 = 30.
Similarly, a₃ = 150 = 6 [tex]$ \times $[/tex] [tex]$ 5^{3 - 1} = 5^2 = 25 $[/tex]
Generalizing this, we have:
aₙ = a₁ . [tex]$ 5^{n - 1} $[/tex]
This is called the recursive formula of the sequence.
The table below shows the numbers of tickets sold at a movie theater on Friday.
NUMBER OF TICKETS SOLD
Day
Adult Tickets
Children's
Tickets
1,678
976
Friday
Saturday
The number of each type of ticket sold on Saturday is described below.
• Adult tickets—2 times as many as the number of adult tickets sold
on Friday
• Children's tickets-3 times as many as the number of children's
tickets sold on Friday
Complete the table above to show the numbers of tickets sold on Saturday.
What is the total number of tickets sold over these two days?
Answer:
Number of Adult's tickets sold on Saturday = 3,356
Number of Children's tickets sold on Saturday = 2, 928
Total number of tickets sold over these two days is 8,938.
Step-by-step explanation:
Here, the number of tickets sold on FRIDAY:
Adult Ticket sold = 1,678
Children's Tickets sold = 976
So, the total number of tickets sold on Friday
= Sum of ( Adult + Children's ) tickets = 1,678 + 976 = 2,654 .... (1)
The number of tickets sold on SATURDAY:
Adult Ticket sold = 2 times the number of adult tickets sold on Friday
= 1,678 x 2 = 3,356
Children's Tickets sold = 3 x the number of children's tickets sold on Friday.
= 976 x 3 = 2, 928
So, the total number of tickets sold on Saturday
= Sum of ( Adult + Children's ) tickets = 3,356 + 2,928 = 6, 284 .... (2)
Now, the total number of tickets booked in these two days :
Sum of tickets booked on (Friday + Saturday)
= 2,654 + 6, 284 = 8,938
Hence, total number of tickets sold over these two days is 8,938
x-4y=-21
8y-x=45
Solve the system
(X,y)=
Answer:
[tex]\displaystyle (3, 6)[/tex]
Step-by-step explanation:
{x -4y = −21
{8y - x = 45
_________
[tex]\displaystyle \frac{4y}{4} = \frac{24}{4} \\ \\ [/tex]
[tex]\displaystyle y = 6[/tex][Plug this back into both equations above to get the x-coordinate of 3]; [tex]\displaystyle 3 = x[/tex]
I am joyous to assist you anytime.
There are 6 lollies in a packet
A teacher buys 25 packets and divides them equally amping her students
Each student gets 4 lollies and there are 22 lollies left over.
How many students are there altogether?
Answer:
5
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
multiply 25×6 =150
subtract 150-22 = 128
128÷4
32
How do I find the coordinates of the point P that lies along the directed segment from C(-3,-2) to D(6,1) and partitions the segment in the ratio 2 to 1?
[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ C(-3,-2)\qquad D(6,1)\qquad \qquad \stackrel{\textit{ratio from C to D}}{2:1} \\\\\\ \cfrac{C\underline{P}}{\underline{P} D} = \cfrac{2}{1}\implies \cfrac{C}{D} = \cfrac{2}{1}\implies 1C=2D\implies 1(-3,-2)=2(6,1)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf P=\left(\cfrac{(1\cdot -3)+(2\cdot 6)}{2+1}\quad ,\quad \cfrac{(1\cdot -2)+(2\cdot 1)}{2+1}\right) \\\\\\ P=\left( \cfrac{-3+12}{3}~~,~~\cfrac{-2+2}{3} \right)\implies P=\left( \cfrac{9}{3}~~,~~\cfrac{0}{3} \right)\implies P=(3~~,~~0)[/tex]
WILL GIVE 15 POINTS!
PLZ HELP FAST!
Which situations can be simulated using this spinner? Select three options.
Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female
Predicting the gender of a randomly chosen history teacher if 12 of 15 history teachers are female
Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female
Predicting the gender of a randomly chosen chemistry teacher if 4 of 9 chemistry teachers are female
Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female
There are 6 sections on the spinner
Answer:
Step-by-step explanation:
- Predicting the gender of an arbitrarily picked craftsmanship educator if 1 of 3 workmanship / art instructors is female .
- Predicting the gender of a haphazardly picked science / biology instructor if 8 of 12 biology educators are female .
- Predicting the gender of a haphazardly picked health educator if 2 of 4 health instructors are female .
Answer:
1/3 8/12 2/4
Step-by-step explanation:
Because they involve 6
When do you need to rationalize the denominator? My physics teacher says that you don't have to if you are isolating a variable.
Answer:
When the denominator is an irrational number in order to make the denominator a rational number we rationalize the denominator.
Step-by-step explanation:
For example,
[tex]\frac{1}{1+\sqrt{2} }[/tex] (here the denominator is an irrational number)
Multiply the numerator and denominator by [tex]1-\sqrt{2}[/tex]
We get [tex]\frac{1-\sqrt{2} }{(1+\sqrt{2})(1-\sqrt{2}) }[/tex]
Here (1+\sqrt{2})(1-\sqrt{2}) = -1
Thus we get [tex]\sqrt{2} -1[/tex]
Here the denominator has become a rational number.
When we are isolating a variable we are only taking the required variables to one side thus it doesn't require rationalization.
[tex]a = \frac{x}{1+\sqrt{2} }[/tex]
Then we can say,
[tex]x = a(1+\sqrt{2})[/tex]
No rationalisation required
Lisa bought six dog toys. Each dog toy costs the same amount. She spent a total of $10.50. Write an expression that represents the situation. Use d to represent the cost of each dog toy.
Answer:
Each dog toy costs $1.75.
Step-by-step explanation:
6x=10.5
x=10.5/6
x=1.75
Five math questions
1.) 7+5 > 6+2
2.) g ≥ 8
3.) s = -2, -8
4.) from the middle and beyond (best way i can answer)
5.)
b < 11 = The board is shorter than 11 cm
b > 11 = The box contains more than 11 books
b < 12 = There are fewer 12 beetles in a jar
b > 12 = The building is taller than 12 ft.
Answer:
1. 6 times 5
2. 7/6 simplified
3. 4 times 13
4. 45 divided by 1 1/6
5. 10 as a proporation
Step-by-step explanation:
you deposited 500 in an account that pays 3.25 annual interest compounded monthly. About how long does it take for the balance to quadruple?
Answer:
42 years, 9 months
Step-by-step explanation:
Using the compound interest formula Accrued Amount = P (1 + r/n)^(nt)
where Accrued amount (A) which is quadruple the initial deposit
A = 4 x 500 = $2000
P = principal; $500
r = 3.25% = 0.0325
t = number of years
n = number of times interest is compounded = 12 for monthly
Therefore
2000 = 500 (1 + 0.0325/12)^(12t)
Therefore
(1.002708)^12t = 2000/500
(1.002708)^12t = 4
finding the log of both sides
12t x log 1.002708 = log 4
12t x 0.001174 = 0.6021
12t = 0.6021/0.001174
12t = 512.83
t = 512.83/12
t = 42.7
which is estimated as 42 years, (0.7 x 12 = 9) months
hence it takes about 43 years to quadruple the deposit
The number of years it will take to be the amount by quadruple will be 42.7 years.
What is compound interest?Compound interest is applicable when there will be a change in the principal amount after the given time period.
As per the given,
The total amount will be,
A = 4 × 500 = $2000
Principle amount P = $500
Rate of interest r = 3.25% = 0.0325
The time period is t.
n = number of times interest is compounded
n = 12
By compound interest formula,
2000 = 500 [tex](1 + 0.0325/12)^{12t}[/tex]
(1.002708)^12t = 2000/500
(1.002708)^12t = 4
Take logs on both sides,
12t × log 1.002708 = log 4
12t × 0.001174 = 0.6021
12t = 0.6021/0.001174
12t = 512.83
t = 512.83/12
t = 42.7
Thus, the time period will be 42.7 years.
Hence "The number of years it will take to be the amount by quadruple will be 42.7 years.".
For more information about compound interest,
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Mrs. Smith needed to split 28 students into 4 equal groups for the race. Which step could help her to work 30 divided by 3?
(A) (27 divided by 9) + (9 divided by 3)
(B) (24 divided by 4) + (4 divided by 4)
(C) (21 divided by 3) + (9 divided by 3)
(D) (20 divided by 4) + (10 divided by 4)
Answer:
Procedure in option C only works.
Step-by-step explanation:
We have to select the process in which Mrs. Smith can help her to work 30 divided by 3.
(A) (27 divided by 9) + (9 divided by 3) = 3 + 3 = 6
But (30 ÷ 3) = 10 ≠ 6
(B) (24 divided by 4) + (4 divided by 4) = 6 + 1 = 7 ≠ 10
(C) (21 divided by 3) + (9 divided by 3) = 7 + 3 = 10
(D) (20 divided by 4) + (10 divided by 4) = 5 + 2.5 = 7.5 ≠ 10
So, procedure in option C only works. (Answer)
Again, we can prove the procedure in the following way:
[tex]\frac{30}{3} = \frac{21 + 9}{3} = \frac{21}{3} + \frac{9}{3}[/tex]
{Which is the distributive property of division}