[tex]\left\{\begin{array}{ccc}2x+2y=8\\3x+2y=12&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+2y=8\\-3x-2y=-12\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-x=-4\to\boxed{x=4}\\\\\text{Put the value of x to the first equation:}\\\\2(4)+2y=8\\8+2y=8\qquad\text{subtract 8 from both sides}\\2y=0\qquad\text{divide both sides by 2}\\\boxed{y=0}\\\\Answer:\ \boxed{x=4\ and\ y=0\to(4,\ 0)}[/tex]
What is total cost of three pairs of socks priced at 1.29 a pair, with a 6% sales tax?
Answer:
$4.10
Step-by-step explanation:
Subtotal = (3 pairs of socks) x (price of socks):
Subtotal = (3 x $1.29) = $3.87
To get the overall total, you add tax, which is 6% of the subtotal:
6% of the subtotal = 0.06 x subtotal = 0.06 x $3.87 = $0.23
Subtotal + tax = $3.87 + $0.23 = $4.10
A garden table and a bench cost $804 combined the garden table costs $46 less than the bench. What is the cost of the bench
Answer:
The cost of the bench is 425 dollars.
Step-by-step explanation:
Let x represent the garden table.
Let y represent the bench.
x + y = 804
x = y - 46
Use the substitution method.
y - 46 + y = 804
2y - 46 = 804
Add 46 to both sides.
2y = 850
Divide both sides by 2.
y = 425
Answer:
The cost of the bench is 425 dollars.
Simplify (√3)(^5√3)
A. 3^1/10
B. 3^3/5
C. 3^9/10
D. 3^7/10
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\text{Therefore}\\\\\sqrt3=3^\frac{1}{2}\\\\\sqrt[5]{3}=3^\frac{1}{5}\\\\\text{We have}\\\\(\sqrt3)(\sqrt[5]3)=3^\frac{1}{2}\cdot3^\frac{1}{5}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=3^{\frac{1}{2}+\frac{1}{5}}=3^{\frac{5}{10}+\frac{2}{10}}=3^{\frac{7}{10}}\\\\Answer:\ \boxed{D.\ 3^{\frac{7}{10}}}[/tex]
Solve the equation for y
Answer: y=1/7am -1/7
Step-by-step explanation:
First: 3y+4y+z =am - z
Second: 7y=am - z
Third: y=1/7am -1/7z
Finally: y=1/7am -1/7
Solve the inequality for u.
.
Simplify your answer as much as possible.
Answer:
u ≤ 4
Step-by-step explanation:
The given inequality
15 ≤ 39 - 6u
Subtract 39 from both sides, we get
15 - 39 ≤ 39 - 6u - 39
-24 ≤ -6u
Dividing both sides by -6, we get
4 ≥ u [Remember, when we divide by negative, the direction of
the inequality changes]
Which is u ≤ 4.
Thank you.
Answer:
U is greater than or equal to 4
Step-by-step explanation:
(pretend theres a line under the <)
15 < 39 - 6u
subtract both sides by 39 to get -6u by itself
-24 < -6u
divide both sides by -6 and get u completely by itself
4 < u
u is greater than or equal to 4.
a pair of shoes cost x dollars. if there is a 30% discount, write the expression to show final amount
Answer:
f = 0.30(x)
Step-by-step explanation:
Let x = # of dollars
Let f = final amount
Note that 30% is the same as 30/100, which in decimal form is 0.30
Set the equation.
Each pair of shoes costs x amount, in which it is decreased by 30%, which leads to the cost in f amount.
~
The data in the table represents a company's profit based on the number of items produced.
Which equation best represents the data?
A) y= -1.026x^2 + 1016.402x - 162075
B) y= -1.036x^2 + 1024.771x - 163710
C) y= 298.214x - 66317.667
D) y= 196.2x - 18710
Answer:
(A) y= -1.026x^2 + 1016.402x - 162075
Step-by-step explanation:
Given is the data 'x' -Items produced. The equation that satisfies the given data can be found by simply substituting the values of x in the given equations. For example:
Substituting the value of x= 100 in the given equations,
A) y= -1.026(100)^2 + 1016.402(100)-162075= -70,500
Similarly you can check the values on the rest of the equations and if they satisfy the equation, then the given is the required equation.
Answer:
(A)
Step-by-step explanation:
WE are given the data which represents the company's profit based on number of items produced.
The equation which best represents the data can be found out by substituting the values of x in the given equations.
So,substituting x=100 in first equation, we have:
[tex]y=-1.026x^{2} +1016.402x-162075[/tex]
[tex]y=-1.026(100^{2})+1016.402(100)-162075[/tex]
[tex]y=-10260+101640.2-162075[/tex]
[tex]y=-70500[/tex]
which satisfies the equation. Hence, option A satisfies.
We can also substitute the different values of x in the equations to check whether it satisfies or not.
PLEASE HELP! I know it’s an easy question, but I don’t remember how to do this. Help
Answer:
Your range is (1,2,4,8)
5 + 2 root 3 / 7 + 4 root 3 equals to a + b root 3
[tex]\dfrac{5+2\sqrt3}{7+4\sqrt3}=\dfrac{5+2\sqrt3}{7+4\sqrt3}\cdot\dfrac{7-4\sqrt3}{7-4\sqrt3}\\\\\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{(5+2\sqrt3)(7-4\sqrt3)}{7^2-(4\sqrt3)^2}\\\\\text{use distributive property}\\\\=\dfrac{(5)(7)+(5)(-4\sqrt3)+(2\sqrt3)(7)+(2\sqrt3)(-4\sqrt3)}{49-4^2(\sqrt3)^2}\\\\=\dfrac{35-20\sqrt3+14\sqrt3-8(3)}{49-16(3)}=\dfrac{35-6\sqrt3-24}{49-48}=\dfrac{11-6\sqrt3}{1}\\\\=11-6\sqrt3\\\\11-6\sqrt3=a+b\sqrt3\to\boxed{a=11\ and\ b=-6}[/tex]
what is the rule for adding and subtracting monomials
Answer:
As shown, both terms are equal to 192. To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same. To subtract two or more monomials that are like terms, subtract the coefficients; keep the variables and exponents on the variables the same.
Step-by-step explanation:
Point E is the midpoint of side BC of parallelogram ABCD (labeled counterclockwise) and AE ∩ BD =F. Find the area of ABCD if the area of △BEF is 3 cm2.
Answer: [tex]36 cm^2[/tex]
Explanation:
Since here ABCD is the parallelogram.
Where E is the mid point of the line segment BC.
And, F is the intersection point of the segments AE and BD,
Also, Area of △BEF is 3 [tex]cm^2[/tex].
We have to find Area of parallelogram ABCD.
Since,In ΔBEF and ΔACD,
∠ADF=∠EBF ( because AD ║ BE )
∠DFA = ∠BFE (vertically opposite angle)
Thus, By AA similarity postulate,
[tex]\triangle BEF \sim \triangle ACD[/tex],
Thus, [tex]\frac{area of \triangle ADF }{area of \triangle BFE} =(\frac{AD}{BE})^2[/tex]
But, AD = 2 BE,
Therefore, [tex]\frac{area of \triangle ADF }{area of \triangle BFE} =(\frac{2BE}{BE})^2[/tex] = 4/1
Thus, area of Δ ADF = [tex]12 cm^2[/tex]
Similarly, [tex]\triangle ADB \sim \triangle BAE[/tex]
Now, let the area of the triangle AFB = x [tex]cm^2[/tex]
Thus, x + 12 = 2(x+3) ( because the area of the ΔADB = 2(area of ΔBAE) )
⇒ x = 6 [tex]cm^2[/tex]
Therefore, area of ΔAFB= 6 [tex]cm^2[/tex]
⇒ area of ΔABD = 12 + 6 = 18 [tex]cm^2[/tex]
By the definition of diagonal of parallelogram,
Area of parallelogram ABCD = 2× area of Δ ABD= 2 × 18 = 36 [tex]cm^2[/tex]
Rewrite the rational exponent as a radical.
(5*3/4 power)2/3 power
[tex]Use:\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\(a^n)^m=a^{nm}\\\\\left(5^{\frac{3}{4}}\right)^{\frac{2}{3}}=5^{\frac{3}{4}\cdot\frac{2}{3}}=5^{\frac{1}{2}\cdot\frac{1}{1}}=5^{\frac{1}{2}}=\sqrt[2]{5}=\boxed{\sqrt5}[/tex]
Find the slope of the line represented by the table of values. A.1/2 B.1 C.2 D.4
X Y
-1 1
1 2
3 3
5 4
7 5
Answer:
The correct option is A.
Step-by-step explanation:
From the given table it is noticed that the line is passing through the points (-1,1), (1,2), (3,3), (5,4) and (7,5).
Slope of a line is calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose any two pair of coordinates from the given points.
Let the line is passing through (5,4) and (7,5).
[tex]m=\frac{5-4}{7-5}[/tex]
[tex]m=\frac{1}{2}[/tex]
Therefore the slope of line is [tex]\frac{1}{2}[/tex] and option A is correct.
Answer:
The actual answer is C
Step-by-step explanation:
what is b if the expression is (4/5 divided by b)+b please explain this = 27
Answer:
b = 26.97 or b = 0.03
Step-by-step explanation:
[tex]\frac{\frac{4}{5} }{b} +b=27[/tex]
[tex]\frac{4}{5b} +b=27[/tex]
[tex]\frac{4+5b^{2} }{5b} =27[/tex]
[tex]4+5b^{2} =135b[/tex]
[tex]5b^{2} -135b+4=0[/tex]
[tex]b=\frac{135+\sqrt{18225-80} }{10}[/tex] or
[tex]b=\frac{135-\sqrt{18225-80} }{10}[/tex]
b = 26.97 or b = 0.03
A car dealer earns a 4% commission on all cars sold. Last month, he earned $7,200 in commission. He wants to earn $8,000 in commission this month. What increase in total sales does he need in order to reach his goal for this month?
Answer:
$800 is the answer because you subtract 7200 from 8000 and you get 800
Final answer:
To earn an $8,000 commission at a rate of 4%, the car dealer needs to increase his total sales by $20,000, from $180,000 last month to $200,000 this month.
Explanation:
The car dealer wishes to increase his commission from $7,200 to $8,000. Since he earns a 4% commission on all cars sold, we first need to determine how much his sales were last month. To do this, we divide his commission for the last month by the commission rate:
Last month's sales = Commission / Commission rate = $7,200 / 0.04 = $180,000
To earn $8,000 this month, we need to find the total sales required:
This month's sales = Desired commission / Commission rate = $8,000 / 0.04 = $200,000
To find the increase in total sales needed, we subtract last month's sales from this month's sales target:
Required increase in sales = This month's sales - Last month's sales = $200,000 - $180,000 = $20,000
I don’t understand
Answer:
1. 1:2
2. 2:2
3. 2:5
4. 2:10
5. 4:10
Step-by-step explanation:
simplify 5^-8 ×5^4 as a fraction
Answer:
Answer is: 5^ -8 * 5^4 = 5^-4
Step-by-step explanation:
To simplify : 5^ -8 * 5^4
This can also be written as :
5^ -8 * 5^4 = 1/5^8 * 5^4
or 5^ -8 * 5^4 = 5^4 / 5^8
or 5^ -8 * 5^4 = 5^(4 - 8)
or 5^ -8 * 5^4 = 5^-4
Hence we got 5^ -8 * 5^4 = 5^-4
What is the sum of 2.5x10^4 and 3.4 x 10^4
Answer: 59,000
Step-by-step explanation:
(2.5 * 10^4) + (3.4 * 10^4)
(2.5 * 10,000) + (3.4 * 10,000)
25,000 + 34,000
59,000
10 • 10 • 10 • 10 = 10,000
(2.5 • 10,000) + (3.4 • 10,000)
25,000 34000
25,000 + 34,000 = 59,000
Can someone give me the answers for these?
Answer:
a. He started with $50 in the the account.
b. The account grow by $10 dollars each week
c see graph
Step-by-step explanation:
y = 50 + 10x
We can rewrite this as
y = 10x+50
This is in the form y = mx+b
where m = 10 which is the slope and b =50 which is the y intercept
The y intercept = 50 is the starting value or the value when x = 0
a. He started with $50 in the the account.
The slope is how much it grows by as x grows. As x increase by 1 , y will grow by the slope or 10, so the account will grow by 10 each week.
b. The account grow by $10 dollars each week
c see graph
Pls help match the following
Answer:
Statement Reason
1. <R=<Q, AS=AT Given
2. <5=<6 Base <'s of isosceles triangles are =
3. <4, <5 are supplementary Exterior sides in opposite rays
and <6, <7 are supplementary
4. <4=<7 Two <'s supplementary to equal <'s are =
5. Triangle RAS congruent to AAS
Triangle QAT
6. RS=QT CPCTE
Step-by-step explanation:
Statement
1. <R=<Q, AS=AT. This is given.
2. <5=<6, because base angles of isosceles triangles are congruent.
3. <4, <5 are supplementary and <6, <7 are supplementary, because they have exterior sides in opposite rays.
4. <4=<7, because two angles supplementary to equal angles are congruent
5. Triangle RAS congruent to Triangle QAT because Angle Angle Side (AAS)
6. RS=QT, because Congruent Parts in Congruent Triangles are equal (CPCTE)
Rachael’s patio has an area of 290 square feet. If the patio is shaped like a square, what is the approximate side length?
A. about 72.5 feet
B. about 145 feet
C. about 17 feet
D. about 24 feet
Answer:
C. about 17 feet
Step-by-step explanation:
Since, we know that,
The area of a square is,
[tex]A=s^2[/tex]
Where,
s = side length,
If A = 290 square feet,
[tex]\implies 290 = s^2[/tex]
[tex]\implies s = \sqrt{290}=17.0294\approx 17[/tex]
Hence, the side length of the patio would be about 17 ft,
OPTION C is correct.
Jerome works as a waiter. He earns $80 each weekend plus 15% in tips on meals served. Jerome served $725 worth of meals last weekend. How much did Jerome earn last weekend? Please show all steps :)
Answer:
well you would need to look at how much he gets a weekend, and then worry anout the tips.
Step-by-step explanation:
He gets paid $80 each weekend, and a 15% with tips.
you would need to figure out the tips, by taking the $725 and timesing it by .15 for the percent.
which would be 108.75
you would now take 108.75 and add 80 to get what he made that weekend.
108.75+80 = 188.75 dollars
I need to know how to do slope
Answer:
slope is easy it is rise over run
Step-by-step explanation:
rise/run
rise means up
run means move sideways
Answer:
Slope = rise/run
Step-by-step explanation:
Example: (6,3) (2, 2)
Add the x's and divide by two and then add the y's and divide by two.
6 + 2 = 8
8/2 = 4
3 + 2 = 5
5/2 = 2.5
So, the slope would be 4/2.5
Simplify the expression
2v+8v-5v
Answer:
5v
Step-by-step explanation:
First you convert all the subtraction to addition: 2v+8v+(-5v)
Then you combine like terms: 2v+3v:
5v
2v + 8v - 5v combine like terms
= (2 + 8 - 5)v
= (10 - 5)v
= 5v
Find the area of a rectangle with length (2x + 3) and width (x - 4).
A) 2x2 - 11x - 12
B) 2x2 - 5x + 12
C) 2x2 + 11x + 12
D) 2x2 - 5x - 12
Answer:
Area = 2x^2 -5x-12
Step-by-step explanation:
Area = length * width
Area = (2x+3) * (x-4)
We will use the FOIL technique to multiply the terms.
First: 2x*x = 2x^2
Outer: 2x* -4 = -8x
Inner: 3*x = 3x
Last = 3* -4 = -12
Add the 4 terms together: 2x^2 -8x+3x -12 = 2x^2 -5x-12
Area = 2x^2 -5x-12
Answer: 2x^2 - 5x - 12
Step-by-step explanation: The correct answer is 2x^2 - 5x - 12. To find the area of a rectangle you multiply the length by the width. So you multiply (2x + 3)(x - 4) using the FOIL method.
A group of friends went to lunch, and their bill was $132.50. An 18% gratuity was added to the bill. What was the total amount of the bill?
Answer:
$156.35
Step-by-step explanation:
we know that
A group of friends went to lunch, and their bill was $132.50
In this problem
$132.50 represent the 100%
100%+18%=118%
so
using proportion
Find out the total amount that represent 118%
Let
x ----> the total amount of the bill
[tex]\frac{\$132.50}{100\%}=\frac{x}{118\%}\\\\x=132.50(118)/100\\\\x=\$156.35[/tex]
Answer:
Step-by-step explanation:
The answer is $156.35
The diameter of a circle is 6 units. What is the radius of the circle?
Answer:
The radius of the circle is 3 unit.
Step-by-step explanation:
Given : The diameter of a circle is 6 units.
To find : What is the radius of the circle?
Solution :
The radius of the circle is [tex]r=\frac{d}{2}[/tex]
Where, d is the diameter d=6 units
Substitute the value,
[tex]r=\frac{6}{2}[/tex]
[tex]r=3[/tex]
Therefore, the radius of the circle is 3 unit.
How long will it take $500 to double at a simple interest rate of 5%? Explain how you found your answer.
HELP IS GREATLY APPRECIATED!
Answer:
20 years
Step-by-step explanation:
Simple interest is only interest on the original principal amount. Every year, you earn the same interest amount.
At 5% simple interest, you earn 5% of the principal each year.
In any year, you earn
5% of $500 = 5% * 500 = 0.05 * 500 = $25
Each year, you earn $25 in interest.
How many years will it take to earn a full $500 by earning $25 per year?
$500/$25 = 20
It takes 20 years to double the $500.
5. Your brother has $2,000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find out how much he can spend for everything else.
Answer:
2000>= 637+ x
1363>= x
He can spend no more than $1363 on everything else
Step-by-step explanation:
If he has 2000 dollars to spend in total, that will go on one side of the inequality. Everything he spends goes on the other. 2000 is the maximum he can spend. He is going to sped 637 on an airline ticket plus x on other expenses.
2000>= 637+ x
Subtract 637 from each side
2000-637 >= 637-637 +x
1363>= x
To find out how much your brother can spend for everything else, subtract the cost of the airplane ticket from his total savings. Your brother can spend up to $1,363 for everything else.
To find out how much your brother can spend for everything else, we need to subtract the cost of the airplane ticket from his total savings. Let's say his total savings is $2,000 and the cost of the airplane ticket is $637. We can write the inequality as:
2000 - 637 ≤ x
Simplifying the inequality, we have:
1363 ≤ x
Therefore, your brother can spend up to $1,363 for everything else.
Learn more about Inequality here:https://brainly.com/question/30231017
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4m+2n=5n solve for m
Answer:
m = [tex]\frac{3n}{4}[/tex]
Step-by-step explanation:
given 4m + 2n = 5n ( subtract 2n from both sides )
4m = 3n ( divide both sides by 4 )
m = [tex]\frac{3n}{4}[/tex]
Answer:
m = 3/4 n
Step-by-step explanation:
4m+2n=5n
Subtract 2n from each side
4m +2n-2n = 5n-2n
4m = 3n
Divide by 4
4m/4 = 3n/4
m = 3/4 n