A company is looking to hire a lawyer. One law firm states that their legal fees can be determined using the expression 350x + 22,000, where x is the number of hours of legal assistance. A second law firm states that their legal fees can be determined using the expression 410x+16,000. The company president wants to know when the legal fees would cost the same for each law firm. What number of hours of legal assistance makes the equation 350x+22,000 = 410x+16,000 true?
Answers
Answer:
100 hours
Step-by-step explanation:
The number of hours of legal assistance that makes the expressions 350x+22,000 = 410x+16,000 true is 100 hours.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
We have,
Two expressions that denoted the legal fees for x hours:
350x + 22,000 ____(1)
410x+16,000 _____(2)
Where x = number of hours
The number of hours where both the legal fees are equal:
350x + 22,000 = 410x + 16,000
Subtract 350x on both sides.
22,000 = 410x -350x+ 16,000
22,000 = 60x + 16,000
Subtract 16,000 on both sides.
22,000 - 16,000 = 60x
6,000 = 60x
Divide both sides by 60.
x = 100
Thus,
The number of hours of legal assistance that makes the expressions 350x+22,000 = 410x+16,000 true is 100 hours.
Learn more about expressions here:
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Related Questions
hi! when finding a ratio, like teeth to no teeth, (pretend theres 9 faces with teeth and 10 with none), do you put the bigger number in front or follow the question and put the 9 faces with teeth first?
Answers
Answer:
it matters what word came first
Step-by-step explanation:
The order of the items in a ratio is very important, and must be respected; whichever word came first in the ratio (when expressed in words), its number must come first in the ratio.
4:3. The order of numbers in a ratio is important. ...
numerator / denominator. A fraction is another way of expressing one number divided by another. ...
24 / 56 = 0.42857.
Proving the Congruent Supplements Theorem
Try
Statements Reasons
Given: 21 and 22 are supplements, 23
and 24 are supplements, and
2124
Prove. 22 23
m2 1 + m 2 = 180
m23+ m24 = 180
21 and 22 are supp.
23 and 24 are supp
21 24
m2 1 + m 2 = m 3 + m24
Statements
Reasons
3
2
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Answers
Answer:
From
m∠1 = m∠4
m∠1 + m∠2 = m∠3 + m∠4
m∠2 = m∠3 [tex]{}[/tex] Identity property
∠2 ≅ ∠3 [tex]{}[/tex] [tex]{}[/tex] Equal angles are congruent
Step-by-step explanation:
Given [tex]{}[/tex] Reason
∠1 and ∠2 are supplementary [tex]{}[/tex] Given
Therefore;
m∠1 + m∠2 = 180° [tex]{}[/tex] Supplementary ∠s sum up to 180°
∠3 and ∠4 are supplementary [tex]{}[/tex] Given
Therefore;
m∠3 + m∠4 = 180° [tex]{}[/tex] Supplementary ∠s sum up to 180°
From which we have;
m∠1 + m∠2 = 180° = m∠3 + m∠4 [tex]{}[/tex] [tex]{}[/tex] Transitive property
m∠1 + m∠2 = m∠3 + m∠4
∠1 ≅ ∠4 [tex]{}[/tex] Given
m∠1 = m∠4 [tex]{}[/tex] Congruent ∠s have equal measure
Therefore;
m∠1 + m∠2 = m∠3 + m∠1 [tex]{}[/tex] [tex]{}[/tex] Transitive property
Therefore;
m∠1 + m∠2 - m∠1= m∠3 + m∠1 - m∠1 [tex]{}[/tex]Subtraction property
m∠1 - m∠1 + m∠2 = m∠3 + m∠1 - m∠1 [tex]{}[/tex]
0 + m∠2 = m∠3 + 0 [tex]{}[/tex] Inverse property
Therefore;
m∠2 = m∠3 [tex]{}[/tex] Identity property
∠2 ≅ ∠3 [tex]{}[/tex] [tex]{}[/tex] Equal angles are congruent.
Answer:
<1 and <2 are supp. givenm <1+ m<2 =180. def. of supplementary angles<1≅<4. given<3 and <4 are supp. givenm< 3 + m<4 = 180. def. of supplementary anglesm<1+m<2 = m< 3 + m<4. substitution propertym<1 = m<4. definition of ≅ anglesm<1+m<2 = m< 3 + m<1. Substitution propertym<2 = m< 3. subtraction property<2 ≅ < 3. definition of ≅ angle
A nurse mixes 50 cc of a 60% saline solution with a 10% saline solution to produce a 20% saline solution. How much of the 10% solution should he use?
Answers
Answer:
The nurse should use 200cc of the 10% saline solution in order to produce a 20% saline solution.
Step-by-step explanation:
to the given mix we add a quantity of a lower mix to generate another.
50cc at 60% + Xcc at 10% = (50 + X)cc at 20%
50 x 60% + X x 10% = (50 + X) x 20%
30 + 0.1X = 10 + 0.2X
30 - 10 = 0.2X - 0.1X
20 = 0.1X
20/0.1 = X
X = 200
The greater of 2 consecutive odd integers is 8
more than 3 times the lesser. Find the integers.
Answers
Step-by-step explanation:
let the odd integers be a, a+2.
a+2=8+3a
collect like term
a-3a=8-2
-2a=6
a=-3
so the integers are -3, -1
Simplify. 2 × (3 – 1) + 3
Answers
100000 inches is equal to how many miles?
Answers
Answer:1.5783 Miles
1.5783 Miles
Step-by-step explanation:
Multiply the value in Inch (in) by 0.0000157828 (the conversion factor). So,
100000 Inch (in) × 0.0000157828 = 1.57828 Mile.
How do we multiply monomial times monomial?
A. Multiply the coefficients, Add the exponents
B. Multiply the coefficients, multiply the exponents
C. Add the coefficients, multiply the exponents
Answers
Answer:
A. Multiply the coefficients, Add the exponents
Step-by-step explanation:
To multiply monomials, multiply the coefficients, and add the exponents of the same variable.
Answer: A. Multiply the coefficients, Add the exponents
Answer:
a- multiply the coefficients, add the exponets.
Step-by-step explanation:
i already did it!
is 4 to 7 the same as 7 to 4? Explain why or why not.
Answers
Answer:
No, 4 to 7 is not the same as 7 to 4.
Order is important when writing a ratio.
The ratio compares the first quantity to the second.
The ratio 4 to 7 means there are more of the second quantity, but 7 to 4 means there are more of the first.
Step-by-step explanation:
Solve the equation,
3(b + 3) - 4(-2+b) = 19
Answers
Answer:
b= -2
Step-by-step explanation:
Answer:
b = -2
Step-by-step explanation:
The first thing we need to do to solve this equation is expand the brackets. To so this we need to multiply the outside term with each of the terms inside the bracket (distributive law).
This gives us:
3xb + 3x3 -4x-2 -4xb = 19
Which multiplies out to:
3b + 9 + 8 -4b = 19
Combine like terms:
-b +17 = 19
From here we move the 17 to the other side by subtracting 17 from both sides
-b +17 -17 = 19 - 17
-b = 2
Divide both sides by -1:
-b/-1 = 2/-1
Which gives us:
b = -2
Hope this helped!
the slope of (-2,3) and (4,-5)
Answers
Answer:
-4/3
Step-by-step explanation:
Slope= - 5-3/4+2
Slope= - 8/6
Slope = - 4/3
answer:
0.75 i think i'm not really sure i hope it helps tho
Step-by-step explanation:
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars
Answers
Answer:$ 44.70
Step-by-step explanation: 250/1.3687 = 182.655-150 =32.655 times 1.3687
Answer:
He has 45 USD left.
Step-by-step explanation:
250 USD = 212 Euros. 250 - 212 = 38. 38 euros - about 45 USD, rounded.
Помогите пожалуйста!
Answers
i don't speak russian bro
5.67
is it rational
Answers
Answer:
Yes
Step-by-step explanation:
It not a continues number like 1.33333... therefore it is rational. If it went on forever it would be concidered irrational.
Answer:
Yes. 5.67 is a rational no.
Step-by-step explanation:
5.67 is a terminating & non-repeating decimal . And we know that a terminating non-repeating (or repeating i.e. the decimal would have a bar) decimal no. is a rational number.
5.67 can also be written as [tex]\frac{567}{100}[/tex] . A rational is always in the form of [tex]\frac{p}{q}[/tex] form where p & q are integers. Hence 5.67 is a rational number.
(x+y+z) (x-y+z)
Thank you
Answers
Answer:
x^2 +2xy + 2xz - y^2 + z^2
Step-by-step explanation:
(x+y+z) (x-y+z)
x^2 + xy + xz + xy - y^2 + yz + xz - yz + z^2
x^2 + xy + xy + xz + xz - y^2 + yz - yz + z^2
x^2 +2xy + 2xz - y^2 + z^2
Answer:
x² +2xy + 2xz - y² + z²
Step-by-step explanation:
What type of move takes Figure A to Figure B?*
Answers
Answer: Rotation
Step-by-step explanation:
From the figure , we can observe that both figure A and b are absolutely congruent.
To translate a figure to make congruent images , we use rigid motions (Translation, Reflection, Rotation)
It is Rotation because of we move Figure A 180 degrees clockwise about the fixed point O, we will get Figure B .
It cannot be reflection because both figures are not mirror images.
It cannot be translation because all points on Figure A is not moving , as point O remained at same position throughout this which is not possible in translation.
Esme buys jacketsfor 500 each and prices them for 700 each.If the selling price is reduced by 20%. how much profitdoes Esme make on each items .
Answers
Answer:
($) 60 is the profit per item when the selling price is reduced by 20%
Step-by-step explanation: 20% of 700 is 140.
The original profit is 700 - 500 = 200. The selling price is 140 less, Subtract 140 from 200. That leaves a profit of 60. (Not necessarily dollars, as the currency was not given in the question.)
A car moves a distance of 100m in 12 seconds. what is the average speed in km/h
Answers
Answer:
30km/h.
Step-by-step explanation:
100m/12s = 0.1km/12s
There are 3600 seconds in an hour.
0.1km/12s = 30km/h.
Determine if the expression -5y^5-y^3−5y5−y3 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomimal.
Answers
Answer:I think it y=73
Step-by-step explanation:
Answer: It is a polynomial, and the degree is 5.
I could be wrong on this but, i'm trying
Step-by-step explanation:
Polynomials in one variable are algebraic expressions that consist of terms in the form axn a x n where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term. The degree of a polynomial in one variable is the largest exponent in the polynomial. Also, all exponents have to be positive in a polynomial. Another rule of thumb is if there are any variables in the denominator of a fraction then the algebraic expression isn’t a polynomial.Note that this doesn’t mean that radicals and fractions aren’t allowed in polynomials. They just can’t involve the variables.
The degree is 5 (since the largest exponent is 5)
Examples of Non- Polynomials
Example Polynomial Explanation
5x^-2 +1 Not a polynomial because a term has a negative exponent
3x^½ +2 Not a polynomial because a term has a fraction exponent
(5x +1) ÷ (3x) Not a polynomial because of the division
Jonathan was thrilled when his boss told him he was going to get a 5% raise. If Jonathan
is currently paid $10,000 per year, how much raise did he get?
Answers
Answer:10,500
Step-by-step explanation:
10,000*5%=500
Given that 6 x − 4 y = 29 Find x when y = 4
Answers
Answer:
[tex]x=15/2=7.5[/tex]
Step-by-step explanation:
So we have the equation:
[tex]6x-4y=29[/tex]
And we want to find x when y is 4.
So, substitute y for 4:
[tex]6x-4(4)=29[/tex]
Multiply:
[tex]6x-16=29[/tex]
Add 16 to both sides:
[tex]6x=45[/tex]
Divide both sides by 6:
[tex]x=45/6[/tex]
Reduce by dividing both layers by 3:
[tex]x=15/2=7.5[/tex]
And this is our answer :)
Answer:
[tex]7.5 \: or \:7\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]6x- 4 y = 29\\x =?\\y =4[/tex]
Substitute 4 for y in the given equation ;
[tex]6x-4(4)=29\\6x -16=29[/tex]
Collect like terms
[tex]6x = 29+16[/tex]
Simplify
[tex]6x = 45[/tex]
Divide both sides of the equation by 6
[tex]\frac{6x}{6} = \frac{45}{6} \\\\x =\frac{15}{2} \:or \: 7.5 \: or \:7\frac{1}{2}[/tex]
Solve for x: 4 - (x + 2) < -3(x + 4) A. x < -7 B. x > -7 C. x < -9 D. x > -9
Answers
Answer:
C is the answer
Step-by-step explanation:
Find the inverse function (find f^-1)
[tex]f(x)=\frac{x-2}{3x+3}[/tex]
I have the correct answer, I just don't know how to get to it.
answer is: [tex]f^{-1} =\frac{-2-3x}{3x-1}[/tex]
Answers
Step-by-step explanation:
f(x) = (x-2)/(3x+3). Let y = f(x).
Then y = (x-2)/(3x+3).
y(3x+3) = x - 2
3xy + 3y = x - 2
3xy - x = -3y - 2
x(3y-1) = -(3y+2)
x = -(3y+2)/(3y-1)
Hence, the inverse of f(x) is -(3x+2)/(3x-1).
What is the sum of 9+10=???
Answers
Answer:
19 but if its is the joke version then 21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
4 more is twice a number is equal to 10 what is the number
Answers
solve for x. 7(x+2)=6(x+5)
Answers
Answer:
16
Step-by-step explanation:
7x+14=6x+30
Move x into one side and whole numbers to the other.
Solve like linear equation.
7x+14=6x+30
7x-6x=30-14
x=16
Answer:
x = 16
Step-by-step explanation:
7(x+2)=6(x+5) multiply
7x + 14 = 6x + 30 add like terms
7x - 6x = 30 - 14
x = 16
If I fall for 18 s what would my final velocity be, if I started from rest.
Answers
Answer:
176.58 m/s
Step-by-step explanation:
assume that the acceleration due to gravity, g = 9.81 m/s²
I also assume we neglect air resistance (hence we assume no terminal velocity)
recall that one of the equations of motions can be expressed as
v = u + at, where
u = initial velocity = 0 (because it says you started from rest)
v = final velocity (we are asked to find this)
a = acceleration due to gravity = 9.81 m/s²
t = time = given as 18s
simply substitute the above into the equation.
v = 0 + (9.81)(18)
v = 176.58 m/s
Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below: He concludes that she is not running fast enough to exceed her fastest time. \
Answers
Answer:
Answer: The question is a multiple choice so it's A and C:
Answer:
He used an incorrect time ratio converting hours to minutes.
He incorrectly concluded that she is not running fast enough.
In the morning the temperature is 0 F. It is drop out rate of 3° perh what is the temperature after five hours
Answers
Answer:
-15 degrees
Step-by-step explanation:
3 times 5 is 15 and its negative because it says it DROPS every hour and its taking the temp every 5 hrs
using appropriate properties, find the value of 249² - 248²
Answers
Answer:
[tex]\boxed{\bold{\huge{\boxed{497}}}}[/tex]
Step-by-step explanation:
=> [tex]\sf 249^2 - 248^2[/tex]
Using Formula [tex]\sf a^2 - b^2 = (a+b)(a-b)[/tex]
Where
a = 249
b = 248
=> [tex]\sf (249+248)(249-248)[/tex]
=> [tex]\sf (497)(1)[/tex]
=> 497
46% of 125.7 is what?
a. 1.22
b. 57.8
C. 5782.2
d. 273.3
Answers
Answer:
B. 57.8
Step-by-step explanation:
Changing 46% to a decimal it would be 0.46
125.7 * 0.46 = ?
125.7 * 0.46 = 57.822
57.822 rounds to 57.8 which is answer B.
Answer:
It's 57.823
Step-by-step explanation:
I looked it up lol