Let a and b = the numbers we must find.
a + 2b = 5.....Equation A
2a + b = 13.......Equation B
We have a system of equations in two variables.
I will solve A for little a.
a + 2b = 5
a = 5 - 2b
Now I will plug 5 - 2b for a in B.
2(5 - 2b) + b = 13
10 - 4b + b = 13
-3b = 3
b = -1
To find a, replace b with -1 in EITHER A or B.
I will use Equation A.
a + 2b = 5
a + 2(-1) = 5
a - 2 = 5
a = 7
The two numbers are -1 and 7.
Understand?
It requires 350 joules to raise a certain amount of a substance from 10. 0°C to 30. 0°C. The specific heat of the substance is 1. 2 J/g°C. What is the mass of the substance? 12 g 15 g 18 g 30 g.
The correct option is B which is 15 g.
Given to us:
the heat [tex]Q= 350\ Joules[/tex],
the specific heat [tex]c= 1.2\ J/g\ ^o C[/tex],
the lower temperature [tex]t_1= 10^o C[/tex],
the higher temperature [tex]t_2= 30^o C[/tex],
Formula for specific heat:
[tex]Q=mc(\Delta T)[/tex]
where,
[tex]m[/tex] is the mass,
[tex](\Delta T)[/tex] is the temperature difference,
Putting in the values;
[tex]350=m\times 1.2\times (30-10)\\\\m= \dfrac{350}{1.2\times (30-10)} \\\\m=14.5833 grams[/tex]
Hence, the mass is 14.5833 grams. therefore, the correct option is B which is 15 g.
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what is the transformation of f(x)=|x-9|
Answer: X=9
Step-by-step explanation:
Answer:
f(x) = x-9 {9 < x}
f(x) = 0 {x = 9}
f(x) = -x - 9 {x < -9}
Step-by-step explanation:
I'm not too sure what transformation you want. However,,,
f(x)=|x-9| can be changed to function
f(x) = x-9 {9 < x}
f(x) = 0 {x = 9}
f(x) = -x - 9 {x < -9}
without absolute value.
A trucking company uses matrix A , shown below, to represent the driving time in hours for 6 trucking routes. A = [ 4 6 8 ]
[6 8 10 ]
The driving time matrix is based on an average speed of 60 miles per hour. This means that the matrix 60 A represents the driving distances in miles for these 6 trucking routes. Which of these is the matrix 60 A ?
Each element of the matrix are multiplied by the scalar to form a matrix of
same size as the original matrix in matrix scalar multiplication.
[tex]60 \cdot A = \left[\begin{array}{ccc}240\4&360&480\\360&480&600\end{array}\right][/tex]Reasons:
The matrix A is presented as follows;
[tex]A = {\left[\begin{array}{ccc}4&6&8\\6&8&10\end{array}\right]}[/tex]
Using the multiplication of a matrix and a scalar, we have;
[tex]60 \cdot A = 60 \cdot \left[\begin{array}{ccc}4&6&8\\6&8&10\end{array}\right] = \left[\begin{array}{ccc}60 \times 4&60 \times 6&60 \times 8\\60 \times 6&60 \times 8&60 \times 10\end{array}\right] = \left[\begin{array}{ccc}\mathbf{240}&\mathbf{360}&\mathbf{480}\\\mathbf{360}&\mathbf{480}&\mathbf{600}\end{array}\right][/tex]
Therefore;
[tex]60 \cdot A = \left[\begin{array}{ccc}240\4&360&480\\360&480&600\end{array}\right][/tex]
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If 7 out of 25 students have a pet, what percent of the class has a pet?
Answer:
28%
Step-by-step explanation:
(25%-7%)×4
100%-28%
what is cosec32°/sec58°=
Answer:
1
Step-by-step explanation:
Using the cofunction identity
sec(90 - x) = cosecx , then
sec(90 - 58)° = cosec32° , so
[tex]\frac{cosec32}{sec58}[/tex]
= [tex]\frac{cosec32}{cosec32}[/tex]
= 1
3 How is the value of 2 - 3 like the value of 3 - 2? How is it different? -
Answer:
They are not diffrent at all. may look diffrent from the question but lets look a little closer!
Step-by-step explanation:
2-3=1 and 3-2=1 both answers look the same because the equion is Both 3s in 3-2 and 2-3 looks no diffrent. To be honest one is only backwords from the other one! But remeber to think BIG and look at those diffrentses.
If x < -4, then -4 is a solution.
True
False
Answer:
true
Step-by-step explanation:
the less than or equal to sign (≤) means that -4 is a solution. if it was the less than sign (<) then -4 would not be included
Answer:
i believe it would be true
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
Henry had beaten 12 levels in a video game. If the ratio of levels he had beaten to not
beaten was 6:1, how many levels does the game have total?
Pls help!!!!!!!!!!!!!
Answer:
eat tacos until you bloat
Step-by-step explanation:
AHAHAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH MAMAMAMAMAMAA
What expression is equivalent too 3(-6h - 4) + 5h?
Answer:
-13h - 12
Step-by-step explanation:
3(-6h - 4) + 5h
-18h - 12 + 5h
-13h - 12
hope this helps! :D
have a miraculous day, and brainliest is immensely appreciated!! <3
What is the selling price of an item if the original cost is $784.50 and the markup on the item is 6.5 percent?
selling price = original cost + markup value
A.
$509.95
B.
$831.57
C.
$835.49
The selling price of the item is $835.49
How to determine the selling price?The given parameters are:
Original cost = $784.50
Markup = 6.5%
The selling price is calculated as
Selling price = Original cost * (1 + Markup)
So, we have:
Selling price =$784.50 * (1 + 6.5%)
Evaluate the expression
Selling price =$835.49
Hence, the selling price of the item is $835.49
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While flying against the wind, the plane covered 1800 km in 2 hours and 40 minutes. On the return flight it spent 16 minutes less because the plane was moving on the direction of the wind. What was the speed of the wind and the speed of the plane?
Answer:
PLANE SPEED --
While flying against the wind - 675 km/h
While flying along with the wind - 750 km/h
WIND SPEED --
Speed of the wind - EXPLANATORY LOOK AT ABOVE DATA
Step-by-step explanation:
If you need the explanation, just comment yes :)
It's a bit long, so I'm not sure if you just wanted the answer or the whole step-by-step explanation.
How do you solve : 3x^4 - 11x^3 -x^2 + 19x + 6
You can't use long division in this equation.
Step-by-step explanation:
This is a polynomial so we can use rational roots Theorem to solve the equation.
The rational roots simply states that the roots of a polynomial, in the form of
[tex]p{x}^{n} + ax {}^{n - 1} + bx {}^{n - 2} .....r {}^{0} [/tex]
The possible roots of the polynomial are the factors of
p/r.
We say r^0 to represent the constant and p to represent the leading coeffceint.
So the rational roots states the possible roots of a polynomial is
the factors of leading coeffceint/ the factors of the constant.
In this case, the polynomial leading coeffecient is 3 and its constant is 6 so we do the factors of 3 divided by the factors of 6.
The factors of 3, are plus or minus 1 and 3. divided by factors of 6 which are plus or minus 1,2,3,6. So our possible roots are
positive or negative (1,1/2, 1/3,1/6, 3, 3/2).
Now, we see which of the following roots will that the polynomial, P will equal zero.
It seems that -1 can work so by definition, (x+1) is the a factor of the polynomial. So now we use synetheic or long division to cancel out that factor.
So our factored version of the polynomial is
[tex](x + 1)(3x {}^{3} - 14 {x}^{2} + 13x + 6)[/tex]
Now can we continue and factor the right side of the factors.
3 also works so x-3 is a factor as well so
[tex](3 {x}^{2} - 5x - 2)(x + 1)(x - 3)[/tex]
Now factor the quadratic using factoring by grouping
[tex]3 {x}^{2} - 5x - 2 = 3 {x}^{2} - 6x + x - 2 = 3x(x - 2) + 1(x - 2) [/tex]
So our factor are
[tex](3x + 1)(x - 2)[/tex]
So in conclusion our factors are
[tex](3x + 1)(x - 2)(x + 1)(x - 3)[/tex]
And our x values are -1/3, 2, -1, and 3.
Solve for X
(10x - 1)=(14x - 37)
(make them equal to each other)
10x-1 = 14x-37
(combine like terms)
-4x = -36
(divide by -4)
x=9
Hope this helps! Have a good day/night!
Last season, your
favorite basketball
team won 20 games. This
season, your favorite
basketball team won 31
games. What is the
percent change in the
number of games that
your favorite team won
from last season to this
season?
Answer:
55%
Step-by-step explanation:
The percent change formula is written like this:
[tex]|\frac{change - original }{original}|[/tex]. In this scenario, the "change" or new value is 31, because it is this season, and the original is last season. Now, 31-20 = 11, and 11/20 = 55%.
What is the relationship between 0.04 and 0.004?
Answer: 0.04 is exactly 10 times as much as 0.004. If we multiply 0.004 by 10, we will get 0.04 as an answer. In other words, we can say that 0.004 is exactly 1/10th of 0.04. It means that if we divide 0.04 by 10, we will get 0.004 as an answer.
Answer:
Look below
Step-by-step explanation:
0.04 means 4 hundredths since if you divide 4 by 100 you get 0.04. You can try it yourself on a calculator. 0.004 is 4 thousandths. Same thing with 0.04, if you divide 4 by 1000 you will get 0.004. Hope this helps! If you want me to explain a bit more I can try
can someone solve this trigonometry question?
What is 1/3 of 9/5 please help.
Answer the ones you want to. Answer at least one.
Have no idea how to do this. Please help I beg you.
Answer:
For 8 b, draw 36 squares and for 8 c, it would be 144:)
A group of 493 people is going on a boat tour. If each boat holds 7 people, how many people will be on the last boat?
Answer:
3 people.
Step-by-step explanation:
493÷7=70 with 3 remaining.
How can I solve this?
Answer:
This is not possible with 2 equal symbols
Nick and Sally run on the 100m straight track,Nicks's speed is 3m/s,Sally's soeed is 2m/s.If they both start from two sides of the track, running towards each other continuously.Then they would meet each other ... times after 10 minutes
They would meet 30 times after 10 minutes.
Since Nick and Sally run on the 100m straight track, and Nicks's speed is 3m / s, while Sally's speed is 2m / s, if they both start from two sides of the track, running towards each other continuously, to determine how many times they would meet each other after 10 minutes the following calculation should be performed:
30 x 20 + 2 x 20 = 60 + 40 = 100 10 minutes = 600 seconds 600/20 = X 30 = X
Therefore, they would meet 30 times after 10 minutes.
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Peggy earned $20 for each lawn she mowed last summer. This summer, she raised her price to $23 per lawn. What is the percent increase of Peggy’s charges?
Answer:
15 percent
Step-by-step explanation: You will substract the new value from the old value.
23-20
Now you will get the difference between them and divide that by the original amount.
3/20
This will equal 0.15 in which you now multiply by 100
15 percent
Convert 53 grams to kilograms. 53,000 kg 0.053 kg 5.3 kg 530 kg
Answer:
0.053 kg
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
Raj pays $7.99 per month for a movie subscription service. One month he also rents 3 movies from the service. His bill for the month is $19.96. How much does Raj pay to rent each movie?
Answer:
Each movie costs 3.99
Step-by-step explanation:
If every month he is paying $7.99 initially for the service, you take $19.96 and subtract the initial cost ($7.99) then your left with $11.97 and since he bought 3 movies then you divide $11.97 by 3 and your left with $3.99 which is your final answer!
Hope this makes sense!
A pancake recipe calls for 4 eggs and 12 cups of flour. How many cups of flour would you need for a single egg?
Answer:
3
Step-by-step explanation:
i'd say 3
i divided 12 by 4 and then multiplied by one, since that is the amount of eggs we want
good luck! <3
Mr. Allen says that the equation y=2x+1 has a solution of (4, 9). Is Mr. Allen right or wrong?
Answer:
right
Step-by-step explanation:
y=2x+1
9=2(4)+1
9=8+1
9=9
Colin invests £2350 into a savings account. The bank gives 4.2% compound
interest for the first 4 years and 4.9% thereafter. How much will Colin have after
10 years to the nearest pound?
Answer:
£3691 (nearest pound)
Step-by-step explanation:
Consider the rate of compound interest is r and the initial amount of savings is P, hence
[tex]P \ + \ P \ \times \ r \ = \ P \ (\ 1 \ + \ r \ ) \qquad (Final \ amount \ for \ the \ 1st \ year ) \\ \\ \ P \ (\ 1 \ + \ r \ ) \ + \ P \ (\ 1 \ + \ r \ ) \ \times \ r \ = \\ \ P\ ( \ 1\ + \ r \ ) \ ( \ 1 \ + \ r \ ) \ = \ P \ {( \ 1 \ + \ r \ )}^2 \qquad (Final \ amount \ for \ the \ 2nd \ year) \\ \\ \ P \ {(\ 1 \ + \ r \ )}^2 \ + \ P \ {(\ 1 \ + \ r \ )}^2 \ \times \ r \ = \\ \ P\ {( \ 1\ + \ r \ )}^2 \ ( \ 1 \ + \ r \ ) \ = \ P \ {( \ 1 \ + \ r \ )}^3 \\ \\ (Final \ amount \ for \ the \ 3rd \ year)...[/tex]
Therefore, the final amount of savings after nth years of compund interest is
[tex]P \ {( \ 1 \ + \ r \ )}^n[/tex].
Given that 4.2% compound interest was used for the first 4 years to a savings of £2350, thus
[tex]Final \ amount \ for \ the \ first \ 4 \ years \ = \ 2350 \ {( \ 1 \ + \ \frac{4.2}{100} \ )}^4 \ = \ 2770.36[/tex]
Then, taking the final amount of savings previously into an initial amount for the next 6 years with 4.9% compound interest.
[tex]2770.36 \ {( \ 1 + \frac{4.9}{100} \ )}^6 \ = \ 3691.40 \ = \ 3691 \ (nearest \ pound)[/tex]
Mae buys 7 boxes of drinks. The cost of each box of drinks is £7 and each box holds 12 cans.She sells 3/4 of the total number of cans for 70p each and the remaining cans for 40p each. WORK OUT THE TOTAL OF PROFIT HE MAKES
Answer:
£3.50
Step-by-step explanation:
The total number of cans Mae bought was ...
(12 cans/box)×(7 boxes) = 84 cans
The revenue from sales is ...
(3/4)(84)(70p) +(1/4)(84)(40p) = 84(3/4×70p +1/4×40p) = 84(52.5p +10p)
= £52.50
The cost of the drinks was ...
(£7/box)×(7 boxes) = £49.00
Mae's profit is the difference between her sales revenue and her cost:
profit = revenue - cost
profit = £52.50 -49.00 = £3.50
What does (-4)+8-9+12-(-3)
10 is the your answer, hope its worth it