Answer:
The solution for the given system of equations is ( 4,-3).
Step-by-step explanation:
Here, the given set of equations is:
7 x - 3 y = 37 .... (1)
14 x + 11 y = 23 .... (2)
Now, we solve this equation by ELIMINATION METHOD,
Multiply the first given equation with ( -2), we get:
(-2) [7 x - 3 y = 37 ] ⇒ -14 x + 6 y = -74 .... (3)
Adding equation (2) and (3), we get:
14 x + 11 y + -14 x + 6 y = 23 -74
or, 17 y = - 51
or, y = -51/17 = 3
⇒ y = -3
Now, out the value of y in the given second equation,we get:
14 x + 11 (-3) = 23
or, 14 x = 23 + 33 = 56
or, x = 56/14 = 4
⇒ x = 4
Hence, the solution for the given system of equations is ( 4,-3).
A group of students goes out to lunch. If two have burritos and five have tacos, the bill will be $19.50. If five students have burritos and two have tacos, the bill will be $22.50. Find the price of each taco and burrito
Answer:
The price of the burrito is $3.5 and the price of the taco is $2.5.
Step-by-step explanation:
2x+5y=19.5
5x+2y=22.5
------------------
5(2x+5y)=5(19.5)
-2(5x+2y)=-2(22.5)
-----------------------------
10x+25y=97.5
-10x-4y=-45
-----------------------
21y=52.5
y=52.5/21=2.5
2x+5(2.5)=19.5
2x+12.5=19.5
2x=19.5-12.5
2x=7
x=7/2=3.5
x=3.5, y=2.5
The price of the burrito is $3.5 and the price of the taco is $2.5.
The required price of the burrito is $3.50 and the price of the taco is $2.50.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's represent the price of a burrito b and the price of a taco t.
If two students have burritos, then the cost of the burritos is 2b.
If five students have tacos, then the cost of the tacos is 5t.
The total cost of the meal is 2b + 5t = $19.50.
Similarly, if five students have burritos, then the cost of the burritos is 5b.
If two students have tacos, then the cost of the tacos is 2t.
The total cost of the meal is 5b + 2t = $22.50.
We can set up a system of equations to solve for b and t:
2b + 5t = $19.50
5b + 2t = $22.50
We can solve this system using the elimination method. Multiplying the first equation by 5 and the second equation by 2, we get:
10b + 25t = 97.50
10b + 4t = 45.00
Subtracting the second equation from the first equation, we get:
21t = 52.50
t = $2.50
Substituting this value for t into the first equation, we get:
2b + 5 x $2.50 = $19.50
2b = $7
b = $3.50
Therefore, the price of a taco is $2.50 and the price of a burrito is $3.50.
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Find the probability of obtaining exactly 3 heads when flipping 4 coins
school starts at 8:55. one day katie was a quarter of an hour late. what time did she arrive
the answer is 9:10 hope it helps
Final answer:
Katie was a quarter of an hour, or 15 minutes, late to school which starts at 8:55 AM. So, she arrived at 9:10 AM.
Explanation:
If school starts at 8:55 AM and Katie was a quarter of an hour late, that means she was 15 minutes late because a quarter of an hour is 15 minutes (60 minutes divided by 4 equals 15 minutes).
To find out what time Katie arrived, we need to add 15 minutes to the starting time of school:
School starts: 8:55 AM
Time late: + 15 minutes
Time of arrival: 9:10 AM
So, Katie arrived at school at 9:10 AM.
Please SHOW me how to complete this problem. 50 points
(10y^3-5y^2-10x+4) ÷(2y-1)
Answer:
10y3 - 5y2 - 10x + 4
————————————————————
2y - 1
Step-by-step explanation:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
Step 2 :
Equation at the end of step 2 :
Step 3 :
10y3 - 5y2 - 10x + 4
Simplify ————————————————————
2y - 1
Checking for a perfect cube :
3.1 10y3 - 5y2 - 10x + 4 is not a perfect cube
Final result :
10y3 - 5y2 - 10x + 4
————————————————————
2y - 1
Answer:
The answer is 10y³-5y²-10x+4 over 2y-1
Step-by-step explanation:
i am pretty sure this the answer because there are no like terms so you can't simplify so you solve it by writing the division as a fraction. but the again im positive this is right but i may be wrong. hope this is right!
this year a softball coach raised $1200 for new equipment. that is 4 percent less then last year. how much did he raise last year?
Answer:
The coach raised $1250 last year
Step-by-step explanation:
Let the amount raised last year be $x
Amount raised this year = $1200
Amount raised this year was less by the 4% of x amount last year:
1200 = x - 4% of x
1200 = x - x (x) 4/100 = 96x/100
x = $1250
The coach raised $1250 last year for the equipment.
How many like terms are in 3x–2y+7?
Answer:
None.
Step-by-step explanation: 3x does not have the same coefficient as 2y or 7
Please help me and explain how you got the answer
Answer:
∠NQP = 74°
Step-by-step explanation:
NPQ is a triangle.
We know the sum of 3 angles of a triangle is 180 degrees. So we can write:
N + P + Q = 180
2x + 34 + 2x + 2 = 180
Now, we can solve for x:
[tex]2x + 34 + 2x + 2 = 180\\4x+36=180\\4x=180-36\\4x=144\\x=\frac{144}{4}\\x=36[/tex]
The measure of NQP is "2x+2", we plug in x = 36, and find the measure of NQP:
∠NQP = 2(36) + 2 = 74°
Item 13
Factor out the coefficient of the variable.
The expression 14y+38 factored is
Answer:
2(7y+19)
Step-by-step explanation:
14y+38=2(7y+19)
Goldberg's sleigh currently runs at 203mph, but he needs it to reach 400mph with all the packages he has to deliver.
If Goldberg is delivering presents at an altitude of 5,813.6ft, with the same drag and weight of a 2019 Challenger SRT® Hellcat Redeye, how much HP would he need to reach 400 mph?
Pro Tips:
100% driveline efficiency
P (air density) at 5813.6 ft = .0019 slug/ft^3
A (Area of Challenger front end) = 26.72 ft^2
C(d) (Coefficient of drag) = .398
Goldberg's sleigh required speed, 400 MPH = 587 ft/sec
F(drag) = 1/2 p x v^2 x C(d)A
P = F(drag) x V
Convert to Horsepower = P ( 1HP/550 ft lbf/sec)
Answer:
5,813 HP
Step-by-step explanation:
P=f*v
f=1/2*p*v^2*C*A
HP=(f*v)/550
Answer:
He needed 3747.61 HP to reach 400 mph.
Step-by-step explanation:
Given data :
P (air density) = 0.0019 slug/ft³
A (Area) = 26.72 ft²
C(d) = 0.398
crr = 0.015
V = 400 mph = 587 ft/sec = 178.92 m/sec
weight = 2019 lb = 8980.96 N [1 pound = 4.44822 N]
[tex]P=\frac{Force\times Displacement}{Time}[/tex]
P = Force × Velocity = FV
F = F(sum) = F(drag) + F(rolling resistance)
F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]
F(rolling resistance) = weight × crr
[tex]HP=\frac{P}{1hp}[/tex] 1hp = 745.7 watts
F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]
[tex]=\frac{1}{2}\times 0.0019\times 587^{2} \times 0.398\times 26.72[/tex]
= 3481.23 [tex]\frac{slug\times ft}{sec^2}[/tex]
convert [tex]\frac{slug\times ft}{sec^2}[/tex] to [tex]\frac{kg\times m}{s^2}[/tex]
1 slug = 14.5939 kg
1 ft = 0.3048 m
[tex]\frac{slug\times ft}{sec^2}[/tex] = 14.5939 × 0.3048 = 4.448 [tex]\frac{kg\times m}{s^2}[/tex] or newton
Since F(drag) = 3481.23 × 4.448 N
= 15484.51 N
P = F(drag) × V
= 15484.51 × 178.92 N m/s
= 2770488.529 watts
F rolling resistance = crr × w
= 0.015 × 8980.96 N
= 134.714 N
Power = (Fdrag + Frolling resistance) × V
= (15484.51 + 134.714) × 178.92
= 15619.224 × 178.92
= 279459.558 watts
Power in HP
[tex]HP=\frac{P}{hp}[/tex]
[tex]=\frac{279459.558}{745.7}[/tex]
= 3747.61 HP
He needed 3747.61 HP to reach 400 mph.
Whats 2÷3/4×6&1/2÷4×8÷11=
Answer:
4/9 and 1/64
Step-by-step explanation:
Do PEMDAS:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionThere are no parentheses or exponents, so move onto step 3 Multiplication
[tex]2 \div \frac{3}{4} \times 6[/tex]
[tex] \frac{3}{4} \times \frac{6}{1} = \frac{18}{4} [/tex]
[tex]2 \div \frac{18}{4} = \frac{2}{1} \times \frac{4}{18} = \frac{8}{18} = \frac{4}{9} [/tex]
4/9 is the answer to the first problem
Again there are no parentheses or exponents, so move onto multiplication
[tex] \frac{1}{2} \div 4 \times 8[/tex]
[tex] \frac{1}{2} \div 32 = \frac{1}{2} \times \frac{1}{32} = \frac{1}{64} [/tex]
1/64 is the answer to the second problem
a pet store had a special offer this weekend. for every $120 that customers spend, $3 is donated to a pet rescue program. How much do customers have to spend in order to raise $1000 for the pet rescue program?
$3 donated_____$120 spent
$1,000 donated__X=$40,000 spent
(1,000*120)/3= 40,000
Answer: The Customers have to spend $4000 in order to raise $1000 for the pet rescue program.
Step-by-step explanation:
Hi, to answer this question we have to write a proportion.
Proportion = money spent / money raised for the pet rescue program
For every $120 that customers spend, $3: 120/3
To raise $100 : x / 100
Where x is the money that customers spent to raise $100 for the pet rescue program.
Solving for x:
120/3 = x /100
(120/3)100=x
x =$4000
A biology test is worth 100 points and has 36 questions
Answer:
whats the question?
Step-by-step explanation:
Stephan, Gavin and Jim share some sweets in the ratio 1:4:4. Stephen gets 13 sweets. How many more sweets does Gavin get over Stephen?
Final answer:
To find out how many more sweets Gavin gets over Stephan, we use the ratio 1:4:4, knowing that Stephan gets 13 sweets. Gavin, who has 4 times Stephan's amount, ends up with 52 sweets, which is 39 sweets more than Stephan.
Explanation:
To determine how many more sweets Gavin gets compared to Stephan, we need to use ratios. Since Stephan, Gavin, and Jim share sweets in the ratio 1:4:4, and Stephan gets 13 sweets, we can assign variables to the parts of the ratio to make this easier to solve. Let's assign 'x' to the value of one part, so Stephan gets 1x=13 sweets.
Since 1x is equal to 13, that means 4x is the amount Gavin gets. Now we calculate 4x, which is 4 [tex]\times[/tex] 13=52 sweets. To find out how many more sweets Gavin gets we subtract Stephan's 13 sweets from Gavin's 52 sweets to get the difference.
So, Gavin gets 52-13=39 sweets more than Stephan.
Which of the following linear equations matches the graph
y = 1/3 x
y = 3/2 x
y = 3x
y = 2x
y = 2/3 x
The only linear equation that matches the graph is: Option E: y = 2/3 x
What is the equation of the line?
The general form for the equation of a Line in slope intercept form is:
y = mx + c
Where:
m is slope
c is y-intercept
We can find the slope between two coordinates using the formula:
m = [tex]\frac{(y_{2} - y_{1}) }{(x_{2} - x_{1})}[/tex]
Using the given coordinates (-3, -2) and (3, 2), we have:
m = (2 - (-2))/(3 - (-3))
m = 4/6 = 2/3
The only equation with slope of 2/3 is Option E
Find the sum of the first 50 terms in this geometric series 1+10/11+100/121
Answer:
10.91
Step-by-step explanation:
The sum of the first 50 terms in this geometric series is 11.00.
What is a geometric series?When all the terms of a geometric sequence are added, then that expression is called geometric series.
Lets suppose its initial term is f=a , multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We are given that;
n=50
Series= 1+10/11+100/121
Now,
To find the sum of the first 50 terms in this geometric series, we need to use the formula:
Sum = [tex]a1(1 - r^n) / (1 - r)[/tex]
where a1 is the first term, r is the common ratio, and n is the number of terms. We can identify that the first term is 1, the common ratio is 10/11, and the number of terms is 50. Plugging these values into the formula, we get:
Sum = 1(1 - (10/11)^50) / (1 - 10/11) Sum = (1 - 0.000000000000000000000000000000000000000000000001) / (1/11) Sum = (0.9999999999999999999999) / (0.09090909) Sum = 10.99998
Rounding this result to two decimal places, we get:
Sum = 11.00
Therefore, by the given geometric sequence the answer will be 11.00.
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What is 4,479,621,002 rounded to the nearest ten million
The nearest ten million is 4,480,000,000.
at a store 20 feet of fencing cost $36 at the rate how much will 15 feet of fencing cost
Answer:
15 feet of fencing costs $27
Step-by-step explanation:
We know 15/20 = 3/4 so...
36 x 3/4 = 27
Another way:
36 divided by 20 = 1.8
1.8 x 15 = 27
answer:
$24
Step-by-step explanation:
36 divided by 15 equals 2.4 then 2.4x5 secne 15 is 5 away from 20 equals 12 then 36 - 12 = 24
4 square meters is equivalent to how many square yards
Answer:
4.8sq. yards
Step-by-step explanation:
Of the total number of spectators at a circus show, 1/4 are men. 2/5 of the remaining number of spectators are women. There are 132 women at the circus show. How many children are at the circus show?
Answer: There are [tex]198[/tex] children at the circus show.
Step-by-step explanation:
Let be "x" the total number of spectators at the circus show and "c" the number of children at the circus show.
Knowing that [tex]\frac{1}{4}[/tex] of the spectators are men, we can find the remaining:
[tex]x-\frac{1}{4}x=\frac{3}{4}x[/tex]
Since [tex]\frac{2}{5}[/tex] of the remaining number of spectaros are women and there are a total of 132 women, we can write the following equation:
[tex](\frac{2}{5})(\frac{3}{4}x)=132[/tex]
Solving for "x", we get:
[tex]x=(132)(\frac{20}{6})\\\\x=440[/tex]
Therefore, we get that "c" is:
[tex]c=440-\frac{1}{4}(440)-132\\\\c=198[/tex]
How much should you invest at 5% simple interest in order to have a balance of 1,200 in two and a half years
Answer:
We should invest 9600 .
Step-by-step explanation:
Interest received in Two and a half year = 1,200
So, Interest that should be received in a year = 1200×[tex]\frac{2}{5}[/tex]
= 480
Interest rate = 5%.
Let we had invested amount X.
Thus 5 % of X we will get in a year as interest
Which is [tex]\frac{5}{100}[/tex]×X = [tex]\frac{X}{20}[/tex].
It is also equal to 480 as calculated above,
So. X = 480×20 = 9600.
Thus,
We should invest 9600 .
Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $90 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2350. How long did each mechanic work?
Answer:
The first mechanic worked for 20 hours and the second mechanic worked for 5 hours
Step-by-step explanation:
Let f be the number of working hours of first mechanic
Let s be the number of working hours of second mechanic
Given that they both worked for a combined total of 25 hours
⇒f + s = 25 → equation 1
First mechanic charged $95 per hour and second mechanic charged $90 per hour and they both together charged $2350
⇒95f + 90s = 2350 → equation 2
Using equation 1 in equation 2:
95f + 90(25-f) = 2350
⇒95f + 2250 - 90f = 2350
⇒5f = 100
or f = 20 hours
⇒s = 25 - f ⇒ s = 5 hours
The first mechanic worked for 20 hours and the second mechanic worked for 5 hours
A. 141
B. 138
C. 282
D. 69
Answer:
D
Step-by-step explanation:
The measure of x is calculated as
x = 0.5( arc CD - arc BD)
= 0.5(210 - 72) = 0.5 × 138 = 69 → D
write an absolute value inequality that has 3 and -6 as two of its solutions
Final answer:
An absolute value inequality that includes 3 and -6 as solutions is |x + 1.5| ≤ 4.5. Both numbers satisfy the inequality when substituted for x.
Explanation:
To write an absolute value inequality that has 3 and -6 as two of its solutions, we must find an inequality such that both of these numbers satisfy the condition when their absolute values are considered. One such inequality is |x + 1.5| ≤ 4.5.
Let's verify the solutions:
For x = 3: |3 + 1.5| = |4.5| = 4.5, which is less than or equal to 4.5.
For x = -6: |-6 + 1.5| = |-4.5| = 4.5, which is also less than or equal to 4.5.
Therefore, the inequality |x + 1.5| ≤ 4.5 is a valid inequality that includes 3 and -6 as solutions.
paul has a total of 15 markers and pencil. Each pencil cost $0.30 and each marker costs $1.25 how many pencils does paul have
Answer:
1
Step-by-step explanation:
Jan walks 1/5 of a mile to the bus stop and then gets on the bus and rides 2/3 of a mile to school find the total distance Jan travels to school
Answer:
13/15
Step-by-step explanation:
Hope it is correct
What is 45 divided by 765
Answer:
.06 rounded to nearest hundreth
Step-by-step explanation:
Answer:
17 I think
Step-by-step explanation:
Don’t understand #3 please help quickly
Answer:
the answer is b
Step-by-step explanation:
Ohio is the home of two of the world’s largest aluminum smelters, in which metal is separated for recycling. Together, these two facilities process an average of 15 million pounds of aluminum each month. How many pounds of aluminum do the Ohio smelting plants average per week?
3.75 million pounds of aluminium
Step-by-step explanation:
The question requires you to perform division operation
Given that 15 million pounds is processed per month
A month has average 4 weeks.
The aluminium smelted per week will be;
15/4 = 3.75 million pounds of aluminium
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Keyword : pounds, average, month, week
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Justin began his walk at 3:05 p.m. He arrived at his destination at 4:32 p.m. How long did Justin walk? Show your work and explain how you found your answer.
PLZZZ HELP!!! 16 POINTS!!!!
Answer:
The answer to this question is it took him an hour and 27 minute
simplify 2.8-5.8n-3n+5
Answer: -8.8n + 7.8
Step-by-step explanation:
2.8 - 5.8n - 3n + 5
Add -5.8n and -3n to get -8.8n
Add 2.8 and 5 together to get 7.8
Answer:
Step-by-step explanation:
7.8-8.8n