The cost to replace a water pump in a car was $816. This included $381 for the water pump and $87 per hour for labor. How many hours of labor were required to replace the water pump?
Graph 5x + 3y = 15.
y
Graph is on the picture.
hope ot helps.
3) Cory is standing on a cliff that is 48 feet above the ground. He throws a rock in to the air. The height, h, of the rock
after t seconds is given by h(t) = -2t+4t +48.
a) What is the initial height?
b) How many seconds does it take to reach the maximum height?
c) What is the rock's maximum height?
d) How many seconds does it take to for the rock to land on the ground?
Answer:
a) The initial height of the rock is of 48 feet.
b) It takes 1 seconds for the rock to reach maximum height.
c) The rock's maximum height is 50 feet.
d) It takes 6 seconds for the rock to land on the ground.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
The height of the ball after t seconds, in feet, is given by:
[tex]h(t) = -2t^2 + 4t + 48[/tex]
Which is a quadratic equation with [tex]a = -2, b = 4, c = 48[/tex]
a) What is the initial height?
This is [tex]h(0) = 48[/tex]. So the initial height of the rock is of 48 feet.
b) How many seconds does it take to reach the maximum height?
This is the value of t at the vertex. So
[tex]t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1[/tex]
It takes 1 seconds for the rock to reach maximum height.
c) What is the rock's maximum height?
This is the height of the ball after 1 second. So
[tex]h(1) = -2(1)^2 + 4(1) + 48 = 50[/tex]
The rock's maximum height is 50 feet.
d) How many seconds does it take to for the rock to land on the ground?
This is t for which [tex]h(t) = 0[/tex], so we solve the quadratic equation.
[tex]\bigtriangleup = (4)^2-4(-2)(48) = 400[/tex]
[tex]t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4[/tex]
[tex]t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6[/tex]
Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.
what is the slope of the line?
Answer:
In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line.
Step-by-step explanation:
the half life of carbon 14 is 5730 years. how much of a 50 gram sample would be left after 15000 years
Answer:
In this question (t½) of C-14 is 5730 years, which means that after 5730 years half of the sample would have decayed and half would be left as it is. After 5730 years ( first half life) 70 /2 = 35 mg decays and 35 g remains left. After another 5730 years ( two half lives or 11460 years) 35 /2 = 17.5mg decays and 17.5 g remains left . After another 5730 years ( three half lives or 17190 years) 17.5 /2 = 8.75mg decays and 8.75g remains left. after three half lives or 17190 years, 8.75 g of C-14 will be left.
Step-by-step explanation:
5.65 x 10 to the 5th power + 4.87 * 10 to the 3rd power
Answer:
569870
Hope this helps you. Do mark me as brainly
Answer:
the answer is very big..... it is 575,876,495
Simplify completely''''
Answer:
[tex]\displaystyle \frac{2(x + 3)}{5x - 2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{2x^2 + 16x + 30}{5x^2 + 13x - 6}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{2(x + 3)(x + 5)}{5x^2 + 13x - 6}[/tex][Fraction] Factor denominator: [tex]\displaystyle \frac{2(x + 3)(x + 5)}{(x + 3)(5x - 2)}[/tex][Fraction] Divide: [tex]\displaystyle \frac{2(x + 3)}{5x - 2}[/tex]5у2 2is a power + бу - 4
Answer:
Its 5000
Step-by-step explanation 4883-3455=5000
Please I need help!!
Answer:
These expressions are both correct because they are equivalent to each other.
5(4) + 7(4) = 20 + 28 = 48
(12 x 8)/2 = 96/2 = 48
Let me know if this helps!
Is 1/4 more than 7/3
Answer:
No
Step-by-step explanation:
Frank is building 2 raised gardens. He needs 3 cubic yards of soil to fill the first garden and 2 1/2 times that amount to fill the second one. How much soil does Frank need to fill the second garden?
Answer:
7.5 cubic yards
Step-by-step explanation:
3* 5/2= 15/2= 7.5 cubic yards
if my answer helps please mark as brainliest.
what do you know to be true about the values of a and b
Answer:
a
Step-by-step explanation:
all angles in a triangle is equal to 180 so
60+50=110 so p =70
80+30=110 so q =70
p=q
Answer:
p=q
Step-by-step explanation:
hiii , does anyone know with work? thank you
Answer:
3√41
Step-by-step explanation:
The diagonal can be gotten using the pythagoras theorem
d² = l²+w²
d² = 12²+15²
d² = 144 + 225
d² = 369
d = √9*41
d = 3√41
Hence the diagonal is 3√41
Type the integer that makes the following addition sentence true:
= 6
39 +
-33
Hope this helps. :)))))
Please help please and thank you
Answer:
Step-by-step explanation:
2x + 3x + 8 - 3x - 2 = 2x + 6
The first and third expressions.
Answer:
1 and 3
Step-by-step explanation:
This should be correct
Perform the indicated operation. (2u2 - 7) ÷ (u + 3)
Answer:
2u+3-7/u
Step-by-step explanation:
factor the numerator and denominator and cancel the common favtors
Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycle? Round your answer to two decimal places, if needed.
Answer:
17 mphStep-by-step explanation:
Miguel's speed = m, Raul's speed = rGivenm = 4rDistance = 68 milesTime difference = 3 hoursSolutiontime = distance/speedSubstitute values and solve for r the equation of the time difference:
68/m + 3 = 68/r68/4r + 3 = 68/r17/r + 3 = 68/r17 + 3r = 683r = 68 - 173r = 51r = 17Raul's speed is 17 mph
Answer:
[tex] \huge \boxed{ \boxed{ \red{ \tt17 \: mph}}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:equationequation word problemsPEMDASgiven:Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycletips and formulas:t=d/sto findhow fast can Raul ride his bicyclelet's solve:let's the speed of Raul be x
likewise
Miguel can drive 4 times as fast as Raul can ride his bicycle
therefore
4x
according to the question
[tex] \sf \frac{68}{4x}+3=\frac{68}{x}[/tex]
[tex] \implies \sf \frac{68 + 12x}{4x} = \frac{68}{x} [/tex]
[tex] \sf factor \: out \: 4 \: and \: reduce \: it : \\ \sf \implies \frac{4(17 + 3x)}{4x} = \frac{68}{x} \\ \\ \implies\sf \frac{17 + 3x}{x} = \frac{68}{x}[/tex]
[tex] \sf multipy \: both \: sides \: by \: x : \\ \sf \implies (\frac{17 +3 x}{x} )x = (\frac{68}{x} )x \\ \implies \sf 17 + 3x = 68[/tex]
[tex] \sf cancel \: 17 \: from \: both \: sides : \\ \implies \sf 17 - 17 + 3x = 68 - 17 \\ \implies \sf 3x = 51[/tex]
[tex] \sf divide \: both \: side s \: by \: 3 : \\ \sf \implies \frac{3x}{3} = \frac{51}{3} \\ \therefore x = 17[/tex]
This relationship is a function.
2
4
5
6
5
6
8
13
True
O False
What is the value of (x^3 − 7x^2 − 18x + 42) when x = 3?
Answer:
-150
Step-by-step explanation:
x^2 - 7x^2 - 18x +42
3^2 - 7(3)^2 - 18(3) + 42
9 - 63 - 54 + 42
-54 -54 + 42
-108 + 42
-150
Artificial grass sells for $10.98 per square yard final cost to buy and install 69.2 square yards if the seller charges $5.15 per square yard for labor round to the nearest cent
Answer:
$1,116.19.
Step-by-step explanation:
Given that artificial grass sells for $ 10.98 per square yard, to determine the final cost to buy and install 69.2 square yards if the seller charges $ 5.15 per square yard for labor, round to the nearest cent, the following calculation must be performed:
69.2 x (10.98 + 5.15) = X
69.2 x 16.13 = X
1,116,196 = X
Thus, the cost to purchase and install 69.2 square yards of artificial grass is $ 1,116.19.
The ratio of cats to dogs is 8:9. If
there are 27 dogs, how many cats
are there
(Help)
Answer:
24 yw :)
Step-by-step explanation:
3. His teacher praised him.
someone please help me i don’t understand
Answer:
Answer B
Step-by-step explanation:
Write out f(x) and g(x) in a column; we will subtract g(x) from f(x):
f(x) = x^2 - 9 or f(x) = x^2 - 9
-g(x) = -(2 - x) or -g(x) = +x -2
---------------------------------
f(x) - g(x) = x^2 + x - 11 (Answer B)
how many hours in 1weak
Answer:
168 hours
Step-by-step explanation:
11 There are 136 people on a train.
34 of the people are children.
What percentage of the people on the train are adults?
Answer:
75%
Step-by-step explanation:
There are 136 people on a train
34 are children
Therefore the percentage of people that are adults can be calculated as follows
= 136-34
= 102
= 102/136 × 100
= 0.75 × 100
= 75%
Hence 75% are adults
Solve the equation for x. 2x + 22 = 4(x+3)
Answer:
x = 5
Step-by-step explanation:
We have the algebraic expression and are asked to solve for x.
To solve, we need to isolate x.
2x + 22 = 4(x + 3)
Distribute :
2x + 22 = (4(x) + 4(3))
2x + 22 = 4x + 12
Subtract 12 from both sides :
2x + 10 = 4x
4x = 2x + 10
Subtract 2x from both sides :
2x = 10
Divide 2 from both sides to get x alone :
x = 5
Answer:
x = 5
Step-by-step explanation:
We have the algebraic expression and are asked to solve for x.
To solve, we need to isolate x.
2x + 22 = 4(x + 3)
Distribute :
2x + 22 = (4(x) + 4(3))
2x + 22 = 4x + 12
Subtract 12 from both sides :
2x + 10 = 4x
4x = 2x + 10
Subtract 2x from both sides :
2x = 10
Divide 2 from both sides to get x alone :
x = 5
Solve for k.
B=1/2kq
Answer:
k= 2b/q
Step-by-step explanation:
see pic for explanation
Three uniform shirts sell for $34.50. How much will 5 uniform shirts cost?
Answer:
57.5
Step-by-step explanation:
Recognize our numbers
3,5,34.50
Three uniform shirts sell for 34.50
34.50/3
=11.5
How much will five cost?
5x11.5
=57.5
Hope this helps!
Answer:
55.25
Step-by-step explanation:
1. First we need to work out the price of ONE shirt. To do that we divide the total price of 3 shirts by 3.
34.50 / 3 = 11.05
2. Now we know that the price of one shirt is $11.05p we can multiply that by 5 to get the price of 5 shirts.
11.05 * 5 = 55.25
= $55.25p
What is the reference angle of 50°?
A store owner purchased 70 soccer balls for $24.50 each. The store owne sold 40 of the soccer balls for $39.75 each. The remainder of the soccer balls were sold for $29.50 each. How much profit did the store owner earn?
Answer:
The stores profit was $757
Step-by-step explanation:
70 x 24.50=1715
they spent 1715 on 70 soccer balls.
They sold 40 of the soccer balls for 39.75 each.
so 40 x 39.75=1590
Then the the remainder of the soccer balls would be 30 since they only started with 70
so they sold 30 soccer balls for 29.50 each.
30 x 29.50= 882
So add 882+1590=2472
then take that number and subtract it from 1715
2472-1715=757 So in profit they made $757 dollars.
