Answer: 95 units.
Step-by-step explanation:
The cost of making x units is:
C(x) = x^2 + 10*x + 45.
Now, if the cost is $10,020, then we can solve this for x as:
C(x) = 10,020 = x^2 + 10*x + 45
x^2 + 10*x + 45 - 10,020 = 0
x^2 + 10*x - 9,975 = 0
Now, remember that for a quadratic equation:
a*x^2 + b*x + c = 0
the solutions are:
[tex]x = \frac{-b +-\sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In this case the solutions are:
x = [tex]x = \frac{-10 +-\sqrt{10^2 - 4*1*(-9,975)} }{2*1} = \frac{-10 +- 200}{2}[/tex]
Then we have two solutions, one for each sign:
x = (-10 -200)/2 = -110
x = (-10 + 200)/2 = 95
Here we must choose the positive option, as x represents a positive quaintity.
Then the number of units manufactured is 95.
Jeremy and Karina are playing the "Integer Card Game". Jeremy drew three cards, -1, 8, and - 3.
What is the sum of the cards in his hand?m?
Answer:
3
Step-by-step explanation:
Answer:
-1 + 8 + (-3) = 4
Step-by-step explanation:
If one gallon of water is approximately 75,000 drops of water, how many gallons is 1 million drops of water
Answer:
13
Step-by-step explanation:
13x75000=975000
Check for reasonableness...
975000/75000=13
So the answer is 13 gallons.
P.S. There will still be 25,000 drops left, which is 1/3 of a gallon.
In the figure shown, AB = 8 and AD = 5. What is BC?
Answer: 5
Step-by-step explanation:
Since we know that equal number of dashes will always be equal to another we can easily solve the question. They said AB=8 and as you can see 8 is represented by two dashes here and if we take in what i said earlier,, that means DC= 8 too. They also said AD= 5. Since 5 is represented by one dash we can easily see that since BC also has one dash,, it is going to be equal to AD which concluded to the answer of 5.
slove the following multi-step equation
-3(3x+8)+2=26-3x
Answer:
x=-8
Step-by-step explanation:
-3(3x+8)+2=26-3x
We move all terms to the left:
-3(3x+8)+2-(26-3x)=0
We add all the numbers together, and all the variables
-3(3x+8)-(-3x+26)+2=0
We multiply parentheses
-9x-(-3x+26)-24+2=0
We get rid of parentheses
-9x+3x-26-24+2=0
We add all the numbers together, and all the variables
-6x-48=0
We move all terms containing x to the left, all other terms to the right
-6x=48
x=48/-6
x=-8
What is 3x + 2 + 4x - 1 after combining like terms
Answer:
7x+1
Step-by-step explanation:
When you look at the expression(3x+2+4x-1), you will notice that some have variables while some are just regular numbers.
First, focus on the variables. 3x and +4x. In the expression, you will have to add it so 3x+4x will be 7x. Now, keep 7x on the side and switch to the numbers.
Next, focus on the numbers. 2 and -1. All you have to do is combine them which will be 2-1 which also equals 1.
Finally, return 7x with 1 which will be 7x+1. The reason you add a + sign instead of a - sign is because you got positive 1, not negative 1.
Your answer is 7x+1.
69 2/3 as a decimal
Answer:
Here you can find 69 2/3 as a decimal, along with useful information regarding 69 2/3 in decimal form. If you have been searching for 69 and 2 over 3 as a decimal, then you are right here, too. The terms used in this article about 69 2/3 as decimal are explained in detail on our home page; check it out if anything remains unclear. Read on to find the answer to the question what is 69 2/3 as a decimal, and make sure to have a look at our converter.
69 2/3 as a decimal = 69.(6)
Step-by-step explanation:
69.67
2/3 as a decimal is .6 repeating which I rounded
Hope it helps!
Plot 4/7 on the number line
Answer:
0.57, which is a number between 0 and 1
Step-by-step explanation:
The fraction 4/7 is approximately equal to 0.57 as a decimal, so you would plot 4/7 where 0.57 should go
Answer:
Between 0 and 1
Step-by-step explanation:
A small town’s raffle has 85 entries and 3 gift baskets that three different people could win. What is the probability of winning a gift basket if you have 1 of the entries
Answer:
[tex]\dfrac{3}{85}[/tex]
Step-by-step explanation:
It is given that a small town’s raffle has 85 entries and 3 gift baskets that three different people could win.
Total number of entries = 85
Total number of gift baskets = 3
We need to find the probability of winning a gift basket.
[tex]\text{Required probability}=\dfrac{\text{Total number of gift baskets}}{\text{Total number of entries}}[/tex]
[tex]\text{required probability}=\dfrac{3}{85}[/tex]
Therefore, the required probability is [tex]\dfrac{3}{85}[/tex].
For f(x)=3x+1 and g(x)= x2-6, find (f/g)(x)
Answer:
(3x+1)/(x^2-6)
Step-by-step explanation:
f/g(x)=f(x)/g(x)=(3x+1)/(x^2-6)
A field in the shape of a trapezoid has an area of 13.687.5 square yards the length of one base is 150 yards and the length of the other base is 215 yards what is the height of the trapezoid
This question is not correctly written
Complete Question
A field in the shape of a trapezoid has an area of 13,687.5 square yards the length of one base is 150 yards and the length of the other base is 215 yards what is the height of the trapezoid
Answer:
The height of the trapezoid is 75 yards
Step-by-step explanation:
Area of a Trapezoid = 1/2(b1 + b2) × h
Where b1 = Length of the first base
b2 = Length of the second base
h = height of the trapezoid
From the question
Area of the trapezoid = 13,687.5 yd²
b1 = Length of the first base = 150 yards
b2 = Length of the second base = 215 yards
h = height of the trapezoid
Hence, we have
13,687.5 = 1/2(150 + 215)h
13,687.5 = 365h/2
13,687.5 × 2 = 365h
h = 13687.5 × 2/365
h = 75 yards
Therefore, the height of the trapezoid is 75 yards.
Short math problem giving brainly!
Answer:
It should be the second one
Step-by-step explanation:
How many solutions does 3x – 1 = 3x + 1 have?
This system 3x – 1 = 3x + 1 has no solution.
How to solve the given system of equations?In order to determine the solution for the given system of equations, we would apply the substitution method. Based on the information provided above, we have the following system of equations:
y = 3x - 1 .......equation 1.
y = 3x + 1 .......equation 2.
By using the substitution method to substitute equation 2 into equation 1, we have the following:
3x - 1 = 3x + 1
3x - 3x = 1 + 1
0 = 2 (False).
Read more on equation here: https://brainly.com/question/31398664
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5 + {2[(48 – 40) ÷ 4 + (2 x 5)]}
Answer:
29.
Step-by-step explanation:
The given expression is
[tex]5+2[(48-40)\div 4+(2\times 5)][/tex]
BODMAS = Bracket, Of, Division, Multiplication, Addition, and Subtraction.
Using BODMAS, we get
[tex]5+2[(8)\div 4+(10)][/tex] (Brackets)
[tex]5+2[2+10][/tex] (Division)
[tex]5+2[12][/tex] (Brackets)
[tex]5+24[/tex] (Multiplication)
[tex]29[/tex] (Addition)
Therefore, the value of given expression is 29.
What are the coordinates of Y if the midpoint of line segment XY is (2,-5) and the coordinates of point X is (4,4)?
Answer:
Y(0, - 14 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ [tex]\frac{1}{2}[/tex] (x₁ + x₂ ), [tex]\frac{1}{2}[/tex] (y₁ + y₂ ) ]
Use the midpoint formula and equate corresponding parts to the coordinates of the given midpoint
let Y = (x, y ), then
[tex]\frac{1}{2}[/tex] (4 + x) = 2 ( multiply both sides by 2 )
4 + x = 4 ( subtract 4 from both sides )
x = 0
and
[tex]\frac{1}{2}[/tex] (4 + y ) = - 5 ( multiply both sides by 2 )
4 + y = - 10 ( subtract 4 from both sides )
y = - 14
Thus
coordinates of Y = (0, - 14 )
If n = 4, all of the following expressions are equivalent except _____. 16 n -2
For n = 4, all of the given expressions are equivalent except 16 and
(n - 2).
What is Substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
The expressions are;
1. 16
2. n - 2
3. 1/16
4. 1/n²
Now, Put n = 4 in all given expression we get;
The first expression is,
16
The second expression is,
n - 2
= 4 - 2
= 2
The third expression is,
1/16
The fourth expression is,
1/n²
= 1/4²
= 1/16
Hence, Third and fourth expression are same.
So, For n = 4, all of the given expressions are equivalent except 16 and
(n - 2).
Learn more about the substitution method visit:
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The complete question is this.
If n = 4, all of the following expressions are equivalent except _____.
16
n -2
1/16
1/n ^ 2
3/7 rounded to the nearest hundredth
Answer:
0.4285714286.
The hundredth place is 2 places to the right of the decimal. In this case, it is 2. So we look to the number to the right of 2 (which is 8). 8 ≥ 5, so the 2 gets rounded to a 3.
0.43
Answer:
The answer is 0.43
Step-by-step explanation:
When you divide 3 by 7, you get 0.42857142857142857142857142857143.
To round to the nearest hundredth, you go 2 numbers after the decimal place. The number on the right of the 2nd number (which is in the hundredths place) will either make the number round up or down. Since the number 8 is greater than 5, the number rounds up.
So, the answer will be 0.43
Need help asap i will help u if u help me
Answer:
(14,5)
Step-by-step explanation
add 9 to 5 and add 4 to 1
hope this helps
Find the distance d(A,B) between points A and B.
A(7-5); B(7,5)
Answer: d(A,B)=
Simplify your answer. Type an exact answer...
Answer:
The answer is 10 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
A(7-5); B(7,5)
The distance between them is
[tex]d = \sqrt{ ({7 - 7})^{2} + ({ - 5 - 5})^{2} } \\ = \sqrt{ {0}^{2} + ( { - 10})^{2} } \\ = \sqrt{100} [/tex]We have the final answer as
10 unitsHope this helps you
Can someone on help me 20 points!
Answer:
7/8
Step-by-step explanation:
No probability numbers have been assigned to the branches, so there is insufficient information.
We note that "at least one head" includes all 7 branches above the last one (which is all tails). If the probabilities are all equal, then ...
p(h > 0) = 7/8
15-12 + 4(3) =
15-12-12
15-1
14
Answer:
15
Step-by-step explanation:
15-12+4(3)
15-12+12
3+12
15
Rewrite the equation for x, and express its value in terms of a. 3/a x - 4 = 20
For this case, we must clear variable "x" from the given equation, expressed in terms of "a".
We have:
3/a x-4=20
By clearing "x" we have:
Adding 4 to both sides of the equation:
3/a x = 20 + 4
Multiplying by a/3 on both sides of the equation:
x=24a/3
x=8a
So, x=8a
Answer:
x=8a
Perform the indicated operation.
f(x)= 3x - 5
g(x) = 4x - 4
Find (5f- 5g)(x)
Answer is -5x-5
write 3 integers less than -27
Answer:
It would be -28, -29, and -30.
Step-by-step explanation: It would be these answers since the numbers are negative the "less than" would be in the other direction.
I will mark brainliest just answer right and fast pls
attached link
Answer:
9,0
Why?
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
— 7 + 4p = -8p + 11
just the answer
or steps if you can
Answer:
p = 1.5
Step-by-step explanation:
— 7 + 4p = -8p + 11
Add 8p to each side
— 7 + 4p+8p = -8p+8p + 11
-7 +12p = 11
Add 7 to each side
-7+7 +12p = 17
12p = 18
Divide each side by 12
12p/12 =18/12
p = 18/12
p = 3/2
p = 1.5
J is between H & K, if HJ=4t-15, JK=5t-6, and KH=15, find JK
Answer:
JK = 39
Step-by-step explanation:
HJ and JK are segments of line segment HK, so they must add up to the length of KH.
HJ + JK = HK
By substituting in the values of each line segment, we can solve for t.
(4t - 15) + (5t - 6) = 15
9t - 21 = 15
9t = 36
t = 9
Now that we have t, we can plug it in in order to find the value of JK.
JK = 5t - 6
5(9) - 6
45 - 6
39
JK = 39
(1/2)+(1/2)
lets see who can solve this problem the fastest
Answer:
1
Step-by-step explanation:
Youll only add the top parts so 1+1=2
now we have [tex]\frac{2}{2}[/tex] which is also equal to 1 so our answer is 1.
What is 1/5 expressed as a percent
Simplify the following expression.
(7x3 + 8 – x2) + (5x3 – 7)
brainlet !!
5/6 + 7 1/3 (pls show how u get the answer)
Answer:
8 1/6
Step-by-step explanation:
5/6 + 7 1/3
Change the fractions to different denominators.
5/6 x 1/1 = 5/6
1/3 x 2/2 = 2/6
5/6 + 2/6 = 7/6
7/6 = 1 1/6
1 1/6 + 7 = 8 1/6