Answer:
To find critical points, take the first derivative and set it equal to zero:
f(x) = -2x^2 + 4x + 5
f'(x) = -4x + 4
-4x+4 = 0
-4x = -4
x = 1
Critical point at x = 1
Alternatively, if you mean zeros, or where the x intersects, you can use the quadratic equation.
What are the measures of Angles a,b, and c? show your work and explain your answers.
Answer:
a=35
b=55
c=110
Step-by-step explanation:
a=35
Opposite angles which are non-adjacent angles formed by two intersecting lines are equal
b+35+90=180 sum of interior angle of a triangle equal to 180
b=180-125
=55
c+70=180 Angles on a straight line add up to 180°
c=180-70
=110
To calculate the volume of a chemical produced in a day a chemical manufacturing company uses the following formula below:
[tex]V(x)=[C_1(x)+C_2(x)](H(x))[/tex]
where represents the number of units produced. This means two chemicals are added together to make a new chemical and the resulting chemical is multiplied by the expression for the holding container with respect to the number of units produced. The equations for the two chemicals added together with respect to the number of unit produced are given below:
[tex]C_1(x)=\frac{x}{x+1} , C_2(x)=\frac{2}{x-3}[/tex]
The equation for the holding container with respect to the number of unit produced is given below:
[tex]H(x)=\frac{x^3-9x}{x}[/tex]
a. What rational expression do you get when you combine the two chemicals?
b. What is the simplified equation of ?
c. What would the volume be if 50, 100, or 1000 units are produced in a day?
d. The company needs a volume of 3000 How many units would need to be produced in a day?
Answer:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]V(50) = 2548.17[/tex] [tex]V(100) = 10098.10[/tex] [tex]V(1000) = 999201.78[/tex]
[tex]x = 54.78[/tex]
Step-by-step explanation:
Given
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
[tex]C_1(x) = \frac{x}{x+1}[/tex]
[tex]C_1(x) = \frac{2}{x-3}[/tex]
[tex]H(x) = \frac{x^3 - 9x}{x}[/tex]
Solving (a): Expression for V(x)
We have:
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
Substitute known values
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solving (b): Simplify V(x)
We have:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solve the expression in bracket
[tex]V(x) = [\frac{x*(x-3) + 2*(x+1)}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-3x + 2x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
Factor out x
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x(x^2 - 9)}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x^2 - 9)[/tex]
Express as difference of two squares
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x- 3)(x + 3)[/tex]
Cancel out x - 3
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)}] *(x + 3)[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Solving (c): V(50), V(100), V(1000)
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Substitute 50 for x
[tex]V(50) = [\frac{(50^2-50+2)(50 + 3)}{(50 + 1)}][/tex]
[tex]V(50) = \frac{(2452)(53)}{(51)}][/tex]
[tex]V(50) = 2548.17[/tex]
Substitute 100 for x
[tex]V(100) = [\frac{(100^2-100+2)(100 + 3)}{(100 + 1)}][/tex]
[tex]V(100) = \frac{9902)(103)}{(101)}[/tex]
[tex]V(100) = 10098.10[/tex]
Substitute 1000 for x
[tex]V(1000) = [\frac{(1000^2-1000+2)(1000 + 3)}{(1000 + 1)}][/tex]
[tex]V(1000) = [\frac{(999002)(10003)}{(10001)}][/tex]
[tex]V(1000) = 999201.78[/tex]
Solving (d): V(x) = 3000, find x
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]3000 = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Cross multiply
[tex]3000(x + 1) = (x^2-x+2)(x + 3)[/tex]
Equate to 0
[tex](x^2-x+2)(x + 3)-3000(x + 1)=0[/tex]
Open brackets
[tex]x^3 - x^2 + 2x + 3x^2 - 3x + 6 - 3000x - 3000 = 0[/tex]
Collect like terms
[tex]x^3 + 3x^2- x^2 + 2x - 3x - 3000x + 6 - 3000 = 0[/tex]
[tex]x^3 + x^2 -3001x -2994 = 0[/tex]
Solve using graphs (see attachment)
[tex]x = -54.783[/tex] or
[tex]x = -0.998[/tex] or
[tex]x = 54.78[/tex]
x can't be negative. So:
[tex]x = 54.78[/tex]
Pls if anyone knows the answer that will be greatly appreciated :) question 1 btw
Answer:
here's the answer to your question
Terry is building a tool shed with a 90 square foot base and a length that is three more than twice the width. This can be modeled by the equation (2w+15) (w-6)= 0. The length of Terry's tool shed is______ feet.
Answer:
l = 15 feet
Step-by-step explanation:
l = 2w + 3
First you solve for the width(w)
(2w+15) (w-6) = 0
This means
2w+15=0 OR. w-6=0
First let’s solve 2w+15=0
2w = -15
w = -7.5
Width can’t be negative so that can’t be the answer. So we look at the second equation w-6=0
w= 6
Since we found the width now we can find the length by using the formula l = 2w + 3
= 2(6) + 3
= 12 + 3
= 15 feet
You can check this by using the given area which is 90.
A = lw = 15*6 = 90
The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side lengths of the right triangle given the perimeter= 60 and it's area= 120
9514 1404 393
Answer:
10 and 24
Step-by-step explanation:
We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).
These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).
For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)
The side lengths are 10 and 24.
__
Check
For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.
__
In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...
x² +y² = (x+2)² ⇒ y² = (x² +4x +4) -x² ⇒ y² = 4x +4 = 4(x +1)
_____
Additional comment
The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.
Using the third equation in the attachment to write an expression for y, we have ...
y = 58 -2x
Substituting that into the second equation gives ...
(x(58 -2x)/2 = 120
29x -x² = 120
x² -29x +120 = 0
(x -5)(x -24) = 0 . . . . x = 5 or 24.
The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.
Quick Test
7. After 12% discounts, the price of a car is RM 44,000. What is the original price?
A. RM 52,800
B. RM 38,720
C. RM 49,280
D. RM 50,000
8. Find the interest on RM 2,800 if the rate is 5% for 4 years.
A. RM 500
B. RM 660
C. RM 460
D. RM 560
9. Find the net price of an item with a list price of RM 80.00 and a trade discount of 12%
A. RM 69.50
B. RM 57.70
C. RM 70.50
D. RM 70.40
10. The price of a hard drive is RM 215. If Andrew is given 6% discounts, find the mark down
amount.
A. RM 202.10
B. RM 86.00
C. RM 129.00
D. RM 12.90
Answer:
number 7 the answer is 50,000
Ell takes the 17 apples home, and the bakes as many apple pies
as he can. He uses 7 apples in each ple. How many apple pies does
El bake? How many apples are left?
Counters
17:7
10
10
c
Boles
pies
apples are en
Answer:
Tedyxhcj eydyfhxrstetdhsawe
If an 8" X 8" square cake serves 8 people, how many 24" X 24" square cakes are needed for a
wedding attended by 144 people?
Answer:
2 24" X 24" square cakes are needed.
Step-by-step explanation:
This question is solved by proportions.
Area of a square:
The area of a square of side l is given by:
[tex]A = l^2[/tex]
8" X 8" square cake serves 8 people
Thus:
[tex]A = 8*8 = 64[/tex]
Area of 64 serves 8 people, so for 1 people, an area of 64/8 = 8 is needed.
144 people
The total area needed is:
[tex]A = 144*8 = 1152[/tex]
How many 24" X 24" square cakes?
24*24 = 576
1 cake - 576
x cakes - 1152
Applying cross multiplication:
1152/576 = 2
2 24" X 24" square cakes are needed.
A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 60 cookies. The mean is 22.36 and the standard deviation is2.97 . Construct a 80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.
Answer:
2.665 < σ < 3.379
Step-by-step explanation:
Given :
s = 2.97
Sample size, n = 60
α = 80%
χ² Critical value (two - tailed), df = (60-1) = 59
χ² = 45.577 ; χ² = 73.279
The 80% confidence interval for the standard deviation :
s * √(n - 1) / χ² critical
2.97 * √(60 - 1) / 73.279 < σ < 2.97 * √(60 - 1) / 45.577
2.665 < σ < 3.379
PLEASE HELP!!!!!!!!! DUE ASAP I WILL GIVE BRAINLIEST!!!!!!!!
Explanation:
A = values on the die greater than 1
A = {2,3,4,5,6}
B = values on the die less than 5
B = {1,2,3,4}
Union those two sets together
C = A u B = {1,2,3,4,5,6}
Effectively, we get every possible value on the die. This is due to the "or" keyword. If it was "and", then it would be a difference story.
So the probability of getting anything in set C is 100% or just 1. We have guaranteed certainty we'll have this event happen.
HELP ASAP PIC IS BELOW!!!
Answer:
55°
Step-by-step explanation:
Vertical angles are similar
Answered by GAUTHMATH
If f(x) = x - 5, what is the value of f(8)? -13 -3 3 13
Answer:
putting the value of X=8 in f(X)
f(8)= 8-5
f(8)= 3
Answer:
3
Step-by-step explanation:
We must plug in 8 into the equation of the function since f(x) = x - 5 for all values of x. Since 8 could be a value of x, we can plug it in:
[tex]f(8) = 8-5[/tex]
The value of 8 minus 5 is 3, so the value of f(8) is 3.
Please help explanation if possible
Answer:
N=18
Step-by-step explanation:
Hope it will help you
If it does pls give me Brainlest
Have a nice day
Answer:
18
Step-by-step explanation:
use the concept of similarity and enlargement.
[tex] \frac{15}{n} = \frac{5}{6 } [/tex]
[tex]n = \frac{15 \times 6}{5} [/tex]
[tex]n = 18[/tex]
Add .003, 265.8, 83.04
and 1972
PLZZZ HELP
This is due in 15 mins
I need 5
But I already have 4
So one more
Answer:
The hottest month for the northern hemisphere is August.
The hottest month for the southern hemisphere is January and February (these top two might be the opposite)
It's globally warmer during the months of June July and August
During april and november, the southern hemisphere and northern hemisphere are the same, or very close.
During July and August the southern and northern hemispheres have the largest difference in temperature
Use the elimination method to solve this system. − 4 x − 2 y = − 12, 4 x + 8 y = − 24
Answer:
x = 6; y = -6
Step-by-step explanation:
-4x - 2y = -12
4x + 8y = -24
Add the two equations, so x is eliminated:
6y = -36
6y/6 = -36/6
y = -6
Plug in y, to solve for x
-4x - 2y = -12
-4x - 2(-6) = -12
-4x +12 = -12
-4x = -12 -12
-4x = -24
-4x/-4 = -24/-4
x = 6
Answer from Gauthmath
Instructions: Find the missing side. Round your answer to the nearest tenth.
22
58°
Answer:
x = 19.2
Step-by-step explanation:
tan(58)=x/12
x=12×tan(58)
x=19.2
Answered by GAUTHMATH
Write an equivalent fraction for each 1/4 = /10
Answer:
[tex]x = \frac{5}{2}[/tex]
Step-by-step explanation:
Step 1: Find an equivalent fraction
[tex]\frac{1}{4} = \frac{x}{10}[/tex]
[tex]4(x) = 1(10)[/tex]
[tex]4x = 10[/tex]
[tex]x = \frac{10}{4}[/tex]
[tex]x = \frac{5}{2}[/tex]
Answer: [tex]x = \frac{5}{2}[/tex]
Reggie and Jay go for a walk every morning. Reggie walks 2 14 miles. Jay walks 138 miles less than Reggie. What is the total distance they walk every morning?
Answer:
They walked a total distance of 290 miles every morning.
Step-by-step explanation:
First, we have to subtract 214 and 138.
= Jay walks 76 miles.
Next, we have add 214 and 76.
= 290 mi.
Rationalize 2 / 2√2
Answer:
[tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{2\sqrt{2} }[/tex] * [tex]\frac{2\sqrt{2} }{2\sqrt{2} }[/tex] =[tex]\frac{4\sqrt{2} }{8}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
1.2 Write the ratio 1:2 in the simplest form.
compute (-12)+(-8)+30
Answer:
10
Step-by-step explanation:
(-12) + (-8) +30
-(12+8)+30
-20 + 30
10
What is 0.25% of K2 000?
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{When you hear/see the word of in mathematics, it usually means }\\\large\text{\bf multiplication. }[/tex]
[tex]\large\text{So, when you think of think of the word \underline{of} think of its asking you to}\\\large\text{\bf multiply }[/tex]
[tex]\large\text{Now that we got that run down out of the way lets answer your given}\\\large\text{question}[/tex]
[tex]\large\textsf{0.25\% of 2,000}[/tex]
[tex]\large\textsf{= 0.25\%} \times \large\textsf{2,000}[/tex]
[tex]\large\textsf{0.25\%} = \mathsf{\bf \dfrac{25}{100}}[/tex]
[tex]\mathsf{= \dfrac{25}{100} \times 2,000}[/tex]
[tex]\mathsf{\dfrac{25}{100}= \bf 0.0025}[/tex]
[tex]\large\textsf{= 0.0025} \times \large\textsf{2,000}[/tex]
[tex]\large\text{= \bf 5}[/tex]
[tex]\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf 5}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
solve this set of equation, using elimination or substitution method.
Answer:
X =224
Y= -10
Step-by-step explanation:
To solve this question it's better to convert the fractions to decimals this way it will be easy to solve.
0.25x+0.6y= -4
0.2x+0.25y=-0.9
0.2(0.25x+0.6y=-4)
0.25(0.2x+0.25y=-0.9)
0.05x+0.12y=-0.8
0.05x+0.06y=-0.225
0.0575y/0.0575=-0.575/0.0575
Y=-10
To find x you replace the value of y in any of the equations
0.25x+0.6y=-4
0.25x+0.6(-10)=-4
0.25x=-4+60
0.25x/0.25=56/0.25
X=224
I hope this helps and sorry if it's wrong
Bob has 40 cents in his pocket. If Bob has no pennies, how many different combinations of quarters, dimes, and/or nickels could he have.
dime: 5 cents
nickel: 10 cents
quarter: 25 cents
let's start with quarters, (2)
25 + 10 + 5
25 + 5 + 5 + 5
nickels, (4)
10 + 10 + 10 + 10
10 + 10 + 10 + 5 + 5
10 + 10 + 5 + 5 + 5 + 5
10 + 5 + 5 + 5 + 5 + 5 + 5
dimes, (1)
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
7 combinations.
hope it helps :)
A company that makes mobile applications surveyed every 10th customer to learn more about how often customers are using one of the company’s new apps. The table shows the results of the survey.
Feedback Number
use frequently
51
use sparingly
23
do not use
12
What is the predicted percentage of customers who use the new app either frequently or sparingly?
A.
59%
B.
74%
C.
85%
D.
86%
Answer:
I hope this helps
Step-by-step explanation:
Books, and then you have 44+45x=?
Answer:
45x=-44
x=-44/45
Step-by-step explanation:
is this a free question?
For Coronado Industries, sales is $500000, variable expenses are $335000, and fixed expenses are $140000. Coronado’s contribution margin ratio is
a) 67%.
b) 33%.
c) 28%.
d) 5%.
Manish writes the functions g(x)= 3 sqrt -x - 72 and h(x) = -(x + 72)^3
Which pair of expressions could Manish use to show that g(x) and h(x) are inverse functions?
Answer:
[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]
Step-by-step explanation:
Given
[tex]g(x) = 3\sqrt x - 72[/tex]
[tex]h(x) = -(x +72)^3[/tex]
Required
Show that they are inverse functions
For g(x) and h(x) to be inverse, then:
[tex]g(h(x)) = h(g(x))[/tex]
We have:
[tex]g(x) = 3\sqrt x - 72[/tex]
Replace x with h(x)
[tex]g(h(x)) = 3\sqrt{h(x)} - 72[/tex]
Substitute value for h(x)
[tex]g(h(x)) = 3\sqrt{-(x +72)^3} - 72[/tex]
Similarly;
[tex]h(x) = -(x +72)^3[/tex]
Replace x with g(x)
[tex]h(g(x)) = -(g(x) +72)^3[/tex]
Substitute value for g(x)
[tex]h(g(x)) = -(3\sqrt x - 72 +72)^3[/tex]
Recall that:
[tex]g(h(x)) = h(g(x))[/tex]
So:
[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]
Its c
explanation:
on edge
give that 1/x+2/y=1/2, express y in terms of x and 2
9514 1404 393
Answer:
y = 4x/(x -2)
Step-by-step explanation:
Subtract 1/x
2/y = 1/2 -1/x
Combine terms
2/y = (x-2)/(2x)
Cross multiply
4x = y(x -2)
Divide by the coefficient of y
y = 4x/(x -2) . . . . simplest
y = 2^2/(x -2) . . . . in terms of x and 2
