Answer:
If one buoy is placed 120 feet away from the left shore, then the distance of the second buoy from the left shore = 480
Step-by-step explanation:
Given that:
The absolute value function:
[tex]d(h) = \dfrac{1}{6}|h - 300| - 50[/tex]
To calculate the position of the buoy where the river bottom is 20 feet below the surface, we equate the absolute value function to the negative value of 20 feet and then solve it for h.
d(h) = -20
[tex]d(h) = \dfrac{1}{6}|h - 300| - 50 = -20[/tex]
Let us add the sum of 50 on both sides, then:
[tex]= \dfrac{1}{6}|h - 300| - 50+50 = -20+50[/tex]
[tex]= \dfrac{1}{6}|h - 300| = 30[/tex]
By multiplying 6 on both sides, we have:
|h - 300| = 30 (6)
|h - 300| = 180
We can attempt the above expression by rewriting it as two equations:
h - 300 = 180 or h - 300 = - 180
Let us add 300 to both sides from the two expressions above:
h - 300 + 300 = 180 + 300 or h - 300 + 300 = -180 + 300
h = 480 or h = 120
Thus, if one buoy is placed 120 feet away from the left shore, then the distance of the second buoy from the left shore = 480
[tex]\mathbf{d(h) = \frac 16|h - 300| - 50}[/tex] is an illustration of an absolute function.
The buoy should be placed at 480 feet from the left shore
The function is given as:
[tex]\mathbf{d(h) = \frac 16|h - 300| - 50}[/tex]
To place a buoy at 20 feet below, means d(h) = -20
So, we have:
[tex]\mathbf{-20 = \frac 16|h - 300| - 50}[/tex]
Add 50 to both sides
[tex]\mathbf{30 = \frac 16|h - 300|}[/tex]
Multiply both sides by 6
[tex]\mathbf{180 = |h - 300|}[/tex]
Remove absolute bracket
[tex]\mathbf{h - 300 = -180}\ or\ \mathbf{h - 300 = 180}[/tex]
Make h the subject
[tex]\mathbf{h = 300-180}\ or\ \mathbf{h = 300+180}[/tex]
[tex]\mathbf{h = 120}\ or\ \mathbf{h = 480}[/tex]
This means that, the buoy should be placed at 480 feet from the left shore
Read more about absolute functions at:
https://brainly.com/question/1389494
The function is f(x)=x^2+7x-8
Need immediately
Rewarding 100 points !!!!
Answer: Vertex is (-7/2, -81/4)
Axis of synmentary is x= -7/2
Directrix is y= -41/2
Step-by-step explanation:
Its on google
This homework is really confusing me. PLEASE HELP SOON. i also haven't been able to understand this topic that well so if someone could explain some stuff that would be good
I've been having some problems too
:/
Which of the following represents the graph and y-intercept of the function 3x + y = -2?
Please help with this question ASAP I will give brainliest !!!
Answer:
(2).
Step-by-step explanation:
We have the expression:
[tex]\displaystye{\ln(\displaystyle{\frac{\sqrt{e}}{y^3})}[/tex]
First, we can use the difference property of logarithms:
[tex]\ln(x/y)=\ln(x)-\ln(y)[/tex]
Hence, this is equivalent to:
[tex]=\ln(\sqrt{e})-\ln(y^3)[/tex]
We can rewrite the left as:
[tex]=\ln(e^\frac{1}{2})-\ln(y^3)[/tex]
Now, we can use the power property:
[tex]\ln(a^b)=b\ln(a)[/tex]
Essentially, we move the exponent to the front.
Hence, this yields:
[tex]=\frac{1}{2}\ln(e)-3\ln(y)[/tex]
The natural log of e is simply 1. Hence:
[tex]=\frac{1}{2}-3\ln(y)[/tex]
Combine fractions:
[tex]\displaystyle{=\frac{1}{2}-\frac{6\ln(y)}{2} \\ =\frac{1-6\ln(y)}{2}}[/tex]
Hence, our answer is (2).
4(3xy^4)^3/(2x^3y^5)^4
Answer:
[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]
Step-by-step explanation:
Given the expression
[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]
solving the expression
[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=4\cdot \:\frac{\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]
[tex]=4\:\frac{27x^3y^{12}}{16x^{12}y^{20}}[/tex]
[tex]=4\cdot \frac{3^3}{2^4x^9y^8}[/tex]
The multiply fractions are defined as
[tex]\:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
so the expression becomes
[tex]=\frac{3^3\cdot \:4}{2^4x^9y^8}[/tex]
[tex]=\frac{3^3\cdot \:2^2}{2^4x^9y^8}[/tex]
[tex]=\frac{3^3}{2^2x^9y^8}[/tex]
Refining
[tex]=\frac{27}{4x^9y^8}[/tex]
Therefore,
[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]
Is the graph linear exponential or neither?
If one angle equals 130 in a triangle and the other equals 96 then what does the angle labelled X equal
Answer:
x = 46
Step-by-step explanation:
This is basic trigonometry, so we can apply this procedure...
- The total sum of all angles in a triangle is 180 (no angle should be more than 180, this is the limit) and we only need to know just one angle labeled as x, this is represented as:
130 + 96 + x = 180
x = 130 + 96 - 180
- Now we just need to obtain x:
x = 130 + 96 - 180
x = 226 - 180
x = 46
Which correctly represents this inequality?
A number times two is less than 20 + 8.
PLS HELP!
Answer:
solving the inequality we get [tex]x < 14[/tex]
Step-by-step explanation:
We need to solve the inequality A number times two is less than 20 + 8
Let the number be x
The inequality will be:
2x < 20+8
Now solving the inequality to find the value of x
[tex]2x < 20+8\\2x < 28\\x<\frac{28}{2}\\x<14[/tex]
So, solving the inequality we get [tex]x < 14[/tex]
In figure a I am attaching the number line for solution.
In figure b I am attaching the graph for solution.
Drag the tiles to the correct boxes to complete the pairs. Match each population trend to a contributing factor. government-sponsored family control programs agricultural economies medical advancements Industrial Revolution high birthrate arrowRight low death rate arrowRight increase in food supply arrowRight low birthrate arrowRight Reset Next
Answer:
Matching the population trend to a contributing factor:
Contributing Factors Population Trends
government-sponsored family control programs Low birth rate
agricultural economies increase in food supply
medical advancements low death rate
Industrial Revolution high birth rate
Step-by-step explanation:
a) Contributing factors are some negative or positive factors that influence or cause a single event or chain of events that result to the incident.
b) Defining population trends:
1) High birth rate: the industrial revolution triggered high birth rate, following increased food supply and medical advancements.
2) Low death rate: medical advancements brought about low death rate as better healthcare is provided to the sick.
3) Increase in food supply: large-scale agricultural economies ensured increasing food production and supply.
4) Low birth rate: when governments started sponsoring family control programs, the resulting effect was low birth rate.
Answer:
The first one is children and adolescents
the second one is adults
the third one is pregnancy
the last one is indivisuals with brittle bones
Step-by-step explanation:
hope this helps :D
Divide. Reduce the answer to lowest terms.
14/3 ÷ 4
Answer:
Work shown below!
Step-by-step explanation:
[tex]\frac{14}{3}[/tex] ÷ [tex]\frac{4}{1}[/tex] = [tex]\frac{14}{3}*\frac{1}{4} = \frac{14}{12}=\frac{7}{6}[/tex]
Answer:
the correct answer is 1 1/6
I WILL GIVE BRAINLIEST! Parallelogram WXYZ has vertices W(-5, 3), X(-2, 0), Y(-4, -2), and Z(-7, 1), as shown in the graph below.
Which statement about parallelogram WXYZ is true?
A. Since two adjacent sides are congruent and have slopes that are negative reciprocals, WXYZ is a square.
B. Since two adjacent sides are not congruent, WXYZ is not a rhombus.
C. Since two adjacent sides have slopes that are negative reciprocals, WXYZ is a rectangle.
D. Since two adjacent sides have slopes that are not negative reciprocals, WXYZ is not a rectangle.
Answer:
d
Step-by-step explanation:
Please help will mark brainliest
Answer: The awnser is B
Step-by-step explanation: ive went over the problem and checked
5x+4=x+44 solve for x
Answer:
x=10
Step-by-step explanation:
hope this helps
5x = x + 44 - 4
5x = x + 40
5x - x = 40
4x=40
x=40/4
x = 10
If f(x) =x 2 + 10, what is f (-5)?
Answer:
f(-5) = 35
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = x² + 10
f(-5) is x = -5
Step 2: Evaluate
Substitute: f(-5) = (-5)² + 10Exponents: f(-5) = 25 + 10Add: f(-5) = 35What's the gcf of 47 and 17
Answer:
The GCF of 47 and 17 is 1
Step-by-step explanation:
What is the slope of the line that
passes through these two points?
(-3, 2)
(4, 2)
Remember, Slope
rise (y2-yı)
run (x2-x1)
Simplify your answer completely.
Answer:
The line has a slope of zero which means the line is a horizontal line.
Step-by-step explanation:
Given that:
The two points are (-3,2) and (4,2)
Slope of a line is given by the formula,
[tex]m = \frac{Rise}{Run} = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Here,
[tex]x_{1}=-3,\ y_{1}=2\\x_{2}=4,\ y_{2}=2[/tex]
Putting these values in formula;
[tex]m=\frac{2-2}{4-(-3)} \\m = \frac{0}{4+3}\\m = \frac{0}{7} = 0[/tex]
Hence,
The line has a slope of zero which means the line is a horizontal line.
(24-2)180 whats the answer?
Answer:
3960 is the answer
Step-by-step explanation:
Answer:
3960
Step-by-step explanation:
...........................
...........................
answer is 3960
what is the vertex of the parabola using this equation y=-x^2+4x+5
Answer:
(2, 9)Step-by-step explanation:
[tex]y=-x^2+4x+5\quad \implies\quad a=-1\,,\ b=4\,,\ c=5\\\\h=\dfrac{-b}{2a}=\dfrac{-4}{2(-1)}=2\\\\k=c-\dfrac{b^2}{4a}=5-\dfrac{4^2}{4(-1)}=5-\dfrac{16}{-4}=5+4=9[/tex]
Or by completing the square:
[tex]y=-x^2+4x+5\\\\y=-(x^2-4x)+5\\\\y=-(\underline{x^2-2\cdot x\cdot 2+2^2}-2^2)+5\\\\y=-\left((x-2)^2-4\right)+5\\\\y=-(x-2)^2+4+5\\\\y=-(x-2)^2+9\quad\implies\quad h=2\,,\ k=9[/tex]
find the lump sum that must be deposited today to have a future value of $25,000 in 9 years if the funds carn 8%, compounded annually. Use the table of values below.
Answer:
The lum sum that must be deposited today is $12,506.25 to have a future value of $25,000 in 9 years if the funds carn 8%, compounded annually.
Step-by-step explanation:
We are given:
Future value (A)=$25,000
Rate r =8% (0.08%)
Time t = 9
Compounded Annually n =1
We need to find:
Principal Amount (P) = ?
The formula used will be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values and finding Principal Amount (P)
[tex]A=P(1+\frac{r}{n})^{nt}\\25000=P(1+\frac{0.08}{1})^{9*1} \\25000=P(1+0.08)^{9} \\25000=P(1.08)^{9} \\25000=P(1+0.08)^{9} \\25000=P(1.9990)\\P=\frac{25000}{1.9990}\\\mathbf{P=12506.25 }[/tex]
So, The lum sum that must be deposited today is $12,506.25 to have a future value of $25,000 in 9 years if the funds carn 8%, compounded annually.
evaluate when a=15:2(a-5)+2
Answer:
22
Step-by-step explanation:
if a=15
then, 2(a-5)+2= 2(15-5)+2 = 2(10)+2= 20+2=22
Can someone please help me with this? I keep getting half of the answer and I'm doing everything right. ------------------------- The perimeter of any triangle is the sum of the lengths its sides. The lengths of the sides of a certain triangle, in feet, are consecutive even integers. The perimeter of this triangle is between 10 feet and 24 feet inclusive. a. Using one variable, write three expressions that represent the lengths of the three sides of the triangle. b. Write a compound inequality to model this problem. c. Solve the inequality. List all possible lengths for the longest side of the triangle. ------------------------- This is what I have so far... (please tell me what I did wrong as well) ------------------------- 10 ≤ x+(x+2)+(x+4) ≤ 24 ------------------------- 10 ≤ 3x+6 ≤ 24 -------------------------4 ≤ 3x ≤ 18 ------------------------- 4/3 ≤ x ≤ 6
9514 1404 393
Answer:
a. x, x+2, x+4
b. 10 ≤ 3x+6 ≤ 24
c. 6 ft, 8 ft, or 10 ft
Step-by-step explanation:
Given:
The lengths of the sides of a certain triangle, in feet, are consecutive even integers.The perimeter of this triangle is between 10 feet and 24 feet inclusive.Find:
a. Using one variable, write three expressions that represent the lengths of the three sides of the triangle.
b. Write a compound inequality to model this problem.
c. Solve the inequality. List all possible lengths for the longest side of the triangle.
Solution:
You have let x represent the shortest side. (Note that the question asks for the length of the longest side.)
a. The expressions for side lengths can be x, x+2, x+4 when x is the shortest side.
__
b. Here is the compound inequality
10 ≤ x+(x+2)+(x+4) ≤ 24
__
c. Here is the solution
10 ≤ 3x+6 ≤ 24 . . . . collect terms
4 ≤ 3x ≤ 18 . . . . . . . subtract 6
4/3 ≤ x ≤ 6 . . . . . . . . divide by 3
Your working is correct, but incomplete. The values of interest are the even integers x+4.
5 1/3 ≤ x+4 ≤ 10
The longest side may be 6 ft, 8 ft, or 10 ft.
Rob loves to snowboard in the winter, so he is looking at the cost of ski lift tickets for different mountains. Peak Point is selling 5-day packs for $275.60. Grand Mountain is selling 3-day packs for $174.75. Which mountain offers the better deal?
Answer: Peak Point offers the better deal.
Step-by-step explanation:
To find which has the best price, we need to know the cost for one day at each mountain. To do this, we would divide the cost of each pack by the number of days it pays for, so
$275.60/5 days
and $174.75/3 days.
Peak Point costs $55.12 per day while Grand mountain costs $58.25 for each day. This shows that Peak Point clearly has the better deal, costing $3.13 less for every day included in the pack.
Help!!! I need the answer!!
Answer:
Step-by-step explanation:
3/4a>-16=
a >- 64/3 or -21 1/3
In the first week of July, a record 1,060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week,140 more people went to the pool than in the second week. In the fourth week, 146 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
there was a total of 954 people at the pool
Step-by-step explanation:
Answer: 246
Step-by-step explanation:
Steven has 10 1/4 pages of homework. If he finishes 2 1/2 pages every ten minutes, how many pages will Steven have left after 10 minutes?
A. He has completed all pages of homework.
B. 12 3/4 pages
C. 7 3/4 pages
D. 2 1/2 pages
Answer: 7 3/4
Step-by-step explanation:
From the question, we are informed that Steven has 10 1/4 pages of homework and that he finishes 2 1/2 pages every ten minutes.
The number of pages that Steven will have left after 10 minutes will be:
= 10 1/4 - 2 1/2
= 7 3/4
He'll have 7 3/4 pages left
If f(y) = 2y - 2/5,
what is f(f^-1(1024))?
Answer:
-0.399
Step-by-step explanation:
f^-1(1024)=(2*1024-2/5)^-1= 0.000488
f(0.000488)=2*0.000488-2/5= -0.399
Please help me out with this question please...
Answer: B) No, every x-value does not have exactly one y-value
Explanation:
We have the input x = 3 map to the outputs y = 2 and y = 8 at the same time. A function is only possible if any given x value goes to exactly one y value.
Put another way, if x repeats itself, then we don't have a function. This assumes we don't repeat the same y value when we repeat the x value.
Please help!!! will give crown
Answer:
Mixed number: 6 1/100
Improper Fraction: 601/100
Step-by-step explanation:
Hope this helps!
Answer:
Mixed number: [tex]6\frac{1}{100}[/tex]
Improper fraction: [tex]\frac{601}{100}[/tex]
Step-by-step explanation:
A mixed number is a fraction that contains an integer and fraction part. An improper fraction is a fraction where the numerator is larger than the denominator.
[tex]6.01[/tex] can be written in the from [tex]\frac{601}{100}[/tex]. This is an improper fraction since the numerator is greater than the denominator.
The mixed number is [tex]6\frac{1}{100}[/tex] since [tex]100[/tex] goes into [tex]601[/tex] six full times with [tex]1[/tex] as the remainder.
Hope this helps :)
Match each explicit formula to its corresponding recursive formula.
Answer:
See attached
Step-by-step explanation:
The answer is in below picture
Which is the answer???