Please help!!!
Find the area of the following figure: (Use π = 3.14 and do NOT include units in your answer.)
Answers
The composite shape's area is 61.12.
Step-by-step explanation:
Step 1; To calculate the value of the composite shapes area we first divide it into shapes whose areas we know. In this case, the composite shape consists of only a circle's half and a triangle attached below it. If we can sum the individual areas of the two shapes we should be able to determine the area of the unknown shape.
Step 2; The triangle has a base length of 8 as it is from (6, 10) to (14, 10) so 14 - 6 = 8 and the height is from (10,10) and (10,1) so the height is 10 -1 = 9. So the area of any given triangle is 0.5 times the product of its base length and height. So area of this triangle = 0.5 × 8 × 9 = 36. The circle is not an entire one but only half so we calculate the entire circle's area and then half it to find its area. The diameter is 8 as the circle's ends are at (6, 10) and (14, 10) and radius = 14 - 6 / 2 = 4. The area of any circle is π times the square of its radius. So area of this circle = π × r²/2= 3.14 × 4²/ 2 = 25.12.
Step 3; Now we calculate the given composite shapes area by summing the two areas i.e areas of the half-circle and the rectangle.
Area of the composite shape = 36 + 25.12 = 61.12.
Related Questions
Which equation describes a linear function? a) y = 3x + 5, b) y = -x^2 -5 , c) y = 3/x, d) y = x^3
Answers
Answer:
A Linear function is an equation whose graph is a straight line. It has the following form; y = a + bx.
A linear function contains one independent variable and one dependent variable. X is the independent variable and y is the dependent variable.
The answer is a) y = 3x + 5
3x1+5= 8
3x2+5= 11
I think A is a linear funtion because everytime getting added 3
Im sorry if im wrong
Mona and Shakira play on a basketball team. In one game, Shakira scored twice as many points as Mona. Together they scored 24 points in that game. How many points did each girl score?
Answers
Answer:
Mona = 8, Shakira = 16
Step-by-step explanation:
S = 2m....m = S/2
2S + S = 24
3S = 24
S = 24/3
S = 8
Mona = 8
Shakira = 16
A group of 86 people consist of men women and children. There are twice as many women then there are men. There are 6 more children than there are women. How many men women and children in group
Answers
Answer: 16 men
32 women
38 children
Step-by-step explanation:
Let x represent the number of men in the group.
Let y represent the number if women in the group.
Let z represent the number of children in the group.
A group of 86 people consist of men women and children. This means that
x + y + z = 86 - - - - - - - - - - - - 1
There are twice as many women than there are men. It means that
x = y/2
There are 6 more children than there are women. This means that
z = y + 6
Substituting x = y/2 and z = y + 6 into equation 1, it becomes
y/2 + y + y + 6 = 86
multiplying through by 2, it becomes
y + 2y + 2y + 12 = 172
5y = 172 - 12 = 160
y = 160/5 = 32
x = y/2 = 32/2
x = 16
z = y + 6 = 32 + 6
z = 38
There are 16 men, 32 women, and 38 children in the group.
Explanation:Let the number of men be M, the number of women be W, and the number of children be C.
From the given information, we have the following equations:
W = 2M (Twice as many women as men)
C = W + 6 (6 more children than women)
The total number of people is given as 86:
M + W + C = 86
Substituting the values of W and C in terms of M into the third equation, we have:
M + 2M + (2M + 6) = 86
5M + 6 = 86
5M = 80
M = 16
Substituting the value of M in the first equation, we have:
W = 2(16) = 32
Finally, substituting the value of W in the second equation, we have:
C = 32 + 6 = 38
Therefore, there are 16 men, 32 women, and 38 children in the group.
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A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?
Answers
What is the near or exact matching of the left and right sides of a three-dimensional for or a two-dimensional composition?
Answers
Answer:
Im pretty sure it is symmetrical-balance
Step-by-step explanation:
Answer:
symmetrical-balance.
Step-by-step explanation:
In design, the near or exact matching of left and right sides of a three-dimensional form or a two-dimensional composition.
Let us first concentrate on the central value. take f0 = n and 0 = . find the central value of fx, in n
Answers
Answer:
Fx=N177.007
Step-by-step explanation:
Let us first concentrate on the central value. Take F0 = 325 and theta 0 = 57 degrees. Find the central value of Fx, in N
can be pu as thus from an online resource
To resolve forces into the horizontal component , we have
Fx=fCosФ
Fx=325Cos57
Fx=N177.007
Take Note that a force is that which tends to change a body's state of rest or uniform motion in a straight line.
Estimate the solution to the graph shown below.
5,-3)
(4,-3)
(-3,4)
Solve the following linear system any way you like.
x+ y= 4
x - y= 2
(2, 0)
(2, 4)
No solution
(0, 6)
(0, 4)
(-6,0)
Answers
Answer:
The answer to your question is 1.- (-3, 4) 2.- (3, 1) None of the choices
Step-by-step explanation:
1.- The solution of a system of equation by the graph method is the point in which the lines cross. In this graph we observe that this point is approximately
(-3, 4).
2.-
Equation 1 x + y = 4
Equation 2 x - y = 2
Solve by the combination method
x + y = 4
x - y = 2
2x 0 = 6
2x = 6
Solve for x
x = 6/2
x = 3
Substitute x in equation 1 to find y
3 + y = 4
Solve for y
y = 4 - 3
y = 1
Solution (3, 1)
How many positive integers $n$ with $n\le 500$ have square roots that can be expressed in the form $a\sqrt{b}$ where $a$ and $b$ are integers with $a\ge 10$?
Answers
Answer:
23
Step-by-step explanation:
We take a methodical approach by considering the different possible values of b when asqrtb is the simplest form of sqrtn.
Case 1: b=1. We can't forget the perfect squares! If n=100, for example, then sqrt100 can be written as 10sqrt1. So, we must include the perfect squares from 10^2=100 up through 22^2 = 484. (All greater squares are greater than 500.) There are 13 such squares.
Case 2: b=2. If b=2, then we have asqrtb = asqrt2 = sqrta^2 x sqrt2 = sqrt2a^2. We still must have a {>_} 10, but now we need 2a^2 to be no greater than 500. This means that a^2 must be no greater than 250, so a can be 10, 11, 12, 13, 14, or 15. There are 6 such values.
Case 3: b=3. We then have asqrtb = asqrt3 = sqrt3a^2. Since 3a^2 {<_} 500, we know that a^2 is less than 167. We still need a {>_} 10, so there are only 3 values of a in this case: 10, 11, 12.
We skip b=4 because then asqrtb would not be in simplest form.
Case 4: b=5. We then have asqrtb = sqrt5a^2, and a=10 is the only possible value for this case.
For any greater value of b, the resulting value of n is greater than 500 when a {>_} 10. So, there are no more possible numbers asqrtb that satisfy the problem. Since each of the 13+6+3+1 = 23 possibilities listed above represent different simplified forms, they give us 23 different possible values of n that satisfy the problem.
There are infinitely many positive integers less than 500 that have square roots in the form of a√b, where a and b are integers with a≥10.
The number of such positive integers n is infinite, as there is no finite value for the count.
Here,
We are looking for positive integers n that are less than 500.
The square roots of these integers can be expressed in the form a√b.
And [tex]a\ge 10[/tex]
To find the number of positive integers less than 500 that have square roots in the form of a√b,
Analyze the possible values of a and b separately:
For a,
We know that it must be an integer greater than or equal to 1. So,
We have a total of a = 10, 11, 12 ..., and so on. (since a ≥ 10)
As for b,
it can be any perfect square less than or equal to 500.
Let's list a few examples:
b = 1, since 1√1 = 1
b = 4, since 1√4 = 2
b = 9, since 1√9 = 3
b = 16, since 1√16 = 4
...
b = 484, since 1√484 = 22
Now, we can count the number of possibilities for a and b.
We have an infinite number of possibilities for a, but b has a finite number of perfect squares less than or equal to 500.
There are 22 perfect squares within this range.
Therefore, the total number of positive integers n, with n < 500, that have square roots in the form of a√b is 22 x infinity = infinity.
Since there are infinitely many possible values for n,
Hence,
We can conclude that there is no finite value for the number of positive integers n that satisfies this condition.
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Rebecca is three years younger than twice Anthony's age. Write an expression that represents the relationship of Rebecca's age in terms of Anthony's age.
Answers
Answer:
X=2y-3
Step-by-step explanation:
Let Rebecca's age be x
Let Anthony's age be y
Twice Anthony =2y
Rebecca's age (x) to be 3 years younger than twice Anthony's =2y-3
So, it's x=2y-3
Three fair dice are rolled, one red, one green and one blue. What is the probability that the upturned faces of the three dice are all of different numbers?
Answers
Answer: [tex]\dfrac{5}{9}[/tex]
Step-by-step explanation:
When we throw a die , Total outcomes =6
When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]
Given : Three fair dice are rolled, one red, one green and one blue.
Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed
By Permutations , the number of favorable outcomes = [tex]^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120[/tex]
The probability that the upturned faces of the three dice are all of different numbers = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{120}{216}=\dfrac{5}{9}[/tex]
The probability that the upturned faces of the three dice are all of different numbers is [tex]\dfrac{5}{9}[/tex] .
Triangle MNO is an equilateral triangle with sides measuring 16 StartRoot 3 EndRoot units. Triangle M N O is an equilateral triangle with sides measuring 16 StartRoot 3 EndRoot units. A perpendicular bisector is drawn from point N to point R on side M O splitting side M O into 2 equal parts. What is the height of the triangle? 12 units 24 units 36 units 72 units
Answers
Answer:
The correct option is second one i.e 24 units.
Therefore the height of the triangle is
[tex]NR=24\ units[/tex]
Step-by-step explanation:
Given:
An equilateral triangle has all sides equal.
ΔMNO is an Equilateral Triangle with sides measuring,
[tex]NM = MO = ON =16\sqrt{3}[/tex]
NR is perpendicular bisector to MO such that
[tex]MR=RO=\dfrac{MO}{2}=\dfrac{16\sqrt{3}}{2}=8\sqrt{3}[/tex] .NR ⊥ Bisector.
To Find:
Height of the triangle = NR = ?
Solution :
Now we have a right angled triangle NRM at ∠R =90°,
So by applying Pythagoras theorem we get
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Substituting the values we get
[tex](MN)^{2} = (MR)^{2}+(NR)^{2}\\\\(16\sqrt{3})^{2}=(8\sqrt{3})^{2}+(NR)^{2}\\\\(NR)^{2}=768-192=576\\Square\ rooting\ we\ get\\NR=\sqrt{576}=24\ units[/tex]
Therefore the height of the triangle is
[tex]NR=24\ units[/tex]
Answer:
b 24
Step-by-step explanation:
The current global human population is about 6.1 billion and is growing at an annual rate of 1.35 percent. If world population were to grow at this rate for the next year, approximately how many people would be added?
Answers
Answer:
Step-by-step explanation:
The current global population is growing at an annual rate of 1.35 percent. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 6.1 × 10^9
r = 1.35% = 1.35/100 = 0.0135
t = 1
Therefore
A = 6.1 × 10^9(1 + 0.0135)^1
A = 6.1 × 10^9(1.0135)^1
A = 6182350000
The number of people that would be added is
6182350000 - 6100000000
= 82350000
If the world population were to keep growing at 1.35%, we number of people who would be added next year is 82,350,000 people.
The population of the world is growing at 1.35%. This means that next year, the number of people added will be 1.35% of the current population.
The current population is 6.1 billion so the number of people who will be added is:
= Population x Incremental rate
= 6,100,000,000 x 1.35%
= 82,350,000 people
In conclusion, 82,350,000 people will be added.
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The RideEm Bicycles factory can produce 100 bicycles in a day at a total cost of $10,500. It can produce 120 bicycles in a day at a total cost of $11,000. What are the company's daily fixed costs, and what is the marginal cost per bicycle?
Answers
Answer:
The company's daily fixed cost=$8000
The marginal cost per cycle=Slope=$ 25
Step-by-step explanation:
We are given that
Factory produces bicycle in a day=[tex]x_1=[/tex]100
Total cost,[tex]y_1=[/tex]$10,500
Factory produces bicycles in a day,[tex]x_2[/tex]=120
Total cost=[tex]y_2=[/tex]$11,000
There are two points (100,10500) and (120,11000)
Slope =[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the formula
[tex]m=\frac{11000-10500}{120-100}=\frac{500}{20}=25[/tex]
Slope-intercept form
[tex]y=mx+c[/tex]
Where m=Slope of line
c=y-intercept
Substitute the values
[tex]10500=25(100)+c[/tex]
[tex]10500=2500+c[/tex]
[tex]c=10500-2500=8000[/tex]
y-intercept=8000
Substitute the values in the equation
[tex]y=25x+8000[/tex]
Therefore, company's daily fixed cost=$8000
The marginal cost per cycle=Slope=$ 25
BRAINLIEST !! Pls at least take a look , answer all or don't answer
Answers
Answer:
1) 706.86
2) 726 cm^3
3) V= 792 km^3
4) 209.4 ft^3
Step-by-step explanation:
#4: V=πr2h
3.14 times the radius, then the height divided by 3
#3 V=lwh
V=lwh3 length times width times height divided by 3
#2 ^same as #3 steps
#1 A=πr2
pi times the radius squared
Answer:
1. 706.5
2. 726
3. 396
4. 130.8
Step-by-step explanation:
1. Area = pi × r²
= 3.14 × 15²
= 706.5 ft²
2. Volume = ⅓ × base area × height
= ⅓ × 11² × 18
= 726 cm³
3. Volume = ⅓ × base area × height
= ⅓ × ½ × 9 × 12 × 22
= 396 km³
4. radius = 10/2 = 5
Volume = ⅓ × base area × height
= ⅓ × 3.14 × 5² × 5
= 130.83333 ft³
PLZ HURRY IT'S URGENT!!
What is the ratio of m to n in simplest form given 10m = 5n?
2/5
1/2
2/1
10/1
Answers
Answer:
1/2.
Step-by-step explanation:
10m = 5n
m = 5n/10
m = n/2
m/n = n/2 * 1/n
m/n = 1/2.
Answer:1/2
Step-by-step explanation:
10m=5n
Divide both sides by 5n
10m/5n=5n/5n
2m/n=1
Therefore m/n=1/2
Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this information, what interval of prices would we expect at least 89% of new car prices to fall within?
Answers
Answer:
($13,300,$46,900)
Step-by-step explanation:
We are given the following in he question:
Mean, μ = $30,100
Standard Deviation, σ = $5,600
Chebyshev's Theorem:
According to theorem atleast [tex]1 - \dfrac{1}{k^2}[/tex] percent of data lies within 2 standard deviations of mean.For k = 3,[tex]1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%[/tex]
Thus, 89% of data lies within three standard deviation of mean.
[tex]\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900[/tex]
Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)
In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon. How much cinnamon does the spice mix contain per pound? A. 5/8 B. 9/10 C. 1 1/9 D. 1 3/5
Answers
Answer:
option C
Step-by-step explanation:
In 3/4 pound of a spice mix, there is 5/6 cup of cinnamon
The ration of spice mix over Cinnamon is
[tex]\frac{\frac{3}{4} }{\frac{5}{6} } =\frac{3}{4} \cdot \frac{6}{5} =\frac{9}{10}[/tex]
Let x be the spice mix per pound
make a proportion
[tex]\frac{9}{10} =\frac{1}{x}[/tex]
cross multiply
[tex]9x=10\\x=\frac{10}{9}\\x= 1 \frac{1}{9}[/tex]
option C is the answer
A triangle has sides with lengths a,b,and c.The longest side is b.Write An Equation or inequality that shows the relationships of the lengths of the three sides
Answers
the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
In a right triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. So, we have:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
This equation represents the relationship among the side lengths of a right triangle.
Therefore, the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
This completes the three relations among a, b, andc.
The complete Question is given below:
A right triangle has side lengths of a,b , and c units. The longest side has a length of c units. Complete each equation show three relations among a,b , and c .
Type the answers in the boxes below.
c^(2)= _____
a^(2)= _____
b^(2)= _____
You are designing a wall Mural that will be composed of squares of different sizes. One of the requirements of your design is that the side length of each square itself is a perfect square. If you represent the side length of the square as x to the power of 2 write an expression for the area of the mural square.
Answers
Answer:
1. Area of a square = (x^2)^2 = x^4
(each side is x^2, area of a square = side^2
so (x^2)(x^2) = x^4 )
2. when x = 5
area = 5^4 = 625
3. when x = 10
area = 10^4 = 10000
Step-by-step explanation:
Hope its right!
Final answer:
The area of a square mural where the side length is a perfect square, represented as x², can be expressed as A = x⁴, which simplifies the concept of multiplying the side length by itself twice.
Explanation:
The area of a mural square, where the side length is a perfect square represented as x to the power of 2 (x²), is calculated by squaring the side length. Therefore, if x itself is a perfect square, the area A of the square mural is given by A = x² * x², which simplifies to A = x⁴. Since the side length is a perfect square, x could be expressed as y² where y is an integer, resulting in the area being y⁴, where y⁴ represents the side length squared twice.
19 in2 17 in2 12 in2 22 in2
Answers
Answer:22in2
Step-by-step explanation:
suppose the model boat were traveling at a rate of 4 feet per second. How long would it take the model boat to get from the edge of the pond to the center
Answers
Answer:
[tex]25\ seconds[/tex]
Step-by-step explanation:
Hi,
Time, speed and distance are related by a very simple formula:
[tex]Distance = Time \times Speed[/tex]
Which can easily be used here to solve the question.
To find the time, we require:
Speed:
This is given in the question as 4 ft/ sec.
Distance:
On a circle, the distance from the end of the circle to the centre is referred to as "Radius". We shall assume the radius here is [tex]r[/tex].
To calculate the radius, we can use the formula of the circumference: [tex]C = 2 \pi r[/tex]
Were are given that C = 628 feet.
Using the formula: [tex]r = \frac{628}{2 \pi} = 100\ feet[/tex]
The distance the boat needs to travel is 100 feet.
Time:
To calculate time, we alter the provided formula to: [tex]Time = \frac{Distance}{Speed}[/tex]
Substituting the values in this: [tex]Time = \frac{r}{4}[/tex]
[tex]Time = \frac{100}{4} = 25\ seconds[/tex]
The boat requires 25 seconds to travel from the edge of the pond to centre.
Leah had 50 stickers. Leah gave 1/2 of the stickers to her sister. Of the amount left, she gave 2/5 to her friend.How many does Leah have left for herself?
Answers
Answer: Leah has 15 stickers left for herself.
Step-by-step explanation:
Total number of stickers that Leah had initially is 50. Leah gave 1/2 of the stickers to her sister. This means that the number of stickers that Leah gave to her sister is
1/2 × 50 = 25 stickers
Of the amount left, she gave 2/5 to her friend. This means that the number of stickers that Leah gave to her friend is
2/5 × 25 = 10 stickers
Therefore, the number of stickers that Leah have left for herself is
50 - (25 + 15)
= 50 - 35
= 15
After giving away some of her stickers to her sister and friend, Leah has 15 stickers left for herself.
Explanation:Leah initially had 50 stickers. She gave half of them to her sister, which left her with 50/2 = 25 stickers. Then, she gave away 2/5 of these remaining stickers to her friend.
To calculate how many she gave her friend, we multiply 25 * 2/5 = 10 stickers.
To find out how many Leah has left for herself, we subtract this from the number she had after giving stickers to her sister: 25 - 10 = 15 stickers.
So, Leah has 15 stickers left for herself.
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Which 2 statements are correct regarding reconciling a bank account in QuickBooks Online? (Select all that apply) You can only undo a bank reconciliation via a link in the Accountant Toolbox To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement Reconciliations must only be run at period end to estimate tax owed To see the Reconciliation report, select View report after you've successfully reconciled the account
Answers
Answer:
The correct statements are:
To successfully reconcile and run a reconciliation report you need to enter the Statement Ending Date and Ending Balance from the relevant bank statement
To see the Reconciliation report, select View report after you've successfully reconciled the account.
EXPLANATION:
The steps to reconciling a bank account using QuickBooks Online include:
1. Click on the Gear button, then on “Tools” and then “Reconcile.”
2. Click on the drop-down menu under “Accounts” and select the account you want to reconcile.
3. Enter the “Ending balance” and “Ending date” based on your bank statement information.
4. Match transactions to your bank statement and check them off one by one.
5. Apply filters so transactions are easier to find.
6. Keep going until the “Difference” field is zero and you see the Success! page.
7. Select "View Report" from the Report period drop-down arrow to view your reconciliation report.
The two options that are correct regarding bank account reconciliation QuickBooks online are:
To see the Reconciliation report, select View report after you've successfully reconciled the account.What is QuickBooks?
Quickbooks is an Accounting Application that aids in the collection, processing, analyses, and reporting of Accounting and Financial Information for organizations.
It is a tool that is very useful for business owners.
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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠H.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠H = °
Answers
Answer:
Step-by-step explanation:
Triangle GHI is a right angle triangle.
From the given right angle triangle,
HI represents the hypotenuse of the right angle triangle.
With m∠H as the reference angle,
GH represents the adjacent side of the right angle triangle.
GI represents the opposite side of the right angle triangle.
To determine m∠H, we would apply
the Sine trigonometric ratio.
Sine θ = opposite side/hypotenuse. Therefore,
Sin H = 9/10 = 0.9
m∠H = Sin^-1(0.9)
m∠H = 64.2° to the nearest tenth.
The level of a lake in inches is falling linearly . The lake level is 452 inches on Jan 1 and then 378 inches on Jan 21. Find a function to represent the lake level
Answers
Answer:
[tex]y=-\frac{74}{21}x+452[/tex]
Step-by-step explanation:
Given:
The level of a lake is falling linearly.
On Jan 1, the level is 452 inches
On Jan 21, the level is 378 inches.
Now, a linear function can be represented in the form:
[tex]y=mx+b[/tex]
Where, 'm' is the rate of change and 'b' is initial level
[tex]x\to number\ of\ days\ passed\ since\ Jan\ 1[/tex]
[tex]y\to Lake\ level[/tex]
So, let Jan 1 corresponds to the initial level and thus b = 452 in
Now, the rate of change is given as the ratio of the change in level of lake to the number of days passed.
So, from Jan 1 to Jan 21, the days passed is 21.
Change in level = Level on Jan 21 - Level on Jan 1
Change in level = 378 in - 452 in = -74 in
Now, rate of change is given as:
[tex]m=\frac{-74}{21}[/tex]
Hence, the function to represent the lake level is [tex]y=-\frac{74}{21}x+452[/tex]
Where, 'x' is the number of days passed since Jan 1.
Final answer:
The lake level can be represented by a linear function L(t) = -3.7t + 452, where L(t) is the lake level in inches and t is the time in days from January 1st.
Explanation:
To find a function representing the lake level as it drops linearly over time, we need to determine the linear equation that corresponds to the change in the lake level.
We are given that the lake level is 452 inches on January 1st and 378 inches on January 21st.
First, we will define the variables where L(t) is the lake level in inches and t is the time in days with t=0 corresponding to January 1st.
We are given two points on the linear function: (0, 452) and (20, 378), since January 21st is 20 days after January 1st.
Next, we calculate the slope of the line using the formula:
slope = (change in lake level) / (change in time) = (378 - 452) / (20 - 0) = -74 / 20 = -3.7 inches per day.
Now, we can use the slope and a point to write the equation of the lake level as a function of time in the slope-intercept form:
L(t) = mt + b
where m is the slope and b is the y-intercept. Plugging in the slope and the point (0, 452):
L(t) = -3.7t + 452
This equation represents the function of the lake level over time.
Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives. Black olives cost three dollars a pound. Green olives cost five dollars a pound. She spends $15.50. How many pounds of each type of olives does she buy? Write and solve a system of equations. Give the answer to in context of the problem.
Answers
Answer:
She buy 0.5 pounds of black olives and 3.5 pounds of green olives.
Step-by-step explanation:
Given:
Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives.
Black olives cost three dollars a pound. Green olives cost five dollars a pound.
She spends $15.50.
Now, to find the pounds of olives she buy.
Let the pounds of black olives be [tex]x.[/tex]
And the pounds of green olives be [tex]y.[/tex]
So, total pounds of olives:
[tex]x+y=4[/tex]
[tex]x=4-y[/tex] ........( 1 )
As, given the cost of black olives $3 a pound.
And cost of green olives $4 a pound.
Now, the total money spends:
[tex]3x+4y=15.50[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]3(4-y)+4y=15.50[/tex]
[tex]12-3y+4y=15.50[/tex]
[tex]12+y=15.50[/tex]
Subtracting both sides by 12 we get:
[tex]y=3.5[/tex]
The green olives = 3.5 pounds.
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=4-y\\x=4-3.5\\x=0.5\ pounds.[/tex]
The black olives = 0.5 pounds.
Therefore, she buy 0.5 pounds of black olives and 3.5 pounds of green olives.
Final answer:
Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party, determined by solving a system of equations representing the total weight and cost of the olives.
Explanation:
How Many Pounds of Black and Green Olives did Susan Buy?
To determine how many pounds of black and green olives Susan bought, we need to create a system of equations based on the information provided:
Let x be the number of pounds of black olives Susan bought, and let y be the number of pounds of green olives.
The first equation will represent the total weight of olives:
1. x + y = 4 (since Susan bought 4 pounds of olives in total)
The second equation will represent the total cost of olives:
2. 3x + 5y = 15.50 (because black olives cost $3 per pound and green olives cost $5 per pound)
Now, let's solve this system of equations:
Multiplying the first equation by 3 gives us a new equation:
3x + 3y = 12
Now, we subtract this new equation from the second equation to find y:
(3x + 5y = 15.50) - (3x + 3y = 12)
2y = 3.50
y = 1.75
So, Susan bought 1.75 pounds of green olives. We can now substitute y into the first equation to find x:
x + 1.75 = 4
x = 4 - 1.75
x = 2.25
Therefore, Susan bought 2.25 pounds of black olives.
In conclusion, Susan bought 2.25 pounds of black olives and 1.75 pounds of green olives for her party.
Find the x- and y-intercepts of 3/5x + 1/3y = 1/15
Answers
Y-intercept: 1/5
You get these by plugging in 0 for the opposite variable you are trying to solve for the intercept.
Answer: X-intercept: 1/9
Y-intercept: 1/5
Step-by-step explanation:
Identify the domain and range of the inverse of f(x) = 0.5^x.
Answers
Answer:
Domain (0, ∞) and Range (-∞, ∞).
Step-by-step explanation:
The domain of f(x) = 0.5^x is all values of x and the range is f(x)>0 as 0.5^x cannot be negative or zero.
In interval form this is Domain is (-∞, ∞) and Range is (0, ∞).
So its inverse has Domain (0, ∞) and Range (-∞, ∞).
The requierd domain (0, ∞) and range (-∞, ∞) of the inverse of f(x) = 0.5ˣ.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The exponential function is given in the question, as follows:
f(x) = 0.5ˣ
Here the domain of f(x) = 0.5ˣ is all values of x and the range is f(x) > 0 as f(x) = 0.5ˣ cannot be negative or zero.
In interval form, the Domain is (-∞, ∞) and the Range is (0, ∞).
As a result, its inverse has Domain (0, ∞) and Range (-∞, ∞)
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If Alex and Brandon work together, they will clean the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself?
Answers
Answer:
I think it is 5 but don't take my word for it
Step-by-step explanation:
I think you minus 20 - 15 which equals to 5 so 20 - 15 = 5 hopefully i was a little helpful just try that if its not correct i'm so sorry i will practice my math and answer this question again thank you for being so understanding
Answer:
Correct answer: Alex can finish the same job in 60 hours
Step-by-step explanation:
The appropriate equation for this situation is:
1/20 + 1/x = 1/15 => (x + 20) / 20x = 1/15 => 15 · (x + 20) = 20x =>
15x + 300 = 20x => 5x = 300 => x = 300/5 = 60 hours
x = 60 hours
God is with you!!!
What is the 6th value in the sequence with the explicit formula an=−2n−14?
Answers
Answer:
-26
Step-by-step explanation:
a(6)=-2(6)-14
a(6)=-12-14
a(6)=-26
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The 6th value in the sequence = an=−2n−14 = -4.3
Take n = 6
⇒ a6 = -2·6 -14 = -12-14 = -26
∴ a= [tex]\frac{-26}{6}[/tex] = -4.3
Explicit formulaThe explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geomrietc, or harmonic sequence.
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