The midpoint is just the average of the coordinates,
M = (1/2) ( (0,2) + (2,8) ) = ((0+2)/2, (2+8)/2) = (1, 5)
Answer: (1,5)
Answer:
(1,5)
Step-by-step explanation:
(0,2) and (2,8)
Midpoint: (0+2)/2, (2+8)/2
2/2, 10/2
(1,5)
a forest ranger in a 140-foot observation tower sees a fire moving in a direct path toward a lake. the angle of depression to the fire is 3° and the angle of depression to the lake is 8°. to the nearest foot, how close is the fire to the lake?
Answer:
1675 ft
Step-by-step explanation:
For us to calculate how close the windmill is to the fire, if we imagine it as a triangle, the distance from watch tower to the fire will be:
tan θ= opposite/adjacent
opposite=140 ft
adjacent = x
θ=3°
Thus;
tan 3 = 140/x
x=140/tan 3
x = 2,671.359 ft
Now, the distance from watch tower to windmill will be:
tan θ=opposite/ adjacent
θ=8°
opposite=140 ft
adjacent=y
thus
tan 8 = 140/y
y = 140/tan8
y=996.15 ft
Now, the distance between fire and wind mill will be:
x - y = 2671.359 - 996.15
x - y = 1675.209 ≈ 1675 ft
Answer:
1675 feet
Step-by-step explanation:
Refer to the image attached for diagrams and better explanations
The population had decreased 300 resident over the past 5 years. The same number of residents left each year.
Answer:
60
Step-by-step explanation:
If the coefficient of determination is a positive value, then the regression equationa.must have a positive slopeb.must have a negative slopec.could have either a positive or a negative sloped.must have a positive y intercept
Answer:
The correct answer is must have a positive slope.
Step-by-step explanation:
The coefficient of determination varies between -1 to 1. It shows the how strong is the relationship between two variables.
Coefficient closer to -1 indicate negative relationship and that y decreases with increase in x and the regression equation has a negative slope.
Coefficient closer to 1 indicate positive relationship and that y increases with increase in x and the regression equation has a positive slope.
Coefficient closer to 0 indicate that there is no possible relationship between the variables under consideration. It is not possible to construct a particular regression equation.
Caleb went into a cave.
The light intensity (in candela per square meter, or \text{cd/sq. m}cd/sq. mstart text, c, d, slash, s, q, point, space, m, end text) as a function of depth inside the cave (in \text{m}mstart text, m, end text) is graphed.
What is the approximate average rate at which the light intensity decreases, as Caleb goes from a depth of 5\text{ m}5 m5, start text, space, m, end text to a depth of 14\text{ m}14 m14, start text, space, m, end text?
graph
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
330\text{ cd/sq. m}330 cd/sq. m330, start text, space, c, d, slash, s, q, point, space, m, end text per \text{m}mstart text, m, end text
(Choice B)
B
360\text{ cd/sq. m}360 cd/sq. m360, start text, space, c, d, slash, s, q, point, space, m, end text per \text{m}mstart text, m, end text
(Choice C)
C
390\text{ cd/sq. m}390 cd/sq. m390, start text, space, c, d, slash, s, q, point, space, m, end text per \text{m}mstart text, m, end text
(Choice D)
D
Answer:
A) 330 cd/sq. M per m
Step-by-step explanation:
To find the average rate at which the light intensity decreases as Caleb goes from a depth of 5m to a depth of 14m inside the cave, we need to calculate the change in light intensity and divide it by the change in depth.
Explanation:To find the average rate at which the light intensity decreases as Caleb goes from a depth of 5m to a depth of 14m, we need to calculate the change in light intensity and divide it by the change in depth.
Let's denote the initial light intensity at 5m as I1 and the final light intensity at 14m as I2. Using the graph, we can estimate the values of I1 and I2.
Then, the average rate of decrease in light intensity is given by:
Average rate = (I2 - I1) / (14m - 5m)
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What’s 68 pt equal to —- qt
Answer:
Around 41 quarts
Step-by-step explanation:
The principal will have to increase the number of eighth grade next year if the seventh grade enrollment exceeds 110% of the current eighth grade enrollment
Answer:
Refer below.
Step-by-step explanation:
The principal will have to increase the number of teachers next year.
We found out that the seventh grade enrollment was 120% of the number of eight graders, which is greater than 110%.
48) A laboratory tested twelve eggs and found that the average amount of cholesterol in each egg was 185 milligrams, with a sample standard deviation of 17.6 mg. Construct a 95% confidence interval for the mean cholesterol content in a typical egg.
Answer:
The C.I. at 95% is 185±9.9583 or C.I.[175 to 195].
Step-by-step explanation:
Given:
Mean =185 mg
Standard deviation=17.6
Total number of samples=12
To Find:
95% of Confidence interval .
Solution:
We know that formula for C.I is given by ,
C.I.=mean±Z[standard deviation/Sqrt(Total no of samples)]
So using all above given values we get ,
Here Zscore at 95% is Z=1.96
So
C.I.=185±1.96[17.6/Sqrt(12)]
=185±1.96[17.6/3.464]
=185±1.965[5.0808]
=185±9.9583
In short C.I. is given as at 95% C.I.[175 to 195].
1. If there is an even number of signs, the
solution is
Final answer:
In mathematics, when an operation involves an even number of signs, the result will be positive. This applies to multiplication and division rules, where similarly signed numbers yield a positive result. Principles of mathematical operations also extend to probabilities, where conditions and the complement of events are crucial to determining event outcomes.
Explanation:
If there is an even number of signs in a mathematical operation, such as multiplication or division, the solution will have a positive sign. This is because multiplying or dividing two positive numbers, or two negative numbers, results in a positive outcome. However, multiplying or dividing numbers with opposite signs results in a negative outcome.
For instance:
When two positive numbers multiply, the answer has a +ve sign, e.g., 2x3 = 6.
When two negative numbers multiply, the answer also has a +ve sign, e.g., (-4) x (-3) = 12.
In probability, events A and B being given conditions, such as event A given B (A GIVEN B) or event B given A (B GIVEN A), can impact the likelihood of those events occurring. The complement of an event (like the complement of A) refers to all outcomes that are not part of the event A.
Principles of Mathematical Operations and Probability
Understanding these principles helps solve many mathematical problems and assess probabilities, especially when working with equations with an unknown squared, which will typically result in two solutions, or when calculating the possibilities of a dice roll in probability exercises.
A "mathematically fair bet" is one in which a gambler bets, say, $100 for a 10 percent chance to win $1,000 ($100 = 0.10 × $1,000). Assuming diminishing marginal utility of dollars, this is not a fair bet in terms of utility because
Answer: the winnings are reduced
Step-by-step explanation:
Given 10 percent chance to win $1,000 for $100. That is
Gain = $900
Assuming diminishing marginal utility of dollars, when the utility of the gain and the money used for bet are considered, it is discovered that the utility of the $100 used to make the bet is greater than the $900 that you might gain if you win the bet.
this is not a fair bet in terms of utility because the winnings are reduced.
A mathematically fair bet does not account for the diminishing marginal utility of money. The expected utility calculated with a utility function might show a different picture, revealing the bet might not be fair in terms of utility. Samuelson's story illustrates statistical independence and that repeated gambles with positive expectations lead to better outcomes.
A "mathematically fair bet" is one where the expected value of the bet is equal to the cost of making the bet. In other words, if you bet $100 for a 10 percent chance to win $1,000, the mathematically calculated expectation would be $100, or 0.10 times $1,000. However, the concept of diminishing marginal utility suggests that the utility or satisfaction derived from each additional dollar decreases as one has more money. Thus, the utility of the potential win cannot simply be calculated by multiplying the probabilities by the monetary outcome.
Under the concept of expected utility, the expected utility of a bet should also be considered. To calculate this, one might use a utility function, like the von Neumann-Morgenstern utility function, to determine the utility of each possible outcome and then finding the average utility. For example, let's assume that the utility function is represented by the square root of the dollar amount (this is just an example, utility functions can take many forms). Hence, the expected utility of winning $1,000 would be the square root of $1,000, not just $1,000.
Paul Samuelson's story illustrates the idea of statistical independence and the law of large numbers, where repeated play of a gamble with positive expectation can lead to more stable and predictable results, as opposed to a single high-risk gamble. This idea reflects human behavior and the role of hope in encouraging smart risk-taking, even when each individual bet may not be favorable in terms of utility.
John's wages, w dollars, for working h hours is modeled by the equation w = 4h. If John has worked for 4 hours, and then he continues to work for another 2 hours, how much does John earn?
Answer:
$24
Step-by-step explanation:
So the total number of hours John has worked after 4 hours plus another 2 hours is h = 4 + 2 = 6 hours.
Given that John's wage is modeled by the equation w = 4h, then his total wage within 6 hours of working is is
w = 4h = 4 * 6 = $24
John earns: [tex]\[\boxed{24}\][/tex] Dollars
To determine how much John earns, we can use the equation provided: w = 4h , where w represents John's wages in dollars and h represents the number of hours worked.
John first worked for 4 hours. Using the wage equation:
[tex]\[w = 4 \times 4 = 16 \text{ dollars}\][/tex]
Next, John continues to work for another 2 hours. The total number of hours he works is now:
[tex]\[4 + 2 = 6 \text{ hours}\][/tex]
Using the wage equation for the total number of hours:
[tex]\[w = 4 \times 6 = 24 \text{ dollars}\][/tex]
Thus, John earns:
[tex]\[\boxed{24}\][/tex] Dollars
1
444 m
What’s the surface area ?
Answer:
The answer to your question is 566 m²
Step-by-step explanation:
Data
length = 19 m
width = 4 m
height = 9 m
Process
1.- Calculate the area of the 6 faces
-Area of the bases
Area = 19 x 4 x 2 = 152 m²
-Area of the lateral faces
Area = 4 x 9 x 2 = 72 m²
-Area of the frontal and the opposite faces
Area = 19 x 9 x 2 = 342 m²
2.- Calculate the total area
Total area = 152 + 72 + 342
= 566 m²
Why were roads important to the military expansion of the Roman Republic?
They provided revenue to help fund the military.
They made it difficult for enemies to attack Rome.
They made it easier to move troops to conflict areas.
They allowed soldiers to work in construction when not fighting.
Answer:
#3
Step-by-step explanation:
Similar to the US highway system Rome realized if they wanted to control their territory they were going to need to be able to squash resistance that wasn't in the immediate area and move resources form place to place easily
Answer:
c
Step-by-step explanation:
i took the test
T.J. is hosting a dinner party. T.J. greets the first guest and they shake hands. The second guest arrives and shakes hands with T.J. and the first guest. The third guest arrives and shakes hands with T.J., the first guest, and the second guest. This pattern continues. How many handshakes have taken place after the ninth guest arrives?
Answer:
45 Handshakes
Step-by-step explanation:
45 Handshakes have taken place all together
Answer:
45
Step-by-step explanation:
What number would you add to both sides of x2 + 7x = 4 to complete the square? 22 72 StartFraction 7 squared Over 2 EndFraction (StartFraction 7 Over 2 EndFraction) squared
Answer:
D on e2020
Step-by-step explanation:
got it right
Answer:
D. (StartFraction 7 Over 2 EndFraction) squared
Step-by-step explanation:
Use 12 cubes to make this square frame that has 4 cubes on each side if she uses 36 cubes to make a square frame how many cubes will be on each side of the frame
Answer:
10 cubes on each side
Step-by-step explanation:
The amount of cubes to make a square frame given was 36
If you start by putting ten cubes on one side then adding nine off of the the end cubes and continue that pattern you end up with 10 cubes on each side.
There will be 6 cubes on each side of the frame.
Explanation:
To understand the relationship between the number of cubes used and the length of the side of the square frame, let's first consider the given example with 12 cubes.
For the smaller frame with 12 cubes, we know that the frame is square and has 4 cubes on each side. This means that the total number of cubes used to make the frame is the perimeter of the square minus the 4 corner cubes, which are counted twice (once for each side they belong to). The perimeter of the smaller square frame is [tex]\(4 \times 4 = 16\)[/tex] cubes, but since we subtract the 4 corner cubes, the total number of cubes needed is [tex]\(16 - 4 = 12\)[/tex] cubes.
Now, we are given that 36 cubes are used to make a larger square frame. Using the same logic, we can find the length of the side of this larger frame. Let \(n\) be the number of cubes on each side of the larger frame. The perimeter of this larger square frame would be [tex]\(4n\)[/tex] , and we would again subtract the 4 corner cubes. Therefore, the equation to find [tex]\(n\)[/tex] is:
[tex]\[4n - 4 = 36\][/tex]
Adding 4 to both sides gives us:
[tex]\[4n = 40\][/tex]
Dividing both sides by 4 gives us:
[tex]\[n = 10\][/tex]
So, there are 10 cubes on each side of the larger frame. However, we need to account for the fact that the frame is hollow, meaning the corner cubes are not present. Since there are 4 corners without cubes, we subtract 1 cube from each side to get the number of cubes actually used for each side:
[tex]\[n - 1 = 10 - 1 = 9\][/tex]
Now, we can calculate the total number of cubes used for the frame with 9 cubes on each side:
[tex]\[4 \times 9 = 36\][/tex]
This confirms that with 9 cubes on each side, we indeed use 36 cubes to make the frame. However, since the question asks for the number of cubes on each side of the frame, we must consider that the 36 cubes include the 4 corner cubes that are counted twice (once for each side). Therefore, we add back the 4 corner cubes to the length of each side:
[tex]\[9 + 1 = 10\][/tex]
Thus, there are 10 cubes on each side of the frame, but since we are considering the outer dimension of the frame (including the corners), we have to add the corner cubes that are shared by two sides. Since there are 4 corners, and each corner contributes 1 cube to 2 sides, we divide by 2 to avoid double counting:
[tex]\[10 + \frac{4}{2} = 10 + 2 = 12\][/tex]
However, this calculation is incorrect because we've already accounted for the corner cubes when we subtracted 4 from the perimeter to get the number of cubes on each side. The correct number of cubes on each side is 9, as calculated previously. Since the question asks for the number of cubes on each side of the frame, not the length of the side including the corners, the correct answer is 9.
Upon reviewing the solution, it is clear that there was an error in the final step. The correct number of cubes on each side of the frame is indeed 9, not 12. Therefore, the final answer should be:
There will be 9 cubes on each side of the frame.
Find the value for each expression where a = 3 and b = 5. Place the expressions in order from least (1) to greatest (5) based on their values. 2a + b2b + a3(a + b)4b − a6a − 2b
To find the value for each expression, substitute a = 3 and b = 5 into the given expressions. The values of the expressions are: 11, 13, 24, 17, 8.
Explanation:To find the value for each expression, we substitute a = 3 and b = 5 into the given expressions. The expressions are:
1. 2a + b: Substituting a = 3 and b = 5, we have 2(3) + 5 = 6 + 5 = 11.
2. 2b + a: Substituting a = 3 and b = 5, we have 2(5) + 3 = 10 + 3 = 13.
3. (a + b)3: Substituting a = 3 and b = 5, we have (3 + 5)3 = 8 × 3 = 24.
4. 4b - a: Substituting a = 3 and b = 5, we have 4(5) - 3 = 20 - 3 = 17.
5. 6a - 2b: Substituting a = 3 and b = 5, we have 6(3) - 2(5) = 18 - 10 = 8.
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Final answer:
After substituting a = 3 and b = 5 into the given expressions, we calculate their values and order them from least to greatest: 6a - 2b = 8, 2a + b = 11, 2b + a = 13, 4b - a = 17, 3(a + b) = 24.
Explanation:
We are given the variables a = 3 and b = 5 and need to find the values of five expressions, then place them in order from least to greatest. Let's calculate each expression step by step:
2a + b = 2×3 + 5 = 6 + 5 = 112b + a = 2×5 + 3 = 10 + 3 = 133(a + b) = 3×(3 + 5) = 3×8 = 244b − a = 4×5 - 3 = 20 - 3 = 176a − 2b = 6×3 - 2×5 = 18 - 10 = 8Now placing them in order from least to greatest, we get:
6a − 2b = 82a + b = 112b + a = 134b − a = 173(a + b) = 24The bicycle wheel shown travels 63 inches in one complete rotation. If the wheel rotates only 120° about the center, how far does it travel?
Answer:
21 inches
Step-by-step explanation:
In 1 rotation the angle at the centre = 360°
For 120° the fraction turned = [tex]\frac{120}{360}[/tex] = [tex]\frac{1}{3}[/tex], thus
distance travelled = [tex]\frac{1}{3}[/tex] × 63 = 21 inches
If the wheel rotates only 120° it travel 21 inches.
How to find distance travel by wheel?The angle at the center of one rotation is 360°.
The fraction for 120° changed[tex]=\frac{120}{360} =\frac{1}{3}[/tex]
Total 63 inches in one complete rotation of a wheel.
Thus distance travelled[tex]=\frac{1}{3}\times 63= 21[/tex]
The wheel travel on the bicycle is 21 inches.
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The table shows the gallons of water in a pool over time.
Choose the term that describes the slope of the line of
a graph representing the data in the table.
The slope of a line graphed to represent the volume of
water in a pool over time would be described as
Time (min)
Water in Pool (gal)
UNAWN -
ITA
INION
undefined
zero
positive
negative
Done
Intro
Answer:
The slope of a line graphed to represent the volume of water in the pool can be described as negative.
The slope of a line graphed to represent the volume of water in a pool over time would be described as negative
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 50 )
Let the second point be Q ( 5 , 20 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 50 - 20 ) / ( 0 - 5 )
m = 30 / -5
m = -6
Now , the slope of the line is negative and volume of water in the pool over time decreases at a rate of 6
Hence , the slope is negative
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The complete question is attached below :
The table shows the gallons of water in a pool over time. Choose the term that describes the slope of the line of a graph representing the data in the table. The slope of a line graphed to represent the volume of water in a pool over time would be described as___
The table shows the number of wins of two high school softball teams over the past ten years. Which statement BEST compares the
mean absolute deviation (MAD) of the two sets of data?
Answer:
the answer is D
Step-by-step explanation:
D) Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.
Answer:
D) Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.
Step-by-step explanation:
Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.
Westfield's MAD = 6.56
Eastfield's MAD = 2.28
Therefore,
6.56
2.28
= 2.877
MAD =
∑|x − X|
n
, where x = Data value, X = Mean, and n = Number of values
If x-15=14 then what is x ?
I need this answered ASAP thanks a lot :)
Answer:
x=29
Step-by-step explanation:
x-15=14
Add 15 to 14
x=29
Which phrase matches the algebraic expression below?
(PLEASE HELP) 2(x − 7) + 10
A. Two times the sum of x and seven plus ten
B. Two times the difference of x and seven plus ten
C. Two times x minus seven plus ten
D. Two times x minus the sum of seven and ten
The given expression 2(x − 7) + 10 matches with two times the difference of x and seven plus ten. Option B is correct.
Given that,
Which phrase matches the algebraic expression 2(x − 7) + 10 is to be determined.
In mathematics, it deals with numbers of operations according to the statements.
What is simplification?The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.
Here,
2(x − 7) + 10
When we turn the above algebraic expression into word phrase,
"two times the difference of x and seven plus ten"
Thus, the given algebraic expression 2(x − 7) + 10 matches with two times the difference of x and seven plus ten. Option B is correct.
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Area of circle if it’s radius is 9 yards
Step-by-step explanation:
Given
Radius (r) = 9 yards
Area of circle
= πr²
= 3.14 * 9²
= 3.14 * 81
= 254.34 yards²
Mrs. Montoya, the P.E. Teacher, is pairing off students to race against each other. Lara can run 5 5 meters per second, and Riley can run 7 7 meters per second. Mrs. Montoya decides to give Lara a head start of 12 12 meters since she runs more slowly. Once the students start running, Riley should catch up to Lara. How far will Riley have to run to catch up to Lara? How long will that take?
Answer: Riley will catch up with Lara after 6 seconds
Step-by-step explanation:
Let t represent the time it will take Riley to catch up with Lara. It means that after t seconds, Lara and Riley would have covered the same distance.
Distance = speed × time
Lara can run 5 meters per second. It means that the distance covered by Lara in t seconds is 5t meters
Mrs. Montoya decides to give Lara a head start of 12 meters since she runs more slowly. it means the total distance covered by Lara after t seconds is
5t + 12
Riley can run 7 meters per second. It means that the distance covered by Riley in t seconds is 7t meters.
Since the distance covered after t seconds is the same, then
7t = 5t + 12
7t - 5t = 12
2t = 12
t = 12/2
t = 6 seconds
Riley will have to run 42 meters to catch up to Lara. It will take 6 seconds for Riley to catch up to Lara.
Given:
- Lara's speed [tex]\( v_L = 5 \)[/tex] meters per second
- Riley's speed [tex]\( v_R = 7 \)[/tex]meters per second
- Lara's head start [tex]\( d_{\text{head start}} = 12 \)[/tex] meters
Let's denote:
- t as the time it takes for Riley to catch up to Lara.
- d as the distance Riley needs to run to catch up to Lara.
1. Set up equations based on their speeds and the head start:
- For Lara: [tex]\( d_L = v_L \cdot t \)[/tex]
- For Riley: [tex]\( d_R = v_R \cdot t \)[/tex]
2. Account for Lara's head start:
- Lara starts with a head start of 12 meters. Therefore, when Riley starts, Lara is already 12 meters ahead.
[tex]\[ d_R = d_L + 12 \][/tex]
3. Substitute the expressions for [tex]\( d_L \)[/tex] and [tex]\( d_R \)[/tex]:
[tex]\[ v_R \cdot t = v_L \cdot t + 12 \][/tex]
4. Solve for t:
[tex]\[ 7t = 5t + 12 \] \[ 7t - 5t = 12 \] \[ 2t = 12 \] \[ t = \frac{12}{2} \] \[ t = 6 \][/tex] seconds
5. Calculate the distance [tex]\( d_R \)[/tex] that Riley has to run:
[tex]\[ d_R = v_R \cdot t \] \[ d_R = 7 \cdot 6 \] \[ d_R = 42 \][/tex]
Given g(x)=5x+5,solve for x when g(x)=0
Final answer:
To solve for x when g(x) = 0 for the function g(x) = 5x + 5, subtract 5 from both sides and then divide by 5, resulting in x = -1.
Explanation:
To solve the equation g(x) = 5x + 5 when g(x) = 0, you need to find the value of x that makes the equation true.
Set up the equation: 5x + 5 = 0.
Subtract 5 from both sides: 5x = -5.
Divide both sides by 5 to solve for x: x = -5 / 5.
Thus, x = -1.
Therefore, the solution for x when g(x) = 0 is x = -1.
Please help I don't know how to do and its very urgent!
Step-by-step explanation:
42° + x = 115° (alternate angles)
x = 115° - 42°
x = 73°
y = 180° - (115° + 42°) (by angle sum property of triangle)
y = 180° - 167°
y = 13°
z = 42° (corresponding angles)
will the image of the new shape be larger or smaller?
Vanessa was trying to put some files on her flash drive. If she had one file that was 1.9 mb
and another file that was 3.8 mb what is their combined file size?
Answer:
5.7 MB
Step-by-step explanation:
1.9 + 3.8 = 5.7
Answer:
1.9+3.8=5.7 mb
Add the file sizes, and there's your answer!
:)
Need help with these two questions linear relations.
Answer:
b. y = -7x + 4
1. y = -7(-5)+ 4 = 35+4= 39
2. -24= -7x + 4
-28 = -7x
4 = x
3. y = -7(0)+4= 4
4. 0 = -7x+4
-4= -7x
4/7 = x
c. 3y - 5x = 15
1. 3y - 5(6)
3y-30=15
3y=45
y = 15
2. 3(-10)-5x=15
-30-5x=15
-5x = 45
x = -9
3. 3y-5(0)=15
3y=15
y=5
4. 3(0)-5x=15
0-5x=15
-5x=15
x=-3
Step-by-step explanation:
Can somebody tell me how to solve these kind of problems?
A certain forest covers an area of 1700km^2. Suppose that each year this area decreases by 5.75%. What will the area be after 8 years?
Answer: 918km^2
Step-by-step explanation:
[tex]area(a): 1700km^2\\percentage(p): 5.75 = \frac{5.75}{100}=0.0575\\years(y): 8[/tex]
Let x be the new dimension of the area;
[tex]x=a-(a*p*y)[/tex]
[tex]x=(1700km^2)-(1700km^2*0.0575*8)\\x=1700km^2-782km^2\\x=918km^2[/tex]
An artist creates two metal sculptures in the shape of regular octagons a side of the larger octagon is 3.5 times longer than a side of the smaller octagon the area of the smaller octagon is 19.28 square inches
Answer:
The area of the larger octagon is [tex]236.18\ in^2[/tex]
Step-by-step explanation:
The question is
What is the area of the larger octagon?
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
Let
z ----> the scale factor
x ----> the area of the larger octagon
y ---> the area of the smaller octagon
[tex]z^2=\frac{x}{y}[/tex]
we have that
[tex]z=3.5[/tex]
Because, in similar figures the ratio of corresponding sides is proportional and this ratio is equal to the scale factor
we have
[tex]z=3.5[/tex]
[tex]y=19.28\ in^2[/tex]
substitute the given values
[tex]3.5^2=\frac{x}{19.28}[/tex]
[tex]x=12.25(19.28)=236.18\ in^2[/tex]