Answer:
Answer is -2/21r + (-19)
Step-by-step explanation:
(-1/7r - 9 -2/3r) - (-5/7r + 10)
= -1/7r - 9 - 2/3r + 5/7r - 10 (distributing the negative sign)
= (-1/7r + 5/7r) + (-2/3r) - 9 - 10 (grouping the like terms)
= 4/7r - 2/3r - 19 (combining the like terms)
= (12r - 14r)/21r - 38r/21r (getting a common denominator)
= -2r/21r - 38r/21r
= (-2r - 38r)/21r
= -40r/21r
= -40/21
Therefore, the simplified expression is B. -2/21r + (-19).
The approximate mass of a hydrogen atom is grams. The mass
of a single lead atom is approximately grams. How many times
heavier is a lead atom than a hydrogen atom?
A lead atom is 200 times heavier than a hydrogen atom.
To determine how many times heavier a lead atom is compared to a hydrogen atom, we can calculate the ratio of their masses.
Mass of hydrogen = 1.7 × 10⁻²⁴ grams
Mass of lead atom = 3.4 × 10⁻²² grams
To find the ratio of their masses, we divide the mass of the lead atom by the mass of the hydrogen atom:
Ratio = 3.4 × 10⁻²² / 1.7 × 10⁻²⁴
= (3.4 / 1.7)× 10⁻²² / 10⁻²⁴
= 2×10²
= 200
Therefore, a lead atom is 200 times heavier than a hydrogen atom.
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The approximate mass of a hydrogen atom is 1.7*10^-24 grams. The mass of a single lead atom is approximately 3.4*10^-22 grams. How many times heavier is a lead atom than a hydrogen atom.
A. 5 times heavier
B. 20 times heavier
C. 50 times heavier
D. 200 times heavier
PLEASE HELP
Lily is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 40w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points)
Part C: Evaluate the composite function in Part A for 35 weeks. (4 points)
Step-by-step explanation:
Part A:
To find the composite function, we need to plug in the expression for s(w) into f(s):
f(s(w)) = 2s(w) + 30
= 2(40w) + 30
= 80w + 30
Therefore, the composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks is f(s(w)) = 80w + 30.
Part B:
The units of measurement for the function f(s(w)) are the same as the units of measurement for f(s) and s(w). From the given information, we know that s(w) represents the number of seeds planted per week and f(s) represents the number of flowers bloomed based on the number of seeds planted. Thus, the units of measurement for f(s(w)) are "flowers" per week.
Part C:
To evaluate the composite function f(s(w)) for 35 weeks, we need to substitute w = 35 into the expression we found in Part A:
f(s(35)) = 80(35) + 30
= 2,830
Therefore, Lily can expect 2,830 flowers to bloom after planting 40 seeds per week for 35 weeks.
Answer: c
Step-by-step explanation:
i took the test
Drew designs and produces vintage looking clothing, but using modern materials. Drew would like to sell the clothing, but does not want to set up a store front either physically or online. What might Drew choose as an option for selling the clothing?
a)mail order
b)door to door sales
c)consignment
d)e-commerce direct
Consignment cab be used as an option for selling the clothing
What is consignment?Consignment involves providing your goods to an established business, like a boutique or vintage store, which then sells the items on your behalf and takes a cut of the profits. This approach lets Drew benefit from the store's customer base and avoids the need to manage a storefront.
Mail order (option a) could also work if Drew is willing to manage shipping and handling, and has a method for advertising the products effectively without a physical or online storefront.
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x-1 is a factor of which of the following?
1.x²+x-2
11.2x2–5x+3
O Neither
OI only
O II only
OI and II
The term (x - 1) is a factor of both of the given polynomials:
x² + x - 2
2x² - 5x + 3
How to check if x - 1 is a factor?
If (x - a) is a factor of a polynomial p(x), then x = a is a zero of the polynomial, which means that:
p(a) =0.
So, if x - 1 is a factor of any of the given polynomials, then we need to evaluate them in x = 1 and check if we get zero.
a) x² + x - 2
Evaluate it in x = 1.
1² + 1 - 2 = 0
it is zero, so (x - 1) is a factor.
b) 2x² - 5x + 3
Evaluating this in x = 1.
2*1² - 5*1 + 3
2 - 5 + 3 = 0
(x - 1) is a factor.
Then the correct option is the last one, it is a factor of both polynomials.
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2( x - 4) + 3(2 - x) + 2x + 7
Answer:
The Answer to This question Is x + 5 So Basically 5
Mean, Fractiles, median, and mode are called the measures of central tendency
The mean monthly income is $3300, the median monthly income is $3000, there is no mode, and the range of the monthly income is $3000.
To find the mean, median, mode, and range of the monthly incomes, we'll perform the following calculations:
Mean:
The mean is calculated by summing all the values and dividing by the total number of values.
Mean = (2000 + 2500 + 3000 + 4000 + 5000) / 5
Mean = 16500 / 5
Mean = 3300
The mean monthly income is $3300.
Median:
The median is the middle value when the data is arranged in ascending order. In this case, since we have an odd number of values, the median is the middle value.
Arranging the incomes in ascending order: $2000, $2500, $3000, $4000, $5000
The median monthly income is $3000.
Mode:
The mode is the value(s) that appear most frequently in the data. In this case, there is no value that appears more than once, so there is no mode.
The data has no mode.
Range:
The range is calculated by subtracting the minimum value from the maximum value.
Range = Maximum Value - Minimum Value
Range = $5000 - $2000
Range = $3000
The range of the monthly income is $3000.
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The complete question is as follows:
Mean, Fractiles, median, and mode are called the measures of central tendency. A group of friends recorded their monthly incomes in dollars. The incomes are as follows: $2000, $2500, $3000, $4000, $5000. Determine the mean, median, mode, and range of their monthly incomes.
Pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4π cm
Step-by-step explanation:
A minute hand travels a full revolution along a circular path in 60 minutes
The distance from the center to the tip of the minute hand = 8 cm
We can consider the movement of the minute hand as being on the circumference of a circle with radius = 8 cm
Circumference = 2π · r
= 2π · 8
= 16π
I5 minutes = 15/60 = 1/4th
So in 15 minutes the minute hand will cover only 1/4th of the full circle
Therefore distance traveled by tip of minute hand
= 1/4 x 16π = 4π cm
You take out a 45-day loan for $2600. At the end of the loan, you owe $70.52 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
Which expression is a function that has zeros at 4 and –3?
Answer:
[tex]f(x) = (x - 4)(x + 3) [/tex]
[tex]f(x) = {x}^{2} - x - 12[/tex]
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
The answer is C. Mean, because Desert Landing is symmetric.
What is distributions?A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.
According to question:To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the Mean, which measures the spread of the middle of the data.
The answer is C. Mean, because Desert Landing is symmetric. depending on the shape of the distributions. If the temperature data in Desert Landing is symmetric, then the Mean would be appropriate to measure the spread of the data. If the temperature data in Sunny Town is skewed, then the Mean would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.
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how many liters each of a 50% acid solution and a 85% acid solution must be used to produce 70 liters of a 75% acid solution
The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.8 pounds with a standard deviation of 1.02 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.73 pounds after one week.
If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 45 individuals will be 1.73 pounds or less?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
The probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.
How to find the probability that the mean weight loss after one week on this pill for a random sample of 45 individuals will be 1.73 pounds or lessCalculating the standard error of the mean (SE) using the formula:
SE = σ / sqrt(n)
where σ is the standard deviation and n is the sample size.
SE = 1.02 / sqrt(45) ≈ 0.1522
We can calculate the z-score using the formula:
z = (x - μ) / SE
where x is the observed mean and μ is the claimed mean.
z = (1.73 - 1.8) / 0.1522 ≈ -0.4582
Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.3231.
Therefore, the probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.
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A cone has a volume of 48 cubic feet and a height of 9 feet. Find the radius.
The radius is ___ ft
Cone - A cone is a three-dimensional geometric object used in mathematics that smoothly taper from a flat, typically circular base to a point known as the apex or vertex.
The following is the formula for a cone's volume:
[tex]V = (1/3)πr^2h[/tex]
where the volume is [tex]V[/tex], the radius is [tex]r[/tex], and the height is [tex]h[/tex].
In putting the values provided yields:
[tex]48 = (1/3)πr^2(9)[/tex]
By dividing both sides by [tex]3[/tex], we arrive at:
[tex]144/π = r^2(9)[/tex]
When we multiply both sides by [tex]9[/tex], we get:
[tex]16/π = r^2[/tex]
When we square the two sides, we obtain:
[tex]r = √(16/π)[/tex]
(Rounded to two decimal places) [tex]r = 2.52 feet[/tex]
As a result, the radius is roughly [tex]2.52 feet.[/tex]
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Triangle BCD with vertices B(-2, 3), C(8, 7), and D(-1,-5): y = x
B' (-3, 2); C'(7,8); D'(-5,-1)
B' (-3,-2); C'(7,8); D'(-5,-1)
B' (3,-2); C'(7,8); D'(-5,-1)
B' (3,-2); C'(7,-8); D'(-5,-1)
Answer:
(c) B'(3, -2); C'(7, 8); D'(-5, -1)
Step-by-step explanation:
Apparently, you want to know the coordinates of B', C', and D' after reflection of B(-2, 3), C(8, 7), and D(-1,-5) in the line y = x.
ReflectionThe reflection in the line y = x has the effect of swapping the x- and y-coordinates:
(x, y) ⇒ (y, x)
No sign changes are involved.
The reflected coordinates are ...
B'(3, -2); C'(7, 8); D'(-5, -1)
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manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.
Note that based on the volume calculations, the manager's statement is NOT correct. The given area of 2m × 2m is insufficient to store all 80 crates.
How is this so ?To verify if the manager's statement is correct, we need to derive the volume of each crate and the total volume required to store all 80 crates.
Volume = Length × Width × Height
Recall that
Length (L) = 690 mm
Width (W) = 445 mm
Height (H) = 180 mm
Thus, the Volume of one crate is
Volume = 690 mm × 445 mm × 180 mm
Converting mm to meters we have,
Volume = (690 / 1000) × (445 / 1000) × (180 / 1000)
= 0.690 × 0.445 × 0.180
= 0.055269 m³
Next , we calculate the total volume required for 80 crates as
Total Volume = Volume of one crate × Number of crates
= 0.055269 m³ × 80
= 4.42152 m³
Recall that the manager stated that all 80 crates can be packed in a 2m × 2m area in the store room.
Since area of store room is
Area = 2 m × 2 m
Area = 4 m²
Comparing the total volume required (4.380208 m³) with the available area (4 m²), we see that the volume exceeds the area. Tus, the manager's statement is incorrect.
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Full question:
Manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.
See attached Image.
1 in 20 children play chess and 1 in 5 children play a musical instrument. Research shows that the probability
of a child playing a musical instrument given that that child plays chess is 0.2.
What is the probability of a randomly chosen child playing chess and playing a musical instrument?
O 0.04
O 0.25
O 0.2
O 0.01
The probability that we will get a lead role, given that we are chosen to be in the play is 0.7.
We have,
Probability is the ratio that shows the likelihood of an event occurring from a given set of possible events.
We can find the required probability below:
The probability that we will be chosen for the play is 0.5.
The probability that we will get the lead role is 0.2.
In this situation, the probability can be found by adding the probability of being chosen and the probability that we will get the lead role.
The probability that we get a lead role, = The probability that we will be chosen for the play + The probability that we will get the lead role
= 0.5 + 0.2
= 0.7
The probability of us getting a lead role given that we have already been chosen for the play is found to be 0.7. The correct answer is option C.
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complete question:
You are trying out for the school play. The probability that you are chosen to
be in the play is 0.5. The probability that you get a lead role is 0.2. What is the
probability that you get a lead role, given that you are chosen to be in the
play?
O A. 0.5
Oo oo
O B. 0.4
O c. o7
O D.0.3
PLEASE HELP!!!!!
Two cards are drawn without replacement from a standard deck of 52
playing cards. What is the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a heart? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
25/51
Step-by-step explanation:
If the first card was a heart, we've drawn one red card already.
The ratio of black to red cards in the deck is now 26:25.
On the second draw, there will be only 51 cards to choose from, rather than 52 because you have already taken out a card. Therefore, you only have a 25/51 chance of drawing a red card compared to the 26/52 or 1/2 chance on the first draw.
Answer is 25/51.
The distance between Marisa's house and the post office is 720 m. If she walks from her house to the post office at an average speed of 80 m/min, how long will she take?
Okay, let's break this down step-by-step:
* The distance between Marisa's house and the post office is 720 m
* Marisa walks at an average speed of 80 m/min
* To calculate the time:
** Distance / Speed = Time
** 720 m / 80 m/min = 9 minutes
Therefore, if the distance is 720 m and Marisa's average walking speed is 80 m/min, it will take her 9 minutes to walk from her house to the post office.
True or false,if f(s)=f(t) then s=t
A football is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t² +27t +
2.4 a) How high is the football after 1 second? b) For how long is the football more than 30 m high? c)
What is the maximum height of the football?
After 1 second the football is 24.5 meters.
Given that, a football is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t² +27t +2.4
a) Here, t=1
Now, h =-4.9(1)²+27(1)+2.4
= -4.9+27+2.4
= 24.5 meters
b) Given that, h=30 meter
30=-4.9t² +27t +2.4
30+4.9t²-27t-2.4=0
4.9t²-27t+27.6=0
Factor and set each factor equal to zero.
Exact Form:
t=(135+√4701)/49, (135−√4701)/49
Decimal Form:
t=4.15436405…, and 1.35584002...
c) To find maximum height, set h=0
-4.9t² +27t +2.4=0
Factor and set each factor equal to zero.
Exact Form:
t=(135+√19401)/49, (135−√19401)/49
Decimal Form:
t=5.59770352…,−0.08749943…
Therefore, after 1 second the football is 24.5 meters.
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Can anyone help me with this <3
Answer:
[tex]3.23*10^{16}[/tex]
Step-by-step explanation:
Just multiply. You have to do:
[tex](1.12*10^7)*(2.88*10^9)\\=3.23*10^{16}[/tex]
A friend has a 80% average before the final exam for a course. The score includes everything but the final, which counts for 15% of the course grade. What is the best course grade your friend can earn? What is the minimum score would your friend need on the final to earn a 75% for the course?
Your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.
Since the final exam counts for 15% of the course grade, the weighted average can be calculated as follows:
Weighted average = (0.85 × 80%) + (0.15 × final exam score)
If we assume that your friend wants to get the highest possible grade, then they would need to get a perfect score on the final exam, which would be 100%.
Plugging this into the equation above, we get:
Weighted average = (0.85 × 80%) + (0.15 × 100%) = 83%
Therefore, the best course grade your friend can earn is 83%.
We can set up an equation where x is the minimum score needed on the final exam:
Weighted average = (0.85 × 80%) + (0.15 × x) = 75%
Simplifying this equation, we get:
0.85 × 80% + 0.15x = 75%
68% + 0.15x = 75%
0.15x = 7%
x = 46.67%
Therefore, your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.
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Calculator
A point is selected at random inside the given figure.
What is the probability the point will be in the region labeled A?
Enter your answer, as a fraction in simplest form, in the box.
P(A) =
Basic
5 in.
B
3 in.
A
C
4 in.
3 in.
D
4 in.
The probability of the point being in region A is 0.5294.
The area of the entire figure can be found by adding the areas of the four triangles:
Area of entire figure
= Area of triangle ABC + Area of triangle ACD + Area of triangle ABD + Area of triangle BCD
= (1/2)(5)(3) + (1/2)(3)(4) + (1/2)(4)(3) + (1/2)(3)(4)
= 7.5 + 6 + 6 + 6
= 25.5 square inches
Similarly, the area of region A can be found by adding the areas of triangles ABC and ABD:
Area of region A
= Area of triangle ABC + Area of triangle ABD
= (1/2)(5)(3) + (1/2)(4)(3)
= 7.5 + 6
= 13.5 square inches
Therefore, the probability of the point being in region A is:
P(A) = Area of region A / Area of entire figure
P(A) = 13.5 / 25.5
P(A) = 0.5294
So the probability of the point being in region A is 0.5294.
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A communications satellite is in a synchronous orbit 18,000 miles above an alien planet's surface. Points B and D in the figure are points of tangency of the satellite signal with the planet. They represent the greatest distance from the satellite at which the signal can be received directly. Point C is the center of the planet, which has a radius of 3,500 miles.
Satellite diagram with satellite at point A, planet with center c and points of tangency with A at B and D. Radius of planet is 3,500 mi and distance from edge of planet to satellite is 18,000 mi.
Find distance
. Round to the nearest mile. Show your process and explain your reasoning.
m∠BAC = 9.4°. If the circumference of the circle represents the the planet's equator, what percent of the planet's equator is within range of the satellite’s signal? Show your process and explain your reasoning.
How much longer does it take a satellite signal to reach point B than it takes to reach point E? Use 186,000 mi/sec as the speed of a satellite signal. Round your answer to the nearest hundredth. Show your process and explain your reasoning.
The satellite is in orbit above the planet's equator. Along with the point directly below it on the planet's surface, the satellite makes one complete revolution every 36 hours. How fast must it travel to complete a revolution in that time? Round your answer to the nearest whole number. Show your process and explain your reasoning.
The distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles. Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).
1. Find the distance from the satellite to the points of tangency Solution: Firstly, we need to draw a rough diagram of the scenario to easily understand it. Consider a satellite revolving around an alien planet in a synchronous orbit 18,000 miles above its surface.
We can see that B and D are the points of tangency of the satellite signal with the planet, and C is the center of the planet. Hence, the figure will look like the following: Image Source: Synchronous Orbit - Wikimedia Commons Now, we need to find the distance from the satellite to the points of tangency.
Hence, the distance from the satellite to the points of tangency, B and D, is 61861.9 miles (approximately 61862 miles).2. Find the percentage of the planet's equator within range of the satellite's signal Solution: We can see that the planet's equator can be represented by a circle with a radius of 3500 miles. Hence, the circumference of the circle would be 2π × 3500 miles ≈ 21991.5 miles.
We know that the satellite's signal can be received directly up to a distance of 61862 miles from it. Hence, the length of the portion of the equator within range of the satellite's signal would be twice the distance from the satellite to the point of tangency, which is 2 × 61862 ≈ 123724 miles. Now, we need to find the percentage of the planet's equator within range of the satellite's signal.
Hence, we need to find the time taken for the satellite signal to reach points B and E. We can see that the distance from the satellite to point B is 61862 miles and the distance from the satellite to point E is 3500 miles. Hence, the time taken for the satellite signal to reach point B would be: Time taken to reach point B = Distance / Speed = 61862 / 186000 ≈ 0.332 seconds Now, we need to find the time taken for the satellite signal to reach point E.
Hence, the time difference between the satellite signal reaching points B and E is approximately 0.07 seconds.4. Find the speed of the satellite Solution: We know that the satellite takes 36 hours to complete one revolution around the planet along with the point directly below it on the planet's surface. Hence, we need to find the distance travelled by the satellite in 36 hours to find its speed.
We can see that the distance travelled by the satellite in one revolution is equal to the circumference of the circle with a radius of 3500 miles, which is 2π × 3500 miles ≈ 21991.5 miles. Hence, the distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles.
Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).
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What is the least common denominator of -2x/x-1 + x+3/x^2-1 =
The least common denominator will be (x-1)(x²-1).
When two or more fractions have the same denominators, they are termed as the common denominators.
The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.
For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators.
The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given.
Given is an expression, -2x/x-1 + x+3/x²-1, we need to find the least common denominator,
So,
-2x/x-1 + x+3/x²-1
Taking the LCM,
-2x(x²-1) + (x+3)(x-1) / (x-1)(x²-1).
Hence the least common denominator will be (x-1)(x²-1).
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what are the coefficients in the polynomial
Answer: 7 and -4
Step-by-step explanation:
Coefficients are numbers in front of variables
6 doesn't have a variable so it's a constant
7 and -4 are the coefficients
What is the measure of angle HEK in this figure?
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
85°
150°
95°
55°
Answer:
Measure of angle HEK is: 85°.
Step-by-step explanation:
Given that point E is the center of the protractor, we have:
angle HEJ = 55° (EH points to 55 degrees)
angle JEK = 30° (EK points to 30 degrees)
Since angle HEJ and angle JEK meets at a point E, then we can find angle HEK by summing up the two angles:
angle HEK = angle HEJ + angle JEK
angle HEK = 55° + 30°
angle HEK = 85°
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
rectangle with a length of x plus 25 and width of x plus 15 with a rectangle in the bottom right corner labeled bench that has a length of 10 and width of 3
Write an equation to determine the area, A, of the patio that will be painted.
A. A = (x + 18)(x + 35)
B. A = (x + 15)(x + 25) + 30
C. A = (x + 5)(x + 22)
D. A = (x + 25)(x + 15) − 30
The correct equation to determine the area, A, of the patio that will be painted is,
D. A = (x + 25)(x + 15) - 30
We have to given that;
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted.
Here, rectangle with a length of x plus 25 and width of x plus 15 with a rectangle.
And, in the bottom right corner labeled bench that has a length of 10 and width of 3.
Hence, Area of rectangle is,
A = (x + 25) (x + 15)
And, Area of bottom right corner is,
A = 10 x 3
A = 30
Thus, The equation to determine the area, A, of the patio that will be painted is,
⇒ A = (x + 25)(x + 15) - 30
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ABDE is a parallelogram.
AB=AC
B
Show that x = 38°
A
C
82°
D
68%
E
Not drawn
accurately
[3 marks]
The proof that the value of x is 38° is shown below
How to show that the value of x is 38°From the question, we have the following parameters that can be used in our computation:
ABDE is a parallelogram.
The measure of the angle opposite the vertex x is
Angle = 180 - 68
Evaluate the like terms
So, we have
Angle = 112
Also, we have
B = 68
AB = AC
So, we have
y = 180 - 68 - 68
y = 44
Using the above as a guide, we have the following:
x + 44 = 82
So, we have
x = 82 - 44
Evaluate
x = 38
Hence, we have shown that the value of x is 38°
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helpppp me please this is really hard for me to do right now
Part A: At her current rate, the distance Amy can ride her bike within 12 minutes is A. 1.6 miles.
Part B: Sebastian can ride his bike for C: 7.5 miles in 1 hour.
Part C: The time it will take for one to wait is B: Amy will have to wait 1.5 minutes for Sebastian.
How to determine the distance a rider can ride his bike?Part A:
To find the distance Amy can ride her bike in 12 minutes, we set up a proportion based on her current rate.
Amy's rate: 4 miles / 30 minutes = x miles / 12 minutes
Cross-multiplying:
30x = 4 * 12
30x = 48
Dividing both sides by 30:
x = 48 / 30
x ≈ 1.6
So, Amy can ride her bike at 1.6 miles in 12 minutes.
Part B:
To find the distance Sebastian can ride his bike in 1 hour, convert the time to minutes first.
1 hour = 60 minutes
Sebastian's rate: 3 miles / 24 minutes = x miles / 60 minutes
Cross-multiplying:
24x = 3 * 60
24x = 180
Dividing both sides by 24:
x = 180 / 24
x ≈ 7.5
Therefore, Sebastian can ride his bike at 7.5 miles in 1 hour.
Part C:
Amy's home to Park = 3 miles,
Park to Sebastian's home = 3 miles.
Amy's rate = 4 miles in 30 minutes, equivalent to 1 mile in 7.5 minutes.
Sebastian's rate = 3 miles in 24 minutes, equivalent to 1 mile in 8 minutes.
Then, we estimate the time it takes for each to cover a distance of 3 miles.
Amy:
Time = Distance / Rate = 3 miles / (2/15 miles/minute)
= 3 * (15/2) minutes
= 22.5 minutes
Sebastian:
Time = Distance / Rate = 3 miles / (1/8 miles/minute)
= 3 * 8 minutes
= 24 minutes
Since Amy= 22.5 mins and Sebastian takes 24 mins,
24 - 22.5 = 1.5
Hence, Amy will have to wait 1.5 minutes for Sebastian.
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