Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine this area.
Answers
Answer:
Using Geometry to answer the question would be the simplest:
Step-by-step explanation:
Remembering the formula for the area of a triangle which is \(A=\frac12bh\). One can then tackle the question by doing the following:
Step 1 Find the y-intercepts
The y-intercepts are found by substituting in \(x=0\).
Which gives you this when you plug it into both equations:
\(-y=1\\y=-1\\y=8\)
So the y-intercepts for the graphs are \((0,-1)\\\), and \((0,8)\) respectively.
Now one has to use elimination to solve the problems by adding up the equations we get:
\(x-y=1\\2x+y=8\\3x=9\\x=3\)
Now to solve for the y component substitute:
\(2(3)+y=8\\y=2\)
Therefore, the graphs intersect at the following:
\((3,2)\)
Now we have our triangle which is accompanied by the graph.
now to solve it we must figure out how long the base is:
\(b=8-(-1)\\b=9\)
The height must also be accounted for which is the following:
\(h=3\)
Now the formula can be used:
\(A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2\)
Answer: 13.5 units²
Step-by-step explanation:
Geometry Solution:
The base is along the y-axis from -1 to 8 = 9 units
The height is the largest x-value = 3
\(Area=\dfrac{base\times height}{2}\quad =\dfrac{9\times 3}{2}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5}\)
Calculus Solution:
\(\int^3_0[(-2x+8)-(x-1)]dx\\\\\\=\int^3_0(-3x+9)dx\\\\\\=\bigg(\dfrac{-3x^2}{2}+9x\bigg)\bigg|^3_0\\\\\\=\bigg(\dfrac{-3(3)^2}{2}+9(3)\bigg)-\bigg(\dfrac{-3(0)^2}{2}+9(0)\bigg)\\\\\\=\dfrac{-27}{2}+27-0-0\\\\\\=\dfrac{27}{2}\quad =\large\boxed{13.5}\)
Related Questions
A restaurant charges $8 per burger basket ordered. The charles family orders at least 3 burger baskets but no more than 7 burger baskets a week. If x, represents the number of burger baskets ordered the total cost can be represented by f(x) = 8.50x. What is the domain of the function for this situation?
A- 8,32,40,48,56
B- 3,4,5,6,7,
C- 3
D- 8
Answers
Answer:
b
Step-by-step explanation:
PLEASE HELP!! Please show me work also!
Answers
Solve for x...........
Answers
Answer:
x=?
Step-by-step explanation:
Write two different inequalities in which one of the solutions is the same as the solution x -23=191
Answers
This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.
1. x + 191 ≥ 214
2. x - 214 ≤ -23
1. To solve this inequality, we add 23 to both sides of the equation: x - 23 = 191.
x + 191 ≥ 214
2. To solve this inequality, we subtract 191 from both sides of the equation: x - 23 = 191.
x - 214 ≤ -23
1. x + 191 ≥ 214
This inequality can be expanded to x + 191 ≥ 214, which means that any value of x that is greater than or equal to 214 satisfies the inequality.
2. x - 214 ≤ -23
This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.
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A car travels 25 m/s for 30 seconds. What distance did the car travel ?
Answers
Answer:
750 meters
Step-by-step explanation:
Answer:
750m
Step-by-step explanation:
Distance= Speed x Time
Speed = 25m/s
Time = 30s
Distance = 25 x 30
= 750 m
Which intervals show f(x) increasing? Choose two options.
[–2.5, –1.6)
[–2, –1]
(–1.6, 0]
[0, 0.8)
(0.8, 2)
(0.8, 2)](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/77q5JNIjK1aaPwG6EzdhZSB0HTASAfz2.png)
Answers
Answer:
C and D
Step-by-step explanation:
The intervals that show f(x) increasing are [–2, –1], and (0.8, 2) as per the given graph.
What is interval?In mathematics, an interval refers to a set of real numbers that includes all the numbers between two given values.
Intervals can be expressed using square brackets [ ] or parentheses ( ), where square brackets denote that the endpoints are included in the interval, and parentheses denote that the endpoints are excluded.
To determine the intervals in which f(x) is increasing, we need to find the portions of the graph where the function is sloping upwards (i.e. where the graph is moving from left to right in an upward direction).
Looking at the graph, we can see that f(x) is increasing on the intervals [–2, –1] and (0.8, 2).
Therefore, the correct options are: [–2, –1], and (0.8, 2).
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What number is 0.409 more than 0.733? HELP
Answers
Answer:
= 1.223
Step-by-step explanation:
0.409 more than 0.733 means the addition of 0.733 + 0.409
0.733 + 0.409
= 1.223
Approximately to one decimal place = 1.2
My friends and i are buying a total of 20 cupcakes. i'd like to buy 10% of the total
Answers
You would like to buy 2 cupcakes out of the total of 20 cupcakes. This proportion represents your share based on the 10% you desire.
If you and your friends are collectively buying 20 cupcakes, and you would like to buy 10% of the total, it means you want to purchase a portion that corresponds to 10% of the whole.
To calculate this, you can multiply the total number of cupcakes (20) by 10% (or 0.10), which represents the fraction or decimal form of 10%.
10% of 20 can be computed as follows:
10% of 20 = 0.10 * 20 = 2
Therefore, you would like to buy 2 cupcakes out of the total of 20 cupcakes. This proportion represents your share based on the 10% you desire.
By purchasing 2 cupcakes, you ensure that you have obtained your desired portion while leaving the remaining 18 cupcakes for your friends to distribute among themselves. This way, everyone gets a fair share, and you are able to satisfy your preference for 10% of the total quantity.
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a 60-year-old female is diagnosed with hyperkalemia. which symptom would most likely be observed?
Answers
Hyperkalemia is a medical condition that refers to an elevated level of potassium in the blood.
This condition can be caused by several factors, including kidney disease, certain medications, and hormone imbalances. Symptoms of hyperkalemia can range from mild to severe, depending on the level of potassium in the blood.
In a 60-year-old female diagnosed with hyperkalemia, the most likely symptom that would be observed is muscle weakness. This is because high levels of potassium can interfere with the normal functioning of muscles, leading to weakness, fatigue, and even paralysis in severe cases.
Other symptoms that may be observed in hyperkalemia include nausea, vomiting, irregular heartbeat, and numbness or tingling in the extremities. Treatment of hyperkalemia typically involves addressing the underlying cause of the condition, as well as managing symptoms through medication and lifestyle changes.
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Can you factor x² + 9?
Answers
Answer:
x square + 3 Square
(x + 3)square
X Square + 3 Square + 2x3
the area of a circular trampoline is 112.07 square feet
Answers
The required answer is the approximately 5.98 feet.
The area of a circular trampoline is given as 112.07 square feet.
To find the radius of the trampoline,
area of a circle:
A = πr^2
where A is the area and r is the radius of the circle.
To find the radius,
r = √(A/π)
Substituting the given area, we have:
r = √(112.07/π)
Now, calculate the value of the radius using a calculator or estimation. the value of π to be approximately 3.14:
r = √(112.07/3.14)
r ≈ √(35.70675)
r ≈ 5.98
Therefore, the radius of the circular trampoline is approximately 5.98 feet.
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Find all of the cube roots of 11 and write the answers in rectangular (standard) form.
Answers
To solve this we must be knowing each and every concept related to cube root and its calculations. Therefore, the cube roots of 11 is 2.223.
What is cube root?In a nutshell, the cube roots of almost any integer is the component that we multiply on its own three times to produce the specific values. Remember that now the cube roots of an integer is the inverse of its cubing.
Only when yyy= x is the cube root of such a number x , a number y. All nonzero real numbers get one actual cube root and two complex conjugated cube roots, while all nonzero complex numbers possess three distinct complex cube roots. The cube roots of 11 is 2.223.
Therefore, the cube roots of 11 is 2.223.
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The circumference of a circle is 25π m. What is the area, in square meters? Express your answer in terms of \piπ.
Answers
Answer:
Area = 156.25π meters
Step-by-step explanation:
In order to identify the area of the circle, you would need the radius. In order to find the radius, you would plug in the circumference (25π) into the equation for the circumference of a circle, like this:
C = 2πr
25π = 2πr
You would then solve the equation for r (the radius)
25π = 2πr
12.5π = πr
12.5 = r
Then you would plug the radius into the equation for the area of a circle.
A = π(r^2)
A = 12.5^2π
A = 156.25π
So your answer would then be 156.25π meters, since that was the unit of measurement
Answer: 156.25π m. Hope this helps.
-2x + 2y = -4 3x - 2y = 4
Answers
Answer:
x=0 and y=−2
keep scrolling it is kind of long
Step-by-step explanation:
−2x+2y=−4,3x−2y=4
−2x+2y=−4for x:
−2x+2y=−4
−2x+2y+−2y=−4+−2y
−2x=−2y−4
-2x/-2=-2y-4/-2
x=y+2
Substitute y +2 for x in3x−2y=4:
3x−2y=4
3(y+2)−2y=4
y+6=4
y+6+−6=4+−6
y=−2
Substitute −2 for y in x=y+2:
x=y+2
x=−2+2
x=0
x=0 and y=−2
Which measurements could not represent the side lengths of a right triangle? answer choices. 6 cm, 8 cm, 10 cm. 12 cm, 35 cm, 37 cm. 4 cm, 6 cm, 10 cm.
Answers
12 cm, 35 cm, 37 cm measurements could not represent the side lengths of a right triangle. So the option C is correct.
The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle must equal the square of the longest side.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two legs (the sides that make the right angle) is equal to the square of the hypotenuse (the side opposite the right angle). Mathematically, this can be written as a² + b² = c².
So the sides of option C "12 cm, 35 cm, 37 cm" could not represent the side lengths of a right triangle because 12 cm² + 35 cm² ≠ 37 cm², these side lengths could not represent a right triangle.
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Pls help
And explain pls
Answers
Answer:
To graph the function
Step-by-step explanation:
You can use negative one zero one and two, or negative 2, negative one, zero and one as x values to help you graph the function.
After graphing the function you can easily determine the domain and range.
A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?
Answers
A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?
step 1
Find the probability that Jill draw an A
P=2/5
step 2
Find the probability that jill draw a C
P=1/4
therefore
the probability that Jill will draw an A and then a C is
P=(2/5)(1/4)
P=2/20
P=1/10 or 10%Find the measure of the arc or angle indicated
Answers
(9) The measure of angle MTS is 48⁰.
(10) The measure of angle CLK is 93⁰.
What is the measure of the arc or angle indicated?The measure of the arc angle indicated is calculated by applying intersecting chord theorem as follows;
(9) The measure of angle MTS is calculated as follows;
arc RMT = 90 x 2 (interior angle of intersecting secants)
arc RMT = 180⁰
arc MR = arc RMT - arc MT
arc MR = 180 - 84⁰
arc MR = 96⁰
angle MTS = ¹/₂ x 96⁰ (interior angle of intersecting secants)
angle MTS = 48⁰
(10) The measure of angle CLK is calculated as follows;
arc CLK = 98⁰ + 76⁰
arc CLK = 174⁰
angle CJK = ¹/₂ X 174⁰ (interior angle of intersecting secant)
angle CJK = 87⁰
angle CLK = 180 - 87⁰ (opposite angles of cyclic quadrilateral are supplementary)
angle CLK = 93⁰
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What is the equation of the line that passes through the point (4, 6) and has an
undefined slope?
Answers
Answer:
x = 4
Step-by-step explanation:
a line with an undefined slope is a vertical line parallel to the y- axis, with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (4, 6 ) with x- coordinate 4 , then
x = 4 ← equation of line
Ricardo is creating a budget for himself to set goals on how much money he wants to save. At his current job, he makes $90 per week, and spends $10 each week on his expenses. If he wants to save a total of at least $1,200, how many weeks at minimum does he have to work for in order to reach his goal?
Answers
Answer: 10 Weeks
Step-by-step explanation: hope this is right
please help, I’m so lost!
Answers
Answer:
B
Step-by-step explanation:
If you distribute:
2(x) + 2(10)
that gives you:
2x + 20
Answer:
B. 2x +20
Step-by-step explanation:
tap on the photo. i don't understand how to do part c.
(c) the element x that does not
change when it is mapped
onto z
Answers
Answer:
it's basically just saying find the X that if it's mapped to Z would still have the same X value
Bag A contains 10 marbles of which 2 are red and 8 are black. Bag B contains 12 marbles of which 4 are red and 8 are black. A ball is drawn at random from each bag.
a) Draw a probability tree diagram to show all the outcomes the experiment.
Answers
Answer: Ok, so the tree would start with the ten marbles going to 1 of the reds, 1 of the black , and get till you used up all the black, then do 2/10 and 8/10 to 12 and repeat the 1 part step, and then do 4/12 and 8/12 and add it all up and place the probability out of 22.
Step-by-step explanation:
PLS HELP WILL MARK BRAINLIEST !
Answers
Answer:
1) 8x³ - x² + 1
2) 5a - 3b - 10c
3 17x²y - 7xy²
Step-by-step explanation:
Just combine like terms, since everything is adding, all you have to do is add everything with the same symbol. Make sure you watch for negatives so you know when to add or subtract you numbers!
Hope this helps!
Choose one for the above
Answers
helppppppppppppppppppp
Answers
Answer:
Im pretty sure the answer is 2,090
Step-by-step explanation:
Answer:2090
15% of 3,800 is 570. This means the population will decrease 570 roaches each year. 570 x the 3 years recorded will be 1710. This means the new population can be figured out by subtracting 3800-1710, which equals 2090. This means in three years 2090 roaches will live in the colony.
I hope this helped & Good Luck <3 !!!!
what is the answer? A B C D
Answers
Answer:
b
Step-by-step explanation:
Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.
the median for week 2 is more than the median for week 1.
the mean for week 2 is less than the mean for week 1.
the range for week 1 is more the range for week 2.
the range for week 1 is less than the range for week 2.
Answers
The mean of week 2 > the mean for week 1.
Range for week 1 = range for week 2.
What is the Range and Median of a Data?The range = greatest value - least value
Median = center of the data.
The center of the data for week 1 = 79, the mean for week 2 is therefore 79.
The center of for week 1 is 73.5. Mean for week 1 is 73.5.
This means mean for week 2 is greater than mean for week 1.
Range for week 1 = 89 - 62 = 27
Range for week 2 = 89 - 62 = 27
This means both weeks have the same range.
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please help i don’t understand
Answers
9514 1404 393
Answer:
3
Step-by-step explanation:
Vertical angles share a vertex point, and have opposite rays for sides. In short, they are across the point of intersection from each other. Vertical angles do not have a common side (they are not adjacent).
The first part of the problem is to identify angle NCA. That is shown in red in the attachment. The vertical angle is across the point of intersection. It is angle 3.
Solve by completing the square.
x2 - 4x – 20 = 0
A. x = {-2±6√2}
B. x = {2+6√2}
C. x = {2+2√6}
D. x = {-2±2√6}
Show your work.
Answers
Step-by-step explanation:
Subtract
20
from both sides of the equation.
x
2
−
4
x
=
−
20
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
−
2
)
2
Add the term to each side of the equation.
x
2
−
4
x
+
(
−
2
)
2
=
−
20
+
(
−
2
)
2
Simplify the equation.
Tap for more steps...
x
2
−
4
x
+
4
=
−
16
Factor the perfect trinomial square into
(
x
−
2
)
2
.
(
x
−
2
)
2
=
−
16
Solve the equation for
x
.
Tap for more steps...
x
=
2
±
4
i