Answer:
Step-by-step explanation:
(3k,4k,5k)
sea k=2
la terna es:
(6,8,10)
sea k=5
la terna sería:
(15,20,25)
If the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units, using integration find the value of a, where a > 0.
The value of a using integration is 2, such that the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units
How to determine the value of a?The given parameters are:
Curve, y² = 4ax
Line, x = 4a
Substitute x = 4a in y² = 4ax
y² = 4a * 4a
Take the square root of both sides
y = ±4a
This means that the point of intersection between the line and the curve is (4a, -4a) and (4a, 4a)
Remove the negative interval
So, we have: (4a, 0) and (4a, 4a)
The area is then calculated as
[tex]A =2 \int\limits^{4a}_0 {\sqrt y} \, dx[/tex]
This gives
[tex]A =2 \int\limits^{4a}_0 {\sqrt {4ax}} \, dx[/tex]
Remove the constant
[tex]A = 2\sqrt{4a}\int\limits^{4a}_0 {\sqrt {x}} \, dx[/tex]
Integrate
[tex]A = 2\sqrt{4a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]
Evaluate the exponent
[tex]A = 4\sqrt{a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]
Expand
[tex]A = 4\sqrt{a} * \frac 23 (4a)^\frac32[/tex]
Rewrite as:
[tex]A = 4 * a^\frac12 * \frac 23 * 4^\frac32 * a^\frac32[/tex]
Evaluate the exponents by the laws of indices
[tex]A = 4 * \frac 23 * 8 * a^2[/tex]
Recall that the area is:
A = 256/3
So, we have:
[tex]\frac{256}3 = 4 * \frac 23 * 8 * a^2[/tex]
Evaluate the quotients
[tex]256 = 4 * 2 * 8 * a^2[/tex]
Divide both sides by 64
4 = a²
Take the square root of both sides
2 = a
Rewrite as:
a = 2
Hence, the value of a is 2
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Find the value of x.
x = [?]
Answer:
x = 14 units
Step-by-step explanation:
Distance of both the chords from the center of the circle is 9 units.-> Both the chords are equal. (Chords equidistant from the center of the circle are equal)Perpendicular drawn from the center of the circle bisects the chord.-> Measure of one chord = 7 + 7 = 14 unit-> Measure of the other chord = 14 units-> x = 14 unitsQuestion 1 Complete the missing reasons for the proof. Given: 4(x - 2) = 6x + 18 Prove: x= -13 Statements Reasons 1.4(x - 2) = 6x +18 given 2. 4x8= 6x +18 distributive property 3.-2-8-18 4.-2x = 26 addition property of equality 5.x = -13 O 3. subtraction property of equality; 5. multiplication property of equality O 3. subtraction property of equality; 5. division property of equality 3. addition property of equality; 5. division property of equality O 3. addition property of equality; 5. multiplication property of equality
Looking at the problem statement, the question is asking us to determine what the missing reasons are. The information that is given to us is a step-by-step process of solving an expression for an unknown. There are also two blanks in the reasons column for steps 3 and 5 which we will need to determine.
For step #3, we can see that they subtracted 6x from both sides which means that options 3 and 4 are automatically out since they reference addition in the first part. The correct reasoning for this part would be Subtraction Property of Equality which states that we subtract the same item from both sides of the expression.
We can see this being done in the following actions
[tex]4x - 8 = 6x + 18[/tex][tex](4x - 6x) - 8 = (6x - 6x) + 18[/tex][tex](4x - 6x) - 8 = 18[/tex][tex]-2x - 8 = 18[/tex]For step #5, we can see that they divided both sides by -2 which means that option 1 is out since it references the multiplication property of equality. The correct reasoning for this part would be Division Property of Equality which states that we divide both sides by the same item.
We can see this being done in the following actions
[tex]-2x = 26[/tex][tex]\frac{-2x}{-2} = \frac{26}{-2}[/tex][tex]x= \frac{26}{-2}[/tex][tex]x= -13[/tex]Therefore, the option that would best fit the description that we provided during our work would be option 2 (3. subtraction property of equality; 5. division property of equality).
Answer:
b) 3. addition property of equality; 5. division property of equality.
Step-by-step explanation:
Given: 4(x - 2) = 6x + 18
Prove: x = -13
Algebraic Properties:
Addition: If a = b, then a + c = b + cSubtraction: If a = b, then a - c = b - cMultiplication: If a = b, then ac = bcDivision: If a = b, then a ÷ c = b ÷ cDistributive: a(b + c) = ab + acSteps:
1. Given:
⟹ 4(x - 2) = 6x + 18
2. Distribute property:
4(x) + 4(-2) = 6x + 18 [distribute 4]
⟹ 4x - 8 = 6x + 18
3. Subtraction property of equality:
4x - 6x - 8 = 6x - 6x + 18 [subtract 6x from both sides]
⟹ -2x - 8 = 18
4. Addition property of equality:
-2x - 8 + 8 = 18 + 8 [add 8 to both sides]
⟹ -2x = 26
5. Division property of equality:
-2x ÷ -2 = 26 ÷ -2 [divide both sides by -2]
⟹ x = -13
In conclusion, the missing reasons are the subtraction and division properties of equality.
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Use the following table of Registered Voters at Kensington College, Registered Voters at Kensington College 2009 2010 640 790 Democrats Republicans 960 410 Independents 320 300 11) What is the probability that a voter registered in Kensington College in 2009 was not a Republican?
Step-by-step explanation:
remember, a probability is ultimately always
desired cases / total possible cases
what are the total possible cases for our question here ?
all registered voters in 2009 :
640 + 960 + 320 = 1920
the desired cases (not republican) out of all these 1920 possibilities are
640 + 320 = 960
so, the probability for a registered voter to not be republican was
960 / 1920 = 1/2 = 0.5
Estimate the product.
14×212
-6>2x+6 ≤18
graph the inequality
Answer:
y= x + b
-6 > 2x+6- graph a doted line that crosses through -6, and 2 shade below the dotted line going to the negative
18 >< 2x+6 graph a solid line through 18 and 2 and shade everything above the line going positive
have a good day hope this helped
Step-by-step explanation:
The base of an isosceles triangle is half
as long as each of the two equal sides.
Write the area of the triangle, A(x), as a
function of the length of the base, x.
A(x) =
Answer:
X * H
-----------
2
Step-by-step explanation:
Base of the triangle (X) times height of triangle, divided by 2
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
The area of the isosceles triangle will be A(x) = √15(x² / 4).
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.
The base of an isosceles triangle is half as long as each of the two equal sides.
Let the base length be x. Then the length of each other legs will be 2x.
A(x) = √[s(s - x)(s - 2x)(s - 2x)]
The value of s is half of the perimeter.
s = (x + 2x + 2x) / 2
s = 5x / 2
Then the area of the isosceles triangle will be
A(x) = √[5x / 2(5x / 2 - x)(5x / 2 - 2x)(5x / 2 - 2x)]
A(x) = √[5x / 2(3x / 2)(x / 2)(x / 2 )]
A(x) = √(15x⁴ / 16)
A(x) = (x² / 4)√15
The area of the isosceles triangle will be A(x) = √15(x² / 4).
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Find the quotient.
7/8 ÷ 2 1/4
WILL GIVE 30 POINTS
Step-by-step explanation:
Hello there!
This is how we solve this problem
7/8 ÷ 2 1/4
[tex] \frac{7}{8} \div 2 \frac{1}{4} \: conveting \: to \: improper \: faction\\ \\ = \frac{7}{8} \div \frac{9}{4} \\ = \frac{7}{8} \times \frac{4}{9} \: multiply \: through \\ = \frac{7}{18} [/tex]
= 7/18
I hope this helps.
Have a nice studies.
( brain + 95 points ) A triangular prism has a height of 10 cm and the triangle has a base of 4 cm and a height of 6 cm. Find the volume of the triangular prism.
Area of base
1/2BH1/2(4)(6)2(6)12cm²Volume
Area of base× height12(10)120cm³28) Which of the following sets of ordered pairs does not represent a linear function?
(a) {(1, 2), (3, 4), (4, 5), (6, 7)}
(b) {(0, 3), (1, 5), (3, 9), (1, 13)}
(c) {(2, 2), (3, 3), (4, 4), (5,5)}
(d) {(1, 2), (2, 2), (3, 5), (4, 8)}
Answer: D
Step-by-step explanation:
Answer: Choice D
Plot the points given for choice D. See below.
It is impossible to draw a single straight line through all of the points.
Therefore, this set of points do not represent a linear function.
What is the measure of angle B in degrees
Angle C and the 112 degree angle are supplementary, so angle C measures 180-112=68 degrees.
This means that by the exterior angle theorem, [tex]m\angle B=51^{\circ}+68^{\circ}=\boxed{119^{\circ}}[/tex]
If √ 24 + √ 96 7 √600 = y√ 6, find the value of y. -
Two triangles are proportional, and the first triangle has a base of 10 cm and a height of 15 cm. If the base of the second triangle is 12 cm, what is the height of the second triangle?
Answer: b1/b1=h1/h2=10/12=15/h2 so use criss cross and equel to 15×12=10h2 both sides devide by 10 and equel 180/10=18
so h2=18
Explain how you would use addition to find the product of -2 and 5
At a basketball game, 6% were supporting the visiting team. If total number of people attending the game was 2500, how many people were supporters of the home team?
There were 2350 people supporting the home team
How to determine the number of supporters?The given parameters are:
Total = 2500
Proportion that supports the visiting team= 6%
Let the number of people that supports the team be x.
So, we have:
x = (1 - Proportion that supports the visiting team) * Total
This gives
x = (1 - 6%) * 2500
Evaluate
x = 2350
Hence, there were 2350 people supporting the home team
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A circular garden has a circumference of 42.3 feet. Find the approximate diameter of the garden. Use 3.14 for π.
Answer:
13.5
Step-by-step explanation:
c = 2πr
42.3 = 2(3.14)r
42.3 = 6.28r
6.74 = r
d = r + r
d = 6.74 + 6.74
d = 13.5
The discussion in this lesson offers two tips for saving money. Write 1-2 paragraphs that describe the following: 1. state the two money saving tips 2. tell why these tips work
The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.
What is saving?Saving is the method of saving your money for the future. We can not predict the future if anything bad happens and we need a large amount of money these savings will help us.
The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.
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The numbers of pages in the books in a library follow a normal distribution. If the mean num
pages, what can you conclude?
O A. About 60% of the books have fewer than 150 pages.
OB.
About 16% of the books have fewer than 150 pages.
OC.
About 95% of the books have more than 150 pages.
About 16% of the books have more than 150 pages.
O D.
Reset
Next
Answer:
For the answer to the question above, the numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30 pages, you can conclude that about 16% of the books have fewer than 150 pages.
can someone help please
Answer:
2 good scoops
Step-by-step explanation:
I got you I think
What is the minimum value of the following function f(x)=(x-1)^2 +1
Answer:
1
Step-by-step explanation:
f(x)=(x-1)²+1
f(1)=(1-1)²+1
f(1)=0²+1
f(1)=0+1
f(1)=1
what is -23/6 - 7/3
A -37/6
B -30/9
C -16/6
D 37/6
Answer:A
Step-by-step explanation:
-23/6 - 7/3 =-6.16666666667
-37/6 = -6.16666666667
Answer:
[tex] \frac{ - 37}{6} [/tex]
Step-by-step explanation:
[tex] \frac{23}{6} - \frac{7}{3} \\ lcm = 6 \\ \frac{ - 23 - 14} {6} = - \frac{ - 37}{6} \\ final \: answer \\ = \frac{ - 37}{6} [/tex]
Which equation is the inverse of 5y+4= (x+3)² + 2?
Solve
x=4
-7x +y =-22
Answer:
y = 6
Step-by-step explanation:
-7 (4) + y = -22
-28 + y = - 22
+28 + 28
y = 6
Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z', then reflected across the x-axis to form triangle X''Y''Z''. Which of the following statements is true for ΔXYZ and ΔX''Y''Z''? Question 25 options: ΔXYZ and ΔX''Y''Z'' are similar ΔXYZ and ΔX''Y''Z'' are congruent ΔXYZ and ΔX''Y''Z'' are neither congruent nor similar There isn't enough information given to identify whether ΔXYZ and ΔX''Y''Z'' are similar or congruent
1.ΔXYZ and ΔX''Y''Z'' are similar
2.ΔXYZ and ΔX''Y''Z'' are congruent
3.ΔXYZ and ΔX''Y''Z'' are neither congruent nor similar
4.There isn't enough information given to identify whether ΔXYZ and ΔX''Y''Z'' are similar or congruent
The statement that is true for ΔXYZ and ΔX''Y''Z'' is; 2: ΔXYZ and ΔX''Y''Z'' are congruent
How to identify coordinates of transformed triangles?We are told that;
- Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z'.
- Thereafter, reflected across the x-axis to form triangle X''Y''Z''
Now, in transformation, Reflection is flipping an object across a line without changing its size or shape while Rotation is rotating an object about a fixed point without changing its size or shape. Thus, it means that the size and shape of the triangle formed is not different from the original one.
Thus, we can say that both triangles are congruent because the shape and size didn't change.
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An eight-sided die is tossed. Determine the odds against rolling an 8.
Reason:
There are 7 outcomes we don't want vs 1 outcome we do want
outcomes we don't want = rolling one of the following {1,2,3,4,5,6,7}
outcome we want = rolling an 8
Which of the following produces an image that is not congruent to the pre-image?
A. translation
B. dilation
C. rotation
D. reflection
Answer:
Dilation
Step-by-step explanation:
it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.
Which of the following statements must be true about parallelogram ABCD?
Options are below
Answer: [tex]\angle A+\angle D=180^{\circ}[/tex]
Step-by-step explanation:
Adjacent angles of a parallelogram are always supplementary.
Evan picks up a cantaloupe that weighs 3.24 pounds. Suppose Evan
could buy 100 cantaloupes that are all this weight. Without using the
multiplication algorithm, explain how Evan could figure out the total
weight of all 100 cantaloupes.
The total weight of the 100 cantaloupe is 324 pounds
How to determine the total weight?The given parameters are:
Weight of each = 3.24 poundsNumber of cantaloupe = 100Since the number of zeros in 100 is 2;
All Evans needs to do is to move the decimal point in 3.24 two places forward.
i.e. 3.24 becomes 324 when the decimal point is moved
Hence, the total weight of the 100 cantaloupe is 324 pounds
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Select the correct answer. If is modified as , what transformations will be seen in the graph? A. The graph will reflect across the x-axis and then shift units up. B. The graph will reflect across the y-axis and then shift units down. C. The graph will reflect across the x-axis and then shift units to left. D. The graph will reflect across the y-axis and then shift units to right.
The transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.
How to determine the transformation?The missing phrase in the question is: "If f(x) = 2ˣ + 1 is modified as g(x) = 2⁻ˣ + 1 - 5"
The functions are given as:
f(x) = 2ˣ + 1
g(x) = 2⁻ˣ + 1 - 5
First, the function f(x) is reflected across the y-axis (this eliminates options a and c)
The rule of this transformation is
(x,y) ⇒ (-x,y)
So, we have:
f'(x) = 2⁻ˣ + 1
Next, the function f(x) is shifted down by 5 units (this eliminates options d)
The rule of this transformation is
(x,y) ⇒ (x,y - 5)
So, we have:
f''(x) = 2⁻ˣ + 1 - 5
By comparing the functions f"(x) and g(x), we have:
g(x) = f''(x) = 2⁻ˣ + 1 - 5
Hence, the transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.
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y = 12•3x for x = -2
Answer:
y=12×3(-2)
y=-72
Step-by-step explanation:
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