Given the following rectangle and circle, what appropriate value of x are the two areas equal? A: x= 3.4 B: x=5.8 C: x= 10.2 D: the curves do not intersect, so there is no solution
Answers
The correct option is D:
the curves do not intersect, so there is no solution
For what values of x are the two areas equal?
The area of the rectangle is given by:
f(x) = (x + 7)*(5x - 3)
f(x) = 5x² -3x + 35x - 21
f(x) = 5x² + 32x - 21
For the circle, the area is:
g(x) = 2*pi*(x + 6)^2
g(x) = 2pi*x^2 + 12pi*x + 72pi
The solution is given g(x) = f(x).
By graphing both functions (the green curve is the area of the rectangle, the orange one is the area of the circle). The two curves never do intercept, so the correct option is D.
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Related Questions
A rectangle is four times as long as it is wide. If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square. What are the rectangle’s dimensions?
Answers
Answer:
Length equals 16 and Width equals 4
Step-by-step explanation:
First let us create an equation. We can use L and W for length and width.
If the length is 4 times the width, then we end up with: L = 4W
It then says, " If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square."
Since a square has an equal length and width then we end up with:
L - 6 = W + 6
Knowing this we can just substitute the first equation into the second one leaving us with: 4W - 6 = W + 6
We then remove a W from both sides so that the right side is left with a 6, and add 6 to both sides to remove the -6 from the left one.
This leaves us with 3W = 12
W = 4, and if we put that into our first equation, L = 4W, then Length equals 16, and Width equals 4. We can check this by putting it into the 2nd equation. 16 - 6 = 4 + 6.
0.65 more than -4.35
Answers
Answer:
-3.7
Step-by-step explanation:
1. More = Addition
2. 0.65 + -4.35 = -3.7
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
0.65 more than -4.35
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The word more means addition, thus
-4.35+0.65=
[tex]\bf{-3.7}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=-3.7}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
can someone help me solve this problem?
Answers
Answer:
13
Step-by-step explanation:
cos17 = x/14
x = 14cos17
x= 13.38826658
to the nearest hundredth
x=13
Which of the following equations describes the graph? Urgent lol
Answers
Answer : I think 3rd is the answer
Can someone help me please?
Answers
Answer:
1. y ax
|
A-------------------------------B
|
------------C---------------------
|
|__________________x ax
for this, your A might be (0,5), B (5,5), C (2,2).
parallel means railroad tracks: same slope, different intercepts.
line AB in this case has a slope of 0, intercept (0,5), so y₁=0x+5 or just y₁=5
the line passing through C also has slope 0, but intercept (0,2), so y₂=0x+2 or just y₂=2
2. perpendicular means that the slopes of two lines multiply out to -1. If line AB has, for example, a slope of 2/3, then the line passing through C would have slope -3/2 (negative reciprocal). To make things easier have either point A or B be on the x or y axis
khan academy has some helpful videos :)
https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/perpendicular-lines
A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of Plot A can be represented by 3x^2 +7x - 5, and the area of Plot B can be represented by 5x^2 - 4x + 11. Write a polynomial that represents the total area of both plots of land.
Answers
Step-by-step explanation:
Combine common terms
(3x²+5x²)+(7x-4x)+(-5+11)
8x²+3x+6
The polynomial that represents the total area of both plots of land will be; 8x²+3x+6
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We are given that ;
The area of Plot A can be represented by 3x² +7x - 5, and the area of Plot B can be represented by 5x² - 4x + 11.
So the polynomial that represents the total area of both plots of land
Now Combine common terms;
(3x²+5x²)+(7x-4x)+(-5+11)
Then we get;
8x²+3x+6
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what are the possible numbers of positive, negative, and complex zeros of f(x)=x^6+x^5+x^4+4x^3-12x^2+12?
Answers
The number of zeros are; Positive; 2 or 0; Negative: 4 or 2 or 0; Complex; 0, 2, 4, 6
How to find the zeros of a Polynomial?We are given the polynomial function as;
f(x) = x⁶ + x⁵ + x⁴ + 4x³ - 12x² + 12
Use Descartes Rule rule of signs allows us to determine the possible number of positive, negative, and complex roots.
For the function f(x), the number of sign changes that occur from term to term will give us the number of positive possible roots.
For the function f(-x), the number of sign changes that occur from term to term will give us the number of negative possible roots.
The numbers of complex roots is the difference between the degree of function and total number of positive and negative roots.
For f(x), the signs change 2 times. Thus, there can only be a possibility of 2 positive roots
For f(-x), we have;
x⁶ - x⁵ + x⁴ - 4x³ - 12x² + 12
Thus, the sign changes 4 times and so we have a possibility of 4 negative roots.
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Write pqqqqrr in exponential form.
Answers
p^1
q^4
r^2
Is this what your asking for and also can you please mark me as brainlist. Thank you
(5 - 1/2- 2)x^2 + ( 1/5 + 1/2 - 1/3 )x + (5/2 - 1/3 - 1/6 ) =
Answers
Answer:
Step-by-step explanation:
Answer:
The answer is
5/2x^2+11/30x+2
[tex] \frac{5}{2}x ^{2} + \frac{11}{30} x + 2[/tex]
this is timed, much help is appreciated:)
Answers
The value of the angle m∠4 is 105 degrees.
How to find angles in a quadrilateral?The sum of angles in a quadrilateral is 360 degrees.
Therefore,
m∠1 + m∠2 + m∠3 + m∠4 = 360°
Hence,
x + x + 10 + x + 20 + x + 30 = 360
4x + 60 = 360
4x = 360 - 60
4x = 300
x = 360 / 4
x = 75
Therefore,
m∠4 = 75 + 30 = 105°
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Solve the rational equation quantity 3 times x minus 5 end quantity divided by 7 equals four sevenths.
Answers
Answer:
3
Step-by-step explanation:
If we write it out, the equation will be 3x-5/7 = 4/7. So first, we can multiply 7 by both sides to get 3x - 5 = 4. Next, we can add 5 to both sides to get 3x = 9. Lastly, we'll divide 3 by both sides to get x = 3.
There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three gardens in square feet.
65
60
62
64
Answers
Answer:
62
Step-by-step explanation:
1. To find the total area, we must find the area of the three individual gardens and sum them together
2. Since the gardens are square, the area is equal to the side length squared
3. Therefore, square the sides and sum:
3^2 = 9
7^2 = 49
2^2 = 4
4+9+49 = 62
help me i dont understand this
Answers
The equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)
Equation of reciprocal of a functionGiven a linear function that contains the coordinate point on its line (5, 7) and (9, 11)
The equation of its reciprocal can be determine by finding the equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)
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A 2012 survey of 2,254 American adults indicates that 17% of cell phone owners do their browsing on their phone rather than a computer or other device. (a) According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones. Conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%. The hypotheses for this test are:
Answers
The hypothesis which can be used to show whether data provide strong evidence or not are: [tex]H_{0}:p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1}:p_{1}=p_{2}[/tex] where [tex]p_{1} and p_{2}[/tex] are the proportions of Americans and chinese people who use mobile phones to access internet.
Given proportion of Americans uses mobile phones is 17%. Proportion of chinese uses mobile phones is 38%.
Hypothesis are the statements which can be tested through its validity. There can be null hypothesis and alternate hypothesis.
The hypothesis which can be used are as under:
[tex]H_{0} :[/tex][tex]p_{1}[/tex]≠[tex]p_{2}[/tex]
[tex]H_{1}:p_{1} =p_{2}[/tex]
We have used equal to signs because we have to check whether they are different or not.
We cannot check hypothesis as we don't have standard deviation.
Hence the hypothesis for this test are: [tex]H_{0} :p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1} :p_{1} =p_{2}[/tex].
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HELP GEOMETRY) Fill in the blanks:
How many degrees is angle LKZ?
How many degrees is angle LMZ?
How many degrees is arc LKZ?
Answers
Answer:
Step-by-step explanation:
Quinn wants to save $300 this year. She saves $25 after her first dog-sitting job. How much more money does Quinn need to reach her goal for the year?
Answers
Quinn needs to save another $275.
How much more money does Quinn need to reach her goal for the year?
The money that she needs will be equal to the difference between the amount that she wants to save, and the amount that she already has.
She wants to save $300.She already has $25The difference is:
D = $300 - $25 = $275
This means that, to reach her goal this year, Quinn needs to save another $275.
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PLS HELP I REALLY NEED HELP
Answers
Answer:
a) AB = 10 unitsb) Midpoint is (2, 6)===================
GivenPoints A( - 1, 10) and B(5, 2)To finda) The length of ABb) The midpoint of ABSolutiona) Use the distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the coordinates and calculate:
[tex]d=\sqrt{(5-(-1))^2+(2-10)^2} =\sqrt{6^2+(-8)^2} =\sqrt{36+64} =\sqrt{100} =10[/tex]
The distance is AB = 10 units
b) Use midpoint formula and find x and y- coordinates of this point:
[tex]x= \cfrac{x_1+x_2}{2}[/tex] and [tex]y= \cfrac{y_1+y_2}{2}[/tex]
Substitute coordinates and find the midpoint:
[tex]x= \cfrac{-1+5}{2} =2[/tex] and [tex]y= \cfrac{10+2}{2}=6[/tex]
The midpoint is (2, 6)
Answer:
Length of line segment AB = 10 units
Midpoint of line segment AB = (2, 6)
Step-by-step explanation:
To find length, apply the distance formula :
AB = √(5 - (-1))² + (2 - 10)²AB = √36 + 64 = √100[tex]\fbox {AB = 10 units}[/tex]To find the midpoint :
M = (-1 + 5 / 2, 10 + 2 / 2)[tex]\fbox {Midpoint = (2, 6)}[/tex]Can someone help me please
measure of angle B = 37 degrees, a = 12, b = 15. Find the measure of angle A to the nearest degree.
Answers
Answer: 28.78
Step-by-step explanation:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}\\\\ \sin A=\frac{a \sin B}{b}\\\\\sin A=\frac{12 \sin 37^{\circ}}{15}\\\\\sin A=0.481452...\\\\A \approx 28.78^{\circ}, 151.21^{\circ}[/tex]
However, we disregard the second case, giving 28.78 degrees.
Use the box-and-whisker plots to determine which statements are true.
Answers
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers and a box. The whiskers represents the minimum and maximum scores. The difference between the minimum and maximum scores is the range.
On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
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f(x)=x^2(x+2)(x-2)(x-5) has zeros at x=-2, x=0, x=2 and x=5. what is the sign of f on the interval -2
Answers
Answer:
f is sometimes positive and sometimes negative on the interval
Step-by-step explanation:
So if you were to expand out the x's you would have x^2 * x * x * x which will result in x^5. and because the leading coefficient is positive, it will be going towards positive infinity as x goes towards positive infinity, and because the degree is odd the end behaviors will be opposite, so as x goes towards negative infinity the value of f(x) will be going towards negative infinity. One other thing to note is that because x^2 technically is two zeroes, with the same value, the zero at x=0 has a multiplicity of 2, meaning that it will not cross the x-axis, but rather have a turning point, once it intersects the x-axis, because the zero has an even multiplicity. Given this information we can draw a graph. So as you can see in the graph, it will sometimes be negative and sometimes positive
GUYS CAN SOMEONE PLEASE HELP ASAP?
THANKS SO MUCH ULL GIVE 40POINTS AND BRAINLIEST
Answers
Answer:
1136/295 cm
Step-by-step explanation:
Corresponding lengths of similar figures are proportional.
If we let the radius of the second cylinder be x,
x/6.4 = 7.1/11.8
x = 6.4(7.1/11.8) = 1136/295 cm
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O A is 3. The length of A A prime is 9.
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation.
What is the scale factor of the dilation?
1/3
3
4
1/4
Answers
Answer:
3
Step-by-step explanation:
9 divided by 3 is 3...
hope this helped
Answer:
its 3
Step-by-step explanation:
im doing summer school rn lol
Please help ASAP
Please help ASAP
Please help ASAP
Please help ASAP
Answers
The volume of the rectangular box is 12 cubic inches
Volume of a boxThe formula for measuring the volume of a rectangular box is expressed as:
V = lwh
l is the length
w is the width
h is the height
Given the following
l = 2in
w = 3in
h = 2in
Substitute
V = 2* 3 * 2
V = 12 cubic inches
Hence the volume of the rectangular box is 12 cubic inches
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the number of men is five eights of the number of women working in a factory if there is 24 more women than men how many workers are all together
Answers
Answer:
104
Step-by-step explanation:
women = 8/8
men = 5/8
all workers = 8/8 + 5/8 = 13/8
extra women workers = 8/8 - 5/8 = 3/8
so...
3/8 = 24
13/8 = x
( cross multiplication method)
3/8 x = 39
x = 104
Hence, there are 104 workers
Answer:
104 workers
Step-by-step explanation:
w = women
m = men = 5/8 w
w - 5/8 w = 24
w = 64 then m = 5/8 * 64 = 40 total = 104
help help help help??
Answers
Answer:
a b f would all be the correct answers
Step-by-step explanation:
Less than looks to the left
Greater than looks right
Which equation correctly describes the relationship between the measure of the inscribed angle and the measure of the intercepted arc in the figure? m∠PQR=360°−mPR⏜ m∠PQR=12mPR⏜ m∠PQR=2(mPR⏜) m∠PQR=mPR⏜ Circle with two chords. Point Q at 10 o clock, point P at 3 o clock, and point R at 6 o clock are on the circle. Segment Q R and Q P share a common end-point at point Q.
Answers
Answer:
Your answer is ∠PQR=(1/2)* m arc PR.
Step-by-step explanation:
The Angle Described is one that has its vertex in the circumference. The inscribed angle measures half of the arc it comprises.
So, in this problem, The inscribed angle=∠PQR
The arc it comprises=m arc PR too.
So therefore:
∠PQR=(1/2)* m arc PR is the answer
if (p,4) is mapped into (q,-3) under a rotation through+90° about origin . then find the values of p and q
Answers
Answer:
p = 3
q = 4
Step-by-step explanation:
Rotation by +90° (clockwise) about the origin: (x, y) → (y, -x)
Therefore, (p, 4) rotated by +90° about the origin:
(p, 4) → (4, -p)
Therefore:
(4, -p) = (q, -3)
⇒ p = 3
⇒ q = 4
Therefore, (3, 4) is mapped into (4, -3) under a rotation by +90° about the origin.
Theodore started watching a movie at 19:30.
The movie was 1 hour and 56 minutes long, but part-way through he
paused it for 12 minutes.
What was the time when the movie finished?
Give your answer using the 24 hour clock.
Answers
The time when movie finished was 21 : 38.
It is given that Theodore started watching movie at 19:30 and length of movie was 1 hour and 56 minutes.
We have to find the time when the movie finished if there was a break of 12 minutes also between movie.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations and the symbols are called variables.
As per the question ;
Theodore started watching movie at 19:30.
The length of movie = 1 hour and 56 minutes
Break = 12 minutes
So ;
Total length of running of movie = 2 hours and 8 minutes
The time when movie finished will be ;
= 19 :30 + 2:08
= 21 : 38
Thus , the time when movie finished was 21 : 38.
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M angle A=
M angle B=
M angle C=
Help me please Stuck on this question thanks
Answers
m<A = 28
m<B = 96
m<C = 56
the area of 4 walls of a room is 120 m^2. if the length and breadth are 7m and 5m respectively, find the height.
Answers
=========================================================
Explanation:
The floor is a 7 meter by 5 meter rectangle. The perimeter is
P = 2(L+W)
P = 2(7+5)
P = 2(12)
P = 24
The perimeter of the floor is 24 meters.
Multiply this perimeter by the unknown height h to get 24h
This expression represents the lateral surface area. This is the combined wall area. Set this equal to 120 and solve for h.
24h = 120
h = 120/24
h = 5
-----------------
Check:
One pair of walls is 7 meters by 5 meters, giving an area of 7*5 = 35 square meters each. So far that's 2*35 = 70 square meters for these two walls combined.
The other pair of walls is 5 by 5. Each has an area of 5*5 = 25 which doubles to 2*25 = 50
The total wall area is 70+50 = 120 to confirm the answer.