Answer:
It’s A, D, and E
The magnetic field lines flow from Earth’s geographic South Pole to Earth’s
geographic North Pole.
The magnetic field is generated in Earth’s core.
The magnetic field is similar to the magnetic field of a bar magnet.
thank youhave a good day
Answer:
It’s A, D, and E.
Step-by-step explanation: Try and find out :)
Jk Jk it's right.
Please help me with these problems
Check the picture below.
HELLLP!!!
Type the correct answer in each box. Write coordinate points in the form (x, y).
Consider the hyperbola represented by the equation .
The center of this hyperbola is . The left vertex, if the hyperbola opens horizontally, or the bottom vertex, if it opens vertically, is . The other vertex is .
Answer:
The center of the hyperbola is (-5 , 7)
The left vertex is (-5 , -6)
The other vertex is (-5 , 20)
Step-by-step explanation:
* Lets explain the equations of the hyperbola
- The standard form of the equation of a hyperbola with center (h , k)
and transverse axis parallel to the x-axis is (x - h)²/a² - (y - k)²/b² = 1
- The hyperbola is open horizontally
- The coordinates of the vertices are (h ± a , k)
- The standard form of the equation of a hyperbola with center (h , k)
and transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1
- The hyperbola is open vertically
- The coordinates of the vertices are (h , k ± a)
* Lets solve the problem
∵ The equation of the hyperbola is - (x + 5)²/9² + (y - 7)²/13² = 1
- Lets rearrange the terms of the equation
∴ The equation is (y - 7)²/13² - (x + 5)²/9² = 1
∴ The hyperbola opens vertically
∵ (y - k)²/a² - (x - h)²/b² = 1
∴ a = 13 , b = 9 , h = -5 , k = 7
∵ The coordinates of its center are (h , k)
∴ The center of the hyperbola is (-5 , 7)
∵ The hyperbola opens vertically
∴ Its vertices are (h , k - a) the bottom one and (h , k + a) the up one
∴ The bottom vertex is (-5 , 7 - 13) = (-5 , -6)
∴ The bottom vertex is (-5 , -6)
∴ The other vertex is (-5 , 7 + 13) = (-5 , 20)
∴ The other vertex is (-5 , 20)
Answer:
Center: (-5,7)
Opens Vertically: (-5,-6)
The other vertext : (-5, 20)
Step-by-step explanation:
Delaware Trust has 450 shares of common stock outstanding at a market price per share of $27. Currently, the firm has excess cash of $400, total assets of $28,900, and net income of $1,320. The firm has decided to pay out all of its excess cash as a cash dividend. What will the earnings per share be after this dividend is paid? A. $2.69 B. $2.86 C. $2.93 D. $3.07 E. $3.24
Answer:
Earnings per share is $2.93
Step-by-step explanation:
Given data
shares = 450
assets = $28,900
net income = $1,320
to find out
earnings per share
solution
Earnings per share is directly calculate by net income / total share
here we know net income and that share i.e.450
so
Earnings per share = net income / total share
Earnings per share = 1,320 / 450
Earnings per share = $2.93
so option C is right i.e. $2.93
Please assist me with these problems.
Answer:
c for the question that says what point is on [tex]y=\log_a(x)[/tex] given the options.
9 for the question that reads: "If [tex]\log_a(9)=4[/tex], what is the value of [tex]a^4[/tex].
Step-by-step explanation:
We are given [tex]y=\log_a(x)[/tex].
There are some domain restrictions:
[tex]a \text {is number between } 0 \text{ and } 1 \text{ or greater than } 1[/tex]
[tex]x \ge 0[/tex]
a) couldn't be it because x=0 in the ordered pair.
b) isn't is either for the same reason.
c) \log_a(1)=0 \text{ because } a^0=1[/tex]
So c is so far it! Since (x,y)=(1,0) gives us [tex]0=\log_a(1)[/tex] where the equivalent exponential form is as I mentioned it two lines ago.
d) Let's plug in the point and see: (x,y)=(a,0) implies [tex]0=\log_a(a)[/tex].
The equivalent exponetial form is [tex]a^0=a[/tex] which is not true because [tex]a^0=1 (\neq a)[/tex].
If [tex]\log_a(9)=4[/tex]. then it's equivalent exponential form is: [tex]a^4=9[/tex].
Guess what it asked for the value of [tex]a^4[/tex] and we already found that by writing your equation [tex]\log_a(9)=4[/tex] in exponential form.
Note:
The equivalent exponential form of [tex]\log_a(x)=y[/tex] implies [tex]a^y=x[/tex].
Find the product of (x − 7)2.
A. x2 − 14x + 49
B. x2 + 14x + 49
C. x2 − 49
D. x2 + 49
Answer:
A.
Step-by-step explanation:
(x − 7)^2=
=x^2 − 14x + 49
Answer:
x^2 -14x+49
Step-by-step explanation:
(x − 7)^2
(x-7) (x-7)
FOIL
first x*x = x^2
outer -7*x = -7x
inner -7*x = -7x
Last = -7*-7 = 49
Add them together
x^2 -7x-7x +49
x^2 -14x+49
Which shows the correct solution of the equation
1/2 a + 2/3b = 50 when b=30
For the given equation, if b=30, then the value of a will be equal to 60.
Like the given equation is a linear equation with two variables (a and b). You can solve this equation replacing b for the informed value (30).
Here it is important to remember the rules to the addition and the mutiplication of integers numbers:
Addition Sign RulesThe rules to addition of numbers are:
+ +
Add Final result (+)
- -
Add Final result (-)
+ -
Subtract Final result (the sign of the integer having greater value )
- +
Subtract Final result (the sign of the integer having greater value )
Multiplication Sign RulesThe rules to multiplication of numbers are:
+ + or - -
The result presents a positive sign (+) because the signs are same.
+ - or - +
The result presents a negative sign (-) because the signs are different.
If b=30, then you can find the value for a from steps below.
[tex]\frac{1}{2}*a +\frac{2}{3} *b=50\\ \\ \frac{1}{2}*a +\frac{2}{3} *30=50\\ \\ \frac{1}{2}*a +2*10=50\\ \\ \frac{1}{2}*a +20=50\\ \\ \frac{1}{2}*a =50-20\\ \\ \frac{1}{2}*a=30\\ \\ a=30*2\\ \\ a=60[/tex]
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Evaluate the expression if a = 4 , b = 9. and c = 1. A. –27 B. –9 C. 9 D. 27
(thanks :)))))))))) )
Answer:
I don't know if you want to find this answer using the quadratic formula or not, the question is no the greatest but i will solve it the best that i can. Or
Step-by-step explanation:
I used the discriminant which is √[tex]b^{2}[/tex]-4ac
Then I filled the numbers in, and found that 9 gets plug in for b and this becomes 9 squared, and that becomes 81. 4 is multiplied to 4 and 1 and becomes 16. Then 81 and 16 are subtracted and we get 65. We then find the square root, and will find that the answer is C.
Hoped this helped thanks, if you need more help let me know.
The required value of the given expression is (-9). which is the correct answer would be an option (B).
What is the quotient?A quotient is defined as when dividing one number by another, the result is called the quotient.
To determine the value of the expression.
The given expression is given in the question.
⇒ 3b ÷ c⁽¹⁻ᵃ⁾
Here a = 4, b = 9, and c = 1
Substitute the value of a,b, and c in the expression
⇒ 3(9) ÷ (1)⁽¹⁻⁴⁾
⇒ 27 ÷ (1)⁽¹⁻⁴⁾
⇒ 27 ÷(1)⁽⁻³⁾
Reciprocal the term in the denominator,
⇒ 27 × (1 /(-3)
⇒ 27/(-3)
Apply the division operation,
⇒ (-9)
Therefore, the required value of the given expression is (-9).
Hence, the correct answer would be an option (B).
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The question seems to be incomplete the correct question would be
Evaluate the expression if a = 4, b = 9, and c = 1.
3b ÷ c⁽¹⁻ᵃ⁾
A. –27 B. –9 C. 9 D. 27
Assume that there is a 55% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on threethree independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is nothing. (Round to four decimal places as needed.) b. With threethree hard disk drives, the probability that catastrophe can be avoided is nothing. (Round to six decimal places as needed.)
Answer:
a. 0.6975
b. 0.833625
Step-by-step explanation:
a. The probability of both drives failing is 0.55² = 0.3025, so the probability that both drives won't fail is 1 -0.3025 = 0.6975.
__
b. The probability of all three drives failing is 0.55³ = 0.166375, so the probability that all three drives won't fail is 1 -0.166375 = 0.833625.
What are the possible numbers of positive, negative, and complex zeros of f(x) = −3x4 + 5x3 − x2 + 8x + 4?
Answer:
Either: 1 neg, 3 pos, 0 imaginary; 1 neg, 1 pos, 2 imaginary
Step-by-step explanation:
Look for the positive possibilities first. Count the numbe of sign changes then subtract 2, if possible, as many times as you can.
There are 3 sign changes. So the possible positive roots are either 3 or 1.
Now look for the negative possibilities. Replace each x with a -x and then count the sign changes. Replacing with -x's gives you this polynomial:
[tex]f(-x)=-3x^4-5x^3-x^2-8x+4[/tex]
There is only one sign change here, so the possible negative roots is 1. Start with the negative roots to find the possible combinations of positive, negative, and imaginary, since there is only 1.
- 1 1
+ 3 1
i 0 2
Since this is a 4th degree, the number of roots we have has to add up to equal 4.
A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? (Round your answer to two decimal places.) ft
The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is:
16.65 ft.
Step-by-step explanation:Let L denote the total length of the ladder.
In right angled triangle i.e. ΔAGB we have:
[tex]L^2=h^2+(x+4)^2[/tex]
( Since by using Pythagorean Theorem)
Also, triangle ΔAGB and ΔCDB are similar.
Hence, the ratio of the corresponding sides are equal.
Hence, we have:
[tex]\dfrac{h}{8}=\dfrac{x+4}{x}[/tex]
i.e.
[tex]h=\dfrac{8(x+4)}{x}[/tex]
Hence, on putting the value of h in equation (1) we get:
[tex]L^2=(\dfrac{8(x+4)}{x})^2+(x+4)^2\\\\i.e.\\\\L^2=\dfrac{64(x+4)^2}{x^2}+(x+4)^2\\\\i.e.\\\\L^2=(x+4)^2[\dfrac{64}{x^2}+1]----------(2)[/tex]
Now, we need to minimize L.
Hence, we use the method of differentiation.
We differentiate with respect to x as follows:
[tex]2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1]+(x+4)^2\times \dfrac{-128}{x^3}\\\\i.e.\\\\2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1+(x+4)\times \dfrac{-64}{x^3}]\\\\\\i.e.\\\\\\2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1-\dfrac{64}{x^2}-\dfrac{256}{x^3}]\\\\\\i.e.\\\\\\2L\dfrac{dL}{dx}=2(x+4)[1-\dfrac{256}{x^3}][/tex]
when the derivative is zero we have:
[tex]2(x+4)[1-\dfrac{256}{x^3}]=0\\\\i.e.\\\\x=-4\ and\ x=\sqrt[3]{256}[/tex]
But x can't be negative.
Hence, we have:
[tex]x=\sqrt[3]{256}[/tex]
Now, on putting this value of x in equation (2) and solving the equation we have:
[tex]L^2=277.14767[/tex]
Hence,
[tex]L=16.6477\ ft.[/tex]
which on rounding to two decimal places is:
[tex]L=16.65\ ft.[/tex]
Using the Pythagorean theorem, the length of the shortest ladder that will reach from the ground over the 8 ft fence to the wall of the building 4 ft away is approximately 8.94 ft.
Explanation:This problem is an example of a right triangle problem in trigonometry. The fence and the ground form the two legs of a right triangle and the ladder forms the hypotenuse. The 8ft fence is perpendicular to the 4ft distance from the building, forming a 90-degree angle.
To find the length of the shortest ladder from the ground over the fence to the wall of the building, we need to use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the formula is h² = a² + b², where h is the length of the ladder (hypotenuse), 'a' is the height of the fence (8 ft), and 'b' is the distance from the fence to the building (4 ft).
Therefore, the length of the shortest ladder can be solved as follows:
h² = 8² + 4² = 64 + 16 = 80
By taking the square root of both sides, we find that h (the length of the ladder) is approximately 8.94 ft, rounded to two decimal places.
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The average price of a gallon of orange juice from October 2013 to September 2014 can be modeled by the function f shown, where x represents the number if months since October 2013,
f(x)=6.12+0.03x
Complete the sentence to describe the change in average price of a gallon of orange juice from October 2013 to September 2014
The average price of a gallon of orange ( 1st-Blank) by (2nd-Blank) each month
1st -Decreased OR Increased
2nd- 3% OR 612% Or $0.03 OR $6.12
Answer:
The average price of a gallon of orange increased by $0.03 each month.
Step-by-step explanation:
It is 11 months between October 2013 and September 2014 so the price after 11 months =
f(11) = 6.12 + 0.03(11)
= 6.12 + 0.33
= $6.45.
This is an increase of 0.33 / 11 = 0.03 / month.
Find the the measure of angle T
Answer:
38.7°
Step-by-step explanation:
Use the Law of Cosines:
[tex]7^2=11^2+10^2-2(11)(10)cosT[/tex] and
49 = 121 + 100 - 220cosT so
-172 = -220cosT and
.781818181 = cosT
Using the inverse cosine function on your calculator, you find that angle T = 38.7 degrees
sin4θ - sin2θ = _____
2cos3θcosθ
2cos3θsinθ
2sin3θcosθ
2sin3θsinθ
Answer:
B. 2cos3θsinθ.
Step-by-step explanation:
Use the identity
sin x - sin y = 2 [cos(x + y)/2]sin [x - y)/2].
So we have:
sin4θ - sin2θ = 2 cos (4θ+2θ)/2 sin (4θ-2θ)/2
= 2cos3θsinθ.
I don't know how to find x. Can someone please explain.
Answer:
x° = 109°
Step-by-step explanation:
x° is a "corresponding angle" to either of the upper left or lower right interior angles of the parallelogram. (The lines marked with a single arrow are parallel, as are the lines marked with a double arrow.)
Either of those angles is supplementary to the one marked 71°, so x° and all corresponding angles are 180° -71° = 109°.
6. For a particular pickup truck, the percent markup is known to be 115% based on cost to the seller. If the seller paid $15,800 for the truck, what would be the percent markup be based on the sale price? (Round to the nearest tenth percent)
Answer:
53.5 %Explanation:
You can convert the percent markup into a multiplicative factor in this way:
Base price: 15,800 . . . (cost to the seller)
Percent mark up: 115% . . . (based on the cost to the seller)
Sale price: 15,800 + 115% of x = 15,800 + 115 × 15,800 /100 =
= 15,800 + 1.15 × 15,800 = 15,800 (2.15) = 33,970
The markup is:
Markup = price paid by the seller - cost to the seller = 33,970 - 15,800 = 18,170 (notice that this is 115% of 15,800)And the percent markup based on the sale price is:
% = (markup / sale price) × 100 = (18,700 / 33,970) × 100 == 53.49 %
Rounding to the nearest tenth percent that is 53.5 %.
Hillary rolls 2 number cubes numbered 1 through 6 while playing her favorite board game. She will get a second turn if she rolls a sum that is an odd number greater than 10.
What are Hillary's chances of getting a second turn when she rolls the number cubes?
1 over 36
1 over 18
1 over 12
1 over 6
Answer:
1 in 18
Step-by-step explanation:
The highest possible number Hillary can get is 12, meaning that the only odd number above 10 which she can get is 11.
There are two possible ways in which Hillary can get 11:
(a) Hillary rolls a 5 on her first cube and a 6 on her second cube
(b) Hillary rolls a 6 on her first cube and a 5 on her second cube
There are 34 other possible outcomes which Hillary can have when rolling her number cubes, for a total of 36 possible outcomes.
Since 2 of these outcomes result in a roll of 11, Hillary has a 2 in 36 chance of rolling an 11, which can be simplified as 1 in 18.
Answer:
1/18
Step-by-step explanation:
Which angle measures create a triangle with three different side lengths. 40°, 40°, and 100° 65°, 65°, and 65° 45°, 45°, and 90° 29°, 58°, and 93°
Answer:
29°, 58°, and 93°
Step-by-step explanation:
If the angles opposite are equal, the sides are equal. In order to have three different side lengths, you must have three different angles.
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 95% confidence if she uses a previous estimate of 0.32?
Answer: 8359
Step-by-step explanation:
The formula for sample size needed for interval estimate of population proportion :-
[tex]n=p(1-p)(\frac{z_{\alpha/2}}{E})^2[/tex]
Given : The significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}}=z_{0.025}=\pm1.96[/tex]
Previous estimate of proportion : [tex]p=0.32[/tex]
Margin of error : [tex]E=0.01[/tex]
Now, the required sample size will be :-
[tex]n=0.32(1-0.32)(\frac{1.96}{0.01})^2=8359.3216\approx8359[/tex]
Hence, the required sample size = 8359
To estimate the proportion of adults with high-speed Internet access with a 95% confidence level and a margin of error of 0.01, a sample size of 752 should be obtained.
Explanation:To estimate the proportion of adults who have high-speed Internet access with a 95% confidence level and a margin of error of 0.01, we can use the formula:
Sample Size = (Z^2 * p * (1-p)) / (E^2)
Where Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion from a previous study, and E is the desired margin of error.
With a previous estimate of 0.32, a confidence level of 95% (corresponding Z-score of 1.96), and a margin of error of 0.01, the sample size required would be:
(1.96^2 * 0.32 * (1-0.32)) / (0.01^2) = 752
A sample size of 752 should be obtained to achieve the desired confidence level.
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The standard formula for the volume of a rectangular pyramid is . If the pyramid is scaled proportionally by a factor of k, its volume becomes V' = V × k3. Use your algebra skills to derive the steps that lead from to V' = V × k3 for a scaled rectangular pyramid. Show your work.
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The volume of a rectangular pyramid is equal to
[tex]V=\frac{1}{3}LWH[/tex]
where
L is the length of the rectangular base
W is the width of the rectangular base
H is the height of the pyramid
If the pyramid is scaled proportionally by a factor of k
then
the new dimensions are
L=kL
W=kW
H=kH
substitute and find the new Volume V'
[tex]V'=\frac{1}{3}(kL)(kW)(kH)[/tex]
[tex]V'=\frac{1}{3}(k^{3})LWH[/tex]
[tex]V'=(k^{3})\frac{1}{3}LWH[/tex]
[tex]V'=(k^{3})V[/tex]
The new volume is equal to the scale factor k elevated to the cube multiplied by the original volume
Answer:
V = πr2h
V' = π × (k × r)2 × (k × h)
= π × k2 r2 × kh
= k3 × πr2h
= k3 × V
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs not all tiles will be used match each quadratic graph to its respective function PLEASE HELPPPP
Answer:
Part 1) The function of the First graph is [tex]f(x)=(x-3)(x+1)[/tex]
Part 2) The function of the Second graph is [tex]f(x)=-2(x-1)(x+3)[/tex]
Part 3) The function of the Third graph is [tex]f(x)=0.5(x-6)(x+2)[/tex]
See the attached figure
Step-by-step explanation:
we know that
The quadratic equation in factored form is equal to
[tex]f(x)=a(x-c)(x-d)[/tex]
where
a is the leading coefficient
c and d are the roots or zeros of the function
Part 1) First graph
we know that
The solutions or zeros of the first graph are
x=-1 and x=3
The parabola open up, so the leading coefficient a is positive
The function is equal to
[tex]f(x)=a(x-3)(x+1)[/tex]
Find the value of the coefficient a
The vertex is equal to the point (1,-4)
substitute and solve for a
[tex]-4=a(1-3)(1+1)[/tex]
[tex]-4=a(-2)(2)[/tex]
[tex]a=1[/tex]
therefore
The function is equal to
[tex]f(x)=(x-3)(x+1)[/tex]
Part 2) Second graph
we know that
The solutions or zeros of the first graph are
x=-3 and x=1
The parabola open down, so the leading coefficient a is negative
The function is equal to
[tex]f(x)=a(x-1)(x+3)[/tex]
Find the value of the coefficient a
The vertex is equal to the point (-1,8)
substitute and solve for a
[tex]8=a(-1-1)(-1+3)[/tex]
[tex]8=a(-2)(2)[/tex]
[tex]a=-2[/tex]
therefore
The function is equal to
[tex]f(x)=-2(x-1)(x+3)[/tex]
Part 3) Third graph
we know that
The solutions or zeros of the first graph are
x=-2 and x=6
The parabola open up, so the leading coefficient a is positive
The function is equal to
[tex]f(x)=a(x-6)(x+2)[/tex]
Find the value of the coefficient a
The vertex is equal to the point (2,-8)
substitute and solve for a
[tex]-8=a(2-6)(2+2)[/tex]
[tex]-8=a(-4)(4)[/tex]
[tex]a=0.5[/tex]
therefore
The function is equal to
[tex]f(x)=0.5(x-6)(x+2)[/tex]
For the first graph the function is f(x) = (x—3)(x + 1), for the second graph the function is f(x) = -2(x—1)(x + 3), and for the third graph the function is f(x) = 0.5(x-6)(x+2).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we can see in the first graph, the x-intercepts are x = -1 and x = 3, and it is opening up-side, so the function:
f(x) = (x - 3)(x + 1)
Second graph: x-intercepts are x = -3 and x = 1 and opening down-side.
Also, the vertex is at (-1, 8) so the function:
f(x) = -2(x - 1)(x + 3)
Third graph: x-intercepts are x = -2 and x = 6, and it is opening up-side, Also the vertex is at (2, -8) so the function:
f(x) = 0.5(x-6)(x+2)
Thus, for the first graph the function is f(x) = (x—3)(x + 1), for the second graph the function is f(x) = -2(x—1)(x + 3), and for the third graph the function is f(x) = 0.5(x-6)(x+2).
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What are the discontinuity and zero of the function f(x) = quantity x squared plus 5 x plus 6 end quantity over quantity x plus 2?
A. Discontinuity at (−2, 1), zero at (3, 0)
B. Discontinuity at (−2, 1), zero at (−3, 0)
C. Discontinuity at (2, 5), zero at (3, 0)
D. Discontinuity at (2, 5), zero at (−3, 0)
Answer:
B. Discontinuity at (−2, 1), zero at (−3, 0)
Step-by-step explanation:
The given function is:
[tex]\frac{x^{2}+5x+6}{x+2}[/tex]
The expression in numerator can be expressed as factors as shown below:
[tex]\frac{x^{2}+5x+6}{x+2}\\\\ =\frac{x^{2}+2x+3x+6}{x+2}\\\\ =\frac{x(x+2)+3(x+2)}{x+2}\\\\ =\frac{(x+2)(x+3)}{x+2}[/tex]
Note that for x = -2, both numerator and denominator will be zero. When both the numerator and denominator of a rational function are zero for a given value of x we get a discontinuity at that point. This discontinuity is known as a hole. This means there is a hole at x = -2
Cancelling the common factor from numerator and denominator we get the expression f(x) = x + 3
Using the value of x = -2 in previous expression we get:
f(x) = -2 + 3 = 1
Thus, there is a discontinuity(hole) at (-2, 1)
For x = -3, the value of the expression is equal to zero. This means x = -3 is a zero or root of the function.
Thus, (-3, 0) is a zero of the function.
Therefore, option B would be the correct answer.
A farmer finds that if she plants 100 trees per acre, each tree will yield 35 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest?
Answer:
126 trees should she plant per acre to maximize her harvest.
Step-by-step explanation:
Let x be the additional tress that must be plant after planting 100 tress.
So, total number of trees = 100 + x trees
Also, Each additional tree planted decreases the yield of each tree by 3 bushels.
So , net bushels by each tree = 35 - 3x
The revenue function becomes
f(x) = (100 + x)(35 - 3x)
Thus,
Differentiating it by using chain rule as:
f'(x) = (100 + x)35 + 100(35 - 3x)
f'(x) = 3500 + 35x + 3500 - 300x
f'(x) = 7000 - 265x
For maxima of f(x), f'(x) = 0
7000 - 265x = 0
Thus,
x = 26.4151
Since, x represents tress, so, x is 26.
So, total tress she would plant to earn maximum revenue = 100 + 26 = 126 trees
A parabola has a vertex at the origin. The equation of the directrix of the parabola is y = 3. What are the coordinates of its focus? (0,3) (3,0) (0,–3) (–3,0)
Answer:
(0, -3)
Step-by-step explanation:
The vertex is halfway between the directrix and the focus. The vertex is at (0, 0) and the directrix is a (0, 3). There are 3 units between them, so that means that the focus is 3 units the other way at (0, -3).
Based on the scenario given above, the the coordinates of its focus is known to be (0, -3).
What is the parabola about?A parabola is known to be a kind of plane curve that is said to be often mirror-symmetrical and it is one that can be called closed to U-shaped.
Note that the vertex is said to be in the middle between the directrix and the focus. So the vertex is at (0, 0) and also the directrix is a (0, 3).
Since there are found to be 3 units between them, we can say that the focus is 3 units the other part at (0, -3).
Therefore, Based on the scenario given above, the the coordinates of its focus is known to be (0, -3).
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Choose the best answer. The diagonals of a rectangle:
A.) are double the shortest side
B.) none of these
C.) are the same length
D.) are the not same length
C.) Are the same length
How you know-
No matter how long the rectangle is the diagonals always will measure the same length. Think about two sides of a square, they have to equal the same length because if they were not the same then the shape wouldn't be a square.
The best answer is the diagonals of the rectangle are the same length.
Diagonals of Rectangle PropertiesThe diagonal of rectangle is a line segment drawn between the opposite vertices of the rectangle. The properties of diagonals of a rectangle are as follows:
1. The two diagonals of a rectangle are congruent. In other words, the length of the diagonals is equal.
2. The two diagonals bisect each other and divide the rectangle into two equal parts.
3. The length of the diagonal of rectangle can be obtained using the Pythagoras theorem.
4. When the diagonals bisect each other, the angles of a rectangle at the center become one obtuse angle and the other an acute angle.
5. When two diagonals bisect each other at 90° it is called a square.
6. Since the diagonal of rectangle divide the rectangle into two right-angled triangles, it is considered the hypotenuse of these triangles.
We know the diagonal property of rectangle that
1. The diagonals of the rectangle bisect each other.
2. The diagonals of the rectangle are equal.
The best answer is the diagonals of the rectangle are the same length.
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What is the area of a rectangle with a length of 3 cm and a width of 4.5 cm?
A) 1.5 cm squared
B) 6.75 cm squared
C) 7 cm squared
D) 13.5 cm squared
(PLEASE EXPLAIN HOW YOU GOT THE ANSWER)
D) 13.5 cm squared (13.5 cm²)
Step-by-step explanation:In this question, it's asking you to find the area of the rectangle.
In order to solve this question, we need to use the helpful information that the question gives us.
Important Information:
Length is 3 cmWidth is 4.5 cmWith the information above, we can solve the problem.
To find the area of the rectangle, we would need to multiply the length times the width.
length × width (or l × w)
We know that the length is 3 and the width is 4.5, so we would multiply 3 and 4.5 in order to get the area of the rectangle.
[tex]3 * 4.5=13.5[/tex]
When you're done multiplying, you should get 13.5. With the unit, it would be 13.5 cm² (area of a rectangle is always squared).
This means that the area of the rectangle is 13.5 cm²
I hope this helped you out.Good luck on your academics.Have a fantastic day!in the xy-plane, the y-axis contains all ordered pairs such that:
Answer:
B, the x coordinate is zero
Step-by-step explanation:
The y axis is the line where the x coordinate is zero
The x axis is the line where the y coordinate is zero
We are looking for the y axis, so x=o
Answer:
For me the answer was B (the x-coordinate is 0)
Step-by-step explanation:
Solve the right triangle. State the side lengths to the nearest tenth and the angle measures to the nearest degree.
Answer:
Option B
Step-by-step explanation:
The two acute angles of a right triangle are equal.
[tex] \angle \: A + 18 = 180[/tex]
[tex]\angle \: A= 90 - 18 = 72 \degree[/tex]
Recall the mnemonics SOH-CAH-TOA
The tangent ratio is opposite over adjacent.
[tex] \tan(18) = \frac{AC}{21} [/tex]
[tex]AC = 21 \tan(18) [/tex]
[tex]AC = 6.8[/tex]
The sine ratio is opposite over hypotenuse
Using the sine ratio,
[tex] \sin(72) = \frac{21}{AB} [/tex]
[tex]AB = \frac{21}{ \sin(72) } = 22.1[/tex]
Answer:
it 55
Step-by-step explanation:
There are 100 students each enrolled in at least one of three science classes. Of those students, 60 are enrolled in chemistry, 45 in physics, and 30 in biology. Some students are enrolled in two science classes, and 10 students are enrolled in all three. (a) How many students are enrolled in exactly two science classes? (b) There are 9 students taking both chemistry and physics (but not biology), and 4 students taking both physics and biology (but not chemistry). How many are taking both chemistry and biology (but not physics)? Lewis, Harry. Essential Discrete Mathematics for Computer Science (p. 57). Princeton University Press. Kindle Edition.
Answer:
a) 15
b) 2
Step-by-step explanation:
a) The sum of the enrollments in chemistry (60), physics (45), and biology (30) counts those triply enrolled 3 times and those doubly-enrolled twice. This sum will exceed the total number of students by 1 times those double-enrolled and twice those triply-enrolled.
We know that there are 10 students triply-enrolled, so the difference ...
(60 +45 +30) -2(10) = 15
is the number of doubly-enrolled students.
There are 15 students enrolled in exactly 2 science classes.
__
b) There are 9+4 = 13 students doubly-enrolled in physics and something else. Using the result from part A, there will be 15 -13 = 2 students doubly-enrolled in chemistry and biology, but not physics.
Answer:
a) 15
b) 2
Step-by-step explanation:
There are 15 students in 2 science classes.
2 students enrolled in both chemistry and biology, but not physics.
15 -13 = 2
Mayra did not have a date on a Friday night so she decided to mix solutions that she obtained from her garage. She has 9 liters of a 4% -saline solution that must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?
Let [tex]x[/tex] be the number of liters of the 10% solution she needs to use. She'd end up with a 6% solution with a volume of [tex]9+x[/tex] liters. The starting solution contains 0.04*9 = 0.36 liter of salt. Each liter of the 10% solution contributes 0.1 liter of salt, so that
[tex]0.36+0.1x=0.06(9+x)[/tex]
Solve for [tex]x[/tex]:
[tex]0.36+0.1x=0.54+0.06x[/tex]
[tex]0.04x=0.18[/tex]
[tex]x=4.5[/tex]
so Mayra needs to add 4.5 liters of the 10% solution.
Complete the synthetic division problem below. What is the quotient in polynomial form?
Answer:
C
Step-by-step explanation:
Answer: OPTION C
Step-by-step explanation:
You need to follow these steps:
- Carry the number 1 down and multiply it by the number 2.
- Place the product obtained above the horizontal line, below the number 5 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number 2.
- Place the product obtained above the horizontal line, below the number -14 and add them.
Then:
[tex]2\ |\ 1\ \ 5\ -14\\\\.\ \ |\ \ \ \ 2\ \ \ 14\\------\\.\ \ \ 1\ \ \ 7\ \ 0[/tex]
Therefore, the quotient in polynomial form is:
[tex]x+7[/tex]