jack is mowing a lawn that has a shed. needs to know area of lawn to mow. dimensions of yard are 5x by 13 x-4 . she'd are 2x by 2x+4. " find polynomial that describes area of lawn needed to mow. Polynomial in answer should have two terms.
please help.
Answers
The area of the lawn needed to be mowed equals to the area of the yard minus the area of the shed
The area of the yard = [tex](5x)(13x-4) = 65 x^{2} -20x[/tex]
The area of the shed = [tex](2x)(2x+4)=4 x^{2} +8x[/tex]
The area of the lawn = [tex]65 x^{2} -20x-(4 x^{2} +8x)[/tex]
The area of the lawn = [tex]65 x^{2} -20x-4 x^{2} -8x[/tex]
The area of the lawn = [tex]61 x^{2} -28x[/tex]
Related Questions
Determine the angular velocity, in radians per second, of 4.3 revolutions in 9 seconds. Round the answer to the nearest tenth.
Answers
simplify away.
Let g(x) = x - 3 and h(x) = x2 + 6. What is (h o g)(1)?
Answers
Which are the roots of the quadratic function f(q) = q2 – 125? Check all that apply. q = 5 q = –5 q = 3 q = –3 q = 25 q = –25
Answers
Answer:
q=5 sqrt 5 and q=-5 sqrt 5
Step-by-step explanation:
got it right on edge :)
The roots of the quadratic function f(q) = q^2 − 125 are q = -5 and q = 5. Other options listed do not satisfy the function. The roots are found by factoring the equation as a difference of squares.
Explanation:The roots of the quadratic function f(q) = q2 − 125 can be found by solving the equation q2 − 125 = 0. To find the roots, we need to factor the quadratic or use the square root property since the equation is already set to zero.
We can see that this is a difference of squares equation, so it factors to (q + 5)(q - 5) = 0. Setting each factor equal to zero gives us q = -5 and q = 5.
So, the roots of the quadratic function are q = -5 and q = 5. The other options given (q = 3, q = -3, q = 25, q = -25) do not satisfy the equation f(q) = q2 − 125 = 0, hence they are not roots of this function.
Complete the pattern ___, ___, ___, 0, 2, 4, 6
Answers
Answer:-6, -4, -2, 0, 2, 4, 6. They continue in increments of +2.
Step-by-step explanation:
Factor 2x^2-128 completely
Answers
2(x² - 64), but (x² - 64) = x² - 8² (difference of 2 squares),[a²-b²=(a-b)(a+b)]
2(x² - 64) = 2(x² - 8²) = 2(x-8)(x+8)
whats the value of the equation
Answers
13x-2(x+4) = 8x+1 =
13x-2x-8 = 8x+1=
11x-8 = 8x+1
-8 =-3x+1=
-9 = -3x
x = -9/-3 = 3
x = 3
Two standard number cubes are thrown, one after the other. What is the probability that the first cube lands showing a 1 and the second cube lands showing a number that is not 1? Round the answer to the nearest thousandth.
Answers
Let B be the probability that you don't throw 1
A and B are independent events
P(A)= 1/6 and P(B)= 5/6
Because they are independent you multiply them: 1/6 x 5/6 = 0.138888...
Rounded to the nearest thousandth is 0.139
Answer:
B on edge
Step-by-step explanation:
What are the values of a1 and r of the geometric series?
2 – 2 + 2 – 2 + 2
Answers
Answer: For the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
Step-by-step explanation: We are given to find the values of [tex]a_1[/tex] and [tex]r[/tex] of the following geometric series:
[tex]2-2+2-2+2-~.~.~..[/tex]
We know that
[tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
[tex]a_1=2.[/tex]
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio [tex]r[/tex] of the given geometric series is
[tex]r=\dfrac{-2}{2}=\dfrac{2}{-2}=~.~.~.~=-1.[/tex]
Thus, for the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
The circle will be dilated by a scale factor of 6. What is the value for n if the expression nPI represents the circumference of the circles in inches?
Answers
So basically N = 12r. You haven't given me any original radius, so I can't give you a constant for N, but if you do have that original radius you can just plug that into 12r.
Based on your comment, N = 12 * 9 = 108 inches
The value of n is 12 .
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
The circle will be dilated by a scale factor of 6 .
so,
New radius of the circle R = 6r
As is it dilated by a scale factor of 6
Now ,
The circumference of the new circles = 2πR
= 2.6π
= [tex]12\pi r[/tex] -------------------- (1)
and given circumference of the new circles = nπ ---------------------(2)
when we compare both n = 12
Hence, the value of n is 12 .
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In the figure below, segment AC is congruent to segment AB:
Triangle ABC with a segment joining vertex A to point D on side BC. Side AB is congruent to side AC
Which statement is used to prove that angle ABD is congruent to angle ACD?
Answers
the answer is A. segment AD bisects angle CAB. I just took the exam and I got it right. hope this helps!
Answer: Isosceles triangle theorem
Step-by-step explanation:
In the given picture, there a triangle whose two sides are equal AB=AC.
Therefore it is an isosceles triangle.
Now, the isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Therefore by isosceles triangle theorem in ΔABC we have
[tex]\angle{B}=\angle{C}[/tex]
Since [tex]\angle{ACD}=\angle{C}[/tex] [Reflexive]
[tex]\angle{ABD}=\angle{B}[/tex] [Reflexive]
Therefore, [tex]\angle{ACD}=\angle{ABD}=[/tex]
Evaluate the surface integral. ∫∫s (x2 + y2 + z2) ds s is the part of the cylinder x2 + y2 = 16 that lies between the planes z = 0 and z = 5, together with its top and bottom disks.
Answers
[tex]\mathbf r_1(u,v)=\begin{cases}x(u,v)=4\cos u\\y(u,v)=4\sin u\\z(u,v)=v\end{cases}[/tex]
where [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le5[/tex],
[tex]\mathbf r_2(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=0\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex], and
[tex]\mathbf r_3(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=5\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex].
For the cylinder, we have
[tex]\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}=\langle4\cos u,4\sin u,0\rangle\implies\left\|\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}\right\|=4[/tex]
and the integral over this surface is
[tex]\displaystyle\iint_{\text{cyl}}(x^2+y^2+z^2)\,\mathrm dS=4\int_{v=0}^{v=5}\int_{u=0}^{u=2\pi}((4\cos u)^2+(4\sin u)^2+v^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle320\int_{u=0}^{u=2\pi}\mathrm du+8\pi\int_{v=0}^{v=5}v^2\,\mathrm dv[/tex]
[tex]=640\pi+\dfrac83\pi(125)[/tex]
[tex]=\dfrac{2920\pi}3[/tex]
Bottom disk:
[tex]\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}=\langle0,0,u\rangle\implies\left\|\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}\right\|=u[/tex]
and the integral over the bottom disk is
[tex]\displaystyle\iint_{z=0}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}u^3\,\mathrm du[/tex]
[tex]=128\pi[/tex]
The setup for the integral along the top disk is similar to that for the bottom disk, except that [tex]z=5[/tex]:
[tex]\displaystyle\iint_{z=5}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2+5^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}(u^3+25u)\,\mathrm du[/tex]
[tex]=528\pi[/tex]
Finally, the value of the integral over the entire surface is the sum of the integrals over the component surfaces:
[tex]\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\frac{2920\pi}3+128\pi+528\pi=\dfrac{4888\pi}3[/tex]
Evaluate the given surface integral by parameterizing the surface and computing the integral on each surface separately. Take the antiderivatives of both dimensions defining the area, from the bounds of the integral for an accurate solution.
Explanation:The problem you've presented is a surface integral in the field of calculus, specifically relating to multivariable calculus. To solve this, we need to evaluate the integral over the specified parts of the cylinder and the top and bottom disks. We start by parameterizing the surface. Given that our cylinder is x² + y² = 16 between z = 0 and z = 5, we can use cylindrical coordinates with the parameterization: r(θ, z) = <4cos(θ), 4sin(θ), z> for 0 ≤ θ ≤ 2π and 0 ≤ z ≤ 5. With this parameterization, you can derive the equation for the surface integral and solve it.
When working with surface integrals, it's essential to remember that you are totaling up the quantity across the entire surface of an object. In such a situation, we could handle this problem by separating it into three parts: the side of the cylinder, the top disk, and the bottom disk, and compute the integral on each surface separately.
The integral can be solved by taking the antiderivatives of both dimensions defining the area, with the edges of the surface in question being the bounds of the integral. You can apply this approach to all the separate parts of this question.
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The rounding rule for the correlation coefficient requires three decimal places true or false
Answers
Answer:
Round the value of r to three decimal places.
Step-by-step explanation:
The rounding rule for the correlation coefficient requires three decimal places
this statement is true.
The correlation coefficient in statistics is a parameter which measures the degree of strength of relation between two variables .
Its value lies between -1 to +1 .
The closer the correlation coefficient will be near to 1 the stronger the correlation will be.
The correlation between two variables can be positive or negative
Correlation coefficients are helpful in determining the functional relationships among the variables
So higher magnitude of correlation coefficients lead to accurate functional relation among variables.
The rounding rule for the correlation coefficient requires three decimal places
this statement is true.
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Write an appropriate inverse variation equation if y = 9 when x = 3.
Answers
y = k/x
so, 9 = k/3
k = 9x3
k = 27
then equation is, y = 27/x
Andrew estimated the weight of his dog to be 60 lb. The dog’s actual weight was 68 lb. What was the percent error in Andrew’s estimate? Round your answer to the nearest tenth of a percent. __________ %
Answers
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 68&100\\ 8&x \end{array}\implies \cfrac{68}{8}=\cfrac{100}{x}[/tex]
what is the other measurement of the shape?
Answers
for the length of the side that is not given:
look at it as part of a triangle with the legs being 4m tall by 6 m wide
so 4^2 + 6^2 = X62
16+36 = 52^2
square root(52) = 7.211 m
does it as to round of to nearest whole number? nearest tenth?
round off answer as needed
which expression represents the distance between the two points x and y on the number line -4 and 3
Answers
Answer with explanation:
The two points on the number line are
x = -4
y=3
The distance is a positive Quantity.
So, Distance between x and y can be written as:
=|x-y| or |y-x|
=|3-(-4)| or |-4-3|
=|3+4| or |-7|
=|7| or |-7|
=7 Units
The expression will be : =|x-y| or |y-x|
=|3-(-4)| or |-4-3|
the quadratic formula gives which roots for the equation 2x^2+x-6=0
Answers
a=2, b=1, c=-6
x = -b+_ /(b^2 - 4ac) ÷ 2a
+_ (plus minus) / ( square root)
X = -1 +_ /1^2 - 4(2)(-6) ÷ 2(2)
= -1 +_ /49 ÷ 4
= -1 +_ 7 ÷ 4
= 6/4 or -8/4
= 3/2 or -2
Hope it helped!
The quadratic formula gives two roots for a quadratic equation. The roots of the equation 2x²+x-6=0 are 1.5 and -2.
Explanation:The quadratic formula gives the roots of a quadratic equation of the form ax²+bx+c=0. For the equation 2x²+x-6=0, the values of a, b, and c are 2, 1, and -6, respectively.
Using the quadratic formula, we can calculate the roots:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula:
x = (-1 ± √(1² - 4*2*(-6))) / (2*2)
Simplifying the expression:
x = (-1 ± √(1 + 48)) / 4
x = (-1 ± √49) / 4
x = (-1 ± 7) / 4
Therefore, the roots of the equation 2x²+x-6=0 are:
x = (-1 + 7) / 4 = 3/2 = 1.5
x = (-1 - 7) / 4 = -8/4 = -2
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"if z is a standard normal variable, find the probability. the probability that z lies between 0 and 3.01"
Answers
P(0<z<3.01) = P(z<3.01) - P(z<0)
Reading from the z-table, we have
P(z<0) = 0.5
P(z<3.01) = 0.9987
Hence, P(0<z<3.01) = 0.9987 - 0.5 = 0.4987
The probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.
What is z- score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.
Given:
Probability between z = 0 and z = 3.01 is given by
As, P(0<z<3.01)
= P(z<3.01) - P(z<0)
So, the z score values are
P(z<0) = 0.5
and, P(z<3.01) = 0.9987
Hence, the probability that z lies between 0 and 3.01 P(0<z<3.01) = 0.4987.
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can anone help me please
Answers
Area= 12
Cost= 84
a. The perimeter of the triangle is 18 cm. b. The area of the triangle is 24 cm². c. Tiling the triangle at $7 per square centimeter would cost $168.
a. Perimeter:
Perimeter} = 5 + 5 + 8 = 18 cm
b. Area:
Use Heron's formula since the sides are known:
[tex]\[ s = \frac{5 + 5 + 8}{2} = 9 \] \[ \text{Area} = \sqrt{s(s-5)(s-5)(s-8)} \] \[ \text{Area} = \sqrt{9 \times 4 \times 4 \times 1} = \sqrt{576} = 24 \, \text{cm}^2 \][/tex]
c. Cost to Tile:
If the cost is $7 per square centimeter:
[tex]\[ \text{Cost} = \text{Area} \times \text{Cost per square centimeter} \] \[ \text{Cost} = 24 \times 7 = 168 \][/tex]
Therefore,
a. Perimeter = 18 cm
b. Area = 24 cm²
c. Cost to Tile = $168
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The law of cosines is a2+b2 - 2abcosC = c^2 find the value of 2abcosC .... A. 40 B. -40 C. 37 D. 20
(The sides are 2,4, and 5; A to B is 2, B to C is 4, and A to C is 5.)
Answers
Аngle C lies opposite to the side AB, so "c" in the formula it is AB in your triangle
4² + 5² - 2abcosC = 2²
16 + 25 - 2abcosC = 4
41 - 4 = 2abcosC
2abcosC = 37
Given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]
Law of Cosines is given as: [tex]a^2+b^2 - 2abcosC = c^2[/tex]
Given also are the sides of a triangle:
a = 4 (side B to C)b = 5 (side A to C)c = 2 (side A to B)Plug in the values into the Law of Cosines, [tex]a^2+b^2 - 2abcosC = c^2[/tex] to find [tex]\mathbf{2abcosC}[/tex]
Thus:[tex]4^2+5^2 - 2abcosC = 2^2\\\\16 + 25 - 2abcosC = 4\\\\41 - 2abcosC = 4[/tex]
Subtract 41 from both sides[tex]41 - 2abcosC - 41 = 4-41\\\\-2abcosC = -37[/tex]
Divide both sides by -1[tex]\mathbf{2abcosC = 37}[/tex]
Therefore, given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]
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Simplify: 4x^2+36/4x•1/5x
Answers
Answer:
Step-by-step explanation:
The given equation is:
[tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex]
On solving the above equation, we get
=[tex]\frac{4x^2+36}{(4x)(5x)}[/tex]
=[tex]\frac{4(x^2+9)}{(4x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(x)(5x)}[/tex]
=[tex]\frac{x^2+9}{(5x^2)}[/tex]
which is the required simplified form.
Thus, the simplified form of the given equation [tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex] is [tex]\frac{x^2+9}{(5x^2)}[/tex].
Which measure of variability is the most appropriate for this set of values?
13, 42, 104, 36, 28, 6, 17
Answers
Answer:
in other words that guy said E
Step-by-step explanation:
Steps to solve y=3x + 8
Answers
[tex]y-8=3x[/tex]
Step 2. Divide both sides by 3
[tex] \frac{y-8}{3} =x[/tex]
Step 3. Switch sides
[tex]x= \frac{y-8}{3} [/tex]
Done! :) Hope this helps!
A population of flies grows according to the function p(x) = 2(4)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 2x + 5. What is the population of flies after two weeks with the introduced spider?
Answers
now, after two weeks, x = 2
[tex]\bf P(x)-s(x)\implies 2(4)^2-[2(2)+5]\implies 32-9[/tex]
Answer:
answer is 23
Step-by-step explanation:
In dogs, the drug carprofen has a half-life of 8 hours. If a veterinarian gives a dog an 80-milligram dose, how long will it take for the amount of carprofen in the dog to reach 10 milligrams?
Answers
N(t)=Ne^(-λt)
or
N(t)=N(1/2)^(t/τ)
where:
t=time
N=initial amount
N(t)=final amount
τ=half-life
thus the time taken for the drug to decay will be:
10=80(1/2)^(t/8)
1/8=(1/2)^(t/8)
introducing natural logs;
ln (1/8)=(t/8)ln (1/2)
thus;
[ln 1/8]/[ln 1/2]=t/8
3=t/8
t=3*8
t=24 hours
the answer is 24 hours
Final answer:
Using the half-life formula, it would take 24 hours for the amount of carprofen to reduce from an initial dose of 80 milligrams to 10 milligrams.
Explanation:
To calculate the time it will take for the amount of carprofen to decrease from 80 milligrams to 10 milligrams in a dog, given the half-life of 8 hours, the exponential decay formula can be used. The half-life formula is:
[tex]C = C0 \times (1/2)^{(t/T)[/tex]
C is the final concentration of the drug.C0 is the initial concentration of the drug.t is the time elapsed.T is the half-life of the drug.Let's set up the equation using the given values:
[tex]10 mg = 80 mg \times (1/2)^{(t/8 hours)[/tex]
Now, we solve for t:
[tex]10/80 = (1/2)^{(t/8)[/tex]
[tex]1/8 = (1/2)^{(t/8)[/tex]
To find the exponent t/8 that makes this equation true, we can use logarithms:
log2(1/8) = t/8
-3 = t/8
t = -3 * 8
t = -24 hours
The negative result is due to the fact that we are finding a factor by which the concentration is reduced. To get the actual time elapsed, we take the absolute value:
t = 24 hours
Therefore, it would take 24 hours for the amount of carprofen to reduce to 10 milligrams.
which expression is equivalent to (4h^7k^2)^4?
A: 16h^11k^6
B: 16h^28k^8
C; 256h^11k^6
D: 256h^28k^8
Answers
The answer is D.
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex](4h^7k^2)^4[/tex]
We need to simplify this :
Here we go:
We will apply :
[tex](a^m)^n=a^{mn}[/tex]
[tex](4h^7k^2)^4\\\\=4^4\times (h^7)^4\times (k^2)^4\\\\=256h^{28}k^8[/tex]
Hence, option 'D' is correct.
To keep heating costs down for a structure, architects want the ratio of surface area to volume as small as possible. An expression for the ratio of the surface area to volume for the square prism shown is . Find the ratio when b = 12 ft and h = 18 ft.
Answers
Hope this helps!
The car salesman tells you that the car can go from a stop position to 60 mph in six seconds he's giving you the cars rate of
Answers
Answer:
acceleration i think
Step-by-step explanation:
If a new car is valued at $13,200 and 6 years later it is valued at $3000, then what is the average rate of change of its value during those six years?
Answers
Lily is standing at horizontal ground level with the base of the Sears Tower. The angle formed by the ground and the line segment from her position to the top of the building is 15.7°. The Sears Tower is 1450 feet tall. Find Lily's distance from the Sears Tower to the nearest foot.
Answers
tan theta=[opposite]/[adjacent]
opposite=1450 ft
adjacent=x ft
theta=15.7
thus;
1450/x=tan15.7
hence;
x=1450/tan15.7
x=5,158.54 ft
x=5,159 (to the nearest foot)