a farmer wants to use 500 feet of fence to create a pasture for his horse. The area created by this is modeled the function A(w)=250w-w^2, where w represent width in feet. What is A(50)

Answer:

1 and 9

Step-by-step explanation:

To complete the square

add ( half the coefficient of the x- term)²

1

x² + 2(- 1)x + (- 1)² = x² - 2x + 1 = (x - 1)²

2

x² + 2(- 3)x + (- 3)² = x² - 6x + 9 = (x - 3)²

To complete the square for the expressions x² - 2x + ___ and x² - 6x + ___, the required values are 1 and 9, respectively, because these are the squares of half the coefficients of the x terms.

To complete the square for a quadratic expression, we need to add a term that will turn the expression into a perfect square trinomial. For the general form x² + bx + c, the value needed to complete the square is (b/2)².

In the case of x² - 2x + ___, the value of b is -2. Therefore, you need to add (-2/2)² = (1)² = 1.

For the second expression, x² - 6x + ___, the value of b is -6. Here, you add (-6/2)² = (3)² = 9.

So, the values needed to complete the square are:

For x² - 2x + ___, the value is 1.

For x² - 6x + ___, the value is 9.

Answer:

B 18*2/9 =4

Step-by-step explanation:

To determine the number of mixed nuts that were almonds, take the number of nuts and multiply by the fraction that were almonds

nuts * 2/9= almonds

18 * 2/9

36/9

4

Hey there! I'm happy to help!

To find the area of a circle, you square the radius and then multiply by pi (3.14 in our case).

The radius is half of the diameter.

12.6/2=6.3

We square this.

6.3²=39.69

We multiply by 3.14

39.69×3.14=124.6266

We round to the nearest hundredth, giving us an area of 124.63 in².

Now you can find the area of a circle! Have a wonderful day! :D

You can use formula for area of circle which simply is pi times square of radius. The radius is half of diameter.

The area of the given circle is 124.63 sq inches

Area of circle using pi = 3.14 and approximated to nearest hundredth.

[tex]\text{Area} = \pi \times r^2[/tex]

[tex]\text{Radius} = \dfrac{\text{diameter}}{2}\\ r = \dfrac{12.6}{2} = 6.3 \: \rm inch[/tex]

[tex]Area = \pi \times r^2 \approx 3.14 \times 6.3^2 \approx 124.626 \approx 124.63 \: \rm inch^2[/tex]

Thus, the area of the given circle is 124.63 sq inches

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Answer:

It is symmetric about the x-axis because cos(3θ) = cos(-3θ).

It is not symmetric about the y-axis because cos(3θ) is not equal to cos(3(pi-θ)).

It is not symmetric about the origin because cos(3θ) is not equal to -cos(3θ).

Answer:

The graph is symmetric about x- axis.

Step-by-step explanation:

We are given that an equation

[tex]r=4 cos 3\theta[/tex]

We have to find the graph is symmetric  about x- axis , y-axis or origin.

We taking r along y-axis and [tex\theta [/tex] along x- axis

When the graph is symmetric about x= axis then (x,y)=(-x,y)

[tex] \theta [/tex] is replaced by [tex]-\theta[/tex] and r remain same then we get

[tex] r=4cos (-3\theta)[/tex]

We know that cos (-x)=cos x

Therefore, [tex] r=4cos 3\theta[/tex]

Hence, the graph is symmetric about x- axis.

When the graph is symmetric about y- axis then (x,y)=(x,-y)

Now, r is replaced by -r then we get

[tex]-r=4cos 3\theta [/tex]

[tex] r=-4 cos {3\theta}[/tex]

[tex] r=4 cos {\pi-3\theta}[/tex]

Therefore, the graph is not symmetric about y-axis.

When the graph is symmetric about y- axis then (x,y)=(x,-y)

Now, r is replaced by -r then we get

[tex]-r=4cos 3\theta [/tex]

[tex] r=-4 cos3\theta[/tex]

[tex] r=4 cos (\pi-3\theta)[/tex]

[tex](\theta,r)\neq (\theta,-r)[/tex]

Therefore, the graph is not symmetric about y-axis.

When the graph is symmetric about origin then (-x,-y)=(x,y)

Replaced r by -r and [tex]\theta [/tex] by-[tex]\theta[/tex]

Then we get [tex] -r=4cos3(-\theta)[/tex]

[tex] -r= 4 cos 3\theta[/tex]

Because cos(-x)=cos x

[tex] r=-4 cos 3\theta [/tex]

[tex](-\theta,-r)\neq(\theta,r)[/tex]

Hence, the graph is not symmetric about origin.

Answer:

True

Step-by-step explanation:

True.

Like the cubic term -3x^3 is negative, for small values of "x", the dependent variable "y" will rise. All this can be verified by looking at the graph.

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{9\times 9}{81}\\ h=&10 \end{cases}\implies V=\cfrac{1}{3}(81)(10)\implies V=270[/tex]

Answer:

a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft

Step-by-step explanation:

i took the test and i got this as the right answer

Answer:

A a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft

Step-by-step explanation:

In order to calculate this, you have to remember that you have a tether that is 18 ft long, thetered to a point, this would make a circle with a radius of 18 ft, but as the center of the circle would be where the theter is knotted, the shed forbids to make a full circle, it rather creates a 3/4 circle, and the dog can acces the other points of the shed, with le length of the theter, that is 8 ft after the long side, and 12 feet after the short side, creating another quarter circle with a radius of 8 and 12 ft.

Answer:

Step-by-step explanation:

The key here is that AB ║ EC. This makes arc AE have the same measure as arc BC. Since those have the same measure as AB and the three arcs together make a semicircle, each has measure 180°/3 = 60°.

Then the various arc measures are:

Then your answers are ...

a) AE = 60°

b) ∠ABD = (1/2)(DE +EA) = (1/2)(100° +60°) = 80°

c) ∠DFC = (1/2)(CD +EB) = (1/2)(80° + (60° +60°)) = 100°

d) ∠P = (1/2)(DA -AB) = (1/2)(100° +60° -60°) = 50°

e) ∠PAB = (1/2)(AB) = (1/2)(60°) = 30°

Answer:

arc BG = 14°

Step-by-step explanation:

∠BMG = [tex]\frac{1}{2}[/tex] ( arc BG + arc JS) = 30

Multiply both sides by 2

arc BG + arc JS = 60, that is

arc BG + 46° = 60° ( subtract 46° from both sides )

arc BG = 14°

Answer:

arc BG= 14°

Step-by-step explanation:

It is given in the figure that  mJS = 46∘ and m∠BMG = 30∘.

If two chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs. So,  

m∠BMG = 12 (mJS +mBG)

Substitute the given values and solve for mBG.

30∘ = 12 (46∘ + mBG)

Multiply by 2.

60∘ = (46∘ + mBG)

Subtract 46∘.

14∘ = mBG

Therefore, mBG = 14∘.

Answer:

option C

40

Step-by-step explanation:

[tex]x_{nm}[/tex]

here n = number of row

        m = number of column

so the labelled 3x3 matrix would be like this

[tex]y=\left[\begin{array}{ccc}y11&y12&y13\\y21&y22&y23\\y31&y32&y33\end{array}\right][/tex]

Given in the question matrixX since matrixY is eaxctly same as matrixX so,  

[tex]y=\left[\begin{array}{ccc}1&6&-7\\-5&0&8.5\\-1&14&27\end{array}\right][/tex]

so

y12 = 6

+

y13 = -7

+

y32 = 14

+

y33 = 27

=

40

Answer:

The answer C, is right!

Step-by-step explanation:

Answer:

Step-by-step explanation: 6?

Answer:

20 bricks

Step-by-step explanation:

So if you multipy the dimentions given, you get 750 inches squred. You now take 15,000 and divide it by 750 to get 20. This is your answer.

A company makes 20 concrete bricks.

Given:

Find:

Solution:

A company makes concrete bricks shaped like rectangular prisms.

So, the volume of the brick = 15*10*5 = 750[tex]inches^{3}[/tex]

Now, to find how many bricks they make we have to divide 750[tex]inches^{3}[/tex] from 15000.

Number of brick = 15000/750 = 20

Hence, the number of bricks that the company makes is 20.

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#SPJ2

Answer:

4.7%

Step-by-step explanation:

Kevin's commission was 4.7% of the price of the house.

Answer:

  x + 4y ≤ 15; y ≥ 0

Step-by-step explanation:

The graph doesn't do a very good job of modeling any of the given equations. However, the equations listed above seem the best fit.

The slope of the top (left) line is negative, so the equation will be of the form ...

  x + 4y = something

When y=0, x=15, so the "something" is expected to be 15.

However, the line appears to go through points (6, 2) and (-2, 4). Both of these points are on the line x + 4y = 14.

The graph is shaded below the line so the values of x and y that are in the shaded area will add to less than 15 (or 14). Hence, the inequality will be ...

  x + 4y ≤ something . . . . . part of the 3rd answer choice

The fact that the shading does not go below y=0 means the other limit is ...

  y ≥ 0 . . . . . part of every answer choice.

86 which equals 90 and then you divide by two

Answer:

x = 53.1°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanx = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{8}{10}[/tex]

x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{10}[/tex] ) ≈ 53.1°

Answer:

negative 2 square root of 10 over 7

Step-by-step explanation:

Check the picture below.

since the diameter of the cone is 6", then its radius is half that or 3", so getting the volume of only the cone, not the top.

1)

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \implies V\approx 37.7[/tex]

2)

now, the top of it, as you notice in the picture, is a semicircle, whose radius is the same as the cone's, 3.

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=3 \end{cases}\implies V=\cfrac{4\pi (3)^3}{3}\implies V=36\pi \\\\\\ \stackrel{\textit{half of that for a semisphere}}{V=18\pi }\implies V\approx 56.55[/tex]

3)

well, you'll be serving the cone and top combined, 12π + 18π = 30π or about 94.25 in³.

4)

pretty much the same thing, we get the volume of the cone and its top, add them up.

[tex]\bf \stackrel{\textit{cone's volume}}{\cfrac{\pi (3)^2(8)}{3}}~~~~+~~~~\stackrel{\stackrel{\textit{half a sphere}}{\textit{top's volume}}}{\cfrac{4\pi 3^3}{3}\div 2}\implies 24\pi +18\pi \implies 42\pi ~~\approx~~131.95~in^[/tex]

Answer:

Here's what I get.

Step-by-step explanation:

Question 4

The general equation for a sine function is

y = a sin[b(x - h)] + k

where a, b, h, and k are the parameters.

Your sine wave is

y = 3sin[4(x + π/4)] - 2

Let's examine each of these parameters.

Case 1. a = 1; b = 1; h = 0; k = 0

y = sin x

This is a normal sine curve (the red line in Fig. 1).

(Sorry. I forgot to label the x-axis, but it's always the horizontal axes)

Case 2. a = 3; b = 1; h = 0; k = 0

y = 3sin x

The amplitude changes from 1 to 3.

The parameter a controls the amplitude of the wave (the blue line in Fig. 1).

Case 3. a = 3; b = 1; h = 0; k = 2

y = 3sin x - 2

The graph shifts down two units.

The parameter k controls the vertical shift of the wave (the green line

in Fig. 1).

Case 4. a = 3; b = 4; h = 0; k = 2

y = 3sin(4x) - 2

The period decreases by a factor of four, from 2π to π/2.

The parameter b controls the period of the wave (the purple line in Fig. 2).

Case 5. a = 3; b = 4; h = -π/4; k = 2

y = 3sin[4(x + π/4)] - 2

The graph shifts π/4 units to the left.

The parameter h controls the horizontal shift of the wave (the black dotted line in Fig. 2).

[tex]\boxed{a = 3; b = 4; h = \frac{\pi}{2}; k = -2}}[/tex]

[tex]\text{amplitude = 3; period = } \dfrac{\pi}{2}}[/tex]

[tex]\textbf{Transformations:}\\\text{1. Dilate across x-axis by a scale factor of 3}\\\text{2. Translate down two units}\\\text{3. Dilate across y-axis by a scale factor of } \frac{1}{4}\\\text{4. Translate left by } \frac{\pi}{4}[/tex]

Question 6

y = -1cos[1(x – π)] + 3

[tex]\boxed{a = -1, b = 1, h = \pi, k = 3}[/tex]

[tex]\boxed{\text{amplitude = 1; period = } \pi}[/tex]

Effect of parameters

Refer to Fig. 3.

Original cosine: Solid red line

m = -1: Dashed blue line (reflected across x-axis)

 k = 3: Dashed green line (shifted up three units)

 b = 1: No change

h = π: Orange line (shifted right by π units)

[tex]\textbf{Transformations:}\\\text{1. Reflect across x-axis}\\\text{2. Translate up three units}\\\text{3. Translate right by } \pi[/tex]

Answer:

X x 26= 26x +840

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

Linear model:

E = 24x + 840   where E is the  enrolment .

If there are 900 students then

900 = 24x + 840

24x = 900-840 = 60

For  E < 900 we have the inequality

24x < 60

x < 2.5

As we are dealing in years our answer is

x <  3 years .

ANSWER

[tex]3\le x\le6[/tex]

EXPLANATION

The given inequality is

[tex] {x}^{2} - 9x + 18 \leqslant 0[/tex]

This is the same as

[tex](x - 3)(x - 6) \leqslant 0[/tex]

The corresponding equation is

[tex](x - 3)(x - 6)= 0[/tex]

By the zero product principle,

[tex]x = 3 \: or \: x = 6[/tex]

We now plot the boundaries and test for the region that satisfies the inequality.

See attachment.

From the graph the solution is

[tex]3\le x\le6[/tex]

Answer:

It's the second choice ⁶√2.

Step-by-step explanation:

Convert to fractional exponents:

√2 = 2^1/2

∛2 = 2^1/3

√2 / ∛2

= 2^1/2 / 2^1/3 = 2^(1/2-1/3)

= 2^(1/6)

Now change back to radicals:

= ⁶√2.

ANSWER

[tex] \frac{3\pi}{4} \: radians[/tex]

EXPLANATION

To convert an angle from degrees measure to radians, we multiply by:

[tex] \frac{\pi}{180 \degree} [/tex]

We want to convert 135° to radians.

This implies that,

[tex]135 \degree = 135\degree \times \frac{\pi}{180 \degree} = \frac{3\pi}{4} \: radians[/tex]

The last option is correct.

Answer:

1.=128     2.= 128      3.= 0      4.= 0

Step-by-step explanation:

Answer:

128 + 0 = 128

128 - 0 = 128

128 x 0 = 0

128 / 0 = 0

Answer:

500 lb

Step-by-step explanation:

You have to make a proportion:

[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]

77 lb is part of the whole weight ( which we don't know) so 77 will go on top

The problem tells us that 15.4% of the total weight is pecans so 15.4 will go over 100 (since % are out of 100)

[tex]\frac{77}{x} = \frac{15.4}{100}[/tex]

Then you cross multiply giving you: 7700 = 15.4x

then you divide 15.4 to both sides to isolate x which will give you 500

Final answer:

To find the total weight of a batch of mixed nuts where pecans make up 15.4% and weigh 77 pounds, we set up a proportion and solve for the total weight, resulting in 500 pounds for the whole batch.

Explanation:

The question asks how many pounds of mixed nuts are in a batch altogether if 77 pounds are pecans, which represent 15.4% of the mix. To find the total weight, we need to set up a proportion where 15.4% corresponds to 77 pounds, and we want to find 100% (the whole mix).

We can set up the equation like so: 15.4 / 100 = 77 / x, where x stands for the total weight of the mixed nuts. To find x, we solve for x using algebra: x = 77 / (15.4 / 100). When you perform the calculation, the result is x = 500 pounds. So, the batch of mixed nuts weighs 500 pounds in total.

The measure of angle K and angle L is 35 degrees and 105 degrees

In Triangle JKL the measure of angle J = 40 and the measure of angle L is 3 times the measure of angle K.

here we assume the angle K be x

So Angle L be 3x

Now

J + K + L = 180

40 + x + 3x = 180

40 + 4x = 180

4x = 180 - 40

4x = 140

x = 35 degrees

So, the angle K be 35 degrees

And, angle L should be 3(35) 105 degrees

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Final answer:

To solve the exponential equation 7^(3x-1) = 5^(x-1) using properties of common logarithms, we can take the natural logarithm (ln) of both sides. By expanding and isolating x, we can solve for x approximately as x ≈ 0.08.

Explanation:

To solve this exponential equation, you can take the natural logarithm of both sides. The natural logarithm (ln) cancels out the exponential function. So, taking the ln of both sides, we have:

ln(7^(3x-1)) = ln(5^(x-1))

Using the property of logarithms, we can bring down the exponents:

(3x-1)ln(7) = (x-1)ln(5)

Now, we can solve for x by isolating it. Let's expand the equation:

3xln(7) - ln(7) = xln(5) - ln(5)

Combining like terms:

3xln(7) - xln(5) = ln(7) - ln(5)

Factoring out x:

x(3ln(7) - ln(5)) = ln(7) - ln(5)

And finally, dividing:

x = (ln(7) - ln(5))/(3ln(7) - ln(5))

Using a calculator or a math software, we can approximate the value of x to the nearest hundredth to find:

x ≈ 0.08

Answer:

Blue: 1/16 square units

Green: 1/64

yes

1/3

Step-by-step explanation:

The areas of these shaded triangles. Orange: 1/4 square units, Blue: 1/16 square units, Green: 1/64 square units

A fraction represents a part of a whole number of equal parts.

The area of the largest triangle is given as 1 square unit.

The area of the triangle is colored and follows a geometric sequence with the common ratio of 1/4.

The area of the non-shaded triangle is given by 1 square unit.

The area of the orange triangle

1 × 1/4 = 1/4 square units.

The area of the blue triangle

1/4 × 1/4 = 1/16 square units.

The area of the green triangle

1/16 × 1/4  = 1/64 square units.

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Answer:sd

D. [tex]f\left(x\right)=2x^2+3x-5[/tex]

Step-by-step explanation:

Given choices are:

[tex]f\left(x\right)=\frac{2}{x^2}[/tex]

[tex]f\left(x\right)=3\left(3-x\right)[/tex]

[tex]f\left(x\right)=7^2[/tex]

[tex]f\left(x\right)=2x^2+3x-5[/tex]

Now we need to find about which of them is the quadratic function.

We know that quadratic function is written in form of [tex]f\left(x\right)=ax^2+bx+c[/tex]

Last choice looks similar to that form.

Hence coorect choice is D. [tex]f\left(x\right)=2x^2+3x-5[/tex]

Answer:

D. f(x) = 2x^2 + 3x - 5

Step-by-step explanation:

C.Government is the answer

Answer:A-Price

Step-by-step explanation:

Real Gross Domestic Product is adjusted for Price changes.

Unlike Nominal GDP Real GDP accounts for the change in prices and provides a better figure than nominal GDP. Real GDP differentiate GDP in different years more significant because it permits comparisons of the real volume of services and goods without taking inflation.