consider the table below.which of the following squares root equation best fits the data in the table?

Step-by-step explanation:

So it's really easy if you read it carefully, the only thing you need to do is 63,000 - 6,922 = _____ and that's it hope it helps

Answer:

2, 4, 4, 6

Step-by-step explanation:

So to get 3 to 2, you'd need to multiply by 2/3, so 2/3 would be the scale factor. 2/3*6=4, 9*2/3=6

Answer:

A. a. 34.5 feet

b. 60 feet

Step-by-step explanation:

Parabola equation

\(y=-0.005x^2+0.3x\)

Differentiating with respect to x we get

\(\dfrac{dy}{dx}=-0.01x+0.3\)

Equating with zero

\(-0.01x+0.3=0\\\Rightarrow -0.01x=-0.3\\\Rightarrow x=\dfrac{0.3}{0.01}\\\Rightarrow x=30\)

Double derivative of the parabolic equation

\(\dfrac{d^2y}{dx^2}=-0.01<0\)

So, \(x=30\) is maximum.

\(y=-0.005\times 30^2+0.3\times 30\\\Rightarrow y=4.5\)

So, the maximum height of the arch will be 4.5 feet.

From the ground the highest point of the arch will be \(30+4.5=34.5\ \text{ft}\)

We are taking the x axis as the width of the bank.

\(0=-0.005x^2+0.3x\\\Rightarrow 0.005x^2=0.3x\\\Rightarrow x=\dfrac{0.3}{0.005}\\\Rightarrow x=60\)

So, the width of the bank will be 60 feet.

Answer:

7a+2b-3c

Step-by-step explanation:

6a+a = 7a

2b stays the same

-3c stays the same

Answer:

Hey mate, here is your answer. Hope it helps you.

7a-3c+2b

Step-by-step explanation:

6a+a-3c+2b

=7a-3c+2b

3c and 2b will be the same because the variables are different. They are not like terms.

To find the confidence interval, we use the following formula.

Where z = 1.96 for a 95% confidence interval. Replacing the given information, we have the following:

So, the confidence interval is

Answer:

5x-2x

Step-by-step explanation:

4x-x = 3x

so,

5x-2x = 3x

The equivalent expression would be; 5x-2x

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We are given that the expression as; 4x - x

We need to find an equivalent expression.

Therefore, solving further;

4x-x = 3x

Thus, we can also create one expression as;

5x-2x = 3x

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Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

The value of the angle θ is approximately 24.2 degrees to 1 decimal place.

In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Given that tan θ = 23/52, we can find the value of the angle θ.

To find the value of θ, we can use the inverse tangent or arctan function. Taking the inverse tangent of both sides of the equation, we have:

θ = arctan(23/52)

Using a calculator or trigonometric tables, we can evaluate the inverse tangent of 23/52. The result is approximately 24.2 degrees.

Note that in the context of a right-angled triangle, the tangent function is defined for acute angles (less than 90 degrees). Since 0 degrees is the smallest possible angle, it is considered an acute angle in this case.

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The value for the Inequality 13x ≤ 200 is x ≤ 15.384.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

13 times a number x is less than or equal to 200.

Now, Writing the Inequality Mathematically

13x ≤ 200

x ≤ 200 / 13

x ≤ 15.384

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The ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

If two solids that are similar to each other, have volumes A and B respectively, and have a scale factor of a:b, thus, the ratio of their volumes would be expressed as:

Volume of solid A/Volume of solid B = a³/b³

or

Volume of solid A : Volume of solid B = a³ : b³

Thus, the given similar solids have a scale factor of 5:3, therefore, the ratio of their volumes would be expressed as shown below:

5³ : 3³

125 : 27

Thus, the ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.

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Answer:

\(C=4\)

Step-by-step explanation:

\(7(c-18)=-98\\7c \frac{-126}{+126}=\frac{-98}{+126} \\\frac{7c}{7}=\frac{28}{7}\\c=4\)

Given:

The base area of a right circular cone is \(\dfrac{1}{4}\) of its total surface area.

To find:

The ratio of the radius  to the slant height.

Solution:

We know that,

Area of base of a right circular cone = \(\pi r^2\)

Total surface area of a right circular cone = \(\pi rl+\pi r^2\)

where, r is radius and l is slant height.

According to the question,

\(\pi r^2=\dfrac{1}{4}(\pi rl+\pi r^2)\)

Multiply both sides by.

\(4\pi r^2=\pi rl+\pi r^2\)

\(4\pi r^2-\pi r^2=\pi rl\)

\(3\pi r^2=\pi rl\)

Cancel out the common factors from both sides.

\(3r=l\)

Now, ratio of the radius  to the slant height is

\(\dfrac{r}{l}=\dfrac{r}{3r}\)

\(\dfrac{r}{l}=\dfrac{1}{3}\)

Therefore, the ratio of the radius  to the slant height is 1:3.

Answer:

it is b

Step-by-step explanation:

The solution is Option A.

The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the coordinates of the point A be A ( x , y )

Now , the vertex A is reflected over the line y = x

When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )

So , the coordinates of the point A' ( -2 , 10 )

Now , the coordinates of the point A will be

A ( x , y ) = A ( 10 , -2 )

Therefore , the value of A is A ( 10 , -2 )

Hence , the coordinates of the point before reflection is A ( 10 , -2 )

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Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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Remove the parentheses and combine the like terms:

7 - -9 = 7+ 9 = 16

6i - -8i = 6i +8i = 14i

The answer is 16 + 14i

The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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Answer:

400 litres

Step-by-step explanation:

The only relative minimum found here is at point F because F is the lowest valley point, we have a relative minimum here.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

F(x) = x2 is an illustration of a basic function. The function f(x) in this function first squares the value of "x". As an illustration, f(3) = 9 if x = 3. There are other other functions that can be used, such as f(x) = sin x, f(x) = x2 + 3, f(x) = 1/x, f(x) = 2x + 3, etc.

A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.

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Answer:

1. H0: u = 500

2. H1: u <500

3. One sample t test

Step-by-step explanation:

1. The null hypothesis in this question would be

H0: u = 500

2. The alternative hypothesis would be

H1: u < 500

3. The test that we are going to be using is the one sample t test. This test is used to test hypothesis. It would make a comparison of h0 to the mean of the sample. Now we are using this here because the sample standard deviation was given

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Option D is the correct answer.

We have,

Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.

In response to this rejection,

Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).

Thus,

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

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\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}\)

\(F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill\)

\(F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill\)

\(D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }\)

Calculate the area of each face that is covered by the paint:

Area of 1 and 4:

Use Pythagorean theorem to find 1/2 b:

Area of 2 and 3:

Area of 5 and 7:

Area of 6 and 8:

Then, the total area cover by the paint is:

The sale price of the sweater is $2.7

From the question, we have the following parameters that can be used in our computation:

Markdown rate = 85% off

Original price of the sweater = $18

The retail price of the coat can be calculated using the following equation

Retail price = original price * (1 - Markdown rate)

Substitute the known values in the above equation, so, we have the following representation

Retail price = 18 * (1 - 85%)

Evaluate the products

Retail price = 2.7

Hence, the sales price is $2.7

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Answer:

Step-by-step explanation:

CE and are the sides making up the sine of an angle.

CE is the side opposite the angle

DE is the side hypotenuse.

<D = 61 degrees

Sin(D) = opposite / hypotenuse

hypotenuse = 8

Sin(61) = 0.8746

CE = ?

sin(61) = CE / 8                multiply both sides  by 8

8 sin(61) = CE

CE = 8 * 0.8746

CE = 6.9969

CE = 7.0

That 0 should be included in the answer, but I think it is safe to say that if you enter 7, you will get it right.

Answer:

7.0

Step-by-step explanation:

Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

Answer:

y=8x+5

Step-by-step explanation:

Answer:

-------------------------

According to the given we can state:

Find arc AB, it is a semicircle of 1 cm radius:

ΔAEO and ΔBEO are both isosceles, hence ∠A and ∠B are both 45°.

Find arcs ABD and BAC:

∠AEB is a right angle since ∠AEO and ∠BEO are both 45°.

Hence ∠CED is also right angle as vertical angle with ∠AEB.

Find the length of EC and ED.

We know AD = BC = 2 cm and ΔAEO is 45° right triangle.

It gives us:

Then:

Find arc ECD:

The perimeter is the sum of all the arc measures:

Answer:

\(\textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}=7.20333649...\; \sf cm\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}\)

To convert degrees to radians, multiply the angle in degrees by π/180°.

Arc AB

As arc AB has center O, the radius of arc AB is OA = 1 cm.

As AB is a straight line, ∠AOB is 180° = π.

Therefore, the length of arc AB is:

\(\implies AB=r \:\theta=1 \cdot \pi = \pi\)

Arc AC

Triangle BOE is a right triangle with base of 1 cm and height of 1 cm.

Therefore, ∠OBE is 45° = π/4

If arc AC has center B, then the radius is AB = 2 cm.

Therefore, the length of arc AC is:

\(\implies AC=r \:\theta=2 \cdot \dfrac{\pi}{4} = \dfrac{\pi}{2}\)

Arc BD

Arc BD is the same as arc AC.

\(\implies BC= \dfrac{\pi}{2}\)

Arc CD

As triangle BOE is a right triangle with base of 1 cm and height of 1 cm, the length of its hypotenuse BE is:

\(\implies BE=\sqrt{1^2+1^2}=\sqrt{2}\)

As arc AC has center B and radius of AB = 2 cm, then BC is also its radius and therefore BC = 2 cm

Therefore:

\(\implies CE=BC-BE\)

\(\implies CE=2-\sqrt{2}\)

The arc CD has center E so its radius is CE = 2-√2.

As ∠BEO and ∠AEO are both 45° then ∠AEB is 90°.

According to the vertical angle theorem, ∠CED is also 90° = π/2.

Therefore, the length of arc CD is:

\(\implies CD=r \:\theta=(2-\sqrt{2}) \cdot \dfrac{\pi}{2} = \dfrac{(2-\sqrt{2})\pi}{2}\)

Perimeter of the egg

The perimeter of the egg is the sum of the found arcs:

\(\implies \textsf{Perimeter}=AB+AC+BD+CD\)

\(\implies \textsf{Perimeter}=\pi+\dfrac{\pi}{2}+\dfrac{\pi}{2}+\dfrac{(2-\sqrt{2})\pi}{2}\)

\(\implies \textsf{Perimeter}=2\pi+\dfrac{(2-\sqrt{2})\pi}{2}\)

\(\implies \textsf{Perimeter}=2\pi+\dfrac{2 \pi}{2}-\dfrac{\sqrt{2}\:\pi}{2}\)

\(\implies \textsf{Perimeter}=3\pi-\dfrac{\sqrt{2}\:\pi}{2}\)

\(\implies \textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}\)

\(\implies \textsf{Perimeter}=7.20333649...\; \sf cm\)