what is the negative square root of 65 over 121

Answer: x=4

Step-by-step explanation:

The perimeter´s formula for this kind of polygons is

The triangle perimeter would be:

(x+2)+(x+3)+(x+3)

And the rectangle:

(x+2)+(x+2)+x+x

For them to have the same value, we should equal them:

(x+2)+(x+3)+(x+3)=(x+2)+(x+2)+x+x

Working with this:

3x+8=4x+4

x=4

Answer:

10^3

Step-by-step explanation:

Answer:

100 small rectangles

Step-by-step explanation:

Number of small rectangles = Area of large rectangle ÷ area of small rectangle

               \(= \frac{25*40}{10}\\\\= 25*4\\= 100\)

Answer:

7

Step-by-step explanation:

180÷12=15 hats and scarves were sold

15 total hats and scarves minus 8 hats is 7

so seven scrapes were sold

180÷12=15

15-8=7

Total 7 unit scarves she sold last week when total of $12 selling she did.

It is given that the Elana makes  knit hats and scarves and sells them in her online store for $12 each. Last week Elena's store made $180 total.

It is required to find the how many scarves she sold if total number of hats sold were 8.

It is defined as the mathematical term that shows how profitable the businness is, both are measure in percentage form.

We have, price of each knit hats and scarves =  $12

Total selling of knit hats and scarves = $180

Total knit hats sold = 8

Total selling price of knit hats = 8×12 ⇒ $96 (∵each item selling price is $12)

Total selling price of scarves = $180 - $96 ⇒ $84

Total number of scarves = \(\rm \frac{84}{12} \Rightarrow 7\) (∵each item selling price is $12)

Thus, total 7 unit scarves she sold last week.

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After d days, the number of lily pads in the pond can be calculated using the formula 2^d. So, if d is the number of days, then the number of lily pads after d days would be 2^d.

Each day, the number of lily pads doubles. So, on the first day, there is 1 lily pad. On the second day, the number doubles to 2. On the third day, it doubles again to 4, and so on. This doubling pattern continues for d days.

To calculate the number of lily pads after d days, we raise 2 to the power of d (2^d). This is because each day, the number of lily pads doubles, which can be represented as 2^1, 2^2, 2^3, and so on. By substituting the value of d into the equation, we can find the number of lily pads after d days.

For example, if d = 5, then the number of lily pads after 5 days would be 2^5 = 32. This means that there would be 32 lily pads in the pond after 5 days.

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Answer:

50°

Step-by-step explanation:

96°+34°=130°

A whole triangle is made up of 180°

So 180°-130°= 50°

Answer: B

Step-by-step explanation: I used a graphing site named Geogebra and found the equation is -x+y=-4 and the slope is up 2, right 2 which would give us 2/2 which simplifies to 1

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

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

Writing linear equations given two points can be a useful skill when graphing linear equations.

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Answer:

Step-by-step explanation:

Given function:

a)  g(2)

b)  g(t - 2)

c)  g(t) - g(2)

Answer:

\(\huge\boxed{4}\)

Step-by-step explanation:

In order to find the slope between two points, we want to find the rise over run. Basically - we find the change in y and divide that by the change in x.

The first y value is 0 and the second is 8. The change here is \(8-0=8\).

The first x value is 1 and the second is 3. Therefore the change here is \(3-1=2\).

Now that we know the change in y and x, we divide.

\(8\div 2 = 4\)

So the slope between these two points is 4.

Hope this helped!

Answer:

Step-by-step explanation:

Piedmont Middle School = 3x

Let the crows = x                     foul balls

x+ 8 = 3x                                    Subtract x from both sides

x-x + 8 = 3x - x

8 = 2x

x = 4

So the crows hit 4 foul balls

The ravens must have hit 12 foul balls.

They did hit 8 more than the crows did.

The signs of functions in each quadrant, and the trigonometric values of common angles, we can evaluate the six trigonometric functions of any angle θ in standard position accurately.

Evaluating the six trigonometric functions of any angle θ in standard position involves understanding reference angles, signs of functions in each quadrant, and the trigonometric values of common angles.

Reference angles help us find the corresponding values in the unit circle. The signs of the functions are positive in the first quadrant, only sine is positive in the second quadrant, tangent is positive in the third quadrant, and cosine is positive in the fourth quadrant. Common angles like 0°, 30°, 45°, 60°, and 90° have well-known trigonometric values. Diagrams and figures can aid in visualizing these concepts.

To evaluate the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) of any angle θ in standard position, we need to consider a few key concepts.

First, reference angles play a crucial role. A reference angle is the acute angle formed between the terminal side of θ and the x-axis. It is always positive and ranges from 0° to 90°. The reference angle allows us to find the corresponding values on the unit circle.

Next, we need to understand the signs of the functions in each quadrant. In the first quadrant (0° to 90°), all functions are positive. In the second quadrant (90° to 180°), only sine is positive. In the third quadrant (180° to 270°), only tangent is positive. In the fourth quadrant (270° to 360°), only cosine is positive. This mnemonic device, "All Students Take Calculus," can help remember the signs: All (positive), Sine (positive), Tangent (positive), Cosine (positive).

Knowing the trigonometric values of common angles is also helpful. For example, at 0°, the values are: sine = 0, cosine = 1, tangent = 0, cosecant = undefined, secant = 1, cotangent = undefined. At 30°, the values are: sine = 1/2, cosine = √3/2, tangent = √3/3, cosecant = 2, secant = 2/√3, cotangent = √3. Similarly, for 45°, the values are: sine = √2/2, cosine = √2/2, tangent = 1, cosecant = √2, secant = √2, cotangent = 1. For 60° and 90°, the values can be derived from the 30° and 45° values.

Visual aids like diagrams and figures can greatly assist in understanding these concepts. The unit circle is a particularly helpful tool to visualize the angles, reference angles, and the corresponding trigonometric values. By familiarizing ourselves with reference angles, the signs of functions in each quadrant, and the trigonometric values of common angles, we can evaluate the six trigonometric functions of any angle θ in standard position accurately.

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Thus, the object travels a distance of 10π units along the given trajectory.

To find out how far an object travels along a given trajectory, we need to calculate the arc length of the curve. The formula for arc length is given by:

L = ∫_a^b √[dx/dt]^2 + [dy/dt]^2 dt

where L is the arc length, a and b are the start and end points of the curve, and dx/dt and dy/dt are the derivatives of x and y with respect to time t.

In this case, we have the trajectory r(t) = (10 cos 2t, 10 sin 2t) for 0 ≤ t ≤ π/2. Therefore, we can calculate the derivatives of x and y as follows:

dx/dt = -20 sin 2t
dy/dt = 20 cos 2t

Substituting these values into the formula for arc length, we get:

L = ∫_0^(π/2) √[(-20 sin 2t)^2 + (20 cos 2t)^2] dt
 = ∫_0^(π/2) √400 dt
 = ∫_0^(π/2) 20 dt
 = 20t |_0^(π/2)
 = 10π

Therefore, the object travels a distance of 10π units along the given trajectory.

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Answer:

Step-by-step explanation:

12

Answer:

12+ 6 = 18

Step-by-step explanation:

parenthesis means distribute

(6x-5)-(-x-4)

6x-5=x+4

6x-x=4+5

5x=9

Answer:

111 cm^2

Step-by-step explanation:

h = 11.4

d = 5  so  r (radius) = 2.5

Surface Area of a Cone Formula: πr^2 + πrs

s represents the slant height of the cone, lets represent this with a drawing.

We have the values of h and r, but we don't have the value of s, meaning we have to find it. We can do this by using pythagorean theorem.

a^2 + b^2 = c^2

These three values can come together to create a right triangle which we can seperate from the rest of the diagram, now we can find s.

s = √(11.4^2 + 2.5^2)   so  s = 11.67

now that we have all of the pieces, we can plug back into the original surface area formula. πr^2 + πrs

π(2.5^2) + π(2.5)(11.67) = 111.29 cm^2 or 111 cm^2

The surface area of the solid cone requiring paint will be 111 square cm.

Let d be the diameter of the base circle, l be the slant height, and h be the height of the cone.

Then the lateral surface area of the cone will be

SA = πrl + πr²

Then the slant height is given as

l² = r² + h²

The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.

Then the radius of the base circle will be

r = 5 / 2

r = 2.5 cm

The length of the slant height will be

l² = 11.4² + 2.5²

l² = 136.21

 l = 11.67

Then the surface area of the solid cone requiring paint will be

SA = π × 2.5 × 11.67 + π × 2.5²

SA = 29.18π + 6.25π

SA = 35.43π

SA = 111.3

SA ≈ 111 square cm

The surface area of the solid cone requiring paint will be 111 square cm.

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9514 1404 393

Answer:

  (d)  8

Step-by-step explanation:

Corresponding sides are proportional.

  ED/EG = EC/EF

  (6x +3)/17 = (8x -1)/21

  21(6x +3) = 17(8x -1)

  126x +63 = 136x -17

  80 = 10x . . . . . . . . . . . add 17-126x

  8 = x . . . . . . . . . . divide by 10

Answer:

-9/14 :)))))))))))))))))))

The pressure per square inch at a depth of 25 feet is approximately 10.9 pounds per square inch.

We have,

We can use the point-slope form of a linear equation to model the pressure as a function of depth.

Let (x1, y1) = (9, 18.7) be a point on the line, and let (x2, y2) = (14, 20.9) be another point on the line.

Then the slope of the line is:

slope = (y2 - y1) / (x2 - x1)

= (20.9 - 18.7) / (14 - 9)

= 0.44

Using the point-slope form with the point (x1, y1):

y - y1 = m(x - x1)

y - 18.7 = 0.44(x - 9)

y = 0.44x - 0.08

So the function that models the amount of pressure as a function of depth is:

y = 0.44x - 0.08

To find the pressure at a depth of 25 feet,

we substitute x = 25 into the equation:

y = 0.44(25) - 0.08

= 10.92

Therefore,

The pressure per square inch at a depth of 25 feet is approximately 10.9 pounds per square inch.

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The distance between the given coordinates  (−5, −19) and (−5, 32) is given by 51 units.

Let us consider the coordinates of two given points be,

(x₁ , y₁ ) = ( -5 , -19 )

(x₂ , y₂ ) = (-5 , 32 )

Distance formula between two points is equals to,

Distance = √ ( y₂ - y₁)² + ( x₂ - x₁ )²

Substitute the values of the coordinates we have,

⇒ Distance = √ ( 32 - (-19))² + ( -5- (-5) )²

⇒ Distance = √ (32 +19)² + (-5 + 5)²

⇒ Distance = √ 51² + 0²

⇒ Distance =  51 units.

Therefore, the distance between the two points is equal to 51 units.

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Answer:

y=-4x-6

Step-by-step explanation:

y=mx+b, where m is the slope and b is the y-intercept

Slope is given as -4, so:

y=-4x+b

To find b, sub in the point we were given (-2,2):

2=-4(-2)+b

2=8+b

b=2-8=-6

So we have: y=-4x-6

Answer:

Step-by-step explanation:

-5n = 13 - 3m

Subtract 13 from both sides

-5n - 13 = -3m

Multiply the whole equation by (-1)

-5n *(-1) - 13*(-1) = -3m*(-1)

5n + 13 = 3m

Divide both sides by 3

\(\dfrac{5n+13}{3}=m\\\\\\m =\dfrac{5n+13}{3}\)

Social scientists gather data from samples instead of populations because c. populations are often too large to test.

Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.

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Answer:

3

Step-by-step explanation:

Just set up the chart and if 3 is a quarter of 12 you have to make the 1\2 hours match up and you would get the answer of 3

Check the picture below, so the shaded area is really just the area of one quarter of a circle's area with a radius of 7, and a triangle whose base is 7 and height is 7, so let's simply sum both of them up.

\(\stackrel{\textit{\Large Areas}}{\stackrel{\textit{quarter of a circle}}{\cfrac{1}{4}(\pi)(7)^2}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(7)}}\implies \cfrac{49\pi }{4}~~ + ~~\cfrac{49}{2}~~ \approx~~63.0\)

Answer:

3(x^3-3x+1)

hope this helps!

Answer:

None.

Step-by-step explanation:

Let blue, green and purple be B, G, and P respectively.

Sample Space = 2+2+2 = 6

p(B) = p(G) = p(P) = 2/6 = 1/3

Probability that the two marbles Ummi selected are of the same color (note that the marbles were replaced after selection)

B = (1/3)•(1/3)

+

G = (1/3)•(1/3)

+

P = (1/3)•(1/3)

= 3•(1/9) = 1/3

.

The same thing goes for Julio.

They have the same chance/probability of picking two marbles of the same color.

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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The approximate area of each tank that will be painted is 2287.08 ft².

The lateral surface area of a cylinder is also called the curved surface area of the cylinder.

Suppose that:

Then, the lateral surface area of that cylinder is:

\(S_L = 2\pi r h \: \rm unit^2\)

The missing image is attached below.

The tank is cylindrical in shape.

For this case, we've got:

Radius = half of diameter = 28/2 = 14 ft

Thus, the curved surface area of each of such tanks is:

\(S_L = 2\pi r h = 2\pi (14)(26) = 728\pi \approx 2287.08 \: \rm ft^2\)

Thus, the approximate area of each tank that will be painted is 2287.08 ft².

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Answer: 2287.08 ft²

Step-by-step explanation: Correct for plato/Edmentum