1. The possible missing terms to make x²_____+100 a perfect square trinomial are
a. 4x and 25x.
b. -10x and 10x.
c. -20x and 20x.
d. -4x and -25x.

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

Answer: .025

Step-by-step explanation: we first have to find the distance between each term we divide 12/5 by 6 you have to change it into multiplication so you invert is to 12/5 times 1/6 you then get 12/30 you reduce that to become 2/5 if you want to test this to make sure it is right then you can. you then use a formula but I can't remember it so then you can just multiply it several times to find the answer. you get the answer by round from the thousandths

Answer: The correct answer is (5, 11π/6). or C

Step-by-step explanation:

The polar coordinates of the point (x, y) = (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

Explanation:

Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

Plugging in the given values:

r = √((5√3/2)^2 + (-5/2)^2)

= √(75/4 + 25/4)

= √(100/4)

= 5

θ = atan2(-5/2, 5√3/2)

≈ 11π/6 radians

So, the correct polar coordinates of the point (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

The resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

The problem we are trying to solve is to determine if the sample proportion of heads obtained from spinning a penny 300 times (134 heads) is significant evidence against equal probabilities of heads and tails. To do this, we will be testing the null hypothesis H0: p = 0.5, which states that the probability of getting heads is equal to 0.5.

We can calculate the z-test statistic using the formula z = (sample proportion - hypothesized proportion) / (standard error). In this case, the z-test statistic is z = (0.444 - 0.5) / (√(0.5 * 0.5 / 300)) = -0.86. This means that the sample proportion of heads is 0.86 standard errors away from the hypothesized proportion of 0.5.

Therefore, the resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

For the transformation 1, we have a reflection, which keeps both the side lengths and the angle measure constant, just changing the orientation of the figure.

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Answer:

The probability that the number chosen is not even = 4/8

Answer:

62 degrees

Step-by-step explanation:

Hope this helps! If it’s wrong I’m really sorry. I used the formula θ = s/r then converted it from radians to degrees.
Pls give brainliest!

Answer:

Area of shaded region:

12r^2 - (2(2r^2) + 2πr^2) =

12r^2 - 4r^2 - 2πr^2 =

(2r^2)(4 - π)

Probability of point chosen in shaded region:

(2r^2)(4 - π)/(12r^2) = (4 - π)/6 = .143 = 14.3%

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

tan theta=5/6

theta=tan-1(5/6)

        =39.8º

Answer:

34.83/.9 = 38.7 g mass (after one hour)

38.7/.9 = 43 g (starting mass)

The starting mass of the ice cube was 43 grams.

[tex]g(x)=\sin^2(x)+3\cos(x) \\\\[-0.35em] ~\dotfill\\\\ g(\pi )=\sin^2(\pi )+3\cos(\pi )\implies g(\pi )=[\sin(\pi )]^2+3\cos(\pi ) \\\\\\ g(\pi )=(0)^2+3(-1)\implies g(\pi )=-3[/tex]

Answer:

AB = (20/√2)(√2/√2) = 10√2

The probability that a student has a dog given that they have a cat is 2/5.

To find the probability that a student has a dog given that they have a cat, we need to use conditional probability. We can use the formula:

P(Dog | Cat) = P(Dog and Cat) / P(Cat)

where P(Dog and Cat) is the probability that a student has both a dog and a cat, and P(Cat) is the probability that a student has a cat.

From the given data table, we can see that there are a total of 25 students in the class, and 15 of them have a cat. Of the 15 students with a cat, 6 also have a dog. Therefore, P(Dog and Cat) = 6/25 and P(Cat) = 15/25.

Substituting these values into the formula, we get:

P(Dog | Cat) = (6/25) / (15/25) = 6/15 = 2/5

Therefore, the probability that a student has a dog given that they have a cat is 2/5 or 0.4.

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Answer:

Step-by-step explanation:

the median would be 9.

Answer: Reduce the height of the ramp from 1 meter to 0.5 meters

Step-by-step explanation:

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

cos(49.4°) = d/16.2

d = 16.2cos(49.4°) = 10.5 feet

Answer:

I assume you are referring to a rectangular prism with dimensions of 7 feet by 13 feet by 5 feet and you are trying to identify which dimension represents the length, width, and height.

In a rectangular prism, the length is typically considered the longest dimension, while the width and height are interchangeable depending on the orientation of the prism.

So, in this case, it is likely that the 13 feet dimension represents the length, while the 7 feet and 5 feet dimensions represent the width and height (in either order). However, it is important to note that without more context, it is impossible to know for sure which dimension is which.

The area of this​ trapezoid is 14.42 square yards.

To compose the trapezoid into a parallelogram, we need to add a triangle to the top of the trapezoid, so that the top and bottom sides are parallel. The area of the triangle is equal to half the product of the base and height.

First, we need to convert the mixed numbers to improper fractions:

Base 1: 6 1/3 yd = 19/3 yd

Base 2: 8 1/5 yd = 41/5 yd

Height: 3 3/4 yd = 15/4 yd

The length of the top side of the triangle is equal to the difference between the two bases:

Top side = 41/5 - 19/3 = (123 - 95)/15 = 28/15

Now we can calculate the area of the triangle:

Triangle area = (1/2) x (28/15) x (15/4) = 7/4

The trapezoid can now be composed into a parallelogram, with base 1 as one side and base 2 as the other side. The height of the parallelogram is the same as the height of the trapezoid, which is 15/4 yd.

The area of a parallelogram is equal to the product of its base and height, so the area of the trapezoid is:

Parallelogram area = (19/3 + 41/5) x (15/4) = 865/60 = 14.42

Therefore, the area of the trapezoid is 14.42 square yards.

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Answer:

The given sequence is decreasing by a factor of 2 each time, so each term is half of the previous term.

We can write the nth term of the sequence as:

a_n = a_1 * (1/2)^(n-1)

where a_1 is the first term of the sequence (12 in this case) and n is the position of the term we want to find.

For example, to find the 4th term of the sequence, we would have:

a_4 = 12 * (1/2)^(4-1)

= 12 * (1/2)^3

= 12 * 1/8

= 1.5

Therefore, the formula for the nth term of the sequence 12, 6, 3, ... is:

a_n = 12 * (1/2)^(n-1)

Answer:

36

Step-by-step explanation

6x6

The surface area of the right cylindrical oil can is 120π in² and the right option is C) 120π in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

To calculate the surface area of the right cylindrical oil can, we us the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the right option is C) 120π in².

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If company's marginal cost function is c(x)= 14 / √x, the total cost of producing the first 25 units is $10.67.

The marginal cost function is given as c(x) = 14 / √x, where x is the number of units produced.

To find the total cost of producing the first 25 units, we need to integrate the marginal cost function from x=0 to x=25, as follows:

Total cost = ∫₀²⁵ 14 / √x dx

We can use integration by substitution to solve this integral. Let u = √x, then du/dx = 1/(2√x), and dx = 2u du. Substituting these into the integral, we get:

Total cost = ∫₀⁵ √14/u du

This can be integrated using the power rule of integration. We have:

Total cost = 2√14 [[tex]u^{(3/2)[/tex]/3]₀⁵

Substituting back u = √x, we get:

Total cost = 2√14 [[tex](\sqrt{x})^{(3/2)[/tex]/3]₀²⁵

= 2√14 [[tex](\sqrt{25})^{(3/2)[/tex]/3 - [tex](\sqrt{0})^{(3/2)[/tex]/3]

= 2√14 (5/3)

= 10.67

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Answer:

63 cubic inches

Step-by-step explanation:

To find the volume of the rectangular prism mini-flashlight, we need to multiply its length, width, and height.

Given that the width is 3 inches, the height is 14 inches, and the length is 1.5 inches, we have:

Volume = length x width x height

Volume = 1.5 in x 3 in x 14 in

Volume = 63 cubic inches

Therefore, the volume of the mini-flashlight is 63 cubic inches.

Answer: The correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,π3) tell us the radius r=4 and the angle θ=π3. So the point should be on the circle labeled 4 and form an angle of π3 with the positive x-axis. Point B is the correct point

To find the domain of a function, we need to determine all values of the independent variable (usually denoted as x) for which the function is defined and has a real output.

For example, if we have the function:

f(x) = 1/(x-3)

We need to exclude any values of x that would make the denominator zero, since division by zero is undefined. Therefore, the domain of this function would be all real numbers except x = 3. We could write this as:

Domain: x ∈ ℝ, x ≠ 3

If we have a more complex function, we need to consider any other restrictions on the independent variable that may be imposed by the function.

For instance, if we have the function:

g(x) = sqrt(x-2)/(x+3)

Here, the square root function is defined only for nonnegative values of its argument. Therefore, we need to ensure that x-2 ≥ 0, or equivalently, x ≥ 2. Additionally, the denominator of the fraction cannot be zero, so we need to exclude x = -3. Combining these two conditions, we get:

Domain: x ∈ [2, ∞), x ≠ -3

This means that the function g(x) is defined and has a real output for all values of x greater than or equal to 2, except x = -3.

In general, to find the domain of a function, we need to consider any restrictions on the independent variable imposed by the function itself (such as division by zero, taking the square root of a negative number, etc.), as well as any restrictions that may be imposed by the context in which the function is used (such as physical or mathematical constraints). We then express the domain as a set of values of x that satisfy all the relevant conditions.

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The maximum value of the data = 64

We know that in the box and whisker plot with the left end of the whisker represents the minimum value of the data and the right end of the whisker represents the maximum value.

From the attached box and whisker plot, we can observe that between two numbers on the number line there are 5 equal units.

So, the value of each unit length = 4 unit

Here, the left end of the whisker has value 8 and the right end of the whisker has value 64

This means that the meaximum value = 64

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Integration of   [tex]\int\limits^6_0 {\frac{8}{1+74e^{-0.3t} } } \, dt[/tex]   is 2.199.

We can solve this integral using the substitution method, where u = 1 + 74[tex]e^{-0.3t}[/tex] . Taking the derivative of both sides, we have du/dt = -222[tex]e^{-0.3t}[/tex] .

We can rewrite the integral in terms of u:

∫[8/(1+74[tex]e^{-0.3t}[/tex] )]dt = ∫[8/u * (-1/222) * (-222[tex]e^{-0.3t}[/tex] )]du

Simplifying this expression, we have:

= (-8/222) ∫[1/u] du

= (-4/111) ln|u| + C

where C is the constant of integration.

Substituting back for u, we have:

= (-4/111) ln|1 + 74[tex]e^{-0.3t}[/tex] | + C

To evaluate the definite integral from 0 to 6, we plug in the limits of integration:

= (-4/111) [ln | 1 + 74[tex]e^{-0.3(6)}[/tex] | - ln | 1 + 74[tex]e^{-0.3(0)}[/tex] |]

= (-4/111) [ln|1 + 74[tex]e^{-1.8}[/tex]| - ln75]

≈ 2.199

Therefore, the value of the definite integral is approximately 2.199.

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