What is the area of one petal of r = 6 sin 2theta?
a. phi /8 b. 9phi/8 c. 25phi/8 d. phi/5 e. 9phi/2 f. 5phi g. phi/20 h. 9phi/5 i. 25phi/2 j. phi/2

Answer:

-2 1/4, -1 1/4, 3/4, abs val 1 1/4, abs val -1 3/4, abs val - 2 1/4

Step-by-step explanation:

When you factor in the abs val, which look like a number stuck between two lines, you measure the distance of the number from zero which is ALWAYS POSITIVE. Therefore, change all the numbers inside abs val signs into positive numbers of the same value, for example abs val -1 3/4 would become 1 3/4 and arrange them from least to greatest.

The roots of the polynomial functions are

(a) x = -1 or x = -1.2 and x = -0.16

(b) x = -1/7 or x = 2

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

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

The roots of the polynomial functions are calculated by setting the functions to 0

So, we have

(x + 1)(5x² + 7x + 1) = 0

(7x + 1) (2x - 4) = 0

Using the zero product property, we have

x + 1 = 0 or 5x² + 7x + 1 = 0 and

7x + 1 = 0 or 2x - 4 = 0

When evaluated, we have

x = -1 or x = -1.2 and x = -0.16

x = -1/7 or x = 2

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Complete question

For each polynomial function below, determine all of the roots.

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

answer:

2

sorry for putting words it wouldnt let me only put 2

Answer:

I believe the answer is 8.16 pardon me if it's wrong.

Answer:

8.18

Step-by-step explanation:

First, note that 8.175 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:

Integer Part: 8

Fractional Part: 175

To round 8.175 to the nearest hundredth means to round the numbers so you only have two digits in the fractional part.

We use the following rules to round 8.175 to the nearest hundredth:

A) If the last digit in the fractional part of 8.175 is less than 5, then simply remove the last the digit of the fractional part.

B) If the last digit in the fractional part of 8.175 is 5 or more and the second digit in the fractional part is less than 9, then add 1 to the second digit of the fractional part and remove the third digit.

C) If the last digit in the fractional part of 8.175 is 5 or more and the second digit in the fractional part is 9, and the first digit in the fractional part is less than 9, then add 1 to the first digit in fractional part and make the second digit in fractional part 0. Then remove the third digit.

D) If the last digit in the fractional part of 8.175 is 5 or more and the second digit in the fractional part is 9, and the first digit in the fractional part is 9, then add 1 to the integer part and make the fractional part 00.

With 8.175, rule B applies and 8.175 rounded to the nearest hundredth is:

8.18

Answer: A child tosses a tennis ball into the air and it lands in the mud. The function h(t)=−16t2+16t+4

h

(

t

)

=

−

16

t

2

+

16

t

+

4

h(t)=−16t

2

+16t+4 gives the ball's height in feet with respect to time in seconds. a. Sketch a graph of y = h(t). Highlight the portion of the curve that fits this situation. b. What is happening to the height of the tennis ball with respect to the time? c. Since velocity is a function of distance traveled overtime, what part of the graph represents the velocity of the ball? What is happening to the velocity of the tennis ball with respect to time? d. Copy and complete the following table of time (s) versus height (ft). $$\begin{matrix}\text{t (s)} & \text{0} & \text{0.25} & \text{0.5} & \text{0.75} & \text{1} & \text{1.25} & \text{1.50}\\text{h (ft)} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{_}\\end{matrix}$$ e. Use the table to determine the ball's average velocity in ft/sec for each 0.25-second time interval. f. Predict the velocity of the ball at t = 0.8 seconds. Be prepared to justify your answer to the class.

Step-by-step explanation:

Adam is correct because this fact can be used to determine the length of the radius of the circle by constructing a perpendicular line from point G to any of the sides of the triangle.

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Since the given circle with center G is the incircle of triangle PQR, we can reasonably infer and logically deduce that Adam is correct because "the radius drawn to the point of tangency is perpendicular to the tangent line of a circle."

In conclusion, the perpendicular line drawn from the center G to the side lengths of triangle PQR would typically be perpendicular to the tangent line of a circle.

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Answer:

b,c, and d

Step-by-step explanation:

its telling you the opposite of the one number

Answer:

I think its B and F

Step-by-step explanation:

Answer:

11.25

Step-by-step explanation:

Answer:

DB = 11.25cm

Step-by-step explanation:

We need to find the diagonal.

d² = 9² + 6.75²

d² = 81 + 45.5625

d² = 126.5625

d = 11.25

Best of Luck!

Answer:

I will list main feature for each property and you can choose. You can comment if you want to check or have questions

Step-by-step explanation:

Isosceles - two sides are equal

Equilateral - all sides are equal

Obtuse - one angle is greater than 90 degrees

Right - one angle is equal to 90 degrees

Scalene - none of the sides is equal

Acute - all angles are less than 90 degrees

Go down the list and see if it's true or false about the given triangle

The value of the expression divide negative 3 and one-sixth ÷ negative 8 and two-fifths is 95 over 252. Option B

A fraction can be defined as the part of a whole item, number or element.

The several types of fractions are;

From the information given, we have that;

-3 1/ 6 ÷ - 8 2/ 5

Turn into improper fractions

-19/ 6 ÷ 42/ 5

Take the inverse of the divisor and multiply

- 19/ 6 × 5/ 42

95/252

Hence, the value is 95/252

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1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.

For given question,

Let x be the quantity ( in liters ) of glycerin added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin,

Thus,

Quantity of glycerin in 12 liters + Quantity of glycerin in x

= Quantity of glycerin in resultant mixture.

⇒ 8% of 12 + 100% of x = 16% of (12 + x )

⇒ 0.08 × 12 + x = 0.16 × ( 12 + x )

⇒ 0.96 + x = 0.16 × 12 + 0.16x

⇒ 0.96 + x = 1.92 + 0.16x

⇒ x - 0.16x = 1.92 - 0.96

⇒ 0.84x = 0.96

⇒ x = 1.143 liters

Therefore, 1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.

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Answer:

C. five samples.

Step-by-step explanation:

Answer:

The possible values of k are 3 and -3

Step-by-step explanation:

Given

Points: (-3,k) and (2,0)

Distance between them = √34

Required

Determine the value of k

The distance between two points is calculated as thus;

\(Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

Let

\((x_1,y_1) = (-3,k)\)

\((x_2,y_2) = (2,0)\)

Substitute these values in the given formula

\(Distance = \sqrt{(-3 - 2)^2 + (k - 0)^2}\)

Evaluate the brackets

\(Distance = \sqrt{-5^2 + k^2}\)

\(Distance = \sqrt{25 + k^2}\)

Recall that Distance = √34

So; we have

\(\sqrt{34} = \sqrt{25 + k^2}\)

Take square of both sides

\(34 = 25 + k^2\)

Collect Like Terms

\(k^2 = 34 - 25\)

\(k^2 = 9\)

Take square root of both sides

\(k = \±3\)

Hence, the possible values of k are 3 and -3

Answer:

The value of x = 1

Step-by-step explanation:

2x+3 = 5

=> 2x = 5-3

=> 2x = 2

=> x = 2/2

=> x = 1

Answer:

Step-by-step explanation:

In this question we are given with an equation that is 2x + 3 = 5 . And we are asked to find the value of x .

Solution : -

\( \longmapsto \qquad \: 2x + 3 = 5\)

Step 1 : Subtracting with 3 on both sides :

\( \longrightarrow \qquad \:2x + \cancel{ 3} - \cancel{3} = 5 - 3\)

On further calculations, We get :

\( \longrightarrow \qquad \:2x = 2\)

Step 2 : Dividing with 2 on both sides :

\( \longrightarrow \qquad \: \dfrac{ \cancel{2}x}{ \cancel{2}} = \cancel{\dfrac{2}{2} }\)

On calculating further, We get :

\( \longrightarrow \qquad \: \blue{\underline{\boxed{ \sf{x = 1}}}} \quad \bigstar\)

Verifying : -

Now we are checking our answer by substituting value of x in the given equation . So ,

Therefore , our answer is correct .

Answer:

8? not sure tho....

Step-by-step explanation:

Answer: D: 0

Step-by-step explanation:

Without doing a long division.

\(Remember:\\\\\\\boxed{a^3+b^3=(a+b)(a^2-ab+b^2)}\\\\\dfrac{x^3+1}{x^2-x+1} =\dfrac{(x+1)(x^2-x+1)}{x^2-x+1} =x+1\\\\remainder\ is\ 0\\\\Answer\ D\\\)

There is an association between birth rate and death rate during this time interval are True.

Interval is a set of values that lie between two given numbers or points. It is used to represent a continuous magnitude, such as distance, temperature, time, or mass. Intervals are commonly used in mathematics, music theory, and statistics. In mathematics, an interval may be a set of real numbers, a set of real numbers and their limits, a set of points in a line, a set of points in a plane, or a set of points in a space. In music theory, an interval is the ratio of two frequencies. In statistics, an interval is the range of values within which a measured value is expected to fall.

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Answer:

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

In the given diagram, the central angle has same measure as given arc.

Hence we can set up the following equation:

The matching choice is D.

Answer is.

Step-by-step explanation:

Here we are given central angle of the circle is 85°

Length of arc is 4x - 5.

Since measure of central angle is equal to measure of an arc of the circle.

Then,

4x + 5 = 85

4x = 85 - 5

4x = 80

x = 80/4

x = 20

So, the value of x is 20

0.0006 .

The probability that both systems of an atomic reactor will fail simultaneously is 0.0006.

This is calculated by multiplying the probability of cooling system A failing (0.02) by the probability of cooling system B failing (0.03) which results in 0.0006, rounded to four decimal places.

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Answer:

2(x+3)=2x+6

Step-by-step explanation:

Because You multiply 2*x and 2*3.

The X is a variable and it actually equals to 1. so it's basically 2*1

After you multiply 2*x and 2*3 you will get 2x+6

Answer: 70

Step-by-step explanation: 528/264 * 35 = 70

Answer:

C. triangle LAP was translated 1 unit to the left and 3 units up to triangle LAP

The parametric equations for the line passing through points A(-3, 2) and B(5, 0) ar; x(t) = -3 + 8t, and y(t) = 2 - 2t.

option C

The parametric equations for the line passing through point A(-3, 2), and point B(5, 0) is calculated as follows;

The x-coordinate (x(t)) of a point on the line is calculated as follows;

\(x(t) = x_A + (x_B - x_A)t\)

Where;

x(t) = -3 + (5 - (-3))t

x(t)  = -3 + 8t

x(t)  = -3 + 8t

The y-coordinate (y(t)) of a point on the line is calculated as;

\(y(t) = y_A + (y_B - y_A)t\)

Where;

y(t) = 2 + (0 - 2)t

y(t)  = 2 - 2t

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Frequency distribution table: class, frequency, and relative frequency. (b) Histogram of frequencies. (c) Mean and standard deviation calculations for the sample using grouped data.

(a) To create a frequency distribution table, we need to group the data into intervals or classes and count the frequency of values falling within each class. The table should have columns for the class intervals, frequency (number of individuals in each interval), and relative frequency (proportion of individuals in each interval).

(b) To draw a histogram of frequencies, we use the frequency distribution table. The horizontal axis represents the class intervals, and the vertical axis represents the frequencies. We draw rectangles or bars for each interval, with the height of each bar corresponding to the frequency.

(c) To calculate the mean and standard deviation of the sample using grouped data, we need to expand the frequency distribution table with additional columns required for the calculations. These columns include the midpoint of each class interval, the product of midpoint and frequency, and the squared deviations from the mean. The mean is calculated by summing the products of the midpoint and frequency and dividing by the total number of individuals. The standard deviation is calculated by summing the squared deviations from the mean, dividing by the total number of individuals, and taking the square root of the result.

For problem 2, part (a), the sample space for each experiment can be determined by listing all possible outcomes. For the experiment of tossing a coin three times, the sample space would consist of all possible sequences of heads (H) and tails (T) in three tosses, such as {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

For the experiment of tossing a coin first and then rolling a dice, the sample space would consist of all possible combinations of the outcomes of the coin toss (H or T) and the dice roll (1, 2, 3, 4, 5, 6), such as {(H,1), (H,2), ..., (T,6)}.

In problem 2, part (b), the sets A, B, and C are defined as A = {0, 1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {1, 3, 5}. To determine the outcomes of the given events, we can use set operations:

A' (A complement) represents all outcomes not in set A, which would be the complement of A with respect to the universal set of possible outcomes.

AUB represents the union of sets A and B, which represents all outcomes that belong to either A or B or both.

BUC represents the union of sets B and C, which represents all outcomes that belong to either B or C or both.

(A∩B)UC represents the union of the intersection of sets A and B with set C, which represents all outcomes that belong to both A and B, and also belong to C or are in C.

(A∩C)UB represents the union of the intersection of sets A and C with set B, which represents all outcomes that belong to both A and C, and also belong to B or are in B.

(A∩C)' represents the complement of the intersection of sets A and C, which represents all outcomes not in the intersection of A and C.

By applying the appropriate set operations to the given sets, we can determine the outcomes for each event.

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Answer:

d

Step-by-step explanation:

The solutions in part (a) are (π/4, 1.414) and (5π/4, -1.414))

The trigonometric inequality expression is given as:

sec(x) ≥ csc (x)

The domain of the trigonometric inequality expression is given as:

0 ≤ x ≤ 2π

Next, we express the trigonometric inequality expression as an equation.

So, we have:

sec(x) = csc (x)

Next, we split the trigonometric inequality as follows:

y = sec(x)

y = csc (x)

Convert to inequalities

y ≥ sec(x)

y ≥ csc (x)

Next, we plot the graphs of the inequalities.

See attachment for the graphs of the inequalities.

From the attached graph, the graphs of the inequalities y ≥ sec(x) and y ≥ csc (x) intersect at points (π/4, 1.414) and (5π/4, -1.414))

Hence, the solutions in part (a) are (π/4, 1.414) and (5π/4, -1.414))

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Answer:

All of them are irrational except √9 which is rational.

Step-by-step explanation:

√5= 2.2606797749(irrational)

√9=3(rational) this one is rational

√7=2.64575131106(irrational)

√3.31662479035(irrational)

hope it helps.

Answer:

132

Step-by-step explanation:

8×4×3 + 3×3×4

96+36=132