The area of the base of a rectangular prism is 18 cm2
. The height of the prism is 912
cm. What is the volume of the prism?

We can use the formula for the equation of a line to determine any missing values. The formula is:

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=

�

�

+

�

y=mx+b

where $m$ is the slope of the line and $b$ is the y-intercept.

We can use the given data points to calculate the slope of the line:

�

=

change in y

change in x

=

�

2

−

�

1

�

2

−

�

1

m=

change in x

change in y

​

=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

where $(x_1, y_1)$ and $(x_2, y_2)$ are any two points on the line. Let's use the points $(-9, 3)$ and $(-6, 2)$:

\begin{align*}

m &= \frac{y_2 - y_1}{x_2 - x_1} \

&= \frac{2 - 3}{-6 - (-9)} \

&= \frac{-1}{3}

\end{align*}

Now we can use the slope-intercept form of the equation of a line to determine any missing values. Let's go through each option:

a. Missing $x:-2$, Missing $y:0$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot (-2) + 3 \

&= \frac{7}{3}

\end{align*}

So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7}{3}}$.

b. Missing $x:0$, Missing $y:1$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-intercept:

\begin{align*}

y &= mx + b \

3 &= -\frac{1}{3} \cdot (-9) + b \

3 &= 3 + b \

b &= 0

\end{align*}

So the y-intercept is $0$. Now we can substitute $b = 0$ and $m = -\frac{1}{3}$ into the formula $y = mx + b$ to find the y-value when $x = 0$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot 0 + 0 \

&= 0

\end{align*}

So the missing value of $y$ when $x = 0$ is $\boxed{0}$.

c. Missing $x:-2$, Missing $y:2$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot (-2) + 3 \

&= \frac{7}{3}

\end{align*}

So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7

Answer:D=12, R=6

A=πr², C=2πr

A=36π, C=12π

A=113.04 ft²

C=37.68 ft

The vector b is [10, 5, 10] and the general solution for [A|b] is [1, 5, -3] + [-3, 2, -1]s

To find the vector b, we need to multiply the matrix A by the vector x and solve for b in the equation Ax = b.

So, we have:

[tex]\left[\begin{array}{ccc}1&3&-3&0&1&-2&3&5&-1\end{array}\right]\left[\begin{array}{c}1&1&-2\end{array}\right] &= \left[\begin{array}{c}10&5&10\end{array}\right][/tex]

Therefore, the vector b is [10, 5, 10].

To find the general solution of [A | b], we need to perform row reduction on the augmented matrix [A | b] and express the pivot variables in terms of the free variables.

[tex]\left[\begin{array}{ccc|c}1&3&-3&10&0&1&-2&5&3&5&-1&10\end{array}\right] &\rightarrow \left[\begin{array}{ccc|c}1&0&3&1&0&1&-2&5&0&0&0&0\end{array}\right][/tex]

The third column does not have a pivot variable, so we can express x3 in terms of the free variables.

Let s be the free variable, then we have:

x3 = -s - 3

We can now express the pivot variables in terms of s:

x1 = 1 - 3s

x2 = 5 + 2s

Thus, the general solution of [A | b] is:

[tex]\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] &= \left[\begin{array}{c}1 - 3s&5 + 2s&-s - 3\end{array}\right] \&= \left[\begin{array}{c}1&5&-3\end{array}\right] + s\left[\begin{array}{c}-3&2&-1\end{array}\right][/tex]

Therefore, the general solution of [A | b] is [1, 5, -3] + [-3, 2, -1]s

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Answer:

Multiply the numerators first together then multiply the denominators together.

Step-by-step explanation:

example  1/2(4/2) =4/4 = 1

Answer:

y = -7x - 3

Step-by-step explanation:

The slope-intercept form of the equation of a line is:

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

Given the slope m = -7 and the y-intercept b = -3, we can write the equation of the line in slope-intercept form as:

y = -7x - 3

Therefore, the equation of the line with slope -7 and y-intercept -3 in slope-intercept form is y = -7x - 3.

The median amount of time Julie's friends spend reading each week is 3 1/2 hours, which is the average of the two middle values when the given values are arranged in order.

To find the median value, we first need to put the given values in order from smallest to largest. The given values are: 1/2, 1/2, 2 1/2, 4 1/2, 7, and 12. When we arrange them in order, we get:

1/2, 1/2, 2 1/2, 4 1/2, 7, 12

The median is the middle value of the ordered list. If there is an odd number of values, the median is simply the middle value. However, in this case, we have an even number of values. Therefore, we take the average of the two middle values to find the median. The two middle values are 2 1/2 and 4 1/2. So, the median is:

(2 1/2 + 4 1/2)/2 = 3 1/2

This means that half of Julie's friends read for more than 3 1/2 hours per week and half of them read for less than 3 1/2 hours per week.

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Answer: I am pretty sure 7

Step-by-step explanation: I think this because 20 is the most and 13 is the leased so 20 -13 =7 but i just got done like a month or 2 ago so i just learned this so dont quote me sorry if it isn't right

Answer:

Step-by-step explanation:

A) To find the area covered by two-way radio A, we need to calculate the area of a circle with a radius of 8 miles:

Area = πr² = 3.14 x 8² = 200.96 square miles

Rounding to the nearest whole number, two-way radio A covers 201 square miles.

B) To find the area covered by two-way radio B, we need to convert the radius from kilometers to miles and then calculate the area of a circle with that radius:

Radius in miles = 11.27 / 1.61 = 6.9988 miles (rounded to 4 decimal places)

Area = πr² = 3.14 x (6.9988)² = 153.94 square miles

Rounding to the nearest whole number, two-way radio B covers 154 square miles.

C) Two-way radio A covers a larger area than two-way radio B (201 square miles vs 154 square miles).

D) The scale factor relationship between the radio coverages can be found by dividing the radius of radio A by the radius of radio B:

Scale factor = radius of A / radius of B = 8 miles / (11.27 km / 1.61 km/mile) = 4.97

This means that the coverage of two-way radio A is almost 5 times larger than that of two-way radio B.

Answer:

Step-by-step explanation:

Center of circle will be at the midpoint of (-2,1) and (4,3):

                     [tex]M=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

                           [tex]=(\frac{-2+4}{2} ,\frac{1+3}{2} )[/tex]

                           [tex]=(1,2)[/tex]

Radius will be distance from circle center (1,2) to edge (4,3):

                       [tex]r=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2 }[/tex]

                           [tex]=\sqrt{(4-1)^2+(3-2)^2 }[/tex]

                           [tex]=\sqrt{3^2+1^2 }[/tex]

                           [tex]=\sqrt{10}[/tex]

Equation of circle with center (1,2) and radius [tex]\sqrt{10}[/tex]:

                      [tex](x-h)^2+(y-k)^2=r^2[/tex]        center (h,k)  radius r

                      [tex](x-1)^2+(y-2)^2=\sqrt{10}^2[/tex]

                      [tex](x-1)^2+(y-2)^2=10[/tex]

SOLUTION: [tex](x-1)^2+(y-2)^2=10[/tex]

a. Sm satisfies all three properties of an equivalence relation, it is indeed an equivalence relation on Real numbers[x].

b. The equivalence class of Sm containing f is the set of all polynomials g that satisfy the condition m | (g - f).

c. The equivalence class of Sm containing the polynomial f(x) = x + 1 is the set {g ∈ Real numbers[x] : g(2) = 3}.

Real numbers are those that can be used to calculate constant values like temperature, time, or distance. They are equivalent to countless decimal increases. They are the sum of all positive and negative integers, fractions, decimals, transcendental numbers, and irrational numbers.

(a) To prove that Sm is an equivalence relation on Real numbers[x], we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any polynomial f ∈ Real numbers[x], we have f − f = 0, which is clearly a multiple of any polynomial m. Therefore, (f, f) ∈ Sm for all f ∈ Real numbers[x], and Sm is reflexive.

Symmetry: If (f, g) ∈ Sm, then m is a factor of g − f. This means that there exists a polynomial q ∈ Real numbers[x] such that g − f = mq. It follows that f − g = −mq, which is a multiple of m. Therefore, (g, f) ∈ Sm, and Sm is symmetric.

Transitivity: If (f, g) ∈ Sm and (g, h) ∈ Sm, then m is a factor of g − f and m is a factor of h − g. This means that there exist polynomials q1 and q2 ∈ Real numbers[x] such that g − f = mq1 and h − g = mq2. It follows that h − f = (h − g) + (g − f) = mq2 + mq1 = m(q2 + q1). Therefore, m is a factor of h − f, and (f, h) ∈ Sm. Thus, Sm is transitive.

Since Sm satisfies all three properties of an equivalence relation, it is indeed an equivalence relation on Real numbers[x].

(b) The division rule for polynomials states that for any polynomials f and g with g ≠ 0, there exist unique polynomials q and r such that f = qg + r and deg r < deg g. The equivalence class of Sm containing f is the set of all polynomials g that satisfy the condition m | (g - f).

Applying the division rule for polynomials to the polynomial g - f, we can write it as g - f = mq + r, where deg r < deg m. This means that g - r = f + mq, and therefore, any polynomial in the equivalence class of Sm containing f can be written as g = r + f + mq, where deg r < deg m. In other words, every equivalence class of Sm contains a polynomial of the form r + f + mq, where r is a polynomial of degree less than deg m.

(c) Let m(x) = x - 2. Then for any polynomial f(x) ∈ Real numbers[x], we have (f, g) ∈ Sm if and only if g(x) - f(x) is a multiple of x - 2. This means that g(2) - f(2) = 0, or in other words, f(2) = g(2). Therefore, the equivalence class of Sm containing the polynomial f(x) = x + 1 is the set {g ∈ Real numbers[x] : g(2) = 3}.

Justification: Let g(x) = (x - 2) + 3. Then g(2) = 3, and g(x) - f(x) = (x - 2) + 3 - (x + 1) = x - 2, which is a multiple of x - 2. Therefore, (f, g) ∈ Sm, and the set {g ∈ Real numbers[x] : g(2) = 3} is an equivalence class of Sm.

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[tex] \:\:\:\:\:\:\star\longrightarrow \sf \underline{y = 5\:x^4\:tanx}\\[/tex]

Differentiating with respect to x-

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{d}{dx}\:y = \dfrac{d}{dx}\: 5\:x^4\:tanx\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}\:= 5\:\dfrac{d}{dx}\: \:x^4\:tanx\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{d}{dx}\:y =5\:\bigg[tanx\times \dfrac{d}{dx}\: \:x^4\:+x^4\times \dfrac{d}{dx} tanx\bigg]\\[/tex]

[tex]\pink{\star}\:\boxed{\sf\sf\dfrac{d}{dx}\bigg[f(x)\:g(x)\bigg] = f(x) \dfrac{d}{dx} g(x) + g(x) \dfrac{d}{dx} f(x)}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}= 5\:\bigg[tanx\times 4\:x^3+ x^4 \times sec^2x \bigg]\\[/tex]

[tex] \qquad\pink{\star}\:\:\:\:\boxed{\sf \dfrac{d}{dx}x^n=nx^{n-1}}\\[/tex]

[tex] \qquad\pink{\star}\:\:\:\:\boxed{\sf \dfrac{d}{dx}tanx=sec^2x}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}= 5\:x^3\:\bigg[4tanx+ x sec^2x \bigg]\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{\dfrac{dy}{dx}= \boxed{\sf5\:x^3\:\bigg[4tanx+ x sec^2x \bigg]}}\\[/tex]

Answer:

70°

Step-by-step explanation:

280°÷4x

what is x?

x=70°

Answer: Let's break down the budget into different categories:

Furniture: 15% of the budget

15% of Rs. 53000 = Rs. 7950

So you can spend Rs. 7950 on furniture.

Cosmetics: 25% of the budget

25% of Rs. 53000 = Rs. 13250

So your cosmetics bill from Makeup4uonline is Rs. 13250.

Appliances: 15% of the budget at 20% discount

15% of Rs. 53000 = Rs. 7950

The appliances are at a 20% discount, so you only need to pay 80% of the price:

80% of Rs. 7950 = Rs. 6360

So you can spend Rs. 6360 on appliances.

Electric works: 5% of the total budget which is 12% of wall décor and lights

12% of the budget = 12/100 x Rs. 53000 = Rs. 6360

5% of the budget = 5/100 x Rs. 53000 = Rs. 2650

So you can spend Rs. 6360 on wall décor and lights, and Rs. 2650 on electric works.

Leftover amount for COVID-19 safety measures

The total amount spent so far is:

Rs. 7950 + Rs. 13250 + Rs. 6360 + Rs. 2650 = Rs. 30110

So the leftover amount for COVID-19 safety measures is:

Rs. 53000 - Rs. 30110 = Rs. 22890

Rate of leftover amount to total budget

The rate of leftover amount to total budget is:

(Rs. 22890 / Rs. 53000) x 100% = 43.2%

So 43.2% of the total budget is leftover for COVID-19 safety measures.

Step-by-step explanation:

Answer:

∠h = 61°

∠g = 119°

∠m = 59°

∠k = 121°

Step-by-step explanation:

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Therefore, as angle g is opposite 119°:

⇒ ∠g = 119°

As angle k is opposite 121°:

⇒ ∠k = 121°

Angles on a straight line sum to 180°.

As angle h and 119° form a straight line:

⇒ ∠h + 119° = 180°

⇒ ∠h + 119° - 119° = 180° - 119°

⇒ ∠h = 61°

As angle m and 121° form a straight line:

⇒ ∠m + 121° = 180°

⇒ ∠m + 121° - 121° = 180° - 121°

⇒ ∠m = 59°

Answer:

Step-by-step explanation:

To find:-

Answer:-

From the given figure we can see that angles k and 121° are vertically opposite angles . Also we know that vertically opposite angles are equal to each other. Hence here we can say that,

[tex]\longrightarrow \boxed{ k = 121^o}\\[/tex]

Secondly, we know the the mesure of angle of a straight line is 180° . So the sum of angles on a straight line would be 180° . If two angles are present we call them linear pair . Hence here , we can see that m and 121° are linear pairs.

So that,

[tex]\longrightarrow m + 121^o = 180^o \\[/tex]

[tex]\longrightarrow m = 180^o-121^o\\[/tex]

[tex]\longrightarrow \boxed{m = 59^o } \\[/tex]

Similarly we can see that g and 119° are vertically opposite angles. Again they will be equal. So ,

[tex]\longrightarrow \boxed{g = 119^o} \\[/tex]

Again, 119° and h form linear pair.So their sum would be 180° .

[tex]\longrightarrow h + 119^o = 180^o \\[/tex]

[tex]\longrightarrow h = 180^o - 119^o\\[/tex]

[tex]\longrightarrow \boxed{ h = 61^o }\\[/tex]

These are the required values of the unknown angles.

The answer should be 2.The lower quartile of the number of absence is 2

0 is the lowest number and then 2 would be lower quartile, The 4 would be the Median or the middle of all the data 7 is the upper quartile and 10 would be the highest number of absences.

The lower quartile, also known as the first quartile, is a measure of central tendency that divides a dataset into four equal parts. It represents the point at which 25% of the data values fall below and 75% of the data values fall above. In other words, the lower quartile marks the boundary between the lowest 25% and the upper 75% of the data. It is often used in statistics to help summarize and analyze datasets, and can be helpful in identifying outliers or unusual values in the lower end of a dataset.

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The probability that more than 2 students have blue eyes is 0.149, the expected number of students out of the 4 with blue eyes is 0.4, the variance is 0.36, and the standard deviation is 0.6.

a) P(X = 3) = (4 choose 3) * [tex](0.10)^3 * (0.90)^1[/tex] = 0.0036

So the probability that exactly 3 of them have blue eyes is 0.0036.

b) P(X = 2) = (4 choose 2) * [tex](0.10)^2 * (0.90)^2[/tex] = 0.0386

So the probability that exactly 2 of them have blue eyes is 0.0386.

c) P(at least 1) = 1 - P(none) = 1 - [tex](0.90)^4[/tex] = 0.3439

So the probability that at least 1 of them has blue eyes is 0.344.

d) P(X > 2) = P(X = 3) + P(X = 4) = (4 choose 3) * [tex](0.10)^3 * (0.90)^1[/tex] + (4 choose 4) * [tex](0.10)^4 * (0.90)^0[/tex] = 0.0001

So the probability that more than 2 have blue eyes is 0.0001.

e) E(X) = n * p = 4 * 0.10 = 0.4

So the expected number of students out of the 4 with blue eyes is 0.4, not 0.291 as provided.

f)Var(X) = n * p * (1 - p) = 4 * 0.10 * 0.90 = 0.36

So the variance is 0.36.

g) SD(X) = sqrt(Var(X)) = sqrt(0.36) = 0.6

Standard deviation is 0.6.

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Answer:

9) x = 12 cm

10) x = 10.4 ft (Rounded)

11) y = 39.7 in (Rounded)

Step-by-step explanation:

Just use Pythagorean theorem

Answer and Explanation:

We can solve for x in these questions using the Pythagorean Theorem:

a² + b² = c²,

where a and b are the legs (shorter sides) of a right triangle, and c is its hypotenuse (longest side).

Applying this theorem to the problems at hand:

9. We are using (10 / 2) as one of the legs.

(10 / 2)² + x² = 13²

↓ simplifying division

5² + x² = 13²

↓ subtracting 5² from both sides

x² = 13² - 5²

↓ simplifying the right side

x² = 169 - 25

x² = 144

↓ taking the square root of both sides

x = 12

10.

6² + x² = 12²

↓ subtracting 6² from both sides

x² = 12² - 6²

↓ simplifying the right side

x² = 144 - 36

x² = 108

↓ taking the square root of both sides

x = [tex]\sqrt{108}[/tex]

↓ simplifying the square root

    [tex]\sqrt{108} = \sqrt{3 \cdot 3 \cdot 3 \cdot 2 \cdot 2} = (3\cdot 2)\sqrt{3} = 6\sqrt3[/tex]

x = 6[tex]\sqrt3[/tex]

11.

24² + 33² = y²

↓ simplifying the right side

576 + 1089 = y²

1665 = y²

↓ taking the square root of both sides

y = [tex]\sqrt{1665}[/tex]

↓ simplifying the square root

    [tex]\sqrt{1665} = \sqrt{3 \cdot 3 \cdot 5 \cdot 37} = 3\sqrt{5 \cdot 37} = 3\sqrt{185}[/tex]

y = 3[tex]\sqrt{185}[/tex]

In the given figure the similarity is angle-angle property.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

Hence, In the given figure the similarity is angle-angle property.

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The distance between the two cruise ships after 2 hours is approximately 4.201 miles.

How to find distance?

To solve this problem, we need to use trigonometry to find the distance between the two cruise ships after 2 hours.

In the diagram, A and B are the two cruise ships, and D is the distance between them after 2 hours. The angle between their paths is 35 degrees.

We can use the formula: distance = speed x time

to find how far each cruise ship travels in 2 hours. For Cruise A, the distance it travels is

[tex]distance_A = 18 \times 2 = 36 \: miles[/tex]

For Cruise B, the distance it travels is

[tex]distance_B = 15 \times 2 = 30 \: miles

[/tex]

Now we can use trigonometry to find the distance between the two cruise ships. We can use the tangent function, since we know the angle and the opposite and adjacent sides of the triangle formed by the two cruise ships and the distance between them:

tan(35°) = D / (36 - 30)

Simplifying this equation, we getting,

D = (36 - 30) x tan(35°)

D = 6 x 0.7002

D ≈ 4.201 miles

Therefore, the distance between the two cruise ships after 2 hours is approximately 4.201 miles.

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Answer:

45/100, 0.45, 9/20

Step-by-step explanation:

Answer 1:  A percentage is part of a number is written in hundredths.  Thus, 45% is the same as 45/100

Answer 2:  To convert 45% to a decimal, you can rewrite 45% as 45.0%.  Then, you can move the decimal two places to the left, which is the same as dividing by 100.  You can also do standard division and you'll find the 45 divided by 100 = 0.45

Answer 3:  45/100 is not the simplest form of this fraction.  To simplify, we must find the greatest common factor of the numerator (45) and the denominator (100).  Both of these numbers can be divided evenly by 5 so 5 is the GCF of the two numbers.

Now, we divide both numbers by 5 to simplify the fraction:

45 / 5 = 9 and 100 / 5 = 20.  Thus, 45/100 reduces down to 9/20

Select any of the two answers available on your worksheet (if I'm reading what you wrote correctly, it seems like the two answer choices they provided were 9/20 and 45/100

According to the information to graph the inequality we have to show a number line with an open circle at -3 and an arrow pointing to the left, with the shaded region to the left of -3 labeled as x < -3.

To graph the inequality x < -3, we need to draw a number line and mark the point -3 on it. Since the inequality is "less than," we want to shade the region to the left of -3 on the number line.

We start by drawing a horizontal line with a labeled point for -3. Then we draw an arrow to the left of -3, to indicate that all the values to the left of -3 satisfy the inequality.

Here are the steps to graph the inequality on the sketchpad:

The resulting graph should show a number line with an open circle at -3 and an arrow pointing to the left, with the shaded region to the left of -3 labeled as x < -3.

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The area of the square is equal to 64 square units.

In this problem we find the representation of a geometric system formed by a circle and a square and we must compute the area of the latter figure. First, find the side length of the square by Pythagorean theorem:

10² = (2 · x)² + (1.5 · x)²

100 = 4 · x² + 2.25 · x²

100 = 6.25 · x²

x² = 16

x = 4

Second, compute the area of the square:

A = (2 · 4)²

A = 64

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Answer:

Step-by-step explanation:

I'm a little confused where the angle is, because I don't understand English units of measurement well, but the answers must be correct!

i use formula  [tex]sin^{2} \alpha + cos^{2} \alpha =1[/tex]

Answer: would be great if you could give the options of the questions?

the equation [tex]r = 3 - 3cos(\theta)[/tex] is symmetric with respect to the vertical line  but not with respect to the origin or the pole .

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides.  

The equation r = 3 - 3cos(θ) represents a polar curve, where r is the distance from the origin to a point on the curve, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

1. Symmetry with respect to the origin: A curve is symmetric with respect to the origin if replacing (r, θ) with (-r, θ + π) gives the same curve. Substituting -r for r and θ + π for θ in the equation, we get:

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

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

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

This is not the same as the original equation, so the curve is not symmetric with respect to the origin.

2.Symmetry with respect to the pole (x-axis): A curve is symmetric with respect to the pole if replacing (r, θ) with (r, -θ) gives the same curve. Substituting -θ for θ in the equation, we get:

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

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

This is not the same as the original equation, so the curve is not symmetric with respect to the pole.

3.Symmetry with respect to the vertical line (y-axis): A curve is symmetric with respect to the vertical line if replacing (r, θ) with (-r, π - θ) gives the same curve. Substituting -r for r and π - θ for θ in the equation, we get:

[tex]-r = 3 - 3cos(π - \theta)[/tex]

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

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

This is the same as the original equation, so the curve is symmetric with respect to the vertical line (y-axis).

Therefore, the equation  [tex]r = 3 - 3cos(\theta)[/tex] is symmetric with respect to the vertical line (y-axis) but not with respect to the origin or the pole (x-axis).

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The graph of r = 3 - 3cos(theta) is symmetric about the x-axis but not about the origin or about the y-axis.

Symmetry is described in geometry as a balanced and proportionate likeness seen in two sides of an object. It signifies that one side is a mirror image of the other. The line of symmetry is the imaginary line or axis along which you can fold a figure to obtain the symmetrical halves.

The symmetry equation is r = 3 -3 cosФ depicts a cardioid-shaped polar graph. We can use the following tests to determine symmetry:

1) We can test for symmetry with regard to the origin by seeing if the equation remains the same after substituting r with -r and Ф with Ф + pi.

r = 3 - 3cosФ - r = 3 - 3cos(Ф + pi)

3 - 3(-cos(Ф)) = r

-r = 3 + 3cos(Ф)

Because this is not equal to the original equation, the graph is not symmetric about the origin.

2) Symmetry with respect to the x-axis: We may test for symmetry with respect to the x-axis by seeing if the equation stays unchanged when theta is replaced with -theta.

r = 3 - 3cos(Ф)

r = 3 - 3cos(-Ф)

r = 3 - 3cos(Ф)

This is the same as the original equation, hence the graph is symmetric about the x-axis.

3) Symmetry with respect to the y-axis: We may test for symmetry with respect to the y-axis by seeing if the equation stays unchanged when theta is replaced with pi - theta.

r = 3 - 3cos(Ф)

r = 3 - 3cos(pi - Ф)

r = 3 + 3cos(Ф)

Because this is not equal to the original equation, the graph is not symmetric about the y-axis.

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Answer:

Use in² for area; use in³ for volume.

Explanation:

When you calculate the area of a rectangle, you multiply length times width. Both units are in inches so:

inches × inches = (inches)² or in²

When you calculate the volume of a box (rectangular prism), you multiply length by width by height. All three units are in inches so:

inches × inches × inches = (inches)³ or in³

Yes,I would have made the same decision to purchase disability insurance .

What is disability insurance?

Disability insurance provides financial protection in the event that you become unable to work due to an illness or injury. It can help you pay for living expenses, medical bills, and other costs while you are unable to work.

When deciding whether or not to purchase disability insurance, it's important to consider your financial situation and your ability to manage expenses if you were to become disabled. If you have a good amount of savings or other sources of income, you may be able to manage without disability insurance. However, if you rely heavily on your income to pay for living expenses and do not have significant savings, disability insurance may be a wise investment.

It's also important to consider the cost of disability insurance and whether it fits within your budget. While the additional $22.70 a month may not seem like a lot, it can add up over time. You should evaluate whether the cost of the insurance is worth the potential benefits it provides.

Ultimately, the decision to purchase disability insurance is a personal one that depends on individual circumstances and priorities. While it's impossible to predict the future, having disability insurance can provide peace of mind and financial protection in case the unexpected happens.

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the correct answer is (D) 8 units to the left. To find the translation direction and number of units, we need to find the vector that takes us from point R to point R'.

Vector RR' can be found by subtracting the coordinates of R from the coordinates of R':

RR' = R' - R = (-7, 4) - (1, 4) = (-8, 0)

This means that the translation moves 8 units to the left, since the x-coordinate of the vector is negative.

To determine the translation direction and number of units required to move R to R', we need to first find the distance between the x-coordinates of R and R'. We can do this by subtracting the x-coordinate of R from the x-coordinate of R': -7 - 1 = -8.

This tells us that we need to move R' 8 units to the left to get to R. However, the question is asking for the translation required to move R to R', not the other way around. Therefore, we need to reverse the direction and say that we need to move R 8 units to the right to get to R'.

We can confirm this by checking the y-coordinates of R and R'. We see that they are both 4, which means there is no vertical translation required. Therefore, the answer is C. 8 units to the right.

Therefore , the correct answer is (D) 8 units to the left.

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Answer:

Step-by-step explanation:

The rule that relates the number of months (m) to the cost (c) of a gym membership is:

c = 15m + 25

To find the cost of a 1 year (12 months) membership, we substitute m = 12 into the equation:

c = 15(12) + 25 = 205

Therefore, the cost of a 1 year membership is $205 (which includes the $25 sign up fee).

The area of the unshaded region is 3x²-3x-8

What is area of rectangle?

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.

The area of a rectangle is expressed as;

A = l× w

Area of the unshaded part = Area of the whole rectangle - area of shaded part

Therefore area of the unshaded part =

5x²+4x-8 -(2x²+7x)

= 5x²+4x-8 -2x²-7x

collect like terms

5x²-2x²+4x-7x-8

= 3x²-3x-8

therefore the area of the unshaded part is 3x²-3x-8

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