Part 2 - Find the error(s) and solve the problem correctly.
Convert the polar equation to rectangular form and identify the graph. Support your answer by sketching the graph. Show and explain your work.
r = − 4 cos θ
Answer:
Cosine graph reflected over x-axis with amplitude 4

Answer:

True.

Step-by-step explanation:

In order for a quadrilateral to be a parallelogram, the top and bottom sides must be congruent, and the left and right must be congruent.

Opposite angles on either side are equal.

\(\frac{7}{8} (-32-48x) + 36 = \frac{2}{3} (-33x-18) -10x\)

\(\frac{7}{8} (-32)+\frac{7}{8} (-48)+36=\frac{2}{3} (-33x)+\frac{2}{3} (-18)-10x\)

\(-28-42+36=-22x-12-10x\)

\(22x+10x=28+42-36-12\)

\(32x=22\)

\(x=\frac{22}{32} =\frac{11}{16} =0,6875\)

Answer: x = 0.6875

Ok done. Thank to me :>

Answer:

x = 2

Step-by-step explanation:

7/8 (-32-48x) + 36 = 2/3 (-33x-18) - 10x

Multiply,

7(-32-48x)/8 + 36 = 2(-33x-18)/3 -10x

Simpliy,

-336(3x+2) + 864 = -48(11x+6) - 240x

Expand,

-1008x + 192 = -768x - 288

Simplify,

-1008x = -768x -480

Simplify,

-240x = -480

Simplify,

x = -480/-240

Answer,

x = 2

Answer: -2/3

Step-by-step explanation:

Answer:

0.5679

Step-by-step explanation:

From. The table Given above :

The probability of female Given an advanced degree ;

P(F|A) = p(FnA) / p(A)

From the table, p(FnA) = 322

P(Advanced degree), P(A) = (245 + 322) = 567

Hence,

P(F|A) = p(FnA) / p(A) = 322 / 567 = 0.5679

Answer:

Step-by-step explanation:

x = 45    {Angles on the same segment of a circle are equal}

EC ---> chord

∠EBC & ∠EDC are on the same segment

The slope-intercept equation of the line with a slope of 8 and a y-intercept of (0, 9) is y = 8x + 9.

To find the slope-intercept equation of a line, we use the form y = mx + b, where m represents the slope and b represents the y-intercept.

Given:

Slope (m) = 8

Y-intercept (0, 9)

We can substitute these values into the slope-intercept form:

y = mx + b

y = 8x + 9

Consequently, y = 8x + 9 represents the slope-intercept equation for the line with a slope of 8 and a y-intercept of (0, 9).

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The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

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Answer:

The slope is:

\( \binom{1}{2} \)

In slope-intercept form the equation is:

\(y = \binom{1}{2} x - 3\)

The table is completed as shown below and total earnings of Lori is found.

What exactly is total earnings of a person?

The wages paid for both regular working hours and other working hours, including extra work or tips are referred to as total earnings.

Consider Tuesday

Hours worked = 4

Base salary = 4 × 7 ( $7 per hour given)

                     = $28

Tips = 18% of food sales = 0.18 × 300 = $54

Total earnings on Tuesday = 28 + 54 = $82

In the similar way the table can be completed as below.

1) The total earnings of Lori for the week = 82+138.9+218.5+173 = $612.4

2) Total earnings in a year = 52 × 612.4 = $31844.8

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Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

Solve for x.  

Step-by-step explanation:

3

x

–

1

<

8

or

x

–

5

>

0

Show Solution

Solve each inequality by isolating the variable.

x

−

5

>

0

OR

3

x

−

1

<

8

+

5

+

5

––––––––––

+

1

+

1

–––––––––––

x

>

5

3

x

–––

<

9

–

3

3

x

<

3

x

>

5

or

x

<

3

Write both inequality solutions as a compound using or, using interval notation.

Answer

Inequality:

x

>

5

or

x

<

3

Interval:

(

−

∞

,

3

)

∪

(

5

,

∞

)

The solution to this compound inequality can also be shown graphically. Sometimes it helps to draw the graph first before writing the solution using interval notation.

the school purchased 742 items in total.

Just add 256+332+154

which equals...742. :)

Answer:

742 items

Step-by-step explanation:

Add up all the items that the cafeteria purchased. 256+332+154=742!

The maximum daily profit the company can earn is $2,350.

It is a set of points in a coordinate plane that represents the values of the function for different inputs.

The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.

Therefore, the maximum daily profit the company can earn is $2,350.

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The values of the variables in the circles are

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

Circles and missing angles (see attachment for the figures)

Circle 1

To determine the unknown variable (a), we make use of the following theorem

The angle subtended by an arc at the circumference is twice the angle subtended at the circumference

Mathematically, this means that

a = 2 * 17 degrees

Evaluate the product

a = 34 degrees

Circle 2

To determine the unknown variable (a), we make use of the following theorem

The angle at the circumference in a semicircle is 90 degrees.

Mathematically, this means that

b = 90 degrees

Also, we have

a + 122 degrees = 180 degrees

Evaluate

a = 58 degrees

Using the theorem in (a), we have

b + a/2 + c = 180

This gives

90 + 58/2 + c = 180

Evaluate the like terms

c = 61 degrees

Hence, the angle c is 61 degrees

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Answer:

choice C: x2 -3x -3

Step-by-step explanation:

(3x^2-7x+2)-(2x^2-4x+5)

becomes

3x^2-7x+2 -2x^2+4x-5

adding

3x^2-2x^2 -7x+4x +2-5

which is

x^2 -3x -3

Answer: 2 is the value of expression 4(6/10 - 1/5) + 0.4.

Step-by-step explanation:

4(6/10 - 1/5) + 0.4

= 4(3/5 - 1/5) + 0.4

= 4(2/5) + 0.4

= 8/5 + 0.4

= 1.6 + 0.4

= 2

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The implicit general solution is 0.5y² = -0.5x² + 0.5x + C, here C should pass through the origin of the circle. The family of curves (T)  represents the integral curve. The graph (T) is represented below.

a. To find the implicit general solution of the given differential equation, we can integrate both sides with respect to x. Let's start by rewriting the equation:

yy' = -x + 1/2

Integrating both sides:

∫ yy' dx = ∫ (-x + 1/2) dx

Using integration by parts on the left side, let u = y and dv = y' dx:

\(\int u dv = uv - \int v du\\\\y\int dy = \int (-x + 1/2) dx\\\\1/2 y^2 = -1/2 x^2 + 1/2 x + C\\\\0.5y^2 = -0.5x^2+0.5x+C\)

Where C is the constant of integration. This is the implicit general solution of the given differential equation.

b. The family of curves (T) that represents the general solution in an orthonormal system is known as the integral curves of the differential equation.

c. To find the graph (T) that passes through the origin O(0, 0), we substitute the point (x, y) = (0, 0) into the implicit general solution and solve for C:

\(1/2(0)^2 = -1/2(0)^2 + 1/2(0) + C\\\\0 = 0 + 0 + C\\\\\C = 0\)

So the graph (T) that passes through the origin is given by:

\(1/2 y^2 = -1/2 x^2 + 1/2 x\)

This equation represents the specific curve that satisfies both the differential equation and the condition of passing through the origin.

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Check the picture below.

The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.

(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.

Step 1: Sum up the number of movies watched by all 25 students:

\(0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70\)

Step 2: Divide the sum from Step 1 by the number of students (25):

70 / 25 = 2.8

So the sample mean X = 2.8

(b) The sample standard deviation s can be calculated using the formula:

\(s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }\)

Where \(X_{mean}\) is the sample mean, n is the sample size, and Σ represents the sum of all values.

Step 1: Calculate \((X - X_{mean})^2\)for each data point and sum up the values:

\((0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36\)

Step 2: Divide the sum from Step 1 by (n - 1) = 24:

31.36 / 24 = 1.31

Step 3: Take the square root of the result from Step 2:

\(\sqrt{1.31} = 1.15\)

So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).

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Answer: y = -2x + 1

Step-by-step explanation:

The formula for slope-intercept form is y = mx + b. Keep y and x as the variables. Replace m with the slope, which can be found by doing rise/run, and replace b with the y-intercept. The y-intercept is the spot where the line intersects the y-axis.

Hope this helps! Have a great day! :)

Answer: 2. They are congruent angles.

Step-by-step explanation:

      Angle 1 and angle 3 are vertical angles. In other words, they are "opposite" each other.

     Vertical angle pairs are congruent angles, meaning the answer to this question is;

              2. They are congruent angles.

Answer: They are congruent angles.

Step-by-step explanation: Complementary means the two angles equal 90°, supplementary angles are next to each other and equal 180° together, and it's obviously not a right angle, (angle that equals 90°) so we know they are congruent angles (this means that they are the same)

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(a) When measuring angle 9 and the lengths of AB and BC, one observation is required.

(b) The line drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord, while the line drawn from the center of a circle to an endpoint of a chord bisects the chord.

a) In the given diagram, we have angle AOB (angle 9) and line segments AB and BC.

To measure angle 9, we use a protractor. We align the baseline of the protractor with the line segment OA, ensuring that the center point of the protractor coincides with the vertex O. Then, we read the degree measurement where the line segment OB intersects the protractor. Let's assume the measurement of angle 9 is x degrees.

To measure the length of line segments AB and BC, we use a ruler. We align the ruler with the line segments and read the length in units (e.g., centimeters or inches).

b) The statements to complete are:

(i) The line drawn from the center of a circle to the midpoint of a chord will be perpendicular to the chord.

(ii) The line drawn from the center of a circle to the endpoint of a chord will bisect the chord.

In a circle, the center of the circle lies on the perpendicular bisector of any chord. This means that if we draw a line from the center of the circle to the midpoint of a chord, it will be perpendicular to the chord (statement i). Similarly, if we draw a line from the center of the circle to one of the endpoints of the chord, it will bisect the chord into two equal parts (statement ii).

These properties hold true for any chord in a circle, and they are based on the geometric properties of circles and perpendicular bisectors.

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Answer:

solution

given

length =3

breadth=6

height=3

volume =?

now,

volume=l*b*h

3*6*3

and 54

Answer:

114

Step-by-step explanation:

break apart the shape into 2 smaller shapes and you'll get 15 and 4 for the 1st shape multiply them and you'll get 60. Then for the second shape you'll get 6 and 9 multiply them and you'll get 54. Last add them together and you get 114. (Sorry if I get it wrong)

Answer:

Step-by-step explanation:

fraction decomposition for the expression

13x - 7/(x+2)(4x-3)

Answer: A

Step-by-step explanation:

Answer:

hey can you give us the buying price of the ticket so we can find the increase? thanks :)

Step-by-step explanation:

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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