Chords AB and CB intersect at E in circle O, as shown in the diagram below. Secant
PFA and tangent PD are drawn to circle O from external point and chord AC is drawn. The ratio of BF:FC:CA:AB = 3:3:4:8. Find the measures of FC,∠P,∠CEA, and ∠ABC.

The length of AB when A'B' is 8 is 12

The measurement of B' when angle B is 40° is also 40°

The measurement of A' when A is 80° is also 80°

The measurement of C using AB is 60°

Similar triangles are triangles that have the same angles and the ratio of their corresponding sides are equal.

Analysis:

ΔCA'B' is similar to ΔCAB.

Which means [tex]\frac{A'B'}{AB}[/tex] = [tex]\frac{CB'}{CB}[/tex] = [tex]\frac{CA'}{CA}[/tex]

A'B' = 8, CA' = 4, CA = 6

[tex]\frac{8}{AB}[/tex] = [tex]\frac{4}{6}[/tex]

4AB = 8 X 6

AB = 48/4 = 12

Line BA nd B'A' are parallel lines joined by two transversals BC and CA.

So, ∠B = ∠B' = 40°( corresponding angles are equal)

Also, ∠A = ∠A' = 80° ( corresponding angles are equal)

∠A + ∠B +∠C = 180( sum of angles in a triangle)

80 + 40 + ∠C = 180

120 + ∠C = 180

∠C = 180 - 120 = 60°

In conclusion,

The length of AB when A'B' is 8 is 12

The measurement of B' when angle B is 40° is also 40°

The measurement of A' when A is 80° is also 80°

The measurement of C using AB is 60°.

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Answer:

  4.23 square units

Step-by-step explanation:

The area of the triangle is given by the formula ...

  K = 1/2ab·sin(C)

__

Filling in the given values, we find the area to be ...

  K = 1/2(4)(5)sin(25°) = 4.23 . . . . square units

Answer:

The arrangements of things following one after another in time

Step-by-step explanation:

well don't breath just collect like terms and booom

Answer:

Step-by-step explanation:

A graph shows real zeros at ±2.203 and -1. The value of f(x) changes sign at each of these.

The positive leading coefficient indicates the graph trends generally upward, so the function will be positive in intervals with an even number of zeros to the right.

There are an even number of zeros to the right of x = 2.203 and the interval (-2.203, -1).

  f(x) is positive in the intervals (-2.203, -1) or (2.203, ∞).

The function will be negative where it is not positive (except at the zeros)

  f(x) is negative in the intervals (-∞, -2.203) or (-1, 2.203).

_____

Additional comment

The graph shows the only rational real root of the function is x=-1. Using synthetic division to reduce the polynomial, we find ...

  f(x) = (x +1)(x^4 -3x^2 -9)

The remaining factor is a quadratic in x^2, which has roots ...

  x = ±√(1.5 ±√11.25)

The real roots are approximately ±2.20320266118. The value 2.203 used above is a stand-in for the exact value √(1.5 +√11.25)).

Answer:

Question 3: [tex]b \geq 2[/tex]

Question 4: [tex]r < -5[/tex]

Question 5: [tex]y \leq -6[/tex]

Step-by-step explanation:

Question 3:

[tex]b + 2 \geq 4\\b + 2 -2 \geq 4 - 2\\b \geq 2\\[/tex]

Question 4:

[tex]13 > 18 + r\\13 - 18 > 18 -18 + r\\\\-5 > r\\ r < -5[/tex]sign flips when r switches sides

Question 5:

[tex]3y \leq 2y - 6\\3y - 2y \leq 2y - 2y - 6\\\\y \leq - 6\\[/tex]

Answer:

x=-108117

Step-by-step explanation:

108105-2+1(2x+10)=1(x-4)

108113+2x=x-4

2x-x=-4-108113

x=-108117

Answer:

here is 1/2 divided displayed mathematically

1/2 ÷ 6

1= numerator

2= denominator

3= whole number

to make it fraction from the answer you keep the

numerator by the whole number to make a new

denominator

___1___ = _1_

2×6 12

thus the answer to 1/2 divided by 6 on fraction form is

1/12 is the answer

Answer:

The answer is 5/36.

Step-by-step explanation:

Test approved.

The probability that she rolls a 1 on the first cube and a number greater than 1 on the second cube is 5/36.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

Given that Stef rolls two six-sided number cubes.

Based on the diagram of the sample space.

Therefore, the probability that she rolls a 1 on the first cube and a number greater than 1 on the second cube

=  5/36.

Hencce, the correct option is B.

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Answer:

[tex] \frac{ - 2x - 2}{ {x}^{2} + 2x - 3 } [/tex]

is the answer

Answer:

C. $16.95

Step-by-step explanation:

Median is putting the numbers in numerical order and finding the middle by  listing a number on each side off.

As there would need to be bigger numbers in order for the $17.99 to be in the middle, the smallest number would mess the order up.

In the end, Fatima only has 0.395 kg of roses, because she used up a total of 0.115 kg of rose petals.

To calculate the amount of rose petals that Fatima has at the end, we must perform the following mathematical operations:

Subtract 0.02kg to 0.454kg

Add 0.056 kg to 0.434 kg

Subtract 0.095kg from 0.49kg

Based on the above, Fatima is wrong because she thinks she should have 0.413 kg of rose petals, but she has 0.395 kg.

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The enlargement or a reduction in the dimensions of a building would cause a change in the scale factor is defined below:

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

A dilation is a transformation that enlarges or reduces a figure in size. This means that the pre image and image are similar and are either reduced or enlarged using a scale factor.

As seen in the graphics below. A reduction (think shrinking) is a dilation that creates a smaller image, and an enlargement (think stretch) is a dilation that creates a larger image.

If the scale factor is between 0 and 1 the image is a reduction.

Using dilation scale factors, we can shrink or expand a figure to the size we desire, knowing that each angle is congruent, each segment is proportional, the slope of each segment is maintained, and the perimeter of the pre image and image have the same scale factor.

Hence, this is how an enlargement or a reduction in the dimensions of a building would cause a change in the scale factor.

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Answer:

The formula for determining the present value of an annuity is PV = dollar amount of an individual annuity payment multiplied by P = PMT * [1 – [ (1 / 1+r)^n] / r] where: P = Present value of your annuity stream. PMT = Dollar amount of each payment. r = Discount or interest rate.

Step-by-step explanation:

Hope this helps :) :)

Answer:

21.5 to 1 decimal place.

Step-by-step explanation:

The total number of marks for all the boys = 28*28 = 784 marks.

The total number of marks for all the girls   = 24*14  = 336 marks.

So the mean mark for the whole group  

= (784+336) / (28+24)

= 1120 / 52

= 21.538

To multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32

To answer the question, we need to know what logarithm of a number is

The logarithm of a number x is the power to base 10 of that number.

So, logarithm of x to base 10 is written as ㏒x.

Since we want to multiply 64 × 83.2, we convert this to logarithmic equation using the addition rule of logarithm.

㏒ab = ㏒a + ㏒b

So, 64 × 8.32 to logarithm is ㏒(64 × 8.32) = ㏒64 + ㏒8.32

So, to multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32

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Answer:

you need to width x height x length b

Step-by-step explanation:

Length, width, and height are measurements that allow us to indicate the volume of geometric bodies. The length (6 cm) and the width (10 cm) correspond to the horizontal dimension. On the other hand, the height      (5 cm)refers to the vertical dimension.

The room, the tables and the guests are illustrations of rectangles and areas.

This is calculated using:

Tables = Guest ÷ Guest per top table

So, we have:

Tables = 120 ÷ 12

Evaluate

Tables = 10

Hence, 10 tables are required for the top table

This is calculated using:

Covers = Number of spring ÷ Cover space

So, we have:

Covers = 3 ÷ 0.6

Evaluate

Covers = 5

Hence, 5 covers are required for each spring

This is calculated using:

Tables = Tables for top table ÷ Spring

So, we have:

Tables = 10 ÷ 3

Evaluate

Tables = 3.33

Remove decimal

Tables = 3

Hence, 3 tables are required for each spring

This is done to allow passage for walkway

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Answer:

Length = 24 yd

Width = 6 yd

Step-by-step explanation:

To start out, we can begin by saying that "l" is the length of the rectangle, and "w" is the width.

Since we know that the length (l) is 4 times its width we can say that 4 times the width is equal to its length. We would write this out this way :

4w = l

Next, we know that the perimeter is 60yd (as it is given in the question). We also know that the perimeter of a rectangle is all of its sides, added. Meaning the length plus the length, plus the width and the width. So, we can use the equation :

2l + 2w = p

"p" being the perimeter. And, since the perimeter is 60, we can place in 60 for "p"

2l + 2w = 60

Now we can use this information to combine the terms, and find the width and length. We first do this by noticing that in the first equation, it shows that "l" (the length) is equal to 4w. This means that we can put 4w in place of the "l" in the second equation. We can do this, becuase we know that "l" is equal to 4w. (from the first eqaution)

2 (4w) + 2w = 60

Now, we solve

2 * 4w = 8w

8w + 2w = 10w

So now we have :

10w = 60

To get the width, all we have to do is simply get "w" alone. We can do this by dividing both sides by 10.

10w = 60

/10     /10

w = 6

Therefore, the width is 6.

Now, going back to the first equaiton, we already know that the length is 4 times the width, meaning all we have to do is multiply 6 by 4 to get the length.

6 * 4 = 24.

Therefore, the length is 24.

Lastly, to check and make sure we are correct, we can go back to the second equation. 2l + 2w = 60

2 (24) + 2 (6) = 60

2 * 24 = 48

2 * 6 = 12

48 + 12 = 60

60 = 60

Now, we officially know that the length of the rectangle is 24 and the width is 6.

Answer: sin(x)=5/11

Step-by-step explanation:

For #7, the hypotenuse is always the longest side of a triangle and in right triangles it's always the side that's opposite the right angle. MO, the side thats 11, is the hypotenuse in this triangle and not the adjacent side which would be NM. Therefore, you need to use sin=opp/hyp and get sin(x)=5/11

Answer: c= [tex]x^{2}[/tex] +4x-10

Step-by-step explanation:

Step 1: Flip the equation.

C+1= [tex]x^{2}[/tex]+4x-9

Step 2: Add -1 to both sides.

c+1+-1=[tex]x^{2}[/tex]+4x-9+-1

c=[tex]x^{2}[/tex]+4x-10

Answer:

415.63

Step-by-step explanation:

Multiply the price by the sales tax to find out how much money the sales tax will add.

Answer:

$415.63

Step-by-step explanation:

475

after 30%

475 times .30 = 142 5

475 - 142.5 = 332.5 <- sale price

332.5 times .25 = 83.125

332.5 + 83.125 = 415.625 <- new price

Answer:

92

Step-by-step explanation:its right

Answer:

m = 2

Step-by-step explanation:

Write the slope formula

Substitute: m = - 13 - 11/ - 9 - 3

Calculate the sum or difference: m = -24 / - 9 - 3

Calculate the sum or difference: m = -24 /-12

Reduce the fraction: m = 2

Answer: m = 2

Answer: m = 2

Step-by-step explanation:

Slope formula = [tex]\frac{y2-y1}{x2-x1}[/tex]

plug in values

[tex]\frac{-13-11}{-9-3}[/tex]

simplify

[tex]\frac{-24}{-12}[/tex]=2

⇒M = 2

Answer:

Your question does not make sence

Answer:

the X axis line which bisects the y axis with an angle of 90 degrees

Based on the number of ways to answer the multiple choice questions and the number of ways to answer true or false, the number of ways to answer the test is 8,192 ways.

This can be found as:

= Total number of ways to answer multiple choice questions + Total ways to answer true or false questions

Solving gives:
= (4 x 4 x 4) x (2 x2 x2 x 2 x 2 x 2 x 2)

= 64 x 128

= 8,192 ways

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