Let A, B, C be three points on a circle

with AB = BC. Let the tangents at A and

B meet at D. Let DC meet again

at E. Prove that the line AE bisects the segment

BD. (Hint: Why do we care about a chord bisecting a tangent line?)​

Answer:

6a³b²

Step-by-step explanation:

3 × 2 = 6

a²× a¹ = a³

b × b = b²

Answer:  -12

Step-by-step explanation:    x is -4 so -(-4) is positive 4. d = 3 so -3 = -3. -3x4 = -12.

The value of b as described in the task content by means of solving the two equations simultaneously is; b= -10.

The given simultaneous equations as indicated have been manipulated to determine the value of a which is; 0.5 in the task content.

Hence, by substituting a= 0.5 into the equation; 5 = 30a + b; we have;

5 = 30(0.5) + b

b = 5- 15 = -10.

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Perimeter → 25cm

Area → 25.5cm²

[tex]perimeter = > 2.5 \times 2 + 5.5 + 3.5 + 6 + 3 + 2 = 5 + 9 + 9 + 2 = 25[/tex]

[tex]area = > 3 \times \frac{1}{2} \times 2 + 3 \times 3.5 + 6 \times 2 = 3 + 12 + 10.5 = 25.5[/tex]

Total of 24.03% of boys choose Niagara falls.

A frequency table is a list of objects with the frequency of each item shown in the table.

The quantity of times that an event or value occurs is its frequency.

A frequency table, then, is a table that contains some facts and their frequency.

Given,

Total number of boys

56 + 74 + 103 = 233

Number of boys who chose Niagara falls = 56

Percentage of 56 out of 233

(56/233) × 100⇒ 24.03%

Hence the percent of the boys chose Niagara Falls will be 24.03%.

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Based on the calculations, the area of a rectangle to the nearest hundredth is equal to 1143.92 ft².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

By drawing a line between the points representing wicket 3 and wicket 9, we can logically deduce that wicket 2 forms a perpendicular bisector. Thus, the distance between the points representing wicket 3 and wicket 9 is given by:

Distance = 1/2 × 36.77

Distance = 36.77/2

Distance = 18.39 ft.

For the height of this triangle, we would apply Pythagorean's theorem:

h² = 25.02² - 18.39²

h² = 626.0004 - 338.1921

h² = 287.8083

h = √287.8083

h = 16.97 ft.

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 36.77 × 16.97

Area of triangle = 311.99 ft².

For area of the rectangle, we have:

Mathematically, the area of a rectangle can be calculated by using this formula;

Area = LW

Area = 36.77 × 31.11

Area = 1143.92 ft².

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Answer:

C

Step-by-step explanation:

The amount we should charge Tommy is $363.

How much should we charge Tommy:

The amount charged for 1000 words = $110

The amount charged per word = $110/1000

Amount to be charged for 3300 words = $(110/1000) × 3300

= $(0.11) × 3300

= $363

The amount we should charge Tommy is $363.

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Answer:

x = 5

Step-by-step explanation:

There's a Secant Theorem that someone else figured out (waaaay back in history) we just need to memorize it. So a secant is a line that touches the circle in two places. Your picture has two secants that both go thru the same point that's outside the circle. The secants each have a bit that's inside the circle and a bit that's outside the circle. And we could add together the inside and outside bits and get a total for the whole thing.

The secant theorem says that the outside piece × the whole thing on one secant = the outside piece × the whole thing on the other secant.

For the secant on top the "outside" bit is 9 and the whole thing is (2x+1+9). We'll times these together.

For the bottom secant the outside piece is 10 and the whole thing is (x+3+10). We'll multiply these together.

9(2x+1+9)=10(x+3+10)

simplify.

9(2x+10) = 10(x+13)

distribute.

18x + 90 = 101x + 130

combine like terms.

8x + 90 = 130

subtract 90

8x = 40

divide by 8

x = 5

see image.

Answer:

39 pages

Step-by-step explanation:

If 13 pages are read in 1/3 of an hour, we need to multiply 13 by 3 to get the number of pages read in 1 hour. 13*3 = 39 pages

Answer:

144

Step-by-step explanation:

First find g(7) --

[tex]g(7)=2(7)-2\\=14-2\\=12[/tex]

Then plug 12 into f(x) --

[tex]f(12)=(12)^{2} \\=144[/tex]

2/3 is 400% of 1/6

0.2 is 12.5% of 1 3/5

From the question, we are to determine what percent of 1/6 is 2/3

Let the value be x

Thus,

We can write that

2/3 is x% of 1/6

This means

2/3 = x/100 × 1/6

Now, solve for x

2/3 = x/100 × 1/6

2/3 = x/600

x = (2×600)/3

x = 400

Hence, 2/3 is 400% of 1/6

We are to determine what percent of 1 3/5 is 0.2

Let the value be y

That is,

0.2 is y% of 1 3/5

This can be written as

0.2 = y% × 1.6

0.2 = y/100 × 1.6

Now, solve for y

0.2 = y/100 × 1.6

0.2 = 1.6y/100

1.6y = 0.2 × 100

1.6y = 20

y = 20/1.6
y = 12.5

Hence, 0.2 is 12.5% of 1 3/5

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Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=9\\ h=7 \end{cases}\implies \begin{array}{llll} A=\cfrac{7(5+9)}{2}\implies A=\cfrac{7(14)}{2} \\\\\\ A=49 \end{array}[/tex]

[tex]x[/tex] and [tex]3x+5[/tex] are being multiplied to form the expression, and are not being added or subtracted.

Here, x and (3x+5) are given in the form of multiplication, instead of being separated by addition or subtraction. This is why x and (3x+5) are factors of the expression x(3x + 5)² and not terms of the expression.

What are terms and factors in an expression?

Terms of an expression can be a variable, a signed number, or a constant multiplied by one or more variables. On the other hand, the factors are the items that have been multiplied by another items. Any integer, variable, phrase, or lengthier expression can be a factor.

For instance, the expression 2x(y - 5) has three components: 2, x, and (y-3). These three components are its factors, since when multiplied, they produce the same expression. The factors may or may not be comprised of more than one terms.

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Answer:

a) x + 10 = 45

b) 3 = 6 - x

c) d = s * t

Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.

SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.

This is all we're really doing.

Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.

Just keep doing this with all the equations.

Hope this helped!

By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.

Notice that the ladder makes a right triangle with the wall.

Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft

If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.

Then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse)

Then:

sin(x) = (13.5ft)/(15ft)

If we use the inverse sine function on both sides, we get:

Asin(sin(x)) = Asin( 13.5ft/15ft)

x = Asin(13.5/15) = 64.2°

So the angle is less than 75°, which means that in fact, the ladder is safe.

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Answer:5SQRT61/

61

Step-by-step explanation:

Answer:

y= -3x+4

Step-by-step explanation:

y=mx+c

m= y2-y1 ÷ x2-x1

m= -3

y=-3x+c

7=-3(-1)+c

c=4

y=-3+4

The value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

The equation is given as:

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000

From the question, we understand that the expression is to be solved from left to right (without using the pemdas mathematical rule)

So, we start by multiplying 2 and 4

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 8 + 48000 / 8 - 1 x 30 x 2 + 40000

Add 8 and 48000

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 48008 / 8 - 1 x 30 x 2 + 40000

Divide 48008 by 8

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6001 - 1 x 30 x 2 + 40000

Subtract 1 from 6001

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6000 x 30 x 2 + 40000

Multiply 6000 and 30

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 180000 x 2 + 40000

Multiply 180000 by 2

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 360000 + 40000

Evaluate the sum

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 400000

Hence, the value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

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the answer is (-4,-1) and (1,-5)

Using the law of sines, it is found that the distance between the kite and the dog is of 284.77 meters.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

For the situation described, we have that:

Hence:

[tex]\frac{\sin{42^\circ}}{h} = \frac{\sin{87^\circ}}{425}[/tex]

Applying cross multiplication:

[tex]h = 425\frac{\sin{42^\circ}}{\sin{87^\circ}}[/tex]

h = 284.77 meters.

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The estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

The thickness of a sheet of paper can be measured using a screw gauge or vernier caliper.

If the thickness of a ream of paper, which contains 500 sheets, is given, a sheet will be x/500 thick.

The thickness of 2 sheets of paper will be the thickness of a sheet multiplied by 2.

Number of reams of paper in a box = 5 reams

1 ream = 500 sheets

500 sheets = 5.4 cm thick

The thickness of 2 sheets of paper = 0.0216 cm {5.4cm x 2/500)}

Thus, the estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

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Assume that one ream of paper is 5.4 cm thick.

Answer:

∠ 3 = 65°

Step-by-step explanation:

∠ 2 and 115° are a linear pair and sum to 180° , that is

∠ 2 + 115° = 180° ( subtract 115° from both sides )

∠ 2 = 65°

∠ 2 and ∠ 3 are corresponding angles and and are congruent , then

∠ 3 = 65°

Answer:

80 cups

Step-by-step explanation:

The perimeter of the bigger octagon that is similar to the smaller one is: 238 units.

An octagon can be described as a polygon that has 8 sides and 8 angles.

What are Similar Octagons?

Octagons are referred to as similar to each other if they have the same angle measure but corresponding sides that are proportional to each other. That is, they have the same shape but different sizes.

How to Find the Perimeter of Similar Polygons?

Given the two octagons in the diagram are similar, and:

Perimeter of the smaller octagon = 34 units

A side of the smaller octagon = 4 units

Perimeter of the bigger octagon = ?

A corresponding side of the bigger octagon = 28 units

Therefore:

Perimeter of the smaller octagon/Perimeter of the bigger octagon = side of the smaller octagon/corresponding side of the bigger octagon

Plug in the values

34/Perimeter of the bigger octagon = 4/28

Perimeter of the bigger octagon = (28 × 34)/4

Perimeter of the bigger octagon = 238 units.

In summary, the perimeter of the bigger octagon is: 238 units.

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Answer: 27°

Step-by-step explanation:

The easiest way to find the measure of angle Z is to know that in a rhombus, the diagonals are perpendicular bisectors of each other. This means that all the four angles in the center are 90°.

Since we know that all angles in a triangle add up to 180°, we can set the sum of z, 63, and 90 to be 180 and solve for z.

[tex]z+63+90=180\\z+153=180\\z=27[/tex]

Hence, z is 27°.

Answer:

4.93

See the discussion below if the number is 4928.

Step-by-step explanation:

Comment

Do you really mean hundred? If you do, the nearest hundred is 0 when the actual value is 4.928

If you mean the nearest hundredth that means that 2 is the value of the hundredth now. Rounded, the answer is 4.93

If the given value is 4928, the hundred's place is the 9. Look at the 10s place (2). Since the 2 is less than 5, the 9 is not changed. 2 zeros are at the end of 49 since the hundreds place is rounded.

4900 is the answer

Hi there,

please see below for solution steps :

__________

Let us revise the rounding rules :

1) if the number you’re rounding to is followed by a number from 0 to 4, you drop that number

2) if the number you’re rounding to is followed by a number equal to 5 or more, you add 1 to that number

________

Now,

Nearest Hundredth => 3 digits after the decimal point

Thus,

4.928 => 4.93

Hope the Answer - and steps - made sense to you,

Happy Studying !!

Frozen Melody

Answer:

See below

Step-by-step explanation:

237/50   =    4    R 37

37/20     =     1     R 17

17 / 10     =     1     R 7

7 / 1         =     7    R 0

4   50gm's      1     20gm       1   10gm       and   7    1g wts

The required number of weights used in chemical balance to weigh 237g is 4,1,1,7 respectively.

What is mathematical expression?

A mathematical expression expression in mathematical is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g.

Now, let us find the number of weights for each weight type :

For 50g weight the maximum number of weights needed will be 4 that is :

50g x 4 = 200g

Now, for 20g weight the maximum number of weights needed will be 1 that is :

20g x 1 = 20g

Now, for 10g weight the maximum number of weights needed will be 1 that is :

10g x 1 = 10g

Now, for 1g weight the maximum number of weights needed will be 7 that is :

1g x 7 = 7g

Adding all the weights we get :

200g + 20g + 10g + 7g = 237g;

which is the required weight and the number of weights used is 4,1,1,7 respectively.

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