30 Points!!!

AOC and BOD are diameters of a circle, centre O.
Prove that triangle ABD and triangle DCA are congruent by RHS.

Answer:

(2[tex]b^{2}[/tex] - 5) (3b + 8)

Step-by-step explanation:

First factor out 2[tex]b^{2}[/tex] from the first set of parentheses and -5 from the second

2[tex]b^{2}[/tex] ( 3b + 8)  - 5 (3b + 8)

Next factor out (3b + 8)

(2[tex]b^{2}[/tex] - 5) (3b + 8)

Answer: [tex]y=x^2 -10x+41[/tex]

Step-by-step explanation:

[tex]y=(x-5)^2 +16\\\\y=x^2 -10x+25+16\\\\y=x^2 -10x+41[/tex]

The number you should multiply 3 1/3 to get a product of 4 is 1 1/5

From the question, the statement is given as

What number should you multiply 3 1/3 to get a product of 4

Let the number be x

So, we have the following representation

3 1/3 * x = 4

Express 3 1/3 as an improper fraction

So, we have the following representation

10/3 * x = 4

Multply both sides by 3

So, we have

10 * x = 12

Divide both sides by 10

This gives

x = 12/10

Express as mixed numbers

x = 1 1/5

Hence, the number is 1 1/5

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After evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

So, -(8⁻²):

Now, evaluate -(8⁻²) as follows:

Therefore, after evaluating the given expression -(8⁻²), the resultant expression is - 1/64.

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Answer: [tex]3.71 \times 10^{-9}[/tex]

Step-by-step explanation:

[tex](2.8 \times 10^{-9})+(9.1 \times 10^{-10})\\\\=10^{-10}(28+9.1)\\\\=10^{-10}(37.1)\\\\=3.71 \times 10^{-9}[/tex]

Answer:

The answer is C: 3.71 × 10−9.

Step-by-step explanation:

a) The minimum number of dogs that could have a mass of more than 27 kg is 4.

b) The maximum number of dogs that could have a mass of more than 27 kg is 17.

The given table shows information about the masses of some dogs.

a) Because we need the minimum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the minimum value out of 13 and 4 is 4.

b) Because we need the maximum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17

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Answer:

Step3

-by-step explanation:

Answer:8.7:1.2

Step-by-step explanation: divide both by 3

Answer:

x = 12

Step-by-step explanation:

Be the 8 consecutive numbers like this:

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) =  124

8x + 28 = 124

8x = 124 - 28

8x = 96

x = 12

Answer:

length = 6m

Step-by-step explanation:

H=5m

V=180m^3

Here

V=l^2 ×H ( being a square)

180=a^2×5

a^2=36

a=6m

Answer:

[tex]x=5/3[/tex]

Step-by-step explanation:

[tex]9x+1=16 \\ \\ 9x=15 \\ \\ x=5/3[/tex]

Answer:

x+46

Step-by-step explanation:

Distribute

Combine like terms

Answer:

I believe it would be "A population of 200 bacteria quintuples every week"

Step-by-step explanation:

If it is quintupling each week then the number is getting larger and larger exponentially.

Yes , ∠WGR is congruent ∠GHR because both angles are on one line.

What does the word "congruent" mean in math?

a) No, ∠PHG is not congruent  ∠MGH because both angles are not equal.

b) No, ∠RHG and ∠MGH are not supplementary angle because in   supplementary angle is equal to 180° .

c) No, ∠SGW  is not congruent   ∠PHV.

d)  Yes , ∠WGR is congruent ∠GHR because both angles are on one line.

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Answer:108 inches

Step-by-step explanation:

to find the area of one of the right triangles you do.

base = 6/2 =3

3x6=18

18/2=9

there are 8 right triangles so you would do

9x8 = 72.

then you would add 72 and the area of the square in the middle

6x6=36

36+72= 108

so Area of SA = 108 inches ^2

Answer:

Step 4

Step-by-step explanation:

Mia made a mistake in step 4.

Step3:  x(x + 6) -2(x + 6)

In both terms, (x + 6) is common.

Step 4: When we take (x + 6) out, it will be (x + 6 ) (x - 2)

Answer:

86

Step-by-step explanation:

average is calculated as

average = [tex]\frac{sum}{count}[/tex]

given her average was 70 in 3 tests , then

[tex]\frac{sum}{3}[/tex] = 70 ( multiply both sides by 3 )

sum = 210

let the score she must get in test 4 be x for an average of 74 , then

[tex]\frac{210+x}{4}[/tex] = 74 ( multiply both sides by 4 )

210 + x = 296 ( subtract 210 from both sides )

x = 86

she must score 86 in her next test

Answer:

[tex]\frac{x}{3}[/tex]= 70

x=210

[tex]\frac{210+x}{4}[/tex] = 74

210+x=74x4

210+x=296

x=296-210

x=86

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Given:

Let the cost of chocolate bar be 'x'.

Cost of chocolate bar is $0.55

The estimate of the average rate of change f is -2

The possible graph that completes the question is added as an attachment

The interval is given as

-1 ≤ x ≤ 0

This can be rewritten as

x = -1 to x = 0

This can also be represented as

(a, b) = (-1, 0)

From the attached graph, we have

f(-1) = 7

f(0) = 5

The estimate (to one decimal place) of the average rate of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(-1) - f(0)]/[-1 - 0]

So, we have

Rate = [7 - 5]/[-1 - 0]

Evaluate

Rate = -2

Hence, the average rate of change f is -22

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[tex] = 2^{3} \\ = 2 \times 2 \times 2 \\ = (2 \times 2) \times 2 \\ = 4 \times 2 \\ = 8[/tex]

ATTACHED IS THE SOLUTION

LAST OPTION IS THE ANSWER.

Answer:

$3,690

Explanation:

The shipping charge for all 3 TVs =$90

Cost of a TV = $1200

Therefore, the cost of 3 TVs = 3 x $1200 =$3,600

The total amount paid by Gordon will be:

=$3600+90

=$3,690

The slope of the ramp is m =  h/√(r² - h²).

What is mean by square root of a number?

A square root of a number is a value that multiplied by itself gives the same number.

Let h = height of the landing.

And, r = the length of the ramp.

Then, the length from the ground where the ramp touches it, to the ground directly below the landing is

⇒ √(r² - h²)

And, The slope of the ramp is m =  h/√(r² - h²)

For example, if the ramp is 5 meters long and the landing height is 3 meters high, the slope of the ramp is 3/4.

As, Slope of the ramp (m) = 3/√(25-9)  = 3/√16  = 3/4

Thus, The slope of the ramp is m =  h/√(r² - h²).

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Answer:

x = 5/3, 1/3

Or

x=1.6 repeating ,0.3 repeating

Answer:

3

Step-by-step explanation:

Absolute value is how far away the value is from 0. The only value of x that would make this equation true is 3.

The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]. The evaluated expression is  3a+4.5b+c=40.5

Given that,

The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]

We have to evaluate the expression

Evaluating an algebraic expression involves determining its value when a particular integer is substituted for a variable. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

Take,

0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]

0.5×81=a×3+b×4.5+c

40.5=3a+4.5b+c

The expression can be written in 4 ways

1st- 3a+4.5b+c=40.5

2nd- a=[tex]\frac{40.4-4.5b-c}{3}[/tex]=13.4-1.5b-c (this is the expression with subject a)

3rd- b= [tex]\frac{40.5-3a-c}{4.5}[/tex]=9-1.6a-c (this is the expression with subject b)

4th- c= 40.5-3a-4.5b (this is the expression with subject c)

Therefore, The evaluated expression is 3a+4.5b+c=40.5

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The number 150 is 0.0000455 % out of 329.5 million

The statement is given as

the percentage of 150 out of 329.5 million

The percentage can be calculated as

Percentage = 150 out of 329.5 million *100%

Express as fraction

So, we have

Percentage = 150/329.5 million *100%

Rewrite as

Percentage = 150 *100/329.5 million %

Evaluate the product

Percentage = 15000/329.5 million %

Evaluate the quotient

Percentage = 0.0000455 %

Hence, the percentage of 150 out of 329.5 million is 0.0000455 %

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Answer: (4) [tex]y=2x[/tex]

When you look at the table, you can see that the y values are double the x values they are associated with. Therefore, to get to the y value, the x values must be multiplied by 2, which would be the equation [tex]y=2x[/tex]

The value obtained for z-score for the given sample mean is 0.5.

For the given question;

The formula for finding the z-score is;

z = (x - μ)/σ

x = sample size

μ = population mean

σ = standard deviation population.

The given values are-

Put the value in the z-score.

z = (35 - 25)/20

z = 10/20

z = 0.5

Therefore, the value obtained for z-score for the given sample mean is 0.5.

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The correct question is-

Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.

Let's call the amount of lugagge the first men had as x, and the amount of lugagge the second men had as y.

Since both had to pay for excess of luggage, both had the permitted amount of luggage plus an extra amount. Let's call the permitted amount as a, the extra the first men had as z, and the extra the second man had as w. Then, our total amounts of luggage can be rewritten as

Since their total amount of luggage added together was 135 kg, this gives to us the following equation

The charge for the extra luggage is a flat rate, let's call it r, then, the price you pay for the extra luggage is given by the product between this rate and the amount of extar luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage, therefore

If we divide one equation by the other, we can write the excess of luggage of one as a function of the other.

If all of the luggage belonged to one person, this person would have to pay $8.10 for the excess. If we call the excess of this person as p, the amount of luggage this person had would be

Using the "rate formula" we created before, we can also write p as a function of z.

Rewritting all the total amounts, we have

If we add the equations for x and y together, we have

From the first equation, we know that the sum between both total amounts of luggage is equal to 135.

Now, we have two equations for our two variables.

If we multiply the first equation by 2, and subtract the second equation, we're going to get a new equation only for a(the amount in kilograms of permitted luggage).

The amount of luggage permitted to bring onto the plane for free is 45 kilograms.

Answer:

$1.53

Step-by-step explanation:

Let x represent each bottle of juice, then the equation will be -->

2.45+18x=29.99

18x=29.99−2.45=27.54

Therefore, x=1.53

Each bottle of juice costs $1.53