Practice
Example 1
PROOF Write each proof.
1. Given: AB || CD, ∠CBD ≅ ∠ADB
Prove: ΔABD ≅ ΔCDB

Answer:

x > 1

Step-by-step explanation:

Add 7 to both sides

x > 1

Answer:

33cm

Step-by-step explanation:

385 / 35 = 11

11 times 3 = 33

Fοr the table 1 data pοints, the cοrrect equatiοn is Equatiοn 3:  y = -5x + 3.

A mathematical definitiοn οf an equatiοn is a claim that twο expressiοns are equal when they are jοined by the equals sign ("=").

Table 1 cοntains the data pοints -

x = -1, 0, 1, 2

y = 8, 3, -2, -7

Substitute the value οf x = -1 intο the fοur equatiοns tο οbtain the value οf y as 8.

Equation 1 is \(y = 5^x\)

On substituting the value of x = -1 -

\(y = 5^{-1}\)

y = 0.2

Therefore, equation 1 is incorrect.

Equation 2 is y = 5x - 2.

On substituting the value of x = -1 -

y = 5(-1) - 2

y = -5 - 2

y = -7

Therefore, equation 2 is incorrect.

Equation 3 is y = -5x + 3.

On substituting the value of x = -1 -

y = -5(-1) + 3

y = 5 + 3

y = 8

Therefore, equation 3 is correct.

Equation 4 is \(y = 5(0.2)^x\)

On substituting the value of x = -1 -

\(y = 5(0.2)^{-1}\)

\(y = 1^{-1}\)

y = 1

Therefore, equation 4 is incorrect.

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Answer:

2..

Step-by-step explanation:

Answer:

Probably 2

Step-by-step explanation:

<3

Thanks for the free points btw! Have a great day

Answer: step by step

Step-by-step explanation:

not totally sure what you're asking but in this equation p=2

Answer:

LL

Step-by-step explanation:

We have two right triangles

The two legs are congruent

We can use the LL congruence theorem

Answer:

X=21

Step-by-step explanation:

3x+5+6x-14=180

9x-9=180

9x=180+9

9x=189

x=21

The domain of the graph of the exponential function is (d) all real numbers

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

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:

B. y=1/2x+7

Step-by-step explanation:

y2-y1/x2-x1 this finds the slope

Then take one of the coordinates: either (2,8) or (4,9) and plug them into x and y to find b (the y-int)

Answer:

Step-by-step explanation:

(2, 8) (4, 9)

(9 - 8)/(4 - 2) = 1/2

y - 8 = 1/2(x - 2)

y - 8 = 1/2x - 1

y = 1/2x + 7

B is the answer

The standard deviation is 1.0319

x values between 10.4681 and 12.5319 are respectively ( 11 , 12 )

The probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value is 0.6740

We are given that: a geologist has collected 14 specimens of basaltic rock and 14 specimens of granite.

Thus total rocks = N = 14 +14 = 28

The geologist instructs a laboratory assistant to randomly select 23 of the specimens for analysis.

Thus sample size = n = 23

Part a) What is the pmf of the number of granite specimens selected for analysis?

x = the number of granite specimens selected

Thus M = Number of granite specimens = 14

Thus x can have the following values:

x n-x = 23-x

9 14

10 13

11 12

12 11

13 10

14 9

We can select a minimum 9 granite specimens, so that total becomes 9 granite specimens + 14 basaltic rock = 23

and maximum 14 granite specimens, so that total becomes 14 granite specimens + 9 basaltic rock = 23

Here x = the number of granite specimens selected follows Hypergeometric distribution with parameters N = 28 ,M=14 , n = 23 .

P(X=9) =0.02037

Similarly, we find all next probabilities:

x P(x)

9 0.0204

10 0.1426

11 0.3370

12 0.3370

13 0.1426

14 0.0204

Part b) What is the probability that all specimens of one of the two types of rock are selected for analysis?

the probability that all specimens of one of the two types of rock are selected

That is:

P( All 14 are granite specimens and rest 9 are basaltic rock OR All 14 are basaltic rock and rest 9 are granite specimens)=......?

That is:

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =......?

From above table in part a) , we have:

P( 14 granite specimens) = 0.0204 , that means

P(14 granite specimens , 9 basaltic rock) = 0.0204

and

P( 9 granite specimens)=0.0204

That is:

P( 14 basaltic rock , 9 granite specimens) = 0.0204

Thus

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =0.0204 + 0.0204

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) = 0.0408

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We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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Answer:

It will take 4 hours and 20 minutes to hike the rest of the 7 miles

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

Exterior angle theorem

Exterior angle = Interior opposite angle 1 + Interior opposite angle 2

(9x + 16)° = 90 + (5x - 14)°

9x + 16 = 90 + 5x - 14

9x - 5x = 90 - 14 - 16

4x = 90 - 30

4x/4 = 60/4

x = 20

Answer:

0!there is no shaped figure

Answer:

\(angle \: 1 = 2x \\ angle 2 = 3x \\ sum = 1 00 \\ 2x + 3x = 100 \\ 5x = 100 \\ divide \: both \: side \: by \: 5 \\ \frac{5x}{5} = \frac{100}{5} \\ x = 20\)

Answer:

f(6)=2

f(2)=4

f(0)=7

f(5)=1.5

f(x)=1 x=4

Step-by-step explanation:

f(x)=y.The numbers represent the x values. As you are plugging in a number for x. Just look at the graph on the x-axis to get the y-values.

Answer:

240cc

Explanation:

From the expression of the relationship between pressure and volume, we can state mathematical that for two successive volume V1 and V2 and Pressure P1 and P2 we have:

P1V1 = P2V2

V2 = P1V1 / P2

=400×300/500= 240cc

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Answer:

We have to find co-ordinates of the fourth vertex.

Let fourth vertex be D(x,y)

Since, ABCD is a parallelogram, the diagonals bisect each other.

Si, co-ordinate of mid-point of AC= Co-ordinate of mid-point of BD.

∴ The fourth vertex is D(−b,b)

Step-by-step explanation:

Answer:

18%

Step-by-step explanation:

Divide 64/303.

Divide 9/303.

Subtract the answers and you'll get 18%.

The percentage of the sample population with brown eyes and black hair is larger than the percentage of the sample population with blue eyes and black hair by 18.25%

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given here, according to the survey, the population with Brown eyes & black hair and Blue eyes and black hair  is 64 and 9 respectively

Also, the marginal total is equal to 303

therefore, the percentages of the two groups are

Brown eyes & black hair =64/303 × 100

                                         = 21.12%

similarly we can calculate  Blue eyes and black hair = 9/303 × 100

                                                                                      = 2.97%

Hence the difference is  21.22% - 2.97% =  18.25% (approx)

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Answer:

Step-by-step explanation:

A. quick math's i mean calculator

The original price was $105.04 and the discount is 10%.

Calculate the discount:

10 * 105.04 / 100 = 10.50

The discount is $10.50

The final (sale) price is:

$105.04 - $10.50 = $94.54

Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

She bought $27.40 worth of roast beef.

Answer:

x-4y=2 can be written as y=(x-2)/4

(2,0) when x=2, y=0 and (6,1) when x=6, y=1

Answer: To find the price of the 3-year old car, we need to determine how much less it is than the new car, which is 23% of the price of the new car.

We can start by finding the value of 23% of the price of the new car, which is: $12,400 x 0.23 = $2,832

Now we know that the price of the 3-year old car is $2,832 less than the price of the new car. To find the price of the 3-year old car, we subtract $2,832 from the price of the new car: $12,400 - $2,832 = $9,568

So the price of the 3-year old car is $9,568.

Step-by-step explanation:

Answer:

badge showing an astronaut's boot touching down on the moon.

Step-by-step explanation:

I cannot really graph it but I will try my best to explain.

When you have a coordinate plane draw from right to left, up to down.

Now starting from righthand top corner, draw a smooth curve just like how you will draw a quadratic equation, through the x axis then curve back making the graph touch the axis at 2 points. That's the 2 real roots

Now make another curve down but this time not touching the x axis and then curving back up to the top left corner, this meant the 2 complex roots.

This is not the only way to do it, as long as one complete curve is not touching the x axis and another complete curve, weather as a whole or combined is touching the x axis at 2 points, it has 2 real and complex roots.