Given this triangle find angle B to the nearest tenth of a degree if b=8 and c=12.

Answer:

Prime

Step-by-step explanation:

Its factors are:1 and itself.

ALL prime numbers have the same 2 factors: 1 and itself.

Answer:

the answer should be 4, you left the - off of the 61

Step-by-step explanation:

Answer:

343

Step-by-step explanation:

7*7*7=343

The factor of the 343 will be 7, 7, and 7. Then the number 343 is a perfect cube of 7.

The integers that are the threefold multiplication with the same number are known as perfect cubes.

To put it another way, a perfect cube is the combination of complex times multiplying a whole integer by itself.

A perfect cube is a quantity that may be stated as the composition of three different numbers.

A. The factor of the 21 will be 3 and 7. It can not be a perfect cube.

B. The factor of the 49 will be 7 and 7. It can not be a perfect cube.

C. The factor of the 343 will be 7, 7, and 7. It is a perfect cube.

D. The factor of the 600 will be 2, 2, 2, 3, 5, and 5. It can not be a perfect cube.

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Answer:

The answer to this question is

As speed increases the height Increases

Step-by-step explanation:

Because increases mean going up so when the speed is going up the height of the speed also increases so that's why when the speed increases also the height increases

I hope this works

YW!

The correct explanation of the graph will be;

''As speed increases, height is decreases.''

Option D is true.

What is an mathematical expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph is shown in figure for the relation of height and speed.

Since, The graph is shows when the speed of any object increase, then its height will also be increase.

Thus,  

The correct explanation of the graph will be;

''As speed increases, height is decreases.''

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What applies here is one of the laws of the factorization of polynomials, called the factor theorem and it states that:

For a polynomial f(x) , if for any value a,  f(a) =0  then (x-a) is factor of f(x)

Example:

Consider the polynomial

[tex]f(x) = x^{3} - 3x^{2} - 8x+4[/tex]

For  a =3,

[tex]f(a) = (3)^{3} - 3(3)^{2} - 8(3)+24[/tex]

= 27-27-24+24 = 0

f (3)= 0

which means (x-3) is a factor of f(x)

Applying the above rule to the question:

if (x + 3) is a factor of a polynomial f(x), then f(-3) = 0

note that (x+3) can also be written  as (x- (-3)).

Researchers can use b) weighting to counter bias in their sampling, which adjusts sample representation to match a desired population. While convenience sampling offers easy data collection, it lacks generalizability, and weighting is necessary to enhance the validity of findings.

To counter bias in their sampling, researchers can employ a method known as b) weighting. This technique adjusts the representation of samples to match a desired population, countering potential biases that may arise from non-random sampling methods such as convenience sampling. It is important to distinguish between non-random sampling methods that are potentially biased and strategies that are used to ensure data accuracy and representativeness.

Convenience sampling, also referred to as availability sampling or haphazard sampling, is a nonprobability sampling strategy where researchers collect data from individuals or elements that are most easily accessible. This approach is useful in exploratory research or student projects where probability sampling is too costly or difficult but does not offer the rigor needed to make generalizations to larger populations. To overcome these limitations and enhance the validity of their findings, researchers may adjust their data using weighting to better reflect the population being studied.

Answer:1250

Step-by-step explanation:

Answer:

value of [tex](f o g)(1)[/tex] is, 17

Step-by-step explanation:

We have to find the [tex](f o g)(1)[/tex]

Using the given tables;

[tex](f o g)(1) = f(g(1))[/tex]   ......[1]

At x = 1

g(1) = 6

Substitute this in [1] we have;

[tex](f o g)(1) = f(6)[/tex]

At x = 6

f(6) = 17

then;

[tex](f o g)(1) = 17[/tex]

Therefore, the value of [tex](f o g)(1)[/tex] is, 17

Answer:

0.5 or half of it (1/2)

The function [tex]\( f(x) = \frac{5x}{x-x^2} \)[/tex] has a removable discontinuity at ( x = 0 ) after canceling the common factor [tex]\( x \).[/tex]

A removable discontinuity occurs at a point where a function is not defined due to a factor in the denominator that could be canceled out with a factor in the numerator.

Let's analyze each function to determine if any of them have a removable discontinuity.

[tex]a. \( g(x) = \frac{2x-1}{x} \)[/tex]

- The denominator ( x ) is zero at ( x = 0 ).

- The numerator ( 2x-1 ) is non-zero at ( x = 0 ).

- Since there is no common factor in the numerator and denominator that could cancel out, the discontinuity at ( x = 0 ) is not removable.

[tex]b. \( p(x) = \frac{x+2}{x^2-x-2} \)[/tex]

- The denominator [tex]\( x^2-x-2 \) factors as \( (x-2)(x+1) \).[/tex]

- The function becomes [tex]\( p(x) = \frac{x+2}{(x-2)(x+1)} \).[/tex]

- The denominator is zero at ( x = 2 ) and ( x = -1 ).

- The numerator ( x+2 ) is zero at ( x = -2 ).

- There is no common factor between the numerator and the denominator that could be canceled out. So, the discontinuities at [tex]\( x = 2 \) and \( x = -1 \)[/tex] are not removable.

[tex]c. \( f(x) = \frac{5x}{x-x^2} \)[/tex]

- The denominator [tex]\( x-x^2 \) factors as \( x(1-x) \).[/tex]

- The function becomes [tex]\( f(x) = \frac{5x}{x(1-x)} = \frac{5x}{x-x^2} \).[/tex]

- The denominator is zero at x = 0  and  x = 1 .

- The numerator ( 5x ) is zero at ( x = 0 ).

- There is a common factor of ( x ) in the numerator and denominator which could be canceled out, making the discontinuity at ( x = 0 ) removable.

- After canceling the common factor ( x ), the function becomes [tex]\( \frac{5}{1-x} \),[/tex] which is defined at ( x = 0 ).

[tex]d. \( h(x) = \frac{x^2 - x + 2}{x + 1} \)[/tex]

- The denominator ( x + 1 ) is zero at ( x = -1 ).

- The numerator [tex]\( x^2 - x + 2 \) is not zero at \( x = -1 \).[/tex]

- There is no common factor in the numerator and denominator that could be canceled out, so the discontinuity at ( x = -1 ) is not removable.

Conclusion

The function [tex]\( f(x) = \frac{5x}{x-x^2} \)[/tex] has a removable discontinuity at ( x = 0 ), because the discontinuity can be removed by canceling the common factor ( x ) in the numerator and the denominator.

So, the correct answer is:

[tex]c. \( f(x) = \frac{5x}{x-x^2} \)[/tex]

As per linear equation, the total cost of the computer is $645.00.

"A linear equation is an equation in which the highest power of the variable is always 1."

Given, the cost of computer is $600.00.

The sales tax rate is 7.5%.

Therefore, the total cost of the computer is

= $[tex][600.00 + \frac{(7.5)(600.00)}{100}][/tex]

= $[tex][600.00 + 45.00][/tex]

= $[tex]645.00[/tex]

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Answer:  The correct option is (B) [tex]f>5.[/tex]

Step-by-step explanation:  Given that Blake has more than five friends.

We are to select the inequality that describes the number of Blake's friends.

The number of Blake's friends is represented by f.

According to the given information, we have

the inequality that describes the number of Blake's friends is given by

[tex]f>5.[/tex]

Thus, (B) is the correct option.

By setting up an equation and solving for the number of students in each club, we find there are 48 students in the science club.

To solve the problem, we can set up an equation based on the information given. Let the number of students in the robotics club be represented by x.

According to the problem, the science club has 12 more students than the robotics club, so the science club has x + 12 students. We also know that there are a total of 84 students in both clubs combined. Therefore, we can set up the following equation:

x + (x + 12) = 84

Combining like terms, we have:

2x + 12 = 84

Subtracting 12 from both sides gives us:

2x = 72

Dividing both sides by 2 gives us:

x = 36

So, there are 36 students in the robotics club. To find the number of students in the science club, we add 12 to the number of students in the robotics club:

36 + 12 = 48

Therefore, there are 48 students in the science club.

The barrel leaks 0.5 L of water each day.

Every year, Luisa puts $10 into her savings account.

Linear functions represent situations with a constant rate of change. Saving $10 every year and a barrel leaking 0.5 L of water each day are examples of linear relationships due to this constant change.

Situations that can be represented by a linear function are those where the rate of change remains constant. Let's analyze the given situations according to this condition:

These two scenarios fit the criteria for being linear because they involve a constant rate of change over time. On the other hand, scenarios like the exponential growth of bacteria or percentage-based population growth are not linear since the rate of change is not constant; these would be represented by exponential functions.

Answer:

The answer is 2.25 times as fast. I just did this one

Step-by-step explanation:

Final answer:

Using the compound interest formula, the total amount after three years for $50 invested at 6% compounded monthly is approximately $59.70.

Explanation:

To calculate the future value of $50 invested at 6% compounded monthly after a period of three years, we use the formula for compound interest:

FV = P × (1 + (r/n))³⁼ ×⁴

where:

FV is the future value of the investment,

P is the principal amount ($50),

r is the annual nominal interest rate (6% or 0.06),

n is the number of times the interest is compounded per year (12, for monthly compounding),

t is the time the money is invested for, in years (3 years).

Using these values, we calculate as follows:

FV = $50 × (1 + (0.06/12))³·×´ = $50 × (1 + 0.005)·¹·´

Now we calculate this raised to the power of 36 (3 years times 12 months):

FV = $50 × (1.005)³···¶ = $50 × 1.194052

Thus, FV ≈ $59.70

The total amount after three years would be approximately $59.70, assuming the interest is compounded monthly at a rate of 6%.

Answer:

It is $787.50.