1.State domain and range
2.Is it a function
3.Is it a one to one function

Answer:

Step-by-step explanation:

OK so i'm not really good at this my self but i'll try my best to help you because I don't really do it for the points I do it because I like to help other people. OK so their blocks have a scale factor of k=4.5. OK so I don't know if this is right but what I would do is there are 8 sides to any cube and you have a scale factor of k=4.5 so I would multiply 4.5 and 8 to get a answer of 36ft.

Answer:

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Vertical compression of a function by a factor of a is:

Vertical compression of a function by a factor of 5 is:

Shifting up by b units is:

If we apply both transformations we get:

Option C is correct.

The two polygons are similar using the SAS criteria.

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end. A polygon's line segments are therefore referred to as its sides or edges. The vertex or corners made by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon. A circle is a planar figure as well, but since it is curved and lacks sides and angles, it is not regarded as a polygon. Hence, we may argue that while all two-dimensional forms are polygons, not all two-dimensional figures are polygons.

For the given polygons we find the scale factor to determine whether the two figures are similar.

The scale factor is given as:

SF = length of original/ length of new image

SF = 4 / 6

SF = 2/3

For the second segment:

SF = 6/9

SF = 2/3

The ratios of the segment are same. Also the angle between the corresponding segments is 86 degrees.

Hence, the two polygons are similar using the SAS criteria.

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Answer:

9

Step-by-step explanation:

The median is the number in the middle of a set of numbers.

Our set of numbers:  1, 1, 2, 3, 7, 9, 10, 10, 15, 17, 19​

In this case the median is 9

Answer:

Let's start by defining some variables to represent the given information:

T0 = 48°F (the current temperature)

deltaT = -1.5°F/hour (the rate of change in temperature)

T = 36°F (the target temperature)

We want to find how many hours it will take for the temperature to drop from 48°F to 36°F, so let's call that time h. We can use the formula for the linear relationship between temperature and time:

T = T0 + deltaT * h

We want to solve for h when T = 36°F, so we can substitute the given values and solve for h:

36 = 48 + (-1.5) * h

-12 = -1.5h

h = 8

Therefore, it will take 8 hours for the temperature to drop from 48°F to 36°F, assuming the temperature continues to decrease at a rate of 1.5°F per hour.

The polynomial function is f(x) = (x + 1)³(x - 1)²(x - 3). A polynomial function is a mathematical expression that consists of variables, constants, and exponents that are combined using the operations of addition, subtraction, multiplication, and division.

The zeros of a polynomial function are the values of x that make the function equal to zero. The given polynomial function has a triple zero at x = -1,

double zero at x = 1, and zero at x = 3.

This means that the factors of the polynomial function are (x + 1)³, (x - 1)², and (x - 3).

Multiplying these factors together gives us the polynomial function:f(x) = (x + 1)³(x - 1)²(x - 3).

To find the value of the constant term, we can use the given point (2, 27). Substituting x = 2 and f(x) = 27 into the polynomial function gives us:

27 = (2 + 1)³(2 - 1)²(2 - 3)27

3³(1)²(-1)27 = 27(-1)27

= -27

To make the function pass through the point (2, 27), we need to multiply the polynomial function by -1:

f(x) = -1(x + 1)³(x - 1)²(x - 3)f(x)

= -(x + 1)³(x - 1)²(x - 3)

Therefore, the polynomial function is f(x) = -(x + 1)³(x - 1)²(x - 3).

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Answer:

To compare 2 2/3 to another mixed number, you need to convert both mixed numbers to improper fractions.

To convert 2 2/3 to an improper fraction, you need to multiply the whole number (2) by the denominator of the fraction (3), and then add the numerator (2). This gives you:

2 2/3 = (2 x 3) + 2/3 = 6 + 2/3 = 20/3

Now that you have the improper fraction for 2 2/3, you can compare it to the improper fraction of another mixed number.

For example, if you want to compare 2 2/3 to 4 1/2, you would convert 4 1/2 to an improper fraction:

4 1/2 = (4 x 2) + 1/2 = 8 + 1/2 = 17/2

Now that you have both mixed numbers as improper fractions, you can compare them by finding a common denominator and then comparing the numerators. In this case, the common denominator is 6, so you need to multiply 17/2 by 3/3 to get:

17/2 = (17 x 3)/(2 x 3) = 51/6

Now you can compare 20/3 and 51/6 by looking at their numerators:

20/3 = 6.666...

51/6 = 8.5

So 2 2/3 is less than 4 1/2.

Step-by-step explanation:

Let the number of students in each van be "x" and the number of students in each bus be "y". We can then set up a system of equations to represent the given information:

From High School A: 8x + 8y = 240

From High School B: 4x + y = 54

We can use the second equation to solve for y in terms of x:

y = 54 - 4x

We can then substitute this expression for y into the first equation and solve for x:

8x + 8(54 - 4x) = 240

8x + 432 - 32x = 240

-24x = -192

x = 8

Now that we know x = 8, we can use the equation for y to solve for y:

y = 54 - 4x = 54 - 4(8) = 22

Therefore, there were 8 students in each van and 22 students in each bus.

The individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

What is the Present Value of an Annuity?

With a specific rate of return, or discount rate, the present value of an annuity is the current value of the future payments from an annuity. The present value of the annuity decreases as the discount rate increases.

To determine the amount needed for retirement, we can use the formula for the present value of an annuity:

  [tex]PV= PMT* \frac{1-\frac{1}{(1+r)^{n} } }{r}[/tex]

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $15,265, r = 4.5%/2 = 0.0225 (since the interest is compounded semi-annually), and n = 35 x 2 = 70 (since there are 70 semiannual periods in 35 years).

Plugging in these values, we get:

[tex]PV = (15,265\times(1 - (1 + 0.0225)^{(-70))) / 0.0225[/tex]

PV = $405,840.13

Therefore, the individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

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Answer:

k = .5 inches

Step-by-step explanation:

To find (f ∘ g)(x), we need to substitute g(x) into f(x) wherever we see x in the expression for f(x).

So we have:

f(g(x)) = f(3x + 1) = (3x + 1)^2 - 8 = 9x^2 + 6x - 7

Therefore, the correct answer is: 9x^2 + 6x - 7.

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hope it helps! :)

Answer:

A perfect square trinomial is a trinomial expression of the form:

a^2 + 2ab + b^2

Where a and b are constants, it can also be written as (a + b)^2.

To identify a perfect square trinomial, we can check if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.

For example, let's consider the expression:

x^2 + 4x + 4

The first term is x^2, which is a perfect square. The last term is 4, which is also a perfect square. The middle term is 4x, twice the product of the square roots of x^2 and 4 (i.e., 2x). Therefore, this expression is a perfect square trinomial:

x^2 + 4x + 4 = (x + 2)^2

To simplify this expression, we can use the fact that (a + b)^2 = a^2 + 2ab + b^2:

(x + 2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4

Therefore, the perfect square trinomial x^2 + 4x + 4 is equivalent to (x + 2)^2.

Step-by-step explanation:

Answer:

3rd choice down

(x + 9) / (x + 1)

Step-by-step explanation:

(2x + 4 - x + 5) / (x + 1) = (2x - x + 4 + 5) / (x+ 1) = (x + 9) / (x + 1)

The function notation for the amount of rainfall after 6 hours of raining is f(t) = 37.

Let's define the function as follows:

f(t) = r

where t represents the time elapsed since the rain started, f(t) represents the amount of rainfall at time t, and r represents the amount of rainfall in millimeters.

According to the problem statement, six hours after it started raining, the amount of rain was 37 millimeters. We can use this information to find the value of r:

f(6) = 37

This means that at time t=6, the amount of rainfall is 37 millimeters.

Now we can write the function in terms of the specific value of r:

f(t) = 37

This means that the amount of rainfall is constant and equal to 37 millimeters for all values of t.

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Answer:

To find out how many books each member read, we can divide the total number of books by the number of members in the reading group:

168 books ÷ 6 members = 28 books per member

Therefore, each member of Dan's reading group read 28 books this year.

168/6 = 28

28 books per member

Answer:

[tex]27\pi[/tex]

Step-by-step explanation:

The area of a circle is given by the formula [tex]A = \pi r^2[/tex].

We are given the radius of this circle, so we can plug in.

[tex]A = \pi r^2\\A=6^2\pi \\A=36\pi[/tex]

Seeing that there is [tex]\frac{3}{4}[/tex] of the circle left, multiply [tex]36\pi[/tex] by [tex]\frac{3}{4}[/tex].

[tex]36\pi(\frac{3}{4})\\ 9\pi (3)\\27\pi[/tex]

a) P (20 < or = X) =  0.8617: This is the probability that 20 or more of the 30 patients will be helped by the medicine.

b) P (18 < or = X < 25) = 0.8557: This is the probability that between 18 and 25 of the 30 patients will be helped by the medicine.

c) P ( X < 16) = 0.0266: This is the probability that less than 16 of the 30 patients will be helped by the medicine.

The given situation can be modeled using a binomial distribution, where the number of trials is 30, and the probability of success is 0.75. We can use the binomial probability formula to find the probabilities for each of the given conditions. The binomial probability formula is:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and (n choose x) is the binomial coefficient.

a) P (20 < or = X) = 1 - P (X < or = 19) = 1 - sum_{x=0}^{19} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8617

b) P (18 < or = X < 25) = P (X < or = 24) - P (X < or = 17) = sum_{x=18}^{24} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8557

c) P ( X < 16) = sum_{x=0}^{15} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.0266

Therefore, the probabilities are 0.8617, 0.8557, and 0.0266 for the conditions a), b), and c) respectively.

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1 gallon of milk is equal to 16 cups of milk (1 gallon = 4 quarts = 16 cups).

Mario poured 4 cups of milk for each of the 4 people, which is a total of 16 cups of milk.

So the amount of milk left is:

16 cups (total) - 16 cups (poured) = 0 cups

Therefore, there is no milk left.

The sum of two exponentials is given by:

A e^(jφ) + B e^(jψ) = (Acosφ + Bcosψ) + j(Asinφ + Bsinψ)

Applying this formula to the given problem:

[tex]33.65 e^{j(377t-25.5)} + 31.39 e^{j(377t+172.8)}[/tex]

[tex]= (33.65cos(377t-25.5) + 31.39cos(377t+172.8)) + j(33.65sin(377t-25.5) + 31.39sin(377t+172.8))[/tex]

This is the final answer, expressed in rectangular form with real and imaginary parts.

In words, the sum of the two exponentials is a complex number with a real part equal to the sum of the cosines of the two phases and an imaginary part equal to the sum of the sines of the two phases. The phase angle of the resulting complex number is determined by the weighted sum of the two original phase angles.

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The greatest common factor (GCF) of the polynomial ab+8a+2b+16 is 2.

To factor the given polynomial ab + 8a + 2b + 16 by grouping, follow these steps:

1. Group the terms in pairs: (ab + 8a) + (2b + 16).

2. Factor out the Greatest Common Factor (GCF) from each group. - For the first group (ab + 8a), the GCF is "a". So, factor out "a" from the group: a(b + 8).

-For the second group (2b + 16), the GCF is "2". So, factor out "2" from the group: 2(b + 8).

3. Notice that both groups have a common factor of (b + 8). So, factor out (b + 8) from the entire expression: (b + 8)(a + 2).

Thus, the factored form of the polynomial ab + 8a + 2b + 16 by grouping is (b + 8)(a + 2).

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x1 = -2, x2 = 1, and x3 = 5.5

This system of equations can be solved by first combining the equations and then isolating one of the variables. To combine the equations, subtract the first equation from the second equation:

4x1 + 5x2 + 5x3 = 9

- (x1 + x2 + 3x3 = -4)

3x1 + 4x2 + 2x3 = 13

Next, isolate one of the variables. In this case, let's isolate x3:

3x1 + 4x2 + 2x3 = 13

- (2x3) - (-2x3) = 0

3x1 + 4x2 = 13

x3 = \frac{13 - (3x1 + 4x2)}{2}

Now that x3 has been isolated, substitute it into one of the original equations and solve for the remaining two variables:

x3 = \frac{13 - (3x1 + 4x2)}{2}

x1 + x2 + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x2:

x2 = \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4}

Substitute this expression for x2 into one of the original equations and solve for x1:

x1 + \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4} + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x1 and then plug this value back into the expression for x2 to find x2:

x1 = -2

x2 = 1

x3 = \frac{13 - (-2 + 4x2)}{2}

x3 = \frac{13 - (-2 + 4 \cdot 1)}{2}

x3 = \frac{13 - 2}{2}

x3 = 5.5

Therefore, the solution to the system of equations is x1 = -2, x2 = 1, and x3 = 5.5.

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The solution to the system of linear equations is (47/16, -161/40, 49/8).

To solve the system of linear equations using Gaussian elimination, we first need to write the equations in matrix form.

[2 -3 -5 | -6]
[-6 2 8 | 11]
[3 -1 3 | 5]

Next, we need to use elementary row operations to transform the matrix into reduced row echelon form (RREF). This means that the matrix will have a leading 1 in each row, and all other entries in that column will be 0.

Step 1: Divide the first row by 2 to get a leading 1.

[1 -3/2 -5/2 | -3]
[-6 2 8 | 11]
[3 -1 3 | 5]

Step 2: Add 6 times the first row to the second row to eliminate the -6 in the second row.

[1 -3/2 -5/2 | -3]
[0 5 7 | 7]
[3 -1 3 | 5]

Step 3: Subtract 3 times the first row from the third row to eliminate the 3 in the third row.

[1 -3/2 -5/2 | -3]
[0 5 7 | 7]
[0 7/2 13/2 | 14]

Step 4: Divide the second row by 5 to get a leading 1.

[1 -3/2 -5/2 | -3]
[0 1 7/5 | 7/5]
[0 7/2 13/2 | 14]

Step 5: Add 3/2 times the second row to the first row to eliminate the -3/2 in the first row.

[1 0 -1/2 | -1/2]
[0 1 7/5 | 7/5]
[0 7/2 13/2 | 14]

Step 6: Subtract 7/2 times the second row from the third row to eliminate the 7/2 in the third row.

[1 0 -1/2 | -1/2]
[0 1 7/5 | 7/5]
[0 0 4/5 | 49/10]

Step 7: Divide the third row by 4/5 to get a leading 1.

[1 0 -1/2 | -1/2]
[0 1 7/5 | 7/5]
[0 0 1 | 49/8]

Step 8: Add 1/2 times the third row to the first row to eliminate the -1/2 in the first row.

[1 0 0 | 47/16]
[0 1 7/5 | 7/5]
[0 0 1 | 49/8]

Step 9: Subtract 7/5 times the third row from the second row to eliminate the 7/5 in the second row.

[1 0 0 | 47/16]
[0 1 0 | -161/40]
[0 0 1 | 49/8]

Now the matrix is in RREF, and we can read off the solutions:

x = 47/16
y = -161/40
z = 49/8

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S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

Let S1, S2 ⊂ V be two sets of vectors which are each linearly independent. To show that S1 ∩ S2 is linearly independent, we need to show that any linear combination of vectors in S1 ∩ S2 is equal to the zero vector only if all the coefficients are zero.

Let v1, v2, ..., vn be the vectors in S1 ∩ S2 and let a1, a2, ..., an be the coefficients in the linear combination a1v1 + a2v2 + ... + anvn = 0.

Since v1, v2, ..., vn are in S1 ∩ S2, they are also in S1 and S2. Therefore, the linear combination a1v1 + a2v2 + ... + anvn = 0 is also a linear combination of vectors in S1 and S2.

Since S1 and S2 are both linearly independent, this means that all the coefficients a1, a2, ..., an must be zero. Therefore, S1 ∩ S2 is also linearly independent.

In conclusion, if S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

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Answer:

I think the question is incomplete

You would receive $13.50 if you cashed in 135 dimes. That's the equivalent of 1,350 pennies.
If you cashed in 135 dimes, you would receive 1,350 pennies.

This is because each dime is worth 0.1 dollars, or 10 pennies. So, to find the total number of pennies you would receive, you can simply multiply the number of dimes by the number of pennies in each dime:
135 dimes * 10 pennies/dime = 1,350 pennies
So, you would receive 1,350 pennies if you cashed in 135 dimes.

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The domain of the function f(x) = 4[(x-2)^(1/2)]-8 is the set of all real numbers x such that x ≥ 2.

This is because the expression (x-2)^(1/2) is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)^(1/2)]-8 is always greater than or equal to -8 for all values of x in the domain.

So, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are:
Domain: [2, ∞)
Range: [-8, ∞)

In conclusion, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are [2, ∞), [-8, ∞).

The domain of the function f(x) = 4[(x-2)1/2]-8 is the set of all real numbers x such that x ≥ 2. This is because the expression (x-2)1/2 is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)1/2]-8 is always greater than or equal to -8 for all values of x in the domain.

So, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are:

Domain: [2, ∞)

Range: [-8, ∞)

In conclusion, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are [2, ∞), [-8, ∞).

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The transformation is (a) Graph opens down, it moves 2 units left and 5 units down.

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

y = -|x + 2| - 5

Where the parent function is

y = |x|

When we modify the equation to y = -|x + 2| - 5, we are applying several transformations to the parent graph:

So the resulting graph (a)

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Answer:

attached is the answer

Step-by-step explanation:

HI

THIS IS THE ANSWER

I HOPE IT HELPS

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