area of composite figures

68 sq. cm
92 sq. cm
72 sq. cm
96 sq. cm
72 sq. cm
90 sq. cm

For this case we must indicate the percentage that represents the following expression:

[tex]\frac {1} {20}[/tex]

By a rule of three we can solve them:

20 ----------> 100%

1 ------------> x

Where the variable x represents the percentage of 1 with a base of 20.

[tex]x = \frac {1 * 100} {20}\\x = 5[/tex]

So, we have that [tex]\frac {1} {20}[/tex] represents 5%

Answer:

Option A

The required  1/20 is equal to 5% when expressed as a percentage. Option A is correct.

To find the percent equivalent to 1/20, we need to express it as a fraction of 100.

First, we can convert 1/20 into a decimal by dividing 1 by 20, which gives us 0.05.

Next, we multiply the decimal by 100 to express it as a percentage: 0.05 * 100 = 5%.

Therefore, 1/20 is equivalent to 5%.

In conclusion, 1/20 is equal to 5% when expressed as a percentage.

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[tex]f(x)=e^{-5x}[/tex] is continuous on [0, 1] and differentiable on (0, 1), so yes, the MVT is satisfied.

By the MVT, there is some [tex]c\in(0,1)[/tex] such that

[tex]f'(c)=\dfrac{f(1)-f(0)}{1-0}[/tex]

The derivative is

[tex]f'(x)=-5e^{-5x}[/tex]

so we get

[tex]-5e^{-5c}=e^{-5}-1\implies e^{-5c}=\dfrac{1-e^{-5}}5\implies-5c=\ln\dfrac{1-e^{-5}}5[/tex]

[tex]\implies\boxed{c=-\dfrac15\ln\dfrac{1-e^{-5}}5}[/tex]

The function f(x) = e^-5x is both continuous and differentiable on the interval [0, 1] and performs according to the Mean Value Theorem. To find the specific numbers, c, that suit the theorem’s conclusion, we must solve the equation f'(c) = [f(b) - f(a)] / (b - a).

The function we are considering is f(x) = e-5x. To check whether it satisfies the Mean Value Theorem (MVT) on the interval [0, 1], we have to ensure two conditions. Firstly, that the function is continuous on the closed interval [0, 1], and secondly, that it is differentiable on the open interval (0, 1).

Given that f(x) = e-5x is an exponential function, it is continuous and differentiable for all x in real numbers, R. Hence, f(x) is continuous and differentiable on [0, 1] and (0, 1), respectively. Therefore, the function satisfies the hypotheses of the Mean Value Theorem.

To find all the numbers c that satisfy the conclusion of the MVT, we have to solve the equation f'(c) = [f(b) - f(a)] / (b - a). Differentiating f(x), we get f'(x) = -5e-5x. On solving this equation for c, the value that satisfies it will be our solution.

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Answer:

1. Range =30

2. Variance =137.6

3. Standard deviation=11.7303

Step-by-step explanation:

This question requires you to find the range, variance and standard deviation of sample data set.

Given the data as; 127 150 121 120 140 128

Arrange the data in ascending order;

sample set S={120, 121, 127, 128, 140, 150}

number of elements, n=6

1. Range = Maximum (S) - Minimum (S) = 150- 120 = 30

⇒Find the mean of the data set

[tex]mean= \frac{120+121+127+128+140+150}{6} = 786/6 = 131[/tex]

2. Variance is the measure of how far a set of data is spread out.Standard deviation is the square-root of variance.To find variance you need to follow the steps below;

Finding the deviations from the mean and their squares

Deviations             Squares of deviations

120-131= -11               -11²=   121

121-131= -10                -10² =100

127-131= -4                  -4² = 16

128-131= -3                   -3= 9

140-131= 9                    9²=  81

150-131= 19                19²=  361

Finding the sum of the squares of the deviations from the mean

[tex]=121+100+16+9+81+361=688[/tex]

Finding the variance

Variance, S²=(sum of squares of deviations from mean)/ n-1

[tex]=\frac{688}{n-1} =\frac{688}{6-1} =\frac{688}{5} =137.6[/tex]

Finding standard deviation

Standard deviation , s , is the square-root of the variance 

[tex]s=\sqrt{137.6} =11.73[/tex]

Final Answer:

- Range: 30 mmHg
- Variance: 137.6 (mmHg)²
- Standard Deviation: Approximately 11.73 mmHg
- Ideal Standard Deviation: 0 mmHg

Explanation:

To find the range, variance, and standard deviation for the given blood pressure readings, we can follow these steps:
1. **Range:**
  - The range is the difference between the highest and lowest values in the data set.
  - Highest reading = 150 mmHg
  - Lowest reading = 120 mmHg
  - Range = Highest reading - Lowest reading = 150 - 120 = 30 mmHg

2. **Variance:**
  - Variance measures the average degree to which each reading differs from the mean of the readings. Because we are dealing with a sample of the population, not the entire population, we'll use the sample variance formula.
  - First, compute the mean of the readings.
  - Mean (average) blood pressure reading = (127 + 150 + 121 + 120 + 140 + 128) / 6
  - Mean = 786 / 6 = 131 mmHg
  - Now, we'll calculate the square of the differences between each reading and the mean, sum those, and divide by (n-1), where n is the number of readings.
  - Differences squared: (127-131)², (150-131)², (121-131)², (120-131)², (140-131)², (128-131)²
  - = (-4)², (19)², (-10)², (-11)², (9)², (-3)²
  - = 16, 361, 100, 121, 81, 9
  - Sum of squared differences = 16 + 361 + 100 + 121 + 81 + 9 = 688
  - Sample variance = 688 / (6 - 1) = 688 / 5 = 137.6 (mmHg)²

3. **Standard Deviation:**
  - The standard deviation is the square root of the variance and provides a measure of the average distance from the mean.
  - Standard deviation = √variance = √137.6 ≈ 11.73 mmHg

4. **Ideal Standard Deviation:**
  - If the subject's blood pressure remains constant, and the measurement technique is applied correctly and without any error, the ideal standard deviation should be zero because all measurements would be the same, resulting in no variability.

In summary:
- Range: 30 mmHg
- Variance: 137.6 (mmHg)²
- Standard Deviation: Approximately 11.73 mmHg
- Ideal Standard Deviation: 0 mmHg

Answer:

Step-by-step explanation:

A) Let x represent acres of pumpkins, and y represent acres of corn. Here are the constraints:

  x ≥ 2y . . . . . pumpkin acres are at least twice corn acres

  x - y ≤ 10 . . . . the difference in acreage will not exceed 10

  12 ≤ x ≤ 18 . . . . pumpkin acres will be between 12 and 18

  0 ≤ y . . . . . the number of corn acres is non-negative

__

B) If we assume the objective is to maximize profit, the profit function we want to maximize is ...

  P = 360x +225y

__

C) see below for a graph

__

D) The profit for an acre of pumpkins is the highest, so the farmer should maximize that acreage. The constraint on the number of acres of pumpkins comes from the requirement that it not exceed 18 acres. Then additional profit is maximized by maximizing acres of corn, which can be at most half the number of acres of pumpkins, hence 9 acres.

So profit is maximized for 18 acres of pumpkins and 9 acres of corn.

Maximum profit is $360·18 +$225·9 = $8505.

We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

[tex]h(t)=-16t^2+25t+5[/tex]

[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16})[/tex]

X-term: [tex]-\frac{25}{16}[/tex]

Half of the x term: [tex]-\frac{25}{32}[/tex]

After squaring: [tex](-\frac{25}{32})^2=\frac{625}{1024}[/tex]

[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16}+\frac{625}{1024}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{5}{16}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{945}{1024}) \\ \\[/tex]

[tex]h(t)=-16[(t-\frac{25}{32})^2-\frac{945}{1024}] \\ \\ \boxed{h(t)=-16(t-\frac{25}{32})^2-\frac{945}{64}}[/tex]

Finally, the vertex of this function is:

[tex](\frac{25}{32},\frac{945}{64})[/tex]

So in this vertex we can find the answer to this problem:

The ball will reach its maximum height at [tex]t=\frac{25}{32}s=0.78s[/tex]

The ball maximum height is [tex]H=\frac{945}{64}=14.76ft[/tex]

Also we will use completing squares. We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:

[tex]R(p)=-5p^2+1230p[/tex]

[tex]R(p)=-5(p^2-246p)[/tex]

X-term: [tex]-246[/tex]

Half of the x term: [tex]-123[/tex]

After squaring: [tex](-123)^2=15129[/tex]

[tex]R(p)=-5(p^2-246p+15129-15129)[/tex]

[tex]R(p)=-5[(x-123p)^2-15129] \\ \\ R(p)=-5(x-123p)^2+75645[/tex]

Finally, the vertex of this function is:

[tex](123,75645)[/tex]

So in this vertex we can find the answer to this problem:

The price will maximize the revenue is [tex]p=123 \ dollars[/tex]

The maximum revenue is [tex]R=75645[/tex]

Answer:

  8 ft

Step-by-step explanation:

The height of the cross section through the apex will be the same as the height of the apex: 8 ft.

Answer:

11.4 million

Step-by-step explanation:

Let's define the variables i and i' to represent the number of infected bacteria initially and after 1 hour, and the variables n and n' to represent the number of non-infected bacteria initially and after 1 hour. The biologist's theory predicts ...

0.50i +0.20n = i'

0.50i +0.80n = n'

In matrix form, the equation looks like ...

[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right] \left[\begin{array}{c}i&n\end{array}\right]=\left[\begin{array}{c}i'&n'\end{array}\right][/tex]

If i''' and n''' indicate the numbers after 3 hours, then (in millions), the numbers are ...

[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right]^3 \left[\begin{array}{c}11&5.2\end{array}\right]=\left[\begin{array}{c}i'''&n'''\end{array}\right][/tex]

Carrying out the math, we find i''' = 4.8006 (million) and n''' = 11.3994 (million).

The population of non-infected bacteria is expected to be about 11.4 million after 3 hours.

Answer:

a. $295

Step-by-step explanation:

Add the net pay and the interest. This is the total net income.

Then add all other amounts separately. These are the expenses.

Subtract the expenses from the total net income.

The answer is a. $295

Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.

It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.

It is given that:

Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet shown in the picture.

From the spreadsheet:

Add the interest to the net pay. The overall net income is shown here.

= 2300 + 200

= $2320

Next, add each additional sum separately. The costs are as follows.

= 800+120+90+45+95+80+275+520

= $2025

From the entire net income, deduct the costs.

= 2320 - 2025

= $295

Thus, Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.

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[tex]\displaystyle\bf\\m \overset{\frown}{HE}=360-m \overset{\frown}{HL}-m \overset{\frown}{EV}-m \overset{\frown}{VL}\\m\overset{\frown}{HE}=360^o-40^o-130^o-110^o=360^o-280^o=80^o\\\\m\widehat{EYH}=m\widehat{EYV}=\frac{m \overset{\frown}{EV}-m\overset{\frown}{HE}}{2}=\frac{130^o-80}{2}=\frac{50^o}{2}=\boxed{\bf25^o}[/tex]

Answer:

B.) Investing has the risk of losing principal, whereas saving does not.

Step-by-step explanation:

Saving can be accomplished a number of ways, including putting the money in a cookie jar (where it will not earn interest). Most savings institutions (banks, credit unions, and the like) are governed by rules that help to ensure the availability and safety of the balance. Often, such institutions are insured so that depositors are protected against loss of principal.

Many investment opportunities are governed by no such rules. The invested amount may be unavailable for perhaps a lengthy period of time, and any return on the investment may be dependent upon factors not under the control of the party accepting the money. There is the opportunity for complete loss of the invested amount, and the possibility of incurring additional liability in some cases.

Investment in certificates that are traded on a regulated exchange will be subject to the exchange rules, generally including the requirement that the investor be fully informed of the risks. That doesn't mean there is no risk—it just means the investor is supposed to be made aware of it.

Answer:

342.24 units²

Step-by-step explanation:

The area of one of the 8 triangular sections of the octagon is ...

A = (1/2)r²·sin(θ) . . . . . where θ is the central angle of the section

The area of the octagon is 8 times that, so is ...

A = 8·(1/2)·11²·sin(360°/8) = 242√2

A ≈ 342.24 units²

The area of the octagon should be 342.24 units²

Since the area of 1 of the 8 triangular sections of the octagon should be.

[tex]A = (1\div 2)r^2.sin(\theta)[/tex]

Here θ represent the central angle of the section

Since

The area of the octagon is 8 times

So,

[tex]A = 8.(1/2).11^2.sin(360\div 8) \\\\= 242\sqrt2[/tex]

A ≈ 342.24 units²

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Start by describing the data given about the flower Heliconia's varieties. Then, conduct a significance test, possibly using ANOVA, to compare their mean lengths. However, the computation for the p-value and F-statistical is not specified in the question. You can just round your numbers according to the instructions.

The first step in a complete analysis is the description of the data. From the question, we have three types of tropical flower Heliconia, namely H. bihai, H. caribaea red, and H. caribaea yellow. We have the respective data points for each class, n, the sample mean, x-bar, standard deviation, s, and the standard error, s_(x-bar).

The next step is to carry out a significance test. This can be done using ANOVA (Analysis of variance), which compares the means of three or more samples. The test statistic in ANOVA is the F statistic, and the null hypothesis is that the population means are equal.

Given numbers, you can compute the F-statistic, but from the question, it's unclear how the actual computation was done. The p-value can also be calculated from the F statistic; it's the probability of getting an extreme or more extreme result in your observed data, assuming the null hypothesis is true.

The instruction is explicit regarding how to round your numbers: sample mean to four decimal places, standard deviation to three decimal places, and your test statistic (F-statistic) to two decimal places. The p-value should also be rounded to three decimal places.

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The slope is 3

I am not that shure on the y intercept

Answer:

Step-by-step explanation:

1. The function is good for years 1880 to 2009, 0 to 129 years after 1880. Values of x can be anything in the domain [0, 129].

__

2. 1950 -1880 = 70. The year 1950 corresponds to x=70, so the function tells us the water level rose ...

  f(70) = 1.6·70 = 112 . . . . . mm

__

3. We want to find x when f(x) = 100. That will be the solution to ...

  100 = 1.6x

  100/1.6 = x = 62.5

Then 62.5 years after 1880 is year 1942.5. The water level was 100 mm higher than in 1880 in the year 1942.

Answer:

  y = 90°

Step-by-step explanation:

The angle y subtends an arc of 180°, so its measure is 180°/2 = 90°. (We know the arc is 180° because the end points of it are on a diameter, so it is half a circle.)

The expression (5x + 2) + (5x + 2) + (5x + 2) simplifies to 15x + 6 by combining like terms; three 5x's give 15x, and three 2's give 6 when added together.

The expression (5x + 2) + (5x + 2) + (5x + 2) is given by adding three identical binomials. To find an equivalent expression, you can use the distributive property of multiplication over addition, which in this case can also be seen as simply combining like terms.

Step-by-step, here's how you simplify the expression:

So, (5x + 2) + (5x + 2) + (5x + 2) is equivalent to 15x + 6 for all values of x.

Answer:

0.74 m

Step-by-step explanation:

The distance around a circle on the other hand is called the circumference (c).

A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d) .

Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).

The circumference of a circle is found using this formula:

C=π⋅d

or

C=2π⋅r

Given r = 119.3 mm

So, C = 2 * 3.14 * 119.3 = 749.2 mm = 0.74 m

2, -2, 2, -2, ...

This is a geometric progression.

First term = 2

The rate of geometric progression = -1

a1 = 2

a2 = a1 × (-1) = -2

a3 = a2 × (-1) = 2

And so on

⇒ This is a infinite geometric sequence

Answer:

Infinite geometric sequence

Step-by-step explanation:

2, -2, 2, -2, ...

Lets find the difference of the terms

-2 -2=0

2-(-2)=0

LEts check with common ratio

-2/2= -1

2/-2=-1

so common ratio r=0, so its geometric

The sequence is repeating because of common ratio -1

So it goes on infinitely

Hence it is Infinite geometric sequence

Answer:

(1,2) is the only solution to the given linear equation

Step-by-step explanation:

To see whether an ordered pair is a solution to an equation, the easiest thing to do would be to plug the pair into the equation and see if it equals the right hand side.

(1,2):

[tex]4*x+7*y=18\\4*(1)+7*(2)=18\\\therefore (1,2) \text{ is a solution}[/tex]

(8,0):

[tex]4*(8)+7*(0)=32\\\therefore (8,0) \text{ is not a solution}[/tex]

(0, -2):

[tex]4*(0)+7*(-2)=-14\\\therefore (0,-2) \text{ is not a solution}[/tex]

The pair (1,2) is a solution to the linear equation 4x+7y=18. However, the pairs (8,0) and (0,-2) are not solutions because they do not satisfy the equation.

a. To determine if the ordered pair (1, 2) is a solution to the linear equation 4x + 7y = 18, we substitute the values of x and y into the equation: 4(1) + 7(2) = 18. This simplifies to 4 + 14 = 18, which is true. Therefore, (1, 2) is a solution to the given linear equation.

b. To determine if the ordered pair (8, 0) is a solution, we substitute the values of x and y into the equation: 4(8) + 7(0) = 18. This simplifies to 32 + 0 = 18, which is false. Therefore, (8, 0) is not a solution to the given linear equation.

c. To determine if the ordered pair (0, -2) is a solution, we substitute the values of x and y into the equation: 4(0) + 7(-2) = 18. This simplifies to 0 - 14 = 18, which is false. Therefore, (0, -2) is not a solution to the given linear equation.

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The complete question is here:

Determine whether each ordered pair is a solution of the given linear equation.

4 x+7 y=18 ;(1,2),(8,0),(0,-2)

a. Is (1,2) a solution to the given linear equation?

No

Yes

b. Is $(8,0)$ a solution to the given linear equation?

Yes

No

c. Is (0,-2) a solution to the given linear equation?

No

Yes

The Lagrangian is

[tex]L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)[/tex]

with partial derivatives (set equal to 0)

[tex]L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0[/tex]

[tex]L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0[/tex]

[tex]L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0[/tex]

[tex]L_\lambda=4x^2+4y^2-z^2=0[/tex]

[tex]L_\mu=2x+4z-2=0\implies x+2z=1[/tex]

Case 1: If [tex]y=0[/tex], then

[tex]4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|[/tex]

Then

[tex]x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23[/tex]

[tex]\implies x=\dfrac15\text{ or }x=-\dfrac13[/tex]

So we have two critical points, [tex]\left(\dfrac15,0,\dfrac25\right)[/tex] and [tex]\left(-\dfrac13,0,\dfrac23\right)[/tex]

Case 2: If [tex]\lambda=-\dfrac14[/tex], then in the first equation we get

[tex]x(1+4\lambda)+\mu=\mu=0[/tex]

and from the third equation,

[tex]z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0[/tex]

Then

[tex]x+2z=1\implies x=1[/tex]

[tex]4x^2+4y^2-z^2=0\implies1+y^2=0[/tex]

but there are no real solutions for [tex]y[/tex], so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

[tex]f\left(\dfrac15,0,\dfrac25\right)=\dfrac15[/tex] (min)

and

[tex]f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59[/tex] (max)

This problem involves using Lagrangian multipliers to optimize a function with two constraints. The maximum and minimum points can be found by solving the Lagrange equations, which are derivatives of the function and constraints. These points can be confirmed by checking the positive or negative value of the second-order derivative.

To find the maximum and minimum values of the function ​f(x,y,z)=x²+y²+z² subject the cone z²=4x²+4y² and the plane 2x+4z=2, we use Lagrange multipliers. We have two constraint functions here, given by the cone and the plane equations.

The first step is to set up the Lagrange equations, with and as Lagrange multipliers. From w=gradientf=gradientg+gradienth, we have three equations: 2x=*8x+2, 2y=*8y+0, 2z=*4. The second step is to solve these three equations, together with the original constraints ​g(x,y,z)=​0 and ​h(x,y,z)=​0.

Solving these equations will give you specific values for x, y, and z that correspond to the maximum and minimum points. To determine if a point is a maximum or minimum, one can compute the second-order partial derivatives and organize them into the Hessian matrix.

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Answer:

  D.  p + q = 7

Step-by-step explanation:

The slope of AB is ...

  slope AB = (1 -4)/(6 -p) = 3/(p -6)

The slope of BC is ...

  slope BC = (q -1)/(9 -6) = (q -1)/3

The product of these is -1, so we have ...

  (slope AB)·(slope BC) = -1 = (3/(p -6))·((q -1)/3)

Multiplying by q -1 gives ...

  -(q -1) = p -6 . . . . . . the factors of 3 in numerator and denominator cancel

  1 = p + q -6 . . . . . . add q

  7 = p + q . . . . . . . . add 6 . . . . matches choice D

Answer:

D. p + q = 7

Step-by-step explanation:

Just did this quiz on edmentum :P

-5

Make the equation into slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept.

In the equation y = -5x - 2/3, the slope is -5 and the y-intercept is -2/3.

For this case we have that the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]y = - \frac {2} {3} -5x[/tex]

Reordering:

[tex]y = -5x- \frac {2} {3}[/tex]

So, we have to:

[tex]m = -5\\b = - \frac {2} {3}[/tex]

Answer:

The slope is -5

Answer:

1. 4n^3

2. 4k^7

3. 3

4. -30x

5. -6

Step-by-step explanation:

1. The prime factorization of 12 is 2 x 2 x 3 and the prime factorization of 16 is 2 x 2 x 2 x 2. When you look at these two expressions you can see the common factors of these two numbers are 2 x 2, which is 4. Next, we look at the GCF of the N's which would be n^3 since n^5 has three N's in it. Therefore, we get 4n^3 when we multiply the two together.

2. The factors of 8 are 1, 2, 4, and 8. Out of these, 1, 2, and 4 are the only factors that 20 shares with it and 4 is the greatest. Then, we look at the K's and the GCF of the K's is k^7 since k^8 has seven K's. We multiply the two and we get 4k^7.

3. Since one of the numbers of the three given here does not include the variable n, there will not be any N's in the GCF of the three, so we don't have to worry about that. Now, we just find the GCF of 18, -24, and -21. The factors of 18 are 1, 2, 3, 6, 9, and 18, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, and lastly, the factors of 21 are 1, 3, 7, and 21. From these, 3 is the biggest common divisor, therefore the GCF is 3.

4. Between the two X's, X^1 is the biggest amount of X's this GCF has, so the final GCF will be some constant multiplies with X. Since we are dealing with bigger numbers on this problem, we should use prime factorization. The prime factorization of 90 is 2 x 3 x 3 x 5, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5. From these expressions, we take the biggest amount of each common factor as we can. Since these expressions both have 2, we take the smaller amount of 2's which is one two. Then we get one three from both expressions, and one five as well. 2 times 3 times 5 equals 30, therefore, we get -30x, and not 30x, because both of these numbers are negatives.

5. All of these numbers do not have an x, so there won't be an x in our GCF. Another method of quickly finding the GCF of numbers is to look at the smallest number's factors first to see what factors it shares with the other numbers. The factors of 12 are 1, 2, 3, 4, 6, and 12. 42 and 30 do not have the factor 12, so we can go down the list and see if 42 and 30 share the factor 6, which they do since 6 times 7 is 42 and 6 times 5 is 30. Since all of these numbers share the negative sign, the GCF of these three numbers is -6.  

Answer:

Option B, two line perpendicular to the same line are parallel.

Step-by-step explanation:

Since DA and CB are perpendicular to AB, they are considered parallel. This is like a transversal line.

Answer:

Definition of right angles.

Step-by-step explanation:

A rectangle is a parallelogram whose opposite sides are parallel to each other. Also, these opposite sides measure the same and all four sides create right angles. In this sense the reason would complete the proof in lines 3 and 5 is the "Definition of right angles". This is because by definition the rectangle is a parallelogram with a right angle, since it is a parallelogram, its opposite is also a right angle. The other angles, which are supplementary to the previous two, add up to 180º. And since they are opposite, they are the same, therefore each of the four is a right angle.

[tex]\angle ABC = \angle BCD = \angle CDA = \angle DAB=90^{\circ}[/tex]

The vertex form of the equation of a parabola is

                     f(x) = a( x − h)^2 + k

where (h,k) is the vertex of the parabola. In this case, we are given that      (h,k) = (5,0). Hence,

                     f(x) = a( x − 5)^2 + 0

                           =a( x − 5)^2

Since we also know the parabola passes through the point (7,−2), we can solve for a because we know that f(7) = −2.

                        a( 7 − 5)^2 = -2

                           a(2)^2 = -2

                              4a = -2

                               a = -1/2

Thus, the given parabola has equation

                      f(x) = -1/2(x − 5)^2

Answer:

i couldnt answer please be more specific

Step-by-step explanation:

Answer: [tex]cos(\pi-x)=-cos(x)[/tex]

Step-by-step explanation:

We need to apply the following identity:

[tex]cos(A - B) = cos A*cos B + sinA*sin B[/tex]

Then, applying this, you know that for [tex]cos(\pi-x)[/tex]:

[tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex]

We need to remember that:

[tex]cos(\pi)=-1[/tex] and [tex]sin(\pi)=0[/tex]

Therefore, we need to substitute these values into [tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex].

Then, you get:

[tex]cos(\pi-x)=(-1)*cos(x)+0*sin(x)[/tex]

[tex]cos(\pi-x)=-1cos(x)+0[/tex]

[tex]cos(\pi-x)=-cos(x)[/tex]

Answer:

C. Domain: (negative infinity, infinity)   Range: (0, infinity)

Step-by-step explanation:

It's correct

The domain of the functions will be (-∞, ∞) and the range of the functions will be (0, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

The functions are given below.

y = f(x)

y = g(x)

y = h(x)

y = k(x)

Then the domain of the functions will be (-∞, ∞) and the range of the functions will be (0, ∞).

Then the correct option is C.

More about the domain and range link is given below.

https://brainly.com/question/12208715

#SPJ2

Answer:

1. [tex]f(x)=-10^{x-1}-10[/tex] - [tex]-\frac{101}{10}[/tex]

2. [tex]f(x)=-3^{x+5}-9[/tex] - [tex]-252[/tex]

3. [tex]f(x)=-3^{x-2}-1[/tex] - [tex]-\frac{10}{9}[/tex]

4.  [tex]f(x)=-17^{x-1}+2[/tex] - [tex]\frac{33}{17}

Step-by-step explanation:

We are given the exponential functions and we are to match them with their y-intercepts.

1. [tex]f(x)=-10^{x-1}-10[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-10^{0-1}-10 = -\frac{101}{10}[/tex]

y-intercept ---> [tex]-\frac{101}{10}[/tex]

2. [tex]f(x)=-3^{x+5}-9[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-3^{x+5}-9=-252[/tex]

y-intercept ---> [tex]-252[/tex]

3. [tex]f(x)=-3^{x-2}-1[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-3^{x-2}-1=-\frac{10}{9}[/tex]

y-intercept ---> [tex]-\frac{10}{9}[/tex]

4. [tex]f(x)=-17^{x-1}+2[/tex]:

Substituting x = 0 to find the y-intercept:

[tex]f(x)=-17^{x-1}+2=\frac{33}{17}[/tex]

y-intercept ---> [tex]\frac{33}{17}

Finding x.

Suzette ran = x

Suzette biked = 4x

7 = x + 4x --) 7 = 5x --)  1.4 = x

Suzette ran for 1.4 hours

Finding y.

Quickest way is to use Suzette biked = 4x and substitute the x for 1.4 to find how much she biked.

4 x 1.4 = 5.6

1.4 + 5.6 = 7 hours the total time exercising

And the mileage adds up to.

5(1.4) + 20(5.6) = 119