I need help with number 5

The value closest to the lateral area of the cylinder is 138. 5cm^2. Option C

The formula for determining the lateral area of a cylinder is expressed as;

Lateral area = 2 πrh

Where;

Note that radius is half the diameter;

radius, r = 5. 8/ 2 = 2. 9 cm

Substitute into the formula

Lateral area = 2 ( 3. 142 × 2. 9 × 7. 6)

Lateral area = 2 ( 69. 249)

Lateral area = 138. 49 cm^2

Thus, the value closest to the lateral area of the cylinder is 138. 5cm^2. Option C

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The value of x is 4 , 12 , - 1 resp. in eq 1 , 2 and 3 .

Finding values of unknown variable x .

Following are linear equations in one variable .

On solving them we get ,

1 )          2 ( 3 x - 5 ) = - 4 x + 30

             6 x - 10 = - 4 x + 30

              10 x =40

                 x = 4

2 )          5 x - 6 - 3 x = 18

              2 x = 18 + 6

              2 x = 24

               x = 12

3 )         - 11 - 5 x = 6 ( 5 x + 4 )

               - 11 - 5 x = 30 x + 24

                 - 35 x = 35

                x = - 1

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If

[tex]f(x) = \dfrac{2ax+b}{x-1}[/tex]

Note that

[tex]f(2) = \dfrac{4a+b}{2-1} = 4a+b[/tex]

From the given information we have

[tex]\displaystyle \lim_{x\to0} f(x) = \lim_{x\to0} \frac{2ax+b}{x-1} = \frac{0+b}{0-1} = -b = -3 \\\\ ~~~~ \implies b=3[/tex]

and

[tex]\displaystyle \lim_{x\to\infty} f(x) = \lim_{x\to\infty} \frac{2ax+b}{x-1} = \lim_{x\to\infty} \frac{2a+\frac bx}{1-\frac1x} = \frac{2a+0}{1-0} = 2a = 4 \\\\ ~~~~ \implies a=2[/tex]

It follows that

[tex]f(2) = 4\cdot2+3 = 11[/tex]

as required.

Answer: 576

Step-by-step explanation:

5+3 = 8

8*72=576

Answer:576

Step-by-step explanation: just add and multiply

Answer:

15

Step-by-step explanation:

The sides add to 63, so:

[tex]11+3x+11+x+2+2x+3=63 \\ \\ 6x+27=63 \\ \\ 6x=36 \\ \\ x=6 \\ \\ \implies AB=2(6)+3=15[/tex]

Step-by-step explanation:

2(x-1) + 5(x-9)

2x - 2 + 5x - 45

2x + 5x - 2 - 45

7x - 47

Answer:

2x -2 + 5x -45       7x -47

Step-by-step explanation:

2*x = 2x

2*-1 = -2

5*x =5x

5*-9 = -45

Answer:

$3285.47

Step-by-step explanation:

We know the value decreased by a factor of 2500/28000 after 5 years.

This means the value decreased by a factor of (2500/28000)⅕ per year.

Therefore, after 3 years, the value is

[tex]28000(2500/28000)^{3/5} \approx 3285.47[/tex]

If the point N lying on the Line segment MP, divides MP such that the ratio of MN to NP is 6 to 1, and the coordinates of M(-13, 20) and P(1-1), then the coordinates of "N" is

As per the question statement, N lying on the Line segment MP, divides MP such that the ratio of MN to NP is 6 to 1.

We are required to find out the coordinates of "N".

To solve this question, we need to know the formula to calculate the coordinates of a point (Say "c") that divides a line segment AB in the ratio of (m:n).

The formula goes as:

Abscissa of c [tex](x_{3})=\frac{mx_{2}-nx_{1} }{m-n}[/tex]

and, Ordinate of c [tex](y_{3})=\frac{my_{2}-ny_{1} }{m-n}[/tex]

where, [tex](x_{1}, y_{1})[/tex] are the coordinates of point A, while

[tex](x_{2}, y_{2})[/tex] are the coordinates of point B.

Using our given data in the above formulae, we get

Abscissa of N =  [tex]\frac{(6*1)-[1*(-13)]}{6-1} =\frac{6-(-13)}{5}=\frac{6+13}{5}=\frac{19}{5}[/tex]

And, Ordinate of N = [tex]\frac{[6*(-1)-(1*20)}{6-1} =\frac{(-6)-20}{5}=\frac{-(20+6)}{5}=\frac{-26}{5}[/tex].

Hence, our concerned point N = [tex](\frac{19}{5}, \frac{-26}{5})\\[/tex].

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Concluding that m∠ J K L = m ∠ Q R S is an example of: substitution property of equality

The substitution property of equality states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.

Now, we are told that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S.

Thus, concluding that m ∠ J K L = m ∠ Q R S is an example of: substitution property of equality

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Answer: [tex]\boxed{y=\frac{2}{5} x-7}\ as\ an\ example[/tex]

Step-by-step explanation:

Find the slope-intercept form:

[tex]2x-5y=30\\\\-5y=-2x+30\\\\y=\frac{-2x+30}{-5} \\\\y=\frac{2}{5} x-6[/tex]

Therefore the slope is 2/5

An example of a line parallel to this line is

[tex]y=\frac{2}{5} x-7[/tex]

The given set is (3, 4, 5, ...} is infinite set.

A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.

The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.

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Answer:

3

Step-by-step explanation:

input -3 into h(x)=x^2-6

h(-3)=-3^2-6=9-6=3

Answer:

$187.5

Step-by-step explanation:

39 (4) + 0.09 (350)

156 + 31.5

$187.5

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Answer:

$187.5

Step-by-step explanation:

You need to multiply the daily cost by the days. In this case, 39*4 = 156. Then, we can get the cost for the miles driven, being 0.09*350 = 31.5.

We can now add the two numbers together:

156 + 31.5 = $187.5

Answer:

1,803.268

Step-by-step explanation:

so thousandths place is three number after the decimal just see the fourth number after the decimal and if it 5 or greater round the (in this case) 8 but since the fourth number was 4 it stays the same but only three numbers

Answer:

k = 1

Step-by-step explanation:

since 360 = 60² , a perfect square , then

360 × 1 ← is a perfect square

that is 360k with k = 1 is a perfect square

Answer: It can.

Step-by-step explanation:

If an 8 oz. cup of juice cost $1.20 and a 12 oz. cup of juice cost $1.44, there is a $0.24 difference between the money and cups of juice in ounces. If there were to be a constant rate of change, a 16 oz. cup of juice MUST cost $1.68

No, the relationship between cost and ounces of juice cannot be described by a constant rate.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Cost of 8 ounce juice= $1.20

Cost of 12 ounce juice= $1.44

Now,

If the relationship between cost and ounces of juice was described by a constant rate, then the cost per ounce would be the same for both the 8-ounce cup and the 12-ounce cup. However, we can see that the cost per ounce is different for each cup:

For the 8-ounce cup: cost per ounce = $1.20 / 8 ounces = $0.15 per ounce

For the 12-ounce cup: cost per ounce = $1.44 / 12 ounces = $0.12 per ounce

Therefore, by algebra the cost per ounce is different for each cup, the relationship between cost and ounces of juice cannot be described by a constant rate.

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Answer:

5/4 > 5/6

Step-by-step explanation:

Answer:

10°C

Step-by-step explanation:

c = [tex]\frac{F - 32}{1.8}[/tex]  Plug in 50 for F and solve for C

c = [tex]\frac{50-32}{1.8}[/tex]

C = [tex]\frac{18}{1.8}[/tex] Divide

c = 10

AAnswer:

AB (-1, 4) = 34^ and B = (3,-1) 249*32 = 20

Step-by-step explanation:

Answer:

[tex]AB=\sqrt{53}\:\sf units[/tex]

[tex]EF=\sqrt{349}\:\sf units[/tex]

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}.[/tex]

Given:

Substitute the given points into the distance formula and solve for AB:

[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-4))^2+(-1-1)^2}\\& =\sqrt{(7)^2+(-2)^2}\\& =\sqrt{49+4}\\& = \sqrt{53}\end{aligned}[/tex]

Given:

Substitute the given points into the distance formula and solve for EF:

[tex]\begin{aligned}\implies EF & =\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\& =\sqrt{(11-(-7))^2+(3-(-2))^2}\\& =\sqrt{18^2+5^2}\\& =\sqrt{324+25}\\& =\sqrt{349}\end{aligned}[/tex]

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answer and steps to get it in the picture

1) Yes, because each value of x maps onto only one value of y.

2) No, because the x-value of 1 maps onto 4 different y values.

Answer:

Step-by-step explanation:

You want to know if the given sets of ordered pairs represent a function.

A function is a relation that maps an input value to a single output value. On a graph, this means no two points are vertically aligned. For a table or set of ordered pairs, it means no input (x) value is repeated.

The input (x) values are {-1, 0, 1, 2} with no repeats. This relation is a function.

The input values are {1, 1, 1, 1} with repeats. This relation is not a function.

If a high school student decides to apply four of six famous colleges, then the four colleges can be selected in as many as 15 different combinations.

As per question statement, a high school student decides to apply four of six famous colleges.

We are required to calculate the number of combinations in which the four colleges can be selected.

To solve this question, we need to know the formula of Combination which goes as [tex](nCr)=\frac{n!}{r!(n-r)!}[/tex]

, i.e., we are to select a set or "r" from a set of "n".

Here, we have to select a combination of 4 from a set of 6.

Therefore applying (nCr) formula with (n = 6) and (r = 4), we get,

[tex](6C4)=\frac{6!}{4!(6-4)!} =\frac{6!}{4!2!}=\frac{4!*5*6}{4!*2}=\frac{5*6}{2}=(5*3)=15[/tex].

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Answer: She can use 4 gigabyte while remaining in her budget.

Step-by-step explanation:

You would first subtract 54  from 70 which leaves you with 16,

Then you would divide 16 by 4 to find how many gigabytes she could use which gives you 4

So she can use 4 gigabyte while remaining in her budget.

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Answer: Answer is 3

Step-by-step explanation:

let the maximum number of gigabytes of data is x

total budget is  $70

then, flat cost is $54 and $5per gigabyte

we get:

54 +5 × x= 70

5x =70 - 54

x = [tex]\frac{16}{5}[/tex]  = 3.2 ≈ 3

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The number of nails in each box is: 1300, 1400, 600, 1200, and 500

Given 5000 nails in five boxes.

Let X denote the universal set.

Then n(X) = 5000.

Let A denote the first box,

B denote the second box,

C denote the third box,

D denote the fourth box, and

E denotes the fifth box.

The first and second boxes have 2700 nails altogether.

⇒n(A ∪ B) = 2700

The second and third boxes have 2000 nails altogether.

⇒n(B ∪ C) = 2000

The third and fourth boxes have 1800 nails altogether.

⇒n(C ∪ D) = 1800

The fourth and fifth boxes have 1700 nails altogether.

⇒n(D ∪ E) = 1700

We need to find out how many nails are there in each box.

That is to find out: n(A), n(B), n(C), n(D), and n(E).

Note that all these five sets are disjoint. This means that the intersection is empty.

n(A ∪ B ∪ C ∪ D) = n(A ∪ B) + n(C ∪ D) = 2700 + 1800 = 4500

n(E) = n(X) - n(A ∪ B ∪ C ∪ D) = 5000 - 4500 = 500

n(D) = n(D ∪ E) - n(E) = 1700 - 500 = 1200

n(C) = n(C ∪ D) - n(D) = 1800 - 1200 = 600

n(B) = n(B U C) - n(C) = 2000 - 600 = 1400

n(A) = n(A U B) - n(B) = 2700 - 1400 = 1300

Therefore, the number of nails in each box is 1300, 1400, 600, 1200, and 500.

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(A) is false. By symmetry,

[tex]\displaystyle f(x) = \int_{-x}^x (|t|_t^2) e^{-t^2} \, dt = 2 \int_0^x (t-t^2) e^{-t^2} \, dt[/tex]

where [tex]|t|=t[/tex] since [tex]x>0[/tex]. Substitute [tex]s=t^2[/tex] to get the equivalent integral,

[tex]\displaystyle f(x) = \int_0^{x^2} (1 - \sqrt s) e^{-s} \, ds[/tex]

Then

[tex]\displaystyle f(x) + g(x) = \int_0^{x^2} e^{-s} \, ds[/tex]

[tex]\displaystyle f(\sqrt{\ln(3)}) + g(\sqrt{\ln(3)}) = \int_0^{\ln(3)} e^{-s} \, ds = \frac23 \neq \frac13[/tex]

(B) is false. Note that [tex]1+\alpha x[/tex] is linear so its derivative is the constant [tex]\alpha[/tex] at every point. We then have

[tex]{\psi_1}'(\alpha) = -e^{-\alpha}+1 = \alpha \implies 1-\alpha = e^{-\alpha}[/tex]

But this has no solutions, since the left side is negative for [tex]\alpha>1[/tex] and the right side is positive for all [tex]\alpha[/tex].

(C) is true. By the same reasoning as in (B), the line [tex]2x(\psi_1(\beta)-1)[/tex] has constant derivative, [tex]2\psi_1(\beta)-2 = 2e^{-\beta+2\beta-2[/tex]. Then

[tex]{\psi_2}'(\beta) = 2\beta-2+2e^{-\beta} = 2e^{-\beta}+2\beta-2[/tex]

holds for all values of [tex]\beta[/tex].

(D) is false. We use the first derivative test. By the fundamental theorem of calculus,

[tex]\displaystyle f(x) = 2 \int_0^x (t-t^2)e^{-t^2}\,dt \implies f'(x) = 2(x-x^2)e^{-x^2}[/tex]

Solve for the critical points.

[tex]f'(x) = 0 \implies x-x^2 = 0 \implies x = 0 \text{ or } x = 1[/tex]

[tex]e^{-x^2}>0[/tex] for all [tex]x[/tex], so the sign of [tex]f'[/tex] depends on the sign of [tex]x-x^2[/tex]. It's easy to see [tex]f'>0[/tex] for [tex]x\in(0,1)[/tex] and [tex]f'<0[/tex] for [tex]x\in\left(0,\frac32\right)[/tex]

Answer:

x = 23 degrees

Because if you look at diagram x is vertical to angle FBC, and angle FEC and angle EBA are alternate interior angles so they are equal to each other, and AC is a straight line which means it equals to 180 degrees.

[tex]4x+65+x = 180[/tex]

x = 23 degrees