For the function f(x) = 3x + 7, find the following:
a) f(2)=
c) f(x) = 8
b) f(-3) =
d) f(x) = 10

Using trigonometric identities, it is found that the exact value of the secant of the angle is given by:

c. [tex]\sec{\theta} = - \sqrt{5}[/tex]

According to the following identity:

[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]

The tangent is the inverse of the cotangent, hence in this problem, we have that:

[tex]\tan{\theta} = -2[/tex]

Then, the secant is given as follows:

[tex]\sec^2{\theta} = 1 + (-2)^2[/tex]

[tex]\sec^2{\theta} = 5[/tex]

[tex]\sec{\theta} = \pm \sqrt{5}[/tex]

The angle is in the second quadrant, where the cosine is negative, hence the secant also is and option c is correct, that is:

c. [tex]\sec{\theta} = - \sqrt{5}[/tex]

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Answer:

  cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

__

We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

The relevant formulas are ...

  V = LWH

  A = 2(LW +H(L +W))

for length L, width W, and height H.

a) prism 1

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

  V = (8 in)(8 in)(5 in) = 320 in³

  A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

b) prism 2

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

  V = (10 in)(8 in)(4 in) = 320 in³

  A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

__

The relevant formulas are ...

  V = πr²h

  A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

  V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

  A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

__

The relevant formulas are ...

  V = 1/3s²h

  A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

  V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

  A = (10 in)(10 in + 2×14 in) = 380 in²

__

The proposed figures have volume and area (rounded to the nearest unit) as follows:

  [tex]\begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}[/tex]

The proposed cylinder requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

Additional comment

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

Answer:

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

[tex]y \geqslant 2x - 15[/tex]

I hope this helps

The correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The inequality which is shown in the figure is y < x and y > 2.We can see in the graph when you plot y > 2 then it will cover all the values greater than 2 in the graph.

Similarly, if we plot the inequality y < x on the graph it will cover all the values of y which are less than x and intersect at the point ( 2, 2).

Therefore the correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2. The graph is attached with the answer below.

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Neither of these statements are true.

x/∞ = 0 is a nonsensical statement. It's more accurate to say

[tex]\displaystyle \lim_{y\to\infty} \frac xy = 0[/tex]

for any real number x. The important bit is that y is an arbitrarily large number as it approaches ∞. To convince yourself that this expression approaches 0 as y gets larger and larger, try fixing x and pick any increasing sequence of numbers for y.

For example, let x = 1 and take y from the sequence of increasing powers of 10, {10, 10², 10³, …}, which grows without bound. Then

1/10 = 0.1

1/10² = 0.01

1/10³ = 0.001

and so on. Naturally, the larger the power of 10 and thus the larger y gets, the closer x/y gets to 0.

Similarly, x/0 is nonsense, but the "limit-ized" version of the claim is also incorrect. For any fixed real number x, the limit

[tex]\displaystyle \lim_{y\to0} \frac xy[/tex]

does not exist. Suppose x > 0. If y approaches 0 from above, then y > 0 and x/y > 0 and

[tex]\displaystyle \lim_{y\to0^+} \frac xy = +\infty[/tex]

which you can convince yourself is true by reversing the example from before. Let x = 1 and take y from the sequence of decreasing powers of 10, {1/10, 1/10², 1/10³, …}, which converges to 0. Then

1/(1/10) = 10

1/(1/10²) = 100

1/(1/10³) = 1000

and so on. The smaller y gets (while still being positive), the larger x/y becomes.

But now suppose y < 0 and that y approaches 0 from below. Then x/y < 0, and

[tex]\displaystyle \lim_{y\to0^-} \frac xy = -\infty[/tex]

The limits from either side do not match, so the limit as y approaches 0 does not exist.

You can use the same reasoning for when x < 0.

The case of x = 0 is special, however. Since y is approaching 0, it's never actually the case that y = 0. 1/y is then some non-zero real number, and multiplying it by x = 0 makes x/y = 0. Then

[tex]\displaystyle \lim_{y\to0} \frac 0y = 0[/tex]

So in general,

[tex]\displaystyle \lim_{y\to0} \frac xy = \begin{cases}0 & \text{if }x = 0 \\ \text{does not exist} & \text{otherwise}\end{cases}[/tex]

Answer:

86 is the score that Maurice must get to average his score to 80

Using it's concept, it is found that the domain of the function is given by:

C. Real numbers between 0 and 12.

The domain of a function is the set that contains all possible input values of the function. In a graph, it is given by the values of the horizontal axis.

In the graph, the function is defined for real numbers between 0 and 12, hence option C is correct.

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64

x=154(vertically opposite angle)

d =p

then mpn =154-90 = 64

angle epm is straight angle

The table shows that it is more likely to wait at red during daytime by 2.92%.

Day

Green = 2 min

Red = 3 min

Yellow = 20 sec = 0.333 min

Total day cycle time= 5.33 min

Night

Green = 3 min

Red = 4 min

Yellow = 30 sec = 0.5 min

Total night cycle time= 7.5 min

Pday= 3 min/5.33 min= 0.5625

Pnight= 4 min/7.5 min= 0.5333

Pdifference= 0.02917 = 2.92%

Therefore it is more likely to wait at red during the daytime by 2.92%.

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The true statements for this graph are:

B. The domain is the set of all real numbers.

D. The range is the set of all real numbers greater than or equal to zero.

A domain can be defined as the set of all real numbers for which a particular function is defined. For this graph, the vertex of the parabola is (1, 0) and as such, the equation will be given by:

y = (x - h)² + k

y = (x - 2)² + 0

y = x² -4x + 4

Therefore, the graph's domain include a set of all real numbers.

A range refers to a set of all real numbers that connects with the elements of a domain. For this graph, we can observe that only real numbers greater than or equal to zero (0) are connected to the values on the x-axis of the domain.

In conclusion, we can logically deduce that the true statements for this graph are:

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Reason:

The friend should have multiplied the exponents.

This is what the steps should look like:

[tex](r^6)^4 = r^{6*4}\\\mbox{ \ \ \ \ \ \ } =r^{24}[/tex]

The reason for the multiplication is because we have four copies of [tex]r^4[/tex] added together. Repeated addition can be shortened to multiplication.

In other words,

[tex](r^6)^4 = (r^6)*(r^6)*(r^6)*(r^6) = r^{6+6+6+6} = r^{6*4} = r^{24}[/tex]

Answer:

9. 20,001

10. 100,001

11. 4,999

12. 999,999

Step-by-step explanation:

Answer:

229

Step-by-step explanation:

(my work for the problem is in the photo I attached)

(I also wrote this step-by-step in the photo because I can explain things better as I do them)

This will be a little bit confusing without me writing out the numbers, so mainly this is if you can't read my handwriting

  -3       + 8         =      5    ;  5       + 8    =     13

(1st term)                   (2nd term)            (3rd term)

Instead of adding 8 repeatedly (repeated addition), we can use multiplication.

To get the 3rd term in this sequence, we had to add 8 twice, which could also be done by multiplying 8 twice (8 x 2)

13 + 8 = 21

         (4th term)

to get the 4th term, we added 8 three times (or, 8 x 3)

So, if we are looking for the 30th term in a sequence, we will have to add 8, 29 times (8 x 29) to our original term.

8 x 29 = 232

-3 + 232 = 229

This means that the 30th term of the sequence will be 229.

Step-by-step explanation:

this is an isoceles, right-angled triangle.

but legs are equally long (6 m), and the baseline is per Pythagoras

baseline² = leg1² + leg2² = 6² + 6² = 36 + 36 = 72

baseline = sqrt(72) = 8.485281374... m

so, the perimeter is

6 + 6 + 8.485281374... = 20.485281374... ≈ 20.5 m

so, B is the right answer.

The Perimeter of Triangle is 6(2 + √2).

A branch of mathematics called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided form can be decomposed into a group of triangles, trigonometry may be found across all of geometry.

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyse this relationship.

Given:

Perpendicular = 6 m

Using Trigonometry

sin 45 = P/H

1/√2 = 6/ H

H= 6√2

and, tan 45 = P/ B

1= 6/ B

B= 6

So, the perimeter of triangle

= 6 + 6 + 6√2

= 12 +6√2

= 6(2 + √2)

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The base area of the prism is 36 square centimeters and the volume of the prism is 288 cubic centimeters

The base area is calculated as:

Base area =Length * Width

From the complete question (see attachment), we have:

Length = 12

Width = 3

So, we have:

Base area = 12 * 3

Base area = 36

The volume is calculated as:

Volume = Base area * Height

So, we have:

Volume = 36 * 8

Evaluate

Volume = 288

Hence, the volume of the prism is 288 cubic centimeters

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Applying the inscribed angle theorem, the measure of the arc from A to B is: 100 degrees.

The inscribed angle theorem states that an inscribed angle in a circle is half the central angle.

Angle BAC = 40 degrees, so, central angle = 80 degrees. Arc BC would also be 80 degrees.

Measure of arc AC through point B = 180 degrees.

Arc AB = 180 - 80 = 100 degrees.

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By knowing the circumference of the base of the cone, we see that the radius is 4 centimeters.

Notice that in the first figure, the length of the arc AB is L = 8π cm.

Then, that arc will be the bottom part of the cone. Then we can see that the circumference of the base of the cone will be equal to the length of the arc.

And remember that for a circle of radius R (like the base of the cone), the circumference is:

C = 2πR.

Then we will get:

8π cm = C =  2πR

( 8π cm)/ 2π = R

4cm = R

The radius of the cone is 4cm.

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The following way is a way which can not be used to represent the solution of 5(x + 2) ≥ 7x + 2(x - 1) is "A number line with a closed circle on 3 and shading to the right".

5(x + 2) ≥ 7x + 2(x - 1)

5x + 10 ≥ 7x + 2x - 2

5x + 10 ≥ 9x - 2

5x - 9x ≥ -2 - 10

-4x ≥ - 12

x ≤ -12/-4

x ≤ 3

Therefore, the correct answer is "A number line with a closed circle on 3 and shading to the right".

The complete question:

Which of the following is not a way to represent the solution of the inequality 5(x + 2) greater than or equal to 7x + 2(x − 1)? . A number line with a closed circle on 3 and shading to the right. . A number line with a closed circle on 3 and shading to the left. . 3 greater than or equal to x . x less than or greater to 3

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The five-number summary as displayed in a box plot attached below, from the least to the greatest is: Minimum < Q1 < Median < Q3 < Maximum

The five-number summary can be described as a set of data points or values that summarizes the distribution of a data.

The diagram attached below shows the five-number summary as displayed by a box plot.

From the least to the greatest, the five-number summary consist of:

Minimum < Q1 < Median < Q3 < Maximum

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Answer:

52 weeks are there in a year

Step-by-step explanation:

365/7

Questions:- perimeter

Explanation:- one side is 10 cm another opposite to it

6+x= 10

x= 4 units

so now perimeter

[tex]8 + 8 + 10 + 8 + 4 + 10 \\ 16 + 8 + 4 + 20 \\ 20 + 8 + 20 \\ 40 + 8 = 48 \: units[/tex]

The probability that a divisor of 2 or 9 is chosen when the spinner is spun once is 2/3.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

P(2 or divisor of 9) = section that has a divisor of 2/ total number of sections + section that has a divisor of 2/ total number of sections

1/3 + 1/ 3 = 2/3

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Using proportions, it is found that the ordered pair that represents the location of the layover is given by: (2.75, 1.5).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the flight distance is partitioned in a ratio of 3:1, hence:

L - Nv = 3/4(Ny - Nv).

This ratio is applied for both coordinates, hence, for the x-coordinate:

[tex]x + 4 = \frac{3}/{4}(5 + 4)[/tex]

[tex]x = \frac{27}{4} - \frac{16}{4}[/tex]

[tex]x = \frac{11}{4}[/tex]

x = 2.75.

For the y-coordinate:

[tex]y = \frac{3}/{4}(2 - 0)[/tex]

[tex]y = \frac{6}{4}[/tex]

x = 1.5.

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Answer:

4

Step-by-step explanation:

The mode is most common, so it is 4.

The value of x and y is (5,2)

We have given that,

4x + 2y = 9 ........(1)

x - 2y = 1.......(2)

We have to solve the simultaneous equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

adding equations 1 and 2 so we get,

4x + 2y = 9

x - 2y = 1

----------------

5x-0y=10

[tex]5x=10\\x=10/2\\x=5[/tex]

Use the value of x in equation 2 so we get,

[tex]5-2y=1[/tex]

[tex]-2y=1-5[/tex]

[tex]-2y=-4[/tex]

[tex]y=-4/-2[/tex]

[tex]y=2[/tex]

Therefore the value of x and y is (5,2)

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The probability that he does not wait for more than five minutes all 5 days this week is 0.16807

The probability that he waits for more than 5 minutes is:

p = 30%

This means that the probability that he does not wait for more than 5 minutes is

q = 70%

If he does not wait for more than five minutes all 5 days this week, the probability is:

P = q^5

This gives

P = (70%)^5

Evaluate

P = 0.16807

Hence, the probability that he does not wait for more than five minutes all 5 days this week is 0.16807

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Answer:

Answer:1296π

Step-by-step explanation:

As we know,

Area of cicle=πr^2

= π(36)^2

=1296π