Find the exact value of sec(theta) if cot(theta)= -1/2 and the terminal side of theta lies in quadrant ii.

a. sec(theta)= -sqrt(5)/2
b. sec(theta)= sqrt(t)/2
c. sec(theta)= -sqrt(5)
d. sec(theta)= sqrt(5)

Answer:

c) 6

Step-by-step explanation:

Given :

⇒ f(x) = x³ + 7x² - x

⇒ g(x) = x² - 3

===============================================================

Finding the degree of g(f(x)) :

⇒ Degree of f(x) = 3

⇒ Degree of g(x) = 2

⇒ Therefore, degree of g(f(x)) = degree of f(x) × degree of g(x)

⇒ Degree of g(f(x)) = 3 × 2

⇒ Degree of g(f(x)) = 6

Degree of g(f(x))

Use Pascal's law

Option C

Answer:

Unlikely

Step-by-step explanation:

well if you want the chance it’s unlikely. This is because you only have 6 defective calculators and the rest or majority are not defective.

In Colorado, the estimated total in-state college tuition cost for two years is $83,832. It is to be noted that this is inclusive of other factors as shown in the computation below.

Given the following:

Base Tuition (Note that this increases by 20% every year) = $12, 650

Off campus Room and Board  - $11, 440

Housing - $5,976

Meals - $ 6, 450

Living Expenses - 1,670

Books and Supplies - $1200

The summary thus is equal to

Base Tuition = $12, 650 * 2 * 1.2

Off campus Room and Board  - $11, 440 * 2

Housing - $5,976  * 2

Meals - $ 6, 450 * 2

Living Expenses - 1,670 *2

Books and Supplies - $1200 *2

This results in:

Base Tuition                               = $30,360

Off campus Room and Board  = $22,880

Housing                                      = $11, 952

Meals                                          = $ 12900

Living Expenses                        = $ 3,340

Books and Supplies                  = $2,400

Grand Total                               = $ 83,832.

Note that the base tuition was estimated to increase at the rate of 20% every year.

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Answer:

c = 10

Step-by-step explanation:

The pythagoras theorem :

a² + b² = c²

a = 6 and b = 8

6² + 8² = c²

36+64 = c²

100 = c²

c = √100

c= 10

Hope this helped and brainliest please

Answer:

the second one

Step-by-step explanation:

just looking at the y values you get

-24y + 32y so that will give u +8y , there is only one answer with that

Answer:

a) 13

b) 1/3

c) -2

d) 1

Step-by-step explanation:

This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:

For example:

f(x) = 3x + 7

f(2) = 3(2) + 7

f(2) = 6 + 7

f(2) = 13

________

f(-3) = 3x + 7

f(-3) = 3(-3) + 7

f(-3) = -9 + 7

f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.

f(-3) = -2

The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:

For example:

f(x) = 8

f(x) = 3x + 7

8 = 3x + 7

8 - 7 = 3x

1 = 3x

x = 1/3

f(x)= 10

f(x) = 3x + 7

10 = 3x + 7

10 - 7 = 3x

3 = 3x

3/3 = x

1 = x

I hope this helps!

Answer:4.6

Step-by-step explanation:

Use the pythagorean theorem, then find the square root using your calculator.

The x-intercept of the line is (4, 0)

The x-intercept of a line is the point where the line crosses the x-axis. Given the equation below:

y=3/4x-3

The x-intercept occurs at the point where y = 0. Substitute:

0 = 3/4x - 3

3/4x  = 3

3x = 12

x = 4

Hence the x-intercept of the line is (4, 0)

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The difference of the earnings of movies C and D for that week is $10,652,270.46 .

Subtraction is used to determine the difference between two or more numbers.

The difference = earnings of movie D - earnings of movie C

$34.311,887.98 - 23,659,617.52 = $10,652,270.46

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Answer:

15 students

Step-by-step explanation:

To solve this question, we can set up a system of equations.

Let's start by naming our variables.

We can call the number of students that rode in a van "x".

Then, let's name the number of students that rode a bus "y".

Knowing this, we can create two equations and then solve.

For High School A, the equation would be as follows:

12x+11y=576

For High School B, it would be:

4x+9y=384

What you have to do now, is to eliminate one of the variables.

I'm going to choose to do it with elimination, but substitution also works.

I'm going to multiply the second equation by 3, so that we can subtract the equations to eliminate the x variable.

3(4x+9y=384)

Since we're multiplying 3 to both sides, the equation will remain true.

12x+27y=1152

Now, let's subtract the other equation from this one:

  12x+27y=1152

-  12x+11y=576

_____________

0x+16y=576

Our new equation is:

16y=576

Divide both sides by 16 to isolate y

y=36

This means that 36 students rode in each bus.

Let's now use this info to solve for x.

We can do this by plugging in 36 for y.

4x+9y=384

4x+9(36)=384

Simplify

4x+324=384

Subtract 324 from both sides

4x=60

Divide both sides by 4

x=15

This means that 15 students rode in each van.

As I mentioned earlier, this could have also been solved by substitution.

You would have had to isolate one variable so that one of the equations read x= something or y= something

After that, you plug that in to the other equation so you're left with only one variable.

You then simplify, and plug the value back in for the other variable.

Given the nature of this question, that would have involved working with decimals, so I chose elimination instead.

Please let me know if you have any questions!

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, we have given that,

Let the number of students in van be 'x' and number of students in bus be 'y' .

According to the question,

Linear equation for class A

[tex]\sf{ 12x + 11y = 576 ...eq(1)}[/tex]

Linear equation for class B

[tex]\sf{ 4x + 9y = 384 ...eq(2) }[/tex]

Subtract eq(2) from eq(1) :-

[tex]\sf{ 12x + 11y -( 4x + 9y) = 576 - 384 }[/tex]

[tex]\sf{ 12x + 11y - 4x - 9y = 192 }[/tex]

[tex]\sf{ 8x + 2y = 192 }[/tex]

[tex]\sf{ 2(4x + y) = 192 }[/tex]

[tex]\sf{ 4x + y = {\dfrac{192}{2}}}[/tex]

[tex]\sf{ 4x + y = 96}[/tex]

[tex]\bold{ y = 96 - 4x ...eq(3) }[/tex]

Subsitute eq (3) in eq(1) :-

[tex]\sf{ 12x + 11( 96 - 4x) = 576 }[/tex]

[tex]\sf{ 12x + 1056 - 44x = 576 }[/tex]

[tex]\sf{ 12x - 44x = 576 - 1056}[/tex]

[tex]\sf{ -32x = - 480 }[/tex]

[tex]\sf{ x = {\dfrac{-480}{-32}}}[/tex]

[tex]\bold{ x = 15 }[/tex]

Thus, The value of x is 15 .

Now, subsitute the value of x in eq(2) :-

[tex]\sf{ 4(15) + 9y = 384 }[/tex]

[tex]\sf{ 60 + 9y = 384 }[/tex]

[tex]\sf{ 9y = 384 - 60 }[/tex]

[tex]\sf{ 9y = 324 }[/tex]

[tex]\sf{ y = {\dfrac{324}{9}}}[/tex]

[tex]\bold{ y = 36 }[/tex]

Thus, The value of y is 36

Therefore,

The number of students in each van = 15

The number of students in each bus = 36

Hence, The number of students rode in each van are 15 .

Answer:

[tex]\alpha =107.4^{o}[/tex]

Step-by-step explanation:

[tex]15=\frac{\pi (8)\alpha }{180}[/tex]

[tex]\alpha =\frac{(15)(180)}{8\pi } =\frac{2700}{25.13}=107.4[/tex]

Hope this helps

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=15\\ r=8 \end{cases}\implies 15=\cfrac{\theta \pi (8)}{180}\implies 15=\cfrac{2\pi \theta }{45} \\\\\\ 675=2\pi \theta \implies \cfrac{657}{2\pi }=\theta \implies 104.56^o\approx \theta =a[/tex]

Answer:

true

false

true

false

true

The ratio of the number of squares to the number of triangles is 5 : 2

The number of triangles that should be added to make the ratio is 6

Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another number.

Ratio of the number of squares to the number of triangles = number of squares : number of triangles

10 : 4

5 : 2

The number of triangles that should be added to make the ratio 1 : 1 - 10 - 4 = 6

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Comparing the two data sets shown below

Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.

Both the mean and the median can be used to describe where the “center” of a dataset is located.

So, the mean of data in 2022 is more than mean of data in 2018.

It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.

As the variance of 2022 more than in variance in 2018.

A high variance indicates that the data points are very spread out from the mean, and from one another.

As the standard deviation of 2022 more than in standard deviation in 2018.

The high standard deviation indicates data are more spread out.

The bigger the range, the more spread out the data.

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Answer:

2nd option

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

given

6xy³z × 3x²yx²

= 6 × 3 × x × x² × x² × y³ × y × z

= 18 × [tex]x^{(1+2+2)}[/tex] × [tex]y^{(3+1)}[/tex] × z

= 18[tex]x^{5}[/tex][tex]y^{4}[/tex]z

Answer:

Let the number of digits be n and the number of elements in set be s.

The pattern we see helps us determine the relationship between s and n as follows.

When set contains n-digit numbers, the set contains:

We have s known, substitute it into equation above and solve for n:

The numbers in the set s are 9-digit long.

The difference of the given functions is x^2 + 10

Given the following functions

f(x) = 2x^2 + 3 and

g(x)=x^2-7

Take the difference

(f-g)(x) = 2x^2 + 3 - (x^2 - 7)

(f-g)(x) = 2x^2 - x^2 +3 + 7

(f-g)(x) = x^2 + 10

Hence the difference of the given functions is x^2 + 10

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The first step is to convert feet to yards.

1 feet = 1/3 yards

Volume of the dirt hauled away = 16 x 13 x 3 = 624 yards³

Number of trips needed to haul away the dirt = 624 / 11 = 56. 7 = 57 trips

Total cost = 57 x 1175 = $66,975

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The combination expression that demonstrates how the 20 is calculated using the combination pattern​ is 6C3

While combination has to do with selection, permutation has to do with arrangement.

According to the combination rule

nCr = n!/(n-r)!r!

The expression that gives the result of 20 is expressed below;

6C3 = 6!/(6-3)!3!

6C3 = 6!/3!3!

6C3 = 6!/6*6
6C3 = 720/36
6C3 =20

Hence the combination expression that demonstrates how the 20 is calculated using the combination pattern​ is 6C3

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The each type of angle are discussed below

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

If the hours hand point to the hour 1 and minute hand at 12 then

angle will be acute.

If the hours hand point to the hour 2 and minute hand at 12  then

angle will be acute.

If the hours hand point to the hour 3 and minute hand at 12  then

angle will be right angle .

If the hours hand point to the hour 4 and minute hand at 12  then

angle will be obtuse.

If the hours hand point to the hour 5 and minute hand at 12  then

angle will be obtuse.

If the hours hand point to the hour 6 and minute hand at 12  then

angle will be straight angle .

If the hours hand point to the hour 7 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 8 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 9 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 10 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 11 and minute hand at 12  then

angle will be reflex.

If the hours hand point to the hour 12 and minute hand at 12  then

angle will be Complete angle.

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Answer:

Step-by-step explanation:

Remark

What you don't know and what makes the problem confusing, is that where to the given arcs start and end. So I am going to say that both arcs start from E and 119 ends at D, and 174 ends at F which means that the arc FD is not known, but it is not hard to find.

The total number of degrees from beginning to end is 360 degrees. The formula for finding FD is

Formula

FD = 360 - (174 - 119)

The formula for x is (ED - FD)/2

Solution

Arc FD = 360 - (174 - 119)

Arc FD = 67

So x = (119 - 67) / 2

x = 52 /2

x = 26

Answer:

D

Step-by-step explanation:

The correct answer should have a 63%.

It's probably D. The terminology is a little confusing.

The equation of the output looks like:

-7.611 + .186(x) = y

x --> Arm span

y --> Foot span

The linear relationship is formed with the armspan.

Sometimes. p ⇒ q is true if both p and q are true, or whenever p is false.

Always. ¬ p ⇒ ¬q is true if ¬p and ¬q are both true (which means p and q are both false), or whenever ¬p is false (p is true).

Answer:

hundred

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

slope-intercept form is [tex]y = mx + b[/tex] with [tex]m[/tex] being the slope of the line and [tex]b[/tex] being the y-intercept (where the line touches the y-axis)

First we can find [tex]m[/tex] using the formula for slope, [tex]\frac{rise}{run}[/tex] (or [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]), which is the change in y over the change in x.

We can use any points on the line, but I am going to use [tex](4, 3)[/tex] and [tex](3, 1)[/tex] for this example. We can now find the slope.

[tex]\frac{3-1}{4-3} = \frac{2}{1}[/tex]

This means your slope is 2, which means [tex]m[/tex] is 2.

Finding the y-intercept is easy. This line crosses the y-axis at -5, and so [tex]b[/tex] is -5.

Now we can plug in the values into our original equation to get the equation of the line.

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

That is the answer

- Kan Academy Advance

Answer:

x = -2+- sqrt(6)

Step-by-step explanation:

Using completing the square, let x^2+4x-2 = 0 and solve the steps to get the answerx^2 + 4x - 2 =0

add 2 to both sides to get x^2 + 4x = 2

then add 4 to both sides to get x^2 + 4x + 4 = 6

Get the left hand side to the square formate: (x+2)^2 = 6

then simplify x+2 = sqrt(6) or x+2 = -sqrt(6)

so x = sqrt(6) - 2 or x = -sqrt(6) -2

Answer:

Hi,

Step-by-step explanation:

1) PC=PD since PC*PA=PD*PB

2)25 since PO²=PA²+r² PO=14.5, PB=14.5+10.5=25

3)

6²=3*x==> x=12

The height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.

In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.

We have a square pyramid.

Length of the pyramid = 23.4 in

The slant height of the pyramid = 93.2 in

From the figure:

Base length CB  = DC = 23.4 in

In a right-angled triangle, BCD

Applying Pythagoras theorem:

DC² + CB² = DB²

23.4² + 23.4² = DB²

DB = 33.092 in

OB = (1/2)DB

OB = (1/2)33.092 = 16.546 in

In the right-angle triangle AOB, again applying Pythagoras theorem:

AO² + OB² = AB²

h² + 16.546² = 93.2²

AO = h (height of the square pyramid)

AB = slant height = 93.2 in

After calculating, we get:

h = 91.719 ≈ 91.72 in

Thus, the height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.

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