Which expression is the best estimate of 1.25 + (-2.69)?

Answer:

Second answer

Step-by-step explanation:

We are given [tex]\displaystyle \large{\sec \theta = -3}[/tex] and [tex]\displaystyle \large{\sin \theta > 0}[/tex]. What we have to find are [tex]\displaystyle \large{\cot \theta}[/tex] and [tex]\displaystyle \large{\cos \theta}[/tex].

First, convert [tex]\displaystyle \large{\sec \theta}[/tex] to [tex]\displaystyle \large{\frac{1}{\cos \theta}}[/tex] via trigonometric identity. That gives us a new equation in form of [tex]\displaystyle \large{\cos \theta}[/tex]:

[tex]\displaystyle \large{\frac{1}{\cos \theta} = -3}[/tex]

Multiply [tex]\displaystyle \large{\cos \theta}[/tex] both sides to get rid of the denominator.

[tex]\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}[/tex]

Then divide both sides by -3 to get [tex]\displaystyle \large{\cos \theta}[/tex].

Hence, [tex]\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}[/tex]

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Next, to find [tex]\displaystyle \large{\cot \theta}[/tex], convert it to [tex]\displaystyle \large{\frac{1}{\tan \theta}}[/tex] via trigonometric identity. Then we have to convert [tex]\displaystyle \large{\tan \theta}[/tex] to [tex]\displaystyle \large{\frac{\sin \theta}{\cos \theta}}[/tex] via another trigonometric identity. That gives us:

[tex]\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}[/tex]

It seems that we do not know what [tex]\displaystyle \large{\sin \theta}[/tex] is but we can find it by using the identity [tex]\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}[/tex]  for [tex]\displaystyle \large{\sin \theta > 0}[/tex].

From [tex]\displaystyle \large{\cos \theta = -\frac{1}{3}}[/tex] then [tex]\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}[/tex].

Therefore:

[tex]\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}[/tex]

Then use the surd property to evaluate the square root.

Hence, [tex]\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}[/tex]

Now that we know what [tex]\displaystyle \large{\sin \theta}[/tex] is. We can evaluate [tex]\displaystyle \large{\frac{\cos \theta}{\sin \theta}}[/tex] which is another form or identity of [tex]\displaystyle \large{\cot \theta}[/tex].

From the boxed values of [tex]\displaystyle \large{\cos \theta}[/tex] and [tex]\displaystyle \large{\sin \theta}[/tex]:-

[tex]\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}[/tex]

Then rationalize the value by multiplying both numerator and denominator with the denominator.

[tex]\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}[/tex]

Hence, [tex]\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}[/tex]

Therefore, the second choice is the answer.

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Summary

[tex]\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}[/tex]

[tex]\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}[/tex]

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = 3/2 , the value of b is -9.

Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.

Given

The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = 3/2 .

The axis of the symmetry is given by;

[tex]\rm x=\dfrac{-b}{2a}[/tex]

The value of x is 3/2 and a is 3.

Substitute all the values in the formula

[tex]\rm x=\dfrac{-b}{2a}\\\\\dfrac{3}{2}=\dfrac{-b}{2 \times 3}\\\\\dfrac{3}{2}=\dfrac{-b}{6}\\\\ -b = \dfrac{6 \times 3}{2}\\\\ b = \dfrac{=18}{2}\\\\b =-9[/tex]

Hence, the value of b is -9.

To know more about the axis of symmetry click the link given below.

https://brainly.com/question/12896816

Answer:

P=18

Step-by-step explanation:

45/20= 40.5/P

45p=810

p=18

Answer:

(© 105 + 90 = (52 - 70)

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{6}{3}=\frac{AC}{6}\\AC=12[/tex]

Answer:

sin(90-25) = sin(65)

Step-by-step explanation:

cos(a) = sin(90-a)

The distributive property is basically expanding brackets.

So if you take 3(x + 4) = 36 and remove the brackets (so multiplying out the 3), you get:

3x + 12 = 36

And from there you simplify :)

3x + 12 = 36

3x = 24

x = 8

The distributive property was used to multiply the 3 through the brackets, thus making the equation easier to solve I guess

Step-by-step explanation:

Answer:

19.5552

Step-by-step explanation:

34.92 x 0.56

Use calculator or use long multiplication.

    3492

       ×56

  20952

+17460  

195552

How many numbers are after the point on both of the numbers?

2 each. 2 + 2 = 4

We will take our result 4 points back or divide it by 10^4

195552 / 10000 = 19.5552

Answer:

K=49π cm^2

Step-by-step explanation:

Area of a circle: πr^2

r=7

7^2=49

Therefore, the answer is 49πcm^2

Answer:

so you don't have to give me points but I can explain how to do it

Step-by-step explanation:

so for number 1. it says y=3x-7 and the equation is 5x+4y=6

so basically your plugging in y so

5x+5(3x-7)=6 and you will get your answer

Answer:

D) 10

Step-by-step explanation:

Singe a right triangle has to be 90 degrees, 60+(3*10)=90:)

therefore x=10

Answer:

D

Step-by-step explanation:

the angles 60 and 3x form a right angle , then

60 + 3x = 90 ( subtract 60 from both sides )

3x = 30 ( divide both sides by 3 )

x = 10 → D

The value of the logarithm function log₅25 is 2. Then the correct option is C.

Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.

The logarithmic form of 25 will be

We know that if the base of the logarithm is the same as the number then the value of the logarithm will be 1 one that is given as

[tex]\rm log_a a = 1[/tex]

Then take the log with the base value of 5.

log₅25 = log₅5²

log₅25 = 2 × log₅5

log₅25 = 2

The value of the logarithm function log₅25 is 2. Then the correct option is C.

More about the logarithm link is given below.

https://brainly.com/question/7302008

Answer:

c

Step-by-step explanation:

Answer:

No, you did not get a B+, you got an 85.6% for the class

Step-by-step explanation:

So, let's split the grades into different parts:

Quiz: 15%

Exam1: 15%

Exam2: 15%

Exam3: 15%

Homework: 10%

Final: 30%

Each part of the grade adds up together to be 100%, so here, we are going to multiply each weighting of the grade with the average amount of points you got for each assignment then add it all up.

(Notice how I convert the percentages to decimals to make it easier to multiply)

Quiz: 0.15(85) = 12.75

Exam1: 0.15(78) = 11.70

Exam2: 0.15(81) = 12.15

Exam3: 0.15(92) = 13.80

Homework: 0.10(85) = 8.50

Final: 0.3(89) = 26.70

Adding these all up:

12.75 + 11.70 + 12.15 + 13.80 + 8.50 + 26.70 = 85.6

You got an 85.6% for the class, which is not a B+

Feel free to ask any questions you may have in the comments! :D

Answer:

a. geometric

b. an =  2(2)^n-1 or an = 2^n

c. an+1 = an x 2

Step-by-step explanation:

The sequence, 2, 4, 8, 16, 32,...

a. The sequence is geometric because there is a common ratio in the numbers of the sequence. Each number is made by multiplying the common ratio and the previous number.

b. The explicit formula that can be used to find any term is an =  2(2)^n-1 or an = 2^n

Note: the variable n and number 1 is written in italics to show that it should be in subscript

an = a1 (r)n-1

With the common ratio of n being 2 and first number being 2, we have:

an =  2(2)^n-1

or

an = 2^n

c. The recursive formula for the sequence is an+1 = an x 2

an+1 = an x r

Plugging in the values, we have

an+1 = an x 2

Your welcome, and comment if you have any questions! If you could mark this answer as brainliest, I would appreciate it very much!

Answer:

Step-by-step explanation: well the  anwser is 48

Answer:

12x-8

Step-by-step explanation:

Answer:

12x-8

Step-by-step explanation:

Answer:

12/52 or 3/13

Step-by-step explanation:

So lets go over what we know:

There are 12 face cards in a deck of cards

There are 52 cards in a deck

So there are 12 face cards out of 52 cards.

The ratio of this is:

12 : 52

This looks like this in fraction form:

[tex]ratio1 : ratio2[/tex] =   [tex]\frac{ratio1}{ratio2}[/tex]

So the ratio 12 : 52 = [tex]\frac{12}{52}[/tex]

So the answer is 12/52(this can be simplified to 3/13)

Hope this helps!

Step-by-step explanation:

You need to find the n( A n B ) and then continue the process, if you have any question revert back to me...

Answer:

(C) 30πcm

Step-by-step explanation:

In order to find circumference you use the formula C (circumference)=2(pi)(r) in which r is the radius. In this case, two and 15 are thirty so to find the circumference all you have is the equation 30 times pi centimeters is equal to the Circumference.

Answer:

R325

Step-by-step explanation:

Cost to buy shoes (x)

x = 175 * 50

x = 8750

At this point they've lost R8750 (-8750)

7500 = -8750 + 16250

To make an overall profit of R7500 they would need to sell the shoes at

16250 / 50 = R325

Color combinations used in a presentation

2

The overall look of a presentation

4

A typeface without decorative extensions on the ends of the letters

5

The difference between objects

3

A tool used in presentation planning

1

The statement that is true about her rate of change in elevation is  She descended at a rate of 920 feet per hour.

From the question, Jacinta traveled from an altitude of 4,450 feet above sea level to an altitude of 150 feet below sea level, then the total distance traveled will be

D = 4450 + 150

D = 4600 feet

If Jacinta drove at a constant speed and the trip took her five hours, her rate will be expressed as:

Rate = Total distance/Time

Rate = 4600/5

Rate = 920 feet perhour

Hence the statement that is true about her rate of change in elevation is  She descended at a rate of 920 feet per hour.

learn more on rate of change here: https://brainly.com/question/8728504

Answer:

Step-by-step explanation:

Answer:

(a) the objective is to determine if the artificial light from e-Readers also disrupted sleep.

sorry thats all i know

Answer:

y=3x-4

Step-by-step explanation:

If we substitute the values of the points (-3, -13) (-1, -7), and (2, 2) into the equation, we can see that it's right.

[tex]6 \frac{2}{3} = \frac{2}{18} = 9[/tex]

[tex]3 \times \frac{1}{2} = \frac{1}{6} = 6[/tex]

6×9=54

Answer:

V= π r2h

is this right