Given Tan A= 2/3 and that angle A is in quadrant 1, find the exact value of sec A in simplest radical form using a rational denominator.

Answers

Answer 1

Answer:

[tex]\sec A =\frac{\sqrt{13}}{3}[/tex]

Step-by-step explanation:

Given

[tex]\tan A = 2/3[/tex]

Required

[tex]\sec\ A[/tex]

First, we have:

[tex]\tan A = \frac{x}{y}[/tex]

Where

[tex]x \to oppo site\\[/tex]

[tex]y \to adja cent[/tex]

[tex]z \to hypotenuse[/tex]

So:

[tex]\tan A = \frac{x}{y} =\frac{2}{3}[/tex]

By comparison:

[tex]x = 2; y =3[/tex]

Using Pythagoras, we have:

[tex]z^2 = x^2 +y^2[/tex]

[tex]z^2 = 2^2 +3^2[/tex]

[tex]z^2 = 13[/tex]

[tex]z = \sqrt{13[/tex]

[tex]\sec A =\frac{z}{y}[/tex]

[tex]\sec A =\frac{\sqrt{13}}{3}[/tex]


Related Questions

Determine if the two triangles are congruent. If they are State how you know. NO LINKS!!!​

Answers

Problem 25

These triangles are congruent.

The reasoning is the AAS congruence theorem. We have two pairs of congruent angles, as shown by the arc markings, and a pair of congruent sides. The sides are not between the angles. That means AAS is slightly different from ASA. The order matters.

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

Problem 26

The triangles are not congruent

Why not? Well it all comes down to the angle placement. For the triangle on the right side, the arc is between the shared segment and the segment with the double tickmarks. The other arc is not in the proper corresponding location to be able to use SAS. It would need to be adjacent to the arc on the right for us to use SAS.

If it's hard to visualize what I mean, refer to the diagram below.

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

Problem 27

The triangles are congruent by SAS

The angles aren't marked, but recall that vertical angles are always congruent. So you could add in angle markers if you wanted, to help complete the diagram. The tickmarks of course tell us which segments are the same length. The angles are between the segments.

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

Problem 28

The triangles are congruent by SSS

Like before, the tickmarks tell us which sides are the same length. So the tickmarks say that we have two pairs of congruent sides. The overlapping sides or shared sides are the third pair of congruent segments. So in reality, we have three pairs of congruent sides. It might help to break up the figure into two separate triangles.

Joseph leans a 20-foot ladder against a wall so that it forms an angle of 69° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest hundredth of a foot if necessary.

Answers

Answer:

18.67 ft

Step-by-step explanation:

     |\

     |   \

     |      \

h    |         \     20 ft

     |            \

     |               \

     |--        69°  \

     ---|----------------

For the 69° angle, h is the opposite leg, and 20 ft is the hypotenuse.

sin A = opp/hyp

sin 69° = h/20

h = 20 * sin 69°

h = 18.67

Answer: 18.67 ft

Could someone help please I'm stuck and need desperate help???

Answers

Answer:

9/64π

Step-by-step explanation:

The area of a circle is given as :

Area = πr²

The diameter of the circle = 3/4 in

Radius of circle = diameter / 2 = (3/4) ÷ 2 = (3/4) * 1/2 = 3/8 in

Area = π(3/8)²

Area = π * 9/64

Area = 9/64π

H Н
Which two statements are both true?
Di Ta and KFT
EH I TĞ and KT | TG
Di I K and Di 1 ET
ET I TĞ and KF | DI

Answers

A and b are not true because

What is the domain of function p?
p(x) = /x-1+2

Answers

Answer:

A.

Step-by-step explanation:

a strange question, as 2 answer options are actually possible, as they define valid domains for this function.

and if the range of the function would include imaginary numbers ("i"), all 4 would be correct.

the problem statement has to be much more precise. you can tell your teacher that.

but I assume, we base just on real numbers and want the biggest domain range. and that is A.

A. for x=1 we get sqrt(0) + 2, which is absolutely valid.

B. a square root of a negative number is undefined in the works of real numbers. we would need "i", the imaginary numbers, to make this a valid function.

C. is also valid. no bad values and expressions involved. it is just a snake range than A.

D. the same a for B.

The domain of the function [tex]f(x) = \sqrt{x - 1} + 2[/tex] is [tex][1,\infty)[/tex]

How to determine the domain?

The function is given as:

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

Set the radicand greater than or equal to 0

[tex]\sqrt{x - 1} \ge 0[/tex]

Take the square of both sides

[tex]x - 1 \ge 0[/tex]

Add 1 to both sides

[tex]x \ge 1[/tex]

This means the possible values of x starts from 1 till infinity

Hence, the domain of [tex]f(x) = \sqrt{x - 1} + 2[/tex] is [tex][1,\infty)[/tex]

Read more about domain at:

https://brainly.com/question/1770447

What is the equation of the line that is parallel to the line defined by the equation y = 3x + 6 and goes through the point (3, 2)?
options:
y = 2x – 1
y = 3x – 7
y = 2x + 4
y = 4x + 3
y = -2x + 9

Answers

Answer:

Step-by-step explanation:

Parallel lines have the same slope. The slope of the given line is 3. The easy way to do this, the one that uses our logical brains as opposed to our mathematical brain, tells us that since there is only one choice that has a given slope of 3, that is the one that we want. The second choice down is the only one that has a slope of 3.

Mathematically,

[tex]y-2=3(x-3)[/tex] and

[tex]y-2=3x=9[/tex] and

[tex]y=3x-9+2[/tex] so

y = 3x - 7 (the second choice)

please answer correctly thanks​

Answers

a = 0.06
b = 0.08
c = 133

George buys a pizza. He eats 3/8 of the pizza for lunch and 1/4 of the pizza for dinner. What fraction of the pizza has George eaten?

Answers

Answer:

5/8

Step-by-step explanation:

Make denominators equal

1/4 = 2/8 (Multiply both sides by 2 to get a common denominator)

2/8 + 3/8 = 5/8

answer:
5/8
step-by-step explanation:
3/8 he ate 3 pieces
1/4 = 2/8 he ate 2 pieces
2 + 3
5/8

Solve the linear equations
1/4(x-5)+4=1/3(2x+7)-5/6

Answers

Answer:

x = 3

Step-by-step explanation:

Given the linear equation :

1/4(x-5)+4=1/3(2x+7)-5/6

(x-5)/4 + 4 = (2x+7)/3 - 5/6

Take the lcm and sum

(x-5+16)/4 = (4x+14-5)/6

(x+11)/4 = (4x+9)/6

Cross multiply

6(x+11) = 4(4x+9)

6x + 66 = 16x + 36

Collect like terms

6x - 16x = 36 - 66

-10x = - 30

x = 30/10

x = 3

How many kiloliters are there in 19,000 milliliters?


A. 19
B. 1.9
C. 0.019
D. 0.0019

Answers

Answer:

C

Step-by-step explanation:

To convert milli- to kilo-, move the decimal point six places to the left

need help asap! The graphs below have the same shape. what is the equation of the red graph?

no links​

Answers

Answer:

B. [tex]g(x) = x^{3} - 5[/tex]

Step-by-step explanation:

The graph of f(x) is the graph of g(x) translated 5 units downwards.

Simplify by combining like terms. − 5 p + 4 m − 2 p + m

Answers

Answer:

-7p  +5m

Step-by-step explanation:

− 5 p + 4 m − 2 p + m

Combine like terms

-5p -2p   +4m +m

-7p  +5m

Answer:

-7p+5m

Step-by-step explanation:

See image below:) :)

help? (the last part of it “what is rhe shortest name lengths” is what i need help) :) (i mark brainlist)

Answers

3
I think the question is referring to the number of letters in a name and 3 is the lowest number of letters in a name in the class

Answer:

8

Step-by-step explanation:

eight letters

there is only one who has 8 letters in the name

3 consecutive integers have a sum of 27. What are the integers?

Answers

Three consecutive integers that add up to 27 are 8, 9, and 10

Hope this helps =)

First represent your 3 consecutive integers as x, x + 1, and x + 2.

Since their sum is 27, our equation reads x + (x + 1) + (x + 2) = 27.

Now simplifying on the left side we get 3x + 3 = 27.

You should be able to easily solve for x and find that x = 8.

Make sure you list all your answers.

If x is 8, then x + 1 is 9 and x + 2 is 10.


X – 10x = 100
Use a trial and improvement method to find this solution.
Give
your answer correct to 1 decimal place.
You must show all your working.
On the same line as your final answer you must write “to 1 decimal place"

Answers

Answer:

x-10x=100

-9x=100

-9x÷-9=100÷-9

x=-11,1

Need help for this please

Answers

Answer:

i think 471.24cm³?

i just found the volume for both the cylinder and cone and added them together.

What is the area and perimeter of the triangle

Answers

Answer:

Area = 20yd

Perimeter = 23 yd

Step-by-step explanation:

Area = 1/2 ×bh

b, which I the base = 10yd

h, which is the height = 4yd

Note: 5yd is the base because when you turn the triangle you will see that 10yd is the base and 5yd is the height not 8yd because 8 yd is not a straight line at a right angle

Therefore;

Area = 1/2× 10 × 4

= 1× 5 × 4

= 20yd

Perimeter = 8yd +5yd +10yd

= 13yd + 10yd

= 23yd

The points (-18, 15) and (-20, 15) lie on a circle with a radius of 1.
Find the coordinates of the center of the circle.​

Answers

Answer:

Step-by-step explanation:

eq. of any circle with center (h,k) and r=1 is

(x-h)²+(y-k)²=1²

points (-18,15) and (-20,15) lie on it.

(-18-h)²+(15-k)²=1

(15-k)²=1-(-18-h)²

and (-20-h)²+(15-k)²=1

(15-k)²=1-(-20-h)²

so 1-(-18-h)²=1-(-20-h)²

-(18+h)²=-(20+h)²

324+36h+h²=400+40h+h²

40h-36h=324-400

4h=-76

h=-19

(15-k)²=1-(-18-(-19))²=1-1=0

k=15

so center is (-19,15)

Sung Lee invests $3,000 at age 18. He hopes the investment will be worth $9,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.​

Answers

Answer:

.169

Step-by-step explanation:

I hoped I helped you solve sorry if I'm wrong

(2x-3)(x+4)=2x2+_-12

Answers

Answer:

_ = 5

Step-by-step explanation:

Which expression is equivalent to Cube root of 343 x Superscript 9 Baseline y Superscript 12 Baseline z Superscript 6?

7x3y4z2
7x3y6z2
49x3y6z2
49x3y4z2

Answers

9514 1404 393

Answer:

  7x^3y^4z^2

Step-by-step explanation:

  [tex]\displaystyle\sqrt[3]{343x^9y^12z^6}=\sqrt[3]{(7x^3y^4z^2)^3}=\boxed{7x^3y^4z^2}[/tex]

Answer:

[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]

Step-by-step explanation:

[tex] \small \sf \leadsto \: \sqrt[3]{343 \: x {}^{9} \: y{}^{12} \: z {}^{6} }[/tex]

[tex] \small \sf \leadsto \: \sqrt[3]{7x {}^{3}y {}^{6}z {}^{2} } [/tex]

[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]

Determine the value of x

1)70
2)140
3)40
4)280

Answers

180-140= 40

Im not so sure of my answer so I might be wrong so enjoy!!

3(7x)-2(4-x) simplify the expression

Answers

Answer:

23x - 8 is the answer in simplify that expression

Answer:

[tex]3(7x)-2(4-x)[/tex]

[tex]21x-2(-x+4)[/tex][tex](21x+2x)-8[/tex][tex]23x-8[/tex]

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

hope it helps...

have a great day!!


Can someone please help me with this problem?

Answers

Answer:

C 6

Step-by-step explanation:

Pythagoras

c² = a² + b²

117 = x² + (x+3)² = x² + x² + 6x + 9 = 2x² + 6x + 9

=>

108 = 2x² + 6x

54 = x² + 3x

0 = x² + 3x - 54 = (x-6)(x+9)

just think by what numbers can we divide 54 without any remainder (so that when multiplying we get 54) ? and which pair of these have a difference of 3 (so that with +/- combination we get "3x" in the multiplication)?

the solutions for x are the 2 numbers that would make one of the bracket expressions 0, as this turns the whole expression to 0.

x = 6 and x = -9

a negative number does not make any sense for a side length.

so, the only possible solution is x = 6

PLEASE HELP!! WILL MARK BRAINLIEST TO WHOEVER GET IT RIGHT

Answers

Answer:

neither, since the gradients are not the same, as well as the c value

Step-by-step explanation:

First line : y = -4x + 7

Second line : y = -4x + 3

We know that the standard form of equation of a line is y = mx + c

where :

m is the slope

c is the y intercept

Comparing both line equations with the standard form, we can notice that :

 Slope of the first line = -4

 Slope of the second line = -4

We know that Slopes of parallel lines are same

So, We can conclude that the given two lines are parallel to each other

Answer : Parallel because the slopes are the same


[tex] \frac{9}{11} = 0. |?| |?| [/tex]
list the digits that repeat​

Answers

Step-by-step explanation:

9/11=0.81818181....

the digits that repeat is 81

Answer:

.81 repeating

Step-by-step explanation:

9/11 = 0.81 repeating.

.An ice cream vendor serves 4 flavors: vanilla, chocolate, strawberry, and mint. If the
vendor selects two flavors at random, what is the probability that vanilla and strawberry
are chosen?

Answers

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

This question may be relatively tricky. Since no specific order is stated or implied, it does not matter whether the vendor chooses vanilla or strawberry first, as long as the vendor chooses both.

Therefore, for the first flavor the vendor can either choose vanilla or strawberry. There is a [tex]\frac{2}{4}=\frac{1}{2}[/tex] chance of this happening.

For the second flavor, the vendor must choose the one they didn't pick for the first flavor (either strawberry or vanilla). There is a [tex]\frac{1}{4}[/tex] chance they do so.

Therefore, there is a [tex]\frac{1}{2}\cdot \frac{1}{4}=\boxed{\frac{1}{8}}[/tex] chance that vanilla and strawberry are chosen.

Deborah finds that the theoretical probability of flipping "heads" on a fair coin was 50%. After she flipped the fair coin 100 times, she calculated that she flipped "heads" 45 times. What is the percent difference in theoretical and experimental probability?

Answers

Answer:

I have the same doubt so pls answer

Step-by-step explanation:

Solve x2 + 13x + 22 = 0 using the quadratic formula.

Answers

x^2 + 13x + 22 = 0

( x + 11 )( x + 2 ) = 0

x = - 11 Or x = - 2

A salesperson at DHL Department Store earns $415 per hour and is paid biweekly. FOr the last pay cycle, a sales rep earned 5% commission on sales amounting to $89,500. Calculate their basic wage if they worked for 40 hours each week. please help me, Thanks

Answers

Answer:

=$21075

Step-by-step explanation:

Given data

Earnings =$415 per hour

Commission =5%

Sales =$89500

Time =40 hours

Let us find the commission

5/100*89500

0.05*89500

=4475

Let us find the amount earned in 40 hours

40*415

=16600

Total

=16600+4475

=21075

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