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.

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.

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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.

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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.

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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.

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

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

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]

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

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)

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:

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

Answer:

C

Step-by-step explanation:

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

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.

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:) :)

Answer:

8

Step-by-step explanation:

eight letters

there is only one who has 8 letters in the name

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.

Answer:

x-10x=100

-9x=100

-9x÷-9=100÷-9

x=-11,1

Answer:

i think 471.24cm³?

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

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

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)

Answer:

.169

Step-by-step explanation:

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

Answer:

_ = 5

Step-by-step explanation:

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]

Answer:

23x - 8 is the answer in simplify that expression

Answer:

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

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

hope it helps...

have a great day!!

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

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

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.

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.

Answer:

I have the same doubt so pls answer

Step-by-step explanation:

x^2 + 13x + 22 = 0

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

x = - 11 Or x = - 2

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