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.

Answer:

[tex]h^{-1}(x) = \frac{4}{3}x + \frac{23}{3}[/tex]

Step-by-step explanation:

Given

Graph h:

[tex](x_1,y_1) = (1,-5)[/tex]

[tex](x_2,y_2) = (9,1)[/tex]

Required

Plot [tex]h^{-1}(x)[/tex]

First, calculate h(x)

Calculate slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{1--5}{9-1}[/tex]

[tex]m = \frac{6}{8}[/tex]

[tex]m = \frac{3}{4}[/tex]

The equation is:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = \frac{3}{4}(x - 1) -5[/tex]

[tex]y = \frac{3}{4}x - \frac{3}{4} -5[/tex]

[tex]y = \frac{3}{4}x + \frac{-3 - 20}{4}[/tex]

[tex]y = \frac{3}{4}x - \frac{23}{4}[/tex]

Next, calculate [tex]h^{-1}(x)[/tex]

Swap y and x

[tex]x = \frac{3}{4}y - \frac{23}{4}[/tex]

Solve for y

[tex]\frac{3}{4}y = x + \frac{23}{4}[/tex]

Multiply through by 4

[tex]3y = 4x + 23[/tex]

Divide through by 3

[tex]y = \frac{4}{3}x + \frac{23}{3}[/tex]

Replace y with [tex]h^{-1}(x)[/tex]

[tex]h^{-1}(x) = \frac{4}{3}x + \frac{23}{3}[/tex]

See attachment for graph

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

Sides of a square is = 7 + 3x

Therefore,

Perimeter of a square = 4 × side

= 4 × (7 + 3x )

= 28 + 12x (Ans)

Answer:

4 mugs of hot chocolate

Step-by-step explanation:

So, we must find out how many mugs of hot chocolate we can make.  

Then we set up a ratio of amount of chocolate to mugs such as  

(2/5) / (1/10) = (2/5)(10/1) = 20/5 = 4 mugs of hot chocolate

Hope this answer helps you :)

Have a great day

Mark brainliest

[tex]\huge\color{purple}\boxed{\colorbox{black}{♡Solution♡}}[/tex]

Step-by-step explanation:

[tex]10 - 5 \frac{2}{3} \\ = 10 - \frac{17}{3} \\ = \frac{10 \times 3}{1 \times 3} - \frac{17}{3} \\ = \frac{30 - 17}{3} \\ = \frac{13}{3} \\ = 4 \frac{1}{3} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer: 28

Step-by-step explanation:

The multiples of 7 that's less than 30 include: 7, 14 , 21 and 28.

From the numbers above,

7 isn't divisible by 4 as it gives a remainder.

14 isn't divisible by 4 as it gives a remainder.

21 isn't divisible by 4 as it gives a remainder.

28 is divisible by 4 without a remainder

Therefore, the correct answer should be 28

Answer:

28

Step-by-step explanation:

28/2=14

28/4=7

28/7=4

28 is an even number

Step-by-step explanation:

28 is the answer

28 is a number between 20 and 30

and divisible by

28/2=14

28/4=7

28/7=4

Answer: Approximately 1.0233 meters

Round this however you need to

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

Work Shown:

Refer to the drawing below.

sin(angle) = opposite/hypotenuse

sin(17) = x/3.5

3.5*sin(17) = x

x = 3.5*sin(17)

x = 1.02330096652958

x = 1.0233

Be sure that your calculator is in degree mode.

Answer:

a rectangle

Step-by-step explanation:

because 2 sides are the same the other 2 arent it has four sides with straight angles

Answer:

B.

Step-by-step explanation:

Answer:

ans: additive inverse is -5

multiplicative inverse is 1/5

Step-by-step explanation:

adding what value to 5 makes it 0 i.e

5 + (- 5)= 0 ( so additive inverse is -5)

multiplying what value to 5 makes it 1 i.e

5×( 1/5)=1 ( so multiplicative inverse is 1/5)

Answer:

0.52

Step-by-step explanation:

100% - 48% = 52%

[tex]\frac{52}{100}[/tex]

0.52

Answer:

-1+i

Step-by-step explanation:

(2+5i)+(-3-4i)

=(2-3)+i(5-4)

=-1+i

Answer:

[tex]−1+i[/tex]

Step-by-step explanation:

[tex](2+5i)+(−3−4i)[/tex]

[tex]2+5i−3−4i[/tex]

[tex]−1+5i−4i[/tex]

[tex]−1+i[/tex]

Answer:

1x= 28

y= v7vub8b9nf7v6v

Answer:

Step-by-step explanation:

(-7*6)(c*c^6) = -42c^7

Answer:

The trace of the water left on the floor is 566 cm.

Step-by-step explanation:

The bicycle wheel has a circular shape, therefore;

1 revolution is the same as the circumference of the wheel. So that 3 revolutions is the same as multiplying the circumference of the wheel by 3.

circumference = 2[tex]\pi[/tex]r

where r is the radius of the wheel (r = 30 cm).

Thus,

circumference = 2 x [tex]\frac{22}{7}[/tex] x 30

                        = [tex]\frac{1320}{7}[/tex]

circumference = 188.57 cm

3 revolutions = 3 x 188.57

                      = 565.71 cm

Therefore, the trace of the water left on the floor is 566 cm.

Answer:

Answer is in picture

Step-by-step explanation:

Hope it is helpful...

answer: 116⁰

z⁰ for y⁰ because it's

equal

Answer:

The car uses less gas

They use the same amount of gas after [tex]\frac{640}{7}[/tex] miles

Step-by-step explanation:

Given

The table represents the car mileage

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

First, calculate the car's slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

From the table, we have:

[tex](x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)[/tex]

So, we have:

[tex]m = \frac{10.5 - 13.5}{180 - 60}[/tex]

[tex]m = \frac{-3}{120}[/tex]

[tex]m = -\frac{1}{40}[/tex]

Calculate the equation using:

[tex]y = -\frac{1}{40}(x - 60)+13.5[/tex]

[tex]y = -\frac{1}{40}x + 1.5+13.5[/tex]

[tex]y = -\frac{1}{40}x + 15[/tex]

[tex]m = -\frac{1}{40}[/tex] implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

By comparison to: [tex]y = mx + b[/tex]

[tex]m = -\frac{1}{5}[/tex]

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

[tex]1/40 < 1/5[/tex]

This means that the car uses less gas

Solving (b): Distance traveled for them to use the same amount of gas.

We have:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

[tex]y = -\frac{1}{40}x + 15[/tex] --- The car

Equate both

[tex]-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15[/tex]

Collect like terms

[tex]\frac{1}{40}x -\frac{1}{5}x =-31 + 15[/tex]

[tex]\frac{1}{40}x -\frac{1}{5}x =-16[/tex]

Take LCM

[tex]\frac{x - 8x}{40} = -16[/tex]

[tex]\frac{- 7x}{40} = -16[/tex]

Solve for -7x

[tex]-7x = -640[/tex]

Solve for x

[tex]x = \frac{640}{7}[/tex]

Answer:

B

Step-by-step explanation:

Have a nice day

Answer:

B as well

Step-by-step explanation:

As you can work out the area of rectangle by l ×w

which is 18×36 =648

and you can also work out the area of a segment which is

[tex]\pi \times {r}^{2} \div 2[/tex]

so pi ×18^2÷2 and then add 648 you get 1156.9.

Answer:

Step-by-step explanation:

By using the utility for the line of best fit,

Equation of the line of best fit will be,

y = 1.5x + 1.32

Here, y - intercept of the line = 1.32

Here, y-intercept represents the amount of bean production when the level of water applied was zero.

Answer:

13510 ft

Step-by-step explanation:

I have attached a triangle diagram to depict this situation.

From the diagram, we see that distance between A and B is denoted by x.

Now, from trigonometric ratios in this type of triangle, let's first find y.

6400/y = tan 36

y = 6400/tan 36

y = 8808.84 ft

Now, we can find x from;

6400/(8808.84 + x) = tan 16

6400/tan 16 = 8808.84 + x

22319.452 = 8808.84 + x

x = 22319.452 - 8808.84

x ≈ 13510 ft

The distance the plane traveled from point A to point B is 13510 ft

Here we assume the distance between A and B should be x.

Now the y value should be

[tex]6400\div y = tan 36\\\\y = 6400\div tan 36[/tex]

y = 8808.84 ft

Now, we can find x

[tex]6400\div (8808.84 + x) = tan\ 16\\\\6400\div tan\ 16 = 8808.84 + x[/tex]

22319.452 = 8808.84 + x

x = 22319.452 - 8808.84

x ≈ 13510 ft

Learn more about distance here: https://brainly.com/question/785292

Answer:

1. B

2. B

3. B

4. A

5. D

6. A

7. C

8. D

9. A

10. C

Answer:

0.0181 probability of choosing a king and then, without replacement, a face card.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability of choosing a king:

There are four kings on a standard deck of 52 cards, so:

[tex]P(A) = \frac{4}{52} = \frac{1}{13}[/tex]

Probability of choosing a face card, considering the previous card was a king.

12 face cards out of 51. So

[tex]P(B|A) = \frac{12}{51}[/tex]

What is the probability of choosing a king and then, without replacement, a face card?

[tex]P(A \cap B) = P(A)P(B|A) = \frac{1}{13} \times \frac{12}{51} = \frac{1*12}{13*51} = 0.0181[/tex]

0.0181 probability of choosing a king and then, without replacement, a face card.

Answer:

a=-4

Step-by-step explanation:

See image below:)

Answer:

After simplify answer will be :[tex]\frac{5p}{18}[/tex]

Step-by-step explanation:

Given data:

[tex]\frac{2p}{3} *\frac{5p}{12}[/tex]

Now,

[tex]\frac{10p}{36}[/tex]

Final answer would be :

[tex]\frac{10p}{36}=\frac{5p}{18}[/tex]

72/360 = x/10pi

1/5 = x/10pi

x = 2pi

6.3 cm

Answer:

X y better because it has X and Y is no no

Answer:

A

Step-by-step explanation:

|4 − y| = 1

drop absolute value lines

create two problems

4 - y = 1

and

4 - y = -1

solve for y

Answer:

x = 4.48

Step-by-step explanation:

read the picture