7. The ratio of the base to height of a triangle is 3:5. If the area of this triangle is 30, find the lengths of the base and height.​

Answer:

y int (0, 13)

x int (-13/6,0)

just make the x = 0 and solve to get y

same with the x make y =0 and solve

Answer:

in order from the top down

2,5,1,4,5

The functions are illustrations of trigonometry ratios

[tex]\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}[/tex]

The sine of an angle is calculated as follows

[tex]\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}[/tex]

So, we have:

[tex]\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}[/tex]

[tex]\mathbf{sin\theta = \sqrt{1 - (15/25)}}[/tex]

Take LCM

[tex]\mathbf{sin\theta = \sqrt{\frac{10}{25}}}[/tex]

[tex]\mathbf{sin\theta = \frac{\sqrt{10}}{5}}[/tex]

[tex]\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}[/tex]

The tangent of an angle is:

[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]

Using Pythagoras theorem, we have:

[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]

So, we have:

[tex]\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}[/tex]

[tex]\mathbf{Hypotenuse^2 = 10 + 4}[/tex]

[tex]\mathbf{Hypotenuse^2 = 14}[/tex]

Take square roots

[tex]\mathbf{Hypotenuse = \sqrt{14}}[/tex]

So, the sine of the angle is:

[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]

[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}[/tex]

Rationalize

[tex]\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}[/tex]

[tex]\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}[/tex]

The sine of the angles is:

[tex]\mathbf{sin \theta = \frac{1}{csc\theta}}[/tex]

So, we have:

[tex]\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}[/tex]

[tex]\mathbf{sin \theta = \frac{3}{\sqrt{15}}}[/tex]

Rationalize

[tex]\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}[/tex]

[tex]\mathbf{sin \theta = \frac{\sqrt{15}}{5}}[/tex]

[tex]\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}[/tex]

The sine of an angle is calculated as follows

[tex]\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}[/tex]

So, we have:

[tex]\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}[/tex]

[tex]\mathbf{sin\theta = \sqrt{(1 - 9/6)}}[/tex]

[tex]\mathbf{sin\theta = \sqrt{( - 3/6)}}[/tex]

The sine of the angle does not have a real value

[tex]\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}[/tex]

Start by calculating the tangent of the angle

[tex]\mathbf{tan\theta = \frac{1}{cot\theta}}[/tex]

So, we have:

[tex]\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}[/tex]

[tex]\mathbf{tan\theta = \frac{2}{\sqrt 6}}[/tex]

Rationalize

[tex]\mathbf{tan\theta = \frac{2\sqrt 6}{6}}[/tex]

[tex]\mathbf{tan\theta = \frac{\sqrt 6}{3}}[/tex]

The tangent of an angle is:

[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]

Using Pythagoras theorem, we have:

[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]

So, we have:

[tex]\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}[/tex]

[tex]\mathbf{Hypotenuse^2 = 6 + 9}[/tex]

[tex]\mathbf{Hypotenuse^2 = 15}[/tex]

Take square roots

[tex]\mathbf{Hypotenuse = \sqrt{15}}[/tex]

So, the sine of the angle is:

[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]

[tex]\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}[/tex]

Rationalize

[tex]\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}[/tex]

Rewrite as:

[tex]\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}[/tex]

[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}[/tex]

Read more about trigonometry ratios at:

https://brainly.com/question/24888715

Answer:  89674 buckets were produced in 4 months

Answer:

Step-by-step explanation:

First you have to do 5263 / 7 = 751.9 (rounded 751.857143)

Then do 751.9x121.6= 91 431

You get 121.6 because that is how many days are in 4 months.

Hope this helps !!!!

Have a good day/night!!<333

Hello Gumiho!

[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

Find the distance.

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

Refer to the attached picture for the steps.

Answer :- The answer will be (c) [tex]\boxed{\boxed{\tt\sqrt{a^{2} + b^{2}}}}[/tex]

__________________

Hope it'll help you!

ℓu¢αzz ッ

Answer: 22/3 I think

sorry if it’s wrong

Answer:

7 1/3

i hope this helps you can do it

Answer:

7/12

1/6 to 2/12 add 5/12 to get 7/12

Price of one unit Sausage =  1.65

Sum ( Price x Quantity) = Total Expenditure  

Price of Bread x Quantity of Bread + Price of Ketchup x Quantity of Ketchup + Price of Sausage x Quantity of Sausage

Total Expenditure Value = 10 - 0.45  = 9.55

Let price of sausage = P

Therefore, 2 (1.40) + 1 (1.80) + 3 P = 9.55

2.80 + 1.80 + 3 Ps = 9.55

4.6 + 3 P = 9.55

3P = 9.55 - 4.60 =  4.95

P = 4.95 / 3 = 1.65

To learn more, refer https://brainly.com/question/16910784?referrer=searchResults

Answer:

f(8) = 13

Step-by-step explanation:

Step 1: Plug in 8 for the value of x.

Step 2: Multiply 2 by 8.

Step 3: Subtract 3 from 16.

Therefore, f(8) = 13.

Answer:

Step-by-step explanation:

Hi there!

Given;

f(x) = 2x - 3

To find: f(8)

Replace 8 in each place where there is "x" in f(x).

or, f(8) = 2*8 -3

           = 16-3

           = 13

Therefore, f(8) = 13.

Hope it helps!

Answer:

A is the answer

trust me

here is your answer and please follow me and Mark me As brain list

A manufacturer of bicycles has determined that 550 bikes per month will be sold at a price of $250. At a price of $150, it is estimated that 750 bikes will be sold.

a) Determine a linear function (equation) that predicts the number of bikes that will be sold each month at any given price.

b) Use your equation from question a to predict how many bikes will be sold at $350.

Step-by-step explanation:

Option A os Correct

Answer: he is currently 69 years old

Step-by-step explanation:

24x3=72-3=69 lol funni number

Answer:

78 years old

Step-by-step explanation:

In 3 years Joanne will be 27. Xavier is 3 times that age by the time Joanne is 27. 27×3=81. but we're looking for Xaviers age today. so we take 81 and subtract 3 which leaves us with 78

Answer:

the answer is 5.50 or the last one

Step-by-step explanation:

hope this helps

Answer:

answer is $7.5

Step-by-step explanation:

1shirt=$5

10 shirt= ?

10*5= $50

$5= 100%

what about 150%

(5*150)÷100= $7.5

Answer:

450,000

Step-by-step explanation:

The ten thousand digit is 4 and if we compare it to 9, it is bigger then 5 therefore it is rounded up and you get the answer of 450,000

Answer:1. They make policies

2. They perform executive duties

3. They plan environmental and land use policy

Step-by-step explanation:

Answer:

To become rich

Step-by-step explanation:

I'm rich so

Answer: A  F D G

Step-by-step explanation:

Answer: 5 to 20 intervals.

Step-by-step explanation:

hope it helps you

can you BRAINLEST me

Answer:

Step-by-step explanation:

Given lines in standard form:

We can see they have same slopes:

The lines after simplification of the second one:

Since the lines are parallel, use the distance formula:

Substitute the values and find d:

Answer:

Y=-3

You see y=-3 does pass through 2,3 and is also parallel to y=6

i had to do the answer as a pic cuz my iPad is gonna die.

sorry <:)

Answer:

Step-by-step explanation:

x = - 23

y = - 5

z = - 10

(x - 12)/(y+z)=

(-23 - 12)/(-5-10)=

45/15=

7/3

Answer:

-4 and -2✓6+3

Step-by-step explanation:

use pemdas

1(1-8)÷✓1 + 3

-7÷1+3

-4

6(6-8)÷✓6+3

-12÷✓6+3

multiply fraction by ✓6 on bottom and top to get rid of square root on bottom

-12✓6÷6+3

divide -12 by 6 and put radical next to it

-2✓6+3

d

8+2x is the correct answer

Answer:

okay, well, is there any link u wanna post for us to help u? maybe we can explain it?

Step-by-step explanation:

Answer:

9 ft

Step-by-step explanation:

Atea = length* width

what two numbers multiply to 72 but are one number apart

9 * 8

9 is the length since the width is given as being shorter.

other numbers can multiply to 72 but they are not one number apart.

Answer:

9ft

Step-by-step explanation:

Answer:

2x/3y

Step-by-step explanation:

√4x^2/3y

√4√x^2/3y

2x/3y

Answer:

sorry I can't understand the word

Answer: =11/4

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

[tex]5(y - 1) = 3(2y - 5) - (1 - 3y) \\ 5y - 5 = 6y - 15 - 1 + 3y \\ 5y - 5 = 9y - 16 \\ 16 - 5 = 9y - 5y \\ 11 = 4y \\ \frac{11}{4} = y \\ 2 \frac{3}{4} = y \\ [/tex]

Answer:

C) Minimum at (3,7)

Step-by-step explanation:

Recall that vertex form is [tex]y=a(x-h)^2+k[/tex]:

[tex]y=x^2-6x+16[/tex]

[tex]y=(x^2-6x+9)+7[/tex]

[tex]y=(x-3)^2+7[/tex]

Therefore, the vertex is [tex](h,k)[/tex] or [tex](3,7)[/tex] in this case. Because the parabola is positive, then the vertex has to be the minimum of the parabola, making choice C correct.

Answer:

Step-by-step explanation:

4x2 - 8x -12 = 0

divide through by 4

x2 - 2x - 3 = 0

x2 - 3x + x - 3 = 0

(x2 - 3x) + (x - 3) = 0

x(x - 3) + 1(x - 3) = 0

(x + 1) (x - 3) = 0

x + 1 = 0 and x - 3 = 0

x = -1 and x = 3

Answer:

B IS THE ANSWER

Step-by-step explanat

(22x2 -  8x) -  12  = 0

  4x2 - 8x - 12  =   4 • (x2 - 2x - 3)

The first term is,  x2  its coefficient is  1 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -2 .

     -3    +    1    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  1  

                    x2 - 3x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-3)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-3)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-3)

            Which is the desired factorization

4 • (x + 1) • (x - 3)  = 0

A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately  

Any solution of term = 0 solves product = 0 as well.

  Solve  :    x+1 = 0

Subtract  1  from both sides of the equation :  

                     x = -1

   Solve  :    x-3 = 0  

Add  3  to both sides of the equation :  

                     x = 3

Answer

A, C, and D

Step-by-step explanation:

You are trying to find the y value in (x,y) form. Therefore, it has to be A, C, and D because they all have a 6 in the y value.