Solve using the zero-factor proper (13x + 7)(6x - 7) = 0​

Answers:

[tex]\text{OA} = \cos(\alpha)\\\\\text{AB} = \sin(\alpha)\\\\\text{DC} = \tan(\alpha)\\\\[/tex]

You can use the word "alpha" without quotes in place of the symbol [tex]\alpha[/tex] if you want (though it will depend if your teacher allows it of course).

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

Explanation:

Focus entirely on triangle AOB.

With respect to reference angle alpha (symbol [tex]\alpha[/tex]), the side OA is the adjacent side since it's the leg closest to or touching the reference angle.

In this same triangle, side OB is the hypotenuse. Because its the radius of the unit circle, we know that OB = 1.

We'll use the cosine rule to connect the adjacent over hypotenuse like so

[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\alpha) = \frac{\text{OA}}{\text{OB}}\\\\\cos(\alpha) = \frac{\text{OA}}{1}\\\\\text{OA} = \cos(\alpha)\\\\[/tex]

So you'll type either [tex]\cos(\alpha)[/tex] or cos(alpha) into the box for OA.

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

We're still working with triangle AOB only.

Side AB is the opposite side with respect to reference angle alpha.

We can say

sin(angle) = opposite/hypotenuse

sin(alpha) = AB/OB

sin(alpha) = AB/1

AB = sin(alpha)

Basically it's almost identical to the previous section's steps, but we're using sine instead of cosine this time. Like before, you can type in either [tex]\sin(\alpha)[/tex] or sin(alpha) depending on your teacher's preferences.

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

This next section can be a bit tricky.

Sides AB and DC are parallel due to them being both vertical. We can use the AA (angle angle) similarity theorem to prove triangle BOA is similar to triangle DOC. The order of the letters is important. The order helps us see how the sides pair up, or how they correspond, so we can form the correct proportion.

The vertical sides of the triangles are AB and DC as mentioned earlier, so they form one fraction AB/DC. I'm dividing small over big.

Another fraction we can form is OA/OC which is dividing the horizontal legs (again small/big).

Overall, due to the similar triangles, we can set up this equation

AB/DC = OA/OC

We'll plug in what we found earlier. Also, OC = 1 because it's another radius of the same unit circle.

Lets solve for side DC.

AB/DC = OA/OC

sin(alpha)/DC= cos(alpha)/1

sin(alpha)*1 = DC*cos(alpha)

DC = sin(alpha)/cos(alpha)

DC = tan(alpha)

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

In summary, segments OA, AB and OC represent the cosine, sine and tangent of the reference angle alpha. These are visual ways to see how the trig ratios correspond to lengths of triangles when connecting them to the unit circle like this.

Side notes:

9514 1404 393

Answer:

  30 grams

Step-by-step explanation:

The time 120 seconds is 4 times the half-life of 30 seconds. That means (1/2)^4 = 1/16 of the original amount will remain. That is (480 g)(1/16) = 30 g.

  30 g of the radioactive rhodium will be left

Answer:

Jenn is correct, as the function has two x-intercepts, at x = -3 and x = 3.

Step-by-step explanation:

x-intercepts of a function:

The x-intercepts of a function are the values of x for which f(x) = 0.

In this question:

[tex]f(x) = x^2 - 9[/tex]

x-intercepts:

[tex]x^2 - 9 = 0[/tex]

[tex]x^2 = 9[/tex]

[tex]x = \pm \sqrt{9}[/tex]

[tex]x = \pm 3[/tex]

Jenn:

Jenn is correct, as the function has two x-intercepts, at x = -3 and x = 3.

Answer:

Step-by-step explanation:

Rhode Island Red chicks = 3.20 Dollars

Buckeye chicks = 3.44 Dollars

For every3 times as 3.44 Dollars, The farmer buys 4 times as 3.20 Dollars so simply Multiply until you reach 70 S0..

3.44 x 3

= 10.32

3.20 x 4

= 12.8

With 7 chicks, combine the prices of the chicks and multiply it by 10.

= 12.8 + 10.32

= 23.12

= 23.12 x 10

= 231.2

So 231.2 Dollars were spent for 70 chicks`in total.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The total cost of farmers' chicks is $231.2

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 5 is an equation.

We have,

Total chicks = 70

4 Rhode Island Red chicks = 3 Buckeye chicks.

Multiply 10 on both sides.

40 Rhode Island Red chicks = 30 Buckeye chicks.

We see that,

40 + 30 = 70

Now,

Rhode Island Red chicks cost = $3.20

Buckeye chicks cost = $3.44

Now,

= 40 x 3.20 + 30 x 3.44

= 128 + 103.2

= $231.2

Thus,

The total cost of farmers' chicks is $231.2

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

1

Step-by-step explanation:

When 1 substract from any number then will get previous number.

Example:

Let any number that is 5

5-1=4

4 is the just previous number of 5

Therefore, number -1 = the previous number

Answer will be 1

The type of sample is a stratified sampling.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data

Given that news reporter at a family amusement park asked a random sample of 20 kids and a random sample of 20 adults about their experience at the park

We need to find the type of sample.

This is a stratified sampling because reporter at a family amusement park asked a random sample of 20 kids and a random sample of 20 adults about their experience at the park

stratified sampling is a method of sampling from a population which can be partitioned into subpopulations.

Hence, the type of sample is a stratified sampling.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ5

Answer:

m-a = n

Step-by-step explanation:

a=m-n

Subtract m from each side

a-m = m-n-m

a-m = -n

Multiply each side by -1

-a+m = n

m-a = n

9514 1404 393

Answer:

  A.  15x +14y = -36

Step-by-step explanation:

Since we are given two points, we can start with the 2-point form of the equation for a line.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (6 -(-9))/(-8 -6)(x -6) +(-9)

  y = 15/-14(x -6) -9

Multiplying by -14, we have ...

  -14y = 15x -90 +126

Adding 14y-36 to both sides gives ...

  -36 = 15x +14y . . . . matches choice A

The standard-form equation is ...

  15x +14y = -36

_____

Additional comments

It can be easier to start with the form ...

  (Δy)x -(Δx)y = (Δy)x1 -(Δx)y1 . . . . . where Δx = x2-x1 and Δy = y2-y1

This gives ...

  (6+9)x -(-8-6)y = 15(6) +14(-9)

  15x +14y = -36 . . . simplified

__

You can also start with the slope-intercept form or the point-slope form, if you're more familiar with those. The result will be the same. I find it handy to be familiar with a number of different forms of the equation for a line.

Answer:

A. A closed plane figure made up of line segments

Step-by-step explanation:

Answer:

A closed plane figure made up of line segments

Answer:

12 / 15

Step-by-step explanation:

4/5 = x /15

15 / 5 = 3

So multiply both numerator and denominator by 3

4/5 * 3/3 = 12 / 15

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

To get this fraction, we multiply top and bottom by 3

4*3 = 12

5*3 = 15

We get the value 3 through trial and error, or you can note how 15/5 = 3.

Step-by-step explanation:

the scale factor k = 5/12

The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

From the figure attached, we are given that Triangle ABC is similar to triangle EFD.

Therefore,

BC/ FD = AC/ ED

These corresponding sides are proportional.

Scale factor;

EF / AB = 5/12

Then Angle between this sides is also equal.

The SAS rule of similarity of triangles states that two triangles will be similar if their corresponding two sides are proportional and the angle between these two sides is equal.

The scale factor k = 5/12 is required to dilate triangle ABC thus, its image, ABC is congruent to triangle EFD.

Learn more about scale factors here:

https://brainly.com/question/11178083

#SPJ2

Answer:

The Question isn't clear

Step-by-step explanation:

Answer:

can someone please answer this question correctly for me. i need it asap

Step-by-step explanation:

Answer:

what's the question???

Answer:

x = 3.721

Step-by-step explanation:

Since, the triangle is right triangle, we can use trignometery equations ;

In this case, we need to use tangent equation in perpendicular :

tan θ = opposite side / adjacent side

Where , we've

tan 28 ° = x / 7

7 × tan 28 ° = 7 × x / 7 ..( Multiply each side by 7 )

7 × tan28° = x

Rewrite

x = 7 tan ×28°

multiply to get

x = 7 × 0.531709432

x = 3.72196602

Answer:

[tex](3 {}^{x} + 2)(3 {}^{x} + 2)[/tex]

hope it is helpful to you

Answer: 139.65 or 25.34.

Step-by-step explanation:

The revenue function will be:

= Price × Quantity

= P × (7,000 - 50p)

= 7000p - 50p²

The coat function is given as:

C = 2,000 + 25q

C = 2000 + 25(7000 - 50p)

C = 2000 + 175000 - 1250p

C = 177000 - 1250p

Then, we'll equate the revenue function to the cost function. This will be:

7000p - 50p² = 177000 - 1250p

-50p² + 7000p + 1250p - 177000 = 0

-50p² + 8250p - 177000 = 0

Divide through by -50

p² - 165 + 3540 = 0

Solving to get the value of P will then give us 139.65 or 25.34.

Answer:

40°

Step-by-step explanation:

because angle In an isosceles triangle base angles are same and angle in a triangle add up to 180° and angle on a straight line add up to 180°

hope this helps:)

1=22e 3663 30-4949-29238342

Answer:

[tex]x = \sqrt{12} = 3.464[/tex]

Step-by-step explanation:

[tex]AC=AD+DC=13\\\text{Because ABC is a right triangle then}\\AB^2=AD.AC\\\Rightarrow AB^2=1 \times 13=13\\\Rightarrow AB = \sqrt{13}\\\text{In the right triangle ABD, since Pythagoras we also have}\\AB^2=AD^2+BD^2\\\Rightarrow BD^2=AB^2-AD^2\\\Rightarrow x^2= 13 - 1=12\\\Rightarrow x = \sqrt{12} = 3.464.[/tex]

Answer:

D. 30

Step-by-step explanation:

f²+g² = (f+g)²-2fg

= 54-24 = 30

12.50 on each ticket

Step-by-step explanation:

12.50 x 4 = 50.00

Answer:

13,456

Step-by-step explanation:

Tn= a+(n-1)d

a is the first term, n is the given number and d is the common difference. d is given by subtracting the first term from the second term or the second from the third. Therefore the the 59th term of the sequence 29, 37, 45 is,

Tn= 29+(59-1)8

=29(58)8

=13,456

Answer:

x=24

Step-by-step explanation:

if x is 24 in x/3, that would give us 24/3 or 8.

8-2=6 :)

Answer:

48.6

Step-by-step explanation:

Given the equation for the line of best fit ; f(x) ≈ 1.8x − 5.4 ;

This equation is used to make prediction for any given value of x ; Here, we are to make prediction for when x = 30

f(x) ≈ 1.8x − 5.4 ; we substitute into the equation, x = 30

f(30) = 1.8(30) - 5.4

f(30) = 54 - 5.4 = 48.6

Prediction at x = 30 is 48.6

Answer:

first one. domain: all real numbers, range: {y | y ≥ 0}

Answer:

The domain is all real numbers

The range is y ≥ 0

Step-by-step explanation:

The domain is the values that x can take

The domain is all real numbers

The range is the values that y can take

The range is y ≥ 0

Answer:

mean = find the total of people in such data by adding up all the totals of people represented by each age then  divide that total by 2.

mean = with cumulative or frequency graphs if the numbers range individually like 25-30 and 30-35 etc and so on then you take the midpoint age and multiply it by the frequency number in new column add up both columns then divide by smaller total.

mean = histogram total number of data ie) from 270 people (80 x 0 = 0), (40 x 2 = 0) and so on multiplying the frequency. then add them all up in new column ie) 380 among 270 people = 1.4  

mode = histogram highest box

median = histogram add up all data number divided by 2 and can draw this on graph as they sort of are in order ie) 15 to the left and 15 to the right

To find standard deviation you need the copulative formula and the notation change for sample shows the small m and s to represent standard deviation ie) m-n is a notation difference for samples of population's

n = number of scores ie)  = 50  

Ex = then sum of x  = would be the collective total  ie) = 270

m = 270/50 = 5.4

Ex^2 = 270 x 270 = 72900   (the square of the total population)

SS = Sum of squares = 72,900 - ( 270^2 / 50) are all the variables.

is the formula  = 71,442

the root of SS -1

S^2 = 270 / (50 -1) =  270/49 = 5.51

S = sqrt S^2 = sqrt SS /n-1 = sq rt 50 = and you get your answer here.

Standard Deviation on data example here shown is;

S = sqrt 5.51 = sqrt 71442 / n-1 = sq rt 71442/ 50-1 = sq rt 71442/49 = 38.1837662  from a 270 population that exists with 50 age group 25 -75 to show the ease here and how to remember.

Just retrace and where 270 is change for total

Where 50 is put 64-25 = 39

and where n-1 is put 39-1 and always subtract first before dividing as the formula protects the brackets as seen in bold.

As your very last formula is S = SS/n-1

Step-by-step explanation:

Answer:

14cm

Step-by-step explanation:

Answer:

28 cm2

14 cm

Step-by-step explanation:

7

___________________

Answer:

C

Step-by-step explanation:

(1/√y)^-1/5

= (1/sqrt(y))^(-1/5)

=sqrt(y)^(1/5)

=y^(1/10)

= (tenth root of y)

=C

:)