Jen factored x² - 4x - 21 as (x - 3)(x + 7) What did she do wrong?

Answer:

[tex]A_{\Delta ABP}=\sin \theta[/tex]

Step-by-step explanation:

Let the center of the circle be O.

Recall that the area of a triangle can be given by:

[tex]\displaystyle A=\frac{1}{2} ab\sin C[/tex]

Where C is the angle between the two sides.

ΔABP is equal to the sum of ΔAPO and ΔBOP.

Let a = OP and b = OB. Since this is the unit circle and PO and BO are radii, they both equal one. C will be θ. Hence, the area of ΔBOP is:

[tex]\displaystyle A_{\Delta BOP}=\frac{1}{2}(1)(1)\sin \theta=\frac{1}{2}\sin\theta[/tex]

For ΔAPO, we can use the two sides OP and OA. Again, they are the radii of the unit circle, so they equal one. The angle in this case will be π - θ radians. Hence:

[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}(1)(1)\sin\left(\pi -\theta\right)=\frac{1}{2}\sin\left(\pi -\theta\right)[/tex]

However, note that sin(π - θ) = sin(θ). Hence:

[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}\sin\left(\theta\right)[/tex]

Hence, the area of ΔABP is:

[tex]\displaystyle A_{\Delta ABP}=\frac{1}{2}\sin \theta+\frac{1}{2}\sin\theta =\sin \theta[/tex]

Answer:

22.5

Step-by-step explanation:

Inscribed Angle =1/2 Intercepted Arc

F = 1/2 (45)

<F = 22.5

Answer:

01:04

Step-by-step explanation:

add 7 minutes to 22:57 to get 23:04. then add 2 hours to get to 01:04.

Answer:

1

Step-by-step explanation:

Answer:

See Below.

Step-by-step explanation:

Problem A)

We have:

[tex]\displaystyle \csc^2\theta \tan^2\theta -1=\tan^2\theta[/tex]

When in doubt, convert all reciprocal trig functions and tangent into terms of sine and cosine.

So, let cscθ = 1/sinθ and tanθ = sinθ/cosθ. Hence:

[tex]\displaystyle \left(\frac{1}{\sin^2\theta}\right)\left(\frac{\sin^2\theta}{\cos^2\theta}\right)-1=\tan^2\theta[/tex]

Cancel:

[tex]\displaystyle \frac{1}{\cos^2\theta}-1=\tan^2\theta[/tex]

Let 1/cosθ = secθ:

[tex]\sec^2\theta -1=\tan^2\theta[/tex]

From the Pythagorean Identity, we know that tan²θ + 1 = sec²θ. Hence, sec²θ - 1 = tan²θ:

[tex]\tan^2\theta =\tan^2\theta[/tex]

Problem B)

We have:

[tex]\sin^3x=\sin x-\sin x \cos^2 x[/tex]

Factor out a sine:

[tex]\sin x(\sin^2 x)=\sin x-\sin x\cos^2 x[/tex]

From the Pythagorean Identity, sin²θ + cos²θ = 1. Hence, sin²θ = 1 - cos²θ:

[tex]\sin x(1-\cos^2 x)=\sin x-\sin x\cos^2x[/tex]

Distribute:

[tex]\sin x- \sin x \cos^2 x=\sin x-\sin x\cos^2 x[/tex]

Problem C)

We have:

[tex]\displaystyle \frac{\cos 2x+1}{\sin 2x}=\cot x[/tex]

Recall that cos2θ = cos²θ - sin²θ and that sin2θ = 2sinθcosθ. Hence:

[tex]\displaystyle \frac{\cos^2 x-\sin^2 x+1}{2\sin x\cos x}=\cot x[/tex]

From the Pythagorean Identity, sin²θ + cos²θ = 1 so cos²θ = 1 - sin²θ:

[tex]\displaystyle \frac{2\cos^2 x}{2\sin x\cos x}=\cot x[/tex]

Cancel:

[tex]\displaystyle \frac{\cos x}{\sin x}=\cot x[/tex]

By definition:

[tex]\cot x = \cot x[/tex]

Answer:

16

Step-by-step explanation:

8/1/2

8 divided by 1/2

8 x 2/1 = 16

Answer:

Step-by-step explanation:

P=8/V

1/2=8/V

do cross multiplication

2*8=V*1

16=V

Step-by-step explanation:

missing where ?

I guess you mean that there is one element missing between 51 and 33 (based on the readable answer options).

if that is true, then the missing element is 42.

the difference between 60 and 51 is 9.

the difference between 51 and 33 is 18.

if there is an engender missing in between 51 and 33, then it is logical to put it in the middle cutting the interval of 18 in half to 2 times 9. which is also supported by the first interval between 60 and 51 (9).

so, it would be 51 -9 = 42

Answers:

These values are approximate

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

Explanation:

The circumference formula is

C = 2*pi*r

which rearranges to

r = C/(2pi)

when solving for r.

Plug in the given circumference to find that

r = C/(2pi)

r = (39,750)/(2pi)

r = 6,326.40898790283

For the sake of the most accuracy possible, I'm using my calculator's stored version of pi (and not something like pi = 3.14); if your teacher requires you to use pi = 3.14 then follow those instructions of course.

The radius is roughly 6326 km when rounded to the nearest integer.

Keep in mind that the earth isn't a perfect sphere, but rather a slightly squished one. This means the earth is slightly fatter than it is tall. However, for the sake of this problem, we'll assume it's a sphere.

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

Once you determine the circumference, aka distance around the circle, we can figure out the next problem: determining the distance from the north pole to the equator. This distance runs along a line of longitude, so it's a north-south distance.

Again, imagine the earth is a perfect sphere. This means that the equator circumference is the same as the circumference as a full longitude line when we travel the globe only along that line. In other words, start at the north pole, travel along that specific longitude only until you reach the south pole. Then staying on that line, travel back to the north pole going around the backend of the earth.

That full circular path we traveled will get cut into 1/4 because 1/2 the circumference is the portion from north to south pole, and then we cut that distance in half when going from north pole to the equator.

(1/4)*(6,326.40898790283) = 1,581.6022469757

That rounds to 1582 km

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

Side notes:

Answer:

(-0.5, -1)

Step-by-step explanation:

A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising)

Answer:

The focus is: [tex](0,2)[/tex]

Step-by-step explanation:

Given

[tex]y = \frac{1}{8}x^2[/tex]

Required

Determine the focus

The focus of a parabola

[tex](x- h)^2 = 4p(y - k)[/tex]

is:

[tex](h,k+p)[/tex]

So, we have:

[tex]y = \frac{1}{8}x^2[/tex]

Cross multiply

[tex]8y = x^2[/tex]

Rewrite as:

[tex]x^2 = 8y[/tex]

Rewrite as:

[tex](x - 0)^2 = 8(y - 0)[/tex]

Express 8 as 4 * 2

[tex](x - 0)^2 = 4 * 2(y - 0)[/tex]

By comparison with: [tex](x- h)^2 = 4p(y - k)[/tex]

[tex]h = 0[/tex]    [tex]p =2[/tex]     [tex]k = 0[/tex]

So, the focus [tex](h,k+p)[/tex] is:

[tex](h,k+p) = (0,0+2)[/tex]

[tex](h,k+p) = (0,2)[/tex]

Answer:

sí, (yo) quiero un chocolate

Answer:

I don't know the answer

Step-by-step explanation:

c.1

Answer:

3/8

Step-by-step explanation:

There is a 1/2 probability one die will be odd because 1, 3, and 5 are the only possible odd numbers.

Since you want 3/4 of the dice to be odd, you multiply 1/2 by 3/4 to get 3/8.

I believe it is 3/8.

Answer:

9/24 or 3/8

Step-by-step explanation:

3/6 (3 out of the 6 sides are odd)

3/4 (3 out of 4 die)

Multiply together

3/6 * 3/4= 9/24

so 9/24 is the answer... you can simplify it to 3/8.

ur welcome :)

[tex]3.09375[/tex] ✅

Step-by-step explanation:

[tex] \frac{11}{8} \div \frac{4}{9} \\ = \frac{11}{8} \times \frac{9}{4} \\ = \frac{11 \times 9}{8 \times 4} \\ = \frac{99}{32} \\ = 3.09375[/tex]

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

9514 1404 393

Answer:

  w = 8t

Step-by-step explanation:

If we assume that the ounces of water are proportional to the time, then the equation will look like ...

  w = kt

for some constant k.

Solving for k, we find ...

  k = w/t

Using the given values, we find k to be ...

  k = (32 ounces)/(4 seconds) = 8 ounces/second

The units are stated in the definitions of the variables, so we can write the equation as ...

  w = 8t

Answer:

They are congruent

Step-by-step explanation:

The reason that WK is congruent to WL is because both come from the same origin of W and they both end up in the same place on their side. Which means if WK and WL are congruent, that means that AK and AL are congruent as well.

The answer is 'Right'.

Step-by-step explanation:

Sum of angles in a triangle = 180°

Angle C = 180 - 58 - 32

= 90°

90° is defined as a right angle.

Therefore, triangle ABC is classified as a right-angled triangle.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

8000, 8000, 7000, 11000, 15000, 17000, 20000, 1000000.

Mean = Σx / n = 1086000 / 8 = 135750

Median = 1/2(n+1)th term = 8000

The lower quartile :

Q1 = 1/4(n+1)th term

Q1 = 8000

Q3 = 3/4 (n+1)th term

Q3 = 18500

IQR = 18500 - 8000 = 10500

OUTLIER :

8000 - (1.5*(10500)) = - 7750

18500 + (1.5*(10500)) = 34250

10% trimmed mean

10% * 8

Cut off 1 from the top and bottom

Data becomes : 8000, 8000, 11000, 15000, 17000, 20000

Trimmed mean = 13166

Answer:

D

Step-by-step explanation:

Pitágoras

A^2 = B^2 + C^2

A^2 = 14^2 +5^2

A^2 = 196 + 25

A = √221

Answer:

tan B =  12 /5

sin B =  12/13

cos B =  5/13

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan B = opp/ adj = 12 /5

sin B = opp/hyp = 12/13

cos B = adj/hyp = 5/13

Answer:

Sine of B = 12/13

Cos of B = 5/13

Tan of B = 12/5

Step-by-step explanation:

In this case, the opposite is 12, the adjacent is 5 and the hypotenuse is 13.

sin is opposite/hypotenuse

cos is adjacent/hypotenuse

and

tan is opposite/adjacent

Answer:

y=mx+b

Step-by-step explanation:

so that is b right?

that means its what number you start the y on

Answer:

[tex] x_{1} = 3 + \sqrt {6} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Step-by-step explanation:

Given the quadratic equation;

x² - 6x + 3 = 0

To find the roots of the quadratic equation, we would use the quadratic formula;

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 1, b = -6 and c = 3

The quadratic equation formula is;

[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]

Substituting into the formula, we have;

[tex] x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - (12)}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - 12}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {24}}{2} [/tex]

[tex] x = \frac {6 \pm 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6 + 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = 3 + \sqrt {6} [/tex]

Or

[tex] x_{2} = \frac {6 - 2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Answer:

160,000

Step-by-step explanation:

                   251

                × 638

     _______________

                2008

                753

    +       1506

__________________

            160138

Product to the  nearest thousand = 160,000            

Answer:

AOB = 65

DOE = 35

AOC = 90

EOB = 115

DOB = 80

Answer:

x=3

Step-by-step explanation:

2 triangles are proportional so we have

4/6=x/4,5

--> x=(4.4,5)/6=3

You can also use sin cos but this way is faster

Answer

Step-by-step explanation:

Replace x and y

[tex](3 \: \: \: 25)[/tex]

[tex]y = 6x + 7 \\ 25 = 6 \times 3 + 7 \\ 25 = 18 + 7 \\ 25 = 25[/tex]

So, the point (3,25) lie on the line y=6x+7

hope this helps you.

Have a nice day!

9=6y + 33 the answer is  y=−4

the next one is   x=10

Step-by-step explanation:

Answer:

hope it helped u :)

Step-by-step explanation:

[tex]9 + 6y = 33\\6y = 33 - 9\\6y = 24\\y = 4\\\\\\-4(2-1.2x) = 40\\-8 + 4.8x = 40\\4.8x = 48\\x = \frac{48}{4.8} = \frac{48 \times 10}{48} = 10[/tex]