trigonometric identities Simplify cos^2 theta -1/ 4 sin^2 theta

To factorize a polynomial you need to find the zeros, and then you can write the polynomial as a product of bynomials.

For a polynomial of the form:

[tex]p(x) = A_n*x^n + A_{n-1}*x^{n-1} + ... + A_1*x + A_0[/tex]

We define the zeros as the values of x such that:

p(x) = 0.

On the above case, the degree of the polynomial is n (the maximum exponent). Then the number of zeros of the polynomial is n (same as the degree).

Once we know the n zeros, we can factorize the polynomial as:

[tex]p(x) = A_n*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]

For example, for the polynomial:

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

The two zeros are x = 2 and x = -2, then it can be rewriten as:

[tex]p(x) = 2*(x + 2)*(x - 2)[/tex]

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Answer:

X=70

Step-by-step explanation:

aw we can for a triangle, where the 2 angles are complementary from the outer ones, so the 2 angles are 50, and 60

so the third one will be 70

Step-by-step explanation:

the median is the value, where half of the other values is smaller (or equal), and the other half bigger (or equal).

with an even number of data points that is not directly possible to find.

in this case the 2 middle values are taken and their mean value is the median.

in our case, the 2 middle values are 12 and 14.

their mean value is

(12+14)/2 = 26/2 = 13

so,

13 is the median (even though if is not a data point itself).

Answer:

2/7  ?

Step-by-step explanation:

Because 1/4 divided by 7/8th is 1/4. Hope this works

Answer:

4x ÷ 7

Step-by-step explanation:

the product of 4 and a number (x)

would be 4x. Then you would divide by 7.

The amount of iced tea left in quartz is  3 quartz

The coach makes 9 quarts of iced tea.

she fills 12 bottles with 2 cups of iced tea each to share with her team.

1 quartz = 4 cups

Therefore, she shared the following amount of tea in cups:

amount shared = 12 × 2 = 24 cups

Then, let's convert to quartz,

4 cups = 1 quartz

24 cups = ?

amount shared in quartz = 24 / 4 = 6 quarts

Therefore,

the amount of ice tea left = 9 - 6 = 3 quartz

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Answer:

10 percent

Step-by-step explanation:

look closl

it's 10 percent ...................... 10%

Answer:

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you 1. 2 M, 2R, 2 P are placed in shelf randomly P(similar a…

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Transcribed image text: Your Turn Find the probability using permutation with repetition 1. There are 2 mystery books, 2 romance books, 2 poetry books to be randomly placed on a shelf. What is the probability that the mystery books are next to each other, the romance books are next to each other, and the poetry books are next to each other? (For example, MMRRPP). 2. The school jazz band has 4 boys and 4 girls, and are randomly lined up for a yearbook photo. Find the probability of getting all of the boys grouped together.

Step-by-step explanation:

CORRECT ME IF IM WRONG

Answer:

41.34

Step-by-step explanation:

We can use the Pythagorean theorem to solve for the distance. First we will create an imaginary triangle with the leg lengths being the x distance and y distance between the 2 points and the hypotenuse being the distance between the 2 points.

x distance =

[tex]15 - (-20) = 35[/tex]

y distance =

[tex] |-17-5| = | - 22| = 22[/tex]

We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle

xdistance²+ydistance²=distance²

35²+22²=distance²

1709=distance²

[tex] \sqrt{1709} = distance[/tex]

In decimal form the distance would be around 41.34.

That is the answer

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Answer:

A rational number is a number that can be expressed as a fraction (the ratio of two integers).  

Integer:  A whole number that can be positive, negative, or zero.

To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:

[tex]\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}[/tex]

[tex]\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}[/tex]

[tex]\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}[/tex]

[tex]\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}[/tex]

Therefore, [tex]\sf \sqrt{12.1}[/tex] is not a rational number.

Step-by-step explanation:

a rhombus is a parallelogram with 4 identical sides.

it has therefore two pairs of equal angles.

as any quadrilateral the sum of all interior angles is 360°.

(and yes, as add-on, the diagonals bisect each other at right angles).

so, one interior angle is 79°.

that means it has a twin that is also 79°.

together they have 79×2 = 158°.

that leaves

360 - 158 = 202°

for the other 2 angles (they must be equal too).

so, each of them has

202/2 = 101°

so, the other 3 angles are

79°, 101°, 101°

Problem 1

Triangle ABE is similar to triangle DCE. This is because we have two pairs of congruent corresponding angles.

Refer to the angle angle (AA) similarity theorem for more info.

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

For the other pair of triangles, we don't have enough info to determine if they are similar or not. We have info about one pair of sides, and a pair of angles, but that's about it.

We need to know if JL is proportional to MO, and in the same ratio as KL & NO are, if we wanted to use the side angle side (SAS) similarity theorem.

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

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

Problem 2

Divide the corresponding sides

We see the three ratios are equal to the same value (2) and that proves the triangles LNM and POQ are similar by the SSS (side side side) similarity theorem.

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

Like before, we'll divide the corresponding sides

We don't have a match. Let's try rotating the second rectangle so that the side '8' is horizontal, and the side '3' is vertical

We don't have a match here either. There are other approaches we could take, but basically the two rectangles are not similar.

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

Answer:

-66

Step-by-step explanation:

add the numbers

-26 -37 = -66

[tex] - 26 - 37 = - 63[/tex]

Whenever the sign of the numbers is same , add them but don't forget the negative sign.

Please give brainliest

Answer:

36

Step-by-step explanation:

Question:

[tex] \bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]

Solution:

Here, we need to use PEMDAS rule, where:

There's a rule as well, the sum given is need to solved from the left, whichever sign is there.

Solved:

[tex]\bigg(\cfrac{10}{2} \bigg)\times 7 + 5 - 4[/tex]

Solve for parentheses first:

[tex] = 5 \times 7 + 5 - 4[/tex]

Then multiplication of course:

[tex] = 35 + 5 - 4[/tex]

Then addition:

[tex] = 4 0 - 4[/tex]

[tex] =36[/tex]

Hence, the answer is 36.

Answer:

4. x = 9 and y = 18

Step-by-step explanation:

Hello there!

When given such a problem we have to methods to handle this:

On this problem, let's limit ourself to substitution method;

x + y = 27 ..................... eq.1

y = 2x ........................ eq.2

Eq.2 is already manipulated. Substitute it into eq.1

x + y = 27

=> x + 2x = 27

3x = 27

x = 9

Substitute x into eq.2

y = 2 (9)

= 18

In terms of x and y;

(x, y) => (9, 18)

I hope this helps you.

Have a nice time and nice studies.

Collin's sampling method will better represent the entire population.

Determine which sampling method will better represent the entire population.

From the question, we understand the Collin selected random names from the school directory.

While Karl surveyed only the students sitting close to him.

Karl's method is biased because students sitting far from him do not have a chance of being surveyed.

Hence, Collin's sampling method will better represent the entire population.

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Answer:

Discount amount = 34

Step-by-step explanation:

Discount amount = 202 - 168 = 34

Answer:

So the two numbers are {15, 25}.

Step-by-step explanation:

Simultaneous Equations:

xy = 375

x = y + 10

Subsitute the Second One into the First:

(y + 10)y = 375

y^2 + 10y - 375 = 0

y = 15 [and not -25 (natural numbers are not negative)]

Solve for x by Substituing y in the Second Equation:

x = 15 + 10

x = 25

Solution:

So the two numbers are {15, 25}.

Answer:

  15 and 25

Step-by-step explanation:

The given relations between the two numbers allow you to write a system of equations. Algebraic solution of the system involves the solution of a quadratic equation. The numbers are "natural numbers", so are both positive integers.

__

Let x and y represent the smaller and larger of the two numbers, respectively. The given relations are ...

  y = x +10 . . . . . . the larger is 10 more than the smaller

  xy = 375 . . . . . . their product is 375

Substituting for y in the second equation, we have ...

  x(x +10) = 375

Adding (10/2)² will complete the square.

  x² +10x +25 = 375 +25 . . . . add 25

  (x +5)² = 400 . . . . . . . . . . . write as a square

  x +5 = √400 = 20 . . . . . . positive square root

  x = 20 -5 = 15

  y = x +10 = 25

Those two numbers are 15 and 25.
__

The attachment shows a graphical solution of the equations.

_____

Additional comment

Your number sense tells you that both numbers end in 5. Their geometric mean is √375 ≈ 19.4, so the first numbers that deserve consideration are numbers ending in 5 that are either side of this value: 15 and 25.

You can also consider their arithmetic mean. If that is represented by z, then we have (z-5)(z+5)=375  ⇒  z²-25=375  ⇒  z²=400  ⇒  z=20, and the two numbers are 20±5.

(x+8/3)²+y²=1

(x+8/3)²+y²+0²+2×0y=1

(x+8/3)²+(y+0)²=(V1)²

->center: C(8/3,0)

-> radius: V1

The value of x for which the lines m and l are parallel is 31 degrees

The given diagram includes two parallel lines m and l, since the line are parallel hence the sum of the angles 105 and 3x - 18 are supplementary that is;

105 + 3x - 18 = 180

Simplify for the value of x

87 + 3x = 180

3x = 180 - 87

3x = 93

x = 93/3

x = 31

Hence the value of x for which the lines m and l are parallel is 31 degrees

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The area of the triangle DEF is 2 square units

The given parameters are:

D(9,-8), E(8,-3), and F(2,-5),

The area of the triangle is calculated using:

Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |

This gives

Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |

Evaluate

Area = 0.5|4|

Expand

Area = 2

Hence, the area of the triangle DEF is 2 square units

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Answer:

see the attachment photo!

The different ways Johnny can improve his meal is 16

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]  ways.

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

Given;

Mother tells him he may only make two additions to his meal

First addition; 1C4

Second addition; 1C4

1C4=4

=4x4

=16

Therefore, by combinations and permutations their will be 16ways

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Answer:

[tex]2( \frac{2}{5} x + 2) = \frac{4}{5} x + 4[/tex]

Step-by-step explanation:

Use the distributive property.

The probability that can be chosen by Jake will be 33.5%.

The area of the whole dartboard will be:

= πr²

where r will be:

= 3 + (4 × 4)

= 3 + 16

= 19

Area = π(19)² = 361π²

The area of 30, 40, and 50 points will be:

= π × [3 + (2 × 4)]²

= 121π²

The probability will be:

= (361π - 121π) × 100

= 33.5%

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