Choose the correct simplification of the expression -5x(4x-6x^2-3)

Use the half-angle identities.

[tex]\sin^2x=\dfrac{1-\cos2x}2[/tex]

[tex]\implies\sin^4x=\left(\dfrac{1-\cos2x}2\right)^2=\dfrac{1-2\cos2x+\cos^22x}4[/tex]

[tex]\cos^2x=\dfrac{1+\cos2x}2[/tex]

[tex]\implies\sin^4x=\dfrac{1-2\cos2x+\frac{1+\cos4x}2}4=\dfrac{3-4\cos2x+\cos4x}8[/tex]

sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.

Rewrite sin^4(x) in terms of cosine by using the Pythagorean identity for trigonometric functions, which relates sin^2(x) and cos^2(x):

sin^2(x) + cos^2(x) = 1

Now, solve for sin^2(x):

sin^2(x) = 1 - cos^2(x)

Now, square sin^2(x) to get sin^4(x):

(sin^2(x))^2 = (1 - cos^2(x))^2

sin^4(x) = (1 - cos^2(x))^2

So, sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.

for such more question on trigonometric functions

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Answer:

C

Step-by-step explanation:

Charlene has 8 more dollars so you would have to add it all together to get 86.

Answer:

16

Step-by-step explanation:

Input it in the calculator

Answer: 16

Step-by-step explanation:

5 1/7 is 36/7=5.142857

3 1/9 is 28/9=3.1

Do 5.142857 times 3.1

And it equals 15.94 but rounds up to 16.

The answer is:

The area that the want to cover with new grass will be:

[tex]Area_{grass}=8x^{2} -12x-22[/tex]

If we want to calculate what is the ara of the region of the backyard that they want to cover with new grass, we need to calculate the area of the backyard, calculate the area of the swimming pool and its patio, and the last step is to subtract the area of the swimming pool and its patio to the total area of the backyard.

So, to calculate the areas, we need to use the following formula:

[tex]Area=Length*Width[/tex]

Also, we need to remember how the distributive property works, since we are going to need it.

We have that:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

We are given the following information:

For the backyard we have:

[tex]Length=3x-2\\Width=3x+1[/tex]

For the swimming pool and its patio:

Since there it's not mentioned, let be the first expression the length, and the second one, the width.

[tex]Length=x+4\\Width=x+5[/tex]

Then, calculating we have:

Backyard:

[tex]Area_{backyard}=(3x-2)*(3x+1)=9x^{2}+3x-6x-2=9x^{2}-3x-2[/tex]

Swimming pool and patio:

[tex]Area_{swimmingpool}=(x+4)*(x+5)=x^{2}+5x+4x+20=x^{2}+9x+20[/tex]

Now, calculating the area that they want to cover with new grass, we have:

[tex]Area_{grass}=Area_{backyard}-Area_{swimmingPool}\\\\Area_{grass}=(9x^{2}-3x-2)-(x^{2}+9x+20)\\\\Area_{grass}=9x^{2} -x^{2} -3x-9x-2-20\\\\Area_{grass}=8x^{2} -12x-22[/tex]

Hence, we have that the area that the want to cover with new grass will be:

[tex]Area_{grass}=8x^{2} -12x-22[/tex]

Have a nice day!

Answer:

-2

Step-by-step explanation:

the coefficient is the number in front of the variable.

Answer:

x = -4 and x = -12

Step-by-step explanation:

x^2 + 16x + 48 = 0 is to be factored.

Note that 48 is the product of 4 and 12 and that the sum of 4 and 12 is 16.

Therefore,

x^2 + 16x + 48 = 0 in factored form is:

(x + 4)(x + 12) = 0, so that x + 4 = 0 → x = -4, and

                                        x + 12 = 0  → x = -12

Answer:

(x + 4) (x + 12)

Step-by-step explanation:

to factor x² + 16x + 48 = 0, you need to find 2 numbers that when multiplied together give you 48 and when added together give you 16

you can list the factors of 48 and see what adds up together to give you 16, but here is a hint:

the numbers probably end in a 2, 4, 0, 6, 5, or 1, as a pair of these numbers added together give us 6. i looked at a factor chart and saw that 12 and 4 that when added together, give us 16 and when multiplied, give us 48

in factored form it looks like the following:

(x + 4) (x + 12)

this would be the answer in factored form

The 1st and 4th ones

Answer: the correct answers are

1. <EGO ≈ <EOG

4. TW = 1/4GO

Step-by-step explanation:

1. all the angles are corresponding therefore it’s correct

4. TW is 1/2 of PQ therefore it would be 1/4 of GO

Answer: b) -5 ≤ y ≤ 1

Step-by-step explanation:

y = 3 cos (4x) - 2

     ↓                 ↓

amplitude       vertical shift

The amplitude is 3 which gives a range of -3 to 3 but there is also a shift down of 2 units so the new range is: -3 - 2 = -5 to 3 - 2 = 1

-5 ≤ y ≤ 1

Answer:

The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).

Step-by-step explanation:

Given : Sample size(n)= 144

Sample mean [tex]\mu= 22 ug/m^3[/tex]

Standard deviation [tex]\sigma=3.5 ug/m^3[/tex]

To find : 99.7% confident that actual concentration of fine particulates at the school is?

Solution :

The formula for confidence interval is

[tex]CI=\mu \pm z\times\dfrac{\sigma}{\sqrt{n}}[/tex]

Substituting the values in the formula,

[tex]CI=22 \pm 3\times\dfrac{3.5}{\sqrt{144}}[/tex]

[tex]CI=22 \pm 3\times\dfrac{3.5}{12}[/tex]

[tex]CI=22 \pm 3\times 0.2916[/tex]

[tex]CI=22 \pm 0.8748[/tex]

[tex]CI=22+0.8748, 22-0.8748[/tex]

[tex]CI=22.8748, 21.1252[/tex]

Therefore, The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).

Answer:

21 ug/m^3 - 23 ug/m^3

Step-by-step explanation:

Just got it right

Answer:

The factorization of [tex]729x^{15} +1000[/tex] is [tex](9x^{5} +10)(81x^{10} -90x^{5} +100)[/tex]

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form [tex](a^{3} +b^{3} )[/tex] or [tex](a^{3} -b^{3})[/tex]. It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of [tex]729x^{15} +1000[/tex] by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation [tex]729x^{15} +1000[/tex], and the exponent of the letter x is divided by 3.

[tex]\sqrt[3]{729x^{15}} =9x^{5}[/tex]

[tex]1000=10^{3}[/tex] then [tex]\sqrt[3]{10^{3}} =10[/tex]

So, we got that

[tex]729x^{15} +1000=(9x^{5})^{3} + (10)^{3}[/tex] which has the form of [tex](a^{3} +b^{3} )[/tex] which means is a sum of cubes.

Sum of cubes

[tex](a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})[/tex]

with [tex]a= 9x^{5}[/tex] y [tex]b=10[/tex]

2.) Solving the sum of cubes.

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )[/tex]

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)[/tex]

.

Answer:

14n-16

Step-by-step explanation:

Given

[tex]2n - 7 + 3(4n - 3)\\[/tex]

Simplification requires the expression to be in its shortest and concise form. The brackets are opened and addition or subtractions are performed

So,

Multiplying 3 inside bracket

[tex]2n - 7 + 12n - 9[/tex]

Combining alike terms:

[tex]2n+12n-7-9[/tex]

Performing addition and subtractions:

[tex]14n-16[/tex]

Hence the simplified form is:

14n-16 ..

Answer:

the pattern would be W

Step-by-step explanation:

W should be the answer. Hope I helped you lots please count me brainy

Answer:

the number of sheet available is 75, 000

you take the total number of pages available = 8 x 75,000

= 600,000 pages

then each notebooks contains 200 pages

= 600,000 / 200

= 3000 notebooks can be made

Step-by-step explanation:

Answer:

3000 notebooks

Step-by-step explanation:

75,000*8=600000

600000/200=3000

Answer:

Yes he is Correct

Step-by-step explanation:

When multiply with numbers like 10,100,1000 ect or even like 20,200,2000 then you have to break it down. Since multiply by zero equals 0 anyways you will only have to focus on the number that is in front of it. And just and the zeros to the back of the number.

Answer:

Yes he is correct

Step-by-step explanation:

Whenever we are multiplying any number with  10 or multiples of ten we simply add the zeros to the end of that number.

For example:

134 x  10   =  1340

As you can see, to get the answer, you simply need to add 0 to the end of 134

Also 10 x 10 = 100

To get the answer we simply added zero to the end of ten which then give us   100

12 x 10= ?  all you need to do is to add zero to the end of 12 which will give us 120

13 x 100 =?  In this case, since the zeros are two, you will simply add two zeros to the end of  13 which will give you the answer 1300

So Marcel can find 52 times 10 by simply adding a 0 to the end of 52 to get 520 as the correct answer.

Answer:

Point S coordinates= (-4,5)

Step-by-step explanation:

If you would just move the point 5 PLACES TO THE RIGHT, you would get -4, 5, which is the correct answer.

Pie. It’s pie 3.14.... the name of that sign is pie

Answer:

That symbol represents pi.

Step-by-step explanation:

Pi is used by mathematicians to represent the ratio of a circle's circumference to its diameter.  It is approximately equal to 3.14159. Hope this helps!

Answer:

- 864

Step-by-step explanation:

In the case of a 2 × 2 matrix the determinant may be defined as:

|A| = [tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]= ad-bc

Given in the question a matrix

[tex]\left[\begin{array}{cc}-30&-6\\6&30\\\end{array}\right][/tex]

(-30)(30) - (-6)(6)

-900 + 36

- 864

Answer:

Option A: -30

For Odyssey

**If you are on the pre-test then you might wanna take your time because they can suspect if you are cheating**

Answer:

1/2

Step-by-step explanation:

3+7+10=20

20/2=10=1/2

Answer:

147

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

here a = 3 and d = 9 - 3 = 15 - 9 = 6, hence

[tex]a_{25}[/tex] = 3 + (24 × 6) = 3 + 144 = 147

Here is the answer:...

Answer:

- Solve for y

- Subtract  2 x  from both sides of the equation then divide by  5 .

-y = 1 − 2 x 5

Step-by-step explanation:

Answer:

The perimeter is 22.

Step-by-step explanation:

The perimeter formula (it sometimes varies) is 2(b+h)

b being base (in this example, 6)

h being height (in this example, 5)

So now, with substitution, we are left with:

2(6+5)

Which simplifies down to:

2(11)

22

Answer:

(1/2)/(3/4) = (1/2)(4/3) = 2/3

Step-by-step explanation:

ANSWER: Multiply out front and multiply under the radicals. "The radical of a product is equal to the product of the radicals of each factor." "The radical of a quotient is equal to the quotient of the radicals of the numerator and denominator."

Answer:

Step-by-step explanation:

Lateral Area:

The formula of a Lateral Area of a cone:

[tex]L.A.=\pi rs[/tex]

r - radius

s - slant height

We have r = 5m and s = 12m. Substitute:

[tex]L.A.=\pi(5)(12)=60\pi\ m^2\\\\\pi\approx3.14\to L.A.\approx(6)(3.14)=188.4\ m^2[/tex]Surface Area:

The formula of a Surfaace Area of a cone:

[tex]S.A.=B+L.A.[/tex]

In the base we have the circle with the radius r = 5m.

The formula of an area of a circle"

[tex]A_O=\pi r^2[/tex]

Substiute:

[tex]B=\pi(5^2)=25\pi\ m^2\approx(25)(3.14)=78.5\ m^2[/tex]

[tex]S.A.=60\pi+25\pi=85\pi\ m^2\approx188.4+78.5=266.9\ m^2[/tex]

Answer:

Not all relationships are functions, but all functions are also relationships

Step-by-step explanation:

A relationship is a correspondence between two sets of values.

A relationship assigns values from an output set called range to a set and input called a domain.

On the other hand, a relation is a function if and only if there is only one value of the output set (Range) assigning to each value of the input set (Domain).

In other words, if an input value [tex]x_1[/tex] is assigned two or more output values [tex]y_1[/tex], [tex]y_2[/tex], [tex]y_3[/tex] .. then the relationship is not a function. This means that not all relationships are functions.

[tex]y=\±\sqrt{x} +3[/tex]   is a relation but it is not a function.

because when x = 4 then y = 1 and y = 5.

Not all relationships are functions, but all functions are also relationships

Final answer:

A relation is a set of ordered pairs, while a function is a relation where each input value is associated with only one output value. Not every relation is a function, but every function is a relation.

Explanation:

A relation is a set of ordered pairs where each input value is associated with one or more output values. On the other hand, a function is a relation where each input value is associated with only one output value.

Not every relation is a function. For example, the relation {(1,2), (1,3), (2,4)} is not a function because the input value 1 is associated with two different output values (2 and 3). However, every function is a relation because it establishes a relationship between the input and output values.

Answer:

the probability is very high 86% > 14%

Step-by-step explanation:

55+20+11= 86%/100% 100-86=14% chance there will not be any rain or lightning

hope this helps!!

Answer:

4/21

Step-by-step explanation:

In this case, carry out the indicated operations from left to right:

8      1

---- * --- = 4/21

7       6

Answer:

the population would be 30.28 billion by 2020

Step-by-step explanation:

y=6.08 + 1.21x

y = 6.08 + 1.21(20)

y = 6.08 + 24.2

y = 30.28

Answer: B=27

Step-by-step explanation:

10.8 x 5=54/2= 27

Answer:

26in.^2 the first choice

Step-by-step explanation:

Just did the QC

Answer:

(x-2)(x+4)

Step-by-step explanation:

So it would be A.

Explanation: The middle number is 2 and the last number is -8.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 2

Multiply together to get -8

Can you think of the two numbers?

Try -2 and 4:

-2+4 = 2

-2*4 = -8

Fill in the blanks in

(x+_)(x+_)

with -2 and 4 to get...

(x-2)(x+4)

Answer:

(x−2)(x+4)

A. (x+4)(x-2). The factorization of the quadratic equation x²+2x-8 given by the graph is (x+4)(x-2).

From the graph shown in the image we can see the parabola's cut points, in the y-axis is -4 and the x-axis is 2, then we write the product changing the signs (x+4)(x-2) = x²+2x-8