Simplify the expression. 1/2 (-sin2x - cos 2x)

Answer:

(2/3)^2

Step-by-step explanation:

A simplification of the expression 4/9 to the second power is [tex](\frac{2}{3} )^2[/tex]

In Mathematics and Geometry, an exponent is a mathematical operation that is commonly used in conjunction with an expression, so as to raise a given quantity to the power of another.

Mathematically, an exponent can be modeled by this mathematical expression;

[tex]b^n[/tex]

Where:

the variables b and n are numerical values, letters, or an expression.

n is known as a power.

By applying the law of indices for powers (division) to the given equation, we would have the following simplified expression:

[tex]\frac{4}{9} =\frac{2^2}{3^2} \\\\\frac{4}{9} =(\frac{2}{3} )^2[/tex]

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Answer:9

Step-by-step explanation:

Answer:

b=8

Step-by-step explanation:

Solution steps:

-7b=-56

b=-56 / -57

b=8

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ b = 8}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 7b = - 56}[/tex]

divide both sides of the equation by -7

[tex] \sf{ \dashrightarrow\frac{ - 7b}{ - 7} = \frac{ - 56}{ - 7} }[/tex]

Calculate

[tex] \dashrightarrow \sf{b = 8}[/tex]

Hope I helped!

Best regards! :D

Answer:

[tex]y = \frac{9x^2}{2} + c[/tex]

Step-by-step explanation:

Given

[tex]\int\limits^ _[/tex][tex](x + 8x) dx[/tex]

Required

(a) Integrate

(b) Check using differentiation

To integrate, we make use of the following formula;

if

[tex]\frac{dy}{dx} = \int\limits^{} _{} ax^n[/tex]

then

[tex]y = \frac{ax^{n+1}}{n+1}[/tex]

So; [tex]\int\limits^ _[/tex][tex](x + 8x) dx[/tex] becomes

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

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

[tex]y = \frac{x^{2}}{2} + 4x^2 + c[/tex]

Take LCM

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

[tex]y = \frac{9x^2}{2} + c[/tex]

To check using differentiation, we make use of

if [tex]y = ax^n[/tex], then

[tex]\frac{dy}{dx} = nax^{n-1}[/tex]

Using this formula

[tex]y = \frac{9x^2}{2} + c[/tex] becomes

[tex]\frac{dy}{dx} = 2 * \frac{9x^{2-1}}{2}[/tex]

[tex]\frac{dy}{dx} = 2 * \frac{9x}{2}[/tex]

[tex]\frac{dy}{dx} =9x[/tex]

[tex]9x = x + 8x[/tex]

So;

[tex]\frac{dy}{dx} = x + 8x[/tex]

In geometry, a line is completely straight and stretches in both directions infinitely. In contrast, a line segment is a line that doesn't go on forever but rather has a fixed set length. A line segment has two endpoints. A ray has only one endpoint and the other side extends forever.

Answer:

Levene confidence intervals ( b )

Step-by-step explanation:

T- test should include all of the following in the results section except the  Levene confidence intervals.The confidence intervals may be constructed for various power values using the binomial distribution.

The dependent measure , the size and the Homogeneity of variance test are all included in the results section of a t-test

No option is greater than the value of 1.45.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values.

Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples.

The given number is 1.45. The given options are:-

A. 0.009

B. 0.019

C. 0.0032

D. 0.0177

All the options are less than the value of 1.45. Therefore, No option is greater than the value of 1.45.

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Answer:

[tex]5x^5+5xyz+7xy+8x[/tex]

Step-by-step explanation:

When putting an equation in standard form, you always prioritize the term with the most variables - unless terms have a greater exponent.

The prioritization order is:

Exponents

Amount of variables

Value of coefficient

So, [tex]5x^5[/tex] is the only term with an exponent in this expression, so it will go first.

Next up, we have to choose between [tex]8x[/tex], [tex]5xyz[/tex], and [tex]7xy[/tex]. We know that [tex]5xyz[/tex] has more variables than the other ones, so it goes next.

Now we're left with [tex]7xy[/tex] and [tex]8x[/tex]. [tex]7xy[/tex] has more variables than [tex]8x[/tex], so it goes next.

This leaves [tex]8x[/tex] last.

So, the expression becomes [tex]5x^5+5xyz+7xy+8x[/tex].

Hope this helped!

Answer:

Step-by-step explanation:

y + 5 = 1(x - 7)

y + 5 = x - 7

y = x - 12

Answer:

(-1,4)

Step-by-step explanation:

(2x+8)/6=1/3(x+4)

3(2x+8)=6(x+4)

6x+24=6x+24.

0=0.

∴There are no real solutions.

Answer:

$1 for one tube

Step-by-step explanation:

Ratio is 10:10

if you keep on reducing it

you will eventually get to 1:1

Therefore, the answer is $1 for one tube

Answer:

4

Step-by-step explanation:

0</x/<5

0</1, 2, 3, 4/>5

(1,2,3,4) there are 4 numbers that are greater than 0 and less than 5.

Answer:

8

Step-by-step explanation:

All possible answers are 1,2,3,4,-1,-2,-3, and -4. Since we are using the absolute value here, the opposites of the positive values are also included.

Answer:

  89/100

Step-by-step explanation:

The average weighted by the number of students is ...

  (90(0.90) +10(0.80))/100 = (81 +8)/100 = 89/100

312 ft²

3 rectangles

2 triangles

4 yd = 12 ft

A = 4ft×12ft + 8ft×12ft + 10ft×12ft + 2×6ft×8ft/2

= 48ft² + 96ft² + 120ft² + 48ft²

= 312 ft²

Answer:

336

Step-by-step explanation:

Got it right

You are welcome :)

Answer:75

Step-by-step explanation:

90-15=75

Answer:

He has 75 tacos left.

90 - 15 = 75.

Answer:

Angle ABC is bisected by BD

BC =Half AC

2 mangle DBC =mangle ABC

Answer:

(a) How many are there to select 2 pairs of gloves?

10 ways

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

130 ways

Step-by-step explanation:

For the above questions we apply that combination formula

(a) How many are there to select 2 pairs of gloves?

There are 5 pairs of gloves according to the question above, hence:

5C2 = 5!/2! × (5 - 2)!

= 5!/2! × 3!

= 5 × 4 × 3 × 2 × 1/2 × 1 × 3 × 2 × 1

= 10 ways.

Therefore, there are 10 ways to select 2 pairs of gloves

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

i) A way to select 4 gloves out of 10 gloves =

10C4 = 10!/4! ×(10 - 4)!

= 10!/ 4! × 6!

= 210 ways

ii) In order for 2 of the 4 gloves selected to be a pair, note that we have 5 pairs of gloves hence:

5 × 2⁴

= 80 ways.

Therefore, the number of ways which we can select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.) = 210 ways - 80 ways

= 130 ways

Step-by-step explanation:

sin(2A)

Use double angle formula:

= 2 sin(A) cos(A)

Use Pythagorean identity.  0 ≤ A ≤ π/2, so cos(A) > 0.

= 2 sin(A) √(1 − sin²(A))

Substitute and simplify.

= 2 (¼) √(1 − (¼)²)

= ½ √(¹⁵/₁₆)

= ⅛ √15

Answer:

B < -76

Step-by-step explanation:

You start out with writing out the equation

8-1/4b> 27

Then, you subtract 8 from each side, so the -1/4b can be by itself

-1/4b>27-8

-1/4b>19

After that, you want to get rid of that -1/4, so you multiply both sides by -4

This makes the > sign flip to <

So, this makes:

b < -76

Answer:

D

Step-by-step explanation:

If the number is positive, the absolute value is the same as the number. If the number is negative, the absolute value is just a positive version of that number. So the absolute value of 0 is 0, -18 is 18, -31 is 31, and -44 is 44. Out if these, D has the greatest absolute value, so it would be D

Answer:

D. -44.

Step-by-step explanation:

Absolute value of -44:

= |-44| = 44

Answer:

1000 m³

Step-by-step explanation:

The base of a cube is just a square.

The area of a square is [tex]l^2[/tex], where l is the length.

Since we know the area of the base (the square) we can find l easily.

[tex]l^2 = 100\\\\l = \sqrt{100}\\\\l=10[/tex]

Now that we know the length of the sides, we have to take note that a cube has side lengths that are all congruent.

This means the height of the cube is also 10m.

Since the volume of a cube is represented as [tex]l^3[/tex], where l is the length, we can substitute 10 in as [tex]l[/tex] to find it's total volume.

[tex]10^3 = 1000[/tex]

So the volume of this cube is 1000 m³.

Hope this helped!

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

Explanation:

He has 90 feet of fencing overall. This is the perimeter of the rectangle as its the distance around all four sides.

Two of the opposite sides are the width = 15 ft. So we have 15+15 = 30 feet taken up and 90-30 = 60 feet left for the other two opposite sides to add to. Call each of those sides x

x+x = 60

2x = 60

x = 60/2

x = 30

The other side must be 30 feet long.

This rectangle is 30 by 15

perimeter = 30+15+30+15 = 45 + 45 = 90

which helps confirm we have the right answer

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

Or you can solve this way

P = 2*(L+W) is the perimeter of a rectangle with length L and width W

Plug in the perimeter P = 90 and the width W = 15. Solve for L

P = 2*(L+W)

90 = 2*(L+15)

2(L+15) = 90

L+15 = 90/2

L+15 = 45

L = 45-15

L = 30

Answer:

a. 17

b. 231

c. 1

d. 23

e. 9

Answer:

10 cm³

Step-by-step explanation:

According to Archimedes, if we place an object in water, the rise of the water in mL will be the volume of the object in cm³.

Without the rock, the water measures 20 mL.

With the rock, the water measures 30 mL.

The change here is [tex]30-20=10[/tex], so 10 cm³ is the volume of the rock.

Hope this helped!

Answer:

238,900 miles away

Answer:

238,900

Step-by-step explanation:

Light travels at a speed of 186,282 miles per second, you multiply this number by 1.25 you get your answer.

Answer:

Answer:

158

Step-by-step explanation:

10.89-2.99 = 7.90

.5/7.90=158

Answer:

158 songs

Step-by-step explanation:

Monthly membership = 2.99

Each song cost = .05

Total Amount spent after 1 month = 10.89

S = Songs purchased

=> 2.99 + .05S = 10.89

=> 2.99 - 2.99 + .05S = 10.89 - 2.99

=> .05S = 7.9

=> .05S / .05 = 7.9 / .05

=> S = 158

So, she purchased 158 songs that month.