Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?

Choose all answers that apply:

Choose all answers that apply:


(Choice A)

A

3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis


(Choice B)

B

(b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis


(Choice C)

C

2(b)+2(3c)2(b)+2(3c)2,

Answer:

Probability of people order a salad or an appetizer P(A∪B) = 62%

Step-by-step explanation:

Given:

Probability of appetizer P(A) = 55%

Probability of salad P(B) = 25%

Probability of choose both P(A∩B) = 18%

Find:

Probability of people order a salad or an appetizer P(A∪B)

Computation:

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 55% + 25% - 18%

P(A∪B) = 62%

Probability of people order a salad or an appetizer P(A∪B) = 62%

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

cosec x = [tex]\frac{1}{sinx}[/tex]

Consider the left side

[tex]\frac{sin0}{1-cos^20}[/tex]

= [tex]\frac{sin0}{sin^20}[/tex] ← cancel sinΘ on numerator/denominator

= [tex]\frac{1}{sin0}[/tex]

= cosecΘ = right side

Scale = 1cm:3km

Therefore area of lake = 81Km

1:3 = x:81

= 27:81

Therefore the area on map is 27cm

Must click thanks and mark brainliest

Answer:

121.5 is answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

3(x-2)

Answer:

CD = 7

Step-by-step explanation:

CD and GI are of same lenghth so

3x - 6 = x + 8

transpose

3x - x = 8+6

2x = 14

x = 14/2

x = 7

It looks like you're trying to evaluate the sum,

[tex]\displaystyle \frac2{4\times7} + \frac2{7\times10} + \frac2{10\times13}+\cdots+\frac2{49\times52}[/tex]

which can be written as

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)}[/tex]

Split up the summand into partial fractions:

[tex]\displaystyle \frac2{(3n+1)(3n+4)} = \frac a{3n+1} + \frac b{3n+4} \\\\ \implies 2 = a(3n+4)+b(3n+1) \\\\ \implies 2 = (3a+3b)n+4a+b[/tex]

so that

3a + 3b = 0, or a = -b

4a + b = 2

Solve for a and b :

4a + (-a) = 3a = 2   ==>   a = 2/3   ==>   b = -2/3

So the sum is

[tex]\displaystyle \frac23 \sum_{n=1}^{16} \left(\frac1{3n+1} - \frac1{3n+4}\right)[/tex]

Write out the first terms and observe that several terms cancel with each other:

2/3 (1/4 - 1/7)

+ 2/3 (1/7 - 1/10)

+ 2/3 (1/10 - 1/13)

+ …

+ 2/3 (1/43 - 1/46)

+ 2/3 (1/46 - 1/49)

+ 2/3 (1/49 - 1/52)

So the sum collapses and simplifies to

[tex]\displaystyle \sum_{n=1}^{16} \frac2{(3n+1)(3n+4)} = \frac23 \left(\frac14 - \frac1{52}\right) = \boxed{\frac2{13}}[/tex]

Answer:

4

Step-by-step explanation:

Let the number be x.

According to the question,

[tex]\dashrightarrow \sf { \dfrac{1}{4}x - \dfrac{1}{5}x= 8 + 10 } \\[/tex]

[tex]\dashrightarrow \sf { \dfrac{5x + 4x}{2}= 18 } \\[/tex]

[tex]\dashrightarrow \sf { \dfrac{9x}{2}= 18 } \\[/tex]

[tex]\dashrightarrow \sf { 9x = 18 \times 2 } \\[/tex]

[tex]\dashrightarrow \sf { 9x = 36 } \\[/tex]

[tex]\dashrightarrow \sf { x =\cancel{ \dfrac{36}{9} }} \\[/tex]

[tex]\dashrightarrow \underline{\boxed{\pmb { \frak {x = 4 }}}} \\[/tex]

The number is 4.

Answer:

123

Step-by-step explanation:

We can square and cube the equation, then multiply the results together.

(a + [tex]\frac{1}{a}[/tex]) = 3 ← square both sides

a² + 2 + [tex]\frac{1}{a^2}[/tex] = 9 ( subtract 2 from both sides )

a² + [tex]\frac{1}{a^2}[/tex] = 7 → (1)

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

Now cube both sides

a³ + [tex]\frac{1}{a^3}[/tex] + 3(a + [tex]\frac{1}{a}[/tex]) = 27

a³ + [tex]\frac{1}{a^3}[/tex] + 3(3) = 27

a³ + [tex]\frac{1}{a^3}[/tex] + 9 = 27 ( subtract 9 from both sides )

a³ + [tex]\frac{1}{a^3}[/tex] = 18 → (2)

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

Multiply (1) and (2)

(a² + [tex]\frac{1}{a^2}[/tex] )(a³ + [tex]\frac{1}{a^3}[/tex] ) = 7(18)

[tex]a^{5}[/tex]  + ( [tex]\frac{1}{a}[/tex] + a) + [tex]\frac{1}{a^5}[/tex] = 126

[tex]a^{5}[/tex] + 3 + [tex]\frac{1}{a^5}[/tex] = 126 ( subtract 3 from both sides )

[tex]a^{5}[/tex] + [tex]\frac{1}{a^5}[/tex] = 123

Answer:

Step-by-step explanation:

Answer:

. an=4(2n−1)

Step-by-step explanation:

Answer:

x = log 10/log 3

Step-by-step explanation:

3^x - 4 = 6

3^x = 10

We take log base 3 of both sides since log_3 3^x is simply x.

log_3 3^x = log_3 10

x = log_3 10

We have an answer for x, but it is a log base 3. We want log base 10.

Now we use the change of base formula.

log_b y = log y/log b

x = log 10/log 3

Answer:

x = (-2 , 4.5)

Step-by-step explanation

Hope it helps! later!

One equation you can use is y = -12x+752 and you plug in x = 8 to find y.

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

Explanation:

x = number of minutes

y = depth of the submarine

Being at sea level means the depth is y = 0. Diving 752 ft below sea level means the depth is y = 752. It's tempting to make this negative since we're below sea level, but depth values are always positive. They are simply distances you are from the surface of the water. Negative distances are never possible. So this concept might be a bit tricky to get used to.

Possibly equally confusing is the fact that the "12 ft per minute" means the slope is -12. This is because the depth is getting smaller as the submarine gets closer to the surface (aka the sub is rising).

The equation is y = -12x+752. The equation is in the form y = mx+b with m = -12 as the slope and b = 752 as the y intercept. Note how the y intercept is the starting depth value.

From here, we plug in x = 8 to find where the sub is

y = -12x+752

y = -12*8+752

y = -96+752

y = 656

The submarine's depth after eight minutes is 656 feet

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

An alternative equation to use is

y = 12x-752

which is very similar to the other one used earlier. All I did was flip the sign of each term. Now y represents the height of the sub. Negative y values indicate we're below the surface of the water. The slope being positive means the submarine is going upward. The negative y intercept indicates we're starting 752 feet below sea level. Plugging in x = 8 will lead to y = -656, which you'll need to make positive (since all depth values are positive).

As you can probably guess, the change from y = -12x+752 and y = 12x-752 is simply multiplying the right hand side by -1, which explains why the signs flip (and explains how the y value sign flips as well)

Answer:

the answer is ; Never

Hope this answer correct :)

Answer:

the answer is never

Step-by-step explanation:

Answer:

[tex]2 \frac{4}{9} [/tex]

[tex] = \frac{ - 5}{6} + 1 \frac{2}{9} [/tex]

[tex] = \frac{ - 5}{6} + \frac{11}{9} [/tex]

[tex] = \frac{ - 5 \times 2 + 11 \times 1}{9} [/tex]

[tex] = \frac{ - 10 + 9}{9} [/tex]

[tex] = \frac{-1}{9} [/tex]

Answer:

It's true. We can write integers in fraction by giving it a denominator of 1.

Answer:

true

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

= 3^3 + (2 x 2 x 3) + 2^2 + ( 3 + 2)^5

= 3^3 + (12) + 2^2 + (3 + 2)^5

= 3^3 + 12 + 2^2 + (5)^5

= 9 + 12 + 2^2 + 5^5

= 9 + 12 + 4 + 5^5

= 9 + 12 + 4 + 25

= 50

Answer:

Step-by-step explanation:

Question 5

Part A

if Sin(x) = - 3/5  and tan(x) < 0

you are told 3 things

tan(x) = Sin(x)/cos(x)

tan(x) = -3/5 // 4/5

Tan(x) = -3/4

Part B

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

cos(2x) = (4/5)^2 - (-3/5)^2

cos(2x) = 16/25 - 9/25

cos(2x) = 7/25

Part B

x + y = 90

sin(x +y) = 1

Sin(x - y) =

Sorry can't do this part. I don't know what this is equal to.

Answer:

30

Step-by-step explanation:

if x is 5, then 6x=______.

sub in the value of x for 5

when a variable and coefficient as next to eachother that means to multiply

so 6*5= 30

Answer:

[tex]\large \boxed{\mathrm{30}}[/tex]

Step-by-step explanation:

[tex]x=5[/tex]

[tex]\sf{Substitute \ x \ as \ 5 \ for \ 6x.}[/tex]

[tex]6(5)[/tex]

[tex]6 \times 5 = 30[/tex]

Answer:

Second option is the correct answer

[tex] {3}^{ - 4} [/tex]

Step-by-step explanation:

[tex] {3}^{ - 8} . {3}^{4} = {3}^{ - 8 + 4} = {3}^{ - 4} [/tex]

Answer:

The answer is D because you multiply the exponents so -8 times 4 is -32

Hope this helps and plz mark branliest!

Step-by-step explanation:

Answer:

5 ml of 50% syrup solution will be used to create the final solution

Step by step Explanation:

Let the amount of 50% solution that was used = b

Which means ( 30 - b ) is the amount of 1/200 solution used then we can derive an equation as follows,

set up will then be,

0.5b +0.05(30 -b) = 1/8 (30)

We can simplifiy this as

0.5b+ 1.5 -0.05b = 3.75

Then make b the subject of the formula we have

0.45b = 2.25

b= 2.25/0.45

b = 5 ml

Therefore, 5ml of 50% syrup solution will be used to create the final solution

Answer:

4

Step-by-step explanation:

Answer:

-26, and -36

Step-by-step explanation:

(-2) (-3) + (4) (-8)

        6 + -32 = -26

(3) (-6) - 18

       -18 + -18 = -36

Step-by-step explanation:

Origin is 5.

Y Axis is 2

Run is 9

Solution of a Line is 13.

Ordered Pairs is 4.

Quadrant is 6.

Solution of Linear Equation is 12.

Slope is 10.

Slope Intercept Form is 16.

Rise is 8.

Y intercept is 15.

Parallel Lines is 17.

X intercept is 14.

X axis is 3.

Linear Equation is 7.

Perpendicular Lines is 18.

Point Slope Form is 11.

Coordinate plane is 1.

Answer:

x = 5/2          x=1/3

Step-by-step explanation:

(2x – 5)(3x – 1) = 0

Using the zero product property

2x-5 =0    3x-1 =0

2x=5         3x =1

x = 5/2          x=1/3

Answer:

C on edg 2021

Step-by-step explanation:

Answer:

0.48

Step-by-step explanation:

hope it can work for you mark me as a brain liest

Answer:

Step-by-step explanation:

[tex]V = ?\\r = 8\\h =5 \\\pi = 3.14\\\\V = \pi r^2 h\\\\V = 3.14 \times 8^2 \times 5\\V = 1004.8 cubic units[/tex]

Answer:

C. 1004.8  cubic units

Step-by-step explanation:

Lets analyze the problem given, we have to find the volume of cylinder and use 3.14 as pi.

We can use the formula V=(3.14)r^2h to find the volume of the cylinder.

Below is the work to solve the formula:

8^2= 64

64(5)=320

320(3.14)=

1004.8  cubic units is our answer.

Answer:

The charge is negative and the amount is 215

Step-by-step explanation:

Electrons are negative

-354

Protons are positive

+139

-354+139

-215

So

Net charge

Negative charge and the amount is 215

Answer:

[tex]\huge\boxed{2k-13}[/tex]

Step-by-step explanation:

[tex]\sf -3(2+4k)+7(2k-1)\\Expanding \ brackets\\-6-12k+14k-7\\Combining \ like \ terms\\-12k+14k-6-7\\2k -13[/tex]

Answer:

In the real world, a consumer may purchase more then one commodity. Let us assume that a consumer purchases two goods X and Y. How does a consumer spend his fixed money income in purchasing two goods so as to maximize his total utility? The law of equi­-marginal utility tells us the way how a consumer maximizes his total utilit

Answer:

B) 24

D) 48

Step-by-step explanation:

Given:

Two fractions

[tex]\dfrac{1}6 \\and\\\dfrac{3}8[/tex]

To find:

Number that can be chosen as Common denominator such that numerator is also a whole number ?

Solution:

Common denominator for two fractions [tex]\frac{p}{q}[/tex] and [tex]\frac{r}{s}[/tex] is chosen as LCM or multiple of LCM of (q, s).

OR

Common denominator for two fractions is chosen as the Least Common Multiple or multiple of LCM of denominators of the two fractions.

The denominators of the given fractions are 6 and 8.

Let us factorize and try to find the LCM of 6 and 8.

[tex]6 = \underline2 \times 3\\8 = \underline2 \times 2\times 2[/tex]

Common part of the denominators (as underlined) will be taken only once.

So, [tex]LCM = 2 \times 3 \times 2 \times 2 =24[/tex]

Multiples of LCM, 24 = 48

So, the correct answers are:

B) 24 and

D) 48

Answer:

(x - 10)(x + 8)

Step-by-step explanation:

x² - 2x - 80

Consider the factors of the constant term (- 80) which sum to give the coefficient of the x- term (- 2)

The factors are - 10 and + 8 , since

- 10 × 8 = - 80 and - 10 + 8 = - 2 , then

x² - 2x - 80 = (x - 10)(x + 8)