i would like if someone helped me with this.

Answer:

L={∅}

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

Step 1: Multiply 4 with X and 3. You'll get 4x+12=x+42

Step 2: Keep the variable on one side and the number on the other side. you would subtract X and subtract 12. You'll get 3x=30

Step 3: Divide by the 3 on both sides and you'll get x=10

Given:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ [/tex]

Solution:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ \\ \\ \tt⇢ 4x + 12 = x + 42 \: \: \\ \\ \\ \tt \: ⇢4x - x = 42 - 12 \: \\ \\ \\ \tt \: ⇢3x = 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: ⇢x = \frac{30}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: \pink{ \pmb{ \mathfrak{⇢x = 10}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ [/tex]

Verification:

[tex] \\ ⇢ \tt \: 4(10+ 3) = 10+ 42 \\ \\ \\ \tt⇢ 40 + 12 = 10 + 42 \: \: \\ \\ \\ \tt \: ⇢52 = 52 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \: ⇢ \purple{ \pmb{ \bold{L.H.S = R.H.S}}}\\ \\ \\ [/tex]

It looks like you have to find the value of the sum,

[tex]C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}[/tex]

so that the n-th term in the sum is

[tex]\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}[/tex]

for 1 ≤ n ≤ 180.

We can then write the sum as

[tex]\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}[/tex]

Break up the summand into partial fractions:

[tex]\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}[/tex]

Combine the fractions into one with a common denominator and set the numerators equal to one another:

[tex]1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)[/tex]

Expand the right side and collect terms with the same power of n :

[tex]1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c[/tex]

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==>   a = 1/2, b = -1, c = 1/2

Now our sum is

[tex]\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)[/tex]

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994

Given:

Total number of people = 10

To find:

The number of ways in which 10 people can be divided into three groups of 2, 3, and 5 people respectively.

Solution:

We know that the number of ways to select r items form n times is:

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

The number of ways to select 2 people from 10 is [tex]^{10}C_2[/tex].

The number of remaining people is [tex]10-2=8[/tex].

The number of ways to select 3 people from 8 is [tex]^{8}C_3[/tex].

The number of remaining people is [tex]8-3=5[/tex].

The number of ways to select 5 people from 5 is [tex]^{5}C_5[/tex].

Now, the total number of ways is:

[tex]Total=^{10}C_2\cdot ^{8}C_3\cdot ^{5}C_5[/tex]

[tex]Total=\dfrac{10!}{2!(10-2)!}\cdot \dfrac{8!}{3!(8-3)!}\cdot \dfrac{5!}{5!(5-5)!}[/tex]

[tex]Total=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}\cdot \dfrac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\cdot 1[/tex]

[tex]Total=45\cdot 56\cdot 1[/tex]

[tex]Total=2520[/tex]

Therefore, the total number of ways is 2520 to divide 10 people into three groups of 2, 3, and 5 people respectively.

Answer:

3.375 cm^2

Step-by-step explanation:

The area of a parallelogram is given by

A = bh  where b is the base and h is the height

A = 2.25 * 1.5

A =3.375 cm^2

Area = length x height

Area = 2.25 x 1.5

Area = 3.375 cm^2

3/7×4/7= (3×4)/(7×7)= 12/49

Answer:

12/49

Step-by-step explanation:

Hi! To start off, I'm going to multiply our numerators, and then our denominators.

3 × 4 = 12

7 × 7 = 49

Usually, if this fraction was not simplified (but it is) we would simplify it (ex. 2/4 to 1/2).

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

4i

Step-by-step explanation:

apply (a+b)^2 formula

Answer:

. .

Step-by-step explanation:

x^2-9x√x-12

solve by using formula (a+b)^2 and open the brackets

Step-by-step explanation:

the probability will be  amount of green marbles over total amount of marbles

if there are 2 green marbles, and 10 total the probability is 2/10, or 20%

Step-by-step explanation:

Explanation is in the attachment

Hope my answer is helpful to you ✌️❣️☪️❇️❇️☪️❣️✌️

Answer:

5

Step-by-step explanation:

VU = VT because they are on two diagonals that intersect at the midpoint

Answer:

[×1] +16=10

×=10-16

×=-6

Answer:

x=5 and x=-5

Step-by-step explanation:

First subtract 16 from both sides.

Then solve for x+1=6 and x+1=-6

you answer should be x=5 and x=-5

Answer:

a) -8x³+x²+6x

d) 16x²-9

Step-by-step explanation:

a) -2x(x+4x²)+3(x²+2x)

Expand each bracket:

-2x(x+4x²)

As the -2x is on the outside of the bracket, you have to times everything inside the bracket by -2x.

-2x times x equals -2x²

-2x times 4x² equals -8x³

Then we expand the other bracket:

3(x²+2x)

3 times x² equals 3x²

3 times 2x equals 6x

We then put all of it together:

-2x²-8x³+3x²+6x

Collect like terms:

-8x³+x²+6x

b) (4x-3)(4x+3)

We will use the FOIL method:

F-First

O-outer

I-Inner

L-Last

Times the first two terms in each bracket:

4x times 4x equals 16x²

Times the outer terms in the bracket:

4x times 3 equals 12x

Times the inside terms in the bracket:

-3 times 4x equals -12x

Times the last terms in the bracket:

-3 times 3 equals -9

Put it together:

16x²+12x-12x-9

The 12x and -12x cancel out to leave 16x²-9

Hope this helps :)

Answer:

(a,a)

Step-by-step explanation:

Keep in mind that the vertical line represents the y axis and the horizontal line represents the x axis

We want to find the coordinates of C

We can do this by looking at the given coordinates and the axis..

We are given that B is at (0,a) and we are given that D is at (a,0)

Now looking at C, we can tell that C shares the same y value as B and the same x value as D

If B has a y value of a and D has an x value of a then C would have an x and y value of a

Hence C would be at (a,a)

2)10,290

105

98

10290

(3y-2z) (3y+2z)

3y(3y+2z)-2z(3y+2z)

9y2+6yz-2z(3y+2z)

9y2+6yz-6yz-4z2

9y2-4z2

Answer:

1

Step-by-step explanation:

add 1/2 + 1/2 = 2/2 = 1

Answer:

x = 126

Step-by-step explanation:

The angles are complementary which means they sum to 180

x+54 =180

x = 180-54

x = 126

Answer:

Yes, the ratio is still 5:4.

Step-by-step explanation:

If you have a class of 5 males and 4 females, both numbers can be multiplied to get an even bigger class but the same ratio.

For example:

5 x 5 = 25 males

4 x 5 = 20 females

The amount of males to females is 25:20 when simplified (divided by 5) gets you back to your ratio of 5:4. You also can't go under this because the two don't have a way to get simplified without going into decimals. And I don't think decimals are very good with the number of students.

Have a good day! :)

x > 0.8

x > -2

hope it helps :)

The solution of the given inequalities will be x > 0.8 and x < -2.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given inequalities are x-0.8>0, and -5x<10. the inequalities will be solved as:-

x-0.8>0

x > 0.8

-5x<10

Take -5 to the right side and divide 10 by -5 and solve further.

x < -10 / 5

x < -2

Therefore, the solution of the given inequalities will be x > 0.8 and x < -2.

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ5

Answer:

27 games

Step-by-step explanation:

The probability of them winning is 3 out of 5 games.

First, multiply 45 by [tex]\frac{3}{5}[/tex]

[tex]\frac{45}{1} *\frac{3}{5}[/tex]

[tex]\frac{135}{5}[/tex]

27 games.

You could also just multiply 45 by 3 then divide by 5. Mostly the same thing

I hope this helps!

Answer:

Step-by-step explanation:

You need to find the model for this situation using the points given. If you are given 13 mg immediately, the coordinate point for that is (0, 13), where the x coordinate is the time in minutes and the y coordinate is the amount of dye in mg.

If after 12 minutes, 4.75 mg remain, the coordinate point for that is (12, 4.75). Just so you know, the time unit always goes in for x, never for y.

Now that we have these coordinates we are going to use them as a system and find the model. Begin with the point (0, 13) in

[tex]A=a(b)^t[/tex] where A is the amount left in the body, a is the initial amount injected, b is the rate at which it decays, and t is the time in minutes. Plug in the first set of coordinates:

[tex]13=a(b)^0[/tex] and since anything raised to the power of 0 is equal to 1, we have

13 = a. Now we can use that and write another equation with the other set of coordinates to solve for b:

[tex]4.75=13(b)^{12}[/tex] and divide both sides by 13 (don't round anything yet) to get

.3653846154 = b¹². Now take the 12th root of both sides (you need a scientific calculator for this) to get that

b = .9195228407  Yikes.

Now for the model, using the fact that a = 13 and b = .9195228407:

[tex]A=13(.9195228407)^t[/tex]  

We are told that the amount that we are allowed to leave with still remaining in our system cannot be more than 2 mg, so we sub in a 2 for A:

[tex]2=13(.9195228407)^t[/tex] and begin by dividing away 13 to get

[tex].1538461538=.9195228407^t[/tex]  Take the natural log of both sides, which allows us to bring the t out front:

ln(.1538461538) = t ln(.9195228407) and finally divide by ln(.9195228407) to get

t = 22.3 minutes

Answer:

A and B

Step-by-step explanation:

A and B are the correct options

Answer:

10

Step-by-step explanation:

The altitude of a graph is displayed as the square root of the two parts of the hypotenuse multiplied together. Over here, the two values are 5 and 15. That means the altitude of the graph is the square root of 5 times 15, which means the altitude of the bigger triangle is equal to the square root of 75. Now, we can use the Pythagorean theorem on the smallest triangle to figure out the value of x. We have:

[tex]5^2+(\sqrt{75})^2=x^2[/tex]

5 squared is 25 and the square root of 75 squared is 75.

[tex]25+75=x^2[/tex]

Combining like terms:

[tex]100=x^2[/tex]

Taking the square root of both sides:

[tex]10=x[/tex]

The value of x is 10.

Answer:

Option C

X>1

Step-by-step explanation:

x-7>-6

x>-6+7

x>1

Please Mark me brainliest

Answer:

C

Step-by-step explanation:

x - 7 > -6

x > -6 + 7

x > 1

• We change the inequality sign if we multiply or divide a negative number from both sides. But since it’s positive and we added it we won’t change the inequality sign.

Answer:

It's D:5.3

Step-by-step explanation:

√28 =5.29

Round off therefore is 5.3

Answer:

Hence the answer is Letter B.

Step-by-step explanation:

° ° °

Answer:

x = 40

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 30² = 50²

x² + 900 = 2500 ( subtract 900 from both sides )

x² = 1600 ( take the square root of both sides )

x = [tex]\sqrt{1600}[/tex] = 40

Answer:

25%

Step-by-step explanation:

1 ÷ 4 = 0.25

0.25 x 100 = 25 = 25%