acyclics

The smallest integer that Pearl wrote down is 15.

Step-by-step explanation:

7 consecutive integers. They are:

a

a+1

a+2

a+3

a+4

a+5

a+6

Sum of the integers:

a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 = 7a + 21

6 times the largest of the seven integers.

The largest is a + 6. So

7a + 21 = 6(a + 6)

7a + 21 = 6a + 36

7a - 6a = 36 - 21

a = 15

The smallest integer that Pearl wrote down is 15.

The probability that a student is chosen randomly from the class plays both basketball and baseball is 4/21

Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

If the total number of people in the class is 21 students, hence the total outcome is 21

Get the number of students that plays both basketball and baseball

n(U) = n(B)only + n(Ba)only + n(BnBa) + n(BuBa)'

21 = 6-x + 14-x + x + 5 

21 = 25 -x

x = 25 - 21

x = 4

Hence 4 students play both basketball and baseball

Pr(basketball and baseball) = 4/21

Hence the probability that a student chosen randomly from the class plays both basketball and baseball is 4/21

The simplification of the given expression is equal to 192524.3.

Step-by-step explanation:

The expression is equal to,

√2 × √6 × √110 × √120 × √450 × √520

Simplify this expression by first simplifying the square roots under the radical signs,

√2 = √(2 × 1) 

     = √2 × √1

√6 = √(2 × 3) 

     = √2 × √3

√110 = √(2 × 5 × 11) 

        = √2 × √5 × √11

√120 = √(2 × 2 × 2 × 3 × 5) 

        = 2√2 × √3 × √5

√450 = √(2 × 3² × 5²) 

         = √2 × (3 × 5)² 

         = 15√2 

√520 = √(2³ × 5 × 13) 

        = 2√2 ×√5 × √13

Substituting these simplifications back into the original expression, we have,

√2 × √6 × √110 × √120 × √450 × √520

= √2 × √2 × √3 × √2 × √5 × √11 × 2√2 × √3 × √5 × 15√2  ×  2√2 ×√5 × √13

= 2⁵ × 3² × 5²√(5 × 11  × 13)

= 7200√715

= 192524.3

23/48

Step-by step explantion.

Let each side of triangle XYZ have length s. We therefore have:

s = YZ = YQ + QR + RZ = x + 2y

Since each side of triangle X1 Y2 Z2 is 3/4 the length of the corresponding side of triangle XYZ, we have:

3/4s = X1 Z1 = X1 Q + QP + P Z1 = 2x +y.

The system of equations:

x + 2y = s

2x + y = 3/4s

Multiply the second equation by 2, then subtract the first equation.

3x = 1/2s, so x = 1/6s.

Now we have y = 3/4s-2x = 5/12s. 

A/[XYZ] = [XYZ] - 3[YPQ]/[XYZ]

= {[XYZ] - 3[(25)/144] * [XYZ]} / [XYZ]

={23/48* [XYZ]} / [XYZ]

= 23/48

Cannot answer " url question "

n = 3.

How to obtain the smallest integer?

The seven integers are consecutive, hence they are represented in function of the smallest integer n as follows:

n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6.

The sum of the integers is equals to 14/3 times the largest integer, which is of (n + 6), hence the expression to obtain n is given as follows:

n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6 = 14/3(n + 6)

7n + 21 = 14n/3 + 28

21n/3 - 14n/3 = 7

7n/3 = 7

7n = 21.

n = 3.

Well ' I ' concluded because from looking at the problem:

a^3-b^3 / a^3b^3+a^2b^4+ab^5 it is a fraction correct?

And from the fraction the calue of variable of a expression are excluded for which expression does not exist, where denominator is going to be zero those value going to be excluded. So making the denominator ( NOT ' 0 ' ) so like in The question best fits the problem: 

I need to find point where it become zero we put 6x²yz equal to 0

6x²yz = 0

Making the new problem of:x² = 0  or y = 0 or z = 0

x² = 0  or y = 0 or z = 0

and concealing the problem making option a correct.

x,y,z=0

Step-by-step explanation:

For this case we have the following expression:
 3x ^ 2y ^ 2-6xz / 6x ^ 2yz
 From here, we must exclude all values that make the denominator equal to zero.
 We have then:
 6x ^ 2yz = 0
 Therefore, the results are:
 x = 0
 y = 0
 z = 0
 Answer:
 The exclusion that fits best with this problem is:
 x, y, z = 0

When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

What are linear equations in one variable?

Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable).

How to solve the given question?

In the question, we are asked to find a number, which satisfies the statement, "Five times a number is divided by 7 more than the number. The result of this division is 2".

We assume the number to be x.

Now we try to form a linear equation in one variable from the given statement.

Five times a number is 5x.

7 more than a number is x + 7.

We are said that five times a number is divided by 7 more than a number. This can be shown as 5x/(x + 7).

Now, the result is given as 2, which can be shown as:

5x/(x+ 7) = 2, which is the required linear equation in one variable.

To get the number, we solve the equation using the following steps:

5x/(x+ 7) = 2

or, {5x/(x+ 7)}*(x + 7) = 2*(x + 7) (Multiplying both sides by (x + 7))

or, 5x = 2x + 14 (Simplifying)

or, 5x - 2x = 2x + 14 - 2x (Subtracting 2x from both sides)

or, 3x = 14 (Simplifying)

or, 3x/3 = 14/3 (Dividing both sides by 3)

or, x = 14/3 (Simplifying)

∴ When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

The tank capacity is 24 gallons

Step-by-step explanation:

Let the tank capacity be c.

Then (1/6)c + 2 = (1/4)c, or (since the LCD is 12):

2c/12 + 24/12 =  3c/12, or

24/12 = c/12

Multiplying both sides by 12, we get:

24 = c

The tank capacity is 24 gallons.

28

Step-by-step explanation

In order to solve this problem we need to find out what $QR$ is.

We know that the perimeter of the parallelogram was given as $24$ and that two of the sides were given as $5$. $5+5=10$ $24-10=14/2=7$. Now we know that the base was $7$.

We can find the height by taking the area that they gave us and dividing that by $7$. We get $4$.

Since we now know that the height of the parallelogram is $4$ that means $OQ$ is also $4$.

Next we need to find what $RT$ is.  

$4^2+B^2=5^2$.

Since we now $5^2$ is $25$ and that $4^2$ is $16$, we can use the following equation.

$25-16=9$. $\sqrt{9}=3$.  

Now we know that $RT$ is $3$ we can start adding the sides.

$7+3=10+4=14 \cdot 2=28$.

28

* I have answered this before so I will put it again *