The number of boys is 3 more than double the girls. Together, there are 54 students in total. How many boys and girls are there?

Answer:

solving the inequality we get [tex]x < 14[/tex]

Step-by-step explanation:

We need to solve the inequality A number times two is less than 20 + 8

Let the number be x

The inequality will be:

2x < 20+8

Now solving the inequality to find the value of x

[tex]2x < 20+8\\2x < 28\\x<\frac{28}{2}\\x<14[/tex]

So, solving the inequality we get [tex]x < 14[/tex]

In figure a I am attaching the number line for solution.

In figure b I am attaching the graph for solution.

Answer:

9, 30, and 15.

Step-by-step explanation:

Let the three numbers be a, b, and c.

The sum of them is 54. So:

[tex]a+b+c=54[/tex]

The third number is 6 more than the first. In other words, c=a+6.

The second number is twice the third. In other words, b=2c.

Let’s write the second number in terms of a. Since b=2c, this means that b=2(a+6).

Let’s substitute them into our equation. So:

[tex]a+2(a+6)+(a+6)=54[/tex]

Solve for a. Distribute:

[tex]a+2a+12+a+6=54[/tex]

Combine like terms:

[tex]4a+18=54[/tex]

Subtract 18 from both sides:

[tex]4a=36[/tex]

Hence, the value of a is:

[tex]a=9[/tex]

So, the first number is 9.

The third number is 6 more than the first, so the third number is 15.

The second number is twice the third. So, the second number is 30.

Therefore, our numbers are:

9, 30, and 15.

Answer: The awnser is B

Step-by-step explanation: ive went over the problem and checked

Answer: B) No, every x-value does not have exactly one y-value

Explanation:

We have the input x = 3 map to the outputs y = 2 and y = 8 at the same time. A function is only possible if any given x value goes to exactly one y value.

Put another way, if x repeats itself, then we don't have a function. This assumes we don't repeat the same y value when we repeat the x value.

The central angle of the circle is given by the equation A = 120°

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

r is the radius of the circle

Central Angle = 2 x Angle in other segment

Given data ,

Let the center of the circle be O

Let the arc be represented as AB

Let the angle be represented as ∠AOB

Now , ∠AOB is a central angle with an intercepted minor arc from A to B.

Substituting the values in the equation , we get

m∠AB = 120º

The measure of the central angle ∠AOB = measure of m∠AB

So ,

The measure of the central angle ∠AOB = 120°

Hence , the central angle is 120°

To learn more about central angle click :

https://brainly.com/question/11877137

#SPJ2

Answer:

Mixed number: 6 1/100

Improper Fraction: 601/100

Step-by-step explanation:

Hope this helps!

Answer:

Mixed number: [tex]6\frac{1}{100}[/tex]

Improper fraction: [tex]\frac{601}{100}[/tex]

Step-by-step explanation:

A mixed number is a fraction that contains an integer and fraction part. An improper fraction is a fraction where the numerator is larger than the denominator.

[tex]6.01[/tex] can be written in the from [tex]\frac{601}{100}[/tex]. This is an improper fraction since the numerator is greater than the denominator.

The mixed number is [tex]6\frac{1}{100}[/tex] since [tex]100[/tex] goes into [tex]601[/tex] six full times with [tex]1[/tex] as the remainder.

Hope this helps :)

Answer:

See attached

Step-by-step explanation:

The answer is in below picture

Answer:

f(-5) = 35

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = x² + 10

f(-5) is x = -5

Step 2: Evaluate

Answer:

x=10

Step-by-step explanation:

hope this helps

5x = x + 44 - 4

5x = x + 40

5x - x = 40

4x=40

x=40/4

x = 10

Answer:

Please, see the explanation.

Step-by-step explanation:

DETERMINING THE EQUATION FOR THE FIRST TABLE

Given the first table

x                     y

-5                   10

-1                    2

0                    0

11                   -22

From the given equation, we can verify and determine that

[tex]y=-2x[/tex] is the required equation that satisfies the table values of the first table.

substituting the table values of all the ordered pairs to check

FOR (-5, 10)

y =-2x

10 = -2(-5)

10 = 10

L.H.S = R.H.S

FOR (-1, 2)

y =-2x

2 = -2(-1)

10 = 2

L.H.S = R.H.S

FOR (0, 0)

y =-2x

0 = -2(0)

0 = 0

L.H.S = R.H.S

FOR (11, -22)

y =-2x

-22 = -2(11)

-22 = -22

L.H.S = R.H.S

As all the ordered pairs of the first table satisfy the equation.

Hence, [tex]y=-2x[/tex] is the equation for the first table.

DETERMINING THE EQUATION FOR THE SECOND TABLE

Given the first table

x                     y

-8                   -11

-2                    -5

1                      -2

7                      4

From the given equation, we can verify and determine that

[tex]y=x-3[/tex] is the required equation that satisfies the table values of the second table.

substituting the table values of all the ordered pairs to check

FOR (-8, -11)

y =x-3

-11 = -8-3

-11 = -11

L.H.S = R.H.S

FOR (-2, -5)

y =x-3

-5= -2-3

-11 = -5

L.H.S = R.H.S

FOR (1, -2)

y = x-3

-2= 1-3

-2 = -2

L.H.S = R.H.S

FOR (7, 4)

y = x-3

4 = 7-3

4 = 4

L.H.S = R.H.S

As all the ordered pairs of the second table satisfy the equation.

Hence, [tex]y = x-3[/tex] is the equation for the second table.

Therefore, the equations are:

[tex]y=-2x[/tex]

[tex]y = x-3[/tex]

Now, let us solve to determine the solution

[tex]\begin{bmatrix}y=-2x\\ y=x-3\end{bmatrix}[/tex]

Arrange equation variables for elimination

[tex]\begin{bmatrix}y+2x=0\\ y-x=-3\end{bmatrix}[/tex]

[tex]y-x=-3[/tex]

[tex]-[/tex]

[tex]\underline{y+2x=0}[/tex]

[tex]-3x=-3[/tex]

[tex]\begin{bmatrix}y+2x=0\\ -3x=-3\end{bmatrix}[/tex]

solving

[tex]-3x=-3[/tex]

[tex]\frac{-3x}{-3}=\frac{-3}{-3}[/tex]

[tex]x=1[/tex]

For [tex]y+2x=0[/tex],  plugin [tex]x = 1[/tex]

[tex]y+2\cdot \:1=0[/tex]

[tex]y+2=0[/tex]

[tex]y=-2[/tex]

Therefore, the solution to the system of equations are:

[tex]y=-2,\:x=1[/tex]

9514 1404 393

Answer:

  a. x, x+2, x+4

  b. 10 ≤ 3x+6 ≤ 24

  c. 6 ft, 8 ft, or 10 ft

Step-by-step explanation:

Given:

Find:

  a. Using one variable, write three expressions that represent the lengths of the three sides of the triangle.

  b. Write a compound inequality to model this problem.

  c. Solve the inequality. List all possible lengths for the longest side of the triangle.

Solution:

You have let x represent the shortest side. (Note that the question asks for the length of the longest side.)

a. The expressions for side lengths can be x, x+2, x+4 when x is the shortest side.

__

b. Here is the compound inequality

  10 ≤ x+(x+2)+(x+4) ≤ 24

__

c. Here is the solution

  10 ≤ 3x+6 ≤ 24 . . . . collect terms

  4 ≤ 3x ≤ 18 . . . . . . . subtract 6

  4/3 ≤ x ≤ 6 . . . . . . . . divide by 3

Your working is correct, but incomplete. The values of interest are the even integers x+4.

  5 1/3 ≤ x+4 ≤ 10

The longest side may be 6 ft, 8 ft, or 10 ft.

[tex] {x}^{3} - {x}^{2} + x - 1 + \frac{2}{x + 1} [/tex]

lmk if u want an explanation for this I can try type it out

Answer:

[tex]x^3-x^2+x-1+\frac{2}{x+1}[/tex]

Step-by-step explanation:

See the picture attached.

Notice how I set up [tex]x^4+1[/tex] as [tex]x^4+0x^3+0x^2+0x+1[/tex], as it makes it easier to solve.

Also, notice that the 2 as the remainder doesn't have anything else to divide to, so that means there will be an extra term [tex]\frac{2}{x+1}[/tex] in the end of the answer.

Answer:

d

Step-by-step explanation:

Answer:

x = 60

Step-by-step explanation:

Given: L ∥ M and the line going through them is transversal

The sum of the interior angles on the same side of a transversal is equal to 180 degrees; therefore, (2x + 5) degrees + (x - 5) degrees = 180 degrees.

2x + 5 + x - 5 = 180

2x + x + 5 - 5 = 180

3x + 0 = 180

3x = 180

x = 180/3

x = 60

Double Check:

2(60) + 5 + (60) - 5 = 180 degrees

120 + 5 + 55 =

125 + 55 =

180 degrees

180 degrees = 180 degrees

Answer:

Below.

Step-by-step explanation:

(a)  There 8 possible outcomes.

HHH TTT HHT HTH THH TTH THT HTT

(b) Prob(No Heads)

= Prob(TTT)

= 1/8.

(c) Possible outcomes of at least 2 tails are:

TTT, TTH THT HTT = 4

So Probability of this  is 4/8 = 1/2.

the answer is x=-4 hope it helps

Answer:

22

Step-by-step explanation:

if a=15

then, 2(a-5)+2= 2(15-5)+2 = 2(10)+2= 20+2=22

Answer:

5. Slope: 2

y-intercept:(0,-6)

y=2x-6

6. Slope:1

y-intercept:(0,-1)

y=x-1

Answer: Vertex is (-7/2, -81/4)

Axis of synmentary is x= -7/2

Directrix is y= -41/2

Step-by-step explanation:

Its on google

Answer:

The lum sum that must be deposited today is $12,506.25 to have a future value of $25,000 in 9 years if the funds carn 8%, compounded annually.

Step-by-step explanation:

We are given:

Future value (A)=$25,000

Rate r =8% (0.08%)

Time t = 9

Compounded Annually n =1

We need to find:

Principal Amount (P) = ?

The formula used will be:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Putting values and finding Principal Amount (P)

[tex]A=P(1+\frac{r}{n})^{nt}\\25000=P(1+\frac{0.08}{1})^{9*1} \\25000=P(1+0.08)^{9} \\25000=P(1.08)^{9} \\25000=P(1+0.08)^{9} \\25000=P(1.9990)\\P=\frac{25000}{1.9990}\\\mathbf{P=12506.25 }[/tex]

So, The lum sum that must be deposited today is $12,506.25 to have a future value of $25,000 in 9 years if the funds carn 8%, compounded annually.

Answer:

x = 6

Step-by-step explanation:

Answer:

(2).

Step-by-step explanation:

We have the expression:

[tex]\displaystye{\ln(\displaystyle{\frac{\sqrt{e}}{y^3})}[/tex]

First, we can use the difference property of logarithms:

[tex]\ln(x/y)=\ln(x)-\ln(y)[/tex]

Hence, this is equivalent to:

[tex]=\ln(\sqrt{e})-\ln(y^3)[/tex]

We can rewrite the left as:

[tex]=\ln(e^\frac{1}{2})-\ln(y^3)[/tex]

Now, we can use the power property:

[tex]\ln(a^b)=b\ln(a)[/tex]

Essentially, we move the exponent to the front.

Hence, this yields:

[tex]=\frac{1}{2}\ln(e)-3\ln(y)[/tex]

The natural log of e is simply 1. Hence:

[tex]=\frac{1}{2}-3\ln(y)[/tex]

Combine fractions:

[tex]\displaystyle{=\frac{1}{2}-\frac{6\ln(y)}{2} \\ =\frac{1-6\ln(y)}{2}}[/tex]

Hence, our answer is (2).

Answer:

[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]

Step-by-step explanation:

Given the expression

[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]

solving the expression

[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=4\cdot \:\frac{\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]

             [tex]=4\:\frac{27x^3y^{12}}{16x^{12}y^{20}}[/tex]

              [tex]=4\cdot \frac{3^3}{2^4x^9y^8}[/tex]

The multiply fractions are defined as

[tex]\:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]

so the expression becomes

                [tex]=\frac{3^3\cdot \:4}{2^4x^9y^8}[/tex]

                [tex]=\frac{3^3\cdot \:2^2}{2^4x^9y^8}[/tex]

                [tex]=\frac{3^3}{2^2x^9y^8}[/tex]

Refining

                 [tex]=\frac{27}{4x^9y^8}[/tex]

Therefore,

[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]            

Step-by-step explanation:

Area of a triangle= 1/2breadth × height

Answer:

x = 46

Step-by-step explanation:

This is basic trigonometry, so we can apply this procedure...

- The total sum of all angles in a triangle is 180 (no angle should be more than 180, this is the limit) and we only need to know just one angle labeled as x, this is represented as:

130 + 96 + x = 180

x = 130 + 96 - 180

- Now we just need to obtain x:

x = 130 + 96 - 180

x = 226 - 180

x = 46

Answer:

3960 is the answer

Step-by-step explanation:

Answer:

3960

Step-by-step explanation:

...........................

...........................

answer is 3960

Answer:

1) 1[tex]\frac{1}{8}[/tex]

2) 2[tex]\frac{5}{7}[/tex]

3) 1[tex]\frac{8}{9}[/tex]

Step-by-step explanation:

Step-by-step explanation:

4 7/8 + __ = 6

__ = 6 - 4 7/8

__ = 1 1/8

3 2/7 + __ = 6

__ = 6 - 3 2/7

__ = 2 5/7

3 1/9 + __ = 5

__ = 5 - 3 1/9

__ = 1 8/9

Topic: Fractions

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

Answer:

Step-by-step explanation:

7x+4=10x-11

4=3x-11

15=3x

x=5