rationalize the denomintaors 3square root of 3 - 3 square root of 3

Answer:

39 tables

Step-by-step explanation:

Given:

third grade= 134

fourth grade=167

total=134+167=301

Now no. of students is 7 times no. of adults,

no. of adults= 301/7

                    =43

Total no. of people =301+43

                                 =344

Each picnic table can seat 9 people, so

No. of tables for 344 people= 344/9

                                              =38.222

39 tables picnic tables will need to be set up for the picnic!

Answer:

R(- 12, 22 )

Step-by-step explanation:

Using the midpoint formula

[tex]\frac{1}{2}[/tex](8 + [tex]x_{R}[/tex] ) = [tex]x_{M}[/tex] = - 2

Multiply both sides by 2

8 + [tex]x_{R}[/tex] = - 4 ( subtract 8 from both sides )

[tex]x_{R}[/tex] = - 12

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

[tex]\frac{1}{2}[/tex](- 10 + [tex]y_{R}[/tex] ) = [tex]y_{M}[/tex] = 6

Multiply both sides by 2

- 10 + [tex]y_{R}[/tex] = 12 ( add 10 to both sides )

[tex]y_{R}[/tex] = 22

The coordinates of R = (- 12, 22 )

Answer:

45°

Step-by-step explanation:

I think you meant m<ACB, and from what I see here, I took half of 90°, which is 45°.

Answer:

The rate of change determines the average speed of the ball when it is dropped from the building.

Step-by-step explanation:

d(t) = 16t^2

when t = 2

d(t) = 16 (2)²

d(t) = 64

when t = 5

d(t) = 16 (5)²

d(t) = 400

Average speed/rate of change = distance/time = 64/2 = 32 feet

Average speed/rate of change = distance/time = 400/5 = 80 feet

The rate of change determines the average speed of the ball when it is dropped from the building.

!!

The average rate of change of d(t) from [tex]\( t = 2 \) to \( t = 5 \)[/tex] represents that the ball traveled at an average rate of 112 feet per second during this time interval.

The average rate of change of a function over a given interval is calculated by finding the difference in the function values at the endpoints of the interval and dividing by the difference in the independent variable values. In this case, we want to find the average rate of change of the function [tex]\( d(t) = 16t^2 \) from \( t = 2 \) to \( t = 5 \).[/tex]

First, we find the values of the function at the endpoints of the interval:

- At [tex]\( t = 2 \), \( d(2) = 16(2)^2 = 64 \)[/tex] feet.

- At [tex]\( t = 5 \), \( d(5) = 16(5)^2 = 400 \)[/tex] feet.

Then, we calculate the difference in the function values:

[tex]\[ \text{Difference in } d(t) = d(5) - d(2) = 400 - 64 = 336 \text{ feet} \][/tex]

Next, we calculate the difference in the independent variable values:

[tex]\[ \text{Difference in } t = 5 - 2 = 3 \text{ seconds} \][/tex]

Finally, we find the average rate of change by dividing the difference in d(t) by the difference in t:

[tex]\[ \text{Average rate of change} = \frac{\text{Difference in } d(t)}{\text{Difference in } t} = \frac{336}{3} = 112 \text{ feet/second} \][/tex]

Answer:

Step-by-step explanation:

x^2 - 36 is the difference of two squares and factors as follows:

        (x - 6)(x + 6)

x^2 - 16 is the difference of two squares and factors as follows:

        (x - 4)(x + 4)

x^2 - 7x + 12 is an easily factored quadratic; the factors are

         (x - 3)(x - 4)

x^2 - x - 20 is an easily factored quadratic; the factors are

         (x - 5)(x + 4)

I conclude that none of the four expressions is prime.

Answer:

B. [tex]x^2+16[/tex]

Step-by-step explanation:

We are asked to find the prime polynomial from our given choices.

We know that a polynomial is prime, when it has only two factors that are 1 and polynomial itself.

Upon looking at our given choices, we can see that each polynomial can be factored except [tex]x^2+16[/tex].

We can see that [tex]x^2+16[/tex] is sum of squares and sum of squares cannot be factored, therefore, polynomial [tex]x^2+16[/tex] is a prime polynomial.

[tex]\huge{\boxed{y=-3x+4}}[/tex]

Slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] represents the slope and [tex]b[/tex] represents the y-intercept.

Substitute in the values. [tex]\boxed{y=-3x+4}[/tex]

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case the slope (m) is -3 and the y-intercept (b) is 4

Your equation is:

y = -3x + 4

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]\large\boxed{(n^3)^2\times(n^5)^4=n^{26}}[/tex]

Step-by-step explanation:

[tex](n^3)^2\times(n^5)^4\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(n^{3\cdot2})\times(n^{5\cdot4})=n^{6}\times n^{20}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=n^{6+20}=n^{26}[/tex]

Answer:

Yes.

Step-by-step explanation:

If we add a fixed number to each term of an arithmetic sequence, we are still going to be having an arithmetic sequence.

For example, given the following sequence:

1, 3, 5, 7, 9, 11...

The difference between consecutive terms  is 2, therefore the pattern is adding two to the previous term.

If we add a fix number, let's say '3':

1+3, 3+3, 5+3, 7+3, 9+3, 11+3...

4, 6, 8, 10, 12, 14...

We notice that the pattern is the same, and it's still an arithmetic sequence.

Answer:

[tex]\boxed{\textbf{1700 yr}}[/tex]

Step-by-step explanation:

[tex]-\dfrac{\text{d}L}{\text{d}t} = kL\\\\\dfrac{dL}{L}=-kdt\\\\\ln L = -kt + C\\\text{At t = 0, L = L$_{0}$, so C = $\ln L_{0}$}\\\ln L = -kt + \ln L_{0}\\\ln L_{0} - \ln L = kt\\\\\ln \dfrac{L_{0}}{L} =kt[/tex]

Data:

L₀ = 24 g

L = 20 g

k = 0.000 11 yr⁻¹

Calculation:

[tex]\ln \dfrac{24}{20} =0.000 11t\\\\\ln 1.2 = 0.000 11t\\\\0.1823 = 0.000 11t\\\\t = \dfrac{0.1823}{0.000 11} = \textbf{1700 yr}\\\\\text{It will take } \boxed{\textbf{1700 yr}}\text{ for the polonium to decay to 20 g}[/tex]

Answer:

Step-by-step explanation:

305p=1,525

305    305

p=5

The solution of the linear equation 305p = 1525 will be 5.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear equation with one variable is given below.

305p = 1525

On simplifying, we have

305p = 1525

      p = 1525 / 305

      p = 5

More about the linear system link is given below.

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Answer:

Third choice.

Step-by-step explanation:

Trinomial means you have 3 terms.

You don't have 3 terms in first two choices so let's not look at them.

Anything of the form [tex]a^2x^2+2abxy+ b^2y^2[/tex] is a perfect square trinomial because it can be written as [tex](ax+by)^2[/tex].

Let's this this:

[tex](ax+by)^2[/tex]

[tex](ax+by)(ax+by)[/tex]

Now foil!

First=ax(ax)=a^2x^2

Outer=ax*by=abxy

Inner=by*ax=abxy

Last=by*by=b^2y^2

Add together and this gives you a^2x^2+2abxy+b^2y^2.

So looking at third choice you can write it as 4^2x^2+24xy+3^2y^2.

Is 2*4*3 equal to 24?  If it is then you have your answer. It is.

We have our answer.

Answer: y=-16

Step-by-step explanation:

Y/-2+5=13

Y/-2=8

Y=-16

Answer:

[tex]x_{1=} \frac{-1+i\sqrt{35} }{6} \\\\x_{2=} \frac{-1-i\sqrt{35} }{6}[/tex]

Step-by-step explanation:

Using the quadratic formula:

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

We will have two solutions:

[tex]x_{1}\\ x_{2}[/tex]

-3x^2-x-3=0     a=-3    b=-1   c=-3

We have:

[tex]x_{1}=\frac{1+\sqrt{-35} }{-6}\\\\x_{2}=\frac{1-\sqrt{-35} }{-6}\\[/tex]

we can write:

[tex]x_{1}=\frac{-1+\sqrt{-35} }{6}\\\\x_{2}=\frac{-1-\sqrt{-35} }{6}\\[/tex]

The solutions are not real numbers.

So, we know: [tex]i=\sqrt{-1}[/tex]

Finally we have:

[tex]x_{1}=\frac{-1+i\sqrt{35} }{6}\\\\x_{2}=\frac{-1-i\sqrt{35} }{6}\\[/tex]

Check the picture below.

Answer:

(a + b)(a + b - 2c)

Step-by-step explanation:

Note that

(a + b)² = a² + b² + 2ab

Given

a² + b² + 2(ab - ac - bc) ← distribute parenthesis

= a² + b² + 2ab - 2ac - 2bc

= (a + b)² - 2ac - 2bc ← factor out - 2c from each term

= (a + b)² - 2c (a + b) ← factor out (a + b) from each term

= (a + b) [ a + b - 2c ]

= (a + b)(a + b - 2c) ← in factored form

The expression a² + b² + 2(ab - ac - bc) cannot be factorized using standard factorization techniques over real numbers, as a² + b² is not factorizable over the reals and there's no common factor for all terms.

To factorize the expression a² + b²+ 2(ab - ac - bc). To factorize this, we will look for a common factor and regroup the terms. Let's see if there's a way to rearrange the terms to resemble a known pattern or factor by grouping.

First, let's rewrite the expression by grouping terms with a common factor:

a² + 2ab - 2ac

b² - 2bc

However, we notice that the expression does not fit into a perfect square or any other easily factorizable form like (a + b)² or (a - b)² due to the nature of the terms a², b², and 2(ab - ac - bc). The expression is already in its simplest factored form as it stands because a²+ b² is not factorizable over the real numbers, and there's no common factor for all terms.

Therefore, the expression a² + b² + 2(ab - ac - bc) does not factorize further using real numbers and the usual factorization techniques.

Answer:

[tex]\large\boxed{-1\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The points on the graph are collinear (they lie on one straight line).

Therefore, average of change is the same as a slope.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We choose two points and put the coordinates to the formula

[tex](1, 4), (3, 1)\\\\\dfrac{1-4}{3-1}=\dfrac{-3}{2}=-1\dfrac{1}{2}[/tex]

The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].

The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.

The points on the graph are collinear (they lie on one straight line).

Therefore, average of change is the same as a slope.

The formula of a slope:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

We choose two points and put the coordinates to the formula

(1, 4), (3, 1)

[tex]\frac{1-4}{3-1} =\frac{-3}{2} =-1\frac{1}{2}[/tex]

The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].

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False.

The Rational Root theorem states that P is a factor of the constant term and q is a factor of the leading coefficient.

Answer:

6^(32)

Also I don't see your choices.

Step-by-step explanation:

I'm going to apply this law of exponents: (x^a)^b=x^(a*b).

It justs says to multiply the exponents in this case so we have 6^(-8*-4)=6^(32).

Answer:

It would be 1/6^32

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

f(n+1) = f(n) -2

We know f(1) = 10

Let n=1

f(1+1) = f(1) -2

f(2) = 10-2 =8

We now know f(2)

Let n=2

f(2+1) = f(2)-2

f(3) = 8 -2=6

f(3) =6

The sum of the three angles of a triangle need to equal 180

To find the third angle subtract the two known angles from 180.

Third angle = 180 - 44 - 72 = 64 degrees.

Answer:

All angles of a triangle add up to 180. Just subtract. -72 --> 108 - 44. 64

Answer:

Part 1) [tex]b=8.2\ units[/tex]

Part 2) [tex]a=10.1\ units[/tex]

Part 3) [tex]A=51\°[/tex] and [tex]C=90\°[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the side b

we know that

In the right triangle ABC

The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)

[tex]sin(B)=AC/AB[/tex]

we have

[tex]AB=c=13\ units[/tex]

[tex]AC=b[/tex]

[tex]B=39\°[/tex]

substitute

[tex]sin(39\°)=b/13[/tex]

solve for b

[tex]b=(13)sin(39\°)[/tex]

[tex]b=8.2\ units[/tex]

step 2

Find the side a

we know that

In the right triangle ABC

The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)

[tex]cos(B)=BC/AB[/tex]

we have

[tex]AB=c=13\ units[/tex]

[tex]BC=a[/tex]

[tex]B=39\°[/tex]

substitute

[tex]cos(39\°)=a/13[/tex]

solve for a

[tex]a=(13)cos(39\°)[/tex]

[tex]a=10.1\ units[/tex]

step 3

Find the measure of angle A

we know that

In the right triangle ABC

[tex]C=90\°[/tex] ----> is a right angle

[tex]B=39\°[/tex]

∠A+∠B=90° ------> by complementary angles

substitute the given value

[tex]A+39\°=90\°[/tex]

[tex]A=90\°-39\°[/tex]

[tex]A=51\°[/tex]

A term is any number, variable or combination of a number and a variable in an equation.

Examples:

In 2x + 5y + 8, 2x is one term,  5y is a second term and 8 is a 3rd term.

In the equation 2x + 3 + 5x -2

Combine the like terms 2x and 5x are like terms because they both have x as a variable, there is a plus sign in fron of the 5x, so you would have 2x +5x = 7x

Then 3 and 3 are like terms, because they are just numbers, there is a subtraction sign in front of the 2, so you have 3-2 = 1

The equation then becomes: 2x + 3 + 5x -2 : 7x + 1

Answer:

n = 16

Step-by-step explanation:

1/2 n = 8 (multiply both sides by 2)

(1/2) (2) n = 8 (2)

n = 8 (2)

n = 16

Answer:

(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].

Please correct if I'm wrong about your expression.  

Step-by-step explanation:

I think you mean [tex]f(x)=3 \cdot 4^x[/tex].

Let's test the point and see.

A. (0,12)?

(0,12)=(x,y)

What happens when x equals 0? Is the result 12?

[tex]3 \cdot 4^0[/tex]

[tex]3 \cdot 1[/tex]

[tex]3(1)[/tex]

[tex]3[/tex]

Yep that isn't 12 so (0,12) is not on the graph of f.

B. (0,0)?

(0,0)=(x,y)

What happens when x equals 0? Is the result 0?

[tex]3 \cdot 4^0[/tex]

We already this and got 3 so (0,0) is not on the graph of f.

C.  (1,12)?

(1,12)=(1,12)

What happens when x equals 1? Is the result 12?

[tex]3 \cdot 4^1[/tex]

[tex]3 \cdot 4[/tex]

[tex]12[/tex]

The result is 12 so (1,12) is on the graph of f.

C.  (12,1)

(12,1)=(x,y)

What happens when x equals 12? Is the result 1?

[tex]3 \cdot 4^{12}[/tex]

This will result in a really big number that isn't 1 so (12,1) is not on the graph of f.

(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].

Answer:

(1,12)

Step-by-step explanation:

ape x

Answer:

$7,434.57

knewton alta 2023

Step-by-step explanation:

Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.

To calculate the amount Edgar will owe on his credit card debt in 2 years with continuous compounding, we can use the formula for compound interest:

A = P*e^(rt)

Where:

Plugging in the values, we have:

A = $5,000 * e^(0.20*2)

Calculating this expression gives the approximate value of $6,360.92. Therefore, Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.

Answer:

Terry has 20 quarters and 18 dimes

Step-by-step explanation:

Let

x -----> the number of quarters

y ----> the number of dimes

Remember that

1 quarter=$0.25

1 dime=$0.10

we know that

x=y+2 ----> equation A

0.25x+0.10y=6.80 -----> equation B

Substitute equation A in equation B and solve for y

0.25(y+2)+0.10y=6.80

0.25y+0.50+0.10y=6.80

0.25y+0.10y=6.80-0.50

0.35y=6.30

y=18 dimes

Find the value of x

x=y+2 -----> x=18+2=20 quarters

therefore

Terry has 20 quarters and 18 dimes

To determine the number of quarters and dimes Terry has, set up two equations based on the information provided, solve one of the equations for one variable, and substitute this into the second equation. Solve the equation to get the number of dimes and substitute it into the first equation to get the number of quarters.

To solve this, we can use algebra, setting up equations to represent the problem and then solve it.

Let F represent the number of dimes (since a dime is worth $0.10) and let Q represent the number of quarters (since a quarter is worth $0.25). We have two key pieces of information:

From the first equation, we can substitute F + 2 for Q in the second equation: 0.10F + 0.25(F + 2) = 6.80.

Solve this equation to find the value of F, representing the number of dimes, Terry has. Then, substitute the value of F into the first equation to determine the number of quarters Terry has.

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Answer:

1. 3x + 6

2. [tex]\frac{99}{14}[/tex] or 7.071

3. [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

1. 3 consecutive even integers

If the first is x, the 2nd is x+2, and the 3rd is x+4

x + (x+2) + (x+4)

= 3x + 6

2. The equation for circumference is

[tex]C=2\pi r[/tex]

If the diameter is [tex]1\frac{4}{5} = \frac{9}{5}[/tex]

The the radius is half of that.

So the circumference is

[tex]\pi * \frac{9}{4} *\frac{1}{2} * 2\\= \pi * \frac{9}{4}\\=\frac{22}{7} * \frac{9}{4}\\= \frac{198}{28}\\ =\frac{99}{14} \\=7.071[/tex]

3. To divide we multiply by the reciprocal.  So flip the fraction that we are dividing by.

[tex]\frac{1}{7} / -\frac{2}{7}\\ = \frac{1}{7} * -\frac{7}{2} \\= -\frac{1}{2}[/tex]

Answer: B. It would be shifted up.

Step-by-step explanation: We are changing the last number only. This number determines where the y-intercept is, which is on the vertical axis. Since the number increases by 4, the y-intercept would be shifted up by 4, without changing the slope. Therefore, the answer would be B. It would be shifted up.

Answer:

Step-by-step explanation:

The tough part of this question is figuring out what to do with √(7^2). You could do it by expanding the square. √(7^2) = √49

Now what is the square root of 49? Is it not 7?

√49 = 7

7^6 * 7^1

7 ^(6 + 1)

7 ^ 7

Answer:

49

Step-by-step explanation:

Answer:

360

Step-by-step explanation: