If a total of 360 students were involved in the evening's activities, how many students attend the school?

Answer:

x = 3, x = -5

Step-by-step explanation:

A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:

a^2 = x^2

a = x

Now, we can substitute x for a in the other expression to create the equation:

2ab = 2x

2(x)b=2x

b = 1

From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:

x^2 + 2x = 15

x^2 + 2x + 1 = 16

Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:

(x + 1)^2 = 16

Now, we take the square root of both sides:

x + 1 = ± 4

We can separate this into two equations and solve:

x + 1 = 4

x = 3

x + 1 = -4

x = -5

Answer:

Step-by-step explanation:

x^2 + 2x = 15

x^2 + 2x + [1/2(2)]^2 = 15 +  [1/2(2)]^2

(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2

(x + 1)^2 = 15 + 1^2

(x + 1)^2 = 15 + 1

(x+1)^2 = 16                       Take the square root of both sides.

sqrt( (x + 1)^2 ) = sqrt(16)

x + 1 = +/- 4

x + 1 = 4

x = 4 - 1 = 3

x + 1 = -4

x = -4 - 1

x = - 5

So the roots are 3 and - 5

Step-by-step explanation:

IN first triangle multiplier factor is 4

and IN second triangle multiplier factor is

[tex] \frac{3}{2} [/tex]

Answer:

the answer is 1959

Step-by-step explanation:

2834-875=1959

Answer:

x = 16

y = 5

Step-by-step explanation:

The three sides of an equilateral triangle are equal. Therefore:

3x + 1 = 49

Solve for x.

3x + 1 - 1 = 49 - 1

3x = 48

3x/3 = 48/3

x = 16

Also

18y - 41 = 49

Solve for y.

18y - 41 + 41 = 49 + 41

18y = 90

18y/18 = 90/18

y = 5

Answer:

f ( -4 ) = 1024 + 8 + 9

Step-by-step explanation:

f ( x ) = 4x⁴ - x² + 9

If f ( - 4 ) then we get

f ( -4 ) = 4 ( -4)⁴ - ( - 4)² + 9

Expand the exponents

f ( - 4 ) = 4 ( 256 ) + 8 + 9

multiply the numbers

f ( -4 ) = 1024 + 8 + 9

Answer:

The second answer.

Step-by-step explanation:

Tim is correct. Absolute value is just the distance away from 0. In this case, both P and Q are 3/8 away from zero, even though they have opposite signs. In fact, opposites signs of the same number will always have the same absolute value because they are the same distance from 0.

So, it is the second one.

Hope this helps!

Answer:

2nd answer choice:

Tim, because each point is 3/8 unit away from 0

Step-by-step explanation:

The absolute value of a number is how far it is from 0 in the number line, not including direction.

On this number line, point P is -3/8 and point Q is 3/8.

In the number line, count how many units each point is away from 0. You will find that they each have a distance of 3/8 from the number line. Therefore they have the same absolute values.

PS: absolute values are NEVER negative.

Hope this helps!

Step-by-step explanation:

For Adding and Subtraction:

1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator).

1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.

1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them).

1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed.

1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed. 5. simplify the numerator by distributing and combining like terms.

1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed. 5. simplify the numerator by distributing and combining like terms. 6. Factor the numerator if can and replace the letters "LCD" with the actual LCD.

1. Find the denominator (bottom number) of each fraction to find the LCD (least common denominator). 2. find the LCD.3. Find the new numerator (top number) for each fraction. To find the new numerators for each fraction, compare the denominator of each of the original fractions to the LCD and write down everything different about the LCD in the numerator of the fraction. (you should also consider using the letters "LCD" in the denominator instead of the actual LCD as it will be less tempting to reduce them). 4. combine the fraction by adding or subtracting the numerators and keeping the LCD. When subtracting, notice that the subtraction sign is moved into the numerator so it can be distributed later if needed. 5. simplify the numerator by distributing and combining like terms. 6. Factor the numerator if can and replace the letters "LCD" with the actual LCD. 7. simplify or reduce the rational expression of you can. Remember, to reduce rational expressions, the factors must be exactly the same in both the numerator and the denominator.

To Multiply:

To Divide:

9514 1404 393

Answer:

Step-by-step explanation:

For multiplication and division, the denominator of the result is developed as part of the algorithm for performing these operations on rational expressions. For example, ...

  (a/b)(c/d) = (ac)/(bd)

  (a/b)/(c/d) = (ad)/(bc)

It is not necessary to make the operands of these operations have a common denominator before the operations are performed. That being said, in some cases, the division operation can be simplified if the operands do have a common denominator or a common numerator:

  (a/b)/(c/b) = a/c

  (a/b)/(a/c) = c/b

__

If the result of addition or subtraction is to be expressed using a single denominator, then the operands must have a common denominator before they can be combined. That denominator can be developed "on the fly" using a suitable formula for the sum or difference, but it is required, nonetheless.

  (a/b) ± (c/d) = (ad ± bc)/(bd)

This formula is equivalent to converting each operand to a common denominator prior to addition/subtraction:

  [tex]\dfrac{a}{b}\pm\dfrac{c}{d}=\dfrac{ad}{bd}\pm\dfrac{bc}{bd}=\dfrac{ad\pm bc}{bd}[/tex]

Note that the denominator 'bd' in this case will not be the "least common denominator" if 'b' and 'd' have common factors. Even use of the "least common denominator" is no guarantee that the resulting rational expression will not have factors common to the numerator and denominator.

For example, ...

  5/6 - 1/3 = 5/6 -2/6 = 3/6 = 1/2

The least common denominator is 6, but the difference 3/6 can still be reduced to lower terms.

If we were to use the above difference formula, we would get ...

  5/6 -1/3 = (15 -6)/18 = 9/18 = 1/2

Answer: x=52

Step-by-step explanation:

x+72=34+90

x+72=124

124-72=x

x=52

Answer:

0.098 , 0.89, 0.98

Step-by-step explanation:

0.098 is the smallest, 0.98 is the closest to 1 so it's the biggest

Answer:

ans:

Match the metric measurement on the left with an equivalent unit of measurement on the right are as follows;

0.3 hectoliter       3 deciliters

0.03 liters             30 milliliters

30 centimeter     3 Deciliters

3000 Milliliters    0.3 Decaliters

A standard unit of measurement is a quantifiable language that describes the magnitude of the quantity.

Match the metric measurement on the left with an equivalent unit of measurement on the right is determined in the following steps given below.

1. 0.3 hectoliter = 0.3 × 10 = 3 deciliters

2. 0.03 liters = 0.03 × 1000 = 30 mililiters

3. 3 Centiliters = 0.3 Deciliters then 30 centimeter = 3 Deciliters

4. 3000 Milliliters = 0.3 Decaliters

Learn more about unit measurement here;

https://brainly.com/question/15402847

#SPJ2

Answer:

7 442,84

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.

tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16   ⇒   sec = -(1/4)√97

cot(θ) = 1/tan(θ) = -4/9

csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81   ⇒   csc = (1/9)√97

sin(θ) = 1/csc(θ) = (9√97)/97

cos(θ) = 1/sec(θ) = (-4√97)/97

9514 1404 393

Answer:

  -3840t^4

Step-by-step explanation:

The k-th term, counting from k=0, is ...

  C(5, k)·(4t)^(5-k)·(-3)^k

Here, we want k=1, so the term is ...

  C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4

__

The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.

Answer:

True

Step-by-step explanation:

if |x| is 3 then x is either -3 or 3. Either way, the distance from 0 is 3.

Hole this helps! :)

Answer:

The best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

Step-by-step explanation:

Best point estimate:

The best point estimate of a population mean is the sample mean.

In this question:

The sample mean amount of money spent for textbooks was $121.60, which means that the best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

Answer:

The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)

Step-by-step explanation:

Hey there!

The probability of first getting a red marble is 1/3 since we have 1 red marble out of 2 + 1 = 3 total.

We put the marble back. The probability of then choosing a black marble is 2/3, since we have 2 black marbles out of 3 total.

So we get 1/3 * 2/3 = 2/9

The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)

Hope this helps, please mark brainliest if possible. Have a nice day. :)

Answer:

We want to find:

[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}[/tex]

Here we can use Stirling's approximation, which says that for large values of n, we get:

[tex]n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n[/tex]

Because here we are taking the limit when n tends to infinity, we can use this approximation.

Then we get.

[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}[/tex]

Now we can just simplify this, so we get:

[tex]\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\[/tex]

And we can rewrite it as:

[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}[/tex]

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.

Thus:

[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}[/tex]

9514 1404 393

Answer:

  $2505.80

Step-by-step explanation:

After the first exchange, the tourist has ...

  $3000(12.90 R/$) = R38,700

After 7 days, she has ...

  R38,700 -7(R900) = R32,400

After the second exchange, she has ...

  R32,400 × ($1/R12.93) = $2505.80

She gets $2505.80 at the second exchange.

Answer:

im doing the same one, i believe it is D

Step-by-step explanation:

Answer:

a- yes because corresponding sides are parallel and have lengths in the ration 4/3

Step-by-step explanation:

just did the test

[tex]f'(4) = 43[/tex]

Explanation:

Given: [tex]f(x)=5x^2 + 3x + 3[/tex]

[tex]\displaystyle f'(x)= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}[/tex]

Note that

[tex]f(x+h) = 5(x+h)^2 + 3(x+h) + 3[/tex]

[tex]\:\:\;\:\:\:\:= 5(x^2 + 2hx + h^2) + 3x + 3h +3[/tex]

[tex]\:\:\;\:\:\:\:= 5x^2 + 10hx + 5h^2 + 3x + 3h +3[/tex]

Substituting the above equation into the expression for f'(x), we can then write f'(x) as

[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{10hx + 3h + 5h^2}{h}[/tex]

[tex]\displaystyle\:\:\;\:\:\:\:= \lim_{h \to 0} (10x +3 +5h)[/tex]

[tex]\:\:\;\:\:\:\:= 10x + 3[/tex]

Therefore,

[tex]f'(4) = 10(4) + 3 = 43[/tex]

Answer:

[tex]y=\frac{5}{2}x-14[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]y=\frac{5}{2}x-10[/tex]

In the given equation, [tex]\frac{5}{2}[/tex] is in the place of m, making it the slope. Because parallel lines have the same slope, the line we're currently solving for therefore has a slope of [tex]\frac{5}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{5}{2}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{5}{2}x+b[/tex]

Plug in the given point (-6,-29) and solve for b

[tex]-29=\frac{5}{2}(-6)+b[/tex]

Simplify -6 and 2

[tex]-29=\frac{5}{1}(-3)+b\\-29=(5)}(-3)+b\\-29=-15+b[/tex]

Add 15 to both sides to isolate b

[tex]-29+15=-15+b+15\\-14=b[/tex]

Therefore, the y-intercept is -14. Plug this back into [tex]y=\frac{5}{2}x+b[/tex]:

[tex]y=\frac{5}{2}x-14[/tex]

I hope this helps!

Answer:

2.52m³

Step-by-step explanation:

volume=L x W x H

V=2 x 1.4 x 1.8

V=5.04

WE DIVIDE 5.04m³ by 2 to get 2.52m³

Have a nice day

Answer:

since it's the lhs we are concerned about, i. e., Y axis, so it must be either up or down. now look at the question, it says 8x2 - (1), it means one lower value of y i. e., 1 unit down

Answer:It is shifted 1 unit down.

Step-by-step explanation:

Answer:

77,786.251

Step-by-step explanation:

Answer:

Answer is 42

Step-by-step explanation:

2^5 + 10

2*2*2*2*2 + 10

32 + 10

42

Answer:

[tex]{ \tt{ w = 2hx - 11x}} \\ \\ { \bf{w = x(2h - 11)}} \\ \\ { \bf{x = \frac{w}{2h - 11} }}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = \frac{w}{(2h - 11)} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]w = 2hx - 11x[/tex]

[tex]✒ \: w = x \: (2h - 11)[/tex]

[tex]✒ \: x = \frac{w}{(2h - 11)} [/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{3}{2} \div 5[/tex]

[tex] = \frac{3}{2} \times \frac{1}{5} [/tex]

[tex] = \frac{3}{10} [/tex]

= 0.3 (Ans)

Answer:

3/10

Step-by-step explanation:

3/2÷5

3/2÷5/1

3/2÷10/2 ( LCM of denominators)

3/2×2/10 ( Reciprocal of 10/2)

3/10 (Cancelling 2 by 2)

Answer:

[tex]Width = 59[/tex]

Step-by-step explanation:

Given

The above data

Required

The class width

To do this, we simply calculate the difference between the class limits of any one of the classes.

Taking 1187–1246 as a point of reference, the class width is:

[tex]Width = 1246 - 1187[/tex]

[tex]Width = 59[/tex]

Answer:

a. Cookbooks

b. 50%

c. 30%

Step-by-step explanation:

According To the Question,

a. Now, Approximately Cookbooks & Textbooks revenue Form 180°, but textbook revenue is more than cookbooks as clearly visible in the diagram

Thus, cookbooks are less than 90°.

Now, we have to find 1/5th of total publisher revenue which is 360°/5= 72°. & the Cookbooks is nearest to 72° ( less than 90°)

So, Answer For (a) is Cookbooks  

b. Here in Diagram Clearly Visible that The Cookbooks & Textbooks Revenue Form 180° which is Approximately 50% of total Publisher's Revenue.

So, the Total Revenue Comes From Textbooks & Cookbooks is 50%.

c. Now We know the Cookbooks + Textbooks Revenue form 180° Approximately & Cookbook is approximately equal to 72° (as we solve above)

So, textbooks are 180°-72° = 108°, which is 30% of 360° ∴ 30% Revenue Come From Textbooks.