What is the next number in the
pattern -3, 6, -9, 12,

Answer:

Explanation:

1. Ratio of campers to counselors in june:

2. Ratio of campers to counselors in july:

3. Equivalent ratios:

Solve for x:

The camp needs approximately 22 counselors in July to maintain the original camper-to-counselor ratio of 12.5:1 that was present in June, when there were 325 campers and 26 counselors.

The question asks how many counselors the camp needs in July to keep an equivalent ratio of campers to counselors from June. In June, the camp had 325 campers and 26 counselors. The ratio of campers to counselors is 325:26, which simplifies to approximately 12.5:1. If 265 campers leave in July and 215 new ones arrive, the total number of campers for July is 325 - 265 + 215 which equals 275. To maintain the same ratio, we divide the number of July campers by the original ratio:

The camp needs approximately 22 counselors in July to maintain the same camper-to-counselor ratio as in June.

Answer:

.4

Step-by-step explanation:

Use a caluculator

Answer:

.4

Step-by-step explanation:

Answer:

2.2

Step-by-step explanation:

It is a 2.2 slope because you just have to divide the depth of water by the time by 2.2 or multiply the time by 2.2 to get the depth of water :)

Answer:

(0,0)&(2,4.4)

(4.4-0)/(2-0)= 4.4/2= 2.2 is the overall slope

To solve the equation 5(2c + 7) - 3c = 7(c + 5), distribute the values inside the parentheses, combine like terms, and solve for c.

To solve the equation 5(2c + 7) - 3c = 7(c + 5), we will distribute the values inside the parentheses. This gives us 10c + 35 - 3c = 7c + 35. Next, we will combine like terms by subtracting 7c from both sides of the equation and adding 3c to both sides. This simplifies the equation to 10c - 7c = 35. By combining the terms on the left side, we get 3c = 35. Finally, we can solve for c by dividing both sides of the equation by 3, which gives us c = 35/3 or 11.67.

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Answer:

The irrational conjugate theorem states that if a polynomial equation has a root (a + √b), then we can say that the conjugate of (a + √b), i.e. (a - √b) will also be another root of the polynomial.

Step-by-step explanation:

The irrational conjugate theorem states that if a polynomial equation has a root (a + √b), then we can say that the conjugate of (a + √b), i.e. (a - √b) will also be another root of the polynomial.

For example, if we consider a quadratic equation x² + 6x + 1 = 0, then two of its roots are - 3 + √8 and - 3 - √8 and they are conjugate of each other. (Answer)

The Irrational Conjugate Theorem states that if a complex number is irrational, then its conjugate is also irrational. It is used in mathematics to prove this relationship. The theorem is based on the definition of the conjugate of a complex number, and a proof by contradiction approach can be used to prove it.

The Irrational Conjugate Theorem is used in mathematics to prove that if a complex number is irrational, then its conjugate is also irrational. This theorem is based on the concept of the rational and irrational parts of a complex number. Let's define a complex number as z = a + bi, where a and b are real numbers and i is the imaginary unit. The conjugate of z, denoted by [tex]\bar Z[/tex], is obtained by changing the sign of the imaginary part. So, if z = a + bi, then [tex]\bar Z = a - bi.[/tex] The Irrational Conjugate Theorem states that if a + bi is an irrational complex number, then a - bi (the conjugate) is also irrational.

To prove this theorem, we can use a proof by contradiction approach. Let's assume that a + bi is irrational and a - bi (the conjugate) is rational. We can then use valid reasoning to arrive at contradictory results. For example, we can add a + bi and a - bi to get 2a, which is a rational number. However, this contradicts our initial assumption that a + bi is irrational. Therefore, our assumption must have been false and the theorem is proven.

Answer:

D. [tex]y=-0.927x+13.634[/tex]

Step-by-step explanation:

We graph the points on the graph. The graph is attached.

Let us take two points (1, 14) and (15, 1), and calculate the slope [tex]m[/tex]between them (we choose these points because the line passing through them will be the best fit for all points)

[tex]m=\frac{14-1}{1-15} =\frac{13}{-14} =-0.9286[/tex]

Thus we have the equation

[tex]y=-0.9286x+b[/tex]

Let us now calculate [tex]b[/tex] from the point [tex](1,14)[/tex]

[tex]14=-0.9286(1)+b[/tex]

[tex]b=14.9286[/tex]

So the equation we get is

[tex]y=-0.9286x+14.9286[/tex]

Let us now turn to the choices given and see which choice is closest to our equation: we see that choice D. [tex]y=-0.927x+13.634[/tex] is the closest one, so we pick it.

Answer:

iT WAS 3 Bum

Step-by-step explanation:

Answer:

2x+2 or 2(x+1)

Step-by-step explanation:

2x-2+4=2x+2

Answer: 46 years

Step-by-step explanation:

Let the father's age be x and the son's age be y, then 3 years ago:

Father = x - 3

son     = y - 3

Then , from the first statement :

x - 3 = 3 ( y - 3 )

x - 3 = 3y - 9

x     = 3y - 9 + 3

x     = 3y - 6 .......................................... equation 1

In five years time

father = x + 5

son = y + 5

Then , from the second statement

x + 5 = 2 ( y + 5 )

x + 5 = 2y + 10

x       = 2y + 10 - 5

x       = 2y + 5 ........................ equation 2

Equating equation 1 and 2 , we have

3y -6 = 2y + 5

add 6 to both sides

3y = 2y + 5 + 6

subtract 2y from both sides

3y - 2y = 11

y = 11

substitute y = 11 into equation 1 to find the value of x

x = 3y - 6

x = 3(11) - 6

x = 33 - 6

x = 27

This means that the father is presently 27 years and the son is presently 11 years.

In four years time

father = 27 + 4 = 31

son = 11 + 4      = 15

sum of their ages in four years time will be

31 + 15 = 46 years

Answer:

46 years

Step-by-step explanation:

Answer:

Step-by-step explanation:

In solving this, we'll make some keen assumptions to solve the question.

We'll represent the father's age with "a"

And represent the sons age as "b"

Lets interpret the question.

3 years ago, (means in the past), we'll subtract.

Therefore:

Father's age = a - 3

Sons age = b - 3

The sentence said, " 3 years ago, father was 3 times the sons age*. Interpreting that becomes:

a - 3 = 3 times (b - 3)

Simplifying that gives :

a - 3 = 3(b - 3)

a - 3 = 3b - 9

a = 3b - 9 + 3

a = 3b - 6 ( FIRST EXPRESSION )

The next line says: In five years time (that's in the future, hence we add) he'll be twice his sons age.

Therefore I become:

Father : a + 5

Son : b + 5

a + 5 = 2(b + 5)

a + 5 = 2b + 10

a = 2b + 5 ( SECOND EXPRESSION)

Equating the first and second equation to solve for "a" - the father's age

3b - 6 = 2b + 5

b = 5 + 6

b = 11 years (Sons age)

Substitute b = 1 in the first expression.

a = 3b - 6

a = 3(11) - 6

a = 33 - 6

a = 27 years (Father's age)

Let resolve, the last sentence:

What will be the sum of their ages in 4 years time. (SINCE IT'S IJ THE FUTURE, WE ADD)

Father's age in four years time: 27 + 4 = 31

Son's age in four years time: 11 + 4 = 15.

The sum of their ages in same four years time becomes:

31 + 15 (years)

46 years

Answer:

X= 7

Step-by-step explanation:

Answers:

1) [tex]cos B=\frac{4}{5}=0.8[/tex]

2) [tex]csc A=\frac{5}{3}=1.66[/tex]

3) [tex]sec B=\frac{5}{4}=1.25[/tex]

4) [tex]tan A=\frac{3}{4}=0.75[/tex]

5) [tex]z=38.65\°[/tex]

Step-by-step explanation:

First exercise:

We have a right triangle with the values of each side an we have to find the following trigonometic functions (taking into account the secant function [tex]sec[/tex] is the inverse of the cosine, the cosecant [tex]csc[/tex] is the inverse of the sine):

1) [tex]cos B=\frac{Adjacent-side}{hypotenuse}[/tex]

[tex]cos B=\frac{4}{5}=0.8[/tex]

2) [tex]csc A=\frac{1}{sin A}[/tex]

[tex]\frac{1}{sin A}=\frac{1}{\frac{5}{3}}[/tex]

Then:

[tex]csc A=\frac{5}{3}=1.66[/tex]

3) [tex]sec B=\frac{1}{cos B}[/tex]

[tex]frac{1}{cos B}=\frac{1}{\frac{4}{5}}[/tex]

Then:

[tex]sec B=\frac{5}{4}=1.25[/tex]

4) [tex]tan A=\frac{opposite-side}{adjacent-side}=\frac{3}{4}[/tex]

Then:

[tex]tan A=\frac{3}{4}=0.75[/tex]

Second exercise:

5) Here, we are given another right triangle and we have to find the measure of the angle [tex]z[/tex].

So, according to the figure, we can use the tangent function:

[tex]tan z=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan z=\frac{8}{10}[/tex]

Finding the value of [tex]z[/tex]:

[tex]z=tan^{-1}\frac{8}{10}[/tex]

[tex]z=38.65\°[/tex]

Answer:

Its 4

Step-by-step explanation:

24÷3=8÷2=4

Answer:

the amount of pennies that Bryan lost is 16

To find the measure of each angle, we can set up an equation and solve it for x, which represents one of the angles. The other angle can be calculated by subtracting x from 90. The answers are x = 63.6° and 90 - 63.6 = 26.4°.

To solve this problem, we need to set up an equation based on the given information. Let x be the measure of one angle, and since the angles are complementary, the other angle will be 90 - x. According to the problem, x is 37.2° more than 90 - x. This can be written as the equation x = 90 - x + 37.2. Solving this equation, we find that x = 63.6°. Therefore, one angle measures 63.6° and the other angle measures 90 - 63.6 = 26.4°.

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Answer:

5/8

Step-by-step explanation:

1/4 = 2/8

2/8 + 3/8 = 5/8

Answer:

5/8

Step-by-step explanation

1/4 has a common denominator as 3/8 and when u find the common denominator add and ur good to go

Answer:

-12

Step-by-step explanation:

Answer:

Your answer

Step-by-step explanation:

When c=4. Then,

c²-9c+8

= 4²-9c+8

= 4*4-9c+8

= 16-94+8

= 78+8

= -86 ans

Answer:

First option:  [tex]6*10^{-4}[/tex]

Step-by-step explanation:

The expression is:

 [tex](6.3*10^{-2})(9.9*10^{-3})[/tex]

Scientific Notation (which is also known as "Standard form"), is a way to write numbers. It is very useful to handle very small numbers and very large numbers.

By definition, Scientific Notation has the following form:

[tex]a*10^n[/tex]

Where the coefficient "a" is a number from 1 to 10 without including 10, and the exponent "n" is an Integer.

Given:

[tex](6.3*10^{-2})(9.9*10^{-3})[/tex]

If you want to estimate the result, you can round the coefficients to the nearest whole number. Since the decimal point must be just after the first digit, you know that:

[tex](6*10^{-2})(10*10^{-3})=(6*10^{-2})(1*10^{-2})[/tex]

Now you need to remember the Product of powers properties:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then, solving the multiplication, you get:

[tex]6*10^{-4}[/tex]

Answer:

the answer is a

Step-by-step explanation:

i took the test... 100% i swear

Answer:

Infinitely Many Solutions

Step-by-step explanation:

Since it's given that x = 3y + 4 we can use this in second expression

3×(3y+4) = 9y + 12 ➡ 9y + 12 = 9y + 12 add the like terms

9y - 9y = 12-12 ➡ 0 = 0 there's infinitely many solutions for second equation

Same goes for first equation.

Answer:

84, 82, 246

Step-by-step explanation:

first multiply by 3 for first term

next term, use previous term minus 2

The actual amount that should be credited is $757.58.

Solution:

Given that,

2% Discount if paid in 10 days.

1% Discount if paid in 15 days, (but greater that 10 days)

Net due in 60 days.

That is,

[tex]\bold{1400\times0.98 = 1372}[/tex] will close the acount on days 1-10

[tex]\bold{1400\times0.99 = 1386}[/tex] will close the acount on days 11-15

And August 8 is Day 15 and falls under the 1% discount rule.

Therefore, we have to divide the partial payment by the complement of the discount rate.

[tex]\bold{\Rightarrow\frac{750}{0.99} = 757.58}[/tex] from the balance, and [tex]\bold{1400.00 - 757.58 = 642.42}[/tex] is due by day 60.

Answer:

$ 322

Step-by-step explanation:

x = his paycheck

x - 1/2x + 55 = 216

1/2x + 55 = 216

1/2x = 216 - 55

1/2x = 161

x = 161 * 2

x = $ 322 <===

Answer:

B, C, and D

Step-by-step explanation:

By doing 5÷8 = .625 you know that Hang can read .625 of a page per minute.

You can do this for the rest of the people finding that Kira reads .5 page per minute which is a slower/ smaller ratio, Joe rate is .66, Quon's ratio is .71 and Lulus rate is .76, the only rate that is smaller than Hangs is Kira,s, leaving you with Joe, Quon, and Lulu to be your answer

Joe, Quon, and Lulu have a greater ratio of pages read to minutes than Hang. Their respective ratios are 0.6667, 0.714, and 0.769, each higher than Hang's ratio of 0.625.

Let's determine who has a greater ratio of pages read to minutes than Hang.

Hang's ratio is 5:8 or 5/8 = 0.625.

ratio = 2/4 = 0.5 (less than 0.625)

    2. Joe: 6 pages in 9 minutes,

ratio = 6/9 = 0.6667 (greater than 0.625)

    3. Quon: 5 pages in 7 minutes,

ratio = 5/7 ≈ 0.714 (greater than 0.625)

    4. Lulu: 10 pages in 13 minutes,

ratio = 10/13 ≈ 0.769 (greater than 0.625)

So, Joe, Quon, and Lulu have a greater ratio of pages read to minutes than Hang.

Answer: 4

Step-by-step explanation:

To solve this problem we can use the Pythagorean Theorem to find the length of the other LEG of a right triangle

Pythagorean Theorem can be written as A^2+B^2=C^2

Now we plug in the values. C represents the hypotenuse while A and B represent the legs. We only are given one leg and the hypotenuse so we will be solving for B. (Or A if you swap the legs around)

3^2+b^2=5^2

9+b^2=25

Subtract 9 from both sides:

16=b^2

Now we take the square root of both sides

b=4

The length of the other leg of the triangle is 4 feet.


This is a basic 3-4-5 Triangle. Anytime the hypotenuse of a triangle is 5 and the leg is 3 the other leg will always be 4.

Answer:

$5952

Step-by-step explanation:

The principal of $4800 will become after 24 months at an interest of 12% APR,

[tex]4800(1 + \frac{2 \times 12}{100}) = 5952[/tex] dollars.

Now, the monthly payment is $135.57 for 24 months.

So, the payment by installment is $(135.57 × 24) = $3253.68.

Therefore, the down payment was $(5952 - 3253.68) = $2698.32.

Therefore, the total paid for the motorcycle including the down payment was $5952. (Answer)

Answer:

y = -1/3x + 2

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals.

The line y = 3x - 2 has slope 3.

The perpendicular line has slope -1/3.

Now we find the equation of the line that has slope -1/3 and passes through (-9, 5).

y = mx + b

y = -1/3x + b

5 = (-1/3)(-9) + b

5 = 3 + b

b = 2

The equation of the perpendicular is

y = -1/3x + 2

it said it was wrong for me

The length of the unknown leg is approximately 35.4 inches.

The image shows a right triangle with the following dimensions:

The base of the triangle is 24 inches.

The height of the triangle is 26 inches.

We can use the Pythagorean theorem to solve for the length of the missing leg. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs.

Let us call the unknown side "ao".

In this case, we can write the equation as follows:

ao^2 = 24^2 + 26^2

where:

ao is the length of the hypotenuse (unknown)

24 is the length of the base

26 is the length of the height

Simplifying the equation:

ao^2 = 576 + 676

ao^2 = 1252

ao = sqrt(1252)

ao ≈ 35.4 inches

Therefore, the length of the unknown leg is approximately 35.4 inches.

Answer:

B, a cold and nasty winter day

Step-by-step explanation:

.

Hello ^w^

I believe the answer you are looking for is A

I found this answer by adding up the lengths of all the sides.

S -> T = 8

S -> R = 7

Q -> R = 6

P -> Q = 6

P -> T = 10

10 + 6 + 6 + 7 + 8 ->  37

A -> 37

If I am incorrect, please inform me.

Have a good day!