Which of the following is equivalent to the expression below?
√(-300)

A. -10i √(3)
B. -3i √(10)
C. 3i √(10)
D. 10i √(3)

Answer:

x = - 7

Step-by-step explanation:

Given

3x + 5 = - 16 ( subtract 5 from both sides )

3x = - 21 ( divide both sides by 3 )

x = - 7

Two-step equations can get more difficult the higher the numbers get, but they're not too hard! ;)

To solve 3x+5=-16:

First subtract 5 from each side

Now its 3x=-21

Next divide 3 from each side

You get x=-7!

Always check your work! To check your work plug your answer "-7" into x.

So it looks like this: 3(-7)+5=-16 then distribute and solve!

You'll get -16=-16, that means its correct/true!

To model the bird population that triples each year starting with 10 birds, an exponential growth function is used: f(x) = 10 × 3^x, where x is the number of years.

To create a function that represents the scenario of birds increasing threefold each year, we need to use an exponential growth model.

The initial population of birds is 10 and then it triples every year.

Therefore, the function that describes the number of birds after x years would be:

f(x) = 10 × 3^x

Here, f(x) represents the number of birds after x years, 10 is the initial number of birds released into the habitat, and 3^x indicates that the population is growing three times each year for x years.

Final answer:

The number of birds after x years can be calculated using the exponential function B(x) = 10 × 3^x, representing the initial population of 10 birds tripling every year.

Explanation:

The scenario describes a population of birds in a new habitat growing exponentially each year. The initial population of birds is 10 (in year 0), and the population triples every year thereafter. To represent this situation mathematically, we can use an exponential function.

To find the number of birds after x years, we can use the following function:

B(x) = 10 × 3^x

Where:

B(x) is the number of birds after x years

10 is the initial number of birds

3 is the growth factor, as the population is tripling each year

x is the number of years since the birds were first released into the habitat

This equation models exponential growth and gives us the predicted population of the birds for any given year x.

Answer:

f(x)=x^3-3x^2+25x-75

Step-by-step explanation:

Solve for x:

x^3 - 3 x^2 + 25 x - 75 = 0

The left hand side factors into a product with two terms:

(x - 3) (x^2 + 25) = 0

Split into two equations:

x - 3 = 0 or x^2 + 25 = 0

Add 3 to both sides:

x = 3 or x^2 + 25 = 0

Subtract 25 from both sides:

x = 3 or x^2 = -25

Take the square root of both sides:

Answer:  x = 3 or x = 5 i or x = -5 i

Answer:

x squared plus two times x minus one = zero.

Step-by-step explanation:

(This is a Quadratic equation in the variable x).

Answer:

One less than the sum of square of a number  and twice the number is 0

Step-by-step explanation:

[tex]x^2+ 2x - 1 = 0[/tex]

x represents any number. x^2 represents square of a number

2x represents twice the number

[tex]x^2+2x[/tex] can be written as sum of square of a number  and twice the number

[tex]x^2+2x-1[/tex]

One less than the sum of square of a number  and twice the number

[tex]x^2+2x-1=0[/tex]

One less than the sum of square of a number  and twice the number is 0

Answer:

z = 5

Step-by-step explanation:

Given

- 0.25z = - 1.25 ( divide both sides by - 0.25

z = [tex]\frac{-1.25}{-0.25}[/tex] = 5

z = 5

Answer:

z = 5.

Step-by-step explanation:

-0.25 z = -1.25

z = -1.25 / -0.25

z = 5.

Answer:

28

Step-by-step explanation:

So this means to replace the r you see in 4r^2-8 with 3.

Let's do that:

4(3)^2-8

Now to simplify this just use pemdas or a calculator:

4(9)-8     since 3^2 means 3*3=9

36-8

28

Answer:

28.

Step-by-step explanation:

Put r =- 3 and work it out:

That would be 4(3)^2 - 8

=  4 * 9 - 8

= 36 - 8

= 28.

Answer:

c

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Let, [tex]P_0[/tex] be the initial population,

Given,

The population is decreasing by 3%  each year,

Thus, the population after t years would be,

[tex]P=P_0 (1-\frac{3}{100})^t[/tex]

[tex]\implies P=P_0(1+\frac{-3}{100})^t[/tex]

Since, if a population is changing by a constant rate then the population after t years is,

[tex]P=P_0(1+\frac{r}{100})^t[/tex]

Where, r is the rate of changing per period.

Hence, in the given situation the population is changing by the constant rate.

Answer:

11/16

Step-by-step explanation:

You could list all the possible fractions you will get:

Here are the's with 4 as the numerator:

4/4

4/5

4/6

4/7

Here are the one's with 5 as the numerator:

5/4

5/5

5/6

5/7

Here are the one's with 6 as the numerator:

6/4

6/5

6/6

6/7

Here are the one's with 7 as the numerator:

7/4

7/5

7/6

7/7

There are 4(4) different numerator-denominator combinations we can get.

Let's see which of these are bigger than 5/6.

If you think it is easier to look at the decimals of all these you can.

5/6=0.8333333333

----

4/4 =1

4/5 =0.8

4/6  =0.6666666666

4/7  =0.5714 (approximately)

There is only 1 bigger than 5/6 in this section.

5/4 =1.25

5/5  =1

5/6  =0.83333333333

5/7  =0.714 (approximately)

There is 2 bigger than 5/6 in this section.

6/4  =1.5

6/5   =1.2

6/6   =1

6/7   =0.857 (approximately)

There is 4 bigger than 5/6 in this section.

7/4

7/5

7/6

7/7

All of these are 1 or bigger because the numerator is bigger than or equal to the denominator so all 4 of these are bigger than 5/6 in this section.

P(fraction being greater than 5/6)=[\tex]\frac{\text{ the numbers I listed bigger than } \frac{5}{6}}{\text{ all the fractions I listed }}[/tex]

P(fraction being greater than 5/6)=[\tex]\frac{4+4+2+1}{4(4)}=\frac{11}{16}{/tex]

11/16

Answer:

1/6 or 11/16

Step-by-step explanation:

If you spin a spinner with the first spin giving the numerator and the second spin giving the denominator of a fraction, the probability of the fraction will be greater is 1/6 or 11/16.

6 - 5/6 = 1/6

However, there are 4 possible spots you could land on so, it would change to 11/16.

Answer:

see explanation

Step-by-step explanation:

These are the terms of an arithmetic sequence

The n th term ( explicit rule ) for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = 9 - 2 = 16 - 9 = 23 - 16 = 30 - 23 = 7 and a₁ = 2, hence

[tex]a_{n}[/tex] = 2 + 7(n - 1) = 2 + 7n - 7 = 7n - 5

The explicit rule for the sequence 2,9,16,23,30... is 7n - 5

2,9,16,23,30

= 7

The explicit rule is defined by

nth term = a + (n - 1) d

= 2 + (n - 1)7

= 2 + 7n - 7

= 7n - 5

Learn more about arithmetic progression:

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Multiply the bracket by 5

I used PEMDAS

P= parenthesis

E= exponents

M=multiplication

D= division

A= addition

S= subtraction

7r+2= 5(r-4)

7r+2= 5r-20

Move 5r to the left hand side . Positive 5r changes to negative 5r

7r-5r+2= 5r-5r-20

2r+2=- 20

2r+2-2= -20-2

Move positive 2 to the right hand side. Changes to negative -2

2r+2-2= -20-2

2r= -22

Divide by 2 for 2r and -22

2r/2= -22/2

r= -11

Answer is r= -11

Answer:

r = (-11)

Step-by-step explanation:

7r + 2 = 5(r – 4) ​

7r + 2 = 5r – 4 * 5

7r + 2 = 5r – 20

7r - 5r = -20 - 2

     2r = -22

       r = -22/2 = (-11)

Answer:

Yes the lines are indeed parallel. The slope of AB is 2

Step-by-step explanation:

Answer:

D. 148°

Step-by-step explanation:

Theorem: The measure of the angle formed by a tangent and a chord is equal to one-half the measure of the intercepted arc.

In your diagram, XZ is the chord, WZ is the tangent, and XYZ is the intercepted arc.

Per the theorem,

mXZW = ½ mXYZ = ½ × 296° = 148°

The measure of the tangent chord angle is 148°.

Answer: D: 148 is correct

Step-by-step explanation: apx :)

Answer:

3

Step-by-step explanation:

Answer:

[tex]\frac{3\pi}{2}[/tex]  units to the right

Step-by-step explanation:

If we have a parent function y = Sin(x), the function

The function given is [tex]y=Sin(x-\frac{3\pi}{2})[/tex]

So from the rules, we can clearly say that it is parent function shifted RIGHT by  [tex]\frac{3\pi}{2}[/tex] units.

2nd answer choice is correct.

Answer:

[tex]\large\boxed{D.\ (x-4)^2=55}[/tex]

Step-by-step explanation:

[tex](a-b)^2=a^2-2ab+b^2\qquad(*)\\\\\\x^2-8x=39\\\\x^2-2(x)(4)=39\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\\underbrace{x^2-2(x)(4)+4^2}_{(*)}=39+16\\\\(x-4)^2=55[/tex]

Answer: the answer is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]3x+1=4x+(-4)\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\3x-4x+1=4x-4x-4\\\\-x+1=-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=-4-1\\\\-x=-5\qquad\text{change the signs}\\\\x=5[/tex]

Answer:

The answer is B. In step one he should have added 3 negative x-tiles to both sides.

Step-by-step explanation:

(0,0) satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4. C

(0,0) satisfies both inequalities.

Answer:

The equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

Step-by-step explanation:

The equation of line for point=slope form is

y-y₁ = m(x-x₁)

Finding Slope m:

m= y₂-y₁/x₂-x₁

here y₂= 6,y₁= 7,x₂= -3,x₁= -6

m = 6-7/-3-(-6)

m = -1/-3+6

m = -1/3

The slope m = -1/3 and considering point (-6,7) the equation is:

y-y₁ = m(x-x₁)

y-7 = (-1/3)(x-(-6))

y-7 = -1/3(x+6)

y-7 = -1/3x -2

y = -1/3x-2+7

y = -1/3x + 5

So, the equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

Answer: 50 degrees.

Step-by-step explanation:

To find the measure of the angle Q, you need to follow these steps:

- Knowing that:

[tex]-980= -(1,360)cos(Q)[/tex]

You can divide both sides of the equation by -1,360:

[tex]\frac{-980}{-1,360}=\frac{-1,360cos(Q)}{-1,360}\\\\\frac{49}{68}=cos(Q)[/tex]

- Finally, using  the inverse function of the cosine, Arccosine, we get:

[tex]Q=Arcos(\frac{49}{68})\\\\Q=49.89\°[/tex]

To the nearest whole degree, this is:

[tex]Q=50\°[/tex]

Answer:

170 m

Step-by-step explanation:

Area of a rectangle is width times length:

A = WL

Given:

A = 1764

W = L + 13

Substitute:

1764 = (L + 13) L

1764 = L² + 13L

0 = L² + 13L − 1764

0 = (L + 49) (L − 36)

L + 49 = 0, L − 36 = 0

L = -49, L = 36

Since length can't be negative, L = 36 m.

So the width is W = L + 13 = 49 m.

Perimeter of a rectangle is twice the width plus twice the length.

P = 2W + 2L

P = 2(49) + 2(36)

P = 170 m

The perimeter is 170 meters.

Answer:

2160

Step-by-step explanation:

36*20=720      720*3=2160

To find the number of square inches of paper needed, multiply the length and width of each drawer to get the area, and then multiply that area by 3.

To find the number of square inches of paper needed, we need to find the area of the bottom of each drawer and then add them together. The area of a rectangle is found by multiplying its length by its width. So, for each drawer, we multiply 36 inches by 20 inches to get an area of 720 square inches.

Since there are 3 drawers, we need to multiply the area of one drawer by 3. So, the total number of square inches of paper needed is 720 square inches times 3, which equals 2160 square inches.

Therefore, the correct answer is D) 2160.

Answer:

false

Step-by-step explanation:

correct me if this is wrong, but it's actually x>1

Answer:

false.

Step-by-step explanation:

Given :  2x+8>10.

To find : the solution to 2x+8>10 is x<1   true or false.

Solution : We have given that  

2x+8>10.

On subtracting both sides by 8

2x > 10 -8.

2x > 2

On dividing both sides by 2

x > 1

So,  given statement false .

Therefore, false.

Yes. You should add commas next time to make it easier to read.

Answer:

Yes this is a function..

Step-by-step explanation:

We have to see the inputs and outputs for the function.

Here x represents input and y represents output.

For a relation to be a function there should be no repition in domain or input of the function i.e. every element in domain should be unique.

The domain for given relation is:

{1,-1,3,5}

All the inputs are only once mapped to the output so this relation is a function ..

Step-by-step explanation:

pt C is (-4,-4)

pt D is (2,-4)

length of CD is 6 units

to form a rectangle AB must be parallel to CD, AC must be parallel to BD and AC and BD must be 6 units

Therefore...A =(-4, 2) and B = (2, 2)

Answer:

x = -7 and x = 2

Step-by-step explanation:

Look for the points on the graph where if you draw a horizontal line at y=1, you will intersect the curve.

By observation, we can see that this happens at x = -7 and x = 2

x = -7 and x = 2

Here in the diagram, we can see that, a curve is present & 6 co-ordinates on that curve are given.

We have to find the values of x correspond with f(x) = 1

f(x) = 1 means y = 1

So, if we draw a horizontal line at y = 1, which is parallel to x-axis.

Then, we can able to observe the points which are on the line y = 1.

So, the points on line y = 1 are (-7, 1) & (2, 1).

Hence, we can say that, input values that correspond with f(x) = 1 are x= -7 & x = 2.

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Answer:

see explanation

Step-by-step explanation:

x³ + y³ ← is a sum of cubes and factors as

(x + y)(x² - xy + y²) ← in factored form

Answer:

½ = x

Step-by-step explanation:

As discussed in one of my You-Tube videos on Exponential Rules, aᵐ\ⁿ, any base to the half power is the SAME AS taking the exponential denominator of that power, and setting that to the square root of the base, leaving the exponential numerator on the outside:

25¹\² = √25

25 = a [Base]

1 = m [Exponential Numerator]

2 = n [Exponential Denominator]

As you can see, it is unnecessary to put the two because by definition, any vacant root is automatically assumed as the square root, and 1, which is the exponential numerator, is on the outside, which again is unnecessary because 5¹ is 5.

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Answer:

F

Step-by-step explanation:

∠C is opposite ( or across from ) side AB

In the same way

∠A is opposite side BC and

∠B is opposite side AC