Question 6 What is the factored form of the expression below? 7 - 16 O OD (x-8)(x - 8) (x - 4)(x + 4) (x - 4)(x - 4) (x-8)(x + 8) Oo

It is to be noted that the correct graph is graph A. This is because it shows the coordinates (2, 25). See the explanation below.

It is information given is the rate of change of the linear relationship between the stated variable variables:

The ratio given is depicted as:

r = [250 bottles]/ [20 mintures]

r = 25/2 bottles per min

By inference, we know that our starting point coordinates (0,0), because zero bottles were filled at zero minutes.

Thus, we must use the point-slope form to arrive at the equation that exhibits or represents the relationship of the linear graph.

The point-slope form is given as:

y-y₁ = m(x-x₁)

Recall that our initial coordinates are (0, 0,) where x₁ = 0 and y₁ = 0. Hence

⇒ y - 0 = 25/2(x-0)

= y = 25x/2

Hence, if x = 2, then y must = 25

Proof: y = 25(2)/2

y = 50/2

y = 25.

Hence, using the principle of linear relationships, the first graph is the right answer, because it shows the points (2,25) which are part of the relation.

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The derivative of the function f(x) = √x-5 is 1/2√(x-5)

Given f(x) = √x-5

from the formula d/dx (√x) = 1/2√x

hence d/dx √x-5 = 1/2√x-5

or

d/dx √x-5 = 1/2 (x-5)¹/²

The formula for the derivative of root x is d(x)/dx = (1/2) x-1/2 or 1/(2x). The exponential function with x as the variable and base equal to 1/2 is the root x provided by x. Utilizing the Power Rule and the First Principle of Derivatives, we can get the derivative of root x.

Hence we get the value as 1/2 (x-5)¹/²

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Inch is one of the units of measuring length.

Converting from inch to meters,

A 12-inch ruler converted to meters will be;

Converting the meter equivalent of the ruler into the sub-units of meters measurement,

From the conversions of metric units of length above, the 12-inch ruler measures 30.48cm which is closest to 30cm

Therefore, the ruler is closest to 30 centimeters

1) rotation 90° clockwise over the origin and a reflection over the x-axis

2) rotation 90° counter clockwise over the origin and reflection over y-axis

Answer:

hey what don't u get? u didn't show the question

The popcorn we can order is either buttered or unbuttered.

Therefore, the probability of choosing buttered popcorn is 1/2

Since the lines r and s are parallel the angles 1 and 2 must be equal

write an equation

solve the equation for x

the value for x in which r and s are parallel must be 14

measure of angle 1 and 2 must be 54°

Here are the steps in multiplying scientific notations:

1. Multiply the coefficients first.

2. Multiply the base 10 by adding their exponents.

3. Connect the result in steps 1 and 2 by the symbol for multiplication.

Hence, the result is 6.6 x 10⁵.

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]2^{-2}[/tex]

[tex]\boxed{\textsf{Exponent rule}: \quad a^{-n}=\dfrac{1}{a^n}}[/tex]

Apply the exponent rule to the given expression:

[tex]\implies 2^{-2}=\dfrac{1}{2^2}[/tex]

Two squared is the same as multiplying 2 by itself, therefore:

[tex]\begin{aligned}\implies 2^{-2}&=\dfrac{1}{2^2}\\\\&=\dfrac{1}{2 \times 2}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]

Solution

[tex]2^{-2}=\dfrac{1}{4}[/tex]

Answer:

1/4

Step-by-step explanation:

Now we have to,

→ find the required value of (2)^-2.

Let's solve the problem,

→ (2)^-2

→ (1/2)² = 1/4

Therefore, the value is 1/4.

Explanation:

The total number of students is

Concept:

To figure out the probability that a student earns grade A,B or C

Will be calculated below as

The Probability of A is

The probabaility of B is

The probabaility of C is

Hence,

By substituting the values in the concept, we will have

Hence,

The final answer is

By applying Kepler's third law of planetary motion, the approximate revolution time for Jupiter is equal to 12 years.

Mathematically, Kepler's third law of planetary motion is given by this mathematical expression:

T² = a³

Where:

Note: Earth has 1 astronomical unit (AU) in 1 year of time.

For this direct variation, the value of the constant of proportionality (k) is given by:

T² = ka³

k = T²/a³

k = 1²/1³

k = 1.

When the semi-major axis or the distance of Jupiter from Sun is 5.2, we have;

T² = ka³

T² = 1 × 5.2³

T² = 140.608

T = √140.608

T = 11.858 ≈ 12 years.

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To solve this question, we shall be using the principle of similar triangles

Firstly, we identify the triamgles

These are JKL and JMN

JKL being the bigger and JMN being the smaller

Mathematically, when two triangles are similar, the ratio of two of their corresponding sides are equal

Thus, we have it that;

9/g + 2h + 5

When g = 3 and h = 6

First, replace the values of g and h by the ones given:

9/(3) + 2(6) + 5

9/3 + 2(6)+5

Then, divide and multiply:

3+12+5

Finally, add

20



Given:

• Number of male who survived = 338

• Number if female sho survived = 316

• Number f children who survived = 57

• Number of male who died = 1352

• Number of female who died = 109

• Number of children who died = 52

• Total number of people = 2224

Let's solve for the following:

(a). Probability of the passenger that survived:

(b). Probability of the female.

We have:

(c). Probability the passenger was female or a child/

(d). Probability that the passenger is female and survived:

(e). Probability the passenger is female and a child:

(f). Probability the passenger is male or died.

Thus, we have:

(g). If a female passenger is selected, what is the probability that she survived.

(h). If a child is slelected at random, what is the probability the child died.

(i). What is the probability the passenger is survived given that the passenger is male.

ANSWER:

• (a). 0.320

• (b). 0.191

• (c). 0.240

• (d). 0.142

• (e). 0.009

• (f). 0.832

• (g) 0.744

• (h). 0.477

• (i) 0.2

The values of f(4) , f(0) and f(-5) are 16/7, -12 and -7/11 respectively.

We are given the function:-

f(x) = (x + 12)/(2x - 1)

We have to find the values of  f(4) , f(0) and f(-5).

Putting x = 4 in the given function, we can write,

f(4) = (4+12)/(2*4-1) = 16/7

Putting x = 0 in the given function, we can write,

f(0) = (0 + 12)/(2*0 - 1) = 12/(-1) = -12

Putting x = -5 in the given function, we can write,

f(-5) = (-5 + 12)/(2*(-5) - 1) = 7/(-10-1) = 7/(-11) = -7/11

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we multiply the first parenthesis by its coefficient

now multiply each value and add the solutions

Irrational

Explanation

Step 1

simplify

Step 2

the square root of 2 is an irrational number,because there is not number such that

and

The square root of 3 is an irrational number √3 cannot be expressed in the form of p/q

hence

the sum of 2 irrational numbers gives a irrational result,Sum of two irrational numbers is always irrational.

so, the answer is

Irrational

I hope this helps you

we have the function

g(x)=(x/3)+2 ---------> interval (-infinite, 1)

g(x)=4x-2 ------> interval [1, infinite)

the given function is not one-to -one function, because don't pass the Horizontal Line Test.

Example

For the horizontal line

y=2

we have the values of

x=0 ---------> g(x)=(x/3)+2

and

x=1 -----------> g(x)=4x-2

that means

two elements in the domain of g(x) correspond to the same element in the range of g(x)

therefore

The surface area of the figure is the sum of the area of the squares. Since they're all equal, is the amount of squares times the area of one square. We have a total of six squares, with a side length equal to 4 units. The area of a square is given by the product of its side length by itself, therefore, the total surface area of this figure is

The area of this figure is 96 ft².

Answer: 72 Square Meters sorry super late

Step-by-step explanation:

STEP - BY - STEP EXPLANATION

What to find?

The average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air.

Given:

Step 1

Differentiate the heigh with reospect to t.

The rate of change of height is the differentiation of the height.

Step 2

Substitute t= 1.25

ANSWER

Average rate = -40 ft / s

Explanation:

To add mixed fractions we have to follow these steps:

1. Add the whole numbers together

2. Add the fractions

3. If the sum of the fractions is an improper fraction then we change it to a mixed number and add the whole part to the whole number we got in step 1.

In this case the sum of the fractions results in a proper fraction, so we can skip this step.

Answer:

The result is:

Kaitlin's family's trip from Washington D.C., to New York City of 227 miles at average rate of 55 miles per hour is 4 hours 8 minutes

information gotten from the question include

Washington D.C., to New York City is 227 miles

Kaitlin's family can drive an average of 55mi / h

Average speed is a function of ratio distance covered with time. this is represented mathematically as

average speed = distance covered / time

55 miles / h = 227 miles / time

time = 227 / 55

time = 4.127 hours

The trip take 4.127 hours

0.127 * 60 = 7.62 ≅ 8 minutes

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Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x

Step-by-step explanation:

I think of a number, represented by the variable/pronumeral x.

I add 5 to it: x + 5

then double the result: 2(x + 5)

I then subtract 10 from this answer: [2(x + 5)] - 10

I then subtract the original number I thought of: [2(x + 5)] - 10 - x

Simplifying the expression will explain why you get the original number.

[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.  

ANSWER:

A. The slope of the line is -1/4

STEP-BY-STEP EXPLANATION:

Given:

(13,1) and (1,4)

The slope can be calculated using the following formula:

We substitute each value and calculate the slope:

Therefore, the correct answer would be:

A. The slope of the line is -1/4

Part 3

An exponential growth function has the general form:

where r is the rate of growth, t is the time, and a is a constant. Notice that if calculate f(t) for t = 0, we have (1 + r)º = 1 (any number with exponent 0 equals 1). So, we obtain:

Thus, the constant a is the initial value of the function.

Now, the rate at which a bacteria grows is exponential. So, the function C(h) is given by:

Notice that we represented the time by the letter h instead of t.

Since C(0) = 10 and C(1) = 12, we can replace h by 1 to find:

Thus, the number of cells C(h) is given by:

Notice that this is valid for C(15) = 154:

Part 1

Then, using this formula, we find:

Part 2

Now, plotting the points, rounded to the nearest whole cell, on the graph, we obtain:

Part 4

Using a calculator, we obtain the following graph of the function C(h):

Comparing the graph to the plot of the data, we see that they match.

Part 5

After a full day, it has passed 24 hours. So, we need to use h = 24 in the function C(h):

Therefore, the answer is 795 cells.

Let's begin by listing out the information given to us:

r (1) = 11.4 cm, θ (1) = 70°, θ (2) = 40°, r(2) = ?

The arc length is the same for the 2 circles

r (1) * θ (1) = r (2) * θ (2)

11.4 * 70° = r (2) * 40°

r (2) = 11.4 * 70 ÷ 40

r (2) = 19.95 cm

Hence, the radius of the larger circle is 19.95 cm

Ok, so

Here we have the function:

Now we want to find the tripling-time for this population of deer.

If we make t=0, we will find the initial population of deer. This is:

Now, we want to find the time "t" such that this population is the triple.

This is:

We got this exponential equation:

As the base is the same, we could equal the exponents:

Therefore, tripling-time for this population of deer are 3 years.

An equation that shows that two ratios are equal is referred to as a true proportion.

This refers to as a mathematical term which is used to show or depict that two expressions are equal and is  usually indicated by the sign = .

In the case in which the equation shows that two ratios are equal is referred to as a true proportion and an example is:

10/5 = 4/2 which when expressed will give the same value which is 2 as the value which makes them equal and is thereby the reason why it was chosen as the correct choice.

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Answer:

(3h+y)*(3h-y)

Step-by-step explanation:

We are given the following expression:

We want to find the LCD for:

9h²-y² and 3h + y.

3h+y is already in it's most simplified way.

9h²-y² , according to the notable product of (a²-b²) = (a-b)*(a+b), can be factored as:

(3h-y)*(3h+y).

The factors of each polynomial is:

3h + y and (3h-y)*(3h+y)

The LCD uses all unique factors(If a factor is present in more than one polynomial, it only appears once).

So the LCD is:

(3h+y)*(3h-y)

Which is option B.

Given,

The initial height of H feet.

The initial velocity of the object is Vo.

The equation of the path of projectile is,

This is the expression of the projectle path.

Hence, the path of the projectile object is y = h + xtan(theta) - x²/2V₀²cos²(theta)