Determine whether the lines are parallel, intersect, or coincideY = 4x - 53x + 4y = 7

Pythagorean theorem

(Type an integer or decimal rounded to the nearest tenth as needed.)

Integer = 8'

decimal rounded to the nearest tenth as needed = 8.1'

"S is the midpoint of BT": this is given.

BO || AT: this is given.

SB = ST: definition of midpoint.

alternate interior

vertical

ΔBOS = ΔTAS: SAS or ASA (both are right).

Explanation:

The zero-factor property states that if ab=0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more factors is zero.

From these options only B and D have factors, but B equals to 3. In D we have that (3x-2) = 0 or the other factor is zero (or both)

Answer:

The correct answer is option D

ANSWER:

The correct option is the following:

C. Find the intersection of the angle bisectors of each angle of the triangle,

EXPLANATION:

The point that equidistant is the point at which the three bisectors of the internal angles of the triangle intersect, and it is the center of the circumference inscribed in the triangle and equidistant from its three sides.

IMPORTANT NOTE:

Any point on the bisector of an angle of a triangle equidistant from the sides that define that angle.

The x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.

For the given question,

The equation of the line is 5x-9y=-12.

For the x intercept, Put y = 0.

5x-9×0=-12.

x = 12/5

x intercept = (12/5, 0)

For y intercept, put x = 0.

5×0-9y=-12

y = -12/9

y = -4/3

y intercept = (0, -4/3)

Thus, the x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.

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We want find the compound interest annualy for 4 years, $8500, at 7%'

The formula for the compound amount over one year is;

1st year:

2nd year:

3rd year:

4th year:

A sequence is called arithmetic if the difference between two consecutives is a constant

In the first case we see a constant difference of 5

every two consecutives have difference of 5, for example 20-15, 30-25 and so on.

In the second case we see the division between two consecutives is a constant . That is called a GEOMETRIC sequence.

the constant in this case is 18/6 =3

lets return to the 1st case find the explicit

An = Ao +(n-1) d

An means the n term in the sucession

Ao means the first term

d means the constant

with that in mind we replace the values obtained

An= 5 + (n-1) •5

now for the recursive

a1= 5

An = An-1 + 5

Now lets go to the second part, the geometric sequence. Just is needed to replace the values in the ABOVE RIGHT formula

so then

An = A1 •(3)^(n-1)

An = 2• (3)^(n-1)

The type of variation that describes each relationship include the following:

An indirect variation simply refers to a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other, which means as one variable increases, the other variable decreases and vice-versa.

Direct variation refers to a type of proportional relationship in which a variable is directly proportional to another variable. This ultimately implies that, a direct variation represents two variables that are directly proportional to each other, which means as one variable increases, the other variable also increases and vice-versa.

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10

10x1=10

Hope this helps

EXPLANATION

As we can see in the graph, we can calculate the slope with the following equation:

Let's consider any ordered pair, as (x1,y1)=(1,7) and (x2,y2)=(5,8), replacing this in the equation will give us:

Answer: the slope is equal to 1/4.

Answer

Option B is correct.

Angle ABC > Angle DBC

Explanation

Since it's been proven that

Angle ABC = Angle ABD + Angle DBC

Since Angle ABD > 0,

Angle ABC > Angle DBC is the part that completes the proof that

Angle ABC > Angle RST

Hope this Helps!!!

Make graph line using the slope and the y-intercept or the point.

m=1/4 and b=3

What is graph ?

graph is a mathematical representation of a networks and it describes that the  relationship between lines and points. A graph consists of some points and lines are  between them. The length of the lines and position of the points do not matter.

Sol-as per the given question y=1/4x+3

The slope-intercept form y=mx+b where m is the slope and b is the y intercept

y=mx+b

Reorder terms

y=1/4x +3

Use the slope-intercept form to find the slope and y-intercept

Slope=1/4

y-intercept :(0,3)

Any line can be graphed using two points is  Select two x

values, and plug them into the equation to find the corresponding Y values.

In record terms -y=1/4 x+3

The table of x and y values are-

X-0,4

Y-3,4

graph the line using the slope and the y-intercept, or the points.

Slope -1/4

y-intercept (0,3)

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Answer: I thought you already asked this question.

Step-by-step explanation:

We have the next function that models the Australian GDP since 1960 :

Where t is the number of years since 1960.

a)If we are in the year 1960, it means t=0

Therefore:

b)Now, we need to find the Australia capita in 1963.

This means t=3

Therefore:

c) We need to find when the function is equal to 100,000.

Therefore we equal the function G(t)=100,000.

Then:

Solve for t:

Divide both sides by 1806:

Add Ln for each side:

Then:

Rounded to the nearest year:

Therefore: 1960 +110 = 2070

On 2070 the Austranlian GDP reaches 100,000 USD

Answer:  B) 46.67% approximately

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Work Shown:

A = it will be cloudy tomorrow

B = it will be rainy tomorrow

P(A) = 0.30

P(B) = 0.15

P(A and B) = 0.14

Apply the conditional probability formula.

P(B given A) = P(A and B)/P(A)

P(B given A) = 0.14/0.30

P(B given A) = 0.4667 approximately

P(B given A) = 46.67% approximately

Answer:

b)  About 46.67%.

Step-by-step explanation:

Let event A = being cloudy.

Let even B = being rainy.

Given probabilities:

Therefore:

Conditional Probability Formula

[tex]\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}[/tex]

The probability of being rainy given it is cloudy = P(B | A).

Substitute the given values into the formula:

[tex]\implies \sf P(B|A)=\dfrac{0.14}{0.3}=0.46666...=46.67\%\;(2\;d.p.)[/tex]

Therefore, the probability of it being rainy if you know it will be cloudy is about 46.67%.

The segments cannot be set equal since the constant terms 15 is greater than two. The variable x remains like a constant term in both sides of the point B.  we say that 15x > 2x

In mathematics, the signs used inequality calculations are

Using the picture as evidence the mark represented by B is not the midpoint hence the equality sign will not be used here. The sign to be used is the inequality sign.

In addition, the constants 15 and 2 shows that 15 is greater than 2. and there is no other addition to the variable x to help check the effect of the greatness of 15

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Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared​

we have that

F=m*a

we have

m=30 kg

F=60 N

substitute in the formula

60=30*a

solve for a

a=60/30

a=2 m/s^2

therefore

Outcome that are in A and B simply means both outcome must be achieved.

Therefore,

Solution

Find the value of x in the triangle shown below:

Calculate the value of x

Opposite = 5

adjacet = x

Therefore the correct value of x = 4.2

SOLUTION

From the question, we want to find the value in dollars of the account after 2 years.

We will usethe formula

Applying this, we have

Hence the answer is 43,548.47 to the nearest cent

We have

Let x = cost of the ticket

After paying for the tickets, Mr. Herman had 125 - x

and Mr Chandra had 80 - x

Then, the equation is:

So, solve for x:

The concert ticket cost is $71

Therefore, Mr. Chandra have left:

Answer: $9

Answer:

whales, walruses, porpoises, dolphins, seals, dugongs, manatees, and sea otters

Step-by-step explanation:

have good day

We have that the floor's dimensions are 15ft x 20ft and the height of the room is 10ft tall. This is

if we extended it we would have:

We want to find how many square foot Brett needs to cover. We just find the area of each side of the studio.

We find it just by multiplying both of its sides (they all are rectangles):

Wall 1

area = 10ft x 15 ft

area = 150 ft²

Wall 2

area = 10ft x 20 ft

area = 200 ft²

Wall 3

area = 10ft x 15 ft

area = 150 ft²

Wall 4

area = 10ft x 20 ft

area = 200 ft²

Floor

area = 15ft x 20 ft

area = 300 ft²

Ceiling

area = 15ft x 20 ft

area = 300 ft²

A condensed way....

TOTAL AREA

Now, we add all the areas found, this will be the total area Brett must cover:

Wall 1 + wall 2 + Wall 3 + Wall 4 + ceiling + floor = total area

150 ft² + 200 ft² + 150 ft² + 200 ft² + 300 ft² + 300 ft² = 1300 ft²

COST

Since the padding costs $2.50 per square foot, and there are 1300 square foot to cover. Brett will spend

$2.50 x 1300 = $3250

Answer: Brett spend on padding $3250

The average rate of change can be calculated as the division of the output of the function on the interest interval by the size of the interval. To do that we have to find the value of "y" at the end of the interval and subtract it by the value of "y" at the beggining. This is shown as an expression below:

For this function the values of x are:

The values for y are:

Using these values we can calculate the average rate of change:

The average rate of change for this function is approximately -3 for the given interval. The correct answer is A.

The Solution:

Let the outcomes when two dice are tossed be as summarized in the picture attached below:

SOLUTION

Step1: write out the giving equation

Step2: Integrate both sides of the equation above

Then simplify by integrating both sides

since the initial value is 25,000, then

the Population function is

b). For the population to reach 50,000 the time will be

Multiply the equation by 3, we have

To solve this we rewrite the function as

The value of t becomes

Then it will take approximately

Answer:

A

Step-by-step explanation:

we have 3/4 in / minute.

so, we divide this by 3/4 to get the time for 1 inch.

and then we multiply by 1/3 to get the time for 1/3 inch.

that combination, dividing by 3/4 and multiplying by 1/3, can be done in any sequence (commutative property of multiplication).

therefore, this can be expressed as 1/3 divided by 3/4. and A is the correct answer.

By definition, an equation is a statement that two mathematical expressions are equal.

Equations always contain the equal sign "="

Out of the 4 expressions listed, number 2. does not contain the equal sign, which means that this expression is not an equation.

All other expressions contain the equal sign, they can be considered equations.

Given the word problem, we can deduce the following information:

The correlation coefficient r is equal to 0.755.

To determine the coefficient of determination and the coefficient of nondetermination, we use the formulas below:

Now, we first plug in r=0.755 to get the coefficient of determination:

Next, we get the coefficient of nondetermination:

Therefore, the answer is:

The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430