when graphed on a coordinate plane,Bumby Avenue can be represented by the equation y=-4x-7. primrose can be represented by the equation 8x+2y=17. Are these streets parallel ?

The amount of money that Joe has left is $1155

Joe earned $2100

He spent 1/5 of the money on rent

1/5 × 2100

= 420

$420 was spent on rent

He spent 1/4 of the money on food

= 1/4 × 2100

= 525

$525 was spent on food

The amount of money left can be calculated as follows

Total amount spent = 525 + 420

                   = 945

Amount left= 2100 - 945

= 1155

Hence Joe has $1155 left

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From the data set given, 3/4 is the length of the shortest feather of fox sparrow.

Given,

The image is attached with this.

The length of fox sparrow feathers studied by Michael.

We have to find the shortest feather in the data set.

Here,

3/4 inches is the shortest feather and only 1 sparrow has the shortest feather.

2 3/4 inches is the longest feather and 3 sparrows have the longest feather.

That is,

From the data set given, 3/4 is the length of the shortest feather of fox sparrow.

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Explanation:

The functions are given below as

Part 1:

To find the value of x(t), we will put t=2

We have to identify the intervals where the function is concave upwards and where is concave downward.

We can differentiate them in a graph as:

We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.

Then, we can write all the intervals as:

The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.

Now that we have two points, we can solve for slope m

Now that we have both m and b. Substitute these values to the slope intercept form

Th formula for the area of the triangle is as follows.

where b is the base of the triangle and h is its height.

Substitute the given values into the formula and then simplify.

Therefore, the area of the triangle is 30 square feet, which is option B.

SOLUTION

(a) Complementary angles are angles that add up to 90 degrees. So the angle that will complement 50 degrees will add to it to get 90. Let the angle be x, we have

Hence the measure of the compelement is 40 degrees

(b) Supplementary angles are angles that add up to 180 degrees. So the angle that will supplement 135 degree will add to it to make it 180 degrees. Let this angle be y, so we have

Hence measure of the supplement is 45 degrees

Alexandre, this is the solution:

Let's recall that the interior angles of a rhombus add up to 360 degrees.

Upon saying that, we have:

4x + 3x + 31 + 6x - 90 + 7x + 19 = 360

20x - 40 = 360

Adding 40 at both sides:

20x - 40 + 40 = 360 + 40

20x = 400

Dividing by 20 at both sides:

20x/20 = 400/20

x = 20

Now, we can calculate each of the angles and prove they add up to 360 degrees, as follows:

• 4x = 4 * 20 =, 80

• 3x + 31 = 3 * 20 + 31 = 60 + 31 =, 91

• 7x + 19 = 7 * 20 + 19 = 140 + 19 = ,159

• 6x - 90 = 6 * 20 - 90 = 120 - 90 = ,30

80 + 91 + 159 + 30 = 360

Answer:

[tex]\frac{5}{2}[/tex] or 2.5cm

Step-by-step explanation:

Hello! Let's help you with your question here!

Let's start by working out what we know and what we need. So, we know that P is a circle and Q is the shape of a quarter circle with a radius of 20cm. The area of Q is 9 times the area of P and we must find the radius of P.

To start, we're looking for area, so we should at least start looking at the area of a circle, given radius, which is:

[tex]A=\pi r^2[/tex]

Now, we don't necessarily know r (radius) and the area either. However, we can try to use the quarter circle as our guide for the full circle. So, we want to find the area of the quarter circle, we can do that by using this formula!

[tex]A=\frac{1}{4} \pi r^2[/tex]

The reason why we put a [tex]\frac{1}{4}[/tex] at the front of [tex]\pi r^{2}[/tex] is because we're only solving for a quarter of a circle instead of the entire circle.

Now that we have our formula! We can calculate the area of the quarter circle as follows:

[tex]A=\frac{1}{4}\pi 15^2[/tex]

[tex]A=\frac{\pi 15^2}{4}[/tex]   -We combine the fraction [tex]\frac{1}{4}[/tex] into the rest of the equation.

[tex]A=\frac{225\pi }{4}[/tex]   - Evaluating [tex]15^2[/tex]

Now that we have the area of the quarter circle, we can now work on the full circle. What we know is that the area of A is 9 times of B, since we're finding the radius of B, we can essentially plug in the area and solve for the radius of the full circle. That would be as such:

[tex]A=9\pi r^2[/tex]   -We're using the area of circle A to find the radius of B.

[tex]\frac{225\pi }{4} =9\pi r^2[/tex]   - Plugging in the area of the quarter circle.

[tex]\frac{225\pi }{4}/9\pi =\frac{9\pi r^2}{9\pi }[/tex]   - We divide [tex]9\pi[/tex] to get rid of it on the right side.

[tex]\frac{25}{4} =r^2[/tex] - When dividing by [tex]\pi[/tex], the numerator [tex]\pi[/tex] gets cancelled out.

[tex]\sqrt{\frac{25}{4} }=r[/tex]   -We square root to get rid of the squared.

[tex]\frac{5}{2}=r[/tex]    - Square rooted both numerator and denominator.

And there we have it! We finally get a radius of [tex]\frac{5}{2}[/tex] or 2.5cm.

Answer:

45

scalene

acute

Step-by-step explanation:

Answer: The triangle classified by the sides is 59 degrees.  The triangle is classified by the angel is 1

Step-by-step explanation:

Given the equation below

Step 1

Collect like terms.

Step 2

Divide both sides of the equation obtained, by the coefficient of the unknown.

Hence, the value of n in the equation is 4

The share price I would expect based on the estimate of the dividend growth rate is $10.70.

In order to determine the share price, the constant growth dividend model would be used. According to the model, the share price is a function of the cost of equity, dividend paid and growth rate.

Share price = next dividend / (cost of equity - growth rate)

Next dividend = current dividend x (1 + growth rate)

$1 x (1 + 0.07)

$1 x 1.07 = $1.07

Share price = $1,07 / (0.08 - 0.07)

$1.07 / 0.01 = $10.70

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a. the amount of liquid in the tank:  5580 liters

b. The amount of liquid should be added  to fill the tank 100% capacity : 450 liters

We have been given a right circular conical tank.

h = 4 m and r = 1.20 m

We know that the formula for the volume of cone is,

V = πr²h/3

The volume of the tank would be,

V = (π × r² × h)/3

V = (π × 1.20² × 4)/3

V = 18.09/3

V = 6.03 m³

Let h1 be the height of liquid level in the tank and  V1 be the volume of the liquid in the tank.

h1 = 3.70 m

V1 = (π × r² × h1)/3

V1 = (π × 1.20² × 3.70)/3

V1 = 16.74 / 3

V1 = 5.58 m³

V1 = 5580 liters

The amount of liquid need to added to fill the tank 100% of capacity.

V2 = V - V1

V2 = 6.03 m³ - 5.58 m³

V2 = 0.45 m³

V2 = 450 liters

Therefore, a. the amount of liquid in the tank:  5580 liters

b. The amount of liquid should be added  to fill the tank 100% capacity : 450 liters

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The set builder notation of "The domain of a function is all whole numbers between 2.5 and 7.5" is Domain = {x: x∈W , 2.5<x<7.5 }.

In the Set Builder form , a statement or expression is used to represent all the elements of the set .

In the question ;

it is given that

the domain of the function is all whole numbers between 2.5 and 7.5 .

the set of whole numbers is represented by W.

Since the numbers between 2.5 and 7.5 are included , so "<" will be used .

The Set Builder notation is Domain = {x: x∈W , 2.5<x<7.5 } .

Therefore , the set builder notation of "The domain of a function is all whole numbers between 2.5 and 7.5" is Domain = {x: x∈W , 2.5<x<7.5 }.

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The largest proper fraction that can be formed is 16/17

What is a fraction?

A fraction (from the Latin fractus, "broken") is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line (or before a slash like 12) and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.

The largest proper fraction that can be formed is

= 1+3+12/11+6 = 16/17

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We are to find an unknown side in a case of a triangle bisected via one of its angles.

We therefore use the bisecting angle theorem:

Which in the case of our image:

can be written as the following proportion:

8 / 4 = y / 6

in order to solve for "y", we multiply both sides by 6:

(8 * 6) / 4 = y

48 / 4 = y

then y = 12

The given statement is true.

This is a question of probability.

It is given in the question that:-

Chance of raining here = 50 %

Chance of raining on Mars = 10 %

The given statement is :-

There is a 45 % chance that it will rain in neither place.

Chance of not raining here = 100 - 50 % = 50 % = 1/2

Chance of not raining on Mars = 100 - 10% = 90 % = 9/10

Hence, chance of raining in neither place = (1/2)*(9/10) = 9/20

9/20 = (9/20)*100 = 45 %.

Hence, the given statement "There is a 45% chance that it will rain in neither place" is true.

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We have the following:

We know that to calculate the average we must add the corresponding values of bronze medals of each nation and then divide by the number of nations like this

the median number of bronze medals for all nations is 5.8

The perimeter of a triangle is given by the sum of all it is sides.

Now, we have the next measures:

- The longest side of a triangle is 5in longer than the shortest side.

- The medium side is 4 inches longer than the shortest side

Then, the perimeter is given by:

P = (s+5)+(s+4)+s

If the perimeter is P=21 inches:

21 = (s+5)+(s+4)+s

Solve for s:

21 = s+5+s+4+s

21 = 3s + 9

21-9 = 3s

12 = 3s

s = 12/3

s= 4

Therefore,

The shortest side of the triangle is 4 inches.

The medium side is s+ 4 = 4+ 4 = 8 inches

The longest side is s+5 = 4+5 = 9 inches

SOLUTION

Step 1 :

In this question, we are meant to know the relationship between Growth factor and Growth Rate.

Growth factor is the factor by which a quantity multiplies itself over time.

Growth rate is the addend by which a quantity increases ( or decreases ) over time.

Step 2 :

From the question, if the growth factor is 1.2 which is also 120 %,

then the growth rate will be ( 120 - 100 ) % = 20 % = 0. 2

CONCLUSION:

The Growth Rate = 0. 2

Note that a quadratic function is increasing and decreasing at exactly half between the roots.

The roots are the point on the ground when tossing the ball into the air.

So we need to get the roots of the given equation.

Roots are the values of x when y = 0

So the roots are 0 and 6, this will be the x coordinate or the point on the ground.

Since the equation is increasing halfway and decreasing up to the ground, the halfway point is the midpoint between the roots.

Midpoint = (0 + 6)/2 = 3

Therefore, the ball's height is always decreasing at 3 < x < 6

The answer is 3 < x < 6

To solve the system of equations

we need to make the coefficients of one of the variables opposite, that is, they need to have the same value with different sign; let's do this with the y variable, so let's multiply the second equation by 0.7 and the first equation by 0.2; then we have:

Now we add the equations and solve the resulting equation for x:

Now that we have the value of x we plug it in one of the original equations and solve for y:

Therefore, the solution of the system of equation is (4,2)

3x + y = 0

5x + y = 14

From the question, It takes Ary an hour to write one thank you card.

So, the rate at which she writes the thank you card is;

To determine the number N of thank you card she would write in 8 hours.

Where;

R is the rate = 1 card/hour

T is the time taken = 8 hours

Substituting the values we have;

The number of thank you cards she write is 8 cards

The volume of a Pyramid

Given a pyramid of base area A and height H, the volume is calculated as:

The base of this pyramid is a right triangle, with a hypotenuse of c=19.3 mm and one leg of a=16.8 mm. The other leg can be calculated by using the Pythagora's Theorem:

Solving for b:

The area of the base is the semi-product of the legs:

Now the volume of the pyramid:

The volume of the figure is 319.2 cubic millimeters

It is to be noted that a relations in math can be represented in 8 different ways. See the examples below.

The relation in mathematics is the relationship between two or more sets of values.

The various types of relations and their examples are:

Empty Relation

An empty relation (or void relation) is one in which no set items are related to one another. For instance, if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8. For an empty relationship,

R = φ ⊂ A × A

Universal Relation

A universal (or complete) relation is one in which every member of a set is connected to one another. Consider the set A = a, b, c. R = x, y will now be one of the universal relations, where |x - y| = 0. In terms of universality,

R = A × A

Identity Relation

Every element of a set is solely related to itself via an identity relation. In a set A = a, b, c, for example, the identity relation will be I = a, a, b, b, c, c. In terms of identity,  I = {(a, a), a ∈ A}

Inverse Relation

When one set includes items that are inverse pairings of another set, there is an inverse connection. For example, if A = (a, b), (c, d), then the inverse relation is R-1 = (b, a), (d, c). As a result, given an inverse relationship,

R-1 = {(b, a): (a, b) ∈ R}

Reflexive Relation

Every element in a reflexive relationship maps to itself. Consider the set A = 1, 2, for example. R = (1, 1), (2, 2), (1, 2), (2, 1) is an example of a reflexive connection. The reflexive relationship is defined as- (a, a) ∈ R

Symmetric Relation

If a=b is true, then b=a is also true in a symmetric relationship. In other words, a relation R is symmetric if and only if (b, a) R holds when (a,b) R. R = (1, 2), (2, 1) for a set A = 1, 2 is an example of a symmetric relation. As a result, with a symmetric relationship, aRb ⇒ bRa, ∀ a, b ∈ A.

Transitive Relation

For transitive relation, if (x, y) ∈ R, (y, z) ∈ R, then (x, z) ∈ R. For a transitive relation, aRb and bRc ⇒ aRc ∀ a, b, c ∈ A

Equivalence Relation

If a relation is reflexive, symmetric and transitive at the same time, it is known as an equivalence relation.

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It is found that a relations in math can be represented in 8 different ways.

The relation in mathematics is defined as the relationship between two or more sets of values.

There various types of relations and their examples:

An empty relation (or void relation) is one in which no set items are related to one another.  if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8.

R = φ ⊂ A × A

Universal Relation; It is one in which every member of a set is connected to one another.

R = A × A

Identity Relation; Every element of a set is solely related to itself via an identity .

In a set A = a, b, c, for example, it is I = a, a, b, b, c, c. I

n terms of identity,  I = {(a, a), a ∈ A}

Inverse Relation; When one set of data includes items that are inverse pairings of another set, there is an inverse connection.

For example, if A = (a, b), (c, d), then the inverse is; R-1 = (b, a), (d, c).

R-1 = {(b, a): (a, b) ∈ R}

Equivalence Relation; When a relation is reflexive, symmetric and transitive at the same time, it is calles as an equivalence relation.

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The equation of the line in slope intercept form is y = -2x - 70

The equation of a line can be represented in different form such as slope intercept form, point slope form and standard form.

The equation of the line can be written is slope intercept form as follows:

y = mx + b

where

Therefore, using the coordinates (0, - 70)(-20, -30)

Let's find the slope,

m = slope = -30 + 70 / -20 - 0

m = 40 / - 20

m = - 2

Let's find the y-intercept using (0, -70)

-70 = -2(0) + b

b = - 70

Therefore, the equation of the line is y = -2x - 70

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1) Since the sum of these angles is written in terms of x, we can write it out:

Notice that to sum these fractions we had to take the LCM(2, 1) = 2 and rewrite it as a sum.

2) Another way of writing the sum of these angles is writing it as a sum of decimal numbers since we can rewrite fractions as decimal numbers.

3/2 = 3÷2 = 1.5

1/2 = 1÷2 =0.5

1

a)

We need to convert 1.96 x 10^-5 meters. into standard notation.

Now, on the scientific notation, the power of ten shows how many places the decimal point has been moved.

- If the exponent is positive then the decimal point has been moved to the left.

- If the exponent is negative, then the decimal point has been moved to the right.

In this case, the power is negative 5 . So, the decimal point has been moved 5 places to the right.

Hence:

1.96 x 10^-5 = 0.0000196

b)

a. Meters

First, we need to convert kilometers into meters using the rule of three:

If 1k = 1000 meters

Then 12,100k = x

Where x = (12,100k*1000m)/ 1k

x =12000000 meters

We need to convert from standard notation to scientific notation:

12000000.0 = 1.2x10^7 meters

The decimal point has been moved 7 places to the left, so the power of then is positive 7.

b) We need to convert 12,100 kilometers into scientific notation:

12,100 = 12,100.0

Converting into scientific notation

1.21x10^4 kilometers

The decimal point has been moved 4 places to the left. Hence, the power of the is positive 4.