Writing Equations of lines

Write the equation of each line with the given information

Slope = 7, y-intercept = -3

Answer:

S(a) = 27,5036  squared units

Step-by-step explanation:

Shaded area is :

S(a)  =  Area of the circle  - area of the regular pentagon      (1)

A(c) = area of the circle

A(c) = π*(r)²    ⇒  A(c) =  π*(6)²     ⇒   A(c) =  36*π   ⇒ A(c) = 113,0976 squared units

Area of a regular pentagon:

a) If we draw a straight line between the center and each vertex we get  5 triangles, and if we draw the apothem for each side, we get 10 triangles. We will calculate the area of one  of these triangles

The first 5 triangles has a central angle equal to 72⁰ according to:

360/5  =  72

When we divide these triangles in two triangles by means of the apothem, each central angle will be of 36⁰, then

sin 36⁰  =  0,58778  and cos 36⁰ = 0,809017    and   sin 36⁰ =  x/6      here x is half of the side of the regular pentagon. Then

0,58778  =  x/6

x = 6*0,58778

x =  3,52668 units of length  

and cos 36⁰ = a/6      where a is the apothem, then

0,809017  = a / 6     ⇒   a  = 6*0,809017

a =  4,8541 units of length

Now we are in conditon to calculate area of the triangles as:

A(t) = (1/2)*b*h

A(t) = (1/2)*x*a     ⇒ A(t) = 0,5* 3,52668*4,8541

A(t) = 8,5594 squared units

Finally we have 10 of these triangles, then

Area of regular pentagon is : 10*A(t) squared units

A(p) = 85,594 squared units

Now plugging these values in equation (1) we get the shaded area

S(a) =  113,0976 - 85,594

S(a) = 27,5036  squared units

The random variable given in the accompanying table is discrete.

A discrete random variable can only take on a countable number of distinct values. In this case, the random variable represents the number of girls, and the values it can take are 0, 1, 2, 3, and 4. These values are countable and separate from each other, indicating that the random variable is discrete.

The probabilities assigned to each value also support the notion of discreteness. Each probability represents the likelihood of observing a specific number of girls, indicating that the random variable is defined for specific outcomes.

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Answer:

81.6

Step-by-step explanation:

8 divided by 5 is 1.6.

Hope this helps! Sorry if it is incorrect :(

Answer:

b) 0.0228

Step-by-step explanation:

We use the z score formula when given random number of samples =

z = (x-μ)/σ/√n where

x is the raw score = $3.5 million

μ is the population mean = $3.26 million

σ is the population standard deviation = $ 1.2 million

n = random number samples = 100

Hence,

z = 3.5 - 32.6/1.2/√100

z = 3.5 - 32.6/1.2/10

z = 3.5 - 3.26/0.12

z =2

Probability value from Z-Table:

P(x<3.5) = 0.97725

P(x>3.5) = 1 - P(x<3.5)

P(x>3.5) = 1 - 0.97725

P(x > 3.5) = 0.02275

Approximately ≈ 0.02278

The approximate probability that the mean salary of the 100 players exceeded $3.5 million is 0.02278

Answer:

6.9

Step-by-step explanation:

Let x be the length of the remaining side.

By the Pythagorean theorem,

4² + x² = 8²

x² = 8² - 4² = 48

x = √48 = 4√3 ≅ 6.9

Answer:

6.9

Step-by-step explanation:

a^2+b^2=c^2

a^2+ 4^2 =8^2

a^2+ 16= 64

a^2= 48

\(\sqrt{a}\\\) = \(\sqrt{48}\)

a= 6.92

The area of a rectangle is 173 unit square.

What is the 30-60-90 triangle?

A 30-60-90 triangle is a right triangle with one leg equal to x, the other leg equal to 2x, and the hypotenuse equal to x*sqrt(3).

We have given,

The rectangle is separated by two triangles.

The length of the common side of triangles and the diagonal of the rectangle which is 20.

We know that each angle of the rectangle is 90°, so triangles become of 30-60-90 triangles.

Given the length of one side of a triangle, we can find the other side(s) without using long-step methods such as Pythagorean Theorem and trigonometric functions.

Solving a 30-60-90 triangle

When the hypotenuse is known, we can find the shorter side by dividing the hypotenuse by 2. The longer side can then be obtained by Pythagoras' Theorem.

Thus,

Shorter side = hypotenuse/2

Shorter side = 20/2 = 10

By using Pythagoras' Theorem:

(longer side)² + (Shorter side)² = (hypotenuse)²

(longer side)² + (10)² = (20)²

(longer side)² = 400 - 100 = 300

longer side = √300 = 17.3

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

so, 17.3 * 10 = 173 unit square.

Hence, the area of a rectangle is 173 unit square.

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Answer:  There is an extra O2 molecule left over.

Step-by-step explanation: A reaction between four oxygen molecules and two methane molecules will not have any leftovers.

There is an extra O2 molecule left over.

In a chemical reaction, one or more substances—also known as reactants—are changed into one or more additional substances—also known as products. Chemical elements or chemical compounds make up substances.

Reactants are the chemicals that take part in a chemical reaction. The resulting materials are referred to as products. The reactants' characteristics are different from those of the products. Additional Names: chemical change, reaction

Given:

C\(H_4\)+2\(O_2\) -> C \(O_2\) + 2\(H_2\)O

So, if we  change the 2 in front of 2O2 to a 3 then we have 4 oxygens to react.

Then, There won't be any byproducts of a reaction between two methane molecules and four oxygen molecules.

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After applying the scale factor, the image is an enlargement.

The new coordinate of the vertex at (3, 3) if the vertex at (0, 0) remains the same is (6, 6).

In Geometry, a dilation is a type of transformation which typically changes the dimension (size) or side lengths of a geometric object, but not its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would increase or decrease depending on the scale factor applied.

In this scenario an exercise, we would dilate the coordinates of the vertex at (3, 3) by applying a scale factor of 2 that is centered at the origin as follows:

Vertex (3, 3) → new coordinate of vertex (3 × 2, 3 × 2) = (6, 6).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

2

Step-by-step explanation:

4²=16

16 × 3 = 48

2²=4

4 × 6 = 24

48 ÷ 24=2

(4² * 3) / (2² * 6)

Answer:

the awnser is 2

Step-by-step explanation:

4 times 6= 24

16 times 3=48

48 divided by 24 =2

Answer:

Part A- yes, because all 3 sides are Equal (each side is 5)

Part B- yes, each rectangle has the dimensions 12*5

Part C- yes- since the sides are 5 and 12 you can determine that the diagonal is 13, using they Pythagorean theorem \(a^{2} +b^{2} =c^{2}\)

\(5^{2} +12^{2} =13^{2} \\25+144=169\)- true statement, so the lateral sides are rectangles, because the corners are 90

Part D-  \(4\sqrt{2}\) (it is a 45-45-90 triangle- so the hypotenuse is the side length times \(\sqrt{2}\)

Part E- the diagonal face as the largest area- dimensions are \(4\sqrt{2} * 12\\\)

the area would be \(48\sqrt{2}\)

Step-by-step explanation:

The square root of the expression -36 is DNE

From the question, we have the following parameters that can be used in our computation:

\((-36)^\frac 12\)

By definition, the square root of negative numbers are complex numbers

using the above as a guide, we have the following:

\((-36)^\frac 12\) is not a real number

Hence, the solution is DNE

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The response choice that include the true statements based on the number line is the second option;

Point B represents \(-2\frac{1}{2}\), Point C represents 1, and 1 > \(-2\frac{1}{2}\)

A number line is a line that contains (equally spaced) markings, which is then used to illustrate mathematical operations.

The number line in the question is presented as follows;

<________|_____|_____|__|__|____|____|____|___|_|____|_____|____>

                -5          A               B                     0       C      D                     5  \({}\)

Therefore, based on the number line, we get;

The location of the point A is 4 units to the left of the point 0, taking the points to the right of zero as positive, we get;

Each unit to the left of point O, is -1 larger than the previous value, moving from right to left.

The coordinates of the point A is therefore, -1 × 4 = -4

The location of the point C is one unit to the right of 0, therefore, the coordinates of the point C is 1

The location of the point C = 1 is further right to 0 than the point B = -2 1/2

Therefore;

The correct option is; Point B represents -2 1/2, Point C represents 1, and 1 > -2 1/2

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\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Linear Algebra

a-2= 3+6a/3

=> 3(a-2)= 3+6a

=> 3a-6= 3+6a

=> -6-3=6a-3a

=> -9=3a

hence, a=-3

Answer:

The quadrilateral'area is 96cm².

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

i+42

Step-by-step explanation:

(3+3i) - (3+2i) + (1+41)

= 3+3i-3-2i+1+41

= 3i-2i+1+41

= i+42

Answer:

Step-by-step explanation:

In this equation, 500 is the coefficient of the variable h, 4,000 is the constant, and E and h are both variables. Therefore, the equation should be written as:

E = 500h + 4000

-0.2

'0

-0.2 = - .2 = - 2/10 = - 1/5

so

answer is -1/5

Answer:

-0.2 = -1/5

Step-by-step explanation:

you have to turn the decimal to a fraction.

0.2/1

multiply 0.2/1 by 10/10 which is 2/10

Since the GCF is 2...

You want to divide 2/10 by 2/2

that is 1/5

Now add the negative number sign

BOOM

Now you got yourself -1/5

I hope I helped! :)

Answer: 6,573.99 cubic meters.

Step-by-step explanation: The volume of a cylinder can be calculated using the formula:

V = πr^2h

where V is the volume, r is the radius, and h is the height of the cylinder.

To find the volume of a cylinder with a diameter of 28 meters, we first need to find the radius:

radius = diameter / 2 = 28 / 2 = 14 meters

Now we can use the formula to find the volume:

V = πr^2h = π(14)^2(9.5) = 6,573.99 cubic meters (rounded to two decimal places)

Therefore, the volume of the cylinder is approximately 6,573.99 cubic meters.

In parallelogram ABCD, which angle is congruent to ?

Let us draw the parallelogram to better understand the problem.

As you can see from the above figure,

∠ABC and ∠CDA are congruent. (drawn in black color)

Also, ∠BCD and ∠DAB are congurent. (drawn in red color)

This means that the opposite angles are congruent in a parallelogram.

Therefore, the correct answer is option C

∠ABC and ∠CDA are congruent.

Answer:

the last one is the only one with a y intercept of -1

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

im assuming the "x" is multiplication so 16 x y is 16y

Step-by-step explanation:

whoever created the original question and then probably the people copying it need to focus on writing these things correctly.

I assume this means

log(9) - log(4) ÷ log(3) - log(2)

or is anything combined in brackets ? like it could be e.g. log(4 ÷ log(3)). just as example.

and I guess we mean logarithm to the base of 10, right ?

anyway, if my assumptions are correct, then we only need to follow the regular priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

so, we need to start with the division in the middle, and then do the subtractions.

log(4) ÷ log(3) = 1.261859507...

log(9) - 1.261859507... = -0.307616998...

-0.307616998... - log(2) = -0.608646993...

or was the original question

(log(9) - log(4)) ÷ (log(3) - log(2))

?

that would be way more interesting.

we use the rules of logarithm :

e.g.

log(a×b) = log(a) + log(b)

log(a/b) = log(a) - log(b)

so, we have then

log(9/4) ÷ log(3/2)

and that is equal to

log(3/2 × 3/2) ÷ log(3/2)

(log(3/2) + log(3/2)) ÷ log(3/2) = 1 + 1 = 2

if that is the case, you really, REALLY need to pay more attention to brackets and other symbols in problem definitions.

Answer:

Step-by-step explanation:

If single rolls are indeed priced at $89 each, the 3-roll package is a much better buy.

We suspect that the single rolls are priced at $0.89 each, which means you can buy 3 of them for less than $2.70. At this price, single rolls are a better buy.

Answer:

Hope this helps you understand

Step-by-step explanation:

-2m-6=-6m+8

Add 6 on both sides

-2m=-6m+14

subtract 14 from both sides.

-2m -14=-6m

Add 2m on both sides

-14=-6m

Do the rest on your own

A graph that represents each set of points is shown below.

A set that represents equivalent ratios include the following: B. (2, 1), (6, 3), (10, 5).

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using the various data points from table D as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 1/2 = 3/6 = 5/10

Constant of proportionality, k = 0.5.

Therefore, the required linear equation is given by;

y = kx

y = 0.5x

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Using a system of equations, the amount of solution a and b required to make the required gallons of the solution are 29.41 and 20.59 respectively.

Let :

a + b = 50 - - - - (1)

0.24a + 0.41b = 50 × 0.31

0.24a + 0.41b = 15.5 - - - - (2)

From (1) :

a = 50 - b - - - - (3)

Substituting (3) into (2)

0.24(50 - b) + 0.41b = 15.5

12 - 0.24b + 0.41b = 15.5

0.17b = 15.5 - 12

0.17b = 3.5

b = 20.588

From (3) :

a = 50 - 20.588

a = 29.412

Therefore, about 29.41 gallons of solution a and 20.59 gallons of solution b is required.

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Answer:19/20

1-20=19

1÷20=0.05

0.05=5%

I hope this is good enough:

answer:

y = -2/5x + 4