The swiss mathematician leonhard euler and the french mathematician rene descartes both discovered a pattern in the numbers of​ edges, vertices, and faces of polyhedrons. solve problems 810.

The equation of the line in point slope form is y - 105 = 4 (x - 10) and the equation of the line in slope intercept form is y = 4x + 65.

Slope is defined as the change in the y coordinates of the point divided by the change in x coordinates of the point.

Slope of a line through any two points (x₁, y₁) and (x₂, y₂) is,

m = (y₂ - y₁) / (x₂ - x₁)

We have the points (10, 105), (15, 125), (20, 145), (25, 165) and (30, 185).

Considering the points (10, 105) and (15, 125),

m = (125 - 105) / (15 - 10) = 20/5 = 4

Equation of a line in point slope form is,

y -  y₁ = m (x - x₁)

Substituting m = 4 and a point (10, 105),

y - 105 = 4 (x - 10)

Equation of a line in slope intercept form is,

y = mx + c, where c is the y intercept which is the point where the line intersects the Y axis. The x coordinate at that point will be zero.

Substituting x = 0 in the point slope form,

y - 105 = 4 (0 - 10)

y - 105 = 4 × -10

y = -40 + 105

y = 65, which is the y intercept.

The equation of the line in slope intercept form is,

y = 4x + 65.

Hence the equation of the line in point slope form and slope intercept form are y - 105 = 4 (x - 10) and y = 4x + 65 respectively.

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The appropriate test statistic for the test is t = 16/0.037.

The appropriate test statistic for the test is obtained by dividing the estimated slope of the regression line (in this case, 16) by the standard error of the slope (0.037). The test statistic measures how many standard deviations the estimated slope is away from the hypothesized value of 0. By calculating the ratio of 16 divided by 0.037, we obtain the t-value, which is used to assess the significance of the estimated slope in relation to the null hypothesis.

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Answer:

4.5

Step-by-step explanation:

Use sin64=x/5 and simplify to

5sin64 and plug it into a calculator to get 4.49 which is 4.5

Answer:

19

Step-by-step explanation:

7x + 2x = 9x

9x = 68 + 103

68 + 103 = 171

9x = 171

Divide it

19

Answer:

I'm sure the correct answer is x = 19

Step-by-step explanation:

7x + 2x = 9x

68 + 103 = 171

divide both sides by 9 and the it gives you x = 19

I did not get Your Question Probably But the way I see it the answer is:

The equation of a circle with center (h, k) and radius r can be written as:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -6). To find the radius, we can use the distance formula between the center and the given point (-√28, 3):

r = √((x₂ - x₁)^2 + (y₂ - y₁)^2)

Plugging in the values:

r = √((-√28 - 0)^2 + (3 - (-6))^2)

Simplifying:

r = √(28 + 81)

r = √109

Therefore, the equation of the circle with center (0, -6) and containing the point (-√28, 3) is:

(x - 0)^2 + (y + 6)^2 = (√109)^2

Simplifying further:

x^2 + (y + 6)^2 = 109

Answer:

The equation of the circle with center (0, -6) containing the point (-√28, 3) is x^2 + (y + 6)^2 = 109.

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is given by the formula:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -6), which means that h = 0 and k = -6. We also know that the circle contains the point (-√28, 3), which means that this point is on the circle and satisfies the equation above.

To find the radius r, we can use the distance formula between the center of the circle and the given point:

r = sqrt((0 - (-√28))^2 + (-6 - 3)^2) = sqrt(28 + 81) = sqrt(109)

Substituting h, k, and r into the equation of the circle, we get:

x^2 + (y + 6)^2 = 109

Therefore, the equation of the circle is x^2 + (y + 6)^2 = 109.

Answer:

P' = (1,5 . 3)

Q' = (1,5 . 4,5)

R' = (1,5 . 1,5)

The quadrilateral that has diagonals that always bisect its angles and also bisect each other is a (1) rhombus.

In a Rhombus, the diagonals are perpendicular bisectors of each other, and they bisect each other at their point of intersection, dividing the rhombus into four congruent triangles.

Each angle of a rhombus is = 180° divided by number of sides, so each angle of a rhombus is 90°.

In a rectangle, the diagonals bisect each other, but they do not necessarily bisect the angles of rectangle.

In a parallelogram, the diagonals bisect each other, but they do not necessarily bisect the angles of parallelogram.

In an isosceles trapezoid, the diagonals do not bisect each other.

Therefore, the correct answer is option (1) rhombus.

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The given question is incomplete, the complete question is

Which quadrilateral has diagonals that always bisect its angles and also bisect each other?

1) rhombus

2) rectangle

3) parallelogram

4) isosceles trapezoid.

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Answer: The point (-2, 4) is on the circle (x - 5)^2 + (y + 3)^2 = 25.

Step-by-step explanation: The point (-2, 4) is on the circle (x - 5)^2 + (y + 3)^2 = 25. To check if a point is on the circle, we can substitute the point's x and y coordinates into the equation of the circle. If the equation is true, then the point is on the circle. In this case, substituting (-2, 4) into the equation of the circle.

The area in square meters will the oil slick cover is 9.5×10⁶ m².

15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:

The total volume of the oil spilt by 15 barrels = 15× 42 gallons.

=630 gallons

1 gallon = 3.78541 liters

Volume in L = 630 gallons × 3.78541 liters/ 1 gallon

= 2384.8083 L

1 L = 10⁻³ m³

2384.8083  L = 2384.8083 × 10⁻³ m³

= 2.3848083 m³

The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.

1 nm = 10⁻⁹ m

Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m

= 2.5×10⁻⁷ m

Area (m²) = volume (m³)/thickness (m)

= 2.3848083 m³/ 2.5×10⁻⁷ m

= 0.95392×10⁷ m²

= 9.5×10⁶ m²

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When talking about constant speed, we are referring to a ray (line with an initial point); in this case, the initial point is the origin (cero), because in cero time the car travels cero distance. On the other side, the problem says that the car is traveling at a constant speed of 92 mph. It means that (92 miles, 1 hour) is a point of the ray. Thus, we just need to graphic or draw the ray that passes through both points.

For the given function f(x) the graph has a domain of (-5 , 0). For the function g(x) represented by the table the domain is given by the values (-3, 3).

The set of all potential inputs or independent variables for which a function is defined is known as the domain of the function in mathematics. In other words, it is the collection of all possible x-values for the function. On the other hand, the collection of all potential dependent variables or outputs that a function may produce for the specified inputs is known as the range of the function. It is the collection of all y-values that the function is capable of producing.

Given that the function f(x) is the graph while the function g(x) is represented by the table.

For the given function f(x) the graph has a domain of (-5 , 0). The range of the function is (4, infinity). The vertex of the function is given by the coordinates (2, 4). The axis of symmetry of the parabola is x = -2.

For the function g(x) represented by the table the domain is given by the values (-3, 3). The range of the function is given as (25, 1). The x-intercept is at the point 2. The y-intercept is at the point 4.

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Answer: 13,36,-2,-2,pi

Step-by-step explanation:

You do exactly what it says for the rule to -6 to get your answer.

Answer:

On-time Buses: 75%

Running late Buses: 13.46%

Step-by-step explanation:

Part 1: Solve for the probability of Jerry owning an "on-time" bus

Of the 48 buses that run on time, Jerry owns 36 of them. Therefore, the probability of a bus running on time being owned by Jerry will be solved with the ratio of 36 buses to 48 buses.

Part 2: Solve for the probability of Jerry owning a "running late" bus

Of the 52 buses that run late, Jerry owns 7 of them. Therefore, the probability of a bus running late & being owned by Jerry will be solved with the ratio of 7 buses to 52 buses.

Given that, parallelogram ABCD is a rectangle. And

AC = 6y − 1 and

BD = 4y + 13.To find AC. To find the value of AC, we can use the properties of a rectangle. In a rectangle, opposite sides are equal and parallel.

So, in parallelogram ABCD, AC is one of the diagonals, and since it is a rectangle, the opposite side is parallel, and they have the same length. So, BD = AC.

Substituting BD = 4y + 13, we get;

AC = 4y + 13 Now, the value of

AC is 4y + 13. Therefore, the answer is 4y + 13. So, in parallelogram ABCD, AC is one of the diagonals, and since it is a rectangle, the opposite side is parallel, and they have the same length. So, BD = AC.

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This question is incomplete because it was a details in the question was not written correctly.

Complete Question:

A sundae requires 2 ice-cream scoops and 4 raspberries, and a milkshake requires 3 ice-cream scoops and 5 raspberries. Laila wants to sell sundaes and milkshakes with at most 80 ice-cream scoops and 150 raspberries. Let S denote the number of sundaes she makes and M the number of milkshakes she makes. Write an inequality that represents the condition based on the number of (ICE-CREAM SCOOPS).

Answer:

An inequality that represents the condition based on the number of (ICE-CREAM SCOOPS) is given as:

2S + 3M ≤ 80

Step-by-step explanation:

From the above question, we are told that:

Let S denote the number of sundaes Laila makes

M the number of milkshakes

a) A sundae requires 2 ice-cream scoops and 4 raspberries

A sundae = 2S and 4S

b) A milkshake requires 3 ice-cream scoops and 5 raspberries.

A milk shake = 3M and 5M

Laila wants to sell sundaes and milkshakes with at most 80 ice-cream scoops and 150 raspberries .

Therefore, an inequality that represents the condition based on the number of (ICE-CREAM SCOOPS) is given as:

2 ice cream scoops + 3 ice cream scoops ≤ 80

2S + 3M ≤ 80

423

To solve the above equation follow the BODMAS rule

That is,

Brackets of Division Multiplication Addition Subtraction

BODMAS rule states that mathematical expressions with multiple operations need to be solved from left to right in the order of BODMAS.

so,

first, calculate the value in the brackets

(144-4)*(12/4)+3 = (140)*(12/4)+3

=140*(3)+3

According to the rule, a division operation is to be performed but there is no division operation in the equation we skip this step and proceed to the next operation

so, multiply 140*3

=420+3

the next operation is the addition

=423

the next operation according to the rule is subtraction which is not required to be performed in the equation.

therefore,

(144-4)*(12/4)+3 = 423

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In the consumption-based asset pricing model, an increase in future dividends can result in a decrease in the current stock price due to the income and substitution effects which prompts stockholders to sell their shares, and the substitution effect, which increases the supply of other assets and the demand for stocks.

The income effect refers to the impact of changes in income on an individual's consumption choices. In this model, an increase in future dividends implies higher expected future income for the stockholders. As a result, stockholders may choose to consume more in the future, reducing their current consumption. To finance this increased consumption in the future, stockholders may decide to sell their shares in the present, leading to a decrease in the stock price.

The substitution effect relates to the trade-off between different assets. An increase in future dividends makes holding stocks more attractive compared to other assets. As a result, investors may choose to reallocate their portfolios by selling other assets and buying more stocks. This increased supply of other assets and increased demand for stocks can lead to a decrease in the price of stocks.

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Answer:

If you guess do this -

.5(9)

Basically about a 4.5% chance of getting all right.

Answer:

Step-by-step explanation:

each question has 2 answer choices, so 1 or the 2 is correct, and to get all 9 in a row correct would be like this

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2

because theres a 1 in 2 chance of getting each question right, and there are 9 questions

1/2^9 = 0.00195 = 0.195%

Answer:

6

Step-by-step explanation:

Okay so you don't have a number of cookie makes it a bit harder but since the answer can only be 5/6 or 6 we'll say there is 45 cookies. So 1/3 of 45 = 15

so 15 divided by 2 1/2 = 6

Answer:

f(x)=2x-10 ______(given)

f(x)=8 _______(given)

Therefore, according to the above problem

2x-10=8

2x=10+8

2x=18

x=18/2

x=9

The value of the input of a function given the output is found by reversing

the operations of the function.

When f(x) = 8, x is 9.

Reasons:

The given function is; f(x) = 2·x - 10

Required:

The value of x if f(x) = 8

Solution:

When f(x) = 8, we have;

f(x) = 2·x - 10 = 8

Which gives;

2·x - 10 + 10 = 8 + 10 = 18

2·x + 0 = 18

\(x = \dfrac{18}{2} = 9\)

x = 9

When f(x) = 8, x = 9

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The margin of error is multiplied by √2. The correct option is B.

The margin of error is affected by the sample size and the standard deviation of the population. When the sample size is cut in half, the margin of error increases because there is more uncertainty in estimating the population mean. The formula for margin of error is:

Margin of Error = Z * (Standard Deviation / √Sample Size)
When the sample size is cut in half, the new margin of error becomes:
New Margin of Error = Z * (Standard Deviation / √(Sample Size / 2))
By factoring out the square root, we get:
New Margin of Error = Z * (Standard Deviation / (√Sample Size * √0.5))
This shows that the original margin of error is multiplied by √2 when the sample size is cut in half.

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Answer:

1. 2/5,-3 2. \(x=\frac{-5+-\sqrt{13} }{6}\)

Step-by-step explanation:

i used the quadratic formula to find x also please note that 2 has 2 answers bc of the +- beofre the sqrt of 13  

Step-by-step explanation:

5x² + 13x - 6 = 0

Using the quadratic formula

\(x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} \)

a = 5 , b = 13 c = - 6

We have

\(x = \frac{ - 13± \sqrt{ {13}^{2} - 4(5)( - 6) } }{2(5)} \)

\(x = \frac{ - 13± \sqrt{169 + 120} }{10} \)

\(x = \frac{ - 13± \sqrt{289} }{10} \)

\(x = \frac{ - 13±17}{10} \)

\(x = \frac{ - 13 + 17}{10} \: \: \: \: \: or \: \: \: \: x = \frac{ - 13 - 17}{10} \)

3x² + 5x + 1 = 0

a = 3 , b = 5 , c = 1

\(x = \frac{ -5 ± \sqrt{ {5}^{2} - 4(3)(1)} }{2(3)} \)

\(x = \frac{ - 5± \sqrt{25 - 12} }{6} \)

\(x = \frac{ - 5± \sqrt{13} }{6} \)

\(x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} \)

Hope this helps you

Answer:

Rajan = 436.36 rupees and Kamal = 363.63 rupees

Step-by-step explanation:

Total ratio = 11/30

Amount to be shared = 800

Rajan = Individual ratio / Total ratio x the total amount to be shared

1/5 ÷11/30 × 800 = 436.36

Kamal = 1/6 ÷ 11/30 × 800 = 363.63

Answer:

25%

Step-by-step explanation:

To find what percentage of 40 is 10, you must do this:

10÷40 = 0.25

Then multiply by 100 to find the percentage:

0.25 × 100 = 25%

The answer is 25%.

Hope this helps. Please mark me as brainliest. Thanks!

Answer:

x=30 degrees

Step-by-step explanation:

there are 3theorems that can be used for this

vertical angle theorem: vertical angles congruent

triangle sum theorem: all angles in triangle add up to 180 degrees

straight line?? i forgot the name: a straight line is 180 degrees

refer to image attached

measure of angle BAC is 36 degrees by vertical angle theorem.

look at the angle 105 degrees. it and a unknown degree to the left equal 180 because it makes a straight line. so measure of angle BDC is 180-105 degrees. measure of angle BDC is 75 degrees

then sum of all the angles in triangle ABD is 180

36 +(39+x) +75=180 degrees

solve equation

x +150=180

x=30 degrees

hope this helps !!

In order to calculate the value of x, we can use the sine relation of angle x.

The sine relation is equal to the length of the opposite leg to the angle over the length of the hypotenuse.

So we have:

Therefore the value of x is 60.78°.

Answer and Step-by-step explanation:(MAKE ME BRAINLIEST)

Answer:

Step-by-step explanation:

Choose your own x values and find the corresponding y values.

Here's a table of values

 x     y= 2x + 3    (x, y)

 0                  3    (0, 3)

 2    2(2) + 3 = 7  (2, 7)

and so on