what is the slope of the line that goes through (0 0) and (6 3)

Answer:

x=-2

Step-by-step explanation:

answer attached

The system of equations plotted on graph 3 has two solutions.

In the given figure, three different parabola and lines are drawn.

The intersection of the parabola and the line represent the solution of that system of equations.

Graph 1:

The parabola and the line do not intersect at each other.

Therefore, the equation has no solution.

Graph 2:

The parabola and the line intersect each other at one point, that is (1, 1).

Therefore, the equation has one solution.

Graph 3:

The parabola and the line intersect each other at two points that is (4, 1) and (0.5, -1).

Therefore, the equation has two solutions.

Therefore, the system of equations plotted on graph 3 has two solutions.

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Answer:

c

Step-by-step explanation:

third graph

If the vertex angle of an isosceles triangle is 40 degrees, the base angle will also be 70 degrees.

An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception. The characteristics of an isosceles triangle are as follows: There is agreement between two parties. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

Here,

The sum of angles of triangle=180 degree

by property of isosceles triangle, two angles are equal.

2y+40=180

2y=140

y=70 degree

The measure of a base angle of an isosceles triangle if the vertex angle is 40 degree will be 70 degrees.

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The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

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If a farmer had twice as many cows as sheep. After he had sold

375 cows and another 12 cows died, he had half as many cows

as sheep left. then he left with 129 cows.

Two or more expressions with an Equal sign is called as Equation.

Let C represents number of cows and S represents sheeps

Given that A farmer had twice as many cows as sheep.

C=2S

375 cows and another 12 cows died,

Now, with C-375-12, then

2(C-375-12)=S

After this he had half as many cows as sheep left.

2(C-375-12)=C/2

1.5C=2×(387)

C=4/3×387

= 4×129=516 and S=258

Now in the end, number of cows=

516-375-12= 129 and S=258

Hence there are 129 cows remained.

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The length of 2 sides and an angle between them is given A = ½ × b × c × sin(α) If two angles and the length between them is given A = For an isosceles right triangle A = ½ × a.

If the height (i.e. the altitude) and base of an isosceles triangle are known, the area can be easily calculated. The area of the isosceles triangle is calculated by multiplying the height by the base and dividing by two. As a result, an isosceles triangle has two equal sides and two equal angles. The name is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

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Answer:

  A)  6.86×10⁴

Step-by-step explanation:

You want to write 68600 in scientific notation.

The number 68600 can be written in expanded form with exponents as ...

  68600 = 6×10⁴ +8×10³ +6×10² +0×10¹ +0×10⁰

The left-most term of this sum tells you the exponent in scientific notation:

  68600 = 6.86×10⁴

Yes, the selling price of an item is a function of the cost of making the item.

A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.

Cost is often the expenditure incurred for producing a product or service that a firm sells. The selling price is the amount paid by the buyer to purchase a product or products.

The selling price of an item is a function of the cost of creating the item since the manufacturer must sell at a price higher than the cost of making the item in order to recoup his investment and make a profit.

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Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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Answer:

39 3/8 ft ^2

Step-by-step explanation:

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

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

On solving the provided question, we can say that equation is 532/13.5 = 39.4 doses

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

equation is

week * 7( days/week) * 24(hours/day) * 19/6(MILIGRAMS/HOURS)

532 milligrams for a week

532/13.5 = 39.4 doses

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Answer: C

Step-by-step explanation:

\(g(7)=\frac{7}{8}(7)-\frac{1}{2}=\frac{49}{8}-\frac{4}{8}=\frac{45}{8}\)

The percentage of the seats that is filled is 39%.

A fraction or share of a whole is expressed as a percentage by dividing it by 100. It is a fundamental idea in arithmetic, finance, statistics, and daily life.

100% is a percentage that denotes the completeness or whole of something. A value is effectively represented as a piece or fraction of the entire when it is expressed as a percentage. "%" is the symbol for percentage.

We can see that the number of the filled seats would be;

1700 -  1037

= 663 seats

Percentage of the filled seats = 663/1700 * 100/1

= 39%

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Missing parts;

A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?

a ruler is not the best tool to use to measure the field of view on medium- and high-power lenses.

Using a ruler to measure the field of view on medium- and high-power lenses would be difficult and inaccurate. This is because the magnification of the lenses changes the field of view, so a ruler would not be able to measure the field of view accurately at different magnifications. Additionally, a ruler is too small to measure the field of view accurately since it is usually measured in degrees. Therefore, Using a ruler to measure the field of view on medium- and high-power lenses is difficult and inaccurate. This is because the magnification of the lenses changes the field of view, and a ruler is not designed to measure this change. A ruler is also too small to measure the field of view accurately since it is usually measured in degrees. Therefore, using a ruler is not the most reliable tool for measuring field of view on medium- and high-power lenses. Instead, it is better to use a protractor or other specialized tools to accurately measure the field of view. Additionally, it is important to remember that the field of view changes with magnification and should be checked at different magnifications to get the most accurate measurement.

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Miles is the number of miles Martin has run, and Total Time is the total time in minutes that he has been running, which is 11Miles + 5.

To create a linear model, we need to find the equation of the line that best fits the data.

We can do this by finding the slope and y-intercept of the line.
First, we need to find the slope, which is the change in y divided by the change in x.

We can choose any two points on the line to calculate the slope.

Let's use the first and second data points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (104 - 60) / (9 - 5)
Slope = 44 / 4
Slope = 11
Now we can use the point-slope form of the equation of a line to find the y-intercept.

We can use the first data point:
The linear model has the form y = mx + b, where y represents the total time (in minutes), x represents the miles run, m is the slope, and b is the y-intercept.

We can use the data points to find the slope (m) as follows: m = (change in total time) / (change in miles)

Using the first two data points, (5, 60) and (9, 104):

m = (104 - 60) / (9 - 5) = 44 / 4 = 11

Now that we have the slope, we can find the y-intercept (b) using one of the data points.

Let's use (5, 60): 60 = 11 * 5 + b 60 = 55 + b b = 5

So the linear model representing Martin's pace is: y = 11x + 5 In this model, x is the miles run, and y is the total time in minutes.
y - y1 = m(x - x1)
y - 60 = 11(x - 5)
y - 60 = 11x - 55
y = 11x + 5
So the linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output is
Total Time = 11Miles + 5

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Answer:

669

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

From the figure attached,

Area of the shaded region = Area of circle - (Area of the ΔOAB + Area of ΔOED)

Area of the circle = πr²

                             = π(5)²

                             = 25π cm²

Area of ΔOAB = 2(Area of ΔOCB)

AB = 6 cm

OC = 5 - 1 = 4 cm

By applying Pythagoras theorem in ΔOCB,

OB² = OC² + BC²

5² = 4² + BC²

BC² = 25 - 16

BC = √9 = 3 cm

Area of ΔOCB = \(\frac{1}{2}(OC)(BC)\)

                        = \(\frac{1}{2}(4)(3)\)

                        = 6 cm²

Area of ΔAOB = 2(6) = 12 cm²

Area of ΔAOB = Area of ΔDOE = 12 cm²

Area of shaded region = 25π - (12 + 12)

                                      = (25π - 24) cm²

Therefore, Option (3) will be the answer.

Answer:

The Cpk of this line is 0.6667.

Step-by-step explanation:

Cpk:

In a process with mean \(\mu\), standard deviation \(\sigma\), upper limit U and lower limit M, the CPK is of:

\(C_{pk} = \text{min}(\frac{U-\mu}{3\sigma}, \frac{\mu-L}{3\sigma})\)

Average of 61 psi with a standard deviation of 2 psi.

This means that \(\mu = 61, \sigma = 2\)

The specification calls for the acceptance range to be from 55 psi to 65 psi.

This means that \(L = 55, U = 65\).

Cpk

\(\frac{U-\mu}{3\sigma} = \frac{65-61}{3(2)} = 0.6667\)

\(\frac{\mu-L}{3\sigma} = \frac{61-55}{3(2)} = 1\)

The minimum of these values is 0.6667, so the Cpk of this line is 0.6667.

The sum (A+B)(x) and difference (A-B)(x) of two quadratic functions A(x) and B(x) were found, along with their values for x=5, vertices, intercepts, and where they are increasing/decreasing.

To find (A+B)(x), we simply add the two functions:

(A+B)(x) = A(x) + B(x) = (\(-0.25x^2+20x\)) + (\(-0.19x^2+15.2x\)) = \(-0.44x^2\) + 35.2x

To find (A-B)(x), we simply subtract B(x) from A(x):

(A-B)(x) = A(x) - B(x) = (\(-0.25x^2+20x\)) - (\(-0.19x^2+15.2x\)) = \(-0.06x^2\) + 4.8x

When x=5, we can evaluate each expression:

(A+B)(5) = \(-0.44(5)^2\) + 35.2(5) = 60

(A-B)(5) = \(-0.06(5)^2\) + 4.8(5) = 12

To find the vertices and intercepts of the functions A(x) and B(x), we can use the vertex and intercept formulas for quadratic functions:

For A(x):

Vertex = (-b/2a, f(-b/2a)) = (-20/-0.5, A(20/-0.5)) = (40, 400)

x-intercepts: 0 = \(-0.25x^2\) + 20x, so x = 0 or x = 80

y-intercept: A(0) = 0

For B(x):

Vertex = (-b/2a, f(-b/2a)) = (-15.2/-0.38, B(15.2/-0.38)) = (40, 304)

x-intercepts: 0 = \(-0.19x^2\) + 15.2x, so x = 0 or x = 80

y-intercept: B(0) = 0

Both functions are decreasing for x < 40, and increasing for x > 40. The vertex (40, 400) is the maximum point for A(x), and the vertex (40, 304) is the maximum point for B(x).

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Answer:

O a=0

Step-by-step explanation:

Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Answer:

that means each side equals 8

Step-by-step explanation:

Answer:

angle a: 70°

angle d: 70°

angle dce: 35°

x: 15m

y: 14m

Step-by-step explanation:

all triangles add to 180° so 35 + 75 = 110 and 180-110 = 70

where the two triangles connect and cross, the angles will be the same so it will have the same angle measures as the first triangle which makes the triangles similar

knowing that they are similar triangles will help with figuring out the lengths of the sides.

since they are similar, their sides will be proportional, we just need to figure out the ratio

if we lay the triangles on top of each other, the two 75° angles match up and therefore the sides do too so we can make a fraction 12/18 = 10/x

now we can solve for x

multiply both sides by x

12x/18 = 10

now multiply both sides by 18

12x = 180

divide both sides by 12

x = 15

now we do the same for y

12/18 = y/21

12*21/18 = y

y = 14

hope this helps!

Answer:

10

Step-by-step explanation:

26×3=78

78÷8=9.75

round up to 10 since you can't buy .75 of a pizza

Answer:

Week 1 = 80

Week 2 =88

Week 3 = 96.8

Week 4 = 106.48

Week 5 = 117.128

Step-by-step explanation:

Given

Week 1 = 80

Growth = 10%

Required

Fill week 1 to 5

We have week 1 already.

Week 2 is calculated as thus:

Week 2 = Week 1 + 10% * Week 1

Week 2 = 80 + 10% * 80

Week 2 = 80 + 8

Week 2 = 88

Week 3 is calculated as thus:

Week 3 = Week 2 + 10% *Week 2

Week 3 = 88 + 10% * 88

Week 3 = 88 + 8.8

Week 3 = 96.8

Week 4 is calculated as thus:

Week 4 = Week 3 + 10% * Week 3

Week 4 = 96.8 * 10% *96.8

Week 4 = 96.8 + 9.68

Week 4 = 106.48

Lastly, week 5 is calculated as thus:

Week 5 = Week 4 + 10% * Week 4

Week 5 = 106.48 + 10% * 106.48

Week 5 = 106.48 + 10.648

Week 5 = 117.128

Answer:

From top to bottom:

\(0, 1, 2, -8, -8\)

Step-by-step explanation:

We are given the piecewise function:

\(g(x) = \left\{ \begin{array}{ll} 0.5x+1 & \text{if } x \leq 2 \\ -8 & \text{if } x > 2 \end{array} \right.\)

Row 1:

We want to find g(-2).

Since -2 is less than (or equal to) 2, we will use the first equation. Thus:

\(g(-2)=0.5(-2)+1=-1+1=0\)

Row 2:

Likewise, 0 is less than or equal to 2. We will continue to use the first equation:

\(g(0)=0.5(0)+1=1\)

Row 3:

2 is not less than 2 but it is equal to 2. So we will continue to use the first equation:

\(g(2)=0.5(2)+1=1+1=2\)

Row 4 and 5:

Both 4 and 6 are greater than 2. Thus, we will use the second equation. Therefore:

\(g(4)=-8\text{ and } g(6)=-8\)

*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though