A certain triathlon consists of a ​2.6 mile ​swim, a ​110 mile bicycle​ ride, and a ​26.2mile run. At one​ point, a participant had completed as many miles as the number of miles left to complete. How many miles had he completed at that​ mark?

Answer:

y = 3x - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3 and c = - [tex]\frac{1}{2}[/tex] , then

y = 3x - [tex]\frac{1}{2}[/tex] ← equation of line

Answer: The answer should be 20 hours

Step-by-step explanation:

That is when the 2 lines meet up so that is when they are the same difference from Kansas City.

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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The missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

What is the quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."

First, let Xa, Xb, Xc, Xd = each factor

Xd = each factor which shows In the graph

Then, we can know that

Xa, Xb are the roots of x² + ___x + 14

Xb, Xd are the roots of x²= 3x - __

Xc, Xd are the roots of x² - __x - 15

Xa, Xc are the roots of x² + 10x + __

Xa * Xb = 14           Xd = 15/10 +Xa

Xb+ Xd = 3            14/Xa + 15/10 +Xa = 3

Xc* Xd = - 15          140 + 29Xa/Xa(10+Xa)

Xa + Xc = -10x        140 + 29Xa = 30Xₐ + 3Xₐ²

Xb = 14/Xa             3Xₐ² + Xₐ² - 140 = 0

14/Xa + Xd = 3       Xa1 = -7   Xa2 = 20/3

Xd = -15/-3             Xb1 = -2   Xb2 = 21/10

Xc = -10 -X1            Xc1 = -3    Xc2 = -30/3

Xc1 = -3     Xc2 = -30/3

Xd1 = 5         Xd2=9/10

There are two kinds of answers.

1) x² + 9x + 1x           Xa1 + Xb1 = -9

x² - 3x + 10           Xb1 * Xd1 = -10

x² - 2x - 15           Xc1 + Xd1 = 2

x² + 10x + 21           Xa1 * Xc1 = 21

2)

x² - (263/30)x + 14           Xa2 * Xb2 = 263/30

x² - 3x - (-189/100)           Xb2 * Xd2 = 189/100

x² - (413/30)x - 15           Xc2 + Xd2 = 413/30

x² + 10x + (1000/9)           Xa2 * Xc2 = 1000/9

Hence, the missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

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The table that represents the function for a lawn being mowed more quickly than by Killian's rate is given as follows:

Second table.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

Killian can cut grass at a rate of 1000 square feet each 10 minutes, hence his average rate of change is given as follows:

1000/10 = 100 square feet per minute.

For the second table, in 7 minutes, 1100 square feet of lawn is mowed, hence the rate is given as follows:

1100/7 = 157 square feet per minute.

It is more quickly than Killian's as the rate of change is greater.

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Answer:

 To find the total number of shirts that would make the total cost for each company the same, we can set the two equations equal to each other and solve for the number of shirts:

Red Nose: t = 3.50r + 79

Green Machine: t = 5r + 40

3.50r + 79 = 5r + 40

Subtracting 3.50r from both sides, we get:

79 = 1.50r + 40

Subtracting 40 from both sides, we get:

39 = 1.50r

Dividing both sides by 1.50, we get:

r = 26

So the total cost for each company would be the same if 26 shirts are ordered.

To find the total cost for each company when 26 shirts are ordered, we can substitute 26 for r in each equation:

Red Nose: t = 3.50(26) + 79 = $192

Green Machine: t = 5(26) + 40 = $170

Therefore, if 26 shirts are ordered, the total cost would be $192 for Red Nose and $170 for Green Machine.

Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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The scaling factor for given transformation is 3.

What exactly is scaling factor?

The scaling factor, also known as the scale factor, is a value that indicates how much a geometric figure is enlarged or reduced. It is the ratio of the length of a side or dimension of the original figure to the length of the corresponding side or dimension of the new figure. The scaling factor can be greater than 1, which indicates an enlargement, or less than 1, which indicates a reduction. When the scaling factor is 1, the two figures are congruent, which means they have the same shape and size.

Now,

We can find the scale factor by comparing the corresponding side lengths of the two polygons. Let's start by finding the side lengths of the original polygon:

HI: √[(4-0)² + (-5+3)²] = √20

IJ: √[(6-4)² + (0-0)²] = 2

JK: √[(4-6)² + (5-0)²] = √41

KL: √[(0-4)² + (3-5)²] = √20

LH: √[(0-0)² + (-3+5)²] = 2

Now let's find the corresponding side lengths of the dilated polygon:

H'I': √[(12-0)² + (-15+9)²] = √600

I'J': √[(18-12)² + (0-0)²] = 6

J'K': √[(12-18)² + (15-0)²] = √600

K'L': √[(0-12)² + (9-0)²] = √600

L'H': √[(0-0)² + (-9+3)²] = 6

We can see that the side lengths of the dilated polygon are all 3 times as long as the corresponding side lengths of the original polygon. Therefore, the scale factor is 3.

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Answer:1 and 2

Step-by-step explanation:

so, they asked 50 students and then that was later broke down to smaller groups.

10,15,25

so, for every 10 students will be one. 1 vote= 10 students.

also, the dinosaur had the greatest number of votes so that explains answer 2.

Using the product rule of logarithms, we can condense the expression as follows:

log(x/3 * y/3 * z/3)

= log((xyz) / 27)

So, the condensed form of the given expression is log((xyz) / 27).

Answer:

Step-by-step explanation:

5/9 + (-4/9) - (-2)

5/9 - 4/9 + 2

[tex]5-4+18/9[/tex]

19/9 or 2.1, 2 1/9

Answer:

(2x)(4x)= 8x^22x + 4x = 6x(x+1)+ 2x = 3x + 1(x+1)(2x) = 2x^2 + 2x3x + (2x) = 5x(3x)(2x) = 6x^2

Step-by-step explanation:

hope this helped

For the given triangular prism, the volume value is obtained as Option B: 31.5 in³.

What is a triangular prism?

The pentahedron Triangular Prism contains nine different nets. The bases' vertices and edges are connected by means of their three rectangular sides. The rectangular sides of the triangular prism are joined to one another side by side. Every cross-section that is perpendicular to the base faces is a triangle.

The height of the triangular prism is given as 2 inches.

The base of the triangular prism is given as 7 inches.

The length of the triangular prism is given as 4.5 inches.

The volume of a triangular prism is given by the formula -

V = (1/2) × b × h × l

where b is the base of the triangle, h is the height of the triangle, and l is the length of the prism.

Substituting these values into the equation, we get -

V = (1/2) × 7 inches × 2 inches × 4.5 inches

V = 7 inches × 1 inch × 4.5 inches

V = 31.5 cubic inches

Therefore, the volume of the triangular prism is 31.5 cubic inches.

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Answer:

D

Step-by-step explanation:

The curve will be wider but the vertex would be in the same position.

If a<1, our function will be wider

If a>1, the function will be more narrow

The correct answer is D

Answer:

Alright

Step-by-step explanation:

50/1.428

Multiply the numerator by the denominator to get 50000/1428

Set equation up in long division format

Divide 50000 by 1428 to get 3

Divide 7160 by 1428 to get 5

Divide 200 by 1428 to get 0

Divide 2000 by 1428 to get 1

Divide 5720 by 1428 to get 4

Divide 80 by 1428 to get 0

Divide 800 by 1428 to get 0

35.014

Answer:

Step-by-step explanation:

Yes, that's correct!

3/5 can be simplified to 12/20 by multiplying the numerator and denominator by 4:

3/5 x 4/4 = 12/20

And 1/20 is already in its simplest form, so it is equal to 1/20.

Answer:0

Step-by-step explanation: just like you did on my question and stole the points :) xx

The x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL, as x-coordinate of AJ'K'L' = -y-coordinate of AJKL and y-coordinate of AJ'K'L' = x-coordinate of AJKL.

We create the x-axis and y-axis in the coordinate plane. the origin, where the x- and y-axes cross, and the coordinates ( 0,0 ). The horizontal axis represents the x-axis. The vertical axis represents the y-axis. The first and second coordinates are for the horizontal and vertical axes, respectively. On the coordinate plane, coordinates are expressed by ( x ,y ). The x-coordinate stands for the first coordinate.

When a point is rotated 90° clockwise about the origin, its x-coordinate becomes the negative of its original y-coordinate, and its y-coordinate becomes the positive of its original x-coordinate.

So, for point A(x,y), its new coordinates after a 90° clockwise rotation about the origin would be A'(-y,x). Similarly, for point J, K, and L, their new coordinates would be J'(-yj,xj), K'(-yk,xk), and L'(-yl,xl) respectively.

Therefore, the x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL as follows:

x-coordinate of AJ'K'L' = -y-coordinate of AJKL

y-coordinate of AJ'K'L' = x-coordinate of AJKL

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Answer:

The answer would be C (1,4)

Step-by-step explanation:

The maximum refers to the highest point on the graph.

In this graph, the highest point lands 1 point to the right of zero and then four points up from there.

Making the maximum (1,4)

Answer:

Step-by-step explanation:

The maximum occurs at (1,4). The maximum is the highest point a function will reach. You can see on the graph that the highest point occurs when x = 1 and y = 4.

So the maximum is at (1,4)

A trick you can use to easily find it next time, imagine a horizontal line is coming down the graph from the top. When the line touches the function, that will be the maximum

Answer:

8 feet.

Step-by-step explanation:

Let's denote the width of the sandbox as "w".

We know that the perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

So, we can plug in the given values:

46 = 2(15 + w)

Now, we can solve for "w":

46 = 30 + 2w

Subtracting 30 from both sides:

16 = 2w

Dividing by 2:

w = 8

Therefore, the width of the sandbox is 8 feet.

Answer:51,000

Step-by-step explanation:

ther is 1000 grams every kilogram so 17x3 is 51 and 51x1000 is 51,000

Answer:

Step-by-step explanation:

Cash

(1)

(7)

(9)

(4)

(8)

(3)

(2)

25,000 (3)

11,900 (5)

9,700 (6)

(8)

James Ralston, Capital

(1)

Accounts Receivable

9,900 (9)

James Ralston, Drawing

7,000

Supplies

12,500

Fees Earned

(4)

The answer to the puzzle is (3)O (7)N which makes word ON, (4)T (10)H (1)E which makes word THE, (6)B (8)E (2)A (9)C (5)H which makes the word BEACH

What is a quadrilateral?

A quadrilateral is a 4 sided polygon. On the basis of its properties quadrilaterals are classified as Trapezium,Kite, Parallelogram, Rectangle, Rhombus and square.

Complete the sentence:

1.Parallelogram-(E)

2.Quadrilateral-(A)

3.Supplementary-(O)

4.Bisect-(T)

5.Congruent-(H)

Using the diagram:

6.Given that KG=17 units, KJ=14 units.

As we know from the figure, GH is congruent to KJ and HJ is congruent to side KG.

Therefore, GH=KJ=14units- (B)

7.∠GKJ=86° and ∠GHJ=(x+6)°

We know that ∠GKJ is congruent to ∠GHJ

Therefore, x+6 = 86

                      x=86-6

                      x=80-(N)

8.Given KH=20 & KF= KH÷2  {diagonal pf parallelogram bisect}

                                  =20 ÷ 2

                                  =10 units-(E)

9.Given ∠HJK=82° & We know ∠HJK+∠GKJ=180°  {consecutive angles}

                                                               ∠GKJ=180-∠HJK

                                                                         =180-82

                                                                         =98°-(C)

10.Give that, ∠HJK=82° & we know  ∠HGK=∠HJK {opposite angles of parallelogram}

                                                            ∠HGK=82°-(H)

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The missing coordinate of line is r = 8.

A straight line is a geometrical object that extends infinitely in both directions and has no curvature or bending. It is a one-dimensional object that is defined by two points on the line, called its endpoints, or by its slope and a point on the line.

the slope formula to find the slope of the line given two points:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Plugging in the coordinates we have:

-4 = (-16 - r) / (1 - (-5))

Simplifying:

-4 = (-16 - r) / 6

Multiplying both sides by 6:

-24 = -16 - r

Adding 16 to both sides:

-8 = -r

Dividing both sides by -1:

r = 8

Therefore, the missing coordinate is r = 8.

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Answer:

     6.75 inches.

Step-by-step explanation:

[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]

[tex]= 56.52 + 18.84h[/tex]

[tex]183.69 - 56.52 = 18.84h[/tex]

[tex]127.17 = 18.84h[/tex]

[tex]=\frac{127.17}{18.84}[/tex]

[tex]=6.75[/tex]

The best way to assign values for a simulation using random digits table will be option A.

The best way to assign values for a simulation using a random digits table would be to use a table with at least 10 digits (0-9) in each row.

For Country X, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. If a digit outside of these ranges is generated, it would be ignored.

For Country Y, we would assign Blood type O with the digits 0-5, Blood type A with digits 6-7, Blood type B with digit 8, and Blood type AB with digit 9. Again, if a digit outside of these ranges is generated, it would be ignored.

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Answer:

168 cm^2

Step-by-step explanation:

This rhombus is made up of two triangles. To find triangle area, base x height/2 (but bc there are two triangles we don’t need to divide by 2). To do this, 14 x 12 to get 168cm^2

The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

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