A long distance runner started on a course running at an average speed of 6mph. half an hour later, a second runner began the same course at an average speed of 7mph. how long after the second runner started will the second runner overtake the first runner?

Answer:

[0,+♾)

Step-by-step explanation:

|x| function is kinda like a half opened book from (0, 0) and |x+5| is from (–5, 0)

So we can't find any changes for y

so the domain is

[0, +♾)

The equation to represent the given scenario is a=b-5 and the age of Ana is 18 years when her sister Beatriz is 23 year old.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Ana is 5 years younger than her sister, Beatriz

1) Let the age of Ana be a and the age of Beatriz be b

Now, a=b-5

2) Beatriz is 23 years old

Substitute b=23 in the equation a=b-5, we get

a=18 years

Therefore, the age of Ana is 18 years when her sister Beatriz is 23 year old.

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"Your question is incomplete, probably the complete question/missing part is:"

Ana is 5 years younger than her sister, Beatriz.

1. Write an equation that represents how old Ana is (a) when Beatriz is b years old.

2. How old is Ana when Beatriz is 23 years old?

Answer:

Part 1: 9:18:27

Part 2: 28:42:84

Step-by-step explanation:

Part 1:

54 pigs are split into the ratio 1:2:3. Treating a "1" ratio as x, we have x:2x:3x is 54 pigs. We can add up all parts of the ratio to become the whole. x+2x+3x=54. Solving, x=9. Substituting, our ratio is 9:18:27.

Part 2:

Similar to part 1, we treat a "1" ratio as y. Our ratio is 2y:3y:6y for a total of 154 chickens. Adding all the parts, we have 2y+3y+6y=154, so y=14. Substituting, our ratio is 28:42:84.

In words (6 + q) - xy is six added to a number subtracted from the product of two numbers

The problem is a algebraic expression

A algebraic expression  a mathematical expression containing one or more variables used to express a word problem

We want to convert the algebraic expression (6 + q) - xy into a word problem.

So, (6 + q) - xy in words is six added to a number subtracted from the product of two numbers

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The rectangular equation for given parametric equations x = 2sin(t) and   y = -3cos(t) on 0 ≤ t ≤ π is  [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex] which is an ellipse.

For given question,

We have been given a pair of parametric equations x = 2sin(t) and           y = -3cos(t) on 0 ≤ t ≤ π.

We need to convert given parametric equations to a rectangular equation and sketch the curve.

Given parametric equations can be written as,

x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.

We know that the trigonometric identity,

sin²t + cos²t = 1

⇒ (x/2)² + (- y/3)² = 1

⇒ [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex]

This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.

The rectangular equation is  [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex]

The graph of the rectangular equation [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex] is as shown below.

Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is  [tex]\frac{x^{2} }{4} +\frac{y^2}{9} =1[/tex] which is an ellipse.

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Answer:22

Step-by-step explanation:

10x2+1x2=

20+2

=22

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\huge\text{10(2) + 1(2)}[/tex]

[tex]\huge\text{= 10 + 10 + 1 + 1}[/tex]

[tex]\huge\text{= 20 + 1 + 1}[/tex]

[tex]\huge\text{= 21 + 1}[/tex]

[tex]\huge\text{= 22}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{22}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

x= -3.936 and -0.064

Step-by-step explanation:

I simplified the equation to 40u^2 +16u + 1. Then I just graphed it and found that the zeroes were -3.936 and -0.064.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Let's calculate its discriminant :

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 = 40[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 - 40 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 1 = 0[/tex]

Here, if we equate it with general equation,

[tex]\qquad \sf  \dashrightarrow \: disciminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (4 \times 4 \times 1) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (16) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(16 - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 240[/tex]

Now, since discriminant is positive ; it has two real roots ~

The roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - b \pm \sqrt{ d } }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm \sqrt{ 240 } }{2 \times 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm 4\sqrt{ 15 } }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ 4(- 4\pm \sqrt{ 15 }) }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4\pm \sqrt{ 15 } }{2} [/tex]

So, the required roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4 - \sqrt{ 15 } }{2} \: \: and \: \: \dfrac{ - 4 + \sqrt{15} }{2} [/tex]

if two occurrences A and B are unrelated to one another. Then, 3/4 or 0.75 is the likelihood of event B.

The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true.. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.

These occurrences are referred to as independent events when the occurrence or non-occurrence of one event has no bearing on the occurrence or non-occurrence of any other events.

Figuratively, we have:

If we have the following, two events A and B are said to be independent.

                            [tex]\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})[/tex]

Events A and B happen apart from one another. P(A) = 1/6, while P(A and B) = 1/8.

The likelihood of the event B will then be.

                            [tex]\begin{aligned}&\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\&\mathrm{P}(\mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} \\&\mathrm{P}(\mathrm{B})=\frac{1 / 8}{1 / 6} \\&\mathrm{P}(\mathrm{B})=\frac{6}{8} \\&\mathrm{P}(\mathrm{B})=\frac{3}{4}=0.75\end{aligned}[/tex]

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I understand that the question you are looking for is:

Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) = 1/8. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.

Answer:

6 days

Step-by-step explanation:

if they are writing at 5,000 words per 6 hours, we divide 120,000 by 5,000 and then multiply by 6: 120,000/5,000 = 24, 24*6 = 144 total hours

There are 24 hours in a day: 144/24 = 6

The factors of the trinomial are:

Options C and E

This is further explained below.

Generally, A trinomial is a kind of polynomial that is used in basic mathematics. It is composed of three components, also known as monomials.

In conclusion, The following expressions are the components of the trinomial: x - 7, x + 2

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To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then [tex]$g(x) =x^2-10[/tex] exists g(10) = 90.

The value of g(10), we have to substitute in every x of f(x), the

[tex]f(x) = 2x + 1[/tex] exists f(90) = 181

Therefore, the value of f[g(10)] exists 181.

To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then

[tex]$g(x) =x^2-10[/tex]

substitute the value of x = 10

[tex]$g(10) = (10)^2-10[/tex]

simplifying the equation, we get

g(10) = 100 - 10

g(10) = 90

We have the value of g(10), we have to substitute in every x of f(x), then

f(x) = 2x + 1

substitute the value of x = 90

f(90) = 2(90) + 1

simplifying the equation, we get

f(90) = 180 + 1

f(90) = 181

The value of f[g(10)] exists 181.

Therefore, the correct answer is option b) 181.

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Answer:

66/65.

Step-by-step explanation:

22/5 / 13/3

Invert the divisor and multiply.

---> 22/5 * 3/13

= 66/ 65

Answer:

x ≤ -2

Step-by-step explanation:

3(x + 2) ≤ 5(-2 - x)

Distribute on both sides.

3x + 6 ≤ -10 - 5x

Add 5x to both sides.

8x + 6 ≤ -10

Subtract 6 from both sides.

8x ≤ -16

Divide both sides by 8.

x ≤ -2

Answer:

[tex]\textsf{D. }x\leq-2[/tex]

Step-by-step explanation:

Given inequality: [tex]3(x+2)\leq5(-2-x)[/tex]

Step 1: Distribute [tex]3[/tex] and [tex]5[/tex] through the parentheses.

[tex]\implies 3(x)+3(2)\leq5(-2)+5(-x)[/tex]

[tex]\implies 3x+6\leq-10-5x[/tex]

Step 2: Subtract [tex]6[/tex] from both sides.

[tex]\implies 3x+6-6\leq-10-6-5x[/tex]

[tex]\implies 3x\leq-16-5x[/tex]

Step 3: Add [tex]5x[/tex] to both sides.

[tex]\implies 3x+5x\leq-16-5x+5x[/tex]

[tex]\implies 8x\leq-16[/tex]

Step 4: Divide both sides by [tex]8[/tex].

[tex]\implies \dfrac{8x}{8}\leq\dfrac{-16}{8}[/tex]

[tex]\implies x\leq-2[/tex]

Step-by-step explanation:

part 1: 64/125 - 2/3

make the denominator ( bottom number) the same

x/125 and x/3

125×3 and 3×125

x/375 and x/375

whatever we do to the denominator we have to do to the numerator ( top number)

64/125

125 × 3

so

64 ×3

=64×3/125×3

=192/375

2/3

3 × 125

so

2 × 125

=2×125/3×125

=250/375

put together:

192/375 - 250/375

denominator is the same so we can simply take 192 from 250

192 - 250 = -58

= -58/375

part 2: + (256/625)-1/4

-58/375 + (256/625)-1/4

do the same for (256/625)-1/4 as in part 1

then add it to -58/375 by making the denominator the same

part 3: + (7/3)​

make the denominator the same and add

part 4: simplify

divide a number from both the top and bottom till there is nothing you can divide from both

Answer: 14 cars.

Step-by-step explanation:

A car can be washed with : 100/11 oz.

1 gallon=128 oz.

Hence,

[tex]\displaystyle\\\frac{128}{\frac{100}{11} } =\frac{128*11}{100} =\frac{1408}{100} =14,08\ (cars).[/tex]

The total number of cars that can be washed with 1 gallon of soap if 100oz Can wash 11 cars would be given as 14 cars

To determine how many cars can be washed with 1 gallon of soap, we need to find the ratio between the amount of soap used and the number of cars washed.

Given that 100 oz of soap can wash 11 cars, we can set up the following proportion:

100 oz soap / 11 cars = 1 gallon soap / x cars

I gallon is given as 128 OZ

Such that we have

128 x 100 / 11

= 14.08 cars

Hence the total number of cars would be given as 14 cars

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Answer:

2280 minutes.

Step-by-step explanation:

Time spent each week in lessons = (Lessons per week)(Time per lesson)

= (6)(38)

= 228 minutes/week

Time spent in a 10-week period:

10 weeks * 228 minutes/week

= 2280 minutes

Use conversion factors to determine the time in the desired units (i.e. Hours, seconds, etc.).

Hope this helps!

The number of two year old boys that wear a size 6 is greater than the number of three year  old boys that wear a size 6  by 35.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines called the whiskers and a box. The whiskers represent the minimum and maximum scores.

On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile

50% of the two year olds wear a size 6 = 50% x 100 = 50

25% of the three year olds wear a size 6 = 25% x 60 = 15

Difference in the number : 50 - 15 = 35

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The identified vertical pair of angles in the given figure is: angle LOP and angle MOE.

A pair of angles are regarded as vertical angles that are formed when two straight line intersect each other. The vertical angles formed are non-adjacent angles. They share a common point or vertex but do not have any shared common side.

According to the vertical angles theorem, this vertical angles pair that are non-adjacent angles have angle measure that is congruent to each other.

In the figure shown below, the shared vertex O. The two non-adjacent angles that share this vertex but share no common sides are angle LOP and angle MOE. These vertical angles that are non-adjacent angles are congruent.

Therefore, the identified vertical pair of angles in the given figure is: angle LOP and angle MOE.

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The solution to the systems if equation y = 4x - 5, y = 2x + 3 is (x, y) = (4, 11)

y = 4x - 5

y = 2x + 3

4x - 5 = 2x + 3

4x - 2x = 3 + 5

2x = 8

x = 8/2

x = 4

y = 4x - 5

= 4(4) - 5

= 16 - 5

y = 11

Therefore, the solution to the system of be equation is x = 4 and y = 11

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Calculate discriminant :

[tex]\qquad \sf  \dashrightarrow \: 3 {x}^{2} + 6x - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 36 - 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} [/tex]

Now, let's calculate it's roots ( x - intercepts )

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} [/tex]

So, the intercepts are :

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} [/tex]

and

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} [/tex]

Answer:

[tex]\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)[/tex]

Explanation:

Given expression:

f(x) = 3x² + 6x - 1

Use quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0[/tex]

Here after finding coefficients:

Applying formula:

[tex]x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}[/tex]

[tex]x = \dfrac{ -6 \pm \sqrt{48}}{6}[/tex]

[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{6}[/tex]

[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}[/tex]

[tex]x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}[/tex]

[tex]x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}[/tex]

The cross-price elasticity of demand between strawberries and whipped cream is (C) -0.5.

Therefore, the cross-price elasticity of demand between strawberries and whipped cream is (C) -0.5.

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The complete question is given below:

When strawberry prices increase by 20 percent, the quantity demanded of whipped cream falls by 10 percent. What is the cross-price elasticity of demand between strawberries and whipped cream?

a. -2

b. 2

c. -0.5

d. 0.5

It should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity.

It should be noted that an identity simply means an equation that is always true no matter the values that are substituted.

In this case, should be noted that sin(sin^-1x) = sin-1(sinx) is not an identity. It's simply the inverse of the sine function.

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The shape that we have here is sued to show the infinite geometric progression.

This is the sequence of numbers that has all the other values in the sequence gotten by the multiplication of a certain factor

In this question or the shape we can see that the triangle is made up of smaller other triangles embedded in it.

The area of the traingle that is in the red color is seen to have been made up of 1/3 of the total triangles that we have in the shape. This can be seen to be similar as the triangles that are represented by the green and the blue color.

Putting a  lot of triangles inside one big triangle gives up a pictorial diagram on how to add infinite amount of things up.

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The factored form of the given trinomial is (x -7)(x +1)

From the question, we are to factor the given trinomials

The given trinomial is

x² + 6x - 7

The trinomial is a quadratic expression. The trinomial/ quadratic expression can be factored as a product of two binomial. When factored, the trinomial will take the form (x + a)(x + b)

Where are a and b are integers.

Factoring the trinomial

x² + 6x - 7

To factor the trinomial, we will find two numbers such that when added, we get the middle term; and when these numbers are multiplied we get the constant term.

The numbers that satisfy this condition are +1x and -7x

x² +x -7x - 7

x (x + 1) -7(x +1)

(x -7)(x +1)

Hence, the factored form of the given trinomial is (x -7)(x +1)

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Given the percentage taken off and the reduced price, the original price of the item is $142.

Given the data in the question;

The original price of the item is at 100%, if the 20% is taken off. The price is now at 80%.

Hence 80% of the original price will give the reduced price.

Let the original price be represented by x

80% × x = $113.60

We solve for x

80/100 × x = $113.60

80x/100 = $113.60

Cross multiply

80x = $11360

x = $11360/80

x = $142

Given the percentage taken off and the reduced price, the original price of the item is $142.

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Answer:

42

Step-by-step explanation:

let the number be x

4/7 of x

(4/7) × x

4x/7

As stated in the question:

x=4x/7+18

=x-4x/7=18

=(7x-4x)/7=18

=3x/7=18

3x= 18×17

3x= 126

x=126/3

x=42

Area of the shaded region is 1397.46 square feet.

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.

We are to find the area of the shaded region. For that, we will divide the figure into smaller shapes, find their areas separately and then add them up.

From the given figure, we can see that there are two semi circles or say one whole circle if we combine them at the ends while 2 rectangles at the top and bottom.

Radius of circle = [tex]\frac{20+7+7}{2}[/tex] = 17

Area of circle = [tex]\pi r^{2}[/tex]

                      = [tex]\pi( 17)^{2}[/tex]

                      = 907.92 square ft.

Area of rectangles =2×(l×b)

                              = 2×20×35

                              = 490 square ft

Then,

Area of the shaded region = 907.92 +490

                                            = 1397.46 square ft

Hence,Area of the shaded region is 1397.46 square ft.

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An equation which best represents the relationship between velocity and time is: B. v = 2.19x + 6.7.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

v = 2.0852x + 6.3978

Therefore, an equation which best represents the relationship between velocity and time is:

v = 2.19x + 6.7.

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