At 10:00 a.m. han and Tyler both start running toward each other from opposite ends of a 10 mile path along the river how han can run at a pace of 12 miles per minute Tyler can run at a pace 15 miles per minute how far does han run after a half an hour

The value of tan 30° after using trigonometric ratio  is  [tex]\frac{1}{\sqrt{3} }[/tex] .

What is trigonometric ratio?

 There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given

=> tan30°

Now ,Tan 30 degrees in radians is written as

=>tan (30° × π/180°)

=> [tex]\frac{1}{\sqrt{3} }[/tex]

Therefore the value of tan30° is  [tex]\frac{1}{\sqrt{3} }[/tex] .

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In the given equation we get the following values:

M = 2

C = 5

Given, we have the equation:

Y = 2x + 5

we are asked to determine the following values of m and c.

The given equation is in the form of slope intercept form.

slope intercept form is given as:

y = mx+c

hence :

M = 2 and

C = 5

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. This relationship will be the equation of a straight line:

hence we get the required values.

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Answer:x^4+6

Step-by-step explanation:

you must combined both x squared to get x^4 and then add the opposite of -4 Which is +4  and what you do to one side you must do to the other therefore you add the 2 to it as well. in conclusion you get x^4+6. hope this helps:)

According to the growth function, the population be in 2050 will be 10,635

Growth function:

The growth function refers the pattern of data that shows greater  increases with passing time, creating the curve of an exponential  function.

Given,

In 1965, the population of a certain town was 2010. In 1995, the population was 3620.

Here we need to find the population in 2050.

While we looking into the given problem, let us consider,

P refers the final population

A refers the the starting population, and

x refers the time passed

Now,  we need to determine the value of the growth factor n and it can be calculated using the information for the years 1965 and 2010.

Here we know that, in 1965, the population of a certain town was 2010. In 1995, the population was 3620.

And the value of x is 30

So, it can be written as,

=> 3620 = 2010eⁿˣ³⁰

=> 3620/2010  = e³⁰ⁿ

=> 362/201 = e³⁰ⁿ

Here by applying ln to both sides of the equation:

⇒ln(362/201) = ln(e³⁰ⁿ)

By, using the laws of logarithms:

=> 30n = ln(362) - ln(201)

=> n = [ln(362) - ln(201)] / 30

=> n = 0.0196

Here we have to use this information to determine P in 2050.

Here the value of A will still be 2010, but x will be 85 years.

Here we have to apply these values then we get,

=> P = 2010e⁰°⁰¹⁹⁶ˣ⁸⁵

=> P = 2010e¹°⁶⁶⁶

=> P = 2010 x 5.2909

=> P = 10635

Therefore, there are 10635 in 2050.

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The value of the unknown angle x would be 43 degrees.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given a right-angle triangle with a perpendicular side of 6 units and a hypotenuse of 10 units.

The unknown angle is x which needs to find.

Therefore, applying trigonometry;

Sin x = perpendicular/hypotenuse

Sin x = 6/10

Sin x = 3/5

Sin x = 0.6

x = Sin inverse (0.6)

x = 43 degrees.

Hence, the value of the unknown angle x would be 43 degrees.

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Check the picture below.

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{16}}\implies cos(\theta )=\cfrac{1}{4}\implies \theta =cos^{-1}\left( \cfrac{1}{4} \right)\implies \theta \approx 75.5^o[/tex]

Make sure your calculator is in Degree mode.

In given order puzzle Aya's bag is the heaviest bag .

What is order puzzle?

 A puzzle is a thing that is difficult to understand or explain. The term also refers to a game, toy, or problem designed to test ingenuity or knowledge. Math puzzles are problems that require mathematical logic and calculation. These types of puzzles carry recreational as well as educational value for the pupils.

Here the given statements ,

=> Alex bag > Hisham bag

And Hisham bag < Aya bag and Irene bag

Now ,

=> Aya bag > Alex bag and Irene bag

Then combine the given ,

=> Aya bag> Alex bag>Irene bag>Hisham bag.

Therefore Aya's bag is the heaviest bag.

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Answer:

y-2

Step-by-step explanation:

Answer:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

The points that are a distance of 5 units from P(-8, 4) will be all the points on the circumference of a circle with center (-8, 4) and radius 5.

Substitute the center and radius into the formula to create an equation of the circle:

[tex]\implies (x+8)^2+(y-4)^2=25[/tex]

The y-value of any point on the x-axis is zero.

Therefore, to find the points on the x-axis that are 5 units from point P, substitute y = 0 into the equation of the circle and solve for x:

[tex]\implies (x+8)^2+(0-4)^2=25[/tex]

[tex]\implies (x+8)^2+(-4)^2=25[/tex]

[tex]\implies (x+8)^2+16=25[/tex]

[tex]\implies (x+8)^2+16-16=25-16[/tex]

[tex]\implies (x+8)^2=9[/tex]

[tex]\implies \sqrt{(x+8)^2}=\sqrt{9}[/tex]

[tex]\implies x+8=\pm3[/tex]

[tex]\implies x+8-8=\pm3-8[/tex]

[tex]\implies x=-8\pm3[/tex]

[tex]\implies x=-11, x=-5[/tex]

Therefore:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

The value of sin(x/2)= √(1-√11/6)/2

The value of cos(x/2)=√(1+√11/6)/2

The value of tan(x/2) = 5/6/(√(1+√11/6)

In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45 and so on. If θ is an angle, then the half angle is represented by θ/2.

In trigonometry, sin( x/2)= √(1-cosx)/2

cos( x/2)= √(1+cosx)/2

tan( x/2)=sinx/1+cosx

if sin (x) = 5/6

this means that 5 is the opposite and 6 is the hypotenuse, then the adjascent is

a= √(6^2-5^2)

a= √36-25

a= √11

therefore if cos x= √11/6

sin(x/2)= √(1-√11/6)/2

cos(x/2)= √(1+√11/6)/2

tan(x/2)=5/6/(√(1+√11/6)

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Answer:

Step-by-step explanation:

a.

f(d)=11(1.01^d

d=6.97 days

b.

t

f(c) represents the size of algae after c days

c.

f(2)=11(1.01)^2

f(7)=11(1.01)^7

[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]

Answer:

  28 mph

Step-by-step explanation:

Given that a car moving 36 mph takes 7 hours for a trip, you want to know the speed if the trip takes 9 hours.

The speed and time vary inversely for the same distance. If the time goes up by a factor of 9/7, the speed will go down by the inverse factor: 7/9.

  7/9 × 36 mph = 28 mph

The speed of the car is 28 mph for the 9-hour trip.

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Answer:

162

Step-by-step explanation:

12²+6² ÷ 2

= 144 + 36 ÷ 2

= 144 + 18

= 162

Answer: The answer to this question would be: 5 days

In this question, there are two kinds of rent pricing and you are asked to find the number of days when both of them will charge the same price.

From the description, you can get an equation of each price which would look like this(x=number of day rent):

cost1= 110 + 46x

cost2= 70 + 54x

Then, the days when the price same would be:

cost1 = cost2

110 + 46x= 70+54x

110-70= 54x - 46x

40= 8x

x=5

Step-by-step explanation:

When talking about a number line, the farther right the digit moves, the large the number. The farther left it goes, the smaller the number.

For example, 81 would be to the right of 80. And 79 would be on the left. The larger the negative number, the smaller it is. So -70 is smaller than -20.

I hope this helps!

If a 40-foot rope is cut into 2 pieces.  the length of the longer rope piece x  is 23ft.

Seven less than 4 times = 4x-7

4x-7=5(40-x)

4x-7=200-5x

Collect like terms

9x=207

Divide both side by 9x

x = 207 /9

x=23 ft  (longer part of the rope)

Shorter part of the rope

40-x where x is 23

40 -23

= 17ft

Therefore the longer part is 23ft.

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Answer:

It is not a solution

Step-by-step explanation:

put in (-9,-5) in for x and y

9(-9)+4(-5)=10

-81-20=10

-101=10

This is false so (-9,-5) is not a solution to the equation 9x+4y=10

Answer:

Below

Step-by-step explanation:

4  3/10   * 3 =   43/10 * 3 = 129 / 10 =  12 9/10 miles

The correct statement will be  "Neither ordered pair is a solution".

What are ordered pairs?

Given equation is:  6x = 14

For ordered pair (-9, 3) ,  the values of x=-9 and y=3

Plugging these values into the given equation

6(-9) = 14

-54 = 14 (False)

Now for ordered pair (2, -4) ,  the values of x=2 and y=-4

Plugging these values into the given equation

6(2) = 14

12 = 14 (False)

The correct statement will be  "Neither ordered pair is a solution".

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The expressions which have only one constant are:

A. 18+5r³

B. 90(h-4)

Given: we have a set of equations.

an equation is  a combination of variables and constants.

In the given set of equations we have a single variable with a single constant.

those are:

→ 18+5r³

→  90(h-4)

In the other equations we don't have constants.

A constant is defined as an object whose value is fixed regardless of changes in its usage.

Even after the expression is changed, these values stay the same.

Natural numbers, whole numbers, real numbers, integers, and decimal numbers are examples of constants in mathematics.

A variable is a thing whose value changes depending on how it's used and isn't fixed.

Hence we get the required answer.

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The simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

What is a radical expression?

An nth root of a number x is a number r that, when multiplied by n, equals x, where n is a positive integer, also known as the degree of the root. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.

We have,

k² = 17

The variable in this non-linear equation needs to be separated. This is achieved by exponentiating both sides by the reciprocal of the exponent of the variable, which in our example is equal to 1/2.

[tex](k^{2} )^{\frac{1}{2} } = 17^{\frac{1}{2} }[/tex]

[tex](k^{2} )^{\frac{1}{2} } = -17^{\frac{1}{2} }[/tex]

[tex]k= 17^{\frac{1}{2} }[/tex]

[tex]k = -17^{\frac{1}{2} }[/tex]

Hence, the simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

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Answer:

6x + 3y

Step-by-step explanation:

=3x + (3)(x) + (3)(y)

=3x + 3x + 3y

=3x + 3x +3y

=(3x + 3x) + (3y)

=6x + 3y

Answer:

I do not see the choices.  There could be more than one right answer

6x + 3y

Step-by-step explanation:

3x + 3(x+y)

3x + 3x + 3y

6x + 3y

The general form of a linear equation is slope m and y-intercept c is given as y = mx + c thus the slope of the line y = -2x + 4 is -2 so option (C) is correct.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given line,

y = -2x + 4

The general form of a linear equation is the slope(m) and y-intercept (c) is given as

y = mx + c

Compare,

m = -2 and c = 4

Slope = -2 and y-intercept = 4

Hence "The slope of the line y = -2x + 4 is -2 and y-intercept is 4".

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The difference in the cost of all 30 pens between two shops is,

£1.05

Given, Eve is going to buy 30 pens from either shop A or shop B.

Shop A: pack of 10 pens for £2

Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.

So, the cost of 30 pens from the shop A is,

as, a pack of 10 pens is of £2

1 pen = 2/10

30 pens = £6

Now, the cost of 30 pens from the shop B is,

as, a pack of 5 for £1.10

1 pen = 1.10/5 = £0.22

also buy 1 and get 1 at half price.

So, 2 pens = 0.22 + 0.11 = £0.33

Therefore, 30 pens = £4.95

So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.

Hence, the difference in the cost of all 30 pens between two shops is,

£1.05

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Step-by-step explanation:

okok

The standard score (z-score) of the given sample is -20.

Given,

[tex]u[/tex] = 35

[tex]o[/tex] = 9

n = 60

x = 32

To calculate standard score (z-score) use formula,

[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]

Thus, the standard score(z-score) of given sample mean is -20.

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The values of the variables a, b and c are; a = 5/19, b = -160/19, c = 960/19

We are given the quadratic function formula as;

p(t) = at² + bt + c

Thus, the equation is now;

p(t) = at² + bt + 0

p(t) = at² + bt

From the graph, we see that when x = 8, y = 0. Thus;

p(8) = a(8²) + 8b + c = 0

64a + 8b + c = 0   ------(1)

From the graph, we know that the axis of symmetry is;

x = -b/2a

Thus;

16 = -b/2a

b = -32a  -----(2)

From the graph, we see that when x = 5, y = 15. Thus;

p(8) = a(5²) + 5b + c = 0

25a + 5b + c = 15   ------(3)

Put -32a for b in eq 1 and 3 to get;

64a + 8(-32a) + c = 0  

-192a + c = 0   ------(4)

25a + 5(-32a) + c = 15

-135a + c = 15   ------(5)

Subtract eq 4 from eq 5 to get;

192a - 135a = 15

57a = 15

a = 15/57

a = 5/19

Thus;

b = -32(5/19) = -160/19

-135(5/19) + c = 15

15 + (675/19) = c

c = 960/19

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