Peter and John are running around the town around the town in opposite directions. Peter can go around the town in 2.5 hours, and John can do the same in 15 hours. Assuming they start at the same time and same place, how many times will they pass each other going in opposite directions in a 24-hour period?

Using cosine law of triangle and using the provided value for the sides, the value of angle C is [tex]118^{o}[/tex] .

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

It is especially helpful for filling in the gaps in a triangle's information. The cosine rule, for instance, enables one to determine any of the angle measurements when all three sides of a triangle are known. Similar to this, using the cosine rule, one can determine the length of the third side given two sides and the angle between them are known.

a=80

b=51

c=113

[tex]cos(C) = \frac {a^{2}+b^{2} - c^{2}}{2ab}[/tex]

cos(c)= -0.4617

C= [tex]118^{o}[/tex]

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An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = ax

Where a>0 and a is not equal to 1.

x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

“x” is a variable

“a” is a constant, which is the base of the function.

An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.

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The transformations of f(x) are (b) horizontally shrunk by a factor of 1/4, vertically stretched by a factor of 5 and then reflected across the x-axis

From the question, we have the following function that can be used in our computation:

f(x) = x²

g(x) = -5(4x)²

Mathematically, these equations can be represented as

g(x) = -5f(4x)

The above equations implies that, we have the transformation to be:

Hence, the transformed function is (b(

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Answer:

Zachary pays $150 per month for his computer

Step-by-step explanation:

after 2 months:

2x + 1100y = 1400..... equation 1

after 4 months:

4x + 800y = 1400...... equation 2

we can either multiply equation 1 by 2 or we can divide equation 2 by 2, the purpose is simply to get the x values equal so it can be eliminated from the equation.

dividing equation 2 by 2:

2x + 400y = 700 ...... equation 3

Now equation 1 minus equation 3:

0x + 700y = 700

700y = 700

y = 700/700

y = 1

substituting y=1 into equation 3

2x + 400(1) = 700

2x = 700 - 400

2x = 300

x = 300/2

x= 150

Therefore it is concluded that Zachary has a payment plan where he pays $150 each month for the computer

Answer: It is perpendicular because it makes a 90-degree angles

Step-by-step explanation: A perpendicular is when it makes a 90-degree angle or has the same length!

The perpendicular equation is y = -1/3x + 10 Option A

You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 3 we flip it and make it a negative and the new slope is -1/3.

Now we can use that and the point to get the y intercept using slope intercept form.

y = mx + c

m = gradient of the line

c = y -intercept

8 = (-1/3)(6) + c

8 = -2 + c

10 = c

And now we can use our new slope and new intercept to model the equation. y = -1/3x + 10

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Answer:

(0,2)

Step-by-step explanation:

im not too educated with this topic but i believe we multiple x and y by 1/2

0x1/2=0

4x1/2=2

(0,2) is the answer

:)

The mean and standard deviation of T, the mean and standard deviation of R, and the mean and standard deviation of Q.

a. The mean and standard deviation of 7-G is

7-1=6 and 0.12, respectively.

b. Let X be the weight of a single grapefruit, so the mean and standard deviation of X are 1 and 0.12, respectively.

The mean and standard deviation of R=G+G+G are

3*1=3

and

√(3)*0.12=0.2, respectively.

c. The mean and standard deviation of

Q=T-R are 7-3=4

√0.2((0.12^2)+(0.2^2))=0.2236 respectively.

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The measure of indicated angle in the given triangle is 71.035°.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given right angled triangle, hypotenuse side is 74 units and the two legs of triangle are 70 units and 24 units.

Let the unknown angle be x.

We know that, tanθ =Perpendicular/Base

Now, tan x= 70/24

tan x= 2.91

x =71.035°

So, one of the angle in the triangle is 71.035°.

Therefore, the measure of unknown angle is 71.035° in the given triangle.

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The resulting triangle is 9/5 the original triangle.

The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).

Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 9/5,

Then changed triangle is  A'B'C'

So, relation between them is A'B'C' = 9/5(ABC)

Thus, the resulting triangle is 9/5 multiple of triangle ABC.

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Answer:

56x-32

Step-by-step explanation:

7x-4 Times 8x+8

7xtimes8x

56x-4times8

56x-32

Answer:

X = 33.19

Step-by-step explanation:

You're welcome.

Answer:

36 ounces or if over 150 lbs drink more water than 36 ounces

Step-by-step explanation:

For every pound of sweat you lose you need to drink 16 ounces of water!

Answer:

C)117

Step-by-step explanation:

50%=1/2

If you want to figure out how much is left of a half all you do is have to divide the total number of whatever it is, in this case, its roses, by 2.

So now that we know that, let's get started.

234/2=117

Which we know is correct because it's one of your answer choices.

So 117 roses are not red. The other half was.

I hope this helps!!!

The inequality does not belong with the other three is  - 1 ≤ x/1.25.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given,

1.  4x ≥ 12 ⇒ x ≥ 3.

2.  - 1 ≤ x/5 ⇒ - 5 ≤ x.

3.  12 > x/1.25 ⇒ x < 15.

4.  2.5x > - 6.4 ⇒ x > - 2.56.

x ≥ 3 and  x < 15 is,    3 ≤  x < 15.

- 5 ≤ x and x > - 2.56 here one common region is x > - 2.56 so - 5 ≤ x does not fit.

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Answer:

time is gold ............

Answer:

q1: it arrived at 11:45

q2: 8 hours and 45 minutes

q3: a: 6:59 AM b: 498 minutes

Step-by-step explanation:

q1: 10:30 + 1:15 = 11:45

q2: 0:30 +7:30 +0:45 +8 hours and 45 minutes

q3: a(8:18 + 10:41 PM = 6:59 AM) b(8x60= 480 +18= 489)

Answer:

D=Trapeador

A=Cubeta

C=Escoba

B=Recogedor

Step-by-step explanation:

One knief costs 5.52 dollars

Let the cost of knief be x dollars and the cost of spoon be y dollars.

A knife costs 3 times the cost of a spoon.

So, we get an equation,

x = 3y                       ..............(1)

9 spoons and 12 knives cost $82.80

So, we get an equation,

12x + 9y = 82.80        .........(2)

Substitute above value of x in equation (2),

12(3y) + 9y = 82.80

45y = 82.8

y = 1.84

Subatitute above value of y in equation (1),

x = 5.52

Therefore, the cost of knief is 5.52 dollars

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Answer:

  1800

Step-by-step explanation:

You want the least common multiple (LCM) of 72 and 150 given their prime factorizations:

The LCM is found as follows:

  LCM(72, 150) = 2³ × 3² × 5² = 1800

The value of the 35x + 10y is 330.

What is the linear equation?

A linear equation is an equation of a straight line, written in the form y = mx + b. In this equation, m is the slope of the line and b is the y-intercept. Linear equations are used to describe relationships between variables, and they can also be used to solve problems with multiple unknowns. For example, if you know the slope of a line and the y-intercept, you can use a linear equation to calculate the x-intercept. Linear equations can also be used to model real-world situations, such as calculating the cost of a product or the amount of money saved over a period of time.

We have given:

the value of 35x + 10y, When x=8 and y=5.

Using substitution, substitute the given values of x and y.

35x + 10y

35(8) + 10(5)

280 + 50 = 330

Hence, the value of the 35x + 10y is 330.

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Complete Question:

Find the value of 35x+10y, When x=8 and y=5

Mia is incorrect, as they both ran the same distance, which is the hypotenuse of a right triangle of dimensions 10m and 16m.

The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the lengths of the sides squared.

The sides are between the angle of 90º, while the hypotenuse is the segment that connects the sides.

From the image given at the end of the answer, the distances ran from each of them are equal, which is the hypotenuse of a right triangle of dimensions 10 m and 16 m, thus the distance is obtained as follows:

d² = 10² + 16²

d = square root of (10² + 16²)

d = 18.87m.

The problem is given by the image shown at the end of the answer.

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Mr. Ramli's investment in the small entrepreneurship will be doubled in 8 year.

For the stated equation-

rate of increase is given as-

dy/dx = 2(x + 121) < - rate of the change

dy = 2(x + 121)dx

Integrating;

∫dy = ∫2(x + 121)dx

y = x² + 242x + C

At x = 0, y(0) = 0 Thus,

(0)² + 242(0) + C = 2000

C = 2000

Now, y = x² + 242x + 2000

Calculate 't' to get the y(t) = 40,000 (double the amount)

4000 = x² + 242x + 2000

x² + 242x - 2000 = 0

Find the factor;

x = 8 and x = -250

As, x is time in year. So, x = 8 years.

Therefore, it takes eight years for his investment capital to double from what he initially put up.

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Answer: [tex]x^{2} -5x+3\\[/tex]

Step-by-step explanation:

Answer:

see attached

Step-by-step explanation:

Step-by-step explanation:

[tex] {x}^{2} - 12x + 36 = - 36[/tex]

[tex](x - 6) {}^{2} = - 36[/tex]

[tex](x - 6) {}^{} = 6i[/tex]

[tex]x = 6 + 6i[/tex]

[tex]x = 6 - 6i[/tex]

Fraction form  12.5%  question did Paul get wrong .

What do math fractions mean?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided.

                                           Both are integers in a simple fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator.

Fraction of incorrect question = 1/8

Present of incorrect question

Computation:

Present of incorrect question = (Fraction of incorrect question)(100)

Present of incorrect question = (1/8)(100)

Present of incorrect question = 12.5%

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The solution of the given system of equations is (-1, 2).

What is system of equations?

A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.

Consider, the given system of equations.

x^2 - x + 3y - 8 = 0           ..(1)

x - y + 3 = 0                       ..(2)

From equation (2),

x = y - 3            ..(3)

Plug the value of x in equation (1).

⇒ (y - 3)^2 - (y - 3)  + 3y - 8 = 0

y^2 - 6y + 9 - y + 3 +3y - 8 = 0

y^2 - 4y + 4 = 0

y^2 - 2y - 2y + 4 = 0

y(y - 2) - 2(y - 2) = 0

(y - 2)(y - 2) = 0

(y - 2)^2 = 0

y = 2

Now plug y = 2 in equation (3)

x = 2 - 3

x = -1

hence, the solution of the given system of equations is (-1, 2).

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Answer:  55.7 inches and 60.3 inches

Step-by-step explanation:

I saw this question before in math class, so I know the answer! Hope you find this helpful!

The lower limit of the confidence interval is 51%, which is above 55%, so the Republican should expect to win.

What does confidence interval mean?

Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

                       If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. In statistics, confidence is another word for probability.

A confidence interval of proportions has two bounds, a lower bound and an upper bound.

These bounds depend on the sample proportion and the margin of error.

The lower bound is the sample proportion subtracted by the margin of error.

The upper bound is the margin of error added to the sample proportion.

In this problem, we have that:

Sample proportion 53%

Margin of error 2%

53 - 2 = 51%

53 + 2 = 55%

Hence, the lower limit of the confidence interval is 51%, which is above 55%, so the Republican should expect to win.

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