Two cars leave towns 850 kilometers apart at the same time and travel toward each other. One car's rate is 16 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.

Answer:

(2x + 3)(x - 5)

Step-by-step explanation:

2x² - 7x - 15

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = - 7

the factors are - 10 and + 3

use these factors to split the x- term

2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )

= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term

= (2x + 3)(x - 5) ← in factored form

Blank 1 is 3

Blank 2 is 5

The area of the required shaded portion is 123 ft²

Given is figure having some shaded portion we need to find the area of the same,

So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,

So, to find the same, we will calculate the area of the triangles and add them,

Area of a triangle = 1/2 x base x height

Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14

= 122.5 ft²

≈ 123 ft²

Hence the area of the required shaded portion is 123 ft²

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area of equilateral triangle =

[tex]( \sqrt{3 } \div 4) \times a {}^{2} [/tex]

(C) area = 84.9 in²

Answer:

  (a)  0.75

Step-by-step explanation:

You want the 10th term of the geometric sequence with a1 = 384 and a7 = 6.

The equation for the n-th term can be written ...

  an = a1·b^(n-1)

Using a1 = 384, we can find b from ...

  a7 = 6 = 384·b^(7-1)

  (6/384)^(1/6) = b

Then the 10th term is ...

  a10 = 384·(6/384)^((10-1)/6) = 0.75

The 10th term of the sequence is 0.75.

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The center of the circumscribed circle is (1, 5).

We calculate the midpoint and slope of the line segment AB:

Midpoint of AB = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Midpoint of AB = ((2 + 0) / 2, (8 + 8) / 2)

Midpoint of AB = (1, 8)

Slope of AB = (y₂ - y₁) / (x₂ - x₁)

= (8 - 8) / (0 - 2)

Slope= 0

We can notice that the equation of the perpendicular bisector of AB is x = 1.

We also find midpoint and slope of the line segment  BC

Midpoint of BC = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

= ((0 + 2) / 2, (8 + 2) / 2)

= (1, 5)

Slope of BC = (y₂ - y₁) / (x₂ - x₁)

= (2 - 8) / (2 - 0)

= -3

y - 5 = -3(x - 1)

y - 5 = -3x + 3

3x + y = 8

we have the equations of two perpendicular bisectors which are

x = 1 and 3x + y = 8.

We Substitute x = 1 into 3x + y = 8:

3(1) + y = 8

3 + y = 8

y = 5

In conclusion, center of the circumscribed circle is (1, 5).

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The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

Sin 40° = x/16

0.6428 = x/16

x = 0.643 × 16

x = 10.2848

x = 10.28

So, the value of x is 10.28 (C)

That's it :)

The solution to the equation 1/3a = -15 is a = -45

from the question, we have the following parameters that can be used in our computation:

1/3a = -15

Multiply 3 to both sides of the equation

so, we have the following representation

3 * 1/3a = -15 * 3

When the products are evalated, we have

a = -45

Hence, the solution to the equation is a = -45

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The statement "If dom(f) = Χ, then f is an n-ary functionon X" means that if the domain   of the function f is equal to the set X, then f is considered an n-ary function on X.

In other words, for each element in X,   the function f can take n arguments or inputs to produce aunique output. The term "n-ary" indicates the number of arguments that the function can accept.

A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is anothername for a statement. The main point is that there should be no uncertainty.

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Answer:

The statement "If dom(f) = X, then f is an n-ary function on X" means that if the domain of a function f is equal to the set X, then f is a function that takes n arguments or inputs from the set X, where the value of n depends on the specific function.

Step-by-step explanation:

The statement "If dom(f) = X", then f is an n-ary function on X" means that if the domain of the function f is equal to the set X, then f is an n-ary function on X.

Here's a breakdown of the terms used in the statement:

- dom(f): The domain of a function f refers to the set of all possible input values for the function. It represents the set of values for which the function is defined.

- X: In this context, X represents a set. It could be any set, and it serves as the domain for the function f.

- n-ary function: An n-ary function is a function that takes n arguments or inputs. The value of n represents the number of inputs the function expects.

Therefore, the statement is saying that if the domain of the function f is equal to the set X, then f is an n-ary function on X. It implies that the function f takes n inputs from the set X, where n is determined by the specific function.

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The value of x in arithmetic progression is 5/3 and the largest angle is 30.

The given sequence is: (2x-7), (x-1), 3x, x, (x+2), 30, 10.

In an arithmetic progression, the common difference (d) between consecutive terms remains constant.

The common difference between the terms = (x - 1) - (2x - 7) = x - 1 - 2x + 7 = 6 - x

6 - x = 3x - (x - 1)

6 - x = 3x - x + 1

6 - x = 2x + 1

-x - 2x = 1 - 6

-3x = -5

x = -5 / -3

x = 5/3

Therefore, the value of x is 5/3.

2x-7 = 2 ×5/3 -7 = -3.66

x-1 = 5/3-7 = -5.33

3x = 3 × 5/3 = 5

x + 2 = 5/3+2 =3.66

Thus, the largest angle is 30.

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Your question is incomplete, most probably the full answer is:

If (2x-7), (x-1), 3x, x, (x+2), 30 and 10 are in AP, then

1. Find the value of x

2. Find the value of the largest angle

The population reached in the year 2079 is 1,65,400 and the total population in the year 2081 would be 1,80,623.

To find the population reached in the year 2079, we need to consider the initial population and the growth rate, as well as the number of people who migrated.

The initial population in 2078 was 1,20,000. The population growth rate is 4.5%, which means the population will increase by 4.5% each year.

To calculate the population in 2079, we first need to calculate the increase in population due to the growth rate:

Population increase due to growth rate = 1,20,000 * (4.5/100) = 5,400

Then we add the number of people who migrated:

Total population in 2079 = Initial population + Population increase due to growth rate + Number of migrants

= 1,20,000 + 5,400 + 20,000

= 1,45,400 + 20,000

= 1,65,400

To calculate the total population in the year 2081, we need to consider the growth rate and the population in 2080.

The population in 2080 would be the population in 2079 plus the population increase due to the growth rate:

Population increase due to growth rate in 2080 = 1,65,400 * (4.5/100) = 7,444

Total population in 2080 = 1,65,400 + 7,444

= 1,72,844

To calculate the total population in 2081, we need to consider the growth rate and the population in 2080:

Population increase due to growth rate in 2081 = 1,72,844 * (4.5/100) = 7,779

Total population in 2081 = Population in 2080 + Population increase due to growth rate in 2081

= 1,72,844 + 7,779

= 1,80,623

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Answer:

13cm

Step-by-step explanation:

The area of a trapezoid is given by the formula:

Area = ½*(b1+b2)*h

where:

In this problem, we are given that b1 = 6 cm, b2 = 15 cm, and Area = 136.5 square centimeters.

Plugging these values into the formula, we get:

136.5 = ½*(6 + 15)*h

Solving for h, we get:

136.5=10.5h

h = 136.5/10.5=13centimeters

Therefore, the height of the trapezoid is 13 centimeters.

Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

Becky contributed $50 towards the building for the aged.

Let's calculate the amounts contributed by each student:

Azar contributed 50% of the total amount:

Amount contributed by Azar = 50% of $200

= (50/100) × $200

= $100

Sunil contributed 25% of the total amount:

Amount contributed by Sunil = 25% of $200

= (25/100) × $200

= $50

Now, we can calculate the amount contributed by Becky:

Total contribution by Azar and Sunil = $100 + $50 = $150

The remaining amount contributed by Becky can be found by subtracting the total contribution by Azar and Sunil from the total amount:

Amount contributed by Becky = Total amount - Total contribution by Azar and Sunil

= $200 - $150

= $50

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In order to expand the properties of logarithms log981x:

log981x = log98 + log1x

One must know that loga + logb = log(ab), and loga + logb = log(ab) may also be represented as loga(b) or logab.

Using this property, we can simplify the expression further:

log981x = log98 + log1x = log9 + log8 + log1 + logx

We know that log9 = 2 and log1 = 0, so we can simplify even further:

log981x = log9 + log8 + log1 + logx = 2 + log8 + 0 + logx = 2 + log8x.

Therefore, the expanded value would be log981x to 2 + log8x.

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The summation of 5 to power of n (where n starts from 1) is determined as 625.

The sum of the expression given is calculated by using the defined expression as sated in the question to perform the summation.

The given summation expression include;

∑5ⁿ

where;

So we are going to sum the number 5ⁿ 4 times.

The expression becomes;

5ⁿ x 5ⁿ x 5ⁿ x 5ⁿ = 5⁴ⁿ

where;

n = 1

The summation becomes;

5⁴ⁿ = 5⁴ = 625

Thus, the summation of 5 to power of n (where n starts from 1) is determined as 625.

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Step-by-step explanation:

1 qt = 2 pts     multiply both sides by two

2 qt = 4 pints

The angle ABC in the circle is 70 degrees.

The intercepted arc is the arc that is inside the inscribed angle and whose

endpoints are on the angle. The arc angle is half the the inscribed angle.

The intercepted arc that is formed is equal to the inscribed angle,

multiplied by two (intercepted arc measure = inscribed angle × 2).

Therefore, let's find the arc angle ABC as follows:

∠ ABC = 1  /2 (360 - 120 - 100)

∠ ABC = 1  /2 (360 - 220)

∠ ABC = 1  /2 (140)

Therefore,

∠ ABC = 70 degrees

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In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.

Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.

Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.

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The full question is:

In the year 2000 the world population was

The correct statement regarding the association in the scatter plot is given as follows:

Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.

There can either be a positive association between variables or a negative association between variables, as follows:

In this problem, we have a decreasing scatter plot, hence there is a negative association between the variables.

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The value of x that makes the rational expression undefined is x = -3.

The rational expression is undefined when the denominator is equal to zero, because division by zero is undefined.

In the given rational expression (x - 3) / (3 + x), we need to find the value of x that makes the denominator (3 + x) equal to zero.

To find this value, we set the denominator equal to zero and solve for x:

3 + x = 0

Subtracting 3 from both sides:

x = -3

Therefore, the value of x that makes the rational expression undefined is x = -3.

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Answer:

There are 20 blue fish in the aquarium.

Step-by-step explanation:

If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.

Hello!

[tex]7p-13p+4-5p\\\\= 7p-13p-5p+4\\\\= -6p-5p+4\\\\\Large\boxed{= -11p + 4}[/tex]

The nearest Whole number, the missing dimension (height) of the cylinder is approximately 39 inches.

The missing dimension of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

Given that the volume is 10,000π in³ and the diameter of the base is 32 inches, we can determine the radius (r) of the cylinder.

The diameter is twice the radius, so the radius is half of the diameter:

r = 32 inches / 2 = 16 inches

Substituting the known values into the volume formula, we have:

10,000π in³ = π * (16 in)^2 * h

Cancelling out the common factor of π, we get:

10,000 = 16^2 * h

Simplifying further:

10,000 = 256 * h

To isolate h, we divide both sides of the equation by 256:

h = 10,000 / 256

Calculating the value of h:

h ≈ 39.06

Rounded to the nearest whole number, the missing dimension (height) of the cylinder is approximately 39 inches.

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Answer:

Refer to the step-by-step, follow along carefully.

Step-by-step explanation:

Verify the given identity.

[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)} =\csc(x)(1+\cos^2(x))[/tex]

Pick the more complicated side to manipulate, so the L.H.S.

(1) - Combine the fractions with a common denominator

[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)}\\\\\Longrightarrow \frac{\sin(x)(1+\cos(x))}{(1-\cos(x))(1+\cos(x))} -\frac{\sin(x)\cos(x)(1-\cos(x))}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos(x)-\sin(x)\cos(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}} \\\\[/tex]

(2) - Simplify the denominator

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}\\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos(x)+\cos(x)-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}}[/tex]

(3) - Apply the following Pythagorean identity to the denominator

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\cos^2(\theta)=\sin^2(\theta)\end{array}\right}[/tex]

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}}[/tex]

(4) - Simplify the fraction and split it up

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}\\\\\Longrightarrow \frac{1+\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \boxed{\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}}[/tex]

(5) - Apply the following reciprocal identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Reciprocal Identitiy:}}\\\\\csc(\theta)=\frac{1}{\sin(\theta)} \end{array}\right}[/tex]

[tex]\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \csc(x)+\frac{1}{\sin(x)}\cos^2(x) \\\\\Longrightarrow \csc(x)+\csc(x)\cos^2(x) \\\\\therefore \boxed{\boxed{\csc(x)(1+\cos^2(x))}}[/tex]

Thus, the identity is verified.

Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown below.

We have to given that,

Expression to verify is,

⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)

Now, We can simplify as,

⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)

⇒ sin x [ 1 / (1 - cos x) - cos x / (1 + cos x)]

⇒ sin x [1 + cos x - cos x (1 - cos x )] / (1 - cos²x)

⇒ sin x [1 + cos x - cos x + cos²x] / sin²x

⇒ (1 + cos²x) / sin x

⇒ cosec x (1 + cos²x)

Thus, Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown above.

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Step-by-step explanation:

To solve this problem, we need to calculate the probability of the first student being a boy and the second student being a girl.

There are a total of 13 boys and 15 girls in the class, making a total of 28 students.

The probability of the first student being a boy is given by:

P(boy) = Number of boys / Total number of students = 13 / 28

After the first student is selected, there are now 27 students remaining (since one student has already been selected). Out of these 27 students, there are still 15 girls remaining.

The probability of the second student being a girl, given that the first student was a boy, is given by:

P(girl|boy) = Number of girls / Remaining number of students = 15 / 27

To find the probability of both events occurring (the first student being a boy and the second student being a girl), we multiply the individual probabilities:

P(boy and girl) = P(boy) * P(girl|boy) = (13/28) * (15/27)

Calculating this expression:

P(boy and girl) ≈ 0.2041

Therefore, the probability that the first student is a boy and the second student is a girl is approximately 0.2041 or 20.41%.