The two bases of a trapezoid measure 14 inches and 10 inches respectively. The trapezoid's height is 8 inches. What is the area of the trapezoid?

Answer:

Step-by-step explanation:

1033

Answer:

999 + 34 is 1033

Step-by-step explanation:

9 +4 = 13

90+ 30 = 120

900 + 120 + 13 = 1033

Answer: (1, 3)

Step-by-step explanation:

There are two ways to solve this problem, 1 without the pythagorean theorem, and 1 with it.  For the sake of simplicity, I will solve it without the pythagorean theorem.

As is visually evident from the graph, the line segment spans 6 units horizontally, and 3 units vertically.  Because the ratio between AP and PB is 1:2, simply divide both the domain and range by 3, to get 2 horizontally, and 1 vertically.  

Then, simply go to point A and respectively add and subtract the horizontal and vertical values to get point A(-1, 4) --> P(1,3)

Hope it helps, and let me know if you want me to solve it an alternate way or go more in depth as to the way it is know.

Answer:

Step-by-step explanation:

Coordinates of A and B:

The partition ratio:

Coordinates of P are:

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

Total Distance : 1*60 +60=120

Total time taken = 1+ 60/30= 1+2=3

Hence average speed for the trip = 120/3= 40 kmph

Hence Answer is 40

Step-by-step explanation:

The average speed is 40 km/h.

The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:

Average Speed = Total distance covered ÷ Total time taken

Example:

sing the average speed formula, find the average speed of Sam, who covers the first 200 kilometers in 4 hours and the next 160 kilometers in another 4 hours.

Solution:

To find the average speed we need the total distance and the total time.

Total distance covered by Sam = 200Km + 160 km = 360 km

Total time taken by Sam = 4 hour + 4 hour = 8 hour

Average Speed = Total distance covered ÷ Total time taken

Average Speed = 360 ÷ 8 = 45km/hr

Given:

d1= 60 km

d2= 30

d3 = 60

Total Distance : 1*60 +60=120

Total time taken = 1+ 60/30= 1+2=3

Now,

average speed = total distance/ total time taken

= 120/3

= 40 kmph

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By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.

Notice that the ladder makes a right triangle with the wall.

Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft

If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.

Then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse)

Then:

sin(x) = (13.5ft)/(15ft)

If we use the inverse sine function on both sides, we get:

Asin(sin(x)) = Asin( 13.5ft/15ft)

x = Asin(13.5/15) = 64.2°

So the angle is less than 75°, which means that in fact, the ladder is safe.

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Answer:

15.01

Step-by-step explanation:

10.95+4.06

Answer:

15.01

Hope that helps :-)

Answer:

United States federal law signed into law by President Bill Clinton on May 20, 1993, and which came into effect on January 1, 1995.

Step-by-step explanation:

Hope It Helps :)

g(x) = 2x + 1

h(x) = x + 2x

(g + h)(x) = (2x + 1) + (x + 2x)

(g + h) (x) = 2x + 1 + x + 2x

(g + h) (x) = 2x + 2x + x + 1

(g + h)(x) = 5x + 1 Result

We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.

To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.

Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:

We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.

To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.

98 ÷ 10 = 9.8

Since 9.8 is still greater than 1, we need to continue dividing by 10.

9.8 ÷ 10 = 0.98

Now, we have reached a value less than 1, so we stop dividing.

From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:

98 =\(10^1\) + 2

Therefore, we can write 98 in exponential form as:

98 = \(10^3\)

In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.

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The percentage of students attend either public school or college will be 90%.

Let the students in public school be 40%

Let the students in college be 50%

Let those who stay at home be 10%

Therefore, the percentage of students attend either public school or college will be:

= 40% + 50%

= 90%

Therefore, the percentage of students attend either public school or college will be 90%.

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In a school, the following information are given:

Public school students = 40

Number of those in college = 50

Number of those at home = 10

What percentage of students attend either public school or college?

a. 90%

b. 50%

c. 40%

d. 10%

Answer:

Step-by-step explanation:

The larger number is four I think

Answer:

5

Step-by-step explanation:

14-2 = 12

12÷4=3 (smaller number)

3+2=5

Answer:

5:8

Step-by-step explanation:

The solution of the system of equations is the point of intersection (4, 2), as shown in the graph below.

Caroline bought 4 soda bottles.

Caroline bought 2 juice bottles.

In order to determine the solution to this problem, use the information given to create two equations.

Number of soda bottle = x.

Number of juice bottle = y.

First Equation for the total number of bottle that Kelvin bought

x + y = 6 --> eqn. 1

Second Equation 2 for the total sugar in the soda bottles and total sugar in juice bottles that equals 150 grams of sugar.

30x + 15y = 150

Simplify by dividing by 5

6x + 3y = 30 --> eqn. 2

Rewrite eqn. 1:

y = 6 - x

Solve simultaneously for the variables of x and y, by substituting the value of y into equation 2:

6x + 3(6 - x) = 30

6x + 18 - 3x = 30

3x + 18 = 30

3x = 30 - 18

3x = 12

3x/3 = 12/3

x = 4

Caroline bought 4 soda bottles.

Substitute x = 4 into equation 1 to find the value of y:

x + y = 6

4 + y = 6

y = 6 - 4

y = 2

Caroline bought 2 juice bottles.

The graph below shows the point of intersection, (4, 2), which is the solution.

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y-intercept is the point in the y-axis that the graph intersects.

From the figure, the graph intersects at point (0, 3)

The y- intercept is (0, 3)

x-intercept is the point in the x-axis that the graph intersects.

Since the graph does not intersects the x-axis, the x-intercept does not exist

Vertex is a point on the graph that is a maximum or a minimum.

The vertex of the graph which is the lowest point as shown in the figure is at point (1, 2)

And this is a minima, since it is the lowest point.

Domain is the set of x-values that exist in the graph, the graph is going infinitely to the left and to the right, therefore the domain is (-∞, ∞)

Range is the set of y-values that exist in the graph, the y values starts from the vertex which is the lowest point at (1, 2) going upward.

So the range is all real numbers greater than or equal to 2. [2, ∞)

End behavior is the behavior of the function at large positive and negative values of x.

when x goes positive infinity, f(x) goes to positive infinity

As x ⇒ ∞, f(x) ⇒ ∞

when x goes negative infinity, f(x) goes to negative infinity

As x ⇒ -∞, f(x) ⇒ -∞

Decreasing interval occurs when the graph is going down, and increasing interval occurs when the graph is going up.

Decreasing interval will be (-∞, 1]

Increasing interval will be [1, ∞)

The answer is 0.471 radians.

FORMULA:

Just do 27° × π/180 = 0.4712rad but then cut off the two.

The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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Answer:

Multiples that are shared by two or more numbers are common multiples.

Step-by-step explanation:

A common multiple is a whole number that is a shared multiple of each set of numbers. The multiples that are common to two or more numbers are referred to as the common multiples of those numbers.

I hope this helps! ^-^

Answer:

3sqrt(5)

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the diagonal of the rectangular box.

The Pythagorean theorem states that for a right triangle with legs of length a and b and hypotenuse of length c, we have:

c^2 = a^2 + b^2

In this case, the legs of the right triangle are 3 inches and 6 inches, and the hypotenuse is the length of the straw. So we have:

straw length^2 = 3^2 + 6^2 straw length^2 = 9 + 36 straw length^2 = 45

Taking the square root of both sides, we get:

straw length = sqrt(45) = sqrt(9*5) = sqrt(9)*sqrt(5) = 3sqrt(5)

Therefore, the length of the straw is 3sqrt(5) inches.

Answer:

D

Step-by-step explanation:

In scientific notation, the number that is being multiplied by the power of ten must be greater than or equal to 1 and less than 10. This eliminates options B, C, and E. The rest of the options are all 5.79 times something. To find that something, we can do 5,790,000 / 5.79 = 1000000 = 10⁶. This means that the answer is D.

Answer:

y=0 and x=6 according to questions

Answer:

Step-by-step explanation:

Domain is values on x-axis

y= 6-3=3 (when x=3)

y= 6-6=0 (when x=6)

y= 6-0=6 (when x=0)

y= 6-(-5)= 6 + 5 = 11 (when x= -5)

To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:

Refer to the attachment below.

There are three pairs of faces on a rectangular prism:

8 cm × 3 cm = 24 cm²

Since there are two of these faces, the total area is:

2 × 24 = 48 cm²

8 cm × 6 cm = 48 cm²

Since there are two of these faces, the total area is:

2 × 48 = 96 cm²

3 cm × 6 cm = 18 cm²

Since there are two of these faces, the total area is:

2 × 18 = 36 cm²

Now, add up the areas of all six faces:

Surface Area = 48 + 96 + 36 = 180 cm²

So, the surface area of the rectangular prism is 180 cm².

________________________________________________________

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The variable is the letter like x or y. The coefficient is the number next to the variable like the 2 in 2x or if its just x it would be 1. The constant is the number by itself usually at the end.

Example 2x+5

Variable is x constant is 5 and coefficient is 2. Sorry i didn't answer the actual question and just told you how to find it but those expressions don't have any of these things.

Answer:

-1 and 1/3

Step-by-step explanation:

I replaced each variable with 1. Other than that I just guessed and got it right lol

We are given the following expression

We are asked to provide justification on how it is being simplified.

Step 1: Justification

Since the base is the same (x) the coefficients are multiplied together.

Step 2: Justification

Combining the like terms together

Step 3: Justification

Apply the exponent's rule (since the base is the same their powers can be added)

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, then none of the statements is false.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

Since a/b = c/d, are proportional then can cross-multiply to get ad = bc.

Now, evaluate each statement -

A. b/a = d/c

Cross-multiplying, it is obtained that bc = ad, which is true based on the original proportion.

Therefore, this statement is true.

B. a/c = b/d

Cross-multiplying, it is obtained ad = bc, which is also true based on the original proportion.

Therefore, this statement is true.

C. b/a = c/d

This is equivalent to the original proportion, so it is true.

D. (a + b)/b = (c + d)/d

Simplify the equation -

d(a + b) = b(c + d)

da + db = bc + bd

da = bc

Cross-multiplying, it is obtained that da = bc, which is true based on the original proportion.

Therefore, this statement is true.

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The monthly Payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.

The monthly payment of a 2-year loan of $1590 with 9% interest which needs to be repaid in 254 equal monthly installments, we need to use the loan repayment formula. The formula is given as:

Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Here,

Loan Amount = $1590

Interest Rate = 9% per annum

Time = 2 years = 24 months

number of Months = 254 (as there are 254 monthly installments)

First, we need to calculate the Monthly Interest Rate using the following formula:

Monthly Interest Rate = Annual Interest Rate / 12

The Annual Interest Rate is 9%,

so the Monthly Interest Rate is:  Monthly Interest Rate = 9 / 12 = 0.75%Putting the given values into the loan repayment formula,

we get: Monthly Payment = (1590 x 0.0075) / (1 - (1 + 0.0075)^(-254))= 11.92 (approx)

Therefore, the monthly payment of a 2-year loan of $1590 with 9% interest that needs to be repaid in 254 equal monthly installments is approximately $11.92.

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Answer:

\(\displaystyle \lim_{x \to \infty} \frac{x^2}{1 + 3x + 5x^2} = \frac{1}{5}\)

General Formulas and Concepts:

Calculus

Step-by-step explanation:

Step 1: Define

\(\displaystyle \lim_{x \to \infty} \frac{x^2}{1 + 3x + 5x^2}\)

Step 2: Determine Rule

If the highest power of x in a rational expression is the same both numerator and denominator, then the limit as x approached ∞ would be the highest term coefficient in the numerator divided by the highest term coefficient in the denominator.

Step 3: Identify

Numerator highest power: x²

Denominator highest power: 5x²

Step 4: Evaluate

Apply rule.

\(\displaystyle \lim_{x \to \infty} \frac{x^2}{1 + 3x + 5x^2} = \frac{1}{5}\)

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Limits

Book: College Calculus 10e

Using Quadratic formula, x = 0.18 ft.

Keep in mind that since the quadratic is downward facing, the vertex will be the highest point, the y-intercept will represent the starting height, and the positive x-intercept will represent the distance to the child.

(a) Locate the y-intercept by setting x = 0 and solving for y.

y = -116(0)2+4(0)+3 = 3 ft

(b) As the maximum height is being requested, determine the vertex's y-value.

Vertex x-value: x=-b/2a=-4/(2*-116)=1/58

Vertex's y-value is given by: y = -116(1/58)2+4(1/58)+3 = 3.03 ft (return the x-value to the equation).

Locate the positive x-intercept (y = 0) in (c).

0 = -116x2+4x+3

Using the quadratic formula because it cannot be factored

x = [-4 ± √(42-4(-116)(3))]

/(2*-116) = -0.14 or 0.18 ft

x = 0.18 ft

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Complete Question -

The height y (in feet) of a ball thrown by a child is  y=−116x2+4x+3

The height y (in feet) of a ball thrown by a child is

y=−116x2+4x+3

where x is the horizontal distance in feet from the point at which the ball is thrown.

(a) How high is the ball when it leaves the child's hand?     feet

(b) What is the maximum height of the ball?    feet

(c) How far from the child does the ball strike the ground? Round your answers to the nearest 0.01.    feet