triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tent if necessary

The set that represents a right triangle has to satisfy Pythagorean's Theorem where the greatest side is the hypothenuse. Let's evaluate each of them until we get the right set.

As you can observe, set B satisfies the theorem.

The equation of a line in slope-intercept form can be written like this:

y = mx + b

Where m is the slope and b is the y-intercept of the line.

In this case, the slope of the line is 1/2, then we can rewrite the above equation like this:

y = (1/2)x + b

We are also told that this line passes through (2, -4), by replacing 2 for x and -4 for y into the above equation, we can solve for the value of b, like this:

-4 = 2(1/2) + b

-4 = 1 + b

-4 - 1 = 1 - 1 + b

-5 = b

b = -5

Then, we can rewrite the equation of the line, like this:

y = (1/2)x - 5

Then, the last option is the correct answer

The word PAYMENT has 7 letters. They can be arranged in groups of 4 like shown below:

PYNT, TA

According to the given data we have the following number:

-10.1

Therefore, the opposite of this given number would be the number 10.1

Instead of -10.1 the opposite would always be with the contrary sign. In this case is the opposite is a positive number.

In this case is -10.1. but for example if we the have to find the opposite number of 1 that would be the -1.

All real number would have and opposite number, except for the number 0.

Solution:

Given:

From the trail lengths given,

The difference in length between the longest trail and the shortest trail:

The sum of the longest trail and the shortest trail.

From the calculations above, the conclusion can be reached that:

Tom's answer does not make sense. His mistake was he did the sum of the longest trail and the shortest trail.

Answer:

Step-by-step explanation:

Given a graph of a probability density function, you want the probabilities ...

The probability of a given range of values of X is the area under the density curve for those values of x.

The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:

  A = 1/2bh

  A = 1/2(16)(0.08) = 0.64

The probability is P(X<16) = 0.64.

The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...

  A = 1/2(b1 +b2)h

  A = 1/2(0.06 +0.10)(8) = 0.64

The probability is P(X>12) = 0.64.

Answer:

the answer is 9.321 miles

Given:

x - 4y = -3

4x - 2y = -12

To determine if the point (3, 1) lies on both of the lines in the system of equations:

Substitute (3, 1) in the first equation, we get

3 - 4(1) = -3

3 - 4 =-3

-1 = -3

But,

Substitute (3, 1) in the second equation, we get

4(3) - 2(1) = -12

12 - 2 = -12

10 = -12

But,

Hence, the answer is, No.

The point (3, 1) does not lie on both of the lines in the system of equations.

Explanation

Part A

The shaded area under the standard normal curve to the left of z=1.00 can be seen below.

Part B

Using the z table, the area under the standard normal curve to the left of z.=1.00 is

Answer: 0.8413

For two given simple statements P and Q, if they are connected with the logical connectivity 'if and only if', then the compund statement is called biconditional statement.

Now,

P: x+4=13

q: x=9

Then, their biconditional statement is x+4=13 if an donly if x=9

Hence the correct answer is (c)

Solution:

Given:

The only acceptable first step in simplifying the expression from the options that would not change or alter the values of the expression is by multiplying (1 + sin x) to both the numerator and the denominator.

Therefore, the correct answer is OPTION B.

Answer:

Choice D: 3 terms

Explanation:

The term of a expressions constant or a variable of an equation, The variable

The property which is used in the following calculation is referred to as Associative Property of Multiplication and is denoted as option D.

This is referred to as the process in which the the result of the multiplication of three numbers is always the same regardless of the way and manner in which they are arranged.

We were given: 4 (18) (5)

= 4 (5) (18)

= 20 (18)

= 360

The multiplication of the numbers will give the same result of 360 no matter how the numbers are arranged which is why it was chosen as the correct choice.

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None of Ari's answer to the question is correct. The right application of the laws of exponents to get the correct answer is explained below.

Some of the laws of exponents can be summarized as follows.

Based on the above laws of exponents, none of Ari's answer is correct. Below are the correct way to solve the questions:

1. [tex]4^2 \times 4^5 = 4^{2 + 5} = 4^7[/tex]

2. [tex](2^{-5})^3 = 2^{-3 \times 5} = 2^{-15} = \frac{1}{2^{15}}[/tex]

3. [tex]\frac{(\frac{1}{4})^4 \times (\frac{1}{4})^5 }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^{4 + 5} }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^9 }{(\frac{1}{4})^3} = (\frac{1}{4})^{9 - 3}} = (\frac{1}{4})^6[/tex]

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Answer

The approximate domain temperature is 10

Step-by-step explanation:

Given the following model function

f(x) = 15x + 145

Mathematically

15x + 145 < 300

Collect the like terms

15x < 300 - 145

15x < 155

Divide both sides by 15

15x/15 < 155/15

x < 10.33

..Given an isosceles trapezoid

The following are the properties of an isosceles trapezoid

The legs are congruent by definition (From the diagram, the legs are JM and KL)

The lower base angles are congruent. The lower base angles are

The upper base angles are congruent. The upper base angles are

Any lower base angle is supplementary to any upper base angle. This means that

Also,

Hence

m∠J = 61⁰

m∠L = 119⁰

m∠M = 119⁰

16 crackers are proportional to 24 grams of carbohydrates. To find the number of grams of carbohydrates in 12 animal crackers, we can use the next proportion:

Solving for x,

Explanation:

This is a function defined by parts. When x is not 3, the function has the equation on top, but when x is 3, the function has one value: 2.

Answer:

f(3) = 2

5 + 6 + 4 = 15

red is 6/15 then taken out

then blue is 5/14

6/15 * 5/14 = 1/7

1/7 or about 0.143

Using the area method in finding the quotient.

The values of A and B are as follows,

A = C/6

B = D/6

A is the quotient of C and 6,

B is the quotient of D and 6.

From the problem, we only have choices of number to input in the boxes.

48, 9, 90, 8, 540, 36 and 0

We will select one to number to be the value of C and the value A must be in the given numbers to be used.

Let's say C = 48

A = 48/6 = 8

Since 8 is included in the list of numbers. This is applicable.

Now for D and B,

Note that the sum of C and D must be equal to the given dividend, the dividend from the problem is 588

Since we already have the value of C = 48, the value of D must be :

588 - C = D

588 - 48 = 540

And 540 is also included in the list of numbers, so D = 540

The value of B will be :

B = D/6

B = 540/6

B = 90

90 is also included in the list of numbers.

The final diagram will be :

For part B, the quotient is the sum of A and B

A = 8, B = 90

Quotient = A + B

= 8 + 90

Quotient = 98

The speed at which diesel train was moving is = 150mph

In the above question, it is given that,

Let the speed of the diesel train which left Abuja be x mph

then, speed of freight train which is moving 50 mph faster than diesel train = (50 + x)mph

Further, the freight train finally caught up the diesel train after three hours

So time taken by freight train = 3 hours

While time taken by diesel train would 1 hour more than freight train as its moving slower = 3 + 1 = 4 hours

Now, it is given that both the trains finally catch up, it means the distance travelled by both the trains would be equal

We know that,

Speed = [tex]\frac{Distance}{Time}[/tex]

Distance = Speed x Time

Distance travelled by Diesel train = distance travelled by Freight train

4x = 3(50 + x)

4x = 150 + 3x

x = 150 mph

Hence, the speed at which diesel train was moving is = 150mph

While, the speed at which freight train was moving is = (150 + x)mph = (150 + 50)= 200mph

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Decreasing order means from largest to smallest

The ordered list is:

54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103

SOLUTION

The triangle XYZ shown below :

The angle with the longest side is said to be the angle with the largest angle:

The largest angle faces the longest side

Hence the Option B is t

A cosine function has the form

Where A is the amplitude, B is 2pi/T, and C is null in this case because the phase is not being specified, and D is the vertical shift (midline).

Using all the given information, we have

Then,

Hence, the function is

81

Explanation

Remember

Step 1

apply

The x-intercept is where the graph passes the x-axis.

The graph extends from {-5 ≤ x ≤ 3}

The x-intercept is {x = -1}.

ANSWER

EXPLANATION

We want to solve for c in:

To do that, we will make c the subject of the formula:

We have solved for c.

we have

step 1

Adds 1 both sides

step 2

Divide by 16 both sides

step 3

Applying square root both sides

Solution

For this case we can use the following formula:

and for this case we have the following:

P= 12600

A= 7100

t = 9 years

And r is the value that we need to find, so we can do the following:

We can do the following:

And we got for r:

And then the rate would be:

6.37%