in a 30 60 90° triangle giving the short leg equals 5 find a hypotenuse of the triangle

To answer this question, we need to remember two theorems of parallelograms:

1. If a quadrilateral is a parallelogram, the two sets of its opposite angles are congruent:

2. The consecutive angles of parallelograms are supplementary (they sum 180 degrees):

Then, with this information, we have that:

And also, we have that the diagonal forms two congruent triangles, and the sum of internal angles of a triangle is equal to 180, then, we have:

Then, we have:

Then, using that the consecutive angles of parallelograms are supplementary (they sum 180 degrees), we have:

Thus, we have that the measure for angle a is:

In summary, we have that (all the measures in degrees):

m< a = 26

m< b = 57

m< c = 97

To find the mile per hour rate equivalent to 40 km per hour, let's convert 40km to miles using the given equivalence in the question.

Therefore, 40 km = 25 miles.

The mile per hour rate equivalent to 40km per hour is 25 miles per hour.

Answer: [tex]y=-\frac{5}{2}x+16[/tex]

Step-by-step explanation:

The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].

[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]

Solution

We are required to determine the expected value of the given distribution

The formula for expected value is shown below

Thus,

The correct option is C

Answer:

D 7.5

Step-by-step explanation:

n + n-3 + 2n-4 = perimeter ≥ 37

4n-7≥37

4n≥30

n≥7.5

Based on the calculations, the numerical value of A is equal to 12.

In this exercise, you're required to determine the numerical value of A when the value of x is equal to 2. Therefore, we would evaluate the given equation based on its exponent as follows:

Numerical value of A = 5x² + 4x² - 2(3x²)

Numerical value of A = 5(2)² + 4(2)² - 2(3 × (2)²)

Numerical value of A = 5(4) + 4(4) - 2(3 × 4)

Numerical value of A = 20 + 16 - 24

Numerical value of A = 36 - 24

Numerical value of A = 12

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Complete Question:

If A = 5x² + 4x² - 2(3x²), find its numerical value for x = 2.

(3+ 1i) (2 - 2i)

open the parenthesis

3(2 - 2i) + 1i(2 - 2i) (note: i² = -1)

6 - 6i + 2i + 2

Rearrange

6 + 2 - 6i + 2i

8 - 4i

comparing with a + bi

The real number a equals 8

The real number b equals -4

The confidence interval depends on the margin of error. When finding the margin of error, the z score corresponding to the 95% confidence level would be multiplied by the square root of the product of the estimated proportion of success and failure divided by the sample size. The greater the sample size, the smaller thie value that would be gotten from this operation. The smaller the sample size, the greater the value that would be gotten from this operation. A greater value would give a bigger margin of error. Thus, the confidence interval would be wider. Hence, the correct option for the sampe size is

A. 40

The acute triangles are those whose all 3 angles have a measure less than 90 degrees.

We need to follow the next image:

Let us check each triangle.

Triangle A:

It has a right angle, hence, it can not be an acute triangle.

Triangle B:

All three sides are less than 90 degrees. Hence, it is an acute triangle

Triangle C:

It has an angle with a measure of more than 90 degrees. Hence, it can not be an acute triangle.

Triangle D

All three sides are less than 90 degrees. Hence, it is an acute triangle.

Triangle E

It has a side with a measure of more than 90 degrees. Hence, it can not be an acute triangle.

Triangle F

It has a right angle, hence, it can not be an acute triangle.

Hence, the correct answer is H. B and D

Hi!

To solve this exercise, we can analyze the sides of this rectangle, which indicate the size of each side.

Let's do it:

On the superior side, we have: x+x+x+x+1, which means 4x+1, right?

On the left side, we have: x+x+1+1+1, or 2x+3

So, we can say that the factors of this rectangle are (4x+1)*(2x+3), last alternative.

ANSWER :

EXPLANATION :

Using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.

So, the amount earned by a person who works 52 hours a week:

So, if a worker works for 52 hours, his salary will be:

Therefore, using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.

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Answer:

100 cans

Explanation:

• The total number of canned food items collected = 3,195

• The number of classrooms that participated = 28

To estimate the number of items each classroom donated, divide 3195 by 28.

Note: Round to a whole number since the number of cans cannot be a decimal.

Each class donated about 100 cans.

Given:

Aim:

We need to find the coordinates and The sign of the equation.

Explanation:

The coefficient of the given functions are

The coefficient is closest to zero.

Comparing the graph of y=A|x| and y=B|x|, we get y=A|x| is wider than y=B|x|.

Comparing the graph of y=C|x| and y=D|x|, we get y=D|x| is wider than y=C|x|.

Comparing the graph of y=A|x| and y=C|x|, we get y=C|x| is wider than y=A|x|.

The coefficient with the greatest value.

Comparing the graph of y=B|x| and y=D|x|, we get y=D|x| is wider than y=B|x|.

We know it's a linear function, which is like

We can find the slope "m" of the linear function doing

There the points x₂, x₁, y₂ and y₁ we can take what's more convenient for us, just be careful, if you do x₁ = 0, you must take the correspondent y₁, the value of y on the same column, therefore y₁ = 3, for example.

I'll do x₁ = 0 which implies y₁ = 3 and x₂ = 1 which implies y₂ = 7. Therefore

Therefore the slope is m = 4, then

To find out the "b" value we can use the fact that when x = 0 we have y = 3, therefore

Then b = 3, our equation is

The correct equation is the letter A.

Answer:

Explanation: We have to write 5.8% In fraction in lowest terms:

This percent number essentially is:

Therefore we can write it as:

In lowest terms, this would be:

Reflection over the x-axis transform the point (x, y) into (x, -y)

Applying this rule to the vertex of the triangle ABC, we get:

A(-6, 6) → A'(-6, -6)

B(-2, 6) → B'(-2, -6)

C(-6, 1) → C'(-6, -1)

Algebraic representation: (x, -y)

EXPLANATION

Rotating the shape , give us the third shape form.

For topic (1), we have the following question:

Which of the following is a function: y=x² or x=y²?

Identify domain and range of each equation.

We can identify a given relation if it is a function or not by identifying the number of possible values of y.

The equations below are both relations.

However, only one of them is a function.

For the first equation, note that for each value of x, there is only one value of y. Some of the points on the equation are as follows.

Thus, the equation passes through the following points.

Notice that no value of x is repeated. Therefore, the given relation is a function.

We can also determine it using graphs. The image below is the graph of the first equation.

If we test it using the vertical line test, no vertical line can pass through the graph twice. Therefore, it shows that the equation is a function.

On the otherhand, the other equation is not a function. This is because when we substitute -2 and 2 to the value of y, we will have the same value of x, which is equal to 4.

Since there are two values of y for only one value of x, the equation must not be a function.

To illustrate this using its graph, we can notice that the vertical line below passes through two points on the graph when x=4.

Therefore, the second equation is not a function.

As for the domain and range, we can obtain it from both graphs.

The domain the set of all possible values of x. Thus, for the first equation, since it extends indefinitely to the left and right, the domain must be from negative infinity to positive infinity.

On the otherhand, since the second equation extends indefinitely to the right from 0, the domain must be from 0 to positive infinity, inclusive.

As for the range, it is the set of all possible values of y.

Thus, for the first equation, since the graph extends indefinitely upwards from 0, the range must be from 0 to positive infinity, inclusive.

On the otherhand, the graph of the second equation extends indefinitely upwards and downwards. Thus, its range must be from negative infinity to positive infinity.

To summarize, here are the questions and the answers for each question.

Which of the following is a function: y=x² or x=y²?

Answer: y=x²

Identify domain and range of each equation.

Answer:

For y=x²:

For x=y²:

(a) Graphing the equation

(i) let x = 0 ; then

y = -0.05 (0) +16

∴ y = 16

Point 1 = ( 0;16 )

(ii) let y = 0 , then

0 = -0.05x +16

0.05x = 16

x = 16 /0.05

∴ x = (320 )

point 2 = ( 320; 0 )

The graph of the line ( y = -0.05x+16) will then be as follows :

{To interpret means to explain in details or translate in writing the meaning of the values of x and y . }

• x represents the number of miles travelled

• y represents gasoline used i gallons

Interpretation:

• when ,x is 0 miles, , the ,gasoline ,is sitting at, 16 gallons.,( this might be the initial stage of travelling)

• however, when the, person has travelled 320 miles,, all gasoline is ,completly used up and sits at 0 gallons, .( this might be the end stage of travelling)

ANSWER and EXPLANATION

We have letter W on the graph.

The cordinates of its vertices are:

(0, 4), (1, 0), (2, 2), (3, 0), (4, 4)

Now, on a cartesian plane, (x - y plane), we have 4 quadrants. The letter is on the first quadrant.

Because it rotates 180 degrees around the origin, it means that it mmoves by 2 quadrants:

So, it moves from quadrant 1 to quadrant 4.

The new cordinates become:

(0, -4), (-1, 0), (-2, -2), (-3, 0), (-4, -4)

Then it is translated 4 units up, so we add 4 units to each of the y values (Remember that cordinates are written as (x, y)):

(0, 0), (-1, 4), (-2, 2), (-3, 4), (-4, 0)

Now, plot those:

a) It forms the letter M.

b) For one shape to be congruent to another, it means that they have the same size. So, yes, the M is congruent to the W.

To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.

To find the length side we will use the following formula:

Where ap is the length of the apothem, and I is the side length.

Substituting the given values, we get:

Solving the equation for I, we get:

Therefore, the perimeter of the hexagon is:

Answer:

STEP 1: Identify and Set Up

We have a trapezoid divided by a straight line that divides it assymetrically. We know from the all too famous geometric rule that adjacent angles in a trapezoid are supplementary. Mathematically, we can express thus:

Hence, from this relation, we can find our unknown angles.

STEP 2: Execute

For <1

<1 = 60 degrees

For <2 & <3

We know from basic geometry that a transversal across two parallel lines gives a pair of alternate angles and as such, <1 = <3 = 60 degrees

We employ our first equation to solve for <2 as seen below:

Therefore, <1 = <3 = 60 degrees and <2 = 20

The fence required is:

For the farmer to build an accurate fence, he needs to know the area of the rose garden. The area is the sum of the area of the rectangle and the area of the semicircle.

The area of the rectangle is:

The area of the semicircle is:

The area of the rose garden is:

Let the number be a

6a x 5a + 8

In the interval where the function is decreasingcreasing, the input or x values increase as the output or y values decrease. Looking at the graph, moving from the left to the right, the values of x are increasing whie the values of y are decreasing. This trend continued till we got to x = 0.5. Thus, in the interval from negative infinity to x = - 0.5, the function was decreasing.

The correct option is C

when evalueatong the expression 13/15,

13 serves as the dividend and

15 is the divisor

Divisor is always placed outside the division sign and the dividend inside.

According to the option, you can see that 15 which is the divisor is placed outside and 13 is placed inside.

check the diagram below:

Option A is the correct answer in this case

Problem

3. In one linear function, when you subtract each y-coordinate from the x-coordinate, the difference is 3. If the x-coordinate is not greater than 10 and the y-coordinate is a positive whole number, how many ordered pairs are there?

Solution

Here are the conditions

x- y= 3

x <10

y >0

And then we have these as possible answers:

4-1 =3

5-2= 3

6-3=3

7-4=3

8-5=3

9-6=3

Then the total possible pairs are: 6