=GEOMETRYPythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Answer:

Explanation:

Here, we want to find the standard form of the equation

We have the standard form as:

We can arrive at this using the two-points form:

This is:

(x1,y1) = (2,3)

(x2,y2) = (2,-5)

Now, as we can see, the line is a vertical line since the x-value is the same

Thus, we have it that:

where c will represent the x-intercept

Thus, we have the equation of the line as:

1) We can do this by listing all the factors of -1, and the leading coefficient 6. So, we can write them as a ratio this way:

Note that p stands for the constant and q the factors of that leading coefficient

2) Now, let's test them by plugging them into the polynomial. If it is a rational root it must yield zero:

3) So the possible roots are:

But there are no actual rational roots.

Since triangles ABC and XYZ are similar, the ratio between their corresponding sides is constant; thus,

Solving for s,

Thus, the result of the cross multiplication is 3s=30 and the answer is s=10

You have:

sin 2A = -√7/4

In order to determine the value of sin A, first calculate the value of angle A by using sin⁻¹ over the previous equation, just as follow:

sin⁻¹(sin 2A) = sin⁻¹(-√7/4) In this way you cancel out the sin

2A = -41.41° divide by 2 both sides

A = -41.41°/2

A = -20.705°

however, take into account that angle A is in the third quadrant. Then, it is necessary to consider the result A=-20.705° is respect to the negative x-axis.

To obtain the angle respect the positive x-axis (the normal way), you simply sum 180° to 20.705°:

20.705 + 180° = 200.705°

Next, use calculator to calculate sinA:

sin(200.705°) = -0.3535

Solution:

In the given figures, angles of the triangle ABC are corresponding equal to triangle DEF and the sides are proportional to each other.

Thus, the triangle ABC is similar to triangle DEF.

Therefore, the relationship between both triangles is the proportional side lengths.

Both triangles are not of the same size as their sides are not equal.

Both triangles are also not congruent as they do not satisfy any five conditions of congruence.

Hence, the correct option is A.

Considering the expression 6+(x+3)^2. the table of at least SIX different values of the expression is

x               y

0            15

1             22

2            31

3            42

4            55

5            70

The table is completed by substituting the values of x in the given expression as follows

6 + (  x + 3 )^2

for x = 0, y = 6 + ( 0 + 3) ^2 = 15

for x = 1, y = 6 + ( 1 + 3) ^2 = 22

for x = 2, y = 6 + ( 2 + 3) ^2 = 31

for x = 3, y = 6 + ( 3 + 3) ^2 = 42

for x = 4, y = 6 + ( 4 + 3) ^2 = 55

for x = 5, y = 6 + ( 5 + 3) ^2 = 70

Learn more about table completion here:

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Given

The equation is given as

Explanation

Factorisation the equation,

Factorise the polynomial.

Hence the answer is

Answer:

Explanation:

To properly classify the traingle, we need to get the length of the sides

To get the length of the sides, we need to get the distance between each two points using the distance between two points formula

Mathematically,we have the formula as:

Where (x1,y1) refers to the coordiantes of the first point while (x2,y2) refers to the coordinates of the second point

let us get the coordinates of the individual points as seen from the plot shown

C (1,8)

A (5,10)

T (7,6)

So, let us find the distance between each two points

For AC, we have:

For AT, we have:

Lastly, for CT, we have:

From our calculations, we can see that AC = AT

If we have a triangle which has two of its sides equal in length (the angle facing these sides would be same too), we call this an isosceles triangle

So, the class of triangle CAT is isosceles triangle

According to visual inspection, shape A has been rotated 180° counterclockwise about the origin and then translated 1 unit to the left.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

The four basic transformations exist:

According to visual inspection, shape A has been rotated 180° counterclockwise about the origin and then translated 1 unit to the left.

Therefore, the correct answer is option C) translated 1 unit to the left and then rotated 180° counterclockwise about the origin

The complete question is:

Describe the transformation that maps the pre-image A to the image A.

A) translated 8 units up and then reflected across the y-axis

B) translated 8 units down and then reflected across the y-axis

C) translated 1 unit to left and then rotated 180° counterclockwise about the origin

D) translated 1 unit to right and then rotated 180° counterclockwise about the origin.

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Answer:

-54

Step-by-step explanation:

Finding a value means you will get a number answer. Since they said x

x = -2

fill in -2 in place of the x.

also they said

y = 6

so fill in 6 wherever you see a y.

2(3x - 6) - 5y

fill in -2 for x and 6 for y.

= 2(3•-2 - 6) - 5•6

Work on parentheses first. Multiply before adding or subtracting.

= 2(-6 - 6) - 5•6

= 2(-12) - 5•6

Again, multiply before adding or subtracting.

= -24 - 30

= -54

The slope is 6 and the y-intercept is 9

The given equation is:

y = 6x + 9

The general form of the equation of a line is

y = mx + c

where m is the slope and c is the y-intercept.

Comparing these equations, we see that

m = 6 and c = 9

Therefore, the slope is 6 and the y-intercept is 9

1) Let's visualize the points

2) To find the equation for the line of best fit we'll need to follow some steps.

2.1 Let's find the mean of the x values and the mean of the Y values

2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.

To make it simpler, let's use this table:

The slope then is the summation of the 5th column over the 6th column, we're using the least square method

The Linear coefficient

3) Finally the equation of the line that best fit is

Looking at the triangles, they are both right triangles. They have congruent legs = 12. They have congruent acute angles of 45 degerees. Thus, they are congruent triangles. The answer is True

Answer:

4

Explanation:

Given the below;

To simplify the above, we have to note that any number or variable raised to the power of 0 is 1.

So, we'll have;

To calculate the equation first we need to choose two points of the table

P1 (1,1)=(x1,y1)

P2(0,9)=(x2,y2)

then we calculated the slope m

substituting the points we have

then we can calculate the equation

the equation is

The general form of the equation of a line is:

y=mx+b

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

Since the intercept is the point where the line intersects the y-axis, if a line goes through the origin, then is intercept equals 0, b = 0, which is the case for the first and last line, then, their equation looks like this:

y=mx

When the slope (m) is a positive number, the line goes up as x increases, when the slope (m) is negative, the line goes down as x increases, then the equation of the first line must be: y=x and y= -x for the last line.

For the second line, we can see that it crosses he axis at y= -3, then its intercept equals -3, that's why the equation of this line is y = x - 3

1. P(video games and kid is 10 to 12 years old)

Therefore,

The P(video games and kid is 10 to 12 years old) = 17/143

2. P(basketball/kid is 13 to 15 years old)

P(basketball/kid is 13 to 15 years old) = 14/45

3. P(kid is 13 to 15 years old/basketball)

P(kid is 13 to 15 years old/basketball) = 7/27

4. P(darts/kid is 10 to 15 years old)

P(darts/kid is 10 to 15 years old) = 27/79

5. P(basketball and darts)

P(basketball and darts) = 0

6. P(basketball and kid is 13 to 18 years old)

P(basketball and kid is 13 to 18 years old) = 2/5

Let's define:

x: pairs of shoes of Shanice

y: pairs of shoes of Ron

Shanice has 4 times as much many pairs of shoes as does her brother Ron, means:

x = 4y (eq. 1)

If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does, means:

x - 12 = 2y (eq. 2)

Replacing equation 1 into equation 2:

4y - 12 = 2y

4y - 2y = 12

2y = 12

y = 12/2

y = 6

and

x = 4*6 = 24

After she gives Ron the shoes, she will have left 24-12 = 12 pairs of shoes

As we know;

We will use this equality. We take the square of the sine of the given angle and subtract it from [tex]1[/tex].

In the third region the sign of cosines is negative. Therefore, our correct answer should be as follows;

According to the problem, the length is 60 cm and the width is 450 mm.

Let's transform 450mm to cm. We know that 1 cm is equivalent to 10 mm. So,

Then, we use the perimeter formula for rectangles.

Where w = 45 cm and l = 60 cm.

However, we know that 1 meter is equivalent to 100 centimeters.

Hence, the perimeter, in meters, is 2.1 meters long.

Part a

Remember that the linear equation in slope-intercept form is

y=mx+b

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

the equation is of the form

C=m(n)+b

where

m=8.50

b=350

therefore

Part b

A reasonable domain for n (number of cups)

Remember that the number of cups cannot be a negative number

so

the domain is the interval [0, infinite)

but a reasonable domain could be [0, 500]

Find out the range

For n=0 -----> C=350

For n=500 ----> C=8.50(500)+350=2,100 ZAR

the range is the interval [350,2,100]

Part c

calculate the cost

For n=100 cups ----> C=8.50(100)+350=1,200 ZAR

For n=200 cups ----> C=8.50(200)+350=2,050 ZAR

For n=400 cups ---> C=8.50(400)+350=3,750 ZAR

Part d

Average cost

Divide the total cost by the number of cups

For 100 cups ------> 1,200/100=12 ZAR per cup

For 200 cups ----> 2,050/200=10.25 ZAR per cup

For 400 cups ----> 3,750/400=9.38 ZAR per cup

Part e

it is better to order more cups, to reduce the initial ZAR 350 cost.

Part f

In this problem we have the ordered pairs

(200, 2150) and (400, 3750)

Find out the slope m

m=(3750-2150)/(400-200)

m=8 ZAR per cup

Find out the linear equation

C=mn+b

we have

m=8

point (200,2150)

substitute and solve for b

2150=8(200)+b

b=2150-1600

b=550

therefore

The linear equation is

Part g

A reasonable domain could be [0, 600]

Find out the range

For n=0 ------> C=550

For n=600 ----> C=8(600)+550=5,350

The range is the interval [550,5350]

Part h

The gradient is the same as the slope

so

slope=8

that means ----> the cost of each cup is 8 ZAR

Part i

For n=600

C=8(600)+550=5,350 ZAR

Part j

we have the inequality

8n+550 < 8.50n+350

Solve for x

550-350 < 8.50n-8n

200 < 0.50n

400 < n

Rewrite

n > 400

For orders more than 400 cups is more effective to order from Cupomatic

Verify

For n=401

C=8n+550=8(401)+550=3,758 ZAR

C=8.50n+350=8.5(401)+350=3,758.5 ZAR

the cost is less in CUPOMATIC, is ok

the answer is

We know that

• Ethan burns 650 calories per hour.

If he runs 5 hours we just have to multiply this time with the given rate.

Answer:

135°

Step-by-step explanation:

To convert an angle from radians to degrees, multiply by [tex]180/\pi[/tex].

[tex]\frac{3\pi}{4} \cdot \frac{180}{\pi}=135^{\circ}[/tex]

1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:

2) So, based on that constant of proportionality (k) we can find the missing leg.

Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.

ANSWER

x = 124

EXPLANATION

First we have to clear the term that contains x in the equation. In this case, this term is the second term. So we have tu subtract 6 from both sides of the equation:

Then, we have to eliminate the root. Note that in the expression inside the root there are two terms. To do this, we have to apply the "opposite" operation on both sides of the equation, which in this case is exponent 5:

Now we do something similar to the first step. We want to leave on one side of the equation only the term that contains x and the rest on the other side. To do this we can either add 2x on both sides, or subtract 249 from both sides. We'll apply the first option because then we'll have a positive coefficient for x:

However, we now have to subtract 1 from both sides of the equation:

Finally, to find x, we have to divide both sides by 2:

Hence, the solution to the equation is x = 124.

Area of shaded triangle = Area of triangle - area of circle

Area of triangle = 1/2 x base x height

Base= 16 yds

Height= 19 yds

Area of triangle = 1/2 x 16 x 19 = 8 x 19 =152 square yard

Area of shaded triangle = 152 - 78.5 =73.5 square yard

The given quadratic equation is:

The quadratic formula is given by the equation:

From the given quadratic equation;

Thus, we have:

Hence, the correct option is Option A

Answer

The power on 2 is either -3.5 in decimal form or (-7/2) in fraction form.

Explanation

To do this, we have to first note that

So, we can then simplify the given expression

Hope this Helps!!!

According to the information given in the exercise:

- Group A contains a total of 155 people.

- One-fifth of that people will be selected to win $20 fuel cards.

- The total number of people in Group B is 686.

Then, you can determine that the number of people that will be selected to win $20 fuel cards is:

Therefore, the number of nonwinners in Group A is:

You know that Group B will receive the same number of fuel cards. Therefore, its number of nonwinners is:

Knowing all this information, you can set up the following ratio of nonwinners in Group A to nonwinners in Group B after the selections are made:

Hence, the answer is:

Answer:

The symmetric is symmetric

The distribution is unimodal

The mean, median, and mode are equal

A normal distribution is appropriate

Explanation:

The normal distribution is symmetric and unimodal, where the mode, the median, and the mean are equal. This distribution has the following shape

Therefore, the normal curve can be used as a model for the distribution.

So, the answers are:

The symmetric is symmetric

The distribution is unimodal

The mean, median, and mode are equal

A normal distribution is appropriate