An isosceles right triangle has 6 cm legs . Find the length of the hypotenuse

The inequality given is

Collecting like terms we will have

With the above solution, we can conclude that y=10 is not a solution to the inequality because the values of y are less than 8

Hence, The answer is NO

1.

It means multiply f(x) and g(x) and then put "2" into it. The solution is what we are looking for. So,

2.

For this we subtract f from g and put -1 into the expression. So

3.

We simply add f and g and put 2 into the final expression.

4.

We divide f by g and put -1 in the final expression. Shown below:

Now, please match each answer with each choice.

Using the Empirical Rule, the correct option regarding the skewness of the distribution is given as follows:

(A) No, the distribution is skewed to the right.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:

In the context of this problem, the mean and the standard deviation are given as follows:

A huge percentage is within one standard deviation of the mean, and the distribution is not symmetric, hence it is not normal.

Since most values are at the lower bounds of the histogram, the distribution is right skewed and option a is correct.

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ANSWER

1.5(x)

EXPLANATION

The tree is originally x feet tall. If it grows 1/2 this height it means that now it is 1/2x taller, or we can express this as a decimal, 0.5x. If we add these two heights we'll have the new height of the tree:

we have the equation

H = -16t^2 + 36t + 56

This equation represents a vertical parabola open downward, which means, the vertex is a maximum

The time t when the ball reaches its maximum value corresponds to the x-coordinate of the vertex

so

Convert the given equation into vertex form

H=a(t-h)^2+k

where

(h,k) is the vertex

step 1

Complete the square

H = -16t^2 + 36t + 56

Factor -16

H=-16(t^2-36/16t)+56

H=-16(t^2-36/16t+81/64)+56+81/4

Rewrite as perfect squares

H=-16(t-9/8)^2+76.25

the vertex is (9/8,76.25)

therefore

SOLUTION

Given:

Now substitute these given into the expression above:

Simplifying further:

The answer therefore is:

a)

In order to find a function M(t), first let's identify two ordered pairs that are solutions to the equation.

From the given information, we have the ordered pairs (1990, 1.16) and (2008, 1.4).

Using these ordered pairs, let's find the slope-intercept form of a linear equation (y = mx + b)

So the equation is M = 0.01333t - 25.3667

The independent variable represents the year (correct option: first one)

b)

The slope represents the change in M over the change in t, that is, it represents the change in attendance over a year (correct option: first one)

c)

For t = 2015, we have:

d)

For M = 1.5, we have:

The store sells a total of 18 types of chairs (this is the sum of all the types of chairs in the two way frequency table). From this table we notice that only two of them are filled with beads and made from velvet. Then the probability of choosing this is:

Therefore the probability is 1/9

We have the following rule for exponents:

then, in this case we have:

we know that

The volume of a cone is equal to

In this problem

we have

V=75pi mm^3

h=9 m------> convert to mm

h=9,000 mm

substitute in the given equation

From the given graph the line is passing through the points (-2,0) and (0,3).

Let,

From the option the equation of the line is y=2x+3

Since on subtituting (0,3) in the above expression the condition satisfys, also on substituting (-1.5,0) in the given expression the condition satisfys.

Thus, the correct option is option A.

Step-by-step explanation:

due to AB being parallel to XZ, we know that ABY and XZY are similar triangles.

therefore, they have the same angles, and there is one common scale factor for all side lengths from one triangle to the other.

so,

AY / XY = AB / XZ

XY = AY + AX = 7 + 6 = 13

7/13 = 14/XZ

XZ×7/13 = 14

XZ×7 = 14×13

XZ = 14×13/7 = 2×13 = 26

Answer:

Step-by-step explanation:

Given a function f(x), a new function g(x) = cf(x), where c is a constant, is a vertical stretch of f(x) when c > 1.

In our case the function f(x) is stretched by a factor of 3.

It means c = 3 and therefore:

Correct choice is B

The perimeter of a quadrilateral is given by the sum of all the sides.

In order to add mixed numbers, let's rewrite them as a sum of the integer part and the fraction part.

So we have:

Therefore the perimeter is 9 1/3 ft.

We are given a graph that shows the depth in meters (y) as a function of the time in minutes (x).

Part A:

Points A, B, and their projection in the point (2, 110) form a similar triangle with the triangle formed by points A, C, and the point (2, 66).

1)

We can find the circumference using the formula

but remember that the diameter is 2 times the radius

So we can use the formula using radius or diameter, the problem gives us the diameter, so let's use it, so the formula will change a little bit

Where "d" is the diameter.

d = 40 yd, and π = 3.14, so the circumference will be

And to find out the area we can use this formula

Or if you prefer use the radius

Let's use the formula with the diameter again

Then the circumference is 125.6 yd and the area is 1256 yd^2

2)

Here we have a compounded figure, we have half of a circle and a triangle, so let's think about how we get the perimeter and the area.

The perimeter will be the sum of the sides of the triangle and half of a circumference, we already know the length of the triangle's side, it's 10.82, we got to find the half of a circle circumference and then sum with the sides.

We know that

And we can see in the figure that d = 12 mm, then

But that's a full circumference, we just want half of it, so let's divide it by 2.

Now we have half of a circumference we can approximate the perimeter of the figure, it will be

The area will be the area of the triangle sum the area of half of a circle

Then let's find the triangle's area first

The base "b" will be the diameter of the circle, and the height "h" will be 9 mm, then

And the half of a circle's area will be

Then the total area will be

Therefore, the perimeter and the area is

The heptagon is a polygon of 7 sides and 7 angles

The heptagon is a closed figure formed from 7 sides

Since every 2 sides connected to form an angle, then

It contains also 7 angles

Then the answer is :

Angles: 7

Sides: 7

9.

Alternative interior angles are congruent

Therefore;

5x + 42 = 18x -12

collect like term

5x - 18x = -12 - 42

-13 x = -54

Divide both-side of the equation by -13

x=4.15

From the figure, we have the coordinates of the vertices:

ABC ==> A(2, 1), B(5, 1), C(1, 5)

A'B'C' ==> A'(-2, 1), B'(-5, 1), C(-1, 5)

Let's determine the type of transformation that occured here.

Apply the rules of rotation.

For a rotation acorss the y-axis, only the x-coordinates of the points will change to the opposite. i.e from negative to positive or from positive to negative.

For a rotation across the y-axis, we have:

(x, y) ==> (-x, y)

From the given graph, we can see that the only the x-coordinates changed from positive to negative.

Therefore, the transformation that occured here is the reflection across the y-axis.

ANSWER:

B) Reflection across the y-axis.

If we sum both equations, we have the next result:

Since we have this, we can say that the system has infinite solutions. We sum both equations, and we finally get that 0 = 0. In this case, the system has infinite solutions.

All these solutions are expressed by (solving for y):

For example, for a value of x = 1, y is a function of x; then, y = 1 + 5 = 6, or (1, 6), and so on.

For the next system of equations:

Adding both equations, we finally have:

Then, solving for x, we have (using the first equation):

Then, this last system has a unique solution, which is (3, 5) or x = 3 and y = 5.

We have that a group of points can be:

Coplanar: if they lie in the same plane

Collinear: if they lie in the same line

For the given question, let the size of the original field = x

Ninety percent of a large field is cleared for planting

So, the size of the cleared land = 90% of x = 0.9x

50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants.

So, the size of the land planted with blueberry plants and strawberry plants =

The remaining will be = 0.9x - 0.81x = 0.09x

Given: the remaining 360 acres of cleared land is planted with gooseberry plants

so,

divide both sides by (0.09) to find x:

So, the answer will be:

The size of the original field = 4,000 acres

Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.

First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:

We can easily find the points (0, -6) and (2, -2).

With this, we can find the equation of the line using the point-slope formula:

Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:

Plugging the coordinates of the points, we get:

Such that:

Rearranging it in the ax + by = c form,

Multiply both sides of the equation by a factor of 2

Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:

All the point (x, y) satisfying this inequality are contained in the shaded region.

Answer:11

Step-by-step explanation:

SOLUTION

We want to perform the following division using synthetic division

This becomes

First we write the problem in a division format as shown below

Next take the following step to perform the division

Now, we have completed the table and we obtained the following coefficients, 1, -1, 1, -1, 4

Note that the first four ( 1, -1, 1, -1) are coefficients of the quotient, while the last one (4) is the coefficient of the remainder.

Hence the quotient is

And the remainder is 4.

Hence

If Jaylen used a 20% discount on a pair of jeans that cost $70 before tax, then the price of the jeans will be $70 - 20%.

Let's calculate the 20% of $70.

So, the discounted price of the jeans before tax is $70 - $14 = $56.

Generally, sales tax is applied to the discounted price, so let's calculate the 6% of $56.

The sales tax is $3.36.

Therefore, the cost of the pair of jeans after tax is $59.36.

Solution:

The modulus of a complex number;

is denoted by;

Thus, given the complex number;

The modulus is;

ANSWER:

The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.

The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.

Ratio = cost / area

750 / 500 = 1.50

1500 / 1000 = 1.50

2,250 / 1500 = 1.50

3000 / 2000 = 1.50

Since the ratios are constant, the relationship is proportional.

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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.

Answer:

your answer is B

Step-by-step explanation:

Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire

The coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.

A connection between a set of variables results in a linear system when presented on a graph. The variable will have a degree of only one.

The linear equation is given below

- 2x - 3y = 6

For the x-intercept, the value of the y will the zero. Then we have

- 2x - 3(0) = 6

-2x = 6

x = -3

The x-intercept is at (-3, 0).

For the y-intercept, the value of the x will the zero. Then we have

- 2(0) - 3y = 6

-3y = 6

x = -2

The y-intercept is at (0, -2).

Thus, the coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.

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