Geometry Problem - Given: segment AB is congruent to segment AD and segment FC is perpendicular to segment BD. Conclusion: Triangle AEG is isosceles. (Reference diagram in picture)

Given the equation:

Solving for x:

Now, we take the square on both sides of the equation:

Now, using the general solution of quadratic equations:

From the problem, we identify:

Then, the solutions are:

But the original equation √(x), so x can not be negative if we want a real equation. Then, the only real solution of the equation is:

Answer:

13.6

Step-by-step explanation:

[tex] \frac{3x}{10.2} - 12.4 = - 8.4[/tex]

[tex] \frac{3x}{10.2} = 4[/tex]

[tex]3x = 40.8[/tex]

[tex]x = 13.6[/tex]

new uniforms = 3

Total amount spent = $486

Amount spent per player = $486 /3 = $162

The resultant answer from computing P(7,4) from probability and statistics is 840.

So, P(7,4):

This is a permutation and can be calculated as:

Put the values in the given formula:

Therefore, the resultant answer from computing P(7,4) from probability and statistics is 840.

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Answer:

1/4

Step-by-step explanation:

Given:

COA is a diameter

O is the origin

OA = 1

m< BOA = 30

Re-drawing the diagram to show the coordinates of the B:

Let the coordinates of B be (x,y)

Using trigonometric ratio, we can find the length of side AB

From trigonometric ratio, we have:

Substituting we have:

Hence, the coordinates of B is (1, 0.58)

To determine the vertex form of a parabola has equation:

where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.

From the question, we have that, the vertex is (-1, 1)

and the leading coefficient is a = 2

We substitute the vertex and the leading coefficient into the vertex form to

get:

The graph of this function is shown in the attachment.

Hence the equation of parabola is

The probability that x will be greater than 45 is 0.1974.

The 90th percentile of x is 63.3786

Given,

The sample size drawn from  a population = 115

The mean of the sample size = 48

Standard deviation of the sample size = 12

a) We have to find the probability that x will be greater than 45.

Here,

Subtract 1 from p value of the z score when x = 45

Then,

z = (x - μ) / σ

z = (45 - 48) / 12 = -3/12 = -0.25

The p value of z score -0.25 is 0.8026

1 - 0.8026 = 0.1974

That is,

The probability that x will be greater than 45 is 0.1974.

b) We have to find the 90th percentile of x.

Here,

p value is 0.90

Then, z score will be equal to 1.28155

Now find x.

z = (x - μ) / σ

1.28155 = (x - 48) / 12

15.3786 = x - 48

x = 15.3786 + 48

x = 63.3786

That is,

The 90th percentile of x is 63.3786

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Michael earned some Money doing odd jobs last summer and put it in a savings account that earns 13% interest compounded quarterly after 2 years there is 100.00 in the account How much did Michael earn doing odd jobs​?

____________________________________

13% interest compounded quarterly

after 2 years there is 100.00

_________________________________-

interest compounded

A = P(1 + r/n)^nt

A= Final amount

P= Principal Amount

r= interest

n= number of compounding periods (year)

t= time (year)

_____________________

Data

A= 100.00

P= Principal Amount (The question)

r= interest (0.13)

n= number of compounding periods (4)

t= time (2)

_________________

Replacing

A = P(1 + r/n)nt

P = A / ((1 + r/n)^nt)

P = 100.00/ ((1 + 0.13/4)^4*5)

P= 100.00/ (1.0325^20)

P= 52

________________

Michael earns doing odd jobs 52 dollars.

then

answer: 1/x

Recall that the probability of a binomial distribution is given by

Where n is the number of trials, p is the probability of success, and x is the variable of interest.

nCr is the number of combinations.

For the given case, we have

n = 18

p = 0.8

x = 15

Let us find the probability P(X=15)

Therefore, the probability P(X=15) is 0.2297

The relation between this two functions is g(x) = -f(x)

This means that g(x) is a reflection of f(x) about the x-axis, that is, a reflection about a horizontal line

SOLUTION:

Step 1:

In this question, we are given the following:

Let the supply and demand functions for sugar be given by the following equations. Bye

Supply: p = 0.4x

Demand: p = 100 - 0.4x

a) Find the equilibrium demand.

Step 2:

At Equilibrium,

collecting like terms, we have that:

Divide both sides by 0.8, we have that:



Step 3:

Recall that:

CONCLUSION:

Equilibrium Demand:

Let:

c = total

a = cost of each book

w = flat shipping fee

Therefore, the total is given by:

where:

b = number of books

The independent variable is:

"b" books

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

Step 02:

simplify (radical):

The answer is:

5x²

In the first bounce, the height is

In the second bounce, the height is

Then, we can note that the pattern is

where n represents the number of bounces of the ball. Then, for n=5 (fifth bounce), we get

which gives

Therefore, by rounding to the nearest thousandths, the answer is 2.758 feet

We will have the following:

*First: We determine the standard deviation of the statistic, this is:

So, we will have:

Then:

And so, we obtain the standar deviation.

*Second: We determine the margin of error:

Here me represents the margin of error, cv represents the critical value and this is multiplied by the standard deviation. We know that the critica value for a 90% confidence interval is of 1.645, so:

*Third: We determine the confidence interval as follows:

Here ci is the confidence interval, ss is the saple statistic and me is the margin of error:

And that is the confidence interval,

From the given expression

a) The linear system of a matrix form is

The linear system of the given matrix will be

b) The entries in A of the matrix is

c) The dimensions of A, X and B are

The equation that represent the situation is as follows:

The three combination of the gift cards you can purchase is as follows:

The store sells gift cards. One can purchase  gift cards for $20 or $30 .

You spent $380 on gift cards. let x be the number of gift cards for $20 And let y be your gift cards for $30 .

The equation in standard form to represent the situation is as follows:

The standard form of a linear equation is A x + By = C.  A, B, and C are

constants, while x and y are variables.

Therefore,

x = number of gift cards for 20 dollars

y = number of gift card for 30 dollars

Hence,

20x + 30y = 380

The three combination one could have purchased is as follows:

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The transformation to get g(x) from f(x) are:

translate 14 units to the left and 10 unit upwards

the transformatio to get h(x) from f(x) are:

translate 14 units to the left and 10 units downwards

SOLUTION:

Step 1:

In this question, we are given the following:

Explain the behavior of :

when x=a.

Give values to x and a such that:

Step 2:

The graph of the function:

are as follows:

Explanation:

From the graph, we can see that the function:

is a horizontal translation, shift to the right of its parent function,

The 5 number summary of the data given is:

Minimum = 59

Q1 = 66.50

Median = 78

Q3 = 90

Maximum = 99

A stem and leaf plot is a table that is used to display a dataset. A stem and leaf plot divides a number into a stem and a leaf. The stem is the first digit in a number while the leaf is the second digit in the number.

The minimum is the smallest number in the stem and leaf plot. This is 59. Q1 is the first quartile.

Q1 = 1/4 x (n + 1)

Where n is the total number in the dataset

1/4 x 19 = 4.75 term

(64 + 69) / 2 = 66.50

Q3 is the third quartile.

Q1 = 3/4 x (n + 1)

Where n is the total number in the dataset

3/4 x 19 = 14.25 term = 90

The median is the number that is at the center of the dataset.

Median = 1/2(n + 1)

1/2 x 19 = 8.5 term

(76 + 80) / 2  = 78

The maximum is the largest number in the dataset. This number is 99.

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We recall that the area of a triangle is defined by the product of the triangle's base times its height divided by 2.

So we notice that in our image, we know the height (6 cm), and we also know the base of the triangle (2 cm)

Therefore the triangles are is easily estimated via the formula:

Then the area is 6 square cm.

Recall that the rule of transformation of a point reflected over the y-axis is as follows:

Therefore, the transformed coordinates of the vertices of the triangle are:

Therefore, the image of the triangle is the triangle with the above vertices.

Answer:

Since the given equation is

If x = 0, then

Then x = 0 is correct because it gives the same value of y in the table

If x = 2

Since the value of y in the table is 4

Then x = 2 is incorrect

Slope is

Then:

Answer: slope = 1

To begin we shall sketch a diagram of the line segments as given in the question

As depicted in the diagram, line segment AC is parallel to line segment DB.

This means angle A and angle B are alternate angles. Hence, angle B equals 41 degrees. Similarly, angle C and angle D are alternate angles, which means angle C equals 56.

Therefore, in triangle EAC,

The measure of angle AEC is 83 degrees

Answer:

Explanation:

Given A = (4, 6) B = (2, 8) C = (5, 10)

SImilarly, for A' = (2, 3) B' = (1, 4) C' = (2.5, 5)

Since it is a dilation, AB/A'B' should be the same as BC/B'C', but that is not the case here.

GIVEN:

We are given the following polynomial;

Required;

We are required to sketch the graph of the function. Also, to use the synthetic division and the remainder theorem to find the zeros.

Step-by-step solution;

We shall begin by sketching a graph of the polynomial function.

From the graph of this polynomial, we can see that there are four points where the graph crosses the x-axis. These are the zeros of the function. One of the zeros is at the point;

That is, where x = -1, and y = 0.

We shall take this factor and divide the polynomial by this factor.

The step by step procedure is shown below;

Now we have the coefficients of the quotient as follows;

That means the quotient is;

We can also divide this by (x - 1) and we'll have;

We now have the coefficients of the quotient after dividing a second time and these are;

The remaining two factors are the factors of the quadratic expression we just arrived at.

We can factorize this and we'll have;

The zeros of this polynomial therefore are;

Therefore;

ANSWER:

In order to sketch the graph we need to find the vertex and two more points to connect with the vertex.

To do so set the inside of absolute value to zero:

The y-coordinate of same is:

So the vertex is (- 3, - 1).

Since the coefficient of the absolute value is positive, the graph opens up, and the vertex is below the x-axis as we found above.

Find the x-intercepts by setting the function equal to zero:

We have two x-intercepts (-4, 0) and (-2, 0).

Now plot all three points and connect the vertex with both x-intercepts.

Now, from the graph we see there is no domain restrictions but the range is restricted to y-coordinate of the vertex.

It can be shown as:

Answer:

Step-by-step explanation:

Given absolute value function:

[tex]f(x)=|x+3|-1[/tex]

The parent function of the given function is:

[tex]f(x)=|x|[/tex]

Graph of the parent absolute function:

Translations

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

Therefore, the given function is the parent function translated 3 units left and 1 unit down.

If the vertex of the parent function is (0, 0) then the vertex of the given function is:

⇒ Vertex = (0 - 3, 0 - 1) = (-3, -1)

To find the y-intercept, substitute x = 0 into the given function:

[tex]\implies \textsf{$y$-intercept}=|0+3|-1=2[/tex]

To find the x-intercepts, set the function to zero and solve for x:

[tex]\implies |x+3|-1=0[/tex]

[tex]\implies |x+3|=1[/tex]

Therefore:

[tex]\implies x+3=1 \implies x=-2[/tex]

[tex]\implies x+3=-1 \implies x=-4[/tex]

Therefore, the x-intercepts are (-2, 0) and (-4, 0).

To sketch the graph:

Note: When sketching a graph, be sure to label all points where the line crosses the axes.

The domain of a function is the set of all possible input values (x-values).

The domain of the given function is unrestricted and therefore (-∞, ∞).

The range of a function is the set of all possible output values (y-values).

The minimum of the function is the y-value of the vertex:  y = -1.

Therefore, the range of the given function is:  [-1, ∞).