State weather the triangles are similar. If so write a similarity statement and that postulate or theorem you used. The diagram is not drawn to scale.

( 9x+70)+(9x+70) + (6x + 80) + (6x+ 80 ) = 360

If you solve the equation you get that

x = --44/5

Now, since

z = ( 6x +80 ) = ( 6*(-44/5) + 80 ) = 136 / 5

So, there you have, x,z

Given:

Number of sophomores attended jazz band concert = 35

Total number of students = 137

Required: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert.

Explanation:

The formula to find probability is

Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert

Option D is correct.

Final Answer: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert is 0.26.

Answer:

(B)

Explanation:

The base of a right rectangular pyramid is a rectangle, so if we cut the pyramid with a plane that is parallel to the base, we will get a cross-section with a rectangular form or (A)

We can also cut the pyramid with a plane that is perpendicular to the base, In this case, we will get a cross-section with a triangular form (C)

Finally, we can cut the pyramid with a transversal plane and get a cross-section with the form of a trapezoid (D)

Therefore, the answer is (B) because a square is not a cross-section for the right rectangular pyramid.

we have the following:

therefore, the answer is 2x

To find the x intercept of the line we have to replace y for 0 and solve for x:

To find the y intercept of the line we have to replace x for o and solve for y:

It means that the x intercept is 0.79 and the y intercept is -0.59.

The mean, mode, and mid-range of the given numbers are 13,13,16 respectively.

The total of all the numbers is represented by the mean. The median is the number in the center of an ordered list. The most frequent number is the mode. The highest number less the smallest number is the range.

Mean = sum of the number/ total no. of observations

​Mean = 117/ 9

Mean = 13

Mode: The unique number that repeatedly comes

Given,

9, 9, 10, 11, 13, 13, 13, 14, 25

Mode = 13

Range: Deduct the smaller number from the greater one.

Range = 25-9

Range = 16

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Given:

Length of a rectangle is a+1

width of a rectangle is a

and solve x

the number is -6.5

Answer

4.5

Step-by-step explanation

Given the equation:

Dividing at both sides by 4.5, we get:

Answer:

Divide each side by 4.5

Step-by-step explanation:

(4.5)x = 264.5456

We want to isolate x

Divide each side by 4.5

(4.5)x / 4.5 = 264.5456/ 4.5

x =58.78791

Given:

The roller-coster is moving in the trajectory of this curve

Step by step solution:

To solve this complete problem we need to draw the estimated graph of this function, so that we can answer this question easily.

First of all, we need to find the roots of the given equation,to plot the curve:

let us put the random numbers that may satisfy the equation:

Let us put x = 1:

From here we can say that 1 is the root of the equation.

We will now divide this function from (x-1), so that we can get the cubic equation:

We will use long division method for division, the result we get after the division is:

We will now try to factorize the cubic equations, by putting the random numbers that may satisfy the equation:

let us put x = 2:

From here we can say that f(2) is also the root of this cubic

We will now divide the cubic equation with (x-2), so we can break the cubic into quadratic:

Upon division the cubic equation break into following factors:

From here we have found out four roots of the initial function that are:

x = 1,2,6,-3

Now we can easily plot the curve:

This is estimated curve, there are no sharp edges.

On the basis of this curve, we can easily answer all the questions related to this curve.

Solution

Explanation:

Given:

(b) Equation of the axis of symmetry

where

The formula for the axis of symmetry and the x value of the vertex

Plug in the value

(d) To find the y value of the vertex, substitute 1 for x in the equation.

The vertex is (-2 , -42) Since a > 0 the vertex is the minimum point and the parabola opens upward.

Hence the vertex = (-2 , -42)

Since this is a right triangle we can use trig functions

First we can find the length of the hypotenuse using the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

28^2 + 45^2 = c^2

784+2025 = c^2

2809 = c^2

Taking the square root of each side

sqrt(2809) = sqrt(c^2)

53 = c

The hypotenuse, DR = 53

Then we can find the measurements of the angles

sin F = opp/ hyp

sin F = 28/53

Taking the inverse sin of each side

sin D = opp/ hyp

sin D = 45/53

Taking the inverse sin of each side

By definition, an equation of a Combined Variation has the following form:

Where "k" is the Constant of Variation.

In this case, you know that the resistance "R" of a wire varies directly as its length and inversely as the square of its diameter.

Then, let be "R" the resistance of the wire (in ohms), "l" its length of the wire (in feet), and "d" its diameter (in inches).

Therefore, you can set up that the equation has this form:

According to the information given in the exercise, when:

The resistance is:

Then, you can substitute values into the equation and solve for "k":

Therefore, you can set up the following equation that represents this situation (using the value of "k"):

Hence, if:

You can substitute these values into the equation and then evaluate, in order to find the corresponding resistance. This is:

Therefore, the answer is:

Find the probability that you will get a 3 on a roll of a die. Since there is only one 3 in a die and there are 6 sides in a die, divide 1 by 6.

Find the probability that you will get a yellow card. Divide the number of yellow cards by the total number of cards.

Since the two events are independent, multiply the obtained probabilities.

I think this is a physics problem.

I'll read it

a) A rectangular prism and a cylinder

b) Volume of the log = pi*r^2 x h

Volume of the log = 3.14*5^2* 30

Volume of the log = 2355 in^3

density = weight / volume

density = 4263 / 2355

density = 1.81 lb/in^3 This is the result

Given:

The radius of the quarter circle is given 3 mm.

To find:

The perimeter of the quarter circle.

Solution:

It is known that the perimeter of the quarter circle is given by:

So, the perimeter of the quarter circle:

Thus, the perimeter of the quarter circle is 10.71 mm.

The lowest value that is needed in order to qualify is given as 216.128

The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from:

z = (raw score - mean) / standard deviation

Given;  mean of 200 and a standard deviation of 20

P(z > c) = 21% = 0.21

1 - P(z < c) = 0.21

P(z < c) = 0.79

we are to find the critical value of z using excel function

=NORM.S.INV(1-0.21)

= 0.806421247

To get the lowest value we would have to put the values in the formula

0.8064 = (x - 200)/20

0.8064 * 20 = (x - 200)

16.128 = (x - 200

take like terms

x = 200 + 16.128

x = 216.128

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The distance travelled by the two boats forms a right triangle. Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.

It is given to us that -

There are two boats

One boat heads north while the other heads east

The boat travelling north has traveled 39 kilometers

The boat travelling south has traveled 52 kilometers

We have to find out the distance between the two boats after they have travelled the respective distances.

It is known to us that one boat heads north while the other heads east. We can see that the trajectory formed between the two boats resembles a right triangle as they start from the same point.

One leg of the right triangle formed equals to the distance travelled by the boat travelling north.

Let us say the distance travelled by the boat travelling north be "a".

=> a = 39 kilometers ----- (1)

Other leg of the right triangle formed equals to the distance travelled by the boat travelling east.

Let us say the distance travelled by the boat travelling east be "b".

=> b = 52 kilometers ------ (2)

Now, the distance between the two boats after they have travelled the respective distances is equal to the value of the hypotenuse of the right triangle formed.

Let us say the hypotenuse of the right triangle formed be "h".

According to the Pythagorean Theorem for a right triangle,

[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (3)

where, a, b = legs of the right triangle

and, h = hypotenuse of the right triangle

Substituting the values of a and b from equations (1) and (2) respectively in equation (3), we have

[tex]a^{2} +b^{2} =h^{2}\\= > 39^{2} +52^{2} =h^{2}\\= > h^{2}=1521+2704\\= > h^{2}=4225\\= > h=65[/tex]

So, the value of the hypotenuse of the right triangle formed is 65 kilometers.

Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.

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We need to find how much will be left after 6 half-lives of a radioactive isotope starting with 130g.

One way to write the amount N of radioactive isotope left after a time t, with an initial amount N₀ and a half-life τ is:

Notice that when t = τ, we have:

In this problem, we have:

Then, we obtain:

Therefore, rounding to the nearest gram, the answer is 2 grams.

Answer

x = 164.9 ft

Explanation:

Given the following figures

To find the distance from the point on the ground, we need to apply the SOH CAH TOA

Therefore, the distance is 164.9 ft

Not, the left graph is discontinuous in x=2, the kind of discontinuity is removable discontinuity. It is not continuous because in x=2 there us a abrupt change in the function value.

To determine if the function is left or right continuous you identify if the function in a jump discontionuity has the defined point on the left or on the right.

The function given in number 11 has a jump discontinuity at x=3, as the defined point is on the part of the graph on the left, you say the function is left continuous at x=3.

When a function is compose by its inverse, the result is its original input. Therefore,

Given: Ted Borrowed $1200 for two years and made monthly payments. The total finance charge is $175.92

Required: To determine the Annual Percentage Rate.

Explanation: The formula for APR is as follows-

where n is the total number of days in the loan term.

Here, the total finance charge is $175.92, and the Principal amount is $1200.

Also, n=2 years or 730 days. Substituting these values into the formula as-

Further solving as-

Final Answer: The Annual Percentage Rate is 7.29%

The rule of the compounded interest is

A is the new amount

P is the initial amount

r is the rate in decimal

n is the number of periods per year

t is the time in years

Since the principal is $1000, then

P = 1000

Since the yearly interest rate is 6%, then change it to decimal by dividing it by 100

r = 6/100 = 0.06

Since the interest is compounded yearly, then

n = 1

Since the time is 10 years, then

t = 10

Substitute them in the rule above

The amount of money in the account after 10 years is $1790.847697

What would happen if X doesn't lie on OM? If it is true that X lies on OM, if we suppose the opposite then we should have a contradiction, so the only way the contradiction doesn't happen is that it is true

1. We know that BX:XA = 1:2

2. We know that M is the middle point between B and P

We need to prove that X lies on OM

Let's suppose X doesn't lie on OM

By 2, we know that 2BM = BP

If X doesn't lie on OM then the intersection between OM and BA is not X

Let's say the line that goes from O to the line BP and intersects BA on X is OX', where X'≠M

Given

perimeter = 42 inches

length of a rectangle is 5 inches more than the width.

Find

width, length

Explanation

Let width of rectangle = x inches

length = 5 + x

Perimeter of rectangle = 2 (l + b) = 2(5+x+x) = 42

width = 8 inches

Length = 5 + 8 = 13 inches

Final Answer

The width of the rectangle is 8 inches.

The length of the rectangle is 13 inches.

If y varies directly as x, we have that

Then

The relationship between x and y is given as

Therefore when x= 12, y=?

Hence, the value of y when x = 12 is 168

Final answer: y = 168

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies {\large \begin{array}{llll} y -5= -(x +1) \end{array}}[/tex]

From the double number line, we can see that the corresponding number of Green and Purple beads needed in each case are stated.

Therefore, for 20 Green beads she will need to use 25 Purple Beads.

Step 1

Given;

Required; To solve by completing the square method.

Step 2

Subtract 15 from both sides of the equation.

Find half of the coefficient of x (i.e 6) and square it

Add it to both sides

Answer;