Find the probability the next person you meet was born either on a Monday or a
Friday.
Show all relevant work. To type a fraction, use the forward slash key on your
keyboard (/), i.e., "1/2". To type an exponent, use the caret (^), i.e., "2^5".

The value of BC is 9cm.

What is a similar triangle?

If two triangles have the same shape or have the same shape as their mirror images, they are said to be comparable. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

Here, we have

Given: BA = 6cm, AC = 8cm

BC =?

In a similar triangle, their side is also proportional.

BA/ED = AC/DF = BC/EF

BA/ED = BC/EF

6/18 = BC/27

18BC = 6×27

BC = 6×27/18

BC = 9cm

Hence, the value of BC is 9cm.

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9514 1404 393

Answer:

  (a)  4/3

  (b)  y -3 = 4/3(x -1)

  (c)  y -3 = -3/4(x -1)

  (d)  r = 5

Step-by-step explanation:

a) The slope is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (7 -3)/(4 -1) = 4/3

__

b) The radius is normal to the circle. The point-slope form of the equation for a line can be useful here:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For slope 4/3, the line through point (1, 3) will have the equation ...

  y -3 = 4/3(x -1) . . . . point-slope equation of the normal

__

c) The tangent is perpendicular to the radius. It will have a slope that is the opposite reciprocal of the slope of the radius: -1/(4/3) = -3/4.

  y -3 = -3/4(x -1) . . . . point-slope equation of the tangent

__

d) The radius can be found from the distance formula.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((4 -1)² +(7 -3)²) = √(3² +4²) = √25 = 5

The radius of the circle is 5.

Answer:

A

Step-by-step explanation:

The function that is  shown in the graph is strictly decreasing

"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."

The given function has a value of (- 5) at a certain point.

After that the function is decreased to a value of (- 10).

Therefore, we can conclude that the function is strictly decreasing.

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Answer:

9 hours

Step-by-step explanation:

$273/13 hours=$21 per hour

$189/$21 =9 hours

S = 30 - 0.15(30) or S = 0.85 can be used to calculate the sale price S of an oil change (30).

By resolving this equation, we find that the value of the variable x is 7. An equation is a mathematical formula that states that two quantities or values are equal, as in the example 6 x 4 = 12 x 2.

S will serve as a stand-in for the sale price of the oil change.

Mr. Allen has a 15% off voucher, and the oil change normally costs $30. The reduction can be shown as 15% of the standard price, or:

0.15 * $30 = $4.50

We can deduct the discount from the list price to determine the oil change's selling price:

S = $30 - $4.50

S = $25.50

As a result, S = 30 - 0.15 can be used to calculate the sale price S of an oil change (30)

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Answer:

The answer is  s=0.85*30=22.50(final sale price)  which will be 15 % of the 30 dollars

Step-by-step explanation:

Answer:

The discount is 22.50 and the final price $52.50

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 75 × 30/100

Discount = 75 x 0.3

You save = $22.50

Final Price = Original Price - Discount

Final Price = 75 - 22.5

Final Price = $52.50

Answer:

0.7

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

e2020

Answer:

8.7

Step-by-step explanation:

Use trigonometry. The ladder and the building form a right triangle with the ground. You are given the length of the hypotenuse and the base angle. You use sine since we are trying to figure out the opposite side from the angle and we have the hypotenuse length. Sin = opposite/hypotenuse. So in this case, sin 60°= x/10. We solve for x by multiplying both sides by 10. Now x= sin 60° (10) = (0.8660)(10) = 8.7 m.

\(\large\underline{\sf{Solution-}}\)

Given:

\( \sf \longmapsto x + \dfrac{1}{9x} = 1\)

Multiplying both sides by 3, we get:

\( \sf \longmapsto 3 \bigg(x + \dfrac{1}{9x} \bigg) = 3 \times 1\)

\( \sf \longmapsto 3x + \dfrac{1}{3x} = 3\)

Cubing on both sides, we get:

\( \sf \longmapsto \bigg(3x + \dfrac{1}{3x} \bigg)^{3} = {3}^{3} \)

\( \sf \longmapsto {(3x)}^{3} + \bigg(\dfrac{1}{3x} \bigg)^{3} + \bigg(3 \times {(3x)}^{2} \times \dfrac{1}{3x} \bigg) + \bigg(3 \times 3x\times \bigg( \dfrac{1}{3x} \bigg)^{2} \bigg) = {3}^{3} \)

\( \sf \longmapsto 27{x}^{3} + \dfrac{1}{27x^{3}} + 9x + \dfrac{1}{x} = {3}^{3} \)

\( \sf \longmapsto 27{x}^{3} + \dfrac{1}{27x^{3}} + 9 \bigg(x + \dfrac{1}{9x} \bigg) = 27\)

As we know that:

\( \sf ,\red\longmapsto x + \dfrac{1}{9x} = 1\)

We get:

\( \sf \longmapsto 27{x}^{3} + \dfrac{1}{27x^{3}} + 9 \times 1 = 27\)

\( \sf \longmapsto 27{x}^{3} + \dfrac{1}{27x^{3}} + 9 = 27\)

\( \sf \longmapsto 27{x}^{3} + \dfrac{1}{27x^{3}} = 18 \: Ans.\)

Answer:

ang 4 = 60°

Step-by-step explanation:

ang 1 and ang 4 are Linear pair or supplementary angles.

ang 1 + ang 4 = 180

120° + ang 4 = 180° (Putting the value of ang 1)

ang 4 = 180° - 120°

ang 4 = 60°

Answer:

\(\large\boxed{\textsf{Option D.}}\)

Step-by-step explanation:

\(\textsf{For this problem, we are asked to compare the areas between Kristin's and Ben's circle.}\)

\(\textsf{To start, we should know that the Radius plays an important role for the area.}\)

\(\Large\underline{\textsf{What is the Radius?}}\)

\(\textsf{The \underline{Radius} is a \underline{line segment} that starts at the \underline{center} of the circle, and ends at}\)

\(\textsf{a point on the \underline{circumference} of the circle. (\underline{Arc})}\)

\(\large\underline{\textsf{Area of a Circle:}}\)

\(\mathtt{Area = \pi (radius)^{2}}\)

\(\textsf{The Radius \underline{determines} what the area of the circle is.}\)

\(\textsf{Because Kristin's radius is 1/2 of Ben's radius, \underline{the area will be 1/2 of Bens}.}\)

\(\large\boxed{\textsf{Option D.}}\)

Answer:

x = 109/21

Step-by-step explanation:

Step 1: Write equation

3(2x + 54) - (27x - 3) = 56

Step 2: Solve for x

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Answer:

Thank yoooooooouuuuuuuuu :)

Answer:

Brittany needs another $3.7405.              

Step-by-step explanation:

Per pound Cost of turkey = $5.96 per pound

The amount Brittany buys the turkey = 2.55 pounds

Brittany's cost for turkey = 2.55 × $5.96 = $15.198

Per pound cost for cheese = $3.35 per pound

The amount Brittany buys the cheese = 3.7 pounds

Brittany's cost for cheese = 2.55 × $3.35 = $8.5425

So,

Brittany's total cost = Turkey cost + Cheese cost

                                = $15.198 + $8.5425

                                = $23.7405

As brittany gave the clerk 20 dollars.

So, the amount she further needs will be:

$23.7405 - $20 =  $3.7405

Therefore, Brittany needs another $3.7405.                                                                      

By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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Answer:

x=5

Step-by-step explanation:

add 5 to both sides

-20+5 = -3x

-15=-3x   (divide)

x=5

Answer:

5x+3

Step-by-step explanation:

1.  Subtract 1 from 4

4+5x-1

2. Solution

5x+3

The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

Answer:

it will be equal and keep it up you will make good grades

Step-by-step explanation:

The design of an experiment in the research to help determine if a set of presentations is simply to consider two groups depending on the gender.

It should be noted that a research simply means an enquiry that is done to achieve a particular information.

In this case, the design of an experiment in the research to help determine if a set of presentations is simply to consider two groups depending on the gender.

Also, the randomization procedure that would achieve this is the ANOVA.

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Answer:

D

Step-by-step explanation:

your domain is all ur X values while ur range is all y values. Just look at the points and determine the coordinates, all the X values belong to the domain and all y values belong to the range

hope this helps

Answer:

4y

Step-by-step explanation:

y - -3y

Subtracting a negative is like adding

y+3y

Combine like terms

4y

Answer:

\(4y\)

Step-by-step explanation:

\(y - ( - 3y) \\ y + 3y \\ = 4y\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

36960 people

Step-by-step explanation:

Answer:

36,960 people

Step-by-step explanation:

\(\frac{is}{of}=\frac{percent}{100}\) is the formula to solve for this equation, here plugging in all our numbers gives us \(\frac{x}{480,000} = \frac{77}{100}\).

We do not know our "is" so we replace it for x and solve → \(x=(480,000)(\frac{77}{100} )\) = 36,960 people

Answer:

C

Step-by-step explanation:

These triangles do look congruent. However, in fact, we don’t have enough information. We need 3 parts of a trainable to be shown congruent for it to be congruent, including HL congruence (because this requires a right angle). In the diagram, only 2 sides are shown to be congruent. This isn’t enough information to prove that the triangles are congruent. Therefore, it is C.

I hope this helps! :)

Answer:

\(\Large \boxed{\sf \bf \ \ 2(x-4)^3(x+2)^2 \ \ }\)

Step-by-step explanation:

Hello, please consider the following.

Construct a polynomial function with the following properties...

... fifth degree

It means that the polynomial can be written as below.

\(a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \ \text{ with }a_5\text{ different from 0}\\\\\text{ or } k(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5) \\\\ \text{ with k different from 0 and } (x_i)_{1\leqi\leq 5 } \text { are the roots.}\)

... 4 is a zero of multiplicity 3

We can write the polynomial as below.

\(k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)=k(x-4)^3(x-x_4)(x-x_5)\)

... −2 is the only other zero

Because this is the only other zero, we can deduce that -2 is a zero of multiplicity 2.

\(k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)\\\\=k(x-4)^3(x-(-2))(x-(-2))\\\\=k(x-4)^3(x+2)^2\)

... leading coefficient is 2.

Finally, it means that k = 2 and then the polynomial function is:

\(\large \boxed{2(x-4)^3(x+2)^2}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

true

Step-by-step explanation:

Answer:

\(2x^{2} - 11x - 11\)

Step-by-step explanation:

The solution is, the perimeter of the parking lot in terms of x is,

2 ( 2x² -11x -6 ) ft.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

here, we have,

from the given figure, we get,

the length of one side = (3x +12) ft

the length of one side = 5x ft

the length of one side = ( 6x - 14 ) ft

the length of one side = (4x+1) ft

the length of one side = ( x² -12x +10) ft

the length of one side = (x² +x -16) ft

now, we know that,

the perimeter = the sum of lengths of out side

so, we get,

perimeter = 2 ( x² -12x +10 + x² +x -16 )

                = 2 ( 2x² -11x -6 )

Hence, The solution is, the perimeter of the parking lot in terms of x is,

2 ( 2x² -11x -6 ) ft.

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Answer:

136 or 34

Step-by-step explanation:

not sure if its right because my math is bad

Answer:

place value of 3 in 783.97 is 3

Step-by-step explanation:

Answer:

Units

Step-by-step explanation:

The units start counting from 3 because after the point that is the 9 start counting tenth

Answer:

77.47°

75.96°

26.57°

Step-by-step explanation:

Given vertices of the triangle:

Find the vectors from A to B, B to C and A to C:

\(\begin{aligned}AB = B - A &=(x_B-x_A,y_B-y_A) \\&=(-3-(-2), 8-4)\\& = (-1, 4) \end{aligned}\)

\(\begin{aligned}BC=C-B &=(x_C-x_B,y_C-y_B)\\ &=(6-(-3),8-8)\\&=(9,0)\end{aligned}\)

\(\begin{aligned}AC = C - A &=(x_C-x_A,y_C-x_A)\\&= (6-(-2), 8-4) \\&= (8, 4)\end{aligned}\)

Use Pythagoras Theorem to calculate the magnitudes of the vectors:

\(|AB| = \sqrt{(-1)^2+4^2}=\sqrt{17}\)

\(|BC|=\sqrt{9^2+0^2}=9\)

\(|AC| = \sqrt{8^2+4^2}=4\sqrt{5}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}\)

Rearrange the dot product formula to make θ the subject:

\(\implies \theta=\cos^{-1}\left(\dfrac{a \cdot b}{|a||b|}\right)\)

Use the rearranged dot product formula to find the angles between two pairs of vectors.

\(\boxed{\begin{minipage}{4 cm}\underline{Dot Product}\\\\$\textbf{u} \cdot \textbf{v}=u_1v_1+u_2v_2$\\\\where:\\ \phantom{ww}$\bullet$ $\textbf{u}=\left\langle u_1,u_2 \right\rangle$ \\\phantom{ww}$\bullet$ $\textbf{v}= \left\langle v_1,v_2 \right\rangle$ \\ \end{minipage}}\)

Angle A

\(\implies A=\cos^{-1}\left(\dfrac{AB \cdot AC}{|AB||AC|}\right)\)

\(\implies A=\cos^{-1}\left(\dfrac{-1 \cdot 8+4 \cdot4}{\sqrt{17} \cdot 4 \sqrt{5}}\right)\)

\(\implies A=\cos^{-1}\left(\dfrac{8}{4 \sqrt{85}}\right)\)

\(\implies A=77.47^{\circ}\; \sf (2 \; d.p.)\)

Angle C

\(\implies C=\cos^{-1}\left(\dfrac{BC \cdot AC}{|BC||AC|}\right)\)

\(\implies C=\cos^{-1}\left(\dfrac{9 \cdot 8+0 \cdot4}{9 \cdot 4 \sqrt{5}}\right)\)

\(\implies C=\cos^{-1}\left(\dfrac{72}{36 \sqrt{5}}\right)\)

\(\implies C=26.57^{\circ}\; \sf (2 \; d.p.)\)

Interior angles of a triangle sum to 180°.

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-77.47^{\circ}-26.57^{\circ}\)

\(\implies B=75.96^{\circ}\)

Therefore, the interior angles of the triangle with the given vertices are: