Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.

W

a system can only be a function if there are no more than one value of y for each value of x. if a value of x is repeated twice or more in a table, it means it is not a function.

Answer:

300 dollars

Step-by-step explanation:

Note that:

{Peter's revenue on Monday: 150 dollars

Peter's revenue on Tuesday: 100 dollars

Peter's revenue on Wednesday: 50 dollars}

---------------------------------------------------------------

In this problem, we need to find how much is Peter's revenue so far (total).

We need to use addition to determine how much Peter's revenue is in total.

So, add 150, 100, and 50.

We get 150 + 100 + 50 = 300

Finally, Peter's revenue in total is 300 dollars.

Answer:

$300

Step-by-step explanation:

add 150+100+50

=300

A parallelogram is a type of quadrilateral that has opposite sides to be equal, and opposite angles to be equal.

Thus to complete the given proof in the question, the required statements and reasons are stated below:

             STATEMENT                                     REASONS

1. AB ≅ CD,                                                    Opposite sides of a

  BC ≅ AD                                                      parallelogram are equal

2. A, B, C, and D form a paralelogram         Given

3. Draw AC and BD                                       Drawing line segments

4. AB = CD,                                                    Equal line segments have

   BC = AD                                                     equal measures

5. ΔABC ≅ ΔCDA                                         SSS criterion for equal

   ΔABD ≅ ΔCDB                                         triangles

6. <BAD ≅ <DCB                                          Corresponding angles of equal

   <ABC ≅  <CDA                                         triangles are equal    

7. AC = AC, and BD = BD                             Reflective property of equality

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The rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].

Hence, the 3rd option is the right choice.

To rewrite any equation, in terms of the other variable, we just need to change the isolation of the variable by rearranging it.

In the question, we are given the equation for the total resistance [tex]R_T[/tex] for a circuit with two resistance R₁ and R₂ connected in parallel as:

[tex]R_T = \frac{R_1R_2}{R_1+R_2}[/tex]

We are asked to rewrite the equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁.

To rewrite the equation, we do as follows:

[tex]R_T = \frac{R_1R_2}{R_1+R_2}\\\Rightarrow R_T(R_1 + R_2) = R_1R_2\\\Rightarrow R_TR_1 + R_TR_2 = R_1R_2\\\Rightarrow R_1R_2 - R_TR_2 = R_TR_1\\\Rightarrow R_2(R_1-R_T) = R_TR_1\\\Rightarrow R_2 = \frac{R_TR_1}{R_1-R_T}[/tex]

Thus, the rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].

Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

Graph is in the attached image.

Question:

A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:

Draw normal curve to help - split into 8 section ( i can't draw it here)

a) 34.13% of cans will be between 480g and 486g.

b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.

Look at the Stand Dev Graph where the give you the number

Step-by-step explanation:

Let me give you a different question and i will answer it, which you help you answer your question.

Answer: -8

Step-by-step explanation:

When x = 5, f(x) = -8.

The value of the function f(5) = -8.

We have,

The concept used to find the value of f(5) is function evaluation.

In this case, we are given a function represented by a table with x and f(x) values.

To evaluate the function at a specific value, such as f(5), we look for the corresponding x-value in the table and determine the corresponding f(x) value.

In this example, we found that when x = 5, f(x) is -8 by looking at the table provided.

To find the value of f(5), we need to look at the table and find the corresponding value of the function when x = 5.

From the given table, when x = 5, f(x) is -8.

Therefore,

The value of the function f(5) = -8.

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The value of A has been illustrated, computed and proven based in the triangle given.

It should be noted that that a triangle is a shape that has three sides and the value of the addition of all the angles are equal to 180°.

Based on the information that's given, it should be noted that the value of angle A, angle B, and angle C will be equal to 180°.

In this case, the following can be deduced:

A = 5x

B = 90°

C = x + 10°

Therefore, A + B + C = 180° (sum of angles in a triangle)

5x + 90 + x + 10 = 180°

6x = 180° - 90° - 10°

6x = 80°

x = 80/6

x = 13 1/3

Therefore, the value of A will be:

= 5x

= 5 × 13 1/3

= 66 2/3

Therefore, A is 66 2/3.

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Answer:

4 and 1

Step-by-step explanation:

The explicit function that defines the sequence is 15/2 - 9n/2

The sequence is given as:

3, -3/2, -6, -21/2

The above sequence is an arithmetic sequence, with the following parameters

The explicit formula is then calculated as:

T(n) = a + (n -1) * d

This gives

T(n) = 3 +(n -1) * -9/2

Expand

T(n) = 3 + 9/2 - 9n/2

Evaluate

T(n) = 15/2 - 9n/2

Hence, the explicit function that defines the sequence is 15/2 - 9n/2

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The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.

Given a fair dice and tossing a fair coin sixteen times.

We have to find the probability that the total number  of heads in all the coin tosses equals 12.

The probability lies between 0 and 1.

Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.

Let X shows the sum of heads while tossing.

P(X=12)=?

We can find the probability using binomial theorem.

=[tex]16C_{12} (0.5)^{12} (0.5)^{2}[/tex]

We have to toss sixteen times and out of 16 times we need head 12 times.

=16!/12!4!*0.00024*0.0625

=1820*0.000015

=0.0273

Hence the probability that the total number of heads in all the coin tosses equals 12 is  0.0273.

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According to the order of operations, brackets are solved first which contains the division operation. Hence, 12 is divided by -6 first.  

Order of Operations

Given expression is,

(12 ÷ (-6))(3) + (-2)

According to the BODMAS rule of operations, the precedence order of operations is as follows,

Brackets > Of > Division > Multiplication > Addition > Subtraction

Hence, we will start by solving the brackets first, then solve the division and then the addition.

Evaluation

Solving the given expression as per the order of operations,

Brackets are solved first, then division followed by multiplication and then addition. Division is always of the highest precedence among all operations after brackets and of.

12 ÷ (-6)(3) + (-2)

= 12 ÷ (-6)(3) - 2   [∵ +(-n) = -n]

= (-2)(3) -2

= -6 - 2

= -8

Thus, solving the +(-2) and then division of 12 by (-6) are the first operations to be performed in order to evaluate the given expression.

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Answer:

1/36

Step-by-step explanation:

The probability for showing a three the first time is 1/6, and then again is another 1/6, multiply and you get 1/36

[tex]P(R \: then \: Y) = \frac{3}{10} \times \frac{1}{10} = \frac{3}{100} [/tex]

[tex]note \: that = \\ order \: matters \: (no \: factorial) \\ replacement \: (equal \: sample \: space)[/tex]

Answer:

c. 3/100

Step-by-step explanation:

there are 10 marbles

First draw (there are 3 red marbles)

[tex]P=\frac{3}{10}[/tex]

Second draw (there is one yellow marble)

[tex]P=\frac{1}{10}[/tex]

probability of the event:

[tex]P=(\frac{3}{10} )(\frac{1}{10} )=\frac{3}{100}[/tex]

Hope this helps

The function with the greatest rate of change over the interval [0, 2] is: D. a.

In Mathematics, the rate of change of a function over a given interval can be determined by calculating the slope of the straight line which connect its end points.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For line a, we have:

Points (x, y) = (0, 1) and (2, 4)

Slope = (4 - 1)/(2 - 0)

Slope = 3/2 or 1.5.

For line b, we have:

Points (x, y) = (0, 0) and (2, 2)

Slope = (2 - 0)/(2 - 0)

Slope = 2/2 or 1.0.

For line c, we have:

Points (x, y) = (0, -1) and (2, 0)

Slope = (0 + 1)/(2 - 0)

Slope = 1/2 or 0.5.

For line d, we have:

Points (x, y) = (0, 0.5) and (2, 2.5)

Slope = (2.5 - 0.5)/(2 - 0)

Slope = 2/2 or 1.

In conclusion, we can logically deduce that "function a" has the greatest rate of change over the interval [0, 2].

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Answer:

y = - [tex]\frac{1}{6}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 2 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then

y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, - 2 ) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line

Answer:

167

Hope this helps you out

Answer:

167

Step-by-step explanation:

Break it into steps.

2+2+5 = 9

69 + 9 = 78

78 + 89 = 167

Hope this helps.

The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.

A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).

The area of a rectangle = (length of rectangle)(width of rectangle).

Given the following parameters for the patio and the bench:

Area to be painted = area of rectangular patio - area of rectangular bench

Area of rectangular patio = (x + 20)(x + 10)

Area of rectangular bench = (6)(2) = 12

Area to be painted = (x + 20)(x + 10) - 12

The answer is: B. A = (x + 20)(x + 10) - 12.

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Answer:

you have a 50/50 chance to get equal number of heads & tails

Answer:

First, transform the given equation into the slope-intercept form, y = mx + b.

2x - 3y < 12

3y > 2x - 12

y > [tex]\frac{2}{3}[/tex]x - 4

Since the equation is y > [tex]\frac{2}{3}[/tex]x - 4, first draw the graph of y = [tex]\frac{2}{3}[/tex]x - 4 with a dotted line (because it is >, not ≥) and shade the area above the dotted line.

Using proportions, it is found that there are 5 cups of milk in each bowl of chocolate pudding.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The cafeteria used 10 quarts for 8 bowls, hence the number of quarts per bowl is:

10/8 = 1.25

Each quart has 4 cups, hence the number of cups is:

4 x 1.25 = 5 cups.

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The surface area of the composite figure shown in the figure attached is 233.6 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²

The surface area of the composite figure shown in the figure attached is 233.6 cm²

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Answer: Option (1)

Step-by-step explanation:

[tex]\angle DMA[/tex] is another name for angle 3, but not [tex]\angle DME[/tex].

The given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

In the question, we are asked for the ordered pair, which is the solution to the system of equations:

2x + 3y= 6 ... (i)

–3x + 5y = 10 ... (ii).

To solve for the solution to the system of equations, we use the elimination method.

We multiply (i) by 3, and (ii) by 2, and then add the resultant equations to eliminate x as follows:

 6x + 9y = 18 {(i) * 3}

-6x + 10y = 20 {(ii) * 2}

_____________

19y = 38,

or, y = 38/19 = 2.

Substituting, y = 2, in (i), we get:

2x + 3y = 6,

or, 2x + 3(2) = 6,

or, 2x + 6 = 6,

or, 2x = 6 - 6 = 0,

or, x = 0/2 = 0.

Thus, the given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

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The complete question is:

"Which ordered pair is a solution to the system of linear equations?

2x + 3y= 6

–3x + 5y = 10

(0,2)

(2,0)

(3,2)

(2,3)"

x<3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

(–10 + 8x) < 6x – 4

8x –6x < –4 + 10

2x < 6

x < 3

Answer:

[tex]0,35[/tex]

Step-by-step explanation:

In view of the fact that our events are independent of each other, we should multiply their probabilities: [tex]P(A \cap B) = P(A) * P(B) = 0,7 * 0,5 = 0,35[/tex].

Answer:

a ≈ 16.5 cm , b ≈ 23.8 cm

Step-by-step explanation:

using the Law of Sines in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

we require to calculate ∠ C

∠ C = 180° - (42 + 75)° = 180° - 117° = 63°

Then to find a

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )

[tex]\frac{a}{sin42}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )

a × sin63° = 22 × sin42° ( divide both sides by sin63° )

a = [tex]\frac{22sin42}{sin63}[/tex] ≈ 16.5 cm ( to the nearest tenth )

similarly to find b

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )

[tex]\frac{b}{sin75}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )

b × sin63° = 22 × sin75° ( divide both sides by sin63° )

b = [tex]\frac{22sin75}{sin63}[/tex] ≈ 23.8 cm ( to the nearest tenth )

Answer:

Step-by-step explanation:

    [tex]\sf \boxed{\bf\dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}=\dfrac{c}{Sin \ C}}[/tex]

Side 'a' faces ∠A.

Side 'b' faces ∠B.

Side 'c' faces ∠C.

We have to find ∠C using angle sum property of triangle.

  ∠C + 75 + 42 = 180

         ∠C +117   = 180

                  ∠C  = 180 - 117

                 ∠C = 63°

[tex]\sf \dfrac{a}{Sin \ 42}= \dfrac{22}{Sin \ 63}\\\\ \dfrac{a}{0.67}=\dfrac{22}{0.89}\\\\[/tex]

   [tex]\sf a = \dfrac{22}{0.89}*0.67\\\\ \boxed{a = 16.56 \ cm }[/tex]

                        [tex]\sf \dfrac{b}{Sin \ B} = \dfrac{c}{Sin \ C}\\\\ \dfrac{b}{Sin \ 75}=\dfrac{22}{Sin 63}\\\\ \dfrac{b}{0.97} =\dfrac{22}{0.89}\\\\[/tex]

                             [tex]\sf b = \dfrac{22}{0.89}*0.97\\\\ \boxed{b =23.98 \ cm }[/tex]

Using the concept of an one-to-one function, it will be one-to-one for c = 13.

A function is said to be one-to-one if each output is mapped to only one input.

In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.

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To start calculating the volume of the cone, we obtain the following data:

To calculate the volume of a cone, we apply the following formula:

[tex]\boldsymbol{\sf{V=\dfrac{\pi r^{2}h }{3} }}[/tex], where

We solve, substituting our data in the formula:

taking the square root

Multiplying

Dividing

Therefore the volume of the cone is 144 cm³.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{\pi \times r^2\times h}{3} = volume}}[/tex]

[tex]\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}[/tex]

[tex]\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}[/tex]

[tex]\huge\textbf{What are the labels in your equation?}[/tex]

[tex]\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}[/tex]

[tex]\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{3\times4\times4\times9}{3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{3\times16\times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{48\times9}{9}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432 \div 3}{3\div3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{144}{1}}}[/tex]

[tex]\large\boxed{\mathsf{= 144\div1}}[/tex]

[tex]\large\boxed{= \textsf{144}}[/tex]

[tex]\huge\textbf{What is the result to this question?}[/tex]

[tex]\huge\boxed{\frak{144\ cm^3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]