in a basketball game Tatiana May 23 baskets each of the baskets was worth either two or three points and Tatiana scored a total of 53 points let x represent the number of two-point baskets she made and why represent the number of three-point baskets she made.part a write a system of equations represent the situation.part b would you use graphing or substitution to solve the system and determine the number of 2.3 point baskets Tatiana made? explain.part c use the method you chose in part b to solve the system and find out how many two point and 3-point baskets Tatiana made.

The proof explained below shows that the triangles are congruent by the AAS congruence theorem.

The AAS congruence theorem states that two triangles can be proven to be congruent to each other if the two angles and a non-included side in one triangle is equal or congruent to two corresponding angles and a corresponding non-included sides in the other triangle.

This implies that, once the criteria needed prove that two triangles are congruent by the AAS congruence theorem are two pairs of congruent angles and a pair of non-included congruent sides.

Using the AAS congruence theorem, the two-column proof that shows each statement and the reason are explained below.

Statement                                   Reason                                        

1. CA bisects angle BAD          1. Given

angle B ≅ angle D                                  

2. Angle CAB ≅ angle CAD     2. Congruent angles formed from bisection

3. Side AC ≅ side CA               3. Reflexive property

4. Triangle ABC ≅ triangle ADC    4. AAS congruence theorem

Thus, the above reasons and statements shows that the two triangles, triangle ABC and triangle ADC, are congruent by the AAS congruence theorem.

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2(5 + X) - 1 = 3X + 9

Step 1: Expand the terms in the bracket

=> 2 x 5 + 2 x X - 1 = 3X + 9

=> 10 + 2X - 1 = 3X + 9

Step 2: collect like terms

=> 2X - 3X = -10 + 1 + 9

=> -X = 0

Answer: A square is a shape with four equal-length sides and four corners that are all right angles.

Hello!

Here are all three solutions to the given equation.

Exact Form:

[tex]w=\frac{21}{20}[/tex]

Decimal Form:

[tex]w=1.05[/tex]

Mixed Number Form:

[tex]w=1\frac{1}{20}[/tex]

Hope this helps!

The result of the algebraic expression is 5x - 2y - 10.

Algebraic Expression:

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

Given,

Here we have the expression 2+4x-12-2y+1x.

Here we have to solve this expression and we have also find simplified form of it.

In order to solve it,

First we have to write the given expression,

=> 2+4x-12-2y+1x

Now, we have to combine the like terms, then we get,

=> (4x + 1x) + (2 - 12) - 2y.

Now, we have to perform the appropriate operation on it,

Then it can be written as,

=> 5x + (-10) - 2y

Now we have to write the equation in the standard form, then we get the result as,

=> 5x - 2y - 10.

Therefore, the resulting standard form of the equation is 5x - 2y - 10.

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Equation:

A =1/2 * r * C

Replace with the values from the table and check the equation:

First row:

50 = 1/2*4*25

50= 50 TRUE

Second row:

78.5= 1/2*5*31.5

78.5= 78.75 FALSE

Since one equality is false, the equation Doesn't describe the relationship-

Answer : NO

The probability that exactly none will graduate is [tex]0.003375[/tex].

What is probability?

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes.

Step-by-step explanation:

Let [tex]X[/tex] be the random variable for the number of students who graduate.

Binomial distribution theorem tells that, [tex]P(X=x)=C(n , x)p^xq^{n-x}[/tex].

Here [tex]p=[/tex]probability of success on a single trial, [tex]q=[/tex]probability of failure on a single trial, [tex]n=[/tex] number of trials.

Given that [tex]p=0.85, q=1-p=1-0.85=0.15[/tex] and [tex]n=3.[/tex]

[tex]P(X=x)=C(3 , x)0.85^x0.15^{3-x}[/tex]

When [tex]3[/tex] students are randomly selected the probability that exactly none will graduate is given by,

[tex]P(X=0)=C(3 , 0)0.85^00.15^{3-0}[/tex]

[tex]P(X=0)=\frac{3!}{0!(3-0)!} 0.15^{3}[/tex]

[tex]P(X=0)=0.15^{3}[/tex]

[tex]P(X=0)=0.003375[/tex]

Hence the probability that exactly none will graduate is [tex]0.003375[/tex].

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Answer:

Part A:

Part B:

Step-by-step explanation:

Part A:

Remember that two parallel lines have the same slope. This way, we can conclude that the slope of this particular line is:

Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:

Therefore, we can conclude that the equation of this line is:

Part B:

Remember that the product between the slopes of two perpendicular lines is -1. This way, we'll have that:

Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:

Therefore, we can conclude that the equation of this line is:

The linear function will be;

⇒ y = - 4x + 5

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The functions are,

1. y = - 3x² + 2

2. y = 2x²

3. y = - 4x + 5

4. y = x³

Now,

Since, The linear function has a variable raised to the first power.

Clearly, In first equation;

The highest power of the variable is 2.

So, It is not a linear function.

Clearly, In second equation;

The highest power of the variable is 2

So, It is not a linear function.

Clearly, In third equation;

The highest power of the variable is 1.

So, It is a linear function.

Clearly, In fourth equation;

The highest power of the variable has power 3.

So, It is not a linear function.

Therefore, The linear function will be;

⇒ y = - 4x + 5

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Answer:

C. The volume is 1/8 the original volume

Explanation:

Step 1. To find how the volume changes if the diameter is reduced to one-half of the original size, we will test two scenarios:

• In the first scenario, the diameter will be 2, and in the second scenario, the diameter will be one-half of 2 which is 1.

We will find the volume for these two cases and see how it changes.

Step 2. For a diameter of d=2.

If the diameter is 2, the radius is:

Using the volume formula for a sphere:

In this case:

We will call this volume, V1:

Step 3. Now we will find the volume for the second case in which the diameter is d=1.

The radius is:

Using the same formula for the volume:

Solving the operations:

We will call this V2:

Step 4. As you can see, the first part of the previous expression is V1:

Therefore:

The second volume is the first volume multiplyed by 1/8 ⇒ it is 1/8 of the original volume.

Answer:

C. The volume is 1/8 the original volume

Answer:  Choice E

Explanation:

The given inequality means n is between -2 and 6. We exclude -2 itself, but include 6.

The set of integer values is -1, 0, 1, 2, ..., all the way up to 6.

The rate at which the area is increasing is 95cm/sec² .

Let us take the variable a to be the length of the rectangle and take the variable to b be the width of the rectangle.

We know that the area of the rectangle is given by A=a × b

Now differentiating with respect to t we get :

[tex]\frac{dA}{dt} = w\times\frac{da}{dt} +l\times\frac{db}{dt}[/tex]

Substituting the values we get that the rate of increase in the area is :

Rate of increase = (32 + 63) cm/sec² = 95 cm/sec²

A constant function is also regarded as linear in this sense because it is a polynomial of degree zero, or the zero polynomial.

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1. Bob's accounting profit is $25,000.

2. Bob's economic loss is $25,000.

3. The implicit cost in this example is the teacher's salary of $50,000 Bob could have got, working as a teacher.

Explicit cost refers to the accounting cost that a business incurs.

Explicit cost is different from implicit cost because implicit cost involves an opportunity cost.

Accounting profit is the difference between total revenue and explicit cost.

Economic profit is the difference between accounting profit and opportunity cost or the cost of forgone alternatives.

Salary as a teacher = $50,000

Explicit restaurant cost = $500,000

Revenue = $525,000

Accounting profit = $25,000 ($525,000 - $500,000)

Economic loss = -$25,000 ($525,000 - $500,000 - $50,000)

Thus, whereas Bob makes an accounting profit of $25,000, he actually incurs an economic loss of $25,000 by forgoing his teacher's salary.

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Answer:

16

Step-by-step explanation:

Two negatives make a positive:

18-7+5

Solve the problem left to right:

18-7=11

11+5=16

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height

V1=LWH= 32

Ex

2*4*4=32

Let's multiply all dimension by 2

4 * 8 * 8 =256

Answer:B. The volume is multiplied by 8.

Answer:

26 pens

Step-by-step explanation:

Let P and R be the numbers of Pens and Rulers Saj purchases.

The cost of P Pens and R Rulers:

Pens = P(20p)

Rulers = R(60p)

P(20p) + R(60p) = £10

P(0.20) + R(0.60) = 10

R = 8

P(0.20) + (8)*(0.60) = 10

P(0.20) + 4.8= 10

P(0.20) = 5.2

P = (5.2/0.20)

P = 26 pens

CHECK:

8 Rulers = 8*(60p) = 480p

26 Pens = 26*(20p) = 520p

Total = £10

We want to graph the line:

For doing so, we will choose two different x-values, and we will find its correspondent y-values. This gives us two different points, and when we trace the line that passes through those points, we will have the line we wanted.

In this exercise, we will choose x=0, and x=5.

For x = 0

This gives us the point (0,3).

For x = 5

This gives us the second point: (5,6).

Now, graphing the points on a cartesian plane, and drawing the line between them, we obtain:

when y = 17/4, x= 3/4

then assume y varies directly as x

then y =kx

k = y/x

k= 17/4× 4/3

k= 17/3

when x= 3/4, y = 27/34

A variation is a relation between a set of values of one component and a set of values of other component.

Direct variation is a type of variation in which two variables go line in line with their values

y= kx where k is the proportionality constant

k = 17/3 when y = 17/4 and x= 3/4

using thesame value of k in the expression k=y/x

and x = 3/4, then

y= 27/34

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The equation of the table in slope intercept form is y = - 5 / 2x - 1

Linear equation can be represented in various form, such as standard form, point slope form and slope intercept form.

But the equation of the table below will be represented in slope intercept form.

The equation in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, using (-4, 9)(-2, 4)

m = 4 - 9 / -2 + 4

m = - 5 / 2

Hence, let's find the y-intercept using (0, -1)

y = - 5 / 2x + b

-1  = - 5 / 2(0) + b

b = -1

Therefore, the equation is y = - 5 / 2x - 1

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Answer:

the mean is 12

Step-by-step explanation:

a mean is a set of numbers of two or more numbers

so becuase 12 repeats there, its your mean

Answer:

3.525/0.25=14.1

Step-by-step explanation:

Answer: 14.1

Step-by-step explanation:

3.525/0.25 = 14.1

Since "quotient" just means the result of two numbers being divided together. Therefore we would divide the two numbers you just gave.

The most appropriate choice for percentage will be given by -

Total salary of Marques in a week = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{x}{10}[/tex])

What is Percentage?

Suppose there is a number and that number has to be expressed as a fraction of 100. The fraction is called percentage. For example 2% means [tex]\frac{2}{100}[/tex]

Here,

Guarantee salary of Marques = $200

Sales made by Marques in a week= $750

Percentage commission on total sales = 10 %

Commission received by Marques = [tex]\frac{10}{100} \times 750\\[/tex]

                                                          = $75

Total salary of Marques in a week = $(750 + 75)

                                                         = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{10}{100}\times x[/tex])

                                                                                            = $([tex]750[/tex] + [tex]\frac{x}{10}[/tex])

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Given functions are

Then,

Thus,

Probability of proportion will be greater than 3.18

Probability of Proportion: Probability represents the chances of some event happening. It is theoretical. Proportion summarizes how frequently some event actually happened

Population Proportion, p=0.52

sample proportion p'=0.45

sample size be n =436

probability of proportion will be greater than 52%

[tex]p(p' > 0.45)=p(p'-p\sqrt{p(1-p)/n} )[/tex]

[tex]=-p(z > (0.45-0.52)/\sqrt{0.52((1-0.52)/436}[/tex]

=P(z>-3.18)

probability of proportion will be greater than 3.18

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The  IRS form is provided at the end of the year by employers, so employees can use it to file taxes is Form W-2.

Form W-2 can be described as the form that is been offered from the  Internal Revenue Service which can be considered as the (IRS) tax form .

It should be noted that this form is been used in the United States so that the wages that is been paid to employees  as well as their taxes can be reported. withheld from them

It should be noted that the form is been provided  when the year is coming to an end by employers.

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Answer:

30 units

Step-by-step explanation:

point D is the midpoint of the bottom line, and we can infer 2 similar triangles from the markings on the triangle,

15  × 2  =ab

as CD is in the middle of the large triangle, the scale factor from the small triangle to the large triangle is 2.

Answer:

Step-by-step explanation:

ABC

ADC

Answer:

1: figures a and b

2: figures a and b

3: figure a

Step-by-step explanation:

2 & 3:

all squares are rectangles, but not all rectangles are squares

Hope this helps!

Answer:

Step-by-step explanation:

if a word ends in a consonant plus "y" , we change "y" to "i" and add "es" to form the plural; "er" for comparative and "est" for superlative

noisiest and noisier

Answer:

Step-by-step explanation:

5