2. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate

Answer:

Ramon deposited $204 monthly

Step-by-step explanation:

Step 1: Firstly convert 2 years to month

1 year = 12 month

∴ 2 years = 24 month

Step 2: Divide $4896 by 24

➟ 4896 ÷ 24

➟ 204

Answer:

1)  -5x² + 13x + 6

2) B(x)  =(4x + 1 )(2x + 3)

  A(x) = (5x +2)(3-x)

Step-by-step explanation:

1) Expand the equation by using distributive property. Then simplify  by combining the like terms.

A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²

         = (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²

         = 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²

         = 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²

        = 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18

       = -5x² + 13x + 6

B(x) = (3x + 2)² - (x - 1)²

Identities:

(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2

(m -n)² = m² - 2mn + n² ; Here m = x & n = 1

2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]

      = 9x² + 12x + 4 - [x² - 2x + 1]

      = 9x² + 12x + 4 - x²+ 2x - 1

     = 9x² - x² + 12x + 2x  + 4 - 1

     = 8x² + 14x +3

Product = 8*3 = 24

Sum = 14

Factors = 2 , 12    {2*12 = 24 & 2 +12= 14}

    = 8x² + 2x + 12x + 3    {Rewrite the middle term}

    = 2x(4x + 1) + 3(4x + 1)      

   = (4x + 1 )(2x + 3)

  A(x) = - 5x² + 13x + 6

       = -5x² + 15x -2x + 6

       = 5x(-x +3) +2 (-x + 3)

       = (5x +2)(3-x)

4) B(x) - 3 = 8x² + 14x + 3 - 3

                = 8x² + 14x

                = 2x *4x + 2x *7

                =2x(4x + 7)

Hence proved.

                           B(x) = 3

            8x²  + 14x + 3 = 3

        8x² + 14x + 3 - 3 = 0

           8x² + 14x         = 0

              2x(4x + 7)     = 0

2x = 0   or    4x + 7 = 0

 x = 0   or          4x = -7

                            [tex]\sf x = \dfrac{-7}{4}[/tex]

  x = 0 or    [tex]\sf \dfrac{-7}{4}[/tex]

Answer:

250 minutes.

Step-by-step explanation:

1/5=50/x

cross product

5*50=1*x

250=x

4.92*10^5 times the annual flow of the Mississippi River fit in the Atlantic Ocean

Given that,

Volume of the Atlantic Ocean = 3.1*10^17cubicmetres

Annual flow of the Mississippi River = 6.3*10^11cubicmeters

Now, we have to find how many times the annual flow of the Mississippi River fit in the Atlantic Ocean

So,

= Volume of the Atlantic Ocean / Annual flow of the Mississippi River

= 3.1*10^17 / 6.3*10^11

= 0.4921*10^6 (Approximately)

=4.92*10^5

Therefore,

It takes 4.92*10^5 times for the Mississippi River to fit into the Atlantic Ocean.

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The mean is  79.5.

The standard deviation is 3.99

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(82 + 78 +  80 +  72 +  85 +  80) / 6 = 477 / 6 =  79.5

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group.

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation:79.50

Determine the difference between each value and the mean and then square the result: (82 - 79.5)² + (78 - 79.5)² + (80- 79.5)² + (72- 79.5) ²+ (85- 79.5)² + (80- 79.5)² = 6.25 + 2.25 + 0.25 + 56.25 + 30.25 + 0.25 = 95.5

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√95.5 / 6 = 3.99

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Answer: 20

Step-by-step explanation:

Everything within the parenthesis gets an exponent of two, so you should have (x^2+y^2).

After this, you plug in the 'x' and 'y' given, so the next part should look like (2^2+(-4)^2)

After step 2, do 2*2 and -4*-4 (exponents ask you to multiply numbers by a specific amount. In this case, both numbers are multiplied by themselves 2 times).

A negative times a negative is a positive, so -4^2 or -4*-4 is 16. 2^2 or 2*2 is simply 4.

Add 4 and 16 together to get your final answer of 20.

Hope this helps!

Answer:

81

Step-by-step explanation:

The Quadratic equation modeled is  [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex].

Quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are numbers and a cannot be 0.

the given equation Much easier to understand with the symbol              [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex]

[tex]3x^{2} -4x+1= 9x^{2} -6x+1\\6x^{2} -2x=0[/tex]

That is how I interpreted the "tile" set up.

Now count up the factors:  

These are (4 -x) and ( x +1) factor of  Quadratic equation.

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The total change in the stock market from the beginning based on the information will be 171 1/4 points.

It should be noted at the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day and at the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day.

Therefore, the total change in the stock market from the beginning will be the difference between the fractions that are given. This will be:

= 120 3/4 - (- 50 1/2)

= 120 3/4 + 50 1/2

= 171 1/4

Therefore, the total change in the stock market from the beginning based on the information will be 171 1/4 points.

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Step-by-step explanation:

here is the answer of each question respectively

Total number of boys in class are 172

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

We have total  number of students in class = 410

We assume that the number of boys in class = X

Number of girls in class is  66 more then boys we assume total number of girls = X+66

If we add number of girls and boys then we found total strength of classX+X+66=4102X+66=4102x=344X=172

Number of boys = 172

Number of girls =238

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The required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.

As given in the question Scarlett left her house at time zero and drove to the store, which is 3 blocks away, at a speed of 1 block per minute.
Then she stopped and went into the store for 4 minutes.
she drove in the identical at a rate of 5 blocks per minute until she got to the bank, which is 15 blocks away from the store.

Here,
1 Approach, Scarlett moves with the speed of a block per minute
Total distance travel = 3 block

Approach 2 Scarlett moves with the speed of 5 blocks per minute for 3 minutes
Total distance travel = 15 block
Approach 3 Scarlett moves with the speed of 3 blocks per minute for 1 minute
Total block traveled = 3 + 15 = 18

Now, Approach 3 is to retrace the path at the rate of 3 blocks per minute,
All these calculations is been shown in the block diagram.

Thus, the required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.

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10⁻² in expanded form is [tex]\frac{1}{100}[/tex] in fractional form or 0.01 is decimal form.

The number 10⁻² is written in scientific notation.

Mathematically 10⁻²= [tex]\frac{1}{10^2}[/tex]=1/100 =0.01

Hence the expanded form of 10⁻²  is 0.01 .

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Answer:

x = 67.5

Step-by-step explanation:

90 + x + 3x = 360            

90 + 4x = 360

4x = 360 - 90

4x = 270

x = 270 / 4

x = 67.5

Hope it helps!!!

Answer: 8.25 miles in 2 3/4 hours

Step-by-step explanation:

Step-by-step explanation:

here you go i don't know if this will be helpful or not

Answer:

If I know how to do math rn, your answer would be v= [tex]\frac{69} {9}[/tex]

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

Hope this helps!

Have a great day and God bless! :)

Answer:
Exact Form:

V = 62/9

Decimal Form:

V = 6.88888 (never-ending 8's)

Mixed Number Form:

V = 6  8/9

Hope this helps <33

The value of 'x' and 'y' is '1' and '3' , respectively.

The substitution method is the algebraic method to solve simultaneous linear equations.

The first step in the substitution method is to find the value of any one of the variables from one equation in terms of the other variable.

Lets solve the given linear equations:

7x − 2y = 1     ... eq. (1)

3x + 4y = 15  ... eq. (2)

By equation 1 we got,

x = (1 + 2y)/7

Now, we will put x = (1 + 2y)/7 in equation 2,

3x + 4y = 15

3 [(1 + 2y)/7] + 4y = 15

 3/7 × (1 + 2y) = 15 - 4y

        3(1 + 2y) = 7(15 - 4y)

           3 + 6y = 105 - 28y

       6y + 28y = 105 - 3

                34y = 102

                    y = 102/34

                     y = 3

Now, put the value y =3 in equation 1,

              7x - 2y    =  1  

           7x - (2×3)   =  1

                 7x - 6   =  1

                      7x   =  1 + 6 = 7

                      7x   =  7/7

                        x  =  1

Hence, the value of x is 1 and y is 3.

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If Malcolm answered 12 questions correctly on his social studies assignment and scored 75%, then the total number of questions on the assignment were 16.

The number of questions on the assignment can be determined by converting the given percentage.

A percentage is a numeral expressed as a fraction of 100

75% = 75 / 100 = 0.75

The equation can be formed as,

75 % of x = 12

Here x is equal to the total number of questions on the assignment

As 75% = 75 / 100 = 0.75

0.75 x = 12

x = 12 ÷ 0.75

x = 16

As x represented the total number of questions, hence the total number of questions on the assignment were calculated to be 16.

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Answer:

y=6x-1

y=3/5x+5

Step-by-step explanation:

6-0= 6= 3/5

5+5 =10

The length of the hypotenuse of the triangle is; AB = 2√106 ≈ 20.591

The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs. Thus;

For median AM, we have;

AM² = CM² +AC² = (BC/2)² +AC²

For median BN, we have;

BN² = CN² +BC² = (AC/2)² +BC²

The sum of these two equations gives us;

AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)

AM² +BN² = (5/4)(AB²)

Thus, we conclude that the length of the hypotenuse of triangle ABC is;

AB = √(4/5(AM² +BN²))

AB = 2√((19² +13²)/5)

AB = 2√106 ≈ 20.591

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Answer:

96 years

Step-by-step explanation:

let Jorge's age be x

then the quotient of his age and 3 is x divided by 3 , so

[tex]\frac{x}{3}[/tex] - 2 = 30 ( add 2 to both sides )

[tex]\frac{x}{3}[/tex] = 32 ( multiply both sides by 3 to clear the fraction )

x = 3 × 32 =96

Jorge is 96 years old

By the commutative property, the value of the expression 7 x 2 x 7 x 5 is 490

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

7 x 2 x 7 x 5

The above expressions are grouped by the product sign

This means that the factors of the expressions can be rearranged by the commutative property

So, we have

7 x 7 x 2 x 5

Group the factors

So, we have

(7 x 7) x (2 x 5)

Evaluate the products

So, we have

49 x 10

Evaluate the products

So, we have

490

Hence, the value of the expression 7 x 2 x 7 x 5 is 490

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Answer is 6.00+0.20-9.40

3.2

or

6.00-0.20-9.40

3.2

Answer:3.2

Step-by-step explanation:

Answer:

y=4x-2

Step-by-step explanation:

m=[tex]\frac{8}{2}[/tex]=4

2=4(1)+b    2=4+b      -2=b

As for the answer, the length of the three sides was x=4.

Let [tex]x[/tex] be the length of the two sides that are the same.

Then the third side would be 2x-3

The perimeter of the triangle will come from adding all of the sides together and setting it equal to the value given, 13.

That is,

x + x + (2x-3)=13

4x-3=13

4x=13+3

4x=16

x=4

The length of each of the common sides is 4, making the third side 5, to get a total perimeter of 13.

The hypotenuse of a right-angled triangle is its longest side, the base is its lower side, and the perpendicular, which stands next to the right angle, is its standing line.

You may determine the sides of a right-angled triangle using a number of techniques, such as the Pythagoras theorem or the triangle's perimeter.

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The solved polynomial is 66x² -304x+94.

We are given a problem related to the polynomial function,  where Polynomial functions are expressions that will contain factors of changing degrees, coefficients, positive types, and constants.

Since the given  equation (11x-47)(6x-2),  both the term are in the form of multiplication, so here we use the distribute rule,

we  multiply the 6x-2 individually  with  the 11x and 47

11x(6x-2) -47(6x-2 )= 66x² -22x -282x + 94

Now,  we have two common variables of coefficients -22 and -282, after adding both of them,  the final outcome  we get  is

= 66x²-304x +94

The solved function for the given equations is 66x2 -304x+94,

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Answer:

71.

Step-by-step explanation:

The "machine" is subtracting 6 from whatever number she puts in. Ergo, 77 - 6 = 71.

The dimension of the triangle whose perimeter is 18 feet will be 4 feet, 6 feet, and 10 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

Let 'x' be the first side of the triangle. Then the second and third sides of the triangle will be (x + 2) and (2 + x + 2). Then the equation is given as,

x + (x + 2) + (x + 2 + 2) = 18

3x + 6 = 18

3x = 12

x = 4

Then the dimension of the triangle will be given as,

x = 4

x + 2 = 4 + 2 = 6

x + 2 + 2 = 4 + 6 = 10

The dimension of the triangle whose perimeter is 18 feet will be 4 feet, 6 feet, and 10 feet.

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