Part 1: Factorial!2. Explain the steps that you took to calculate it on your calculator.

Answer:

-26

Step-by-step explanation:

Q = -18

-18 - 8

-26

Hope this helps! :)

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

B: played by solo instrument with orchestral accompaniment.

The answer is Adjacent angles that form a linear pair are supplementary.

Answer:

-2, 6 or -2/6 is what im seeing i could be wrong though

Step-by-step explanation:

sub to imaginefn

The correct option C: y = (x + 2)(x -3)²(x - 1)² is function which correctly represents the given graph.

For the given graph;

Select one coordinate of the curve from the graph.

Point (0, 18); in which y is 18 for x = 0.

Now, go by option and put the value of x = 0 and find the correct value of y.

Option C:   y = (x + 2)(x -3)²(x - 1)²

Put x = 0

y = (0 + 2)(0 -3)²(0 - 1)²

y = (2)(-3)²(- 1)²

y = 18

We, get the correct coordinates (0, 18).

Thus, the correct option is C, which satisfies the given graph.

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Are the proof and the identity valid? if not, what is the invalid step in the proof

Step 1: x (9x+3) +3(x+3)=9x²+6x+9

Step 2: =(3x+3)²

Step 3: =(3(x+1))²

Step 4: =9(x+1)²



A) the proof is valid

B) step 2 is not valid

C) step 1 is not valid

D) step 3 is not valid​

Verify each step

step 1

x (9x+3) +3(x+3)

=9x^2+3x+3x+9

=9x^2+6x+9

step 1 is correct

step 2

Complete squares

9x^2+6x+9=0

Factor 9

9(x^2+6/9x)+9=0

9(x^2+2/3x)+9=0

9(x^2+2/3x+4/36-4/36)+9=0

9(x^2+2/3x+4/36)+9-1=0

9(x^2+2/3x+4/36)+8=0

9(x+2/6)^2=-8

therefore

Solution

For this case we can do the following:

And if we simplify we got:

Final answer would be:

-4x+7 /( 2(x-2))

GROUP THE LIKE TERMS FIRST.

[tex]9x - 3x = 7 + 9[/tex]

WHEN TERMS CROSS THE EQUAL SIGN THEY CHANGE SIGN.

[tex]6x = 16 \\ \frac{6x}{6} = \frac{16}{6} \\ x = \frac{16}{6} [/tex]

x can be simplified further

[tex]x = \frac{8}{3} [/tex]

HOPE THIS HELPS.

Answer:

The answer should be x=2.6

Step-by-step explanation:

9x-9=3x+7

-first you should move the numbers so you can get all your x values on one side and all your regular numbers on the other like this

9x-3x=7+9

-What i basically did was i passed the 3x from the right side to the left side of the equation, since in adding the 3x originaly, when i pass it to the left side itll be subtracting. then i passed my -9 to the right side of my equation, since i was subtracting originaly ill have to now switch it to adding

-after you do this you are going to want to want to combine like terms

6x=16

-then you are going to want to devide on both sides so you can get x alone

x=2.6

Answer:

x = 3500

Step-by-step explanation:

2580 + 2920 + x

------------------------ = 3000

           3

      5500 + x

------------------------ = 3000(3)

           3(3)

5500 + x = 9000

-5500         -5500

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

x = 3500

I hope this helps!

Given the area of a rhombus is 208 cm square and the perimeter of rhombus is 64 cm.

Recall that all the sides of the rhombus are equal.

Hence,

Area of rhombus is :

Hence the altitude of the Rhombus is 13 cm.

we know that

the total cans are 100

number of cans of root beer=24

number of cans of orange soda=12

number of cans of cola=16

therefore

the probability is equal to

P=(24+12+16)/100

P=52/100

P=0.52 or P=52%

as fraction is 52/100=26/50=13/25

The interest amounts on December 31st and April 30th are $100, $33, and $67. Also, the journal entries are mentioned below.

The Computation of the interest amount is shown below:-

Particulars           Total through     Through maturity   Through maturity

                             Maturity              Dec 31                            Apr 30

Principal               $4,000                 $4,000                     $4,000

Rate                          5%                       5%                               5%

Time                     180 ÷ 360            60 ÷ 360                  120 ÷ 360

Total interest         $100                    $33                             $67

2. The Journal entries are shown below:-

a. Notes receivable Dr, $4,000

        To accounts receivable $4,000

(Being issuance of notes is recorded)

b. Interest receivable Dr, $33

       To Interest revenue $33

(Being interest revenue is recorded)  

c. Cash Dr, $4,100

       To Notes receivable  $4,000

       To Interest revenue  $67

       To Interest receivable $33

(Being cash received is recorded)

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Given data:

The given graph.

The equation of the line when x is less than or equal to 1 is,

x+1

he equation of the linne when x is greater than 1 is,

-x+2.

Thus, the correct option is (c).

The unit rate for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound

What is unit rate and how to compute it?

Unit rate is the rate for 1 unit and to compute the unit rate we divide the total price by the total number of elements

We are given certain price we have to find there unit rate

a) $45 for 9 pound

Divide both sides by 9 to find the unit rate

we get $5 for 1 pound

a) $24 for 3 pound

Divide both sides by 3 to find the unit rate

we get $8 for 1 pound

a) $390 for 6 pound

Divide both sides by 6 to find the unit rate

we get $65 for 1 pound

a) $42 for 21 pound

Divide both sides by 21 to find the unit rate

we get $2 for 1 pound

a) $180 for 10 pound

Divide both sides by 10 to find the unit rate

we get $18 for 1 pound

a) $864 for 8 pound

Divide both sides by 8 to find the unit rate

we get $108 for 1 pound

Hence the unit rates are for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound

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The Solution:

Given:

We are asked to find the probability of selecting a black cat.

By formula,

Thus,

Therefore, the correct answer is 7/11

Given that

The vertices of a quadrilateral are A(-5, 7), B(6,-3), C(10, 2), and D(-1, 12).

So we have to find the type of quadrilateral ABCD.

Explanation -

First, we have to find the length of each side AB, BC, CD, and DA.

We will use the distance formula to find the length of each side

Now we will find the sides by substituting the value,

So we found that the opposite sides are equal. So it can be a parallelogram or a rectangle.

Now, we will check the triangular part ABC, by applying Pythagoras' theorem.

So it is a parallelogram. Then option D is correct.

Final answer -

Given data:

The given table is shown.

Draw the points on the graph paper as shown below.

The number of children's tickets sold is 13750.

Let the number of children be x and the number of adults be y.

The total number of attendance at the amusement park is 25,000.

So we have an equation

x + y = 25000 ......(i)

The cost for children is $15 and the cost for adults is $35, and the total money earned by the park is $600,000.

So we have another equation,

15x + 35y = 600,000

3x + 7y = 120,000 ......(ii)

Multiplying equation (i) with 3 we get

3x + 3y = 75000

3x + 7y = 120,000

Now subtract both the equation we have,

4y = 45000

y = 11250

Now put the value of y in equation (i) we get

x + 11250 = 25000

x = 13750

Where x is the number of children's tickets sold.

Therefore the number of children's tickets sold is 13750.

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We can conclude that Jeffry will reach his home in the time of 9 hours.

So, the time taken by Jeffrey to get home:

Now calculate time as follows:

Rounding off: 9 hours

Therefore, we can conclude that Jeffry will reach his home in the time of 9 hours.

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Answer:

D) 10

Step-by-step explanation:

2x - 2 < 8 + x

add 2 to both sides:

2x - 2 + 2 < 8 + x + 2

2x < 10 + x

subtract x from both sides:

2x - x < 10 + x - x

x < 10

Part A: The vertex, domain, and range of the function g(x) = |x-5|  is

( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).

Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y - coordinate of the vertex is shifted by 3 units.

In Part A:

The given function is;

g(x) = | x - 5 |.

Now, The x - coordinate of the vertex will be:

x - 5 = 0

x = 5

Therefore, the y- coordinate of the vertex will be:

y = g(x) = | x - 5 |

y = g(7) = | 5 - 5|

y = 0

So, The vertex of the absolute function is ( 5, 0 ).

Since, All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this case, the phrase is defined even if there is no real number.

Hence, In Interval Notation the domain is;

⇒ ( - ∞ , ∞ )

And, The set of all legitimate y values is the range.

Hence, In Interval Notation the range is:

⇒ [0, ∞ )

Now, In Part B:

Function h(x) = |x| + 3 is the transformed version of the parent function

f(x) = |x|.

For the parent function f(x) = |x|, the vertex is ( 0, 0).

Since, The range of an absolute function in the form c( | ax + b | ) + k is

f(x) ≥ k.

Therefore, The range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).

For the transformed function h(x) = |x| + 3.

The vertex of the function is ( 0, 3 ).

The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).

Hence, the y coordinate of the vertex is transformed by 3 from f (x) to h(x).

So, Part A: The vertex, domain, and range of the function g(x) = |x-7|  is  

( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).

Part B: The function f(x) = |x| is vertically shifted by 2 units to get the function h(x) = |x| + 3. The y coordinate of the vertex is shifted by 3 units.

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line 1 = y = 5/3 x - 6

Find the slope of the line by comaring it with y = mx+ b

m= 5/3

Line 2

Write the equation in the form y =mx +b and find the slope m

10x - 6y = 8

6y = 10x - 8

Divide through by 6

y = 10/6 x - 8/6

y = 5/3 x - 4/3

m= 5/3

Line 3

3y = 5x + 7

Also write in the form y =mx + b and find the slope m

y = 5/3 x + 7/3

m = 5/3

Line 1 and line 2 are parallel since they have the same slope

Line 1 and 3 are parallel (they have the same slope)

Line 2 and 3 are parallel, they have the same slope

The unit rate for calories per cup is 100 calories per cup.

There is 400 calories in 4 cup of cereal.

Given,

The amount of calories in 3/4 of the cup = 75 calories

That is,

Unit rate of calories = 75 / (3/4)

Unit rate of calories = 75 × (4/3)

Unit rate of calories = 25 × 4

Unit rate of calories = 100

There are 100 calories in a cup of cereals.

Now,

Calories in 4 cup = Calories in one cup × 4

Calories in 4 cup = 100 × 4

Calories in 4 cup = 400

So,

There are 400 calories in 4 cup of cereals.

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Answer:

Step-by-step explanation:

Given

To find the slope plug in the coordinates of the given point, x = 10 and y = 10 and solve for m:

The line is:

∠GJI ≅ ∠LKF is proved below.

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical. If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

Given Data

EF║GH

AB║CD

In given figure,

AB║CD,

While line segment GH is the transversal line.

So,

∠GJI ≅ ∠JLK (because it is corresponding angle) ..(1)

Also,

EF ║GH

Line segment DL  is the transversal line.

So,

∠JLK ≅ ∠LKF (because it is interior alternate angle)..(2)

From (1) and (2)

∠GJI ≅ ∠LKF

Hence, proved.

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Its a decreasing function, and the y-intercept is NOT on (0, -2).

The correct option is A

(A) As the value of x increases, the value of f(x) moves towards a constant

For the given system of equations 4x + 6y=24 and 2x + 3y=8, there is no solution exists.

For the given system of equation,

4x + 6y =24  ......eq 1

and 2x + 3y = 8 ..... eq2

use elimination method.

Multiply eq 2 with 2 and subtract from eq 1.

0 = 16

But 0 ≠ 16, the system of equation becomes untrue.

As, the values o f the variables x and y are getting cancelled. So, the there is no solution existed for the given system.

Also,the ratio of 4x/2x = 2 and 6y/3y = 2 is same thus, no solution is possible for the system.

Now, when the we triple each side of the first equation 4x+6y=24, we have 12x+18y=72.

The new system 12x+18y=72 and 2x+3y=8

Then, also 12x/2x = 6 and 18y/3y = 6 is also same. Then, also the system of equation does not have any solution of the system.

Thus, the system of equation does not have any solution.

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Answer:

B. The graph is incorrect and the line should go through the point (3, 13.5)

Step-by-step explanation:

The equation is y = 4.5x

y = the y-axis/dependent variable

x = the x-axis/independent variable

4.5 x 1 = 4.5

4.5 x 2 = 9

4.5 x 3 = 13.5

Therefore the written ordered pairs would look like this.

(1, 4.5)

(2, 9)

(3, 13.5)

In the graph, (3, 13.5) is graphed as (13.5, 3) making the graph incorrect.

The statement which is true about the graph shown is that: the graph is incorrect and the line should go through the point (3, 13.5).

Generally speaking, the graph of any linear function is always modeled by a straight line and it indicates a proportional relationship because it starts from the origin (0, 0).

Mathematically, a proportional relationship can be represented or modeled by the following linear equation:

y = kx

Where:

At data point (4.5, 4.5), we have:

y = 4.5x

y = 4.5(4.5)

y = 20.25 (incorrect).

At data point (3, 13.5), we have:

y = 4.5x

y = 4.5(3)

y = 13.35 (correct).

Therefore, we can logically deduce that this graph is incorrect because its line didn't pass through the data point (3, 13.5).

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