Data collected on types of fruit is given below.R = Red Fruit. B = Berries Given that:r1 =49r2 =10r3 =5r4 = 8A) how many types of fruit are not red?B) how many types of fruit are berries?C) how many types of fruit are red berries D) how many types of fruit are not red and not berries

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

Solution:

Let A be the first aircraft

Let B be the second aircraft

Let C be the third aircraft

Here is the information that is given in the question:

The first aircraft has 65 more seats than the second aircraft:

A = B + 65

The third aircraft has 41 fewer seats than the second aircraft

C = B - 41

their total number of seats is 402

A + B + C = 402

Now substitute the values in the 1st and 2nd equations into the 3rd.

(B+65) + B + (B-41) = 402

this is equivalent to:

3B + (65-41) = 402

this is equivalent to:

3B + 24 = 402

this is equivalent to:

3B = 402 - 24 = 378

solving for B, we get:

We can conclude that the correct answer is:

first aircraft A:

A = B + 65 = 126 + 65 = 191

that is:

A = 191

second aircraft:

B = 126

third aircraft:

C = B - 41 = 126 - 41 = 85

that is:

C = 85

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!

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

B: played by solo instrument with orchestral accompaniment.

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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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

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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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:

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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The minimum number of friends for which Jump it Up is 7

A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).

Sky high pricing:

$50 for <=10 people and $5 per person after that

Jump it Up pricing:

Set up charges = $70

Per person charges = $2

Let p be the number of people

Formulating the equation we get:

50 + 5p = 70 + 2p

3p = 20

p = 6.66

or p =7

So, Jump it up will be less expensive for 7 friends

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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).

Answer:

-26

Step-by-step explanation:

Q = -18

-18 - 8

-26

Hope this helps! :)

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

∠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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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 Solution:

Given:

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

By formula,

Thus,

Therefore, the correct answer is 7/11

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:

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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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 -

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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Solution

For this case we can do the following:

And if we simplify we got:

Final answer would be:

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

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

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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The quotient in this division problem is 3,4.

What is division problem?
There are three main parts to a division problem that are -the dividend, the divisor, and the quotient. The dividend is the number that will be the  divided. The division is the number of (people )that the the  number is being divided by  among And The quotient is the answer.
a division is a process of a  splitting a specific of amount  into the equal parts.

Sol-
The formula is -
a/b=?
b×?=a
We can write a division statement as a multiplication statment
12/4=3
4×3=12
Thus
The quotients in this division problem are 3 and 4.

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