The art club in Northwestern middle school is selling candy bars as a fundraiser. each art club member....

The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to  [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex]  and it can be determined by using LCM and fraction.

[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]

If no denominator equals zero,

Which expression is equivalent to the given expression?

Expression;

[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]

If no denominator equals zero,

To determine the equivalent relation of the given equation following all the steps given below.

                   [tex]\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}[/tex]

                   [tex]\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}\\\\[/tex]

Hence, The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to  [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] .

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Answer:

heart

Step-by-step explanation:

Answer:

  heart

Step-by-step explanation:

The 36th shape will be the last shape in the 12th repeat of the sequence.

The 35th shape is next-to-last: heart.

Answer:

Figure a) 2

figure b) 4

figure c) 5

Step-by-step explanation:

Answer:

y= 0.75x + -0.50

A or B is what im guessing

Answer:

To prove: The equation x2+px−1=0 has real and distinct roots for all real values of p.

Consider x2+px−1=0

Discriminant D=p2−4(1)(−1)=p2+4

We know p2≥0 for all values of p

⇒p2+4≥0 (since 4>0)

Therefore D≥0

Hence the equation x2+px−1=0 has real and distinct roots for all real values of p

The total number of cars both the student and the teacher made is 49

let

total cars = x

cars made by student = s

cars made by teacher = t

Total = student + teacher

x = s + t

s = 2/7x

So,

x = 2/7x + t

x - 2/7x = t

t = (7x - 2x) / 7

t = 5/7x

Similarly,

s = t - 21

s = 5/7x - 21

equate both s equation

2/7x = 5/7x - 21

2/7x - 5/7x = -21

(2x - 5x) / 7 = -21

- 3/7x = -21

x = -21 ÷ -3/7

= -21 × - 7/3

= (-21 × -7) / 3

= 147/3

x = 49

Therefore, the total number of cars both the student and the teacher made is 49

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Answer:

Hopefully this explains o_O, also Merry Christmas!

Step-by-step explanation:

9 x 10^2 = 9 x 100 = 900

3 x 10^-2 = 3 x 1/100 = 0.03

Ratio of 900:0.03

The first one is 30000 bigger than the second

Answer:

Step-by-step explanation:

Given:

y1 = 5.2

y2 = 1

x1 = 0

x2 = -1.5

Solution:

m = ( y2 - y1 ) / ( x2 - x1 )

m = ( 1 - 5.2 ) / ( -1.5 - 0 )

m = -4.2 / -1.5

m = 2.8

then

y - y1 = m ( x - x1 )

y - 5.2 = 2.8 ( x - 0 )

y - 5.2 = 2.8x - 0

y = 2.8x + 5.2

Answer:

D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

697.19248074 is the answer

Answer:

fortnit 90s

Step-by-step explanation:

crank and c until u get too 90 height

Using the arrangements formula, it is found that there are 720 words that can be formed.

The number of possible arrangements of n elements is the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem:

[tex]T = 6 \times 5! = 6! = 720[/tex]

There are 720 words that can be formed.

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Answer:

The answer is C, y = 2/3x -2

Step-by-step explanation:

Use the rise over run strategy on linear functions such as this one

Answer:62

Step-by-step explanation:

2 times 5=10-5=5

8 times 7=56+7= 63-6=57+5=62!

No solution. hope this helps

Answer:

13 cm

Step-by-step explanation:

The scale of the drawing was 1 centimeter : 4 meters.

x cm : 52 m   Divide by 4

13 cm : 52 m

The cost of the 6 books if you buy the set is $11.75 less.

The given parameters:

The total cost of the 6 books when bought separately is calculated as follows;

Cost = 6 x $38.25

Cost = $229.5

The difference in price is calculated as follows;

= $241.25 - $229.5

= $11.75

Thus, the cost of the 6 books if you buy the set is $11.75 less.

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Step-by-step explanation:

(note: I'm only answering the ones I know vs giving you wrong answers for the others!)

1. ROS=Obtuse (larger then ninty degrees)

2. octagon has 8 angles (octo means eight, after all!)

3. If a figure has three sides, it is a triagle (not positive on this one)

4. symmetric property of congruence (this one's a simple search :p )

5. N/A (although I believe its angle BEC=124 degrees, as every other choice Is proven to be true)

6. congruent complements theorem (this is because we are given that 3 is a suppliment of 4. we are also given that 2=4. Based on this, then 1=3 is congruent based on 1 being suppliment of 2, 2=4, and 3 being a suppliment of 4)

7. N/A

8. N/A (the picture is too fuzzy for me to make any ideas)

I'm sorry I couldn't solve them all, but I hope this at least gets you somewhere! Have a great day!

Answer:

People who bought tickets = 100%

                                             = 8000

People who bought their tickets in person = (100%-60%-15%) × 8000

                                                                       = 2000

The number of tickets sold online is 4800, by phone is 1200, and in person is 2000.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that there were 8000 people at the festival. people bought their tickets online, by phone, or in person. based on a random sample of people at the festival, 60% bought their tickets online, and 15% bought their tickets by phone.

The number of the tickets will be calculated as below:-

Total tickets = 8000

Online tickets = 60% of 8000 = 8000 x 0.6 = 4800

By phone = 15% of 8000 = 8000 x 0.15 = 1200

In-person = 25% x 8000 = 0.25 x 89000 = 2000

Therefore, the number of tickets sold online is 4800, by phone is 1200, and in person is 2000.

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Answer:

  (a)  (2x +7), (x -4)

  (b)  (-7/2, 0), (4, 0)

Step-by-step explanation:

When looking for integer factors of a quadratic of the for ax² +bx +c = 0, it is useful to start by looking for factor pairs whose product is a·c and whose sum is b.

Here, that means you're examining the factors of 2·(-28) = -56, and looking for a pair that have a sum of -1. We can start by examining the ways that -56 can be factored:

  -56 = -56(1) = -28(2) = -14(4) = -8(7)

Sums of these factor pairs are -55, -26, -10, -1, so it is the last pair we're interested in.

At this point, you can rewrite the x-term using these factors and then factor the quadratic by pairs.

  2x² -8x +7x -28 = 0 . . . . . . . use -x = -8x+7x

  (2x² -8x) +(7x -28) = 0 . . . . group into pairs of terms

  2x(x -4) +7(x -4) = 0 . . . . . . factor each pair of terms

  (2x +7)(x -4) = 0 . . . . . . . . . the factored equation

The factors of this equation are (2x +7) and (x -4).

__

The x-intercepts are the values of x that make the factors zero.

  2x +7 = 0 . . . looking for x that makes the first factor zero

  2x = -7 . . . . . subtract 7

  x = -7/2 . . . . divide by the coefficient of x

__

  x -4 = 0 . . . . looking for x that makes the second factor zero

  x = 4 . . . . . . add 4

The x-intercepts are x = -7/2 and x = 4.

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\huge\bold\orange{QUESTIONS:}[/tex]

3. Given this quadratic equation, 2x²-x-28= 0.

(a) List the factors of this equation.

(b) Determine the x-intercepts

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\huge\bold\orange{ANSWER:}[/tex]

(a) (x-4) and (2x+7)

(b) x=4 and x=-7/2

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\huge\bold\orange{SOLUTION:}[/tex]

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

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a) Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

b) since  the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equation

In order to show if the given point corresponds to the given function, we will have to substitute the value of x into the function to see if we will have its corresponding y-value

For the point (-0.8, -0.6), substitute x = -0.8 into both functions as shown:

f(x)  = 2x + 1

f(-0.8) = 2(-0.8) + 1

f(-0.8) = -1.6  + 1

f(-0.8) = -0.6

Simiarly;

y = -3(-0.8)- 3

y = 2.4 - 3

y = -0.6

Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

For the point (1/3, 2), substitute x = 1/3 into both functions as shown:

x = (y+2)/2

x = (2+2)/2

x = 4/2

x = 2

Simiarly;

x + 2 = 3

x = 3-2

x = 1

Since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equations

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Answer:

Hypotenuse: 20√2

Acute Angle measurements: 45

Step-by-step explanation:

Note that the two leg sides are both 20 measurements, suggesting that it is an isosceles triangle.

By definition of a isosceles triangle, the angles will be 45-45-90, and the sides will follow the 1-1-√2 rule, in which the 1 stands for the legs, and the √2 stands for the hypotenuse.

Note that the leg side measures 20. Multiply:

20 * √2 = 20√2.

Hypotenuse: 20√2

Acute Angle measurements: 45

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Step-by-step explanation:

Answer:

24cm

Step-by-step explanation:

because 6 x 4 = 24 centimeters

Answer:

45

Step-by-step explanation:

I think so i dont know

Answer:

45

Step-by-step explanation:

Just do the regular number sequence (1-44) but add 1 since this specific sequence starts with 2.

Answer: i think you should label it with numbers first

maybe??

Step-by-step explanation:

Answer:

(6 + n) - 8

Hope this helps.

Pls mark brainliest. :D

Answer:x < 2

Step-by-step explanation: 6+x < 8

x < (8-6)

x < 2

As the distance from the lighthouse, LH, increases, the angle of elevation,

reduces.

Reasons:

The distance of point A from the light house = 968 feet

Angle of elevation from point A to the lighthouse = 7°

Angle of elevation from point B to the lighthouse = 3°

Required:

The distance from point A to point B.

Solution:

[tex]\displaystyle tan(\theta) = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle} = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{Horizontal \ from \ boat \ to \ the\ LH}}[/tex]

Which gives;

[tex]\displaystyle tan(7^{\circ}) = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{968 \ feet}}[/tex]

Height to the lighthouse = tan(7°) × 968 feet  ≈ 118.86 feet

From point B, we have;

[tex]\displaystyle tan(3^{\circ}) = \mathbf{ \frac{118.86 \ feet }{Horizontal \ distance \ from \ point \ B\ to \ LH}}[/tex]

Therefore;

[tex]\displaystyle Horizontal \ distance \ from \ boat \ to \ LH = \frac{118.86 \ feet }{tan(3^{\circ})} \approx \mathbf{2237.9 \, feet}[/tex]

Therefore;

Distance from A to B = D

D = Horizontal distance from B to LH - Horizontal distance from A to LH

Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet

The distance from point A to point B, D ≈ 1,269.9 feet

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Answer:

Step-by-step explanation: