Which expressions are equivalent to -6n+(-12)+4n

Expand to get 35x^3+49x^2-20x-28

Answer:

3x(3x + 2)

Step-by-step explanation:

Answer:

Let 5 consecutive no's be x,x+1,x+2,x+3,x+4

90 = x+ x+1+x+2+ x+3+x+4

90 = 5x+10

18 = x+2

x= 16

so smallest is 16

greatest = 16+4 = 20

sum = 16 +20 = 36

Answer:

B.) transitive property of equality

Step-by-step explanation:

x = –3 and –3 = z, then x = z.

Symmetric property of equality: if a = b then b = a

Transitive property of equality:  if a = b and b = c, then a = c

Closure property of multiplication:  the set is closed under multiplication

Closure property of addition:  the set is closed under addition

Answer:

y=5x+17

Step-by-step explanation:

perpendicular slope is 5

y-7=5(x+2) convert this equation into slope intercept and that's your answer

[ Answer ]

Y = -9

[ Explanation ]

Subtract 15 from both sides:

2/3y + 15 - 15 = 9 - 15

Simplify:

2/3y = -6

Multiply each side by 3:

3 * 2/3y = 3 (-6)

Simplify:

2y = -18

Divide both sides by 2:

2y / 2 = -18/2

y = -9

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Using the simplification, it is proven that the y = -9 from the equation 2/3y + 15 = 9.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given that 2/3y + 15 = 9

Subtract 15 from both sides;

2/3y + 15 - 15 = 9 - 15

Now Simplify,

2/3y = -6

Multiply each side by 3,

3  (2/3y) = 3 (-6)

2y = -18

y = -9

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Answer:

Each pound of chocolate costs $7.30

Step-by-step explanation:

if 5 pounds of chocolate costs $36.50 then you could simply divide the $36.50 by 5 to calculate the cost of 1 pound of chocolate.

So, 36.50 ÷ 5 = 7.30

Each pound of chocolate costs $7.30

To find the cost of each pound of chocolate, you divide the total cost by the total number of pounds. Given a total cost of $36.50 for 5 pounds of chocolate, the resulting calculation is $36.50 ÷ 5 = $7.30. Thus, each pound costs $7.30.

If you have 5 pounds of chocolate that cost $36.50 in total, and you need to find the cost of each pound of chocolate, you can determine this by dividing the total cost by the number of pounds. This is similar to how in our reference material, to compute the cost of each piece of fruit, you divided the total expense by the quantity of fruit.

In this case, you need to divide the total cost, which is $36.50, by the quantity, which is 5 pounds. So the calculation is $36.50 ÷ 5 = $7.30. Therefore, each pound of chocolate costs $7.30.

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Answer: The price per pound is $18

Final answer:

Since ΔACD is an isosceles right triangle, the two legs AC and CD are equal. Given CD = 6 √ 3, AC is also 6 √ 3 units.

Explanation:

In triangle ΔABC, we are given that m∠ACB = 90°, meaning that ΔACB is a right-angled triangle. We are also given that CD is perpendicular to AB and that m∠ACD = 45°. Since CD is perpendicular to AB at D, triangle ΔACD is also a right-angled triangle with a 45° angle, which makes it an isosceles right triangle. In an isosceles right triangle, the lengths of the legs are equal. Therefore, AC will be equal to CD which is given as 6 √ 3.

The length of AC in triangle ΔACB can be found using Pythagoras' theorem, AC = √(AB² + BC²). But here we need only the length of AC in the right-angled ΔACD where AC equals CD.

Hence, AC = 6 √ 3 units.

The average acceleration of the car is 4 m/s²

The given parameters:

initial velocity of the car, u = 2 m/s

final velocity of the car, v = 16 m/s

time of motion of the car, t = 3.5 s

To find:

The average acceleration of the car is calculated as the change in velocity per change in time.

The formula for average acceleration is given below;

[tex]a = \frac{\Delta v}{\Delta t} = \frac{v- u}{t} = \frac{16 - 2}{3.5} = 4 \ m/s^2[/tex]

Thus, the average acceleration of the car is 4 m/s²

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Answer:

The domain is all real numbers. The range is {y|y ≤ 16}.

Step-by-step explanation:

The vertex of a parabola is given by

[tex](\frac{-b}{2a}, \frac{4ac-b^2}{4a})[/tex].

As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).

As a is negative, it opens downward, so the range is  {y|y ≤ 16}.

Meanwhile, all parabolic functions have a domain of [tex]\mathbb{R}[/tex].

Answer:

SEgment AC is congruent to segment AB

Step-by-step explanation:

given is a triangle ABC with a segment joining A to D on side BC.

To prove that ABD is congruent to ACD

Let us compare these two triangles.

AD = AD (reflexive) Thus one side is equal.

IF AB = AC, then by isosceles triangles property we have angle B = angle C

Thus we get two sides equal.  But this is a necessary condition not sufficient.

Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB

Thus if either AD is angle bisector, or D is mid point besides AC = AB we get

the two triangles are congruent.

Answer:

2.3 degrees.      

Step-by-step explanation:

Please find the attachment.

We are told that an airplane must clear a 60-foot pole at the end of a runway 500 yards long.

Let us convert 500 yards to feet.

1 yard= 3 feet.

500 yards= 3*500 feet= 1500 feet.

We can see from our attachment pole and runway are in form of a right triangle. The pole is opposite to angle of elevation of plane and length of runway is adjacent.

Since tangent represents the relation between opposite and adjacent of right triangle, So we will use tangent to find angle of elevation that plane must ascend to clear the pole.  

[tex]tan(\theta)=\frac{60}{1500}[/tex]    

[tex]\theta=\tan^{-1}(\frac{60}{1500} )[/tex]

[tex]\theta=\tan^{-1}(0.04)[/tex]

[tex]\theta=2.290610042639[/tex]

Therefore, the airplane must ascend 2.3 degrees to clear the pole.

Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer:

DAB must equal 52 because same side interior angles are supplementary. Supplementary describes 2 angles whose measures add up to 180

Answer: May or may not be

Step-by-step explanation:

check the picture and trust me

Answer:

True

Step-by-step explanation:

Each week the amount of radio active material is 100*(1/4)^x which is correct.

So at the end of 4 weeks she will have

amount = 100*(1/4)^x

amount = 100*(1/4)^4

amount = 100 * (1/256)

amount = 0.390625 grams after 4 weeks.

Answer:

Step-by-step explanation:

There is the answer.

Answer:

20%

Step-by-step explanation:

Percent increase is difference/original

360-300) / 300

60/300 / 60/60 = 1/5 * 20/20 = 20/100

Percent is out of 100

Answer:

A. The equation has no solution

Answer:

Step-by-step explanation:

3x + 5 = 19 - 4x     subtract 5 from both sides

3x = 14 - 4x      add 4x to both sides

7x = 14    divide both sides by 7

x = 2

Answer:

x=2

Step-by-step explanation:

3x + 5 = 19 - 4x

Add 4x to each side

3x + 5 +4x= 19 - 4x+4x

7x+5 = 19

Subtract 5 from each side

7x+5-5 =19-5

7x =14

Divide each side by 7

7x/7 = 14/7

x = 2

The complete statement is a division of long form ends with zeroes as remainders

We have the following statement -

A division of _____ ends?

The complete statement is -

A division of long division form ends with zeroes as remainders

Therefore, the complete statement is a division of long form ends with zeroes as remainders.

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PL= sqrt(4^2+12^2)=4sqrt(1+9)=4sqrt(10)

Using similarity gives that AM=4/3.

ML=40/3

[PLMU]=40/3 * 4 = 160/3 (53.33)

Or

PM= sqrt(4^2+16/9)=sqrt(160/9)=4sqrt(10)/3

4sqrt(10)*4sqrt(10)/3=160/3 or approximately 53.33

Answer:

y = 8

Step-by-step explanation:

If y varies directly as x we can write y = kx where k is some constant.

Y = 8 when x = 2 so  8 = k*2

k = 8/2 = 4

so y = 4x

This is the equation of variation.

When x = 6, y = 4*6 = 24  (answer).

Answer:

y =24

Step-by-step explanation:

The equation for direct variation is

y =kx

If we know x and y we can solve for k

y=kx

8 =k*2

Divide each side by 2

8/2 = k2/2

4 =k

y =4x

We want to find y when x=6

y =4*6

y =24

Answer: the answer is 23

Step-by-step explanation: since you are trying to find the number of boxes, b, the first thing you do is isolate it by dividing 4b by 4 this eliminates the 4, and because you did it on one side you have to do it on the other so you work would look like this 4b/4=92/4 you equation would look like this when done b=23

To find the number of boxes Mr. Reed bought, we solve the equation 4b = 92. This involves dividing 92 by 4 which results in 23 boxes of markers.

The subject of this question is Mathematics, particularly algebra. We need to solve the equation 4b = 92, where 'b' represents the number of boxes Mr.Reed bought.

Step 1: Write down the equation: 4b = 92.

Step 2: We solve for 'b' by dividing each side of the equation by 4. This gives us: b = 92/4.

Step 3: Doing the division, we find that 'b' is 23. Therefore, Mr. Reed purchased 23 boxes of markers with $92.

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It's not a rectangle. Look at the picture.

It is a parallelogram.

The area of the red rectangle:

[tex]A_{\boxed{ \ }}=(4+8)(6+3)=(12)(9)=108[/tex]

The areas of the right triangles:

[tex]A_1=\dfrac{1}{2}(3)(4)=6\\\\A_2=\dfrac{1}{2}(6)(8)=24[/tex]

The area of a parallelogram:

[tex]A=A_{\boxed{ \ }}-(2A_1+2A_2)\\\\A=108-(2\cdot6+2\cdot24)=108-(12+48)=108-60=48[/tex]

[tex](f-g)(x)=f(x)-g(x)\\\\\text{We have}\ f(x)=2x^2-5\ \text{and}\ g(x)=3x+3.\ \text{Substitute:}\\\\(f-g)(x)=(2x^2-5)-(3x+3)=2x^2-5-3x-3=2x^2-3x-8\\\\Answer:\ \boxed{(f-g)(x)=2x^2-3x-8}[/tex]

Answer:

The answer would be 998.4

Step-by-step explanation:

251,589 divided by 252 = 998.36

round it to 998.4

Answer:

Step-by-step explanation:

Please find attachment for step by step explanation.