30233088 in index form

Answer:

[tex]m=\frac{-3}{2}[/tex]

Step-by-step explanation:

We can see certain points plotted which are  (-1, 2) (1,-1) and (3, -4)

We use the slope formula to find slope with any two points that were given

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

The explicit rule for the sequence is Tn = 2n - 1

Given the sequence 1, 3, 5, 7, 9...

The explicit formula for the nth term is expressed as:

[tex]T_n=a+(n-1)d[/tex]

a is the first term = 1

d is the common difference = 3 - 1 = 5 - 3 = 2

n is the number of terms

Substitute the given parameters into the formula to have;

[tex]T_n = 1+(n-1)(2)\\T_n=1+2n-2\\T_n=2n-1[/tex]

Hence the explicit rule for the sequence is Tn = 2n - 1

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Answer:

1st: 1+(k-1)2

2nd: 399

3rd: C

4th: 40,000

Answer:

The first, third, and fourth answers are correct!

Answer:

2 days

Step-by-step explanation:

12 - 4 = 8

8/3 = 2.7

9514 1404 393

Answer:

  B

Step-by-step explanation:

The associative property just moves parentheses, without changing the values or order of the operands. The only expression for which that is true is ...

  B.  (6·1/3)·7/5

Using the concept of arithmetic sequence, the 5000th term can be obtained using the relation 4 + (5000 - 1)9

For an arithmetic sequence, the nth term is calculated using the relation :

Here,

First term, a = 4

Common difference = 2nd term - 1st term = 13 - 4 = 9

nth term = 5000th term

The expression would be :

The required expression would be : T(5000) = 4 + (5000 - 1)9

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Answer:

3 : 1

Step-by-step explanation:

The values must be in the same quantity

1 Kg = 1000 g

4.5 Kg = 4.5 × 1000 = 4500 g

Then

4.5 Kg : 1500 g

= 4500 g : 1500 g ( divide both parts by 1500 )

= 3 : 1 ( in simplest form )

The simplified form of the ratio, 4.5 kg : 1,500 g is 3 : 1

A ratio is a measure of the number of times one quantity is contained in or contains another quantity.

To write the the ratio 4.5 kg : 1,500 g as a ratio in its simplest form, both quantities are to be expressed in the same unit.

1 kg = 1,000g

Therefore, 4.5 kg = 1,000 g/kg × 4.5 kg = 4,500 g

The ratio 4.5 kg : 1,500 g can be written as follows;

4,500 g : 1,500 g

The above ratio can be simplified by dividing both terms by the greatest common divisor, (GCD). The GCD of 4,500 and 1,500 is 1,500, therefore, we divide both terms by 1,500 to get;

4,500 g : 1,500 g = (4,500 ÷ 1,500) : (1,500 ÷ 1,500)  = 3 : 1

Therefore, the ratio 4.5 kg : 1,500 g simplifies to 3 : 1

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Answer:

absolute value is the same number just positive and cha never be negative.

Answer:

I think its 6/5 or 2/3

Step-by-step explanation:

Answer:

1. A

2. C

3. D

4. C

5. D

Step-by-step explanation:

You're welcome

The derivative of [tex]f(x) = 2\cdot x^{2}-9[/tex] is [tex]f'(x) = 4\cdot x[/tex].

In this exercise we must apply the definition of derivative, which is described below:

[tex]f'(x) = \lim_{x \to 0} a_n \frac{f(x+h)-f(x)}{h}[/tex] (1)

If we know that [tex]f(x) = 2\cdot x^{2}-9[/tex], then the derivative of the expression is:

[tex]f'(x) = \lim_{h \to 0} \frac{2\cdot (x+h)^{2}-9-2\cdot x^{2}+9}{h}[/tex]

[tex]f'(x) = 2\cdot \lim_{h \to 0} \frac{x^{2}+2\cdot h\cdot x + h^{2}-2\cdot x^{2}}{h}[/tex]

[tex]f'(x) = 2\cdot \lim_{h \to 0} 2\cdot x + h[/tex]

[tex]f'(x) = 4\cdot x[/tex]

The derivative of [tex]f(x) = 2\cdot x^{2}-9[/tex] is [tex]f'(x) = 4\cdot x[/tex].

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Answer:4 1/3

Step-by-step explanation:

Answer:

8/3, or 2 if you want a whole number

Step-by-step explanation:

Well, the simple answer is 2/(3/4). This is nothing but 2*4/3, which is just 8/3. (I used the theorem that states that dividing is the same as multiplying by the reciprocal)

One apple cost $1.8 while the money that Philip has is $24.90

Let x represent the cost of each apple and y represent the money he has presently.

He can buy 15 apples if he had $2.10 more money than he has now, hence:

15x = y + 2.1

15x - y = 2.1     (1)

Also, if he buys 12 apples, how would have $3.30 left of the money he has now. Hence:

12x + 3.3 = y

12x - y = -3.3   (2)

Solving equations 1 and 2 gives:

x = 1.8, y = 24.9

Hence one apple cost $1.8 while the money that Philip has is $24.90

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Answer:

No -5/2 is not greater than three.

Step-by-step explanation:

You could solve this without doing any math. You know that a negative divided by a positive is still a negative and that negative numbers are never greater than positive numbers so therefore you got the answer. No, -5/2 is not greater than positive 3.

Answer:

No

Step-by-step explanation:

[tex]-\frac{5}{2}[/tex] is not greater than 3; it is less than 3. Positives are greater than negatives. To know if an integer is negative, you should see something like this: - in front of the number.

Positive integers don't have a plus sign in front of it because we already assume it is there.

Answer:

After 7 seconds it hits the ground.

h= -16^2 + 80x + 224

(I'm assuming this is what you meant, because these problems are generally quadratic)

Use quadratic formula to find when it hits the ground (get zeros)

x = -2, x = 7

After 7 seconds it hits the ground.

Answer:

3.Top: |-80| + |50| = 80 + 50 = 130m

Bottom: same as top

Left: |50| + |-20| = 50 + 20 = 70m

Right: same as left

4.

130m+130m+70m+70m=400m

The perimeter is 400 meters

Answer:

Well the ineqaulity here would be

y/8 > 10

Or in simpler terms

y ÷ 8 > 10

If you were to solve

y > 80

Answer:

y=30

x=3

Step-by-step explanation:

~may it help you~

Answer:

8.x=7

7.x=12

Step-by-step explanation:

8.The two Base angles are equal

7. The exterior(outside) angle is equal to the sum of the two interior(inside) angles.

Answer:

4 mi²

Step-by-step explanation:

Area of Square: Length x Length

=> Area of Square: 2 x 2

=> Area of Square: 4 mi²

Therefore, the area of the square is 4 mi².

Hoped this helped

Answer:

4 mi²

Step-by-step explanation:

Area of Square: Length x Length

=> Area of Square: 2 x 2

=> Area of Square: 4 mi²

Therefore, the area of the square is 4 mi².

Answer:

0.83

Step-by-step explanation:

volume = length*height*width

1500=L*30*60

1500=1800L

1500/1800 = 0.83

length = 0.83

Answer:

[tex](2,1)[/tex]

Step-by-step explanation:

Let's first write down the first in traditional form:

[tex]\left \{3x-y=5} \atop {2x+y=5}} \right.[/tex]

At this point, let's choose the order we want to do it.

Eliminating x: Let's multiply the first by 2, the second by 3, and subtract one from the other. Rest is simple algebra

[tex]2I-3II: 6x-2y -6x-3y = 10-15\\-5y=-5 \rightarrow y=1[/tex]

Eliminating y: Let's simply add the two equations together. Rest is simple algebra

[tex]I+II:3x-y+2x+y = 10\\5x=10 \rightarrow x = 2[/tex]

The angle of depression is the angle formed with the horizontal, when an object is viewed below the horizontal level. Thus, the height of the cliff is approximately 123.86 m.

Let the height of the cliff be represented by h, so that:

From the triangle 1, we have:

tan [tex]32^{o}[/tex] = [tex]\frac{h}{x}[/tex]

⇒ h = tan [tex]32^{o}[/tex]*x

    h = x tan [tex]32^{o}[/tex] ............. 1

Also, from the bigger triangle, we have:

tan [tex]24^{o}[/tex] = [tex]\frac{h}{80 + x}[/tex]

⇒ h = tan [tex]24^{o}[/tex] (80 + x) .........  2

Now equating the expressions for h in equations 1 and 2, we have:

x tan [tex]32^{o}[/tex] = tan [tex]24^{o}[/tex] (80 + x)

0.6249x = 0.4452 (80 + x)

               = 35.616 + 0.4452x

0.6249x - 0.4452x = 35.616

0.1797 x = 35.616

x = [tex]\frac{35.616}{0.1797}[/tex]

x = 198.2 m

Substitute the value of x in equation 1;

h = x tan [tex]32^{o}[/tex]

  = 198.2 * 0.6249

 = 123.8552

h = 123.86 m

Therefore, the height of the cliff is approximately 123.86 m.

A sketch to this question is attached.

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Answer:

B

Step-by-step explanation:

He added 4 to 2 instead of multiplying.

Answer:

answer attached

Step-by-step explanation:

Answer:

B 13/2

Step-by-step explanation:

2x² + 7x - 15 = 0

First we want to find the two solutions

We can do this by using the quadratic formula

Quadratic formula:

[tex] \frac{- b + or - \sqrt{b {}^{2} - 4(a)(c)} }{2(a)} [/tex]

Where the values of a,b and c are derived from the equation.

The equation is put in ax² + bx + c = 0 form

2x² + 7x - 15 = 0

so a = 2, b = 7 and c = - 15

We now plug these values into the quadratic formula

(-(7) + or - √7² - 4(2)(-15) ) / 2(2)

first solution: -(7) + √7² - 4(2)(-15) ) / 2(2)

remove parenthesis on 7

(-7 + √7² - 4(2)(-15) ) /2(2)

Apply exponents 7²

(-7 + √49 - 4(2)(-15) ) /2(2)

Multiply -4,2 and -15

(-7 + √49 + 120 ) / 2(2)

add 49 and 120

(-7 + √ 169 ) / 2(2)

Take square root of 169

(-7 + 13 ) / 2(2)

add 13 and -7

6/2(2)

multiply 2 and 2

= 6/4

The first solution is 6/4 or 1.5

Now the second solution: -(7) - √7² - 4(2)(-15) ) / 2(2)

For the second solution we basically go through the same steps as for finding the first solution, the only difference is instead of adding -b and √b² - 4(a)(c) we are subtracting.

So we would have ( -7 - 13 ) / 2(2) instead of (-7+13)/2(2)

So second solution: ( -7 - 13 ) / 2(2)

subtract 13 from -7

-20/2(2)

multiply 2 and 2

-20/4

divide

The second solution is -5

Now that we have found the solutions we want to find r - s if r and s are the solutions to the equation and that r > s

The two solutions are 6/4 and -5.

6/4 > -5 so we know that r must equal 6/4 and s must equal -5 because r has to be greater than s

So if r = 6/4 and s = -5

Then r - s = 6/4 - (-5) = 6/4 + 5 = 13/2

So the answer is B. 13/2

Answer: 0= -32

Step-by-step explanation:

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