Simplify the following expression: 3x^3-2x^2+4-(3x^2+5x^2-2)

Answer:

20 so the fractions would be 3/4=15/20 and 9/10=18/20

Step-by-step explanation:

because 4 x 5 = 20 and 10 x 2 = 20

Answer:

LCD=20

Step-by-step explanation:

Step-by-step explanation:

Notice that KM = 0.5BC, KL = 0.5AC

and ML = 0.5AB. Therefore the perimeter of triangle KLM is half of the perimeter of triangle ABC. => 0.5 * 24cm = 12cm.

Each of the 3 purple triangles have perimeters which are 1/4 of the perimeter of triangle ABC. (Their vertices are midpoints of midpoints => 1/2 * 1/2)

Perimeter of 3 small purple triangles

= 3 * [24cm * (1/4)]

= 3 * 6cm = 18cm.

Hence Total perimeter of shaded parts

= 12cm + 18cm = 30cm.

Answer:

D

Step-by-step explanation:

It is D because the scuba diver was 35 m below the surface of the water at the start of the ascent. Meaning that the Y value is showing how deep the diver was in the water

Answer:

771.18

Step-by-step explanation:

The Amount given is  943

13% of amount will be =  943 x 13%

                         =

Decreasing 13% from 943 we get = 943-122.59

                        =820.41

Now the ammount = 820.41

for finding the final amount

find 6% of amount (820.41) we get =  820.41x 6%

                               =

Decreasing 6% from 820.41 we get final amount= 820.41- 49.23

                                   =771.18

so the final amount is 771.18

9514 1404 393

Answer:

  60 miles per hour

Step-by-step explanation:

Speed in miles per hour is found by dividing miles by hours:

  (120 mi)/(2 h) = (120/2) mi/h = 60 mi/h

Answer:

MP is approximately equal to ON because one side of a rectangle is always the same as another side of a rectangle.  

Step-by-step explanation:

Answer:

y=13.15x+14

Step-by-step explanation:

That is the equation, if you need the graph lmk

Answer:

?=14+13.15x

14+13.15x=?

?=13.15x+14

13.15x+14=?

Answer: Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

Step-by-step explanation:

When dividing fractions, the second term becomes the reciprocal.

Fractions are numbers which are of the form a/b where a and b are real numbers which implies that 'a' parts of a number 'b'.

Here, a is called the numerator and b is called the denominator.

Let a/b and c/d be the two fractions.

Division of these fractions will result as a/b ÷ c/d.

Now the second term c/d will change into d/c and the operation changed into multiplication.

a/b ÷ c/d = a/b × d/c

For example, let 1/2 and 3/4 are two fractions.

We have to divide 3/4 into 1/2 parts.

The actual operation is 3/4 ÷ 1/2.

But using the reciprocal and change in the operation, we will get it as,

3/4 ÷ 1/2 = 3/4 × 2/1 = 3/4 × 2

Dividing 3/4 into 1/2 parts is same as doubling 3/4.

Hence the second term will become reciprocal in the division of fractions.

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Answer:let the original number of boys be x

x:2x=1:2

x+2:2x+2=5:9

9x+18=10x+10

x=8

2x=16

Step-by-step explanation:

Answer:

(1)  4

Step-by-step explanation:

Isolate x.

[tex]\frac{x-2}{3}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{5}{6}[/tex]

[tex]\frac{x-2}{3}[/tex] = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex]

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

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

x - 2 = 2

x = 2 + 2

x = 4

Answer:

[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]

Step-by-step explanation:

Given

[tex](81x^4y^{16})^{\frac{1}{2}}[/tex]

Required

Determine an equivalent expression

Express 81 as [tex]9^2[/tex]

[tex](9^2x^4y^{16})^{\frac{1}{2}}[/tex]

Apply law of indices

[tex]9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}[/tex]

[tex]9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}[/tex]

[tex]9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}[/tex]

[tex]9^1 * x^2 * y^8[/tex]

[tex]9 * x^2 * y^8[/tex]

[tex]9 x^2 y^8[/tex]

Hence:

[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]

Answer:

The explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]

Option A is correct option.

Step-by-step explanation:

Third term of sequence is 18

Sixth term of sequence is 33

We need to find the explicit equation for the sequence.

The explicit sequence is [tex]a_n=a_1+(n-1)d[/tex]

We need to find a_1 the first term and common difference d

We have a₃=18

We can write it as: [tex]a_3=a_1+(3-1)d\\[/tex]

[tex]18=a_1+2d[/tex]

a₆=33

We can write it as: [tex]a_6=a_1+(6-1)d\\33=a_1+5d[/tex]

Now, solving these equation s we can find value of d

[tex]18=a_1+2d[/tex]

[tex]33=a_1+5d[/tex]

Subtract both equations

[tex]18=a_1+2d[/tex]

[tex]33=a_1+5d[/tex]

[tex]--------\\-15=-3d\\d=\frac{-15}{-3}\\d=5[/tex]

So, we get common difference d = 5

Now finding a_1

Put value of d in equation [tex]18=a_1+2d[/tex]

[tex]18=a_1+2(5)\\18=a_1+10\\a_1=18-10\\a_1=8[/tex]

So, we get a₁ = 12

Now, the explicit equation is:

[tex]a_n=a_1+(n-1)d\\a_n=8+(n-1)5\\a_n=8+5n-5\\a_n=5n+3[/tex]

So, the explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]

Option A is correct option.

Answer:

13.75

Step-by-step explanation:

6.25+7.50=13.75

Answer:

$11.05

Step-by-step explanation:

The hot dog is $3.55, and the cheeseburger is $7.50. Thus, adding them together, the whole total is $11.05.

Hope this helps

Answer:

-25

Step-by-step explanation:

When subtracting a negative from a negative, ignore the negative sign, ADD the 2 numbers, then add a negative sign to the sum.

Answer:

The probability is 63/1000 or 0.063

Step-by-step explanation:

Here, given that she takes 3 coins , we want to calculate the probability that the sum is £2.50

What we simply have to do here is to get the different ways to arrange £2.50 within 3 selections ONLY

we can only have this as;

taking 2 £1 coins and 1 50 pence coins

The probability of taking a £1 coin is 3/10

The probability of taking a 50 pence coin is 7/10

So the probability of 2 £1 coins and 1 50 pence coins will be;

3/10 * 3/10 * 7/10 = 63/1000

Answer:

multiply 0.05 by amount of grid cubes!

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer:

The number of

Dimes = d = 20 dimes

Quarters = q = 10 quarters

Step-by-step explanation:

Let us represent

The number of :

Dimes = d

Quarters = q

Note that:

A dime is worth 10 cents = 0.10d

A quarter is worth 25 cents = 0.25q

A Wonsan has 30 coins in her pocket, all of which are dimes and quarters .

d + q = 30...... Equation 1

d = 30 - q

If the total value of the coins is $4.50

0.10d + 0.25 q = 4.50.....Equation 2

We substitute 30 - q for d in Equation 2

0.10(30 - q) + 0.25q = 4.50

3 - 0.10q + 0.25q = 4.50

- 0.10q + 0.25q = 4.50 - 3

0.15q = 1.5

q = 1.5/0.15

q = 10 quarters

Solving for d

d = 30 - q

d = 30 - 10

d = 20 dimes

Therefore:

The number of

Dimes = d = 20 dimes

Quarters = q = 10 quarters

Answer:

wheres the rest

Step-by-step explanation:

Answer:

B) [3, 5]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, the line's y-values span from 3 to 5. Since both are closed dot, they are inclusive in the range:

[3, 5] or 3 ≤ y ≤ 5

Answer:

$5.60

Step-by-step explanation:

So each pound equals to $1.75 which means that we need to multiply by 3.2 because we're trying to find the number of money we'll spend on a certain amount of coffee. So if we multiply, we get 5.6. Though in context with the problem, it should be $5.60.

0.75x+3=15

16 chocolate bars

Answer:

a= 15 = 3+ .75c

b= 16 chocolate bars

Step-by-step explanation:

15 = 3 + .75c

c= chocolate bars

to solve for the number of chocolate bars:

subtract three for the snowcone he bought= 12=.75c

then just divide by .75 = 16 = c=16

Answer:

B. 18x3 + 6x2 + 14x - 72

Answer:

B

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

From analysis, it is seen that the probability of winning when playing regular defense is higher than the probability of winning with *prevent* defence.

We will assume that a total of 100 games were reviewed.

50 games used regular defense method.

The remaining 50 games used the prevent defense method.

Out of the 50 regular defense games, 38 were win while 12 games were lose.

Out of 50 prevent defense game, 29 were win, while 21 games were lose.

Thus, the Probability of winning by regular defense is:

P(win | regular) = 38/50

P(win | regular) = 0.76

Probability of winning by playing prevent defense is:

P(win | prevent) = 29/50 = 0.58

From the above analysis we observe that the probability of winning by using the regular defense method is greater than the probability of winning by prevent defense method.

That is 0.76 > 0.58.

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Given:

The equation of a circle is

[tex]10y+x^2=-18+5x-y^2[/tex]

To find:

The center and radius of the given equation by completing the square.

Solution:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]            ...(i)

where, (h,k) is center and r is radius of the circle.

We have,

[tex]10y+x^2=-18+5x-y^2[/tex]

It can be written as

[tex](x^2-5x)+(y^2+10y)=-18[/tex]

[tex]\left(x^2-5x+\left(\dfrac{5}{2}\right)^2\right)+\left(y^2+10y+\left(\dfrac{10}{2}\right)^2\right)=-18+\left(\dfrac{5}{2}\right)^2+\left(\dfrac{10}{2}\right)^2[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+\left(y^2+10y+5^2\right)=-18+\dfrac{25}{4}+5^2[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=-18+\dfrac{25}{4}+25[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{-72+25+100}{4}[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{53}{4}[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\left(\dfrac{\sqrt{53}}{2}\right)^2[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]h=\dfrac{5}{2},k=-5,r=\dfrac{\sqrt{53}}{2}[/tex]

Therefore, the center is [tex]\left(\dfrac{5}{2},-5\right)[/tex] and the radius is [tex]\dfrac{\sqrt{53}}{2}[/tex] units.

Answer:

Step-by-step explanation:

(a)Total number of candies = 120

The number of candies in the rows form AP sequence:

The first term is a=3 and common difference is d=2

Sum of n terms:

Substitute values and solve for n:

Correct choice is (ii) 10

(b) Formula for nth term:

Correct choice is (ii) 21

(c) Use same formula:

Correct choice is (i) 8

(d) Sum of candies in 15 rows

Correct choice is (iii) 255

(e) Number of candies in 12th row:

Correct choice is (iii) 25