Which expressions are equivalent to the given equation. Logarithmic form

The total distance travelled is 1075.91 km.

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.

45 * (x +12)= 50* 1/5 + 1/2 *x

45x + 540= 10+ 0.5 x

44.5 x = 530

x= 11.91 (neglect the negative sign cause time can't be negative)

So, distance= 45* 23.91 = 1075.91 Km

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The journal entry on July 24 to record payment of the balance due is $2156

Discount period is the time period given by the supplier to the consumer for getting discount if the payment is made by the due date.

                                                                          Debit                          Credit

Accounts payable (2300-100 )                       2200

Cash (2200 - (2200* 2%))                                                                   2156

Purchase Discount / Merchandise Inventory                                     44

To record the payment of accounts within discount period

Amount Paid = 2300 - 200 -44 = 2156

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Answer:

18

Step-by-step explanation:

20*3=60 so do 6*3 to get your answer

Answer: 2

Step-by-step explanation:

When x = 3, y = -2.

When x = 6, y = 4.

The average rate of change over the interval is:

[tex]\frac{-2-4}{3-6}=\frac{-6}{-3}=\boxed{2}[/tex]

Answer:

Step-by-step explanation:

The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.

__

Let x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...

  0.15x +0.07(70000-x) = 9000

__

Simplifying the equation gives a 2-step linear equation.

  0.08x +4900 = 9000 . . . . simplified

  0.08x = 4100 . . . . . . . . . . subtract 4900

  x = 51,250 . . . . . . . . . . . .divide by 0.08

  70000 -x = 18,750

The woman should invest $51,250 at 15% and $18,750 at 7%.

Answer: C

Step-by-step explanation:

just took it

The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.

Given that, the surface area of a cone is 250 square centimetres. The height of the cone is double the length of its radius.

We need to find what is the height of the cone to the nearest centimetre.

The area occupied by the surface/boundary of a cone is known as the surface area of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as a curved surface area.

If the radius of the base of the cone is "r" and the slant height of the cone is "l", the surface area of a cone is given as total surface area, T = πr(r + l) square units

Now, let the radius of a cone be x.

Then the height of the cone is 2x.

Slant height=√x²+4x²

=√5x

So, the surface area of cone=πx(x+2.24x)

⇒250=3.14 × 3.24x²

⇒x²=24.57

⇒x=4.95≈5 centimetre

So, height=2x=10 centimetre

The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.

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We know immediately that the line must pass through (-4, 3).

Answer:

15 cm

Step-by-step explanation:

The length of the shorter pole can be found by forming and subsequently solving 2 equations.

Start by defining the variables that are going to be used in the working.

Let the original length of the shorter pole be a cm and that of the longer pole be b cm.

'Product' refers to the multiplication operation.

ab= 285 -----(1)

On the other hand, 'sum' refers to the addition operation.

Length of shorter pole after cutting= a -2

Length of longer pole after cutting= b -2

(a -2) +(b-2)= 30

a +b -4= 30

Adding 4 to both sides:

a +b= 30 +4

a +b= 34 -----(2)

From (2):

a= 34 -b -----(3)

Let's solve by substitution:

Substitute (3) into (1):

b(34 -b)= 285

Expand:

34b -b²= 285

b² -34b +285= 0

Factorise:

(b -15)(b -19)= 0

b -15= 0       or       b -19= 0

b= 15            or             b= 19

Substitute into (1):

a(15)= 285       or       a(19)= 285

a= 285 ÷15      or             a= 285 ÷19

a= 19                or             a= 15

Since a <b, a= 15 and b= 19.

Thus, the length of the shorter pole is 15 cm.

Answer:

=================

Let the initial price be x.

After the first sales quarter the price is reduced by 10% and became:

After the second sales quarter the price is reduced by 20% and became:

The decrease over the two quarters is:

This is equivalent of 28%, hence the correct answer choice is B.

Answer:

3 miles

2.73 miles=3 miles

Answer:

(-2, 0)

Step-by-step explanation:

The solution to the system is the point where the graphs intersect.

Answer:

The answer be the 2 one

Step-by-step explanation:

I do it and it come right

Answer:

d. 11:15

Step-by-step explanation:

1) officer1: distance 75 miles, velocity 60mil/h; officer2: distance 25 miles, velocity 55mil/h;

2) time, which is spent officer1 is: 75/60=1.25[h]=75 [min]. If the officer1 leaves his office at 10:00, the arrival time is 11:15;

3) time which is spent officer2 is: 25/55=5/11[h]≈27[min]. The arrival time is 10:27.

4) finally, the both officers are in the required location at 11:15.

Answer:

  see attached

Step-by-step explanation:

You recognize the equation of the line as being given in point-slope form:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y +3 = 2(x +3) . . . . . . given equation

This tells you the point is (h, k) = (-3, -3), and the slope is m = 2.

__

You can graph the equation by plotting the point (-3, -3) and drawing a line with a slope of 2. It will rise 2 units for each unit to the right.

Answer:

x = 5 and 6

Step-by-step explanation:

1. Square both sides
x - 5 = (x - 5)(x - 5)
2. Simplify the right side
x - 5 = x^2 - 10x + 25
3. Add 5 to both sides
x = x^2 - 10x + 30
4. Subtract x from both sides
0 = x^2 - 11x + 30
5. Factor
0 = (x-5)(x-6)
x = 5,6

Answer:

x = 5 , x = 6

Step-by-step explanation:

[tex]\sqrt{x-5}[/tex] = x - 5 ( square both sides )

x - 5 = (x - 5)² ← expand using FOIL

x - 5 = x² - 10x + 25 ← subtract x - 5 from both sides

0 = x² - 11x + 30 ← in standard form

0 = (x - 5)(x - 6) ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x - 6 = 0 ⇒ x = 6

As a check

substitute these values into the equation and if both sides are equal then these values are the solutions.

x = 5

left side = [tex]\sqrt{5-5}[/tex] = [tex]\sqrt{0}[/tex] = 0

right side = 5 - 5 = 0

then x = 5 is a solution

----------------------------------

x = 6

left side = [tex]\sqrt{6-5}[/tex] = [tex]\sqrt{1}[/tex] = 1

right side = 6 - 5 = 1

then x = 6 is a solution

Answer:

first 1*3+1-3*4+1

then it is in fraction

the answer is -5

If the number of multiple-choice questions is x and the number of short answer questions is y, then:

[tex]x+y=28\\\\3x+5y=100[/tex]

Answer:

y=-2x -1

Step-by-step explanation:

(y-y1) = m(x-x1)

y-(-11) = -2(x-5)

y+11 = -2x + 10

subtract 11 on both sides thus

y = -2x -1

Answer:

Decimal: 1.75

Percentage: 175%

Hey there!

1 3/4

= 1 * 4 + 3 / 4

= 4 + 3 / 4

= 7 / 4

= 7 ÷ 4

= 1.75

= 1.75 * 100

= 175%

Therefore, your answer should be:

• 1.75 (as your decimal form)
• 175% (as your percentage form)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

x = 2

y = 4

Step-by-step explanation:

Let's start with the 7 in the middle. Subtract the 1 on its upper left to get 6.

Add the 3 on its lower left to get 10.

so, 3 - x = 1. x = 2

17 - y = 13. y = 4

Answer: Each child gets 1/3

Step-by-step explanation: x/3

Answer:

[tex]=\frac{4y^2}{x^2}[/tex]

Step-by-step explanation:

[tex]\frac{(8x^2y^3)}{(2x^4y)}[/tex]

[tex]=\frac{(8x^2y^3)}{(2x^4y)}\\[/tex]

[tex]=\frac{8y^2}{2x^2}[/tex]

[tex]=\frac{4y^2}{x^2}[/tex]

I Hope This helps :)

This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.

Answer:

11 + x = 28

Step-by-step explanation:

The number of books they bought must add to 28.

The percentage change in G is 21 %

Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.

It is given that

G = ab

when a is increased by 10% the new a will be = 1.1 a

When b is increased by 10% the new b will be 1.1 b

So,

G' = 1.1a *1.1 b

G' = 1.21 ab

G' = 1.21

(G' - G)*100/G = (1.21-1)*100/1

The percentage change is 21 %

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Answer:

3/2

Step-by-step explanation:

comparing the straight line with ax + bx + c = 0,

we get a = 3 and b = -2

we know,

slope of line = -a/b

= -3/-2

= 3/2

Hope it helped

Answer:

[tex]\frac{187}{112}[/tex]

Step-by-step explanation:

Just add them all up in the calculator and divide by the number of numbers, which in this case is 4

Step-by-step explanation:

follow the steps in the attached

Data set two has the greater variability option (2) Data set two has the greater variability is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Two sets of scores have the same mean, but different standard deviations.

σ₁ and σ₂   (σ₂ > σ₁)

Coefficient of variation  = [SD/(mean)]×100

[tex]\rm CV = \dfrac{\sigma }{|x|}\times100[/tex]

σ₂ > σ₁

Divide by |x| on both sides

σ₂/|x| > σ₁/|x|

[tex]\rm \dfrac{\sigma }{|x_1|}\times100 > \dfrac{\sigma }{|x_2|}\times100[/tex]

(CV)₂ > (CV)₁

Thus, data set two has the greater variability option (2) Data set two has the greater variability is correct.

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Answer: (23, 46)

Step-by-step explanation:

The equation of the line is y = 2x, and we can thus represent point P as (x, 2x)

Substituting into the distance formula,

[tex]\sqrt{2645}=\sqrt{(x)^{2}+(2x)^{2}}\\\\2645=x^2 + (2x)^2\\\\2645=x^2 + 4x^2\\\\2645=5x^2\\\\529=x^2\\\\x=23[/tex]

Thus, the coordinates of P are (23, 46)