Expand the expression.
log(7x3y)

There are 1680 digits 2, 0, 2, and 2 as a 4-digit consecutively ordered block with no other digits between them

To determine the number of whole numbers, the following must be true

Case 1: If the sequence starts from the first digit

So, we have:

[tex]Case\ 1 = 3 * 1 * 2 * 1 * 10 * 10[/tex]

[tex]Case\ 1 = 600[/tex]

Case 2: If the sequence starts from the second digit

So, we have:

[tex]Case\ 2 = 9 * 3 * 1 * 2 * 1 * 10[/tex]

[tex]Case\ 2 = 540[/tex]

Case 2: If the sequence starts from the third digit

So, we have:

[tex]Case\ 3 = 9 * 10 * 3 * 1 * 2 * 1[/tex]

[tex]Case\ 3 = 540[/tex]

The total number of whole numbers is:

[tex]Total = 600 + 540 + 540[/tex]

[tex]Total = 1680[/tex]

Hence, there are 1680 6-digit whole numbers that the digits

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Given:

[tex]cos(2x)=1-sin(x)[/tex]

Expanding using double angle formula,

[tex]1 - 2 \sin^{2} (x) = 1 - \sin(x) [/tex]

Rearranging into a single equation,

[tex]1 - 2 \sin^{2}(x) - 1 + \sin(x) = 0[/tex]

Combining like terms,

[tex] - 2 \sin^{2} (x) + \sin(x) = 0[/tex]

Now multiplying each term by -1,

[tex]2 \sin^{2} (x) - \sin(x) = 0[/tex]

Factor greatest common factors out,

[tex] \sin(x)(2 \sin(x) - 1) = 0[/tex]

Applying Zero property rule,

[tex] \sin(x) = 0 \: or \: 2 \sin(x) - 1 = 0[/tex]

• Solve the trignometric equation to find a particular solution,

[tex]x = 0 \: or \: x = π[/tex]

[tex] = > x = 2nπ \: or \: x = π + 2nπ[/tex]

• Find the union of the solution sets,

[tex]x = nπ[/tex]}

• Rearrange unknown terms to the left side,

[tex]2 \sin(x) = 1[/tex]

• Divide both sides of the equation by the coefficient of variable,

[tex] \sin(x) = \frac{1}{2} [/tex]

• Solve the trignometric equation to find a particular solution,

[tex]x = \frac{π}{6} \: or \: x = \frac{5π}{6} [/tex]

[tex] = > x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z[/tex]

}

☆ Now finding the union of both sets

[tex]x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z[/tex]

Hence, the answer is [tex]x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z[/tex]

Answer:

25%

Step-by-step explanation:

Let George's salary = $50,000 per year

If his salary dropped by 20%, then his salary would be 80% of his previous salary (as 100% - 20% = 80%).

Convert 80% to a decimal: 80% = 80/100 = 0.8

Therefore, 80% of 50000 = 0.8 x 50000 = $40,000

We wish to increase his salary back to the original amount of $50,000.

The difference between the two salaries is : 50000 - 40000 = 10000

Therefore, we need to calculate the percentage that $10,000 is of $40,000.

⇒ (10000 / 40000) x 100 = 25%

So George's salary needs to increase by 25% to get back to where it was before the salary drop.

Answer:

2.08 × 10^11

Step-by-step explanation:

Answer:

i think it is 300 miles,,,,.......

Answer:

The answer should be 236g.

Step-by-step explanation:

If we take the amount of flour used for the cake as 'x,' the flour used to make the scones would be (500-x)×2/3 as 2/3 of the remaining is used for the scones.

We know that 60g more flour is used for the cake.

So,

x-60=(500-x)×2/3

Cross multiply, and brng the 3 to the other side.

3(x-60)=(500-x)2

3x-180=1000-2x

Bring the x-terms to one side and the numbers to one side.

3x+2x=1000+180

5x=1180

Divide both sides by 5 to find x(the amount of flour used to make the cake)

Therefore,

x=236g

[tex]\begin{cases} -x+3y=9\\\\ y=\cfrac{2}{3}x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -x+3y=9\implies 3y=9+x\implies \underline{3y-9=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting ont the 2nd equation}}{y=\cfrac{2}{3}(\underline{3y-9})\implies 3y=2(3y-9)}\implies 3y=6y-18\implies 18+3y=6y \\\\\\ 18=3y\implies \cfrac{18}{3}=y\implies \boxed{6=y}[/tex]

Answer:

C

Step-by-step explanation:

Because 80% of 5,000=4,000 and if there is 5,000 then what is left?

1,000 because 4,000 to 5,000 is 1 more thousand

Also I need my tickets to the concert!

Answer:

y=8

Step-by-step explanation:

Hope this helps!!

Answer:

81

Step-by-step explanation:

9, 30, 93, 282, 849

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

Explanation:

The first term is 9 because of the notation [tex]a_1 = 9[/tex]

To get the second term, we use the recursive rule given to us which is

[tex]a_n = 3a_{n-1} + 3[/tex]

I recommend using parenthesis to separate things like this

[tex]a_n = 3(a_{n-1}) + 3[/tex]

If n = 2, then,

[tex]a_n = 3(a_{n-1}) + 3\\\\a_2 = 3(a_{2-1}) + 3\\\\a_2 = 3(a_{1}) + 3\\\\a_2 = 3(9) + 3\\\\a_2 = 27 + 3\\\\a_2 = 30[/tex]

The second term is 30.

You can use the same idea as above to find the third term, or you can use this slightly different approach

[tex]\text{third term} = 3*(\text{second term}) + 3\\\\\text{third term} = 3*(30) + 3\\\\\text{third term} = 90 + 3\\\\\text{third term} = 93[/tex]

To generate any new term, we first triple the previous term and then add on 3.

Answer:

Side BC and AD are the same lengths so a=21

Side BC = 14

Side AB = 37

Side CD = 37

Step-by-step explanation:

Hope this helps!

please mark as brainliest =D

Answer:

-52/7 or 7 3/7

Step-by-step explanation:

-5 is also -35/7

2 3/7 is also 17/7

-35/7-17/7 = -52/7

-52/7 = 7 3/7

Answer:

-7 3/7

Step-by-step explanation:

-5 -2 3/7

Factor out the negative sign

-(5 + 2 3/7)

Write as a sum

-(5 + 2 + 3/7)

Calculate

-(7 + 3/7)

Write as a mixed number

-7 3/7

Hope this helps :)

Answer:

a = 11c - 4

Step-by-step explanation:

7,18,29,40

constant difference = 11

now,

an = a+(n-1)d

or, an = 7+(n-1)11

or, an = 7 + 11n - 11

or, an = 11n - 4

Step-by-step explanation:

(-3,5) and (x,y)

Slope = (y - 5)/[x - (-3)] = (y - 5)/(x + 3)

(y - 5)/(x + 3) = -1/4

y - 5 = -1/4(x + 3)

y - 5 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 5

y = (-1/4)x + 17/4.

Answer:

Step-by-step explanation:

If it is on a regular dart board and the dart is thrown four times, the probability of hitting the centre would be slim (obviously) but to be more precise it would be 1/4 - if not none at all.

I know this isn't as specific but I hope it will help :)

Answer:

1440°

Step-by-step explanation:

(n - 2)180° - (10 - 2)180° = 8(180°) = 1440°

Answer:

1440 degrees

Step-by-step explanation:

formula for calculating sum of angles in a polygon is (n-2) 180 where n is 10 that's 10-2 which is 8 and 8 * 180 which is 1440

Answer:

3.5 Hours

Step-by-step explanation:

I do not know what measurement or timelapse you're looking for. But this should be the answer to it, no I don't have an explanation though.

The distance between the city and the house is 260 miles.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 = 15, for instance. There are different types of equations like linear, quadratic, cubic, etc.

t              d

1             195

2            130

2.5         97.5

The distance will be calculated by the equation of the line,

y = mx + c

m = ( 130 - 195 ) / ( 2 - 1 )

m = -65

y = -65x + c

195 = -65 + c

c = 260miles

Hence, the distance will be 260 miles.

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Answer: 2nd option

Step-by-step explanation:

Answer:

1.) 5 1/4

2.)1 1/2

Step-by-step explanation:

umm.....

Answer:

1)  5 2/8

2) 1 2/6

Step-by-step explanation:

1) 2 7/8 + 2 3/8

Write these fractions as improper fractions.

23/8 + 19/8

Add the fractions

42/8

Write the answer as a mixed number.

5 2/8

2) 3 1/4 -1 3/4

Write these fractions as improper fractions.

13/4 - 7/4

Subtract the fractions

6/4

Write these fractions as improper fractions.

1 2/6

Answer:

option C gives, x = 8

Step-by-step explanation:

A.

[tex]\frac{5}{2}x+\frac{7}{2}=\frac{3}{4}x+14[/tex]

[tex]\frac{5}{2} x-\frac{3}{4} x = 14-3.5[/tex]

[tex]\frac{10}{4} x-\frac{3}{4} x = 10.5[/tex]

[tex]\frac{7}{4} x = 10.5[/tex]

[tex]x=\frac{10.5*4}{7}[/tex]

[tex]x = 6[/tex]

B.

[tex]\frac{5}{4}x-9=\frac{3}{2}x-12[/tex]

[tex]\frac{5}{4}x-\frac{3}{2}x=-12+9[/tex]

[tex]\frac{5-6}{4} x = -3[/tex]

[tex]-x = 4(-3)[/tex]

[tex]x =12[/tex]

C.

[tex]\frac{5}{4}x-2=\frac{3}{2}x-4[/tex]

[tex]\frac{5}{4}x-\frac{3}{2}x=-4+2[/tex]

[tex]\frac{5}{4}x-\frac{6}{4}x=-2[/tex]

[tex]-x = (-2)*4[/tex]

[tex]x=8[/tex]

D.

[tex]\frac{5}{2} x-7 = \frac{3}{4}x+14[/tex]

[tex]\frac{5}{2} x-\frac{3}{4}x = +14+7[/tex]

[tex]\frac{10}{4} x-\frac{3}{4}x = +21[/tex]

[tex]\frac{7}{4} x=21[/tex]

[tex]x= \frac{21*4}{7}[/tex]

[tex]x = 12[/tex]

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

According to the diagram:

The area is:

Answer:

The slope is 3/1

Y-intercept is at 0,1

Step-by-step explanation:

Step-by-step explanation:

1. cd and dg

2. angle 2

3. angle gde

4. angle cdh

5. cde is st line

6.cdf = cdh+hdf = 42+117= 159

7. angle fde = 90-73=17

The term n is the initial amount that the television is to be sold.

We are told that the television in this case is to be sold at a discount piece. The implication of this is that there is something that has to be removed from the price of the television as it is sold.

We are told that what they are to remove from the price of the television is about $75  and that when this is done, the price of the television would be about $300. Thus n is the original price of the television.

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The variable n represents the initial value of the television

From the question, we have the following parameters that can be used in our computation:

Amount off = $75

New price = $300

When represented as the equation, we have

n - 75 = 300

Add 75 to both sides of the equation

So, we have the following representation

n = 375

This means that the initial price of the television is $375

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The equation illustrates that the number of students that Branch B have will be 2100.

From the question, the number of students taking classes at RSM Branch A is 1.4 more than the number of students taking classes at RSM Branch B. If

Since Branch A has 1,650 students, the number of students that Branch B have will be:

= 1500(1.4)

= 2100

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Answer:

g(x) = 3^x -7

Step-by-step explanation:

In an exponential function like this, the constant at the end of the function represents the vertical shift. This means that the original function is shifted 2 units up. So, 9 units lower than +2 is -7. Thus, the new function, g(x), is g(x)=3^x - 7.
We can prove that g(x) is 9 units lower through y-intercepts. The function f(x) has a y-intercept of 3 and g(x) is -6. Since -6 is 9 lower than 3, we know that there is a 9 unit difference between the functions.

Given :-

To Do :-

Solution :-

Given equation to us is ,

→ y = 3x -1

As we know that , the slope intercept form of the line is ,

→ y = mx + c

where m is the slope and c is the y intercept .On comparing both , we have ,

So the graph will cut the y axis at (0,-1) . And will have a slope of 3 .

When y coordinate is 0 ,

So that ,

→ x - 0 / 0 -(-1) = 3

→ x/0+1 = 3

→ x/1 = 3

→ x = 3

Hence one other point is (3,0 ).

Now we may plot the graph using these two points (3,0) and (0,-1) .

For graph see attachment .

I hope this helps .