How would three billion, nine hundred seventy-six thousand, twelve be written in standard form?

Answer:

Step-by-step explanation:

When the base of a logarithm is not specified, it is assumed that the base is 10. Therefore we have:

[tex]log_1_0(x^2-15)=log_1_0(2x)[/tex]

Intuitively you can see that if the two arguments inside of the logarithm equal each other, then both sides will be equal to each other. Therefore, you can say the following requirement:

[tex]x^2-15=2x[/tex]

Subtract 2x on both sides to get:

[tex]x^2-2x-15=0[/tex]

Use the quadratic formula to solve for 'x' to get:

[tex]x=(-b+\sqrt{b^2-4ac} )/2a[/tex]

[tex]x=(-b-\sqrt{b^2-4ac} )/2a[/tex]

Beginning with the first solution:

[tex]x=(-(-2)+\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]

[tex]x=2+\sqrt{4+60} )/2[/tex]

[tex]x=(2+\sqrt{64}) /2[/tex]

[tex]x=(2+8)/2[/tex]

[tex]x=5[/tex]

Second solution:

[tex]x=(-(-2)-\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]

[tex]x=(2-\sqrt{4+60} )/2[/tex]

[tex]x=(2-8)/2[/tex]

[tex]x=-6/2[/tex]

[tex]x=-3[/tex]

Since the 'x' value inside of the logarith is squared, the -3 is a valid solution. Ordinarily, the log function cannot take on negative values.

Answer:

y = 2x + 1

Step-by-step explanation:

You can see a pattern in the group of x's that the numbers go up by 1 Also in the y-set that the numbers go up by 2. So this pattern is linear, that means the "rule" you are looking for does not have exponents or square roots or any very complicated stuff. You can use a guess and check method. Say to yourself how can I get a 7 out, when I put a 3 in? "times by2 and plus 1" works.

3 times 2, and plus1

gives you 7.

Test it on the other numbers.

-1 times2, and plus1

2(-1)+1 = -1

2(0)+1 = 1

2(1)+1 = 3

2(2)+1 = 5

It works for all the numbers.

You can calculate it also, using any two pairs of (x,y) from the data set. Put y-y on top of a fraction and x-x on the bottom. You will get the slope and that is the 2 in the "rule"

(3,7) and (2,5) for example. 7-5 so put 2 on top and 3-2 so put 1 on the bottom. 2/1 is just 2. From the point (0,1) we know the y-intercept is 1. This also gives the equation y=2x+1.

If you are just starting to learn this, probably just guess and check a rule. The rule has to work for all the points.

Answer:

-x + 1

Step-by-step explanation:

f(x) = 2x + 3

g(x) = 3x + 2

we want to find (f-g)(x)

(f-g)(x) is the same as saying f(x) - g(x)

f(x) - g(x) = (2x + 3) - (3x + 2)

==> remove parenthesis and apply negative sign

f(x) - g(x) = 2x + 3 - 3x - 2

==> combine like terms

f(x) - g(x) = -x + 1

Put values

Answer:

3/4

Step-by-step explanation:

[tex]y = 6x - 2[/tex]

I believe this is correct

Answer:

D

Step-by-step explanation:

Consecutive integers are integers with the progression n, n+1, n+2 (EXAMPLE)

Since w, x, y are consecutive integers, that means w, w+1, w+2; x = w+1, y = w+2

By referring to D,

w + x + y = w + w+1 + w+2

= 3w + 3

Hence, D is true.

Answer:

D

Step-by-step explanation:

A is wrong because if w is -1, x is 0, and y is 1, then wy is negative.

B is wrong because if w is -1, x is 0, and y is 1, then -1 + 1 = 0, which is x.

C is wrong because if w is -1, x is 0, and y is 1, then w³ + 3 = -1 + 3 = 2, which is greater than w + x + y which is 0.

D is correct because w + x + y is always equal to 3w + 3. For example, if w is 1, x is 2, and y is 3, then w + x + y = 6. 3w + 3 = 3(1) + 3 = 6.

E is wrong because if w is 1, x is 2, and y is 3, then wx is 2 and xy is 6, which means xy is greater than wx.

I hope this helps and please mark me as brainliest!

Answer:

4.06.

Step-by-step explanation:

Where x = 1.01,  y = (1.01)^4 + 1 = 1.0406 + 1

= 2.0406

So the gradient between (1, 2) and (1.01, 2.0406)

= (2.0406 - 1)/(1.01 - 1)

= 4.06.

Answer:

3.38 cm^3

Step-by-step explanation:

volume of cylinder = pi r^2 h

    10.14 / pi  = r^2 h

volume of a cone =  1/3  pi r^2  h

     V  = 1/3 pi  (10.14/pi)   = 3.38

Answer:

can you add more context to the question it makes no sense with current given clues

Answer:

5

Step-by-step explanation:

54÷8 x 4 ÷2 means that your answer would be 12

Answer:

4.9 units

Step-by-step explanation:

Answer:

#1: 4) D

#2: 1) 34.89 = 3 × C

#3: 4) 6y + 18

Step-by-step explanation:

#1

Using the distributive property:

3 × 5z = 15z

3 × -3 = -9

The correct expression is 15z - 9. Hence, D is the right option.

#2

You need to find the cost of each box.

3 × C = 34.89

34.89 ÷ 3 = 11.63

3 × 11.63 = 34.89

Hence, 1) is the right option.

#3

Using the distributive property:

6 × y = 6y

6 × 3 = 18

The expression is 6y + 18. Hence, 4) is the right option.

hope this helps!! p.s. i really need brainliest :)

Answer:

1. #4, D

2. #1, 34.89 = 3 x c

3. #4, 6y + 18

Step-by-step explanation:

1. Which pair of expression are equivalent (=)?

A.

10c + 20 = 5(5c + 4) <== distribute

10c + 20 = 25c + 20

This pair is not equivalent

B.

3(4e -  2) = 7e - 5 <== distribute

12e - 6 = 7e - 5

This pair is not equivalent

C.

4(4h + 6) = 16 + 24 <== distribute

16h + 24 = 16 + 24

This pair is not equivalent (look carefully, it's missing an h)

D.

15z - 9 = 3(5z - 3) <== distribute

15 - 9 = 15z - 3

This pair is equivalent

Therefore, the correct answer is D

2. Mr. James bought 3 boxes of pencils for $34.89. Each box of pencils costs the same. Which equaiton can be used to find the cost, c, of each box?

We know that 3 boxes of pecils cost $34.89, and c represents the cost of one box. If c represents the cost of one box and there are 3 boxes, it would be 3c or 3 x c.

Looking at the answer choices, #1 is the only option that represents that.

Therefore, the correct answer is 1) 34.89 = 3 x c

3. Aidan wrote an expression 6(y + 3). Which expression is equivalent to the one Aidan wrote?

6(y + 3) <== distribute

6y + 18

Therefore, the answer is 4) 6y + 18

Hope this helps!

Answer:

58%

Step-by-step explanation:

vertical angles are always the same

Answer:

y = 1566.67x + 1716.67

is the actual answer..

The linear equation that can be used to approximate the data distribution is y = 1566.67x + 1716.67.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given two points on the line.

(0.5, 2500) and (3.5, 7200)

Slope intercept form of a linear equation is y = mx + c, where m is the slope and c is the y intercept.

Slope = (7200 - 2500) / (3.5 - 0.5)

          = 4700 / 3

          = 1566.67

So the equation is, y = 1566.67x + c

Substitute the point (0.5, 2500) to the equation.

2500 = (1566.67 × 0.5) + c

c = 1716.67

So the equation is, y = 1566.67x + 1716.67

Hence the required equation is y = 1566.67x + 1716.67.

Learn more about Linear Equations here :

https://brainly.com/question/29739212

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Answer: I think its D

Step-by-step explanation:

Using relations in a right triangle, it is found that it's area is of 302.2 units squared.

The relations in a right triangle are given as follows:

In this problem, we have that the opposite side to the angle of 25º is of x, while the adjacent side is of 36, hence:

[tex]\tan{25^\circ} = \frac{x}{36}[/tex]

[tex]x = 36\tan{25^\circ}[/tex]

x = 16.79.

It is given by half the multiplication of it's sides, hence:

A = 0.5 x 16.79 x 36 = 302.2 units squared.

More can be learned about relations in a right triangle at https://brainly.com/question/26396675

Answer:

D

Step-by-step explanation:

15/2= 7.5

square root of 64= 8

8  1/7= 8.14285...

Answer:

11

Step-by-step explanation:

11 is ur answer to the question.

I hope it helped yoy

Answer:

Step-by-step explanation:

Total surface area comprises one rectangular base and two pairs of diferent triangles.

Area of rectangle

Area of triangle

Substitute and find

Area of base rectangle

Area of rest triangles

Now

TSA

Answer:

$724.11

Step-by-step explanation:

This requires the use of the growth formula.

Growth Formula:

[tex]y = a*(1+r)^x[/tex]

y = total/answer

a = starting value

r = rate (1.25 = 25%)

x = the amount of time (years/months)

Equation:

[tex]y = 6200 * (1+0.028)^4[/tex]

Solving:

y = $6924.11

$6924.11 - $6200 =  total interest

$724.11

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$6200\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (6200)(0.028)(4)\implies I=694.4[/tex]

Answer:

I give answers I think their correct but as humans we make mistakes so there may be errors

Answer:

Round 55.99 to the nearest tenth is: 56.0

Answer:

-5, -1

-9, 3

5, -11

-8, 2

-18, 12

Step-by-step explanation:

Answer:

_8 2. c. bbx. hx xhdj audiovisual audible Suffolk erudition Ayrshire Ysidro rump sidi ecru his

Answer:

88 ft

Step-by-step explanation:

The perimeter of a shape is the sum of the lengths of all its sides.

Perimeter of rectangle

= 2(length +breadth)

= 2(18 +26)

= 2(44)

= 88 ft

The wedge is an illustration of arc lengths, and Tyler's ledge is larger than Priya's wedge

From the question, the arc length of Tyler's wedge is:

L = 12 cm

For Priya's wedge, we have the following highlights:

Radius = 9 cm

Angle = 60 degrees i.e. the angle when a circle is divided into 6 sectors

Priya's arc length is then calculated as:

[tex]L = \frac{\theta}{360} * 2\pi r[/tex]

This gives

[tex]L = \frac{60}{360} * 2 * 3.14 * 9[/tex]

Evaluate

L = 9.42

By comparing the arc lengths 9.42 and 12 cm, we have 12 cm > 9.42 cm

Hence, Tyler's ledge is larger than Priya's wedge

#SPJ1

Read more about arc lengths at:

https://brainly.com/question/15589041

Answer:

20

Step-by-step explanation:

Since it's a multiple of 5 between 18 and 30, possible answers are:

20 and 25
The GCF of 18, 36, and the number is 2, and 25 is not divisible by 2, leaving only 20.

I think answer is 4

Step-by-step explanation:

I think so the answer is 4 because the questoin is 2x <9 2 time x =the answer and 2 times 4 = 8 and it is smaller than 9 and if we will do the same with the other numbers it will be greter than 9

solution:

2 x < 9

x = 4

2 × 4 = 8

and it is smaller than 9

like this :

8 < 9

this is what I think other wise I am not sure thankyou

The fraction computed shows that the number of peanut butter sandwiches that can be made will be 14.

From the information given, it was stated that there are 2 1/3 cup of peanut butter and that they put 1/16 cup of peanut butter on each sandwich.

Therefore, the number of peanut butter sandwiches that can be made will be:

= 2 1/3 ÷ 1/6

= 7/3 × 6/1

= 14

In conclusion, the correct option is 14.

Learn more about fractions on:

https://brainly.com/question/78672

Answer: 297 in.^2

Step-by-step explanation:

Area of a triangle: b*h/2 ---> (9*12)/2=544 triangles--->4*54(area of triangle)= 216Area of square: b*h ----> 9*9 = 81Add area of all four triangles plus are of square-----> 216+81 = 297 in.^2