combining like terms -3(5x+4)-(2x+2)-3x+6

[tex]\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 5\log(x)+6\log(x+7)\implies \log(x^5)+\log\left[ \left( x+7 \right)^6 \right] \implies \log\left[ x^5\left( x+7 \right)^6 \right][/tex]

Answer: log(x^5(x+7)^6)

Hope that helps! (:

Answer:

7.5 inches.

Step-by-step explanation:

Angular velocity  (ω) in radians per minute

= 16* 2π    (as there are 2π radians in 1 revolution)

= 32π radians per minute.

= ω.

Linear velocity V =  ω r      where r = the radius of the circle.

Therefore:  240π = 32π r

r = 240 / 32

r = 7.5 inches.

Answer:

[tex]x=29[/tex]

Step-by-step explanation:

Given equation :

[tex]\frac{(7+2x)}{5} =13[/tex]

Making the terms of 'x' to one side and constants to the other.

                   [tex](7+2x)=13*5[/tex]

                       [tex]7+2x=65[/tex]

                            [tex]2x=65-7[/tex]

                              [tex]2x=58[/tex]

                                [tex]x=\frac{58}{2}[/tex]

                                  [tex]x=29[/tex]

So, the value of 'x' is 29.

Answer:

x = 29

Explanation:

7 + 2x / 5 = 13

Multiply both sides by 5

7 + 2x / 5 = 13 · (5) = (13) · (5)

7 + 2x = 65

Simplify both sides of the equation

2x + 7 = 65

Subtract 7 from both sides

2x + 7 − 7 = 65 − 7

2x = 58

Divide both sides by 2

2x / 2 = 58 / 2

x = 29

Answer:

2170 kg

Step-by-step explanation:

since there are 7 days in a week first you calculate the days

930 plus 930 equals 1860 which can feed a pair of elephants for 6 days

then since in one day it takes 310 kg then add 1860 plus 310

and then you get 2170

so, you need 2170 kg of food to feed a pair of elephants in a week

Answer:

x=15

Step-by-step explanation:

x+3=18

x+3-3=18-3

x+0=15

x=15

Answer:

the total mass is 456 grams.

Step-by-step explanation:

Answer:

The answer is b or d, but most likely d.

Answer:

B. 13,809 = 3,000+10,000+9+800

Step-by-step explanation:

13,809 = 10,000 + 3000 + 800 + 9

Answer: x= 178. Meaning that x can only equal 178, so that statement can be true. Any other number makes this statement false.

Step-by-step explanation:

Answer:

Lemme break it down for ya. Something plus seventy- two equal two hundred fifty. And if you want or need the answer, all you got to do is subtract 250 and 72. You're welcome. And please follow me.

The value of sin(a)cos(a) = 0.32

Step-by-step explanation:

Step 1: Given details are sin(a) - cos(a) = 0.6

Step 2: Square the given equation on both sides.

⇒ (sin(a) - cos(a))² = (0.6)²

⇒ sin²a + cos²a - 2 sin(a)cos(a) = 0.36

⇒ 1 - 2 sin(a)cos(a) = 0.36 since sin²a + cos²a=1

⇒ - 2 sin(a)cos(a) = - 0.64

⇒ 2 sin(a)cos(a) = 0.64

⇒ sin(a)cos(a) = 0.32

The solution is 2 and -7.

To find two numbers that multiply to -14 and add to -5, we can set up a system of equations based on the properties of multiplication and addition of numbers with different signs.

Let x and y be the two numbers we are looking for, with the following conditions:

x * y = -14 (Multiplication condition)

x + y = -5 (Addition condition)

Using the addition rules, we know that if we have two numbers with opposite signs, the sign of the larger (absolute value) number will dictate the sign of the result. Similarly, the multiplication rules tell us that two numbers with different signs will give a product with a negative sign.

Applying these principles, we can guess that one number is positive and the other negative since their product is -14. We also know that the number with the greater absolute value must be negative since their sum is -5. We can begin by listing pairs of factors of 14 (since the product is -14) keeping the sign in mind:

1 and -14

-1 and 14

2 and -7

-2 and 7

From this list, the pair that adds up to -5 is 2 and -7. Hence, the two numbers are 2 and -7.

They are not all squares because a rhombus has all sides of equal length, but NO right angles. A square is a rhombus WITH right angles.

Hope that clears things up.

Answer:

-2x - 10 = -2(x + 5)

Step-by-step explanation:

-2x - 10 is already simplified, but in order to understand the solution, we need to simplify -2(x + 5) in order to show that it is an equivalent expression:

-2(x + 5) = -2x - 2(5)

Further simplify:

-2x - 10

This proves that -2x - 10 = -2(x + 5) is an equivalent expression.

Answer: [tex]Percent\ change=37.5\%[/tex]  (It is an increase)

Step-by-step explanation:

You need to use the following formula to find the Percent change:

[tex]Percent\ change=\frac{V_2-V_1}{|V_1|}*100[/tex]

Where [tex]V_1[/tex]  is the Initial value and [tex]V_2[/tex] is the Final value.

According to the information given in the exercise, there were 800 visitors on Saturday and 1,100 visitors on Sunday. Then, you can identify that:

[tex]V_1=800\\\\V_2=1,100[/tex]

Then, knowing these values, you must substitute them into the formula:

[tex]Percent\ change=\frac{1,100-800}{|800|}*100[/tex]

Finally, you must evaluate in order to find the Percent change from the number of park visitors on Saturday to the number of park visitors on Sunday.

You get that this is:

[tex]Percent\ change=\frac{300}{|800|}*100\\\\Percent\ change=37.5\%[/tex]

Since it is positive, it is an increase.

Answer:

37.5 percent

Step-by-step explanation:

Final answer:

To find how much money Ethan gave to Dakota, we need to set up and solve an equation based on the given conditions, include the initial difference of $8, the 1/4 transfer of funds, and the resulting 5:2 ratio of their money.

Explanation:

Ethan had $8 more than Dakota. When he gave 1/4 of his money to Dakota, the ratio of Ethan's money to Dakota's became 5:2. To solve this, let's assume Dakota originally had D dollars and Ethan had D + 8 dollars. After giving away 1/4 of his money to Dakota, Ethan would have 3/4 of D + 8, and Dakota would have D plus 1/4 of D + 8.

The new ratio of Ethan's money to Dakota's money is 5/2, leading us to the equation 3/4(D + 8) / (D + 1/4(D + 8)) = 5/2. Solving this equation will not only give us the initial amounts of money each person had but also allow us to calculate the exact amount Ethan gave to Dakota, which is the 1/4 of Ethan's original money.

Answer:

The equation is [tex]y=-3x-5[/tex]

Step-by-step explanation:

We are given;

Assuming the question requires we determine the equation of a line perpendicular to the given line and passing through the point given.

Step 1: Determine the slope of the given line

To determine the slope from an equation requires we write the equation in the form, y = mx + c, where m will be the gradient.

In this case;

[tex]3y = x - 4\\ y = \frac{1}{3}x-\frac{4}{3}[/tex]

Therefore, the slope is [tex]\frac{1}{3}[/tex]

Step 3: Determine the slope of the line in question

We know that the product of the slope of two perpendicular line is -1

That is;

m₁ × m₂=-1

Thus;

1/3 × m₂ -1

Hence; m₂ = -3

Step 3: Determine the equation of the line in question;

We have its slope, m₂ = -3

A point (-2, 1)

Taking another point (x,y)

Thus;

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

Therefore, the required equation is [tex]y=-3x-5[/tex]

The equation of the line perpendicular to the line and passing through the point is y = -3x - 5

Given the equation 3y = x - 4

Find the slope of the line

y = 1/3 x - 4/3

The slope of the line is 1/3 and the slope of the line perpendicular is -3

Substitute the point (-2, 1) and the slope into equation

y - y1 = m(x-x1)

y - 1 = -3(x+2)
y - 1 = -3x - 6
y = -3x - 5

Hence the equation of the line perpendicular to the line and passing through the point is y = -3x - 5

Learn more on equation of a line here; https://brainly.com/question/13763238

Answer:

x=7

Step-by-step explanation:

3x + 2(4 + 6x)= 113

you multiply 2 to 4 that gives you 8 and 2 to 6 that gives you 12x because the 6 has x on it

so it will be 3x + 8 + 12x= 113 then you add 3x to 12x

then you would have 15x+8=113 then subtract 8 to 113 then divide that number to 15 and you get x=7

Final answer:

The expression 3 (4x-2) is not equivalent to 12x-2, as it simplifies to 12x-6, not 12x-2.

Explanation:

The expression 3 (4x-2) is not equivalent to 12x-2 because when we distribute the 3 across the terms inside the parenthesis of the first expression, we get 12x-6, not 12x-2.

To show this step-by-step:

Multiply 3 by 4x to get 12x.

Multiply 3 by -2 to get -6.

Combine these to get 12x-6.

As a result, 3 (4x-2) simplifies to 12x-6, and this is not equal to 12x-2 unless we are considering a special case where x equals to a value that makes -6 equal to -2, which generally isn't the case.

Answer: it’s D

Step-by-step explanation:

I completed it

The relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)}

does not represent the function.

An expression in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). For example -

f(x) = 4x + 6

Given are the set of ordered pairs as given in the question.

It can be clearly seen that the relation set -

{(9, 1), (6,2), (3, 3), (6,4), (9,5)}

does not represent the function as for x = 6, there are two possible values of [y] given, which is not possible.

Therefore, the relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)}

does not represent the function.

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Answer:

3/2 m / sec²

Step-by-step explanation:

acceleration = change in velocity / time

Here, that would be

acc'n = 15 m/s  /  10 s = 3/2 m / sec²

Answer:

4√10

Step-by-step explanation:

√(8) √(20)

= √(8 x 20)

= √(160)

= √(16 x 10)

= √(16) x √(10)

= 4 x √10

= 4√10

Answer:

4[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

[tex]\sqrt{8}[/tex] × [tex]\sqrt{20}[/tex]

= [tex]\sqrt{8(20)}[/tex]

= [tex]\sqrt{160}[/tex]

= [tex]\sqrt{16(10)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{10}[/tex]

= 4[tex]\sqrt{10}[/tex]

Answer:

The speed of the car is 42 mph.

Step-by-step explanation:

Speed = distance / time. 84 / 2 = 42

Answer:

x = (2/5); y = (-2/5)

Step-by-step explanation:

x + y = 0

13x + 8y = 2

Multiply so the "x" variables are opposite with the same absolute value.

(-13) x + y = 0 (-13) ⇒ -13x - 13y = 0

(1) 13x + 8y = 2 (1)  ⇒  13x + 8y = 2

Add the two equations.

(13x - 13x) + (8y - 13y) = (2 - 0)

-5y = 2

Divide both sides by -5

y = [tex]-\frac{2}{5}[/tex]

Plug the value of "y" into either equations.

x + [tex](-\frac{2}{5})[/tex] = 0

Add [tex]\frac{2}{5}[/tex] to both sides.

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

After adding his phone/internet/cable, electric bill, and health insurance premium costs, Chester spends $696 on bills each month. With monthly earnings of $2800, he therefore should have around $2104 left over after paying these bills.

To figure out how much money Chester will have left after paying his bills, you first have to add up all his bills. So, he pays on average $120 for his phone/internet/cable service, $277 for his electric bill, and $299 for his health insurance premium.

To add these together: 120 + 277 + 299 = $696. This is the total amount Chester pays for his bills each month.

Now, subtract this total from Chester's monthly earnings. So, Chester earns $2800 per month, and his bills total $696. So, 2800 - 696 = $2104. Therefore, Chester will have around $2104 left each month after paying these bills.

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Answer:

Step-by-step explanation:

first you find that it is t=Tracy and d= Daniel

so the equation is t= d-38*3 now find the answer

Daniel spent $16.

Let's denote the amount Daniel spent as x dollars.

According to the given information, Tracy spent $38 less than 3 times what Daniel spent. Therefore, Tracy's expenditure can be represented as [tex]\( 3x - 38 \)[/tex] dollars.

Given that Tracy spent $10, we can set up the equation:

[tex]\[ 3x - 38 = 10 \][/tex]

Now, let's solve for x:

[tex]\[ 3x = 10 + 38 \][/tex]

[tex]\[ 3x = 48 \][/tex]

[tex]\[ x = \frac{48}{3} \][/tex]

[tex]\[ x = 16 \][/tex]

So, Daniel spent $16.

The complete Question is given below:

While shopping for clothes, tracy spent $38 less than 3 times what daniel spent. write and solve an equation to find out how much daniel spent. let x represent how much daniel spnet. tracy spent 10$

[tex]13\frac{1}{6}-3\frac{4}{5}=(13*6+1)/6-(3*5+4)/5=79/6-19/5=(395-114)/30=\\ \\=281/30=9\frac{11}{30}[/tex]

Hey there! Since my last answer got reported and deleted because I messed it up, here is a second answer for you!

Answer:

Exact form : 281/30

Decimal form : 9.36 (please a line over the six to represent that the six is repeating itself. It will look like this...9.3666666666...)

Mixed Number form : 9 11/30

Step-by-step explanation: Convert the mixed number to improper fractions, then find the LCD (Least Common Denomintor) and then combine.

Hope this helps you out.

Answer:

length of the prism = 244 - (width x height) / width + height)

Step-by-step explanation:

Let length be a and width be b and height be c

2 (a * b) + 2 (b* c) + 2 (a * c) = 488

2ab+ 2bc + 2ac = 488

ab + bc + ac = 244

ab + ac = 244 - ac

a (b + c) = 244-ac

a = 244-bc / b + c

Therefore the length of the prism = 244 - (width x height) / width + height)

Answer:

teh answer is 14

Step-by-step explanation:

use teh equation for surface are

A=2(lw+hl+wh)

plug in the values

488=2(6*8+6*x+x*8)

to get x=14

which is the length

THIS IS CORRECT CAUSE I HAD TO DO IT FOR CLASS AND I GOT IT RIGHT BTW. :)

Answer:

plug -3 as x to find f(-3)

Step-by-step explanation:

Answer:

(cos a cos b - sin a sin b)

Step-by-step explanation:

It's easy

Answer:

  π

Step-by-step explanation:

The integral decomposes into the sum ...

  [tex]\displaystyle\int_{-2}^2{\left(x^3\cos{\dfrac{x}{2}}\right)\sqrt{4-x^2}}\, dx+\dfrac{1}{2}\int_{-2}^2{\sqrt{4-x^2}}\, dx[/tex]

The first term of this sum is the integral of an odd function, so is zero. The second term of this sum is 1/2 the area under a semicircle of radius 2, so is ...

  A = (1/2)(1/2)π·2² = π

The value of the integral is π.

Answer:

≈268.08 [tex]ft^{3}[/tex]

C. 267.9 [tex]ft^{3}[/tex]

Step-by-step explanation:

Equation of volume of a sphere:

Plug in radius (r) into the equation:

Solve using a calculator:

≈268.08 [tex]ft^{3}[/tex]