Solve each equation for x.
4(x+4)+2x=52

Answer:Commutative property

Step-by-step explanation:

The relationship between a + b and b + a is the commutative property.

The information related to the commutative property is as follows:

Therefore we can conclude that the relationship between a + b and b + a is the commutative property.

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Answer:

32 inches or [tex]2\dfrac{2}{3}[/tex] feet

Step-by-step explanation:

1 foot = 12 inches

2 feet = 24 inches

Initially, the hole was 2 feet deep, after 3 days, the hole sank 8 inches further, so after 3 days, the hole was 2 feet 8 inches deep.

2 feet 8 inches = 24 inches + 8 inches = 32 inches

Now,

1 inch [tex]=\dfrac{1}{12}[/tex] foot

Then

32 inches [tex]=\dfrac{32}{12}=\dfrac{8}{3}=2\dfrac{2}{3}[/tex] inches

Good morning

______

Answer:

2/3 < 3/4​

___________________

Step-by-step explanation:

2/3 = (2*4)/(3*4)=8/12

3/4 = (3*3)/(4*3)=9/12

Since 9/12>8/12 then 3/4>2/3

:)

Answer:

16 = f(6)

12 = f(4)

Step-by-step explanation:

[tex]2(6) + 4 = 12 + 4 = 16 \\ \\ 2(4) + 4 = 8 + 4 = 12[/tex]

I am joyous to assist you anytime.

Answer:

Answer B and C are correct.

Step-by-step explanation:

Vertical angles opposite each other when two lines cross.

"Vertical" refers to the vertex (where they cross), NOT up/down. They are equal.

Answer:

[tex]\angle EYL[/tex] and [tex]\angle AYS[/tex]

[tex]\angle SYL[/tex] and [tex]\angle EYA[/tex]

Step-by-step explanation:

Vertical angles can be defined as the pair of angle which are opposite when two lines crosses, as the image attached shows.

Now, [tex]\angle EYL[/tex] and [tex]\angle AYS[/tex] are vertical angles, because they are opposite when lines ES and AL cross at point Y.

Another pair of vertical angles are [tex]\angle SYL[/tex] and [tex]\angle EYA[/tex], because they are opposite when lines ES and AL cross at point Y.

Therefore, all pair of angles which are vertical angles are

[tex]\angle EYL[/tex] and [tex]\angle AYS[/tex]

[tex]\angle SYL[/tex] and [tex]\angle EYA[/tex]

Answer:

x = 5

Step-by-step explanation:

8x - 8 = 4x + 12

     +8         +8

8x = 4x + 20

-4x  -4x + 20

4x = 20

4x/4  20/4

x = 5

Math is a language that people use to describe the world around them and because the language of math includes numbers, we can use it to describe things very precisely. Sometimes we use symbols to stand for special numbers like π.

Answer:

B. 86.3%

Step-by-step explanation:

The correct answer is C. 88.7%.

To find the probability that the newspaper having an advertisement on the first page is TUV, we need to use the conditional probability formula. The probability that an event A occurs given that event B has occurred is given by:

[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]

In this case, event A is that the newspaper is TUV, and event B is that the newspaper has an advertisement on the front page. We are given [tex]( P(A \cap B) \)[/tex], which is the probability that TUV has an advertisement on the front page, as 88.7%. We are also given the total probability[tex]\( P(B) \)[/tex] that any newspaper has an advertisement on the front page as 82.4%.

Using the conditional probability formula, we get:

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{P(\text{TUV} \cap \text{Ad})}{P(\text{Ad})} \][/tex]

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{88.7\%}{82.4\%} \][/tex]

Now, we calculate this probability:

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{88.7}{100} \times \frac{100}{82.4} \][/tex]

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{88.7}{82.4} \][/tex]

[tex]\[ P(\text{TUV}|\text{Ad}) \approx 1.0765 \][/tex]

However, probabilities cannot be greater than 1, so we must have made a mistake in our calculation. The correct approach is to realize that the total probability of 82.4% already includes the probability of TUV having an advertisement. Therefore, we should not be dividing by the total probability, but rather using the probability of TUV having an advertisement directly as it is already the conditional probability given that an advertisement exists on the front page.

The equation that represents a line parallel to 3x + 5y = –3 is A. 3x + 5y = 2, as it only differs in the y-intercept from the original line, therefore having the same slope which ensures it's parallel.

To determine which equation represents a line parallel to the given line 3x + 5y = –3, we should know that parallel lines have the same slope. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Let's first rewrite the given equation in slope-intercept form.

3x + 5y = –3
5y = -3x - 3
y = -3/5x - 3/5

The slope of this line is -3/5. We now look for an equation among the options which has the same slope of -3/5.

A. 3x + 5y = 2 is the correct choice as it only differs in the y-intercept, which makes it parallel to the original.

B. 6x + 10y = –6 is actually equivalent to the original equation when divided by 2, hence it's the same line, not merely parallel.

C. –5x + 3y = 2 has a different slope.

D. –3x + 5y = –3 has a different slope.

Answer:

Step-by-step explanation:

1. Answer below

[tex]2x = \sqrt[3]{125}[/tex]

[tex]2x = 5[/tex]

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

[tex]x = 2.5[/tex]

2. Answer below

[tex]x + 3^{2} = \sqrt[3]{27}[/tex]

[tex]x + 9 = 3[/tex]

[tex]x = -6[/tex]

Answer:

None of the above (x=3/7)

Step-by-step explanation:

9+3.5x=11-0.5

9+3.5x=10.5

+3.5x=10.5-9

3.5x=1.5

x=1.5/3.5

x= 15/35=3/7

Answer:

HEY THERE THE ANSWER IS C

Step-by-step explanation:

I believe this is the equation you meant to put, 9+3.5x=11-0.5x. In that case the answer iis C which is 2 :) hope this helps and someone doesn't delete my answer for the 3rd time

Answer:

6

Step-by-step explanation: The absolute value is defined as the distance of the value from 0, and thus, is the original number, but always in positive form. So,

-1 - 5 = -6

But since the absolute value is always positive, it goes from -6 to 6, or positive 6.

Answer:

10

Step-by-step explanation:

p=8

18-p

18-8=10

replace 10 for p

Answer:

(4x^3 -5y^2) (16x^6 + 20x^3y^2 + 25y^4)

Step-by-step explanation:

Use a^3 - b^3 formula which is (a-b) (a^2 + ab + b^2)

Here a is 4x^3 and b is 5y^2.

You get (4x^3 -5y^2) (16x^6 + 20x^3y^2 + 25y^4)

Let me know if this helps!

Answer:

0.3212, 0.332, 0.340, 0.3412, 0.342, 0.348, 0.35, 0.352

Answer:

See below.

Step-by-step explanation:

0.3212, 0.332, 0.340, 0.3412, 0.342, 0.348, 0.35, 0.352.

Answer is 90.49095 i think not sure yet

Answer:

2^(-n^2+n+1)

Step-by-step explanation:

2^(n+2)*2^(n-1)*2^(-n(n-1))=2^((n+2)+(n-1)-(n^2-n))=2^(-n^2+3n+1)

I can do it because they have the same base, so I can add the exponents.

I can write 4^n=2^2n. So I have 2^(-n^2+3n+1) / 2^2n and they have the same base again (2), so we can subtract the exponents.

2^((-n^2+3n+1)-2n)=2^(-n^2+n+1)

Answer: 47/8

Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we will put our new number over our old denominator and we have our answer which is 47/8.

Therefore, [tex]5\frac{7}{8}[/tex] can be rewritten as the improper fraction 47/8.

The answers to Unit 3 Homework 1 in an AP Chemistry subject are listed with careful instruction to students to understand the related concepts and why the answers are correct.

Based on the data provided it appears you are referring to Unit 3 Homework 1 of an Advanced Placement Chemistry subject. Here's a breakdown of the answers:

Please make sure to review each question individually, understand the related concepts and why these answers are correct. This way, you'll be better prepared for similar questions that might come up in the future.

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You're looking for an inequality of the form [tex]|t-b|\le a[/tex], or [tex]-a\le t-b\le a[/tex], or [tex]b-a\le t\le b+a[/tex].

Start with

[tex]350^\circ\le t\le400^\circ[/tex]

Notice that 375º is the midpoint of this interval of temperatures. If we subtract all sides by 375º, then we get

[tex]-25^\circ\le t-375^\circ\le25^\circ[/tex]

so we can set [tex]a=25^\circ[/tex] and [tex]b=375^\circ[/tex], and we can rewrite this inequality in terms of absolute values as

[tex]|t-375^\circ|\le25^\circ[/tex]

Answer:

scale factor = 1.2

Step-by-step explanation:

To determine the scale factor, calculate the ratio of the length of the second rectangle to the length of the first rectangle. The corresponding ratio of widths should also equal the same ratio.

scale factor = [tex]\frac{14.4}{12}[/tex] = [tex]\frac{6}{5}[/tex] = 1.2

Final answer:

The scale factor used to get from the first rectangle to the second one is 1.2.

Explanation:

The scale factor used to get from the first rectangle to the second one can be found by comparing the dimensions of the two rectangles. The length of the first rectangle is 12 and the length of the second rectangle is 14.4. Dividing the length of the second rectangle by the length of the first rectangle gives us:

Scale factor = length of second rectangle / length of first rectangle = 14.4 / 12 = 1.2

So, the scale factor used to get from the first rectangle to the second one is 1.2.

Final answer:

The domain for Susan's backpack situation is {0, 1, 2, 3, 4}, representing the number of books she can carry, while the range is from 0 to 14 pounds, representing the total weight of the books she might carry.

Explanation:

To find a reasonable domain and range for Susan's backpack situation, we need to consider the lightest and heaviest books she might carry. Since Susan can carry at most 4 books and each book weighs between 1 pound to 3.5 pounds, we can define the possible weights of the books.

For the domain, we consider the number of books Susan could possibly carry. The domain would therefore be: {0, 1, 2, 3, 4}. She could carry no books or up to 4 books.

For the range, we consider the total weight of the backpack based on carrying the lightest to the heaviest books. The minimum weight would be 0 pounds (if she carries no books) and the maximum weight would be 3.5 pounds  imes 4 books = 14 pounds. So the range of weights would be from 0 to 14 pounds. However, we must remember that the weight can also be any reasonable value in between, for instance when carrying books of varying weights.

In conclusion, the domain for the number of books would be {0, 1, 2, 3, 4} and the range for the total weight of the books would be any value between 0 to 14 pounds, inclusive.

Answer:

Step-by-step explanation:

The summation formula (  arithmetic sequence when the first terme is : A1 = 13

and the coomo diff is d= -4

Sn = n/2(A1 +An)

An = A1+(n-1)d

An = 13 +(n-1)(-4)

An = -4n +17

Sn = n/2(13+17-4n) = n/2(30-4n)

Sn = -2n² +15n

in this exercice : n =4      S4 = -2(4)² +15(4) = -32+60 = 28

verify : 13 + 9 + 5 + 1 =28   ......right

Answer:

5

Step-by-step explanation:

You do 125/25 to find the number of ml of aminophylline. Answer: 5

To administer a dose of 125 mg of aminophylline, one must inject 5 ml.

The student is asking how many milliliters (ml) must be injected to administer a dose of 125 mg of aminophylline when the vial is labeled 25 mg per ml. To calculate this, we use the formula:

Dose (mg) = Volume (ml) times Concentration (mg/ml)

Since we need to administer 125 mg and we know the concentration is 25 mg/ml, we arrange the formula to solve for volume:

Volume (ml) = Dose (mg) / Concentration (mg/ml)

Volume (ml) = 125 mg / 25 mg/ml = 5 ml

Answer: Last option.

Step-by-step explanation:

Given the expression:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}[/tex]

The Quotient of powers property states that:

[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]

And the Power of a powet property states that:

[tex](a^m)^n=a^{mn}[/tex]

Then, applying these properties, you get:

[tex]=\sqrt{\frac{(2^3)^26y}{x^2}[/tex]

Now you must remember that:

[tex]\sqrt[a]{a^n}=a[/tex]

Therefore, simpliying the expression, you get:

[tex]=\frac{2^3\sqrt{y}}{x}=\frac{8\sqrt{y}}{x}[/tex]

Answer:

D. 8√y/x

Step-by-step explanation:

Answer:

The system consists of parallel lines ⇒ 2nd answer

Both lines have the same slope ⇒ 3rd answer

Step-by-step explanation:

Lets revise the types of the solutions of the system of equations

Case 1:

→ If the two equations have the same coefficients of the two variables

   and different numerical terms then the two equations represented

   by two parallel lines

Ex: ax + by = c , ax + by = d

Case 2:

→ If the two equations have the same coefficients of the two variables

   and same numerical term then the two equations represented

   by the same line

Ex: ax + by = c , ax + by = c

Case 3:

→ If the two equations have different coefficients of one of the variables

   or the two variables then they represented by two intersected lines

   and the system has one solution

Ex: ax + by = c , dx + ey = f

The system of equation is

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

* 3 y - x = -7

Multiply the first equation by 3

∴ 3 y = x - 12

Subtract both sides by x

∴ 3 y - x = - 12 ⇒ (1)

∵ 3 y - x = - 7 ⇒ (2)

The system of equations has same x-coefficient and same y-coefficient

in both equations but the numerical terms are different, then they

represented by two parallel lines as first case above

and parallel lines have the same slope

The system consists of parallel lines

Both lines have the same slope

Answer:

BC

Step-by-step explanation:

[tex]\bf A=bx+cx+d\implies A-d=bx+cx\implies A-d=\stackrel{\textit{common factor}}{x(b+c)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{A-d}{b+c}=x~\hfill[/tex]

Check the picture below.

[tex]\bf \textit{area of a trapezoid}\\\\A=\cfrac{h(a+b)}{2}~~\begin{cases}a,b=\stackrel{bases}{parallel}\\\qquad ~sides\\h=height\\\cline{1-1}a=4\\b=7\\h=7\end{cases}\implies A=\cfrac{7(4+7)}{2}\implies A=\cfrac{7(11)}{2}\\\\\\A=\cfrac{77}{2}\implies A=38\frac{1}{2}[/tex]

The area of polygon ABCD is found by dividing it into two rectangles and calculating their areas separately, which are then added together to get a total area of 77 square units.

Calculating the Area of Polygon ABCD:

The area of polygon ABCD with vertices at A(-4,2), B(3,2), C(3,-5), and D(-4,-2), we can split the polygon into two rectangles. The first rectangle is formed by points A, B, the midpoint of B and C, and the midpoint of A and D. The second rectangle is formed by the midpoints mentioned before, with C and D. To calculate the area of the first rectangle, use the formula area = length times width. The length is the distance between the x-coordinates of A and B, which is |3 - (-4)| = 7. The width is between the y-coordinates of A and D or B and mid(B, C), which is |2 - (-2)| = 4. Thus, the area of the first rectangle is 7 times 4 = 28 square units.

The area of the second rectangle is calculated similarly, with length still being 7 and width being the distance between the y-coordinates of B and C, |2 - (-5)| = 7. Therefore, the area of the second rectangle is 7 times 7 = 49 square units. Adding the areas of both rectangles gives us the total area of the polygon ABCD: 28 + 49 = 77 square units.

Answer:

the correct answer is C.

Step-by-step explanation:

You take the area of the square which is 20x20 = 400.

There is 5 squares 400x5 = 2000

There is 4 triangles--which is 1/2 the area of 1 square (In this case).

One triangle = 200

200x4 = 800

2000 + 800 = 2800

You take the area of the square which is 20x20 = 400.

There is 5 squares 400x5 = 2000

There are 4 triangles--which is 1/2 the area of 1 square (In this case).

One triangle = 200

200x4 = 800

2000 + 800 = 2800.

Multiply length × width.

For example, let's say that, for a rectangular area, you measure a length of 4 inches and a width of 3 inches. In this case, the area within your rectangle is 4 × 3 = 12 square inches.

Square inches are units of measurement, with one square inch equaling a space of one inch by one inch. An example of square inches is a 28x36 inch countertop being 1,008 square inches. noun. Plural form of a square inch. noun.

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