Which of the following statements is always true for all values of a
A) -a = a
B) |a| = -a
C) |a| = a
D) -(-a) = a

We know: 9 = 3²

Therefore [tex]\dfrac{1}{9}=\dfrac{1}{3^2}[/tex]

We know the property:

[tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex]

Therefore [tex]\dfrac{1}{9}\cdot3^x=\dfrac{3^x}{3^2}=3^{x-2}[/tex]

We must find f(5). Put x = 5 to the equation of the function:

[tex]f(5)=3^{5-2}=3^3=3\cdot3\cdot3=27[/tex]

The value of f(5) is 27 of function f(x) = 1/9(3)ˣ

The function is defined as mathematics expression defines a relationship between one variable and another variable. When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that  value of x determines what value of  y  will be. This relationship can be expressed as follows: y = f (x)

An exponential function is defined as function has a constant as its base and a variable as its exponent.

In mathematical form an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function.

For the function f defined by f(x) given as :

f(x) = 1/9(3)ˣ ,

To determine the value of f(5).​

f(x) = 1/9(3)ˣ,

Substitute the value of x = 5 in the function,

f(5) = 1/9(3)⁵ ,    [ 3⁵ = 243 ]

f(5) = 1/9(243),

f(5) = 27

Hence, the value of f(5) is 27.​

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31=2y-5

Add 5 on both -5+5 which cancels out and 31+5 which is 36 and then divide 36 by 2 which equals to 18.

So y=18 hope this helped (':

Hey!

[tex]31=2y-5[/tex]

First, this problem should be switch sides.

[tex]2y-5=31[/tex]

Secondly, add 5 from both sides of equation.

[tex]2y-5+5=31+5[/tex]

Then, simplify

[tex]2y=36[/tex]

In fact, you had to divide 2 from both sides of equation.

[tex]\frac{2y}{2}=\frac{36}{2}[/tex]

Finally, simplify

[tex]y=18[/tex]

And the answer is [tex]y=18[/tex]

I hope this helped!

Thank you for posting your question.

-Charlie

Answer:

355,000

Step-by-step explanation:

the 6 is greater than 5, so it would make the 4 a 5

To calculate simple interest, use the formula Simple Interest = Principal × Rate × Time. If the rate is increased by 1%, the simple interest will increase. If the time is increased by 1 year, the simple interest will also increase.

To calculate the simple interest on a deposit, you can use the formula:

Simple Interest = Principal × Rate × Time

Now let’s address the first part of the question. If the rate is increased by 1%, the new rate would be 3% + 1% = 4%. Using the same formula, the simple interest would now be:

Simple Interest = $1200 × 0.04 × 5 = $240

Now, let’s move on to the second part of the question. If the time is increased by 1 year, the new time would be 5 years + 1 year = 6 years. Using the same rate of 3%, the simple interest would now be:

Simple Interest = $1200 × 0.03 × 6 = $216

m^2-36

(m+6)(m-6)

or

m(m-6)+6(m-6)

(m+6)(m-6)

3(x + 7) ≥ 2x + 6

Distributive property.

3x + 21 ≥ 2x + 6

Subtract 2x from both sides.

x + 21 ≥ 6

Subtract 21 from both sides.

x ≥ -15

The solution to the inequality is [tex]\(x \geq -15\)[/tex].

To translate the given statement into an inequality, you can follow these steps:

1. **Translate the first part of the sentence:**

  "Three times the sum of x and seven" can be written as \(3(x + 7)\).

2. **Translate the second part of the sentence:**

  "The sum of two x and six" can be written as \(2x + 6\).

3. **Combine the translated parts with the inequality:**

  "Three times the sum of x and seven is greater than or equal to the sum of two x and six" can be translated into the following inequality:  

[tex]\[3(x + 7) \geq 2x + 6\][/tex]

4. **Solve the inequality for x:**

  Distribute the 3 on the left side:  

[tex]\[3x + 21 \geq 2x + 6\][/tex]

  Move the \(2x\) term to the left side by subtracting \(2x\) from both sides:

[tex]\[3x - 2x + 21 \geq 6\][/tex]

  Simplify:

[tex]\[x + 21 \geq 6\][/tex]

  Move the 21 to the right side by subtracting 21 from both sides:

[tex]\[x \geq -15\][/tex]

So, the solution to the inequality is \(x \geq -15\). This means any value of \(x\) greater than or equal to -15 will satisfy the given inequality.

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Answer:

Step-by-step explanation:

Do you mean 2 x 4 x 7 x 4 = 224

Paula has a staggering total of 224 choices to choose from when customizing her friend's birthday card. That's a lot of possibilities!

Paula has quite a variety of choices for customizing her friend's birthday card!

Let's calculate the total number of different combinations she can create:

Number of sizes = 222

Number of colors = 444

Number of phrases = 777

Number of pictures = 444

To find the total number of combinations, we multiply the number of choices for each element:

2* 4* 7* 4 = 224

Complete Question:

Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.) How many different card designs are possible?

"38 below zero" can be displayed as -38.

The negative sign implies that the number is whatever the value is less than the value of 0.

Thus, -38 + 38 = 0.

the integer is -38 because an integer can not be a fraction or a decimal.. and the problem says that mercury melts at 38 below zero, so, this would be 0-38=-38

28 divided by 7 days a week would be 4 a day

The band makes $300 from selling merchandise.

I found this out by finding the LCD for 3 and 5, which is 15.

Then I multiplied the 2 from 2/3 by 5, and the 1 from 1/5 by 3, which results in 10/15 and 3/15.

Next I divided 1500 by 15, which is 100.

Then I multiplied 100 by 3, and got 300.

The band earns $450 from selling merchandise.

To find out how much money the band earns from selling merchandise, we need to determine what fraction of their profit comes from merchandise sales. We know that the band earns 2/3 of their profit from selling concert tickets, which equals $1500. Let's use this information to find the total profit.

Since 2/3 of the profit is $1500, we can find the total profit by multiplying $1500 by 3/2. $1500 x 3/2 = $2250. Therefore, the total profit the band earns is $2250.

Next, we need to find out how much money the band earns from selling merchandise, which is 1/5 of the total profit. To find this amount, we can multiply the total profit of $2250 by 1/5. $2250 x 1/5 = $450. So, the band earns $450 from selling merchandise.

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1/2 divided by 4 would become 1/2 times 1/4 (Since you change the division sign into multiplication and you'd flip the 4 into 1/4), so the final answer would be 1/8

Hello there!

This question is so super easy to me.

1/2÷4

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓

First you had to used apply fraction rule.

[tex]\frac{1}{2*4}[/tex]

Then multiply by the numbers.

[tex]2*4=8[/tex]

[tex]=\frac{1}{8}[/tex]

Answer⇒⇒⇒1/8

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

1/2 Hour = 20 Minutes

25 miles in 20 minutes

75 miles in 60 minutes

225-25=200

200/75= 2 1/3

3:00 PM + 2:30 = 5:30 PM

They will arrive at the desired destination in 2:30 minutes, which is 5:30 PM

:)

Hello there!

The answer should be the last option D.

This question is so easy to me.

[tex]9=w-14[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓

First you had to switch sides of the equation.

[tex]w-14=9[/tex]

Then you add 14 from both sides of the equation.

[tex]w-14+14=9+14[/tex]

Simplify it should be the right answer.

[tex]w=23[/tex]

Answer⇒⇒⇒w=23

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

( - 10, - 22 )

using the midpoint formula,

let the other endpoint have coordinates (x, y) then

[tex]\frac{1}{2}[/tex] (2 + x ) = - 4 ( multiply through by 2 )

2 + x = - 8 ( subtract 2 from both sides ) then

x = -8 - 2 = - 10 ← value of x-coordinate

Similarly for y-coordinate

[tex]\frac{1}{2}[/tex] (8 + y ) = - 7 ( multiply through by 2 )

8 + y = - 14 ( subtract 8 from both sides )

y = - 14 - 8 = - 22 ← y -coordinate

the other endpoint is ( - 10, - 22 )

To determine the maximum number of sandwiches that can be made with the given turkey and cheese slices, we need to divide the total number of each type of slice by the number of slices needed for one sandwich. The minimum of these two results gives us the maximum number of sandwiches. In this case, the maximum number of sandwiches that can be made is 18.

In this case, we have 72 turkey slices and 18 cheese slices.

Therefore, the maximum number of sandwiches that can be made is the minimum of the number of turkey sandwiches and the number of cheese sandwiches, which is 18.

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there are 1300 millimeters in 1.3 meters

1 meter = 100 centimeters  

1 centimeter = 10 millimeters  

So 1 meter = 100(10) millimeters = 1000 millimeters  

Then 1.3 meters = 1300  millimeters

Answer:

Step-by-step explanation:

Option A is the correct option as X is let smallest integer in both. solution is given in attachment.

one fifth of the boys in the classroom have brown hair.

b hope this helps i think

Answer:

C lots of available jobs

When rotating a point 180 degrees about the origin, you are simply inverting the points.

(5, -2) rotated 180 degrees results in (-5, 2).

To rotate point B(5, -2) 180 degrees about the origin, its image would have coordinates (-5, 2).

To rotate a point about the origin, we can use the formula (x', y') = (-x, -y). In this case, point B has coordinates (5, -2). To rotate it 180 degrees about the origin, we substitute the coordinates into the formula:

(x', y') = (-5, 2)

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Choose an object and rotate it up to 180 degrees around its center. If at any point the object appears exactly like it did before the rotation, then the object has rotational symmetry.

Step-by-step explanation:

We are asked to determine when does a figure have rotational symmetry.

We know a figure has a rotational symmetry, when the figure maps onto itself after rotating it less than 180 degrees.  

In other words, we can say it is the property that a shape has when it looks the exactly same after some rotation.

When a figure maps onto itself exactly at 180 degrees, then the figure has a point symmetry.

Therefore, a figure has rotational symmetry if it maps onto itself after a rotation less than 180 degrees.

Answer: $750

Step-by-step explanation:

If the band is earning $1,500 on ticket sales, that is equal to 2/3 aka 6/15. 1/5,or, 3/15 is earned on merchandise. Since 3/15 is half of 6/15, that means that merchandise makes half of $1,500, (1500÷2) or $750.

So, the band earns $750 from merchandise

750

In order to solve this, first add 10p on both sides of the equation to get the variable on one side only.

[tex]-8p-10=-10p+10[/tex]

[tex]-8p+10p-10=-10p+10p+10[/tex]

[tex]2p-10=10[/tex]

Now add 10 on both sides of the equation.

[tex]2p-10+10=10+10[/tex]

[tex]2p=20[/tex]

Divide both sides by 2 for x.

[tex]\frac{2p}{2}[/tex]=[tex]\frac{20}{2}[/tex]

[tex]p=10[/tex]

Hello!

Answer: ⇒⇒⇒⇒⇒⇒⇒ p=10

Step-by-step explanation:

First you had to add by 10 from both sides of equation.

[tex]-8p-10+10=-10p+10+10[/tex]

Simplify.

[tex]-8p=-10p+20[/tex]

Add by 10p from both sides of equation.

[tex]-8p+10p=-10p+20+10p[/tex]

Simplify.

[tex]2p=20[/tex]

Divide by 2 from both sides of equation.

[tex]\frac{2p}{2}=\frac{20}{2}[/tex]

Simplify.

[tex]p=10[/tex]

Hope this helps!

Thank you for posting your question at here on brainly.

Have a great day!

-Charlie

1/3, 2/6, 3/9, 5/15, 6/18, And so on...

There are infinite equivalent fractions to 4/12.

The five fractions equivalent to 4/12 are 8/24, 12/36, 16/48, 20/60, and 24/72.

We have to determine five fractions equivalent to 4/12.

According to the question

To determine the fraction following all the steps given below.

The five fractions of the 4/12 are as follows;

1. The first fraction is equivalent to 4/12 is determined by multiplying and dividing by 2.

[tex]= \dfrac{4}{12}\\\\= \dfrac{4}{12} \times \dfrac{2}{2}\\\\= \dfrac{8}{24}[/tex]

The first fraction equivalent to 4/12 is 8/24.

2.  The second fraction is equivalent to 4/12 is determined by multiplying and dividing by 3.

[tex]= \dfrac{4}{12}\\\\= \dfrac{4}{12} \times \dfrac{2}{2}\\\\= \dfrac{8}{24}[/tex]

The second fraction equivalent to 4/12 is 12/36.

3.  The third fraction is equivalent to 4/12 is determined by multiplying and dividing by 4.

[tex]= \dfrac{4}{12}\\\\= \dfrac{4}{12} \times \dfrac{4}{4}\\\\= \dfrac{16}{48}[/tex]

The third fraction equivalent to 4/12 is 16/48.

4. The fourth fraction is equivalent to 4/12 is determined by multiplying and dividing by 5.

[tex]= \dfrac{4}{12}\\\\= \dfrac{4}{12} \times \dfrac{5}{5}\\\\= \dfrac{20}{60}[/tex]

The fourth fraction equivalent to 4/12 is 20/60.

5.  The fifth fraction is equivalent to 4/12 is determined by multiplying and dividing by 6.

[tex]= \dfrac{4}{12}\\\\= \dfrac{4}{12} \times \dfrac{6}{6}\\\\= \dfrac{24}{72}[/tex]

The fifth fraction equivalent to 4/12 is 24/72.

Hence, the five fractions equivalent to 4/12 are 8/24, 12/36, 16/48, 20/60, and 24/72.

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Answer:

C) 20 + 36 = 4(5 + 9)

Step-by-step explanation:

The distributive property:

a(b + c) = ab + ac

Therefore your answer is C)

4(5 + 9) = (4)(5) + (4)(9) = 20 + 36

Answer: c

Step-by-step explanation: 20 + 36 = 36 x 20