Find the circumference of the circle to the nearest tenth. Use 3.14 for pi.

Answer:

c^5 *d^5

Step-by-step explanation:

Answer:

(- 3, - 5)

Step-by-step explanation:

A translation of 1 unit left, subtract 1 from x- coordinate

A translation of 3 units down, subtract 3 from y- coordinate

The translation rule is

(x, y) → (x - 1, y - 3), hence

(-2, - 2) → (- 2 - 1, - 2 - 3) → (- 3, - 5)

Answer: third option.

Step-by-step explanation:

You know that:

- There are 10⁹ bytes in a gigabyte.

- There are 10⁶  bytes in a megabyte.

Then, to know how many times greater  the storage capacity of a 1-gigabyte flash drive is than a 1-megabyte flash drive, you must divide 10⁹ bytes by 10⁶ bytes.

Remember the quotient of powers property:

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

Then:

[tex]=\frac{10^9}{10^6}=10^3=1,000[/tex] times greater

Answer:

1,000

Step-by-step explanation:

Answer:

[tex]y=-6(x-1)^{2}-7[/tex]

Step-by-step explanation:

we have

[tex]6x^{2} -12x+y+13=0[/tex]

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y+13=-6x^{2} +12x[/tex]

Factor the leading coefficient

[tex]y+13=-6(x^{2} -2x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]y+13-6=-6(x^{2} -2x+1)[/tex]

[tex]y+7=-6(x^{2} -2x+1)[/tex]

Rewrite as perfect squares

[tex]y+7=-6(x-1)^{2}[/tex]

[tex]y=-6(x-1)^{2}-7[/tex] -----> equation of the parabola in vertex form

The vertex is (1,-7) is a maximum, the parabola open downward

To convert 6x^2 - 12x + y + 13 = 0 to vertex form, follow the steps to complete the square and rewrite the equation as (x - 1)^2 = -y/6 - 7/6.

The equation 6x^2-12x+y+13=0 is in the general form of a quadratic equation. To convert it into the vertex form, we need to complete the square.

First, let's group the x terms together: 6x^2 - 12x = -(y + 13).

Next, let's complete the square: 6(x^2 - 2x) = -(y + 13).

Now, we can add (2/2)^2 = 1 to both sides to complete the square: 6(x^2 - 2x + 1) = -(y + 13) + 6.

Simplifying further, we get 6(x - 1)^2 = -y - 7.

Finally, we can write the equation in vertex form by dividing both sides by 6: (x - 1)^2 = -y/6 - 7/6.

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Answer:

Is it a map? To me that makes the most logical sense.

Answer:

A map

Step-by-step explanation:

A map has cities, mountains, and water. It doesn't show houses, trees, or fish because it doesn't show specific things.

Answer:

The answer is b

thank you

Answer:

-1

Step-by-step explanation:

to find the axis of symmetry, the formula is X= -b/ 2a

a is the 2 from 2x2

and b is 4 from 4x

then plug them to the formula

-b= -4 because of the negative in -b

and 2a is 2(2)

-4/4 is -1

so x= -1

hope im right

hope it helps

Answer:   3

Step-by-step explanation:

[tex]x^3-27=0\\\\x^3=27\\\\\sqrt[3]{x^3}=\sqrt[3]{27}\\\\x=\sqrt[3]{3\cdot 3\cdot 3} \\\\x=3[/tex]

Answer:

C

Step-by-step explanation:

1/2 is positive unlike the other two so it is obviously last.

Now it's between -3/4 and -2/3

-3/4 = -0.75

-2/3 = -0.67

Since -0.75 < -0.67, -3/4 is first and -2/3 is second.

Answer:

Your answer would be C.

Step-by-step explanation:

Answer:

[tex]\boxed{\bold{Not \ Statistical}}[/tex]

Step By Step Explanation:

Statistical: A survey, branch or mathematics consisting of data collection, organization, analysis, interpretation and presentation.

A statistical question deals with social problems, people, or something that must be studied and data gained. Statistical questions must have data sets and data gained. They also must have answers that vary from side to side or opinion to opinion, in order to be qualified as a 'statistical question'.

"An Antique Collector wants to know the age or a particular chair in a shop"

                                                V

Statistical                       Not Statistical

[tex]\boxed{\bold{>}}[/tex] This is not a statistical question because there is no data that needs to be collected, no surveys that need to be filled out and no analysis, interpretation and presentation. The answer to this question does not vary. It is simply a fact.

16 x 14 = 224

[tex]answer = {224cm}^{2} [/tex]

Answer: 7 + i

Step by step:

Remove parentheses.

5 + 3i + 2 - 2i

Add 5 and 2

7 + 3i - 2i

Subtract 2i and 3i

7 + i

The sum of the complex numbers (5+3i) and (2-2i) is 7+i. You add the real parts to get 7 and the imaginary parts to get i, then combine them.

Adding two complex numbers: (5+3i)+(2-2i). To perform this addition, we simply add the real parts and the imaginary parts separately. The real parts are 5 and 2, and when we add them together we get 7. The imaginary parts are 3i and -2i, which sum up to 1i (or just i). Hence, the result of the addition of these two complex numbers is 7+i.

To further clarify with an example similar to the student's question: (3+4i) + (−2+7i) = (3 - 2) + (4 + 7)i = 1 + 11i. The process is straightforward—add the real numbers, add the imaginary numbers, and combine them into one complex number.

Answer:

option (a)

x - √7x / x - 7

Step-by-step explanation:

Given the expression in the question

  √x / (√x + √7)

 There are 3 steps to follow

Multiply by √x - √7

√x (√x - √7) /  (√x + √7)(√x - √7)

√x .√x - √7.√x / (√x + √7)(√x - √7)

a² - b² = (a+b)(a-b)

√x² - √7x / √x² - √7²

x - √7x / x - 7

An equation f(4)=16 means that when the input value is 4, the output value is 16.

An equation in the form f(4)=16 means that when the input value of the function f is 4, the output value is 16.

For example, if f represents the function that multiplies an input by 4, then f(4)=16 because 4 multiplied by 4 equals 16.

In terms of input and output values, f(4)=16 means that when the input value is 4, the function will return an output value of 16.

Answer:

Step-by-step explanation:

What you are trying to do is a nice way to solve this problem. Without knowing any physics, you are using what math you know to get the answer. You are actually very close to being correct, and you are right. You do have to divide by 60.

Here's why and it is the one bit of physics you have to know.

The speed is km/hour. That word hour is the culprit. Your time is in minutes and you have to get it into hours. In physics, the units have to be consistent.

So ...

b1 = 19 minutes which is 19 min [1 hour / 60 minutes] = 19/60 = 0.31667 hour

b2 = 26 minutes which is 26 min [ 1 hour/60 minutes] =  26/60 = 0.4333 hour

h = 40 km/hour

Area = (0.31667 hour + 0.4333 hour)*40 km/hour /2

Area = 0.75 hour * 40 km/hr //2

Area = 15 km

Answer:

t = 4

Step-by-step explanation:

To solve for t, convert the numbers to improper functions. Then multiply by 16/3 on each side.

t ÷ 5 1/3 = 3/4

t ÷ 16/3 = 3/4

t = 16/3 * 3/4

t = 48/12

t = 4

Answer:

27th

Step-by-step explanation:

Every 4 days=4m

Every 3days=3s

Costco =2c

When does 4m=D=3s?

When m=0=s and when m=3 and s=4

4•3=12=3•4

Can 2c=12? Yes, when c=6

So 12 days from now, mall, store and Costco will all happen.

15+12=27

Square, Rectangle and Rhombus

Answer:

Step-by-step explanation:

We know:

If a ≤ b ≤ c are the sides of a triangle, then a + b > c.

We have a = x, b = 2x and c = 15 cm.

Therefore x ≤ 15 and 2x ≤ 15 ⇒ x ≤ 7.5

Therefore we have the inequality:

x + 2x > 15

3x > 15          divide both sides by 3

x > 5 and x ≤ 7.5

Finally x = 6

Answer:

[tex]\large{\boxed{\text{the multiplication property of equality}}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x}{5}+5=20\qquad\text{subtract 5 from both sides}\\\boxed{\text{the subtraction property of equality}}\\\\\dfrac{3x}{5}+5-5=20-5\\\\\dfrac{3x}{5}=15\qquad\text{multiply both sides by}\ \dfrac{5}{3}\\\boxed{\text{the multiplication property of equality}}\\\\\dfrac{3\!\!\!\!\diagup^1}{5\!\!\!\!\diagup_1}\cdot\dfrac{5\!\!\!\!\diagup^1x}{3\!\!\!\!\diagup_1}=\dfrac{5}{3\!\!\!\!\diagup_1}\cdot15\!\!\!\!\!\diagup^5\\\\x=(5)(5)\\\\x=25[/tex]

Answer: C

Step-by-step explanation:

Answer:

Part a) The weight of the original statue is [tex]9,483\ pounds[/tex]

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is [tex]8.4^{3}[/tex]

Part b)  [tex]221,184\ pounds[/tex]

Step-by-step explanation:

Part a)

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its volumes or weights is equal to the scale factor elevated to the cube

step 1

Find the scale factor

remember that

[tex]1\ ft=12\ in[/tex]

The original statue is 7 ft tall

Convert to inches

[tex]7\ ft=7*12=84\ in[/tex]

Divide the height of the original statue by the height of the model to find the scale factor

[tex]\frac{84}{10}=8.4[/tex]

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=8.4[/tex]

[tex]y=16\ lb[/tex]

substitute

[tex]8.4^{3}=\frac{x}{16}[/tex]

[tex]x=16(8.4^{3})=9,483\ pounds[/tex]

The weight of the original statue is [tex]9,483\ pounds[/tex]

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is [tex]8.4^{3}[/tex]

Part b) If the original statue were 20 ft tall, how much would it weight?

step 1

Find the scale factor

remember that

[tex]1\ ft=12\ in[/tex]

The original statue is 20 ft tall

Convert to inches

[tex]20\ ft=20*12=240\ in[/tex]

Divide the height of the original statue by the height of the model to find the scale factor

[tex]\frac{240}{10}=24[/tex]

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=24[/tex]

[tex]y=16\ lb[/tex]

substitute

[tex]24^{3}=\frac{x}{16}[/tex]

[tex]x=16(24^{3})=221,184\ pounds[/tex]

Answer:

The absolute number of a number a is written as

|a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation

|x|=a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

|x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

or

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality

|x|<2

Represents the distance between x and 0 that is less than 2

picture42

Whereas the inequality

|x|>2

Represents the distance between x and 0 that is greater than 2

picture43

You can write an absolute value inequality as a compound inequality.

$$\left | x \right |<2\: or

−2<x<2

This holds true for all absolute value inequalities.

|ax+b|<c,wherec>0

=−c<ax+b<c

|ax+b|>c,wherec>0

=ax+b<−corax+b>c

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

Sorry If its not what your looking for but i tried

Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems.

Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems. Here's how you can do it:

Representing Constraints with "less than" or "greater than" inequalities:

Suppose you have a variable "x" and a fixed value "a." If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than some constant "k," you can write it as:

| x - a | < k

For example, if you want to constrain "x" to be within 3 units from 5, you write:

| x - 5 | < 3

Representing Constraints with "less than or equal to" or "greater than or equal to" inequalities:

If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than or equal to some constant "k," you can write it as:

| x - a | ≤ k

For example, if you want to constrain "x" to be within 2 units from 8, you write:

| x - 8 | ≤ 2

Using absolute value equations allows you to handle situations where the variable needs to be close to a certain value or within a specific range, regardless of whether it is greater or smaller than that value. This flexibility is particularly useful in various mathematical and optimization problems, including linear programming and constrained optimization.

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Answer:

11 inches

Step-by-step explanation:

17/0.85 * 0.55

20 * 0.55

11.

Answer:

OPTION B:  [tex]2(3x+5)[/tex]

Step-by-step explanation:

To solve the exercise you can simplify the expression given in the problem, as following:

- Add the like terms:

[tex]3x+3x+5+5\\6x+10[/tex]

- Find the greatest common factor (GCF) of 6 and 10:

[tex]6=2*3\\10=2*5\\\\GCF=2[/tex]

- Factor ir out.

Then, you obtain the following equivalent expression:

[tex]2(3x+5)[/tex]

Answer:

6x + 10

Step-by-step explanation:

Combine like terms:

3x + 3x = 6x, and

5+5 = 10

and so the final sum is 6x + 10

The answer is A.) 5 because it’s the smaller number

Answer:

Volume of cube= a^3

=(2/√3)^3

=8/3√3 cubic units. (~1.5396 cubic units)

Step-by-step explanation:

Such a cube has diagonal lengths (DF, AG, EC & HB)=diameter of sphere=2 units.

Let the sides of the cube (FG, GC, CB, BF, etc.) be 'a'.

Hence facial diagonal of the cube (FC, BG, FH, etc.) will be √2a (Pythagoras' Theorem).

Applying Pythagoras' theorem for △DFC:

FC²+DC²=FD²

⇒(√2a)²+a²=2²

⇒3a²=4

⇒a=2/√3 units

Answer:

C. 27 40 cubic yard

Step-by-step explanation:

The base area is 9 10 square yard and a height of 3 4 yard.

Volume of the prism will be given by the formula;

= Base area × height

=  9 10 square yard × 3 4 yard

= 27 40 cubic yard

We can make and use the equation: A = 160( 1.03 )^y: A = amount, 160 = amount put in, 1 + .03 = 1.03 = interest, and y as the number of years, as the money is compounded every year. (This is the compound interest equation, but I put in the numbers)

A) 160 * 1.03 = $164.80, 160 * 1.03² = $169.744 ≈ $169.74

B) 160 * 1.03⁵ = 185.48385 ≈ $185.48

The expression is the same as saying (((((160 * 1.03)1.03)1.03)1.03)1.03). This is like multiplying 160 * 1.03, which gives the amount for the first year. Then, that amount is multiplied by 1.03, which is the amount for the second year. This isi repeated until 5 years.

C) 160(1.03)³⁰

Claire will have $164.80 after 1 year and $169.74 after 2 years in her savings account due to the 3% interest rate. After 5 years, she will have $185.86. The expression for the amount after 30 years is $160 × (1.03)³⁰.

When Claire deposited $160 into her savings account at a 3% interest rate per year, she initiated a process of compound interest. This means each year, the amount of money in her account will increase by 3% of the amount from the previous year. The way to find out how much money she will have after a certain number of years is to multiply the initial amount by 1.03 raised to the power of the number of years.

Interest After 1 Year

After 1 year: $160 × 1.03 = $164.80

Interest After 2 Years

After 2 years: $160 × (1.03)² = $169.74

Interest After 5 Years

After 5 years: $160 × (1.03)⁵ = $185.86. This is calculated using the formula for compound interest: $160 × 1.03 raised to the fifth power.

Interest After 30 Years

To write an expression for the amount of money she will have in 30 years: $160 × (1.03)³⁰. This follows the general formula for compound interest, which is the initial amount times one plus the interest rate raised to the number of years.

Answer:

The answer should be A) be square root of 11 is 3.3

Step-by-step explanation:

Answer:

angle = 35 degrees

Step-by-step explanation:

The rocket traveled

5 miles in the       x direction

3.5 miles in the    y direction

The rocket was launched with a slope of

m =y/x = 3.5 miles / 5 miles   = 0.7

The slope is equal to the tangent of the angle of elevation

tan (angle) = m

angle  =  tan^-1 (0.7)

angle = 34.99 ≈ 35 degrees

To determine the angle of elevation, we use the tangent function: the angle θ is the arctan of the altitude over the horizontal distance, which is approximately 35 degrees.

The angle of elevation that the rocket was launched at can be determined using trigonometric functions. Specifically, we can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side (altitude in this case) over the adjacent side (horizontal distance).

The formula is:

tan(\(\theta\)) = \(\frac{{opposite}}{{adjacent}}\).

So, the angle \(\theta\) is:

\(\theta = tan^{-1}\left(\frac{{3.5 \text{{ miles}}}}{{5 \text{{ miles}}}}\right)\).

Using a calculator, we find that:

\(\theta\approx 35.0^\circ).

The rocket was thus launched at an angle of approximately 35 degrees.

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