Find the distance between -3 and 4. A) -12 eliminate b) -7 c) -1 d) 7

Hello!

The function f/g means that that f(x) is written in the numerator and g(x) is written in the denominator because we are dividing the functions f(x) and g(x). (f/g = f(x)/g(x))

f(x)/g(x) is shown as: (3x - 6)/(x - 2).

The function shown above can be factored before we find the domain, since the greatest common factor of the numerator is 3.

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

f(x)/g(x) = 3

The function y = 3 is a horizontal line, so it has a domain of all real numbers.

Therefore, f/g is 3, and its domain is all real numbers, which is choice D.

Final answer:

The quotient of the functions f(x) = 3x - 6 and g(x) = x - 2 is 3. The domain of this quotient function is all real numbers except x = 2.

Explanation:

To find the quotient of the functions f(x) = 3x - 6 and g(x) = x - 2, we divide f(x) by g(x):

f/g = (3x - 6) / (x - 2).

Simplifying the expression:

f/g = 3(x - 2) / (x - 2).

Since (x - 2) is a common factor in both the numerator and the denominator, we can cancel it out as long as x is not equal to 2 (since division by zero is undefined):

f/g = 3; for all x ≠ 2.

Therefore, the quotient of f and g is 3, and the domain of this quotient function is all real numbers except x = 2.

about 3 beats per second

note 1 minute = 60 seconds

divide beats per minute by 60 for beats per second

[tex]\frac{200}{60}[/tex] = 3.333.... ≈ 3 beats per second

To estimate Camila's heart beats per second, divide her target heart rate of 200 bpm by 60 to get 3.33 beats per second.

To estimate the number of times Camila's heart will beat in one second, we need to convert her target heart rate from beats per minute (bpm) to beats per second. To do this, we divide her target heart rate by 60 (since there are 60 seconds in a minute). So, for Camila, her target heart rate in beats per second would be:

200 bpm ÷ 60 = 3.33 beats per second

Therefore, Camila's heart will beat approximately 3.33 times in one second.

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We are given the equation:

[tex]6(x-5)^{4}+4(x-5)^{2}+6=0[/tex]..........(1)

Now we have to write it in quadratic form using substitution.

The general form of quadratic equation is given by:

[tex]ax^{2}+bx+c=0[/tex]

So let us say

[tex](x-5)^{2}=u[/tex].......(2)

Plugging the value of (x-5)² from equation (2) in (1),

[tex]6u^{2}+4u+6=0[/tex]

Answer : Option B. [tex]6u^{2}+4u+6=0[/tex]

Answer:

B

Step-by-step explanation:

THE ANSWER IS 24

A and b are in parenthesis and there is no sign next to them, so you automatically have to multiply.

If that is supposed to be ab^2 then:

First you multiply 4 and 3 to get 12.

Then you multiply 12 by itself to get 144.

If it is supposed to be 2ab then:

First multiply 4 and 3 to get 12.

Then multiply 12 and 2 to get 24.

Step 1. Use Multiplication Distributive Property

-3 * 2^4x^4(4x^5y)^2

Step 2. Simplify 2^4 to 16

-3 * 16x^4(4x^5y)^2

Step 3. Use Multiplication Distributive Property

-3 * 16x^4 * 4^2(x^5)^2y^2

Step 4. Simplify 4^2 to 16

-3 * 16x^4 * 16(x^5)^2y^2

Step 5. Use the Power Rule

-3 * 16x^4 * 16x^10y^2

Step 6. Take out the constants

-(3 * 16 * 16)x^4x^10y^2

Step 7. Simplify 3 *16 * 16 to 768

-768x^4x^10y^2

Step 8. Use the Product Rule

-768x^4 + 10y^2

Step 9. Simplify 4 + 10 to 14

-768x^14y^2

​-3(2x)⁴(4x⁵y)² = When a power is raised to a power the exponents have to be multiplied.

​-3(2⁴x⁴)(4²x⁽⁵*²⁾y²) = We can take out the constants.

=-3*16*16(x⁴)(x¹⁰y²) = We can group the same variables​.

=-768(x⁴x¹⁰)(y²) = When multiplying two powers that have the same base, you have to add the exponents.​

​=-768x⁽⁴⁺¹⁰⁾y² = -768x¹⁴y²

​Answer : -768x¹⁴y²

Hope this helps!​​​​​

​​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

Let x mi/h be the speed of the boat in still water and y mi/h be the speed of stream.

1) Downstream.

The speed of the boat travelling downstream is x+y mi/h. Then

[tex](x+y)\cdot 10=280.[/tex]

2) Upstream.

The speed of the boat travelling upstream is x-y mi/h. Then

[tex](x-y)\cdot 20=280.[/tex]

3) Solve the system of equations:

[tex]\left\{\begin{array}{l}(x+y)\cdot 10=280\\ \\(x-y)\cdot 20=280\end{array}\right.\Rightarrow \left\{\begin{array}{l}x+y=28\\ \\x-y=14\end{array}\right..[/tex]

Add these two equations:

[tex]x+y+x-y=28+14,\\ \\2x=42,\\ \\x=21\text{ mi/h}.[/tex]

Subtract these two equations:

[tex]x+y-x+y=28-14,\\ \\2y=14,\\ \\y=7\text{ mi/h}.[/tex]

Answer: the speed of the boat in still water is 21 miles per hour and the speed of the stream is 7 miles per hour.

1. 5(5 + w) = 25 + 5w

2. 1.5(3 - 8c) = 4.5 - 12c

You simply use the distributive property to distribute the number outside of the parentheses to each term within the parentheses.

(A) j || k by the converse of the same-side interior angle Theorem is your answer

Note that " j || k" means that line j & k are parallel (True)

Note that both ∠1 & ∠2 are on the same side, and that they are located inside the parallelogram produced by the transversal lines (Same Side - Interior Angle Theorem)

Therefore, (A) is your answer

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~Rise Above the Ordinary

Lines are parallel if they have the same slope, not necessarily if the sum of their angles equals to 180.

The statement 'm1 + m2 = 180' typically holds true for two lines that are straight, where m1 and m2 are the angles measured from each line to a common line. If the sum of m1 and m2 adds up to 180º, the lines are supplementary, meaning they add up to form a straight line. However, they are not parallel.

In the context of lines that are parallel, they would have the same slope, but not necessarily the same angle. For instance, in a coordinate plane, the lines y = 4x + 1 and y = 4x - 3 are parallel because they have the same slope (4), but their y-intercepts are different.

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Add 15 to both sides.

8a>88

divide by 8

a>11

so b

8a-15>73

8a-15+15>73+15

Add 15 to both sides

8÷8a>88÷8

Divide both sides by 8

a>11

So you answer is B because the sign is only greater than and not and greater than equal to sign. Also remember if the sign is going > than the line goes to your right and if the sign is < than the line goes to the left of it.

Answer:

 729 is a perfect cube. The number whose cube is 729 is 9.

Explanation:

 Let us find the cubes of natural numbers from starting

     1 x 1 x 1 = 1

     2 x 2 x 2 = 8

     3 x 3 x 3 = 27

     4 x 4 x 4 = 64

     5 x 5 x 5 = 125

     6 x 6 x 6 = 216

     7 x 7 x 7 = 343

     8 x 8 x 8 = 512

     9 x 9 x 9 = 729

    10 x 10 x 10 = 1000

So we got that 729 is the cube of 9, so 729 is a perfect cube.

The number whose cube is 729 is 9.

Final answer:

Yes, 729 is a perfect cube and the number whose cube is 729 is 9.

Explanation:

Yes, 729 is a perfect cube.

To find the number whose cube is 729, we can take the cube root of 729, which is denoted as ∛729.

∛729 = 9

Therefore, the number whose cube is 729 is 9.

If the velocity of the rower is V1=3mph and velocity of the river is V2=7mph and

V1 ⊥V2 then

tanα=7/3 => tanα ≈ 2.33 => α≈ 66.8° ≈ 67°

The correct answer is 67°

Good luck!!!

Final answer:

To find the angle at which the man drifts downstream, we use the arctangent function on the ratio of the river's speed to the man's rowing speed. The calculation is θ ≈ arctan(7/3), which results in an angle of approximately 67 degrees.

Explanation:

The student's question involves finding the angle of drift for a man rowing across a river with a current. The man rows at 3 mph in still water, while the river flows at 7 mph. To find the angle of drift, we must use the concept of vectors and solve a vector addition problem, where one vector represents the man's rowing speed and the other represents the current of the river.

We can visualize this with a right triangle where the horizontal side represents the river flow and the vertical side represents the man's rowing speed. The angle of drift (\( \theta \)) between the resulting vector (the hypotenuse) and the direction the man is heading (across the river) can be found using the arctangent function:

[tex]\( \theta = \arctan(\frac{river\ speed}{man's\ rowing\ speed}) \)[/tex]

[tex]\( \theta = \arctan(\frac{7\ mph}{3\ mph}) \)Solving this, we find:[/tex]

[tex]\( \theta \approx \arctan(2.333) \)\( \theta \approx 66.8^\circ \)[/tex]

Therefore, rounding to the nearest degree, the angle to the line on which he is heading that the man drifts downstream is approximately 67 degrees.

The vertex of  f ( x )  is at  x  =  − 8/ 2   =  − 4

Answer:

Correct answer is D (-1,9)

A.

(-4,2)

B.

(4,-2)

C.

(1,-9)

D.

(-1,9)

Step-by-step explanation:

Final answer:

If we want to plot the graph of the equation y = -56x - 4, we can select two points on the line by choosing arbitrary values for x and then calculating the corresponding y-values.

Step-by-step explanation:

Let's choose x = 0 and x = 1 for simplicity:

1. When x = 0:

- Substitute x = 0 into the equation: y = -56(0) - 4

- Simplify the expression: y = 0 - 4 = -4

- So, the first point is (0, -4).

2. When x = 1:

- Substitute x = 1 into the equation: y = -56(1) - 4

- Simplify the expression: y = -56 - 4 = -60

- So, the second point is (1, -60).

Now we have two points on the line: (0, -4) and (1, -60). We can plot these points on a coordinate plane and draw a straight line passing through them to graph the equation y = -56x - 4.

If you look at the circle, center is B. It's located right in the center of the circle.

Answer

A. B

The center of the circle in the given figure is B.

Option A is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is given as πr².

We have,

The given figure has:

AB = radius

Ay = chord

B is the center

Thus,

The center of the circle is B.

Learn more about circle here:

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Answer:

A) (3, 12)

Step-by-step explanation:

For such a problem, I like to use a graphing calculator. It shows the answer quickly without a lot of fuss.

_____

If you want to solve this analytically, set the difference in y-values equal to zero and solve the resulting quadratic in the usual way. This will give the x-value at which the y-values are equal. (After we find x, we still need to find y.)

... y - y = 0

... x² -2x +9 -4x = 0

... x² -6x +9 = 0 . . . . . . collect terms. Recognize this as a perfect square.

... (x -3)² = 0

... x = 3 is the solution to this

... y = 4x = 4·3 = 12

The point on each of the given curves is (x, y) = (3, 12). The line is tangent to the parabola there, so there is only one point of intersection.

The line y = 4x and the parabola y = x^2 - 2x + 9 intersect at the point (3, 12).

To find the intersection points of the line y = 4x and the parabola y = x^2 - 2x + 9, we set the two equations equal to each other and solve for x. Hence the equation to solve is 4x = x^2 - 2x + 9. Rearranging this gives the quadratic equation x^2 - 6x + 9 = 0. This factors to (x - 3)^2 = 0, so x = 3 is the only solution, meaning the line and the parabola intersect at x = 3. Substituting x = 3 back into either the line or parabola equation gives y = 12, so the point of intersection is (3, 12).

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So the y would be hopefully that helps you ❤.

y = 2/9

2/3+y-1/9=7/9

=> 2/3+y=7/9+1/9

=> 6/9+y=8/9

So, y=2/9

Answer : $1,174.70

A circular pool has  diameter of 18 ft will have a uniform 4 ft concrete walkway   around it.

Diameter = 18ft . So radius = [tex]\frac{18}{2} = 9ft[/tex]

Area of circular pool = [tex]\pi r^2= 3.14 *9*9= 254.34 ft^2[/tex]

Radius of the pool with concrete = 9 + 4= 13

Area of circular pool with concrete=  [tex]\pi r^2= 3.14 *13*13= 530.66 ft^2[/tex]

Now surface area of concrete = area of pool with concrete - area of pool

Surface area = 530.66 - 254.34 = 276.32 square feet

the concrete cost $4.25 a square foot of surface area

So the cost for the concrete =  276.32 * 4.25 = $ 1174.36

We used the approximate value of pi that is 3.14 . so we got approximate answer

The option close to our answer is $1,174.70

$1,174.70 is the cost for the concrete

You did everything right all the way up to one small thing at the end.  When you moved the decimal to the left and made 10.35 into 1.035, you would need to make the exponent an 11.  Raising the exponent will show that you have moved the decimal more than the original problem started with.  

Hope this helps?

In the second to the last step (10.35 x 10¹⁰), you moved the decimal of 10.35 one place to the left but you did not balance it by moving 10¹⁰ one place to the right. FYI: Moving the exponent one place to the right means to add one to the exponent.

The correct answer: 1.035 x 10¹¹

Since there's a negative in front of the parenthesis, it switches the values inside. So that it's -2h+18=7h. h = 2

-68x + p = qx + 34

p - 34 = qx + 68x    added 68x to both sides & subtracted 34 from both sides.

p - 34 = x(q + 68)

[tex]\frac{p - 34}{q + 68} = x[/tex]

The denominator cannot be equal to zero so q + 68 ≠ 0   ⇒   q ≠ -68

You didn't upload the options but look for the one that has q = -68.

The initial number of transactions that took place in the first hour of Monday, which was 10, will not have any impact or bearing on the transactions for the rest of the day. Likewise, the initial number of transactions will not be affected by any other transactions or any other parameter. Thus, we can safely say that the initial number of transactions is neither an independent or a dependent variable.

Thus, out of the given options, Option C is the correct answer.

my brain tells me that the Correct answer is B my duuuuuuuddddeee

For this case we have the following data:

If we divide the volume of the container between the volume of the boxes, we obtain the number of boxes that fit in the container. Therefore:

[tex]\frac{50.148}{2.786}=18[/tex]

Answer:

the shipping container holds:

Option D

Answer:

Option (a) is correct.

The interest that Perry will earn each month on $650 is $ 2.70

Step-by-step explanation:

Given : Perry earns 5 percent simple interest annually on his savings account.

We have to determine the interest that  Perry will earn each month on $650.

Since, Given Perry rate of interest is 5%

So , her monthly rate of interest will be [tex]\frac{5}{1200}[/tex]

Using Formula for Simple interest

[tex]S.I = P\times r\times t[/tex]

Thus, for principal $ 650 at rate of interest [tex]\frac{5}{1200}[/tex] for one month .

Perry interest will be,

[tex]S.I.=650\cdot\frac{5}{1200}\cdot1[/tex]

Simplify, we get ,

Simple interest = $ 2.70

Thus, The interest that Perry will earn each month on $650 is $ 2.70