Suppose that the functions r and s are defined for all real numbers x as follows.
r(x) = x-1
s(x) = 3x^2
Write the expressions for (r+s) (x) and (r*s) (x) and evaluate (r-s) (-3).
(r+s) (x) =
(r*s) (x) =
(r-s) (-3) =

Please help.

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:

Answer:

168  which is not listed

Step-by-step explanation:

Do what is inside the brackets first. Subtract the two terms

52 - 10 = 42

Now multiply by 4

42 * 4 = 168 which is none of your answers. There must be more to the problem.

Yes, there is.

Two variable are in a proportional relationship if one is a multiple of other, i.e. if their ratio is constant.

In fact, two equivalent ways of saying that x and y are in a proportional relationship are saying that there exists a number k such that

[tex] y = kx\quad\text{or}\quad \dfrac{y}{x}=k [/tex]

In this case, you can see that the perimeter is always three times the side, which makes sense, because the perimeter of an equilateral triangle is composed of three "copies" of the side of the triangle.

So, the perimeter is a multiple of the side (with k=3), and in fact you have

[tex] p = 3s \iff \dfrac{p}{s} = 3 [/tex]

which are the two equivalent ways of saying that p and s are in a proportional relationship.

Yes, there is a proportional relationship between the perimeter and the side length of an equilateral triangle as indicated by the equation p = 3s. If you double the side length, the perimeter also doubles.

Yes, there is a proportional relationship between the perimeter and the side length of an equilateral triangle. This can be observed from the equation p = 3s, which indicates that the perimeter is always three times the length of each side. In terms of proportionality, if you double the side length of the triangle (for instance), the perimeter also doubles. This is because the three sides of an equilateral triangle are of equal length, so any change in side length will cause a proportional change in the perimeter.

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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

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.

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]​​​​​​

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

there is a 1:8 ratio so there will be 40 nickels and 5 dimes

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.

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.

-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.

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.

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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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

∠BEC ≅ ∠CED          definition of angle bisector

∠BEC = ∠CED           definition of congruency

∠AEB , ∠BEC, and ∠CED are supplementary    

∠AEB + ∠BEC + ∠CED = 180    definition of supplementary angles

∠AEB + ∠CED + ∠CED = 180    substitution

11x - 12 + 4x + 1 + 4x + 1 = 180    substitution

19x - 10 = 180              simplified (added like terms)

19x = 190                    addition property of equality

  x = 10                       division property of equality

*****************************************************************

∠AEB = 11x - 12

         = 11(10) - 12

          = 110 - 12

          = 98

∠BEC = ∠CED = 4x + 1

                        = 4(10) + 1

                         = 40 + 1

                          = 41

********************************************************************

∠AEB + ∠BEC = ∠AEC   segment addition property

98 + 41 = ∠AEC               substitution

 139 = ∠AEC                  simplified (added like terms)

Answer: 139°

An angle bisector divides an angle into two equal halves. The measure of angle AEC is: [tex]139^o[/tex]

Given that:

[tex]\angle AEB = 11x - 12[/tex]

[tex]\angle CED = 4x + 1[/tex]

Since ray BD bisects [tex]\angle BED[/tex], then:

[tex]\angle BEC = \angle CED[/tex]

This implies that:

[tex]\angle BEC = 4x + 1[/tex]

[tex]\angle AEC[/tex] is calculated as:

[tex]\angle AEC = \angle AEB + \angle BEC[/tex]

This gives:

[tex]\angle AEC = 11x - 12 + 4x + 1[/tex]

Collect like terms

[tex]\angle AEC = 11x + 4x- 12 + 1[/tex]

[tex]\angle AEC = 15x-11[/tex]

Next, we calculate the value of x as follows:

[tex]\angle AEB + \angle CED + \angle BEC = 180[/tex] --- angle on a straight line.

This gives:

[tex]11x - 12 + 4x + 1 + 4x + 1 = 180[/tex]

Collect like terms

[tex]11x + 4x + 4x = 180+12-1-1[/tex]

[tex]19x = 190[/tex]

Divide by 19

[tex]x = 10[/tex]

Substitute 10 for x in [tex]\angle AEC = 15x-11[/tex]

[tex]\angle AEC= 15 \times 10 - 11[/tex]

[tex]\angle AEC= 139^o[/tex]

Hence, the measure of [tex]\angle AEC[/tex] is [tex]139^o[/tex]

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a) substitution   (refer to statements 1 and 2)

b) definition of supplementary

c) subtraction property of equality

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:

The graph of the line is obtained as the straight line passes through (-2.667,0) and (0,2).

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the equation of the line is f(x)=3/4x+2.

We have to draw the graph using the two points. The point through which the line passes.

The slope of the given line is -3/4 and having an intercept of 2.

Thus, the graph of the line is obtained as the straight line passes through (-2.667,0) and (0,2).

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To graph the line y = (3/4)x + 2, choose two points and connect them by drawing a straight line.

To graph the line y = (3/4)x + 2, we can select two points and connect them. Let's choose the points (0, 2) and (4, 5). Substitute the x-values into the equation to find the corresponding y-values:

Plot these two points on the graph and draw a straight line passing through them. Label the graph with f(x) and x.

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.

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.

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.

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.

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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