For f(x)=5x−x2 , use the definition of a derivative to find f′(x)

Answer:

25.8°

Step-by-step explanation:

The wall is vertical so it makes 90°  with the ground.

The ladder forms a right triangle of base = 45 ft and hypotenuse = 50 ft

To find the angle (x) the ladder makes with the ground:

Cos x = [tex]\frac{45}{50}[/tex] = 0.9

[tex]Cos^{-1}[/tex] 0.9 = 25.8° (answer rounded up to nearest tenth)

The angle that the bottom of the ladder makes with the ground in a scenario where a 50ft ladder is leaning against a wall, with the base of the ladder being 45ft from the base of the wall, can be found using basic trigonometry. By using the cosine law, we find that the angle is approximately 25.84 degrees.

To find the angle the bottom of the ladder makes with the ground, we can use basic trigonometry. In this situation, we have a right-angled triangle formed by the wall, the ground, and the ladder, and we are given that the adjacent side (base of the ladder in relation to the vertical wall) is 45 feet and the hypotenuse (the ladder) is 50 feet.

Using the cosine law, the cosine of the angle is equal to the adjacent side divided by the hypotenuse, so:

cosine(Angle) = Adjacent/hypotenuse = 45ft/50ft = 0.9.

Now, we just need to find the inverse cosine (or acos) of 0.9 to find our angle:

Angle = acos(0.9) = 25.84 degrees approximately.

So, the angle that the bottom of the ladder makes with the ground is approximately 25.84 degrees. This result is independent of the length of the ladder.

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[tex]\frac{-3}{8}[/tex] ÷[tex]\frac{-1}{3}[/tex]

When dividing fractions these are the steps you will take:

1. The first number in the expression stays the same  

[tex]\frac{-3}{8}[/tex] ÷[tex]\frac{-1}{3}[/tex]

2. Change the division sign into a multiplication sign

[tex]\frac{-3}{8}[/tex] × [tex]\frac{-1}{3}[/tex]

3. Take the reciprocal (switch the places of numerator and denominator) of the second number in the expression

[tex]\frac{-3}{8}[/tex] × [tex]\frac{-3}{1}[/tex]

4. Multiply across

[tex]\frac{-3*-3}{8*1}[/tex]

[tex]\frac{9}{8}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

The quotient of -3/8 and negative 1/3 is 9/8. To get this result, multiply the first fraction by the reciprocal of the second fraction, and since both fractions are negative, the result is positive.

Explanation:

The question asks about the quotient when dividing two negative fractions, specifically -3/8 and negative 1/3. When dividing fractions, the rule is to multiply the first fraction by the reciprocal of the second fraction. Also, when dividing two negative numbers, the result is positive because a negative divided by a negative equals a positive.

To find the reciprocal of negative 1/3, we flip the numerator and denominator to get -3/1, which is -3. Then we keep the first fraction, change division to multiplication, and multiply by the reciprocal of the second fraction:

-3/8 × -3 (which is the reciprocal of negative 1/3)

When we multiply these, the negative signs cancel out and we get 3/8 × 3/1 = 9/8

Therefore, the quotient of -3/8 and negative 1/3 is 9/8, which is a positive number because the negatives cancel each other out as per the multiplication rules for signs.

Answer:

(fog)(-3) = 125

Step-by-step explanation:

So, we need to first evaluate g(-3) and then plug the value of g(-3) into f(x) to find (fog)(-3). So, let's do that:

[tex]g(-3) = -3-2 = -5[/tex]

[tex]f(g(-3)) = f(-5) = 5(-5)^2 = 5(25) = 125[/tex]

Thus, (fog)(-3) = 125.

Answer:

D

Step-by-step explanation:

The ratio of corresponding sides are equal, that is

[tex]\frac{4}{8}[/tex] = [tex]\frac{y}{14}[/tex]

Answer:

90° counter clockwise rotation of point 0(x, y) about origin = (-y, x)

Step-by-step explanation:

Following are the rules for a counter clockwise rotation of 90 degrees about the origin for a point O(x,y):

1. Invert the sign of the value of y.

2. Switch x and y with each other.

For example, a point A(5,2) after rotation gives a point B(-2,5) using the rules given above. The points on the x-y plane are shown in the image attached.

Answer:

x = - 2, x = 6

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make the expression undefined.

Equating the denominator to zero and solving gives the values that x cannot be.

Solve

- 3x² + 12x + 36 = 0 ( divide through by - 3 )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

x = - 2 and x = 6 ← are the excluded values

ANSWER

The correct answer is D

EXPLANATION

According to the Rational Roots Theorem, the possible rational roots are all the factors of the constant term expressed over the factors of the leading coefficient of the polynomial function.

Based on this we conclude that,

[tex] - \frac{ 2}{5} [/tex]

is a potential rational root of

[tex]f(x) = 25 {x}^{4} - 7 {x}^{2} + x + 4[/tex]

The reason is that the numerator of this rational root is a factor of 4 and the denominator is a factor of 25.

Answer: the correct answer is D

==================================================

Explanation:

If we had a pit stop every 1 mile, then we would have 36 pit stops. Note how 36/1 = 36.

If we had a pit stop every 2 miles, then we would have 18 pit stops because 36/2 = 18

If we had a pit stop every 3 miles, then we would have 12 pit stops because 36/3 = 12

And so on.

As you can see, we divide the total length 36 over the number of miles between pit stops. This applies even to fractions as well

Divide 36 over 4/6 to get

[tex]36 \div \frac{4}{6} = 36 \times \frac{6}{4} = 36 \times 1.5 = 54[/tex]

Recall that when you divide by a fraction, you flip the second fraction and multiply. The action of "flipping" is known as applying the reciprocal.

So this means there are 54 pit stops in total.

An alternative method to get the answer is to note that 4/6 = 0.66666667 approximately, and 36/0.66666667 = 53.99999973 which is very close to 54 that we got above. The reason why its not exactly 54 is because of rounding error. The more decimal digits you use, the more accurate the result will be.

Answer:

The solution set is {1, -2/3, 2/3}.

Step-by-step explanation:

81m^3-81m^2-36m+36=0

9(9m^3 - 9m^2 - 4m + 4) = 0

Looks  like 1 might be  one root:

f(1) = = 9*1 - 9*1 - 4*1  + 4 = 0  so one factor is (x - 1).

Divide the function  by x - 1:

        9m^2 - 4  <------------------Quotient

        ----------------------------------

m - 1 ) 9m^3 - 9m^2  - 4m + 4

         9m^3-9m^2

         -----------------------

                       -4m + 4

                        -4m + 2

                         ..............

Now :

9m^2 - 4 = (3m - 2)(3m + 2).

so  m - 1 = 0  or 3m - 2 = 0 or 3m + 2 = 0

m = 1 , 2/3,  -2/3.

The vertical asymptotes of the function is the point where the denominator of the function is zero. The vertical asymptote of the function is x = 3

Given the function expressed as:

f(x) = 6/x - 3

The vertical asymptotes of the function is the point where the denominator of the function is zero

x - 3 = 0

x = 0 + 3

x = 3

Hence the vertical asymptote of the function is x = 3

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Answer:

A  viable solution is the ordered pair (0,0)

Step-by-step explanation:

we know that

The number of books cannot be a negative number

The number of books is a positive integer

The weight cannot be a negative number

therefore

A  viable solution is the ordered pair (0,0)

Answer:

The third option

Step-by-step explanation:

Trust me ;) I got it right

Answer:

x = 1

y = 3

Step-by-step explanation:

We can solve this problem by inputting the second equation into the first equation by replacing the y variable with the second equation.

x + 3y = 10

y = x + 2

x + 3(x + 2) = 10

Now, distribute three with x and 2

3 * x = 3x

3 * 2 - 6

x + 3x + 6 = 10

4x + 6 = 10

Subtract 6 from both sides

4x = 4

So, x = 1

Solve for y by replacing x in the second equation with 1.

y = 1 + 2

y = 3

The solution to the system of equations is x = 1 and y = 3.

To solve the system of equations using the substitution method, we can start by substituting the value of y from the second equation into the first equation. Let's proceed step by step:

Step 1: Given equations:

1) x + 3y = 10

2) y = x + 2

Step 2: Substitute the value of y from equation (2) into equation (1):

x + 3(x + 2) = 10

Step 3: Distribute the 3 on the left side of the equation:

x + 3x + 6 = 10

Step 4: Combine like terms:

4x + 6 = 10

Step 5: Move the constant term to the other side of the equation:

4x = 10 - 6

Step 6: Simplify the right side:

4x = 4

Step 7: Divide both sides by 4 to solve for x:

x = 4/4

x = 1

Step 8: Now that we have the value of x, substitute it back into equation (2) to find y:

y = x + 2

y = 1 + 2

y = 3

Step 9: Check the solution by substituting the values of x and y into the original equations:

Equation 1: 1 + 3(3) = 10

1 + 9 = 10 (True)

Equation 2: 3 = 1 + 2

3 = 3 (True)

The solution to the system of equations is x = 1 and y = 3.

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Answer:

12

Step-by-step explanation:

√(9×16) =√9×√16 = 3 ×4 = 12

Answer:

Diameter: 4

Radius: 2

Equation: ( x-3 ) + ( y + 2) = 4

Final answer:

The length of the diameter is 4 units, the radius of the circle is 2 units, and the equation of the circle, with its center at (3,-2), is (x - 3)² + (y + 2)² = 4.

Explanation:

The diameter of a circle is the distance between two points on the circumference of the circle which pass through the center of the circle. The two points given are (5,-2) and (1,-2), which both lie on a horizontal line since their y-coordinates are the same. To find the length of the diameter, you calculate the distance between these two points using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

For these points, it becomes:

d = √((1 - 5)² + (-2 - (-2))²) = √((-4)² + (0)²) = √(16) = 4

Therefore, the length of the diameter of the circle is 4 units.

To find the radius of the circle, which is half the diameter, divide the diameter by 2:

r = d / 2 = 4 / 2 = 2 units

The equation of a circle in the standard form is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Given that the center is the midpoint between (5,-2) and (1,-2), which is (3,-2), the equation of the circle with a radius of 2 would be:

(x - 3)² + (y + 2)² = 2²

(x - 3)² + (y + 2)² = 4

Answer:

x<48.83778966 :) have a great day!

Step-by-step explanation:

Answer:  The required solution is x < 48.837.

Step-by-step explanation:  We are given to solve the following inequality for the value of x :

[tex]11.22x-200<347.96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the above inequality, we need to take all the constant terms on one side and the term involving unknown variable on the other.

The solution of inequality (i) is as follows :

[tex]11.22x-200<347.96\\\\\Rightarrow 11.22x<347.96+200\\\\\Rightarrow 11.22x<547.96\\\\\Rightarrow x<\dfrac{547.96}{11.22}\\\\\Rightarrow 48.837.[/tex]

Thus, the required solution is x < 48.837.

Answer:

Exponential

Step-by-step explanation:

As the x value is increasing by 1, the Y value is multiplying by 3. Since the value is increasing rapidly from 3 to 9 to 27 to 81 to 243, this is an exponential function.

The type of function which  is represented by the table of values below is:

                               B. Exponential

We are given a table of values as:

              x                 y

              1                  3

              2                 9

              3                 27

              4                 81

              5                 243  

We can model this equation by the formula:

[tex]y=3^x[/tex]

Since, when x=1 we have:

[tex]y=3^1\\\\i.e.\\\\y=3[/tex]

when x=2 we have:

[tex]y=3^2\\\\i.e.\\\\y=9[/tex]

when x=3 we have:

[tex]y=3^3\\\\i.e.\\\\y=27[/tex]

and so on.

Hence, the function is exponential.

          i.e.  [tex]y=3^x[/tex]

Answer:

The answer is C

Step-by-step explanation:

The correct option is c.

The following information should be considered:

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Answer:

RAGE

Step-by-step explanation:

Answer:

k = 10

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠ZYM is an exterior angle and

∠YZX and ∠ZXY are the 2 opposite interior angles, hence

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{5x^2+8x+7}{4x}[/tex]

Divide each term on the numerator by 4x

= [tex]\frac{5x^2}{4x}[/tex] + [tex]\frac{8x}{4x}[/tex] + [tex]\frac{7}{4x}[/tex]

= [tex]\frac{5x}{4}[/tex] + 2 + [tex]\frac{7}{4x}[/tex]

Answer:

a = k / (4 + 9b)

Step-by-step explanation:

k = 4a + 9ab

Factor out a:

k = a (4 + 9b)

Divide by 4 + 9b:

k / (4 + 9b) = a

Answer:

In my opinion the answer is y = 6

Step-by-step explanation:

We have two unknowns from the equation therefore, two equations are needed. These equations are:

3x + y = 9  

y = –4x +10  

To solve for y, we first substitute the second equation to the first one.

3x + –4x +10= 9  

x = 1

We substitute the value of x to either of the equations and solve for y.

y = –4(1) +10  

y = 6

Answer:

y=6

Step-by-step explanation:

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

[tex]y = -4x + 10[/tex]

Substitute the value of y in the first equation:

[tex]3x + (-4x + 10) = 9[/tex]

Apply the subtraction property of equality:

[tex]-x + 10 = 9[/tex]

[tex]-x=-1[/tex]

x=1

Substitute 1 for x in the given y equation

[tex]y = -4x + 10[/tex]

[tex]y = -4(1)+ 10[/tex]

y=6

Answer:

radius is perpendicular to the chord

The radius of a circle that bisects a chord is perpendicular to that chord.

If a radius of a circle bisects a chord, then it is perpendicular to that chord. By definition, the radius that bisects the chord also bisects the angle at the center of the circle which subtends the chord. This is a direct consequence of a theorem in geometry which states that in a circle, the radius that bisects an angle at the centre is perpendicular to the chord which subtends the angle and bisects the chord itself. This perpendicularity is an important property as it asserts that the bisector of the chord is the shortest path from the circle's center to the chord and it cuts the chord into two equal segments, thus verifying the right angle formed between the radius and the chord.

Answer:

[tex]\frac{(k+5)}{12(k+2)}[/tex]

Step-by-step explanation:

We need to perform the folowing operation:

[tex]\frac{k^{2} + 3k - 10 }{36}[/tex] × [tex]\frac{3}{k^{2} -4 }[/tex]

Factorizing we have:

[tex]\frac{(k-2)(k+5)}{36}[/tex]  × [tex]\frac{3}{(k+2)(k-2)}[/tex]

Simplifying, we get:

[tex]\frac{(k+5)}{12(k+2)}[/tex]

Answer:

64

Step-by-step explanation:

Volume of a cube is:

V = s³

When s = 8 in:

V = (8 in)³ = 512 in³

When s is doubled (s = 16 in):

V = (16 in)³ = 4096 in³

Now we can write a proportion:

8 mugs / 512 in³ = x mugs / 4096 in³

x = 64

The maximum number of mugs that the larger box can hold is:

                                     64

The edge length of box is:  8 inches.

This means that the volume of box is: 8×8×8=512 cubic inches.

Also, the number of mugs a box of edge length 8 in. can hold is: 8

Hence, volume of 1 mug= Volume of box/Number of mugs

Volume of 1 mug= 512/8=64 cubic inches

Now, if the dimension of the box is doubled.

This means that the Volume of new box= 8×Volume of old box

Volume of new  box=8×512=4096 cubic inches

Let n be the number of mugs that the new box can hold.

Volume of new box=n×Volume of  1 mug

⇒   4096=n×64

⇒   n=4096/64

⇒  n=64

               Hence, the answer is:

                            64

Answer: 75

Step-by-step explanation:

The area formula for a trapzoid is area= 1/2 (a+b) h

In this equasion, the substitution would be area=1/2 (10+15) 6

Following PEMDAS, enter the numbers within the parenthases (10+15)

Divide the 25 in half, then multiply by 6. This comes out to 75.

For this case we have that by definition, the area of a trapezoid is given by:

[tex]A = \frac {1} {2} (B + b) * h[/tex]

Where:

B: It is the major base

b: It is the minor base

h: It's the height

According to the figure we have the following data:

[tex]B = 15ft\\b = 10ft\\h = 6ft[/tex]

Substituting in the formula:

[tex]A = \frac {1} {2} (15 + 10) * 6\\A = \frac {1} {2} (25) * 6\\A = \frac {1} {2} 150\\A = 75[/tex]

Finally, the area of the trapezoid is[tex]75ft ^ 2[/tex]

Answer:

[tex]75ft ^ 2[/tex]

The key aspect of a function's graph in Mathematics is its ability to visually illustrate relationships, patterns, and comparisons. Different types of graphs, like line, bar, and pie, provide different ways to interpret the data. Understanding these graphs helps in mathematical analysis and solving problems.

The question involves analyzing functions' graphs and matching them with their meanings. In Mathematics, a function's graph can represent different types of information based on its structure. For example, a line graph signifies a linear relationship between two variables denoted on the horizontal and vertical axis. The height of the curve at any point on the graph represents the value of the function at that point.

Three distinct types of graphs are the line, bar, and pie graph. A line graph shows the relationship between two variables with one variable being represented on the horizontal axis and the other on the vertical axis. A bar graph utilises the height of the bars to signify a relationship, with each bar representing a distinct entity like a group of people or a country. A pie graph is used to show how something is distributed, with each slice representing the corresponding percentage of the whole.

Deciphering this information from a graph includes recognizing patterns, comparisons, and trends, providing an intuitive sense of relationships in the data.

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Here are the matches: f(x) > 0: Intervals of the domain where the graph is above the x-axis. f(x) < 0: Intervals of the domain where the graph is below the x-axis. Y-intercept: Location on the graph where the output is zero. X-intercept: Location on the graph where the input is zero.

In a function f(x), when f(x) > 0, it indicates the intervals on the domain where the function's values are positive, corresponding to regions above the x-axis. Conversely, when f(x) < 0, it denotes intervals where the function's values are negative, representing areas below the x-axis.

The y-intercept is the point where the graph intersects the y-axis, highlighting where the output (function value) is zero. On the other hand, the x-intercept is where the graph crosses the x-axis, signifying the point where the input (x-value) is zero, resulting in a zero output. These aspects provide valuable insights into a function's behavior and characteristics.

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Answer:

1/5

Step-by-step explanation:

There are 10 marbles and two white marbles.

make a probability.

2/10

simplify= 1/5

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

i had the same problem on acellus and 1/5 was the right answer for me not 4/5

Answer:

2 1/24

Step-by-step explanation:

2/3 =    16/24

3/4=      18/24

5/8=       15/24

16+18+15=49

49-24=  25-24=1

2 1/24

Answer:

The cost of one ticket is $9

Step-by-step explanation:

we have

4x+12=48

where

x represents the cost of a ticket

Solve for x

Subtract 12 both sides

4x=48-12

4x=36

Divide by 4 both sides

x=36/4=9

therefore

The cost of one ticket is $9