Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.
y=6x

ANSWER 1

Note that,

[tex]f(u)=tan^{-1}(u)[/tex]

is the same as

[tex]f(u)=arctan(u)[/tex]

We apply the product rule.

[tex]f(x)=x^2tan^{-1}(x)[/tex]

So we keep the second function and differentiate the first,plus we keep the first function and differentiate the second.

[tex]f'(x)=(x^2)'tan^{-1}(x)+x^2(tan^{-1}(x))' [/tex]

Recall that,

If

[tex]f(u)=tan^{-1}(u)[/tex]

Then,

[tex]f'(u)=\frac{1}{1+u^2}} \times u'[/tex]

This implies that,

[tex]f'(x)=2xtan^{-1}(x)+\frac{x^2}{x^2+1} [/tex]

ANSWER 2

We apply the product rule and the chain rules of differentiation here.

[tex]f(x)=xsin^{-1}(1-x^2)[/tex]

[tex]f'(x)=x'sin^{-1}(1-x^2)+x(sin^{-1}(1-x^2))' [/tex]

Recall that,

If

[tex]f(u)=sin^{-1}(u)[/tex]

Then,

[tex]f'(u)=\frac{1}{\sqrt{1-u^2}} \times u'[/tex]

This implies that,

[tex]f'(x)=sin^{-1}(1-x^2)+x \times \frac{1}{\sqrt{1-(1-x^2)^2}}\times (-2x) [/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-(1-2x^2+x^4)}} [/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-1+2x^2-x^4}}[/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{2x^2-x^4}}[/tex]

Part (a)

The variable y is the dependent variable and the variable x is the independent variable.

Part (b)

The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:

[tex]0.75\times 18=13.5[/tex] dollars

Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.

Therefore, the price of the fair admission is: $33.50-$13.50=$20

If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be  written as:

[tex]y=0.75x+20[/tex]......Equation 1

Part (c)

The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.

Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.

the sum of the angles in a triangle = 180°, thus

x + [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{6}[/tex] x = 180

multiply through by 6

6x + 3x + x = 1080

10x = 1080 ( divide both sides by 10 )

x = 108

the angles are 108°, 54° and 18°

Since all the angles are different and the largest is 108°

The triangle is an obtuse scalene triangle

The measures of the angles of the triangle are approximately 108 degrees, 54 degrees, and 18 degrees. This type of triangle is a scalene triangle, as all of its angles are different.

To find the measures of the angles of a triangle whose angles are x, 1/2x, and 1/6x, we will use the fact that the sum of the angles in a triangle is always 180 degrees. The equation representing this is:

x + 1/2x + 1/6x = 180

Combine like terms:

1.6667x = 180

Then solve for x:

x ≈ 108 degrees

Now plug x into the original angle measures to get:

Angle 1 = 108 degrees

Angle 2 = 1/2x = 54 degrees

Angle 3 = 1/6x = 18 degrees

Lastly, in terms of the type of triangle, this is a scalene triangle because all of its angles are different.

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[tex]x=0.\overline{37}\\\\100x=37.\overline{37}\\\\100x-x=37.\overline{37}-0.\overline{37}\\\\99x=37\\\\x=\dfrac{37}{99}[/tex]

The angle in the dilated figure is the same as the original angle in each case, a fact that should be confirmed by the way the answer choices are shown.

∠A = ∠A'

... 4x -4 = 51 -x

... 5x = 55

... x = 11

∠A = 4·11 -4 = 40 . . . . . . doesn't match any offered choice

___

∠B = ∠B'

... 6x -1 = 4x +21

... 2x = 22

... x = 11

... ∠B = 6·11 -1

... ∠B = ∠B' = 65 . . . . . matches selection D)

_____

∠C = ∠C'

... 8x -13 = 6x +9

... 2x = 22

... x = 11

... ∠C = 6·11 +9 = 75

... ∠C = ∠C' = 75 . . . . . matches selection D)

Angles B and C are alternate interior angles where transversal BC cuts parallel lines AB and CD. Thus angles B and C are equal. Angle B is 65°.

Angle AEC is the exterior angle opposite interior angles A and B, which means its value is the sum of angles A and B.

∠AEC = ∠A +∠B = 47° +65°

∠AEC = 112°

Let's form the difference of the two expressions and see what we can learn.

(2y -x) -(2x -y) = 2y -x -2x +y = 3y -3x = 3(y -x)

Since y > x, this is positive, so 2y -x is greater than 2x -y.

let Leo's speed = x mile/hr

so Ethan speed = (x + 6) miles per hour

Distance = Speed × Time

so distance traveled by Leo in 2 hours = x × 2 = 2x

and distance traveled by Ethan in 1.5 hours = 1.5( x + 6 ) = 1.5x + 9

since  they meet on the path , After Ethan has ridden 1.5 hours and Leo has ridden 2 hours , so together the have traveled on complete path that is 65 miles.

⇒  distance traveled by leo in 2 hours + distance traveled by Ethan in 1.5 hours = 65

⇒  2x + 1.5x + 9 = 65

⇒ 3.5x = 56

⇒ x = 16

Hence Leo's speed = x miles/hr = 16 miles/hour

and Ethan's speed = (x + 6) miles/hr = 16 +6 = 22 mile/hour

Answer:

Leo's Speed = 16

Ethan's Speed = 22

Step-by-step explanation:

Into each bowl, he will pour

... (1/3)×(7 1/5) = (1/3)×(6 6/5) = 2 2/5 . . . liters of juice

_____

Here, we have elected to rewrite 7 1/5 as 6 6/5 so each part of the number (whole number, fraction) will be divisible by 3.

You may have been taught to convert 7 1/5 to an improper fraction before doing the multiplication. That method looks like ...

... (1/3)×(36/5) = 12/5 = 2 2/5 . . . . same result

The third angle of the triangle will be the supplement of the sum of the given angles. In order for the triangle to be isosceles, two of the three angles must have the same value.

a) 180 -40 -75 = 65 . . . not isosceles

b) 180 -30 -100 = 50 . . . not isosceles

c) 180 -35 -70 = 75 . . . not isosceles

d) 180 -50 -80 = 50 . . . matches one of the other angles. This triangle is isosceles.

The appropriate choice is ...

... 50 and 80

Area is the product of length and width. If you assume the dimensions are integers, you are looking for factors of 117 that differ by 4.

117 = 1×117 = 3×39 = 9×13

These last two factors differ by 4, so we know the dimensions of the barn are ...

... 9 ft wide by 13 ft long

i think it will be c not really 100 percent sure

Answer:

C 767

Step-by-step explanation:

2031 ÷ 3 = 767

and took test

Answer:

f(-1) = -1 . . . . matches the last selection

Step-by-step explanation:

When evaluating piecewise functions, the first step is to determine the applicable piece. The argument -1 is in the range of the middle definition, (-2, 1). So, the function value is ...

... (-1)³ = -1

Answers: The statement that express the same scale are Options B and C.

Solution:

A. 5 cm on the map represents 50 m in Chicago?

Rule of three:

1 cm represents 100 m

5 cm represents    x

x=(5 cm).(100 m) / (1 cm)

x=500 m

5 cm on the map represents 500 m in Chicago.

The statement A doesn't express the same scale.

B. 1 mm on the map represents 10 m in Chicago?

1 mm = 0.1 cm

Rule of three:

1 cm    represents 100 m

0.1 cm represents    x

x=(0.1 cm).(100 m) / (1 cm)

x=10 m

1 mm = 0.1 cm on the map represents 10 m in Chicago.

The statement B expresses the same scale.

C. 1 km in Chicago is represented by 10 cm on the map?

1 km = 1,000 m

Rule of three:

1 cm    represents 100 m

x         represents  1,000 m

x=(1 cm).(1,000 m) / (100 m)

x=10 cm

1 km = 1,000 m in Chicago is represented by 10 cm on the map.

The statement C expresses the same scale.

D. 100 cm in Chicago is represented by 1 m on the map?

100 cm = 1 m

Rule of three:

1 cm    represents 100 m

x         represents  1 m

x=(1 cm).(1 m) / (100 m)

x=0.01 cm

100 cm = 1 m in Chicago is represented by 0.01 cm on the map.

The statement D doesn't express the same scale.

Answer:

a,b,c d is incorrect but a,b,c is right

Step-by-step explanation:

just took the test

There are 5 days to a school week: Monday, Tuesday, Wednesday, Thursday and Friday.

Divide number of school days by 5 to find the number of weeks:

171 / 5 = 34.2 weeks.

The weeks start with Monday, so there would be 35 Mondays. ( 34 full weeks and the partial week would begin with a Monday)

Divide 171 by 7 (as there are 7 days in each week), obtaining 24.4.  There's one Monday in every 7 days, so in 168 days there'd be exactly 24 Mondays, and in 171 days there'd still be exactly 24 Mondays, with 3 days left over.

The first question probably has a drawing that is not included. Can you please include whatever drawing cam with it?

The Qeustion 2:

starting with writing the complementary angles:

The angles <a and <b being complementary means that

<b = 180 - <a

The angles <b and <c are complementary - that means

<c = 180 - <b

now plug in the first equation for <b to get:

<c = 180 - (180 - <a) = 180-180+<a= <a

so

<c = <a

which was to be proved!

The equation would be 4y=5x       4(x+15)=5x             x+15=y

let x be the amount that Shelia deposits each time

let y represent the amount that Sherri deposits each time

4(x+15)=5x

4x+60=5x

-4x       -4x

60=x

Check:

x+15=y                  60+15=y                        y=75

4(75)=5(60)

300=300

Shelia deposits $60 each time.

DERIVAR :

(2x – 1) / √ x2 + 1

∠1 and ∠2 are alternate exterior angles where transversal BE crosses parallel lines AC and DF, therefore they are equal. ∠2 and ∠3 are opposite angles of a parallelogram, therefore they are equal.

... ∠1 = ∠2

... 3x -5 = 2x +15 . . . . substitute the given values

... x = 20 . . . . . . . . . . . add 5-2x

The measures of angles 1, 2, and 3 are 2·20+15 = 55 . . . degrees.

29°

Consider the right triangle between the plank and the ground

the angle can be found using tangent ratio

tanx° = [tex]\frac{opposite}{adjacent}[/tex]

where adjacent = 18 and opposite = 10

tanx° = [tex]\frac{10}{18}[/tex]

x = [tex]tan^{-1}[/tex]([tex]\frac{10}{18}[/tex]) = 29.0546 ≈ 29°

Answer:

29 degrees to nearest degree.

Step-by-step explanation:

This is the angle whose tangent is  10/18 or 5/9.

this = 29 degrees

Answer:

1. B) 7

2. B) {y|y ≤ -1}

Step-by-step explanation:

1. Put -4 where x is in the function definition and do the arithmetic.

... 3 - (-4) = 3 +4 = 7

2. If the maximum function value is -1 and the values extend to -∞ from there, then the range is (-∞, -1]. In your notation, that is ...

... {y | y ≤ -1}

B and B

f(x) → 3 - x

to evaluate f(- 4 ) substitute x = - 4 into f(x)

f(- 4 ) = 3 - (- 4 ) = 3 + 4 = 7 → B

the range of a function are the values of y for the function

this function ( probably quadratic ) has a vertex at (0, - 1), that is the y-value is - 1

Since the function opens down then the values of y are tending to negative infinity

so the range of values for y are less than or equal to - 1 to negative infinity

{y | y ≤ - 1 } → B

A

note that r = 3.75% = 0.0375

A(9) = 10500 × [tex]e^{0.0375(9)}[/tex] = 10500 × [tex]e^{0.3375}[/tex] = 14, 715.12

We are given formula for continuous change function A(t) = Pe^rt.

We need to find the value of $10,500 investment amount grows 3.75% each year after 9 years.

Plugging values of P=10500

r= 3.75% = 0.0375 and

t=9 in given formula.

We get

[tex]A(9) = 10500e^{0.0375\times 9}[/tex]

Let us simplify it now.

[tex]e^{0.0375\times 9}=e^{0.3375}=1.40144[/tex]

[tex]=10500\times \:1.40144\dots[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:10500\times \:1.40144\dots =14715.11589\dots[/tex]

Rounding it to the nearest cents.

=14715.12.

We know:

The product of two negative numbers is positive.

Therefore

(-12)(12)(-6.3)(-0.2)(-15.9) = (-12)(-6.3) (-0.2)(-15.9)(12) > 0  ANSWER

(12)(-6.3)(-0.2)(-15.9) < 0

(-12)(12)(-6.3)(-0.2)(-15.9)(0) = 0

(12)(12)(6.3)(0.2)(-15.9) < 0

Every 3 feet is $18. 18 divided by 3 equals 6.

24 divided by 6 equals 4. (So the second one is correct)

30 divided by 6 is 5, so the answer is not 30. it'd be 36.

48 divided by 6 is 8, so it is not 7.

72 divided by 6 is 12. But 6 multiplied by 9 equals 52. So, your answer is 52.

Hoped this helped,

-Anime

Answer: Step 2. She incorrectly squared the numbers.

Solution:

The correct steps are:

1. a^2+7^2=25^2

2. a^2+49=625

3. a^2=576

4. a=24

In which step did Shawna make an error?

Step 2. She incorrectly squared the numbers.

Since, we are given right angled triangle

so, we use pythagoras theorem to find 'a'

step-1:

Using pythagoras theorem

[tex]a^2+7^2=25^2[/tex]

step-2:

we know that

[tex]7^2=7\times 7 =49[/tex]

[tex]25^2=25\times 25 =625[/tex]

so, we get

[tex]a^2+49=625[/tex]

she made error in second step

step-3:

Subtract both sides by 49

[tex]a^2+49-49=625-49[/tex]

[tex]a^2=576[/tex]

step-4:

Take sqrt both sides

we get

[tex]a=24[/tex]

so,

Answer is:

Step 2. She incorrectly squared the numbers.

The yearly membership cost plus the cost per visit was set equal to the non-member cost per visit, and solving the equation gave us the result.

We need to find the number of visits it would take for the total cost of a member and a non-member to be the same if they both use the waterpark at each visit. Let's denote the number of visits as x.

The yearly membership cost is $275, and each visit to the waterpark costs an additional $5 for a member. So, for x visits, the total cost for a member is:

Member cost = $275 + $5x

Non-members pay $6 for parking, $15 for admission to the park, and $9 for the waterpark per visit. Therefore, the total cost for a non-member is:

Non-member cost = ($6 + $15 + $9)x = $30x

Setting both costs equal to find the number of visits where the costs are the same:

$275 + $5x = $30x

Now we solve for x:

$275 = $30x - $5x

$275 = $25x

x = $275/$25

x = 11

Therefore, it would take 11 visits for the total cost to be the same for a member and a non-member if they both use the waterpark at each visit.

Assuming one electrician-day is the same as another, the total job is ...

... (18 electricians)×(35 days) = 630 electrician·days

When that work is split among 28 electricians, it can be expected to take ...

... (630 electrician·days)/(28 electricians) = 22.5 days

Answer:

1. (0, -2/3), (2, 0)

2. y = x-6

Step-by-step explanation:

1. Since the equation is in slope-intercept form, you know the y-intercept is -2/3. The x-coordinate there is 0, so the ordered pair is (0, -2/3).

Substituting y=0 into the equation gives the value of the x-intercept.

... 0 = 1/3x -2/3

... 0 = x - 2 . . . . . multiply by 3

... 2 = x . . . . . . . . add 2

The x-intercept is (2, 0).

2. The given line has slope -1, so the perpendicular line has a slope that is the negative reciprocal of that: -1/-1 = 1. Then the point-slope equation of the line can be written ...

... y = 1(x -8) +2

... y = x - 6 . . . . simplify

(1)

to find the intercepts

• let x = 0, in the equation for y-intercept

• let y = 0, in the equation for x-intercept

x = 0 : y = - [tex]\frac{2}{3}[/tex] → (0, - [tex]\frac{2}{3}[/tex]) ← y-intercept

y = 0 : [tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] = 0 ( multiply by 3 )

x - 2 = 0 → x = 2 → (2, 0 ) ← x- intercept

(2)

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - x is in this form with slope m = - 1

the slope of a perpendicular line = - [tex]\frac{1}{m}[/tex] = 1

the partial equation of the perpendicular line is

y = x + c

to find c substitute (8, 2 ) into the partial equation

2 = 8 + c → c = 2 - 8 = - 6

y = x - 6 ← equation of perpendicular line

32 inches³

the volume V of a pyramid = [tex]\frac{1}{3}[/tex] × area of base × height

area of base = 4² = 16 and h = 6

V = [tex]\frac{1}{3}[/tex] × 16 × 6 = 32