1) Suppose f(x) = x2 and g(x) = |x|. Then the composites (fog)(x) = |x|2 = x2 and (gof)(x) = |x2| = x2 are both differentiable at x = 0 even though g itself is not differentiable at x = 0. Does this contradict the chain rule? Explain.

Answer:

Step-by-step explanation:

A of triangle = 1/2 * b * h

b = 6

h = 2

2 * 6 * 0.5

= 12 * 0.5

A of square = l * w

2 * 2

A of Triangle = 1/2 * b * h

2 * 2 * 0.5 =

4 * 0.5

2 + 4 + 6

= 6 + 6

Answer:

Step-by-step explanation:

∠OAB is 90 degrees, tangent and a radius met at 90 degree angle

∠OCB=90 degrees, tan and radius meet at 90 degrees angle

OB=12

find angle BOC:

triangle BOA is right angle triangle:

cos(AOB)=adj/hyp=7/12=54.33

angle B= 180-(90+54.33)=35.67

angle COB=54.33 equal to angle AOB

angle AOC=54.33+54.33=108.66

the sum of angles of circle =360

360-108.66= 251.34( exterior angle at the center AOC)

length of the arc= angle (251.34 degrees*7)

convert degrees to radians=4.386 (251.34/π)

length=r*angle in radian=4.386*7=30.71

( i hope this is the answer)

Answer:

did you already try A???

Answer:

Probability : [tex]\frac{5}{33}[/tex]

Step-by-step explanation:

The probability of drawing an orange on the first attempt would be 5 / 12, considering that in this first attempt their are 5 oranges present out of a total of 12 fruits. Now after that fruit is chosen their are 4 out of 11 oranges present, such that the probability of drawing an orange on the second attempt would be 4 / 11.

Probability of choosing an orange on the first try : [tex]5 / 12[/tex]

Probability of choosing an orange on the second try : [tex]4 / 11[/tex]

Probability of selecting two oranges in a row ( blindfolded ) : [tex]5 / 12 * 4 / 11[/tex]

[tex]\frac{5}{12}\cdot \frac{4}{11}[/tex] ( cross cancel common factor 4 )

[tex]\frac{5}{3}\cdot \frac{1}{11}[/tex] ( multiply fractions )

[tex]\frac{5\cdot \:1}{3\cdot \:11}[/tex] = [tex]\frac{5}{3\cdot \:11}[/tex] = [tex]\frac{5}{33}[/tex] - the probability of selecting two oranges in a row blindfolded, is [tex]\frac{5}{33}[/tex].

Answer:

Step-by-step explanation:

[tex]x^2+19x+70\ \implies a=1\,,\ b=19\,,\ c=70\\\\x=\frac{-19\pm\sqrt{19^2-4\cdot1\cdot70}}{2\cdot1}=\frac{-19\pm\sqrt{361-280}}{2}=\frac{-19\pm9}{2}\ \Rightarrow\ x_1=-14\,,\ x_2=-5\\\\x^2+19x+70=(x+14)(x+5)\\\\\\x^2-225=x^2-(15)^2=(x-15)(x+15)\\\\\\x^2-5x-150\ \implies a=1\,,\ b=-5\,,\ c=-150\\\\x=\frac{-(-5)\pm\sqrt{(-5)^2-4\cdot1\cdot(-150)}}{2\cdot1}=\frac{5\pm\sqrt{25+600}}{2}=\frac{5\pm25}{2}\ \Rightarrow\ x_1=-10\,,\ x_2=15\\\\x^2-5x-150=(x+10)(x-15)[/tex]

[tex]x^2+24x+140\ \implies a=1\,,\ b=24\,,\ c=140\\\\x=\frac{-24\pm\sqrt{24^2-4\cdot1\cdot140}}{2\cdot1}=\frac{-24\pm\sqrt{576-560}}{2}=\frac{-24\pm4}{2}\ \Rightarrow\ x_1=-14\,,\ x_2=-10\\\\x^2-5x-150=(x+14)(x+10)[/tex]

[tex]\dfrac{x^2+19x+70}{x^2-225}\,\cdot\,\dfrac{x^2-5x-150}{x^2+24x+140}=\dfrac{(x+14)(x+5)}{(x-15)(x+15)}\cdot\dfrac{(x+10)(x-15)}{(x+14)(x+10)}=\\\\\\=\dfrac{(x+14)(x+5)}{(x-15)(x+15)}\cdot\dfrac{x-15}{x+14}=\dfrac{x+5}{x+15}\cdot\dfrac11=\boxed{\dfrac{x+5}{x+15}}[/tex]

Answer:

The answer is option 3.

Step-by-step explanation:

First, you have to factorize the expressions :

[tex] \frac{ {x}^{2} + 19x + 70 }{ {x}^{2} - 225 } \times \frac{ {x}^{2} - 5x - 150}{ {x}^{2}24x + 140 } [/tex]

[tex] = \frac{(x + 5)(x + 14)}{(x + 15)(x - 15)} \times \frac{(x - 15)(x + 10)}{(x + 10)(x + 14)} [/tex]

Next, you have to cut out the common terms like (x + 14), (x - 15) and (x + 10):

[tex] \frac{(x + 5)(x + 14)}{(x + 15)(x - 15)} \times \frac{(x - 15)(x + 10)}{(x + 10)(x + 14)} [/tex]

[tex] = \frac{x + 5}{x + 15} [/tex]

Step-by-step explanation:

The equation is   sinθ * cosθ - sinθ = 0

θ = 0 + 2kπ

θ = 2kπ where k is any integer

The solutions to the equation are: {0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

Hence, the correct option is C.

The given equation is:

sin theta × cos theta - sin theta = 0

We can factor out the sine theta:

sin theta (cos theta - 1) = 0

This means that either sin theta = 0 or cos theta - 1 = 0.

If sin theta = 0, then theta = 0, 180 degrees, 360 degrees, etc.

If cos theta - 1 = 0, then cos theta = 1, which means that theta = 0 degrees and 360 degrees.

Therefore, the solutions to the equation are:

{0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

So the answer is C.

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Answer:

44°

Step-by-step explanation:

The secant- secant angle y is half the difference of the measure of its intercepted arcs, that is

[tex]\frac{1}{2}[/tex](BHF - CGJ ) = y , that is

[tex]\frac{1}{2}[/tex](156 - CGH) = 56° ( multiply both sides by 2 )

156 - CGH = 112° , thus

CGH = 156° - 112° = 44°

Answer:

Step-by-step explanation:

-9x + 6y = -30

-7x + 12y = -16

18x - 12y = 60

 -7x + 12y = -16

11x = 44

x = 4

-36 + 6y = -30

6y = 6

y = 1

(4,1)

Answer:

(4,1)

Step-by-step explanation:

-9x + 6y = -30.............(1)

-7x + 12y = -16 ............(2)

(2) - 2(1)

-7x+12y - 2(-9x+6y) = -16 - 2(-30)

simplify

11x = 44

or

x = 4 .......................(3a)

substitute (3) in (1)

-9(4) + 6y = -30

6y = -30 + 36

6y = 6

y =  1 ......................(3b)

Using results from (3a) and (3b), we have

solution :  (4,1)

Answer:

? = 3

Step-by-step explanation:

The parallel segments shown divide the sides in the ratio

[tex]\frac{6}{4}[/tex] = [tex]\frac{?}{2}[/tex] ( cross- multiply )

4? = 12 ( divide both sides by 4 )

? = 3

Answer:

16.704m

Step-by-step explanation:

To solve the above question, we are going to use the Trigonometric function of Sine.

sin θ = Opposite side/Hypotenuse

Where are given θ = 8°

Sin 8° = 0.1392

In the question, we are told that ,

A car travels 120m along a straight road that is inclined at 8° to the horizontal, hence,

Hypotenuse = 120m

We are asked to calculate the vertical distance through which the car rises hence,

Opposite side = vertical distance.

Therefore,

Sin 8° = Opposite/ 120m

Opposite = Sin 8° × 120m

Opposite = 0.1392 × 120m

Opposite = 16.704m

Therefore, the vertical distance through which the car rises is 16.704m

Answer:

P(X > 112) = 0.21186.

Step-by-step explanation:

We are given that the random variable X is normally distributed, with mean [tex]\mu[/tex] = 100 and standard deviation [tex]\sigma[/tex] = 15.

Let X = a random variable

The z-score probability distribution for the normal distribution is given by;

                               Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 100

            [tex]\sigma[/tex] = standard deviaton = 15

Now, the probability that the random variable X is greater than 112 is given by = P(X > 112)

      P(X > 112) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{112-100}{15}[/tex] ) = P(Z > 0.80) = 1- P(Z [tex]\leq[/tex] 0.80)

                                                       = 1 - 0.78814 = 0.21186  

The above probability is calculated by looking at the value of x = 0.80 in the z table which has an area of 0.78814.

Answer:

$3750 and $4250

Step-by-step explanation:

x + 500 = y

.045x + .035y = 317.50

.045x + .035(x + 500) = 317.50

.045x + .035x + 17.5 = 317.50

.08x = 300.00

x = 3750

y = 4250

Answer:

100.

Step-by-step explanation:

Let the number of robberies be x ( in 2013).

Then x - 0.10x = 90

0.90x = 90

x = 90 / 0.90

= 100.

Answer:

The maximum rectangular area will have the length 400 meters and width 200 meters with one side of the length against an existing building.

Step-by-step explanation:

From the given information;

The perimeter of a rectangle = 2 (L+B)

here;

L = the length of the side of the fence

B = the width of the fence

So; The perimeter of a rectangle = 2L+2B

we are also being told that;

One side of the area will be against an existing building

i.e

The perimeter of a rectangle is now =  L + 2B = 800 meters

L = 800 - 2B

Similarly; Area of a rectangle = L × B

Area of a rectangle = ( 800 - 2B) × B

Area of a rectangle =  800B - 2B²

assuming A(B) to represent the Area;

Then the maximum area A'(B) = 0 ;

Thus,

A'(B) = 800 - 4B = 0

-4B = - 800

4B = 800

B = 200

Therefore; the maximum area have a width = 200 meters and a length 800 - 2(200) =  800 - 400 = 400 meters

Answer:

Option : Statistic because the value is a numerical measurement describing a characteristic of a sample.

Step-by-step explanation:

A sample of professors is selected and it is found that Modifying 35 % with underline own a television.

The 35% is the value that summarizes the characteristic of the sample taken from the population. Thus, the value 35% is a statistic.

While a parameter gives a value describing the characteristic of the population itself

Given: Sample proportion is (P)=[tex]35%[/tex]%.

Statistics are the constants that are computed from sample observations alone. This is a simple definition of statistics.

Answer: The correct statement is  Statistic because the value is a numerical measurement describing a characteristic of a population.

Explanation: That is, statistic because the value is a numerical measurement describing the characteristic of a sample.

The remaining statements are incorrect.

As parameters are the constants of the population. They describe only the population not the sample.

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Answer: it 70

Step-by-step explanation:

Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation.

How much is left in Latesha’s lunch account after she has had lunch for 5 days?

$15

$67

$82

you tube guests are for hire

Answer: 1/2

Step-by-step explanation:

solving bracket first we get

2 - 9/6

multiplying and dividing 2 by 6 we get

12/6 - 9/6

=3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

(6-4)-9/6

= (2)-9/6

= 12/6-9/6

= 3/6

= 1/2

Answer: D) Construct the perpendicular bisectors for AB and AC.

The intersection of all three perpendicular bisectors will form the circumcenter, which is the center of the circumcircle. This circle goes through all three corner points of the triangle. At minimum, you only need two perpendicular bisectors to get the job done. Choice B is close, but is missing that second perpendicular bisector.

The angle bisectors intersect to form the incenter, which is the center of the incircle (it's the largest possible circle to fit inside the triangle without spilling over).

Answer:

D.  Construct the perpendicular of ab and ac

Step-by-step explanation:

Circumscribe a Circle on a Triangle

Construct the perpendicular bisector of one side of the triangle.

Construct the perpendicular bisector of another side.

Where they cross is the center of the Circumscribed circle.

Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle

Mark me as brainliest

Answer:

Postulate 3: Through any three points that are not one line, exactly one plane exists. State the postulate that verifies line segment AB is in plane Q when points A and B are in Q.

Step-by-step explanation:

Postulate 4: If two points lie in a plane, the line containing them lies in that plane. hope this helps you :)

Answer:

It took 31 days for the patch to cover half the lake

Step-by-step explanation:

The patch grows to double its size everyday

the patch completely covers the lake in 32 days

Since the patch doubles itself everyday, this means that the previous day before the 32nd day, the lake was just half covered.

Therefore, the the patch covered half the lake on the 31st day, i.e it took 31 days for the patch to cover half the lake

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

The point-slope form of an equation of a line:

y - y₁ = m(x - x₁)

(x₁, y₁) - point on a line

m - slope

We have the line y - 9 = 7(x + 5). The slope m = 7.

A) y - 9 = 3x + 4 → m = 3

B) y = -9x - 5 → m = -9

C) y + 5 = 7(x - 9) → m = 7

D) y - 9 = 5(x + 4) → m = 5

The line C) y + 5 = 7(x - 9) has the same slope.

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex]y = - 2x + 4...........(i)[/tex]

[tex]y = x - 5..........(ii)[/tex]

Equate ( i ) and ( ii ),

[tex] - 2x + 4 = x - 5[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - 2x - x = - 5 - 4[/tex]

Calculate

[tex] - 3x = - 9[/tex]

Divide both sides of the equation by -3

[tex] \frac{ - 3x}{ - 3} = \frac{ - 9}{ - 3} [/tex]

Any expression divided by itself equals 1

[tex]x = \frac{ - 9}{ - 3} [/tex]

Dividing two negatives equals a positive [tex]( - ) \div ( - ) = ( + )[/tex]

[tex]x = \frac{9}{3} [/tex]

calculate the quotient

[tex]x = 3[/tex]

Value of X is 3

Now, put the value of X in equation ( i ) in order to find the value of y

[tex]y = x - 5[/tex]

plug the value of X

[tex] = 3 - 5[/tex]

Calculate

[tex] = - 2[/tex]

Value of y is -2

So, ( 3 , -2 ) is the solution of the given equation.

Hope this helps ....

Best regards!!

Answer:

We have the problem:

|3r−15| if r<5

First we see the equality, if r = 5 we have:

I3r - 15I = I3*5 - 15I = I0I = 0.

Then the only restriction that we have is:

I3r - 15I > 0.

now, we could simplify it a bit further:

if r < 5, then the thing inside the absolute value will always be negative:

Then we can write:

I3*r - 15I = -(3*r -15) > 0

multiplying by -1 in both sides

(3r - 15) < 0.

if we keep simplifying this, we will get our initial restriction:

3r - 15 < 0

3r < 15

r < 15/3 = 5

r < 5

Answer:

The lengths 14, 24, and 26 cannot be the sides of a right triangle.  The lengths 30, 72, 78 can be the sides of a right triangle.

Step-by-step explanation:

To prove that the lengths 14, 24, and 26 cannot be the sides of a right triangle:

a=14, b=24, c=26

Pythagoreon theorem: a^2+b^2=c^2

substitute values in: 14^2+24^2=26^2

simplify: 196+576=676

simplify again: 772=676, which is not true

This proves that the lengths 14, 24, and 26 cannot be the sides of a right triangle.

To prove that the lengths 30, 72, and 78 can be the sides of a right triangle:

a=30, b=72, c=78

Pythagoreon theorem: a^2+b^2=c^2

substitute values in: 30^2+72^2=78^2

simplify: 900+5184=6084

simplify again: 6084=6084, which is true

This proves that the lengths 30, 72, and 78 can be the sides of a right triangle.

Answer:

true, true, false,false,  false,true,true,false

See explanations below

Step-by-step explanation:

If three sides can make a RIGHT triangle, then the sum of squares of the two shorter sides EQUALS the square of the third side, using the Pythatorean theorem.

Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements?

The lengths 14, 24 and 26 cannot be sides of a right triangle.

TRUE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 can be sides of a right triangle.

TRUE, A^2+B^2-C^2= 0

The lengths 14, 24 and 26 can be sides of a right triangle.

FALSE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 cannot be sides of a right triangle.

FALSE, A^2+B^2-C^2= 0

The lengths 14, 24 and 26 can be sides of a right triangle.

FALSE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 can be sides of a right triangle.

TRUE, A^2+B^2-C^2= 0

The lengths 14, 24 and 26 cannot be sides of a right triangle.

TRUE, A^2+B^2-C^2=4sqrt(6)

The lengths 30, 72, and 78 cannot be sides of a right triangle.

FALSE, A^2+B^2-C^2= 0

Hey there! I'm happy to help!

The slope is the steepness or incline of a line. From a graph, it is known as the rise over the run between two integer values. If you have a point at (1,1) and a point at (2,2), the rise (vertical difference) between them in 1 unit, and the run (horizontal difference) is 1 unit. 1/1 is 1, so the slope of a line that passes through these points is 1. This means that for every one unit to the right it goes, it goes one unit up.

The intercepts are where the line hits the x and y axes. By looking at a graph, you can find the y-intercept by seeing on what y-value the line intersects with the y-axis, and for the x-intercept you do so with the x-axis.

The slope-intercept equation is y=mx+b. This b is the y-intercept. To find the x-intercept, you plug in the value 0 for y and solve for x. This is because the x-axis is the line y=0, so you will see where the x is if y is equal to 0.

Linear equations and functions can be written in slope intercept form (y=mx+b), standard form (Ax+By=C), and point slope form [tex]y-y_{1} =m(x-x_{1} )[/tex].

They can be graphed by finding the y and x intercepts from the equation and then connecting the points to draw the line!

Have a wonderful day! :D

Answer:

5.6

Step-by-step explanation:

(3÷3/4)÷5/7

[tex] \frac{3 \times 4}{3} \div \frac{5}{7} [/tex]

[tex]4 \div \frac{5}{7} [/tex]

[tex]4 \times \frac{7}{5} [/tex]

[tex] \frac{28}{5} [/tex]

=5.6

use "keep, change, flip " when dividing a number by a fraction.

keep the whole number

flip the divide sign to multiply

change the placement of number e.g. 5/7 becomes 7/8

then solve

Answer:

190

Step-by-step explanation:

the weight is 191 lbs rounded is 190

Answer:

x = 28 degrees. 180 degrees in a triangle, 180-85-67=28

Answer:

28 degrees

Step-by-step explanation:

The interior angles of a triangle add up to 180 degrees.

The three angles given are: x, 85, and 67.

Therefore, these three angles must add to 180.

x+85+67=180

Combine like terms on the left. Add 85 and 67.

x+ (85+67)=180

x+152=180

We want to find x. We need to get x by itself. 152 is being added to x. The inverse of addition is subtraction. Subtract 152 from both sides.

x+152-152=180-152

x=180-152

x=28

x is 28 degrees.

Answer:

The first term is 12. The common difference is 4.

Step-by-step explanation:

[tex] a_n = a_1 + d(n - 1) [/tex]

The difference between the third and seventh terms is

36 - 20 = 16

The 7th term is the 4th term after the 3rd term, so the common difference is

16/4 = 4

[tex] a_3 = a_1 + 4(3 - 1) [/tex]

[tex] 20 = a_1 + 4(3 - 1) [/tex]

[tex] 20 = a_1 + 8 [/tex]

[tex] a_1 = 12 [/tex]

Answer: The first term is 12. The common difference is 4.

Answer:

both are at the same distance

Step-by-step explanation:

Answer:

Austin and Devyn both have 1/3 of the way left on their way to school. They both also have walked the same amount.

Step-by-step explanation:

If Austin has to walk to his school, which could be said as 3/3 and Austin has already walked 2/3. Then if we conduct the equation 3/3-2/3=x. x=1/3. Now Devyn has already walked 4/6 of the way to school. If she has to walk a total of 6/6, then we can again make an equation 6/6-4/6=2/6. Now if we take the distance that they both have left to their school, its 1/3 and 2/6. These are both equavalent fractions because if you scale up 1/3, it equals to 2/6. Since they both have an equal amount of distance to travel, that must mean that they both have covered the same amount of distance already. We can double check to be sure. 2/3 *2/2=4/6. The reason we used 2/2 is because4/2=2 and 6/3=2.

Answer:

[tex]y=9x+33[/tex]

33 gallons of water to begin with.

Step-by-step explanation:

So, we are essentially given two coordinates: (6,87) and (21,222). To find an equation, we will need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.

Using the slope formula, the slope is:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{222-87}{21-6}=135/15=9[/tex]

So, the rate at which the stream flows is 9 gallons per minute.

Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).

Point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

Substitute:

[tex]y-(87)=9(x-(6))[/tex]

Distribute:

[tex]y-87=9x-54[/tex]

Therefore:

[tex]y=9x+33[/tex]

So, there were 33 gallons of water in the tank to begin with.