2.7.2 : Checkup - Practice Problems

Answer:

False because $296=$296

Answer:

1: -80

3: 21.7

5: inf many solutions? (i cant do that one without a problem)

7: 21

9: - 2/3

11: 6 and 3/8

13: 0.4

15: inf many? (cant solve again)

Step-by-step explanation:

Answer:

please which level is this

and also is it core maths or elective math

Answer:

Some demerits of classical probability are provided throughout the following portion.

Step-by-step explanation:

Answer:

Relative minimum: [tex]\left(-\frac{5}{2}, -\frac{33}{4}\right)[/tex], Relative maximum: [tex]DNE[/tex]

Step-by-step explanation:

First, we obtain the First and Second Derivatives of the polynomic function:

First Derivative

[tex]f'(x) = 2\cdot x + 5[/tex] (1)

Second Derivative

[tex]f''(x) = 2[/tex] (2)

Now, we proceed with the First Derivative Test on (1):

[tex]2\cdot x + 5 = 0[/tex]

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

The critical point is [tex]-\frac{5}{2}[/tex].

As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since [tex]f\left(-\frac{5}{2}\right) > 0[/tex].

Lastly, we find the remaining component associated with the critical point by direct evaluation of the function:

[tex]f\left(-\frac{5}{2} \right) = \left(-\frac{5}{2} \right)^{2} + 5\cdot \left(-\frac{5}{2} \right) - 2[/tex]

[tex]f\left(-\frac{5}{2} \right) = -\frac{33}{4}[/tex]

There are relative maxima.

Answer:

x = 5±√3

Step-by-step explanation:

Equation: (x-5)² = 3

Step 1: Take the square root of both side of the equation

√(x-5)² = ±√3

x-5 = ±√3

Step 2: add 5 to both side of the equation

x-5+5 = 5±√3

x = 5±√3

Hence, from the options above, the right answer is

B. x = 5±√3

Answer:

[tex]x = - \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]x = \frac{ - b}{2a} = \frac{1}{ - 2} [/tex]

I believe this is your question:

A.) find an angle between 0 degrees and 360 degrees that is coterminal with 570 degrees.

Answer:

210 degrees

Explanation:

Coterminal angles begin on the same initial side and end or terminate on the same side as an angle. Example 45 degrees and 405 degrees are coterminal angles because they both begin and end on the same side.

To find an angle between 0 and 360 that is coterminal with 570 degrees, w simply subtract 360 degrees from 570, hence:

570-360=210 degrees

570 degrees is coterminal with 210 degrees

Answer:

B

Step-by-step explanation:

49x^2=9

solve for x

x^2= 9/49

x=± [tex]\sqrt{9/49\\}[/tex]

which is x = ±3/7 (B)

Answer: b x=1/9 and x=-1/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 2 different ways to do this: calculus and by completing the square. In this particular instance, calculus is WAY easier, and since I don't know for what class you are doing this, I'll do both ways. First the calculus way. We know the position equation, and the first derivative of the position is velocity. We also know that when the velocity is equal to 0 is when the object is at its max height. So we'll find the derivative first, then solve it for t:

If [tex]s(t)=-3t^2+20t+2[/tex] then the first derivative is

v(t) = -6t + 20 Solving for t requires that we set the velocity equal to 0 (again, this is where the object is at its max height), so

0 = -6t + 20 and

-20 = -6t so

t = 3.3 seconds. Now that we know that at 3.3 seconds the object is at its highest point, we sub that time into the position function to see where it is at that time:

s(3.3) = [tex]-3(3.3)^2+20(3.3)+2[/tex] and

s(3.3) = 35.3 meters.

Now onto the more difficult way...completing the square. Begin by setting the position function equal to 0 and then move over the constant to get:

[tex]-3t^2+20t=-2[/tex] Since the leading coefficient is not a 1 (it's a 3), we have to factor out the 3, leaving us with:

[tex]-3(t^2-\frac{20}{3}t)=-2[/tex] Now the rule is to take half the linear term, square it, and add it to both sides. Our linear term is [tex]\frac{20}{3}[/tex] and half of that is [tex]\frac{20}{6}[/tex]. Squaring that:

[tex](\frac{20}{6})^2=\frac{400}{36}=\frac{100}{9}[/tex]. We will add that in to both sides. On the left it's easy, but on the right we have to take into account that we still have that -3 sitting out front, refusing to be ignored. So we have to multiply it in when we add it to the right. Doing that gives us:

[tex]-3(t^2-\frac{20}{3}t+\frac{100}{9})=-2-\frac{100}{3}[/tex] We will clean this up a bit now. The reason we do this is because on the left we have created a perfect square binomial which will give us the time we are looking for to answer this question. Simplifying the right and at the same time writing the perfect square binomial  gives us:

[tex]-3(t-\frac{20}{6})^2=-\frac{106}{3}[/tex] Now the last step is to move the constant back over and set the quadratic back equal to y:

[tex]y=-3(t-\frac{20}{6})^2+\frac{106}{3}[/tex].  The vertex of this quadratic is

[tex](\frac{20}{6},\frac{106}{3})[/tex] where

[tex]\frac{20}{6}=3.3[/tex] as the time it takes for the ball to reach its max height of

[tex]\frac{106}{3}=35.3[/tex] meters.

I'd say if you plan on taking calculus cuz you're not there yet, you'll see that many of these types of problems become much simpler when you know it!

Answer:

1716 ways

Step-by-step explanation:

Given that :

Number of entrants = 13

The number of ways of attaining first, second and third position :

The number of ways of attaining first ; only 1 person can be first ;

Using permutation :

nPr = n! ÷(n-r)!

13P1 = 13! ÷ 12! = 13

Second position :

We have 12 entrants left :

nPr = n! ÷(n-r)!

12P1 = 12! ÷ 11! = 12

Third position :

We have 11 entrants left :

nPr = n! ÷(n-r)!

11P1 = 11! ÷ 10! = 11

Hence, Number of ways = (13 * 12 * 11) = 1716 ways

Answer:

its all of them

Step-by-step explanation:

since its the same shape as the old one all the measurements are the same.

Answer:

its all of them

Step-by-step explanation:

Answer:

Step-by-step explanation:

Turgor pressure is the force within the cell that pushes the plasma membrane against the cell wall. It is also called hydrostatic pressure, and defined as the pressure measured by a fluid, measured at a certain point within itself when at equilibrium.

Answer:

A. ¼

Step-by-step explanation:

Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:

Where,

[tex] (4, 1) = (x_1, y_1) [/tex]

[tex] (-4, -1) = (x_2, y_2) [/tex]

Plug in the values

Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]

= [tex] \frac{-2}{-8} [/tex]

= [tex] \frac{1}{4} [/tex]

Rate of change = ¼

Answer:

4

9

Step-by-step explanation:

If X has 5 elements, and Y has 4 elements, and all 4 of Y's elements are the same as 4 of X's elements, then the intersection of the sets has 4 elements.

If X has 5 elements and Y has 4 elements, and they are all different, then the union of the sets has 9 elements.

Answer:

4

9

Answer:

16x4−4x2+4x−116x4−4x2+4x−1

=16x4−(4x2−4x+1)=16x4−(4x2−4x+1)

=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2

=(4x2−2x+1)(4x2+2x−1)∵a2−b2=(a−b)(a+b

Step-by-step explanation:

Answer:

[tex]A"B" = \frac{AB}{2}[/tex]

Step-by-step explanation:

Given

[tex]k = \frac{1}{2}[/tex] --- scale factor

Required

Relationship between AB and A"B"

[tex]k = \frac{1}{2}[/tex] implies that the sides of A"B"C" are smaller than ABC

i.e.

[tex]A"B" = k * AB[/tex]

[tex]A"B" = \frac{1}{2} * AB[/tex]

This gives:

[tex]A"B" = \frac{AB}{2}[/tex]

Answer:

10/1 is the largest because 10÷1 = 10

Answer:

10/1 =  10 and is by far the biggest value in the list

Step-by-step explanation:

Answer:

7/30

Step-by-step explanation:

P = 1/15 + 1/6 = (2+5)/30 = 7/30

This is one single number that's slightly smaller than 400 thousand.

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

Explanation:

There are 26 letters in the english alphabet. We don't use letters i or o, so we have 26-2 = 24 choices for that first slot.

Then we have 10 choices for the second slot because there are 10 single digits 0 (zero) through 9.

After making the selection for the second slot, we have 10-1 = 9 choices left for the third slot. The fourth slot has 10-2 = 8 digits to pick from. The subtraction occurs because we cannot reuse the digits.

Finally, the last slot will be a letter. We have 24-1 = 23 letters left to pick from.

Overall, we have 24*10*9*8*23 = 397,440 different license plates possible.

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

Extra info (optional section)

You may be wondering "why do we multiply those values?". Well consider a simple example of having only 2 slots instead of 5.

Let's say the first slot is a letter A to Z, excluding letters i and o. The second slot will be the digit from 0 through 9.

If you make a table with 24 rows and 10 columns, then you'll have 24*10 = 240 cells overall. Notice the multiplication here. The 24 rows represent each letter, and the 10 columns are the digit numeric digits.

Each inner cell is a different two character license plate. For example A5 is one such plate. This idea can be extended to have 5 characters.

Answer:

the answers are on the picture but the numbers may be rounded

Answer:

52/3

Step-by-step explanation:

Use basic Thales therom,

[tex]\frac{3x}{4x}=\frac{3x+7}{5x-8}\\\\\frac{3}{4}=\frac{3x+7}{5x-8}\\[/tex]

Cross multiply,

3*(5x-8)=4*(3x+7)

3*5x - 3*8 = 4*3x + 4*7

15x - 24 = 12x +28

Add 24 to both sides

15x = 12x + 28 + 24

15x = 12x + 52

Subtract 12x from both sides

15x-12x =52

3x = 52

Divide both sides by 3

x = 52/3

Answer: 12

Step-by-step explanation: Whenever you have a minus a negative in a problem, you can change it to plus a positive.

So we can think of 7 - (-5) as 7 + (+5).

Whenever we have two negatives in a row, we can think of those

negatives as being multiplied together and a negative times a negative

will always result in a positive.

So just add 7 + 5 to get 12.

Answer:

14) 4x+10=8x-26 (corresponding angles are equal)

4x-8x=-26-10

-4x=-36

x= -36/-4= 9

x=9

15) perimeter of rectangle= 2(l+b)

2( l+ [tex]\frac{2l}{3}[/tex]) = 40m

2l+ [tex]\frac{4l}{3}[/tex] =40

Take LCM as 3

[tex]\frac{2l}{1}[/tex] * [tex]\frac{3}{3}[/tex] + [tex]\frac{4l}{3}[/tex] =40

[tex]\frac{6l+4l}{3}[/tex] = 40

[tex]\frac{10l}{3}[/tex] = 40

10l=40*3

10l = 120

l= 120/10 =12 cm

l=12cm

b= 2/3 *12 = 8cm

16) 2:3:4

It can be written as 2x+3x+4x

sum of angles of a triangle =180 degree

so 2x+3x+4x=180

9x=180

x=180/9=20 degree

1st angle=2x=2*20= 40 degree

2nd angle= 3x=3*20 =60 degree

3rd angle= 4x=4*20= 80 degree

17) sum of interior angles of a pentagon is 540 degree

so, 125+88+128+60+x=540 degree

401 +x= 540 degree

x=540-401= 139 degree

Hope this helps

Please mark me as brainliest

Hello,

[tex]\dfrac{d(2^x)}{dx} =2^x*ln(2)\\[/tex]

Answer:

pretty sure it could

Step-by-step explanation:

Answer:

What it's asking is for 2 angles at different angles of attack, are parallel

Step-by-step explanation:

for example, // these two slashes are parallel because they wont ever touch, it wants you to find if the angles are parallel or not.

Answer:

[tex]82\sqrt{21}\text{ or approximately 375.77 miles per hour}[/tex]

Step-by-step explanation:

Please refer to the diagram below. R is the radar station and x is the distance from the station to the plane.

We are given that the plane is flying horizontally at an altitude of two miles and at a speed of 410 mph. And we want to find the rate at which the distance from the plane to the station is increasing when it is five miles away from the station.

In other words, given da/dt = 410 and x = 5, find dx/dt.

From the Pythagorean Theorem:

[tex]a^2+4=x^2[/tex]

Implicitly differentiate both sides with respect to time t. Both a and x are functions of t. Hence:

[tex]\displaystyle 2a\frac{da}{dt}=2x\frac{dx}{dt}[/tex]

Simplify:

[tex]\displaystyle a\frac{da}{dt}=x\frac{dx}{dt}[/tex]

Find a when x = 5:

[tex]a=\sqrt{5^2-2^2}=\sqrt{21}[/tex]

Therefore, dx/dt when da/dt = 410, x = 5, and a = √(21) is:

[tex]\displaystyle \frac{dx}{dt}=\frac{(\sqrt{21})(410)}{5}=82\sqrt{21}\approx 375.77\text{ mph}[/tex]

The rate at which is distance from the plane to the radar station is increasing at a rate of approximately 375.77 miles per hour.

Answer:

$637.50

Step-by-step explanation:

According to the Question,

Thus, the first months interest is

$200,000 list price x 0.90 = $180,000 contract sales price.

Since lender always uses the less of the appraised value or the contract sales price, use $180,00 for the remainder of the calculations.

Answer:

$637.50

Step-by-step explanation:

The appraised value is irrelevant. The lender will consider the lower of the appraised value or the agreed purchase price.

The term of the loan is also irrelevant. It is not an amortization problem.

The first month’s interest is $637.50.

Hello!

(6x⁵z)³/4x⁴z² =

= 216x¹⁵z³/4x⁴z² =

= 54x¹¹z

Good luck! :)

Answer:

simple interest=principal x rate x time÷100

amount borrowed=$8593

125days to year

365 days=1 year

125=125/365x1

0.3424657534246575year

in all there is 3+0.3424657534246575=3.3424657534246575years

I=$8593 x 15.5 x 3.3424657534246575÷100

I= $4451.8802739726026941125

total amount to be repaid=amount borrowed+interest

$8593+$ 4451.8802739726026941125

$13044.8802739726026941125

rounded to the nearest cent=$13045.00