06.10 Module Six Practice Test
Est. Length: 2:00:00 Wyatt Stewart: Attempt 1
What is the value of the expression 22 +42 = 22? (1 point)
O 1) 3
O2) 6
0 3 8
04) 16​

Answer:

Function #2 has a greater minimum.

#3 < #1 < #2

Step-by-step explanation:

In the picture attached, the question is shown.

The minimum of Function #1 is located at (3, -1). This is seen in the picture.

The minimum of Function #2 is located at (1.5, 1). We can see in the table that the function is symmetric respect 1.5 (half-point between 1 and 2).

The function y = x² + 3x - 4 has its minimum at its vertex:

x-coordinate of vertex: x = -b/(2a) = -3/(2*1) = -1.5

y-coordinate of vertex: y = (-1.5)² + 3(-1.5) - 4 = -6.25

So, the minimum of Function #3 is located at (-1.5, -6.25)

Answer:

The other guy is right

Step-by-step explanation:

Answer:  6.25    IF my assumption is correct about the missing x!

The Other way around:   4.5  with    2x² + y² / 3

Step-by-step explanation:  2y² + y² / 3  assuming the 2nd y should have been x, 1st y  is y,  and all divided by 3

2(3)² + (1.5)² / 3

2(9) + 2.25   /3

18 + 2.25  /3

20.25/3

6.25

Edited to correct!________ OR 2y² + y² / 3  assuming the 1st y should have been x, 2nd y  is y,  and all divided by 3

2(1.5)² + (3)² / 3

2(2.25) + 9  / 3

4.5 + 9  /3

13.5 /3

4.5

Answer:

[tex]\frac{13.5}{3}[/tex]

Step-by-step explanation:

=> [tex]2x^2+y^2/3[/tex]

Where x = 1.5, y = 3

=> 2(1.5)²+(3)² / 3

=> 2(2.25)+9 / 3

=> 4.5 + 9 / 3

=> 13.5 / 3

=> [tex]\frac{13.5}{3}[/tex]

Answer:  c) [tex]\dfrac{3}{2}[/tex] .

Step-by-step explanation:

Mean value theorem : If f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that

[tex]\begin{displaymath}f'(c) = \frac{f(b) - f(a)}{b-a} \cdot\end{displaymath}[/tex]

Given function : [tex]f(x) = x^2[/tex]

Interval : [0,3]

Then, by the mean value theorem, there is at least one number c in the interval (0,3) such that

[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}\\\\=\dfrac{3^2-0^2}{3}=\dfrac{9}{3}\\\\=3[/tex]

[tex]\Rightarrow\ f'(c)=3\ \ \ ...(i)[/tex]

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

then, at x=c, [tex]f'(c)=2c\ \ \ ...(ii)[/tex]

From (i) and (ii), we have

[tex]2c=3\\\\\Rightarrow\ c=\dfrac{3}{2}[/tex]

Hence, the correct option is c) [tex]\dfrac{3}{2}[/tex] .

Answer:

10 brownies.

Step-by-step explanation:

First, subtract 4 from 24 bc she gave 4 to her bro. So she has 20 brownie pieces left. Then do 20/2=10. Therfore, the math and art teacher both get 10 brownies.

Answer:

10 for each teacher

Step-by-step explanation:

1. She gave 4 brownies to her brother which is 24-4=20

2. There were 2 teachers, the art and mathematics and both got the same amount so 20 divided 2

3. 20 divided 2 equals 10

so therefore each of the 2 teachers will get 10 brownies each

Answer:

15

Step-by-step explanation:

lets begin to set up this question. i personally find questions like these easiest when i begin to set up ideas to help my brain process it better, for example:

person a

person b

person c

person d

we know that each (person) must receive at least 1 candy. we also know that we have 7 candies. therefore if we want do draw this out :

person a- 1

person b- 1

person c- 1

person d -1

notice that we now have given away 4 of the 7 candies. now we have 3 candies left. we can simply:

person a- 2

person b-2

person c-2

person d- 1

but, keep in mind that there are still many more ways that we can distribute the candies to other kids. the question we are asked is how may ways can we do this. since i have already illustrated the question, you can either learn how to put this into an equation, or experiment how many variations there are. the answer, either way is 15.

Answer:

The Quotient Property.

Step-by-step explanation:

Since all three logarithms have the same base (base-5), and you are subtracting 6 and 3, to solve this all you need to do is 6 / 3 because of the Quotient Property.

You aren't multiplying anything, so you wouldn't use the Product Property.

You are not messing around with powers, so you wouldn't use the Power Property.

And you aren't using addition or multiplication, so you wouldn't use the Commutative Property.

Hope this helps!

Answer:

z = -9.5

Step-by-step explanation:

Well to get rid of the 2 in the following expression,

[tex]-4.75 = \frac{z}{2}[/tex]

We multiply everything by 2.

-4.75 * 2 = -9.5

z * 2 = 2

-9.5 = z

This question is incomplete because the options were not properly written.

Complete Question

Which of the following applies the law of cosines correctly and could be solved to find m∠E? ANSWERS:

A) cos E = 31²+ 39² – 2(31)(39)

C) 56² = 39² – 2(39) ⋅ cos E

D) 56² = 31² + 39² – 2(31)(39) ⋅ cos E

Answer:

D) 56² = 31² + 39² – 2(31)(39) ⋅ cos E

Step-by-step explanation:

From the above diagram, we see are told to apply the law of cosines to solve for m∠E i.e Angle E

The formula for the Law of Cosines is given as:

c² = a² + b² − 2ab cos(C)

Because we have sides d , e and f and we are the look for m∠E the law of cosines would be:

e² = d² + f² - 2df cos (E)

e = 56

d = 39

f = 31

56² = 39² + 31² - (2 × 39 × 31) × cos E

Therefore, from the above calculation and step by step calculation, the option that applies the law of cosines correctly and could be solved to find m∠E

Is option D: 56² = 31² + 39² – 2(31)(39) ⋅ cos E

Answer:

[tex]56^2 = 31^2 + 39^2 minus 2(31)(39) cos E[/tex]

Step-by-step explanation:

Hello, I just took the exam got the answer correct

Answer:

16

Step-by-step explanation:

[tex] {w}^{2} - 8w + { {4}^{2} } \\ = {w}^{2} - 8w + \boxed{ 16} \\= (w-4)^2 [/tex]

Answer:

Step-by-step explanation:

a² + 2ab +b² = (a+ b)²

w² - 8w + _?___

a = w

2ab = -8w

2*w*b = -8w

b = -8w/2w

b = 4

8w = 2 * 4*w

w² - 8w + 4² =w² -8w + 16

Answer:

15 miles

Step-by-step explanation:

Currently, he can run 3.5 * 2 = 7 mph. Adding 1/2 mph to that gives us 7.5 mph, so therefore, in 2 hours he can run 7.5 * 2 = 15 miles.

Answer:

15

Step-by-step explanation:

because its correct just did the thing.

Question

x+5/x+2 - x+1/x²+2x

Answer:

= (x² - 4x - 1)/[x (x+2)]

= (x² - 4x - 1)/[x² + 2x]

Step-by-step explanation:

x + 5/x + 2 - x + 1/x² + 2x

We factorise the second denominator to give us :

x + 5/x + 2 - x + 1/x(x + 2)

We find the L.C.M of both denominators which is x(x+2).

[x(x + 5)-(x + 1)] / (x (x + 2))

Expand the bracket

=[x² +5x - x -1] / [x (x + 2)]

=(x² - 4x - 1) / [x (x + 2)]

= (x² - 4x - 1)/ [x (x + 2)]

= (x² - 4x - 1) / [x² + 2x]

Answer:

Correct

Step-by-step explanation:

Everything seems correct.  I would just put the two answers for questions 3 & 4 in the separate boxes, instead of having two answers in each box.

Answer:

30x > 1470 + 150

30x > 1620

x > 54

Answer:

[tex]\huge\boxed{x>54\to x\in(54;\ \infty)}[/tex]

Step-by-step explanation:

[tex]30x>1,470+150\\\\30x>1,620\qquad\text{divide both sides by 30}\\\\\dfrac{30x}{30}>\dfrac{1,620}{30}\\\\x>54[/tex]

Answer:

There are only 6 numbers that fit that description. (4,12,24,32,44,52)

Answer:

last one

Step-by-step explanation:

"no more than" indicates that we need to use the sign ≤, which eliminates the first and third options. The expression we can use to calculate her cost is 2s + 5 so the answer is 2s + 5 ≤ 40.

Answer:

the 4th one, 2s + 5 ≤ 40

Step-by-step explanation:

Answer:

I guess that you want to calculate the difference between the annual healt care costs in 1950 and today.

The equation is:

C(x) = $620*(1.082)^x

in 1950, we have x = 0 (because is the initial year)

then the cost is:

C(0) = $620*1 = $620.

Now, today, in 2020, we have:

x = 2020 - 1950 = 70

then we have:

C(70) = $620*(1.082)^70 = $154,276.7

So, according to this equation, te difference is:

$154,276.7 -  $620 = $153,656.6

Answer:

I believe the answer Is A

Step-by-step explanation:

If its asking for the shape, the peak would be three because it has the most variables in it which is also 3 variables

Answer:

Step-by-step explanation:

From the information given,

For null hypothesis,

H0:μ=25

For alternative hypothesis,

Ha:μ > 25

It is a right-tailed test due to the inequality sign in the alternative hypothesis.

The decision rule would be to reject the null hypothesis if the significance level is greater than the p value.

Since the significance level, 0.05 is < p-value, 0.41, then we fail to reject H0. Therefore,

At the 5% significance level, the data do not provide sufficient evidence to conclude that the average distance a reader lives from the newspaper's headquarters is greater than 25 miles.

Answer:

a) half life is 3h 17 minutes

b) function of residue drug after t hours with initial quantity = 500 mg

        f(t) = 500 (0.81^t)

c) drug left in patient's system after 24 hours

   = 0.00 grams (to the hundredth of a gram.

Step-by-step explanation:

Given:

Drug initial active weight, A = 500 mg

Residue active weight, f(t) = A 0.81^t

t = time in hours.

a) half life

Half life is T, such that f(T) = 0.5A =>

0.5A = A(0.81^t)

0.81^t = 0.5

t*log(0.81) = log(0.5)

t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours

= 3 h 17.36 minutes

b) Equation of function of residue drug as a function of time t in hours

A=500 mg

f(t) = A(0.81^t)    substitute A = 500 mg

= 500(0.81^t)  mg

c) weight of residue drug after 24 hours to the hundredth of a gram.

t=24 hours

A=500

f(t) = 500(0.81^t)    substitute t=24 hours

= 500(0.81^24)

= 3.181 mg

= 0.003181 g

Answer:

i. The y -axis starts at zero but has different intervals.

ii. Different bar widths are used on the same graph.

iii. The y -axis doesn't start at zero.

Step-by-step explanation:

A graph is a plot showing accurate representation and presentation of correlation among variables of a given data. It is a tool that can be used to summarize all information about a given data for easy understanding and deductions.

A misleading graph is one that has an inappropriate representation of data, thus a wrong conclusion would be deduced or obtained from this type of graph. Misleading graph is majorly due to inconsistency, and errors in plot (axis or scale used).

Answer:

The y-axis doesn't start at zero.

The intervals on the y-axis are too large.

Different bar widths are used on the same graph.

The y-axis starts at zero but has different intervals.

Step-by-step explanation:

I have this lesson on Odyessyware

Please mark brainliest if this helps.

Answer:

C. $0.56

Step-by-step explanation:

26 x $2.15= $55.9

$55.9 - $41.34= $14.56

$14.56 / 26= $0.56

Answer:

You'd be saving $0.56 per pound of chicken.

Step-by-step explanation:

The regular price for 26 lb of chicken would be ($2.15/lb)(26 lb) = $55.90.

Subtracting $41.34 from that figure, we get $14.56.

Dividing that result by 26 lb results in $0.56.

You'd be saving $0.56 per pound of chicken.

Answer:

2/3 of a quart

Step-by-step explanation:

2 coats on a 9X10=1 coat on a 18X10. Since 18X10 is 1.5 times 12X10, the 12X10 will need 2/3 of the paint

Answer:

2/3 quart

Step-by-step explanation:

The 10 by 12 ft wall has an area of 120 ft^2.  The 9 by 10 ft wall has an area of 90 ft^2.

Thus, the following equation of ratios provides us with the answer:

  90         (1/2)

--------- = -----------

 120            x

or 3/4 = 1/(2x), or

6x = 4.  Thus, x = 4/6 or 2/3.

2/3 of a quart would be enough for one coat on the 10 by 12 ft wall.  Note that only 1/2 of a quart would suffice for one coat on a 9 by 10 ft wall (for comparison).

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (5, - 8)

m = [tex]\frac{-8-1}{5-2}[/tex] = [tex]\frac{-9}{3}[/tex] = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 1) , then

1 = - 6 + c ⇒ c = 1 + 6 = 7

y = - 3x + 7 ← equation of line

Answer:

y - 1 = -3(x - 2)

Step-by-step explanation:

Sounds as though you want the equation of the line through (2, 1) and (5, -8).

As we move from (2, 1) to (5, -8), x (the "run") increases by 3 and y (the "rise") decreases by 9.  Thus, the slope of this line is m = rise / run = -9/3, or m = -3.

Let's use the point-slope formula for a straight line here:  The point (h, k) is (2, 1) and the slope is -3. Then y - k = m(x - h) becomes:

y - 1 = -3(x - 2)

Answer:

1. 31.14

2. 46

Step-by-step explanation:

1. Using order of operations, we first simplify what's in the parentheses, so we do 4.1-(-6.2), or 4.1+6.2. This gives us -5+3.8(10.3). Next is multiplication, so we do 3.8(10.3), which gets us to -5+39.14. Lastly, we add, to get 31.14.

2. First, we solve in the parentheses. Within the parentheses, we do multiplication first, so we first do 3*-2, to get us 8-4(-6+(-13))÷2. Then, we solve inside the parentheses, so we do -6+(-13), to get 8-4(-19) ÷2.

Next, since multiplication and division are on the same level, we go from left to right, so we do -4*-19 first, to get 8+76÷2. Now we do division, to get 8+38. Lastly, we add, to get 46.

Answer:

9) 34.14

10) 46

Step-by-step explanation:

Answer:

61 wins

Step-by-step explanation:

60 + 1/2*100=110 wins (team A)

110-49=61

Team B needs to win 61 more games to have the same number of wins as team A.

Answer:

25 train routes

Step-by-step explanation:

The train routes go from 1-2, 2-3, 3-4, 4-5, ,and so on, but there is also one that goes from 25-1. If you notice, there when we get to 4-5, there are 4 train routes which means that if there are 25 towns, then there are 24 train routes, but since 25 and 1 are connected then there are 25 routes. Hope this helps!

Answer:

300

Step-by-step explanation:

25·24/2=300

Answer:

True

Step-by-step explanation:

For every kilogram, there are 1000 grams

Answer:

8

Step-by-step explanation:

21-13=8

m=8

Answer:

m= -8

Step-by-step explanation:

13= m+21

-21      -21

subtract 21 from both sides to get "m" alone

-8=m