Question 5(Multiple Choice Worth 2 points)
(07.01 MC)
What is the range of the function f(x) = x - 3?

Answer:

Is there more information?  There is not enough to find the slope of a line.  I'll answer with an equation that works, but I suspect it won't be correct.

Step-by-step explanation:

If the only requirement is to have a line that goes through (4,3).  Then one could simply say:

y = 4

This is a horizonal line that goes through (3,4), and will always produce a y value of 4 regardless of x.  No, it will not pass through (4,3) since y is aleways 4, regardless of x.

If you wanted to get fancier, we could write a needlessly more complex equation:

y = (4/3)x

When x = 3, y = 4, so (3,4) is on this line.  But (4,3) is not.  y = (4/3)(4) means y = (16/3), not 4.

The roots of the given polynomials exist  [tex]$x=8+\sqrt{10}$[/tex], and [tex]$x=8-\sqrt{10}$[/tex].

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]

Therefore by using the formula we have

[tex]$x^{2}-16 x+54=0$$[/tex]

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$$[/tex]

simplifying the equation, we get

[tex]$&x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]$&x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]$&x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]

Therefore, the roots of the given polynomials are [tex]$x=8+\sqrt{10}$[/tex], and

[tex]$x=8-\sqrt{10}$[/tex].

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Answer:

x=8-[tex]\sqrt{10}[/tex] and x=8+[tex]\sqrt{10}[/tex]

Step-by-step explanation:

It was right for me

Answer:

Step-by-step explanatio

Answer:

C. 206 unit^2.

Step-by-step explanation:

Area = 2*11*5 + 2*11*3 + 2*3*5

         = 110 + 66 + 30

         =  206.

The Five number summary for the given data:

Minimum: 24

Lower quartile: Q1 = 29

Median: 43

Upper quartile: Q3 = 50

Maximum: 56

Interquartile range: IQR = 21

The interquartile range is calculated by

IQR = Q3 - Q1

Where Q3 - upper quartile and Q1 - lower quartile

Q3 = 3/4(n + 1) th term

Q1 = 1/4(n + 1) th term

The given data points are

24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56

where n = 13

Maximum data value = 56

Minimum data value = 24

Calculating Median:

Median = (n+1)/2 th term

⇒ Median = (13 + 1)/2 = 7th term

∴ Median = 43

Calculating the quartiles:

Upper quartile Q3 = 3/4(n + 1)th term

⇒ Q3 = 3/4(13 + 1) = 10.5

⇒ Q3 = 10th term + 1/2(11th term - 10th term)

⇒ Q3 = 49 + 1/2(51 - 49)

⇒ Q3 = 49 + 1

∴ Q = 50

Lower quartile Q1 = 1/4(n + 1)th term

⇒ Q1 = 1/4(13 + 1) = 3.5

⇒ Q1 = 3rd term + 1/2(4th term - 3rd term)

⇒ Q1 = 29 + 1/2(29 - 29)

∴ Q1 = 29

Calculating the IQR:

IQR = Q3 - Q1

      = 50 - 29

      = 21

Thus, the interquartile range is 21.

Therefore, the five-number summary for the given data:

Minimum: 24

Lower quartile: Q1 = 29

Median: 43

Upper quartile: Q3 = 50

Maximum: 56

Interquartile range: IQR = 21

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Answer:

A = 20%

B = 33.33%

C = 46.67%

Step-by-step explanation:

Ok we need to add up 3, 5, and 7

3+5+7 = 15

405/15 = 27.

27*3 = A

27*5 = B

27*7 = C

A = 81 / 20%

B = 135 / 33.33%

C = 189 / 46.67%

Answer:

15

Step-by-step explanation:

Note: Take note , absolute value will give the magnitude of the value. (Which means ignoring the + / - signs.)

Eg. | - 19 | = 19

Therefore,

[tex] \frac{12(30 - (9 + {4}^{2})) }{10 - | - 6| } \\ = \frac{12(30 - (9 + 16))}{10 - 6} \\ = \frac{12(30 - 25)}{4} \\ = \frac{12(5)}{4} \\ = \frac{60}{4} \\ = 15[/tex]

Answer:

1. Transversal y intersects lines m and n; <1 ~= <2 (Given)

2. <1 ~= <3 (Vertical Angles Theorem)

3. <2 ~= <3 (Transitive Property of Congruence)

4. m || n (Converse of Alternate Interior Angles Theorem)

Answer:

680

Step-by-step explanation:

x = total number

.6x  = bus riders = 408              (.6 is decimal for 60%)

.6x = 408

x = 408/.6 = 680

The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

To find the minimum value of 10x (3y/5):

Given - y = 3/(2x)

So, we want the bare minimum of,

Take the derivative to obtain:

When you set it to zero, you get:

So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.

Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

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[tex]5(1.5)=\boxed{7.5 \text{ yd}}[/tex]

The length of the curved border or arc is 7.5 yards.

the length of the arc = [tex]\theta \times r[/tex]

given that [tex]\theta[/tex] = 1.5 radian

radius = 5 yards

then the length of arc from the above formula

[tex]l = \theta \times r\\l = 1.5 \times 5 = 7.5[/tex] yards

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Answer:

Step-by-step explanation:

If 12 men are needed to run 4 machines. How many men are needed to run 20

we can solve with an equation

12 : 4 = x : 20

x = 12 * 20 : 4

x = 240 : 4

x = 60

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

check

12 : 4 = 60 : 20

3 = 3

the answer is good

The perimeter of the triangle can be express as follows:

12b + 11d + 2c

The perimeter of a figure is the sum of the whole sides of the figure.

A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.

Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.

Hence, the perimeter of the triangle can be represented as follows:

Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c

Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c

Perimeter of the triangle = 12b + 11d + 2c

Therefore, the perimeter of the triangle can be express as follows:

12b + 11d + 2c

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Answer:

irrational,  it can't be written as a fraction

Step-by-step explanation:

The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.

let

x + y = 15

2x + y = 21

From equation (1)

x = 15 - y

2x + y = 21

2(15 - y) + y = 21

30 - 2y + y = 21

- 2y + y = 21 - 30

-y = -9

y = 9

Substitute y = 9 into

x + y = 15

x + 9 = 15

x = 15 - 9

x = 6

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From the given similar triangles we can conclude that the length of Side SQ is; 4

We are given that;

PQ is parallel and congruent to MT.

Now, from the concept of similar triangles , we can say that;

PS/TS = QS/MS

From the given triangle we see that;

PS = 3 - 2x

QS = 6x - 1

MS = 30

TS = 10

Thus;

(3 - 2x)/10 = (6x - 1)/30

Cross multiply to get;

3(3 - 2x) = 6x - 1

9 - 6x = 6x - 1

Rearranging gives;

6x + 6x = 9 + 1

12x = 10

x = 10/12

x = 5/6

Thus;

SQ = 6(5/6) - 1

SQ = 4

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Hi :)

Let's use some Algebra skills to find w ^•^

First off, let's subtract both sides by 6

[tex]\longrightarrow\darkblue\sf{-9-6 > 5w}[/tex]

[tex]\longrightarrow\darkblue\sf{-15 < 5w}[/tex]

Divide both sides by 5

[tex]\longrightarrow\sf{-3 < w}[/tex]

Or

[tex]\longrightarrow\sf{w > -3}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

Answer: 15

Step-by-step explanation:

First step is to find the slope of the line given

y = -x - 2

y = mx + c where m is the slope of the line so the slope of the line is -1

If 2 lines are perpendicular to one another, the product of the slopes is -1 so the slope of the perpendicular line is -1/-1 = 1

y = 1x + c or y = x + c

As the line passes through the coordinate (-5,10), we can substitute the x and y value of the coordinates into the equation

10 = -5 + c

c = 15

So the equation of the line is y = x + 15

area is 1/2 times base times height

triangle A

1/2 times 7 times 9

answer 31.5

Triangle B

1/2 times 7 times 5

answer 17.5

Answer:

B

Step-by-step explanation:

The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.

The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value of the investment can also be determined using an online finance calculator, as follows.

Then the interest is the difference between the future value and the present value.

Initial deposit = $8,241.78

Interest rate = 5.5% compounded daily

Investment period = 31 days

N (# of periods) = 31 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $8,241.78

PMT (Periodic Payment) = $0

Results:

FV = $8,280.37

Total Interest $38.59 ($8,280.37 - $8,241.78)

Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.

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0.9544 = 95.44% of scores lie between 220 and 380 points.

Normal distribution problems can be solved using the Z-score formula.

With a set of means and standard deviations, the Z-score for measure X is given by: After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is less than X. H. Percentile of X. Subtract 1 from the p-value to get the probability that the value of the measure is greater than X.

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

We are given mean 300, standard deviation 40.

This means that µ= 300, σ = 40

What proportion of scores lie between 220 and 380 points?

This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.

X = 380

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

Z= (380-300)/40

Z= 2

Z=2 has a p-value of 0.9772.

X=300

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

Z= (220-380)/40

Z=-2

Z=-2 has a p-value of 0.9772.

0,9772 - 0,0228 = 0,9544

0.9544 = 95.44% of scores lie between 220 and 380 points.

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The points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).

Given:

f(x) = -0.5x+2

g(x) = x³ - 5x² + 3

The point of intersection exists the point where f(x) = g(x)

x³ - 5x² + 3 = - 0.5x + 2

x³ - 5x² + 3 + 0.5x - 2 = 0

x³ - 5x² + 0.5x + 1 = 0

Factorize and estimate the value of x

Let x = 0.53 and 4.85

substitute the value of x = 0.53

f(0.53) = -0.5(0.53) + 2

f(0.53) = -0.265 + 2

f(0.53) = 1.375

If x = 4.85

f(4.85) = -0.5(4.85) + 2

f(4.85) = -2.425 + 2

f(4.85) = -0.245

Therefore, the points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).

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the unit price is $3 per pound, the correct option is the second one.

The unit price for the oranges is just the price for one pound of oranges.

Here we know that the price of 4 lb of oranges is $12, with that we want to get the cost of a single lb of oranges, so we can write:

4lb = $12

If we divide both sides by 4, then we get:

4lb/4 = $12/4

1lb = $3

This means that the price of 1 pound of oranges is $3, then the unit price is $3 per pound, the correct option is the second one.

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Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.

According to the statement

we have to tell and explain about the types of shapes which are required for the creations of 3-D figure.

For this purpose, Firstly we have to know about the 3-D figures.

So,

A shape is a graphical representation of an object or its external boundary and outline, as opposed to other properties such as color, texture, or material type.

A plane shape is constrained to lie on a plane, in contrast to solid 3-D shapes.

After that we know that the

When the all dimensions of a given shape can be observed at the same time, then its is said to be in a 3-D. However, polygons are shapes which has 3 or mores sides. Examples are: trigon, hexagon, octagon etc.

Thus, since the in the 3-D figure have 8 sides connected which is greater than their width.

This confirms that the sides of the figure made up of eight congruent rectangles, because the 3-D figure has eight regular sides. Then, the height of the figure would be the length of the rectangles.

After that all this condition, Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.

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Answer:

Smallest number: 5555789

Largest number: 9999875

Step-by-step explanation:

Since each digit must be used at least once, the smallest number that can be formed with the digits 5, 7, 8 and 9 is 5555789 (ascending order of digits with smallest digit used four times

The largest number is 9999875 (descending order of digits with largest digit used four times)

Using the permutation formula, the number of different options for the top three finishers is given as follows:

[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]

The order in which the players are chosen is important, as A, B, C is a different outcome than C,B,A for example, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 students will be chosen from a set of 14, hence the number of ways is:

[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]

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Answer:

you need all of them?

Step-by-step explanation: