Tell which of the following is a linear equation in one variable:
a) x² - 4x + 3 = 0
b) 6x - 2y = 7
c) 3x - 1 = -2x
d) pq - 3 = p
e) 3x + 2 = 4 ( x +7 ) + 9

For 100 Points

Question 10

Lines a and b by the converse of the consecutive interior angles theorem

Question 11

Lines e and f by the converse of the alternate interior angles theorem

[tex]0.744\div6[/tex]

Simplify:

[tex]\frac{0.744}{6}[/tex]

[tex]=0.124[/tex]

Answer:

x < 5

Step-by-step explanation:

[tex]2x - 4 < 6[/tex]

[tex]2x < 10[/tex]

[tex]x < 5[/tex]

.........................................................

The measure that would most correctly answer this question is standard deviation.

What is standard deviation?

The standard deviation is measure of how spread out data from mean.

Step-by-step explanation:

Average age of respondents in a survey is [tex]49[/tex] years. Researcher interested in finding out if most respondents are close to [tex]49[/tex] years or not.

Hence here measures of dispersion fact will be used.

Measures of dispersion are range and standard deviation.

Range is nothing but the difference between maximum and minimum values of the data.

Standard deviation gives proper idea about how far the data values are scattered from the mean point [tex]49[/tex] years.

Therefore the correct option is standard deviation.

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The salesman used 460 order forms in total, when he used three types of order forms: a, b, c.

Given that,

A salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b

A = 50

B = 4A + 0.5C = 200+ 0.5C  .......... (i)

C =  A +  0.5B =  50 + 0.5 B  .......... (ii)

multiply (ii) with 2

B = 2C -50              .......... (iii)

B = 0.5C + 160        ...........(i)

subtract (i) from (iii)

0 = 1.5C -210

C = 420/3 = 140

put in (i)

B = 200 + 0.5(140) = 270

Total forms = A+B+C = 50 + 270 + 140 = 460

Therefore, he used 460 forms altogether.

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39,916,800 color combinations are possible

Here, we want to get the possible number of color combinations possible.

Since any number of colors can be chosen, there are no restrictions here

That means the number of possible color combinations will be;

11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800 color combinations

Answer:

x = 11,2 inchs

Step-by-step explanation:

I infer that the units are in inches.

8-3 = 5

Then:

By the Pythagorean Teorem:

x² = 10² + 5²

x² = 100 + 25

x² = 125

√x² = √125

x = 11.18

to the nearest tenth:

x = 11.2 inches

The speed of the tennis ball is 6.2 metres per seconds.

Speed is measured as the ratio of distance to the time in which the distance was covered.

Therefore, speed can be represented mathematically as follows;

speed = distance / time

Hence, the table tennis travels 12.4 metres south in 2 seconds.

The speed of the tennis can be computed as follows:

distance = 12. 4 metres

time = 2 seconds

Therefore,

speed = 12.4 / 2

speed = 6.2 meters per seconds.

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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.

Given that,

Katie and her best friend Liam play tennis every Saturday morning.

When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.

The speed of the tennis can be found by using formula

speed=distance/time

distance = 12. 4 metres

time = 2 seconds

Now speed=12.4/2

speed=6.2

Hence speed of the tennis ball is 6.2m/s

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The Solution:

Given the graph of f(x), we are required to determine whether the degree of the function is ODD or EVEN, and also to determine whether the function itself is ODD.

An odd function is defined as a function that has f(–x) = –f(x) for any value of x. The opposite input gives the opposite output.

From the given graph of f(x), the function f(x) is ODD.

The degree of the function f(x) is odd since the f(x) itself is odd.

Answer:

1/x to the -8 power simplified would be x^8

Step-by-step explanation:

When there is a negative exponent you put the fraction under 1

[tex]\frac{1}{\frac{1}{x^{8} } }[/tex]  and its the same as x^8

The simplified expression is [tex]x^8[/tex].

Exponent is the power of the variable or constant to which it is raised.

The expression 1 over x is denoted by 1/x.

The exponent of the obtained expression will be -8. So, the expression will be [tex](\frac{1}{x})^{-8}=\frac{1}{x^{-8}}[/tex].

The exponents of the denominator change from negative to positive when they move from denominator to numerator.

[tex]\frac{1}{x^{-8}}=x^8[/tex]

Thus, the simplified expression will be x raised to the power 8.

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For the given tables, we have that:

a. The grids are given at the end of the answer.

b. The functions are classified as follows: f(x) exponential, g(x) linear.

c. When x increases by one unit from left to right, we have that:

d. The functions are equal for a value between 1 and 2, as at x = 1 g(x) is greater while at x = 2 f(x) is greater.

The difference between exponential and linear functions is in the rate of change, as:

Hence the functions are classified as follows:

We have one exponential and one linear function, so it is quite difficult to solve an equation to verify where they are equal. We have that:

This means that at one point between x = 1 and x = 2, they intersected, that is, they had the same function values.

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Answer:

Step-by-step explanation:

solve for x

2x+14=-21-5

2x+14=-26

subtract 14 from both sides

2x+(14-14)=-14-26

2x=-14-26

2x=-40

divide both sides of 2x = -40 by 2

[tex]\frac{2x}{2} =\frac{-40}{2}[/tex]

2/2=1

x=[tex]\frac{-40}{2}[/tex]

x= -20

Answer: b=13

Step-by-step explanation:

b=39/3

b=13

Answer:  its 13  

Step-by-step explanation

Answer:

769 and 858

Step-by-step explanation:

Every hour, the distance between the two planes increases by 2x + 89

2 hours = 4x + 178

3254 = 4x + 178

4x = 3076

x = 769

The following investments were done:

In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:

Metal: x

Glass: 2 · x

Paper: 8,000 - 3 · x

And the yield function is equal to:

280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)

280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x

120 =  0.08 · x

x = 1500

The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.

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The probability that their hospital stay is greater than 6 days is equal to 0.67724 and the probability that their hospital stay is from 5 to 6 days is equal to 0.108

Mean (μ) = 7.37

Standard deviation (σ) = 3

we need to calculate probability that their hospital stay is from 5 to 6 days i.e.

⇒ P(5 < X < 6) = P(X < 6)-P(X < 5)

Here we will use standard normal distribution where,

Z-score = (X -μ )/ σ = (6 - 7.37)/3 = -0.46

Z-score = (5 - 7.37)/3 = -0.79

from Z table we found p-value

⇒P(5<X<6) = P(X<6) - P(X<5) = 0.32276 - 0.21476 = 0.108

So there is 0.108 probability that their hospital stay is from 5 to 6 days.

we need to calculate probability that their hospital stay is greater than 6 days i.e.

We get: P(X > 6) = 1 − P(X < 6)

Here we will use standard normal distribution where,

Z-score = (X - μ)/σ = (6 - 7.37)/3 = -0.46

from Z table we found p-value

P(X > 6) = 1 - P(X<6) = 1 - 0.32276 = 0.67724

So there is 0.67724 probability that their hospital stay is greater than 6 days.

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The picture is represented by the absolute value function g(x) = |x - 5| - 4. (Correct choice: A)

Absolute values are functions defined by the following piecewise function:

The function in the picture is the consequence of the following rigid transformations:

Now we proceed to obtain the image of f(x):

Horizontal translation

f'(x) = |x - 5|

Vertical translation

g(x) = |x - 5| - 4

The picture is represented by the function g(x) = |x - 5| - 4.

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The dimensions are Width = 7 feets ; length = 20 feets

As given,

Meadow area is 140 square feet.

Height = W (smaller dimension and 2 sides)

Height = L (longer dimension and 1 side)

Fence yards equal 34 feet;

Hence,

L + W = 34

L + 2W = 34

L = 34 - 2W - - - (1)

Recall:

Area = L * W = 140

Substitute value of L

140 = (34 - 2W) * W

140 = 34W - 2W²

2W² - 34W + 140 = 0

W² - 17W + 70 = 0

W² - 10W - 7W + 70 = 0

W(W - 10) - 7(W - 10) = 0

(W - 10) = 0 or (W - 7) =0

W = 10 or W = 7

We choose the shorter width because length should be as long as possible:

W = 7

L + 2W = 34

L = 30 - 14

L = 20 feets

Therefore, The measurements are 7 feet wide and 20 feet long.

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Answer:

SSS

Step-by-step explanation:

We know the length of DE and JK are the same because as shown in the diagram, they are both equal to 15 cm. While we know that EF and KL are congruent because it is shown that both sides are 8 cm long. Even though we are not sure of the exact lengths of FD or LJ, we are aware that they are the same length sue to the ticks found on both sides on the triangles, indicating that they are both the same length.

623 / 7 = 89

Result = 89

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

Explanation:

Anything perpendicular to Ax+By = C is of the form Bx-Ay = D

The given equation is x-y = -2 showing that A = 1, B = -1 and C = -2.

So Bx-Ay = D will update to -x-y = D

Plug in the coordinates of (-4,1) to find D.

-x-y = D

D = -x-y

D = -(-4)-1

D = 4-1

D = 3

We go from -x-y = D to -x - y = 3

Then multiply both sides by -1 to end up with x + y = -3

A) A function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days is; T = 25n + 15

B) The total cost to stay for 6 nights is; $165

C) No, 3 night does not cost half as much as the cost for 6 nights due to the addition mandatory cost of $15.

We are told that a pet hotel charges $25 per night to keep a dog. We are also told that there is a mandatory $15 examination fee when the dog arrives there.

A) If the number of nights spent is n, then the function rule here for the total cost  is;

T = 25n + 15

B) We are told that the number of nights is 6 nights. Thus, we will just plug in 6 for n into the total cost equation to get;

T(6) = 25(6) + 15

T(6) = $165

C) The cost of 3 nights would be;

T(3) = 25(3) + 15

T(3) = $90

This is more than half of the cost of 6 nights.

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On solving using combinations (C) we get the answers for part a)the probability that you will be assigned none of the tasks that you want = 0.035% b) the Probability that I am assigned exactly 7 of the tasks that I want = 0.0427 c)The probability that I am assigned at least one of the tasks I want = 0.9996 d)Probability that I am assigned at least 7 of the tasks I want = 0.049

a) There are 27 tasks and 10 tasks I want to do. Thus there are 17 tasks I do not want to do. I am randomly assigned 12 tasks. The probability that I will be assigned none of the tasks that I want is p = 17C12 / 27C12 = 3. 55 * 10 ^ (-4) = 0.035 %

b) The probability that I am assigned exactly 7 of the tasks that I want

p = 10C7 * 17C5 / 27C12 =  0.0427  = 4.27%

c) The probability that I am assigned at least one of the tasks I want

p = 1 - 17C12 / 27C12    where 17C12 / 27C12 is the probability that I get assigned 0 tasks I want.

Thus, p = 1 - (7/19665) = 0.9996

d)Probability that I am assigned at least 7 of the tasks I want

p = (10C7*17C5+10C8*17C4 + 10C9*17C3 + 10C10*17C2) / 27C12

⇒ p = 17 / 345 = 0.049 = 4.9%

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The function that represents the total charge for renting a truck for a certain number of hours is f(h) = 90 + 20h What is the value of the function for an input 5 represent : $190, which is the total charge in dollars for renting a truck for 5 hours.

Given data :

Charges = $90 + $20 per hour

Value = 5

Now let formulate an equation

f(h) = 90 + 20h

Where,

h = 5

So,

Total charge = 90+ 20 ×5

Total charge = 90 + 100

Total charge =190

Therefore  the correct option is B.

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Answer:

Explanation:

• Loan Amount = $500

• Time = 2 weeks

• The amount paid pack = $520

We want to determine the simple interest rate.

First, find the amount paid as interest:

Answer:

[tex]x = 4 \pm \sqrt7[/tex]

Step-by-step explanation:

Hello!

Standard form of a Quadratic: [tex]ax^2 + bx + c= 0[/tex]

Given the Equation: [tex]x^2 -8x+9=0[/tex]

Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\[/tex]

Solve by substituting the values into the Quadratic Formula.

The solution to the quadratic is [tex]x = 4 \pm \sqrt7[/tex].

We need to know how to interpret a graph to solve the problem. (a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

(a) h is a function of t since the height of the projectile varies with time. The input values of the function is the time interval and the output values is the height of the projectile.

(b) The approximate height of the projectile after 0.5 second according to the graph is 20 feet and the height of the projectile after 1.25 second according to the graph is 30 feet.

(c)The domain of the function is [0,2.5] and the range of the function is [0,30].

(d) t is not a function of h.

Therefore a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

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Solution

We will draw a diagram to illustrate the information

Using the concept of SOHCAHTOA

We are given adjacent and we want to find opposite

Therefore, the answer is

Answer: y = 15

Step-by-step explanation:

Combine multiplied terms into a single fraction

-6 = -2y/5

Then, multiply both sides by 5 to get:

-30 = -2y

Last, you divide both sides by -2 to get:

15 = y or y = 15

Hope this helps!

Draw of a modelled object