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Alexxx [7]
3 years ago
14

If the point (2, 5) is a solution to the system of equations shown below, then determine the missing values of b and m. Show how

you arrive at your answer.
Mathematics
1 answer:
antoniya [11.8K]3 years ago
6 0

Complete Question:

If the point (2, 5) is a solution to the system of equations shown below, then determine the missing values of b and m. Show how you arrive at your answer.

1. y = 3x + b

2. y = mx + 9

Answer:

1. Intercept, b = -1

2. Slope, m = -2

Step-by-step explanation:

Given the following data;

Points on the line (x, y) = (2, 5)

To find the missing values;

Mathematically, the equation of a straight line is given by the formula;

y = mx + b

Where;

  • m is the slope.
  • x and y are the points
  • b is the intercept.

1. y = 3x + b

Substituting the value of x and y, we have;

5 = 3(2) + b

5 = 6 + b

b = 5 - 6

<em>Intercept, b = -1</em>

2. y = mx + 9

Substituting the value of x and y, we have;

5 = m(2) + 9

5 = 2m + 9

2m = 5 - 9

2m = -4

m = -4/2

<em>Slope, m = -2</em>

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Answer:

285°

Step-by-step explanation:

105+180=285

7 0
3 years ago
How many times greater is the value of the digit 8 in 82.77 than the value of the digit 8 in 20.18
Kitty [74]

Answer:

Option 3. 1,000 times

Step-by-step explanation:

we know that

The value of digit 8 in 82.77 is equal to 80

The value of digit 8 in 20.18 is 0.08

so

Divide 80 by 0.08

80/0.08=1,000 times

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3 years ago
When a frequency distribution is exhaustive, each individual, object, or measurement from a sample or population must appear in
KiRa [710]

Answer:

a. True

Step-by-step explanation:

The frequency distribution is a summary of the gathered data set, in which the interval of values is divided into classes.

A requirement for a frequency distribution is for the classes to be mutually exclusive and exhaustive. That is, each individual, object, or measurement in the data set must belong to <em>one and only one</em> class.

Then, we can conclude that each individual, object, or measurement must appear in at least one (in fact, only in one) category or class.

4 0
3 years ago
We discovered that 650 GSS respondents in 2006 watched television for an average of 2.98 hrs/day, with a standard deviation of 2
Aliun [14]

Answer:

a) 2.09167

b) 0.2

c) 130 correspondents

d) 5.38 hours per day

e) 69%

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Mean = 2.98hrs/day, Standard Deviation = 2.4

a) What is the Z score for a person who watches more than 8 hrs/day.

z = 8 - 2.98/2.4

= 2.09167

b) What proportion of people watch 5 hrs/day or more television?

z = 5 - 2.98/2.4

z = 0.84167

Determining the Probabilityvalue from Z-Table:

P(x<5) = 0.80001

The proportion of people watch 5 hrs/day or more television

P(x>5) = 1 - P(x<5) = 0.19999

Approximately = 0.2

c) How many does this correspond to in the sample?

From the question above, we are told that: there are 650 GSS respondents in 2006 watched television

Hence the proportion that corresponds to Question b is

0.2 × 650

= 130 correspondents

Therefore, 130 correspondents watch 5 hrs a day or more television

d) What number of television hours per day corresponds to a Z = +1.

z score formula is given as:

z = (x-μ)/σ

Z = +1

x = unknown

Mean = 2.98

Standard deviation = 2.4

Hence:

1 = x - 2.98/2.4

Cross Multiply

1 × 2.4 = x - 2.98

2.4 = x - 2.98

2.4 + 2.98 + x

= 5.38 hours per day.

e)What is the percentage of people who watch between 1 and 6 hours of television per day?

For x = 1

z = 1 - 2.98/2.4

z = -0.825

Probability value from Z-Table:

P(x= 1) = 0.20469

For x = 6

z = 6 - 2.98/2.4

z = 1.25833

Probability value from Z-Table:

P(x = 6) = 0.89586

The percentage of people who watch between 1 and 6 hours of television per day is calculated as:

P(x = 6) - P(x = 1)

0.89586 - 0.20469

= 0.69117

Converting to percentage,

0.69117 × 100%

= 69.117%

To the nearest whole number = 69%

Therefore, 69% of the people who watch between 1 and 6 hours of television per day

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3 years ago
Dad gave Tyler and Emily the same amount of pocket money Emily bought a t shirt for $41 and she had $6 left how much money did d
Lady_Fox [76]

Answer:

Dad gave Tyler $47.

Step-by-step explanation:

You add the money that Emily had left and the cost of the t-shirt.

41+6= 17

6 0
3 years ago
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