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1 year ago

What is the value of x which proves that the runways are parallel? What is the measure of the larger angle?

Mathematics

2 answers:

Semenov [28]1 year ago

6 0

The answer is<u> C) x = 25; 107 degrees </u>

Temka [501]1 year ago

3 0

Answer:

The correct option is C.

Step-by-step explanation:

if a transversal line intersect two parallel lines then the sum of two consecutive exterior angles is 180 degrees.

The two consecutive exterior angles are 3x+32 and x+48.

$3x+32+x+48=180$

$4x+80=180$

$4x=180-80$

$4x=100$

$x=25$

The value of x is 25.

The measure of two consecutive exterior angles are

$3x+32=3(25)+32=107$

$x+48=25+48=73$

The measure of the larger angle is 107 degrees.

Therefore the correct option is C.

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What is the value of k such that x-5 is a factor of x3 – x2 + kx - 30?

Paraphin [41]

Answer:

k = - 14

Step-by-step explanation:

given that (x - 5) is a factor of the polynomial then x = 5 is a root and

x³ - x² + kx - 30 = 0 for x = 5, that is

5³ - 5² + 5k - 30 = 0

125 - 25 + 5k - 30 = 0

70 + 5k = 0 ( subtract 70 from both sides )

5k = - 70 ( divide both sides by 5 )

k = - 14

5 0

1 year ago

If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this

otez555 [7]

Answer:

Step-by-step explanation:

If there is a direct relation between two variables x and y then it can be represented as

y = kx ,

where y is dependent variable

x is independent variable

k is constant of variation

_____________________________

First condition

y = 400

x = r

using y = kx then relationship will be

400 = kr

finding k here

k = 400/r

Second condition

y = r

x = 4

using y = kx then relationship will be

r = 4k

finding k

k = r/4

since in both condition equation is same

thus, value of k will also be same

thus,

400/r = r/4

=> 400*4 = r*r

=> 1600 = r^2

$\sqrt{r^{2} } = \sqrt{1600} \\r = 40$

Thus, 40 is the value of r

k = r/4 = 40/4 = 10

Thus, constant of variation is 10 which is correct choice.

To cross validate

k = 400/r = 400/40 = 10

7 0

1 year ago

Read 2 more answers

The CEO of a local tech company wants to estimate the proportion of employees that are pleased with the cleanliness of the break

Zigmanuir [339]

Answer:

Methods of obtaining a sample of 600 employees from the 4,700 workforce:

Part A: The type of sampling method proposed by the CEO is Convenience Sampling.

Part B: When there are equal number of participants in both campuses, stratification by campus would give a more precise approximation of the proportion of employees who are satisfied with the cleanliness of the breakrooms than stratification by gender. Another method to ensure that stratification by campus gives a more precise approximation of the proportion of employees who are satisfied with the cleanliness of the breakrooms than stratification by gender is to ensure that the sample is proportional to the proportion of each campus to the whole population or workforce.

Step-by-step explanation:

A Convenience Sampling technique is a non-probability (non-random) sampling method and the participants are selected based on availability (early attendees). The early attendees might be different from the late attendees in characteristics such as age, sex, etc. Therefore, sampling biases are present. All non-probability sampling methods are prone to volunteer bias.

Stratified sampling is more accurate and representative of the population. It reduces sampling bias. The difficulty arises in choosing the characteristic to stratify by.

3 0

1 year ago

Part A: Consider the distance from the school to the coffee shop and the distance from the library to the coffee shop. Draw thei

N76 [4]

Answer:

See below

Step-by-step explanation:

<em>Refer to attached. All answers included.</em>

<u>Note. Will mainly refer to y-coordinates in distance questions</u>

Distance from coffee shop to library: 16 -8 = 8
Distance from coffee shop to school: 16 - 10 = 6 = x
Distance from school to library: 10 - 8 = 2 = y
Ratio x:y = 6: 2 = 3:1

Distance from Sergio's home to Saskia's home: 19 -3 = 16
Distance from Sergio's home to Post office: 16*1/4 = 4
Coordinates of post office: x = 16+4/4= 17, y = 19-16/4= 15

Distance from Kay's home to twin theater: 20 - 4 = 16
Distance from twin theater to market: 16*3/4 = 12
Coordinates of market: x = 5+4/4= 6, y = 4 + 16/4= 8

5 0

1 year ago

Estimate the sum of 196 and 482

k0ka [10]

The answer to this problem would be 700. if you need the sum that isnt estimated, its 678.

4 0

1 year ago