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3 years ago

Solve for x in the diagram below.

Mathematics

2 answers:

OlgaM077 [116]3 years ago

8 0

Answer:

Step-by-step explanation:

2x+45+x=180 simplify to 3x+45=180. Subtract 45 on both sides then divide by 3 to get 45

Anastasy [175]3 years ago

5 0

Answer:

Step-by-step explanation:

2x + 45 + x = 180 {linear pair}

3x + 45 = 180

3x = 180 -45

3x = 135

x = 135/3

x = 45

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A devastating freeze in California's Central Valley in January 2007 wiped out approximately 75% of the state's citrus crop. It t

solniwko [45]

The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

The linear equation of the function is: $g(P) = 22.9P+7$ .
The inverse function is: $g^{-1}(c) = \frac{1}{22.9}(c - 7)$ .
A practical domain is from 0% to 100%
A practical range is from 7 to 29.9

A. Input quantity

The input quantity is the percentage of frozen citrus crop

B. Output quantity

The output quantity is the cost of box of oranges

C. The linear function

We have:

$(P_1,c_1) = (20\%,11.58)\\(P_2,c_2) = (80\%,25.32)$

Calculate the slope of the function

$m = \frac{c_2 - c_1}{P_2 - P_1}$

$m = \frac{25.32 - 11.58}{80\%-20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

The linear equation is calculated as follows:

$c -c_1 = m(P-P_1)$

$c -11.58= 22.9(P-20\%)$

$c-11.58 = 22.9P-4.58$

D. Rewrite as y = mx + b

We have:

$c-11.58 = 22.9P-4.58$

Collect like terms

$c = 22.9P - 4.58 + 11.58$

$c = 22.9P+7$

The function is:

$g(P) = 22.9P+7$

E. A practical domain

The domain is the possible values of P. Because P is a percentage, its possible values are 0% to 100%.

The domain of the function is: $[0\%,100\%]$

F. A practical range

When P = 0%

$c = 22.9 \times 0\% + 7 = 7$

When P = 100%

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

G. The meaning of $g^{-1}(12)$

The inverse function of g(P) is $g^{-1}(P)$

So:

$g^{-1}(12)$ is the percentage of frozen citrus crop, when the cost is $12.

H. The inverse formula

We have:

$c = 22.9P+7$

Subtract 7 from both sides

$c - 7 = 22.9P$

Make P the subject

$P = \frac{1}{22.9}(c - 7)$

So, the inverse formula is:

$g^{-1}(c) = \frac{1}{22.9}(c - 7)$

Substitute 12 for c

$g^{-1}(12) = \frac{1}{22.9}(12 - 7)$

$g^{-1}(12) = \frac{1}{22.9} \times 5$

$g^{-1}(12) = 22\%$

Read more about linear equations at:

brainly.com/question/19770987

6 0

3 years ago

John works Monday to Friday. He buys his lunch on his way to work. Each day John buys a sandwich, a bottle of water and a bag of

kipiarov [429]

Complete question

Shop A _________________ shop B £3

Any sandwich - £2.85 ___ sandwich, water crisp

A bottle of water - 60p

A bag of crisp - 85p

Answer:

£6.50, John is incorrect

Step-by-step explanation:

Number of working days = 5 = number of days meal is purchased

Total cost per meal, shop A :

£(2.85 + 0.60 + 0.85) = £4.3

Total cost for the week = 4.3 * 5 = £21.50

Total cost per meal cost Shop B = £3

Total cost for the week = 3 * 5 = £15

Difference :

£21.50 - £15 = £6.50

Hence, Amount John saves by buying from shop B is £6.50

Numbe

4 0

3 years ago

If a stadium has 15,000 seats sold at $10.00, $12.50, and $15.00 equally distributed in three sections, how much can be made if

ELEN [110]

If it is equally distrubuted in 3 sections then we would divide 15,000 by 3. Now we take one section which would cost $10.00 and multiply it by the 5,000 since we divided. We would do the same with all three and then add it together.

$10 * 5,000 = $50,000 section one can sell this much
$12.50 * 5,000 = $62,500 section two can sell this much
$15 * 5,000 = $75,000 section three can sell this much

If all the seats are sold than 50k + 62.5k + 75k = $187,500 can be made

3 0

3 years ago

Please help as soon as possible

Studentka2010 [4]

The lines are reciprocal because they cross to form an X. Also 4/5 is the reciprocal of 5/4

4 0

3 years ago

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The school nurse is packing first aid kits. the ratio of bandages to gloves is 9:2. if she has 48 gloves, how many bandages will

Naily [24]

Answer:

Step-by-step explanation: