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Dahasolnce [82]

3 years ago

10

Last week, the price, in dollars, of a gallon of gasoline was g. This week the price of gasoline per gallon increased by 5%. Whi

ch expressions represent this weeks price, in dollars, of a gallon of gasoline?
A. g+0.05
B. g+0.05g
C. 1.05g
D. 0.05g
E. (1+0.05)g

1 answer:

dmitriy555 [2]3 years ago

4 0

The price of gasoline in this week is 1.05g. Option C

Step-by-step explanation:

Given,

The price of a gallon of gasoline = g in last week.

The price of gasoline increased by 5% this week.

To find the price of gasoline this week.

Formula

If an original price of an object a increased by b% the final price will be = a× $\frac{100+b}{100}$

So,

The price of gasoline in this week = g×1.05 = 1.05g

[ Please note: Here option C and E have same value. So, both are correct].

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Just need help on #7 thru 8(a), b and c

Stella [2.4K]

7

a. The slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

b. The distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

c. The midpoint of the R(3, 5) and H(-1,2) is (2, 4)

8.

a. The transformation rule is (x,y) → (x + 1, y - 1)

b.

The x-coordinate is shifted 1 unit to the left and

The y - coordinate is shifted 1 unit downwards.

c. The image of B' the pre-image of B(5, 6) is (6, 5)

<h3 /><h3>7 a. How to find the slope of the line?</h3>

The slope of a line passing through the points (x₁, y₁) and (x₂,y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

So, m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 5)/(-1 - 3)

m = -3/-4

m = -3/4

So, the slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

<h3>b. The distance between the points</h3>

The distance between two points (x₁, y₁) and (x₂,y₂) is d = √[(y₂ - y₁)² + (x₂ - x₁)²]

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

d = √[(2 - 5)² + (-1 - 3)²]

d = √[(-3)² + (-4)²]

d = √[9 + 16]

d = √25

d = 5 units

So, the distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

<h3>7 c How to find the midpoint of the R(3, 5) and H(-1,2) </h3>

The midpoint of the the points (x₁, y₁) and (x₂,y₂) is (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

So, the midpoint (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(x, y) = [(3 + (-1))/2, (5 + 3)/2]

(x, y) = [(3 - 1)/2, (5 + 3)/2]

(x, y) = [4/2, 8/2]

(x, y) = (2, 4)

So, the midpoint of the R(3, 5) and H(-1,2) is (2, 4)

<h3>8. a The rule for the transformation of point A(1, 4) to point B(2, 3)</h3>

Given that point A(1, 4) and point B(2, 3) we see that point B(1 + 1, 4 - 1).

Let pont A be (x,y).

So, point B = (x + 1, y - 1)

So, the transformation rule is (x,y) → (x + 1, y - 1)

<h3>b. Describe the transformation</h3>

Since the transformation rule is (x,y) → (x + 1, y - 1), we see that

the x-coordinate is shifted 1 unit to the left and
the y - coordinate is shifted 1 unit downwards.

<h3>c. The image of B' the pre-image of B(5, 6)</h3>

Since the transformation rule is (x,y) → (x + 1, y - 1) and point B is (5, 6), thus the image of B' is

(x,y) → (x + 1, y - 1)

(5,6) → (5 + 1, 6 - 1)

(5,6) → (6, 5)

So, the image of B' the pre-image of B(5, 6) is (6, 5)

Learn more about slope of a line here:

brainly.com/question/1617757

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1 year ago

Marlow types 90 words in 3 minutes. How many words does he type in 7 hours?<br>

Contact [7]

Answer:

if I am right it is 12,600 words

Step-by-step explanation: 90 divided by 3 which is 30 420x30=12,600

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3 years ago

Tyler’s height is 57 inches. What could be his height in centimeters? Explain your reasoning. (1 inch= 2.54 cm)

Nina [5.8K]

Answer:

144.78 cm

Step-by-step explanation:

57 times 2.54

6 0

2 years ago

Read 2 more answers

7. Are the ordered pairs below an arithmetic sequence or geometric

DochEvi [55]

Answer:

8. Arithmetic Progression

9. $f(9) = 300$

Step-by-step explanation:

Given

$\{(1,55)\ (2, 45)\ (3, 35)\ (4, 25)\}$

Solving (8): Arithmetic or Geometric

We start by checking if it is arithmetic by checking for common difference (d).

$d = y_2 - y_1 = y_3 - y_2 = y_4 - y_3$

This gives:

$d = 45 - 55 = 35 - 45 = 25 - 35$

$d = -10 = -10 = -10$

$d=-10$

<em>Because the common difference is equal, then it is an arithmetic progression</em>

<em></em>

Solving (8):

$f(n) = f(1) + f(n-1)$

To find f(9), we substitute 9 for n

$f(9) = f(1) + f(9-1)$

$f(9) = f(1) + f(8)$

We need to solve for f(8); substitute 8 for n

$f(8) = f(1) + f(8 - 1)$

$f(8) = f(1) + f(7)$

We need to solve for f(7); substitute 7 for n

$f(7) = f(1) + f(7 - 1)$

$f(7) = f(1) + f(6)$

We need to solve for f(6); substitute 6 for n

$f(6) = f(1) + f(6 - 1)$

$f(6) = f(1) + f(5)$

We need to solve for f(5); substitute 6 for n

$f(5) = f(1) + f(5 - 1)$

$f(5) = f(1) + f(4)$

From the function, f(4) = 25 and f(1) = 55.

So:

$f(5)=55 + 25$

$f(5)=80$

$f(6) = f(1) + f(5)$

$f(6) = 55 + 80$

$f(6) = 135$

$f(7) = f(1) + f(6)$

$f(7) = 55 + 135$

$f(7) = 190$

$f(8) = f(1) + f(7)$

$f(8) = 55 + 190$

$f(8) = 245$

$f(9) = f(1) + f(8)$

$f(9) = 55 + 245$

$f(9) = 300$

8 0

3 years ago

Help me please with my math

motikmotik

Answer:

P = 47.1 units

Step-by-step explanation:

the perimeter of the pair of straight opposite sides is 11+11, or 22

now you have 2 semi-circles, which equals 1 full circle which, if we find the circumference to then we just add it to 22 to get the entire answer

Circumference of circle with diameter of 8:

C = 2πr

C = 2π(4)

C = 8π

C = 25.13

now add 22 + 25.13 to get 47.1 rounded to nearest tenths place

5 0

2 years ago