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3 years ago

12

Henry is buying school supplies for the start of th school year. For every 3 pencils he buys 2 pens . If Henry buys 21 pencils.h

ow many total pencils and pens did Henry purchase

2 answers:

Lilit [14]3 years ago

7 0

Answer: He bought 7 pens.

Step-by-step explanation:

21/3 = 7

Tpy6a [65]3 years ago

6 0

Answer:

14

Step-by-step explanation:

So For every 3 pencils he buys, he buys 2 pens. The ratio is 3:2. You want to find another ratio that is 21:x, because he bought 21 pencils, but you don't know how many pens. You could also rewrite ratios into fractions so you would get 3/2 = 21/x. Move the variable and get 3/2x=21. So 3/2 multiplied by what is equal to 21? 3/2 multiplied by 14 is 21.

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The corners of a meadow are shown on a coordinate grid. Ethan wants to fence the meadow. What length of fencing is required?

Nuetrik [128]

Answer:

34.6 units

Step-by-step explanation:

The lenght of fencing required is the total distance between point A to B, B to C, C to D, and D to A. That is the distance between all 4 corners of the meadow.

The coordinates of the corners of the meadow is shown on a coordinate plane in the attachment. (See attachment below).

Let's use the distance formula to calculate the distance between the 4 corners of the meadow using their coordinates as follows:

Distance between point A(-6, 2) and point B(2, 6):

$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$A(-6, 2)) = (x_1, y_1)$

$B(2, 6) = (x_2, y_2)$

$AB = \sqrt{(2 - (-6))^2 + (6 - 2)^2}$

$AB = \sqrt{(8)^2 + (4)^2}$

$AB = \sqrt{64 + 16} = \sqrt{80}$

$AB = 8.9$ (nearest tenth)

Distance between B(2, 6) and C(7, 1):

$BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$B(2, 6) = (x_1, y_1)$

$C(7, 1) = (x_2, y_2)$

$BC = \sqrt{(7 - 2)^2 + (1 - 6)^2}$

$BC = \sqrt{(5)^2 + (-5)^2}$

$BC = \sqrt{25 + 25} = \sqrt{50}$

$BC = 7.1$ (nearest tenth)

Distance between C(7, 1) and D(3, -5):

$CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$C(7, 1) = (x_1, y_1)$

$D(3, -5) = (x_2, y_2)$

$CD = \sqrt{(3 - 7)^2 + (-5 - 1)^2}$

$CD = \sqrt{(-4)^2 + (-6)^2}$

$CD = \sqrt{16 + 36} = \sqrt{52}$

$CD = 7.2$ (nearest tenth)

Distance between D(3, -5) and A(-6, 2):

$DA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$D(3, -5) = (x_1, y_1)$

$A(-6, 2) = (x_2, y_2)$

$DA = \sqrt{(-6 - 3)^2 + (2 - (-5))^2}$

$DA = \sqrt{(-9)^2 + (7)^2}$

$DA = \sqrt{81 + 49} = \sqrt{130}$

$DA = 11.4$ (nearest tenth)

Length of fencing required = 8.9 + 7.1 + 7.2 + 11.4 = 34.6 units

8 0

3 years ago

Line AC and line DB intersect at point P. Solve for angle BPQ.

taurus [48]

Answer:

Angle BPQ = 64°

Step-by-step explanation:

4x + 12 +2x = 90

6x + 12 = 90

- 12 -12

6x = 78

x = 13°

BPQ = ((4(13) + 12)°

(52 + 12)°

64°

8 0

2 years ago

Jina wanted to study how the area of a rectangle changes with the length if it’s width is fixed. She computed the areas of sever

olganol [36]

Answer:

The domain and the range of the function are, respectively:

$Dom\{f\} = [0\,m,5\,m]$

$Ran\{f\} = [0\,m^{2}, 10\,m^{2}]$

Step-by-step explanation:

Jina represented a function by a graphic approach, where the length, measured in meters, is the domain of the function, whereas the area, measured in square meters, is its range.

$Dom\{f\} = [0\,m,5\,m]$

$Ran\{f\} = [0\,m^{2}, 10\,m^{2}]$

8 0

3 years ago

Need help with school

zepelin [54]

Answer:

x=6°

Step-by-step explanation:

The value of x is 6°.

5 0

2 years ago

The number of users of a cell tower in a small, developing town increased by a factor of 1.5 every year from 2010 to 2019. The f

polet [3.4K]

Answer:

B

Step-by-step explanation:

From the statement, we are given a function that shows the number of cell tower users f(x) after x years, from the year 2010 to 2019, so, to solve the problem, we need to remember that the domain is equal to all the values that the variable (x for this case) could take making the function itself exist.

So, the given function is a function of years, and we know that "x" represents the years from 2010 (starting value), to 2019 (ending value) meaning that the domain is located between those two values.

Hence, the correct option is:

B. 0 ≤ x ≤ 5,000

3 0

3 years ago

Read 2 more answers