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2 years ago

14

A school bought $548 in basketball equipment and uniforms costing $29.50 each. The total cost was $2023. Write an equation u can

use to find the number of uniforms the school purchased.

1 answer:

Marta_Voda [28]2 years ago

4 0

2023-548=X÷29.50
I think

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Answer please cuz I'm very confused

Anestetic [448]

5x + 3y = - 53

the equation of a line in ' slope- intercept form ' is y = mx + c

where m is the slope and c the y-intercept

rearrange 3x - 5y = - 15 into this form to obtain m → (subtract 3x from both sides)

- 5y = - 3x - 15 → divide all terms by - 5 )

y = $\frac{3}{5}$ x + 3 → in slope-intercept form with m = $\frac{3}{5}$

given a line with slope m then the slope m₁ of a line perpendicular to it is

m₁ = - $\frac{1}{m}$ = - 1 ÷ $\frac{3}{5}$ = - $\frac{5}{3}$

partial equation is y = - $\frac{5}{3}$ x + c

to find c substitute ( - 7, - 6) into the partial equation

- 6 = $\frac{35}{3}$ + c ⇒ c = - 6 - $\frac{35}{3}$ = - $\frac{53}{3}$

y = - $\frac{5}{3}$ x - $\frac{53}{3}$ → in slope intercept form

multiply all terms by 3

3y = - 5x - 53 → ( add 5x to both sides )

5x + 3y = - 53 → in standard form

6 0

3 years ago

Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

<h3>16</h3>

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

<h3>17</h3>

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

<h3>18</h3>

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

<h3>15</h3>

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

2 years ago

The length of a rectangle is 9 feet more than the width. If the perimeter is 198 feet, what are the length and width?

stiks02 [169]

THE PERSON BELOW ME OR ABOVE ME IS CORRECT

8 0

1 year ago

(math problem in picture)

In-s [12.5K]

Answer:

the answer of the question is b. 8.2 mm

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2 years ago

Read 2 more answers

To become a member at All Sport Gym, you must first pay a one time fee of $25. After that, the cost of membership is $10 per mon

rodikova [14]

Answer:

25-10=15

Step-by-step explanation:

8 0

2 years ago