A value of θ for which sec θ = csc (θ − 20°) is A. 70° B. 60° C. 55° D. 30°

Suppose that y is directly proportional to x and that y = 10 when x = 3. Complete parts (a) and (b). (a) Find the constant of pr

Yuliya22 [10]

For this case we have that if "y" varies directly with "x", then it is true that:

$y = kx$

Where:

k: It is the constant of proportionality

We have according to the data that:

$10 = k (3)$

We find the value of "k":

$k = \frac {10} {3}$

Having "k", we find "y" when $x = 6$ :

$y = \frac {10} {3} (6)\\y = \frac {60} {3}\\y = 20$

ANswer:

$k = \frac {10} {3}\\y = 20$

4 0

3 years ago

Consider the 30°-60° right triangle shown whose hypotenuse is equal to one. Clearly this triangle is half of an equilateral tria

Bad White [126]

Answer:

Step-by-step explanation:

Given triangle ABC is a right triangle.

m∠ACB = 60°

m∠CAB = 30°

m(AC) = 1 unit

A). Shorter side of the given triangle = Side BC

By applying cosine rule,

cos(∠C) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

cos(60°) = $\frac{BC}{AC}$

BC = $\frac{1}{2}(AC)$

BC = $\frac{1}{2}$

Length of the shorter side = 0.5 units

B). Longer side of the given triangle = side AB

By applying Pythagoras theorem in the given triangle,

AC² = AB² + BC²

1² = AB² + $(\frac{1}{2})^2$

1 = AB² + $\frac{1}{4}$

AB = $\sqrt{1-\frac{1}{4}}$

AB = $\sqrt{\frac{3}{4}}$

AB = $\frac{\sqrt{3} }{2}$

Length of the longer side = $\frac{\sqrt{3}}{2}$

3 0

3 years ago

Here is a picture of a cube, and the net of this cube. What is the surface area of this cube? Enter your answer in the box. mm²

UNO [17]

you times everything by 2 and get 144+16+1=161 milliliters i hope this helped have a great day

6 0

4 years ago

Read 2 more answers

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y. Corn costs $215 per acre to produce, and cotton costs

hodyreva [135]

Answer:

x + y = 500

215x + 615y = 187,500

Step-by-step explanation:

The first equation can show the amount of land. The farmer has 500 acres to plant corn, x, and cotton, y.

x + y = 500

The second equation can show the cost. The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.

215x + 615y = 187,500

The system of equations is

x + y = 500

215x + 615y = 187,500

4 0

3 years ago

How much money left after spending $8, $7 and $13, then received $10 and spent $15. now $12 is left. how much money did one have

Inessa [10]

$8 + $7 + $13 + 15 = $43
$x - $43 = $12
x = $55

i am a mathematics teacher. if anything to ask please pm me

4 0

3 years ago