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3 years ago

Find the area of the rhombus.

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

7 0

The formula for the area of a rhombus using the diagonal dimensions is 1/2 * d1*d2.

Area = 1/2 * 10 * 18 = 90 m^2.

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part 3. Find the value of the trig function indicated, use Pythagorean theorem to find the third side if you need it.

Nat2105 [25]

Answer: $\bold{9)\ \sin \theta=\dfrac{1}{3}\qquad 10)\ \sin \theta = \dfrac{4}{5}\qquad 11)\ \cos \theta = \dfrac{\sqrt{11}}{6}\qquad 12)\ \tan \theta = \dfrac{17\sqrt2}{26}}$

Step-by-step explanation:

Pythagorean Theorem is: a² + b² = c² , where "c" is the hypotenuse

$9)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{12}\quad \rightarrow \large\boxed{\dfrac{1}{3}}$

Note: 4² + (8√2)² = hypotenuse² → hypotenuse = 12

$10)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{16}{20}\quad \rightarrow \large\boxed{\dfrac{4}{5}}$

Note: 12² + opposite² = 20² → opposite = 16

$11)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{\sqrt{11}}{6}\quad =\large\boxed{\dfrac{\sqrt{11}}{6}}$

Note: adjacent² + 5² = 6² → adjacent = √11

$12)\ \tan \theta=\dfrac{\text{side opposite of}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{17}{13\sqrt2}\quad =\large\boxed{\dfrac{17\sqrt2}{26}}$

Note: adjacent² + 7² = (13√2)² → adjacent = 17

5 0

3 years ago

the recipe for pumpking pie instructs you to bake the pie at 425∘F, for 15 minutes and then reduce the oven temperature to 350∘F

lakkis [162]

Answer:

ΔT = -75°F

Step-by-step explanation:

ΔT = T₁ - T₀ = 350 - 425 = -75°F

4 0

3 years ago

Members of a soccer team raised $1946.50 to go to a tournament. They rented a bus for $974.50 and budgeted $60.75 per player for

liubo4ka [24]

Answer:

16 players can be brought to the tournament. The equation is written within my step-by-step explanation.

Step-by-step explanation:

Variable p = number of players

Set up an equation:

974.50 + 60.75p = 1946.50

Isolate variable p:

60.75p = 972

Divide:

p = 16

Check your work:

974.50 + 60.75(16) = 1946.50

974.50 + 972 = 1946.50

1946.50 = 1946.50

Correct!

3 0

2 years ago

A fisherman can row upstream at 5mph and downstream at 10mph he started rowing upstream until he got tired and then rowed downst

AlekseyPX

We have been given that the upstream speed is $5 mph$ and the down stream speed is $10mph$ .

Let the fisherman traveled a distance of x miles.

The total time of the trip is 6 hours.

Relations between speed (s), time (t) and distance (d) is $s = \frac{d}{t}$

Hence, $t= \frac{d}{s}$

Time upstream + time downstream = 6

$\frac{x}{5} +\frac{x}{10} =6$

lcm = 10

$\frac{2x+x}{10} =6$

=> $\frac{3x}{10} =6$

Cross multiplying, $3x= 60$

x = 20 miles .. Answer.

8 0

3 years ago

there are 3/4 as many boys as girls in a class of fifth-graders if there are 35 students in the class how many a

Arlecino [84]

Alright so turn 3/4 into a decimal.
3/4 =.75

We need to set up an equation. To do that are need to give boys and girls their own variables.

Girls= X

And since there is 3/4 as many boys
Boys=. 75X

Now we know the sum of boys and girls equals 35
X+.75X=35

X+.75X=1.75X
Now we have 1.75X=35

Divide by 1.75 and get
20=X

Now plug 20 into the equations got from before.
Boys =. 75*X = 20 *. 75 = 15
Girls = X =20

Your Answer:
15 boys
20 girls

You can check
20+15=35
15/20=3/4

8 0

3 years ago

Read 2 more answers