The price of an electronic puzzle was reduced be $7

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

7 0

Answer:

Step-by-step explanation:

total price was reduced by $ 7

let x = the total price........ x - 7

he bought 10.....and it cost him $ 130

10(x - 7) = 130

10x - 70 = 130

10x = 130 + 70

10x = 200

x = 200/10

x = 20 <====== original price

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If tan 0=5/4, calculate the value of cos 0

emmasim [6.3K]

5
If tan θ = —— , calculate the value of cos θ:
 4

Recall the definition of the tangent function:

 sin θ
tan θ = ————
cos θ

5 sin θ
—— = ————
4 cos θ

Cross multiply:

5 · cos θ = 4 · sin θ

Square both sides:

(5 · cos θ)² = (4 · sin θ)²

5² · cos² θ = 4² · sin² θ

25 · cos² θ = 16 · sin² θ

But sin² θ = 1 – cos² θ. Substitute that for sin² θ into the equation above, then you get

25 · cos² θ = 16 · (1 – cos² θ)

25 · cos² θ = 16 – 16 · cos² θ

Isolate cos² θ:

25 · cos² θ + 16 · cos² θ = 16

(25 + 16) · cos² θ = 16

41 · cos² θ = 16

 16
cos² θ = ———
 41

 4²
cos² θ = ————
(√41)²

Take square root of both sides:

 4
cos θ = ± ———
√41

 4 4
cos θ = – ——— or cos θ = ——— ✔
 √41 √41

The sign of cos θ depends on which quadrant θ lies. Since you first have a positive value for tan θ, then that means θ lies either in the 1st or the 3rd quadrant.

• If θ is a 1st quadrant angle, then

cos θ > 0

 4
cos θ = ——— ✔
√41

• If θ is a 3rd quadrant angle, then

cos θ < 0

 4
cos θ = – ——— ✔
 √41

I hope this helps. =)

3 0

3 years ago

four-fifths of the senior class went to prom. if 324 seniors went to prom, how many are there in the senior class

romanna [79]

The answer to your question is 405, because look divide 324 by 4 becasue thats how many fifths are being used then multiply the answer which is 81 by 405

3 0

3 years ago

On the first day of her 5-day trip, Miss Gordon drove 435 km in 5.3 hours. On the next three days, she drove 80.78 kilometers in

vova2212 [387]

516.66 km

There are 100 m in 1 km
Therefore : 880 m = 0.88 km
435 km + 80.78 km + 0.88 km = 516.66 km

4 0

3 years ago

#12 with explanation please

4vir4ik [10]

Answer:

30.01 units

Step-by-step explanation:

Given vertices WXYZ:

W(-4,5), X(2,4), Y(3, -4), Z(-1, -6)

Perimeter is the sum of the side length.

Use distance formula to find each side:

WX = $\sqrt{(2+4)^2+(4-5)^2} =\sqrt{37}$ ≈ 6.08
XY = $\sqrt{(3-2)^2+(-4-4)^2} =\sqrt{65}$ ≈ 8.06
YZ = $\sqrt{(-1-3)^2+(-6+4)^2} =\sqrt{20}$ ≈ 4.47
WZ = $\sqrt{(-1+4)^2+(-6-5)^2} =\sqrt{130}$ $\sqrt{(-1+4)^2+(-6-5)^2}=\sqrt{130}$ ≈ 11.40