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3 years ago

Write as a single term: sin(25°) cos(10°) − cos(25°) sin(10°).

Mathematics

1 answer:

eduard3 years ago

3 0

Answer: cos (25° + 10°)

Step-by-step explanation: The expression:

sin(25°) cos(10°) − cos(25°) sin(10°)

is associated to the expression for the cosine of the sum of two angles that is:

cos (α+β) = sinα *cosβ -cosα*sinβ

Hence if we do α = 25° and β = 10°

by subtitution we get:

cos (25° + 10°) = sin(25°) cos(10°) − cos(25°) sin(10°)

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QUESTION 11.1

lawyer [7]

The group paid $ 5250 at first city and $ 6250 at second city

Solution:

Let x = the charge in 1st city before taxes

Let y = the charge in 2nd city before taxes

The hotel charge before tax in the second city was $1000 higher than in the first

Then the charge at the second hotel before tax will be x + 1000

y = x + 1000 ----- eqn 1

The tax in the first city was 8.5% and the tax in the second city was 5.5%

The total hotel tax paid for the two cities was $790

Therefore, a equation is framed as:

8.5 % of x + 5.5 % of y = 790

$\frac{8.5}{100} \times x + \frac{5.5}{100} \times y = 790$

0.085x + 0.055y = 790 ------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

0.085x + 0.055(x + 1000) = 790

0.085x + 0.055x + 55 = 790

0.14x = 790 - 55

0.14x = 735

Substitute x = 5250 in eqn 1

y = 5250 + 1000

Thus the group paid $ 5250 at first city and $ 6250 at second city

8 0

3 years ago

PLEASE HURRY XX Find a equation that matches the graph.

Galina-37 [17]

Answer:

x ≥ 3

Step-by-step explanation:

The closed dot represents ≥ and ≤

The dot is located on the number "3"

The closed dot essentially shows that the solution is nothing more than 3 and up.

Let "x" be the variable we use.

x ≥ 3

Best of Luck!

3 0

4 years ago

Read 2 more answers

The cost of putting on a play is $500 for the theater rental, $500 for the

Kamila [148]

You need to add all of them together
Therefore the answer is 1,225

3 0

3 years ago

Serena makes $9 per hour cutting lawns. Each day, she earns about $15 in tips. If Serena made no less than $110 on Monday, which

aleksandrvk [35]

Hourly rate: $9
daily tips: $15
minimum earnings: $110

The inequality that represents h, the number of hours she worked Monday is:

9h + 15 > 110

8 0

3 years ago

The dimensions of two square pyramids formed of sand are shown. How much more sand is in the pyramid with the greater volume?

SSSSS [86.1K]

Answer:

The pyramid with the greater volume has 5in^3 more sand

Step-by-step explanation:

Given

Pyramid A

$B = 25in^2$ -- Base Area

$h = 9in$ --- height

Pyramid B

$B = 30in^2$

$h = 7in$

See attachment for pyramids

The volume of a square pyramid is:

$V = \frac{1}{3}Bh$

First, calculate the volume of pyramid A

$V_A = \frac{1}{3} * 25in^2 * 9in$

$V_A = 25in^2 * 3in$

$V_A = 75in^3$

Next, the volume of pyramid B

$V_B = \frac{1}{3} * 30in^2 * 7in$

$V_B = 10in^2 * 7in$

$V_B = 70in^3$

To calculate how much more sand the greater pyramid has, we simply calculate the absolute difference (d) between their volumes

$d = |V_B - V_A|$

$d = |70in^3 - 75in^3|$

$d = |- 5in^3|$

$d = 5in^3$

8 0

3 years ago