prove the following identity showing all steps:
[tex]\frac{cos(x+30)-sin(x+60)}{sin(x)cos(x)} =-sec(x)[/tex]
please help fast
Answer:
See solution below
Step-by-step explanation:
Given the expression
[tex]\frac{cos(x+30)-sin(x+60)}{sin(x)cos(x)} \\[/tex]
Recall that
cos x = sin(90-x)
cos(x+30 ) = sin (90-(x+30)
= sin(90-x-30)
= sin(60-x)
Substitute
[tex]\frac{sin(60-x)-sin(x+60)}{sin(x)cos(x)} \\= \frac{sin60cosx-cos60sinx)-sinxcos60-cosxsin60)}{sin(x)cos(x)} \\= \frac{-2cos60sinx)}{sin(x)cos(x)} \\= \frac{-2(1/2)sinx)}{sin(x)cos(x)} \\= \frac{-1}{cos(x)}\\= \frac{1}{cos(x)}\\ \\= -sec(x) Proved[/tex]
What is the length of the hypotenuse in the following figure.
Answer:
5
Step-by-step explanation:
what do you mean ?? its already written there
Answer:
The answer is 5
Step-by-step explanation:
The answer is 5 because the length across from the right angle is always the hypotenuse.
What is the area, in square centimeters, of the trapezoid shown below?
3 cm
9 cm
12 cm
Please help
PLSS HELP ME ASAP!! I WILL GIVE YOU BRAINLYEST!
A tree casts a 9-foot shadow while a 5-foot
pole casts a 2h foot shadow. How tall is the
tree?
the answer tho this is that the tree is 14ft
Answer:
22.5
Step-by-step explanation:
20 ft for an 8 foot shadow but since you need 1 more foot
take half of 5 (2.5) and you get 22.5
Elizabeth is going to invest $480 and leave it in an account for 8 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Elizabeth to end up with $670?
Answer:
4.2
Step-by-step explanation:
took a bullet for the team
Elizabeth would need an interest rate of 4.25% to make a profit of $670, to the closest hundredth of a percent.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, Elizabeth is going to invest $480 and leave it in an account for 8 years.
from the formula of compound interest
A = P(1 + r/n) ^nt
in our case,
A =670
P = 480
t = 8
Thus,
670 = 480(1 + r)^8
r = 4.25%
Therefore, an interest rate, to the nearest tenth of a percent, would be 4.25% required in order for Elizabeth to end up with $670
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A cereal box has a length of 8 inches, a width of 1 3/4 inches, and a height of 12 1/8 inches what is the volume of the cereal box?
Answer:
169 3/4 in³
Step-by-step explanation:
v=l×w×h
v=8× 1 3/4× 12 1/8
21 7/32×8= 169 3/4 in³
You borrow $500 to buy a computer. The simple interest rate is 15%. You pay off the loan after 4 years. How much do you pay for the loan?
Answer:
133.33
Step-by-step explanation:
sorry if im incorrect
Answer:
800
Step-by-step explanation:
PLEASE IM IN CLASS PLEASE
Answer:
71.88
Step-by-step explanation:
........................
So if 9 of the 32 are women, then everybody left would be a guy. That's 32 - 9 = 23 men. To turn that into a percentage, just divide the number of men by the total amount of people in the class: 23/32 = 71.875% which rounded is 71.88%
Mario shot 30 baskets in 6 minutes. Chris shot 48 baskets in 8 minutes. How many more baskets did Chris shoot per minute?
Answer:
6
Step-by-step explanation:
You would first divide 48/8 than you would get 8 baskets per minute.
Answer:
6
Step-by-step explanation:
Mario: 1 minute = 5 baskets and 5 x 6 = 30.
Chris: 1 minute = 6 baskets and 6 x 8 = 48.
¿Cuáles son las famosas razones trigonométricas y sus inversas?
Answer:
Razones trigonométricas inversas: cosecante, secante y cotangente. ... Dado un triángulo rectángulo, definimos la cosecante, la secante y cotangente de un ángulo como las razones inversas del seno, coseno y tangente, respectivamente.
Step-by-step explanation:
espero y te ayude
A t-shirt company spent 28% of its annual budget developing a new heat-press machine. What fraction of the company's budget was spent developing the new machine?
Answer:
7/25
Step-by-step explanation:
In a class test, +4 marks were awarded for the correct answers and -1 mark for the wrong answers. Student scores 40 marks. If his correct answers were 11, find his wrong answers. *
4 Wrong Answers
[tex]Correct = 11*4=44[/tex]
[tex]Incorrect = Correct - 40 = 4[/tex]
can someone help me I will give you a brainliest
2√3+6√2
hope this helps :D
Answer:
Step-by-step explanation:
2√3+6√2
Which number is rational?
/2
10
O
16
Answer:
16
Step-by-step explanation:
Square root of 2 is irrational. This has been proven by the Pythagoreans (there is a simple proof of that).
pi is also known to be irrational although the proof is a bit more demanding.
Square root of 10 can be written as a product of square root of 5 and square root of 2, which themselves are irrational. Any product involving an irrational number is irrational
Square root of 16 = 4. 4 can be written as a fraction 4/1, or 8/2, 16/4, etc. and therefore is rational by definition.
In the right triangle shown, m
[tex] \tan(30) = \frac{x}{ \sqrt{72} } [/tex]
[tex] \sqrt{72} \tan(30) = x[/tex]
x equals about 4.9 rounded to the hundredths place.
The right rectangular prisms are similar.
Which statements are correct? Check all that apply.
3.2 AT
The angles in the smaller prism measure 90
degrees.
The perimeter of the rectangular bases changes by
a factor of 2.
The surface area changes by a factor of 8.
The larger prism has twice the volume of the
smaller prism.
The area of the rectangular bases changes by a
factor of 4.
1.6
-
-
-
-
-
-
10.4
V
0.8
2.2.
Answer:
A)The angles in the smaller prism measure 90 degrees.
B)The perimeter of the rectangular bases changes by a factor of 2.
E)The area of the rectangular bases changes by a factor of 4.
Step-by-step explanation:
The right rectangular prisms are similar.
Which statements are correct? Check all that apply.
A)The angles in the smaller prism measure 90 degrees.
B)The perimeter of the rectangular bases changes by a factor of 2.
C)The surface area changes by a factor of 8.
D)The larger prism has twice the volume of the smaller prism.
E)The area of the rectangular bases changes by a factor of 4.
Solution:
Two polygons are said to be similar if they have the same shape, the ratio of their sides are in the same proportion and they have the same size of angles.
A) Since the bigger prism has angles with measure of 90°, hence the angles in the smaller prism will also measure 90.
Option A is correct.
B) Perimeter of bigger prism base = 2(2.2 + 0.8) = 6
Perimeter of smaller prism base = 2(1.1 + 0.4) = 3
The perimeter of the rectangular bases changes by a factor of 2 (6 / 3).
Option B is correct.
C) Surface area of bigger prism = 2(3.2*0.8 + 2.2*0.8 + 3.2*2.2) = 22.72
Surface area of smaller prism = 2(1.6*0.4 + 1.1*0.4 + 1.6*1.1) = 5.68
The surface area does not change by a factor of 8 (22.72 / 5.68 ≠ 8)
Option C is wrong
D) Volume of bigger prism = 2.2 * 3.2 * 0.8 = 5.632
Volume of smaller prism = 1.1 * 1.6 * 0.4 = 0.704
The larger prism volume is not twice of the smaller prism
Option D is wrong
E) Area of bigger prism base = 2.2*0.8 = 1.76
Area of smaller prism base = 2.2*0.8 = 0.44
The area of the rectangular bases changes by a factor of 4 (1.76 / 0.44 = 4)
This is a lot but please help me I’ll mark u as brilliant
Answer:
see below
Step-by-step explanation:
2:
# of sides = 3
# of vertices = 3
name of shape: triangle
3.
# of sides = 4
# of vertices = 4
name of shape: quadrilateral
4.
# of sides = 5
# of vertices = 5
name of shape: pentagon
5.
# of sides = 6
# of vertices = 6
name of shape: hexagon
6.
# of sides = 8
# of vertices = 8
name of shape: octagon
jason is closing on a $430,000 home. he made a 10% down payment and is borrowing the rest. closing costs are 3.5 percent of the mortgage.
a. what is the down payment?
b. what is the amount of the mortgage?
c. what are the closing costs?
d. what is the total amount of the mortgage if they finance the closing costs with the mortgage
The total Amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.
a) The down payment of Jason is 10% of $430,000 =$43,000b) The amount of the mortgage is the difference between the home value and the down payment.
Mathematically, $430,000 - $43,000 = $387,000.c) The closing costs are 3.5% of the mortgage. So, 3.5% of $387,000 is: 0.035 × $387,000 = $13,545.
Hence, the closing costs are $13,545. d) The total amount of the mortgage if they finance the closing costs with the mortgage is the sum of the amount of mortgage and the closing cost.
So, the total amount of the mortgage is: $387,000 + $13,545 = $400,545.Solution:a) Jason's down payment is 10% of the cost of the house, which is given as $430,000.
To calculate the down payment, multiply the cost of the house by 10%.Down payment = $430,000 x 10% = $43,000
Therefore, Jason's down payment is $43,000.b)
The amount of the mortgage is the difference between the total cost of the house and the down payment. The cost of the house is given as $430,000.
Thus, we have:Mortgage amount = Total cost - Down paymentMortgage amount = $430,000 - $43,000Mortgage amount = $387,000
Therefore, the amount of the mortgage is $387,000.c) The closing costs are 3.5% of the mortgage.
Using the mortgage amount calculated in part b), we can compute the closing costs as follows:Closing costs = 3.5% x Mortgage amountClosing costs = 3.5% x $387,000
Closing costs = $13,545
Therefore, the closing costs are $13,545.
d) If the closing costs are financed with the mortgage, we simply need to add the closing costs to the mortgage amount calculated in part b):Total amount of the mortgage = Mortgage amount + Closing costsTotal amount of the mortgage = $387,000 + $13,545
Total amount of the mortgage = $400,545
Therefore, the total amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.
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find the slope, (-2,-2) and (1,4)
Solve the system and find the values of x and y
Answer:
x = [tex]\frac{(a+b)}{2}[/tex]
[tex]y=\frac{a-b}{2}[/tex]
Step-by-step explanation:
System of equations has been given as,
x + y = a ----------(1)
x - y = b ---------(2)
By adding equation (1) and (2)
(x + y) + (x - y) = a + b
2x = a + b
x = [tex]\frac{(a+b)}{2}[/tex]
By substituting these values in equation (2),
x - y = b
[tex]\frac{a+b}{2}-y=b[/tex]
[tex]\frac{a+b}{2}-b=y[/tex]
[tex]\frac{a+b-2b}{2}=y[/tex]
[tex]\frac{a-b}{2}=y[/tex]
Need help, have to submit this very soon!!
Answer:
see explanation
Step-by-step explanation:
length = [tex]\frac{60}{8}[/tex] = 7.5 in
scale factor = [tex]\frac{image}{original}[/tex] = [tex]\frac{8}{60}[/tex] = [tex]\frac{2}{15}[/tex]
---------------------------------------------------
length = [tex]\frac{192}{4}[/tex] = 48 cm
scale factor = [tex]\frac{omage}{original}[/tex] = [tex]\frac{4}{192}[/tex] = [tex]\frac{1}{48}[/tex]
Evaluate the expression when
x= -2 and y = 4
Expression: x² - 8
у
Answer:
x= -2 , y = 4
then
R/ (-2)² - 8(4)
R/ 4-32
R/ -28
Step-by-step explanation:
Can someone help me please
Answer:
That would seem like a b
Step by step explanation: (>) means greater than and b is stating that element a is higher than element c
Can someone please help me with this ❤️❤️
Answer:
See below for answers
Step-by-step explanation:
y=5(2)ˣ
y=5(2)⁻²=5(1/2²)=5(1/4)=5/4
y=5(2)⁻¹=5(1/2¹)=5(1/2)=5/2
y=5(2)⁰=5(1)=5
y=5(2)¹=5(2)=10
y=5(2)²=5(4)=20
Use the tables to complete the statements,
Single Taxpayers: Income Brackets
Tax Rate Income Bracket
10%
O to 9,525
12% 9,526 to 38,700
22% 38,701 to 82,500
24% 82,501 to 157,500
32% 157,501 to 200,000
35% 200,001 to 500,000
37%
> 500,000
Single Taxpayers: Qualified
Dividends and Long-Term
Capital Gains
Tax Rate
Income Bracket
0%
O to 38,600
15% 38,601 to 425,800
20%
> 425,800
If she earned
Rita has a taxable income of $85,000. She sold stock after owning it for six months, resulting in a
$5,000 on the sale of the stock, Rita must pay $ In taxes on the gain,
Answer:
Short term Capital gain and $1200
Step-by-step explanation:
Any investment held under a year falls under short term capital gain
5,000 X 0.24 = 1,200
Answer:
Short term Capital gain and $1200.
Step-by-step explanation:
short term capitalGains earned by selling assets you’ve held for a year or less are called short-term capital gains, and they generally are taxed at the same rate as your ordinary income, anywhere from 10% to 37%.
Since Rita has a taxable income of $85,000.
So , she fall 24% 82,501 to 157,500 Tax rate bracket.
Therefore 5,000 X 0.24 = 1,200
Thus Rita must pay $1200 in taxes on the Short term Capital gain made by her.
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The radius of the base of a cone is 6 inches the height of the cone is 6 inches. Which is closest to the volume of the cone
Answer:
V = 226.19
Step-by-step explanation:
v=(Pi)(r^2)(h/3) = 3.14(6^2)(6/3) = 3.1415(36)(2) = 226.19
The closest to the volume of the cone is given by 226.19.
We have given that,
The radius of the base of a cone is 6 inches the height of the cone is 6 inches.
What is the formula of the volume cone?V=(Pi)(r^2)(h/3)
V= 3.14(6^2)(6/3)
V= 3.1415(36)(2)
V= 226.19
Therefore, The closest to the volume of the cone is given by 226.19.
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PLS help plssss 30 points plssss and how how u know it’s math plssssss helppppp plsssss
Answer:
Complementary angles sum to 90°
x + 73° = 90°x = 90° - 73°x = 17°can someone solve this for me?
Answer:
A, C, D
Step-by-step explanation:
42 + 14 = 56
38 + 18 = 56
67 + 33 = 100
70 + 30 = 100
93 + 35 = 128
95 + 33 = 128
B)
40 + 22 = 62
32 + 10 = 42
62 ≠ 42
Employees at a company are given £1,200 to spend on items for the office.
They decide to buy a coffee machine and as many bean bags as possible.
Bean bags cost £40 with an offer of "Buy at least 15 get 10% off the price."
The coffee machine costs £280.
How much will they have left over from the £1,200?
Answer:
380
Step-by-step explanation:
280 coffe machine
15 bag multiple for 40= 600 - 15%= 540
540+280=820
1200-820=380
A=144pi^2 ft. Find the radius