Answer:
[tex]cos(\alpha )=\frac{\sqrt{11} }{6}[/tex] and [tex]tan(\alpha )=\frac{5\sqrt{11} }{11}[/tex]
Step-by-step explanation:
First we would need to solve for the missing leg in order to figure out the remaining answers.
To do this we can use the Pythagorean Theorem a² + b² = c²
Our missing leg in this case is a, so solving for a gives us [tex]a=\sqrt{c^{2} -b^{2} }[/tex]
Here our b is 5 and our c is 6. So plugging in these values we get [tex]a=\sqrt{(6)^{2}-(5)^{2} } =\sqrt{36-25} =\sqrt{11}[/tex]
With this missing leg being solved, we can use trig identities to solve for cos and tan
I used the trig identity [tex]sin(\alpha )=\frac{opposite}{hypotenuse}[/tex] to set up the triangle in the attached image. We can use the trig identity [tex]cos(\alpha)=\frac{adjacent}{hypotenuse}[/tex] which would give us [tex]cos(\alpha )=\frac{\sqrt{11} }{6}[/tex] and we can use the trig identity [tex]tan(\alpha ) = \frac{opposite}{adjacent}[/tex] which would give us [tex]tan(\alpha )=\frac{5}{\sqrt{11} } =\frac{5\sqrt{11} }{11}[/tex]
Answer:
As trigonometry property:
(sinO)^2 + (cosO)^2 = 1
tanO = sinO/cosO
Then, if sinO = 5/6 = 0.83
=> (5/6)^2 + (cosO)^2 = 1
=> cosO = +/- sqrt(1 - (5/6)^2) = +/- 0.55
=>tanO = +/- 0.83/0.55 = +/- 1.51
Hope this helps!
:)
Does the point (5, 10) satisfy the inequality y>x+5
Help Me Please!!!!1
A basketball has a diameter of 14 inches. If it fits inside a cube-shaped box that has a side length of 13
inches, what is the volume, rounded to the nearest hundredth of a cubic inch, of the space inside the box
that is not taken up by the basketball?
Answer:
The space inside the box = 2197 in³ - 1436.76 in³ is 760.245 in³.
Step-by-step explanation:
Here we have the volume of the cube box given by the following relation;
Volume of cube = Length. L × Breadth, B × Height, h
However, in a cube Length. L = Breadth, B = Height, h
Therefore, volume of cube = L×L×L = 13³ = 2197 in³
Volume of the basketball is given by the volume of a sphere as follows;
Volume = [tex]\frac{4}{3} \pi r^3[/tex]
Where:
r = Radius = Diameter/2 = 14/2 = 7in
∴ Volume of the basketball = [tex]\frac{4}{3} \times \pi \times 7^3 = 1436.76 \ in^3[/tex]
Therefore, the space inside the box that is not taken up by the basketball is found by subtracting the volume of the basketball from the volume of the cube box, thus;
The space inside the box = 2197 in³ - 1436.76 in³ = 760.245 in³.
Which equation is perpendicular to 3x - y = 9 and goes through the point (6,6)
Answer:
y = - [tex]\frac{1}{3}[/tex] x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3x - y = 9 into this form by subtracting 3x from both sides
- y = - 3x + 9 ( divide all terms by - 1 )
y = 3x - 9 ← in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex], thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (6, 6) into the partial equation
6 = - 2 + c ⇒ c = 6 + 2 = 8
y = - [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line
john runs 3 miles in 1/2 of an hour at the same pace how many miles will he run in 1 hour
Answer:
6
Step-by-step explanation:
3miles=30mins
? miles=60mins
=6miles
For 8x2 - 2x-3=0, a = 8, b=_
Answer:
A = 8 B = -2 C = -3
Step-by-step explanation:
The standard form for a quadratic equations is
Ax^2 + Bx +C =0
8x2 - 2x-3=0
A = 8 B = -2 C = -3
Can someone please answer this question? Thanks! What is x? 1/2x = 3
Answer:
x=6
Step-by-step explanation:
hope this helps:)
Answer:
It depends. If x is part of the denominator, then x=1/6. If it is x/2, x=6
Step-by-step explanation:
1/(1/3)=3
1/3*1/2=1/6
x/2=3
2*3=6
Which triangle side lengths form a right triangle? Choose all that apply.
5,6,7
6,8,14
8.15, 17
10, 12, 15
15,20.25
16, 18, 20
Answer:
all
Step-by-step explanation:
What should you NOT use a loan to purchase?
A car
A house
Tuition for higher education
Airline tickets to your dream vacation
Answer:
Airline tickets
Step-by-step explanation:
The other three could be considered important. Your dream vacation may seem important to you, but is something you should only do if you can pay for it. Never go in debt for it.
While loans can be beneficial for purchasing items that generate a return or are necessary, such as a house, car, or higher education, it's generally unwise to take out a loan for things like vacations, which do not provide a return on investment.
Explanation:While it can be tempting to use a loan for many things, there are certain items that are typically seen as poor investments. A house, car, and higher education tuition are often considered acceptable things to take out a loan for, as they can provide a return on your investment and can be seen as necessary for longer term wealth-building. On the other hand, an airline ticket for a vacation is generally not a recommended use for a loan.
The primary reason being that it is not an investment that will appreciate in value or generate income. In fact, it's a depreciating asset because once you've taken the vacation, you have nothing to show for your money, except for the experience and memories. Additionally, taking a loan for such purposes might lead to a situation where you may struggle to repay the debt once you are back from vacation, which can lead to cascading debts and bad credit.
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Tobias sent a chain letter to his friends, asking them to forward the letter to more friends. The number of people who receive the email increases by a factor of
4
44 every
9.1
9.19, point, 1 weeks, and can be modeled by a function,
P
PP, which depends on the amount of time,
t
tt (in weeks).
Tobias initially sent the chain letter to
37
3737 friends.
Answer:
[tex]P(t)=37\cdot 4^{t/9.1}[/tex]
Step-by-step explanation:
The number of people who receive the email increases by a factor of 4 every 9.1 weeks.
This is an exponential growth of the form:
[tex]A=A_o(r)^{t/k}[/tex]
Where:
[tex]A_o =$Initial value\\r=Growth rate\\k=Growth Period\\t=time[/tex]
In this case:
[tex]A_o =37\\r=4\\k=9.1\:weeks[/tex]
Therefore at any time t, the function describing this scenario is:
[tex]P(t)=37\cdot 4^{t/9.1}[/tex] where t is in weeks.
a and b are positive integers and a–b = 3. Evaluate the following:
Plz, help FAST!!!!
Answer:
[tex]3^{b-a}[/tex]
hope this helped!
ASAP for brainlist first correct answer
Answer:
314.16 : 100
Step-by-step explanation:
brainliest?
Answer: about 1:8
Step-by-step explanation: volume of the cone is about 314.16 and the volume of the square pyramid is about 2500 and 314.16 is about 314
314/2500 = .1256 or .125 = 1/8
Denise had a bag full of 24 cubes consisting of red, blue, and black cubes. She concluded that
the probability of picking a blue cube from the bag without looking is neither a likely nor an
unlikely event. How many blue cubes could there be in the bag?
А 3
B 8
с 12
D 20
Answer:
I think it is 12
Step-by-step explanation:
What is the constant rate of change in the function y=5x? *
a.1/5
b.x
c.5
d.1
This is the same as the slope because this is a linear equation
y = 5x is the same as y = 5x+0 which compares to y = mx+b
m = 5 is the slope = rate of change
b = 0 is the y intercept = starting amount
Solve y = x2 - 18 for x.
Answer:
Step-by-step explanation:
assuming that x2 = x², then the equation is y= x²-18
y= x²-18
y-18=x²
[tex]\sqrt{y-18}=\sqrt{x^{2} }[/tex]
[tex]\sqrt{y-18}= x\\[/tex]
so x = [tex]\sqrt{y-18\\}[/tex]
Find the value for x to the nearest tenth.
Answer:
6.2
Step-by-step explanation:
the real answer is 6.24896, but its rounding to the nearest tenth.
A farmer wants to fence a rectangular area for her cows. The area is 200 yards by 423 yards. How many yards of
fencing does she need?
Answer:
1246 yards
Step-by-step explanation:
To find the yard of fencing she needs for he cows, we simply need to find the perimeter of the rectangular area.
The area is 200 yards by 423 yards.
The perimeter is the sum of all the sides of a rectangle and it is given by:
P = 2(L + B)
P = 2(200 + 423) = 2(623)
P = 1246 yards.
She needs 1246 yards of fencing.
Find the value of c that completes the square for x2+12x+c .
3. Who set up their equation correctly for the following question?
Tamara's backyard is rectangular with a length of 5/2 miles. If the area of
the backyard is 3/9 square miles, what is its width? *
Answer:
Step-by-step explanation:100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000$
Final answer:
The correct width of Tamara's backyard is calculated by dividing the area by the length, resulting in a width of 2/15 miles.
Explanation:
The student's question involves setting up an equation to find the width of a rectangular backyard given its length and area. To find the width, we use the formula for the area of a rectangle, which is Length × Width = Area. Tamara's backyard has a length of 5/2 miles and an area of 3/9 square miles. Setting up the equation correctly, we have:
(5/2 miles) × Width = 3/9 square miles
To find the width, we divide both sides of the equation by the length:
Width = (3/9 square miles) / (5/2 miles)
After simplification, which we can do by multiplying by the reciprocal of 5/2, we get:
Width = (3/9) × (2/5) miles
Width = (3 × 2) / (9 × 5) miles
Width = 6/45 miles
After further simplification:
Width = 2/15 miles
Therefore, the correct width of Tamara's backyard is 2/15 miles.
PLS HELP NOW
What is the area of the rectangle, in square feet?
9 ft
20 ft
A.29
B.58
C.120
D.180
Answer:D,180
Step-by-step explanation:
Answer:
9 x 20ft = 180
If one of those values 8ft and 20ft is the diagonal then we deduct the square of thise numbers being √400 - √81 = √309 and find √309 square of 17.57ft
17.57 x 9 = 158.13
so √158.12 = 12.57
and √162 = 12.72
But your question was just a case of finding how to do area and for that we use L x W to find area
A = 9 x 20 = 180ft^2
Step-by-step explanation:
How did British scientists test Einstein theory of relativity
Answer: Arthur Stanley Eddington's 1919 expedition confirmed Einstein's prediction for the deflection of light by the Sun during the total solar eclipse of 29 May 1919 which helped to cement the status of general relativity as a true theory. Since then many observations have confirmed the correctness of general relativity.
Hope this helps. Also gimme brainliest.
Tina brought two less than one-fourth of the number of t-shirts as Maria. If Tina brought
three shirts, how many did Maria bring?
20 t-shirts
15 t-shirts
9 t-shirts
5 t-shirts
The local cell phone tower service for your provider has the best service when you are 15 miles from the tower, if the school is 12 miles east and 11 miles south then will you receive the most bars?
Answer:
No, since the total distance to the cell tower is 16.28 miles, which is farther away than the distance needed to get the best possible service. You are 1.28 miles too far.
Step-by-step explanation:
you have a triangle with sides 12 miles and 11 miles long, so all you need to do is calculate the hypotenuse:
h² = 12² + 11²
h² = 144 + 121
h² = 265
h = √265
h = 16.28 miles
The diameter of a tennis ball is 2 cm and the diameter of the softball is 1 cm. About how many times as
great is the surface area of a half of the tennis ball as to the surface area of a half of the softball? If
necessary, round to the nearest whole number.
Step-by-step explanation:
It is given that,
The diameter of a tennis ball is 2 cm and the diameter of the softball is 1 cm. So, radius of tennis ball is 1 cm and radius of softball is 0.5 cm.
Both balls are in the shape of sphere. Half of the balls will becomes hemisphere. The surface area of hemisphere is given by :
[tex]A=2\pi r^2[/tex]
Taking ratio of both balls, i.e.
[tex]\dfrac{A_1}{A_2}=\dfrac{r_1^2}{r_2^2}[/tex]
[tex]\dfrac{A_t}{A_s}=\dfrac{r_t^2}{r_s^2}\\\\\dfrac{A_t}{A_s}=\dfrac{1^2}{(0.5)^2}\\\\\dfrac{A_t}{A_s}=4[/tex]
So, the surface area of a half of the tennis ball is 4 times of he surface area of a half of the softball.
The surface area of half of a tennis ball is 4 times greater than the surface area of half of a softball.
To find how many times greater the surface area of half of a tennis ball to that of half of a softball is, we need to use the formula for the surface area of a sphere: Surface Area = 4πr².
Since we are dealing with half-spheres, we can halve this formula, so the surface area of the half-sphere is 2πr².
First, we calculate the surface area for half of a tennis ball. The radius of the tennis ball is 2 cm / 2 = 1 cm. Thus, the surface area is:
Surface Area of Tennis Ball Half-Sphere = 2π(1)² = 2π cm²
Next, we do the same for the softball. The radius of the softball is 1 cm / 2 = 0.5 cm. Therefore, the surface area of half of the softball is:
Surface Area of Softball Half-Sphere = 2π(0.5)² = 0.5π cm²
To find the ratio of the tennis ball surface area to the softball surface area, we divide the two results:
(2π) / (0.5π) = 4
Thus, the surface area of half of a tennis ball is 4 times greater than that of half of a softball.
A pizzeria sells 452 pizzas in a day .The price for a pizza is £5.45 and the costs per pizza is £3.05.Calculate the profit if this pizzeria opens for 6 days in the week
Answer:
$807.554098
Step-by-step explanation:
Answer:
Profit is PRICE — COST
so;
[tex]452(5.45 - 3.05) \times 6[/tex]
hope u understand!
What is the simplified expression that is equivalent to (3x^3)^2 . (25x^6)1/2 ?
Answer:
9x⁵ · 25x⁶
Step-by-step explanation:
(3x³)²·(25x⁶)·[tex]\frac{1}{2}[/tex] =9x⁵ · 25x⁶
Please mark me as the brainliest
Final answer:
The simplified expression equivalent to ((3x^3)^2 · (25x^6)^{1/2}) is 45x^9. This is obtained by applying exponent rules, such as power to a power and multiplying terms with the same base resulting in the addition of their exponents.
Explanation:
The expression in question is (3x^3)^2 · (25x^6)^{1/2}. To simplify this expression, we need to apply the exponent rules. When we raise a power to a power as in (a^m)^n, the exponents are multiplied, so (3x^3)^2 becomes 3^2 · x^{3×2}, which simplifies to 9x^6.
Next, taking the square root, which is the same as raising to the power of 1/2, we apply it to (25x^6)^{1/2}. The square root of 25 is 5, and raising x^6 to the 1/2 power gives x^{6×1/2}, or x^3. Therefore, we have 5x^3 as the simplified result of (25x^6)^{1/2}.
Multiplying these results together, we combine 9x^6 and 5x^3. When we multiply terms with the same base, we add their exponents, therefore we get 9×5 · x^{6+3}, resulting in 45x^9.
what is the mean ? 2 6 9 8 6 6 3 8
Answer:
6
Step-by-step explanation:
add all up (is 48), then divide by 8
hope this helped :))
Answer:
6
Step-by-step explanation:
To find the mean
Add up all the number
(2+6+9+8+6+6+3+8) = 48
Divide by the number of numbers
48/8 = 6
Check all of the expressions that are equal to the one below.
(7-11) • (5)
O
A. (5) • 7 + (5) • (-11)
B. -(-7 +11) • (5)
C. (5) • 7 -(5) • 11
OD. (7 +11) • (5)
WILL GIVE BRAINLIEST
ANSWER IN THE NEXT 20 SECONDS FOR BONUS POINTS
Answer:
p^2-3
Step-by-step explanation:
Which would be a correct first step to solve the following system of linear equations using the elimination method? 2x+3y=6
-x+3y=15
Answer:
Subtract
Step-by-step explanation:
Subtract to eliminate the y value so all that is left to slove is the x value. Once you have the x value, you can plug it in to find the y value.
Your soccer club wants to sell frozen yogurt to raise money for new uniforms. The club has the choice of the two different size containers shown. Each container costs the club the same amount. The club plans to charge customers $2.50. Which container should the club buy? Explain.
Answer:
they should buy the smaller one. the yogurt will cost money too. that is why other companys put ice, or empty spaces in cups.
Step-by-step explanation:
The soccer club should choose either Container A or Container B, as both options would generate the same profit of $1.00 per container sold, assuming the cost price is $1.50 and the selling price is $2.50.
To determine which container is more profitable, we need to calculate the profit from each option. For both containers, the selling price is $2.50.
Let's assume the cost of each container is $1.50, which includes the frozen yogurt, packaging, and other associated costs.
Container A Profit:
Selling Price: $2.50
Cost Price: $1.50
Profit per Container: $2.50 - $1.50 = $1.00
Container B Profit:
Selling Price: $2.50
Cost Price: $1.50
Profit per Container: $2.50 - $1.50 = $1.00
As we can see, both Container A and Container B would yield the same profit of $1.00 per container, given the assumed cost price and selling price.
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