With the given conditions of angle A being 30 degrees, side a being 1.5 cm, and side b being 2 cm in a triangle, only one possible triangle satisfies these properties according to the Law of Sines.
Explanation:The question relates to determining the number of possible triangles given certain conditions. Specifically, it refers to a triangle with an angle A of 30 degrees, a side a of 1.5 cm opposite to A, and another side b of 2 cm. To decide the number of possible triangles that fit these criteria, we make use of the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
In the given scenario, since side a (1.5 cm), opposite to angle A (30 degrees), is shorter than side b (2 cm), it is possible that two different triangles could exist, often referred to as the ambiguous case in the Law of Sines. However, the fact that side a is shorter than side b coupled with angle A being acute (30 degrees) leaves us with only one possible triangle. This is because the side opposite the smallest angle (A) cannot form a valid triangle if it's longer than the other given side. Therefore, there is just one solution to this problem.
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One estimate of the population of the world on January 1, 2005, is 6,486,915,022. The population is estimated to be increasing at the rate of 1.4 percent per year. At this rate, what will the population of the world be on January 1, 2024? Round your answer to the nearest whole number. ...?
what is the simplest form of 32/72
What is the difference between 90p and £3.25?
The difference between 90 pence and 3 pounds 25 pence is 235 pence, or 2 pounds 35 pence.
Explanation:The question is asking for the difference between two amounts of money, 90 pence (90p) and 3 pounds 25 pence (£3.25). To find the difference, you would subtract the smaller amount from the larger amount. In this scenario, since both amounts are in British currency, it is a straightforward subtraction.
£3.25 is equal to 325 pence (since there are 100 pence in a pound). Now, subtract:
325p - 90p = 235p
Therefore, the difference between 90p and £3.25 is 235 pence, which can also be expressed as £2.35.
Jose bought 750 bags of peanuts for $375.00. He intends to sell each bag for $0.15 more than he paid. How much should he charge for each bag?
Which statement is true about 109?
a. it is a prime number.
b. it is a composite number.
c. it is a whole number that is neither prime nor composite.
d. it is not a whole number.
Answer:
its a
Step-by-step explanation:
(-3x+7)+(-6x+9) what is the sum
HELP PLEASE?!
Multiply: 3x4(4x4 − x5 + 2)
A.) 7x8 − 3x9 + 6x4
B.) 12x8 − 3x9 + 6x4
C.) 12x4 − x9 + 6x4
D.) 12x16 − 3x20 + 6x4
Answer:
[tex]12x^8-3x^9+6x^4[/tex]
B is the correct option.
Step-by-step explanation:
We have to multiply the expression
[tex]3x^4(4x^4-x^5+2)
Using the distributive property a(b+c)=ab+ac
[tex]3x^4\times4x^4+3x^4\times(-x^5)+3x^4\times2[/tex]
Now, using the exponent rule [tex]x^a\times x^b=x^{a+b}[/tex]
[tex]12x^{4+4}-3x^{4+5}+6x^4[/tex]
On simplifying, we get
[tex]12x^8-3x^9+6x^4[/tex]
B is the correct option.
Ivan, Bella, and Ian agreed to share a pizza which was cut into 101010 slices. Ivan ate 40\%40%40, percent of the pizza.
How many slices did he eat?
slices
Answer: 4 slices
Step-by-step explanation:
They divided the pizza into 10 slices and Ivan ate 40% of the pizza. Each piece of pizza is 10% because a full pizza is 100% and there are 10 pieces, so 10% per each slice. So, he ate 4 slices
Frankos pizza is selling pizza for 35% cheaper than usual. if a pizza normally costs 12.00 how much is it now
A population of insects doubles every month. If there are 100 insects to start with, how many will there be after 7 months?
After 7 month, the population of insects are 12800.
Here,
A population of insects doubles every month.
There are 100 insects to start with.
We have to find the population of insects after 7 month.
What is exponential form?
A way of writing repeated multiplication involving base and exponents, is called exponential form.
Now,
A population of insects doubles every month.
There are 100 insects to start with.
Let the population is P.
Hence, The situation is express in exponential form as;
[tex]P = 100 (2)^n[/tex]
Where, n is the number of month.
So, The population after 7 month is calculate as;
[tex]P = 100 (2)^7=100*128= 12800[/tex]
Therefore, After 7 month the population of insects are 12800.
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David invests £5000 in a savings account.
The account pays 3.2% compound interest per year.
Works out the value of his investment after 3 years.
Give your answer to the nearest penny.
What value in place of the question mark, makes the polynomial below a perfect square trinomial?
x2+24x+? ...?
What is 1/10 of 0.092?
given the expression below, which is the best process for simplifying the expression?
(-5sqrt[2]-sqrt[6])(sqrt[3]+2sqrt[2])
a. combine like terms, distribute the radicals; simplify the radicals
b. combine like terms, simplify the radicals; distribute radicals
c. distribute the radicals, simplify the radicals, combine like terms
d. none of the above. ...?
Answer:
distribute the radicals, simplify the radicals, combine like terms
Step-by-step explanation:
(-5sqrt[2]-sqrt[6])(sqrt[3]+2sqrt[2])
[tex](-5\sqrt{2})-\sqrt{6} )(\sqrt{3} +2\sqrt{2} )[/tex]
To multiply it , we apply FOIL method
Distribute the radicals inside the second parenthesis
After distributing the radicals inside the second parenthesis we multiply and simplify the radical as much as we can
Then we combine like terms to simplify further
distribute the radicals, simplify the radicals, combine like terms
the following equation can be used to predict the average height of boys anywhere b/w birth and 15 years old: y=2.79x+25.64, where x is the age(in yrs) and y is the height (in inches). what does the slope represent? interpret the slope in the cintext of the problem. What does the y-intercept represent in this problem? intercept the y-intercept in the context of the problem. ...?
slope = growth during 1 year y-intercept = their original height i.e. the height when they were born
The standard linear equation is given by :-
[tex]y=mx+c[/tex], where m is the slope and c is the y-intercept.
Given equation to predict the average height of boys anywhere b/w birth and 15 years old:
[tex]y=2.79x+25.64[/tex], where x is the age(in yrs) and y is the height (in inches).
By comparing this equation to the standard linear equation, we have
Slope = 2.79 and y-intercept = 25.64
The slope tells that the rate of change of average height of boys with respect to age is 2.79 .
The y-intercept tells that the initial average height of boys =25.64 inches
If darren completed 25% of his science project on monday what percentage of his project is left to complete
Answer:
75%
Step-by-step explanation:
8% of rides in the park are water rides. If there are 4 water rides, how many rides are there in total
Answer:
50
Step-by-step explanation:
So 8 percent equals to 4 so just multiply the reciprocal of 8/100 and you get 50
Mr hower can buy a computer with a down payment of 510$ and 8 monthly payments of 35.75 if he pays cash for the computer the cost is 699.99$ how much will he save if he pays cash the computer instead of paying for it in monthly payments
Bradley and Kelly are out flying kites at a park one afternoon. A model of Bradley and Kelly's kites are shown below on the coordinate plane as kites BRAD and KELY, respectively:
Which statement is correct about the two kites?
They are similar because Segment BR to segment DB is 1:2 and Segment KE to segment YK 1:2.
They are not similar because Segment BR to segment DB is 1:5 and Segment KE to segment YK is 1:2.
They are not similar because Segment BR to segment DB is 1:2 and Segment KE to segment YK is 1:5.
They are similar because Segment BR to segment DB is 1:5 and Segment KE to segment YK is 1:5.
1. The vertices B, D and R have coordinates (9,9), (1,5) and (11,5), respectively. Then
[tex] BR=\sqrt{(11-9)^2+(5-9)^2}=\sqrt{4+16} = 2\sqrt{5} ,\\BD=\sqrt{(1-9)^2+(5-9)^2}=\sqrt{64+16} = 4\sqrt{5}. [/tex]
The ratio
[tex] \dfrac{BR}{BD}= \dfrac{2\sqrt{5}}{4\sqrt{5}} =\dfrac{1}{2}. [/tex]
2. The vertices K, E and Y have coordinates (13,9), (14,10) and (14,2), respectively. Then
[tex] KE=\sqrt{(13-14)^2+(9-10)^2}=\sqrt{1+1} = \sqrt{2} ,\\KY=\sqrt{(13-14)^2+(9-2)^2}=\sqrt{1+49} = 5\sqrt{2}. [/tex]
The ratio
[tex] \dfrac{KE}{KY}= \dfrac{\sqrt{2}}{5\sqrt{2}} =\dfrac{1}{5}. [/tex]
Answer: correct answer is C (they are not similar because segment BR to segment DB is 1:2 and segment KE to segment YK is 1:5.)
A regular box of cereal holds 14 ounces. If an economy box is made by doubling all the dimensions of the regular-sized box, how many ounces will the economy box hold? ...?
Answer: The economy box will hold 112 ounces.
Step-by-step explanation:
Since we have given that
A regular box of cereal holds = 14 ounces
Let the dimesion of regular box be x .
so, Volume of regular box is given by
[tex]x\times x\times x =x^3= 14[/tex]
According to question, if the box is made by doubling all the dimensions of the regular sized box.
So, volume becomes
[tex]2x\times 2x\times 2x\\\\=2^3\times x^3\\\\=8\times x^3\\\\=8\times 14\\\\=112\ ounces[/tex]
Hence, The economy box will hold 112 ounces.
what is equivalent to 625/1000
luke has $5 more than sam . together they have $73.how much does each have
FlybynightSavings.com is offering a savings account that pays 28% compounded continuously. How much interest would a deposit of $3,000 earn over 5 years? (Round your answer to the nearest cent.)
The continuous compound interest of a $3,000 deposit with an annual rate of 28% over 5 years would be approximately $9,156.58.
Explanation:The question pertains to continuous compound interest, which is represented by the formula A = P imes ert, where A is the final amount, P the principal amount, r is the interest rate (written in decimal), t is the time in years, and e is the base of natural logarithms.
Given that P=$3,000, r=28/100=0.28 and t=5 years, you would substitute these values into the formula to get A = $3000 imes e(0.28 imes 5).
Computing this, gives:
A = $3000 imes e1.4 = $3000 imes 4.0552 (approximately).
So, A = $12156.58 (rounded to the nearest cent).
The interest earned would therefore be: A - P.
Thus, the interest would be $12156.58 - $3000 = $9156.58.
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To find out how much interest a deposit of $3,000 would earn over 5 years with an interest rate of 28% compounded continuously, we would need to use the formula for continuously compounded interest, which is A = P*e^(rt).
Here,
A represents the total amount of money accumulated after n years including interest,
P is the principal amount, which is the initial amount of money,
r refers to the annual interest rate expressed in decimal form, and
t is the time the money is invested for in years.
Given in the problem we have P = $3000, r = 28% = 0.28, and t = 5 years.
Substituting these values into the formula we get:
A = 3000 * e^(0.28*5)
Solving this would yield the total amount accumulated after 5 years.
Next, we would need to calculate the accrued interest. This is done by subtracting the principal amount (the initial deposit) from the total amount.
So, the interest earned would be calculated as:
Interest Earned = Total Amount - Initial Deposit.
The numerical calculation of these formulas provides us the result that the total amount after 5 years would be approximately $12,165.60 and the interest earned would be approximately $9,165.60.
Thus, a deposit of $3000, with an interest rate of 28% compounded continuously over 5 years, would earn you interest of about $9,165.60.
This is of course rounded to the nearest cent as required.
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Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.
p: An isosceles triangle has two congruent sides.
q: A right angle measures 90°.
r: Four points are always coplanar.
s: A decagon has 12 sides.
the following is a conjunction
p∧q: An isosceles triangle has two congruent sides and a right angle measures 90°.
this statement is true because both p and q are true.
The following is a disjunction :
r∨s: Four points are always coplanar or A decagon has 12 sides.
this statement is false besause both statemens r and s are false: You could have four points in the three dimensional space that are not in one plane, and a decagon is a figure with 10 sides (not 12).
A light bulb consumes 2400 watt-hours per day. How long does it take to consume 11400 watt-hours?
Answer: 4 days and 18 hours
Step-by-step explanation:
Mel Garrett needs four new tires for his car. He can buy one tire for $87, two tires for $174, three tires for $261, or four tires for $348. Which is the best buy?
Check all of the values that have three significant figures
a) 1.04
b) 44.65
c) 0.0760
d) 1089 ...?
State if the three numbers can be the measures of the sides of a triangle
In mathematics, specifically geometry, we can determine whether three given numbers can be the sides of a triangle by applying the Pythagorean theorem (a² + b² = c²). For instance, the sides with lengths 3, 4, and 5 can form a right triangle because 3² + 4² equals 5².
Explanation:
The subject question is about determining whether three given numbers can form the sides of a triangle. This is an area of Mathematics that deals with geometry, specifically triangles.
The knowledge of Pythagorean theorem which states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, often written as a² + b² = c², helps to verify if the three given numbers are the lengths of the sides of a triangle.For example, if given lengths are 3, 4, and 5. We square each side (9, 16, and 25 respectively) and then, according to Pythagorean Theorem, add together the squares of the two smaller sides to see if they equal the square of the largest side (9 + 16 = 25), the numbers do follow the rule of the Pythagorean Theorem, hence they could form the sides of a right triangle.Learn more about Pythagorean theorem here:
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Describe the roots of the equation shown below.
3x^2-10x-5=0
A. There are two real, irrational roots.
B. There is one real, double root.
C. There are two real, rational roots.
D. There are two complex roots.
...?
Merle Fonda opened a new savings account. She deposited $40,000 at 10 percent compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10 percent. At the end of 6 years, the balance in Merle's account is:
Answer:
$98,636.72
Step-by-step explanation: