Law of cosines: a2 = b2 + c2 – 2bccos(A)
Which equation correctly uses the law of cosines to solve for y?
92 = y2 + 192 – 2(y)(19)cos(41°)
y2 = 92 + 192 – 2(y)(19)cos(41°)
92 = y2 + 192 – 2(9)(19)cos(41°)
y2 = 92 + 192 – 2(9)(19)cos(41°)
Answers
a = y
b = 9
c = 19
So...
[tex]a^2 = b^2 + c^2 - 2bc*\cos(A)[/tex]
[tex]y^2 = 9^2 + 19^2 - 2*9*19*\cos(41^{\circ})[/tex]
which means the answer is choice D
Related Questions
Answer in factored form x^2-2x-35
Answers
the bigger factor is negative since they add to a negative number
add factors, bigger one is negative
1-35=-34, nope
5-7=-2, yep
(x+5)(x-7)
What is the slope of the line whose equation is 2x−4y=102x−4y=10 ?
Answers
2x - 4y + 4y = 10 + 4y ... see note 1
2x = 10+4y
2x-10 = 10+4y-10 ... see note 2
2x-10 = 4y
4y = 2x-10
4y/4 = 2x/4-10/4 ... see note 3
y = (1/2)x - 5/2
note 1: add 4y to both sides
note 2: subtract 10 from both sides
note 3: divide every term by 4
After all that work, we end up with y = (1/2)x - 5/2
it's in y = mx+b form where m = 1/2 is the slope
Answer:
That's the correct answer!!
Step-by-step explanation:
Book World receives 12 boxes of books. Each box contains 16 copies of the new best-seller, Norton’s Last Laugh. How many copies of Norton’s Last Laugh does the store receive?
Answers
12 x 16 = 192
what decimal is equivalent to 8%
(a). 8.0
(b). 0.8
(c). 0.08
Answers
Sarah's investment in jet blue stock grew 28% to $448 how much did she originally invest?
Answers
X = 448 divide by 1.28
Final answer:
Sarah's original investment was calculated by dividing the final amount of $448 by 1 plus the percentage increase in decimal form, which gives us $350 as the original investment before a 28% growth.
Explanation:
The student is asking to calculate the original investment amount before a 28% increase resulted in a final amount of $448. To find the original investment, we divide the final amount by 1 plus the percentage increase in decimal form. In this case, the percentage increase is 28%, which is 0.28 in decimal form.
The formula to find the original investment (O) is:
O = Final Amount / (1 + Percentage Increase)
So, the original investment would be calculated as follows:
O = $448 / (1 + 0.28) = $448 / 1.28
After performing the division, we find the original investment is:
O = $350
Therefore, Sarah originally invested $350 in JetBlue stock.
without a calculator work out 0.5 multiplied by 0.8
Answers
sooo 0.4 is the answer i believe lemme know if i am wrong
0.5*0.8 = ?
First we need to convert 0.5 and 0.8 into fractions.
The first number after the decimal point (0.#) is in the tenths place, which is to say that the value there is 1/10 of 1. Simplified version... take the number (Example 5 in the number 0.5) and put it over 10. Do it for both numbers!
[tex] \frac{5}{10}* \frac{8}{10} [/tex]
Before we multiply we should reduce them to simplest forms. 5/10 can be divided by 5 on both terms. 8/10 can be reduced by 2 on both terms. Let's look at the new problem:
[tex] \frac{1}{2}* \frac{4}{5} [/tex]
Multiply across! Multiply the numerator with the numerator, and denominator with the denominator... remember:
[tex] \frac{numerator}{denominator} [/tex]
[tex] \frac{1*4}{2*5} [/tex] = [tex] \frac{4}{10} [/tex]
Reduce the fraction by dividing each number by 2.
So our final answer is:
[tex] \frac{2}{5} [/tex] or 0.4
Help me understand this MATH problem...MR.LARSON IS PLANNING THE SEATING FOR A SCHOOL RECITAL. HE NEEDS TO RESERVE 1/3 OF THE SEATS FOR STUDENTS AND 1/6 OF THE SAETS FOR PARENTS.
A. AFTER RESEVING SEATS FOR STUDENTS AND PARENTS, WHAT FRACTION OF THE SEATS IN THE AUDITORIUM ARE LEFT?
B. MR.LARSON's PRINCIPAL TELLS HIM THAT HE ALSO NEEDS TO RESREVE 1/8 OF THE SEATS FOR TEACHERS AND SCHOOL OFFICIALS. THE REMAINDER CAN BE USED FOR OPEN SEATING. WHAT FRACTION OF THE SEATS ARE NOW LEFT FOR OPEN SEATING?
C. LATER, MR.LARSON's PRINCIPAL SAYS HE SHOULD RESERVE 1/4 OF THE SAETS FOR STDENTS FROM OTHER MIDDLE SCHOOLS. ARE THERE ENOUGH SEATS LEFT? IF NOT, EXPLAIN WHY NOT; OTHERWISE, STATE WHAT FRACTION OF THE SEATS WILL BE AVAILABLE FOR OPEN SEATING.
Answers
The graph y=ln(x) is translated 7 units to the left and 4 units upward. The transformed equation is ____.
Answers
When y is replaced by y - k, the graph shifts k units up if k is positive, and k units down is k is negative.
Pool is 25ft long and 15 ft wide and the width of the walkway is to be the same all around the pool. How wide do I make the walkway?
Answers
The price, s, of a mountain bike at Speed Cycling is $290 less than twice the price, d, of the same bike at Downhill Racing. The difference in price between the bike at Speed Cycling and Downhill Racing is $304. Which system of equations can be used to determine the price of the bike at each store?
s - 2d = -290
s - d = -304
2s - d = 290
s - d = -304
2s - 2d = 290
s - d = -304
s - 2d = -290
s - d = 304
Answers
s - d = 304
The system of equations that can be used to determine the price of the mountain bike at each store is:
s - 2d = -290
s - d = 304
Let's determine the correct system of equations to find the prices of the mountain bike at Speed Cycling (s) and Downhill Racing (d).
Given:
The price at Speed Cycling (s) is $290 less than twice the price at Downhill Racing (d). This can be expressed as s = 2d - 290.
The price difference between Speed Cycling and Downhill Racing is $304. This can be expressed as s - d = 304.
Now, we have the two equations:
s = 2d - 290
s - d = 304
These equations form a system that can be used to determine the prices of the bike at each store.
To solve for s and d, you can use the method of substitution or elimination. By substituting the value of s from the first equation into the second equation, you can find the prices of the bike at each store:
Substitute s from the first equation into the second equation:
(2d - 290) - d = 304
Now, solve for d:
d - 290 = 304
Add 290 to both sides:
d = 304 + 290
d = 594
Now that you've found the price at Downhill Racing (d), you can find the price at Speed Cycling (s) by using the first equation:
s = 2d - 290
s = 2 * 594 - 290
s = 1188 - 290
s = 898
So, the price of the mountain bike at Downhill Racing (d) is $594, and the price at Speed Cycling (s) is $898.
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If g(x) = 4x - 4^x, what is the value of g(3/2)?
Answers
To calculate g(3/2) for the function g(x) = 4x - 4^x, we first multiply 4 by 3/2 to get 6, then calculate 4 raised to the power of 3/2 to get 8, and subtract the latter from the former to obtain the final result of -2.
Explanation:To find the value of g(3/2) for the function g(x) = 4x - 4x, we simply substitute x with 3/2. The calculation involves two parts: multiplying 4 by 3/2, and then raising 4 to the power of 3/2.
For the first part, 4 multiplied by 3/2 equals 6.For the second part, 4 raised to the power of 3/2 is the square root of 4 cubed, which equals the square root of 64, giving us 8.Finally, subtract the second part from the first to get g(3/2) = 6 - 8, which equals -2.Therefore, the value of g(3/2) is -2.
If [tex]g(x) = 4x - 4^x[/tex], what is the value of g(3/2) is -2.
To find the value of g(3/2), you need to substitute x = 3/2 into the given function [tex]g(x) = 4x - 4^x.[/tex]
g(3/2) = [tex]4(3/2) - 4^\frac{3}{2}[/tex]
Now, let's simplify this expression:
[tex]g(3/2) = 6 - 4^\frac{3}{2}[/tex]
The value of 4^(3/2) is the square root of 4 cubed, which is [tex]2^3[/tex] = 8. Therefore:
g(3/2) = 6 - 8
Now, subtract 8 from 6:
g(3/2) = -2
So, the value of g(3/2) is -2.
you can afford a $800 per mpnth mortgage payment .youve found a 30 year loan at 8%interest.
A. How bit of a lone can you afford?
B How much total money will you pat the loan company?
C How much of that is interest?
thanks for your help!!!
Answers
The total interest paid for a mortgage at 8% interest rate with a $800 monthly payment.
A. To find the maximum loan amount you can afford:
Calculate the monthly payment using the formula: $800 = P * [r(1 + r)^n] / [(1 + r)^n - 1], where P = Loan amount, r = monthly interest rate, and n = number of payments.Substitute the values: r = 8% / 12, n = 30 years * 12 months, and solve for P to find the maximum loan amount.B. Total payment over 30 years = Monthly payment * 12 months * 30 years.
C. Total interest paid = Total payment - Loan amount.
the longer leg of a right triangle is 3m longer than the shorter leg. the hypotenuse is 6m longer than the shorter leg. find the side lengths of the triangle
Answers
Final answer:
Using the Pythagorean theorem, we find that the side lengths of the right triangle are 9m for the shorter leg, 12m for the longer leg, and 15m for the hypotenuse.
Explanation:
We are asked to find the side lengths of a right triangle, with the condition that the longer leg is 3m longer than the shorter leg, and the hypotenuse is 6m longer than the shorter leg. We can name the shorter leg 'x'. Therefore, the longer leg will be 'x + 3' and the hypotenuse will be 'x + 6'. According to the Pythagorean theorem (a² + b² = c²), we can set up the equation x² + (x + 3)² = (x + 6)².
First, we expand the equations: x² + (x² + 6x + 9) = (x² + 12x + 36).
Combining like terms, we get 2x² + 6x + 9 = x² + 12x + 36. Simplifying further, we get x² - 6x - 27 = 0.
This is a quadratic equation that can be factored as (x - 9)(x + 3) = 0, which gives us the solutions x = 9 and x = -3. Since a side length cannot be negative, we discard the negative value.
Thus, the lengths of the sides of the triangle are: shorter leg x = 9m, longer leg x + 3 = 12m, and hypotenuse x + 6 = 15m.
Gabrielle is 10 years younger than Mikhail. The sum of their ages is 56 . What is Mikhail's age?
Answers
Mikhail is 33
You can figure this out by subtracting 10 from 56.
Write the ratio 8:20 in the simplest form
Answers
what is the mean of 23,25,24,26,23,25,22,22,23,40
Answers
all numbers added give = 253
mean = 253/ 10 = 25.3
mean = 25.3
:)
A total of 304 tickets were sold for the school play. They were either adult or student tickets. The number of student tickets were sold was three times the number of the adult tickets sold. How many adult tickets were sold?
Answers
76 adult tickets were sold.
Explanation:Let's assume the number of adult tickets sold is x. Since the number of student tickets sold was three times the number of adult tickets sold, we can represent it as 3x.
According to the problem, the total number of tickets sold was 304. So, we can write the equation:
x + 3x = 304
Combining like terms, we get:
4x = 304
Divide both sides by 4:
x = 76
Therefore, 76 adult tickets were sold.
write an equation of the line containing the given point and perpendicular to the given line. express your answer in the form y=mx+b. (3,7); 7x+y=4. simplify
Answers
Subtract 7x from both sides to accomplish this
7x+y=4
7x+y-7x=4-7x
y = -7x+4
This equation has a slope of -7. This is the same as -7/1
Flip the fraction to get -1/7 and then flip the sign from negative to positive to get +1/7 = 1/7
The slope of this unknown perpendicular line is going to be m = 1/7
We now use the point (3,7) to figure out the value of b
y = mx + b
y = (1/7)*x + b ... plug in the value of m found earlier
7 = (1/7)*3 + b ... plug in the given point; solve for b
7 = (3/7) + b
7-(3/7) = b
49/7 - 3/7 = b
b = 46/7
So the answer in y = mx+b form is
y = (1/7)x + 46/7
where
m = 1/7 is the slope
b = 46/7 is the y intercept
Please help ASAP
Find how long it takes $1500 to double if it is invested at 7% interest compound semiannually. Use the formula A=P (1+r/n)^nt to solve the compound interest problem.
It will take approximately how many Years ?
Round to the nearest tenth as needed.
Answers
A=future amount
P=present amount
r=rate in decimal
n=number of times per year compounded
t=time in years
how many years to double
basically
A=2P at t=?
so we can simplify and ignore the pricipal given and do
[tex]2=(1+ \frac{r}{n})^ \frac{t}{n} [/tex]
r=7%=0.07
n=2 (semiannualy means 2 times per year)
t=t
[tex]2=(1+ \frac{0.07}{2})^ \frac{t}{2} [/tex]
[tex]2=(1+ 0.035)^ \frac{t}{2} [/tex]
[tex]2=(1.035)^ \frac{t}{2} [/tex]
take the ln of both sides
[tex]ln2=(\frac{t}{2})ln1.035 [/tex]
divide both sides by ln1.035
[tex] \frac{ln2}{ln1.035} = \frac{t}{2} [/tex]
times 2 both sides
[tex] \frac{2ln2}{ln1.035} =t [/tex]
use calculator
40.2976=t
nearest tenth
40.3
about 40.3 years
You are purchasing office supplies. Because of the volume of your orders your company receives 15% off all purchases. You buy a case of paper for $24.95 and a toner refill at $35.99. You find discontinued ink for $49.95 at 50% off. The local sales tax is 4.5%. What do you spend
Answers
Now you take 49.95 divided by 2. you should get: 24.975.
add 24.975 with 60.94. You get 85.915
take 85.915 and multiply it by 0.15. You get 12.88725.
Subtract 85.915 by 12.88725. You should get 73.02775.
Now multiply that by 0.045. you should get 3.28624875.
Add that onto 73.02775, and you get 76.31399875.
Round that to the nearest hundredth, and your done!
(The answer is: 76.31!)
How many hundredths are in 401.308
Answers
That easy
which capital letter appears to have parallel line segments?
A.D
B.L
C.N
D.T
Answers
This is because parallel lines are two lines that will never meet. The two lines on N's outside will never meet
combine like terms to simplify 2xy-xy-y+7y-xy
Answers
All the "xy" terms can combine.
2xy - xy - xy
(Imagine there is a 1 in front of the variables— 2-1-1=0)
Now you're left with the -y + 7y.
Your answer after combining like terms is 6y.
43. Cost of Natural Gas In April 2009, Peoples Energy had the following rate schedule for natural gas usage in single- family residences:
Monthly service charge $15.95 Per therm service charge
1st 50 therms $0.33606/therm
Over 50 therms $0.10580/therm
Gas charge $0.3940/therm
(a) What is the charge for using 50 therms in a month?
(b) What is the charge for using 500 therms in a month?
(c) Develop a model that relates the monthly charge C for
x therms of gas.
(d) Graph the function found in part (c).
Source: Peoples Energy, Chicago, Illinois, 2009
Answers
The charge for using 50 therms is $16.803, while the charge for using 500 therms is $64.413. The model that relates the monthly charge for x therms of gas can be computed using specific conditions. Graphing the function will result in a piecewise linear graph with different slopes for different ranges of therms.
Explanation:To find the charge for using 50 therms in a month, we can use the rate schedule provided. The charge for the first 50 therms is $0.33606 per therm. So, the charge for using 50 therms would be 50 x $0.33606 = $16.803.
For using 500 therms in a month, we need to consider both the charge for the first 50 therms and the charge for the additional therms. The charge for the first 50 therms is $0.33606 per therm, and for the additional therms (450 therms), the charge is $0.10580 per therm. So, the total charge would be (50 x $0.33606) + (450 x $0.10580) = $16.803 + $47.610 = $64.413.
The model that relates the monthly charge for x therms of gas can be represented as follows:
C(x) = $15.95 + ($0.33606 x therms) if x ≤ 50
C(x) = $15.95 + ($0.33606 x 50) + ($0.10580 x (therms-50)) if x > 50
Graphing this function will result in a piecewise linear graph with a slope of $0.33606 for the first 50 therms and a slope of $0.10580 for any additional therms beyond 50.
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The lottery in an extremely small state consists of picking two different numbers from 1 to 10. Ten Ping-Pong balls numbered 1 through 10 are dropped into a fish bowl, and two are selected at random. Suppose you bet on 2 and 9. What is the probability that you won the lottery?
Answers
To win the lottery by betting on numbers 2 and 9, the combined probability is calculated by multiplying the individual probabilities of drawing each number. The probability of drawing number 2 is 1/10, and subsequently drawing number 9 is 1/9, resulting in a combined probability of 1/90.
Explanation:The question asks about the probability of winning a lottery by correctly guessing two specific numbers out of ten. To determine this probability, we must consider the two stages of the lottery separately. Initially, any one of the ten balls can be drawn, so the probability of drawing the first number you bet on, which is 2 in this case, is 1/10. Once the first ball is chosen, it is not replaced, meaning the second selection will be made from the remaining nine balls. Therefore, the probability of drawing the second number you bet on, number 9, after having already drawn number 2, is 1/9. We use the product rule because we need the outcome of drawing both numbers.
Using the product rule, the combined probability of drawing both numbers in the correct order is calculated by multiplying the probabilities of each individual event. Therefore, the combined probability is (1/10) x (1/9), which simplifies to 1/90. This is the probability of winning the lottery by betting on numbers 2 and 9.
I need help on how to solve this equation C+(4-3c)-2=0 stp by step
Answers
c + 4 - 3c -2 = 0
Step 2- Simplify c + 4 - 3c -2 to -2c + 4 - 2
-2c + 4 - 2 = 0
Step 3- Simplify -2c + 4 - 2 to 2c + 2
-2c + 2 = 0
Step 4- Subtract 2 from both sides
-2c = -2
Step 5- Divide both sides by -2
Answer: c = 1
over a 2 hr time period a snail moved 50in how much is that in yards
Answers
1/36 = x / 50....1 yd to 36 in = x yds to 50 in
cross multiply
36x = 50
x = 50/36
x = 1.3889 yds
Please help ASAP
Find how long it takes $1500 to double if it is invested at 7% interest compound semiannually. Use the formula A=P (1+r/n)^nt to solve the compound interest problem.
It will take approximately ? Years .
Round to the nearest tenth as needed.
Answers
A=future amount
P=present amount
r=rate in decimal
n=number of times per year compounded
t=time in years
how many years to double
basically
A=2P at t=?
so we can simplify and ignore the pricipal given and do
[tex]2=(1+ \frac{r}{n})^ \frac{t}{n} [/tex]
r=7%=0.07
n=2 (semiannualy means 2 times per year)
t=t
[tex]2=(1+ \frac{0.07}{2})^ \frac{t}{2} [/tex]
[tex]2=(1+ 0.035)^ \frac{t}{2} [/tex]
[tex]2=(1.035)^ \frac{t}{2} [/tex]
take the ln of both sides
[tex]ln2=(\frac{t}{2})ln1.035 [/tex]
divide both sides by ln1.035
[tex] \frac{ln2}{ln1.035} = \frac{t}{2} [/tex]
times 2 both sides
[tex] \frac{2ln2}{ln1.035} =t [/tex]
use calculator
40.2976=t
nearest tenth
40.3
about 40.3 years
Simplified ratio 0.4
Answers
It can also be expressed as 2 to 5 or 2/5
what are the steps to solve a^2+6a+9/a-10?
Answers
a^2\1+6a\1+9\a-10\1(multiply a by everything on the numerator and everything on the denominator by 1
a*a^2\a*1+a*6a\a*1+9\a-a*10\a*1
=a^3\a+6a^2\a+9\a-10a\a
answer=a^3+6a^2+9-10a everything over a
The value of the expression at a - 10 = 0 is 169.
We have,
Expression:
a² + 6a + 9 _________(1)
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
From the expression a - 10 = 0.
Find the value of a.
a = 10
Now,
Substituting a = 10 in (1).
a² + 6a + 9
Simplify the expression.
10² + 6 x 10 + 9
100 + 60 + 9
Add the like terms in the expression.
100 + 69
169
Thus,
The value of the expression at a - 10 = 0 is 169.
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The complete question:
what are the steps to solve a^2 + 6a + 9 when a - 10 = 0.