Answer:
y 1 = StartFraction log x Over log 0.5 EndFraction, y 2 = StartFraction log 2 Over log 3 EndFraction + x
Step-by-step explanation:
To solve the log equation, the appropriate system of equations is y₁ = log₀.₅ x and y₂ = log₃(2+x) as these correspond to the format of the original log equation, where we can equate the two and solve for x.
Explanation:To solve the equation log₀.₅ₓ = log₃ (2+x), we can rewrite it in a form that helps us find a system of equations.
First, apply the change of base formula for logarithms:
log ab/ log ac = log cb.
Using this formula, we can rewrite the given equation as:
log 0.5x / log₀.₅ 10 = log₃(2+x) / log₃10
Now, we can create a system of equations with the following relationships:
y₁ = log₀.₅ x / log₀.₅10
y₂ = log₃(2+x) / log₃10
Therefore, the correct choice is:
y₁ = logₓ/log₀.₅ , y₂= log(2+x)/ log 3
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An icicle drips at a rate that can be represented by the function f(x) = −x2 + 9x − 18, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.
x = −3 and x = 6
x = 3 and x = −6
x = 3 and x = 6
x = −3 and x = −6
Answer: x=3 and x=6
Step-by-step explanation:
Put the first equation in math-way and find the roots/zeros
An icicle drips at a rate that can be represented by the function
[tex]f(x) = -x^2 + 9x - 18[/tex], where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. So, The solution are x = 3 and x = 6.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
An icicle drips at a rate that can be represented by the function
[tex]f(x) = -x^2 + 9x - 18[/tex],
where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen.
First, we have to find its solution since it is a quadratic function;
[tex]f(x) = -x^2 + 9x - 18\\\\f(x) = -x^2 + 3x+ 6x - 18\\\\f(x) = x (3-x) - 6(3-x)\\\\f(x) = (3-x)(x-6)[/tex]
So, The solution are x = 3 and x = 6.
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Plz help i will give brainliest
Answer:
$96
Step-by-step explanation:
First, let's find the price for a ticket with the markup.
Normally, you pay for 100% of the ticket price, but now you also have to pay an extra 20% of the ticket price.
100%+20%=120%
So, you are basically paying for 120% of the normal ticket price, $16
Multiply 120% and $16
120%*16
Convert 120% to a decimal by dividing by 100, or moving the decimal place 2 spots to the left
120%/100=1.20
120.0-->12.0-->1.20
1.20*16=19.2
Now, each adult ticket costs $19.20
Next, find how much 5 tickets will cost.
Multiply 5 and $19.20
5*19.20=96
5 adults will pay $96 with the ticket markup
Which answer choice shows the decimals in order from greatest to least?
A. 0.013, 0.0104, 0.0118, 0.0108, 0.00149
B. 0.00149, 0.0104, 0.0108, 0.0118, 0.013
C. 0.013, 0.0118, 0.0108, 0.0104, 0.00149
D. 0.013. 0.0118. 0.0108. 0.00149. 0.0104
Answer:
B.) 0.00149, 0.0104, 0.0108, 0.0118, 0.013
Step-by-step explanation:
The more decimal places, the lower the number.
What is the circumference of the sun?
Answer:
2.720984 million miles
Step-by-step explanation:
Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
We have been given that a parabola has vertex [tex](-8,-7)[/tex] and also passes through the point [tex](-7,-4)[/tex]. We are asked to write the equation of the parabola in vertex form.
We know that vertex form of parabola in format [tex]y=a(x-h)^2+k[/tex], with a vertex at point (h,k).
Let us write equation of parabola using our given information as:
[tex]y=a(x-(-8))^2-7[/tex]
[tex]y=a(x+8)^2-7[/tex]
Now we will substitute the coordinates of point [tex](-7,-4)[/tex] to solve for a as:
[tex]-4=a(-7+8)^2-7[/tex]
[tex]-4=a(1)^2-7[/tex]
[tex]-4+7=a-7+7[/tex]
[tex]3=a[/tex]
Therefore, our required equation would be [tex]y=3(x+8)^2-7[/tex].
a sound wave is traveling at 3,810 m/s and has a wave length of 8 m. what is the frequency of the wave?
Answer:
476.25 hertz
Step-by-step explanation:
Since the speed of a wave is the wave length multiplied by the frequency, the frequency can be written as the speed divided by the wave length. 3810/8=476.25 hZ. Hope this helps!
What is the mean of the normal distribution shown below?
-3 -2 -1
0
1
2
3
00.00
Answer:
mean = 0
Step-by-step explanation:
-3 -2 -1
0
1
2
3
if your set is -3, -2, -1, 0, 1, 2, 3 the your mean = 0
A new laptop computer costs $800. The sales tax on the computer is $48. What is the PERCENT of the sales tax?
Answer:
6% sales tax
Step-by-step explanation:
48 / 800 = x / 100
What did you do to turn 800 into 100? Divide by 8.
Since we divided the denominator by 8, we also divide the numerator by 8.
48 / 8 = 6
6% sales tax
Final answer:
The percent of the sales tax on an $800 laptop computer with a $48 sales tax is 6%. This is found by dividing the sales tax by the cost of the computer and then multiplying by 100.
Explanation:
To calculate the percent of the sales tax for the laptop computer, you need to follow these steps:
Convert the sales tax amount to a decimal by dividing the sales tax by the cost of the item before tax.
For example: $48 (sales tax) ÷ $800 (cost of the laptop) = 0.06.
Then, convert the decimal to a percentage by multiplying it by 100.
Continuing the example: 0.06 × 100 = 6%.
Therefore, the sales tax rate for the laptop computer is 6%.
Find the percent of change. Round to the nearest tenth of a percent if necessary. 10 inches to 25 inches. ___ % increase.
Answer:
150% change
Step-by-step explanation:
Formula for Percent change = C =[ (new - old)/ old ]* 100%
C = [ (25 in. - 10 in.) / 10 in. ] = [15/10 ] * 100% = 150 %
As the administration looks ahead to next year, Kyra is concentrating on finishing up this year well. Students at her school receive 4 quarter grades, a mid-term exam grade, and a final exam grade for each class. The quarter grades are all weighted equally, the mid-term exam grade is double the weight of a quarter grade, and the final exam grade is four times the weight of a quarter grade. What fraction of the final course grade is the final exam grade? Express your answer as a common fraction.
Answer:
2/5
Step-by-step explanation:
Defining x the weight of each quarter grades (4x for the 4 quarter grades), then the weight of the mid-term exam grade is 2x, and the weight of the final exam is 4x. The addition of all grades is 4x + 2x + 4x = 10x (this represents the combination of grades that makes the final course grade).
So, the final exam grade represents 4x/10x = 2/5 of the final course grade.
Answer:
2/5
Step-by-step explanation:
just did the test
Geno signed up for a text messaging plan. He pays a $5.00 monthly fee and $0.04 per text message.
Which expression can Geno use to find the cost for one month if he used n messages?
A: 0.02
B: 5.041
C: 0.04r + 5.00
D: 5.00n +0.04
Answer:
The correct answer is [C.) 0.04r + 5.00}
Step-by-step explanation:
hope this hlps
Plz I need answer ASAP
Answer:
a³ - 5a² + 4a + 5
Step-by-step explanation:
To solve this, remove the parentheses. If you were subtracting the two phrases, you would distribute the negative sign to the second phrase, but you are adding so you will not have to do this
4a - a³ - 3 + 2a³ - 5a² + 8
a³ - 5a² + 4a + 5
What is the domain of the function y=3x?
Answer:
The domain is all real numbers
Step-by-step explanation:
if y = 3x and x can be any number
you can do 3 times -29 or 3 times 1/3
HELP PLEASE VERY QUICK, I'LL MARK AS BRAINLIEST!
Answer:
Greater ; Greater
Smaller ; Greater
Step-by-step explanation:
Slopes
First row
A: 15/2
B: (25-12.5)/(4-2) = 12.5/2
A has a greater slope than B
-4x + 2y = 8
2y = 4x + 8
y = 2x + 4
A: 2
B: 3/2
A has a greater slope than B
Second Row
A: (2.6-2)/(3-0) = 0.6/3 = 0.1
B: (5-4)/(4-0) = 1/4 = 0.25
A has a smaller slope than B
A: 60
B: (325-50)/5-0) = 275/5 = 55
A has a greater slope than B
Which point lies on the line x-5 =0
Answer:
see explanation
Step-by-step explanation:
Any point with an x- coordinate of 5 will lie on the line, that is
(5 , - 2), (5, 0), (5, 10)
since 5 - 5 = 0 makes the equation true
A person places $82100 in an investment account earning an annual rate of 4.3%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 2 years.
The future value of $82,100 invested at a 4.3% annual interest rate compounded continuously for 2 years using the formula V = Pe^{rt}, will be approximately $90,137.30.
Explanation:Your question involves the calculation of the future value of an investment using the formula for continuous compound interest, in this case $82,100 invested at an annual rate of 4.3%, over 2 years. This scenario relies on the mathematical concept of compound interest, which means the interest earned on the initial investment is added to the principal, and this combined amount earns interest as well.
Using the formula V = Pe^{rt}. where:
P = principal amount (initial investment) = $82,100,
r = annual nominal interest rate (decimal) = 4.3/100 = .043,
t = time the money is invested for = 2 years,
e = Euler's number (approx. 2.71828).
The calculation then becomes: V = $82,100 * e^(0.043 * 2) = $82,100 * e^(0.086). Using a calculator to do the exponentiation and the multiplication, the balance in the account after 2 years would approximately be $90,137.30.
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Show that (x+1)(x+3)(x+5) can be written in the form ax^3+bx^2+cx+d where a,b and c are all positive integers, and d is a negative integer
The expression (x+1)(x+3)(x+5) can be expanded to the form ax^3+bx^2+cx+d with a, b, and c as positive integers and d as negative by first multiplying (x+1) and (x+3) to get x^2+4x+3, which is then multiplied by (x+5) to obtain x^3+9x^2+23x+15.
Explanation:To show that
(x+1)(x+3)(x+5)
can be written in the form
ax^3+bx^2+cx+d where a,b and c are all positive integers, and d is a negative integer, perform multiplication for the given factors as follows:
Firstly, multiply (x+1) and (x+3) which yields x^2+4x+3.
Then, multiply this result by (x+5) which gives the final form: x^3+9x^2+23x+15.
So, a=1, b=9, c=23, and d=15 proving the original expression can be written in the stated form.
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$ 20,000 is invested at a rate of 5% compounded quarterly. Identify the compound interest function ta model the situation. Then find the balance after 5 years.
Answer:
the balance after 5 years is: 26540.744
Step-by-step explanation:
Given the information:
P = initial balance = $ 20,000r = interest rate (decimal) = 5% = 0.05n = number of times compounded annually = 4t = time = 5We have the compound interest function ta model the situation is:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
<=> A = [tex]20000(1+\frac{0.05}{4} )^{4*5}[/tex]
<=> A = $26540.744
Hence, the balance after 5 years is: $26540.744
Answer:
$25,640.74
Step-by-step explanation:
The total compound interest is $5,640.74.
The final balance is $25,640.74.
with zero additional deposits
hope this helps:)
Given the equation below, what is the value of 3 + 6(79 – s)?
7= -s+ 82
Answer:
1 expression) 477 - 6s
2 equation) s = 75
Step-by-step explanation:
Also, the first expression is simplified
Find the value of r .
Answer:
0.5
Step-by-step explanation:
hypotenuse/adjacent=r
7/14=0.5
What angle is included by AC and BC?
A.
B.
C.
Answer:
B is the answer to this question due to the angle being a 90 degree angle
If the perimeter of a square is 60 inches, how long is each side?
Answer:
15
Step-by-step explanation:
Since a square has 4 sides, that means that each side is equal to the other three sides because it is a square. If so, we do 60/4 to get is 15. To check the answer 15x4 is equal to 60.
Answer:
each side will be 15
Step-by-step explanation:
because if its a square and all the sides are the same lengh and one of the sides are 15 then all of the other sides will also be 15,so that will equal 60.
I need help? With proof for this one.
Answer:
See below.
Step-by-step explanation:
ABC is an isosceles triangle with BA = BC.
That makes angles A and C congruent.
ABD is an isosceles triangle with AB = AD.
That makes angles ABD and ADB congruent.
Since m<ABD = 72 deg, then m<ADB = 72 deg.
Angles ADB and CDB are a linear pair which makes them supplementary.
m<ADB + m<BDC = 180 deg
72 deg + m<BDC = 180 deg
m<CDB = 108 deg
In triangle ABD, the sum of the measures of the angles is 180 deg.
m<A + m<ADB + m<ABD = 180 deg
m<A + 72 deg + 72 deg = 180 deg
m<A = 36 deg
m<C = 36 deg
In triangle BCD, the sum of the measures of the angles is 180 deg.
m<CBD + m<C + m<BDC = 180 deg
m<CBD + 36 deg + 108 deg = 180 deg
m<CBD = 36 deg
In triangle CBD, angles C and CBD measure 36 deg making them congruent.
Opposite sides DB and DC are congruent making triangle BCD isosceles.
Identify two factors that have a product of 1 7/8.
Will give Brainliest
Answer:
17×1= 17, and 8×1= 8
17 and 8 is ur answer
i hope its right...
Step-by-step explanation:
1 7/8 into an improper fraction is 15/8
You can say that
3 5
---- x ----
2 4
GIVING BRAINLIEST ANSWER QUICK!!
Fala is painting the stairs on her deck. she has 6/4 quarts of paint. She needs 4/8 quart of paint for each stair-step.
Fala can paint ______ one whole step.
Fala can paint exactly ______ step(s) with the paint she has.
Answer:
1. Fala can paint more than one whole step
2. She can paint 3 steps
Step-by-step explanation:
1. In the second question we found that she has enough for 3 steps and 3 is more than 1 so she can paint more than one step
2. 6/4=12/8 so she has 12/8 quarts and needs 4/8 for each step
Divide 12 by 4 = 3 So she has enough paint for 3 steps
Answer: more than,3
Step-by-step explanation:
if one letter is chosen at random from the word substitute, what is the probability that the letter chosen will be a "t"?
Please show the work. Thank you
Answer:
3/10
Step-by-step explanation:
there are 10 letters in substitute
there are 3 t's
3/10
The probability of choosing the letter 't' will be 3 / 10.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
If one letter is chosen at random from the word substitute.what is the probability that the letter chosen will be a "t"?The probability will be calculated as:-
There are 10 letters in the word SUBSTITUTE.
Out of these 10 letters, t is three times in the word
So probability will be:-
P = 3 / 10
Therefore the probability of choosing the letter 't' will be 3 / 10.
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PLEASE HELP!!!!whats the first step of factoring 4x^2+10x-24
Answer
2(2x-3)(x+4)
Step-by-step explanation:
Answer:
Exponents
Step-by-step explanation:
First its parentheses but you don't have any and then its exponents and then you multiply and divide and lastly you add or subtract
Which of the following can have a NEGATIVE impact on your credit score
1) paying bills on time
2) paying down balances on your credit card accounts
3) applying for multiple credit cards in a short period of time (e.g., a week)
The answer option which can have a negative impact on your credit score is: 3) applying for multiple credit cards in a short period of time (e.g., a week).
A credit score refers to a numerical expression between 300 to 850, that typically represents an individual's financial history and credit worthiness.
This ultimately implies that, the higher your credit score, the higher and better it is to obtain a credit (money) from a potential lender.
Generally, the ratings of a credit score by FICO include the following;
A credit score ranging from 670 to 739 is considered to be a good credit score.A credit score of 740 to 799 is better.A credit score of 800 to 850 is considered to be excellent.Generally, the best ways to improve your credit score are;
1. You should ensure you don't pay less than the minimum amount due.
2. You should ensure you pay your bills on time or as at when due.
3. You shouldn't move credit card debt around.
4. You should pay down balances on your credit card accounts.
However, when you apply for multiple credit cards in a short period of time (e.g., a week), it is most likely to have a negative impact on your credit score.
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Josh wanted to buy a new shirt for a school dance. At the store, he couldn't decide between a purple plaid shirt and a scarlet striped shirt. Since the shirts were on sale for $19.95 each, Josh decided to buy them both. He saved a total of $9.10. If he saved the same amount on each shirt, what was the original price of each one? $
Answer:
$24.50
Step-by-step explanation:
Answer:
24.50
Step-by-step explanation:
The screen shows Roberto's video game card activity. A negative number represents
money spent on games. A positive number represents money added to the card.
Card Activity
Games
-$2
Deposits
$8
- 4 - 2
0
2
4
6
-10-8-6
S
10
) How much money does Roberto have
on his card?
Answer: 6
Step-by-step explanation: