You want to find t such that
45 - 7t - 6t² = 25
or
6t² + 7t = 20
Solve for t. By completing the square, we have
6t² + 7t = 20
t² + 7/6 t = 10/3
t² + 7/6 t + (7/12)² = 10/3 + (7/12)²
(t + 7/12)² = 529/144
t + 7/12 = ± 23/12
t = -7/12 ± 23/12
t = -5/2 or t = 4/3
We ignore the negative solution, so the ball reaches a height of 25 feet at t = 4/3 seconds, or about 1.33 seconds after being thrown.
1. If you roll two fair dice, what is the probability that the sum of both rolls is 8?
Answer:
1/4
Step-by-step explanation:
Sample space = 12
Prob of sum = 8 is:
[2,6], [3,5]. [4,4]
That is 3/12 = 1/4
[tex]f(x) = {x}^{3 } + {3x}^{2} - 9x + 5[/tex]
which of the following are roots of a polynomial function?
check all that apply
a[tex]1 - \sqrt{3} [/tex]
b
[tex]1 + \sqrt{3} [/tex]
c
[tex] - 5[/tex]
D
[tex]3 - \sqrt{2} [/tex]
E
[tex]3 + \sqrt{2} [/tex]
F
[tex]1[/tex]
Answer:
[tex]f(1) = {(1)}^{3} + 3 {(1)}^{2} - 9(1) + 5 \\ (x - 1) = 0 \rightarrow \: x = 1 \\\frac{{x}^{3 } + {3x}^{2} - 9x + 5}{x - 1} = {x}^{2} + 4x - 5 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1 \\ \color{red}\boxed{x_{1} = 1} \\\color{yellow} \boxed {x_{2} = 1} \\ \color{green}\boxed{x_{3} = - 5} [/tex]
The answer would be C and F
Answer: 1 & -5
Step-by-step explanation
The Hayes family and the Rodrigues family use their sprinklers last summer. The water output rate for the Hayes family sprinkler was 15 L per hour. The water Output rate for the Rodriguez family speakers is 30 L per hour.Families used their sprinklers for a combined total of 75 hour result in a total water of output of 1725 L how long was a sprinkler used?
Answer:
Hayes family: 35 hoursRodrigues family: 40 hoursStep-by-step explanation:
Let x and y represent the usage hours by the Hayes and Rodrigues families, respectively. The problem statement gives us relations that can be used to write equations for volume of use and for total hours.
15x +30y = 1725 . . . . . total liters of use
x + y = 75 . . . . . . . . . total hours of use
The second equation lets us write an expression for y:
y = 75 -x
This can be substituted into the first equation to give ...
15x +30(75 -x) = 1725
-15x + 2250 = 1725 . . . . . . simplify
-15x = -525 . . . . . . . . . . . subtract 2250
x = 35 . . . . . . . . . . . . . . divide by -15
y = 75 -35 = 40
The Hayes family used their sprinklers for 35 hours; the Rodrigues family used theirs for 40 hours.
I thought of a number. This number double is 7 less than 29. What is my number? hurry please
Answer:
11
Step-by-step explanation:
11*2=22
29-7 =22
Answer:
11
Step-by-step explanation:
Let x be your number
Is means equals
2x = 29-7
2x= 22
2x/2 = 22/2
x =11
Choose a way to solve.
Write or draw to explain.
2. Greg has Il shirts.
3 have long sleeves.
The rest have short sleeves.
How many short-sleeve
shirts does Greg have?
Help please! Thank you in advance!!
Answer:
8 short sleeve shirts
Step-by-step explanation:
Subtract the total amount of of shirts by the number of shirts with long sleeves to find your answer.
Use the GCF and the Distributive property to find the sum of 66+78
Here is ur answer of your question
Choose the fraction that goes in the blank. 5/12< _____<3/4
Answer:
7/12 or 8/12 are both good options
Step-by-step explanation:
nvr mind, its 7/12 only
Can someone please explain step by step on how I subtract fractions like for an a example!
7/8 - 3/8 ?
Keep the denominators the same and subtract the numerators. So for example in your example:
7/8 - 3/8
Leave the 8 alone. Subtract 3 from 7.
7 - 3 = 4
So answer is:
4/8
Sometimes they may have to simplify the answer, and in this case, 4/8 could be simplified to 1/2
A car traveled 133 miles in 4 3/4 hours. What was the cars average speed in miles per hour?
4 3/4 = 19/4
133/(19/4) = 133(4/19) = 1197/19 = 63 mph
Prove that
sin 75-sin 15=cos 105+cos 15
Answer:
Step-by-step explanation
RHS = cos 105° + cos 15°
= cos (90° + 15°) + cos (90° – 75°)
= – sin 15° + sin 75°
= sin 75° – sin 15°
= LHS
Answer:
Step-by-step explanation:
sin75-sin15
=sin (90-15)-(-cos (90+15))
=cos 15+cos 105
12. After 80 years of 5.8% interest compounded monthly, an account has $102,393.44. What was the
original deposit amount?
Answer:
12195508,42
Step-by-step explanation:
A(1-R) NA is the depositR is the % presentN is the time period (exponent)A(1-5.8%)80=102,393.44An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
What is meant by deposit?A deposit is money held at a bank. A deposit is a monetary transaction in which money is transferred to another party for safekeeping.A deposit is money placed in a bank account. Deposits are classified into two types: demand deposits and time deposits. Checking, savings, and money market accounts are all examples of demand deposit accounts. Certificates of deposit (CD) and individual retirement accounts are examples of time deposit accounts.Therefore,
Assume that each year has 52 weeks: then compounding occurs.
n = 52 × 80n
times and the rate for each compounding is
[tex]$i=\frac{5.8 \%}{52}=\frac{0.058}{52}$[/tex]
If the original deposit amount is
PV
then the future value
FV
is equal to
[tex]$$F V=P V \cdot(1+i)^n=P V \cdot\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}$$[/tex]
We know the future value (which is given as $ 102,393.44), so calculating the present value is simple:
[tex]P V=F \frac{V}{(1+i)^n}=\frac{\$ 102,393.44}{\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}}[/tex]
The simplest way to compute this is to use a calculator:
[tex]$P V \approx \$ 991.45 .$$[/tex]
We can simplify this expression with great precision just for fun. It is well known that
[tex]$\left(1+\frac{1}{n}\right)^n \rightarrow e$[/tex]
which easily implies that
[tex]$\left(1+\frac{a}{n}\right)^n \rightarrow e^a$[/tex]
Here,
[tex]$$\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}=\left(\left(1+\frac{0.058}{52}\right)^{52}\right)^{80} \approx\left(e^{0.058}\right)^{80}=e^{0.058 .80}=e^{4.64}[/tex]
That is, [tex]P V \approx F V e^{-4.64}$.[/tex]
Hence, An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.
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Solve the inequality 15 ≥ q + 3
Answer:
[tex]q\le \:12[/tex]
Step-by-step explanation:
Solving
[tex]\mathrm{Switch\:sides}[/tex] (Not a required step)
[tex]q+3\le \:15[/tex]
[tex]\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}[/tex]
[tex]q+3-3\le \:15-3\\=q\le \:12[/tex]
[tex]\bold{q\le \:12}[/tex]
Graphing
y = 30.078(1.003)*.
Question 1
? Question
Use the exponential model to make predictions about closing prices of this stock. Remember that x
represents the number of weeks since the first data point, so the value of x today would be 260.
Type the correct answer in each box. If necessary, round the answers to the nearest cent.
One week from today, the stock is predicted to close at $
One month from today, the stock is predicted to close at $
One year from today, the stock is predicted to close at $
Using the exponential function, it is found that:
One week from today, the stock is predicted to close at $65,734.37.One month from today, the stock is predicted to close at $66,327.75.One year from today, the stock is predicted to close at $76,584.35.The exponential function is:
[tex]y(x) = 30078(1.003)^x[/tex]
x represents the number of weeks since the first data point, so the value of x today would be 260.Hence, considering today as an starting point, the function is:
[tex]y(x) = 30078(1.003)^{x + 260}[/tex]
One week from now, we have y(1), hence:
[tex]y(1) = 30078(1.003)^{1 + 260} = 65734.37[/tex]
One week from today, the stock is predicted to close at $65,734.37.
One month from now, we have y(4), hence:
[tex]y(4) = 30078(1.003)^{4 + 260} = 66327.75[/tex]
One month from today, the stock is predicted to close at $66,327.75.
One year from now, we have y(52), hence:
[tex]y(52) = 30078(1.003)^{52 + 260} = 76584.35[/tex]
One year from today, the stock is predicted to close at $76,584.35.
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Answer:
One week from today, the stock is predicted to close at $65,734.37.
One month from today, the stock is predicted to close at $66,327.75.
One year from today, the stock is predicted to close at $76,584.35.
Step-by-step explanation:
Raven can walk 2 2/5 miles in 3/5 hour. At this rate, how far can she walk in 1 hour? You might want to change 2 2/5 to an improper fraction in order to make the math easier for you to do.
The distance traveled by Raven in 1 hour at the given rate is 4.0 miles.
The given parameters:
Distance traveled by Raven = 2 2/5 milesTime of motion, t = 3/5 hourThe speed of Raven motion is calculated as follows;
[tex]V = \frac{Distance}{Time} \\\\V = Distance\ \times \ \frac{1}{Time} \\\\V = 2\frac{2}{5} \ miles \ \ \times \ \ \frac{1}{3/5 \ hr} \\\\V = \frac{12}{5} \ miles \ \ \times \ \ \frac{5}{3 hr} \\\\V = 4 \ mph[/tex]
The distance traveled by Raven in 1 hour at the given rate is calculated as follows;
[tex]D = 4 \times 1\\\\D = 4 \ miles[/tex]
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The length of my rectangular calculator lid is 11 mm more than the width. The area is 152 square
mm. Find the dimensions of the lid.
Answer:
The dimensions of the lid are 8mm by 19mm.
w = 8
l = 19
Step-by-step explanation:
[tex]l=w+11\\l\times w=152[/tex]
where l is length and w is width. This can be solved as a system of equations.
[tex]l\times w=152\\(w+11)\times w=152\\w(w+11)=152\\w^2+11w=152\\w^2+11w-152=0[/tex]
At this point, it gets a little tough. I might be unnecessarily overcomplicating things, but this is the only way I see to solve the problem.
=================== Skip down below if you don't care about factoring
You need to factor the newly created trinomial.
[tex]ax^2+bx+c[/tex]
With a trinomial in this form, you need to find 2 numbers that add together to make b and multiply together to make ac.
Here, we need 2 numbers that add to 11 and multiply to -152. First, factor 152:
1, 152
2, 76
4, 38
8, 19
Then the reverse of all of those is true too, of course:
19, 8
38, 4
etc
In our case, we're looking for -152, so one of our factors will be negative. We're also looking for factors that add up to 11. Looking at these factors, you can see that 19 - 8 = 11, so our factors are 19 and -8.
Finally, you can use those to factor our trinomial. Split up the middle number (11w) into two:
[tex]w^2+11w-152=0\\w^2-8w+19w-152=0[/tex]
And now, you can factor by grouping:
[tex]w^2-8w+19w-152=0\\w(w-8)+19(w-8)=0\\(w+19)(w-8)=0[/tex]
===================
Now that the number is factored, you can finally find w:
[tex](w+19)(w-8)=0[/tex]
Here, you can see that the equation will be true when w = -19 or w = 8. Those are our solutions, but we can't have a negative distance, so it's just
[tex]w=8[/tex]
Going all the way back to the top, now you can use the width to find the length.
[tex]l=w+11\\l=8+11\\l=19[/tex]
That one was much easier.
The dimensions of the lid are 8mm by 19mm.
Finally, check that with both of the original equations to make sure it's correct.
[tex]l=w+11\\19=8+11\\19=19\\\\l\times w=152\\19\times8=152\\152=152[/tex]
Find the area of the equilateral triangle.
Answer:
try 6.93 for answer on equilqteral triangle
Suppose that sin a= 15/17 and 90 degrees
plz help me to answer
Answer:
H=2 r=1
Step-by-step explanation:
P= 2h+4r + πr = π+8
h= π+8- πr -4r/2
(pls give brainliest if helps!)
A2 + B2
Best answer gets a brainliest and thank and 5 star
Answer:
a+b)(a-b)
(Step-by-step explanation:
What is the value of the expression
Answer:
C. 9
Step-by-step explanation:
K(3)=3*3=9........................
1. Gavin buys 89 blue pansies and
86 yellow pansies. He will plant the flowers
in 5 rows with an equal number of plants
in each row. Draw a bar model to help you
find how many plants will be in each row,
O
17
Spiral Review
nose nilo que dise perdoooooooon xd
Rewrite in simplest terms: (-9x + 7y) - (-9x + 5y)
Answer:
3y
Step-by-step explanation:
(-9x+7y)-(-9x+5y)
Distribute the negative(-)
-9x+7y+9x-5y
-9 and 9 cancel each other
3y
The simplest terms of the given expression (-9x + 7y) - (-9x + 5y) will be 2y.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
(-9x + 7y) - (-9x + 5y)
Open the bracket
-9x + 7y + 9x - 5y
Combined likely terms together
-9x + 9x + 7y - 5y
0 + 2y = 2y
Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".
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wren is going to add an ordered pair to the table that will cause the table to no longer be a function. Which could be the ordered pair?
X Y
-3 7
-1 5
0 3
2 6
_ _
Answer:
(0,-2)
Step-by-step explanation:
Carson bought 50 pounds of rice for his restaurant. He cooked the rice and wanted to evenly divide it into 9 containers to be served later. How many pounds of rice should Carson put in each container?
help plss
Answer:
Step-by-step explanation: there you go
(a) The area of a rectangular parking lot is 7050 m².
If the length of the parking lot is 94 m, what is its width?
(b) The perimetel of a rectangular pool is 356 m.
If the width of the pool is 82 m, what is its length?
Length of the pool: Im
Answer:
75 m, 96 m
Step-by-step explanation:
a. Area = length x width
7050 = 94 x width
7050/94 = w
75 m is width
b. perimeter = 2L + 2W
356 = 2L + 2(82)
356 = 2L + 164
192 = 2L
96 m = L
The population of a slowly growing bacterial colony after t hours is given by
p(t) = 4t² + 27t + 150. Find the growth rate after 2 hours.
bacteria/hour
Submit Question
A function is an expression that defines a relationship between an independent variable and a dependent variable.
The number of bacteria colonies after 2 hours is 220.
What is a function?It is an expression that defines a relationship between an independent variable and a dependent variable.
We have,
P(t) = 4t² + 27t + 150
Where t = time
P(t) = population of a slowly growing bacteria colony after a particular time
The growth rate after 2 hours:
P(2) = 4 x (2)² + 27 x 2 + 150
P (2) = 16 + 54 + 150
P (2) = 220
Thus the number of bacteria colonies after 2 hours is 220.
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4.6 + 3.28 + 1.03 = ___
8.91
8.81
8.37
8.18
Answer: The answer is 8.91.
Answer : 8.91
Step - by - step explanation :
Sometimes if a question is to big for you - it's best to start off small . . .
4.60 + 3.28 = 7.88
7.88 + 1.03 = 8.91
Please help!!!!!!!!!!!!!!
Answer:
The answer is A.
Step-by-step explanation:
1 plus 2x (276-5y) + 69= A.
Assume running consumes 95 cal per mile. If you run 9- minute miles, what is your average power output in watts
The amount of money charged to borrow money, expressed as a percentage,
is called the
A. collateral
B. interest rate
O C. principal
D. loan term
Answer:
Interest rate
Step-by-step explanation:
The amount owed is called the principal and the price of borrowing money is called interest. Some people spend a day's pay (or more) per week repaying the interest and principal owed on car loans, credit card bills, student loans, and other consumer debts.