Answer:
20
Step-by-step explanation:
start by using system of equations
x = cola
y = root beer
x + y = 30
x = 2y
now either use substitution or elimination. for me, substitution is easier.
the second equation already has one variable isolated ( x ) so, plug that into the first equation.
2y + y = 30
y = 10
now plug your answer into the original equation.
x + 10 = 30
x = 20
hope this helps :)
A culture of bacteria has an initial population of 12000 bacteria and doubles every 6 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 17 hours, to the nearest whole number?
Answer:
85,524 bacteria
Step-by-step explanation:
Given the population of bacteria modelled by the equation where;
[tex]P_t = P_0\cdot 2^{\frac{t}{d}[/tex]
P0 is the initial population
t is the time in hours
d is the doubling time
If the culture of bacteria has an initial population of 12000 bacteria, this means that;
at t = 0, P0 = 12000
substitute into the modelled function
[tex]P_t = P_0\cdot 2^{\frac{t}{d}\\\\P_t = 12000\cdot 2^{\frac{0}{d}\\\\\\P_t =12000\cdot 2^{0}\\\\P_t = 12000[/tex]
If the population doubles every 6 hours
at t = 6, Pt = 24000
[tex]P_t = P_0\cdot 2^{\frac{t}{d}\\\\\\24000 = 12000\cdot 2^{\frac{6}{d}\\\\\\\\24000/12000 = 2^{\frac{6}{d}\\\\\\\\[/tex]
[tex]2 = 2^{\frac{6}{d} }\\1 = 6/d\\d = 6\\[/tex]
Next is to get the population of bacteria in the culture after 17 hours
at t = 17, Pt = ?
[tex]P_t = P_0\cdot 2^{\frac{t}{d}\\\\P_t = 12000\cdot 2^{\frac{17}{6}\\\\\\\\P_t = 12000\cdot 2^{ 2.833 }\\P_t = 12000\cdot 2^{ 2.833 }\\P_t = 12000 * 7.127\\P_t = 85,524.3[/tex]
Hence the population of bacteria in the culture after 17 hours, to the nearest whole number is 85,524 bacteria
Answer:Pt 85526.2769 = 85526
Step-by-step explanation:
An object is thrown off a 256-foot-tall building, and the distance of the object from the ground is measured every second. The function that models the height, h, of the object after t seconds is h(t) = –16t2 + 96t + 256. Determine the time when the object hits the ground
Answer:
The object hits the ground 8 seconds after launch.
Step-by-step explanation:
Let [tex]h(t) =-16\cdot t^{2}+96\cdot t + 256[/tex], where [tex]h[/tex] is the height of the object above the ground, measured in feet, and [tex]t[/tex] is time, measured in seconds. We notice that given expression is a second-order polynomial and hence, there are two roots, one of them corresponding to the instant when the object hits the ground. If [tex]h(t) = 0[/tex], we get the following expression:
[tex]-16\cdot t^{2}+96\cdot t +256 = 0[/tex] (Eq. 1)
Roots are found by applying the Quadratic Formula:
[tex]t_{1,2} = \frac{-96\pm\sqrt{96^{2}-4\cdot (-16)\cdot (256)}}{2\cdot (-16)}[/tex]
[tex]t_1 = 8\,s[/tex] or [tex]t_{2} = -2[/tex]
Only the first root offer a solution that is physically reasonable. Thus, the object hits the ground 8 seconds after launch.
Susan received $27 for 6 hours of work. Ricky received $14.25 for 3 hours of work. Which statement is true about there hourly rate? Answer choices: A:Susan's rate was closer to $5.00 B:Susan's rate was $0.70 more per hour C: Rickys rate was 0.25 more per hour D:Ricky was paid at half Susan's rate
Answer: C. Rickys rate was 0.25 more per hour" .
Step-by-step explanation:
Susan received $27 for 6 hours of work. Susan's rate we hour will be:
= $27/6
= $4.5
Ricky received $14.25 for 3 hours of work. Ricky's rate will be:
= $14.25/3
= $4.75
From the option given, the correct option is C "Rickys rate was 0.25 more per hour" .
This is because $4.75 - $4.5 = $0.25
; the boy to girl ratio is 10 to 8. If there are 16 girls in the class, how many boys are there?
Answer:
There are 20 boys
Step-by-step explanation:
Please help me with this and show the steps. Will give brainliest if correct.
Answer:
X =1/(b2x+2b)
Step-by-step explanation:
bx2 +2x +1/b = 0
bx2+2x=1/b
bx2(b) +2bx = 1
x(b2x+2b)=1
x=1/(b2x+2b)
write the decimal expansion of 16 by 3125
Answer:
That will be 0.00512
The sum of two numbers is 14 and their product is 45. Represent an equation that could find the two numbers
Please help!
Four more than twice a number is –10.
(I have 15 mins!)
Answer: -7
Step-by-step explanation:
2X + 4= -10
2X= -10 -4
2X= -14
X= -7
2x + y = 7
this is my first day in algebra and i have no clue how to solve a literal equation
Answer:
y = 7 - 2x
Step-by-step explanation:
Step 1:
2x + y = 7 Equation
Step 2:
y = 7 - 2x Subtract 2x on both sides
Answer:
y = 7 - 2x
Hope This Helps :)
how would you substitute this equation?
If y = x and y = z, then by substitution we can say x = z.
In this case, substitution gives us
-1/2 x - 2 = -3/2 x + 2
and we can solve for x :
3/2 x - 1/2 x = 2 + 2
x = 4
then solve for y :
y = -1/2 x - 2
y = -1/2 * 4 - 2
y = -2 - 2
y = -4
At the Sunshine Bakery, 351 loaves of seven-grain bread were baked in six hours and 15 minutes. Estimate how many loaves were baked in one hour.
60
55
65
70
Answer:
B
Step-by-step explanation:
We know that 351 loaves were baked in six hours and 15 minutes.
First, let's convert the time to minutes. 6 hours is 360 minutes, so 6 hours and 15 minutes is 360 + 15 = 375 minutes.
Therefore, we can write the following ratio:
[tex]\frac{351\text{ loaves}}{375\text{ minutes}}[/tex]
We want to estimate how many loaves were baked in one hour or 60 minutes. So, we can write the following proportion:
[tex]\frac{351\text{ loaves}}{375\text{ minutes}}=\frac{x\text{ loaves}}{60\text{ minutes}}[/tex]
Note that the loaves and time align horizontally, while the rates align vertically.
Since we're estimating, let's change 351 to 350 (I'm also going to remove the words, since they're not necessary). So:
[tex]\frac{350}{375}=\frac{x}{60}[/tex]
We can reduce the left by dividing by 25. This yields:
[tex]\frac{14}{15}=\frac{x}{60}[/tex]
Cross multiply:
[tex]15x=60(14)[/tex]
Multiply and solve for x. So:
[tex]15x=840\\\Rightarrow x=56\approx55\text{ loaves}[/tex]
Therefore, approximately 55 loaves were baked in one hour.
So, our answer is B.
And we're done!
Answer:
B) 55Step-by-step explanation:
given
351 loaves baked in 6 hrs and 15 min.
15 min x (1 hr / 60 min) = 0.25 hr
find:
Estimate how many loaves were baked in one hour.
its a ratio and proportion:
351 loaves = x loaves ( just cross multiply)
6.25 hr 1 hr.
x loaves = 351 loaves ( 1 hr.)
6.25 hr.
= 56 ------->>> say 55
1. The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets
Answer:
Y= 12.5+X
Step-by-step explanation:
Y=43.75
X=1.25x25=31.25
so 43.75 minus 31.25= 12.5
he spent 12.5 on fair addmition
2. JI. has coordinates J(-6, 1) and Z(-4, 3). Find the coordinates of the midpoint.
Answer:
(- 5, 2 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (- 4, 3) thus
midpoint = [tex]\frac{-6-4}{2}[/tex], [tex]\frac{1+3}{2}[/tex] ) = ( [tex]\frac{-10}{2}[/tex], [tex]\frac{4}{2}[/tex] ) = (- 5, 2 )
Choose all the number sentences that have a difference less than 7,650?
A) 12,355 – 4,575
B) 19,345 – 12,000
C) 21,675 – 13,055
D) 24,356 – 18,560
E) 10,500 – 3,560
The local meteorologist claims that the temperature is going to steadily drop over the next 4 hours. If the temperature changes by the same amount each hour, and it changes by a total of -28°F, how much will it change each hour? Explain how you got your answer in two or more complete sentences. plz answer with a real answer will give brainlyest
Answer:
-7°F/hour.
Step-by-step explanation:
If the total change is -28°F, and we know it took 4 hours, we just have to divide the total change by hours taken to get the change per hour.
So we do the following: [tex]\frac{-28F}{4} = -7F/h[/tex]
So the temperature changes (drops) by -7°F/hour.
Which equation could be represented by the number line?
A. -5 + 6 = 1
B. -6 + 5 = -1
O c. 1 +(-7) = -6
D. 1 + (-6) = -5
Help!!!
Answer:
I think it’s C
Step-by-step explanation:
80+1246√16
What is the answer please I only have 10 minutes left
Answer:
7556
Step-by-step explanation:
Can You Please give me a Brainlies or how ever you spell it
Answer:
5304
Step-by-step explanation:
80+1246√16
= 1326√16
= 5304.
Are BD and CE congruent? Explain.
Answer:
The answer is D: Yes, BD = 7 and CE = 7
Step-by-step explanation:
B--> -5
D --> 2
-5 + BD = 2
BD = 7
C--> 0
E --> 7
0+CE=7
CE = 7
The answer is D
Please evaluate the given equation, and then see how many solutions the equation has. No. 1
here I am! dunno if this is the question you meant but you haven't gotten an answer here yet.
Answer:
B) Exactly one solution. (-3.5)
Step-by-step explanation:
5x + 8 - 7x = -4x + 1
combine like terms
5x - 7x + 8 = -4x + 1
-2x + 8 = -4x + 1
add 4x to both sides
-2x + 4x + 8 = -4x + 1 + 4x
2x + 8 = 1
subtract 8 from both sides
2x + 8 - 8 = 1 - 8
2x = -7
divide both sides by 2.
x = -3.5
3.5, clearly, is only one number.
On a snowy day, only 7/12 of the students attended Calvin Middle School. Among the students that missed school, about 4/5 students call the school to inform the school office. What was the fraction of all students that called in to inform the school about missing school this day?
Answer:
1/3 of all the students called in to inform the school about missing school this day
Step-by-step explanation:
4/5 = students that call the school to inform the school office
only 7/12 attended Calvin Middle School
To get the number of students that missed Calvin Middle School = 1 - number of students that attended Calvin Middle School
= 1 - 7/12 = (12-7) / 12
= 5 /12
The fraction of all students that called in to inform the school about missing school this day is:
5/12 x 4/5 = 1/3
3sinA=4cosA so find tansquareA_sinsquareA
Step-by-step explanation:
Do you mean?
[tex] \frac{ { \tan(x) }^{2} }{ \ { \sin(x) }^{2} } [/tex]
If so:
[tex]3 \sin(x) = 4 \cos(x) \\ \frac{3 \sin(x) }{ \cos(x) } = 4 \\ \frac{ \sin(x) }{ \cos(x) } = \frac{4}{3} \\ \tan(x) = \frac{4}{3} [/tex]
Did the question specify which quadrant? I'm just going to assume that it's the first
(as tangent = opp/adj)
hence
Hypotenuse:
[tex] \sqrt{{3}^{2} + {4}^{2} } = 5[/tex]
[tex] \sin(x) = \frac{4}{5} [/tex]
Finally,
[tex] \frac{ { \tan(x) }^{2} }{ { \sin(x) }^{2} } = \frac{ { \frac{4}{3} }^{2} }{ { \frac{4}{5} }^{2} } \\ = 2 \frac{7}{9} [/tex]
Solve for the indicated variable.
L = M - N for N
How do I slove this eqaution, and whats the answer?
-3(n+6)+10=-9
Answer:
[tex]n = \frac{1}{3}[/tex]
Step-by-step explanation:
Apply the distributed property, so it now looks like this: -3n + -18 + 10 = -9Combine like terms: -3n + -8 = -9Simplify: -3n - 8 = -9Add 8 to each side, so it now looks like this: -3n = -1Divide each side by -3 to cancel out the -3 next to n. It should now look like this: n = 1/3I hope this helps!
Use the distributive property to remove the parentheses -8(3v-w-4)
Joseph is shopping for school supplies. He can buy a box of 24 pens for $4.32 or a box of 36 pens for $5.76. Which is a better buy? Explain your reasoning.
Answer:
the better one to buy is a box of 36 pens for $5.76. because it is cheaper per pen.
Step-by-step explanation:
4.32 / 24 = 0.18 cents a pen
5.76 / 36 = 0.16 cents a pen
if a and b are integers,what conditions would make a×b > 0?
Answer:
a and b must be positive integers
Step-by-step explanation:
for example- a= (+1)x(+2)
= (+2)
= (+2)>0
= axb>0
Thank U
What is 1 3/4 divided by 3?
Answer:
7/12 is the answer
Arbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165. The equation represents the $495 total cost that Barbara paid to Dance Unlimited. 495 = 165 + 55m How many months, m, did Barbara receive dance lessons from Dance Unlimited?
Given:
Per month fee = $55
One-time recital fee = $165
The equation represents the $495 total cost that Barbara paid to Dance Unlimited.
[tex]495=165+55m[/tex]
To find:
We need to find the number of month Barbara receive dance lessons from Dance Unlimited.
Solution:
We have,
[tex]495=165+55m[/tex]
Here, m is number of months. We need to isolate m.
Subtract 165 from both sides.
[tex]495-165=55m[/tex]
[tex]330=55m[/tex]
Divide both sides by 55.
[tex]\dfrac{330}{55}=m[/tex]
[tex]6=m[/tex]
The value of m is 6. So, the required number of month Barbara receive dance lessons from Dance Unlimited is 6.
What is the value of the expression x2+(2+x5) when x=15.
Answer:
759,602
Step-by-step explanation:
Evaluate (x^5 + 2) + x^2 where x = 15:
(x^5 + 2) + x^2 = 15^2 + (15^5 + 2)
| 1 | 5
× | 1 | 5
| 7 | 5
1 | 5 | 0
2 | 2 | 5:
225 + 2 + 15^5
15^5 = 15×15^4 = 15 (15^2)^2:
225 + 2 + 15 (15^2)^2
| 1 | 5
× | 1 | 5
| 7 | 5
1 | 5 | 0
2 | 2 | 5:
225 + 2 + 15×225^2
| | 2 | 2 | 5
× | | 2 | 2 | 5
| 1 | 1 | 2 | 5
| 4 | 5 | 0 | 0
4 | 5 | 0 | 0 | 0
5 | 0 | 6 | 2 | 5:
225 + 2 + 15×50625
| 5 | 0 | 6 | 2 | 5
× | | | | 1 | 5
2 | 5 | 3 | 1 | 2 | 5
5 | 0 | 6 | 2 | 5 | 0
7 | 5 | 9 | 3 | 7 | 5:
225 + 2 + 759375
| | | | 1 | 1 |
| 7 | 5 | 9 | 3 | 7 | 5
| | | | 2 | 2 | 5
+ | | | | | | 2
| 7 | 5 | 9 | 6 | 0 | 2:
Answer: 759602
Answer:
759,602
Step-by-step explanation:
In this problem you would replace the x with 15 and break down the answer.
[tex]x^{2} +(2 + x^{5} )[/tex] = [tex]15^{2} + (2 + 15^{5} )[/tex]
Now that you know the equation, break it down.
15² = 225
225 + (2 + [tex]15^{5}[/tex])
After rewriting the equation, do the work inside the parenthesis.
(2 + [tex]15^{5}[/tex]) = (2 + 759,375) = 759,377
The equation will now look like this.
225 + (759,377)
Solve!
759, 602
An expert diver is looking for a particular species of fish along the coast line. He dives 25 feet below the surface of the ocean. Then he dives down 10 more feet. He swims back up 7 feet and down another 3 feet before he finds the species of fish he is looking for. What was the depth at which the diver finds the fish?
Answer:
31
Step-by-step explanation:
Depth Changes:
1. down 25 feet
2. down 10 feet
3. up 7 feet
4. down 3 feet
If we form this into an equation, we get:
25+10-7+3 = 31