Question:
At midnight, the temperature in a city was 5 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour.
Write an inequality that represents t, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning.
Answer:
[tex]t > 4.5[/tex]
Step-by-step explanation:
Given
Let T = temperature and t = hours past midnight
So, we have:
[tex](t_1,T_1) = (0,5)[/tex] --- at midnight
[tex]m = -2[/tex] --- rate (it is negative because the temperature drops)
Required
Determine the inequality when the temperature is colder than -4 degrees
First, we calculate the hours when the temperature at -4 degrees
This is represented as:
[tex](t_2,T_2) = (t,-4)[/tex]
[tex](t_1,x_1) = (0,5)[/tex]
Using the slope formula, we have:
[tex]m = \frac{T_2 -T_1}{t_2 - t_1}[/tex]
[tex]-2 = \frac{-4-5}{t -0}[/tex]
[tex]-2 = \frac{-9}{t}[/tex]
Solve for t
[tex]t = \frac{-9}{-2}[/tex]
[tex]t = 4.5[/tex]
This implies that: at 4.5 hours, the temperature is at -4 degrees Celsius.
So, the inequality is:
[tex]t > 4.5[/tex]
Solve the equation and check.
37x + 16 = 6(6x + 6)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is
(Simplify your answer.)
B. The solution is all real numbers.
OC. There is no solution.
Answer:
x = 20.
Step-by-step explanation:
37x + 16 = 6(6x + 6)
Distribute.
37x + 16 = 36x + 36
Subtract 36x from both sides.
x + 16 = 36
Subtract 16 from both sides.
x = 20.
The solution is 20.
Proof
37x + 16 = 6(6x + 6)
37(20) + 16 = 6(6(20) + 6)
740 + 16 = 6(120 + 6)
756 = 6(126)
756 = 756.
Find the inverse of each function. g(x)=∛(x-2)
Please show the steps. I can show you what I have so far if you want, too.
Just please don't put some Ludacris thing, like "ldsnvlsjdsv" Okay? thankyou :)
Answer:
x=2
Step-by-step explanation:
g(x)=∛(x-2) -Substitute g(x)=0
0=∛(x-2) -Swap the sides of the equation
∛(x-2)=0
∛(x-2)=0 -Set the radicand equal to 0
x-2=0
x-2=0 -Move the constant to the right hand side and change its sign
x=2
I Hope this helps! If you are good at geometry I really need help. Please let me know! :)))
Find the sum of (4 + 3x) + (2 + x).
Answer:
Your answer would be 8x+2
Step-by-step explanation:
4x+3x+x+2
Combine the like terms
Which gives you 8x+2
plz help I am being timed
Answer:
24
Step-by-step explanation:
What is 0.00047 in standard form.
Step-by-step explanation:
0.00047. = 47÷10 000
=4.7×10/10^-5
= 4.7×10^-4
A model rocket is launched vertically from a platform 64 feet above the ground. The height of the rocket reaches during the flight is modeled by the equation h(t) = -16t² + 128x, where h is the height of the rocket and t is the time in seconds since the launch. Determine algebraically the time when the ball hits the ground.
Answer:
do not know why asking questions
The following table is for which exponential function?
Find all of the missing angles, #1-22. pleasssseeee helpppppp
[tex]2x-7y=9\\x+2y=10[/tex]
Answer:
x=8 y=1
Step-by-step explanation:
you have first and second equation, YOU MUST FIND THE THIRD EQUATION
SOLUTION
FIND equation 3 from 2
x+2y=10
x=10-2y...........3
Substitute equation 3 from first (not from the equation where you got equation 3)
2 (10-2y)-7y=9
20-4y-7y=9
-11y=9-20
-11y= -11
-11y/-11= -11/-11
y=1
Find the value of x from the third equation
x=10-2 (1)
x=8
A $100 tablet is marked up by 10% and then the new price is marked down by 10%. What is the final price?
Answer:
$99
Step-by-step explanation:
So the initial price of the tablet was $100. It was marked up by 10% and then marked down by 10%. We are asked to find the final price.
To find the final price, lets first find the price after the tablet price was marked up by 10%. This means that the tablet price increased by 10%. To find the price, we can add 10% of the new original price (or 10% times $100) original price ($100):
$100 + ($100 × 0.1) = $100 + $10 = $110
We could have also multiplied $100 by 1.1 (or 1 + 10%) to find the new price.
So now we know that the new price after the tablet is marked up by 10% is $110. Now, to find the final price, we have to find the price after the new price is marked down by 10%. We can do this by taking the new price ($110) and subtracting 10% of the new price (or 10% times $110):
$110 - ($110 × 0.1) = $110 - $11 = $99
So the final price of the tablet would be $99.
I hope you find my answer to be helpful. Happy studying.
HELPPPPPPPPPPPPPPPPppppppppppppppp
Answer:
i go for 3
Step-by-step explanation:
Factor the following quadratic expression n^2+ 4n-12
Answer:
(n + 6)(n - 2)
Step-by-step explanation:
Given
n² + 4n - 12
Consider the factors of the constant term (- 12) which sum to give the coefficient of the n- term (+ 4)
The factors are + 6 and - 2 , since
6 × - 2 = - 12 and 6 - 2 = + 4
Then
n² + 4n - 12 = (n + 6)(n - 2) ← in factored form
Nine scores have an average of 8. Scores x and x+1 are added, and these increase the average to 9. Find x
Answer:
x must be 13
Step-by-step explanation:
Represent the nine scores by a, b, c, d, e, f, g, h, i.
Write the following equation to indicate that the average of these nine scores is 8:
a+b+c+d+e+f+g+h+i
----------------------------- = 8, or a+b+c+d+e+f+g+h+i = 72 if we multiply both
9 sides of this equation by 9.
Next, we add scores x and x+ 1 to
a+b+c+d+e+f+g+h+i + x + x + 1
and divide the result by 11, as there are now 11 scores instead of just 9:
a+b+c+d+e+f+g+h+i + x + x + 1
----------------------------------------------
11
Earlier, we saw that a+b+c+d+e+f+g+h+i = 72. We can now replace
a+b+c+d+e+f+g+h+i in the above fraction by 72:
72 + 2x + 1
------------------- = 9 (as the new average is 9)
11
Multiplying both sides of this equation by 11 results in:
73 + 2x = 99, or 2x = 26.
Then x must be 13, and x + 1 must be 14.
The sum of two numbers is 54 and the difference is 8. What are the numbers?
Answer:
23 and 31 are the numbers you are searching for.
Step-by-step explanation:
23 + 31 = 54
31 - 23 = 8
Have a nice day!
What is the value of x?
Which inequality does the graph represent?
1. x>17
2.x<17
3.x<_17
4.x>_17
Answer:
1. x > 17
Step-by-step explanation:
When the point on the graph is an open circle you are going to be using < or > as an open circle means greater than or less than
Immediately we can eliminate number 3 and 4
When the line is going in the direction of the right than the inequality sign will face the variable (x)
the numbers are getting larger meaning that x is greater than the constant (17)
Hence, your answer is x > 17
Extra notes:
when the point on the graph is a closed circle ( filled in ) then you will use ≤ or ≥ as a closed circle means greater than or equal to or less than or equal to
Answer:
1. x > 17
Step-by-step explanation:
I l l l
17 18 19 20
-------------------------------->
Hope this helps
A certain forest covers an area of 4900 km². Suppose that each year this area decreases by 5.75%. What will the area be after
5 years?
Answer:
3,644 km²
Step-by-step explanation:
y = 4900(1 - .0575)^5
y = 4900(0.9425)^5
y = 3644.21
1. Jake makes $11.00 per hour. He is getting a raise of 20% to his hourly pay. How much
will he make per hour after his raise? Show your calculation.
Answer:
$11,00 x ( 100% + 20%) = $13.2 /h
Step-by-step explanation:
Find the missing height of the solid figure
9514 1404 393
Answer:
5 in
Step-by-step explanation:
The figure's angles are presumed to be right angles everywhere, so the left-side vertical dimension is equal to the right-side vertical dimension.
The right side is marked as 15 inches.
The left side has two vertical segments, one of which is 10 inches. Since the total left-side height must be the same as the right-side height, we have ...
10 in + ? = 15 in
? = 5 in . . . . . . subtract 10 in
The missing height is 5 inches.
What is the value of x ??
Answer:
b. 8
Step-by-step explanation:
What is the measure, in degrees, of the missing interior angle?
O 70
O 40
O 10
O 170
(pls help)
Answer:
A) 70
Step-by-step explanation:
180 - 120 = 60
? = x
x + 50 + 60 = 180
x + 110 = 180
x = 70
When the function ƒ(x) = 4x−2 is evaluated for x = 3, the output is:
-4
-6
-16
-none
Answer:
None
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
f(x) = 4x - 2
x = 3
Step 2: Evaluate
Substitute in x [Function]: f(3) = 4(3) - 2Multiply: f(3) = 12 - 2Subtract: f(3) = 10Find the slope of the line passing through the points D(10,8) and E(-4, 4)
Answer: 2/7
Step-by-step explanation:
Slope form: y2-y1/x2-x1
4-8/-4-10 ==> -4/-14 ==> 2/7
given the following sequences : -17 -25 -33 -41... write an explicit formula and find the 28th term in this sequence
Answer:
a(n) = -8n -9
a(28) = -233
Step-by-step explanation:
a(n) = a(1) + (n - 1)d
n is the nth term, a(1) is the first term, d is the common difference.
*d = -25 - (-17) = -8
a(n) = -17 + (n - 1)(-8)
= -17 + (-8n + 8)
= -17 - 8n + 8
= -8n - 9
For the 28th term
a(28) = -8(28) - 9
= -224 - 9
= -233
Someone help and plz make sure it’s right plz :)
Answer:
6.3
Step-by-step explanation:
square root of (14.9k^2 - 13.5k^2)
please how do you solve 60cos25
Answer:
60cos(25)=54.378467222199
pls help me multiple choice!
Answer:
100. degrees was right for me so it could be for you
If a fair die is rolled twice and two numbers X1=result of the first roll and X2=result of the second roll are obtained. Given that X1+X2=7, what is the probability that X1 =4 or X2 =4
Answer:
P = 2/3 = 0.67
Step-by-step explanation:
Assuming that X1 + X2 = 7
The total number of outcomes such that X1 + X2 = 7 are:
X1 = 3, X2 = 4
X1 = 4, X2 = 3
X1 = 1, X2 = 6
X1 = 6, X2 = 1
X1 = 2, X2 = 5
X1 = 5, X2 = 2
So there are 6 total outcomes such that X1 + X2 = 7
Now, the probability that X1 = 4 is equal to the quotient between the number of outcomes where X1 = 4 (only one outcome) and the total number of outcomes (6)
Then:
p = 1/6
And the probability that X2 = 4 is calculated in the same way, then the probability is:
q = 1/6
Now, the probability that X1 = 4 or X2 = 4 is the sum of both probabilities we've found above, then:
P = p + q = 1/6 + 1/6 = 2/6 = 2/3 = 0.67
Write the equation of the line, in slope-intercept form, with the
following information:
slope: -2
y-intercept: (0, -3)
What is the dominan and range of the relation below? Answer using set notation.
Answer:
domain: -2 < x < 4
range: -3 < y < 1