Answer:
y = -4/3x + 2
Step-by-step explanation:
Slope intercept form is y = mx + b.
Rearrange the equation into slope intercept form by isolating y:
12x + 9y = 18
9y = -12x + 18
Divide each side by 9:
y = -4/3x + 2
So, the equation is y = -4/3x + 2
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
What happens when the multiplicity of a real root is even?
Answer:
Step-by-step explanation:
The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.
A trinomial is a perfect square when two terms are
a. Positive
b.negative
c. Neither positve
d. Either negative
Answer:
a trinomial is a perfect square trinomial if it can be factorized into a binomial multiplies to itself. In a perfect square trinomial, two of your terms will be perfect squares.
..A tin of paint was 2/3 litres full. Tom used 1/2 of
the paint to paint his table. How much was left ?
Multiply the amount of paint started with by the amount used:
2/3 x 1/2 = (2 x 1) / (3 x 2) = 2/6 = 1/3
There is 1/3 liter left
Let a, b, c be the three observations. The mean of these observations is.
(a) a+b+c2 (b) a×b×c2 (c) a+b+c3 (d) a+bc
Answer: a+b+c/3
Step-by-step explanation:
mean= sum of all values/number of values
What does a right angle look like
Answer:
It's a 90 angle, straight up and down, moving into straight right and left.
Find the coefficient of the t4
term in the expansion of
(4t – 375
a
9514 1404 393
Answer:
-3840t^4
Step-by-step explanation:
The k-th term, counting from k=0, is ...
C(5, k)·(4t)^(5-k)·(-3)^k
Here, we want k=1, so the term is ...
C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4
__
The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.
a tank is 2m long, 1.4m wide and 1.8m high.find the volume of water in the tank when it is half full.
Answer:
2.52m³
Step-by-step explanation:
volume=L x W x H
V=2 x 1.4 x 1.8
V=5.04
WE DIVIDE 5.04m³ by 2 to get 2.52m³
Have a nice day
Analyze the key features of the graph of f(x) shown below.
Use rules of transformations and the parent function to formulate an equation for the rational function shown in the graph. Show all your work.
Answer:
y = -2+1/3x
Step-by-step explanation:
Slope = -2
x - intercept = -3
To make the x-intercept positive you make it 1/3.
y = -2 +1/3x
What transformation of the parent function f(x) is made to get f(−x)+1
Answer:
It moved one space to the right , so it is a translation.
Step-by-step explanation:
shown below.
Answer:
Handling Data and probability
find f(1)' If u know that
g(1)=1 , g'(1)= -1
h(1)= -2 , h'(1) 3
Step-by-step explanation:
[tex]f(x) = g(x)h(x)[/tex]
Taking the derivative of f(x), we get
[tex]f'(x) = g'(x)h(x) + g(x)h'(x)[/tex]
Then [tex]f'(1)[/tex] becomes
[tex]f'(1) = (-1)(-2) + (1)(3) = 5[/tex]
The sound pressure P for a given sound is given by:
P= 10 log W/ Wo
Its units are decibels (dB). W is the size of a variable energy source (called the sound power), measured in Watts. Wo is the lowest threshold of sound that humans can typically hear. It is a constant given by:
Wo=10^-12 W/m2
a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.
b) If the variable sound power W is given by W = t2 +t +1, find the rate of change of the sound pressure P, at time t = 3s.
c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)
Answer:
a. 0.302 dB/s
b. 2.34 dB/s
c. 1.24 dB/s
Step-by-step explanation:
a) Find the rate of change of the sound pressure P with respect to time if W=7.2 and dW/dt = 0.5 at some given time t.
Since P = 10log(W/W₀), its rate of change with respect to time is
dP/dt = dP/dW × dW/dt
dP/dW = d[10logW - 10logW₀]/dt
dP/dW = d[10lnW/2.303 - 10logW₀]/dt
= 10/2.303W - 0
= 10/(2.303W)
dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × dW/dt
Since dW/dt = 0.5 when W = 7.2, then
dP/dt = 10/(2.303 × 7.2) × 0.5
dP/dt = 10/16.5816 × 0.5
dP/dt = 0.603 × 0.5
dP/dt = 0.302 dB/s
b) If the variable sound power W is given by W = t² + t + 1, find the rate of change of the sound pressure P, at time t = 3s.
Since P = 10log(W/W₀), its rate of change with respect to time is
dP/dt = dP/dW × dW/dt
dP/dW = d[10logW - 10logW₀]/dt
dP/dW = d[10lnW/2.303 - 10logW₀]/dt
= 10/2.303W - 0
= 10/(2.303W)
and dW/dt = d(t² + t + 1)/dt = 2t + 1
So, dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × (2t + 1)
dP/dt = 10(2t + 1)/(2.303W)
dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]
we then substitute t = 3 into the equation
dP/dt = 10(2t + 1)/[2.303(t² + t + 1)]
dP/dt = 10(2(3) + 1)/[2.303((3)² + 3 + 1)]
dP/dt = 10(6 + 1)/[2.303(9 + 3 + 1)]
dP/dt = 10(7)/[2.303(13)]
dP/dt = 70/29.939
dP/dt = 2.34 dB/s
c) If W = cos 0.2t, find the rate of change of the sound pressure P, at time t = 15 (calculators in radians)
Since dP/dt = dP/dW × dW/dt and dP/dW = 10/(2.303W) and W = cos(0.2t), dW/dt = -0.2sin(0.2t)
So, dP/dt = dP/dW × dW/dt
dP/dt = 10/(2.303W) × -0.2sin(0.2t)
dP/dt = -20sin(0.2t)/(2.303W)
dP/dt = -20sin(0.2t)/(2.303cos(0.2t))
dP/dt = -20tan(0.2t)/2.303
when t = 15, we have
dP/dt = -20tan(0.2 × 15)/2.303
dP/dt = -20tan3/2.303
dP/dt = -20 × -0.1425/2.303
dP/dt = 2.8509/2.303
dP/dt = 1.238
dP/dt ≅ 1.24 dB/s
A driver leaves home for a business trip and drives at a constant speed of 60 miles per hour for 2 hours. Her car gets a flat tire, and she spends 30 minutes changing the tire. She resumes driving and drives at 30 miles per hour for the remaining one hour until she reaches her destination. For what interval of time would a graph that models the driver's distance from home consist of a horizontal line?
Answer:
The 30 minutes that she is changing the flat
Step-by-step explanation:
What is the cube root of -1,000p12q3?
O-1004
O - 10pta
O 1004
O 10pta
Answer:
Your options are not clear
Step-by-step explanation:
[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]
(2x - y + 3) (2x - y - 3)using identities
Step-by-step explanation:
(2x-y+3)(2x-y-3)=
4x²-2xy-6x-2xy+y²+3y+6x-3y-9=
4x²-4xy+y²-9=
(2x-y)²-9
Two similar triangles are shown below:
Which two sets of angles are corresponding angles
Answer:
angle w and angle v; angle x and angle y (option 1)
Step-by-step explanation:
the little arc things are what tell you two angles are corresponding m
angles w and v both have two arc drawing things.
angle x and y have one
and the other angles that aren't labeled have three
PROBIBILITY HELP ME PLZ Mike is playing a game where a ball is hidden under one of 5 cups. Mike guesses which cup contains the ball 20 times and chooses correctly 6 times. Mike wants to simulate the game to determine if his results are the same as what would be expected by random chance.
Answer:
Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.
Step-by-step explanation:
Given
[tex]Cups = 5[/tex]
[tex]Ball=1[/tex]
[tex]Trials = 20[/tex]
See attachment
Required
Simulate the above experiment (fill in the gaps)
The probability of choosing a ball correctly in each trial are independent, and each probability is calculated as:
[tex]P(Correct) = \frac{Ball}{Cups}[/tex]
This gives:
[tex]P(Correct) = \frac{1}{5}[/tex]
The number of times (i.e. 6) he chose correctly is not a factor in his simulation
So, a correct simulation of the experiment is as follows:
Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.
The selected ball represents the number of balls hidden (i.e. 1 ball).
The total number of balls (5 balls; i.e. 1 red and 4 white) represent the number of cups (5 cups)
The 20 times represent the number of times the experiment is repeated.
A fair charges an admission fee of 4 dollars for eacg person. Let C be the cost of admission in dollars for P people. Write an equation relating C to P. Then graph your equation using the axes
Answer:
Equation is C = 4P
Graph is shown below
============================================================
Explanation:
The equation is C = 4P since it costs $4 per person. We just multiply 4 with the number of people (P) to get the cost (C).
Let's say 0 people show up, so that means C = 4*P = 4*0 = 0
The input P = 0 leads to the output C = 0. This is basically the same as saying x = 0 leads to y = 0. The point (0,0) is on the graph.
Repeat for P = 1 and you'll find that C = 4. This is the same as x = 1 leading to y = 4. The point (1,4) is on the graph.
If you keep going for various values of P, you'll get corresponding values of C. It turns out that all you need are 2 points to graph this line. Plot (0,0) and (1,4) on the same xy grid. Draw a line through them to complete the graph.
The graph is shown below.
A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
1460
Step-by-step explanation:
Suppose a jar contains 8 red marbles and 25 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.
Answer: [tex]\dfrac{7}{132}[/tex]
Step-by-step explanation:
Total marbles in the jar = 8+25 = 33
Using combinations, the number of ways of choosing two marbles out of 33= [tex]\dfrac{33!}{2!(33-2)!}\\\\=\dfrac{33!}{2\times31!}\\\\=\dfrac{33\times32}{2}=528[/tex] (total outcomes)
Similarly, the number of ways of choosing two red marbles =
[tex]\dfrac{8!}{2!6!}\\\\=\dfrac{8\times7}{2}=28[/tex](favorable outcomes)
Required probability = [tex]\dfrac{\text{favorable outcomes}}{\text{total outcomes}}[/tex]
[tex]=\dfrac{28}{528}\\\\=\dfrac{7}{132}[/tex]
hence, required probability = [tex]\dfrac{7}{132}[/tex]
how many kilometers are there in 9000000cm
Answer:
90 kilometers
Step-by-step explanation:
https://www.bing.com/search?q=kilometers+are+there+in+9000000cm
The weight, in pounds , of Mike's five pet dogs are listed below.What is the mean absolute deviation (MAD) of the weights?
16 , 23 , 27 , 41 , 53
Type the answer in the box.
______ pounds
Answer:
it would be 32
Step-by-step explanation:
you would add them all up then divide it by five
Answer: The answer is 32
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
You borrow $16,000 with a term of four years at an APR of 5% to buy a truck. What is your monthly payment? (Round your answer to the nearest cent.)
$
How much total interest is paid? (Round your answer to the nearest cent.)
$
Answer:
368.47
1686.56
Step-by-step explanation:
effective rate: .05/12=.00416666667
payment=x
[tex]16000=x\frac{1-(1+.00416666667)^{-48}}{.00416666667}\\x=368.47[/tex]
Interest:
368.47*48-16000=1686.56
Answer:
Answer:
368.47
1686.56
Step-by-step explanation:
effective rate: .05/12=.00416666667
payment=x
\begin{gathered}16000=x\frac{1-(1+.00416666667)^{-48}}{.00416666667}\\x=368.47\end{gathered}
16000=x
.00416666667
1−(1+.00416666667)
−48
x=368.47
Interest:
368.47*48-16000=1686.56
What is the volume of a rectangular prism that has a length of 15 mm, a width of 11 mm, and a height of 4 mm?
269 mm 3
660 mm 3
538 mm 3
1,320 mm 3
Answer:
Option 2: 660
Step-by-step explanation:
Multiply the three numbers together
Answer:
660mm 3
Step-by-step explanation:
Rectangular prism formula: V=LWH
15 x 11 x 4 = 660mm 3
Hope that helps <3
Solve this equation for x. Round your answer to
the nearest hundredth.
0 = In(x + 6)
Answer:
-5 =x
Step-by-step explanation:
0 = In(x + 6)
Raise each side to base e
e^0 = e^ ln (x+6)
1 = x+6
Subtract 6 from each side
1-6 = x
-5 =x
Trig Equation from a Graph
Answer:
Step-by-step explanation:
Please help I have gotten through every problem except this one!
Answer:
Step-by-step explanation:
BUG is 30 degrees more than GUY
So that means if <GUY = x
< BUG = <GUY + 30
Together they make 180 degrees
<BUG + <GUY = 180 Substitute for <BUG
<GUY + 30 <GUY = 180 Combine
2*<GUY + 30 = 180 Subtract 30 from both sides
2*<GUY = 150 Divide by 2
<GUY = 150/2
<GUY = 75
<BUG = 75 + 30
<BUG = 105
rewrite x+2y=-4 in slope intercept
Answer:
y= - 1/2 x-2 ( SEE IMAGE BELOW)
Step-by-step explanation:
FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
Answer:
How do you write
x+2y=4
into slope intercept form?
Answer is:
y=−12x+2
Step-by-step explanation:
Slope intercept form can be represented as
y=mx+b
To get an equation into this form, we should try to get y all alone.
So then from x+2y=4
first, we can subtract x from both sidesand get 2y=−x+4
then, we can divide both sides by 2 to get it in slope intercept form
y=−12x+2
I think is like this. Hope it helps>3
What is the equation of the line? Plsss helppp
Answer:
y = -7
Step-by-step explanation:
Slope: 0
y-intercept: (0,−7)
Since the line doesn't change up, down, right, or left, and it stays on the y-axis, that's how u get y = . The straight line runs along -7 . That's how u get -7 . so when u put it all together u get: y = -7 .
Hope that helps. Tried to explain the best I could :)
PLEASE HELP ME WILL MARK IF YOU CAN HELP
Answer:
d = 52°
Step-by-step explanation:
The two sides with little marks are congruent.
That means that the opposite angles are congruent.
One angle measures 76°.
The other to angles measure d each.
d + d + 76 = 180
2d + 76 = 180
2d = 104
d = 52