Answer:
[tex]t = -7\ \ \ or\ \ t = 10[/tex]
Step-by-step explanation:
Given
[tex]f(t) = 2t^2 - 6t[/tex]
Required
Find t, when [tex]f(t) = 140[/tex]
Substitute 140 for f(t) in [tex]f(t) = 2t^2 - 6t[/tex]
[tex]140 = 2t^2 - 6t[/tex]
Divide through by 2
[tex]\frac{140}{2} = \frac{2t^2 - 6t}{2}[/tex]
[tex]70 = t^2 - 3t[/tex]
[tex]t^2 - 3t = 70[/tex]
Subtract 70 from both sides
[tex]t^2 - 3t - 70= 70 - 70[/tex]
[tex]t^2 - 3t - 70= 0[/tex]
Expand
[tex]t^2 -10t + 7t - 70 = 0[/tex]
Factorize:
[tex]t(t - 10) + 7(t - 10) = 0[/tex]
[tex](t + 7)(t - 10) = 0[/tex]
Split:
[tex]t + 7 = 0\ \ \ or\ \ t - 10 = 0[/tex]
[tex]t = -7\ \ \ or\ \ t = 10[/tex]
Hence, the values of t are -7 and 10
whats a linear model?
Answer:
A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.
:)
Answer: A linear model is an equation that represents a relationship between two quantities at a constant rate of change.
A linear line can be represented by the equation: y=mx+b. This is also known as the linear equation.
t is the letters in the word thinking
Answer:
u is the one on my mind rn
Step-by-step explanation:
HAHAHAHAHHAA XD
10 Which of these transformations make the pre-image
and image congruent?
a) Reflection
b) Dilation
c) Translation
d) Rotation
Answer:
reflection and rotation
Step-by-step explanation:
HELP!!!!
Which type of angle is Angle A B C?
Angle A B C is a straight angle.
Angle A B C is a vertical angle.
Angle A B C is a right angle.
Angle A B C is a complementary angle.
Answer:
Angle ABC is a right angle. So option C is correct.
What is the right triangle?
A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.
The angle of a right angle is always 90 degrees.
IT is given that the Angle A B C is intersected by a line to form angles 25 degrees and 65 degrees.
If we add up 25 and 65 degrees, we get 90 degrees.
25 + 65 = 90
Thus, Angle ABC is a right angle because right angles are 90 degrees.
Therefore Angle ABC is a right angle. So option C is correct.
Step-by-step explanation:
Complete the given proof.
If f′(x) = 3x^2 + 2x and f(2) = 3, then f(1) =
The distribution of the heights of students in a large class is roughly Normal. Moreover, the mean height is 68 inches, and approximately 95% of the heights are between 62 and 74inches. Thus, the standard deviation of the height distribution is approximately equal to
Answer:
Probably equal to 6 or 7.
Step-by-step explanation:
Which of the following is a difference of perfect square?
A) 4x^(2)+36
B) x^2+4
C) 9x^2-100
D) x^2-18
I think b. is the answer
but i am not sure..
[tex] Find the area of the shape shown below.[/tex]
Answer:
60
Step-by-step explanation:
shape can be made into a trapezoid and square
rectangle area= a*b
triangle = 1/2 a*b
rectangle = 64
triangle = 4
64-4=60
in one town, 76% of adults have health insurance. what is the probability that 7 adults selected at random from the town all have health insurance?
Answer:
15% probability that 7 adults selected at random from the town all have health insurance.
Step-by-step explanation:
(sample/population)^number of times selected
(76/100)^7 = (0.76)^7 = 0.15 = 15%
Given point A (-9, -9) and B (5, -2) find the coordinates of point P on the directed line segment AB in the ratio 3:4.
Answer:
We have point P(-3,-6).
Step-by-step explanation:
We want to find a point P(x,y).
Since it is on the directed line segment AB in the ratio 3:4, it means that:
[tex]P - A = \frac{3}{3+4}(B - A)[/tex]
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
We apply this to both the x-coordinate and y-coordinate of P.
x-coordinate:
x-coordinate of A: -9
x-coordinate of B: 5
x-coordinate of P: x
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
[tex]x - (-9) = \frac{3}{7}(5-(-9))[/tex]
[tex]x + 9 = \frac{3}{7} \times 14[/tex]
[tex]x + 9 = 6[/tex]
[tex]x = -3[/tex]
y-coordinate:
y-coordinate of A: -9
y-coordinate of B: -2
y-coordinate of P: y
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
[tex]y - (-9) = \frac{3}{7}(-2-(-9))[/tex]
[tex]y + 9 = \frac{3}{7} \times 7[/tex]
[tex]y + 9 = 3[/tex]
[tex]y = -6[/tex]
We have point P(-3,-6).
AABC = AGMN
mzA = 35°, m_M = 4x + 5°, m N = 6x, Find x
Answer:
35+4x+5+6x=180
10x=180-40
x=140/10
x=14
3 lets We State
2 in
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8 in
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10 in
empty box
If a=-2 and b=-4 find the value of 3a+b+4
Answer:
-6
Step-by-step explanation:
hey laudu
[tex]3a + b + 4[/tex]
[tex]3( - 2) + ( - 4) + 4[/tex]
[tex] - 6 - 4 + 4[/tex]
[tex] - 6[/tex]
Step-by-step explanation:
❀ [tex] \underline{ \underline{ \text{Given}}} : [/tex]
a = -2 & b = - 4❀ [tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
value of 3a + b + 4✏ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]
All you need to do is plug the value and simplify !
⟶ [tex] \tt{3 \times ( - 2) + ( - 4) + 4}[/tex]
⟶ [tex] \tt{ - 6 + ( - 4) + 4}[/tex]
⟶ [tex] \tt{ - 6 - 4 + 4}[/tex]
⟶ [tex] \tt{ - 10 + 4}[/tex]
⟶ [tex] \boxed{ \tt{ - 6}}[/tex]
[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ - 6}}}}}}[/tex]
Hope I helped ! ♪
Have a wonderful day / night ! ♡
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60% of 300 equal . 60 of what is equal to 300. 60 out of 300 is how many percent
Step-by-step explanation:
6/10*300=180
60% of 500 is 300
6/10x=300 x=500
60/300=1/5=20%
A tank contains 100 kg of salt and 2000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.
Required:
a. What is the concentration of our solution in the tank initially?
b. Find the amount of salt in the tank after 4.5 hours.
c. Find the concentration of salt in the solution in the tank as time approaches infinity.
a. The concentration of the solution is 0.05 kg/L. b. The amount of salt is 154 kg after 4.5 hours. c. The concentration of salt in the solution in the tank approaches 0 as the time approaches infinity.
a. The concentration of the salt in the tank initially is given by the amount of salt divided by the volume of water:
0.025 kg/L = 100 kg / 2000 L = 0.05 kg/L
b. Let t be the time in minutes. The amount of salt in the tank after t minutes is given by:
100 kg + 0.025 kg/L × 8 L/min × t
To find the amount of salt after 4.5 hours, we convert the time to minutes:
4.5 hours × 60 minutes/hour = 270 minutes
And substitute this value of t into the equation:
100 kg + 0.025 kg/L × 8 L/min × 270 min = 100 kg + 54 kg = 154 kg
c. The concentration of salt in the solution in the tank as the time approaches infinity is given by:
154 kg / (2000 L + 8 L/min × t) as t approaches infinity
As t approaches infinity, the volume of water in the tank approaches infinity, so the concentration of salt in the solution approaches 0.
So, the concentration of salt in the solution in the tank approaches 0 as the time approaches infinity.
Learn more about the concentration of the salt here:
https://brainly.com/question/14177007
#SPJ1
A box contains 4 red marbles, 3 green marbles and 2 blue marbles. One marble is removed from the box and it is NOT replaced. Another marble is drawn from the box. What is the probability that the first marble is blue and the second marble is green?
The required probability is [tex]\dfrac{1}{12}[/tex].
Important information:
Red marbles = 4Green marbles = 3Blue marbles = 2Probability:Total number of marbles is:
[tex]4+3+2=9[/tex]
The probability of getting a blue marble is [tex]\frac{2}{9}[/tex].
After removing a marble, the number of remaining marbles is 8. So, the probability of getting a green marble is [tex]\frac{3}{8}[/tex].
Now, the probability that the first marble is blue and the second marble is green is:
[tex]P=\dfrac{2}{9}\times \dfrac{3}{8}[/tex]
[tex]P=\dfrac{1}{12}[/tex]
Therefore, the required probability is [tex]\dfrac{1}{12}[/tex].
Find out more about 'Probability' here:
https://brainly.com/question/10697254
William was parasailing at about 900 feet in the air while a shark swam
directly below him at 30 feet below the surface of the ocean. How far is
William from the shark?*
Answer:
930m
Step-by-step explanation:
It says they were 900 feet in the air below him is the ocean so thats 900 meters away from him and the shark is 30 feat below the surface of the ocean so you would do 900+30=930m so the shark is 930m away from him
25 feet in 4 seconds; 80 feet in x seconds write a proportion for each phrase and solve it
Answer:
12.8 seconds
Step-by-step explanation:
Create a proportion where x is the number of seconds for 80 feet
[tex]\frac{25}{4}[/tex] = [tex]\frac{80}{x}[/tex]
Cross multiply and solve for x
25x = 320
x = 12.8
So, the answer is 12.8 seconds
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Also, for the select the options are 23 or 16
Answer:
23
Step-by-step explanation:
Abigail tosses a coin off a bridge into the stream below. The distance, in feet, the coin above the water is modeled by the equation y=−16x2+96x+112 When does the coin hit the water?
Answer:
7 seconds
Step-by-step explanation:
Distance of the coin above the water is modeled by the equation
[tex]y=-16x^2+96x+112[/tex]
where [tex]x[/tex] is time taken to cover the distance
Now equating with zero.
[tex]0=-16x^2+96x+112\\\Rightarrow 16x^2-96x-112=0\\\Rightarrow x=\dfrac{-\left(-96\right)\pm \sqrt{\left(-96\right)^2-4\times \:16\left(-112\right)}}{2\times \:16}\\\Rightarrow x=7, -1[/tex]
So, time taken by the coin to hit the water is 7 seconds.
Change 4.8 meters into centimetres
Answer:
4.80
Step-by-step explanation:
Solve for y: 2x+3y=15
Answer:
[tex]\huge\boxed{y=5-\frac{2}{3}x}[/tex]
Step-by-step explanation:
With the equation [tex]\displaystyle 2x+3y=15[/tex], we can solve for y by algebraically manipulating the question until we have y isolated on one side.
It's important to note that if we do something to one side, we have to do it to another. Just as [tex]5=5[/tex], adding two to both sides still makes it true [tex]5+2=5+2, 7=7[/tex].
[tex]2x+3y=15[/tex] [tex]\displaystyle \frac{2x}{3} + \frac{3y}{3} = \frac{15}{3}[/tex] [tex]\displaystyle \frac{2}{3}x+y=5[/tex] [tex]\displaystyle \frac{2}{3}x - \frac{2}{3}x +y=5 - \frac{2}{3}x[/tex] [tex]\displaystyle y = 5 - \frac{2}{3}x[/tex]Therefore, this equation for y is [tex]\displaystyle y = 5 - \frac{2}{3}x[/tex] .
Hope this helped!
2x + 3y = 15
3y = 15 - 2x
y = 15 - 2x/3
9x81 simplfy in distributive proper
Answer:
the answer is 729.........
what is the y-intercept of the line?
Answer:
the y-intercept is -2, hope this helps! :]
(0, -2)
Solution:The y-intercept is the point where the graph touches the y-axis.The y-intercept is usually written as (0, b) where "b" is the y-intercept.The graph touches the y-axis at (0, -2).Therefore, the y-intercept is (0, -2) or -2.Hope it helps.
Do comment if you have any query.
Pls help with this ASAP
Answer:
answer is A
Step-by-step explanation:
hope this helps!
Two square rooms have a total floor area of 230 m2, and one is 4 metres bigger each way than
the other. Let the smaller room have a length x. Find the dimensions of the room.
Please explain your answer
Answer:
12.54m by 12.54 and 8.54m by 8.54m
Step-by-step explanation:
Area of a square = L²
L is the side length of the room
The total area of the two square room = A₁+A₂
T = A₁+A₂
T = L₁²+x²
If the two square rooms have a total floor area of 230 m², then;
L₁²+x² = 230. ..... 1
If one room is 4 meters bigger each way than other, then;
L₁ = x + 4 .... 2
where x is the length of the smaller room
Substitute equation 2 into 1;
From 1: L₁²+x² = 230
(x+4)²+x² = 230
x²+8x+16+x² = 230
2x²+8x+16-230 = 0
2x²+8x-214 = 0
x²+4x-107 = 0
x = -4±√16-4(-107)/2
x = -4±√16+428/2
x = -4±21.07/2
x = 17.07/2
x = 8.54m
L₁ = x+4
L₁ = 8.54+4
L₁ = 12.54m
Hence the dimensions of the room is 12.54m by 12.54 and 8.54m by 8.54m
what is the ratio of
5/30=3/c
Answer:
18
Step-by-step explanation:
Solve for c by cross multiplying
A bottle rocket is shot off a bridge into the stream below. The height of the rocket (in feet) above
the water is modeled by h (t) = -1662 +96t + 112, where t represents time (in seconds).
How many seconds will it take for the rocket to reach its maximum height?
seconds
What is the maximum height the rocket will reach?
feet
How many second will it take for the rocket to hit the water?
seconds
The correct model of the height of rocket above water is;
h(t) = -16t² + 96t + 112
Answer:
time to reach max height = 3 seconds
h_max = 256 ft
Time to hit the water = 7 seconds
Step-by-step explanation:
We are given height of water above rocket;
h(t) = -16t² + 96t + 112
From labeling quadratic equations, we know that from the equation given, we have;
a = -16 and b = 96 and c = 112
To find the time to reach maximum height, we will use the vertex formula which is; -b/2a
t_max = -96/(2 × -16)
t_max = 3 seconds
Thus, maximum height will be at t = 3 secs
Thus;
h_max = h(3) = -16(3)² + 96(3) + 112
h_max = -144 + 288 + 112
h_max = 256 ft
Time for it to hit the water means that height is zero.
Thus;
-16t² + 96t + 112 = 0
From online quadratic formula, we have;
t = 7 seconds
simplify 12p + 15 - 13- 12p
Answer: 2
Step-by-step explanation:You have to combine like terms
Answer:
the answwer is D
Step-by-step explanation:
hope it helps
