We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression. We take out brackets by expanding them, often known as multiplying out. It is the factorization procedure in reverse.
(t -t2)(t +5)(t-4) (t-4)
Replacing it with: f(t) = (t -t2)(t +5) (t-4)
Instead, resolve: d/dt ((t -t2)(t +5)(t-4) )
Solution:
(t -t2)(t +5)(t-4) (t-4)
Expand:
(t -t2) (t +5) (t-4) ; t³ - t²- 22t + 40
Steps:
(t -t2)(t +5)(t-4) (t-4)
Parentheses distributed as: t ²t+ t² (-4)+3tt+3t(-4)-10t-10t-10(-4)
Reduce t ²t+ t² (-4)+3tt+3t(-4)-10t-10t-10(-4);
t³-t²-22t+40.
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Stephanie is collecting data on the reaction of bacteria to different antibodies. She did not measure the area of the bacteria in the dish when she began the experiment but measured 20 cm2 of bacteria after 1 hour. She continued to measure the bacteria each hour and entered the data in the table. show the explicit function. How much area would you predict the bacteria to have when measured during the 5th hour?
We take a look at the reduction in the area of the bacteria.
In the first hour, its arae is 20cm2. Following that, it reduces 1.25x, to 16. Then another 1.25x, from 16 to 12.8. And another 1.25x, from 12.8 to 10.24.
So, every hour, the bacteria's area reduces by 1.25x
Therefore, in the 5th hour (prediction probably if this is all a coincidence), the bacteria's area will be : 10.24 : 1.25 = 8.192 cm2.
A bus carrying students stops every 30 minutes between 6am and 11am.students arrive at the bus top at random times. the time that a student waits is uniformly distributed from 0-30 mins. 1. calculate the area under the curve 2.calculate the mean 3.calculate the standard deviation 4.what is the probability that a student will wait more than 25 mins for a bus?
Using the uniform distribution, it is found that:
1. The area under the curve is of 1.
2. The mean is of 15 minutes.
3. The standard deviation is of 8.7 minutes.
4. The probability that a student will wait more than 25 mins for a bus is of 1/6.
What is the uniform probability distribution?The uniform distribution has two bounds, given by a and b, in which each possible outcome is equally as likely.
The area under the curve gives the sum of the probabilities of all outcomes, hence it is of 1, as the sum of the probabilities is of 1 = 100%.
The time that a student waits is uniformly distributed from 0-30 mins, hence the bounds of the interval are given by:
a = 0, b = 30.
The mean is given by:
M = (a + b)/2 = 30/2 = 15 minutes.
The standard deviation is given by:
[tex]S = \sqrt{\frac{(b - a)^2}{12}} = \sqrt{\frac{900}{12}} = 8.7[/tex]
The probability of finding a value higher than a measure x is given by:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Considering the bounds in this problem, the probability that a student will wait more than 25 mins for a bus is:
P(X > 25) = (30 - 25)/(30 - 0) = 5/30 = 1/6.
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This is the graph of f(x). What is the value of f(2)?10 УA. 6ОВ. 2С. 5ООD. 9
To solve this problem we must take into account that the y-axis has intervals of 2 units length, and the x-axis has intervals of 1 unit length. We want to know the value of the function when x = 2, so we look for that value of x in the x-axis, we trace a vertical line from x = 2 to the curve that represents the function, and then a horizontal line to the y-axis, and we read the value of y:
Answer: D. 9
You are going to the carnival and your guardians said you can spend no more than $24 on rides. if rides cost $0.75 each, how many rides can you go on?
If a rectangle is 13 units wide and x units long what is the area
The area of Rectangle is 13x (13*x)
How to find area of rectangle ?
The formula of Area of Rectangle is A = W*L
A = area
W = width
L = length
so , to find area of rectangle
we have wide of 13 units , length x units
apply this in formula,
a = 13*x
so the area =13x
Some formulas of rectangle :
Area a = length * widthPerimeter p = 2( l +w)Diagonal d = [tex]\sqrt{W^{2} + L^{2} }[/tex]To learn more about find about rectangle refer :
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A used car was bought for $15,000. When the car was new, it sold for
$25000. If the car depreciates exponentially at a rate of 6% per year, approximately
how old is the car?
Answer:
around 6.66 year old
Step-by-step explanation:
The area of a circular rug is 78.5ft. What is the diameter of the rug, to the nearest whole foot?
area = 78.5 ft squared
diameter = ?
[tex]\begin{gathered} \text{area of a circular rug=}\pi r^2 \\ 78.5=3.14\times(\frac{d}{2})^2 \\ 78.5=3.14\times\frac{d^2}{4} \\ 78.5=\frac{3.14d^2}{4} \\ \text{cross multiply} \\ 3.14d^2=314 \\ d^2=\frac{314}{3.14} \\ d^2=100 \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]
An ice cube has lengths 25mm.
It has a mass of 2.325g.
Work out the density in g/cm³.
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
-10 9
Click twice to plot each segment.
Click a segment to delete it.
34
8
Answer:
slope = rise /run
Step-by-step explanation:
hysnsk
What property is illustrated in the
example below?
94 (x + 2) = 94x + 188
A. Associative
B. Distribuive
C. Commutative
Answer:
B. Distributive
Step-by-step explanation:
Hello, there!
The number outside of the parentheses are being multiplied within the parentheses separated by a symbol, so distributive. (:
Hope this helped, and best of luck with the rest of your assignment.
through (-3,5), slope=4 slope intercept
The most appropriate choice for equation of line in slope intercept form will be given by-
y = 4x + 17 is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope = 4
The line passes through (-3,5)
Equation of line = y - 5 = 4[x - (-3)]
y - 5 = 4x + 12
y = 4x+ 12 + 5
y = 4x + 17
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9. Brenna wants an easier way to write 0.0000000000000000587.
0.0000000000000000587 is written as______
x 10____
in scientific notation.
Answer:
5.87 x [tex]10^{-17}[/tex]
Step-by-step explanation:
You need to write the number as 1 or larger than 1, but less than 10. That means that I need to put the decimal between the 5 and the 8. Now I have to count how many places I moved the decimal. I think that I counted right. It was moved 17 places. Since the number in standard form is much smaller than 5.87, the exponent will be negative.
Kiersti drove 58 mph for 1 hour and 52 minutes. Estimate the distance she traveled
Answer:
110 miles
Step-by-step explanation:
58 (1 + 52/60)
= 58 (1 + 13/15)
= 58 + 50.267
= 108.267 miles
= approximately 110 miles
help pls due tmrw..pls
1) The equation of line is; y = (1/3)x + 1
2) The x - intercept is -3 and the y-intercept is 2
3) Area of CAT is; 6 sq.units
4) Perimeter is; 14.325 units
What is the equation of the Line?
1) The coordinates of the line AC on the graph are;
A(-3, 0) and C(3, 2)
Thus, equation of line is gotten from the formula;
(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)
(2 - 0)/(3 + 3) = (y - 0)/(x + 3)
2/6 = y/(x + 3)
3y = x + 3
y = (1/3)x + 1
2) The x - intercept is -3 and the y-intercept is 2
3) Area of CAT is;
Area = 1/2 * base * height
Area = 1/2 * 6 * 2
Area = 6 sq.units
4) Perimeter of ACT is gotten by;
AT + CT + AC
AC = √((2 - 0)² + (3 + 3)²)
AC = √40
Thus;
Perimeter = 2 + 6 + √40
Perimeter = 14.325
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Open Ended You are given the point Q(-2,-5), A. Identify a point (x, y,) that along with point Q defines a line with a positive slope.
Slope m is positive when
x₁≥ -2
y₁ ≥ -5
Define slope.Slope, usually referred to as rise over run, is the "steepness" of the line. By dividing the difference in y values between two points by the difference in x values, we may determine slope. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope, if you view the line from left to right.
Given,
Point (-2. -5)
Slope = [tex]\frac{y_{1}-(-5) }{x_{1}-(-2) }[/tex]
Slope = [tex]\frac{y_{1}+5 }{x_{1}+2 }[/tex]
Slope m is positive when
x₁≥ -2
y₁ ≥ -5
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Graph of the function
f(x) = -x² - 4x - 1 is the equation of the parabola in the graph.
What is the equation of the graph?From the graph, the parabola passes through point (-1,2) and has a vertex at point (-2,3).
For a parabola with a vertex (h,k), the general equation is expressed as;
y = a( x - h)² + k
First we find 'a', plug in the given coordinates into the equation.
y = a( x - h)² + k
2 = a( -1 - (-2))² + 3
Solve for a
2 = a( -1 + 2 )² + 3
2 = a( 1 )² + 3
2 = a + 3
a = 2 - 3
a = -1
Now substitute the vertex (-2,3 and a ( -1 ) into the general equation.
y = a( x - h)² + k
y = -1( x - (-2))² + 3
Simplify
y = -1( x + 2 )² + 3
Expand using FOIL method
y = -1( (x + 2)(x+2) ) + 3
y = -1( x² + 2x + 2x + 4 ) + 3
y = -1( x² + 4x + 4 ) + 3
Apply distributive property
y = -x² - 4x - 4 + 3
Add like terms
y = -x² - 4x - 1
f(x) = -x² - 4x - 1
Therefore, the equation of the graph is f(x) = -x² - 4x - 1.
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Seth traveled 1 mile in 57.1 seconds.About how fast does seth travel in miles per hour.
Show your work its about unit rates
Answer:
63.04728546 miles an hour
Step-by-step explanation:
to figure out how many miles an hour Seth travels we are gonna start with how far he goes in one min.to do that we are gonna do 60÷57.1 ( we do this to figure the distance he goes in a minute)60÷57.1=1.050788091Now we know he travels 1.050788091 in one minutewe know that there are 60 mins in an hour so we are gonna multiply that but the miles a second60×1.050788091=63.04728546If you need to figure out any other unit of measurement an hour you do it like this:example: we need to convert miles to kmwe know that 1 mile is 1.60934 kmso we do 1mile in 57.1 seconds is 1.60934km in 57.1 seconds then do the steps aboveI recommend that you do the conversion in the beginning so you don't have to handle really big decimalsif you dilate something by 1 half, what would you have to dilate it to to get it back to the same number.
If I dilate a number by 1 half, then I will have to dilate it again by 2, to get the same to the same number.
As per the question statement, I dilate a number by 1 half.
We are required to calculate that by what should I dilate the result, to reverb back to the same number that I started with.
To solve this question, first we need to understand the concept of Dilation.
Dilation means to create an Image.If dilation of a number or object enlarges it, then it is known as enlargement.On the other hand, if dilation creates a smaller image, then it is known as Reduction.Here, since our first dilation of the original number, say "x" reduces it by 1 half, that is, x becomes (x/2),
To get back to x, we will need to multiply (x/2) by 2 again.
[(x/2) * 2] = x.
Therefore, I will need to enlarge our result with a multiplication with 2 to get back to our original number.
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write 4 2/4 as an improper fraction
Tell whether the events are independent or dependent. Explain.You throw the bowling ball at the pins.You have two throws to knock down ten pins.First throw:You knock down 6 pins.Second throw:You knock down 1 pin.
Given
You throw the bowling ball at the pins.You have two throws to knock down ten pins.
Procedure
The events are not independent. Before the first throw, there will be 10 pins to knockdown. Let the number of pins knocked down in the first throw is x.
In the second throw, there will not be 10 pins to knockdown. The number of pins to knockdown in the second throw depends on the number of pins being knocked down in the first throw. Hence, the number of pins to knockdown in the second throw is (10 - x). Thus, the events are dependent
(2x+5)(4x-3) find the product
[tex]2x(4x - 3) + 5(4x -3 ) \\ = {8x}^{2} - 6x + 20x - 15 \\ = 8 {x}^{2} + 14x - 15[/tex]
ATTACHED IS THE SOLUTION
Answer:
I think it would be 8x2^ + 14x − 15
a fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes. assume that this claim is true.one percent of response times take at least how many minutes?
If this claim is true then one percent of response times take at least [tex]38.077[/tex] minutes.
In the given question,
A fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes.
We have to assuming that the claim is true and finding that one percent of response times take at least how many minutes.
From the question,
Mean [tex]\mu=22[/tex] minutes
Standard deviation [tex]\sigma=6.9[/tex] minutes.
Since the given percentage is [tex]1\%[/tex] and percentage means division of [tex]100[/tex] so we can write [tex]1\%=1/100=0.01[/tex]
So the one percent of response times take at least how many minutes is
[tex]P(x\geq a)=0.01[/tex]
[tex]P(x\geq \frac{a-\mu}{\sigma})=0.01[/tex]
As we know the all values. SO putting the values in the formula
[tex]P(x\geq \frac{a-22}{6.9})=0.01\dots\dots[/tex]Equation 1
From the z table
[tex]P(z\geq 2.33)=0.01\dots\dots[/tex]Equation 2
Now from Equation 1 and Equation 2
[tex]\frac{a-22}{6.9}=2.33[/tex]
Multiply by [tex]6.9[/tex] on both side
[tex]\frac{a-22}{6.9}\times6.9=2.33\times6.9[/tex]
Simplifying
[tex]a-22=2.33\times6.9[/tex]
[tex]a-22=16.077[/tex]
Add [tex]22[/tex] on both side
[tex]a-22+22=16.077+22[/tex]
[tex]a=38.077[/tex]
Hence, if this claim is true then one percent of response times take at least [tex]38.077[/tex] minutes.
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Write an equation in slope-intercept form for the line with slope 1/3 and y-intercept -7 then graph the line
The equation of the line is y = 1/3x - 7
The definition of linear equationsLinear equations are equations that have constant average rates of change.
How to determine the equation of the line?The given parameters are
Slope, m = 1/3
y-intercept, c = -7
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = mx + c
Where m = 1/3 and c = -7
So, we have
y = 1/3x - 7
Hence. the linear equation is y = 1/3x - 7
See attachment for the graph
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Which dimensions cannot create a triangle?
three angles measuring 10 degrees, 25 degrees, and 145 degrees
three sides measuring 9 m, 15 m, and 9 m
three angles measuring 40 degrees, 70 degrees, and 65 degrees
three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
10,25, and 145
Step-by-step explanation:
to see if it can make a triangle you have to add 2 of the angles together and it has to be more than the other angle
(ex:40+70>65)
a triangle
(ex:10+25<145)
not a triangle
A bus driver makes $14 per hour and works 2,000 hours each year. He
also gets a fee of $50 for each new driver he recruits. If the bus driver
recruits 7 new drivers, what are his total earnings?
The total earnings of the bus driver in a year is $28500.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The bus driver works 2000 hours each year and makes $14 per hour.
If the bus driver gets $50 for each new recruit he hired.
Let y be his total earnings and x be the number of new drivers he recruits.
Then his total earnings can be represented by the function:
y = 14 × 2000 + 50 × x
If the bus driver recruits x = 7 new drivers.
y = 28000 + 50 × 7
y = 28000 + 350
y = $28350
The total earnings of the bus driver are $2850.
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Can someone pls help me right quick what’s the answer
Answer:
3rd one
Step-by-step explanation:
if h (x) = 2x2 - 5x + 7, find the value of h (-3)
^ (to the second power)
By evaluating h(x) in x = ^-3 and then squaring it, we will see that:
h(-3) = 1,600
How to fid the value of h(3)^2?
Here we have the function:
h(x) = 2x^2 - 5x + 7
First let's evaluate it in x = -3, to do so we just need to replace the variable x by the number 3, we will get:
h(-3) =2*(-3)^2 - 5*-3 + 7
h(-3) = 2*9 + 15 + 7 = 18 + 15 + 7
h(-3) = 40
Now we square it:
h(-3)^2 = 40^2
h(-3)^2 = 1,600
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Analiza lo siguiente ¿qué sucede si divides el número acumulado del año 2 entre el
dinero del año 1, posteriormente divide la cantidad acumulada del año 3 entre la
cantidad acumulada del año 2 y así sucesivamente?
Answer:
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
There are 4 Proof and statements that I need. Given AC=BD, and AB and CD bisect each other. Prove:
Given AC=BD.It is also said AB and CD bisect each other.
Since AB and CD bisect each other at O, we can write
AO=OB
CO=OD
Since the three sides of triangle AOC is equal to the corresponding sides of triangle BOD, both the traingles are congruent.
The angles opposite to equal sides of triangles are also equal.
Since AO and
how many different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it?
10 different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it
What is permutation and combination?Permutations and combinations are the many methods for picking objects from a set to form subsets, usually without replacing them. When the order of selection is a factor, this selection of subsets is known as a permutation; when the order of selection is not a factor, this selection of subsets is known as a combination.
CalculationI think it is only 10 ways.
Put the teal bead on first. It is the marker bead. This takes care of the rotation aspect.
Then you have 2 lots of 3 identical beads. so that is 6!/(3!3!) ways to place them. Which is 20 ways.
But the bracelet can be flipped so I think this will halve the number of possibilities
For instance TOOOBBB is the same as TBBBOOO
So I think the answer is 10 ways.
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