Answer:
Factored form: [tex](x-3)(x+1)(x^2+9)[/tex]
Expanded form: [tex]x^4-2x^3+6x^2-18x-27[/tex]
Step-by-step explanation:
[tex](x-3)(x+1)(x^2+9)[/tex]
[tex](x^2-2x-3)(x^2+9)[/tex]
[tex]x^4+9x^2-2x^3-18x-3x^2-27[/tex]
[tex]x^4-2x^3+6x^2-18x-27[/tex]
[tex]x-3=0[/tex] has a solution of [tex]x=3[/tex]
[tex]x+1=0[/tex] has a solution of [tex]x=-1[/tex]
[tex]x^2+9=0[/tex] has a solution of [tex]x=\pm 3i[/tex]
The graph represents an object that is shot upwards from a tower and then falls to the ground.
1. How tall is the tower from which the object was shot?
2. When did the object hit the ground?
3. Estimate the greatest height the object reached and the time it took to reach that height. I indicate this situation on the graph.
Answer:
1: The tower is around 93 meters tall. 2: The object hit the ground at 6 seconds. 3: 3 seconds to get to about 93 meters up.
Step-by-step explanation:
1: The tower is around 93 meters tall.
2: The object hit the ground at 6 seconds.
3: the time it took to reach that height is 3 seconds to get to about 93 meters up.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Linear function is a function whose graph is a straight line
1. Since the shot was made from the top of the tower, the starting height of the object (time zero) is equal to the height of the tower.
It represent in the graph by the y-intercept of the function, that is, the value of y when x=0.
The y-intercept is at (0,10) which shows that the height of the tower is 10m
2. The point where the object hit the ground, the height is zero meters, thus
The coordinates of the x-intercept are (6,0)
This shows that the object hit the ground 6 seconds after being shot.
3.The y-coordinate of the vertex shows the highest point of the object, which is 93 meters.
The x-coordinate of the vertex shows the time it took the object to reach said height, which is 2.8 seconds
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46. A sphere shaped bowl has a radius of 5.5 inches How much water can the bowl hold? Round to the nearest tenth.
Answer:
try 17.89 cm..then 18 for answer
In ΔMNO,
m
∠
M
=
(
6
x
+
1
)
∘
m∠M=(6x+1)
∘
,
m
∠
N
=
(
3
x
−
10
)
∘
m∠N=(3x−10)
∘
, and
m
∠
O
=
(
x
+
19
)
∘
m∠O=(x+19)
∘
. Find
m
∠
N
.
m∠N.
Answer:
Step-by-step explanation:
All the angles in a triangle add up to 180°
So you need to add up all your angles and set them equal to 180°
angleM + angleN + angleO=180
(6x+1) + (3x-10) + (x+19)= 180
We don't actually need all these parentheses; this is all just addition and subtraction.
6x+1+3x-10+x+19 =180
Add all the x terms together. Add all the constants (plain numbers) together.
10x + 10 =180
Subtract 10 from both sides
10x =170
Divide by 10.
x = 17
But you need one more step because if you reread the question, you are being asked for the measure of angle N, which is 3x - 10
3*17 - 10 =
51 - 10 =
41
The measure of angle N is 41°
Is -4 a real or imaginary number?
Answer:
Real number
Step-by-step explanation:
Unless it has an i with it then it's an imaginary number but because it doesn't have an i with it it's real
Answer:
real number
Step-by-step explanation:
Hi! -4 is a real number because imaginary numbers are characterized as i= sqrt -1
If you see a number with an i in it, then it is imaginary. In this case, however, we have a real number.
I hope this helps!
1 6. ) b) The weight of an object on moon is 1/6 of its weight on Earth. If weight of an object on Earth is 18/5 kg, what would be its weight on moon? Plzz help me
Answer:
Solution given:
weight of moon=1/6 th of Earth
If weight of Earth is 18/5 kg
weight of moon=?
we have
weight of moon: 1/6 of weight of Earth
=1/6*18/5
=3/5kg
Its weight on moon is 3/5 kg
how do you write 8.16 × 101 in standard form?
What is the common denominator of y StartFraction y minus 3 Over 3 EndFraction in the complex fraction y StartFraction y minus 3 Over 3 EndFraction divided by five-ninths StartFraction 2 Over 3 y EndFraction?.
The common denominator of the given expression is [tex]5y+6.[/tex]
Given expression,
[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }[/tex].
We have to find the common denominator.
On solving the numerator and denominator of the given expression,
[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{\frac{3y+y-3}{3} }{\frac{5y+6}{9y} }[/tex]
[tex]= \dfrac{\frac{4y-3}{3} }{\frac{5y+6}{9y} }[/tex]
[tex]= \dfrac{4y-3}{3} \times\dfrac{9y}{5y+6}[/tex]
Or,[tex]\dfrac{y+\frac{y-3}{3} }{\frac{5}{9} +\frac{2}{3y} }= \dfrac{3y(4y-3)}{5y+6}[/tex]
Hence the common denominator of the above expression is given by [tex]5y+6.[/tex]
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Answer:
Not A 3y(y – 3)
Not B y(y – 3)
it is either C 3Y or D 3
Need some help with this one.
Answer:
y = -3x + 7
Step-by-step explanation:
Answer:
y = -3x + 7 (above)
Step-by-step explanation:
To add on, the person above me is correct. The equation of the line is in mx + b, where m is slope and b is the y-intercept.
We see the line intercepts the y axis at (0,7). Therefore the equation is y= mx +7
Now we look for m, the slope. If you may remember slope is also change in y over change in x, or rise/run. If you look at the graph, for each unit to the right, the line drops 3 units(it goes down, so negative). Therefore the slipe would be -3/1, or -3.
Plugging that in,
y = -3x + 7
Which expression is equivalent to 7x + 5x?
a. 12x
b.12x^2
c. 35x
d. 35x^2
Answer:
12x
Step-by-step explanation:
make t the subject q= 1+3t/2-t
Answer:
t = dfrac-1 + 2 q3 + q.
Step-by-step explanation:
Matthew spent 2/3 of his birthday on books and 1/4 of his birthday money on snacks. He says he spent 3/7 of his birthday money.
Which statement is most accurate?
*Disclaimer* show work
Answer:
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{8+3}{12}[/tex] = [tex]\frac{11}{12}[/tex] ≈ 1
The correct answer is the last one (C)
Evaluate the numerical expression 24
Enter your answer in the grid below.
Answer:
what grid below
Step-by-step explanation:
Answer:
what grid below
Step-by-step explanation:
Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It costs a player £1.40 for a turn.A player can win £6 or £3 as in the diagrams:If 216 people are to play, how much profit can Ayo expect to make?
Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.
The expected value is given by the sum of each outcome multiplied by it's respective probability.
In this problem:
The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is [tex]\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}[/tex].The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is [tex]\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}[/tex]In the other cases, Ayo wins £1.40, with [tex]1 - \frac{18}{72} = \frac{54}{72}[/tex] probability.Hence, his expected profit for a single game is:
[tex]E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583[/tex]
For 216 games, the expected value is:
[tex]E = 216(0.2583) = 55.8[/tex]
Ayo can be expected to make a profit of £55.8.
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what is the equation of the line with slope -7 which goes through the point (2,5)
Answer:
y=-7x+19
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-7(x-2)
y=-7x+14+5
y=-7x+19
The equation of the line with slope - 7 which goes through the point (2, 5) is
y = - 7x - 19.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line passes through points (2, 5) with a slope of - 7.
∴ 5 = -7(2) + b in slope-intercept form.
5 = - 14 + b.
b = - 19.
y = - 7x - 19.
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16. If a triangle has two side lengths of 8 inches and 23 inches, describe the possible lengths for the third
side?
Answer:
24
Step-by-step explanation:
Anya purchased $124.35 worth of home improvement items at the hardware store. If the sales tax rate in her city is 6.75%, what is the total cost of her purchase?
Answer:
$132.74
Step-by-step explanation:
6.75% = 0.0675
Multiply 124.35 by 1.0675 because sales tax is added to original cost.
(124.35)(1.0675) = 132.74
The total cost of Anya's purchase of home improvement hardware is 132.74 dollars.
What is percentage?The percentage is the value per hundredth.
According to the given question, the sales tax is 6.75% which is not included in the home improvement hardware which cost Anya 124.35 dollars.
∴ The total cost of Anya's purchase including the sales tax is ( 100 + 6.75)% = 106.75% of 124.35 dollars which is,
= (106.75/100)×124.35 dollars.
= 1.0675×124.35 dollars.
= 132.74 dollars.
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how do you write 100 s a fraction, mixed number, or whole number
X=?
38 degrees 75 degrees
Answer:
67
Step-by-step explanation:
pls help me with this:((((
If measure of angle 3 = 74° find each measure NEED HELP ASAP
What is 1+1 equal? Explain in paragraph form! 5 or more sentences!
Point A=(7,9) is dilated from the origin by scale factor of r=11. what are the coordinates of point A
Answer:
42 and 54
Step-by-step explanation:
Asha bought 60 fruit baskets.
25% of the fruit baskets have 12 pieces of fruit in each basket.
The remaining 75% of the baskets have 15 pieces of fruits in each basket.
Answer:
Answer: 855
Step-by-step explanation:
I take it you want the total number of fruit? You should state the question. I will assume I am correct.
So 25% of 60 baskets = 25/100 * 60 = 15 baskets.
Each basic contains 12 pieces of fruits 12 * 15 = 180
And 75% of 60 baskets = 0.75 * 60 = 45 baskets.
Each contains 15 pieces 45 * 15 = 675
The total number of fruit in all is 855
Solve for X. Please help ASAP.
Answer:
x = 36.87
Step-by-step explanation:
Find the length of the missing side.
x^2 + 12^2 = 15^2
x^2 + 144 = 225
x^2 = 81
x = 9
Now use the law of sines:
sin(90)/15 = sin(x)/9
Multiply each side by 9
9 * sin(90)/15 = sin(x)
0.6 = sinx
sin^-1 = 36.86989 rounded to 36.87
What’s the slope of a line that goes through (0,2)(7,5)
Answer:
slope = 3/7 or 0.43
Step-by-step explanation:
use the slope(gradient) formula
Need some help :(
A)12.7
B)13.3
C)12.4
Answer:
i am just here for points
Step-by-step explanation:
Please help Question in picture
Also could you please dm me on insta gram: yourdealerjeremi
I need some help with a few more questions but im out of brainly points
Answer:
10,9
Step-by-step explanation:
On the coordinate plane you see that the point A has to go 6 to the right and 3 up. So the ratio is: for every 2 side, there is one up. Point A does this 3 times to get to M so do three times. 6 to the right and 3 up and B is on 10,9.
Triangle J K L is shown. Point M is the midpoint of side K L and point J is the midpoint of side J L. The length of K J is 12. 8 meters, the lengths of J N and N L are 3. 7 meters, and the lengths of K M and M L are 5. 9 meters. Which statements about triangle JKL are true? Select two options. M is the midpoint of line segment KJ. N is the midpoint of line segment JL. MN = One-halfKJ MN = 4. 4m MN = ML.
The true statements are: M is the midpoint of line segment KJ and N is the midpoint of line segment JL
The given parameters are:
[tex]KJ = 12.8m[/tex]
[tex]JL = 7.4m[/tex]
[tex]KL = 11.8m[/tex]
From the figure (see attachment), we have the following highlights
Either sides of point M on line segment KL is 5.9 metersEither sides of point N on line segment JL is 3.7 metersThe midpoint of a line segment divides the line segment into equal halves.
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Answer:
Correct answer is A & B on edge
Step-by-step explanation:
7. What is the slope of the line that goes through (0,0) and (5, -1)7
1/2
-1/2
2
-2
Answer:
-1/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-0)/(5-0)
m=-1/5
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 5 hours of burning, a candle has a height of 26 centimeters. After 24 hours of burning, its height is 14.6 centimeters. What is the height of the candle after 18 hours?
Answer:Let Y = height
Let X = time
Height is a linear function of time, so Y = mX + b, where m is the slope and b is the y-intercept.
We can calculate the slope from the given values (8,20.4) and (19,18.2)
Slope = (y2 - y1) / (x2 - x1) = (18.2 - 20.4) / (19 - 8) = -2.2 / 11 = -0.2
This means that the height of the candle is going down by 0.2 cm per hour
Since 16 hours is 8 hours after the first data point of (8,20.4), the height will go down by 8 * (-0.2) = -1.6 cm in the 8 hours between hour 8 and hour 16.
So the height of the candle after 16 hours = 20.4 - 1.6 = 18.8 centimeters
Step-by-step explanation: