Hi there!
[tex]\large\boxed{(x -3)(x + 2)(x + 1)}[/tex]
We can use long division to find the other roots of p(x).
We know that x + 1 is a factor, so:
Set up:
Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.
x² - x - 6
x + 1 | x³ + 0x² - 7x - 6
x³ + x²
0 - x² - 7x
- x² - x
0 - 6x - 6
-6x - 6
0 0
Therefore, x² - x - 6 is another factor. We can factor this further:
Find two numbers that add up to -1 and multiply into -6. We get:
-3, 2
(x - 3)(x + 2)
The entire polynomial factored is:
(x -3)(x + 2)(x + 1)
There is a rack of 15 billiard balls. Balls numbered 1 through 8 are solid-colored. Balsa numbered 9 through 15 contain stripes. If one ball is selected at random, determine the odds for it being striped.
If one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
What do we know?
We know that there are 15 billiard balls.
We also know that balls numbered 1 through 8 are solid-colored, so we have 8 solid-colored balls.
And the other 7 balls are striped.
Now we want to find the probability for a randomly selected ball to be a striped ball.
Because all the balls have the same probability of being randomly selected, the probability of randomly selecting a striped ball is equal to the quotient between the number of striped balls (7) and the total number of balls (15).
Then we have:
P = 7/15 = 0.467
That quotient is also what is called the "odds"
So if one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
If you want to learn more, you can read:
https://brainly.com/question/23044118
The soil samples for the next field indicate that fertilizer coverage needs to be
greater. To achieve this, you need to increase flow rate. How would you achieve
this?
A. Increase speed to approximately 7.1 mph so that you cover the field more
quickly
B. Increase the engine speed to approximately 2,000 rpm
C. Decrease speed to approximately 6.0 mph so that you cover the field more
slowly
D. Shift to second gear so that the engine speed slows
Answer:
A. Increase speed to approximately 7.1 mph so that you cover the field more.
Step-by-step explanation:
The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.
A sample of 34 observations is selected from a normal population. The sample mean is 15, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 14 H1: μ > 14
Required:
a. Compute the value of the test statistic.
b. What is the p-value?
Answer:
1.944 ;
0.026
Step-by-step explanation:
Given :
Sample size, n = 34
Sample mean, xbar = 15
Population standard deviation, σ = 3
The hypothesis :
H0: μ ≤ 14
H1: μ > 14
The test statistic :
Test statistic = (xbar - μ) ÷ (σ/√(n))
Test statistic = (15 - 14) ÷ (3/√(34))
Test statistic = 1 / 0.5144957
Test statistic, Z = 1.944
The Pvalue :
Using the Pvalue from test statistic value :
Pvalue(1.944) = 0.026
Pvalue < α ; Reject H0
If the cost, C, for manufacturing x units of a certain product is given by c=x^2-5x+65, find the number of units manufactured at a cost of 13,865.
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Answer:
120
Step-by-step explanation:
I find it pretty easy to obtain the solution by graphing ...
c(x) -13865 = 0
The positive value of x that makes this so is x = 120.
120 units will have a cost of 13,865 to manufacture.
__
If you like to solve this algebraically, you can probably do it most easily by completing the square.
x^2 -5x = -65 +13865
x^2 -5x +6.25 = 13806.25 . . . . . add the square of (-5/2)
(x -2.5)² = 13806.25
x -2.5 = √13806.25 = 117.5 . . . . only the positive square root is interesting
x = 117.5 +2.5 = 120
Given the similarity statement
AJKL ANOP, what's the
corresponding side of ON ?
Answer:
ON = KJ
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
We are looking for ON = KJ
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Answer:
(d) KJ
Step-by-step explanation:
The segment of interest is named using the 2nd and 1st letters of the right side of the similarity statement.
The corresponding segment will be named using the 2nd and 1st letters of the left side of the similarity statement: KJ.
The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 12 cm and the width is 8 cm, how fast is the area of the rectangle increasing
Answer:
Step-by-step explanation:
This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.
We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is
[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:
[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:
The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];
the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];
and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:
[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and
[tex]\frac{dA}{dt}=72+56[/tex] so
[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]
Which best describes the relationship between the line that passes through the points (6, –1) and (11, 2) and the line that passes through the points (5, –7) and (8, –2)?
A. same line
B. neither perpendicular nor parallel
C. perpendicular
D. parallel
Answer:
Step-by-step explanation:
slope of line through (6,-1) and (11,2) = (-1 - 2)/(6 - 11) = 3/5
slope of line through (5,-7) and (8,-2) = (-7 - (-2))/(8 - 5) = -5/3
product of the slopes = -1, so the lines are perpendicular.
Couldn’t figure this out help please
(B)
Step-by-step explanation:
Rewrite the equations into their standard forms. The first one can be rewritten as
[tex]10x - 12y = -5[/tex]
and the 2nd can be rewritten as
[tex]3x + 5y = -1[/tex]
Solving this system either by substitution or elimination, we get
[tex]x = -\dfrac{37}{86}\:\:\text{and}\:\:y= \dfrac{25}{86}[/tex]
If you add x + y, you'll get a negative number.
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Answer:
B. x + y < 0
Step-by-step explanation:
The two equations can be cleared of fractions by multiplying by 15.
15(2/3(x +1) -4/5y) = 15(1/3)
10(x +1) -12y = 5
10x -12y = -5
and
15(2/5x +1/3(2y +1)) = 15(1/5)
6x +5(2y +1) = 3
6x +10y = -2
3x +5y = -1 . . . . . eliminate common factor of 2
__
You can find the solutions any way you like, but you can answer the question without doing that. The lines are not parallel, nor coincident, so there is exactly one solution. (choices C and D are incorrect)
If we can locate the solution relative to the line x + y = 0, we can tell if choice A or choice B is correct. A quick look at the intercepts of the equations tells us the solution cannot lie in quadrants 1 or 4. The negative y-intercept and shallow slope (-3/5) of the second equation tells us the solution must lie below the line x + y = 0. That means x+y < 0, choice B.
_____
In the attached graph, the line x+y=0 is dashed orange. Above that line, x+y>0; below that line, x+y<0. We see the intersection point of the red and blue lines is in the region where x+y < 0.
For standard form equation ax+by = c, the x- and y-intercepts are c/a and c/b, respectively, so are easy to find from that form. Knowing these makes it easy to make a sketch of the graph, locating the solution point relative to the line x+y = 0.
Solve the system using substitution. x+y=-2 and x-y=-8
Answer:
1) x+y=-2
x=-2-y
2) x-y=-8
substitude value of x
(-2-y)-y=-8
-2-2y=-8
-2y=-6
y=3
Substitute value of y in 1
x=-2-3
x=-5
Brainliest please~
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.
Group of answer choices
A. 0.1946
B. 0.1285
C. 0.1469
D. 0.1346
Answer:
b. 01285 esa es, espero este buena y que te ayude
Select the correct answer from each drop-down menu?
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Answer:
second3firstisStep-by-step explanation:
We observe that the second equation of System B has had the x-term eliminated. That can be accomplished by adding 3 times the first equation to the second.
"To get System B, the second equation in System A was replaced by the sum of that equation and 3 times the first equation. The solution is the same as the solution to System A."
Tony calculates that 3 cubic metres of concrete is enough for the path.
He decides to use a concrete mix which has:
• cement = 1 part
• sand = 2 parts
gravel = 3 parts
How many cubic metres of gravel does Tony need?
0.5
Answer:
1.5 cubic metres
Step-by-step explanation:
Given that in a concrete mix, cement makes up 1 part, sand makes up 2 parts and gravel makes up 3 parts.
The total number of parts = 1 + 2 + 3 = 6 parts.
The amount of marvel present the concrete mix = amount of marvel / total mix
= 3 parts / 6 parts = 1/2
Since 3 cubic metres of concrete is enough for the path, hence the amount of gravel needed is:
Amount of gravel = 1/2 * 3 cubic metres of concrete = 1.5 cubic metres
The product of two numbers is 60 and thei r sum is it, find the Numbers
PLEASE HELP WILL MARK BRAINLIEST! Also please explain the answer
Answer:
Each triangle is a right triangle.
Step-by-step explanation:
You can see each one has one 90 degree corner.
Answer:
13. True
14. True
15. False
Step-by-step explanation:
By using the Pythagorean Theorem a^2+b^2=c^2, you can evaluate whether or not the triangles are right triangles.
13. 8^2+15^2=17^2 -> 64+225=289 -> TRUE
14. 50^2+120^2=130^2 -> 2500+14400=16900 -> TRUE
15. 12^2+35^2=36^2 -> 144+1225 =/=1296 -> FALSE
50 POINTS PLEASE HELP ME
Hello!
f(g(x)) = 4 - 2 × (3x²) <=>
<=> f(g(x)) = 4 - 6x²
Answer: B. f(g(x)) = 4 - 6x²
Good luck! :)
Let we find the composition,
→ f(g(x)) = 4 (-2 × 3x²)
→ f(g(x)) = 4 -6x²
Hence, option (B) is the answer.
Marilyn is retiring and wants to set up a 25-year annuity with 140 000 of her savings . The annuity earns 7.7 compounded monthly How much will Marilyn receive every month ?
Answer:
marilyn isrestiring and wants to set up a 25-year annuity earns 7.
For the parallelogram, if m∠2=4x+30 and m∠4=2x+70, find m∠3.
Polynomial: 3x^4 + 5x - 4; Divisor: x - 1
Answer:
3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]
Step-by-step explanation:
You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.
Which answer explains the correct way to move the decimal to find the quotient of 14.6 ÷ 10,000?
three places to the right.
three places to the left.
four places to the left.
four places to the right
Answer:
Four places to the left.
Step-by-step explanation:
14.6/10000
=> 1.46/1000 [Shifted 1 decimal place after dividing by 10]
=> 0.146/100 [Shifted 1 decimal place after dividing by 10]
=> 0.0146/10 [Shifted 1 decimal place after dividing by 10]
=> 0.00146 [Shifted 1 decimal place after dividing by 10]
Number of decimal places = 1+1+1+1=4
Four places to the left.
In the picture below, which lines are lines of symmetry for the figure?
A. 1 and 3
B. only 3
C. 2
D. 1, 2, and 3
A line of symmetry would separate a shape to make multiple shapes that are exactly the same.
The answer is C.2
We are given both the slope and y-intercept so writing the equation in slope-intercept form is a breeze! Label both the slope and y-intercept and them substitute them into the general form of slope-intercept form. So, y=4x−3.
Answer:
below
Step-by-step explanation:
hope it is well understood?
The slope is 4 and y- intercept is 13
What is slope?A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
Given
Slope
y = 4x-3
dy/dx = 4
slope = 4
intercepts y = 4(4) 3
y = 16-3
y = 13
To learn more about slope refer to:
https://brainly.com/question/1570952
#SPJ2
what is 2 1/2 divided by 1/3 {pls hurry the teacher is not letting us use brainly}
Answer:
7 1/2
Step-by-step explanation:
2 1/2 ÷ 1/3
Change to an improper fraction
(2*1+2)/2 ÷ 1/3
5/2 ÷1/3
Copy dot flip
5/2 * 3/1
15/2
Change to a mixed number
7 1/2
Complete the square to solve the equation below.
Check all that apply.
x^2-10x-4=10
1. Move terms to the left side
2.Subtract the numbers
3.Use the quadratic formula
4.Simplify
5.Separate the equations
6.Solve
Rearrange and isolate the variable to find each solution.
Solution,
Solution
x=5±√39
On her summer abroad in France, Jane bought a pair of shoes for 54.82 euros. The store owner only had francs to give her as change. She gave him 55 euros. How much did he give her back in francs
Answer:
0.19
Step-by-step explanation:
Jane bought a shoe for 54.82 euros
She gave the store owner 55 euros
= 55-54.82
= 0.18 euros to franc
= 0.18× 1.08222
= 0.19 franc
What is the answer to this question in the picture
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Answer:
[tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]
Step-by-step explanation:
It's pretty straightforward. You want ...
f(x) - g(x)
Substituting the given function definitions gives ...
[tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]
I need help with this
Answer:
Statement A is correct
Step-by-step explanation:
Statement A is correct: Model A1 (0.25) is more prefered than Model C3 (0.15)
classmate Date 8) Solve the word problems a) If 576 balls are arranged in equal number of rows and columns, find the numbers of rows.
Answer:
24
Step-by-step explanation:
The number of rows (x) should b equal to the number of columns (x).
x²=576
x=√576 taking the square root of the product
x=24
If\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\]where $a$ and $b$ are integers and $b$ is as small as possible, find $a+b.$
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Answer:
12
Step-by-step explanation:
Apparently, you want the sum a+b when ...
[tex]\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\][/tex]
A calculator can show you the expression on the left evaluates to √243. In simplest terms, that is 9√3, so we have a=9, b=3 and ...
a+b = 9+3 = 12
Answer:
12
Step-by-step explanation:
A tent maker wishes to support a 8-ft tent wall by attaching cable to the top of it, and then
anchoring the cable 7 feet from the base of the tent.
How long of a cable is needed?
Round your answer to the nearest tenth of a foot.
Answer with a numeric value only. That is, do not include "ft" or "feet" with your response.
Cable
Ground
Answer:
10.6
Step-by-step explanation:
A simple sketch of the question would give a right angled triangle. So that we can easily apply the Pythagoras theorem to determine the length of the cable required.
Let the length of the cable required be represented by x.
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]7^{2}[/tex]
= 64 + 49
[tex]x^{2}[/tex] = 113
x = [tex]\sqrt{113}[/tex]
= 10.63
x = 10.6
The length of the cable required is 10.6 in feet.
The length of the cable needed to support the tenth wall is approximately 10.6 ft.
The situation forms a right angle triangle.
Right angle triangle:Right angle triangle has one of it side as 90 degrees.
Therefore,
The tent wall is the opposite side of the triangle.
The table feet from the base of the tent is the adjacent side of the triangle.
Using Pythagoras's theorem the cable needed can be found.
Therefore,
c² = 8² + 7²c² = 64 + 49
c = √113
c = 10.6301458127
length of the cable ≈ 10.6 feet
learn more on right triangle here: https://brainly.com/question/22734015
I need two examples of rounding to the thousandths place. SHOW ALL WORK!
Answer:
3.418
Step-by-step explanation:
3.4175
3.4178
u round if the number behind it is higher than 5
