9514 1404 393
Answer:
zeros: {-2, -1, 7}P(x) = (x +2)(x +1)(x -7)Step-by-step explanation:
Descarte's rule of signs tells you there is 1 positive real root. The rational root theorem tells you any real roots are factors of ±14, so will be ±1, ±2, ±7, or ±14.
We note that the sum of all coefficients is negative, so +1 is not a root.
We note that the sum of coefficients of odd-degree terms is 1-19 = -18, and the sum of coefficients of even-dgree terms is -4-14 = -18. These are the same value, indicating that -1 is a root. The corresponding factor is (x +1).
The result of dividing the factor (x+1) from the polynomial using synthetic division is shown in the first attachment. The coefficients found mean the quotient is ...
Q(x) = x^2 -5x -14
Factoring this using any method you like gives ...
Q(x) = (x +2)(x -7)
This means the full set of zeros is {-2, -1, +7} and the factorization is ...
P(x) = (x +2)(x +1)(x -7)
_____
Additional comment
My personal favorite method of finding the zeros is to let a graphing calculator show them to me. That result is shown in the second attachment.
solve the question
Answer:
40*40=1600
PLS MARK BRAINLIEST
Please answer the following.
Answer:
[tex] \sqrt{4 \times 5 + \sqrt{4 \times 9} } [/tex]
A pile of 15 boxes is 3 metres high. What is the depth of each box?
5 m
0.002 km
200 cm
200 mm
pls help
化學製程中溫度的影響 為研究化學製程中溫度對產量之影響,我們在 3 種溫度下各生產 3批產品,結果如下表。請建立 ANOVA 表。在 0.05 顯著水準檢定不同的溫度是否會影響平均產量。
溫度
50℃ 60 ℃ 70℃
產品1 14 20 13
產品2 15 11 18
產品3 12 15 16
Answer:
Step-by-step explanation:
產品 1 14 20 13
產品 2 15 11 18
產品 3 12 15 16
what percentage is the following 3 upon 4 of 3 upon 8
Step-by-step explanation:
the answer is in the image above
Step-by-step explanation:
3/4×3/8
9/32
9/32×100
~28%
pls help! show your work!
(3sqrt4)/(3sqrt5)
Answer:
3sqaure root 100/5
Step-by-step explanation:
It would look like this picture Below
If f(x) = 3x⁴ - 13x, find f(-2)
Answer:
answer is
74....................
Help. Volume question in math.
Answer:
c-635.25pi
Step-by-step explanation:
volume of cylinder is pi*radius squared*height(here they gave you the diameter so you'll have to divide it by 2 to get the radius)
so pi*(11/2)^2*21
and you end up with 635.25pi
please help me look at the photo!
When wiring a house, an electrician knows that the time she will take is given by the formula Time= 2 hours + 12 minutes per lightswitch. She charges her customers a call out fee of £35, plus £20 per hour. How much should a customer be charged for wiring a house with 10 lightswitches?
Answer:
Step-by-step explanation:
Time = 2 hrs + 12 min (10) = 4 hrs.
Cost = 35 + 20*4
Cost = 35+80
Cost = 115
9514 1404 393
Answer:
£155
Step-by-step explanation:
We can write the function describing the charges as a composition.
t(s) = 2 + 12/60s = 2 +s/5 . . . . . hours for s switches
c(h) = 35 +30h . . . . . . . . . . . . . charge for h hours
Then the charge for s switches is ...
f(s) = c(t(s)) = 35 +30(2 +s/5) = 35 +60 +6s
f(s) = 95 +6s . . . . . . . charge for installing s switches
The charge for 10 switches is then ...
f(10) = 95 +6·10 = 95 +60
f(10) = 155 . . . . pounds
The electrician should charge her customer £155 for wiring a house with 10 switches.
A cube with side lengths of 4 cm has a density of 3 grams/cubic centimeters. The mass of the cube is _____ grams?
9514 1404 393
Answer:
21 1/3 grams
Step-by-step explanation:
The mass is the product of the volume and the density. The volume of a cube is the cube of its edge dimension.
M = Vρ
M = (4 cm)³×(3 g/cm³) = 64/3 g
The mass of the cube is 64/3 = 21 1/3 grams.
When traveling to work, Cherise averages 60 miles per hour.Because of heavy traffic in the evening, she averages only 40 miles per hour. If the distance from home to work is 80 miles, how much longer does it take Cherise to make the drive home?
============================================================
Explanation:
The distance traveled is d = 80 miles.
When going to work, her speed is r = 60 mph. She takes t = d/r = 80/60 = 4/3 hours which converts to 80 minutes. Multiply by 60 to go from hours to minutes.
Notice how the '80' shows up twice (in "80 miles" and "80 minutes"). This is because traveling 60 mph is the same as traveling 1 mile per minute.
-----------------
Now as she's coming home, her speed becomes r = 40 and she takes t = d/r = 80/40 = 2 hours = 120 minutes.
The difference in time values is 120 - 80 = 40 minutes.
Her commute back home takes 40 more minutes compared to the morning drive to work.
What is an equation of the line that passes through the points (5, 0) and (-5, -8)
Answer:
Step-by-step explanation:
m = (y2-y1) / (x2-x1)
m = (-8-0) / (-5-5) = 4/5
note that it does not matter which points you chose to be second or first
then use slope point equation again it does not matter which point from the slope you use
y - y1 = m ( x - x1 )
y - 0 = 4/5 ( x - 5)
y = 4/5x -4
please if you find my answer helpful mark it brainiest
Use the digits 0 - 9 to fill in the blank.
[tex]243 \frac{1}{5} = blank[/tex]
Answer:
use 0-9 to fill in blanks
Step-by-step explanation:
write 145,567 in expanded notation
Answer:
100000+45000+500+60+7
A trailer is 22 feet long. 9 feet wide,
and 7 feet high. What is the volume of
the trailer?
Answer:
1386
Step-by-step explanation:
22 × 9 × 7 = 1386 cubic feet
Mass of a proton: 1.007825 units
Mass of a neutron: 1.008665 units
Calculate the mass Defect of 214 N has actual mass of 14.0031 u.
Given:-
mass of proton = 1.007825 umass of neuron = 2.008625 u .Actual mass = 14.0031 uTo find:-
The mass defect.Answer:-
Mass defect arises when the mass of the atom differs from the sum of masses of nucleons . As we know that the nucleus of an atom is made up of neutrons(n) and protons (p) , and the total mass of a atom is the mass of nucleons ( protons and neutrons ) as electrons have mass very low as compared to that of n or p .
If we denote mass number by [tex]\green{A}[/tex] , then ;
[tex]\implies A = n_{\rm neutrons} + n_{\rm protons} [/tex]
Let [tex] Z[/tex] be the atomic number, then ;
[tex]\implies n_p = Z [/tex]
So, the number of neutrons will be;
[tex]\implies n_n = (A-Z) [/tex]
Therefore total mass would be ;
[tex]\implies M = m_pZ +m_n (A-Z) [/tex]
Then the mass defect would be ,
[tex]\implies\underline{\underline{\green{ \Delta M = [Zm_p + (A-Z)m_n - M ] }}} [/tex]
where ,
[tex]Z [/tex] = atomic number[tex] A[/tex] = mass number[tex] m_p [/tex] = mass of a proton[tex] m_n [/tex] = mass of a neutron_______________________________________
Now we know that the Atomic number of Nitrogen is 7(Z) and its mass number is 14(A) .
Now substitute the respective values,
[tex]\implies \Delta M = 7(1.007825) + (14-7)1.008665 - 14.0031 \\ [/tex]
[tex]\implies \Delta M = 7.054775 + 7(1.008665) - 14.00 31 [/tex]
[tex]\implies \Delta M = 7.054775 + 7.060655 - 14.0031 [/tex]
[tex]\implies \Delta M = 14.11543 - 14.0031 [/tex]
[tex]\implies \underline{\underline{\green{ \Delta M = 0.11233 \ u }}}[/tex]
Hence the mass defect is 0.11233 u .
Also this mass defect appears as energy which is responsible for the binding of nucleons together.
and we are done!
Find all solutions to the equation.
cos^2 x +2cosx+1=0
[tex]x= \pi[/tex]
Step-by-step explanation:
[tex]\cos^2x+\cos x+1=0[/tex]
Let [tex]u= \cos x[/tex]
Then [tex]u^2+2u+1=(u+1)^2=0[/tex]
or
[tex]\cos x = -1[/tex]
This gives us [tex]x= \pi[/tex] or all integer multiples of [tex]\pi (n \pi)[/tex]
What is cos(A)? please explain
Answer:
cos(A) = adjacent side / hypotenuse
= 4/5
Answer:
[tex] \small \sf \: cos ( A ) = \green{ \frac{ 4}{ 5}} \\ [/tex]
Step-by-step explanation:
[tex] \small \sf \: cos ( A ) = \frac{ adjacent \: side }{ Hypotenuse} \\ [/tex]
Where, we have given
adjacent side is 4 Hypotenuse is 5substitute the values that are given
[tex] \small \sf \: cos ( A ) = \green{ \frac{ 4}{ 5}} \\ [/tex]
in which quadrant or axis will the poit lie if...
Step-by-step explanation:
a.fourth quadrent
b.third quadrent.
Rafael ate one-fourth of a pizza and Rocco ate one-third of it. What fraction of the pizza did they eat?
They ate
Answer:
7/12
Step-by-step explanation:
They ate 1/4 and 1/3
1/4 +1/3
Get a common denominator
1/4 *3/3 + 1/3 *4/4
3/12 + 4/12
7/12
Write as many observations as you can for 5k + 23 - 4
Answer:
5k+19
Step-by-step explanation:
Subtract 4 from 23
The mapping shows a relationship between input and output values.
Answer:
where is the photo
Step-by-step explanation:
Nikki grows 20 tomato plants.
She measures their heights to the nearest centimeter and writes them down.
15 14 12 17 18
11 16 14 21 19
10 16 16 13 17
9 15 20 19 9
Complete the frequency table.
Answer:
I found answer
Step-by-step explanation:
1) 9
2) 12
3)15
4)20
Which best explains whether or not ABC = LMN?
Answer:
If I've done it right the answer should be A, the figures are congruent because a 270 rotation about the origin a d a reflection of the x-axis
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For the following right triangle find the side length x
Step-by-step explanation:
everything can be found in the picture
Answer:
x=15
Step-by-step explanation:
Hi there!
We're given a right triangle with the measures of the 2 legs (sides that make up the right angle). We're also given the measure of the hypotenuse (the side opposite to the right angle) as x
We need to find x
The Pythagorean Theorem states that if a and b are the legs and c is the hypotenuse, then a²+b²=c²
Let's label the values of a, b, and c to avoid any confusion first
a=12
b=9
c=x
now substitute into the theorem
12²+9²=x²
raise everything to the second power
144+81=x²
add 144 and 81 together
225=x²
take the square root of 225
15=x (note: -15=x is technically also an answer, but since lengths cannot be negative, it's an extraneous solution in this case)
Therefore, the side length of x is 15
Hope this helps! :)
On a coordinate plane, a line goes through (negative 3, negative 3) and (negative 1, 5). What is the equation of the line parallel to the given line with an x-intercept of 4?
Answer:
4, -16
Step-by-step explanation:
PLEASE HELP! I'm lost. :(
In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean
µ = 520 and population standard deviation = 115.
What math SAT score is 1.5 standard deviations above the mean? Round answer to a whole number.
Answer:
A math SAT score of 693 is 1.5 standard deviations above the mean
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean µ = 520 and population standard deviation = 115.
This means that [tex]\mu = 520, \sigma = 115[/tex]
What math SAT score is 1.5 standard deviations above the mean?
This is X when [tex]Z = 1.5[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.5 = \frac{X - 520}{115}[/tex]
[tex]X - 520 = 1.5*115[/tex]
[tex]X = 693[/tex]
A math SAT score of 693 is 1.5 standard deviations above the mean
d= (r+c)t
how do i solve for t?
Answer:
[tex] { \tt{d = (r + c)t}}[/tex]
Divide ( r+c ) on both sides:
[tex]{ \tt{t = { \frac{d}{(r + c)} }}}[/tex]
Answer:
d / ( r + c) = t
Step-by-step explanation:
d = ( r + c ) t
Divide each side by ( r + c)
d / (r + c ) = ( r + c ) t / ( r + c)
d / ( r + c) = t