Which of the following polynomial equations has 1, 4, -5 as three of its roots?
x 2+4x-5=0
x 4+2x 3-5x+10=0
x 3-21x+20=0*
Answer: x³-21x+20=0
Step-by-step explanation:
To find which polynomial has 1, 4, -5 as the roots, all we have to do is equal each root to 0 and multiply all factors together.
1 is (x-1)=0
4 is (x-4)=0
-5 is (x+5)=0
Now, we just multiply them together.
(x-1)(x-4)(x+5)=0 [FOIL]
(x²-4x-x+4)(x+5)=0 [combine like terms]
(x²-5x+4)(x+5)=0 [FOIL]
x³+5x²-5x²-25x+4x+20=0 [combine like terms]
x³-21x+20=0
Now we know x³-21x+20=0 is the polynomial with those roots.
There are 38 chocolates in a box, all identically shaped. There are 8 filled with nuts, 16 with caramel, and 14 are solid chocolate. You randomly select one piece, eat it and then select a second piece. Find the probability of selecting 2 solid chocolate in a row
Answer:
0.1294
Step-by-step explanation:
Number of chocolates in box = 38
Number of nuts = 8
Number of caramel = 16
Number of solid chocolate = 14
Since 2 are selected in a row and not replaced, then;
Probability of first being solid chocolate = 14/38
Probability of second being solid chocolate after first one = 13/37
Thus;
P(2 selected in a row being solid chocolate) = 14/38 × 13/37 = 0.1294
Bond and DePaulo (2006) analyzed the results from 384 studies that tested the lie-detecting ability of more than 24,000 people and found that: Group of answer choices about 50% of people are especially clairvoyant and able to discern truths from lies. the accuracy rate of most people is barely above the 50% guessing level. most people can rather accurately guess whether they are told the truth or a lie. training people can substantially increase their lie-detecting ability.
Answer:
B: the accuracy rate of most people is barely above the 50% guessing level
Step-by-step explanation:
Bond and DePaul carried out a research and analysis on the accuracy of deception judgments in 2016.
This research involved synthesizing of results gotten from 206 research documents as well as a total of 24483 judges.
In this research and analysis, there were a couple of discoveries when people tried to discriminate lies from the truth and these discoveries include; average percentage of correct lie-truth judgments, percentage of those who correctly classified lies as deception and also percentage of those who classified truths as non-deceptive e.t.c. In conclusion, part of their discoveries was that the accuracy rate of most people is barely above the 50% guessing level.
This corresponds to option B.
A photograph has a length that is 2 inches longer than its width, x. So its area is given by the expression x(x + 2) square inches. If the area of thi
photograph is 48 square inches, what is the width of the photograph?
The width of the photograph is
inches.
suppose the function g(x) doubles the square of the input and then subtracts 13. what is g(3)?
Given:
The function [tex]g(x)[/tex] doubles the square of the input and then subtracts 13.
To find:
The value of [tex]g(3)[/tex].
Solution:
Let [tex]x[/tex] be the input value.
The square of the input is [tex]x^2[/tex].
Doubles the square of the input [tex]2x^2[/tex].
Doubles the square of the input and then subtracts 13, i.e., [tex]2x^2-13[/tex].
So, the function is:
[tex]g(x)=2x^2-13[/tex]
Putting [tex]x=3[/tex] in the above function, we get
[tex]g(3)=2(3)^2-13[/tex]
[tex]g(3)=2(9)-13[/tex]
[tex]g(3)=18-13[/tex]
[tex]g(3)=5[/tex]
Therefore, the value of [tex]g(3)[/tex] is 5.
Find the measure of one interior angle for the following regular polygon
Answer:
120
Step-by-step explanation:
All the interior angles in a regular hexagon are 120 degrees.
A triangle, where the two angles are 30° and 90°, what are the remaining angles
Answer:
60⁰
Step-by-step explanation:
A triangle has three angles.
The sum of its angles = 180⁰
[ By angle sum property ]
Let the unknown angle be 'x'
Then,
30⁰ + 90⁰ + x = 180⁰
120⁰ + x = 180⁰
x = 180⁰ - 120⁰
x = 60⁰
Therefore, the unknown angle will be equal to 60⁰
A group of rowdy teenagers near a wind turbine decide to place a pair of
pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.
a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.
b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.
Answer:
a) Sinusoidal functions are y = a sin [b(x-h)] + k (or)
y = a cos [b(x-h)] + k
Where a is amplitude a= (max-min)/2=(16-2)/2=7
period p= 2π/b
b=2π/30
Horizontal transformation to 10 units right h=10
k= (max+min)/2=(16+2)/2=9
h = 7 cos [π/15(t-10)]+ 9
b) t=10min=600 sec
substitue in the above equation
h=5.5m
Can u help me solve this
Answer:
V = 5,324 in^3
Step-by-step explanation:
V = 4([tex]\pi[/tex]r^3)/3
= 4(3)(11^3)/3
= 12(11)(11)(11)/3
= 12(1,331)/3
= 15,972/3
V = 5,324 in^3
Answer:
5575.28 or 5,324 depending on use of pie.
Step-by-step explanation
V=4/3πr3=4/3·π·113≈5575.27976
Hope this helps :)!
This is the answer if pie is used as 3.14.
V = 5,324 in^3 if pie used as 3.
V = 5575.28 in^3 if pie used as 3.14.
please someone help me! asap!!
Answer:
Last option= 30 minutes
Finding the missing length in a figure
Answer:
8 cm
Step-by-step explanation:
The length of the whole shape is 13. On the right side, it says the length is 5 cm. You use 13-5 to get the missing length.
Answer:
the answer is 8 cm
Step-by-step explanation:
What is the nineteenth term of an arithmetic sequence with first term 9 and common difference 5?
Answer:
The 19th term is 99.
Step-by-step explanation:
We can write a direct formula and use it to find the 19th term. Recall that the direct formula for an arithmetic sequence is given by:
[tex]x_n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
Since the first term is 9 and the common difference is 5:
[tex]\displaystyle x _ n = 9+5(n-1)[/tex]
To find the 19th term, let n = 19. Thus:
[tex]x_{19} = 9+5(19-1)[/tex]
And evaluate:
[tex]\displaystyle \begin{aligned} x_{19} &= 9+5(18) \\ &= 9+90 \\ &= 99\end{aligned}[/tex]
The 19th term is 99.
Given that 3=a+r/a-r,make r the subject of the formula?
Answer:
Step-by-step explanation:
[tex]3=\frac{a+r}{a-r} \\3a-3r=a+r\\3a-a=r+3r\\4r=2a\\r=\frac{1}{2} a[/tex]
Inverse trigonometry functions I need help finding the answers everything I’ve tried says it’s wrong
Answer:
see below
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hypotenuse
cos x = 13/20
Taking the inverse cos of each side
arccos ( cos x ) = arccos( 13/20)
x = arccos ( 13/20)
x =49.45839
x = 49 to the nearest whole number
sin theta = opp/ hyp
sin y = 13/20
Taking the inverse sin of each side
arcsin ( sin y ) = arcsin( 13/20)
y = arcsin ( 13/20)
y=40.5416
y = 41 to the nearest whole number
I do not understand this question can someone help me with good explanation will give Brainliest
Answer:
60 (E)
Step-by-step explanation:
He plants seeds -> plants grow to 12 times the original weight of the seeds -> he sells 50 tonnes from the harvest -> remainder is used as the next batch of seeds
He harvested 120 tonnes this year which means the original weight of the seeds planted was 120÷12 = 10 tonnes. This means that last years harvest would be the 10 tonnes used as seeds plus the 50 tonnes that would have been sold immediately, 10+50 = 60 tonnes
Y’all plss plss help me, it super ugent, I’ll mark the brainlest
Plsssssss, it Imp not spamming,, I’m serious I’ll report u
Answer:
the answer is correct
Step-by-step explanation:
hope u like
What is the range of the function$$f(x) = \frac{1}{1-x}~?$$Express your answer in interval notation.
I think you tried copy pasting the thing in here. usually written equations on tests or whatever don't copy paste well
Given: AABC is a right triangle.
BC =5, AC = 20
Determine the length of the missing side of AABC. When applicable, simplify radicals and show all of your work.
Answer:
19.365
Step-by-step explanation:
The Pythagoreum Theorum tells us that:
a² + b² = c²
where a and b are the legs and c is the hypotenuse.
BC is a leg; we'll lable it a.
AC is the hypotenuse thus labled c.
Plugging their lengths into the above formula will solve for the missing leg length.
5² + x² = 20²
25 + x² = 400
x² = 375
✓x = ✓3 x (5 x 5) x 5
x = 5✓15
x = 19.365
The mean length of a group of fish is 14.2 inches. A fish that is 41 inches long
joins the group. How does this fish's length affect the mean?
A. The new mean length will be less than 14.2 inches.
B. The new mean length will still be 14.2 inches.
C. The new mean length will be 41 inches.
D. The new mean length will be greater than 14.2 inches.
The fish's length will affect the mean because the new mean length will be less than 14.2 inches. That is option A.
What is mean?Mean is defined as the sum of all the data values divided by the count of values in a data set.
What a new value is added to a data set such as the group of fishes, it will affect the fish mean by reducing it to less than its former mean value which is 14.2 inches.
Therefore, the fish's length will affect the mean because the new mean length will be less than 14.2 inches.
Learn more about mean here:
https://brainly.com/question/1136789
#SPJ1
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answer:
B, pi
Step-by-step explanation:
The sine wave shown above has two waves until it reaches 2 pi, making the period of the sine graph 2pi divided by the two waves, making the answer pi.
The value of n from the set {6, 7, 8, 9} that holds true for 4n − 12 < 2n + 2 is .
Answer:
6
Step-by-step explanation:
4n - 12 < 2n + 2 is for n=6
4×6 -12 < 2×6 +2
24 - 12 < 12 + 2
12 < 14 correct
for n=7
4×7 - 12 < 2×7 + 2
16 < 16 incorrect
for n=8
4×8 - 12 < 2×8 + 2
20 < 18 incorrect
for n=9
4×9 - 12 < 2×9 + 2
24 < 20 incorrect
so, only for n=6 is the expression true.
Answer:
6
Step-by-step explanation:
4n - 12 < 2n + 2 is for n=6
4×6 -12 < 2×6 +2
24 - 12 < 12 + 2
12 < 14 correct
for n=7
4×7 - 12 < 2×7 + 2
16 < 16 incorrect
for n=8
4×8 - 12 < 2×8 + 2
20 < 18 incorrect
for n=9
4×9 - 12 < 2×9 + 2
24 < 20 incorrect
so, only for n=6 is the expression true.Step-by-step explanation:
Could someone please help me?
Answer:
ab=9 and ac=12
Step-by-step explanation:
Help ME PLS IM FAILING PYTHAGOREAN THEOREM I NEED HELP NOW
Answer:
3.9
Step-by-step explanation:
We can use the Pythagorean theorem
a^2 +b^2 =c^2 where a and b are the legs and c is the hypotenuse
7^2 + h^2 = 8^2
49 + h^2 = 64
h^2 = 64-49
h^2 = 15
Taking the square root of each side
sqrt(h^2) = sqrt(15)
h = 3.87298
To the nearest tenth
h = 3.9
PLEASE DO THIS ASAP!
NO LINKS!
Answer:
x =6
Step-by-step explanation:
5(x-2) = 14+x
Distribute
5x-10 = 14+x
Subtract x from each side
5x-x -10 = 14+x-x
4x-10 = 14
Add 10 to each side
4x-10+10 = 14+10
4x= 24
Divide by 4
4x/4 = 24/4
x =6
Answer:
5(×-2)=14+×
5x-10=14+x
5x-x=14+10
4x=24
x=6
Do you think mathematics is used when collecting and reporting your data ? Give your reasons.
What is the degree of this polynomial?
5 + 2s
=====================================================
Explanation:
We can rewrite 5 as 5s^0, since s^0 = 1 where s is nonzero.
Think of 2s as 2s^1
With those ideas in mind, the original polynomial turns into 5s^0 + 2s^1
Sorting the terms so that the largest exponent is first gets us the standard form 2s^1 + 5s^0
The largest exponent is the degree, so the degree is 1.
Side note: This trick only works for single variable polynomials.
Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.
The Euler's formula relates the vertices, faces and the edges of a polyhedron.
The correct option is (e) [tex]V = 6[/tex] [tex]E = 10[/tex] [tex]F = 6[/tex] [tex]6- 10 + 6 = 2[/tex]
First, we count the number of faces. This is the flat parts of the shape.
The attached shape has 6 flat surfaces.
So:
[tex]F = 6[/tex]
Next, we count the number of edges. This is where two faces meet.
The attached shape has 10 edges;
So:
[tex]E = 10[/tex]
Lastly, we count the number of vertices. This is where two edges meet.
The attached shape has 6 vertices.
So:
[tex]V = 6[/tex]
Using Euler's formula, we have:
[tex]V - E + F = 2[/tex]
Substitute values for V, E and F
[tex]6- 10 + 6 = 2[/tex]
[tex]2 = 2[/tex]
Hence, the polyhedron has 6 vertices, 10 edges and 6 faces
Read more vertices, edges, and faces at:
https://brainly.com/question/23347978
Complete the paragraph proof.
Given: and are right angles
Line segment A B is-congruent-to line segment B C Line segment B C is-congruent-to line segment A C
Prove: Line A R bisects Angle B A C
Answer:
wea did tha r come from??
Step-by-step explanation:
it is supposed to be d
helpp me solve it and pls explain
tyyy
Answer:
2=124 124/2
4=248 248/4
5=310 310/5
8=496 496/8
Step-by-step explanation:
40 + 22 = 62
62 x 2 = 124
62 x 4 = 248
62 x 5 = 310
62 x 8 = 496
i think
LOL….HEY
(Btw I’m not new to brainly, but I just forgot my old password) *sigh* ughh I start school August second and it’s gonna be my first year in high-school ….I- first of all summer break was wayyyyyyyyy too short basically 2 months and a half while the rest of the year I have to bust my behind preparing for test that don’t have anything to do with MY future plans….eeeee every time I think about it my anxiety levels raise higher and higher …..if any upper class men have some advice plz tell me…cuz I am legit terrified ngl (I checked out some freshmen tips on yxutube but that didn’t really help that much) *and btw this is kind of academically related so need to report me*
Answer:not a man but I think you should just relax and be yourself, high school isn’t scary at all. When you go in for orientation walk around the school and find your classes so you have a good map of where you need to go in your head already! Best of luck
Step-by-step explanation:
