Answer:
A
[tex]f(x) = x^3 - 2x^2 -3x + 6[/tex]
Step-by-step explanation:
According to the Factor Theorem, if (x - k) is a factor of a polynomial P(x), then P(k) must equal zero.
We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let k = 2, √3, -√3.
So, according to the Factor Theorem, P(2), P(√3) and P(-√3) must equal 0.
Testing each choice, we can see that only A is true:
[tex]\displaystyle f(x) = x^3 - 2x^2 - 3x + 6[/tex]
Testing all three values yields that:
[tex]\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \end{aligned}[/tex]
Hence, our answer is A.
Help me plz 20 points to who ever gets it right
Step-by-step explanation:
2., 3., 4., 5.
yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.
you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).
2.
(-4, 6) to (10, -10)
in x the distance is 10 - -4 = 14. half is 7.
in y the distance is |-10 - 6| = |-16| = 16. half is 8.
so the midpoint is
(-4 + 7, 6 - 8) = (3, -2)
remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).
3.
(-3, -8) to (-6.5, -4.5)
in x distance : -3 - -6.5 = 3.5. half is 1.75
in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75
midpoint is
(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)
4.
(3, 7) to (-8, -10)
x : 3 - -8 = 11. half is 5.5
y : 7 - -10 = 17. half is 8.5
midpoint is
(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)
5.
(-6, -13) to (-6.4, -3.8)
x : -6 - -6.4 = 0.4. half is 0.2
y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6
midpoint is
(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)
6.
(-1, 7) to (5, 1)
x : -1 - 5 = |-6| = 6. 1/3 is 2.
y : 7 - 1 = 6. 1/3 is 2.
1/3 from C to D
(-1 + 2, 7 - 2) = (1, 5)
7.
2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).
again
(1, 5)
8.
2/3 of the way from C to D.
so, we need to double what we added in 6.
(-1 + 4, 7 - 4) = (3, 3)
9.
1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).
again
(3, 3)
10.
exactly. Pythagoras.
the square root of the sum of the squares of the coordinate differences.
distance = sqrt((x1 - x2)² + (y1 - y2)²)
11.
(6, 8) to (-1, 8)
distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7
12.
(5, -6) to (5, 6)
sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12
13.
(-2, 0) to (11, 0)
sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13
14.
(1, -5) to (9, 1)
sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10
15.
ST and MT are basically the same equation.
MT is half of ST.
ST equation based on 2 points :
y – yS={(yT – yS)/(xT – xS)}(x – xS)
M = (xS + (xT - xS)/2, yS +(yT - yS)/2)
so, let's put that into the general equation :
y - yM={(yT - yM)/(xT - xM)}(x - xM)
y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))
16.
the two corners farthest away are (5, 10) and (9, 6).
what distance from (0, 0) is now bigger ?
since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.
5² + 10² = 125
9² + 6² = 117
so, the corner (5, 10) is the farthest away.
Solve
0.9(7x + 14) = 1.5 - (x + 2)
[tex]\\ \sf\longmapsto 0.9(7x+14)=1.5-(x+2)[/tex]
[tex]\\ \sf\longmapsto 6.3x+12.6=1.5-x-2[/tex]
[tex]\\ \sf\longmapsto 63x+12.6=-x-0.5[/tex]
[tex]\\ \sf\longmapsto 63x+x=-0.5-12.6[/tex]
[tex]\\ \sf\longmapsto 64x=-13.1[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-13.1}{64}[/tex]
[tex]\\ \sf\longmapsto x=0.2[/tex]
Find two consecutive whole numbers that 29 lies between.
Answer:
28 and 30
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Simplify: 2(6+1)-|-10|+3x2
Answer:
10
Step-by-step explanation:
2(6+1)-|-10|+3*2
First start with the absolute values and parentheses
2(7)-10+3*2
Then multiply from left to right
14 -10 +6
Then add and subtract from left to right
4 +6
10
The charge of eletricity for the first 20 unit is Rs 80 and Rs 7 per unit from 21 unit to 30 units. If service is Rs 75 find the total charge of 28 units
A ball is thrown straight up into the air from an initial height of 5 feet at time t = 0. The height, in feet, of the ball above the ground is given by h(t), where t is measured in seconds for 0 ≤ t ≤ 15. Based on the values of t and h(t) given in the table, for which value of t would the speed of the ball most likely be the greatest?
t (seconds) 0 3 6 9 12 15
h(t) (feet) 5 12 15 11 6 0
Select one:
a. 2 seconds
b. 5 seconds
c. 9 seconds
d. 15 seconds
Answer:
5 seconds
Step-by-step explanation:
The speed of an object is the rate of distance over time. The value of time (t) at the greatest speed of the ball is at 2 seconds
First, we calculate the speed using:
[tex]Speed = \frac{h(t)}{t}[/tex] --- i.e. distance/time
At t = 0, h(t) = 5
So;
[tex]Speed = \frac{5}{0} = unde fine d[/tex]
At t = 3, h(t) = 12
[tex]Speed = \frac{12}{3} = 4[/tex]
At t = 6, h(t) = 15
[tex]Speed = \frac{15}{6} = 2.5[/tex]
At t = 9, h(t) = 11
[tex]Speed = \frac{11}{9} = 1.2[/tex]
At t = 12, h(t) = 6
[tex]Speed = \frac{6}{12} = 0.5[/tex]
At t = 15, h(t) = 0
[tex]Speed = \frac{0}{15} = 0[/tex]
By comparing the above values, we notice that as time and height increases, the value of speed reduces.
This means that the greatest value of speed will be at the least value of time (t).
From the given options, the least value of time is at:
[tex]t = 2[/tex]
Hence, the value of time (t) at the greatest speed of the ball is at 2 seconds
Read more about speed at:
https://brainly.com/question/7359669
Write decimal for each model
Answer:
Please attach a picture or more details about "each model" so we can help you!
Step-by-step explanation:
(4.8 × 10⁷) + 6,500,000
Answer:
5.45 * 10^7
Step-by-step explanation:
[tex](4.8 * 10^7) +6,500,000[/tex]
= [tex](4.8 * 10^7) + 6.5 * 10^6[/tex]
= [tex](4.8 * 10^7) + (0.65 * 10^7)[/tex]
= [tex]5.45 * 10 ^7[/tex]
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
Step-by-step explanation:
4x - 13 = x + 5 Add 13 to both sides
4x = x + 18 Subtract x
3x = 18 Divide by 3
x = 6
Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6
Answer:
Step-by-step explanation:
I assume the sequence is 0, 2, 4, 6
nth term = 2(n-1)
✓ 1 N 3 4 5 6 Conv A rectangular field is 300 meters long and 250 meters wide. What is the area of the field in square kilometers? Do not round your answer. 1000 millimet 100 centimet 10 decimet 1 decame 2 km Х X 5. ? 1 hectomei 1
Answer:
75 km
Step-by-step explanation:
Area = Length × Width
= 300m and 250m
= 75000m
M to Km => ÷1000
= 75000m ÷ 1000
= 75 km #
Find the first six terms of the sequence. a1 = 1, an = 4 • an-1
Answer:
1,4,16,64,245,1024
Step-by-step explanation:
a1 =1
an = 4 * an-1
Let n = 2
a2 = 4*a1 = 4*1=4
Let n = 3
a3 = 4*a2 = 4*4 = 16
Let n = 4
a4 = 4*a3 = 4*16 = 64
Let n = 5
a5 = 4*a4 = 4*64 = 256
Let n = 6
a6 = 4*a5 = 4*256 = 1024
find the missing side round to the nearest tenth
Answer:
23.6
Step-by-step explanation:
cos38=x/30
x= 30cos38= 23.6 (nearest tenth)
Dan scored 1/4 of the points at last nights basketball game. What percentage of the total points did he score
Divide 1 by 4 to get a decimal:
1 / 4 = 0.25
Multiply by 100 to get percent:
0.25 x 100 = 25%
Answer: 25%
Points scored by dan = 1/4
Percentage = 1/4×100
= 25%
Therefore he scored 25% of total points.
Must click thanks and mark brainliest
Find the area of the shaded figure
Please help I apréciate everything
Answer:
2000*pi
Step-by-step explanation:
Shaded area= Area of bigger circle - Area of smaller circle
Shaded area= pi*(60)^2-pi*(40)^2=(60+40)(60-40)*pi=2000*pi
ch of the following collections are w A collection of first six even number A collection of tall girls of class X. A collection of good football player A collection of wild animals. A collection of days of a week. he symbols e or €: {a, e, i, o, u}
Pls Tell question corretly
find the surface area of the prism HURRY HURRY
Answer:
should be 192
Step-by-step explanation:
Maggie's brother is 6 years younger than four times her age. The sum of their ages is
59.
How old is Maggie?
Maggie is
years old.
Answer:
Maggie is 11 years old
Step-by-step explanation:
let m be Maggie and b be her brother.
[tex]m+b=59[/tex]
[tex]b=4m-6[/tex]
substitute for b.
[tex]m+4m-6=59[/tex]
[tex]5m-6=59[/tex]
add 6 to both sides
[tex]5m=55[/tex]
divide by 5 on both sides
[tex]m=11[/tex]
double check by finding the brother's age by substituting for m
[tex]11+b=59[/tex]
[tex]b=48[/tex]
This graph represents which of these expressions?
Answer:
x > 43
Step-by-step explanation:
Open circle at 43, which means it is not equal to 43
Line goes to the right, which means x is greater than
x > 43
Answer:
B
Step-by-step explanation:
Let a and b be real numbers, where a<b, and let A=(a,a^2) and B= (b,b^2) The line AB (meaning the unique line that contains the point A and the point B) has x-intercept (-3/2,0) and y-intercept (0,3). Find a and b. Express your answer as the ordered pair (a,b)
The slope of the line passing through points A and B is
slope = (b ² - a ²) / (b - a) = ((b - a) (b + a)) / (b - a) = b + a
Since this line passes through (0, 3), its equation would be
y - 3 = (b + a) (x - 0) ==> y = (b + a) x + 3
It also passes through (-3/2, 0), so that
y - 0 = (b + a) (x + 3/2) ==> y = (b + a) x + 3/2 (b + a)
If these equations describe the same line, then they must have the same slope and y-intercept, so that
3 = 3/2 (b + a) ==> a + b = 2
It also passes through (a, a ²), so that
a ² = (b + a) a + 3 ==> a ² = ab + a ² + 3 ==> ab = -3
Solving for b in the first underlined equation, we get
b = 2 - a
Substituting into the second equation and solving for a gives
a (2 - a) = -3 ==> 2a - a ² = -3 ==> a ² - 2a - 3 = (a - 3) (a + 1) = 0
==> a = 3 or a = -1
==> b = -1 or b = 3
Since a < b, we pick a = -1 and b = 3, so the solution is (a, b) = (-1, 3).
What is lim j(x)?
X-3
9514 1404 393
Answer:
(b) 4
Step-by-step explanation:
The point (3, 4) is a "hole" in the graph. The function approaches the value y=4 from either direction, so that is the limit as x → 3.
[tex]\displaystyle\lim_{x\to3}f(x)=4[/tex]
What is the slope? Please Help
Answer:
-1
Step-by-step explanation:
Pick two points on the line
(0,2) and (2,0)
Using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 0-2)/(2-0)
= -2/2
= -1
Answer:
-1
Step-by-step explanation:
Use two points on the line to find the slope, using rise over run.
We can use the points (0, 2) and (2, 0).
From the first point to the other, the y value decreases by 2 and the x value increases by 2.
Use rise (change in y value) over run (change in x value):
-2 / 2
= -1
So, the slope is -1.
Tables A telephone exchange operator assumes that 8%8% of the phone calls are wrong numbers. If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 535535 phone calls would differ from the population proportion by more than 3%3%
Answer:
0,375
Step-by-step explanation:
Divide de 3 percent from 8 percent den u get your answer
Pleasure helping you, hope it was helpful
Use the Laplace transform to solve the given system of differential equations. d2x dt2 + x − y = 0 d2y dt2 + y − x = 0 x(0) = 0, x'(0) = −6, y(0) = 0, y'(0) = 1
I'm going to assume that "−" is supposed to be some kind of minus character, so that the given system of DEs is supposed to be
[tex]\begin{cases}\dfrac{\mathrm d^2x}{\mathrm dt^2} + x - y = 0 \\ \dfrac{\mathrm d^2y}{\mathrm dt^2} + y - x = 0 \\ x(0) = 0, x'(0) = -6, y(0) = 0, y'(0) = 1\end{cases}[/tex]
Take the Laplace transform of both sides of both equations. Recall the transform for a second-order derivative,
[tex]L_s\left\{\dfrac{\mathrm d^2f(t)}{\mathrm dt^2}\right\} = s^2 F(s) - sf(0) - f'(0)[/tex]
where F(s) denotes the transform of f(t). You end up with
[tex]\begin{cases}s^2X(s)-sx(0)-x'(0) + X(s) - Y(s) = 0 \\ s^2Y(s) - sy(0) - y'(0) + Y(s) - X(s) = 0\end{cases} \\\\ \begin{cases}(s^2+1)X(s) - Y(s) = -6 \\ (s^2+1)Y(s) - X(s) = 1\end{cases}[/tex]
and solving for X(s) and Y(s) (nothing tricky here, just two linear equations) gives
[tex]X(s) = -\dfrac{6s^2+5}{s^2(s^2+2)} \text{ and } Y(s) = \dfrac{s^2-5}{s^2(s^2+2)}[/tex]
Now solve for x(t) and y(t) by computing the inverse transforms. To start, split up both X(s) and Y(s) into partial fractions.
• Solving for x(t) :
[tex]-\dfrac{6s^2+5}{s^2(s^2+2)} = \dfrac as + \dfrac b{s^2} + \dfrac{cs+d}{s^2+2} \\\\ -6s^2-5 = as(s^2+2) + b(s^2+2) + (cs+d)s^2 \\\\ -6s^2-5 = (a+c)s^3 + (b+d)s^2 + 2as + 2b \\\\ \implies \begin{cases}a+c=0\\b+d=-6\\2a=0\\2b=-5\end{cases} \implies a=c=0, b=-\dfrac52, d=-\dfrac72[/tex]
[tex]\implies X(s) = -\dfrac5{2s^2} - \dfrac7{2(s^2+2)}[/tex]
Taking the inverse transform, you get
[tex]L^{-1}_t\left\{X(s)\right\} = -\dfrac52 L^{-1}_t\left\{\dfrac{1!}{s^{1+1}}\right\} - \dfrac7{2\sqrt2} L^{-1}_t\left\{\dfrac{\sqrt2}{s^2+(\sqrt2)^2}\right\} \\\\ \implies \boxed{x(t) = -\dfrac52 t - \dfrac7{2\sqrt2}\sin(\sqrt2\,t)}[/tex]
• Solving for y(t) :
[tex]\dfrac{s^2-5}{s^2(s^2+2)} = \dfrac as + \dfrac b{s^2} + \dfrac{cs+d}{s^2+2} \\\\ s^2 - 5 = as(s^2+2) + b(s^2+2) + (cs+d)s^2 \\\\ s^2 - 5 = (a+c)s^3 + (b+d)s^2 + 2as + 2b \\\\ \implies \begin{cases}a+c=0\\b+d=1\\2a=0\\2b=-5\end{cases} \implies a=c=0, b=-\dfrac52, d=\dfrac72[/tex]
[tex]\implies Y(s) = -\dfrac5{2s^2} + \dfrac7{2(s^2+2)}[/tex]
Inverse transform:
[tex]L^{-1}_t\left\{Y(s)\right\} = -\dfrac52 L^{-1}_t\left\{\dfrac{1!}{s^{1+1}}\right\} + \dfrac7{2\sqrt2} L^{-1}_t\left\{\dfrac{\sqrt 2}{s^2+(\sqrt2)^2}\right\} \\\\ \implies \boxed{y(t) = -\dfrac52 t + \dfrac7{\sqrt2} \sin(\sqrt2\,t)}[/tex]
Wyatt is making a salad using tomatoes, cucumbers, and carrots. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Wyatt uses:
Ingredient Price per kilogram Amount
Tomatoes 3.30dollars per kilogram 0.3
Cucumbers x dollars per kilogram y kilograms
Carrots z dollars per kilogram 0.20
The total amount Wyatt spends on ingredients is C dollars.
Write an equation that relates x, y, z, and C.
According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:
[tex]C = 0.99 + xy + 0.2z[/tex]
Cost:
0.3 kilograms of tomatoes, at 3.30 dollars per kilogram.
Thus, the cost starts at:
[tex]C = 0.3*3.3 = 0.99[/tex]
y kilograms of cucumbers, at x dollars per kilogram.
Considering this, the cost will now be of:
[tex]C = 0.99 + xy[/tex]
0.2 kilograms of carrots, at z dollars per kilogram:
Now, we have to consider this for the cost, so:
[tex]C = 0.99 + xy + 0.2z[/tex]
A similar example is given at https://brainly.com/question/14544759
Question 6. Which expression is equivalent to 3x(x-6)+5(x-4)?
Answer:
8x- 38
Step-by-step explanation:
3(x-6)+5(x-4)
Distribute
3x- 18+5x -20
Combine like terms
3x+5x -18-20
8x- 38
Answer:
[tex]3(x-6)+5(x-4)[/tex]
[tex]3x-18+5x-20[/tex]
[tex]=(3+5)x-(20x+18)[/tex]
Add:- 3+5= 8, and 20+18= 38
[tex]=8x-38[/tex]
OAmalOHopeO
Kế hoạch đi dã ngoại của một gia đình sẽ bị hủy nếu trời có mây hoặc mưa. Biết xác suất để trời có mây là có mưa là có cả mây và mưa là . Tính xác suất để kế hoạch được thực hiện.
Answer:
itditsktxjtcv6tgcxufh-&#€#€($*:'₹€$*^'ditx_*^,tsitsitxmvditxitsitsjfxkhcoucuofoydoy
In order to pass a class, Amanda needs to have a score higher than 86 on her final. Which graph represents possible scores that Amanda could get to pass this class?
Answer:
graph C
Step-by-step explanation:
Amanda needs to have a score higher than 86 on her final.
That means she can't get lower than 86 (Obviously) but not even an 86.
It has to be higher than 86 for her to pass
Let x represent Amanda's score
[tex]x>86[/tex]
Bolded dots on graphs mean that she can have a 86 but if it's not a bolded dot she can have either higher or lower
Just keep that in mind
The answer will be C. because it describes Amanda's score higher than 86
Answer:
c
Step-by-step explanation:
Write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -6.
Answer:
y=mx+b
Step-by-step explanation:
m=4/3×-6
I think this is the answer
Determine whether the ordered pair is a solution of the equation. Show your work to receive credit.
9. Is (-1,3) a solution to the equation y = -3x + 10?
10. Is (7,-2) a solution to the equation x – 4y = 15?
Please show work to help me understand.
Answer:
3=3 + 10
3 = 13(NO)
x-4y=15
7--8=15
15=15(YES)
