The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
x = 3, −2+4i, −2−4i
To find the zeros of the polynomial p(x), we need to find the values of x such that p(x) = 0.
One way to do this is to use the rational root theorem, which states that if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors), then p must divide the constant term and q must divide the leading coefficient.
For the polynomial, [tex]p(x) = x^3 + x^2 + 8x - 60,[/tex] the constant term is -60 and the leading coefficient is 1.
Therefore, the possible rational roots are:
±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60
We can then use synthetic division or long division to check which of these roots are actually zeros of the polynomial.
Trying the possible roots, we find that x = 3 is a zero of the polynomial, since p(3) = 0.
Using long division or synthetic division, we can then divide p(x) by (x - 3) to get a quadratic factor:
[tex]x^3 + x^2 + 8x - 60 = (x - 3)(x^2 + 4x + 20)[/tex]
The quadratic factor [tex]x^2 + 4x + 20[/tex] has no real roots since its discriminant [tex](b^2 - 4ac)[/tex] is negative. Therefore, the zeros of the polynomial p(x) are:
x = 3 (with multiplicity 1)
x = -2 ± 4i (with multiplicity 1 each)
Therefore, the zeros of the polynomial p(x) are 3, -2 + 4i, and -2 - 4i.
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Dina draws marbles of the same size and shape out of a bag. The probability of randomly drawing a green marble is 30%. The probability of randomly drawing a yellow marble is 25%. What is the probability Dina will randomly draw a marble that is not green, replace it, then randomly draw a yellow marble? Enter your answer as a %.
After analysing the given data we conclude that the probability that Dina will randomly choose that is not green and change it and again randomly choose a marble that is yellow is 17.5%.
The given probability of Dina drawing a green marble is 30%. Then, the probability of her not drawing a green marble is 70%. It can be said that probability of her drawing a yellow marble is 25%. Hence, the probability of her not drawing a yellow marble is 75%.
The probability of Dina drawing a marble that is not green and then replacing it is
70% × 100% = 70%.
The probability of her then drawing a yellow marble is 25%. Therefore, the probability of Dina randomly drawing a marble that is not green, replace it, then randomly draw a yellow marble is
70% × 25% = 1750
1750× 100 = 17.5%.
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# (-20
01
160 Minutes boseng
and (4,0)
1. Use the equation to answer the question.
x² + 12x - 85
A
(x + 6)² = 11
B (x + 6)² = 9
C (x + 6)² = 7
D (x + 6)² = 15
D. They
Billy is completing the square to rewrite the equation. Which
equation could be his result?
A8 2002 2x2
bow 212
Edavad id doow to 202
12
AREI.4
After completing the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we find that the possible result is [tex]\((x + 6)^2 = 49\)[/tex].
To complete the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we follow these steps:
1. Take half of the coefficient of the [tex]x[/tex] term, which is [tex]\(12/2 = 6\)[/tex].
2. Square this result, [tex]\(6^2 = 36\)[/tex].
3. Add this value, 36, to both sides of the equation to maintain balance:
[tex]\[x^2 + 12x + 36 - 85 = 36 - 85.\][/tex]
4. Simplify both sides of the equation by combining like terms:
[tex]\[(x + 6)^2 - 49 = 0.\][/tex]
5. Rearrange the equation to isolate the perfect square term:
[tex]\[(x + 6)^2 = 49.\][/tex]
From this process, we can conclude that the equation [tex]\((x + 6)^2 = 49\)[/tex] could be the result of completing the square for the given equation [tex]\(x^2 + 12x - 85\)[/tex]. This equation represents a perfect square trinomial with a perfect square term, and it allows us to solve for the value of [tex]x[/tex] by taking the square root of both sides.
It's important to note that completing the square allows us to rewrite quadratic equations in a form that reveals key properties and facilitates solving for unknowns.
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Refer to the painting.
110°
7x
Write an equation that can be used to find the value of x.
An equation that can be used to find the value of x include the following: 110° + 7x = 180°.
What is a supplementary angle?In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:
110 + 7x = 180°
7x = 180° - 110°
7x = 70°
x = 70°/7
x = 10°
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What is the square root of 25*25*64*221?
8/5÷6=
i need help on this
Answer:
2 forms
Step-by-step explanation:
hope this helps <3
[tex] \sf \longrightarrow \: \frac{8}{5} \div 6 \\ [/tex]
[tex] \sf \longrightarrow \: \frac{5}{8} \times 6 \\ [/tex]
[tex] \sf \longrightarrow \: \frac{5 \times 6}{8} \\ [/tex]
[tex] \sf \longrightarrow \: \frac{30}{8} \\ [/tex]
[tex] \sf \longrightarrow \: \frac{8}{30} \\ [/tex]
[tex] \sf \longrightarrow \: 0.26 \\ [/tex]
_____________________________
When the sun is at its highest point in the sky, Hong goes to fly a kite in a flat field. He lets out 42.9 feet of string, and the spool of string is 3.4 feet above the ground. The shadow that the kite makes (directly below the kite on the ground) is 16.5 feet away from Hong. How high is the kite off the ground? Round your answer to two decimal places.
The height of the kite off the ground is approximately 17.87 feet rounded to two decimal places.
To solve the problem can use similar triangles.
Let's draw a diagram:
A
|\
| \
h | \ x
| \
|____\
d B
Point A represents the kite, point B represents the tip of the kite's shadow on the ground and point D represents the point directly below the spool of string on the ground.
The height of the kite represented by h.
The length of the string is 42.9 feet so the distance from point A to point D is also 42.9 feet.
The distance from point B to point D is 16.5 feet.
These two lengths to find the length of segment AB:
AB/AD = BD/AD
AB/42.9 = 16.5/42.9
AB = 16.5
So AB is 16.5 feet.
Now we can use the similar triangles to find h.
We have:
h/x = AB/AD
h/x = 16.5/42.9
h = x × 16.5/42.9
We need to find x.
The spool of string is 3.4 feet above the ground and we know that the kite is directly above the spool when it is at its highest point in the sky.
So the height of the kite above the ground is the same as the height of the spool above the ground plus the length of string that has been let out:
x = 3.4 + 42.9
= 46.3
Now we can substitute this value of x into the previous equation to find h:
h = 46.3 × 16.5/42.9
= 17.87
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Tyler is 8 years old his sister Olivia is 4 years less than twice his age write a numerical expression for Olivia’s age
Answer: yes
Step-by-step explanation:
In the following rectangle, AC = 2x + 7 and BD = 5x - 14. Solve for x.
A
D
2=
B
C
Answer:
7
Step-by-step explanation:
yw ;)
find lim x approaches 3
f(x) = x^2 - 2
f(x) = -3x + 15. x> 3
The value of the limit of the function f(x) = x² - 2 is 7.
The value of the limit of the function f(x) = -3x + 15 is -6.
We have,
To evaluate the limit as x approaches 3, we need to find the limit of function f(x) as x approaches 3 from both sides of 3.
First, let's evaluate the limit from the left side of 3:
lim x → 3⁻ f(x) = lim x → 3⁻ (x^2 - 2)
Substituting x = 3 - h (where h approaches zero) gives:
lim h → 0⁺ [(3 - h)^2 - 2]
= lim h → 0⁺ [9 - 6h + h^2 - 2]
= lim h → 0⁺ [h^2 - 6h + 7]
= 7
(since the limit of a quadratic function as h approaches zero is the constant term)
Next, let's evaluate the limit from the right side of 3:
lim x → 3⁺ f(x)
= lim x → 3⁺ (-3x + 15)
= -6
Since the limit from the left side is not equal to the limit from the right side, the limit of f(x) as x approaches 3 does not exist.
Thus,
The value of the limit of the function f(x) = x² - 2 is 7.
The value of the limit of the function f(x) = -3x + 15 is -6.
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Can someone please help me? I need this fast and it’s really important that I get it right. Graph the function shown in the image.
Answer: attached in image, look at both
Step-by-step explanation:
Please Help! 13 points!
a) The first mistake that Fatima made was in the first step.
b) She incorrectly changed the place value of 0.02 in the subtraction operation.
c) Based on the correct subtraction operation and place value in step one, Fatima has 0.395 kilograms of rose petals left.
What is a place value?The place value shows the position of a digit in a number.
The right place values are essential for correct mathematical operations.
The quantity of rose petals that Fatima bought initially = 0.454 kilograms
The quantity of rose petals used for making rose water = 0.02 kilograms
The remaining quantity of rose petals = 0.434 (0.454 - 0.02)
The additional quantity of rose petals Fatima bought = 0.056
The quantity of rose petals used for making the second rose water = 0.095
The quantity of rose petals left = 0.395 (0.434 + 0.056 - 0.095)
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the diagram shows a regular pentagon a) work out the interior angle , b) work out the size of one angle
pls help
Measure of one exterior angle = 30 degree
Measure of one interior angle = 150 degree
In the given regular pentagon
Number of terms = 12
We know that,
Sum of all exterior angles = 360 degree
To find one exterior angle,
Divide the complete angle by number of terms
Therefore,
One exterior angle = 360/12 = 30 degree
Since,
Sum of all interior angles = 180 degree
And To find one interior angle,
subtract the interior angle by one exterior angle
Therefore,
One exterior angle = 180 - 30 = 150 degree
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Xavier drew a map of an island using a scale in which 2 inches represents 50 feet. The length of the island is 400 feet. What is the length of the island on the map in inches?
Answer:
16 in
Step-by-step explanation:
50 ft x 12 in/ft = 600 in
Scale factor: 2 : 600 = 1 : 300
x = length of island on the map
400 ft = 4800 in
1/300 = x/4800
x = 4800/300 = 16 in
PA HELP PO SA STATS TOPIC PO "RANDOM SAMPLING AND SAMPLING DISTRIBUTION" THANKYOU
1) Note that the population mean is 153.
2) there are 36 possible random samples of size two that can be selected from a population of nine.
How did we arrive at the above?1) Population Mean = (172 + 148 + 156 + 170 + 161 + 138 + 142 + 156 + 134) / 9
= 1377 / 9
Population Mean = 153
2) To get the number of possible random samples, we must use Combination whose equation is given as
nCr = n! / (r! (n-r)!)
nC2 = 9! / (2!(9-2)!)
= 9! / (2! 7!)
= (9 x 8 x 7!) / (2!7!)
= (9 x 8) / 2
= 36
Thus, the number of random samples that can be selected form a population of 9 is 36.
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plessee help me i dont know the answerr
volume: 2,160cm
please let me know if this was what you needed or if it was something else.
How to get the square root of a number?
Answer:
Step-by-step explanation:
What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number.
The square root of a number "a" is denoted by the symbol "√a" or "a^(1/2)." For example, the square root of 9 is 3 because 3 * 3 = 9.
What is the range of the function y=−7x−5?
Step-by-step explanation:
"Range'' is the values of 'y' that a graph can have....there are no limits on this one
(-∞,+∞)
What is the break-even point? A graph has units on the x-axis, and cost (dollars) on the y-axis. 2 lines intersect at (11, 44). a. 11 units c. 3 units b. 44 units d. 6 units
The break-even point would be when the cost is equal to 44 dollars.
Option B is the correct answer.
We have,
The break-even point represents the point at which the cost equals the revenue or the point where there is no profit or loss.
Now,
In this case, if the graph represents the cost (dollars) on the y-axis and units on the x-axis, the break-even point occurs when the cost is equal to the revenue or total sales.
Given that two lines intersect at (11, 44),
The break-even point would be when the cost is equal to 44 dollars.
Thus,
The break-even point would be when the cost is equal to 44 dollars.
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I will give brainliest and ratings if you get this correct
1. The product of MG is as follows;
[tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36 \\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]
2. The values are k₁ = -9, k₂ = -9, t₁ = 0 and t₂ = -1 given that G = M⁻¹
How do we find the product MG?Matrix M and matrix G are given as
M = [1, 4, 5; t₁, 3, -1; 1, t₂, 1] and
G = [2, k₁, -19; 1, -4, k₂; -1, 5, 11]
MG becomes
1×2 + 4×1 + 5×-1 1k₁+4×-4+ 5×5 1×-19+4k₂+5×11
t₁×2+3×1+-1×-1 t₁k₁+3×-4+-1×5 t₁×-19+3k₂+-1×11
1×2+t₂×1+1×-1 1k₁+t₂×-4+-1×5 1×-19+t₂k₂+1×11
=
1 k₁+9 4k₂+36
2t₁ k₁t₁-17 3k₂-19t₁-11
t₂+1 k₁-4t₂+5 k₂t₂-8
To solve G = M⁻¹ we know it is an identity matrix
I = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
We can equate the elements of MG and I to find the values of t₁, t₂, k₁, and k₂:
1 = 1, k₁+9 = 0, 4k₂+36 = 0
2t₁ = 0 k₁t₁-17 = 1 3k₂-19t₁-11 = 0
t₂+1 = 0 k₁-4t₂+5 = 0 k₂t₂-8 = 1
k₁+9 = 0 4k₂+36 = 0 2t₁ = 0 t₂+1 = 0
k₁ = -9 k₂ = -9 t₁ = 0 t₂ = -1
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12. In the figure, AB is a diameter, and ABL CD The figure is not drawn to scale.
If m AC-54°, what is m BD
(1 point)
0 36°
O 108
O 126°
O 144°
20 points
In the figure, AB is a diameter, and AB⊥CD, If m AC = 54°, BD is 36°. Option A
How do we calculate the line BD given the that AB is a diameter, and AB⊥CD?In a circle, a diameter divides it into two equal parts and forms a straight line that measures 180°.
Given that AB is a diameter = 180°.
AB is perpendicular to CD, therefore m∠AC + m∠BD = 90°.
Substituting m∠AC =54°, we get m∠BD + 54° = 90°.
Solving for m∠BD, we get 90° - 54° = 36°.
There BD is 36°.
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The P(tossing a head) is 50%. Ann tossed a coin 100 times. It landed on heads 40 times. Did the
experimental match the theoretical probability?
The experimental probability did not match the theoretical probability.
How to find the experimental probability ?The experimental probability is the chance that is determined from the real results of an experiment or event. It is based on practical observations or information, rather than a mathematical expression.
The theoretical probability is the chance that is worked out using a mathematical equation founded on the assumptions and situations of the event or experiment.
The experimental probability of landing on heads :
= 40 / 100
= 40 %
The theoretical probability is 50 % which means the experimental and theoretical did not match.
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What is the surface area of the cylinder with height 8 cm and radius 4 cm? Round your answer to the nearest thousandth.
Answer:
301.59289cm²
Step-by-step explanation:
What is the answer to this expression?
3⋅10+3⋅5 ^2 +3 ?
Pls help
Will leave gd rating
Answer:
Step-by-step explanation:
PEMDAS (order in which to do operations)
P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction
there are no parentheses so skip that
5^2 is an exponent so do that first
3x10 + 3x5^2 + 3 --> 3 x 10 + 3 x 25 + 3
Next, do multiplication/division operations from left to right
3 x 10 + 3 x 25 + 3 --> 30 + 75 + 3
Finally, do the addition operations
30 + 75 + 3 = 108
final answer: 108
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 24
minutes of calls is $22.12, and the remaining credit after 63 minutes of calls is $17.44. What is the remaining credit after 91 minutes of calls?
The remaining credit after 91 minutes of calls is $16.76.
We are given that;
(24, 22.12) and (63, 17.44)
Now,
To find the slope and the y-intercept of the function. You can write your solution as:
Slope = (y2 - y1) / (x2 - x1) = (17.44 - 22.12) / (63 - 24) = -0.08 y-intercept = y - mx = 22.12 - (-0.08)(24) = 24.04 Equation: y = -0.08x + 24.04
To find the remaining credit after 91 minutes of calls, you need to substitute x = 91 in the equation and simplify. You can write your answer as:
y = -0.08(91) + 24.04 y = -7.28 + 24.04 y = 16.76
Therefore, by the intercept the answer will be $16.76.
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How many yards are equivalent to two miles
Answer:
2 miles = 3,520 yards
Step-by-step explanation:
You multiply the length value by 1,760.
3520 yards is equivalent to 2 miles.
Hope this helped! Have a nice day. :)Diana walks around a circular swimming pool of diameter 14 feet. What is the distance she has walked?
Step-by-step explanation:
She walks the entire CIRCUMFERENCE of the circle
circumference = pi X diameter
= pi X 14 ft = 43.98 ft = ~ 44 ft (rounded)
Theprofit(indollars)earnedbysellingwappletreesisrepresentedby w2 − 4w + 14. The profit (in dollars) earned by selling w pear trees is
represented by 2w + 10. Write a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
[tex]w^2 - 6w + 4[/tex] is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
The profit earned by selling w pear trees is 2w + 10
To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:
[tex](w^2 - 4w + 14) - (2w + 10)[/tex]
Simplifying the expression:
[tex]w^2 - 6w + 4[/tex]
Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is [tex]w^2 - 6w + 4[/tex].
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Identify the center, radius, domain and range of the circle eith equation. Make sure to scroll down through all thr answer choices
(x+2)^2+(y-5)^2 = 9
Answer: Centre: (-2,5)
Radius = 3
so
Diameter = 6
Domain: (-5,1)
Range: (2,8)
Answer:
center (-2,5)
radius =3
domain = -5< x <1
range 2 <y<8
Step-by-step explanation:
siiuu
Two systems of linear equations in two variables, x and y, are given.
System P:
(3x-10y=8
7x+2y=6
The two systems have the same solution..
What are the values of b and c?
b=
System T:
bx - 10 y + 10 y = 38
cx + 10 y = 30
=
C =
Answer:
Step-by-step explanation:
Select the correct answer.
Which expression is equivalent to the given expression?
(14x³y^-4) (4x^-5y^4)
OA. 56/x^2
OB. 56x^2y
OC. 56y/x^2
OD. 56x^2
please help i need the answer!!
Answer:
The correct answer is D. 56x^2.