The roots of the polynomial equation x²−12x−64=0 are 16 and -4. These roots are calculated using the quadratic formula and represent the points where the function intersects the x-axis. The importance of finding real roots in quadratic equations is significant in solving real-world problems.
Explanation:Roots of Polynomial Equation
The roots or solutions of the polynomial equation x²−12x−64=0 can be calculated using quadratic formula. In general, the quadratic function is written as ax²+bx+c=0 and its roots are given by -b ± √(b² - 4ac) / 2a. In this case, a=1, b=-12 and c=-64.
Applying those values into the formula we get 12 ± √((-12)² - 4(1)(-64)) / 2(1) = 12 ± √(144 + 256) / 2 = 12 ± √400 / 2 = 12 ± 20 / 2. This gives us two possible roots: 16 and -4.
Graphically, these roots represent the x coordinates or points where the quadratic function intersects the x-axis on a two-dimensional graph. It is important to note that quadratic equations constructed on physical data always have real roots, which are important for solving real-world problems.
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Solve the system of equations. 2.5y + 3x = 27 5x – 2.5y = 5 What equation is the result of adding the two equations? –8x = 328x = 325y + 8x = 328x – 5y = 32 What is the solution to the system? (–4, 6)(–2.75, 8.6)(2.75, 3.5)(4, 6)
Answer:
8x=32
(4,6)
Step-by-step explanation:
What is the point called where the perpendicular bisectors of the sides of a triangle intersect
You asked your classmates to name their favorite type of music. You found that 12 students like rock, 8 like rap, 6 like R&B, and 4 like jazz. Suppose you made a pie chart to display the data. How many degrees of the circle should represent rock music?
Can someone help me?
Classify the number as natural, whole, integer, rational, and/or irrational. Select all terms that are correct. 7√
Factor ab + bc + b2 + ac.
Anybody have the proper answer to this
Jermaine did this work to solve an equation. Did he make an error?
The solution for the below equation is required:
4x + 6 - x = 2x + 3
The work done by the Jermaine is presented below :
4x + 6 - x = 2x + 3
5x + 6 = 2x + 3
Instead of adding 4x with -1x to make it 3x , he added 4x with 1x to make it 5x.
So, the correct option is
Jermaine did make an error. He should have combined 4x and -1x to make 3x
3x + 6 = 2x + 3
Hope it helps..!!
Answer:
Step-by-step explanation:
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc is th
Select all of the following expressions that are equal to 2.5.
5 ÷ 2
-2(-1.25)
(-0.5)^2
-1 + (-1.5)
The temperature of a liquid during an experiment can be modeled by the function f(x)=3.8cos(πx20)+2.2 , where f(x) is the temperature in °C and x is the number of minutes into the experiment.
What is the lowest temperature the liquid reached during the experiment?
Michaela uses measuring tape to measure a piece of paper. The measuring tape has an accuracy to the nearest centimeter. She uses her measurements to calculate the area of the piece of paper. Which of the answer choices show the degree of precision she can use to report the area?
13) Suppose a coffee cup has a diameter of 8 cm and a height of 9 cm. What is the volume of the cup? (to nearest whole number)
Answer:
[tex]452\ cm^{3}[/tex]
Step-by-step explanation:
we know that
the volume of a cylinder (coffe cup) is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=8/2=4\ cm[/tex] -----> the radius is half the diameter
[tex]h=9\ cm[/tex]
substitute
[tex]V=\pi (4^{2})(9)=452.4\ cm^{3}[/tex]
Round to the nearest whole number
[tex]452.4\ cm^{3}=452\ cm^{3}[/tex]
Marie earns $96 in interest each year on an investment what is the rate of simple interest if her principal was $800
The rate of simple interest that Marie earns on her $800 investment is 12% per year, calculated by dividing the annual interest earned ($96) by the principal amount ($800).
To find the rate of simple interest, we can use the formula Interest = Principal * rate * time. Given that Marie earns $96 in interest each year on an investment and her principal was $800, we can rearrange the formula to solve for the rate.
The formula for simple interest is:
Interest = Principal * rate * time
Assuming the interest earned is for one year, we have:
$96 = $800 * rate * 1 year
To find the rate, we divide both sides by $800:
rate = $96 / $800
rate = 0.12
Converting into a percentage, the simple interest rate is 12% per year.
in the diagram, the areas of ADC and DCB are in a ratio of 3:4. what are the coordinates of point C
the complete question in the attached figure
we know that
dAB=dAC+dCB
dAC=√((8-1)²+(-2+9)²)=√98
Area triangle ADC=dAC*CD/2
Area triangle DCB=dCB*CD/2
Area triangle ADC/Area triangle DCB=3/4
[dAC*CD/2]/[dCB*CD/2]=3/4
dAC=(3/4)*dCB-----------------------> equation (1)
dAB=dAC+dCB=√98
dAC=√98-dCB------------------------ > equation (2)
(1)=(2)
(3/4)*dCB=√98-dCB------------------> (7/4)*dCB=√98
dCB=(4/7)√98
dAC=√98-dCB-------- > √98-(4/7)√98-----à (3/7) )√98
dAC=(3/7) )√98
find the slope point A (1.-9) and point B (8,-2)
m=(-2+9)/(8-1)=7/7=1-------------- > 45°
dAC=(3/7)√98
the component x of dAC is
dACx=(3/7)√98*cos45°=(3/7)√98*√2/2=(3/7)√196=3
the component y of dAC is
dACy=dACx=3
the coordinates of the point C are
point A(1.-9)
Cx=Ax+dACx----------> 1+3=4
Cy=Ay+dACy----------> -9+3=-6
the coordinates C(4,-6)
the answer is C(4,-6)
Answer:
C(4,-6) is correct on plato
Step-by-step explanation:
Trapezoid RSTV∼trapezoid WXYZ .
What is the scale factor of a dilation from RSTV to WXYZ ?
a. 14/25
b. 4/5
c. 7/8
d. 7/10
Answer:
Correct option is D
Scale factor of dilation is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
Given the two similar figures
Trapezoid RSTV∼trapezoid WXYZ
We have to scale factor of dilation from RSTV to WXYZ.
As the two trapezoid are similar therefore their ratio of corresponding sides gives the scale factor of dilation.
Hence, [tex]\text{scale factor of dilation is=}\frac{WX}{RS}=\frac{WZ}{RV}[/tex]
i.e [tex]\frac{28}{40}=\frac{35}{50}=\frac{7}{10}[/tex]
Hence, scale factor of dilation is [tex]\frac{7}{10}[/tex]
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The gum you like to is on sale. it is regularly priced at $1.59. Write and equation that will help determine how much you’ll save if you buy the pack today.
S=sale price
C=cost savings
Which equation has the graph that is a parabola with a vertex at 5,3
Write an expression to represent: four more than the product of three and a number xxx.
Answer:
x-4
Step-by-step explanation:
A ladder is leaning against the side of a building. The building and the ground form a right angle. How high on the building will the ladder touch if the ladder is 10 ft long and the base of the ladder is 6 ft from the base of the building?
The given question describes a right triangle with the hypotenuse as 10 ft and one of the legs as 6 ft.
We can make use of Pythagoras theorem to evaluate the length of the other side.
We know that by Pythagoras theorem, the square root of the sum of the squares of the legs of a right triangle gives the hypotenuse. Let the length of the required leg be x, then
[tex] x^2+6^2=10^2\\ \\ \Rightarrow x^2=100-36=64\\ \\ \Rightarrow x=\sqrt{64}=8. [/tex]
Therefore, the ladder reached 8 ft high on the building.
What is the perimeter of this equilateral triangle?
Equilateral triangle with one side labeled 13 meters.
this is a physics question that requires a lot of math. Hoping on of you genius could help me.
Q: You're driving down the highway late one night at 16m/s when a deer steps onto the road 44m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s2 .
How much distance is between you and the deer. I solved this =23m
What is the maximum speed you could have and still not hit the deer?
The answer is 25 m/s. A lot of people had stated to use the quadratic formula. I just don't know where to begin.
Fiecare dintre cei 25 de elevi ai clasei a |||-a a realizat un jurnal al luni . Stiind ca pentru fiecare zi s-a folosit o pagina si ca luna are 31 de zile,afla cate pagini au jurnalele tuturor elevilor.
Solve the system of equations using the linear combination method. {5m+3n=41 {3m−6n=9 Enter your answers in the boxes. m = n =
Answer:
n=2 m=7
Step-by-step explanation:
Find the 200th term, given the first term and the common difference. A1=34 and d=15
How do you write
2/4
as a percentage?
What is the answer to this problem?
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The expression x²-14x+31=63 is a quadratic equation. To solve it, you must order it:
x²-14x+31-63=0
x²-14x-32=0
Then, you must apply the quadratic formula, which is shown below:
x=(-b±√(b^2-4ac))/2a
So you have the values of a,b and c:
:
a=1
b=-14
c=-32
When you substitute those values in the quadratic formula, you obtain:
x=(-(-14)±√((-14)^2-4(1)(-32))/2(1)
x1=-2
x2=16
So, the correct option is the third one: x=-2 or x=16
the elevation in denver colorado is 13 times greater than that of waikapu, hawaii. the sum of their elevations is 5600 feet. find the elevation of each city
what do all similar circles have in common
a) congruent circumference value
b) congruent diameters
c) π
All the similar circles have π in common.
Thus, option (c) is correct.
When two circles are similar, it means they have the same shape but possibly different sizes.
However, the ratio of their corresponding lengths, including the circumference, remains constant.
Second, the ratio of the diameter will be constant but not congruent.
Third, the value of π is the universal constant whose value is 22/7 or 3.14.....
which is the same for every similar circle.
Thus, π has a common value.
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