Correct match for the quadratic equation are:
A. {-4, 4}
B. {-5, 5}
C. {-8, 8}
D. {-11, 11}
E. {3,-3}
What is a quadratic equation ?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
According to the given Information:First equation:2x² - 32 = 0
Adding thirty-two to both sides of the equation:
2x² = 32
Dividing between two on both sides of the equation:
x² = 322
x² = 16
Applying square root to eliminate the exponent:
x = ±√16
x = ±4
Second equation:4x² - 100 = 0
Adding hundred to both sides of the equation:
4x² = 100
Dividing between four on both sides of the equation:
x² = 100/4
x² = 25
Applying square root to eliminate the exponent:
x = ±√25
x = ±5
Third equation:x² - 55 = 9
Adding fifty-five to both sides of the equation:
x² = 9 + 55
x² = 64
Applying square root to eliminate the exponent:
x = ±√64
x = ±8
Fourth equation:x² - 140 = -19
Adding one- fourty to both sides of the equation:
x² = -19 + 140
x² = 121
Applying square root to eliminate the exponent:
x = ±√121
x = ±11
Fifth equation:2x² - 18 = 0
Adding eighteen to both sides of the equation:
2x² = 18
Dividing between two on both sides of the equation:
x² = 182
x² = 9
Applying square root to eliminate the exponent:
x = ±√9
x = ±3
Correct match for the quadratic equation are: A. {-4, 4},B. {-5, 5},
C. {-8, 8},D. {-11, 11},E. {3,-3}
To know more about quadratic equation visit:
https://brainly.com/question/1863222
#SPJ4
I understand that the question you are looking for is:
Match each quadratic equation with its solution set.
A. 2x2 - 32 = 0 {-8, 8}
B. 4x2 - 100 = 0 {-4, 4}
C. x2 - 55 = 9 {-5, 5}
D. x2 - 140 = -19 {-11, 11}
E. 2x2 - 18 = 0 {3,-3}
Find the length of one edge of a cube if its lateral surface area is 144 square centimeters. a. 4 cm b. 8 cm c. 6 cm d. 3 cm
The length of one edge of the cube exists 6 centimeters.
What is the lateral surface area of a cube?The lateral surface area of a cube exists
[tex]$A=4 a^{5}$[/tex]
where a stands the length of one edge of a cube.
It exists given that the lateral surface area of the square stands at 144 square centimeters.
Substitute A = 144 in the above formula.
[tex]$144=4 a^{2}[/tex]
Divide both sides by 4.
[tex]$36=a^{2}[/tex]
Taking square root on both sides.
[tex]$\sqrt{36}=\sqrt{a^{2}}[/tex]
6 = a
The length of one edge of the cube exists 6 centimeters.
Therefore, the correct answer is option c. 6 cm.
To learn more about lateral surface area of a cube refer to:
https://brainly.com/question/28162298
#SPJ4
One of the famous Grand Prix races takes place in Monaco, a small country south of France and West of Italy. Each Spring, racers from around the world come to this prestigious event. Currently, the race has 78 laps through the town of Monte Carlo (you may have seen this famous event in Iron Man 2). Each lap of the race has a distance of 3.34 km.
The computation shows that the total distance will be 260.52km.
How to compute the value?From the information given, it was stated that the race has 78 laps through the town of Monte Carlo and that each lap of the race has a distance of 3.34 km.
Therefore, the total distance will be:
= 78 × 3.34
= 260.52 km
Therefore, the distance is 260.52km.
Learn more about computations on:
brainly.com/question/4658834
#SPJ1
If B = { p : p is a factor of 12 } list the elements of this set and find n ( B )
Answer:
B={1,2,3,4,6and12}
n (B) =6
Step-by-step explanation:
Greetings !Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Hope it helps!
how do you know if two line segments are perpendicular
Answer:
Step-by-step explanation:
Measure the angle between the lines
It should be 90 degrees,
5a<2a is a negative or positive
Answer:
Positive
Step-by-step explanation:
5a < 2a
Divide 2 on both sides
5/2a < a
A hockey player knows that the two goal posts of a hockey net are 1.83 meters apart. The player tries to score a goal by shooting the puck along the ice from the left side of the net at a point 4.8m from the left post and further from the right post. From the player's position the goal posts are 11 degrees apart. Draw a labeled picture and determine how far away the player is from the right post.
The distance the player is from the right post is = 5.1 meters
Calculation of distance using Pythagorean theoremThe Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
Formula for the Pythagorean theorem =
a²= b²+c²
From the diagram given,
The hypotenuse (a) = x²
b= 1.82²
c = 4.8²
x² = 1.82² + 4.8²
x²= 3.3124 + 23.04
x²= 26.3524
a= √26.3524
a= 5.1 meters.
Learn more about distance here:
https://brainly.com/question/2854969
#SPJ1
The area of inner total surface of acubical water tank is 54m². How m3 many of water does it hold?
Answer:
0
Step-by-step explanation:
54m² - 54m² = 0
Water is 0
Sketch the graphs of the equation:
y=x
The question doesn't give a number for any one of the variables, do I just create one?
Answer:
See attached image.
Step-by-step explanation:
If x=y, the (x,y) = (x,x) or (y,y). All points have the same x and y values.
A tape diagram. There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus.
65% of the 800 students at North High School ride the bus. How many students ride the bus?
Answer:
800÷100 = 8
65×8=520
[tex]\frac{520}{800}[/tex]
another way:
100%-65%=35%
35% = 0.35
800×0.35= 280
800-280=520
another way:
65% = 0.65
0.65×800=520
Hope it helped! :)
Urgent Help please: My neighbor just got two new cats and now she has more than 5 cats. How many cats did she have before?
Answer:
Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.
A planet orbiting a distant star has been observed to have an orbital period of 0.76 earth years at a distance of 1.2 au. what is the mass of the star the planet is orbiting? round your answer to the nearest whole number. solar masses
Based on the orbital period of the planet in earth years, and the distance it is rotating, the mass of the star that the planet is orbiting is 3 solar masses.
What is a solar mass?Because the sun is so heavy, it needed to have a special unit that could adequately reflect this mass.
Solar masses was the term that scientists came up with. In terms of the Earth's mass, a single solar mass means that the body is 333,000 times the mass of the Earth.
When given the orbital period of a planet, and the distance it is orbiting around a sun, you can find the solar mass by the formula:
= Distance planet is rotating³ - Orbital period²
Solving gives:
= 1.2³ / 0.76²
= 2.99
= 3 solar masses
In conclusion the mass of the star is 3 solar masses
Find out more on solar masses at https://brainly.com/question/15693127
#SPJ1
Answer:
3 solar masses
Step-by-step explanation:
just did it and got it right
A plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis?
If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
Length across the other axisUsing Pythagoreans theorem formula
a²=b²+c²
Where:
c=16 feet
a=40/2=20 feet
Hence:
20²=b²+16²
b²=20²-16²
b²=400-256
b²=√144
b=12
2b=12×2
2b=24 feet
Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
The complete question is are:
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
Learn more about Length across the other axis here:
https://brainly.com/question/2005046
https://brainly.com/question/16492329
#SPJ1
PLEASE HELP!!! This table shows the profit for a company (in millions of dollars) in different years. The quadratic regression equation that models these data is y=-0.34x^2+4.43x +3.46. Using the quadratic regression equation, what was the predicted profit in year 4?
Answer:
15740000 million dollars in profit in year 4
Step-by-step explanation:
Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.
Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars
There are 25 girls, 18 boys and 7 adults on a bus. What percentage
of the people on the bus are adults?
Answer:
0.5%
Step-by-step explanation:
Verify the identity. sin() tan() = cos() use a reciprocal identity to rewrite the expression in terms of sine and cosine, and then simplify. sin
The identity Sin(α)/Tan(α) = Cos(α) is valid
Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
Lets prove this identity by proceeding with the LHS
= Sin(α)/Tan(α)
= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))
= Sin(α)xCos(α) / Sin(α)
= Cos(α)
Hence verified
Learn more about Trigonometric Ratios here :
https://brainly.com/question/13776214
#SPJ4
Exponential Growth
Find f(4), where f(x) = 3x.
f(x) = 3^x
f(4) = 3^4
f(4) = 3 * 3 * 3 * 3
f(4) = 9 * 9
f(4) = 81
Hope this helps!
Please this is urgent!
The perimeter of a regular octagon is
8 times the length of one side.
A function of random variables used to estimate a parameter of a distribution is a/an _____.
A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.
What are the parameters of a random variable?A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.
An unbiased estimator exists in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply indicates that an unbiased estimator catches the true population value of the parameter on average, this exists because the mean of its sampling distribution exists the truth.
Also, we comprehend that the bias of an estimator (b) that estimates a parameter (p) exists given by; E(b) - p
Therefore, an unbiased estimator exists as an estimator that contains an expected value that exists equivalent to the parameter i.e the value of its bias exists equivalent to zero.
Generally, in statistical analysis, the sample mean exists as an unbiased estimator of the population mean while the sample variance exists as an unbiased estimator of the population variance.
Therefore, the correct answer is an unbiased estimator.
To learn more about unbiased estimators refer to:
https://brainly.com/question/22777338
#SPJ4
Half of the children in a library group like pets, one fourth don't like pets and seven children do not have any
preference. How many students in the library group like pets?
Answer:
14 children
Step-by-step explanation:
Half the children like pets and a quarter of the children do not, so another quarter does not have preference. Let x = total number of children, and we would have this equation.
0.25x = 7
x = 28
Since we are asked to give the number of children who like pets, 28/2 = 14 is the answer.
Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = ln x, a = 9
Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have
f(x) = ln(x)
[tex]f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }[/tex]
.
.
.
Since we need to have it centered at 9, we must take the value of f(9), and so on.
f(9) = ln(9)
[tex]f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }[/tex]
.
.
.
Following the pattern, we can see that for [tex]f^{n}(x)[/tex],
[tex]f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}[/tex]
This applies for n ≥ 1, Expressing f(x) in summation, we have
[tex]\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}[/tex]
Combining ln2 with the rest of series, we have
[tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
Find out more information about taylor series here
brainly.com/question/13057266
#SPJ4
In kickboxing, it is found that the force, fneeded to break a board, varies inversely with the length, of the board. If it takes 8 pounds of pressure to break a board that is 3 feet long, how long is a board that requires 5 pounds of pressure to break?
The board with a length of 4.8 feet would require 5 pounds of pressure to break.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let p represent the pressure and l represent the length.
l ∝ 1/p
l = k/p (k is constant)
When l = 3, p = 8, hence:
3 = k/8
k = 24
For p = 5:
l = k/p = 24/5 = 4.8 feet
The board with a length of 4.8 feet would require 5 pounds of pressure to break.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
system of equations 9x+8y=-19 ; 7x+9y=-12
Answer:
(-3,1)
Step-by-step explanation:
9x+8y=-19
7x+9y=-12
I'll assume the question is to find the solution to these equations. The solution will be the point (x,y) where the two lines intersect. The intersection is the one point that satisfies both equations (the smae value of (x,y) works in both.
We can either solve matematically of graph to find the intersection. I'll do both, and hope the answers are identical.
Matematically
Rearrange either equation to isolate one of the variables (either x or y). I'll take the second and isolate x:
7x+9y=-12
7x = -9y - 12
x = (-9y - 12)/7
Now use this definition of x in the other equation:
9x+8y=-19
9((-9y - 12)/7) + 8y = -19
(-81y - 108)/7 + 8y = -19
-81y - 108 + 56y = - 133
-25y = -25
y = 1
If y = 1, then:
9x+8y=-19
9x+8(1)=-19
9x = -27
x = -3
The solution is (-3,1)
Graphing
Graph both lines and look for the intersection. The attached graph shows the lines cross at (-3,1).
The solution, bu both approachjes, is (-3,1)
3(x - 5) = 2(x - 5) + x
Solve for x please helppp
Answer: No solution
Distribute the parenthesis
3x-15=2x-10+x
Combine like terms
3x-15=3x-10
This answer has no solution for x.
In a grade 11 class there are 30 learners. 16 of them are girls. there are 7 girls and 6 boys with blue eyes. a student is selected at random tone the class monitor what is the probability that the class monitor is a girl
Answer:
8/15
Step-by-step explanation:
possibilities/ sample size=16 girls/30 "learners"=8/15
Juliana is training to run a marathon. in her second week of training she ran 13 km more than she did during her first week of training. she ran a total of 145 km during the first two weeks of training. how far did she run during her first week of training?
Solve the following equation for a. t=G/a+h
Answer:
t = G/(a + h)
t(a + h) = G
a + h = G/t
a = (G/t) - h
t = (G/a) + h
t - h = G/a
a(t - h) = G
a = G/(t - h)
Write an equation that represents the line
Use exact. Numbers
Answer soon please
PLS HELP ASAP! Ty
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
The value of the function (h-g)(2.1) is -3.51
How to determine the function value?The equations of the functions are given as:
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
To calculate or find (h-g)(2.1), we start by calculating h(2.1) and g(2.1)
This is calculated as follows:
g(2.1)= 2(2.1)^2+3(2.1)-9
Evaluate
g(2.1)= 6.12
h(2.1)=(2.1)^2+2(2.1)-6
Evaluate
h(2.1)=2.61
The function is then calculated as:
(h-g)(2.1) = h(2.1) - g(2.1)
This gives
(h-g)(2.1) = 2.61 - 6.12
Evaluate the difference
(h-g)(2.1) = -3.51
Hence, the value of the function (h-g)(2.1) is -3.51
As a breakdown
g(x)= 2x^2+3x-9
h(x)=x^2+2x-6
g(2.1)= 2(2.1)^2+3(2.1)-9
g(2.1)= 6.12
h(2.1)=(2.1)^2+2(2.1)-6
h(2.1)=2.61
(h-g)(2.1) = h(2.1) - g(2.1)
(h-g)(2.1) = 2.61 - 6.12
(h-g)(2.1) = -3.51
Read more about composite functions at:
https://brainly.com/question/10687170
#SPJ1
Given 8 different toppings to choose from, how many 3-topping pizzas are possible?
Answer:
336 ways
Step-by-step explanation:
Use nPk which is [tex]\frac{n!}{(n-k)!}[/tex]. This is [tex]\frac{8!}{5!}[/tex]. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.
Total number of possible 3-topping pizzas are 336 ways.
How do you calculate the number of possible ways something can be arranged?In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!
Given that,
Total number of items n = 8
number of picking item k = 3
Now,
p(n,k) = [tex]\frac{n!}{(n -k)!}[/tex]
p(8,5) = [tex]\frac{8!}{(8 -3)!}[/tex]
= [tex]\frac{8!}{5!}[/tex]
= [tex]\frac{8.7.6.5! }{5! }[/tex]
= 8 × 7 ×6
p(8,5) = 336 ways
Hence, Total number of possible 3-topping pizzas are 336 ways.
To learn more about number of Possible ways from the given link:
https://brainly.com/question/4658834
#SPJ4
Nuber 17 pls (question on quadratics)
Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.
The graph is the one given at the side of the question.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:
y = a(x - 2)² - 1
The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.
y = a(x - 2)² - 1
4 = a(3 - 2)² - 1
a = 5.
Hence the equation is:
y = 5(x - 2)² - 1
Placing it into standard form, we have that:
y = 5(x² - 4x + 4) - 1
y = 5x² - 20x + 19
Hence the coefficients are:
p = 5, q = -20, r = 19.
More can be learned about the equation of a parabola at https://brainly.com/question/17987697
#SPJ1
