By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
How to solve a quadratic function by the quadratic formula
Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] (1)
Where a, b, c are the coefficients of the quadratic function.
In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:
[tex]x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{1} = \frac{2 + \sqrt{4-40}}{4}[/tex]
x₁ = 0.5 + i 1.5
[tex]x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{2} = \frac{2 - \sqrt{4-40}}{4}[/tex]
x₂ = 0.5 - i 1.5
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
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Alice weighs 20 dogs and 20 cats. The mean weight for the dogs is 32kg and the mean weight for cats is 4kg. The range in weight for dogs is 45kg and the range in weight for cats is 0.5kg. State two conclusions you can draw from this information.
With the mean and range, we can estimate the weights of the smallest and largest animals in each group.
For cats the interval is [ 3.75kg, 4.25kg] and for dogs is [9.5kg, 54.5kg]
Which conclusions can be made with the given information?
We know that the mean weight for cats is 4kg, and the range (difference between the largest value and smallest value) is 0.5kg.
From that, we can conclude with some confidence (but not exactly), that the largest cat weights 4kg + 0.5kg/2 = 4.25kgAnd the smallest cat weights 4kg - 0.5kg/2 = 3.75kg(Assuming a normal distribution).
Similar for the dogs, the mean weight is 32kg and the range is 45kg, then:
The largest dog weights 32kg + 45kg/2 = 54.5kgThe smallest dog weights 32kg - 45kg/2 = 9.5kg(again, assuming a normal distribution).
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Find the equation of the line through the points (-2,4) and (3,-5) using point-slope form. Then rewrite the equation in slope-intercept form.
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-5 -4}{3 +2}\implies \cfrac{-9}{5}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{9}{5}}(x-\stackrel{x_1}{(-2)})\implies y-4=-\cfrac{9}{5}(x+2) \\\\\\ y-4=-\cfrac{9}{5}x-\cfrac{18}{5}\implies y=-\cfrac{9}{5}x-\cfrac{18}{5}+4\implies y=-\cfrac{9}{5}x+\cfrac{2}{5}[/tex]
Think about triangles that have
a perimeter of 15cm,
two or more equal sides,
and each side a whole number of centimetres.
Prove that there are only four of these triangles. i
In order to prove that there are only four of these triangles, we need to first restate the formula for the perimeter of a triangle which is given as: P = a + b + c. Hence, we must identify all the triangles that have two or more equal sides, and each side is a whole number.
What is the proof?
Step 1 - First, we state all the possible combination three whole numbers which when added together result in fifteen.
The numbers are given as:
1 1 132 2 113 3 94 4 75 5 56 6 37 7 1Step 2 - Eliminate options where a side is more than the sum of the other two sides
Hence,
are eliminated. The remaining triangles are four in number.
QED.
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What is m/D?
118°
B
87°
A
D
23/24-
A
12
Answer:
[tex]62^\circ[/tex]
Step-by-step explanation:
This is a cyclic quadrilateral (all points of the quadrilateral are on the circle), meaning opposite angles are supplementary (add up to [tex]180^\circ[/tex]).
[tex]\angle D[/tex] is opposite [tex]\angle B[/tex], which is equal to [tex]118^\circ[/tex]. This means [tex]\angle D[/tex] is equal to [tex]180^\circ - 118^\circ[/tex], which is [tex]\boxed{62^\circ}[/tex].
A trellis consists of overlapping wooden slats.
1.What is the position of the indicated angles?
2.What should the value of x be in order for the two slats to be parallel?
3. Which theorem or postulate will you use to prove the parallel slats?
4. Find the measure of the indicated angle.
The value of x in order for the two slats to be parallel is 6.
The measure of the indicated angle is 42°
What is an angle?
The angle is the measure of how inclined are the two surfaces, or lines with respect to each other.
For the slats to be parallel. both the given angles must be equal
So,
(3x +24)° = 7x°
Solving this expression, we get
7x -3x = 24
4x =24
x = 6°
The measure of the indicated angle is
(3x +24)° = 3x6 +24
(3x +24)° = 18+24
(3x +24)° =42°
and 7x = 7x6 =42°
Thus, the measure of the angle is 42°
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Please solve (30 points)
A real life example of an acute angle is the angle that's made in letter V.
What is a acute angle?It should be noted that an acute triangle simply means an angle that measures less than 90 degrees.
In this case, the real life example of an acute angle is the angle that's made in letter V. Other examples include slizing a pizza into different shapes.
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PLEASE PLEASE HELP ILL LIKE AND ITS WORTH 20 POINTS !!
Answer:
Left one: 27.755 Right one: 3487.5
Step-by-step explanation:
You have to use sin of angle to find the area.
Katy invests a total of $13,000 in two accounts paying 2% and 7% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $310.00.
Invested at 2%___?
Invested at 7%___?
Answer:
2 % amount = 12000 7% amount = 1000 dollars
Step-by-step explanation:
x = 2% amount
then 13 000 - x = 7% amount
.02x + .07 (13000-x) = 310
-.05x + 910 = 310
.05x = 600
x = 600/.05 = 12000 then the 7% amount is 1000
2x-y=7
x+y=5
Use elimination
In other words, x = 4 and y = 1
==============================================
Explanation:
Add the equations straight down.
The x terms add to 3x because 2x+x = 3xThe y terms go away when you add them since -y+y = 0y = 0The terms on the right hand sides add to 7+5 = 12After those three sets of adding terms, we end up with 3x = 12. This solves to x = 4 when you divide both sides by 3.
Use this x value to find y.
2x-y = 7
2(4)-y = 7
8-y = 7
-y = 7-8
-y = -1
y = 1
or
x+y = 5
4+y = 5
y = 5-4
y = 1
Your best best is probably to use the second equation, but it doesn't hurt to have practice with both equations. Getting the same y value helps confirm we have the correct x value.
Therefore, the solution is the ordered pair (x,y) = (4,1). Meaning that x = 4 and y = 1 pair up together.
Visual confirmation can be done by using a graphing tool like Desmos. The two lines intersect at (4, 1). See below.
Simplify as far as possible without a calculator.
3√7(2√2+4√7)
Answer:
[tex]6 \sqrt{14} + 84[/tex]
Step-by-step explanation:
distribute 3√7 by multiplying to each term In parenthesis
3√7×2√2+3√7×4√7
6√14+12√49
6√14+12(7)
6√14+84
6√14 + 84
or
106.449944321
Step-by-step explanation:
have √7 behave like a variable like x
have √4 behave like a variable like y
3√7(2√2+4√7)
(3√7*2√2)+ (3√7*4√7)
6√14 + (12*7)
6√14 + (84)
6√14 + (6 * 14)
If the mean annual wage of her career is $35,240.00, what will her lifetime earnings be when she retires at the age of 60?
Answer:
2,114,400
Step-by-step explanation:
35,250 x 60 = 2,114,400
PLEASE HELP ASAP <3
Evaluate: 23+x/8 for x = 8
O 24
O 3.875
O 20
O 18
Answer:
Your first step would be to rewrite the equation, were x =8 so it would look like this
Step-by-step explanation:
23 + 8/8 = ?
than solve. 8/ 8 = 1 and 23+1 = 24
NEED ASAP PLS HELP
given: XZ WY, WXZ and YXZ are right triangles. Step 1: cos(W)=WZ/y; ycos(W)=Wz. Which step contains the first error in calculation
The sine ratio that was applied in step 2 is incorrect, therefore, the first error is in: B. step 2.
How to Apply the Sine Ratio?The sine ratio that is applied when we want to solve a right triangle is, sin ∅ = opposite length / hypotenuse length.
In step 2, the sine ratio applied is wrong because:
∅ = WOpposite length = XZHypotenuse length = yThus, we should have:
sin(W) = XZ/y
The first error is in: B. step 2.
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What is the equation of the function shown in the graph, given that the equation of the parent function is f(x)=(1/7)^x
The equation of the graphed function is given as follows:
g(x) = (1/7)^x - 4.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
f(x) = (1/7)^x.
(which has an asymptote at y = 0).
The function was shifted down 4 units, meaning that the translated function is given as follows:
g(x) = (1/7)^x - 4.
And the correct option is given by the first option.
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Are the equations 1/2x-8=9 and x-8=18 equivalent?
Answer:
not equivalent
Step-by-step explanation:
solve for x to see if they are equivalent
1/2x-8=9 and x-8=18
1/2x=17
x=34
x-8=18
x = 36
no they are not equivalent
Please help with the Area
I'm pretty sure it is, but it just seems so onesided so I wanted to make sure, is this correct?
1. On a train ride cross-country, the trees, buildings, and people appear to be speeding by the window. This is because the train is our _____
2. Scientists use the ______
system for making measurements.
3. Physical science studies the relationships between ____,____,
and ______.
4. If 6.6 tyrannosaurs weigh 30,000 kg, then what does one tyrannosaur weigh?
5. For most activities, the ___
makes a handy frame of reference.
On a train ride cross-country, the trees, buildings, and people appear to be speeding by the window. While traveling in a train, it appears that the trees near the track are moving whereas co-passengers appear to be stationary.
How to explain the measurements?When measuring, scientists use a shared system of measurement, called the International System of Units (SI). Physical science is concerned with the study of natural but non-living objects.
If 6 tyrannosaurs weigh 30,000 kg, the weight of one tyrannosaur will be;
= 30000/6
= 5000kg
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A student claims that tan^2 0+1 = sec^2 0 can be converted to sin^2 0 + cos^2 0 = 1. which sequence of steps supports this claim?
Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.
Here,
tan²θ + 1 = sec²θ
sin²θ/cos²θ + 1 = 1/cos²θ
By taking LCM, we get
(sin²θ + cos²θ)/cos²θ = 1/cos²θ
(sin²θ + cos²θ) = cos²θ/cos²θ
(sin²θ + cos²θ) = 1
Thus, Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
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help please! will give brainle giving 20 points love !
Answer:
D. 75%
Step-by-step explanation:
100% - 25% = 75%
Answer:
D. 75%
Step-by-step explanation:
If 25% get into an accident then how many teenagers don't? :
100% - 25% = 75%
Have a great day! :)
help me please, i need an answer asap
Answer:
answer is A - library books by genre and by Adult or Child
Step-by-step explanation:
your column on the left will have different genre of books
your top column will have children or adults
What are the coordinates of the vertices of the image?
Translate the shape A four squares right and two squares down.
Answer:
see explanation
Step-by-step explanation:
a translation of 4 squares right means add 4 to the x- coordinate
a translation of 2 squares down means subtract 2 from the y- coordinate
then
(1, 1 ) → (1 + 4, 1 - 2 ) → (5, - 1 )
(3, 1 ) → (3 + 4, 1 - 2 ) → (7, - 1 )
(1, 4 ) → (1 + 4, 4 - 2 ) → (5, 2 )
NoT YellInG ThIS IS JuSt TO AtTRaCT AtTeNTiOn 50 POiNtS PLeaSE ANswER I Am NoT WasTiNg PoInTS!!! Find the range of 1 1/4, 5/8, 3/4, 1/2, 1 1/2, and 1 3/4
Answer:
Range = 1 1/4
Step-by-step explanation:
Range = Maximum - Minimum
Arranging the data in ascending order :
1/2, 5/8, 3/4, 1 1/4, 1 1/2, 1 3/4Solving for range :
Range = 1 3/4 - 1/2Range = 1 3/4 - 2/4Range = 7/4 - 2/4Range = 5/4Range = 1 1/4Guys please can you help with this question i dont get it at all. 10 x (-8)
Answer:
80 maybe no ummm udk sorry I might
Step-by-step explanation:
I got you I think
Astrid travels 130 km in 2 hours and then at 85 km/h for another 3 hours to reach her
destination. On the return journey home, she travels a total of 5 hours.
Determine the speed of the car that Astrid will travel to get home.
Answer:
[tex]\huge\boxed{\sf Speed = 77\ km/hr}[/tex]
Step-by-step explanation:
Formula to be used in the question:Speed = Distance / TimeDistance for the first 2 hours:= 130 km
Distance for the next 3 hours:Speed = 85 km/h
Time = 3 hours
So,
Distance = Speed × Time
Distance = 85 × 3
Distance = 255 km
So,
Total distance from home to destination:= 130 + 255
= 385 km
Speed on the return journey:Total distance = 385 km
Time = 5 hours
Speed = Distance / Time
Speed = 385 / 5
Speed = 77 km/hr
[tex]\rule[225]{225}{2}[/tex]
PLEASE HELP QUICK :(
Answer:
A
Step-by-step explanation:
Thats how the mean works lol
Find the distance between the points with coordinates (0,-2,0), (3,0,-6).
Answer:
[tex]C)~ 7~ \text{units}.[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1,z_1) = (0,-2,0)~ \text{and}~ (x_2,y_2,z_2) = (3,0,-6)\\\\\text{Distance,}~ d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\\\\~~~~~~~~~~~~~~~=\sqrt{(3-0)^2 + (0+2)^2 +(-6-0)^2}\\\\~~~~~~~~~~~~~~~=\sqrt{3^2 +2^2 +(-6)^2}\\\\~~~~~~~~~~~~~~~=\sqrt{9+4+36}\\\\~~~~~~~~~~~~~~~=\sqrt{49}\\\\~~~~~~~~~~~~~~~=7~ \text{units}.[/tex]
10 + (2 x 3)2 ÷ 4 × 1 over 2 to the power of 3
Answer:
1.4375
Step-by-step explanation:
[tex]\frac{10 + (2 x 3)^{2} / (4)(1)}{2^{3}} \\[/tex]
[tex]\frac{10 + (6)^{2} /4}{8} \\[/tex]
[tex]\frac{10 + 36 / 4}{8} \\[/tex]
[tex]\frac{46 /4}{8} \\[/tex] = [tex]\frac{11.5}{8} \\[/tex]
Determine the solution for the following equation: (8x-8) 3/2 = 64
x = 3
x = 5
x = 13
x = 65
The correct answer is option A which is x = 3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The expression will be solved as:-
( 8x - 8 )[tex]^\dfrac{3}{2}[/tex] = 64
We can write 64 as [tex]16^{\dfrac{3}{2}}[/tex]
( 8x - 8 )[tex]^\dfrac{3}{2}[/tex] = [tex]16^{\dfrac{3}{2}}[/tex]
8x - 8 = 16
8x = 24
x = 3
Therefore the correct answer is option A which is x = 3.
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Answer:
A. x=3.
Step-by-step explanation:
Edge 2022.
30,098 in standard form
30,098 to four significant figures