Answers
The equation that expresses the solution to the quadratic equation x² - 10x + 13 = 0 is [tex]x =5 \pm 2\sqrt{3}[/tex]
How to express the solution?The equation is given as:
x² - 10x + 13 = 0
The solution to a quadratic equation is represented by:
[tex]x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
So, we have:
[tex]x =\frac{10 \pm \sqrt{(-10)^2 -4 * 1 * 13}}{2 * 1}[/tex]
Evaluate the radicand
[tex]x =\frac{10 \pm \sqrt{48}}{2}[/tex]
Take the square root of 48
[tex]x =\frac{10 \pm 4\sqrt{3}}{2}[/tex]
Divide
[tex]x =5 \pm 2\sqrt{3}[/tex]
Hence, the equation that expresses the solution to the quadratic equation x² - 10x + 13 = 0 is [tex]x =5 \pm 2\sqrt{3}[/tex]
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Related Questions
A bag of candy contains 5 red, 4 blue, 6 green, and 3 yellow candies. what is the probability of randomly selecting one candy that is blue or yellow? ( answers 1.)38.9% 2.) 55.6% 3.)16.7 4.)22.2%
Answers
Answer:
1) 38.9%
Step-by-step explanation:
There are 18 total pieces of candy, 4 of which are blue, and 3 of which are yellow. So the probability of randomly selecting one blue or one yellow piece of candy is
[tex] \frac{3}{18} + \frac{4}{18} = \frac{7}{18} = 38.9\%[/tex]
Scientists have sent a 62 kg rover to a new planet. The rover's force of gravity on this planet is 334.8 N. What is the gravity constant for this new planet?
Answers
Answer:
5.4 meters per square second
Step-by-step explanation:
If that rover was on the Earth the weight of it would be 620 N (62*10)
In the new planet the gravitational acceleration is not same as the earth it's definitely less than that of the earth
Let's take the gravity constant of the plant as x.
so, 62*x= 334.8 N
x= 334.8/62
x= 5.4
help me please help
Answers
Step-by-step explanation:
n + 34 = 34 + n
commutative means you can change the sequence of the parts without changing the overall result.
g × h = h × g
s + 0 = s
b × 1 = b
the identity property points are to show that adding 0 or multiplying by 1 does not change anything.
Kanya is comparing the rate for shipping and handling for two online shopping websites. For the item she has selected, Big Bargain Bonanza charges $8.00 for handling and $1.25 per pound for shipping. Discount Deals Depot charges $9.50 for handling and $0.95 per pound for shipping for the same item. If her item weighs 6 lbs, which website charges less for shipping and handling, and how much does it charge?
A. Big Bargain Bonanza; $15.50
B. Discount Deals Depot; $10.45
C. Big Bargain Bonanza; $9.25
D. Discount Deals Depot; $15.20
Answers
D. Discount Deals Depot; $15.20
Why?
Lets do Big Bargain Bonanza first.
$8.00 would stay the same as it is for handling. The only number that would change is $1.25, it uses the the words PER pound for shipping.
Your equation would look like this with p being how many pounds Kanya is shipping:
$8.00+$1.25p
Now we just plug in the numbers.
$8.00+$1.25(6)=
$8.00+$7.50=
$15.50
The same games for Discount Deals Depot.
$9.50+$0.95(6)=
$9.50+$5.70=
$15.20
So in conclusion Discount Deals Depot; $15.20 is cheaper than Big Bargain Bonanza;$15.50
Kai had a gross weekly paycheck of $616 last week. Kai worked 6 hours for 4 of the days and 8 hours on 1 day. What
is Kai's hourly rate of pay?
a $16.21
b. $19.25
C. $20.53
d $25.67
Please select the best answer from the choices provided
Ο Α
OD
Mark this and retum
Save and Frit
Answers
Answer:
Kia makes 19.25 dollars an hour.
Step-by-step explanation:
6x4+8=32 (hours: 6 hours for 4 days, and 8 hours for 1 day)
616 divided by 32 = 19.25
What is the range of y=-3x+1 for the domain of {2, 8}
Answers
Answer:
[0,∞), {y|y≥0}
Step-by-step expl
The graph of y =|3x + 1| is attached.
By observation, we can see that the the least y-value that the graph can take is y =0 (i.e the x-axis) and the greatest y-value that the graph can take is positive infinity.
Hence the range is [0,∞), {y|y≥0}
Step-by-step explanation:
the domain is the set or interval of all valid x-values.
the range is the set of interval of all valid y-values.
the function is a line function, so it's values will continuously increase with increasing x-valies.
therefore we can simply take the 2 interval ends of the domain as the x-values that create the lowest and the highest functions value in that interval.
the function does not make any large twists and turns in that interval.
y = 3x + 1
for x = 2
y = 3×2 + 1 = 6 + 1 = 7
for x = 8
y = 3×8 + 1 = 24 + 1 = 25
so, the range is [7, 25]
need help please !!!
Answers
Answer:
7.8
Step-by-step explanation:
since the shape is a right angled triangle,
we use Pythagoras theorem to find
X= ✓6^2+5^2 = √36+25=. √61 =7.8
A courier service delivers packages which cost $1.60 per package to deliver. The fixed cost to run the delivery van is $56.00 per day. If the company charges $5.60 per package, how many packages must be delivered daily to break even?
Answers
Answer:
14 packages
Step-by-step explanation:
profit = revenue - expenses
we want profit to be 0
0 = revenue - expenses
revenue = 5.60 per package = 5.60 * number of packages
expenses = 56 + 1.60 per package = 56 + 1.6 * number of packages
0 = revenue - expenses
let's say the number of packages = n
0 = 5.6 * n - (56 + 1.6 * n)
= 5.6n - 56 - 1.6n
= -56 + 4n
add 56 to both sides to isolate the variable and its coefficient
56 = 4n
divide both sides by 4 to isolate the variable
n = 14
À point has been translated left and down. Based on the graph, which could be true? Check all that apply.
Answers
Answer:
Step-by-step explanation:
B is the image of D
6 left
2 down
Answer: C (in choices)
B is the image E
6 down
5 left
Answer: D (in choices)
C is the image of D
1 left
2 down
Answer: F (in choices)
Find the surface area?
Answers
20x10.5x20= 4200
So it would be 4200
I need help graphing I’m not sure where to start
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1. The most common type of item found during clean up was small plastic pieces.
2. The least common type of item found during clean up was food wrappers.
3. In my opinion, the litter from our clean up that is most harmful to our aquatic ecosystem is the small plastic pieces. Researchers estimate that over one million animals die each year after ingesting, or becoming entrapped in, improperly discarded trash.
Plastic litter is the most common killer of animals, and marine animals are the most notably affected. Each year over 100,000 dolphins, fish, whales, turtles, and more drown after becoming entangled in or digesting plastic litter. This is why the small plastic pieces are the most harmful in my opinion.
The distance between A(-4,2) and B(4,2) is a.6 b.8 c.4
Answers
Answer:
We can see that our y-value of our coordinates do not change so we can just subtract the first x-value from the second x-value.
[tex]x_2 - x_1[/tex]
[tex]4 - (-4)[/tex]
[tex]8[/tex]
The option that best matches our answer is Option B, [tex]8[/tex]
Hope this helps! Let me know if you have any questions
A drawing of a box with flowers painted on it. The length of the box is marked l, the width is marked 6 inches and the height is marked 2 inches.
Answers
Answer: If this is a 2D box, the length would be 2
Step-by-step explanation:
pleaseeeeeeeeee help me
Answers
Answer:
x=66
Step-by-step explanation:
35-13=22
22*3=66
x=66
Answer:
X=66
Step-by-step explanation:
66 divided by 3 =22
13+22=35
TAKE TIME AND HELP FOR BRAINLIEST!
Graph the function with domain of all the real numbers: f(x) = 5 for x ≥ 3, and f(x) = -6 for x < 3
Answers
Answer:
I used Desmos to graph your requirements, and i took a screenshot of the graph. Credit to Desmos for the great graphing system.
Step-by-step explanation:
Answer:
see image
Step-by-step explanation:
Anytime you see f(x) that just means y.
So f(x)=5 just means
y = 5
Anytime you have an equation to graph that is in the format
"y= anumber", that is a Horizontal line. So the first piece of your graph is the horizontal line thru 5. But also that's only for x>=3. It includes the 3 with the "or=to" underline. So the point must be a solid filled-in point. (Some weird books or teachers use a [ square bracket.) Same logic works for the second piece of the function. f(x) = -6 is the same as y= -6 and is a horizontal line thru -6. But the point at (3, -6) is an Open dot! See image.
What is the slope of the line that passes through the points ( 1 , − 1 ) (1,−1) and ( − 8 , − 7 ) (−8,−7)? Write your answer in simplest form.
Answers
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-8}-\underset{x_1}{1}}}\implies \cfrac{-7+1}{-9}\implies \cfrac{-6}{-9}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3}[/tex]
The slope of the line that passes through the points (1,−1) and (−8,−7) is m = 2/3.
What is the slope of a straight line?Slope tells how vertical a line is. The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
Its slope would be: [tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
If a line passes through two points, then its slope can be calculated with the following :
[tex]m = \dfrac{y-q}{x-p}[/tex]
Plugging in our values, we get:
[tex]m = \dfrac{-7 + 1}{-8 - 1}[/tex]
Now, let's simplify our result:
[tex]m = \dfrac{-7 + 1}{-8 - 1}\\\\m = \dfrac{-6}{-9}[/tex]
m = 2/3
Therefore, the slope of the line that passes through the points (1,−1) and (−8,−7) is m = 2/3.
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Anybody want to help with math?
(5x^4+6x^3-9x^2)-(-6x^4-6x^3+8x)
Ty :D
Answers
Answer:
11x⁴+12x³-9x²-8x
Step-by-step explanation:
M.a.t.h.w.a.y
Find the probability of each event
Ashley is carrying ten pages of math
homework and three pages of English
homework. A gust of wind blows the
pages out of her hands and she is only able
to recover ten random pages. What is the
probability that she recovers all of her
math homework?
Answers
Answer:
Around 77%
Step-by-step explanation:
10/13 = 0.769
In six hours, yokai reads 36 chapters. What is her rate in chapters per hour?
Answers
Answer:
her rate in chapters per hour is:
6 chapters per hour
2: The only contents of a bag are 4
red balls and 6 blue balls. What is the
probability that two balls drawn at
random from the bag will be red if
the first ball drawn is not replaced?
Answers
Answer:
2÷15Step-by-step
the total number of balls in the in the bag is 10
Then
the probability of drawing a red ball on the first draw is 4/10.
…………………………………………………………
Now , if the first ball drawn is not replaced.
Then
the probability of drawing a red ball on the Second draw is 3/9.
……………………………………………
Conclusion:
the probability that two balls drawn at random from the bag will be red if the first ball drawn is not replaced is :
(4÷10)×(3÷9)
= (2÷5)×(1÷3)
= 2÷15
= 0.133333333333
Given the following triangle:
В(2x+4)
A(2x-9)
Find the measure of angle A:
Find the measure of angle B:
Answers
Answer:
A=61, B=74
Step-by-step explanation:
Because all the angles in a triangle add up to 180:
(2x+4) + (2x-9) + x = 180
If you solve that for x, you will get that x=35. Now you just plug in x to the angles A and B.
Why is not the term perimeter used instead of circumference?
Answers
Answer:
Circumference is a special case of perimeter. Both describe the total length of the boundary of a two dimensional figure, but circumference specifically refers to the perimeter of a curved figure or arc. Therefore it only applies to circles, ovals, ellipses, arcs, etc.
Answer:
Both words are used to talk about how long the boundary is of a 2D figure. Think of circumference as a special case of finding the perimeter. The term circumference refers to the perimeter of a figure without sides or something like a circle or arc.
So if we were to look at a rectangle and try to determine how long the boundary is we would use perimeter. On the other hand, if we have a circle we have no way to track how long each side is therefore we use circumference.
:D Can someone help me?
Answers
Answer:
A and D are correct.
How many groups of 1/4 are in 9
Answers
Answer:
36 quarters
9 / 0.25 = 36
The theoretical probability of a couple having a baby girl is . what is p(girl, girl, girl)?
Answers
The value of the probability expression p(girl, girl, girl) is 1/8
How to determine the probability?The theoretical probability is given as:
P(girl) = 1/2
The value of p(girl, girl, girl) is calculated using:
p(girl, girl, girl) = p(girl) * p(girl) * p(girl)
So, we have:
p(girl, girl, girl) = 1/2 * 1/2 * 1/2
Evaluate
p(girl, girl, girl) = 1/8
Hence, the value of the probability expression p(girl, girl, girl) is 1/8
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Express tan J as a fraction in simplest terms. Leg=13 Leg=9 hyp=?
Answers
From the figure, the value of tan j is 13/9
How to determine the value of tan j?The tangent of an angle is represented as: :
tan(j) = opposite leg/adjacent leg
From the figure, we have:
opposite leg = 13
adjacent leg = 9
Substitute these values in the above equation of tangent
tan(j) = 13/9
Hence, the value of tan j is 13/9
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what is the product of 2/3 and 1/5
Answers
2 * 1 is 2
3 * 5 is 15
One force of 8 pounds and one force of 2 pounds act on a body at the same point so that the resultant force is 8. 8 pounds. find the angle between the two original forces, to the nearest 10th of a degree
Answers
Answer:
1,280 I'm sure that's is answer thank youevaluate |-7| + 3|4|
Answers
|-7| + 3|4|
7 + 12
19
hope it helps...!!!
Answer: Heyaa! ~
Your Answer Is 19, Which is C.
Step-by-step explanation:
The absolute value of a number is always positive, so |-7| is 7 and |4| is 4. 4 * 3 = 12 and 12 + 7 is 19.Order of operations:
PEMDAS
ParenthesisExponentMultiplyDivideAddSubtractHopefully this helps you! ^
guys,help please with geometry if u can)
1. In triangle ABC, angle A is 30, angle B is 45, AC=9 Find BC.
2. Sides AB and AC of triangle ABC are 6 and 10 respectively, angle BAC is 120 Find the length of side BC.
3. In the triangle ABC BC35, AC13, AB43. Find the angle C. Give the answer in degrees.
maybe give me answers to two of them, don't really care,just try please.
Answers
Answer:
1.6.36 cm
2
Step-by-step explanation:
Using sine rule to find the length of the BC.
