do this problem using the quadratic equation formula! (using the formula I did oh yes also please correct my number 1 answer)
1.x²+7x+12=0
2.x²-12x+21=0
3.18+6y-y²=0
4.3x²+14×+15=0
5.5x²-18x+12=0
Answers
The required answers for the given questions is question are 1) x = -4, 2) x = 6 - √15, 3) x = 3 + 3√3, 4) x = -3, and 5)x = -9 - √21 / 5
The quadratic Equation formula is x = -b ± √(b² - 4ac) / 2a
1. x² + 7x + 12 = 0
By using the above formula
Here a = 1, b = 7, c = 12
x = -7 ± √(7² - 4*1*12) / 2*1
x = -7 ± √(49 - 48) / 2
x = -7 ± √1 / 2
x = -7 ±1 /2
x = -7+1 /2 x = -7 - 1 / 2
x = - 6 / 2 x = -8 / 2
x = -3 x = -4
2) x²-12x+21=0
By using the above formula
Here a = 1, b = -12, c = 21
x = -(-12) ± √((-12)² - 4*1*21) / 2*1
x = 12 ± √(144 - 84) / 2
x = 12 ± √60 / 2
x = 12 ±2√15 /2
x = 12 + 2√15 /2 x = 12 - 2√15 / 2
x = 6 + √15 x = 6 - √15
3. 18+6y-y²=0
By using the above formula
Here a = -1, b = 6, c = 18
x = -6 ± √((6² - 4*(-1)*18) / 2*(-1)
x = -6 ± √(36 + 72) / -2
x = -6 ± √108 / -2
x = -6 ± 6√3 / -2
x = -6+6√3 /-2 x = -6 - 6√3 / -2
x = 3-3√3 x = 3 + 3√3
4. 3x²+14×+15=0
By using the above formula
Here a = 3, b = 14, c = 15
x = -14 ± √((14² - 4*(3)*15) / 2*(3)
x = -14 ± √(196 - 180) / 6
x = -14 ± √16 / 6
x = -14 ± 4 / 6
x = -14 + 4 /6 x = -14 - 4 / 6
x = -10 / 6 x = -18 / 6
x = -5/3 x = -3
5.5x²-18x+12=0
By using the above formula
Here a = 5, b = -18, c = 12
x = -18 ± √((18² - 4*(5)*12) / 2*(5)
x = -18 ± √(324 - 240) / 10
x = -18 ± √84 / 10
x = -18 ± 2√21 / 10
x = -18 + 2√21 /10 x = -18 - 2√21 / 10
x = -9 + √21 / 5 x = -9 - √21 / 5
Hence, the values of the given question are 1) x = -4, 2) x = 6 - √15, 3) x = 3 + 3√3, 4) x = -3, and 5)x = -9 - √21 / 5
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Related Questions
Under his cell phone plan, William pays a flat cost of $54.50 per month and $3 per gigabyte. He wants to keep his bill at $66.20 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data William can use while staying within his budget.
Answers
Answer: 66.2=54.5+3gg
gg=3.9 gigabytes
Step-by-step explanation:
66.2=54.5+3gg
3gg=66.2-54.5
3gg=11.7
gg=3.9 gigabytes
3.9 number of gigabytes of data William can use while staying within his budget.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
William pays a flat cost of $54.50 per month and $3 per gigabyte.
He wants to keep his bill at $66.20 per month.
We need to solve this and to find number of gigabytes of data William can use while staying within his budget.
This can be written as equation
66.2=54.5+3gg
Subtract 54.5 from both sides
66.2=54.5+3gg
3gg=66.2-54.5
3gg=11.7
Divide both sides by 3
gg=3.9 gigabytes
Hence, 3.9 number of gigabytes of data William can use while staying within his budget.
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Which expression is equivalent to 3/2^3 HELP ASAP
Answers
Answer:
3rd option
Step-by-step explanation:
One of our exponent rules tells us that [tex](\frac{x}{y} )^{z}[/tex] = [tex]\frac{x^{z} }{y^{z} }[/tex]. So, knowing that exponent rule, we know that it has to be the third option. But what if we didn't know that rule? Then how could we solve this?
We know that 3/2 = 1.5. Do some math and you can figure out that 1.5^3 is 3.375. If we were to evaluate expression number 3, we would get 27/8, which, if you were to further evaluate it, you would also get 3.375.
Let me know if you have any questions!
Use the diagram to find the following measures
A) triangle angle sum equation
B) value of x = ———- degrees
Answers
Answer:
x = 71°
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
The measure of two angles out of three is given, we will use the following equation to find the value of the missing angle:
82 + 27 + x = 180 add like terms
109 + x = 180 subtract 109 from both sides
x = 71
Which shape has at least one pair of perpendicular sides?
Answers
∠A and \angle B∠B are vertical angles. If m\angle A=(5x+5)^{\circ}∠A=(5x+5)
∘
and m\angle B=(6x-8)^{\circ}∠B=(6x−8)
∘
, then find the value of x.
Answers
Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles. The value of x is 13.
What are vertical angles?Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles.
Given that ∠A and ∠B are vertical angles. Therefore, the measure of the two of the given angle will be equal to each other. Thus, we can write the measure of the two angles as,
∠A = ∠B
(5x + 5)° = (6x - 8)°
5x + 5 = 6x - 8
Bring the like terms on the same side of the equation,
5 + 8 = 6x - 5x
13 = x
x = 13
Hence, the value of x is 13.
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Rewrite using an exponent.
Answers
Answer:
2[tex] {}^{5} [/tex]
Step-by-step explanation:
2×2×2×2×2 = 2[tex] {}^{5} [/tex]
explain why the statement x < 3 or > 5 cannot be written 5 < x < 3
Answers
Answer:
This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.
Step-by-step explanation:
x < 3 or x > 5
This means, x is less than 3, but greater than 5.
Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.
I need help to find x and y
Answers
The system of nonlinear equations have two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).
What is the solution of a system of nonlinear equations?In this problem we find a system of two nonlinear equations involving radical expressions. We proceed to resolve the system of nonlinear equations by algebra properties:
(2 · x - 1)² + 8√(2 · x · y) = 4
8√(2 · x · y) = 4 - (2 · x - 1)²
8√(2 · x · y) = 4 - 4 · x² + 4 · x - 1
8√(2 · x · y) = 4 · x - 4 · x² + 3
64 · (2 · x · y) = [(4 · x + 3) - 4 · x²]²
128 · x · y = (4 · x + 3)² - 8 · (4 · x + 3) · x² + 64 · x⁴
128 · x · y = 16 · x² + 24 · x + 9 - 32 · x³ - 24 · x² + 64 · x⁴ (1)
4 · y - √(8 · x · y - 1) = 1
4 · y - 1 = √(8 · x · y - 1)
(4 · y - 1)² = 8 · x · y - 1
16 · y² - 8 · y + 2 = 8 · x · y (2)
Now we plot two equations on a graphing tool and find that the system has the following two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).
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solve the problem
(4 1/3) (-2) (5/13)
Answers
The solution of the given expression (4 1/3) (-2) (5/13) is -130/13.
According to the given question.
We have an expression (4 1/3) (-2) (5/13).
Here, we have to solve the given expression.
So, the solution of the expression (4 1/3) (-2) (5/13) is given by
(4 1/3) (-2) (5/13)
= (13/3)(-2)(5/-13) (by converting the mixed fraction into improper fraction)
= (-26/13)(5/13)
= -130/13
Hence, the solution of the given expression (4 1/3) (-2) (5/13) is -130/13.
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Полоску бумаги разрезали на 7 частей. После этого самую большую
из полученных частей снова разрезали на 7 частей. Затем снова самую большую
из полученных частей разрезали на 7 частей. Так поступили много раз: на
каждом шаге самую большую часть разрезали на 7 частей. Могло ли в итоге
получиться 500 частей?
Answers
Answer:
2556285=68358556
Step-by-step explanation:
+58385-5838688(68589)8999=9858288
Given the graphs of f(x) and g(z) below, find the composition of functions f(g(-1)).
Answers
The composition of the functions, f(g(-1)) = 2.
How to Find the Composition of Functions?To find the composition of the functions, f(g(-1)), first, find the function, g(-1) by tracing the value of y that will give an x-value of -1 on the function graph.
The next step is to use the value you get in the first step to trace which value of y will give an x-value equivalent to what you got in the first step on the second function graph.
Thus, from the graph of g(x), g(-1) = 0. Using the graph of f(x), the value of y when x = 0 is 2.
Therefore, the composition of the functions, f(g(-1)) = 2.
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explain square root of 3 rational number
Answers
Answer:
[tex]\sqrt{4}[/tex], [tex]\sqrt{9}[/tex], [tex]\sqrt{16}[/tex]
Step-by-step explanation:
I think that you are asking for 3 examples of square roots that are rational. All perfect squares are rational. If the square root is not a perfect square then the number is irrational.
[tex]\sqrt{4[/tex] = 2 and -2. The number multiplied by itself is an integer. Integers are the whole numbers and their opposites: ...-3, -2, -1, 0, 1, 2, 3...
1/2 is not an integers. 0.75 is not an integer.
[tex]\sqrt{9}[/tex] is 3 and -3
[tex]\sqrt{16}[/tex] is 4 and -4
Numbers like:
[tex]\sqrt{3}[/tex] is irrational because this number in a decimal form never terminates or repeats.
Calculus 1 question
Answers
Which would increase an object’s temperature
Answers
Temperature is a physical quantity that expresses the hotness of matter or radiation. The heat increases an objects temperature.
What is temperature?
Temperature is a physical quantity that expresses the hotness of matter or radiation.
The temperature of the object increases due to the absorbed part of the heat. An object decreases its temperature by releasing energy in the form of heat to its surroundings. And an object increases its temperature by gaining energy in the form of heat from its surroundings.
So the temperature changes according to the heat of the surrounding.
Therefore the heat increases an objects temperature.
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One state has a 6% sales tax on clothing items priced at $75 or higher, and no sales tax on clothing items priced under $75. What is the total tax on the items in the table above?
Answers
For percentages, we turn it into a decimal (move it 2 places to the left) and then multiply by the number. Let’s use the example of 75 dollars. To find its tax, we would multiply $75 by .06. This equals $4.5. This means that the tax is equal to $4.5. Now we need to add this tax to our $75. 75 + 4.5 = $79.5. Our total price for this piece of clothing would be $79.5.
Let’s use another random price as an example - $84.95. $84.95 times .06 = $5.097. Now we add the tax. We would get a total of $90.047 (or $90.05, since we round to our nearest tenth in money).
For your table, you would find the tax for every individual clothing above $75. Your table says to add the total tax (NOT the totals of the prices) together. So, using the numbers I did, we would add $4.5 + $5.097. This equals $9.597, or $9.60 total tax for these items. (Note: You can just ignore items under $75)
what are the slope and the y intercept of the linear function represented by the equation y=9x-2
Answers
Answer:
the slope is 9 and the y-intercept is -2
Tatianna and Genesis are both saving money to buy new dolls. The
ratio of Tatianna's saving to Genesis's saving is 3:1. If they have
saved $400, how much has each girl saved?
Answers
Answer:
tianna has saved $300 and genesis has saved $100
Step-by-step explanation:
3 plus 1 is 4
400 divided by four is 100
3 times 100 is 300
1 times 100 is 100
tianna saved 300
genesis saved 100
help please rn please help
Answers
Answer: the answer is MO=5
Step-by-step explanation:
is it possible for a binomial and trinomial to have the same degree?
Answers
Answer:
No
Step-by-step explanation:
B/c trinomial has exactly 3 terms and binomial only have 2
Make a conjecture about each pattern. Then write the next two items. 4. 1, 2, 2, 4, 8, 32, . . .
Answers
Answer:
256, 8192
{This is an educated guess}
Step-by-step explanation:
The problem seems to be a variation of the Fibonacci sequence: 1, 1, 2, 3, 5, 8...
1 ⇒ 2: 1*2
2 ⇒ 2: 2*1
2 ⇒ 4: 2*2
4⇒8:4*2
8⇒32:8*4
32⇒256: 32*8
256*32 = 8192
how to simplify 4x5 / 1+9
Answers
Answer:
29
Step-by-step explanation:
when you multiply 4x5 you get 20
when you and 1+9 you get 10
so dividing 20/10 you get 2
Gina is making a scrapbook and is putting 6 pictures on each page. She has completed 12 pages so far. How many pictures has she used? What is the problem asking you?
PLS HELP 100 POINT QUESTION
Answers
20 points!!!What is a two step problem with variables on each side equal 20? (Please help)
Answers
5x • 4 = 2 • 10x
20x = 20x
5x-15=5+4x
+15 +5
5x=20+4x
-4x -4x
x= 20
Step-by-step explanation:
Find the vertex of the quadratic function f(x)=(x+3)2−4
Answers
The vertex of the quadratic function f(x) = (x + 3)² - 4 is (-3,-4)
How to find the vertex of the quadratic function?Given a quadratic function, the equation of the quadratic function in vertex form is given by f(x) = a(x - h)² + k where
h = x - coordinate of vertex and k = y-coordinate of vertex and (h, k) is the vertexNow, given the quadratic function f(x) = (x + 3)² - 4, we require the vertex of the quadratic function.
Comparing the function f(x) = (x + 3)² - 4 with f(x) a(x - h)² + k, we see that
a = 1, h = -3 and k = -4.Since the vertex of the quadratic function is (h, k), we see that the vertex of the quadratic function f(x) is (-3,-4)
So, the vertex of the quadratic function is (-3,-4)
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Solve the equation by the zero factor property
b^2-8b+15=0
Answers
Answer:
(b-5)(b-3)
Step-by-step explanation:
To factor this equation we have to find 2 numbers that combine to equal -8 and multiply together to equal 15
these numbers would be -3 and -5
after that you just put them in an equation like so:
(b-5)(b-3)
you can check your work by just multiplying those back together
If you want future explanation on how to do this just ask
hope this helps :D
what is the domain and range of the question below
domain=
range =
Answers
The Domain is [-4, -2] U [-1, 1) and range is [4, 0)
What is Domain and Range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
Given:
The left piece has its other endpoint at x = -2.
So, the interval for the domain is [-4, -2] and the other part is [-1, 1)
So, the domain is [-4, -2] U [-1, 1)
and the range is the vertical range of the right part.
So, range is [4, 0)
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the graph of function y
[tex]y = x ^{2} [/tex]
Answers
And both sides are symmetrical
How can i upgrade now during the trial?
Answers
Express 88 kilometers per hour in miles per hour.
mi/hr
(Round to the nearest hundredth as needed.)
Answers
88 kilometers per hour in miles per hour is 54.68 mi/hr
Converting kilometers per hour to miles per hourNote that:
1 km = 0.6214 miles
The measurement to convert is 88 kilometers per hour
Multiply 88 kilometers per hour by 0.6214 to convert to miles per hour
88 kilometers per hour = 88 x 0.6214 miles per hour
88 kilometers per hour = 54.6832 miles per hour
88 kilometers per hour = 54.68 mi/hr
Therefore, 88 kilometers per hour in miles per hour is 54.68 mi/hr
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One side of a rectangle is 4 m longer than four times another side. The area of the rectangle is 224 m².
Find the length of the shorter side.
m
Answers
Let the another side be x m.
Therefore, the longer side = (4 + 4x) m.
Now,
[tex]{\sf{→x \times (4 + 4x) = 224 \\ →4x + 4x {}^{2} - 224 = 0 \\→ x {}^{2} + x - 56 = 0 \\ →x {}^{2} + 8x - 7x - 56 = 0 \\ →x(x + 8) - 7(x + 8) = 0 \\ →(x - 7)(x +8 ) = 0 \\ →x = 7 \: or \: x = - 8 \\ \\ length \: cannot \: be \: negative \\ possible \: solution \: (x) = 7}}[/tex]
Length of shorter side = x = 7 metres.
[tex]{\sf{answer\: \\ss}}[/tex]