Answer:
1) 1x² - 9x - 109 = 0
2) 3x² -12x -15 = 0
3) 3x² + 13x - 27 = 0
4) 6x² + 84x + 236 = 0
5) -16x² + 8x + 383 = 0
Step-by-step explanation:
The standard form of the quadratic equation is ax² + bx + c where a, b and c are constants.
So we have to convert each of the equations into a form that resembles the above
(1) 11x² -98 = 11 + 9x
Simplify both sides of the equation.(2) (2x - 1)² = (x + 4) ²
Simplify both sides of the equation(3) 4x² + 2x − 9 = (x − 2)(x − 9)
Simplify (x−2)(x−9)(4) 0 = 6(x +7 )² - 58
Switch sides:(5) -1/2 ( x - 1/4 )² + 12 = 0
Calculate [tex]-\dfrac{1}{2} (x - \dfrac{1}{4})^2 = -\dfrac{1}{2} (x^2 - 2\(\dfrac{1}{4}x + \dfrac{1}{16})[/tex]which is the factor of 6z² - 3z -2 + 4?
Answer: 5732
Step-by-step explanation:
Answer: 6z^2-3z-2
Step-by-step explanation: hope this helps a little !!!!
a stick is broken into 3 pieces, by randomly choosing two points along its unit length, and cutting it. what is the expected length of the middle part?
The expected length of the middle part of the stick is 1/3
We know that the Symmetry Principal,
When n points are drooped on a unit segment, the distributions of lengths of the so obtained n + 1 pieces are all the same.
Let the two points have coordinates x and y. Then the expected value of the middle segment is:
[tex]\int\limits^1_0 \int\limits^1_0 {x-y} \, dx~ dy = \frac{1}{3}[/tex]
Let L be the expected value of the length of the middle part of a stick. Since, according to the Symmetry Principle, the lengths of all three segments have the same distribution, their lengths have the same expected value, viz., L.
But in any experiment, the lengths of the three pieces add up to 1.
⇒ 3L= 1
⇒ L = 1/3
Therefore, the expected length of the middle part of the stick is 1/3
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Quadrilateral ABCD - quadrilateral WXYZ, AB = 14 cm, BC = 28 cm, CD = 21 cm, and the scale factor of ABCD to WXYZ is 3/7. Find XY.
The length of the side of the quadrilateral is 12 cm.
A closed quadrilateral has a total of four sides, four angles and four vertices.
It is a form of polygon. In order to create it, four are joined(not colinear ). Quadrilaterals always have a total internal angle of 360 degrees.Typically, quadrilaterals will have four-sided standard shapes like rectangles, squares, trapezoids, and kites or they may be irregular and undefined.Following is another approach to group different kinds of quadrilaterals: Quadrilaterals that are convex have two diagonals that are entirely enclosed within the figure.Concave Quadrilaterals: At least one diagonal extends partially or completely beyond the boundaries of the figure.Quadrilaterals that intersect: Quadrilaterals that intersect don't just have two non-adjacent sides cross each other.Quadrilaterals of this type are referred to as self-intersecting .from the scale factor properties of quadrilaterals we know that:
Scale factor = BC ÷ XY
Now we substitute the values to find the length of XY.
[tex]or, \frac{3}{7} =\frac{BC}{XY} \\\\or, \frac{3}{7} =\frac{28}{XY}\\\\or, XY = 65.33..\\\\or, XY\approx65.33[/tex]
Hence the length of XY is 65.33 cm.
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-12=6+2/3y pls helpppp
Answer:
Y= (-27)
Step-by-step explanation:
Well, I am assuming your just looking for Y. So what I did was you'd want to get rid of the fraction first. I multiplied 3 to all the numbers. so -12(3) = 6(3) + 2y since the bottom 3 from the fraction cancelled out with the (3). so now it would be -36=18+2y. -54/2=2y/2 which leads to -27. So I think Y= -27.
Which is an equivalent expression for 4 times d raised to the negative fifth power all over quantity 18 times d raised to the ninth power end quantity?
0.2d14
negative 2 over quantity 9 times d raised to the fourth power end quantity
72 over d raised to the fourteenth power
2 over quantity 9 times d raised to the fourteenth power end quantity
The equivalent expression using laws of exponents gives us; 2 over quantity 9 times d raised to the negative fourteenth power end quantity
How to use laws of exponents?
We want to write an equivalent expression for 4 times d raised to the negative fifth power all over quantity 18 times d raised to the ninth power end quantity. This can be expressed as;
4d⁻⁵/18d⁹
Now, according to laws of exponents, we know that;
x²/x³ = x²⁻³ = x⁻¹
Applying that law to our question gives us;
4d⁻⁵/18d⁹ = (4/18)(d⁻⁵⁻⁹)
= (4/18)(d⁻¹⁴)
Now, the expression 4/18 can be broken down to 2/9. Thus, our final expression is; ²/₉d⁻¹⁴
Writing that in words gives;
2 over quantity 9 times d raised to the negative fourteenth power end quantity
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Answer: 2/9d^14 or 2 over 9 times d to the 14th power
Step-by-step explanation: AFOKE88 gave the same answer. this answer is correct you just have to understand how to write this equation in word form to understand them. they also gave a great explanation for those who need it.
Which perfect squares are nearest the square root of 11?
The perfect squares which are nearest to the square root of 11 as in the task content are; 1 and 4.
Which perfect squares are nearest the square root of 11?It follows from the task content that the perfect squares which are nearest to the square root of 11 are to be determined.
Hence, one must first determine what the square root of 11 is as follows.
The square root of 11 as given in the task content is; √11 = 3.32.
Hence, the numbers which are perfect squares and closest to the number 3.32 are; 1 and 4.
Consequently, it follows that the perfect squares as required are; 1 and 4.
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f(x) = 3x + 5
g(x) = 4x² - 2
h(x) = x²-3x+1
Find f(x) + g(x) - h(x).
O 3x² + 6x + 2
-O 3x²+2
O 6x2² +6x-1
O 5x² +4
After solving the expression we get 3x² ₊ 6x ₊ 2 .
Given f(x) = 3x₊5
g(x) = 4x² ₋ 2
h(x) = x² ₋ 3x ₊ 1
f(x) ₊ g(x) ₋ h(x)
substitute the values.
3x ₊ 5 ₊ 4x² ₋ 2 ₋ (x² ₋ 3x ₊ 1)
4x² ₊ 3x ₊ 3 ₋ x² ₊ 3x ₋ 1
3x² ₊ 6x ₊ 2
hence we get 3x² ₊ 6x ₊ 2 .
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-8|x/3+1|>-8
Please help me
Answer:
-6<x<0
Step-by-step explanation:
-8|x/3+1|>-8
-8|x/3+1|/(-8)>-8/(-8)
|x/3+1|<1
x/3+1<1
x/3<0
x<0
x/3+1>-1
x/3>-2
x>-6
-6<x<0
$2.71 divided by 2.75 round to the nearest cent?
Answer: $0.99
Step-by-step explanation:
2.71/2.75=
0.98545=
0.98545=$0.99
pls help! if the present value of an item is P and we experience an inflation rate of r for t years, blah blah blah I dont feel like writing the rest.
Answer: 89633.78
Step-by-step explanation: Hope this helps :)
Rewrite the expression in an equivalent form where the radicand is a positive integer
with no perfect square factors.
√-12
The equivalent expression of √-12 is 2√-3
How to rewrite the expression?The expression is given as
√-12
Express 12 as 3 * 4
So, we have
√-12 = √(-3 * 4)
Expand the expression
So, we have
√-12 = √-3 * √4
Take the square root of 4
√-12 = √-3 * 2
Evaluate
√-12 = 2√-3
Hence, the equivalent expression of √-12 is 2√-3
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If the theoretical value of a quantity is 3.142, and the calculated value is 3.16, what is the fractional error?
The fractional error for given example is 0.0057
For given question,
the theoretical value of a quantity is 3.142,
and the calculated value is 3.16
We know that, the fractional error is the ratio of the absolute difference and the accepted value.
Fractional error = absolute difference / accepted value
Fractional error = |E - A| / A
Here, A = 3.142
E = 3.16
So, the absolute difference would be,
|E - A| = |3.16 - 3.142|
= 0.018
Now we find the fractional error.
⇒ Fractional error = |E - A| / A
⇒ Fractional error = 0.018 / 3.142
⇒ Fractional error = 0.0057
Therefore, the fractional error for given example is 0.0057
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ms. justen had 250 students. every year after she had 100 students. calculate the amount of students she's had in 7 years
The students she's had in 7 years is 850.
How to calculate the value?It should be noted that we want to find the 7th term. This will be:
a + (n - 1)d
a = First term = 250
d = Difference = 100
n = Number = 7
Therefore, a + (n - 1)d
= 250 + (7 - 1)100
= 250 + 600
= 850
Therefore, the students she's had in 7 years is 850.
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PLEASE HElP 25 points math
Answer: 4q^2
Step-by-step explanation:
(-2q)^2=
(-2*q)^2=
(-2)^2 * q^2=
4 * q^2=4q^2
please help!!!
i need to find the area of a rectangle with length of three inches and width of 8 inches.
Answer:
24 inches square
Step-by-step explanation:
Area = length x width
A = 3 x 8 = 24
What is −10 + |−4| − |−12|?
−6
−12
−18
−22
Answer:
24
Step-by-step explanation:
write the equation of each line in slope-intercept form. then graph the line described by the equation
passes through (5,-4) and (-6,5)
(the question is number 6)
for each part, compare distributions (1) and (2) based on their means and standard deviations. you do not need to calculate these statistics; simply state how the means and the standard deviations compare
(a) The mean of (2) will be greater than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the maximum of (1) is smaller than the maximum of (2)
(b) The mean of (2) will be smaller than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the minimum of (2) is smaller but negative than the minimum of (1) which is also negative.
(c) The mean of (2) will be more than the mean of (1) and the distribution of (2) will have more variation as compared to the distribution of (1) because the maximum of (1) is smaller than the maximum of (2)
(d) The mean of (2) will be smaller than the mean of (1) and the distribution of (2) will have smaller variation as compared to the distribution of (1) because the range of (1) is greater than the range of (2)
Define mean and distribution?The mean is a measure of the central trend of a probability distribution along the median and the mode.
a distribution is the set of all possible values for terms representing defined events.
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Please help with problem 10
Answer: 13 ==> B
Step-by-step explanation:
x=-3, y=4, z=-1
|2x-3y|+5z=
|2(-3)-3(4)|+5(-1)=
|-6-12|-5=
|-18|-5=
18-5=13 ==> B
90% is 60 of what number
Answer:
Step-by-step explanation:
150 90x 100/60
Which of the following is the inverse of F(x)= 3-x/5
A. F-1(x)= 3 - x/5
B. F-1(x)= 5+x/3
C. F-1(x)= 5x - 3
D. F-1(x)= 3-5x
Answer:
Step-by-step explanation:
B
Explain why subtracting a positive number is the same as adding its inverse.
Explanation:
To add a negative number, we are basically subtracting it because of this:
Example:
10 - 5 = 5
10 + (-5) = 5
The negative sign cancels out the positive which makes it into a subtraction problem instead.
05-x=13 solve for x
i need help ASAP
Answer: X= -8
Step-by-step explanation:
Rearrange your terms:
5-X=13
-x+5+13
Subtract 5 from both sides
Simplify those = -X = 8
Dive both sides by same factor, -1
Simplify again
Solution= X= -8
A small airplane flew 104 miles in 50 minutes.at this rate,how many miles can it fly in one hour? (50 minutes = 5/6 hour)
Answer:
124.8 miles
Step-by-step explanation:
We know that if the rate of change of distance with respect to time remains constant, then the distance and time are proportional .Given : A small airplane flew 104 miles in 50 minutes. Let x be the distance traveled in 1 hour. Also, it is given that Then we have the following proportional equation:-
Hence, it can fly 124.8 miles in an hour.
A square pyramid has a volume of 4320 cubic inches. What is the volume of this pyramid in cubic feet?
The volume of the given square pyramid in cubic feet is 2.5 cubic feet.
Given that, a square pyramid has a volume of 4320 cubic inches.
We need to find the volume of this pyramid in cubic feet.
What is the volume of a square pyramid?The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height).
To convert from cubic inches to cubic feet, divide your cubic inches figure by 1728.
Now, 4320/1728 = 2.5 cubic feet
Therefore, the volume of the given square pyramid in cubic feet is 2.5 cubic feet.
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if a figure is a rectangle, then it has four sides
Answer:
True
(If it has 4 sides it is also known as a Quadrilateral!)
Step-by-step explanation:
Answer:
yes
the reson for htis is b/c retangles are qudrilateral and quadtrialterals have four sides
You start a savings account with $200 and save $30 each month. Let f(n) be the amount in the account before the nth month. How much money will you have invested at one year?
The money you will have invested at one year is $560
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How much money will you have invested at one year?The given parameters are:
Initial = $200
Rate = $30
Let the number of months be n
So, we have
f(n) = Initial + Rate * n
This gives
f(n) = 200 + 30n
There are 12 months in a year
So, we have:
f(12) = 200 + 30 * 12
Evaluate
f(12) = 560
Hence, the money you will have invested at one year is $560
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pls help What is the sum? will mark brainiest
47+ 85⎯⎯⎯⎯⎯⎯⎯
Answer:
132
Step-by-step explanation:
Confused with this problem please help. "The measure of the supplement of an angle exceeds 3 times the measure of the complement by 30. Find the measure of the supplement."
Evaluate the expression (p + 4)^2 for p = -5 and g = -2.
^2 is square 2
=================
Work Shown:
(p+4)^2
(-5+4)^2
(-1)^2
1
Explanation:
We replace p with -5, since p = -5. Then use the order of operations PEMDAS to simplify. Keep in mind that (-1)^2 = (-1)*(-1) = 1. The two negatives cancel out. The value of g is never used.