Answer:
x=1+2√2 or x=1−2√2
Step-by-step explanation:
Let's solve your equation step-by-step.
3x2−6x=21
Step 1: Since the coefficient of 3x^2 is 3, divide both sides by 3.
3x2−6x
3
=
21
3
x2−2x=7
Step 2: The coefficient of -2x is -2. Let b=-2.
Then we need to add (b/2)^2=1 to both sides to complete the square.
Add 1 to both sides.
x2−2x+1=7+1
x2−2x+1=8
Step 3: Factor left side.
(x−1)2=8
Step 4: Take square root.
x−1=±√8
Step 5: Add 1 to both sides.
x−1+1=1±√8
x=1±√8
x=1+2√2 or x=1−2√2
31. Last month, Sharon's Deli charged the Business Club $231
for 18 chicken lunches and 14 ham lunches. This month,
the charge was $225.00 for 15 chicken lunches and 16 ham
lunches. The bill does not list the price of a single chicken
or ham lunch, but you need to know this so you can bill the
members individually. How much did a single chicken
lunch cost?
A. $6.00
B. $6.50
C. $7.00
D. $7.25
E. $7.50
A single chicken lunch will cost $7 so option (C) will be correct.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say the cost of chicken = c
cost of ham = h
Given,
Sharon's Deli charged the Business Club $231 for 18 chicken lunches and 14 ham lunches.
So,
18c + 14h = 231
And,
$225.00 for 15 chicken lunches and 16 ham
So,
15c + 16h = 225
By solving both equations
h = 7.5 and c = 7
Hence, a single chicken lunch will cost $7
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what is the surface area of a cylinder in terms of pi height 10in radius 5in
ANSWER
[tex]T.S.A = 150\pi[/tex] square inches.
EXPLANATION
The total surface area of a cylinder is given by;
[tex]T.S.A = 2\pi \: r(r + h)[/tex]
The height of the cylinder is , h=10in.
The radius of the cylinder is, r=5in.
We substitute the known values into the formula to obtain;
[tex]T.S.A = 2\pi \times 5(5+ 10)[/tex]
[tex]T.S.A = 10\pi(15)[/tex]
In terms of π, the total surface area is
[tex]T.S.A = 150\pi in^2[/tex]
find the roots of the polynomial equation x3 - 2x2 + 10x + 136 = 0
Answer: x=-4,3+5x; 3,-5x
step-by-step explanation: I just used ,athway. this is what is told me. i hope this helps
Which function corresponds to the table?
x y
0 3
1 1
2 -1
A) y = 3x - 2
B) y = 2x + 3
C) y = -2x + 3
D) y = -3x + 2
Answer:
c
Step-by-step explanation:
Use the following matrices, A, B, C and D to perform each operation.
A = |3 1|
|5 7|
B = |4 1|
|6 0|
C = |-2 3 1|
|-1 0 4|
D = |-2 3 4|
|0 -2 1|
|3 4 -1|
40. A + B
41. B - A
42. 3C
43. CD
44. 2D + 3C
Step-by-step explanation:
[tex]\bold{40.}\\\\A+B=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right] +\left[\begin{array}{ccc}4&1\\6&0\end{array}\right] =\left[\begin{array}{ccc}3+4&1+1\\5+6&7+0\end{array}\right]=\left[\begin{array}{ccc}7&1\\11&7\end{array}\right][/tex]
[tex]\bold{41.}\\\\B-A=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]-\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]=\left[\begin{array}{ccc}4-3&1-1\\6-5&0-7\end{array}\right]=\left[\begin{array}{ccc}1&0\\1&-7\end{array}\right][/tex]
[tex]\bold{42.}\\\\3C=3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]=\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]=\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]
[tex]\bold{43.}\\\\CD=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]\\\\=\left[\begin{array}{ccc}(-2)(-2)+(3)(0)+(1)(3)&(-2)(3)+(3)(-2)+(1)(4)&(-2)(4)+(3)(1)+(1)(-1)\\(-1)(-2)+(0)(0)+(4)(3)&(-1)(3)+(0)(-2)+(4)(4)&(-1)(4)+(0)(1)+(4)(-1)\end{array}\right]\\\\=\left[\begin{array}{ccc}4+0+1&-6-6+4&-8+3-1\\2+0+12&-3+0+16&-4+0-4\end{array}\right]\\\\=\left[\begin{array}{ccc}5&-8&-6\\14&13&-8\end{array}\right][/tex]
[tex]\bold{44.}\\\\2D+3C=2\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]+3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\\\\=\left[\begin{array}{ccc}(2)(-2)&(2)(3)&(2)(4)\\(2)(0)&(2)(-2)&(2)(1)\\(2)(3)&(2)(4)&(2)(-1)\end{array}\right]+\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]\\\\=\left[\begin{array}{ccc}-4&6&8\\0&-4&2\\6&8&-2\end{array}\right]+\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]
[tex]\large\bold{You\ can\ not\ add\ matrices\ of\ different\ dimensions!!!}[/tex]
Find the polynomial f(x) of degree 3 with real coefficients that has a y-intercept of 60 and zeros 3 and 1+3i.
[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=1+3i\implies &x-1-3i=0\\ x=1-3i\implies &x-1+3i=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x-3)(x-1-3i)(x-1+3i)=0 \\\\\\ (x-3)\underset{\textit{difference of squares}}{([x-1]-3i)([x-1]+3i)}=0\implies (x-3)([x-1]^2-[3i]^2)=0 \\\\\\ (x-3)([x^2-2x+1]-[3^2i^2])=0\implies (x-3)([x^2-2x+1]-[9(-1)])=0[/tex]
[ correction added, Thanks to @stef68 ]
[tex]\bf (x-3)([x^2-2x+1]+9)=0\implies (x-3)(x^2-2x+10)=0 \\\\\\ x^3-2x^2+10x-3x^2+6x-30=0\implies x^3-5x^2+16x-30=f(x) \\\\\\ \stackrel{\textit{applying a translation with a -2f(x)}}{-2(x^3-5x^2+16x-30)=f(x)}\implies -2x^3+10x^2-32x+60=f(x)[/tex]
To find the polynomial of degree 3 with real coefficients and specific zeros and y-intercept, we use the fact that complex zeros occur in conjugate pairs. We can express the polynomial as f(x) = a(x-3)(x-(1+3i))(x-(1-3i)), where a is a constant. By plugging in the y-intercept value, we can solve for the constant a.
Explanation:To find the polynomial with degree 3 and real coefficients that has a y-intercept of 60 and zeros 3 and 1+3i, we can use the fact that complex zeros occur in conjugate pairs. Given that 1+3i is a zero, its conjugate 1-3i is also a zero. Therefore, the polynomial can be expressed as f(x) = a(x-3)(x-(1+3i))(x-(1-3i)), where a is a constant.
Since the polynomial has a y-intercept of 60, we know that f(0) = 60. Plugging in x=0, we can solve for the constant a:
f(0) = a(0-3)(0-(1+3i))(0-(1-3i)) = 60
Since the constant a is the only unknown variable, we can solve for it:
-3*(1+3i)*(1-3i) = 60/a
-3*(1-9i^2) = 60/a
12 = 60/a
a = 5
Therefore, the polynomial f(x) = 5(x-3)(x-(1+3i))(x-(1-3i)) has the desired properties.
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What numbers are multiples
of 9 and factors of 36?
Answer:
9,18, and 36
Step-by-step explanation:
9*4=36 and 9*1=9
18*2=36 and 9*2=18
36*1=36 and 9*4=36
Answer:
multiples of 9: 9, 18, 27, 36, 45, 54, 63,72, 81, 90, 99, 108, etc.
factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step-by-step explanation:
A living room rug has an area of 63 square feet. The width is 7 feet. What is the length ?
Answer:
lenght = 9
Step-by-step explanation: Area =L×W
Area = 63 7 . x= 63 x=63÷7 x=9 9×7=63
A point located at (-5, 2) is translated right 3 units. What are the coordinates of the image? (-5, 5) (-2, 5) (-5, -1) (-2, 2)
ANSWER
(-2,2)
EXPLANATION
The rule for translating a point 'k' units to the right is
[tex](x,y)\to (x+k,y)[/tex]
If the point located at (-5, 2) is translated right 3 units, the coordinates of the image is obtained by adding 3 to the x-coordinate.
This implies that,
[tex]( - 5,2)\to ( - 5+3,2)[/tex]
[tex]( - 5,2)\to ( -2,2)[/tex]
Therefore the image is:
(-2,2)
Answer:
(-2, 2)
Step-by-step explanation:
We are given the following coordinates of a point:
[tex](-5, 2)[/tex]
If this point is translated to the right for 3 units, what will be the coordinates of its image?
Translation towards right side for 3 units means that 3 units are added to its x coordinate so the new point will be:
[tex] ( - 5 , 2 ) [/tex] [tex] \implies [/tex] [tex] ( - 5 + 3 , 2 ) = [/tex] (-2, 2)
What are some characteristics of the graph of a square root function?
Step-by-step explanation:
Domain and range of a basic square root function are restricted, because the square root of a negative number does not exist. Both domain and range of the basic function are from zero to infinity. 3. Horizontal translation occurs when we add or subtract a number under the square root sign.Some characteristics of the graph of a square root function are: both the domain and range consist of real numbers greater than and equal to zero, start from origin, etc.
What is the square root function?The square root function is the function that is represented by the following:
f(x) = √x
Some characteristics of a square root graph are listed below:We are asked to give some characteristics of a square root graph.
The characteristics are given below:
The domain of a square root function consists of all real numbers greater than and equal to zero.
The range of a square root function consists of all real numbers greater than and equal to zero.
The graph of the square root function starts at the origin.
The graph of a square root function is an increasing graph.
The graph of the square root function is a one-to-one function. This means each domain value and range value has only one corresponding domain and range value.
Therefore, we have given some characteristics of the graph of a square root function.
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Solve the system by substitution. Check your solution.
a - 1.2b = -3
0.2b + 0.6a = 12
a.
(15, 15)
c.
(13, 12)
b.
(10, 12)
d.
(7, 9)
Answer:
a. (15, 15)
Step-by-step explanation:
We start with those two equations:
1) a - 1.2b = -3
2) 0.2b + 0.6a = 12
We'll begin by modifying equation #1 to isolate a:
a = -3 + 1.2b
Then we'll use this value for a in the second equation:
0.2b + 0.6 (-3 + 1.2b) = 12
0.2b - 1.8 + 0.72b = 12
0.92b = 13.8
b = 15
Then we'll place that value of b in the first equation to find a:
a - 1.2 (15) = -3
a - 18 = -3
a = 15
Answer:
(15,15) is right
Step-by-step explanation:
simplify the expression (- 13/17) + 4/17
Answer:
-9/17 is the answer
68 is 85% of what number
Hello! Based on this problem, 68 is part of a whole. To solve it, we can write and solve a proportion. Set it up like this:
68/x = 85/100
Cross multiply the sections. 68 * 100 is 6,800 and 85 * x is 85x. So you get 6,800 = 85x. Now, divide each side by 85 to isolate the x. 85x/85 cancels out. 6,800/85 is 80. We can check this answer by multiplying 80 by 85%. 80 * 85% (0.85) is 68. There's our answer. 68 is 85% of 80.
The number whose 85 percent gives 68 is 8000.
What is the number whose 85 percent gives 68?Given the parameters in the question:
Given Value = 68
Percentage = 85%
To find the number whose 85 percent gives 68, we can use the following formula:
Number = (Given Value / Percentage) × 100
First, convert 85% from percent to decimal:
85% = 85/100 = 0.85
Now, plug these values into the above formula:
Number = (Given Value / Percentage) × 100
Number = ( 68 / 0.85 ) × 100
Number = 80 × 100
Number = 8,000
Therefore, 68 is 85% of the number 8000.
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On the number line below, length
AB= {?}
Answer:
29 units
Step-by-step explanation:
The length of a segment of a number line is the difference of the coordinates of the end points:
45 -16 = 29
What is the reciprocal of (13xz)/(31zy)?
Answer:
(31zy)/(13xz)
Step-by-step explanation:
A reciprocal is a number that you can multiply the original number by and get a product of 1. To find the reciprocal of a fraction, flip it upside down, putting the numerator in the denominator, and the denominator in the numerator:
[tex]\frac{31zy}{13xz}[/tex]
If we multiply this fraction by the other, we would end up simplifying it to 1 by cross multiplication.
Stefan’s family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee?
Answer:
$3
Step-by-step explanation:
Whenever some type of expenditure is made, there are usually 2 types of costs available: the fixed cost and the variable cost. Former is the constant cost which has to be incurred in order to gain the advantage from the expense. Latter is the cost that varies with the duration of the expense. Therefore, total costs (TC) = fixed costs (FC) + variable costs (VC). VC can be expressed as: VC = price per hour (p) * number of hours (h). So the equation becomes TC = FC + p*h. In this question, FC = $43, TC = $64, h = 7 hours, and p is unknown. So plugging in the values give:
64 = 43 + 7p.
Solving the equation for p gives:
p = 21/7. This implies that p = 3.
Therefore, the hourly fee is $3!!!
Answer:
7h+43=64
$3 the hourly fee for the rototiller
Step-by-step explanation:
it takes 3.5 minutes to upload 12 photographs from a smartphone to a computer and then an additional 1.25 minutes to upload the photographs to a website. At this rate, about how long will it take to upload 20 photographs from a smart phone to a computer and then to a website?
The answere is simple.All yyou have to do is sum up the time required to upload aphoto frim a phone to a website.Then find the time it takes to upload ten photos and multiply it by 2.
Answer:
8 minutes.
Step-by-step explanation:
Time taken to upload 12 photographs from a smartphone to a computer = 3.5 minutes
Time taken to upload that 12 photographs from computer to a website = 1.25 minutes.
∵ The time taken for 12 photographs to upload from smartphone to a computer then to a website = 3.5 + 1.25 = 4.75 minutes.
∴ The time taken for 1 photograph to upload to a website = [tex]\frac{4.75}{12}[/tex]
∴ Time taken to upload 20 photographs from a smartphone to a computer then to a website = [tex]\frac{4.75}{12}\times 20[/tex]
= 7.916 ≈ 8 minutes.
It will take 8 minutes to upload 20 photographs.
x2 + 3x - 108 = 0
What is the answer?
Answer:
The answer is x=9 and/or x = -12
Step-by-step explanation:
This is a quadratic formula meaning that you must take the a value (1) b value (3) and the c value (108) and plug it into the quadratic formula.
[tex]\frac{-3±\sqrt{9+4*1*-108} }{2}[/tex]
which simplifies to -3 add or subtract the sqrt of 441 divided by two.
To solve the equation x² + 3x - 108 = 0, we use the quadratic formula, which gives two solutions: x = 9 and x = -12.
The question asks to solve the quadratic equation x2 + 3x - 108 = 0. To solve this equation, we will use the quadratic formula, which is given by x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax2 + bx + c = 0. In our case, a = 1, b = 3, and c = -108.
Substituting these values into the quadratic formula gives us:
x = (-(3) ± √((3)2 - 4 ×(1) ×(-108))) / (2 ×(1))
x = (-3 ± √(9 + 432)) / 2
x = (-3 ± √441) / 2
x = (-3 ± 21) / 2
This results in two possible values for x:
x = 9x = -12So, the solutions to the equation x2 + 3x - 108 = 0 are x = 9 and x = -12.
if the side of a regular hexagon is 10 cm then the radius of its circumcircle is?
Answer:
10 cms.
Step-by-step explanation:
The circumcircle passes through each vertex of the hexagon so the radius is equal to one of the 2 equal sides of an isosceles triangle with base = 10 cm and vertex = 60 degrees.
So considering this triangle the base angles are ( 180 - 60) / 2 = 60 degrees. So we have an equilateral triangle with each side = 10 cm.
Therefore the radius is 10 cm. long.
The radius of the circumcircle of the regular hexagon is approximately 5.77 cm.
In a regular hexagon:
- Each side length s = 10 cm.
- The circumcircle passes through all vertices of the hexagon, making it the circle that circumscribes the hexagon.
The radius R of the circumcircle of a regular hexagon can be related to its side length s by the formula:
[tex]\[ R = \frac{s}{\sqrt{3}} \][/tex]
Let's apply this formula:
[tex]\[ R = \frac{10}{\sqrt{3}} \][/tex]
To simplify [tex]\( \frac{10}{\sqrt{3}} \)[/tex], multiply the numerator and the denominator by [tex]\( \sqrt{3} \)[/tex]
[tex]\[ R = \frac{10 \cdot \sqrt{3}}{3} \][/tex]
Therefore, the radius of the circumcircle of the regular hexagon with a side length of 10 cm is [tex]\( \frac{10 \sqrt{3}}{3} \)[/tex] cm. This is the exact value of the radius in terms of [tex]\( \sqrt{3} \)[/tex]. If you need a numerical approximation, you can calculate it as follows:
[tex]\[ R \approx \frac{10 \times 1.732}{3} \approx \frac{17.32}{3} \approx 5.77 \text{ cm} \][/tex]
according to the synthetic division below which of the following statements is true
Answer:
A, D, and F.
Step-by-step explanation:
A:
The remainder is 0, thereby satisfying the factor theorem.
D: Synthetic division is in the form p(x)/(x-a). Since -4 is the number, the factor must be (x--4) or (x+4)
F: Refer to D.
ax-bx+y=z which of the following represents the formula that could be used to find x?
Step by step explanation:
You first subtract z on both sides of the equal sign
ax-bx=(z-y)
Since a and b both have a "x" you can subtract them
(a-b)x=(z-y)
then you divide "x" on both sides of the equal sign
[tex]\frac{a - b}{x} = \: \frac{z - y}{x} [/tex]
To find x in the equation ax-bx+y=z, combine like terms, subtract y from both sides, and then divide by (a-b) to get the formula x = (z-y)/(a-b).
To find the value of x in the equation ax - bx + y = z, you can follow these steps:
Combine like terms by factoring out x from the terms ax and -bx, which gives you x(a - b).Subtract y from both sides of the equation to isolate the term with x on one side, resulting in x(a - b) = z - y.Finally, divide both sides by (a - b) to solve for x, assuming that a ≠ b, which gives the formula x = (z - y) / (a - b).This step-by-step process allows you to solve for x in terms of a, b, y, and z.
For the geometric series
1+ 4+ 16 + 64 + 256
what is the value of n?
Answer:
(n×4)
Step-by-step explanation:
Divide the 2nd term by the first to find the ratio which is also n.
Answer:
n=5.
Step-by-step explanation:
The given geometric series is
1+ 4 +16 + 64 + 256
In the given G.P. the number of terms is 5 and n represents the number of terms in a G.P. So, n=5.
Alternate method:
Here the first term is 1 and the common ratio is
[tex]r=\dfrac{a_2}{a_1}=\dfrac{4}{1}=4[/tex]
The nth term of a G.P. is
[tex]a_n=ar^{n-1}[/tex]
where, a is first term and r is common ratio.
Substitute a=1, an=256 and r=4 in the above formula.
[tex]256=(1)(4)^{n-1}[/tex]
[tex]4^4=4^{n-1}[/tex]
On comparing both sides we get
[tex]4=n-1[/tex]
Add 1 on both sides.
[tex]5=n[/tex]
Therefore, the value of n is 5.
what is the constant term of -3x^4-7x+2
Answer:
The equation written in the standard form is written as
ax^4 + bx+c
where a and b are the coefficients of the second-order and first-order term, while c is the constant term.
The equation we have in this problem is
By comparing (1) with (2), we immediately see that
A = -3x^4
B = 7x
C = 2
Step-by-step explanation:
Hope this helps :)
Final answer:
The constant term in the polynomial [tex]-3x^4 - 7x + 2[/tex] is 2, as it is the term without any variables.
Explanation:
The constant term in the polynomial [tex]-3x^4 - 7x + 2[/tex] is the term that does not contain any variables. In this polynomial, the terms are classified based on their variable's degree. In this case, -3x^4 is the term with the variable raised to the fourth power, -7x is the term with the variable to the first power, and 2 is the term with no variable, which makes it the constant term. Therefore, the constant term is 2.
WILL MARK BRAINLIEST HELP ASAP
Answer:chicken nuggie
Step-by-step explanation:
5 yards 2 feet × 2=
Answer:
11 and 1/3 yards
Step-by-step explanation:
5 yards and 2 feet = 5 and 2/3 yards = 17/3 yards
(17/3 yards)(2) = 34/3 yards = 11 and 1/3 yards
The equivalent value of 5 yards 2 feet × 2 is 11 and 1/3 yards.
Given,
5 yards 2 feet × 2
Here,
Firstly convert feet to yard,
1 yard = 1/3 feet
So,
2 feet = 2/3 yard
So,
5 yards and 2 feet = 5 and 2/3 yards
= 17/3 yards
Now,
(17/3 yards)(2) = 34/3 yards
= 11 and 1/3 yards
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PLEASE HELP RIGHT AWAY
ANSWER
The fifth term is 27
EXPLANATION
The explicit rule for the given sequence is
[tex]t_n= {2}^{n} - n[/tex]
To find the fifth term, we substitute n=5 to get,
[tex]t_5= {2}^{5} - 5[/tex]
[tex]t_5= 32 - 5[/tex]
Simplify:
[tex]t_5= 27[/tex]
The fifth term is 27
Part A: Factor x2a2 + 3xa2 + 2a2. Show your work. (4 points)
Hope this is what you need
Answer:
I am not sure of the equation but I interpreted it as x^2a^2+3xa^2+2a^2
Step-by-step explanation:
X^2a^2+3xa^2+2a^2
1. a^2 (x^2+3x+2)
2.a^2(x^2+2x+x+2)
3. a^2(x(x+2)+x+2)
4. a^2(x+2)(x+1)
math im soooooooooooooo baaaaaaaaaaaadddddddddddddd
Answer:
The correct answer is A, 73
Step-by-step explanation:
First we have to arrange the whole numbers in ascending order. i-e from smallest to largest. Showing it as follows:
53 54 59 62 64 65 66 68 70 71 75 78 79 79 83 83 86 90 91 94
Now we would find the median by taking the middle number. But this series consists of even numbers. There are 20 numbers. So we will take the middle two numbers and find their average like follows:
71 + 75 = 146/2 = 73
The answer is 73
Answer:
median =73
Step-by-step explanation:
Given list of data is
{94,79,83,78,70,66,68,75,53,54.79,59,83,91,64,65,71,62,86,90}.
Now we need to find about what is the median for the data listed above.
So first we need to rearrange the given data in increasing order. then we can easily find the middle number as median.
Sorted list of data is:
{53, 54, 59, 62, 64, 65, 66, 68, 70, 71, 75, 78, 79, 79, 83, 83, 86, 90, 91, 94}
there are two numbers at the middle 71 and 75
then median = (71+75)/2=146/2=73
PLEASE HELP ME!!!!!!
Answer:
Sample size is 6, event of rolling an even number is 3/6 (or 1/2)
Step-by-step explanation: When you roll a dice it could be 1, 2, 3, 4, 5, or 6. Count those up and you'll have the sample size. Odds of rolling a 2, 4, or 6 (even number) is 3/6 or 1/2, or 50%
What is the solution of 9|2x – 1| + 4 < 49?
Answer: [tex]-2<x<3[/tex]
Step-by-step explanation:
You need to set up two cases (Positive case and negative case) and solve for "x".
- POSITIVE CASE IF: [tex]2x-1>0[/tex]
[tex]9(2x -1) + 4 < 49\\18x-9<49-4\\18x<54\\x<3[/tex]
- NEGATIVE CASE IF: [tex]2x-1<0[/tex]
[tex]-9(2x -1) + 4 < 49\\-18x+9<49-4\\-18x<36\\x>-2[/tex]
Therefore, the solution is:
[tex]-2<x<3[/tex]
Answer:
see explanation
Step-by-step explanation:
Given
9 | 2x - 1 | + 4 < 49 ( subtract 4 from both sides )
9 | 2x - 1 | < 45 ( divide both sides by 9 )
| 2x - 1 | < 5
Inequalities of the type | x | < a always have solutions of the form
- a < x < a, thus
- 5 < 2x - 1 < 5 ( add 1 to all 3 intervals )
- 4 < 2x < 6 ( divide all 3 intervals by 2 )
- 2 < x < 3