Answer:
[tex]\displaystyle x=\frac{-1 \pm i\sqrt{535}}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Multiple RootsStandard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]Algebra II
Imaginary Root i = √-1Step-by-step explanation:
Step 1: Define
Identify
2x² + x + 67 = 0
a = 2
b = 1
c = 67
Step 2: Solve for x
Substitute in variables [Quadratic Formula]: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1^2-4(2)(67)}}{2(1)}[/tex]Multiply: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1^2-4(2)(67)}}{2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1-4(2)(67)}}{2}[/tex][√Radical] Multiply: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1-536}}{2}[/tex][√Radical] Subtract: [tex]\displaystyle x=\frac{-1 \pm \sqrt{-535}}{2}[/tex][√Radical] Simplify: [tex]\displaystyle x=\frac{-1 \pm i\sqrt{535}}{2}[/tex]how does the graph of g(x)=3(2)^x -5 compare to the graph of g(x)=2^x
Answer:
Step-by-step explanation:
The graph of g(x)=3(2)^x -5 is vertically stretched as compared with that of h(x) = 2^x. Also, the graph of g(x)=3(2)^x -5 has been translated downward by 5 units.
To obtain the graph of g(x)=3(2)^x -5, we start by graphing g(x)= 2^x, whose y-intercept is (0, 1). We then stretch this new graph vertically by a factor of 3; the y-intercept becomes (0, 3). Finally, we translate the entire new graph downward 5 units.
The actual amount in a 12-ounce container of a certain brand of orange juice is normally distributed with mean μ = 12.34 ounces and standard deviation σ = 0.04 ounce. What percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice?
Answer:
15.25%
Step-by-step explanation:
The actual amount in a 12-ounce container of a certain brand of orange juice is normally distributed with mean μ = 12.34 ounces and standard deviation σ = 0.04 ounce. What percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice?
We solve using the z score formula
z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean = μ = 12.34 ounces
σ is the population standard deviation = σ = 0.04 ounce
For x = 12.24
z = 12.24 - 12.34/0.04
z = -2.5
Probability value from Z-Table:
P(x = 12.24) = 0.0062097
For x = 12.30
z= 12.30 - 12.34/0.04
z = -1
Probability value from Z-Table:
P(x = 12.30) = 0.15866
Hence, the probability of the juice bottles contain between 12.24 and 12.30 ounces of orange juice
P(x = 12.30) - P(x = 12.24)
= 0.15866 - 0.0062097
= 0.1524503
Therefore, the percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice is calculated as:
= 0.1524503 × 100
= 15.24503%
= 15.25%
Derek can carry 65% of his weight in
his backpack while camping. If his
backpack weighs 88.4 pounds, how
much does Derek weigh?
URGENT HELP NEEDED!!!!!
Find the simple interest earned at the end of 1 year. Show your calculations as best as possible (1 mark) correct answer (1mark) P = $1800 R = 5% T = 1 year
What is the total amount earned at the end of 3 years? P = $2600 R = 12% T = 3 years
1 point
$936
$3 536
$93 600
Both A and B
What principal would give an interest of $36 in 3 years at 3% p.a.? Show your calculations as best as possible (1 mark) correct answer (1mark)
In how many years will $600 double itself at 10% simple interest?
1 point
8 years and 4 months
8 years and 1/3
100 Months
All of the above
Both A and B
In what time will $400 amount to $512 if the simple interest is the calculated at 14% p.a.? Write your answer
Imagine you have a friend who doesn't quite understand what investing money into a bank means. Think of a financial situation and use the following words and numbers to help teach them. (principal $1200, interest earned, interest rate 4%, total amount, term, per anum). This is worth 8 marks.
Answer:
k
Step-by-step explanation:
a=8 and b=2.25 but what is k
Answer:
a = 8, b = 2.25, k = 27Step-by-step explanation:
y = abˣPoints on the graph:
(0, 8), (1, 18), (1.5, k)Substitute coordinates into equation and solve for and and b:
8 = ab⁰ ⇒ 8 = a*1 ⇒ a = 818 = 8b ⇒ b = 18/8 ⇒ b = 2.25Find k:
k = 8*[tex]2.25^{1.5}[/tex] = 27Answer:
a=8
b=9/4
k = 27
Step-by-step explanation:
y = ab^x
We know that a is the initial value or when x = 0
We know the point (0,8) so a = 8
y = 8 b^x
Using the point (1,18) for x and y we can find b
18 = 8 * b^1
18/8 = b
9/4 = b
Now
y = 8 * ( 9/4) ^ x
Letting x = 1.5
k = 8 *(9/4)^1.5
k = 27
is the ordered pair a solution of the equation?
y= 3x + 4; (4, 16)
Answer: Yes.
Step-by-step explanation: Plug in your values. Does y=16 when x=4? 16 = 3(4) +4, which equals 16, so yes.
Please HELP WITH THIS !!!
Simplify √49 + [√81 - x(9x = 14)]
[tex]\longrightarrow{\green{- 9 {x}^{2} + 14x + 16}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \sqrt{49} + [ \sqrt{81} - x \: (9x - 14) ] \\ \\ = \sqrt{7 \times 7} + [ \sqrt{9 \times 9} - 9 {x}^{2} + 14x] \\ \\ = \sqrt{( {7})^{2} } + [ \sqrt{ ({9})^{2} } - 9 {x}^{2} + 14x ] \\ \\ (∵ \sqrt{ ({x})^{2} } = x ) \\ \\ = 7 + (9 - 9 {x}^{2} + 14x) \\ \\ = 7 + 9 - 9 {x}^{2} + 14x \\ \\ = - 9 {x}^{2} + 14x + 16[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Which are correct representations of the inequality 6x2 3 + 4(2x – 1)? Select three options.
12 2x
6x > 3 + 8x - 4
O
-1.5
-1
-0.5
0
0.5
1
1.5
-1.5
-0.5
0
0.5
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
The proper way to express the above inequality is 6x4(2x-1) is x2.
What is inequality?A mathematical statement that has two mathematical expressions on each side of the inequality sign is called an inequality. The indicators for inequality are,, >, or.
6x4(2x-1) is the given inequality.
So, 6x≥8x-4
6x off of both sides gives us
6x-6x≥8x-4-6x
0≥8x-6x-4
0≥2x-4
4 added on both sides give us
0+4≥2x-4+4
4≥2x
By dividing both sides by half, we obtain
(1/2)×4≥(1/2)×2x
2≥x
x≤2
Therefore, x≤2 is the correct representation.
Learn more about inequality here:
brainly.com/question/19498063
#SPJ7
Can some one help me out with this please?
Answer:
GOD BLESS YOU
Step-by-step explanation:
I need help please and thank you!!
Answer:
Option 4
Step-by-step explanation:
2x² + 32 = 0
2x² = -32
x² = -16
sqrt(-16) got no real solution. (no real number multiplied by itself will be negative)
If 5400=54(100x+54), then x=?
Answer:
x=23/50
Step-by-step explanation:
Answer:
0.46
Step-by-step explanation:
Divide 5400 by 54 to get rid of it from the right side.
You will get 100=100x+54
Then subtract 54 from 100.
46=100x
Lastly, divide your number by 100 to get x.
The slope of the line passing through the points (6, -1) and (7, -2) is
-3
-1
1
Answer:
-1
Step-by-step explanation:
when inputting our values into the formula for slope, we get (-2 - -1)/(7 - 6). Subtracting gives us -1/1 and our final answer is -1.
p.s tysm
- 4x < 68
A. Solve by adding 4 to each side.
B. The solution is x>-17.
a or b will mark as brainliest
(ignore the last thing)
Answer:
B.x>-17
Step-by-step explanation:
1. Divide both sides by -4:
-4x/-4<68/-4
2.< will change to > since you are dividing by negative
3.your final answer will be x>-17
Please help!! I'm in summer school and I can't fail
Answer and Step-by-step explanation:
The slope would be positive 1. (Third answer choice).
This is because, using the Rise over Run method of finding slope, we go 1 unit up and 1 unit to the right, showing that it is going in the positive direction (up and right) and has a slope of 1.
#teamtrees #PAW (Plant And Water)
slope:1/6 point: (24 ,4)
Answer:
y -4 = 1/6(x-24)
y = 1/6x -2
Step-by-step explanation:
We can point slope form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y -4 = 1/6(x-24)
Or we can write slope intercept form
y = mx+b where m is the slope and b is the y intercept
Substituting the points
4 = 1/6(24)+b
4 = 6+b
4-6 = b
-2 =b
y = 1/6x -2
Answer:
[tex]y = mx + c \\ 4 = (\frac{1}{6} \times 24) + c \\ 4 = 4 + c \\ c = 0 \\ y = \frac{1}{6} x[/tex]
How do you perform constructions related to circles? What theorems and explanations can be used to justify these constructions? How do you perform constructions related to circles? What theorems and explanations can be used to justify these constructions?
Answer and explanation:
To construct a circle, draw a line that represents the diameter of the circle. Bisect the line so that it is a perpendicular bisector of the diameter of the circle. Place your compass at the bisection point/midpoint and draw an arc or better still the whole circle.
Theorem: the perpendicular bisector of a chord passes through the center of a circle.
Note: a diameter of a circle is a chord that passes through the center of a circle.
HELP ASAP NEED HELP. WILL GIVE BRAINIEST AND 100 POINTS.
Algebra 1
Use the function f(x) = 4x^2 - 7x - 15 to answer the questions.
Part a: completely factor f(x).
Part b: what are the x-intercepts of the graph of f(x)? Show your work.
Part C: describe the end behavior of the graph of f(x). Explain.
Part D: what are the steps you would use to graph f(x)? Justify that you can use the answers obtained in part B and part C to draw the graph.
Answer:
A: [tex]f(x)=(4x+5)(x-3)[/tex]
B: [tex](-\frac{5}{4} , 0)[/tex] and [tex](3, 0)[/tex]
C: They are parallel, which means they have no endpoint.
tan150 cos135 cos100÷sin585 cos150 sin170
Answer:
-0.66
Step-by-step explanation:
use the calculator
Directions: Solve for X Round your answer to the nearest tenth. Make sure you calculator
is in degree model
12
Answer:
36.87
Step-by-step explanation:
Using tan inverse of 9 over 12
Answer:
x ≈ 36.9°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{12}[/tex] , then
x = [tex]tan^{-1}[/tex] ([tex]\frac{9}{12}[/tex] ) ≈ 36.9° ( to the nearest tenth )
20 POINTS
The function f(x)=45x represents the number of jumping jacks j(x) you can do in x minutes. How many jumpibg jacks can you do in 10 minutes
Answer:
450 jumping jacks
Step-by-step explanation:
f(10) = 45 (10)
45 * 10 is just 450 :)
Answer:
450.
Step-by-step explanation:
f(10) = 45 * 10 = 450 jumping jacks.
express . 05 as a proper fraction in its lowest terms
The number -2 is a solution to which of the following inequalities?
x + 7 > 5
-3 x < 1
x - 7 < -4
Answer:
The answer is the third one, x - 7 < 4
Step-by-step explanation:
Which equation can be used to solve a - 5 = 30?A. a = 30 - 5 B. a = 30 + 5 C a = 30 + 5 = 5 D a = 30.5
Which equation can be used to solve a - 5 = 30
answer= a=30+5
HOPE THIS HELPS YOU......
Find the y-intercept of the line which passes through (-2,-2) and (2,-4). O A. (0, -3) O B. (-3,0) O C. (0, -6) O D. (-6,0) O E. (0,-5)
9514 1404 393
Answer:
A. (0, -3)
Step-by-step explanation:
Graphing the given points shows you the y-intercept is between them. The x-coordinate of the y-intercept is always 0, so the only viable answer choice is ...
(0, -3)
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^2+232x+134
Answer:
Step-by-step explanation:
when it touch the ground,y=0
-16x²+232x+134=0
-16(x²-29/2 x+(-29/4)²-(-29/4)²)=-134
-16(x-29/4)²-16(-861/16)=-134
-16(x-29/4)²+861=-134
-16(x-29/4)²=-134-861
(x-29/4)²=-995/-16=995/16
x-29/4=±√995/4
rejecting negative sign
x=29/4+√995/4=(29+√995)/4≈15.14 second
Which statements about the factors of the terms in the expression 12 x + 18 x y minus 24 y are true? Select three options.
The factors common to 12x and 18xy are 1, 2, 3, 6, x, and y.
The factors common to 12x and 18xy are 1, 2, 3, 6, and x.
The factors common to 12x and 24y are 1, 2, 3, 4, 6, and 12.
The GCF of the expression is 6xy.
The GCF of the expression is 6.
Answer:
i think the answer is Options B, C and E holds.
Step-by-step explanation:
this makes options B and C a choice:
Given the expression: 12x+18xy-24y
Factors of 12x=1,2,3,4,6,12 and x
Factors of 18xy=1,2,3,6,9,18,x and y.
Factors of 24y=1,2,3,4,6,8,12,24 and y.
next for E this is why its a choice:
12x+18xy-24y=6(2x+3xy-4y)
Answer:
bce
Step-by-step explanation:
Solve the formula d = rt for r.
315,728 rouned to the nearest ten thousand
Answer:
320,000 is the answer
Step-by-step explanation:
have a good day!!
help pls i beg youuu
Answer:
height = 10 m
Step-by-step explanation:
base area of rectangular pyramid =180 m^2
volume of rectangular pyramid = lwh/3
600 = 180*h/3
600*3 = 180*h
1800/180 =h
10 = h
Answer:
I think the answer to the question is 10
