answer:
[tex]\frac{-23}{6}[/tex] or -3.8333 (repeating)
100 POINTS
Solve x4 - 10x² + 9 = 0.
Answer:
[tex]x=\pm1 \:\textsf{or}\:x=\pm3[/tex]
Step-by-step explanation:
[tex]x^4-10x^2+9=0[/tex]
[tex]\textsf{let}\:x^2=y[/tex]
[tex]\implies y^2-10y+9=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find 2 two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
⇒ two numbers that multiply to 9 and sum to -10: -9 and -1
Rewrite [tex]b[/tex] as the sum of these 2 numbers:
[tex]\implies y^2-y-9y+9=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies y(y-1)-9(y-1)=0[/tex]
Factor out the common term [tex](y-1)[/tex]:
[tex]\implies (y-9)(y-1)=0[/tex]
[tex]\implies (y-9)=0 \implies y=9[/tex]
[tex]\implies (y-1)=0 \implies y=1[/tex]
Change [tex]y[/tex] back to [tex]x^2[/tex]:
[tex]\implies x^2=9\implies x=\pm3[/tex]
[tex]\implies x^2=1\implies x=\pm 1[/tex]
[tex]\textsf{So}\: x=\pm1 \:\textsf{or}\:x=\pm3[/tex]
Answer:
[tex]$x=\pm1\;\textrm{or}\;x=\pm3$[/tex]
Step-by-step explanation:
Substitute [tex]u = x^2[/tex] into the equation. This will make the quadratic formula easy to use.
[tex]\implies u^2 - 10u + 9 = 0[/tex]
Consider the form [tex]x^2 + bx + c = 0[/tex]. Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]c[/tex]. In this case, whose product is [tex]9[/tex]and whose sum is [tex]10[/tex]. And write the factored form using the integers.
[tex]\implies (u - 9)(u - 1) = 0[/tex]
If any individual factor on the left side of the equation is equal to [tex]0[/tex], the entire expression will be equal to [tex]0[/tex].
[tex]\implies \begin{cases}u - 9 = 0 \\ \\ u - 1 = 0\end{cases}[/tex]
Set [tex]u - 9[/tex] equal to [tex]0[/tex] and solve for [tex]u[/tex]. Similarly, Set [tex]u - 1[/tex] equal to [tex]0[/tex] and solve for [tex]u[/tex].
[tex]\implies \begin{cases}u = 9 \\ \\ u = 1\end{cases}[/tex]
Substitute the real value of [tex]u = x^2[/tex] back into the solved equation.
[tex]\implies \begin{cases}x^2 = 9 \\ \\ x^2 = 1\end{cases}[/tex]
Take the square root of both sides of the equations to eliminate the exponent on the left side.
[tex]\implies \begin{cases}x = \sqrt{9} \\ \\ x = \sqrt{1}\end{cases}[/tex]
Solve both the equations for the value of [tex]x[/tex].
[tex]\implies \begin{cases}x = \pm3 \\ \\ x = \pm1\end{cases}[/tex]
Hence, this is our required solution for this question.
[tex]\rule{300}{1}[/tex]
Additional information:
There are three ways to solve a quadratic equation:
FactoringComplete the SquareQuadratic FormulaFactoring uses the logic that the product of any number and zero is zero. Complete the square method uses square root, and the quadratic formula is the simpler method of it.
Quadratic Formula [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
-Applications using z-scores-
(Note: draw the bell shape curve and convert data values to z-score)
A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr?
Answer: 16%
step explanation:
100 m/hr is ONE S.D. (10) above 90
z - score = .8413 (Form Z-score chart)
means 84 % of cars are travelling less than 100 m/hr
~ 16% are traveling 100 or more
4. The number of feet in a yard can be represented by a graph. Circle the graph(s) that could
be used to represent the number of feet, y, in x yards.
GRAPH A
GRAPH B
GRAPH
GRAPHD
27
26
21
18
LS
60
54
48
42
36
30
20
18
12
135
12
105
9
75
6
60
54
40
42
36
30
24
18
12
9
45
3
3
15
6
Ye Li drew another quadrilateral it is a parallelogram and has four right angles can it be rhombus?
Answer:
A rhombus is both a rectangle and a rhombus. All the sides are equal and each angle measure 90 degrees. So yes it can be a rhombus.
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
A squares angles are all 90 degree, a rhombus however, has perpendicular angles crossing each other that are equal to 90 degress.
5* 3 1/3 I have to have my math done in an hour and I don’t know this
16.65... .... ..... ...
Answer: 16.65
Step-by-step explanation:
1/3 is equivalent to the decimal value .33
so, use the equation:
5x(3+.33) or 5x3.33, which equals 16.65
same homework. different question.
Answer:
Answer = B. Obtuse.
Step-by-step explanation:
Trey caught a 3 1/4 pound fish. How much did it weigh in ounces?
Answer: 52 ounces
multiply the mass value by 16
using appropriate property find -2/5 ×1/5 + 2/5 × 1/5
Answer:
simply cut 5 and solve if no property needed but if needed use distributive
Choose the graph below that meets all three of the following requirements: Limit as x approaches 1 minusf(x) = 3 Limit as x approaches 1 plusf(x)= –1 Limit as x approaches 4f(x) = 2 On a coordinate plane, a horizontal line at y = 3 goes to open circle (1, 3). It then goes down to point (2, negative 1) and up to open circle (4, 2). It then increases through (7, 4). On a coordinate plane, a horizontal line starts at open circle (negative 1, 3) and decreases through (negative 3, 0). A curve starts at closed circle (1, negative 1), curves up to (4, 2), and curves down through (6, 0). On a coordinate plane, a line starts at (1, 3) and increases through (0, 4). A line starts at closed circle (4, 3) and decreases through (5, 2). A horizontal line starts at (1, negative 1) and goes to open circle (4, negative 1). On a coordinate plane, a curve starts at open circle (1, 3), increases to (0, 4), and curves down through (negative 2, 1). A line starts at closed circle (1, negative 1) and goes up through (4, 2).
Graph D (last one)
Step-by-step explanation:
edge
Answer:
the last graph is d
Step-by-step explanation:
PLS HELP ILL MARK AS BRAINLEST
find the slope that goes through the following points
Answer:
The slope is 3
Step-by-step explanation:
The formula for slope is m = (y₂-y₁)/(x₂-x₁)
We assign
y₂ = -1y₁ = -4x₂ = 0x₁ = -1Note: You can choose any set of points as long as you assign y₂ and y₁ to y coordinates and x₂ and x₁ to x coordinates.
m = (-1+4)/(0+1) = 3/1 = 3
Answer:
D. 3 :)
Step-by-step explanation:
As the x value increases, so does the y value but in bigger jumps. It increases by 3 :)
Have an amazing day!!
Please rate and mark brainliest!!
help me please…………..
. If 27 and 45 are two lengths of a right triangle, what is the third length of the right triangle?'
Answer:
36 ( or possibly sqrt (2754) )
Step-by-step explanation:
Use the Pythagorean Theorem to find the missing side (you will have to try two different times because you do not know what is missing....a leg or the hypotenuse)
27^2 + 45^2 = x^2 x = sqrt2754=52.4786 although this is one true answer, I do not think it is what the question seeks
let's try
27^2 + x^2 = 45^2 x = 36 Check !
Hey can somebody help me on this?
Answer: 7
Step-by-step explanation: g = 8 ( given ) g/2+3 plugging the value of g 8/2+3
8+3x2
2
8+6
2
14
7
= 2
{4x+y=9 and 5x +2y=9
use substitution method to find all solutions of the system of equations
(X,y)=
Answer:
x=3,y=-3
Step-by-step explanation:
Isolate x for 4x +y=9: x=9-y/4
Substitute x = 9-y/4
[5 x 9-y/4+2y =9]
Isolate y for (45+3y/4)=9:
y=-3
For x= 9-y/4
Substitute y = -3
x= 9-(-3)/4
9-(-3)/4=3
X=3
The solutions to the system of equations are:
x=3 y= -3
5 lb of apples at 2 lb for $0.80
Answer:
2 dollars for 5 lb
Step-by-step explanation:
^
For what values of b will F(x) log, xbe a decreasing function?
O A. 0> b>-1
B. b> 0
O C. b<0
O D. 0 < b<1
Step-by-step explanation:
Have a Great day✧◝(⁰▿⁰)◜✧The correct values for b is,
⇒ 0 < b < 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
F (x) = [tex]log_{b} x[/tex]
Now, We know that;
As the logarithm of a negative number is undefined, b should be a positive number (b>0 ).
Therefore, the value of b must be in the range of 1 > b > 0 for the function to be a decreasing function.
Thus, The correct values for b is,
⇒ 0 < b < 1
Learn more about the function visit:
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After arguing for two weeks, Seth convinced his parents to have his birthday party at FlyZone trampoline park. As soon as he gets there, Seth spends time practicing flips on the trampolines. Then, he spends
1/2
of an hour eating birthday cake with his friends. In all, Seth spends 1 1/4
hours at FlyZone.
Which equation can you use to find the amount of time t Seth practices flips?
Answer:
[tex]t + \frac{1}{2} = 1 \frac{1}{4} [/tex]
Shiho recorded the data below as she timed
how long it took for a car to go down a track.
Car Trial
Time
Trial 1
3.3 seconds
Trial 2
3.8 seconds
Trial 3
4.1 seconds
Trial 4
4.1 seconds
Trial 5
3.1 seconds
If Shiho wanted to determine the average time
it took the car to go down the track, which
measure should she find? (5 points)
A mean is an arithmetic average of a set of observations. The average time taken by Shiho to complete the track is 3.7 seconds.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]
The reading of the 5 trials of Shiho is 3.3 seconds, 3.8 seconds, 4.1 seconds, 4.1 seconds, and 3.1 seconds. Therefore, the average or the meantime of Shiho can be written as,
[tex]\rm \text{Average Time} = \dfrac{\text{Sum of all observations}}{\text{Number of trials}}\\\\\text{Avrage Time} = \dfrac{3.3+3.8+4.1+4.1+3.1}{5}=\dfrac{18.4}{5}= 3.68\approx 3.7\ seconds[/tex]
Hence, the average time taken by Shiho to complete the track is 3.7 seconds.
Learn more about Mean:
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what's the estimate of 6.48 + 9.34
Answer:
6+9=15
Step-by-step explanation:
hope this helps :D
pls helpp i need it i give 23 points
Find the equation of the tangent to the curve y = 4x³- 5x² + x - 3 at the point where it crosses the y axis.
Answer:
y = x-3
Step-by-step explanation:
When the graph of this equation crosses the y - axis , the value of x is = 0.
sub in zero to find this y value = -3
so the point is (0, -3)
Now find the drivative of this equation....the derivative tells you the slope of the original graph at any given point
derivative = 12x^2-10x+1 this , when x = 0 shows slope = 1
the equation then becomes y = (1) x -3 or just y = x-3
See image below
Answer:
-3
Step-by-step explanation:
put x= 0
For a ride on a rental scooter, David paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for David's ride was $22.69. For how many minutes did David ride the scooter? minutes X
For $22.69 dollars I can ride the scooter for 179 minutes.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, A scooter ride has a starting fee of $3 and then 11 cents per mile.
Assuming with $22.69 I can ride x no. of minutes.
∴ 0.11x + 3 = 22.69.
0.11x = 19.69.
x = 19.69/0.11.
x = 179 minutes.
learn more about equations here :
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3)
A mobile phone company uses the formula C = 10t + 20m to calculate the total cost
of a bill.
C is the total cost of the bill in pence
t is the number of text messages
m is the number of minutes of call time
Calculate the total cost for 150 texts and 50 minutes of call time.
р
Answer:
2500 pence (C = 2500)
Step-by-step explanation:
[tex]C = 10t + 20m[/tex]
From the given information, t is the number of texts so essentially you will plug in the number of texts provided (150) in the place of the variable t.
[tex]C = 10(150) + 20m[/tex]
Apply the same thing to minutes, plug in the number of minutes (50) in the place of the variable m.
[tex]C = 10(150) + 20(50)[/tex]
Now multiply the substitutes with the co-efficient.
[tex]C = 1500 + 1000[/tex] (10*150=1500 & 20*50=1000)
Add the addends
C = 2500
Vigorous intensity physical activity target heart rate ranges between
A. 80-90%
B. 70-80%
C. 75-85%
D. 65-75%
pls help i need an A my mom is going to get mad at me pls help i will give 62 points
Answer:
I would say the second one
Step-by-step explanation: Good luck! :)
A sum of money was distributed among some boys. Had there been two boys more, each would have received Rs. 10 less. Had there been two boys less, each would have received Rs. 15 more. Find the number of boys and the sum received by each.
Given -
A sum of money was distributed among some boys.Had there been two boys more, each would have received Rs. 10 less.Had there been two boys less, each would have received Rs. 15 more.To find -
the number of boys and the sum received by each.Explanation -
Here as we are required to find the value of two different individuals hence first we will from 2 linear equations into two variables (taking each to be value as x and y or whatever you like, I will take them as a and b) will solve the equation by any method of your choice (explanation for them is in the link, below, it is given by the same me)
https://brainly.com/question/27161912?utm_source=android&utm_medium=share&utm_campaign=question
Solution -
Let the sum of money that was given to each boy be a and the number of boys be b. Hence, the total no. of money distributed to b no. of boys is ab.
According to the question,
Scenario 1 -
➡ (a + 2)(b - 10) = ab
Solving it further,
➡ a(b - 10) + 2(b - 10)= ab
➡ ab - 10a + 2b - 20= ab
Cancelling ab,
➡ 10a - 2b + 20 = 0
➡ 10a = 2b - 20
➡ a = 2(b - 10)/10
➡ a = (b - 10)/5
Scenario 2 -
➡ (a - 2)(b + 15) = ab
Solving it further,
➡ a(b + 15) - 2(b + 15)= ab
➡ ab + 15a - 2b - 30= ab
Cancelling ab,
➡ 15a - 2b - 30 = 0
Substituting the value of a in the equation,
➡ 15{(b - 10)/5} - 2b - 30 = 0
➡ 3(b - 10) - 2b - 30 = 0
➡ 3b - 30 - 2b - 30 = 0
➡ 3b - 2b -60 = 0
➡ b = 60
Substituting the value of b in a = (b - 10)/5,
➡ a = (60 - 10)/5
➡ a = 50/5
➡ a = 10
[Here we have used the substitution method]
Henceforth, the total number of boys is 60 and the sum received by each is Rs. 10 .
50 points!!! Please help ASAP!!
The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -6
Answer:
Step-by-step explanation:
Ryan invested $257 in an account paying an interest rate of 3.9% compounded weekly.
What is the equation?
Answer:
The equation is 257/x = x/3.9
Step-by-step explanation:
A house on the market was valued at $396,000. After several years, the value increased by 8%. By how much did the house's value increase in dollars? What is the current value of the house?
Answer:
The value of the house increased $31,680.
The current value of the house is $427,680
Step-by-step explanation:
Each set of ordered pairs ( x , y ) represents a relationship with input x and output y . Which relationships do not represent a function? Select two correct answers. A. { ( ¯ 3 , 9 ), ( ¯ 1 , 1 ), ( 1 , 1 ), ( 3 , 9 ) } B. { ( ¯ 6 , 8 ), ( ¯ 6 , 4 ), ( 0 , 0 ), ( 3 , ¯ 4 ) } C. { ( 9 , ¯ 8 ), ( 8 , ¯ 9 ), ( ¯ 9 , 8 ), ( ¯ 8 , 9 ) } D. { ( ¯ 5 , ¯ 2 ), ( ¯ 1 , 3 ), ( 4 , 8 ), ( ¯ 1 , 13 ) } E. { ( ¯ 9 , ¯ 2 ), ( ¯ 5 , 11 ), ( 4 , ¯ 6 ), ( 1 , 17 ) }
Answer:
B and D
Why?
Well when looking for a function you have to look at the X Values. Why the X values? Well if they are different it is considered a function. If it is the same it will NOT be considered a function