Answers
x-intercept: -4
Related Questions
100 POINTS
Solve x4 - 10x² + 9 = 0.
Answers
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]
Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a decimal to the nearest hundredth.
Answers
The probability that the next customer will pay with a credit card will be 0.26 or 26%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Bilquis owns a small business selling used books. She knows that in the last week 49 customers paid cash, 42 customers used a debit card, and 32 customers used a credit card.
Then the probability that the next customer will pay with a credit card will be
[tex]\rm P = \dfrac{32}{123}\\\\ P = 0.26[/tex]
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Answer:
The answer is .26
Step-by-step explanation:
32/123
0.260162...
Vigorous intensity physical activity target heart rate ranges between
A. 80-90%
B. 70-80%
C. 75-85%
D. 65-75%
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The point A(5.
7) is reflected over the
What are the coordinates of point B?
point (6,
6) and its
image is point B.
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The point (6, 6) is the mid-point of A and B. Then the coordinate of the point B is (7, 5).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point A (5, 7) is reflected over the point (6, 6) and its image is point B. Then the point (6, 6) is the mid-point of the A and B. Then the coordinate of the point B will be
[tex]\rm (x_2 , y_2) = (2x -x _1, 2y - y_1)\\\\(x_2 , y_2) = (2 \times 6 - 5, 2 \times 6- 7)\\\\(x_2 , y_2) = (12-5,12-7)\\\\(x_2 , y_2) = (7, 5)[/tex]
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using appropriate property find -2/5 ×1/5 + 2/5 × 1/5
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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).
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Graph D (last one)
Step-by-step explanation:
edge
Answer:
the last graph is d
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
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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
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Which of the following options have the same value as 10 % , percent of 33?
Answers
Answer:
3.3
Step-by-step explanation:
33 x .10 = 3.3
Ye Li drew another quadrilateral it is a parallelogram and has four right angles can it be rhombus?
Answers
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.
which number has a 9 with a value ten times greater than the 9 in 4 903
Answers
Answer:
49030
Step-by-step explanation:
we multiply it by ten so
4903×10=49030
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)
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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.
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{4x+y=9 and 5x +2y=9
use substitution method to find all solutions of the system of equations
(X,y)=
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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
same homework. different question.
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Answer:
Answer = B. Obtuse.
Step-by-step explanation:
A factory makes aquariums. Each aquarium is in the shape of a triangular prism, as shown below. If the factory makes 288 aquariums, how much water will be needed to fill all of them (in cubic feet)?
Answers
Answer:
384
Step-by-step explanation:
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
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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
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Answer:
Step-by-step explanation:
13.
Hamza made 6 calls in
one day. Each call cost the
same amount of
money. The next day he made a
call that cost $4. Which expression
represents the total cost of the calls Hamza made during the two
days?
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Answer:
6x +4 where x is amount for standard call
Step-by-step explanation:
Answer:
4c+6
Step-by-step explanation:
Right on my test
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
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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
Ryan invested $257 in an account paying an interest rate of 3.9% compounded weekly.
What is the equation?
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Answer:
The equation is 257/x = x/3.9
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 ) }
Answers
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
pls help i need an A my mom is going to get mad at me pls help i will give 62 points
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Answer:
I would say the second one
Step-by-step explanation: Good luck! :)
Find the equation of the tangent to the curve y = 4x³- 5x² + x - 3 at the point where it crosses the y axis.
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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
what's the estimate of 6.48 + 9.34
Answers
Answer:
6+9=15
Step-by-step explanation:
hope this helps :D
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.
Answers
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 .
5* 3 1/3 I have to have my math done in an hour and I don’t know this
Answers
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
help me please…………..
Answers
answer: b
explained below
Since both terms are perfect squares, factor using the difference of squares formula
Find two positive numbers whose difference is 27 and whose product is 874.
Answers
Find the minimum value of X²+6X-5
Answers
Answer:
x = -3, y = -14
Step-by-step explanation:
Graph it
Graph it
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?
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Answer:
The value of the house increased $31,680.
The current value of the house is $427,680
Step-by-step explanation:
Hey can somebody help me on this?
Answers
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