The factorization of x² - 2x - 3 is (x+1)(x-3).
The given quadratic equation is,
x² - 2x - 3
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
Hence to factorize we can write the given quadratic equation as,
⇒ x² - 3x + x - 3
⇒ x(x-3) + (x - 3)
⇒ (x+1)(x-3)
Hence,
x² - 2x - 3 = (x+1)(x-3)
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x+y=13
2x-y=5
solve using any method
Answer:
x = 6 , y = 7
Step-by-step explanation:
solving by substitution method
x + y = 13
x = 13 - y equation (i)
2x - y = 5
substitute the value of x
2(13 - y) - y = 5
26 - 2y - y = 5
26 - 3y = 5
26 - 5 = 3y
21/3 = y
7 = y
substitute the value of y in equation (i)
x = 13 - y
x = 13 - 7
x = 6
Write an equation of a line that is parallel to 6x - 2y = -3 and passes through the point (1, 3).
Answer:
Step-by-step explanation:
hope this video link be helpfull to you
You get a $600 bonus from work and want to share with your two kids. How much money will each of the three of you get if you split it evenly?
Answer:
$200 each.
Step-by-step explanation:
You are sharing the $600 bonus with 2 of your kids, meaning that the money will be evenly divided between 3 people. Divide the total amount of money with the total amount of people:
$600/3 persons = $200/person
Each person obtains $200.
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Which of the following is most likely the next step in the series?
Answer:
B
Step-by-step explanation:
Hi there!
TL;DR: Observe the vertices of the shapes inside the circles and their relationship with the circle.
For the first figure, the rectangle has 4 vertices and there are 4 dots on the perimeter of the circle.
For the second figure, the triangle has 3 vertices and there are 3 dots on the perimeter of the circle.
For the third figure, the line has 2 points and there are 2 dots on the perimeter of the circle.
For the fourth figure, there would most likely be only one dot on the perimeter of the circle (4, 3, 2, 1). The only option that shows this is B.
I hope this helps!
how do you find the rate of change for a function over a given interval
Step-by-step explanation:
Differentiate it. You will be given a value of x. Substitute into the differentiated equation use the formula for rate of change. You will find the answerFormula:
[tex]\frac{\alpha y}{\alpha x} =\frac{dy}{dx }[/tex]
Which statement or inequalities describe the number line graph?
Answer:
Step-by-step explanation:
( - ∞ , - 3 ) ∪ [ - 1 , ∞ )
find the y-intercept for the parabola
defined by this same equation:
y = 2x2 – 8x + 5
Answer:
y=5
y int
x=0
y=2(0)^2-8(0)+5
y=5
note everything multiplied by 0 is 0
4. It was 68.7°F at midday, then it rose 9°F in the afternoon and dropped another 12.3°F by 7:00 p.m. What was the temperature at 7:00p.m.?
The temperature rose so you add the amount it rose to the starting temperature
68.7 + 9 = 77.7 degrees
It then dropped so mow you subtract t the amount it dropped:
77.7 - 12.3 = 65.4 degrees
The answer is 65.4 degrees
In the expression below, the
3 is the
of x.
3x + 2
A. Coefficient
B. Constant
C. Operator
D. Variable
A) Coefficient is the correct answer.
Step-by-step explanation:
The 3 is a coefficient. The x is the variable.
Which fraction is represented by point A on the number line?
0
А
-0 -1
о
IT
os
O 1
Customers at a restaurant can build their own burrito by choosing one item from each category shown in the table.
Answer:
E
Step-by-step explanation:
Beans: 2 possibilities
Meat: 3 possibilities
Vegetables: 4 posibilities
Toppings: 4 possibilities
Then mulltiply the numbers:
2 x 3 x 4 x 4 which equals 96
Set up an algebraic equation that could represent the following situation:
Nkateko sells bananas at the low but fixed price of R3/kg. In order to ensure that she makes a reasonable profit, she adds a certain fixed amount of money to any quantity of bananas purchased. A customer who bought 4 kg of bananas was observed paying R14.
Answer:
The profit for any purchased of bananas is R2.
Step-by-step explanation:
Cost of 1 kg banana = R 3
Banana purchased = 4 kg
So, the cost of 4 kg bananas = 4 x 3 = R 12
Amount paid = R 14
Profit = R 14 - R 12 = R 2
So, the profit on any purchased of bananas is R 2.
example of expressions to represent length and width
Answer:
lxwxh
Step-by-step explanation:
Length x width x height
Help with number 4 I'm stuck on this algebra test with my kid and neither of us understand it
Answer:
a) x = 4
b) x = 8
c) y = -7
d) y = -10
Step-by-step explanation:
Solve by substitution on all
a)
3x + 2y = -5
3x +2 * -17/2 = -5
3x - 17 = -5
3x = -5+17
3x = 12
x = 12/3
x = 4
A vault contains 3000 worth of nickels.
How many nickels are in the vault
Answer:
600 nickels
Step-by-step explanation:
Andy is comparing how long two tablets can be used after being fully charged.
-
Tablet A Tablet B
(minutes) (minutes)
540
593
Mean
Median
580
589
NOR
21
13
MAD
6
2
Answer:
Part A: On average Tablet B's battery will last longer.
Part B: The MAD is lower in tablet B's battery life so Tablet B is more consistent.
Step-by-step explanation:
The rule as a mapping for the translation of a rectangle is (x, y) = (x - 2, y + 7). Which describes this translation?
O a translation of 2 units down and 7 units to the right
O a translation
of 2 units down and 7 units to the left
O a translation of 2 units to the right and 7 units up
O a translation of 2 units to the left and 7 units up
Mark this and retum
Answer:
a translation of 2 units to the left and 7 units up
Step-by-step explanation:
Translation of points (x,y)
At point x, the function can be translated to the left or to the right.
(x-a) is the translation of the point a units to the left, and (x+a) is the translation of the point a units to the right.
At point x, the function can be translated up or down. y+a represents a shift of a units up, and y-a represents a shift of a units down.
(x, y) = (x - 2, y + 7)
x - 2: 2 units to the left.
y + 7: 7 units up
So the fouth option is correct.
How much would nick have over the span of 20 years if he put $1000 in his savings account with 10% of simple interest
Step-by-step explanation:
use the simple interest formula
A person must score in the upper of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of and a standard deviation of , what score must a person have to qualify for Mensa (to whole number)
Answer:
The person must score at least [tex]X = \mu + Z\sigma[/tex], in which Z has a p-value of [tex]1 - \frac{p}{100}[/tex], considering p the upper percentage the person must score, [tex]\mu[/tex] is the mean IQ score for the population and [tex]\sigma[/tex] is the standard deviation.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
What score must a person have to qualify for Mensa?
Score of at least X, given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]X - \mu = Z\sigma[/tex]
[tex]X = \mu + Z\sigma[/tex]
In which Z has a p-value of [tex]1 - \frac{p}{100}[/tex], considering p the upper percentage the person must score.
HELPP DONT SEND A FILE WHATS the surface area explain step by step too
Answer:6
Step-by-step explanation:
What is the value of X?
Answer:
The answer is 46'
Step-by-step explanation:
The first triangle is:85'+53'+Y=180' so y=42'
The second triangle with X is:92+42'+X=180' so X=46'
please answer this , like ASAP
Answer:
let total be U and strawberry be S and.apple be A .
now
n[U]=200
n[S]=56% 0f 200=112
n[A]=44%of 200=88
n[A n S]=30%of 200=60
now
[tex] \bar {A U S}=?[/tex]
we have
n[U]=n[A] +n[B]-n[ A n B]+[tex] \bar{A U S}[/tex]
[tex] \bar{A U S}[/tex]=200-112-88+60=60
option C. 60 is a required answer.
Hope this help!!!
Have a nice day!!!
Can y’all help me on question 28?!
Answer:
C. It the correct answer
i need help, this is for a final
Step-by-step explanation:
Since the two triangles are similar
Then the ratio of sides are equal
Then MK:ML =JH:JI
Sub in this and you will get x =64.1
Roderick has an Internet service that charges by the hour. This piecewise function shows the cost of the Internet service based on the number of hours that Roderick uses
the Internet.
when x 34
10
(10 + 2.50(x-4)
when x > 4
Last month, Roderick used the Internet for 7.5 hours. What was he charged?
Helppppp Plssssssss
Answer:
18.75 is the answer
Step-by-step explanation:
since the internet usage is more than 4 hrs, the second equation will be used. that is
cost = (10 + 2.50 (x - 4)) where x is the usage hours.
thus
[tex]cost = 10 + (2.5 \times (7.5 - 4)) \\ = 10 + (2.5 \times 3.5) \\ = 10 + 8.75 \\ = 18.75[/tex]
You measure 34 textbooks' weights, and find they have a mean weight of 69 ounces. Assume the population standard deviation is 8.2 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places
Answer:
The 95% confidence interval for the true population mean textbook weight is between 66.24 and 71.76 ounces.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{8.2}{\sqrt{34}} = 2.76[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 69 - 2.76 = 66.24 ounces
The upper end of the interval is the sample mean added to M. So it is 69 + 2.76 = 71.76 ounces.
The 95% confidence interval for the true population mean textbook weight is between 66.24 and 71.76 ounces.
if the equation 2x^2+ bx+ 5=0 has no real solutions, which of the following must be true A. b^2 < 10 B. b^2> 10 C. b^240
Answer:
C. b²< 40
Step-by-step explanation:
2x²+ bx + 5=0 has no real solutions
=> D< 0
b² < 4ac
b²< 4(2)(5)
b²< 40
How many rows of seats are needed to seat 673 people at a concert when the rows seat 37 people each?
Answer:
18.189 rows
Step-by-step explanation:
673 / 37 = 18.189189189
Hope this helps!
it says 10^-4
please help give brainliest
Answer:
jane is correct
Step-by-step explanation:
10⁻⁴ can be written as [tex]\frac{1}{10000}[/tex] and as 0.0001
Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x) = -3x^4 - 2x - 5
Neither
Even
Odd
Answer:
Neither
Step-by-step explanation:
