Given:
[tex]y=2x^2-8x-10[/tex]
To find:
The interval(s) on which the given function is positive.
Solution:
We have,
[tex]y=2x^2-8x-10[/tex]
[tex]y=2(x^2-4x-5)[/tex]
[tex]y=2(x^2-5x+x-5)[/tex]
[tex]y=2(x(x-5)+1(x-5))[/tex]
[tex]y=2(x+1)(x-5)[/tex]
For zeroes, [tex]y=0[/tex]
[tex]2(x+1)(x-5)=0[/tex]
[tex]x=-1,x=5[/tex]
-1 and 5 divide the number line in three parts [tex](-\infty , -1),(-1,5),(5,\infty )[/tex].
Interval Selected Value [tex]y=2(x+1)(x-5)[/tex] Sign
[tex](-\infty,-1)[/tex] -2 [tex]y=2(-2+1)(-2-5)=14[/tex] +
[tex](-1,5)[/tex] 0 [tex]y=2(0+1)(0-5)=-10[/tex] -
[tex](5,\infty)[/tex] 6 [tex]y=2(6+1)(6-5)=14[/tex] +
So, the function is positive for interval [tex](-\infty,-1)[/tex] and [tex](5,\infty)[/tex].
We can say that the function is positive for interval x < -1 and x > 5.
Therefore, the correct option is B.
Tamara is bringing refreshments to a
reception for 23 people. She estimates one
liter of juice for 5 people. How much juice should Tamara buy in liters.How many milliliters of juice is this.
Solve the inequality.
X + 25 < 33
O A. x< 58
B. x < 8
C. X> 58
O
D. X > 8
Answer:
x < 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
x + 25 < 33
Step 2: Solve for x
Subtract 25 on both sides: x < 8Here we see that any value x smaller than 8 would work as a solution to the inequality.
Which graph represents y = √ X
Explanation:
[tex]\displaystyle [9, 3] → 3 = \sqrt{9} \\ [4, 2] → 2 = \sqrt{4} \\ [1, 1] → 1 = \sqrt{1} \\ [0, 0] → 0 = \sqrt{0}[/tex]
**In this case, we want NON-NEGATIVE terms.
I am joyous to assist you at any time.
Find the measure of angle b (15
Answer:
Angle b is 15 measure the scale
At Smith’s Bike Rentals, it cost $27 to rent a bike for 6 hours. How many dollars does it cost per hour of bike use
Answer:
$4.50 per hour
Step-by-step explanation:
Step 1: 27 divided by 6 is 4.50
Step 2: Double check your work by multiplying 4.50 times 6 to make sure you get 27
Consider the following frequency table representing the scores on a test.
Scores on a Test
Class Frequency
40–43 7
44–47 7
48–51 7
52–55 8
56–59 4
Required:
a. Determine the lower class boundary for the fifth class.
b. Determine the upper class boundary for the second class.
c. Determine the class width of each class.
d. Determine the number of scores between 39.5 and 55.5
Answer:
(a)56
(b)47
(c)3
(d)29
Step-by-step explanation:
From the given frequency
(a) Fifth class is 56-59.
The lower class boundary for the fifth class is 56.
(b) Second class is 44-47.
The upper-class boundary for the second class is 47.
(c) Class width = 47-44 = 3, 47-44 = 3.
(d) Number of scores between 39.5 and 55.5 is
=7 + 7+ 7 + 8 =29
heres more lolllllllllllll
Answer:
Awwww ty <3
You are too nice lollllllllllllll
Step-by-step explanation:
Consider all four-digit numbers that can be made from the digits 0-9 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is less than or equal to 5000
Answer: 0.44
Step-by-step explanation:
First, let's count the total number of four-digit numbers.
Let's think it as four empty slots:
_ _ _ _
In each slot, we can put a single digit.
In the first slot, we have 9 options {1, 2, 3, 4, 5, 6, 7, 8, 9}
The zero is not an option here, because if there was a 0, this would be a 3 digit number, then the 0 can not be in the first slot.
For the second slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
for the third slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
for the fourth slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
The total number of combinations is equal to the product between the numbers of options for each slot, this means that we have:
Combinations = 9*10*10*10 = 9000
So there are 9000 different 4 digit numbers.
Now we want to find the probability of selecting a number at random that is equal or smaller than 5000.
Let's see the number of 4-digit numbers that are equal or smaller than 5000.
The smallest 4-digit number is 1000.
Then the number of numbers between 1000 and 5000 is:
5000 - 1000 = 4000
This means that there are 4000 4-digit numbers that are equal or smaller than 5000.
Now, the probability of selecting one of them at random is equal to the quotient between the number of 4-digit numbers that meet the condition (4000) and the total number of 4-digits (9000)
Then te probability is:
P = 4000/9000 = 4/9 = 0.44
T
What equation is a proportion?
7/9 = 21=28
1/3 = 1/4
5/8 = 20/32
3/4 = 6/9
Answer:
5/8=20/32
Step-by-step explanation:
HELP NOW PLSSSSS
(where the longer it takes to solve a problem and the fewer people who answer it correctly, the more difficult it is). On each subsection, question 1 will be "easy" and question 15 will be considered "difficult." However, the ascending difficulty resets from easy to hard on the grid-ins.
Hence, multiple choice questions are arranged in increasing difficulty (questions 1 and 2 will be the easiest, questions 14 and 15 will be the hardest), but the difficulty level resets for the grid-in section (meaning questions 16 and 17 will again be "easy" and questions 19 and 20 will be very difficult).
the answer is 4/.12
:)
Answer:
Hence, multiple choice questions are arranged in increasing difficulty (questions 1 and 2 will be the easiest, questions 14 and 15 will be the hardest), but the difficulty level resets for the grid-in section (meaning questions 16 and 17 will again be "easy" and questions 19 and 20 will be very difficult).
What is the question??
a circle has a center at (-2,7). if a point on the circle has coordinates (3,-1) then which of the following would be the length of the radius of the circle
Answer:
square root of 65 or 8.06
Step-by-step explanation:
(x-2)^2+(y-7)^2+65
hope this helps
The length of radius is 7.81 unit.
What is Distance Formula?The distance between two points P(a, b)a nd Q(c, d) is
D = √(c- a)² + (d- b)²
Given:
Center at (-2,7) if a point on the circle has coordinates (3,-1).
Using Distance Formula
D = √( 3-(-2))² + (1-7)²
D = √ (3 +2)² + (-6)²
D = √5² + 36
D = √25+36
D = √61
D= 7.81 unit
Hence, the length of radius is 7.81 unit.
Learn more about distance formula here:
https://brainly.com/question/28956738
#SPJ2
if a bike race covers 120 mi over 6 days and the cyclists ride the same distance every day how many miles does each cyclist ride each day
FinWhat is the perimeter of the triangle in the graph? Round your answer to the nearest tenth if necessary. (1 point) 8.9 8.0 12.9 8.5d the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4), N(1,2), O(4, y)
Answer:
man did you ever find out the answer bc I'm dying I cannot fail this test-
Answer:
12.9
Step-by-step explanation:
it is common sense
also i just took test
What is the least common denominator of 1/4 and 7/9
Answer: It is 36
Step-by-step explanation:
Sketch a graph that shows the
relationship between grams of honey and
grams of salt needed for a bakery recipe.
Show on the graph how much honey is
needed for 70 grams of salt.
salt
honey
flour
(c)
10
14
4
25
35
10
1 Add file
Delta Airlines' flights from Boston to Seattle are on time 70 % of the time. Suppose 6 flights are randomly selected, and the number on-time flights is recorded. 1.The probability that at least 4 flights are on time is
Answer:
P(at least 4) = 0.74431
Step-by-step explanation:
Here
Probability of the flights on time is = 70% = 70/100= 0.7
q= 0.3
n= 6
As the probability of success and failure is constant and the n is also fixed then the binomail probability distribution can be used to solve this.
P (x= 4) = 6c4 *(0.7)^4 (0.3)^2= 15*0.2401* 0.09= 0.324135
P (x= 5) = 6c5 *(0.7)^5(0.3)^1= 6*0.16807* 0.3=0.302526
P (x= 6) = 6c6 *(0.7)^6 (0.3)^0= 0.117649P
P (x= 0) = 6c0 *(0.7)^0 (0.3)^6= 0.000729
P (x= 1) = 6c1 *(0.7)^1 (0.3)^5=0.010206
P (x= 2) = 6c 2*(0.7)^2 (0.3)^4=0.059535
P (x= 3) = 6c3 *(0.7)^3 (0.3)^3=0.18522
Probability of at least 4 means that probability of greater than 4 inclusive of 4.
This can be obtained in two ways.
First is by subtracting the probabilities of less than 4.
Second is by adding probabilities greater than 4 including 4.
We get the same answer with any of the two methods used.
P(at least 4) = 1- P(x<4)
= 1- [ 0.000729+ 0.010206 +0.059535+ 0.18522]
= 1- 0.25569
= 0.74431
P (at least 4) = P(x=4) +P(X=5) + P(x=6)
=0.324135+ 0.302526+ 0.117649
=0.74431
whats the value of v 69 = 7v – 6
Answer:
75/7
Step-by-step explanation:
69=7v-6 rewrite as 69+6=7v
75 = 7v
75/7 = v
A small business earns a profit of $4,500 in
March and $9,500 in July. What is the rate
of change in profit for this time period?
Answer:
$2750/month
Step-by-step explanation:
What would you tip for a $22 meal if you wanted to leave 15%?
$18.70
$4.40
$3.30
$25.30
help me , my project is do soon .
Answer:
whats the question
Step-by-step explanation:
Part A : At Mountain Park Middle school, there are 250 seventh-grade students who are not in advanced math. Let a represent the number of seventh-grade students who are not in advanced math?
Part B: How many students are NOT in advanced math?
Answer:
hard to explain
Step-by-step explanation:
Answer:I think 80 at bottom like
Step-by-step explanation:
n − 32 5 = 10 help plz
Answer:
n=335
Step-by-step explanation:
Answer:
Step-by-step explanation:
Here you go mate
Step 1
n − 325 = 10 equation
Step 2
n − 325 = 10 simplify by adding 325 to both sides
Answer
n=335
Rewrite the expression as the sum of two numbers 7(2+5)
answer:
its 7 x 7 or 49
explanation:
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.8 and 51 min.
Answer: the probability that the class length is between 50.8 and 51 min is 0.1 ≈ 10%
Step-by-step explanation:
Given data;
lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min
hence, height = 1 / ( 52.0 - 50.0) = 1 / 2
now the probability that the class length is between 50.8 and 51 min = ?
P( 50.8 < X < 51 ) = base × height
= ( 51 - 50.8) × 1/2
= 0.2 × 0.5
= 0.1 ≈ 10%
therefore the probability that the class length is between 50.8 and 51 min is 0.1 ≈ 10%
Given the diagram below, solve for the value of x.
==========================================================
Explanation:
Sides ED and FD are the same length due to the red tickmarks.
The angles opposite these side lengths, angle E and angle F, are congruent as well. So angle F is also x.
For any triangle, the three angles always add to 180
F+E+D = 180
x+x+74 = 180
2x+74 = 180
2x+74-74 = 180-74 .... subtract 74 from both sides
2x = 106
2x/2 = 106/2 ... divide both sides by 2
x = 53
As a check,
F+E+D = x+x+74 = 53+53+74 = 180
which verifies the answer.
What is the slope of a line parallel to the line 2x + 3y = 5?
i think its 2/3 but im not sure .
Answer:
D
Step-by-step explanation:
Parallel lines have same slope
Write the equation in slope - intercept form
2x + 3y =5
3y = -2x + 5
Divide the equation by 3
[tex]y = \frac{-2}{3}x +\frac{5}{3}[/tex]
So, slope = (-2/3)
Suzi starts her hike at 275 feet below sea level. When she reaches the end of the hike, she is still below sea level at −135 feet. What was the change in elevation from the beginning of Suzi's hike to the end of the hike?
Answer:
Have a nice day!
Step-by-step explanation:
Answer:
140
Step-by-step explanation:
Hi there!
This problem may seem tricky because of the negative sea level, os let’s set up an equation.
[tex]-275+x=-135[/tex] where x = the change in elevation.
Using orders of operations, add 275 to both sides and you will end with
x = 140
Her change in elevation is 140 feet.
I hope this helps!
Find the value of x.
4x + 5
2x + 21, smby help me wit dis pls
Answer: x = 8
Step-by-step explanation:
4x + 5 = 2x + 21
4x + 5 - 2x = -2x + 2x +21 (Subtract 2x from both sides)
2x + 5 = 21
2x + 5 - 5 = 21 - 5 (Subtract 5 from both sides)
2x = 16
2x/2 = 16/2 (Divide both sides by 2)
x = 8
Jeffrey is 5 years older than his brother. If j represents Jeffrey’s age, the expression j−5 can be used to find his brother’s age. If Jeffrey is 23, how old is his brother?
If j=23 and j-5 is how old Jeffery's brother is then Jeffrey's brother is 17 years old.
So j=17
The Molina family went to a concert together. They purchased 4 concert tickets for $25 each, 3T -shirts for $15 each, and a poster for $10.Write an expression for the total cost. Then find the total cost.
Answer:
155
Step-by-step explanation:
( 25 x 4 ) + ( 3 x 15 ) + 10 = 155