Answers
Answer:
Step-by-step explanation:
The catch is to put this into the quadratic and solve for a b and c in three equations.
x = 1
a(1)^2 + b(1) + c= 0
a + b + c + 0 (1)
x = - 1
a(-1)^2 + b(-1) + c = 2
a - b + c = 2 (2)
x = 2
a(2)^2 + b(2) + c = 8
4a + 2b + c = 8 (3)
===================
Add 1 and 2 together
a + b + c = 0
a - b + c = 2
2a + 2c = 2 Divide by 2
a + c = 1 (4)
=====================
Multiply (2) by 2
2a - 2b + 2c = 4 (5)
======================
Add (5) + (3)
2a - 2b + 2c = 4
4a + 2b + c = 8
6a + 3c = 12 (6)
=====================
Multiply (4) by 3
3a + 3c = 3 (7)
===================
Subtract (7) from (6)
6a + 3c = 12
3a + 3c = 3
3a = 9 Divide by 3
3a/3 = 9/3
a = 3
=============
Use (4) to find c
a + c = 1
3 + c = 1 Subtract 3 from both sides
3-3 + c = 1-3
c = - 2
=================
Use 1 to find b
3 + b - 2 = 0 Combine 3 and -2
1 + b = 0 Subtract 1 from both sides
b = - 1
====================
Answers
a = 3
b = - 1
c = - 2
Related Questions
The Question is posted above ⤴
Answers
Answer:
Step-by-step explanation:
I think 9. 10/50
10. 6/50
11. 44/50
what is the solution set for |x/2|=8
Answers
Answer:
The correct answer option is x = -16 and x = 16.
Step-by-step explanation:
We are given the following equation and we are to find the solution for this equation:
[tex] | \frac { x } { 2 } | = 8 [/tex]
For the given equation, involving the modulus, we will have a positive as well as a negative value for it in order to find its solution set.
[tex] \frac { x } { 2 } = - 8 [/tex] and [tex] \frac { x } { 2 } = 8 [/tex]
[tex] x = 8 \times 2 [/tex] and [tex] x = - 8 \times 2 [/tex]
x = -16 and x = 16
Answer:
The correct answer is last option
x = -16 or x = 16
Step-by-step explanation:
it is given that,
|x/2| = 8
To find the solution set
From this we can understand that , the value of x/2 = - 8 or x/2 = 8
If x/2 = -8 then x = -8 * 2 = = -16
If x/2 = 8 then x = 8 * 2 = 16
Therefore the solutions are
x = -16 or x = 16
a fruit drink is made by mixing lemon juice, orange juice and lime juice in the ratio 5:2:3 james makes 400ml of the fruit drink how much lemon juice is used
Answers
Answer:
200ml
Step-by-step explanation:
5+2+3=10
400/10=40
Since lemon's ratio is 5, you multiply 40 by 5 to get 200.
Factor this trinomial: x2−2x−24
Then, select both correct factors below.
Question 4 options:
(x−6)
(x−4)
(x−2)
(x+6)
(x+4)
Answers
It’s (x-6)(x+4) so the first one and last one
For this case we must factor the following expression:
[tex]x ^ 2-2x-24[/tex]
We must find two numbers that when added together give "-2" and when multiplied by "-24"
These numbers are:
[tex]-6\ and\ +4\\-6 + 4 = -2\\-6 * + 4 = -24[/tex]
So:
[tex]x ^ 2-2x-24 = (x-6) (x + 4)[/tex]
Answer:
[tex](x-6) (x + 4)[/tex]
Option A and D
Find the value of y. Round answer to the nearest tenth if needed
Answers
Answer:
y = 54.1
Step-by-step explanation:
The big triangle is divided in two: one on the left and one on the right. Lets start working with the right one.
We know the right triangle is a right triangle with legs 24 and 36, so we can use Pitagoras to find the hypotenuse (h), in a way that:
24^2 + 36^2 = h^2
1872 = h^2
Applying sqr root in both sides:
h = 43.27
So, the hypotenuse measures 43.27 or 43.3.
Now lets do the same with the triangle of the right which legs are 36 and y, lets find it hypotenuse (g):
36^2 + y^2 = g^2
1296 + y^2 = g^2
Now we will pass to the large triangle, which is composed by the left and the right triangles and has legs of 43.3 and g, and the hypotenuse is 24+y. Lets apply Pitagoras:
43.3^2 + g^2 = (24+y)^2
1875 + 1296 + y^2 = 24^2 + 48y + y^2
3171 + y^2 = 576 + 48y + y^2
As we have y^2 in both sides we can eliminate them
3171 + = 576 + 48y
Now subtract 576 in both sides:
3171 -576 = 576 + 48y - 576
2595 = 48y
Divide both sides by 48:
2595/48 = 48y/48
54.1 = y
So, the large hypotenuse measures 54.1+24 = 78.1. Lets verify:
43.3 ^2 + 1296 + 54.2^2 = 6,108.53
And the sqrd root of 6,108.53 is approximately 78.1. Verified!!!!
So, we can confirm: y = 54.1
There are 5 red pens,3 blue pens and 2 green pens in a box. Gary takes at random a pen from the box and gives the pen to his friend. Gary then takes at random another pen from the box . work out the probability that both pens are the same colour.
please help
Answers
➷ Find the total number of pens:
5 + 3 + 2 = 10
The probability of taking a red the first time is 5/10
The probability of taking a blue the first time is 3/10
The probability of taking a green the first time is 2/10
If you want to take the same colored pen again, there would be 1 less of the total pen (as it hasn't been replaced) and there would be one less of that color (as one has already been taken)
Therefore:
The probability of taking a red again is 4/9
The probability of taking a blue again is 2/9
The probability of taking a green again is 1/9
Multiply the values for the same color together:
5/10 x 4/9 = 20/90
3/10 x 2/9 = 6/90
2/10 x 1/9 = 2/90
Add these values together:
20/90 + 6/90 + 2/90 = 28/90
Your answer is 28/90
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
1. Andrew will roll a number cube and flip a coin for a probability experiment. The faces of the number cube are labeled 1 through 6. The coin can land on heads or tails. If Andrew rolls the number cube once and flips the coin once, write a list that contains only the outcomes in which the number cube lands on a number less than 3? 2. A study of a population of 1,500 dogs revealed that 15 out of every 125 dogs in the population have spots on their back. Based on the results of this study, how many dogs in the population do NOT have spots on their back? 3. For his lunch, David is making a sandwich that must consist of bread, cheese, and meat. David can choose from white, French or rye bread, either American or Swiss cheese, and the choice of turkey, ham or pastrami as a meat. Create a tree diagram to represent the combinations of bread, cheese, and meat David could make for his sandwich. 4. Joel has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Joel's Jumble has 2 classical songs, 13 rock songs, and 5 rap songs on it. What is the probability that the first song that Joel hears is a rap song? 5. You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you'll be a magic elf?
Answers
Answer:
Part 1)
(1,H),(2,H)(1,T),(2,T)
Part 2)
1320
Part 4)
1/4
Part 5)
1/15
Step-by-step explanation:
Part 1)
Possible outcomes of cube={1,2,3,4,5,6}
Possible outcomes of coin=(H,t}
Now, Andrew rolls the number cube once and flips the coin once
then possible outcome that contains only the outcomes in which the number cube lands on a number less than 3 are:
(1,H),(2,H)(1,T),(2,T)
Part 2)
Given:
population=1500 dogs
spots containing dogs= 15 out of every 125 dogs in the population have spots
spots containing dogs:
=1500/125
=12
=12*15
=180
dogs in the population that do NOT have spots on their back
=1500-180=1320
Part 4)
Given:
classical songs=2
rock songs=13
rap=5
total songs= 2+13+5
=20
probability that the first song that Joel hears is a rap song= 5/20
=1/4
Part 5)
Given:
3 Characters= elf, hobbit, or human
4 tools= magic, sword, shield, slingshot, or umbrella
Probability of first event , P(C)= 1/3
Probability of second event, P(T)=1/5
As both events are mutually exclusive so
P(magic elf)= P(C)*P(T)
=1/3+1/5
=1/15 !
Point W(5, -6) is reflected across the line y = -x. Which of the following is the location of its image, W’.
(-5, -6)
(5, 6)
(-6, 5)
(6, -5)
Answers
(6, -5)
Key Concepts for Reflections:if (a, b) is reflected on the x-axis, the image is the point (a, -b)if (a, b) is reflected on the y-axis, the image is the point (-a, b)if (a, b) is reflected on the line y = x, the image is the point (b, a)if (a, b) is reflected on the line y = -x, the image is the point (-b, -a)(5, -6) --> (-5, 6)
Hope this helps!!
I'd right the key concepts for future reference!
:D
Answer:
(6,-5)
Step-by-step explanation:
Can someone please help me find the DBE=
Answers
Answer:
∠DBE = 105°Step-by-step explanation:
Angles on one side of a straight line always add to 180°.
Therefore we have the equation:
[tex]35+(3x-15)+x=180[/tex]
[tex]35+3x-15+x=180[/tex] combine like terms
[tex](35-15)+(3x+x)=180[/tex]
[tex]20+4x=180[/tex] subtract 20 from both sides
[tex]4x=160[/tex] divide both sides by 4
[tex]x=40[/tex]
∠DBE = 3x - 15. Substitute:
[tex]\angle DBE=\bigg(3(40)-15\bigg)^o=\bigg(120-15\bigg)^o=105^o[/tex]
Please help me. Thank you
Answers
Step-by-step explanation
i had to turn my laptop just to read that
My
Both rectangles have the same dimensions and shape. P'Q'R'S' is a translated image of PQRS, shifted 3 units right and 3 units up. They are congruent but not identical due to their position.
Step-by-step comparison of rectangles PQRS and P'Q'R'S':
1. Original coordinates:
Assume specific coordinates for the vertices of rectangle PQRS. For example, let P = (1, 2), Q = (5, 2), R = (5, 6), and S = (1, 6).
2. Translation:
A translation moves every point in the shape the same distance and in the same direction. Since Rashid translated rectangle 3 units up and 3 units to the right, add 3 to x-coordinate and 3 to y-coordinate of each point in PQRS to find corresponding points in P'Q'R'S'.
3. New coordinates:
P' = (1 + 3, 2 + 3) = (4, 5)
Q' = (5 + 3, 2 + 3) = (8, 5)
R' = (5 + 3, 6 + 3) = (8, 9)
S' = (1 + 3, 6 + 3) = (4, 9)
4. Comparison:
Shape:
Both rectangles PQRS and P'Q'R'S' are rectangles because a translation preserves the shape of the original figure.
Size:
They have the same dimensions (length and width) as the translation only shifts the position without altering the size.
Orientation:
They maintain the same orientation relative to the axes, meaning their sides remain parallel and perpendicular to the x and y axes.
Position:
The key difference lies in their position. P'Q'R'S' is located 3 units to the right and 3 units above PQRS.
5. Rectangles PQRS and P'Q'R'S' are congruent (same size and shape) but not identical (different positions).
P'Q'R'S' is a translated image of PQRS, moved 3 units to the right and 3 units up.
Habeas Corpus: legal writ or order. Guarantees a prisoner the right to be heard in a court
write a short sentence using the word habeas corpus in it.
Answers
Habeas corpus is the right to have one’s detention reviewed by a judge
Answer:
a prisoner’s right to inquire why he or she is being detained
Step-by-step explanation:
Can someone help me pls
Answers
Answer:
D. $240,000
Step-by-step explanation:
find $40,000 on the chart - then find 45 years old / 60% - go down the chart and over to the right and you'll find 6.0
multiply 40,000 * 6.0 = 240,000
hope this helps!!
The answer is D. 240,000
Hope this helps : )
given -1/2 x>6.choose the solution set
Answers
Answer: x < -12
Step-by-step explanation:
[tex]-\dfrac{1}{2}x>6\\\\\\\text{Multiply both sides by -2}\\\\(-2)\dfrac{-1}{2}x>(-2)6\\\\\\\text{Simplify - remember to flip the inequality symbol}\\x<-12[/tex]
Graph: ←-----------o -12
Interval Notation: (-∞, -12)
Answer:
x<-3
Step-by-step explanation:
ben wants to bike 12 miles. so far he has biked 2/3 of those 12 miles. How many miles has Ben biked
Answers
Answer:
Ben had biked 8 miles
Step-by-step explanation:
You would need to take 12 and divide it by three . That would make 4. After that you would take 4 and multiply it by 2 since he rode 2/3 miles of 12. Then you would end up with 8.
Final answer:
Ben has biked 8 miles of the 12 miles he wants to, as he has completed 2/3 of his intended distance.
Explanation:
To calculate the number of miles Ben has biked, we simply need to multiply the total distance he wants to bike by the fraction of the trip he has completed. Ben wants to bike 12 miles, and he has biked 2/3 of that distance. Multiplying these together gives us 2/3 * 12 = 8 miles. Therefore, Ben has biked 8 miles so far.
What is the product of (2x^2+5x-3) and (3x+7)
Answers
Answer: option D.
Step-by-step explanation:
To solve this exercise you must apply the proccedure shown below:
- Apply the Distributive property (Remember that when you multiply two powers with the same base, you must add the exponents).
[tex]b^m*b^n=b^{(m+n)}[/tex]
- Add the like terms.
Therefore, you obtain that the product is:
[tex](2x^2+5x-3)(3x+7)=6x^3+14x^2+15x^2+35x-9x-21\\=6x^3+29x^2+26x-21[/tex]
An expression is defined as a set of numbers, variables, and mathematical operations. The product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The product of (2x²+5x-3) and (3x+7) can be done as,
(2x²+5x-3) × (3x+7)
= 3x(2x²+5x-3) + 7(2x²+5x-3)
= 6x³ + 15x² - 9x + 14x² + 35x - 21
= 6x³ + 29x² + 26x - 21
Hence, the product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ2
The parallel lines on top of each other confuse me,any help?
Answers
Set it up.
Make the equations equal to 180° because they are on a straight line. And a straight line adds up to 180°
Help!! Not good with Slope! especially with no dots! Brianliest answer offered!!
Answers
Find two "dots" where the line crosses the X and Y axis at real numbers.
(0,3) and (6,-1)
Now find the slope which is the difference in Y over the difference in x.
Slope = (-1 - 3) / (6-0) = -4 / 6 = -2/3
The answer is D.
Write an equation of the line that passes through the point (12.2) and has a slape of -1/4
Answers
answer :
y=-1/4x+5
my work:
y=mx+b
2=-1/4(12)+b
2=-3+b
+3 +3
5=b
y=-1/4x+5
Answer:
y = - [tex]\frac{1}{4}[/tex] x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{4}[/tex], hence
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
To find c substitute (12, 2) into the partial equation
2 = - 3 + c ⇒ c = 2 + 3 = 5
y = - [tex]\frac{1}{4}[/tex] x + 5 ← equation of line
PERFORM THE MULTIPLICATION
(x–3)^2(x+3)^2
SOMEONE PLZZZ HELP
Answers
Answer:
81 is the answer
Step-by-step explanation:
Answer:
Hold up im solving it
Step-by-step explanation:
i need a little help because i forgot how to do this
simplify. y^2y^3
Answers
Answer:
[tex]y^{5}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
Hence
[tex]y^{2}[/tex] × [tex]y^{3}[/tex] = [tex]y^{(2+3)}[/tex] = [tex]y^{5}[/tex]
On a number line 7.35 would be located?
Answers
Answer: B, C, and D are all correct.
Step-by-step explanation:
Answer: B and D
Step-by-step explanation:
It would go between 7.32 and 7.37
During the spring and summer months, the Happy Home Motel sees a rise in travelers. The manager of the motel turned in this report of how many travelers stayed at the Happy Home Motel. Month Number of Travelers March 217 April 232 May 252 June 277 July 307 August ? If the Happy Home Motel continues to follow this pattern, how many travelers will stay during August?
Answers
Answer:
342
Step-by-step explanation:
Let's see the difference is each successive values:
232 - 217 = 15
252 - 232 = 20
277 - 252 = 25
307 - 277 = 30
As we can see, each month the increase is 5 more than previous months' increase. Clearly from the pattern we can surmise that the next month (August), it will increase by 35 from the value of July.
Number of visitors in August = Number of Visitors in July + 35 = 307 + 35 = 342
Answer:
342
Step-by-step explanation:
how do I find the x value of this triangle? thank youuuu
Answers
answer = 42
if you look at the triangle you see a small square in the corner indicating that the triangle is a 90 degree angle, therefore all the sides add up to 90. With this knowledge just add the values of the two known sides, 18 and 30, which is 48 and then subtract 48 from 90 which gives you the value of x, 42
x ^2 + 18 ^2 = 30 ^ 2
x^2 = 30^2-18^2
x^2 = 900-324
x^2 = 576
x = 24 Answer
Is there a proportional relationship between x and y? Explain.
x 8 10 12 14
y 5 7 9 11
Answers
Yes there is because the change of rate for both the x and y-values is 2. It has a consistant rate of change.
The isosceles triangle has two sides of equal length , a , that are longer than the length of the base , b. The perimeter of the triangle is 15.7 centimeters. The equation 2a+b=15.7 models this information.
If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base ?
Answers
Answer:
Step-by-step explanation:
Since the length of one of the longer sides, a, has been given to be 6.3, plug it into the equation.
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 15.7 - 12.6
b = 3.1
Answer:
Equation that can be used to find length of the base is b + 12.6 = 15.7 and the length of the base we get from this equation is 3.1 cm
Step-by-step explanation:
Given:
Length of the equal side of the Isosceles Triangle = a
Length of the base of the triangle = b
Equal sides are longer than base of the triangle.
Perimeter of the triangle = 15.7 cm
Equation representing given information = 2a + b = 15.7
To find: Equation that represent or can be used to find length of the base if longer side = 6.3 cm
Given Equation is the Equation representing the perimeter of the isosceles triangle.
Longer side = 6.3 cm = Length of the Equal Sides of the triangle.
So, a = 6.3 cm
Now,
2 × 6.3 + b = 15.7
b + 12.6 = 15.7
b = 15.7 - 12.6
b = 3.1 cm
Therefore, Equation that can be used to find length of the base is b + 12.6 = 15.7 and the length of the base we get from this equation is 3.1 cm
Please please please please PLEASE answer
Answers
Yea it’s the second one
Given that the circles are congruent, can you conclude that YZ=BC?
Answer options: yes, no
Answers
Answer:
Answer is yes
Step-by-step explanation:
Given in the picture are two circles which are congruent.
This suggests that the radii of the two circles are equal.
Also the central angle of the two circles are congruent (given)
Consider triangles ABC and XYZ,
AC =XY: AB = YZ:
Angle A = Angle X
By SAS theorem, the two triangles are congruent.
Hence BC = YZ
So yes is answer.
find the height, round to the nearest hundredth
Area is 72units squared
Answers
Answer:
[tex]\large\boxed{h=10\dfrac{2}{7}}[/tex]
Step-by-step explanation:
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
We ahve b = 14 and A = 72. Substitute:
[tex]72=\dfrac{14h}{2}[/tex] multiply both sides by 2
[tex]144=14h[/tex] divide both sides by 14
[tex]h=\dfrac{144}{14}\\\\h=\dfrac{144:2}{14:2}\\\\h=\dfrac{72}{7}\\\\h=10\dfrac{2}{7}[/tex]
Help me plz show work
Answers
Answer: F) (x, y) → (x - 6, y + 2)
Step-by-step explanation:
6 units to the left means subtract 6 from the x-value --> x - 6
2 units up means add 2 to the y-value --> y + 2
PLZ HURRY IT'S URGENT!!!!
What is 3/25 written as a decimal? A. 0.3 B. 0.12 C. 0.15 D. 0.22
Answers
Answer:
B. .12 is the decimal
Step-by-step explanation:
What you do is you divide 25 by 3. That will already give you a decimal and when you divide it out your answer is .12.
3/25=.12.
Answer:
The correct answer is 0.12
Step-by-step explanation:
3 = numerator
25 = denominator
Divide the numerator by the denominator to convert a fraction to a decimal.
3 ÷ 25 = 0.12
as a decimal is
0.12
.
Answer: The answer is B. 0.12
Step-by-step explanation: