The parabola $y = ax^2 + bx + c$ is graphed below. Find $a+b+c$. (The grid lines are one unit apart.)
Answers
If [tex]x=0[/tex], then [tex]y=a\cdot0^2+b\cdot0+c=5[/tex], so [tex]c=5[/tex].
If [tex]x=1[/tex], then [tex]y=a\cdot1^2+b\cdot1+c=2[/tex], so [tex]a+b+5=2[/tex] or [tex]a+b=-3[/tex].
If [tex]x=2[/tex], then [tex]y=a\cdot2^2+b\cdot2+c=1[/tex], so [tex]4a+2b+5=1[/tex] or [tex]2a+b=-2[/tex].
We have
[tex]a+b=-3\implies -a-b=3[/tex]
[tex](2a+b)+(-a-b)=-2+3[/tex]
[tex]\implies a=1\implies b=-4[/tex]
So we end up with
[tex]a+b+c=1+(-4)+5=\boxed{2}[/tex]
Related Questions
what number set 1/2 belongs to? rational, irrational, integer, or natural
Answers
Answer:
Rational
Step-by-step explanation:
1/2 would be 0.5 and 0.5 goes into the Rational catagory.
help me with this plzzzzz
Answers
Answer:
C
Step-by-step:
The answer is c because 7.6 & 8.2 are both rational numbers and it goes onto natural numbers. They are also ordered in the from least to greatest like on a number line, 7.6, 8.2, 50, 65, 78. Plus, I'm kinda on the same unit.
Convert the angle to degrees, minutes, and seconds. 292.41°
Answers
Answer:
292° 24' 36"
Step-by-step explanation:
d = int(292.41°) = 292°
m = int((292.41° - 292°) × 60) = 24'
s = (292.41° - 292° - 24'/60) × 3600 = 36"
292.41°
= 292° 24' 36"
Answer:
292 degrees 24 minutes and 36 seconds:
292° 24' 36"
Step-by-step explanation:
There are 60 minutes in a degree and 60 seconds in a minute.
so 0.41 degrees = 0.41 * 60 = 24.6 minutes
and 0.6 of a minute = 0.6 * 60 = 36 seconds.
If p, q and r were three statements such that p → q and q → r then p → r, this is called
Answers
Answer: Law of syllogism
Step-by-step explanation:
Law of Syllogism is described as
a logical reasoning by using transitivity.a valid argument that applies deductive reasoning to get the final statement. it is similar to transitive property that if a=b and b=c then a=c.So if p, q and r were three statements such that p → q and q → r then p → r, this is called law of syllogism.
For example: When Rita gets internet Shamy gets internet. When Shamy gets internet Raj gets internet.
By law of syllogism : When Rita gets internet Raj gets internet.
There are 7 pens in a bag. Four of the pens are blue and the other 3 are red. What's the probability of pulling out a red
pen? Write your answer as a fraction.
Answers
Answer:
3/7
Step-by-step explanation:
P(red) = number of red pens / total number of pens
= 3/7
Answer:
3/7
Step-by-step explanation:
Total pens = 7
Blue pens = 4
Red pens = 3
probability of pulling out a red pen
= No of red pens / Total pens
= 3/7
3x + 5 = 2x + 2 -(x-3) Pls show work too, thanks :)
Answers
Answer:
X=0
Step-by-step explanation:
1.Remove the parentheses
3x + 5 = 2x + 2 -(x-3) -> 3x+5=2x+2-x+3
2.Combine like terms
3x+5=2x+2-x+3 -> 3x+5=x+5
3.Cancel Equal Terms
3x+5=x+5 -> (subtract 5 from both sides) 3x=x
(subtract x from both sides) 3x=x -> 3x-x=0
4.Combine like terms
3x-x=0 -> 2x=0
5.Get rid 2 so divide both sides by 2
2x= 0 -> [tex]\frac{2x}{2}[/tex]=[tex]\frac{0}{2}[/tex] ->
x=0
If 225 is the dividend and 15 is the divisor, then what is the quotient?
Answers
Answer:
The answer is 15.
Step-by-step explanation:
When dividing 225 by 15 you can multiply 15 by 15 and you will get 225.
What is the change in temperature from 20 degrees to -8 degrees ?
Answers
Answer:
28 degrees relatively
Step-by-step explanation:
20-(-8)
Answer:
20 degrees Celsius to Fahrenheit
20 degrees Celsius (ºC) are equal to 68 degrees Fahrenheit (ºF):
20ºC = 68ºF
Calculation
The temperature T in degrees Fahrenheit (ºF) is equal to 20 degrees Celsius (ºC) times 9/5 plus 32:
T(ºF) = 20ºC × 9/5 + 32 = 68ºF
On Monday the temperature was 32° On Tuesday the temperature was -5°. What was
the change in temperature?
Answers
Answer:
37°
Step-by-step explanation:
Think of 0° as a reference point. Then 32° is above this reference by 32 degrees, and -5° is below it by 5 degrees. Summing up 32 and 5, we get 37. The change in temperature was 37°
Make x the subject of the formula a(x-b)=a^2+bx
Answers
Answer:
x = [tex]\frac{a(a + b)}{a-b}[/tex]
Step-by-step explanation:
Step 1: Write out formula
a(x - b) = a² + bx
Step 2: Distribute
ax - ab = a² + bx
Step 3: Add ab to both sides
ax = a² + bx + ab
Step 4: Subtract bx on both sides
ax - bx = a² + ab
Step 5: Factor
x(a - b) = a² + ab
Step 6: Divide (a - b) on both sides
x = [tex]\frac{a^{2} + ab}{a-b}[/tex]
Step 7: Factor
x = [tex]\frac{a(a + b)}{a-b}[/tex]
And we have our final answer!
7n+5=96 so what is the answer
Answers
Answer:
n = 13
Step-by-step explanation:
7n + 5 = 96
Subtract 5 from both sides to get rid of the 5 on the right side:
7n + 5 - 5 = 96 - 5
7n = 91
Divide both sides by 7 to get rid of the coefficient of n:
7n / 7 = 91 / 7
n = 13
Answer: [tex]n=13[/tex]
Subtract 5 from both sides
[tex]7n+5-5=96-5\\7n=91[/tex]
Divide both sides by 7
[tex]7n/7=91/7\\x=13[/tex]
What value of x will make each equation below true? 4x-1=4x+7
Answers
Answer:
4X-1=4X+7
4x - 4x = 1 + 7
0 = 8
Step-by-step explanation:
Since there is no value of x that will make this true,
this has no solution and x is the empty set.
Answer:
Step-by-step explanation:
4x-1=4x+7
4x-1-4x=4x+7-4x
-1=7
Please solve #5 and show your work! Will give BRAINLIST!!
Answers
Answer:
damita
Step-by-step explanation:
erin: 2/12 = 0.1666667
damita: 4/16 = 0.25
jayden: 3/15 = 0.2
0.25 is the highest concentration
(20pts)prove that the difference of the squares of two consecutive integers is equal to the sum of the integers, whenever the larger of the two integers comes first
Answers
Answer:
see below (I hope this helps!)
Step-by-step explanation:
If the two numbers are x and x + 1, then:
(x + 1)² - x²
= x² + 2x + 1 - x²
= 2x + 1
= x + (x + 1)
This year,a farm planted 400,000corn stalks.Last year,the farm planted 275,650cornstalks. How many more cornstalks did the farm plants this year than last year?
Answers
Answer:
The farm planted 124,350 more cornstalks
Step-by-step explanation:
Here in this question, we want to know how much more corn stalks did a farm plant this year compared to last year.
Let’s picture it this way;
Possibly due to expansion purposes, the farm planted more cornstalks this year than last year. So to find the difference in the cornstalks planter between the two years, what needs to be done is simply to subtract the number of corn stalks planted last year from the number of corn stalks planted this year.
From the question, the number of cornstalks planted last year was 275,650 while the number of cornstalks planted this year was 400,000; So the difference between the two will be ;
400,000 - 275,650 = 124,350 cornstalks
Last one, use trigonometry to help you solve for y given that one side is 4 and there is an angle of 50 degrees.
Answers
Answer:
y = 6.22
You can solve this in two ways.
1.) Use SOH CAH TOA:
I typically start off by labeling the sides of the triangle with H (hypotenuse), O (opposite), and A (adjacent). Because I need to figure out what y is when given an angle and 4, I will use CAH, or cosine.
[tex] \cos(angle) = \frac{adjacent}{hypotenuse} [/tex]
[tex] \cos(50) = \frac{4}{y} [/tex]
[tex] \cos(50) \times y = 4[/tex]
[tex]y = \frac{4}{ \cos(50) } [/tex]
[tex]y = 6.22[/tex]
2.) Use Law of Sines:
Solve for the last angle inside the triangle first.
[tex]180 - (50 + 90) = 40[/tex]
Then use the angle you found (40°) in the equation.
[tex] \frac{4}{ \sin(40) } = \frac{y}{ \sin(90) } [/tex]
[tex] \frac{4}{ \sin(40) } \times \sin(90) = y[/tex]
[tex]y = 6.22[/tex]
Find the area of the triangle below. Be sure to include the correct unit in your answer. I need help please
Answers
hope this helps!
Solve for x: the quantity of x plus 20 over 2 = 3x
Answers
Answer:
x = 4
Step-by-step explanation:
For this problem, we simply need to convert the words into the left hand side of the equation and solve for x:
The quantity of implies a grouping
x plus 20 is the quantity
And we want the quantity over 2 all equal to 3x:
( x + 20 ) / 2 = 3x
( x + 20 ) = 6x
20 = 5x
4 = x
And now we can check to see if x is correct by plugging back into the equation:
( x + 20 ) / 2 = 3x
( (4) + 20 ) / 2 ?= 3(4)
( 24 ) / 2 ?= 12
12 == 12
Therefore, we have shown the value of x to be equal to 4.
Cheers.
Answer:
x+20/2=3x.
6x=x+20.
6x-x=20.
5x=20.
x=4.
8.45 +0.7 correct to 3 decimal places
Answers
Answer:
9.15
Step-by-step explanation:
Answer:
9.15 or 9.150
Step-by-step explanation:
The correct answer base on the numbers given is 9.15. But for you to get the 3 decimal answer of 9.150 you would add two 0's to the .7 making it .700.
8.45
+ .700
9.150
Mrs. Lawrie tried to write this number in standard form and made a mistake. What was Mrs. Lawrie's mistake? 600,000 + 8,000 + 500 + 70 + 3 = 68,573 what did she do wrong
Answers
Answer:
Mrs. Lawrie forgot the 600,000 in the equation. Answer = 608,573
Step-by-step explanation:
The equation was:
600,000 + 8,000 + 500 + 70 + 3 = 608,573
Mrs. Lawrie got 68,573, while the answer was 608,573
A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,
45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog
show?
Answers
Answer:
[tex] \boxed{ \bold{ \sf{Mean \: = 41.5}}}[/tex]
[tex] \boxed{ \bold{ \sf{Median = \: 41}}}[/tex]
Step-by-step explanation:
Given weights of the dogs :
38 , 40 , 42 , 46 , 45 , 39 , 42 , 40
Find the sum of the whole data:
sum of all items ( Σx ) = 38 + 40 + 42 + 46 + 45 + 39 + 42 + 40 = 332
Number of items ( n ) = 8
To find mean, divide the sum by the total number of data.
Finding the mean weights:
[tex] \boxed{ \sf{Mean = \: \frac{ Σx}{n}}} [/tex]
⇒[tex] \sf{ \frac{332}{8} }[/tex]
⇒[tex] \sf{41.5}[/tex]
Mean weights = 41.5
-----------------------------------------------------------------------
Finding the median
To find the median, arrange the given data in ascending order.
Given data : 38, 40 , 42 , 46 , 45 , 39 , 42 , 40
Arranging the data in ascending order :
38 , 39 , 40 , 40 , 42 , 42 , 45 , 46
Total number of observation ( n ) = 8
Finding the position of median
[tex] \boxed{ \sf{Position \: of \: median = ( \frac{n + 1}{2} ) ^{th} item}}[/tex]
⇒[tex] \sf{( \frac{8 + 1}{2} ) ^{th} item}[/tex]
⇒[tex] \sf{( \frac{9}{2} ) ^{th} item}[/tex]
⇒[tex] \sf{ {4.5}^{th} item}[/tex]
4.5 th item is the average of 4 th and 5th items .
Here, 4 th item = 40
5 th item = 42
Finding the median
[tex] \boxed{ \sf{Median = ( \frac{{4}^{th} \: item + {5}^{th} item}{2}) }}[/tex]
⇒[tex] \sf{ \frac{40 + 42}{2} }[/tex]
⇒[tex] \sf{ \frac{82}{2} }[/tex]
⇒[tex] \sf{41 }[/tex]
Hope I helped!
Best regards!!
Answer:
A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,
45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog
show?
Step-by-step explanation:
I need help! I can’t understand!
Answers
Hailey divided 92 ÷ 5. Her work is shown below.
92 divided by 5. 5 goes into 9 1 time. 9 minus 5 = 4. 5 goes into 42 8 times. 42 minus 40 = 2. The answer is 18 R 2. There are 5 groups of 1 ten plus 8 ones.
Which statements are true about Hailey’s work? Check all that apply.
Hailey found the correct quotient.
The “1” in the quotient represents the number of tens in each of the 5 groups.
Hailey placed the dividend and divisor in the wrong places in the problem.
The “R2” represents the number of ones in each of the 5 groups.
Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.
Answers
Answer:
The “1” in the quotient represents the number of tens in each of the 5 groups.
Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.
Step-by-step explanation:
Given:
92÷5
Hailey's workings:
92 divided by 5.
5 goes into 9 1 time.
9 minus 5 = 4.
5 goes into 42 8 times.
42 minus 40 = 2.
The answer is 18 R 2.
The true statements about Hailey's work are:
The “1” in the quotient represents the number of tens in each of the 5 groups.
Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.
It’s either D or E; please help
Thirty overweight males agree to participate in a study of the effectiveness of three weight-loss treatments: X, Y, and Z. The researcher calculates the
body fat composition of each subject. The response variable is the reduction in body fat after six weeks of treatment. Previous studies have shown the
effects of a diet may vary based on a subject's initial body fat composition. How should the subjects be blocked? Explain.
They should be blocked alphabetically so the subjects are as different as possible.
They should be blocked by age because weight loss is more difficult to achieve as you get older.
They should be blocked by height because weight loss is easier to achieve for taller people.
They should be blocked by body fat composition so the subjects are as similar as possible.
Blocking should not be used in this experiment.
Answers
Answer:
They should be blocked by body fat composition so the subjects are as similar as possible.
Step-by-step explanation:
It's D .
Blocking here means how should the subjects be arranged in terms of body fat or weight.
Option A is wrong because alphabetically controlling body fat would not get desired results.
Option B is wrong because different age groups would yield different results.
Option C is wrong also because weight loss is not dependent on taller people.
Option D is correct because controlling body fat would yield best possible results in ascending or descending order
Option E is incorrect because arranging data in ascending or descending order would simplify the researches experiments.
Solve the equation x/2-6=y for x
Answers
x/2-6=y
multiply both sides by 2
2(x/2-6)=2(y)
2x/2-12=2y
x-12=2y
add 12 to the both sides
x=2y+12
hope this helps <3
Answer:
x = 2y + 12Step-by-step explanation:
x/2 - 6 = y+6 +6
x/2 = y + 6×2 ×2
x = 2(y + 6) x = 2y + 12Pls halp due today >_<. Thank you
Answers
Answer:
-√(1/4) is smaller
Step-by-step explanation:
Step 1: Evaluate -√(1/4)
-√(1/4) = -(0.5) = -0.5
Step 2: Evaluate -1/5
-1/5 = -0.2
Step 3: Align
-0.5 < -0.2
Idk how to do this!!?!?
Answers
Answer:
∠ AED = 130°
Step-by-step explanation:
CD is a straight line, thus
∠ AEC + ∠ AED = 180° , that is
50° + ∠ AED = 180° ( subtract 50° from both sides )
∠ AED = 130°
Ben rents a car for one day. The charge is $20 plus the $0.12 per mile. He wants to spend exactly $80. How many miles can he drive? Write and solve an equation to find how many miles Ben can driv
Answers
Answer:
Ben can drive 500 miles for $ 80
Step-by-step explanation:
Let y be the cost of traveling and x be the number of miles . The charge is $20 plus the $0.12 per mile which means the cost $ 20 is constant and an additional cost of $ 0.12 is spent on every mile. Then according to the given conditions the equation will be
y = $20 + $ 0.12(x) where x is the number of miles
Now we can solve x for y= 80
$ 80= $20 + 0.12 (x)
$ 60 = 0.12x
x= 60/ 0.12= 500
Ben can drive 500 miles for $ 80
At a height of 3,281 feet, Angel Falls in Venezuela is the tallest waterfall in the world. Niagara Falls in the United States is only 190 feet tall. About how much taller is Angel Fall
Answers
Answer:
Angel Fall is 3091 ft taller.
Step-by-step explanation:
Height of Angel fall = 3281 ft
Height of Niagara falls in the United States = 190 ft
Angel fall is taller than Niagara Fall by
==> 3281 - 190 = 3091 ft
evaluate the expression m + p for m = 9 and p =7
Answers
Answer:
16
Step-by-step explanation:
Step 1: Write out expression
m + p
Step 2: Define variables
m = 9
p = 7
Step 3: Plug in variables
9 + 7
Step 4: Evaluate
16