Answers
If you are in calculus, then you would apply the derivative to get
h(x) = x^2 - 2x + 3
h ' (x) = 2x - 2
The gradient, or slope of the tangent line, is negative when the derivative is negative.
So we need to solve h ' (x) < 0.
h ' (x) < 0
2x-2 < 0
2x < 2
x < 2/2
x < 1
Any x value smaller than x = 1 will lead to a negative gradient.
-----------------------------------
If you are not in calculus, then you can determine the vertex of the function
Note that y = x^2 - 2x + 3 is in the form y = ax^2 + bx + c with
a = 1
b = -2
c = 3
The x coordinate of the vertex is
h = -b/(2a)
h = -(-2)/(2*1)
h = 1
The x coordinate of the vertex is x = 1. Anything to the left of this will represent a negative gradient. This is because the given parabola opens upward (note how a = 1 is positive).
The graph goes downhill on the interval [tex]-\infty < x < 1[/tex] and it goes uphill on the interval [tex]1 < x < \infty[/tex] as shown below.
Related Questions
State the slope (m) and the y-intercept (b) for the problem below.
m
4. y=-2x + 4
b =
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Answer:
The slope is -2. The y intercept is 4.
Step-by-step explanation:
My math problem went from 10a+15=65 to 10a+15-15=65-15. Explain what happened in this step.
Answers
Answer:
You are subtracting 15 from both side to isolate 10 a it would look like this afterwards:
10a=65-15
And you continue to solve
Step-by-step explanation:
Help me plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
u = 12
Step-by-step explanation:
.................
please help me i do not want to fail my class
Answers
Answer:
sdsdsdsdsdsd
Step-sdsdsdsdsd-step explanation:
Answer:
I think its 11
Step-by-step explanation:
NEED HELP NOW Tell whether the sequence is arithmetic. If it is, identify the common difference.
2.9, 4.1, 5.3, 6.5, …
Answers
Here you go! hope this is what you were looking for!
Eight is greater than or equal to the sum of a number and 3.
Answers
Answer:
8 >_ 3 +x
Step-by-step explanation:
X = 5 and any numbers below 5
Answer:
8 ( > or equal to) n + 3
Step-by-step explanation:
I hope this helps :)
Can someone please answer this for me please??
I honestly do not understand, can someone please help me understand?
Answers
Answer:
15/16
Step-by-step explanation:
Using the order of operations, we need to multiply in the parentheses first...
3/5*25/24=75/120, which simplifies to 5/8.
Next, we need to divide 5/8 by 2/3. To divide, we can actually multiply by the reciprocal, which is flipping the fraction that you are dividing by. In this case, we need to multiply 5/8 by the reciprocal of 2/3. The reciprocal of 2/3 is 3/2, so we need to multiply 5/8 by 3/2.
5/8*3/2=15/16
This is the final answer!
I hope this helped you out!! Have an amazing day φ(゜▽゜*)♪
Originally, Juan borrowed $10, but his mother loaned him $3 more, so he borrowed a total of $13. He sells $25 worth of lemonade in his first week. After Juan pays his mother back the $13 he borrowed, his profit is $12.
If Juan’s mother forgave (or took away) his debt of –13, what equation shows the amount of money Juan will have?
Answers
Answer:
Step-by-step explanation:
10+3+25=
13+25=
38
Answer:
Its c if you have the drop down menu
Step-by-step explanation:
Originally, Juan borrowed $10, but his mother loaned him $3 more, so he borrowed a total of $13. He sells $25 worth of lemonade in his first week. After Juan pays his mother back the $13 he borrowed, his profit is $12.
12(-13)=25 So its c
**IM BEING TIMED XD PLEASE ANSWER**
-Evaluate Function Expressions-
3.f(-4)-3.g(-2)=
Answers
Answer:
3•f(-4) - 3•g(-2) = -27Step-by-step explanation:
When the graph is evaluated, you will find that
f(-4) = -3, and g(-2) = 6.
Therefore:
3•f(-4) - 3•g(-2) = 3•-3 - 3•6 = -9 - 18 = -27
-2 ≤ x + 3 ≤ 7
Solve !!
Answers
Answer:
Step-by-step explanation:
-2 <= x + 3
x >= -5
x+3 <= 7
x <= 4
Answer:
x ∈[-5,4]
Step-by-step explanation:
Hi. I need help with these questions.
See age for question.
Answer 11,12
Answers
Answer:
11) k = -112) (i) 4, (ii) 6.5Step-by-step explanation:
11. ......................................................
Given equationx² + (k - 1)x - k = 0The roots are equalTo findThe value of kSolutionWhen the roots are equal, the discriminant equals zero
D = 0b² - 4ac = 0Substituting the values and solving for k:
(k - 1)² - 4*1*(-k) = 0k² - 2k + 1 - 4k = 0k² + 2k + 1 = 0(k + 1)² = 0k + 1 = 0k = -112. ......................................................
Given equation2x² - 6x + 1 = 0The roots are α and βTo findThe values of
(i) 2αβ² + 2α²β + 2αβ(ii) α² - 3αβ + β²SolutionThe sum and the product of the roots is:
α + β = - b/a = - ( - 6)/2 = 3αβ = c/a = 1/2(i)
2αβ² + 2α²β + 2αβ =2αβ ( α + β + 1) = 2(1/2)(3 + 1) =1(4) =4(ii)
α² - 3αβ + β² =(α + β)² - 5αβ = 3² - 5(1/2) =9 - 5/2 =6.5please help brainliset, thanks, and five star
Answers
Answer:
15x+30y-220
Step-by-step explanation:
[tex]30(\frac{1}{2}x-2)+40(\frac{3}{4} x-4 )\\\\(15x-60)+(30x-160)\\\\15x+30y-220[/tex]
Please can u help me
Answers
Answer: p=8
Step-by-step explanation:
FH ≅ FJ --> diagonals bisect in parallelograms--> rectangle is a form of a parallelogram 4p-22 = p+2 --> Transitivity p = 8 --> Algebraa cheetah ran 120 meters in 4 seconds how many meters did it run per second?
Answers
Answer:
30 meters/second
Step-by-step explanation:
120/4 = 30
help this is for my friend
Answers
Answer: stop climbing the volcano im jk any way .7-10sec
What is the slope of the line?
2x-5y=9
Answers
Answer:
m(slope)=2/5
Step-by-step explanation:
y2-y1/x2-x1
HELP! !A small pool is being drained. There are 1,320 gallons of water remaining in the pool after 2 minutes and 1,040 gallons after 9 minutes.
Answers
Answer:
35
Step-by-step explanation:
Translate each verbal phrase into an algebraic expression or equation.
1. Seven less than a number
2. The total of 5 and c
3. 7 less than m
4. The sum of a number and 16
5. the score increased by 8 points
6. The quotient of w and 10
7. 17 more than some number
8. $12 less than the original price
Answers
2. 5+c
Hi. I need help with these
See image for question
Answer no 8 ,9 and 10
Answers
Answer:
8) 4 + 2q²/p² - 4r/p + r²/p²9) (3/4, -9/4)10) (3/8, 41/16)Step-by-step explanation:
8. ============
Given
α and β are roots of px² + qx + r = 0The sum of the roots is α + β = -q/p, the product of then roots αβ = r/p
(2 + α²)(2 + β²) = 4 + 2(α² + β²) + (αβ)² =4 + 2((α + β)² -2αβ) + (αβ)² =4 + 2((-q/p)² - 2r/p) + (r/p)² =4 + 2q²/p² - 4r/p + r²/p²------------------------------
9. ============
Given function
y = 2x² - 3x - 1The minimum point is reached at vertex
The vertex is:
x = -b/2ax = -(-3)/2*2 = 3/4The corresponding y-coordinate is:
y = 2(3/4)² - 3(3/4) - 1 = 9/8 - 9/4 - 1 = 1/8(9 - 18 - 9) = - 18/8 = - 9/4So the point is:
(3/4, -9/4)---------------
10. ============
Given function
y = 2 - 3x - 4x²The maximum is reached at vertex
The vertex is:
x = -b/2ax = -(-3)/2(-4) = -3/8The corresponding y-coordinate is:
y = 2 - 3(-3/8) -4(-3/8)² = 2 + 9/8 - 9/16 = 1/16(32 + 18 - 9) = 41/16So the maximum point is:
(3/8, 41/16)area of a trapezium
Answers
Answer:
The area of a trapezium is computed with the following formula: Area = 1 2 × Sum of parallel sides × Distance between them.
Step-by-step explanation:
Hope it help! :)
Work out the value of the expression 2(a +5b) when a=4 and b=3
Answers
Answer:
38
Step-by-step explanation:
2(4+5(3))
2(4+15)
2(19)
38
Answer:
38
Step-by-step explanation:
2(4+5*3)
2(4+15)
2(19)
38
it's it's urgent can someone please help me
Answers
Answer:
1. D
2. F
3. F
4. C
5. F
6. B
Step-by-step explanation:
1. To find the slope, take two points from the table (in this case I'll use points (-3, 7) and (-1, 4)) and put them into the expression: [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{4-7}{-1-(-3)}[/tex]
Solve:
4 - 7 = -3
-1 - (-3) = -1 + 3 = 2
The slope is -[tex]\frac{3}{2}[/tex]
2. I used the same process I used in number 1 using the points (-2, 4) and
(1, -1)
3. The slope of both equations represents how much each t-shirt was sold for. This means that whichever equation has a higher slope made greater profits. The slope of store B is 3.75 - we know this because the equation given is in y = mx, where m is the slope. To find the slope of store A, use the method I used in question 1 using two points from the graph ( I used points (0, 0) and (10, 40)). The slope of store A is 4, which is greater than 3.75, meaning that Store A made a greater profit per t-shirt.
4. To find the slope and y-intercept of this equation, let's convert the equation to slope-intercept form, y= mx + b, where m is the slope and b is the y-intercept. To do this we have to isolate the y:
y + 9x = -6
Subtract 9x from both sides to isolate the y:
y + 9x - 9x = -6 - 9x
y = -6 - 9x
This equation can also be written as: y = -9x - 6
Now we can see that the slope is -9 and the y-intercept is -6.
5. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Slope is also known as rise over run. Looking the graph, for every 2 points it decreases on the y-axis, it increases by 1 on the x-axis. This can be written as -2/1, or simply -2. To find the y-intercept, find the point on the graph where the line intersects the y-axis. In this case, it's at y = -1. Now that we know the values of our slope and y-intercept, we can put them into the equation:
y = mx + b
y = -2x - 1
6. The y-intercept represents the amount Alice will have to pay for the game center before she pays for any guests. This value is $100.
10,24,26 determine whether the triangle is obtuse, right, acute, or not a triangle
Answers
Answer:
right triangle
Step-by-step explanation:
10 + 24 = 34
34 > 26
Therefore, there is a triangle.
Now we use the Pythagorean theorem.
10^2 + 24^2 = 100 + 576 = 676
26^2 = 676
Since 10^2 + 24^2 = 26^2, the triangle is a right triangle.
The average weight of adult females is 166.3 pounds, with a standard deviation of 14 pounds and a normal distribution. Karys weighs 163.2 pounds. What is the standardized score for Karys's weight? (5 points)
-0.22
.22
-0.78
0.78
Unable to determine the standardized score
Answers
Answer:
Standardized score is -0.22
Step-by-step explanation:
Here, we want to calculate z-score
z-score = (x - mean)/SD
z-score = (163.2-166.3)/14 = -0.22
Answer? I’m confused
Answers
5m + 10
You solve this my using distributive property
Step 1:
Break it apart
5(m) + 5(2)
Step 2:
Use order of operations to solve the rest
5m + 10
How many solutions does the following equation have?
9x - 4 = - 3x + 5 + 12x
O One Solution
O No Solution
O Infinitely Many Solutions
Answers
Answer:
There will be No solution for the equation [tex]9x - 4 = - 3x + 5 + 12x[/tex]. Option B is correct.
Step-by-step explanation:
We need to determine how many solutions the equation [tex]9x - 4 = - 3x + 5 + 12x[/tex] have.
Solving the equation and finding the solutions
[tex]9x - 4 = - 3x + 5 + 12x[/tex]
Combining like terms, Moving 3x and 12x to left side of equality and changing their signs and moving 4 on right side of equation and changing sign.
[tex]9x +3x-12x = 5 + 4[/tex]
Simplifying
[tex]12x-12x = 9\\0=9[/tex]
Solving the equation we get 0=9 which is false. So, there will be No solution for the equation [tex]9x - 4 = - 3x + 5 + 12x[/tex]. Option B is correct.
what's the answer to this question= 4(3x + 2) + 2(x + 3)
A. 12x + 16
B. 24x + 48
C. 10x + 2
D. 14x2 + 48
E. 14x + 14
F. 9x2 + 5
Answers
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{14x + 14}}}}[/tex]
Option E is the best choice.
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☯ Question : Simplify
4 ( 3x + 2 ) + 2 ( x + 3 )
☯ Available options :
☐ 12x + 16
☐ 24x + 48
☐ 10x + 2
☐ 14x + 48
☑ 14x + 14
☐ 9x + 5
✎ Step - by - step explanation :
[tex] \sf{4(3x + 2) + 2(x + 3)}[/tex]Distribute 4 through the parentheses
[tex] \dashrightarrow{ \sf{12x + 8 + 2(x + 3)}}[/tex]
Distribute 2 through the parentheses
[tex] \dashrightarrow{ \sf{12x + 8 + 2x + 6}}[/tex]
Combine like terms. Only coefficients of like terms can be added or subtracted
[tex] \dashrightarrow{ \sf{12x + 2x + 8 + 6}}[/tex]
[tex] \dashrightarrow{ \sf{14x + 8 + 6}}[/tex]
Add the numbers : 8 and 6
[tex] \dashrightarrow{ \boxed{ \sf{14x + 14}}}[/tex]
Hope I helped!
Have a wonderful time ツ
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Three consecutive integers have a sum of 72. Find the integers.
Answers
Answer:The three consecutive integers are 23, 24 and 25
Step-by-step explanation:
23+24+25=72
(For 5th graders)
150 divided by 10
Answers
Answer:
150 divided by 10 is 15
Hope This Helps!
Nemos aquarium is filled with 2400 cm of water the base of the aquarium is 20 cm long and 12 cm wide what is the height of the water in Nemo’s aquarium
Answers
The answer to this question is 10 cm
In this question, you asked the height and given the volume of water(2400cm3), aquarium length(20cm), and aquarium width(12cm).
Then you need to divide the volume with the length and width. The equation would be:
Aquarium height= volume / length / width
Aquarium height= 2400 cm3 / 20cm / 12 cm = 10cm.