Answer:
1
Step-by-step explanation:
It's just 1
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h(x) = -(x - 5)(x – 13)
1) What are the zeros of the function?
Write the smaller x first, and the larger x second.
smaller =
larger x =
2) What is the vertex of the parabola?
Let h(x) = 0.
Set each factor to 0 and solve for x.
-(x - 5) = 0
Disregard the negative sign in front of the parentheses.
x - 5 = 0
x = 5 is a zero.
x - 13 = 0
x = 13 is another zero.
The smaller zero is 5.
The larger zero is 13.
Both numbers make the quadratic function become zero.
Use the FOIL METHOD to express h(x) in standard form.
h(x) = -(x - 5)*x - 13)
After using FOIL, we get -x^2 + 18x - 65.
The square x term has a -1 in front. This number is the value of a in the formula below. The coefficient of x is 18. This is our b value.
x = -b/2a
x = -(18)/2(-1)
x = 18/2
x = 9
This number 9 just found is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, replace every x you see in the quadratic equation above with 9 and simplify.
h(9) = -(9)^2 + 18(9) - 65
h(9) = 16
The vertex is located at the point (9, 16).
The smaller zero is 5 and larger zero is 13. The vertex is located at the point (9, 16).
How to find the vertex of the parabola?Let h(x) = 0.
A. Now Set each factor to 0 and solve for x.
-(x - 5) = 0
Disregard the negative sign;
x - 5 = 0
x = 5 is a zero.
x - 13 = 0
x = 13 is another zero.
The smaller zero is 5 and larger zero is 13.
B. Both numbers make the quadratic function become zero.
So, Use the FOIL METHOD to express h(x) in standard form.
h(x) = -(x - 5)(x - 13)
we get -x^2 + 18x - 65.
x = -b/2a
x = -(18)/2(-1)
x = 18/2
x = 9
Hence, This number 9 just found is the x-coordinate of the vertex.
In order to find the y-coordinate of the vertex, replace every x you see in the quadratic equation above with 9 and simplify;
h(9) = -(9)^2 + 18(9) - 65
h(9) = 16
Hence, The vertex is located at the point (9, 16).
Learn more about the vertex form here:
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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.
Answer:
35
Step-by-step explanation:
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
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
How many solutions does the following equation have?
9x - 4 = - 3x + 5 + 12x
O One Solution
O No Solution
O Infinitely Many Solutions
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.
area of a trapezium
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! :)
Please can u help me
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 --> Algebraplease help brainliset, thanks, and five star
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]
Can someone please answer this for me please??
I honestly do not understand, can someone please help me understand?
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(゜▽゜*)♪
Solve for x: −2x + 5 < 7
Inequality Form = X > -1
Interval Notation = (-1,∞)
Answer:
x>-1
Step-by-step explanation:
move the 5 to the other side by subtracting both sides by 5:
-2x+5-5<7-5
=
-2x<2
Divide by negative 2
(Reminder when you divide or multiply anything by negative you need to switch the signs to the other side)
x>-1
Hope this helps!
Answer? I’m confused
-2 ≤ x + 3 ≤ 7
Solve !!
Answer:
Step-by-step explanation:
-2 <= x + 3
x >= -5
x+3 <= 7
x <= 4
Answer:
x ∈[-5,4]
Step-by-step explanation:
What is the slope of the line?
2x-5y=9
Answer:
m(slope)=2/5
Step-by-step explanation:
y2-y1/x2-x1
**IM BEING TIMED XD PLEASE ANSWER**
-Evaluate Function Expressions-
3.f(-4)-3.g(-2)=
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
a cheetah ran 120 meters in 4 seconds how many meters did it run per second?
Answer:
30 meters/second
Step-by-step explanation:
120/4 = 30
State the slope (m) and the y-intercept (b) for the problem below.
m
4. y=-2x + 4
b =
Answer:
The slope is -2. The y intercept is 4.
Step-by-step explanation:
2x×5x+83=3what is x
Answer:
x= 2i√2
Step-by-step explanation:
Combine terms 10x^2+83=3
Subtract 83 from both sides 10x^2=-80
Divide 10 from both sides x^2=-8
Take square root of each side x= square root of -8
Since there is no perfect square we do prime factorization of the 8 we get 4 and 2.
4 is a perfect square so it stays outside (but remember that what stays outside has the be result of the square so its a 2) and two stays inside the square
2√2
Remember that the response was negative so we have to add i.
Therefore, x= 2i√2
Find the angle measure.
Angle E
Triangle ABC is an isosceles triangle. This means that base angles A and C are the same measure.
Triangle CDE is also isosceles. This means that angles C and D are the same measure.
The hatch marks shown in both triangles clearly indicate this fact of geometry.
So, if angle C is 40 degrees, C and D must be 70 degrees each because the sum of the angles in a triangle is 180 degrees.
Angle C = 70 degrees.
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?
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
NEED HELP NOW Tell whether the sequence is arithmetic. If it is, identify the common difference.
2.9, 4.1, 5.3, 6.5, …
Here you go! hope this is what you were looking for!
My math problem went from 10a+15=65 to 10a+15-15=65-15. Explain what happened in this step.
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:
13) maths equations answer??.. .
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
[tex] \frac{3x}{x - 2} = 7 \\ [/tex]
Multiply sides by ( x - 2 )
[tex](x - 2) \times \frac{3x}{x - 2} = (x - 2) \times 7 \\ [/tex]
Simplification
[tex]3x = 7x - 14[/tex]
Subtract sides 7x
[tex] - 7x + 3x = - 7x + 7x - 14[/tex]
Simplification
[tex] - 4x = - 14[/tex]
Negatives simpliflies
[tex]4x = 14[/tex]
Divide sides by 4
[tex] \frac{4x}{4} = \frac{14}{4} \\ [/tex]
[tex]x = \frac{7}{2} \\ [/tex]
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Answer:
x = [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3x}{x-2}[/tex] = 7 ( multiply both sides by x - 2 )
3x = 7(x - 2) ← distribute
3x = 7x - 14 ( subtract 3x from both sides )
0 = 4x - 14 ( add 14 to both sides )
14 = 4x ( divide both sides by 4 )
[tex]\frac{14}{4}[/tex] = x , that is
x = [tex]\frac{7}{2}[/tex]
(For 5th graders)
150 divided by 10
Answer:
150 divided by 10 is 15
Hope This Helps!
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
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
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.
Write an integer for the situation: 1,464 feet above sea level
Answer:
The answer is 1,464.
The answer will be -1,464, when 1464 is "below sea level".
I hope it help you...
Hi. I need help with these questions.
See age for question.
Answer 11,12
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 =6.5Eight is greater than or equal to the sum of a number and 3.
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 :)
Help me plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
u = 12
Step-by-step explanation:
.................
Three consecutive integers have a sum of 72. Find the integers.
Answer:The three consecutive integers are 23, 24 and 25
Step-by-step explanation:
23+24+25=72
it's it's urgent can someone please help me
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.