The zeros of the function h(r) = r² + 11r - 26 are r = -13, r = 2 and the vertex is (-11/2, -225/4).
What are the zeros and vertex of the function?Given the function in the question:
h(r) = r² + 11r - 26
To find the zeros of the function h(r) = r² + 11r - 26, we need to solve the equation h(r) = 0.
Using factoring:
r² + 11r - 26 = 0
Find two numbers whose sum is 11 and whose product is -26.
The numbers are -2 and 13.
Factor the equation:
(r - 2)(r + 13) = 0
Hence:
r - 2 = 0 and r + 13 = 0
Therefore, smaller r = -13, larger r = 2.
Next, we determine the vertex of the function:
Using the formula for the x-coordinate of the vertex, which is given -b/2a.
Here, the coefficient of r² is 1 (a = 1),
The coefficient of r is 11 (b = 11).
Substituting these values into the formula, we get:
r = -b/2a
= -11/( 2×1 )
= -11/2
The x-coordinate of the vertex is -11/2.
To find the y-coordinate, we can substitute r = -11/2 value back into the function:
h(r) = r² + 11r - 26
h(-11/2) = (-11/2)² + 11(-11/2) - 26
= 121/4 - 121/2 - 26
= 121/4 - 242/4 - 104/4
= (121 - 242 - 104)/4
= -225/4
Therefore, the vertex is (-11/2, -225/4).
Learn more about quadratic equations here:https://brainly.com/question/4038687
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What is the solution to -4|-2x + 6|= -24?
O x=0
O x=0 or x = -6
O x= 0 or x = 6
O no solution
Answer:
x=0 or x=6
Step-by-step explanation:
-4|-2x+6| = -24
|-2x+6| = 6
-2x+6 = 6
-2x = 0
x = 0
-2x+6 = -6
-2x = -12
x = 6
Therefore, x=0 or x=6
Pls look at the picture for question.
Answer:
-5, -2, 3, 4
They are in the correct order already :)
Step-by-step explanation:
They greater a negative number is the less it becomes and positive numbers are always greater than negative ones.
Good luck :)
Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 924 square milimetres and its perimeter is 122 milimetres.
Length =l
Height = h
Area function = l * h = 924
Perimeter function = 2i + 2h = 122
Divide by 2
I + h = 61.
Plug in I or h for the other variable
I * (61 - I) = 924
61i - i^2 = 924
Factor the function
(-I + 28)(I - 33) = 0
l = 33 as l cannot be negative
61 - 33 = 28
h = 28
Difference between h and l is 33-28=5
equations 50 - 3x = 110
Answer:
x = -20
Step-by-step explanation:
50 - 3x = 110
=> -3x = 110 - 50
=> -3x = 60
=> x = -20
Hoped this helped.
Step-by-step explanation:
50 - 3x = 110
3x = 110 - 50
3x = -60
x = -20
Hello hello there help
Answer:
Step-by-step explanation:
A translation 1 unit left and 2 units down :)
What is the height of a cylinder if the radius is 6 cm and volume is 904.78
Answer:
8 cm
Step-by-step explanation:
h = v/(pi r^2)
h = 904.78/ (3.1415 * 6^2)
What is (are) the x-value(s) that solve the system of equations y = x and y = 2x – 1?
Answer:
y=1 x=1
y = 2x – 1
replace y with x
x=2x-1
x-2x = - 1
-x = -1
x= 1
y=x =1
A sandwich costs $4.25 and a fruit drink costs $1.85. How much change will you get from a $10 bill?
Follow: Maddie Edits
Answer:
3.90
Step-by-step explanation:
4.25
+1.85=6.10
10-6.10=3.9
======================================================
Work Shown:
4.25+1.85 = 6.10
It costs $6.10 to get the sandwich and drink.
If the customer pays with a $10 bill, then they get 10.00 - 6.10 = 3.90 dollars in change.
One way to represent $3.90 is to have:
3 dollar bills = 3 dollars3 quarters = 3*25 = 75 cents1 dime = 10 cents1 nickel = 5 centsThe coins add up in value to 75+10+5 = 90 cents.
Or another option is to have 9 dimes and no other coins. Or perhaps you could have nothing but nickels and you'd need 18 nickels. There are a few ways to determine what coins to use.
find the missing side of each triangle
Answer:
where is the triangle
Step-by-step explanation:
I don't no where is the triangle
A group of 90 students plan to go camping over the weekend. At the last minute, some of the students decide not to go. The students who do go separated into four camps, where [tex]\frac{1}{7}[/tex] of the students stay at Hill Camp; [tex]\frac{1}{3}[/tex] of the students stay at Forest Camp; [tex]\frac{1}{4}[/tex] of the students stay at Field Camp; and the remaining students stay at Lake Camp. How many students were at Lake Camp?
Using fractions, it is found that of the students that went camping, [tex]\mathbf{\frac{23}{84}}[/tex] were at Lake Camp.
The students who went camping are divided according to the following fractions:
[tex]\frac{1}{7}[/tex] stayed at Hill Camp.[tex]\frac{1}{3}[/tex] stayed at Forest Camp.[tex]\frac{1}{4}[/tex] stayed at Field Camp.The remaining x stayed at Lake Camp.The sum of all these fractions is 100% = 1, hence:
[tex]\frac{1}{7} + \frac{1}{3} + \frac{1}{4} + x = 1[/tex]
[tex]\frac{12 + 28 + 21 + 84x}{84} = 1[/tex]
[tex]84x + 61 = 84[/tex]
[tex]84x = 23[/tex]
[tex]x = \frac{23}{84}[/tex]
Of the students that went camping, [tex]\mathbf{\frac{23}{84}}[/tex] were at Lake Camp.
A similar problem is given at https://brainly.com/question/24372153
Can someone help me with this
Hello! Please mark Brainliest for the explanation!
Answer:
Area: 10 inches
Step-by-step explanation:
As the paper itself states, the area of a triangle would be
1/2bh
Simply plug the given values in!
1/2(5)(4) =
1/2(20)=
10
Have a wonderful day!
Answer:
Area = 10 units
Skills needed: Triangle Theory, Substitution of Values
Step-by-step explanation:
1) We are given that the formula to finding the area of the triangle is [tex]\frac{1}{2}bh[/tex].... this essentially means that it is: [tex]\frac{1}{2}[/tex] times base (b) times height (h)
2) We can then use substitution to solve this. IN the diagram shown there, 4 is the base, and the height is 5 (since b = base, and h = height).
Area is [tex]\frac{1}{2} * b * h[/tex] in general (the * means multiplication)
Substitute in the values and it is: [tex]\frac{1}{2} * 4 * 5[/tex]
--> [tex]4*5=20[/tex]
--> [tex]\frac{1}{2} * 4*5 = \frac{1}{2} * 20 = 10[/tex]
1/2 of 20 is ten, so that is how we arrive at that final answer.
Hope you understand, have a great day :)
Emilio has 8 large bottles of soda and 12 large jugs of water. Emilio wants to set up identical tables and have no drinks left over. What is the greatest number of tables that he can set up?
Answer:
4
Step-by-step explanation:
Think about the ratio between the current number of large bottles of soda(8) and the current number of jugs of water (12)
By finding the GCF (Greatest Common Factor) of the two numbers, we can conclude that if both numbers were to be divided by the GCF, 4, we would get a 2:3 ratio.
For every 2 bottles of soda, 3 jugs of water will be placed. Keep doing this until we run out of both sources of liquid, in this case, 4 tables where we would use all the bottles of soda and the jugs of water.
Find the value of x in the figure below
Answer:
37
Step-by-step explanation:
Both the x and the 53 add up to 90 so you subtract 53 from 90 and you get 37
Jackie runs and dances for 75 minutes every day.
She dances 25 minutes more than she runs.
What is the greatest amount of time she could spend dancing every day,
given she will take a run.
Answer:
I think it is 50 because 75-25=50
look at this digram a. what fraction is shaded b. what percentage is shaded
Plz answer ASAP
I need help
Answer:
a:6÷9
b:0.666% are the answers
help i need help look at question
Answer:
A
Step-by-step explanation:
because 12 is the smallest number/angle
A fabric store sells close-out fabrics for $2.14 a yard. A customer buys 8 yards of fabric. How much does the customer pay for the fabric? Show your work.
Answer:
$17.12
Step-by-step explanation:
2.14 · 8 = 17.12
a painter has 3 gallons of paint and each will cover 420 ft of wall space. if the total area was 1800 ft what percent of the job could the painter finish with the paint he already has?
Answer:
23.33333%
Step-by-step explanation:
Which item produces the magnetic field in the electromagnet?
A-paperclips
B- a switch
C-paint brushes
D- a magnet
Answer:
Its ethier a switch or magnet
Karen stacks a set of cans as shown. The top can has a diameter of 2 inches, the middle can has a diameter of 5 inches, and the bottom can has a diameter of 6 inches.
Answer:
Unknown
Step-by-step explanation:
What is the question? You have the information listed but you forgot to ask the question.
There is a line that includes the point (1,6) and has a slope of 4. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=4x+2
Step-by-step explanation:
So we start with the slope, which is bad.
But I have an idea
lets write it as
y=4x+? and since x=1 and y=6
6=4+?
Therefore, the y, intercept must be two
Answer:
y=4x+2
Step-by-step explanation:
y-y1=m(x-x1)
y-6=4(x-1)
y=4x-4+6
y=4x+2
Find the sum of the first 11 terms of the geometric sequence shown below.
2, 6, 18, 54, ...
Answer:
177146
Step-by-step explanation:
2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098
What are the consecutive numbers that follow the number 686
Answer:
687, 688, 689, 690, ...
Step-by-step explanation:
Each in a list of consecutive integers is 1 more than the previous number. Consecutive integers following 686 are ...
687, 688, 689, 690, ...
please help ill mark brainliest
Answer:
x=28
Step-by-step explanation:
Pls help I’ll brainlest and add extra points
Answer:
slope is -3
y intercept is 6
Step-by-step explanation:
The y intercept is where it crosses the y axis
It crosses the y axis at 6
We need two points to find the slope (0,6) and (2,0)
m = ( y2-y1)/(x2-x1)
= (0-6)/(2-0)
= -6/2
= -3
The slope is -3
Plssss help!!! Asap tyyy.
Answer:
1):Reaction
2):Action
3):Thought
4): Dialogue
Step-by-step explanation:
Answer:
Mrs. Boggs's generously inspired us to study harder - Reaction Mrs. Boggs agreed to tutor us all before the test - Action I believe that Mrs. Boggs is the most caring teacher I know - Thought "Of course I will tutor you before the test" she said - DialogueStep-by-step explanation:
Hoped this helped.
If you have a book to read that is 20 pages, and you have read 15% of the book, how many pages as you read?
Answer:
3
Step-by-step explanation:
20*.15=3
What is the x-value of the vertex of f(x) = -x2 + 9x - 11 ?
Answer:
I believe it would be 9/2 !
Step-by-step explanation:
A $300 bike is marked down to $175. Find the percent markdown to the nearest whole percent.
Answer:
58
Step-by-step explanation:
58 because you divide 200 by 100 then getting that answer (3) then divide 175 by 3 which equals one percent and you get 58.333 you round it to the nearest whole and u get 58
Subtract 95 800 by 28 766 ?
please please please help!!
Answer: 95,800 - 28,766 = 67,034
Step-by-step explanation: hope this helps :)