Plot the axis of symmetry and the point where the maximum value occurs for this function: h(x) = -(x 2)2 8.
Answers
See attachment for the axis of symmetry and maximum point.
What is a function?A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depends on another quantity.To plot the axis of symmetry:
The given function is: [tex]h(x) = -(x+2)^{2} +8[/tex]This function is in the form: [tex]g(x) = a(x-h)^{2} +k[/tex]Where the axis of symmetry is given by, x = h.y comparison, we have -h=2.This implies h=-2Therefore the axis of symmetry is x = -2.
Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).
So, see attachment for the axis of symmetry and maximum point.
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Related Questions
A straight line passes through the points (1,3) and (2,2). What is the x-intercept of this line?
Answers
Answer:
x-int: (4, 0)
Step-by-step explanation:
First, we need to find the equation of the line.
The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Thus, we need to find the slope first by using the slope formula:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\[/tex] or change in y / change in x
So we have: [tex]\frac{3-2}{1-2}=\frac{1}{-1}=-1=m[/tex]
We must plug in the slope to find the y-intercept:
[tex]3=-1(1)+b\\3=-1+b\\4=b[/tex]
So the equation of the line is y = -x + 4
The x-intercept means that the y coordinate is 0 so we can use the equation:
[tex]0=-x+4\\-4=-x\\4=x[/tex]
A conical circus tent has a 20 ft central pole that supports it. the slant height of the tent is 26 ft long. explain how to find the angle the tent pole makes with the sides of the tent.
Answers
The angle the pole makes with the tent is 39.7°.
What is an angle?An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles formed by two rays are located in the plane containing the rays.Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.
Let θ represent the angle the pole makes with the tent.
Using trigonometric ratios:
cos(θ) = 20/26θ = 39.7°Therefore, the angle the pole makes with the tent is 39.7°.
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Help is needed!!!!! im bad at math :,)
Answers
Answer:
Step-by-step explanation:
A= π(5)²
= 3.14(5)²
= 3.14(25)
= 78.5 ans
-5/3×3/8+3/8+6/9+14/3
Answers
Answer:
Exact Form:
61/12
Decimal Form:
5.083 with 3 repeating
Mixed Number Form:
5 1/12
Step-by-Step Explanation:
-5/3×3/8 = -5/8
-5/8+3/8= -1/4
-1/4+6/9=5/12
5/12+14/3=61/12
The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
Answers
The y-intercept of the linear equation that models the data indicates that:
There was 1 inch of water on the tub when the water was turned on.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, when x changes by 1, y changes by 2, hence the slope is of 2. Hence, since when x = 1, y = 3, when x = 0, y = 3 - 2 = 1, which means that the y-intercept is of 1, and the correct interpretation is:
There was 1 inch of water on the tub when the water was turned on.
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Marcus needs to add a query for multiple tables in his database. he is using access 2016. which tab should he use to add the query? home external data create database tools
Answers
He is using Access 2016 Database tools are the tab that should he use for the add a query for multiple tables in his database.
What is In databases?Databases and a desk is hard and fast of records elements (values) the usage of a version of vertical columns (identifiable with the aid of using the name) and horizontal rows, the cell being the unit wherein a row and column intersect.
Tables are database gadgets that incorporate all of the records in a database. In tables, records is logically prepared in a row-and-column layout much like a spreadsheet.
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The above question is incomplete:
Marcus needs to add a query for multiple tables in his database. He is using Access 2016. Which tab should he use
to add the query?
Home
External data
Create
Database tools
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Lee wants to fence off a rectangular area that is 36 feet squared in size for a vegetable garden. He is considering three garden lengths of 6 ft, 9 ft, and 12 ft. He wants to determine which garden would require the least amount of fencing.
Determine the dimensions of the garden that would require the least amount of fencing.
Answers
tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.
The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.
The dimensions are the sides of a geometric shape.
The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.
If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:
The width of the garden with a length of 6 ft [tex]= \dfrac{36}{6} = 6\ ft[/tex]
The width of the garden with a length of 9 ft [tex]= \dfrac{36}{9} = 4\ ft[/tex]
The width of the garden with a length of 6 ft [tex]= \dfrac{36}{12} = 3\ ft[/tex]
The parameters are calculated as:
The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft
The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft
The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft
The least of the parameter is of the garden with dimensions (6 ft, 6 ft).
Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.
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The graph of the function C(x) = −0.74x2 + 22x + 75 is shown. The function models the production cost, C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands:
graph of a parabola opening down passing through points negative 4 and 57 hundredths comma zero, zero comma 62, 1 and 12 hundredths comma 75, 17 and 65 hundredths comma 167 and 55 hundredths, 34 and 18 hundredths comma 75, and 39 and 87 hundredths comma zero
If the company wants to keep its production costs under $175,000, then which constraint is reasonable for the model?
Answers
If the company wants to keep its production costs under $175,000, then 5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.
Which constraint is reasonable for the model:A constraint is a condition of an optimization problem that should be satisfied the condition.
From the we have the function,
⇒ C(x) = −0.74x² + 22x + 75
the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.
In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.
The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).
This means that above the point (5.6, 175) the graph has the value greater than 175000 and below the point the graph has the value below 175000.Similarly, below the point (24.13, 175) the graph has the value greater than $175,000 and above the point the graph has the value below $175,000.Therefore, x ≥ 5.6 and x ≤ 24.13
⇒ 5.6 ≤ x ≤ 24.13
Hence if the company wants to keep its production costs under $175,000, then 5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.
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Answer:
0 ≤ x < 5.6 and 24.13 < x ≤ 32.82
Step-by-step explanation:
A 3 metre long piece of ribbon is cut into
two pieces in the ratio 3:2.
How long is the shorter piece?
Answers
Step-by-step explanation:
3 meters = 300 cm
anyway, the ratio tells us that the whole ribbon can be seen as the combination of 3 + 2 = 5 equally long parts.
one such part is then
3 m / 5 = 0.6 m or 60 cm
the shorter piece is 2 of these parts long :
2 × 0.6 = 1.2 m or 120 cm
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
The equivalent expression of the radical expression ∛1080 is 6∛5
How to evaluate the radical expression?The radical expression is given as
∛1080
Express 1080 as 216 * 5
∛1080 = ∛(216 * 5)
Split the factors
∛1080 = ∛216 * ∛5
Evaluate the cube root of 216
∛1080 = 6 * ∛5
Evaluate the product
∛1080 = 6∛5
Hence, the equivalent expression of the radical expression ∛1080 is 6∛5
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Choose the correct discount or markup. if an item has a retail price = $995 and a discount of 15%, how much is the discount? it is $ .
Answers
Answer:
$149.25
Step-by-step explanation:
The discount is 15% of $995
Find the Discount[tex]15\%\times995[/tex]
Note that percentages can also be written as that number over 100.
[tex]\frac{15}{100}\times995[/tex]
Simplify the fraction
[tex]\frac{3}{20}\times995=\frac{2985}{20}=149.25[/tex]
Therefore the discount is $149.25.
Answer:
$149.25
Step-by-step explanation:
Geometry: fill in the blanks (ASAP! It’s urgent)
Answers
a. altitude = CE
b. bisector = BD
c. exterior angle = ∠ABE
d. median = CF
e. remote interior angles = ∠BCE and ∠CEB
GeometryFrom the question, we are to fill in the blanks
In ΔBCE, we have that ∠BCE is a right angle
Thus,
a. altitude = CE
Also, we have that
∠EBD ≅ ∠CBD
Thus, BD is a bisector
b. bisector = BD
The exterior angle of the triangle is ∠ABE
c. exterior angle = ∠ABE
From the given information,
BF ≅ EF
∴ F is the midpoint of BE
NOTE: Median is a line segment joining the vertex of one side of the triangle to the midpoint of its opposite side.
The median of the triangle is CF
d. median = CF
The remote interior angles of the triangle are ∠BCE and ∠CEB
e. remote interior angles = ∠BCE and ∠CEB
Hence,
a. altitude = CE
b. bisector = BD
c. exterior angle = ∠ABE
d. median = CF
e. remote interior angles = ∠BCE and ∠CEB
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Suppose you set up a function to show how many hot dogs you will purchase for a dinner when you have already bought two packages but must buy more, . What is the domain of this function?
Answers
The domain of the function is:
h > 0, only integers.
Then the correct option is the first one.
What is the domain of the given function?For a function f(x), we define the domain as the set of the possible values of x that we can use as inputs in the given function.
Here the function is:
f(h) = 6*h + 12
Where h is the number of packages that you buy.
Then h can be only integers larger than zero (as you can't buy half a package or something like that).
Then we conclude that the correct option is the first option.
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PLS HELP ME OUT ON THIS QUESTION. I’m trying to study!
Answers
Answer: 3
Step-by-step explanation:
We can solve this problem by recognizing that z is the geometric mean of 9 and 9+4. This property is outlined in the following formula:
[tex]\frac{hypotenuse}{leg}=\frac{leg}{part}[/tex]
where hypotenuse is the longest side of the triangle, leg is the side of the triangle we are calculating for, and part is the part of the hypotenuse on the side of the leg.
Here, the hypotenuse is 13, or 4 + 9. The leg is z, as it is the side of the triangle we are trying to find. Finally, the part is 9. It is the part of the hypotenuse that is on the side of the leg.
Let's plug in these values:
[tex]\frac{13}{z}=\frac{z}{9}\\117=z^2\\z=\sqrt{117}[/tex]
117 is the product of 9 and 13. Since 9 is a perfect square, we can take it out from the square root.
[tex]z=\sqrt{9*13}\\z=\sqrt{9}*\sqrt{13}\\z=3\sqrt{13}[/tex]
The "?" must be a 3.
Legs: The two ________ sides of a right triangle; the sides that meet at ___ degrees.
Answers
2. 90* degrees
I hope this helps you mate
Legs: The two smaller sides of a right triangle; the sides that meet at 90°.
In Pythagorean Theorem, all three sides of a right triangle have names and certain measurements that explain their names. The legs of a right triangle are the two smaller sides; they meet at a 90° angle and form a square to ensure the 90°. The bigger side of a right triangle is what we call the hypotenuse. The hypotenuse equals what the legs squared add up to. For example, we can take the three measurements:
12 cm, 5 cm, 13 cm
Since the two smaller numbers are 5 and 12, those would be our legs in the right triangle. Because 13 is the largest, it would be our hypotenuse. To identify the equivalence of the equation, we would square 5 and 12 to see if it equals up to 13 squared
5 squared is 25, and 12 squared is 144. Because 144 + 25 = 169, and 13 squared is 169, we know that the right triangle exists. If you need a further explanation, let me know and I will gladly assist you.
What is the value of x that makes l1||l2?
A. 14
B. 11.6
C. 10
D. 26.7
Answers
Answer:
10
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]4x=2x+20 \\ \\ 2x=20 \\ \\ x=10[/tex]
If a sample mean is 32, which of the following is most likely the range of
possible values that best describes an estimate for the population mean?
Answers
Answer:
(28.36)
Step-by-step explanation:
An astronaut who weighed 150 pounds on earth found that his weight on jupiter was 400 pounds. he captured an alien that weighed 120 pounds on jupiter. what is the alien's weight on earth? a. 45 pounds c. 500 pounds b. 30 pounds d. 320 pounds
Answers
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane. y > 2x + 4 x + y ≤ 6 I really need help can someone do it a put the prove that they got it right on edmetom the exact graph
Answers
The solution to the system of inequalities y > 2x + 4 and x + y ≤ 6 on the coordinate plane is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequalities is an expression that shows the non equal comparison of two or more numbers and variables.
The solution to the system of inequalities y > 2x + 4 and x + y ≤ 6 on the coordinate plane is the darker region shown in the graph.
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Determine what type of model best fits the given situation: water leaking from a local reservior at the rate of 500 gallons per hour.
Answers
The type of model that best fits the given situation is; A linear equation Model
What is the model of the equation?Right inside the local reservoir we will have an initial amount of water A.
Now, for every hour that passes by, the amount of water in the reservoir decreases by 500 gals.
Thus, after t hours, the amount of water in the reservoir is expressed as:
W = A - 500gal * t
This is clearly a linear equation model and so we can conclude that the model that fits best in the given situation is a linear model.
The domain of this model is restricted because we can't have a negative amount of water in the reservoir, and as such the maximum value of t accepted is: W = 0 = A - 500gal*t
t = A/500 hours
Therefore, the domain of this linear relation is: t ∈ {0h, A/500 }
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Which of the following graphs represents the inequality? 4 ⪰ b
Answers
The solution to the inequality 4 ≥ b is represented in the graph
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Inequality shows the non equal comparison between two or more numbers and variables.
Given the inequality:
4 ≥ b
Rearranging gives:
b ≤ 4
The solution to the inequality 4 ≥ b is represented in the graph
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AB=
BC=
Help me please!! Asap thanks so much
Answers
Answer:
5 and 5
Step-by-step explanation:
[tex]AB = BC =\sqrt{(4-0)^2+(3-0)^2}=5[/tex]
Answer:
AB = 5
BC = 5
Step-by-step explanation:
The formula to find the distance between two points is: [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
AB: 5
The two points are A(-4,0) and B(0,3).
In the formula, it will be expressed as:
[tex]\sqrt{(0-(-4))^2+(3-0)^2}[/tex]
--> [tex]\sqrt{4^2+3^2}[/tex] .
--> [tex]\sqrt{16+9}[/tex]
--> [tex]\sqrt{25}[/tex]
--> 5
BC: 5
The two points are: B(0,3) and C(4,0)
In the formula, it will be expressed as:
[tex]\sqrt{(4-0)^2+(0-3)^2}[/tex]
--> [tex]\sqrt{(4)^2 + (-3)^2}[/tex]
--> [tex]\sqrt{16 + 9}[/tex]
--> [tex]\sqrt{25}[/tex]
--> 5
So both AB and BC is 5.
PLLLLLEASE T_T PLLLEASE
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
let's solve ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{y - 6} + \cfrac{5}{y + 3} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4(y + 3) + 5(y - 6)}{(y - 6)(y + 3)} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4y + 12 + 5y - 30}{ {y}^{2} + 3y - 6y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{9y - 18}{ {y}^{2} - 3y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: 9y - 18 = 7y - 4[/tex]
[ denominator is same, so numerator must have same value to be equal ]
[tex]\qquad \sf \dashrightarrow \: 9y - 7y = - 4 + 18[/tex]
[tex]\qquad \sf \dashrightarrow \: 2y = 14[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 7[/tex]
Rose and Tyler divided their 1.5kg of pizza
dough in the ratio 2:3.
How much did Rose receive?
Answers
Answer:
0.6kg
Step-by-step explanation:
first roses share becomes 2:5
then you change the kilograms into grams for an easier working
then you multiply 2:5 by 1500g to get roses share
Find the area of a circle with a diameter of 16.
Either enter an exact answer in terms T or use 3.14 for TT and enter your answer as a decimal
Answers
Answer:
Step-by-step explanation:
Area of circle:
area = π · r · r
Radius= [tex]\frac{16}{2}[/tex]= 8
[tex]3.14\times { 8 }^{ 2 }[/tex] = 200.96 [tex]cm^2\\[/tex]
Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the bird reaches Bob, it turns around immediately and starts flying toward Alice at the same speed, turning around immediately when it reaches Alice, and repeating this procedure until Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the bird has flown, in feet?
Answers
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
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What steps do you use to solve y=x+12 and y=-x+17 an unknown number y is 12 more than an u known number x the number y is also x less than 17 the equations to find x and y are show
Answers
Answer:
x=2.5
Step-by-step explanation:
Solve for x in this systems of equations, we already have two values which equal y so half the work is finished for us.
Starting with the equation:
[tex]x+12=17-x[/tex]
Add x to both sides to remove the negative x on the right side of the equation:
[tex]2x+12=17[/tex]
Subtract 12 from both sides to remove the 12 on the left side of the equation:
[tex]2x=5[/tex]
Divide both sides by 2 to cancel out the x coefficient
[tex]x=2.5[/tex]
A central role of members at this time is to recognize and deal with the many forms of?
Answers
Answer:
Resistance
Step-by-step explanation:
Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b to complete the solutions.
Answers
The roots of the given polynomials exists
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex]
What is the formula of the quadratic equation?For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Therefore by using the formula we have
[tex]$x^{2}-16 x+54=0[/tex]
Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get
[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]
simplifying the equation, we get
[tex]$x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1}[/tex]
[tex]$x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1}$[/tex]
[tex]$x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]
Therefore, the roots of the given polynomials are
[tex]$x=8+\sqrt{10},[/tex] and [tex]$ x=8-\sqrt{10}[/tex].
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Emma learned in science class that fruit fly populations can increase by about 30% each day.
She found 7 fruit flies on a rotten banana today, and she is curious how many fruit flies could
be on the banana in a few days. You can use a function to approximate the number of fruit
flies on the banana after x days.
Write an equation for the function. If it is linear, write it in the form h(x) = mx + b. If it is
exponential, write it in the form h(x) = a(b)*.
h(x) =
DIO
89
Answers
Answer:
[tex]h(x)=7(1.3)^x[/tex]
Step-by-step explanation:
Since this is an exponential equation we will use
[tex]h(x)=a(b)^x[/tex]
[tex]a[/tex] Is your starting value, 7
[tex]b[/tex] Is your percentage of change, remember its not 0.3, as that would hint the population is decreasing by thirds exponentially, instead we will use 1.3 as our percent of change, as the 1 maintains the original value and the 0.3 adds 30%, now all we have to do is put it all together!
[tex]h(x)=7(1.3)^x[/tex]
