The general form of a quadratic equation is given by the expression:
[tex]ax^2+bx+c=0[/tex]A quadratic equation having a maximum value or point is one that has its value of a to be lesser than zero
(a < 0). Such a graph opens downwards
Therefore, any quadratic equation that has the a-value to be lesser than zero has a maximum point
Mathematically expressed as:
[tex]\begin{gathered} y=-x^2 \\ \Rightarrow a=-1 \end{gathered}[/tex]what is the range of the function g(x) = -(x+ 2)^2+ 4
Operations of rational algebraic expression 3/4.9/2
The solution for the algebraic expression is [tex]3\frac{3}{8}[/tex].
The problem we are dealing with is related to the PEMDAS order of operations, where P stand for parentheses, E stands for Exponents, M stands for Multiplying, D stands for Divide, A stands for Add, and last S stands for Subtract. It's the order we follow to solve a rational algebraic expression.
For the given expression 3/4.9/2, we start solving it from the direction left to right, according to PEMDAS we multiply first followed by dividing
=3x9/4 x2
=27/4/2
=27/8
simplifying the improper fraction to a mixed number
= [tex]3\frac{3}{8}[/tex]
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May you help me the drop down options are down below
Hello! First, let's analyze the information contained in the exercise:
[tex]\frac{p}{q}>\frac{r}{s}>\frac{t}{u}[/tex]So, according to this, we also can say that:
[tex]\frac{p}{q}>\frac{t}{u}[/tex]Now, let's draw it in a line for better understanding:
Now, let's analyze the line and select the correspondent answer:
On a number line, p/q is to the right of r/s.
Use Heron's formula to find the area of the triangle. Round to the nearest square foot.Side a=7 feetSide b=7 feetSide c=5 feet
The area is approximately 16 square feet.
Step - by -Step Explanation
What to find? Area of the triangle using Heron's formula.
Given:
• Side a=7 feet
,• Side b=7 feet
,• Side c=5 feet
The Heron's formula is given below:
[tex]\text{Area}=\sqrt[]{p(p-a)(p-b)(p-c)}[/tex]Where P is the perimeter of the triangle.
a, b and c are the sides of the triangle.
We need to first find the half perimeter of the triangle.
P = a+b+c /2
= 7+7+5 /2=19/2 = 9.5
Substitute the value of p, a, b and c into the formula and simplify.
[tex]\text{Area}=\sqrt[]{9.5(9.5-7)(9.5-7)(9.5-5)}[/tex][tex]=\sqrt[]{9.5\times2.5\times2.5\times4.5}[/tex][tex]=\sqrt[]{267.1875}[/tex][tex]\approx16\text{ square f}eet[/tex]Hence, the area of the triangle is approximately 16 square feet.
Evaluate (10 – 41) ÷ (5 + 1).
Step-by-step explanation:
option B is correct answer
Hello I need help with a question if you are able to assist.
We are given an equation that represents the path of the longest shot put by the women's track team as:
[tex]h(x)=-0.017x^2\text{ + 1.08x + 5.8}[/tex]Where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground.
Solution:
(a) The vertex of the model:
Method 1: We can plot the model on a graph and identify the vertex from the graph. The vertex is the lowest/highest point on the curve.
The graph is shown below:
From the graph, we can see that the vertex of the model is : (31.765, 22.953)
Method 2: The vertex of the model can also be calculated using the formula:
First, we find the x-coordinate using the formula:
[tex]x\text{ = -}\frac{b}{2a}[/tex]Substituting, we have:
[tex]\begin{gathered} x\text{ = -}\frac{1.08}{2\text{ }\times\text{ -0.017}} \\ x\text{ = 31.765} \end{gathered}[/tex]The y-coordinate of the vertex can be obtained by substituting the x-coordinate into the model. So, we have the y-coordinate to be:
[tex]\begin{gathered} y\text{ = h(31.765)} \\ y=-0.017(31.765)^2\text{ + 1.08(31.765) + 5.8} \\ y\text{ = 22.953} \end{gathered}[/tex]Hence, the vertex is : (31.765, 22.953)
(b) The maximum height
The horizontal distance of the maximum height of the shot put from the starting point is :
From the plot, the starting point is -4.98
[tex]\begin{gathered} \text{Horizontal distance = 31.765 + 4.98} \\ =\text{ 36.745 f}eet \end{gathered}[/tex]The maximum height of the shot put is 22.953 feet, 36.745 feet away from the starting point.
(c) The vertical intercept
The vertical intercept is the point where the curve cuts the y-axis.
From the graph, the point is (0, 5.8).
At this point where the horizontal distance is 4.98 feet away from the starting point, the shot put is 5.8 feet above the ground.
(d) The distance from the starting point to when the shot-put stikes the ground is:
From the plot, the intercepts on the x-axis are (-4.98, 0) and (68.509, 0).
Hence, the distance is:
[tex]\begin{gathered} =\text{ 68.509 + 4.98} \\ =\text{ 73.489} \\ \cong\text{ 73.49 f}eet\text{ (2.d.p)} \end{gathered}[/tex]Question Below: It's about functions
Based on the calculations, the value of function g(f(x)) is equal to: g(f(x)) = x + 10.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable (x-value) to an output variable (y-value).
In this exercise, you're required to determine the value of g(f(x)) and we are given the following functions:
f(x) = (x + 3)² ........function 1.
g(x) = √x + 7 ........function 2.
Next, we would substitute function 1 into function 2 as follows:
g(f(x)) = √((x + 3)²) + 7
g(f(x)) = (x + 3) + 7
g(f(x)) = x + 3 + 7
g(f(x)) = x + 10
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The wait time of a line x hours after a store opens is given by the expression:40x-12x+23
What does the value 23 represent?
Question 1 options:
the total rate of change in people per hour
the total number of people in line
the rate at which people join the line
the number of people in line when the store opened
Answer:
Step-by-step explanation:
The wait time of a line x hours after a store opens is given by the expression:40x-12x+23What does the value 23 represent?Question 1 options:the total rate of change in people per hourthe total number of people in linethe rate at which people join the linethe number of people in line when the store opened
Which set of sides would make a right triangle? 5,10,12 8,10,12 5,12,13 4,5,6
Our answer are the sides 5,12 and 13 which represent a Pythagoraen triple
The sides of a triangle that would make a right-triangle are collectively called a Pythagorean triple
These measures stem from the Pythagoras theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides
At any point in time, the hypotenuse refers to the longest side in the triangle
So basically, to get the correct answer from these options, if we square the longest side, and the sum of the squares of the two other sides equal the square of this longest side, the side that provides us with this would be our answer
So let us consider the options individually;
[tex]\begin{gathered} 12^2\text{ }\ne5^2+10^2 \\ \\ 12^2\ne8^2+10^2 \\ \\ 6^2\text{ }\ne4^2+5^2 \\ \\ \text{But;} \\ \\ 13^2=5^2+12^2 \end{gathered}[/tex]A map is drawn using a scale of 1 inch : 4 meters. If the length of a paved path on a map is 16 inches, then find the actual length of the paved path.
Nana, this is the solution to the exercise:
Scale 1 inch : 4 meters
For solving this exercise, we will use the Direct Rule of Three, as follows:
Length on the map (inches) - Actual length (meters)
______________________________________________
1 4
16 x
_______________________________________________
1 * x = 16 * 4
x = 64
The actual length of the paved path is 64 meters
If xy=8 inches, wy=24 inches and xz=48, The height from the ground the base of the window is ___ inches
Given:
[tex]\begin{gathered} XY=8in \\ WY=24in \\ XZ=48in \end{gathered}[/tex]To find:
The height from the ground to the base of the window.
Explanation:
Since the triangles XWY and XVZ are similar by AA similarity.
So we can write,
[tex][/tex]The value of a stock decreases by an average of 12 dollars each week. Which of the following represents the total average decrease in the stock after 4 weeks? |−12| − 4 = 8 dollars 4|−12| = 48 dollars |−12| − |4| = 8 dollars −4|12| = 48 dollars
The equation that represents the total average decrease in the stock after 4 weeks is 4|−12| = 48 dollars.
What is the total average decrease?When the value of a stock decreases, the number is a negative number. A negative number is a number that is less than zero. A negative number would have a negative sign in front of it. Thus, a $12 stock decrease would be written as -12.
The total stock decrease in 4 weeks can be determined by multiplying $-12 by 4 weeks. Multiplication is the operation that is used to determine the product of two or more numbers.
Total stock decrease = decrease per week x number of weeks
-12 x 4 = -48 or |-48| dollars
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When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?
Answer:
- 200,5
Some words for 20 symbols
What does approximate value of the area of Circumference mean
Let's assume that we have a circle of radius r. Its circumference or perimeter C and its surface area A are given by the following formulas:
[tex]\begin{gathered} C=2\pi r \\ A=\pi r^2 \end{gathered}[/tex]We must find the radius or diameter of a circle where C and A are equal. Then we can construct an equation for r by equalizing A and C:
[tex]\begin{gathered} A=C \\ \pi r^2=2\pi r \end{gathered}[/tex]We can divide both sides by π and r (it is important to note that we can divide by r because we know that r is not 0). Then we get:
[tex]\begin{gathered} \frac{\pi\cdot r^2}{\pi\cdot r}=\frac{2\pi\cdot r}{\pi\cdot r} \\ r=2 \end{gathered}[/tex]AnswerSo the radius is 2 (of any unit). Then the answer is the first option.
How do I find the correct options for the reasons?
Answer:
Explanation:
Statement: Triangle QRT and Triangle STR are Isosceles Triangles.
Angles QRT is congruent to Angle STR.
Reason: Converse of Alternate Interior Angles
Statement: RQ=RT, TR=TS
Reason: Definition of an Isosceles Triangle
Statement: TR = RT
Reason: Reflexive Property
Statement: RQ=TS
Reason: Transitive Property
Statement: RQ||TS
Reason: Opposite sides are congruent and parallel.
Statement: QRST is a parallelogram.
Reason:
Mariano is standing at the top of a hill when he kicks a soccer ball up into the air. The height of the hill is h feet,and the ball is kicked with an initial velocity of v feet per second. The height of the ball above the bottom of thehill after t seconds is given by the polynomial -16 + vt + h. Find the height of the ball after 2 seconds if it waskicked from the top of a 20 foot tall hill at 72 feet per second.O 100 ftO 32 ftO 20 ftO 132 ft
we have the equation
[tex]f(t)=-16t^2+vt+h[/tex]given values
t=2 sec
v=72 ft/sec
h=20 ft
substitute given values
[tex]\begin{gathered} f(t)=-16(2)^2+72\cdot2+20 \\ f(t)=100\text{ ft} \end{gathered}[/tex]therefore
the answer is the first optionWhat is the slope of the line that passes through (2,2) and (10,6)
A Banks loan officer rates applicants for credit the ratings can be described by a normal model with a mean of 200 and a standard deviation of 50. If an applicant is selected what percentage can be between 200 and 275?
Answer:
43%
Step-by-step explanation:
You want to know the percentage of applicants having a rating between 200 and 275, given that applicants have ratings normally distributed with a mean of 200 and a standard deviation of 50.
Area under the Normal PDFThe given percentage can be found using a spreadsheet, suitable calculator, or table of values of the Normal probability function. The attached calculator display shows the percentage to be ...
0.433 × 100% = 43.3%
About 43% of applicants will have a rating between 200 and 275.
An animal gained 5 kilograms steadily over 25 years. What is the unit rate of kilograms per year?
Answer:
0.2kg
Step-by-step explanation:
5/25 = 0.2 which is the rate of kg per year
Does coordinates s or coordinate t represent a greater number in the following
parallelogram?
(-2,3)
(s, -1)
(0, -1)
(t, 3)
Thus, t has a greater value than s for the co-ordinates (s, -1) and (t, 3).
How to analyze points of an axis for a two dimensional entity?
We can use the fact that both points on the x-axis to compare the values of s and t for the provided parallelogram. As a result, each point that is closest to the x coordinate reflects a higher value than its equivalent counterparts.
Given, the co-ordinates of the parallelogram are: (-2, 3), (s, -1), (0, -1),
(t, 3).
Also, the co-ordinates of the parallelogram are also shown in the figure below.
To compare for the values of s and t for the given parallelogram,
we can analyze that both s and t represent points on the x-axis, therefore any point that stands rightmost with the x co-ordinate represents a higher value than the corresponding counterparts.
Therefore, t has a greater value than s for the co-ordinates (s, -1) and (t, 3), since t is on the right side from s.
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which of the following fractions is the biggest: 1/6,3/8,1/4,4/9,2/7
Answer:
4/9
Step-by-step explanation:
Inequality graph the solution x-4<-5
Answer: x < -1
Step-by-step explanation:
So you are starting with x-4<-5
Cancel the -4 on the left side by adding 4 to both sides:
x-4<-5
+4 +4
So you end up with x < -1 which would be your answer.
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so far carmella has collected 14 boxes of baseball cards there are 315 cards in each box carm,ella estimsates that she has about 3,000 cards so she buys 6 albuns that hold 500 cards each.how many cards does carmella have?
Carmella has 9 albums and 4410 cards.
A unitary method is defined.The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Due to that,
There are 315 cards in each box.
14, the number of boxes.
(b) Total number of cards is the sum of the boxes plus the number of cards in each box.
= 14 × 315
= 4410
(a) Carmella purchased a six-album set of 500 cards since she thought she had 3,000 cards. Six albums are not enough because she calculated the quantity of cards incorrectly. There are 4410 cards in total, but she thought there were only 3000.
(c). Total number of albums required = [tex]\dfrac{Total number of cards}{Number of card 1 album can hold}[/tex]
= [tex]\frac{4410}{500}[/tex]
= 8.82 ≅9
Carmella have 4410 cards, 9 albums.
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What would step 3 look like after you have added the two equations?
Adding the two equations will be adding similar terms to both equations. That is:
8x + (-8x) = 0
-10y + (-6y) = -16y
20 + (-4) = 16
Therefore, adding the two equations will look like -16y = 16. (Option 3)
Find the perimeter of a square with the sides of length 9x+11 and 13x-1
The perimeter of the square has a value of 260 units
How to determine the perimeter?From the question, the given parameters are
Shape = Square
Side lengths = 9x + 11 and 13x - 1
The side lengths of a square are congruent
This means that
9x + 11 = 13x - 1
Collect the like terms in the equation
So, we have
13x - 9x = 11 + 1
Evaluate the like terms
2x = 12
Divide both sides by 2
x = 6
The perimeter of the square is then calculated as
P = 4 * (9x + 11)
Where x = 6
So, we have
P = 4 * (9 x 6 + 11)
Evaluate
P = 260
Hence, the perimeter is 260 units
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Lexi opened her account with less money and accrues interest at a greater rate.
What is meant by interest?
In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principle amount (the amount borrowed). The charge that the borrower may be required to pay the lender or another entity is not the same as interest. Interest also differs from dividends, which are distributed by businesses to their shareholders from their profits or reserves, but not at a set rate but rather on a pro rata basis as a portion of the rewards received by risk-takers when revenue generated exceeds total expenditures. The amount of interest paid or received during a specific time period divided by the total amount borrowed or lent is the rate of interest.
The correct answer is option (E):
Lexi opened her account with less money and accrues interest at a greater rate.
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K
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of
producing x units of tile is given by C(x)=200x+900, while the revenue in dollars, R(x), from the sale of x units of tile
is given by R(x) = 230x. Find the break-even point and the cost and revenue at the break-even point.
The break-even point is
units.
The cost at the break-even point is $
The revenue at the break-even point is
Answer: 30, 6900, 6900
Step-by-step explanation:
The break-even point is when cost equals revenue.
[tex]230x=200x+900\\\\30x=900\\\\x=30[/tex]
The cost and revenue at x=30 are both $6900.
how many many eighths are in 8/9
There are 1/9 eighths in 8/9
A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Which diagram best represents this information?
The diagram which best represents the hiking track of the hiker is attached below.
Speed = Distance / Time
As time increases, speed is constant, i.e., 214 miles per hour
So, the distance increases with an increase in time.
Speed = Distance/Time
Let, Distance = D and Time = T,
214 = D / T
D = 214T
Let, D = Y coordinate, Time = X coordinate
y = 214 x→→Equation of the line passing through the origin and slope 214.
For the given situation, the equation is a linear equation and the equation will be on the y-axis.
Hence, a diagram that represents this information is:
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Choose the graph of y = 2 cos x. (2
the expression is
y = 2cos x
when x = 0 degrees
y = 2 x cos0
y = 2 x 1
y = 2
so it is