Describe the features of the function that can be easily seen when a quadratic function is givenin the form: y = a (x – a)(x - b) and how they can be identified from the equation.
Answers
When we write a quadratic function as
\(y=a(x-b)(x-c)\)We can easily identify the roots of this function, and they are given by the numbers b and c.
Related Questions
What is the ratio of the number of days in the week that do not begin with the letter "T" to the number of days in the week that do begin with the letter "T"? (1 point)
Answers
Answer:
5:7
Step-by-step explanation:
The days in the week whose names don't begin with 'T' are Sunday, Monday, Wednesday, Friday, and Saturday. I counted them, and found that there are five (5) of them. Then I counted the number of days in a full week, no matter how they're spelled. I counted seven (7) that time. The ratio of 5 to 7 is. 5:7 or 5/7.
Help me please and thank you, and I will mark you brainliest!!
Answers
Answer:
270m^2
Step-by-step explanation:
30m*18m/2 = 270m^2
Answer:
270
Step-by-step explanation:
Use the verticals line test to determine if y is a function of x in the graph
Which of the following statements is correct?
a) y is a function of x
B) y is not a function of x
Answers
Using the vertical line test we conclude that y is not a function of x.
How to use the vertical line test?When we have the graph of a relation, the vertical line test says that if we draw a vertical line over the graph and it intercepts the graph in more than one point, then the graph does not represent a function.
Here we have the graph of a circle, and there are multiple lines that intercept the graph twice (for example the line x = 0)
So we can conclude that this is not a function, thus, the correct option is A.
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A topological group G is a group that is also a topological space satisfying the T1 axiom, such that the map of G×G into G sending x×y into x⋅y, and the map of G into G sending x into x−1, are continuous maps.
Answers
The topological group G is a group that is also a topological space satisfying the T1 Axiom that is, there is a topology on the elements of G and all sets of a finite number .
Given :
A topological group G is a group that is also a topological space satisfying the T1 axiom, such that the map of G * G into G sending x * y into x⋅y, and the map of G into G sending x into x^−1, are continuous maps.
When we say the map of G * G into G defined as (x, y) 7 → x·y is continuous, we use the product topology on G * G. Since inversion maps G to G, the topology on G is used both in the domain and co - domain.
Every group G is a topological group. We just equip G with the discrete
topology. Continuity of the binary operation follows at (x, y) ∈ G * G by taking the open set O = { x · y } (the “δ set” ) for any given open set in G * G containing (x, y) (the “ε set”).
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A coin is tossed twice. Let
E
be the event "the first toss shows heads" and
F
the event "the second toss shows heads".
(a) Are the events
E
and
F
independent?
Input Yes or No:
(b) Find the probability of showing heads on both tosses. Write your answer as a reduced fraction.
Answer:
Answers
Answer:
(a) Yes, E and F are independent events.
(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4
Right triangle with a hypotenuse of 159 ft and Angle A = 34 degree
Calculate the length of the sides they should be rounded to the nearest whole foot. The rounded for the legs (side) should be used to calculate the area of the triangle
Answers
the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.
Given: The hypotenuse of the right triangle,
c = 159 ft; angle A = 34°
We know that, in a right-angled triangle:
\($$\sin\theta=\frac{\text{opposite}}\)
\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)
\({\text{hypotenuse}}$$\)
We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:
\($$\sin\theta=\frac{\text{opposite}}\)
\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)
\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)
\({\text{adjacent}}$$\) Length of side a is:
\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)
Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:
\($$\text{Area} = \frac{1}{2}ab$$\)
Putting the values of a and b:
\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)
Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.
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Calculator
B(1,5)
5
What is the area of
strapezoid ABCD
3
A(-3,2)
2
Enter your answer as a decimal or whole number in the box. Do
not round at any steps.
1
0
-5
4
3
-2
1
1.
2
3
4
6
units
D(
0-2)
-
C(7-3)
-5
1
2
3
4
5
Next >
Answers
9514 1404 393
Answer:
37.5 square units
Step-by-step explanation:
When the points are plotted on a graph, you can see that the sides of the trapezoid are the hypotenuse of a 3-4-5 right triangle (or multiple thereof). The grid lines make up the legs of the triangle, and the edge of the figure makes up the hypotenuse. Side BC is clearly twice as long as side AD.
The area formula for a trapezoid applies:
A = 1/2(b1 +b2)h
A = 1/2(5 +10)(5) = 1/2(75) = 37.5 . . . . square units area
Someone help me with this question please. I attached the screenshot. Thanks.
Answers
Because it’s the only number that does not go on forever.
Use the defined variables for the verbal model to write an equation in slope-intercept form that relates the variables.
Answers
Answer:
y = 3x + 4
Step-By Step Explanation:
Let's first define the variables:
m = slope
x = independent variable
y = dependent variable
b = y-intercept
Now, let's write an equation in slope-intercept form that relates these variables:
y = mx + b
Explanation:
The equation y = mx + b is known as the slope-intercept form. It is a linear equation that is used to describe the relationship between two variables, x and y. The equation states that y is equal to the slope (m) multiplied by the independent variable (x) plus the y-intercept (b).
Which of the following is most likely the next step in the series?
Answers
It takes 6 hours to clean and detail a luxury car. During the morning of
cleaning, the workers were able to clean for 4 hours. If the variable t stands
for the amount of time the workers have left to clean the windows after lunch,
which of the following units could apply to this variable?
Answers
William leaves his home at 15:03 and walks for 12 minutes to Euston station.
He spends 4 minutes buying a ticket and then catches the next train to Bletchley.
What time will he arrive at Bletchley?
Train timetable
Euston
14:49 15:18 15:29
14:52
15:32 15:35
Harrow
Watford 15:01
15:30
15:41 15:44 16:11
Hemel
15:39 15:50
15:53
16:20
Tring
15:31
16:00
Q
16:14 16:41
Bletchley 15:47
16:16
16:30
Bedford 15:54 16:23 16:34 16:37 17:04
15:32 15:59
Answers
To find out what time he will arrive at Bletchley, we need to look at the arrival time for the train that departs Euston at 15:32. According to the timetable, this train arrives at Bletchley at 16:16.
William spends 12 minutes walking to Euston station and 4 minutes buying a ticket, so his total journey time is 12 + 4 + 44 = 60 minutes (since there are 60 minutes in an hour). Therefore, he will arrive at Bletchley at 16:16 + 60 minutes = 17:16.
So, William will arrive at Bletchley at 17:16.
*Answer*
15:47
Step-by-step explanation:
He left; 15:03
Walk for; 12mins
Spends extra;4min
So by my side,
I'll sum up those values we're having to find the total time that was spent
12+4= 16mins
So, at that time when he reached at the station it was 15:19 when we add those extra mins
And so I think it'll 15:47
My thought told me so though
The graph below represents the function f(x) and the translated function g(x) .
If f(x) = x ^ 2 , which of the following functions could be an algebraic representation of g(x) ?
Answers
Answer: D. \(g(x) = (x-b)^2\)
Explanation:
If we want to shift the curve some distance b to the right, then we'll need to replace x with x-b. What this effectively does is shift the xy axis itself b units to the left while the curve is fixed in place. This gives the illusion of the curve moving b units to the right.
Put another way: the old input x is updated to the new input x-b which is smaller by b units. This helps explain why the xy axis is shifted to the left this amount.
So that's how we go from \(f(x) = x^2\) to \(g(x) = (x-b)^2\). You can think of it as \(g(x) = f(x-b) = (x-b)^2\)
A man pulled a cart filled with stones that had a total mass of 60 kg.
He increased the amount of force used to pull the cart from 60 N to 90 N, what is the new
acceleration of the cart?
Answers
a1 = f/m
a1 = 60/60 = 1ms^-2
a2 = f2/m
a2 = 90/60
a2 = 1.5ms^-2
The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²
What is Force ?The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.
Formula of force,
F = ma
Given that,
A man pulled a cart filled with stones that had a total mass of 60 kg
He increased the amount of force used to pull the cart from 60 N to 90 N
New acceleration of cart = ?
F = ma
Old acceleration,
60 = 60a
a = 1 m/s²
New acceleration,
90 = 60a
a = 90/60
a = 3/2
a = 1.5 m/s²
Hence, the new acceleration is 1.5 m/s²
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Which is more, 5 meters or 4,996 millimeters?
Answers
Answer:
5 meters in milli is 5,000. 5,000 is more than 4996
Step-by-step explanation:
Answer:
5 meters
Step-by-step explanation:
one meter equals 1000 millimeters so obv 5 meters is bigger
Seven students were surveyed on the number of pets in their house. The results are shown below:
2, 2, 2, 3, 4, 4, 11
What is the mean number of pets?
Answers
Answer:
the mean number of pets is 4.
Step-by-step explanation:
if you add all of the numbers together, you get 28. Then you divide 28 by the amount of students.
A kitche sa tabletop that is a rectangle 24 in long and 18 in wide.Rita is an interior designer and wants to cover the tabletop in small tiles.She knows the area each bag of tiles covers, but only in square centimeters.(a) Find the area of the tabletop in square centimeters. Do notround intermediate computations and round your finalanswer to two decimal places. Use the table of conversionfacts, as needed.cm(b) The designer wants to cover the tabletop with tiles. Shedoesn't have any to begin with and she can't buy partialbags of tiles. Each bag of tiles covers 260 cm². How manywhole bags of tiles does the designer need to buy tocompletely cover the tabletop?bags(c) If each bag of tiles costs $3.76, how much will she need tospend on tile? Write your answer to the nearest cent.ExplanationCheckConversion facts for length2.54 centimeters (cm)= 30.48 centimeters (cm)≈ 0.91 meters (m)1 inch (in)1 foot (ft)1 yard (yd)1 mile (mi)XNote that means "is approximately equal to".For this problem, treat as if it were = .1.61 kilometers (km)5?I need help with this math problem.
Answers
Given: a tabletop that is a rectangle 24 in long and 18 in wide.
Find: (a) the area of the tabletop in square centimeters
(b) The designer wants to cover the tabletop with tiles. She doesn't have any to begin with and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm². number of bags of tiles does the designer need to buy to completely cover the tabletop
(c)If each bag of tiles costs $3.76, how much will she need to spend on tiles.
Explanation: (a)
\(1\text{ inch= 2.54cm}\)so the length of the tabletop in cm will be
\(24\times2.54=60.96cm\)and the breadth of the tabletop in cm will be
\(18\times2.54=45.72cm\)the area of the tabletop will be
\(\begin{gathered} l\times b \\ =60.96\times45.72 \\ =2787.09cm^2 \end{gathered}\)(b) The designer wants to cover the tabletop with tiles and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm² so the numbe rof bags designer needs to buy to cover the tabletop is
\(\begin{gathered} \frac{2787.09}{260} \\ =10.71 \end{gathered}\)it means that designer needs to buy 11 bags of tiles to cover the tabletop.
(c) If each bag of tiles costs $3.76.the the total cost will be equal to
\(3.76\times11=41.36\text{ \$}\)Suppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the
sample is less than 0.7.
Answers
The probability that the third largest observation in the sample is less than 0.7 is 0.2401 = 24.01%.
How do we calculate?The sample size n = 5,
Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.
Probability that X₃ is less than 0.7:
Since X₃ is the third largest observation = (X₁ and X₂) < 0.7.
The probability that X₃ is less than 0.7 is (0.7)² = 0.49.
The Probability that X₁ and X₂ < or equal to 0.7 is found as:.
The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.
We then get the product of both cases:
Probability = 0.49 * 0.49 = 0.2401
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Solve for x in the following 4/2.6=5/x
Answers
The value of X is 3.25
Look at the attached picture
Hope it will help you
Good luck on your assignment
Which of the following functions is graphed below? HELP
Answers
The solution is: Piece-wise function
f(x)=x+6 , x≤1
f(x) = x^2 + 3 , x>1, the following functions is graphed below.
Option C is correct.
Explanation:
We are given a graph of piece-wise function which break at x=1
We need to choose correct option for graph.
Function is break at x=1.
We will get two function
For x≤1 and x>1
As we can see x≤1, graph is linear and x>1 graph is parabolic.
Equation of linear graph, x≤1
Take two point of graph (0,6) and (-6,0)
Equation of line:
y-y1/y2-y1 = x-x1/x2-x1
y = x+1
f(x)=x+6 , x≤1
Equation of parabolic graph, x>1
f(x) = x^2 + 3
Piece-wise function
f(x)=x+6 , x≤1
f(x) = x^2 + 3 , x>1
Please see the attached figure.
Hence, The option C is correct.
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consider the two triangles. to prove that the triangles are similar by the sas similiarity theorem it needs to be shown that
Answers
The triangles are similar by the sas similarity theorem.
What is similarity of triangle?The similarity theorem for tri angles states that if two triangles have the same shape, then their corresponding angles are equal and their corresponding sides are proportional.
More specifically, if we have two triangles, Triangle ABC and Triangle DEF, such that:
Angle A = Angle D
Angle B = Angle E
Angle C = Angle F
And also, their corresponding sides are proportional:
AB/DE = BC/EF = AC/DF
Then, we can say that Triangle ABC is similar to Triangle DEF. This means that these two triangles have the same shape and they are only different in size.
The similarity theorem is important in geometry, as it allows us to determine unknown side lengths or angle measures of similar triangles by using proportions. It is also useful in real-life situations where we need to determine the size of objects that are not directly measurable
To prove that two triangles are similar using the SAS (Side-Angle-Side) similarity theorem, you need to show that:
Two pairs of corresponding sides are proportional (have the same ratio).
The included angles (the angle between these two pairs of corresponding sides) are congruent.
So, for the SAS similarity theorem to apply, you need to have two triangles where two pairs of corresponding sides are proportional and the included angle between these sides is congruent. If these conditions are met, then the triangles are similar.
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please some body help me
Answers
10 - $62.50
m - ?
She would need to sell 24 masks to make $150.
In ΔMNO, the measure of ∠O=90°, MN = 99 feet, and OM = 52 feet. Find the measure of ∠M to the nearest degree.
Answers
Answer:
58 is the answer I got and I think it should be right but yeah math is confusing sometimes lol
Answer:
58
Step-by-step explanation:
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
Answers
The factors of the polynomial function f(x) must be x, x + 6 and x + 3
How to determine the factorsFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
On the graph, we have the zeros of the function to be
x = -6, x = -3 and x = 0
Set the equations to 0
So, we have the following representation
x + 6 = 0, x + 3 = 0 and x = 0
This means that the factors are
x, x + 6 and x + 3
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In a certain video game, there is a mini-game where the main character can choose from a selection of twenty
presents. The presents are wrapped, so the character does not know what is in them. If 7 presents contain money, 3
presents contain gems, 6 presents contain ore, and 4 presents contain fish, what is the probability that the main
character does not choose a present that contains a gem?
Your answer should be an exact decimal value.
The probability of randomly selecting a present that does not contain a gem is
Answers
Answer:
There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.
The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.
hope it helps you...
fill in missing value
2 log₂ 5 = log₂ _
Answers
The missing value in the equation is 25.
What is Value?Value is the worth or importance that is placed on something. It is typically determined by factors such as quality, cost, and utility. It is an intangible concept that is highly subjective and is based on an individual’s perception of what something is worth to them. Value can also refer to a measure of worth, such as a financial value or a moral value.
This can be determined by using the following equation: 2log₂5 = log₂25. This equation is based on the fact that logarithmic equations are based on powers and that the logarithm of a number raised to a power is equal to that power multiplied by the logarithm of the number. Therefore, the missing value in the equation is 25.
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1. Mrs. Verner's class has
a total of 15 students. If 8
of them are girls, what
percentage are boys?
Answers
Answer:
46.7%
Step-by-step explanation:
Given:
Total number of students in Mrs. Verner's class = 15
Number of girls = 8
To find: percentage are boys
Solution:
Percentage of boys = ( Number of boys / Total number of students ) × 100
Number of boys = Total number of students - Number of girls = 15 - 8 = 7
So,
Percentage of boys = \(\frac{7}{15}\) × 100 = 46.7%
Help quick please look at pic to solve
Answers
The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
Given the diagram of the hanger which one side has 10 + 5x and other side has 11.
To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.
Thus, the equation is 10 + 5x = 11.
Consider the equation 10 + 5x = 11
On subtracting 10 from each side gives,
5x = 1
Divide each side by 5 gives,
x = 1/5.
Hence, the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
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PLS I REALLY NEED HELP WITH THIS. THANK YOU SO MUCH!!
Cedric earned $50 doing yard work. Cedric spent d dollars on a gift for his family and had X dollars left over.
Explain whether this equation is correct or not:
50 – X = d
Answers
Cedric starts with $50, and takes away x many dollars. His remaining total would be D many dollars. Variables are just letters representing an unknown amount. :)
Can someone make a free brainliest post so i can get too 5 crowns ?
Answers
Answer:
hi I'm Anna achooooooo
Answer:
How many crowns do you need to get to your next rank?
Step-by-step explanation:
I'm willing to help.