The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
F(x)= 2(x-2)^2 + 2 is the correct equation of F(x)
A quadratic function is a polynomial function of the second degree. The general form of a quadratic function is this: f (x) = ax^2 + bx + c, where a, b, and c are real numbers and a≠ 0.
Graphs of quadratic functions
The term "parabola" refers to the graph of a quadratic function. A parabola essentially resembles the letter "U," yet it can be inverted or exactly this shape depending on the situation. The leading coefficient determines whether the graph of a quadratic function opens up or down; if it is more than zero, the parabola opens up; if it is less than zero, the parabola opens down.
It is given that graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat.
We need to find the equation of F(x)
In the figure, parabola opens up, the leading coefficient is greater than zero ,So option (d) is correct
Hence the equation of F(x) is 2(x-2)^2 + 2
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Which equation represents a population of 250 animals that decreases at an annual rate of 12% ?
Answer:
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
Step-by-step explanation:
Use the formula f(t)=P(1+b)^t
Plug in the information.
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
The only thing I did in the second equation is I subtract 0.12 from 1.
Hope this helps!
Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 14 inches, and the width QR is labeled as 7 inches. The side LM of the square is labeled as 7 inches.
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answer:
Incorrect
Step-by-step explanation:
Formula:
the Diagonal of a square with side square of lengths a
is equal to a√2.
=============
Then
Diagonal of LMNO : 7√2
Then
OM = 7√2
…………………………………………
Using the Pythagorean theorem:
The diagonal of the rectangle PQRS is equal to :
√(14²+7²) = √245 = 7√5
Then
SQ = 7√5
………………
Conclusion:
7√5 ≠ 2×(7√2)
Therefore
Anna is not correct.
Figure ABCD is a rhombus. Rhombus A B C D is shown. Angle A is (5 x 25) degrees and angle D is (7 x minus 1) degrees. What is the value of x
Answer: 18
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so
[tex]5 \times 25=7x-1\\\\125=7x-1\\\\126=7x\\\\x=18[/tex]
Find the nth term of the sequence 4, 7, 10, 13, …
Answer:
3n+1
Step-by-step explanation:
Subtract one from all the values, you get multiples of 3 in the equation 3n=nth term
So when you add one back, your equation is 3n+1=nth term
Solve for X.
X = [?]
5x - 16 X + 10
[tex] \boxed{ \sf{ \color{purple}\huge Answer :}}[/tex]
[tex] \: \: [/tex]
[tex] \large \tt \purple↪ \: \: \: \: \: 5x - 16 = x + 10 [/tex]
[tex] \: \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \:5x - x = 10 + 16 [/tex]
[tex] \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \: 4x = 26[/tex]
[tex] \: [/tex]
[tex]\large \tt \purple↪ \: \: \: \: \: x = \cancel\frac{26}{4} [/tex]
[tex] \: \: [/tex]
[tex] \underline{ \boxed{\large \tt \purple↪ \red{ \: \: \: \: x = \frac{13}{2} }}}{ \large✓}[/tex]
[tex] \: \: [/tex]
hope helps ~
Olga has a drawer of socks with four red pears, two gray pears, and a black hairs. she also has a bag of hair bands with 10 red, six gray, and 24 black hair bands if she selects randomly what is the probability that olga will select a red pair of socks and a red hairband
The probability that olga will select a red pair of socks and a red hairband is 14/47
Probability defines the likelihood of an event occurring. There are many situations in real life where we may need to predict the outcome of an event. We may or may not be certain of the outcome of the event. In such cases, we say that there is a probability that the event will or will not occur. Probability in general has great applications in games, in business for probabilistic predictions, and also probability has extensive applications in this new field of artificial intelligence.
The probability of an event can be calculated using the probability formula simply by dividing the number of favorable outcomes by the total number of possible outcomes. The value of the probability of an event occurring can lie between 0 and 1 because the number of favorable outcomes can never exceed the total number of outcomes. Also, a favorable number of results cannot be negative
For an experiment that has "n" number of outcomes, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is as follows.
Probability (event) = favorable outcomes/total outcomes = x/n
Olga has a drawer of socks with four red pears, two gray pears, and a black hairs. she also has a bag of hair bands with 10 red, six gray, and 24 black hair bands
Therefore total number of items are = 4 + 2 + 1 + 10 + 6 + 24 = 47
Probability that olga will select a red pair of socks and a red hairband is 4/47 + 10/47
= 14/47
Hence the probability that olga will select a red pair of socks and a red hairband is 14/47
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Move the sliders to set the values of r, h, and k, and record at least three different sets of data. also record the equations of the corresponding circles.
The equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
The question seems incomplete and complete question given in the image !!!!
A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)
We know that the general equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where ( h, k ) is the center and r is the radius.
According to the question
The equation of circle given is [tex]x^2+y^2=1[/tex]
Center at origin
i.e
(h,k) = (0,0)
and radius = 1 unit
Now ,
By changing changing center (h,k) and radius of equation it will give following equations
h k r equation of circle
0 1 3 [tex](x-0)^2+(y-0)^2=3^2[/tex]
2 2 3 [tex](x-2)^2+(y-2)^2=3^2[/tex]
1 1 1 [tex](x-1)^2+(y-1)^2=1^2[/tex]
-2 -1 2 [tex](x+2)^2+(y+1)^2=2^2[/tex]
3 2 1 [tex](x-3)^2+(y-2)^2=1^2[/tex]
-5 1 3 [tex](x+5)^2+(y-1)^2=3^2[/tex]
Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
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Select the correct answer.
Consider these functions:
f(x) = 4x³ - 10
g(x) = 3x - 4/2
What is the value of g(f2))?
Answer:
3x - 4/2
Step-by-step explanation:
2 result(s) for "f(x) = 4x³ - 10 g(x)
PLS HELP ME PLEASE
To measure the distance across a lake, a surveyor has taken the measurements shown in the diagram below. Determine the distance across the lake.
Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.In this problem, the parameters are:
a = 800, b = 900, C = 70º.
Hence the distance across the lake is c, found as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
c² = 800² + 900² - 2(800)(900)cos(70º)
c² = 957491
[tex]c = \sqrt{957491}[/tex]
c = 978.5.
The distance across the lake is of 978.5 feet.
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Find the perimeter of each of these rectangles
Answer:
a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm
b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)
= 4√10 cm
c) Simplifying √72: √36 x √2 = 6√2
Simplifying √18: √9 x √2 = 3√2
Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm
what is the coefficient of (3y^2 + 9)5
The coefficient of (3y² + 9)5 is 15.
A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.
Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.
a₀ is the leading coefficient.
In the question, we are asked to identify the coefficient of (3y² + 9)5.
First, we expand the given expression:
(3y² + 9)5
= 15y² + 45.
Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.
Thus, the coefficient of (3y² + 9)5 is 15.
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Graph the function shown g(x)=-|x-4|
Using translation concepts, the graph of g(x) = -|x - 4| is shown at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The graph of g(x) = -|x - 4| is the graph of f(x) = |x| with these following changes:
Reflection over the x-axis.Shift right of 4 units.At the end of the answer, the graph shows functions f(x) in red and g(x) in blue.
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In a bag there are 3 red 4 white, and 5 blue marbles. once a marble is selected it is not required. find: p(white, red) find: p(blue, white, red.)
Answer:
Below in bold.
Step-by-step explanation:
Total number of marbles = 3+4+5 = 12
P(white, red) = 4/12 * 3/11
= 12/132
= 1/11,
P(blue, white, red) = 5/12 * 4/11* 3/10
= 60/1320
= 6/132
= 1/22.
Find the number of terms in this series: 3x + 5x + 7x + ... + 23x
Help asap please and thank you!
Your professor selects three students from your Stats class to form a study team. How many study teams are possible from a class of 30 students
Total number of teams are 10
Linear EquationAn equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is one that includes a variable, such as x.
As given in the problem,
total number of students in class=30
now professor want to create study teams .
one team consist of 3 members,
lets suppose professor will form n teams
So,
3×n=30
solve this equation to get value of n
n=30÷3
n=10 teams
hence total number of teams are 10 .
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Homer mowed 5 lawns in his first month and increased the number he mows by two for each month following. Which of the following is the correct interpretation of the rate of change and the initial value?
The equation which represent the interpretation of the scenario is 5 + 2x
AlgebraNumber of lawns Homer mowed = 5Additional laws mowed each month = 2Number of months = xTotal laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)
= 5 + (2 × x)
= 5 + 2x
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Find the surface area of the composite figure. Round to the nearest tenth if necessary.
The surface area of the composite figure shown in the figure attached is 233.6 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²
The surface area of the composite figure shown in the figure attached is 233.6 cm²
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Sumaya's smoothie store is planning to sell an extra-large size. the extra-large size will have three times the volume of the small size (the small size is (8,4) ). it will cost twice as much as the small size.
which coordinate pair represents the volume and cost of the extra-large size?
The coordinate pair that represents the volume and cost of the extra-large size is (24, 8).
A coordinate plane is a plane that can be used to represent the position of a point. The plane consists of x-axes and y-axes. The position of a point is referenced from the origin.
The small size of a pizza is represented by the coordinate pair (8, 4) ⇒ (volume, cost)
Since the volume of the extra-large size will have three times the volume of the small size, hence:
Volume of extra-large size = 8 * 3 = 24
The cost of an extra large is twice as much as the small size, hence:
Cost of extra large = 4 * 2 = 8
A coordinate plane is a graphing and outline machine for factors and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants inside the coordinate plane. The point at which these strains join is known as the starting place (0, zero).
Coordinates are written as (x, y) meaning the point on the x-axis is written first, followed by the point on the y-axis. a few children can be taught to keep in mind this with the phrase 'along the hall, up the stairs, that means that they must observe the x-axis first after which the y.
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A balloon is falling. it falls 200 feet each minute. how far will it in 3 minutes?
Answer:
600ft
Step-by-step explanation:
The balloon falls 200 feet in one minute and we need the amount it fell in 3 minutes: 200feet*3minutes = 600 ft
Suppose the diameter is 35cm. what is its curumference?include the unit measure in your answer
The circumference of the circle of diameter 35cm is 109.9 cm.
Given the diameter of the circle is 35 cm.
We are required to find the circumference of the circle.
The circumference is the arc length of the circle, The perimeter is the curve length around any closed figure. It is equat to the length of the outer ring of a circle.
Formula of circumference=2πr where r is the radius of the circle.
Diameter=35 cm
Radius=35/2 cm (Radius is half of diameter)
Circumference=2π*35/2
=35π
Put the value of π =3.14 (it can be 22/7 as well.)
=35*3.14
=109.9 cm
Hence the circumference of the circle is 109.9 cm.
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On a sunny day, Andrew, who is 1.9 m tall, casts a shadow that is 3.5 m long. A nearby tree casts a shadow that is 28.0 m long. To the nearest tenth of a metre, how tall is the tree?
Answer:
15.2
Step-by-step explanation:
The explanation is in the photo.. but basically this question is about similar triangles and you need to find the scale factor to find the height.
Hope it helps
the height of the tree is approximately 15.2 meters.
To find the height of the tree, we can set up a proportion between Andrew's height and the height of the tree based on their respective shadow lengths.
Let's denote the height of the tree as "h" meters.
The proportion between the height and shadow lengths can be written as:
h / 28.0 = 1.9 / 3.5
Now, we can solve for "h":
h = (1.9 / 3.5) * 28.0
h ≈ 15.2 meters
To the nearest tenth of a meter, the height of the tree is approximately 15.2 meters.
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Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats . what is the probability that a kid who goes the doctor has a sore throat given that he has a fever? (when entering your answer remember that the probability is a number between 0 and 1)
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%. Computed using conditional probability.
The probability of any event A given that event B has already taken place is found using the formula P(A|B) = P(A ∩ B)/P(B). This is known as conditional probability, where P(A ∩ B) is the probability of events A and B, and P(B) is the probability of event B.
In the question, we are given that 70% of kids who visit a doctor have a fever and 21% of kids have a fever and sore throats.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever.
We suppose the event of going to the doctor while having a fever to be B, and going to a doctor while having a sore throat to be A.
We are given that 70% of kids who visit a doctor have a fever, that is, the probability of event B, P(B) = 70% = 0.7.
We are given that 21% of kids who visit a doctor have a fever and sore throats, that is, the probability of event A and event B, P(A ∩ B) = 21% = 0.21.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever, that is, we are asked to find the conditional probability of event A, when event B has already taken place, that is, P(A|B).
By formula, we know that:
P(A|B) = P(A ∩ B)/P(B) = 0.21/0.70 = 0.30.
Thus, the probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%.
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PLEASE HELP IM STUCK
Answer:
y = 7.25 + 0.65x
Step-by-step explanation:
y = total cost
x = each mile
it starts at 7.25
any mile after that is an extra $0.65
y = 7.25 + 0.65x
There are n cities in a OneWayCountry (country in which every road is a One-Way road). Every pair of cities is connected by exactly one direct one-way road. Show that there exists a city which can be reached from every other city either directly or via at most one other city.
The cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from [tex]C_{i}[/tex]-1 to [tex]c_{n}+1[/tex] and from [tex]c_{n}+1[/tex] to [tex]C_{i}[/tex]. Place [tex]c_{n}+1[/tex] between [tex]C_{i}[/tex]−1 and [tex]C_{i}[/tex] to get the desired path.
What is mathematical induction method?Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. By generalizing this in form of a principle which we would use to prove any mathematical statement is 'Principle of Mathematical Induction'.
The question says that between any two cities X and Y, either there’s an
one-way road from X to Y or from Y to X, but not both. Then show that
there is a path from some city A which visits all the cities exactly once.
This problem is very similar to the Football league problem #7 in Homework 1. This problem can be modeled as a directed graph in which cities
are represented as vertices and there’s an edge from vertices X to Y if
there’s a road from cities X to Y. And then, our goal is to find a path
in this graph which visits every vertex in the graph.
The rest of the solution is very similar to the argument in Problem 7 of
homework 1. We use induction of number of cities, say n.
As a base case, if n = 2, there are only two cities X and Y and the path
is simply the edge between X and Y.
For induction hypothesis, assume that the statement is true for any set
of n cities. That is’ for any set of n cities, we can find a path which visits
all the cities exactly once.
Let’s prove the statement for n + 1 cities. Leave out n + 1 th city (say,
[tex]c_{n}+1[/tex]) and for the remaining n cities, by induction hypothesis, we can find a path which visits all these n cities exactly once. Let us label the cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from [tex]C_{i}[/tex]-1 to [tex]c_{n}+1[/tex] and from [tex]c_{n}+1[/tex] to [tex]C_{i}[/tex]. Place [tex]c_{n}+1[/tex] between [tex]C_{i}[/tex]−1 and [tex]C_{i}[/tex] to get the desired path.
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Louis is very hungry when he spots a hot dog stand. The stand sells soft drinks for $1.25 each and hot dogs for $2.50 each. Louis has $21 in his pocket and he really wants to buy one soft drink and as many hot dogs as he can purchase. How many hot dogs can he buy?
Answer:
7 hot dogs
Step-by-step explanation:
Set up an equation:
2.5x + 1.25 = 21
2.5x = 19.75
x = 7.9
You cannot buy .9 of a hot dog, so the answer is 7
Travis jogged to his friend's house 10 miles away and then got a ride back home. It took him 2 hours longer to jog there than ride back. His jogging rate was 16 mph slower than the rate when he was riding. What was his jogging rate?
Answer asap please :)))
Using the relation between velocity, distance and time, it is found that his jogging rate was of 4.5 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, his velocity was of v, while the time was of t + 2, for a distance of 10 miles, hence:
[tex]v = \frac{10}{t + 2}[/tex]
Riding, his velocity was of 16, while the time was of t, also for a distance of 10 miles, hence:
[tex]v + 16 = \frac{10}{t}[/tex]
Then, considering the first equation and replacing in the second:
[tex]\frac{10}{t + 2} + 16 = \frac{10}{t}[/tex]
[tex]\frac{10}{t} - \frac{10}{t + 2} = 16[/tex]
[tex]\frac{10t + 20 - 10t}{t(t + 2)} = 16[/tex]
16t² + 32t - 20 = 0 -> t = 0.5.
Then his jogging rate in mph was:
[tex]v = \frac{10}{0.5 + 2} = 4.5[/tex]
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Select the correct answer. What is the approximate solution to this equation? 4lnx - 8 = 12
A. x = 148.4
B. x = 10.5
C. x = 1.61
D. x = 59,874
Answer:
Step-by-step explanation:
hello :
4lnx - 8 = 12
4lnx - 8 +8= 12+8
4lnx =20
lnx =5
coclusion : x =e^5
A. x = 148.4
Which expression is equivalent to startfraction 3 x superscript negative 6 baseline y superscript negative 3 baseline over 15 x squared y superscript 10 baseline endfraction? assume x not-equals 0, y not-equals 0.
The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline endFraction.
Given expression [tex](3x)^-6*y^-3/ 15x^2*y^10[/tex]
Lets simplify the equation:
[tex]= > (3x)^-6*y^-3/ 15x^2*y^10\\=1/5 x^-8*y^-13[/tex]
Expression:
An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
Hence the correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction.
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The product of two fractions is 9/3/ 5. if one of them is 9/ 3/7. find the other
The other fraction is [tex]1\frac{1}{55}[/tex].
The calculation to find out other fractionProvided that ,
One fraction = [tex]9\frac{3}{7}[/tex] = [tex]\frac{66}{7}[/tex]
The product of their fraction = [tex]9\frac{3}{5}[/tex] = [tex]\frac{48}{5}[/tex]
We have to find out the other fraction.
When one fraction and their product are given, the formula to find out another fraction = product / one fraction
So, the other fraction = [tex]\frac{48}{5}[/tex] / [tex]\frac{66}{7}[/tex]
= [tex]\frac{48}{5} * \frac{7}{66}[/tex]
= 336/330
= 56/55 [divided both the numerator & denominator by 6]
= [tex]1\frac{1}{55}[/tex]
Therefore it is concluded that the other fraction is [tex]1\frac{1}{55}[/tex] .
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