The function's y = 3(x + 5)² +11 width will be narrower.
What are functions?In mathematics, a function from a set x to a set y assigns each element of x precisely one element of y. The subsets x and y are referenced to as the function's domain and codomain, correspondingly. A relationship between a number of inputs and one output per input is referred to as a function. Simply described, a function is an association between inputs in which each piece of data is connected to exactly one output. There is a domain and a codomain, or range, for every function. A function is a type of rule that produces one output from one input. y = x² is a good illustration of this. Any information for x yields a single output for y.
A parabola is made narrow by a large positive value of a and wide by a large positive value of a that is close to 0.
Compare the given equation y = 3(x + 5)² + 11 with y = x² + c
So, a = 3
Therefore, the function will be narrower.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the parabola is open downwards
From the given parabola
The vertex of the parabola is at (-2, 2)
The vertex of the parabola is defined as the the point at the intersection of the parabola and its line of symmetry.
The line of symmetry is at x = -2
The parabola is open downwards
Hence, the vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the given parabola is open downwards
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7 yd.
24 yd.
What is the length of the hypotenuse?
yards
C=
Answer:
25
Step-by-step explanation:
the equation is a^2+b^2=c^2
7^2=49
24^2=576
49+576=625
the square root of 625 is 25
Two of the exterior angles of an n-sided polygon are 25° and 26°, three of its interior angles are 161° each and the remaining interior angles are 159° each. Calculate the value of n.
The required value of the number of sides ( n ) is 17.
What is polygon?
A closed, two-dimensional object composed of straight lines is called a polygon. In most cases, we can quickly determine the polygon's number of sides from its name.
Given, two of the exterior angles of an n-sided polygon are 25° & 26°
So, the sum of exterior angle = 25° + 26° = 51°
three of its interior angles are 161º each
So, each exterior angle = 180° - 161° = 19° .
sum of three exterior angles = 19*3 = 57° .
Then,
Remaining total angles = n - (2 + 3) = (n - 5).
And, the remaining interior angles are 159° each.
So, each exterior angle of the remaining angles = 180° - 159° = 21°.
sum of all (n -5) exterior angles remaining = 21(n - 5) = (21n - 105°) .
Now,
Sum of all exterior angles = 360°
or, 51° + 57° + (21n - 105°) = 360°
or, 21n + 108° - 105° = 360°
or, 21n + 3° = 360°
or, 21n = 360° - 3°
or, 21n = 357°
or, n = 357/21 = 17
Hence, The required value of n is 17.
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How long would the minute hand of a clock have to be if its end were to move at 100km/hour?
To move at 100 km/hour at its end, the length of the minute hand that has an angular velocity of 2·π radians per hour, has to be approximately 15.92 kilometers
What is angular velocity?Angular velocity is the rate and direction of rotation of a body about an axis.
The required linear speed of the minute hand = 100 km/hour
The formula to convert angular speed to linear speed is presented as follows;
[tex]\omega = \dfrac{v}{r}[/tex]Which gives;
[tex]r = \dfrac{v}{\omega}[/tex]The angular speed of the minute hand = 2·π rad/hour
The required length of the minute hand is therefore;
[tex]r = \dfrac{100 \ km/hour}{2\cdot \pi/hour} = \dfrac{50}{\pi}\, km \approx 15.92 \, km[/tex]
The length of the minute hand that that give a motion of 100 km/hour at the end is approximately 15.92 km
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Angel typically orders a 12-ounce Frappuccino that has 430 calories. If she orders the 20 ounce version, how many calories does it
have? Round to the nearest whole number.
Answer: ___ calories
Answer:717 calories
Step-by-step explanation:
first you need to find what one ounce would be:
430/12=35.83...
then you multiply the answer by 20
35.83*20=716.6...=717
Isabel and Khalil buy peaches and apricots. At the fruit stand, peaches cost $0.85 each, and apricots cost $0.55 each. Tax is included in the cost of each fruit. The friends have $5 to spend. Which is a possible combination of the number of peaches and apricots they can get for $5? Responses 1 peach, 8 apricots 1 peach, 8 apricots 2 peaches, 5 apricots 2 peaches, 5 apricots 3 peaches, 7 apricots 3 peaches, 7 apricots 4 peaches, 3 apricots 4 peaches, 3 apricots
The possible combination of the number of peaches and apricots they can get for $5 is 2 peaches and 5 apricots.
What is the possible combination?The equation that represents the total cost of peaches and apricots is:
Total cost = (number of peaches x cost of one peach) + (number of apricots x number of apricots)
$5 = ($0.85 x p) + ($0.55 x a)
Total cost of buying 1 peach and 8 apricots:
($0.85 x 1) + ($0.55 x 8) = $5.25
Total cost of buying 2 peaches and 5 apricots:
($0.85 x 2) + ($0.55 x 5) = $4.45
Total cost of buying 3 peaches and 7 apricots:
($0.85 x 3) + ($0.55 x 7) = $6.40
Total cost of buying 4 peaches and 3 apricots:
($0.85 x 4) + ($0.55 x 3) = $5.05
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. Kendra has a painting canvas that is 23 inches wide by 33 inches high. She painted a red
rose, which covered 30% of the canvas. What was the area of the canvas which was
covered by the red rose?
Answer:
227.7 in²
Step-by-step explanation:
You want to know the area that is 30% of a canvas that is 23 inches by 33 inches.
AreaThe area of the canvas is the product of its length and width.
A = LW
A = (33 in)(23 in) = 759 in²
RoseThe rose covers 30% of that area, so an area of ...
rose = 0.30 × 759 in² = 227.7 in²
The area of the canvas covered by the rose was 227.7 square inches.
To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
A. Write an expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs.
B. What does the coefficient of the expression in part (a) represent?
I need help asap thx u if you can.
A. The expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs is 195x
B. The coefficient of the expression in part (a) represents D. The the total amount the animal shelter earns when x dogs are adopted
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this situation, to adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
Therefore, the expression to adopt x dogs will be:
= 80(x) + 65(x) + 50(x)
= 80x + 65x + 50x
= 195x
This is the cost for x dogs.
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the measure of each side of an equilateral triangle whose are is [tex]\sqrt{3}[/tex] cm² is
Brainlist
The measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.
We have been given the measure of each side of an equilateral triangle whose area is √3 cm².
Let the measure of each side would be "a"
We know that,
Area of an equilateral triangle = √3a² / 4
As per the question,
⇒ √3 cm²= √3a² / 4
⇒ √3a² = 4√3 / √3
⇒ a² = 4 = √4
⇒ a = 2 cm
Thus, the measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.
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Jerome invested 260000 for 2 years at a rate of 8%p.a. 1)calculate the simple interest 2)calculate the investment at compound interim interest 3)amount at the end of the simple interest 4)amount at the end of compound 5)difference between the amount at simple interest and compound interest
1) Simple interest is $41600, 2) compound interest is $ 43264, 3) Amount at the end of Simple interest is $301600, 4) Amount at the end of Compound interest is $303264, 5) Difference in the amount of simple and compound interest is $ 1664.
Here it is given:
Principle (P) =$ 260000
Time(t) = 2 years
Rate (R) = 8%
1) We have to find the simple interest:
Simple interest(SI) = P× t × R/ 100
= 260000× 2× 8/ 100
= $41600
2) We have to find Compound Interest
Compound interest(CI) =P( 1 + R/100[tex])^{t}[/tex]- P
= 260000( 1 + 8/100[tex])^{2}[/tex]- 260000
= 260000( 27/25[tex])^{2}[/tex] - 260000
= 303264 - 260000
= $43264
3) Amount at the end of simple interest
Amount = P + SI
= 260000 + 41600
=$301600
4) Amount at the end of compound interest
Amount = P + CI
= 260000+ 43264
= $303264
5) Difference between the amount at simple interest and compound interest
Difference = 303264 - 301600
= $1664
Therefore the simple interest is $41600, the compound interest is $43264, the Amount at the end of simple interest is $ 301600, the amount at the end of the compound interest is $303264, and the difference in the amount of simple interest and compound interest is $1664.
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Jumpin' Dolphin Boat Tours takes tourists into the Gulf of Mexico to see dolphins. Tourists buy tickets and pay extra for tour pictures. The total price for t tickets and p pictures is 10t+5p dollars. The Kelley family went on a tour this afternoon. They bought 4 tickets and 3 pictures.
What was the total cost of the Kelley family's tour?
If Kelley family went on a tour this afternoon and they bought 4 tickets and 3 pictures. The total cost of the Kelley family's tour is $55.
How to find the total cost?Given data
Total price = 10t+5p dollars
Where:
t = tickets =4
p = pictures = 3
Now let find the total cost
Total cost = 10t+5p
Total cost = 10(4) + 5(3)
Total cost =40 +15
Total cost =$55
Therefore we can conclude that the total cost is the amount of $55.
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<
>
<
In the following diagram, BC is parallel to DE.
What is the measure of Zx?
Angles are not necessarily drawn to scale.
B
D
F
54°
105°
A
E
And please explain how I get the answer pls
The value of Angle DAF, x is 21°
Given,
Line BC parallel to line DE
The value of Angle ABC = 54°
The value of Angle BAC = 105°
We have to find the value of angle DAF
Here,
Angle DAF = x
Now,
Angle ABC = Angle DAB (Alternate interior angles)
So,
Angle DAB = 54°
Then,
Angle DAF, x = 180 - (105 + 54) (Linear pair of angles)
Linear Pair of Angles;
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
That is,
Angle DAF, x = 180 - 159
Angle DAF, x = 21°
Therefore,
The value of Angle DAF, x is 21°
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Determine whether each statement is always, sometimes, or never true.
13. For a 0, the value of a¹ is positive. ●
14. If n is an integer, then 3" 3" equals 1.
15. If 6P 0, then p > 0. 16. 4* equals 1. 4*
17. If m is an integer, then the value of 2m is negative
Problem 13
Answer: Sometimes trueReason:
If a > 0, then the statement would always be true. However, if 'a' was negative, then the statement is false.
For example, if a = -2 then:
[tex]a^{-1} = (-2)^{-1} = \frac{1}{(-2)^1} = -\frac{1}{2} = -0.5[/tex]
In short,
[tex]a^{-1} = -0.5 \ \ \text{ when } a = -2[/tex]
This is one of infinitely many counter-examples to prove the original statement isn't always true.
===================================================
Problem 14
Answer: Always trueReason:
The rule to use here is [tex]a^b*a^c = a^{b+c}[/tex]
We add exponents b and c, while the base 'a' stays the same the whole time.
In this problem we have: [tex]3^n*3^{-n} = 3^{n+(-n)} = 3^{n-n} = 3^0 = 1[/tex]
Therefore [tex]3^n*3^{-n} = 1[/tex] is always true regardless of what you replace n with. The variable n doesn't have to be an integer.
===================================================
Problem 15
Answer: Sometimes trueReason:
Let's say p = -1 is plugged into the expression
[tex]6^p = 6^{-1} = \frac{1}{6^1} = \frac{1}{6} \approx 0.1667[/tex]
which is a positive outcome showing that [tex]6^p > 0[/tex] doesn't automatically guarantee that p > 0. Feel free to try other negative values as counter-examples. Also p = 0 works as well. It turns out that [tex]6^p[/tex] is always positive regardless of what real number you use for p.
===================================================
Problem 16
Answer: Always trueReason:
The rule used here is [tex]a^{-b} = \frac{1}{a^b}[/tex]
An equivalent rule is [tex]\left(\frac{a}{b}\right)^{-c} = \left(\frac{b}{a}\right)^c[/tex]
The idea is to flip the fraction to turn the exponent positive.
Examples: [tex]2^{-5} = \frac{1}{2^5} \ \ \text{ and } \ \ \left(\frac{7}{9}\right)^{-3} = \left(\frac{9}{7}\right)^{3}[/tex]
===================================================
Problem 17
Answer: Never trueReason:
This is similar to problem 15 in that [tex]2^m[/tex] is always positive regardless if m is negative, zero, or positive. It might help to graph out [tex]y = 2^x[/tex] and see that the curve never dips below the x axis.
46 ---> ? ---> ? = 460
complete this function machine by usin two of the functions shown below
a) times by a 100 b) divide by 10 c) times by 10,000 d) divide by 1000 e) times by 10
f) times by a thousand
Answer:
e)times by 10
Step-by-step explanation:
collects like term
?=x
x=460÷46
=10
Lucy's penny bank is 2/3 full. After she removes 120 pennies it's 1/2 full.How many pennies can Lucy's bank hold
Answer:
Her piggy bank can hold 720 pennies.
Step-by-step explanation:
1/2= 3/6, and 2/3=4/6, meaning the difference of 1/6=120 pennies. 120x6=720.
help for the rest pls
Answer :
9 girls and 18 boys don't have a voucher
Step-by-step explanation :
There are 38 boys and 22 girls. The total number of children is 60. We know that 33 children have a voucher. 27 children don't have a voucher. ( 60 - 33 = 27 ) .
"Twice as many boys as girls do not have a voucher."
We can now make an equation.
The girls who do not have a voucher will be x, boys who don't have a voucher will be 2x, since it says twice as many boys.
We can now make our equation.
x + 2x = 27
Add x and 2x
3x = 27
Divide both sides by 3
x = 9
We know now that girls who don't have a voucher is 9.
The boys who don't have a voucher is 2x, so we plug 9 instead of x.
2(9) = 18.
18 boys do not have a voucher.
If you would like the rest for the frequency tree...
Total students : 60
Boys : 38
Boys who don't have a voucher : 18
Boys who have a voucher : 20
Girls : 22
Girls who don't have a voucher : 9
Girls who have a voucher : 13
Hope this helped.
The scatter plot shows the number of strawberries that have been picked on the farm during the month of February
1001
Number of Strawberries
116ITTIS ITT2TTAS
Days in February
Part A: Using computer software, a correlation coefficient of r= 0. 01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why
or why not? (5 points)
Part B. Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for
strawberries picked on the farm. (5 points)
Part A:because the data points are far away from each other.
Part B: A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.
What is Correlation Coefficient?
Correlation coefficient, r, is quantitative measure that measures the extent to which two variables are associated.
The closer the data points are on a scatter plot, the closer the value of r is to 1 or -1.
Part A:
The data points in the scatter plot are farther apart and the trend slopes upwards to the right, this means that the correlation coefficient, r, would be positive but very low.
Thus, based on the scatter plot given, the correlation coefficient of r = 0.01 is most likely accurate because the data points are far away from each other.
Part B:
A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.
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Explain how the function y=-1/3|x+2|+5 is transformed from the original function of y=-1/3|x|.
The original function of y = -1/3|x| was translated 2 units to the right and 5 units up.
The types of transformation.In Mathematics, there are four (4) main types of transformation and these include the following:
DilationRotationReflectionTranslationWhat is a translation?In Mathematics, the translation of a geometric figure (shape) to the right simply means adding a digit to the numerical value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure (shape) that is translated up simply means adding a digit to the numerical value on the y-coordinate (y-axis) of the pre-image.
In this scenario, the original function was shifted 2 units to the right and then shifted 5 units up to produce the new function as follows:
Original function (x, y) → New function (x + 2, y + 5)
y = -1/3|x| → y = -1/3|x + 2| + 5
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victor, a student at um, conducted a similar survey among undergraduate students at the university of michigan using a random sample of the same size from the study conducted at cornell university and obtained the same sample proportion. the undergraduate student body at the university of michigan is almost twice as large as the undergraduate student body at cornell university. victor is concerned that the computation of the margin of error for a confidence interval for the population proportion will be affected by the population size. do you agree with victor's concern?
Yes, Victor needs to have similar portion of the population in the sample.
What is population size?
The number of objects inside a geographical area that has been arbitrary assigned as the population size.
In a fair, unbiased poll
Population proportion plus random error equals sample proportion.
According to the Normal Approximation, the standard deviation of the distribution of these random mistakes across all feasible samples is
[tex]\sqrt{\frac{\text{Population proportion}(1-\text{Population proportion})}{n}}[/tex]
The sample estimate's variance from the actual population value is known as the random error. Numerous alternative summaries, such as sample averages or discrepancies between two sample proportions or averages, are likewise consistent with the observation that random mistakes follow the normal curve.
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2^(x+3) = ((1)/(8))^(x+2) solve for x
step by step exlanation
Darren is building a fence using panels that are sold in 5ft lengths. The perimeter of the fence is 42yds. How many fence panels should Darren buy?
Answer:
6666667
Step-by-step explanation:
PLEASE HELP
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In one study of burmese pythons it took a snake an a stage of 25/4 days to gain 1/8 of weight. at that rate how long does it take a snake to gain 1 pound?
At the rate of variation of 50 days/pound the snake gain 1 pound.
The mathematical expression for the percentage difference change over a predetermined period is called the rate of variation, which also denotes the movement of a variable. It allows us to understand how 2 factors that are changing interact with one another.
A snake takes 25 ÷ 4 days to gain 1 ÷ 8 pounds of weight,
a) Gain 1 pound need take: (25 ÷ 4) × 8 = 50 days
b) In one year = 365 days
= (25 ÷ 4) × (1 ÷ 8)
= (25 ÷ 4) × 8
= 50 days/pound.
So, the snake gained(1 ÷ 50) pounds one day.
In one year: (1 ÷ 50) × 365 = 7.3 pound
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Match the vocabulary word with the correct definition.
Base
Exponent
Scientific Notation
a.
The number that is going to be raised to a power.
b.
The number that tells you how many times you will multiply the base number.
c.
A way of writing VERY large or VERY small numbers so the numbers are easier to compare or calculate.
Answer:
Exponent: B
Base: A
Scientific Notation: C
Step-by-step explanation:
vocabulary
Answer:
Exponent and A
Base and B
Scientific Notation and C
Step-by-step explanation:
Because the Exponent is the number that is going to raise the Base and that Base is the number that you are going to multiply by.
How do I find the missing angle of an intersecting line?
Answer:
Read the given problem, look at the given figure of intersecting lines, and identify the angle given and the unknown angles.
Step-by-step explanation:
At the bowling alley kai rented shoes and purchased 3 games of bowling for $6.50.
Jack rented shoes and purchases 5 games of bowling for $9.50 Caelan has $17 if she rents shoes how many games of bowling can she purchase
Caelan must spend a total cost of $ 17 for 10 bowling games.
How many bowling games can Caelan purchase?
The total cost consists in the sum of a fixed cost, represented by rent of shoes, and a variable cost, represented by the number of bowling games, whose model is presented below:
c' = c + r · n
Where:
c - Fixed cost, in monetary units.r - Cost of each rent, in monetary units.n - Number of rented games.First, construct the system of equations related to Kai and Jack:
Kai
c + 3 · r = 6.50
Jack
c + 5 · r = 9.50
Second, solve the system of linear equations by numerical methods:
(c, r) = (2, 1.5)
Third, write the resulting function:
c' = 2 + 1.5 · n
Fourth, evaluate the function for the situation of Caelan:
17 = 2 + 1.5 · n
1.5 · n = 15
n = 10
Caelan rents 10 bowling games for $ 17.
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Find the value of n+p-2q when n=p=q
The value of expression n + p - 2q when n = p = q is 0
In this question, we have been given an expression n+p-2q
We need to find the value of given expression when n=p=q
Consider given expression,
n + p - 2q
Substitute n = p
= p + p - 2q
= 2p - 2q
Now we substitute p = q in above expression,
= 2q - 2q
= 0
Therefore, the value of expression n + p - 2q when n = p = q is 0
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Solve the equation A=s^2 for s. Assume s>0 answer in form s=….
For the equation A=s² for s. Assume s > 0, then s = [tex]\sqrt{A}[/tex].
What are squares and square roots?
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.
For the given equation, A = s², we have to find the value of s.
thus, taking the square root on both sides, we get
s = [tex]\sqrt{A}[/tex].
Hence, the value of s = [tex]\sqrt{A}[/tex].
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Determine the values of A, B, and C when y – 7=3(x+4) is written in standard form, Ax+By=C.
Answer:
A=-3,b=1,C=19
Step-by-step explanation:
y-7=3(x+4)
we will just simplify the bracket like this
y-7=3x+12
y=3x+12+7
y=3x+19
y-3x=19
A=-3,b=1,C=19
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1) 2 more than 5 times x
2) 9 Multiply n by 6, and then divide the product by 5.
Answer:
1. 5x +2
2. 6x/5
Step-by-step explanation: