Answers
Using translation concepts, it is found that:
a.
The equation is: y = -1.5(x + 4)² + 9.The domain is all real values.The range is y ≤ 9.b.
The rule is [tex]y = -\sqrt{x + 5} + 10[/tex].The domain is x ≥ -5.The range is y ≤ 10.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Quadratic functionThe quadratic function has vertex at (-4,-6), hence:
y = a(x + 4)² - 6
When x = -6, y = 0, hence we use it to find a as follows:
0 = 4a - 6
a = 1.5.
Hence the function is:
y = 1.5(x + 4)² - 6.
When it is reflected over the x-axis, we have that:
y -> -y.
Hence:
y = -1.5(x + 4)² + 6.
When it is moved up 3 units, we have that y -> y + 3, hence:
y = -1.5(x + 4)² + 9.
The function is defined for all real values, assuming values from negative infinity to 9, hence:
The equation is: y = -1.5(x + 4)² + 9.The domain is all real values.The range is y ≤ 9.Square root functionThe parent square root function is given by:
[tex]y = \sqrt{x}[/tex]
From the graph, it is found that:
The function was reflected over the x-axis, hence y -> -y.The function was shifted one unit to right, hence x -> x - 1.The function was shifted two units up, hence y -> y + 2.Hence the rule is:
[tex]y = -\sqrt{x - 1} + 2[/tex]
The translations given by the item are:
6 units left, hence x -> x + 6.8 units up, hence y -> y + 8.Thus:
[tex]y = -\sqrt{x + 5} + 10[/tex]
Then the function will be defined for values of -5 and greater, assuming values of 10 and less, hence:
The rule is [tex]y = -\sqrt{x + 5} + 10[/tex].The domain is x ≥ -5.The range is y ≤ 10.More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
Related Questions
Make sense of problems. Determine the number , and explain how you came up with he solution
Answers
Answer:
5
Step-by-step explanation:
because 5x3=15
15 + 5 = 20
Answer:
5
Step-by-step explanation:
work backwards. Start with 20. minus 5 equals 15. Divide by 3 is 5.
double-check by going the other way.
5x3=15
15+5=20
-12 < 7x + 9 < 16
What is the solution?
Answers
-3 < x < 1
Answer:
-3<x<1
(-3,1)
Step-by-step explanation:
subtract 9 to all 3 sides to get -21<7x<7divide by 7 on all 3 sides to get -3<x<1it is shown as (-3,1) because x is anything inbetween -3 and 1 and those numbers are not included so you use ( ) as opposed to [ ]
A basketball player makes 7/10 free throws. Based on her results, how many of her next 40 free throws will she not make
Answers
Answer: 12 free throws
Step-by-step explanation:
40 * 7/10=
280/10=28 free throws made
40-28=12 free throws missed
write the number in two other forms (fraction, decimals, or percent 19/20 9/16 0.4 0.22
Answers
Answer:
Hope this helps :)
19/20 = 95/100 = 95%
9/16 = 0.5625 = 56.25%
0.4 = 4/10 → 40/100 = 40%
0.22 = 22/100 = 22%
In a restaurant there are 7 starter dishes, 14 main dishes and 9 desserts. phil is going to choose one of the combinations for his meal. a starter dish and a main dish, a main dish and dessert, a starter dish, main dish and dessert dish. how many different ways are there for him to choose the meal.
Answers
There are 1106 different ways for him to choose the meal.
For given question,
In a restaurant there are 7 starter dishes, 14 main dishes and 9 desserts.
The possibilities of selecting a starter = 7
The possibilities of selecting a main dish = 14
The possibilities of selecting a dessert = 9
The meal combinations are: a starter dish and a main dish; a main dish and dessert; a starter dish, main dish and dessert dish.
The possibility of selecting each meal combinations would be,
1) a starter dish and a main dish = 7 × 14
= 98
2) a main dish and dessert = 14 × 9
= 126
3) a starter dish, main dish and dessert dish
= 7 × 9 × 14
= 882
We need to find the total number of different ways to choose the meal.
= 98 + 126 + 882
= 1106
Therefore, there are 1106 different ways for him to choose the meal.
Learn more about different possibilities here:
https://brainly.com/question/14833898
#SPJ4
Please Please help asap!!! Thank you
Answers
Step-by-step explanation:
well, the starting equation and the target format have been given.
let's do the multiplications and compare the target with the starting information.
from there we see what is different or missing.
x² + 14x + 13 = 0
and
(x - p)² = q
x² - 2px + p² = q
x² - 2px + (p² - q) = 0
now let's compare the different parts :
x² = x²
-2px = 14x
-2p = 14
p = -7
p² - q = 13
-7² - q = 13
49 - q = 13
36 - q = 0
q = 36
so, the square (x - p)² = (x + 7)² is completed when
x² + 14x + 49 = 0
but we have only "+ 13". so we need to add 36 to get 49. but we need to do it on both sides, to keep the equation true :
x² + 14x + 13 + 36 = 36
x² + 14x + 49 = 36
(x + 7)² = 36
just as we calculated already above.
and now this can be solved by pulling the square root on both sides (a quadratic equation has always 2 solutions)
x + 7 = ±6
x1 = 6 - 7 = -1
x2 = -6 - 7 = -13
Kurt organized a bike race that was 84 miles long. All 469 riders completed the race. How many miles were biked in all?
Answers
Kurt organized a bike race that was 84 miles long. All 469 riders completed the race. 39,396 miles were biked in all
Kurt organized a bike race = 84 miles long
All 469 riders completed the race
miles were biked in all :
Total miles =84 Multiply By 469
=39,396 miles
39,396 miles were biked in all
Miles :
A mile is a unit of distance equal to 1760 yards or approximately 1.6 kilometers
Learn more about Speed- Distance Problems: brainly.com/question/23245414
#SPJ1
A 84-mile cycling race that Kurt planned took place. The race was completed by all 469 cyclists. All told, 39,396 miles were pedaled
Kurt planned an 84-mile cycling race.
The race was completed by all 469 cyclists.
total number of miles cycled:
Miles total = 84; multiply by 469.
=39,396 miles
All told, 39,396 miles were pedaled
Miles:
Approximately 1.6 kilometers or 1760 yards make up a mile as a unit of measurement.
An interior designer charges $80 to visit a site, plus $65 to design each room. Identify a function that represents
the total amount he charges for designing a certain number of rooms. What is the value of the function for an
input of 5, and what does it represent?
Answers
The function that represents the total amount he charges is y = 80 + 65x and the total amount he charges for designing 5 rooms is $405
Identify a function that represents the total amount he charges for designing a certain number of roomsThe given parameters are
Charge = $80
Rate = $65 per design
The function is then calculated as
y = Charge + Rate * x
Where
y represents the total amount
x represents the number of rooms
So, we have
y = 80 + 65x
What is the value of the function for an input of 5, and what does it represent?Here, we have
x = 5
So, we have
y = 80 + 65 x 5
Evaluate
y = 405
Hence, the total amount he charges for designing 5 rooms is $405
Read more about linear functions at
https://brainly.com/question/15602982
#SPJ1
ayuda por favor no le entiendo
Answers
la 2. es multiplicand 20 por 18 da 360 y ese número se multiplicand por 500 da 180000 . 3se suma y da 1025 la.4 se reparte en 9625 a cada amigo
Mathematicians use multiplicand to calculate the merchandise of two or more numbers. it's a fundamental operation in mathematics that is frequently utilized in everyday life. once we need to combine groups of similar sizes, we utilize multiplicand. On this page, let's study more about multiplicand.
The fundamental concept of repeatedly adding the same number is represented by the process of the multiplicand. The results of multiplying two or more numbers are referred to as the product of those numbers, and therefore the factors that are multiplicand are referred to as the factors. Repeated addition of the identification number is made easier by multiplying the numbers.
To learn more about multiplicand from the given link:
brainly.com/question/24291636
#SPJ9
BRO ILL GIVE U 100 POINTS BRO PLEASE
The local gym holds two 45-minute workout sessions and four 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?
Answers
Answer:
170 minutes
Step-by-step explanation:
Weekly gym sessions:
Two 45-minute workout sessions.Four 30-minutes sessions.Therefore, the total time for all sessions is:
[tex]\begin{aligned}\implies \sf Total\:time & = \sf 2 \times 45 + 4 \times 30\\& = \sf 90 + 120 \\& = \sf 210 \:\:minutes\end{aligned}[/tex]
If Judy attended all sessions, yet
left 10 minutes early during the 45-minute sessions, andleft 5 minutes early during the 30-minute sessions.[tex]\begin{aligned}\implies \sf Total\:time\:Judy\:lost& = \sf 2 \times 10 + 4 \times 5\\& = \sf 20 + 20 \\& = \sf 40\:\:minutes\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies \sf Total\:time\:Judy\:worked\:out & = \textsf{Total time of sessions}-\textsf{Total time Judy lost}\\& = \sf 210-40\\& = \sf 170\:\:minutes\end{aligned}[/tex]
So Judy worked out for a total of 170 minutes for the week
A blank number is a whole number greater than 1 that has more than two factors
Answers
A composite number is a whole number greater than 1 that has more than two factors
Given,
The conditions,
The number is a whole number greater then 1.Its has more than two factorsWe know, composite number is a number that has more than 2 factors
Prime number is a number that has two factors, one and itself.
Here, number is a whole number greater than 1 that has more than two factors
So, the given number is composite number
Hence, a composite number is a whole number greater than 1 that has more than two factors
Learn more about composite number here
brainly.com/question/28199758
#SPJ4
Hola, everyone! Zay here <3 just to make sure you are correct if you answer this question make sure you have an explanation , and a good one with that.
ex; you took the test and have proof you took it.
ex; explaining how you got your answer
also if you happen to need this "⎯⎯" you can just copy paste that and put it in the answer
that's all, thanks for reading this :D
Answers
Answer: $5.25
Step-by-step explanation:
Brianna bought 1 3/4 pounds of cheese
Each pound cost $3.00
1 3/4 x $3
Turn this into an improper fraction, you get 7/4
7/4 x $3
$21 over 4
Do the division, you get $5.25
Answer:
Step-by-step explanation:
1 pound price= 3 dollars
Then she has to pay= (7/4)*3 = 5.25 dollars
Given △XYZ with vertices X(2, 4), Y(6, 0), and Z(7, 2) what is its image after the composition
Translation: (x, y) → (x + 12, y + 4)
Translation: (x, y) → (x − 5, y − 9)
Answers
The image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)
How to determine the image after the composition?The vertices of the triangle are given as:
X(2, 4), Y(6, 0), and Z(7, 2)
The compositions of translations are given as:
Translation: (x, y) → (x + 12, y + 4)
Translation: (x, y) → (x − 5, y − 9)
So, we have:
Translation: (x, y) → (x + 12, y + 4)
X'(2 + 12, 4 +4), Y'(6 + 12, 0 + 4), and Z'(7 + 12, 2 + 4)
Evaluate
X'(14, 8), Y'(18, 4), and Z'(19, 6)
Translation: (x, y) → (x − 5, y − 9)
X''(14 - 5, 8 - 9), Y'(18 - 5, 4 - 9), and Z'(19 - 5, 6 - 9)
Evaluate
X''(9, -1), Y'(13, -5), and Z''(14, -3)
Hence, the image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)
Read more about transformation at:
https://brainly.com/question/4289712
#SPJ1
Eight friends went to the movies. Each ticket cost $6.75. How much did the tickets cost all together?
Answers
Answer:
$54
Step-by-step explanation:
6.75*8=54
Answer:54
Step-by-step explanation:8x6.75=54
A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top. The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a volume of 11,475(3.14) ft cubed
Answers
The height of the silo is 56 feet.
Here, we are given that a large grain silo is to be constructed in the shape of a circular cylinder.
The diameter of the silo = 30 feet
⇒ The radius of the cylinder = 15 feet
and also the radius of the hemisphere = 15 feet
The volume of a hemisphere = 2πr^3/3
Volume = 2 × π × 15 × 15 × 15 × 1/3
Volume of cube = 2250π
Thus, the volume of cylinder = volume of the silo - volume of the hemisphere
= 11,475(3.14) - 2250π
π = 3.14
⇒ 11,475(3.14) - 2250(3.14)
3.14 (11,475 - 2250)
= 3.14 (9225)
= 9225π
Now, the volume of cylinder = πr^2h
Thus, 9225π = π(15) (15) h
9225π/ 225π = h
h = 9225/225
h = 41
Thus, the height of the cylinder = 41
The height of the silo will be the height of hemisphere + height of the cylinder = 15 + 41 = 56 feet.
Learn more about volume here-
https://brainly.in/question/15637217
#SPJ9
Simplify the radical expression ∛81x^7y^9z^5. Show your work! Show the step-by-step process on how you got your answer so I can understand how to do it. Brainliest to the best answer that shows all steps!!
Answers
The simplified radical expression for this problem is given by:
[tex]3x^2y^3z\sqrt[3]{3xz^2}[/tex]
How to simplify the given radical expression?To simplify the given radical expression, we divide all the exponents by 3, and the ones that can be simplified are placed outside the root, multiplying.
Looking at each term, we have that:
81 is equivalent to 3^4, hence [tex]\sqrt[3]{81} = \sqrt[3]{3^4} = 3\sqrt[3]{3}[/tex], as 4 divided by 3 has quotient 1 and remainder 1.For x^7, we have that 7 divided by 3 has quotient 2 and remainder 1, hence [tex]\sqrt[3]{x^7} = x^2\sqrt[3]{x}[/tex].For y^9, we have that 9 divided by 3 has quotient 3, hence [tex]\sqrt[3]{y^9} = y^3[/tex]For z^5, we have that 5 divided by 3 has quotient 1 and remainder 2, hence [tex]\sqrt[3]{z^5} = z\sqrt[3]{z^2}[/tex].Thus, the simplified radical is given by:
[tex]3 \times \sqrt[3]{3} \times x^2 \times \sqrt[3]{x} \times y^3 \times z \times \sqrt[3]{z^2}[/tex]
[tex]3x^2y^3z\sqrt[3]{3xz^2}[/tex]
More can be learned about simplified radical expressions at https://brainly.com/question/738531
#SPJ1
Loudres plans to jog at least 1.5 miles. write and solve an inequality to find x, the number of hours lopudres bwill have to jog.
Answers
The number of hours lopudres will have to jog is .4 hours.
Lord wants to run at least 1.5 miles, and her pace is shown in the picture as 3.75 miles per hour, and the question asks us to construct an inequality expressing x for the amount of hours she would have to run. To meet this inequality, we'll need to apply how quickly or how many miles she wants to cover with how fast she's going to run, so we'll divide 1.5 miles by her rate of 3.75 miles per hour, and when you divide you'll get a number of hours, which comes out to 0.4 hours.
To learn more about inequality from the given link:
https://brainly.com/question/20383699
#SPJ9
-15X(-3) please help
Answers
Answer:
45x
Hope this helps :)
Step-by-step explanation:
- 15x (- 3) = 45 x
Please help with problem 26
Answers
Answer:
Step-by-step explanation:
Please help me find the rule of this linear function:
x-intercept: (-3.667,0)
y-intercept: (0,5.5)
Answers
Step-by-step explanation:
what do you mean by "rule" ?
the line equation (in slope-intercept form ? or any other ?) ?
or only the slope of the line ?
I assume you need the slope-intercept line equation.
this looks like
y = ax + b
"a" is the slope of the line, "b" is the y-intercept (the y value when x = 0).
"b" we know already from the specified intercept points : 5.5
the slope of a line is simply the ratio
(y coordinate change / x coordinate change)
when going from one point on the line to another.
and the axis-intercept points are points on the line too. so, we can use them.
so, we see
x changes by +3.667
(= 3 2/3 = 3×3/3 + 2/3 = (3×3 + 2)/3 = 11/3)
from -3.667 to 0.
y changes by +5.5
(= 5 1/2 = 5×2/2 + 1/2 = (5×2 + 1)/2 = 11/2)
from 0 to 5.5
the slope is therefore
5.5 / 3.667 = 11/2 / 11/3 = 11/2 × 3/11 = 3×11 / 2×11 = 3/2
and so, the line equation is
y = 3/2 x + 5.5
or
y = 3/2 x + 11/2 = 1/2 × (3x + 11)
Arne and Falk are playing Rock, Paper, Scissors. Arne has won 5/8 of the total number of games, g, they
have played. Falk has won 1/4 of the games which is 6 less than Arne. How many total games did they
play?
Answers
Answer:
They have played 14 games
Step-by-step explanation:
5/8 and 2/8 is 7/8 of the time, but if 3/8 is 6 then 1/8 is 2, 2*7 is 14
Which equation is true if b = 2?
2b + 24 = 30
3b - 2 = 4
B + 4 = 8
2b - 3 = 0
Answers
Answer:
2nd equation is correct.
Step-by-step explanation:
1) 2b + 24 = 30
→ 2(2) + 24 = 30
→ 4 + 24 = 30
→ 28 ≠ 30
Hence, it is false.
2) 3b - 2 = 4
→ 3(2) - 2 = 4
→ 6 - 2 = 4
→ 4 = 4
Hence, it is true.
3) B + 4 = 8
→ 2 + 4 = 8
→ 6 ≠ 8
Hence, it is false.
4) 2b - 3 = 0
→ 2(2) - 3 = 0
→ 4 - 3 = 0
→ 1 ≠ 0
Hence, it is false.
Use the formula for arc length to find the value of the unknown quantity.
s=rθ
Answers
The unknown quantity which is the radius has a length of 49752/π yards.
How to find arc length?The formula for the length of arc is;
S = rθ
where;
r is radius
θ is the central angle in radians
Now, we are given;
θ = 3π/4
S = 4146 * 9 yards
Thus, making r the subject and solving gives;
r = S/θ
r = (4146 * 9)/(3π/4)
r = 49752/π
Thus, the unknown quantity which is the radius has a length of 49752/π yards.
Read more about Arc Length at; https://brainly.com/question/2005046
#SPJ1
if x is a positive integer, for how many different values of x is startroot startfraction 48 over x endfraction endroot a whole number?236
Answers
There are 3 whole number with different values of x.
What is a whole number?
All positive integers from 0 to infinity are included in the group of numbers known as whole numbers. The number line has these numbers. They are all genuine numbers as a result. Although not all real numbers are whole numbers, we may argue that all whole numbers are real numbers. As a result, the set of natural numbers plus zero may be used to define whole numbers. The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0. Natural numbers, whole numbers, integers, and fractions all fall under the category of real numbers.
Whole numbers refer to all natural numbers, including '0,' in their entirety. Examples include: 0, 11,1,2,3,4 etc
As stated in the question,
Accordingly, "x" is a positive integer. In order for the value of [tex]\sqrt{\frac{48}{x} }[/tex]to be a whole number, we must determine how many alternative values there are for the variable "x".Then, in order to determine which values of "x" the given fraction is a square for, we must first locate them.
We are aware that the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Now, from the above factors of 48 only (3,12 & 48) of can give us a square number.
Therefore,
If x is 3 then [tex]\sqrt{\frac{48}{3} }[/tex]=[tex]\sqrt{16}[/tex]=4If x is 12 then[tex]\sqrt{\frac{48}{12} }[/tex]=[tex]\sqrt{4}[/tex]=2If x is 48 then[tex]\sqrt{\frac{48}{48} }[/tex]=[tex]\sqrt{1}[/tex]=1Hence, There are 3 whole number with different values of x.
To learn more about whole number , visit:
https://brainly.com/question/28281521
#SPJ4
rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. (1 point) three to the one third power all over three to the one sixth power
Answers
The expression with rational exponents as a radical expression by extending the properties of integer exponents is, [tex]\sqrt[6]{3}[/tex]
Define exponents for integers?The exponents that should be integers are those that are. It may be an integer that is either positive or negative. It specifies how many times the base number should be multiplied by itself using positive integer exponents.
Given:
The given expression is,
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6} } }[/tex]
We know that,
[tex]\frac{x^{a} }{x^{b}}= x^{a-b}[/tex]
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}} = 3^{\frac{1}{3}-\frac{1}{6}}[/tex]
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}=3^{\frac{1}{6} }[/tex]
Therefore,
[tex]\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}=\sqrt[6]{3}[/tex]
To learn more about Integer exponents, visit:
https://brainly.com/question/12389529
#SPJ4
what are the two next numbers in this sequence.
12,14,18,26,42, ,
Answers
Answer:
74 , 138
Step-by-step explanation:
12 + 2 = 14
14 + 4 = 18
18 + 8 = 26
26+16 = 42
42+32= 74
74+64 =138
please make my answer as brainelist
Kinsley bought 8.01 ounces of chocolate. 3.89 ounces of it was milk chocolate and the
rest was dark chocolate. How much dark chocolate did Kinsley buy?
Answers
Answer:
4.12
Step-by-step explanation:
Using the chart in problem 1, what is the least place value of 0.24
Answers
Answer:
The thousandths place.
Step-by-step explanation:
4 is furthest away from the decimal on the right side and it is in the thousandths place.
Diven that 4x^3+x^(5/2) all over √x can be written in the form 4x^a+x^b, write down the value of a and the value of b
Answers
The value of a and the value of b is 6 and 5.
We can solve this problem by few steps, If we change the representation of power by replacing all powers according to √x or [tex] {x}^{1/2} [/tex]. We know that, [tex] {x}^{m/n × n/b } = {x}^{m/b} [/tex]
So, using this we can write, [tex] {4x}^{1/2 \times 6} + {x}^{1/2 \times 10/2} = {4 \sqrt{x} }^{6} + { \sqrt{x} }^{5} [/tex]..............(1)
Now if we compare the value of ( 1 ) with
[tex] {4 \sqrt{x} }^{a} + { \sqrt{x} }^{b} [/tex], we can easily find out the value of a and b and it is, a = 6 and b = 5
Thus, the value of a and b is 6 and 5.
To know more about the fraction -
https://brainly.com/question/17220365
#SPJ4
The complete question is -
Driven that 4x^ 3+x^ (5/2) all over √x can be written in the form 4√x^a+√x^ b, write down the value of a and the value of b.
Transformation that result in a change in the size of a figure are called ____.
Answers
Answer:
Transformation that result in a change in the size of a figure are called dilations.