ANSWER
[tex]f(x) = 4 {(x - 7)}^{2} - 19[/tex]
EXPLANATION
The given equation is
[tex]g(x) = 4 {x}^{2} - 16[/tex]
If the equation is shifted 7 units to the right and 3 units down, then the new equation becomes.
[tex]f(x) = g(x - 7) - 3[/tex]
This implies that,
[tex]f(x) = 4 {(x - 7)}^{2} - 16 - 3[/tex]
The required equation is
[tex]f(x) = 4 {(x - 7)}^{2} - 19[/tex]
Mr Gan has fewer than 20 candies.He wants to pack them into plastic bags.If he packs 3 candies in each bag,he will have 4 extra candies left over.If he packs 5 candies in each bag,he will be short of 2 candies.How many candies does he have?
Answer:
y = 13
Step-by-step explanation:
If Mr Gan packs 3 candies in each bag, he will have 4 extra candies left over. Therefore
3x + 4 = y
where 'x' represents the number of bags, and 'y' the total number of candies he has.
If Mr. Gan packs 5 candies in each bag, he will be short of 2 candies.
5x - 2 = y
To find the number of candies he has, we need to solve the system of equations ove:
3x + 4 = 5x - 2
6 = 2x
x = 3
Now, to find 'y':
5(3) - 2 = y
y = 13
Therefore, Mr. Gan has 13 candies.
Mr. Gan could have 7, 10, 13, or 16 candies.
Explanation:Let's assume that Mr. Gan has x candies.
If he packs 3 candies in each bag, he will have 4 extra candies left over. This means that the total number of candies can be expressed as 3n + 4, where n is the number of bags. Since we know that Mr. Gan has fewer than 20 candies, we can set up the inequality:
3n + 4 < 20
Solving this inequality, we find that n < 5.
If he packs 5 candies in each bag, he will be short of 2 candies. This means that the total number of candies can be expressed as 5m - 2, where m is the number of bags. Using the same reasoning, we can set up the inequality:
5m - 2 < 20
Solving this inequality, we find that m < 4.
Combining the two inequalities, we know that n < 5 and m < 4. Since n and m represent the number of bags, they must be positive integers. So the possible values for n are 1, 2, 3, and 4, and the possible values for m are 1, 2, and 3.
If we substitute these values into the equations, we can find the corresponding number of candies:
If n = 1, then 3n + 4 = 7 candies.
If n = 2, then 3n + 4 = 10 candies.
If n = 3, then 3n + 4 = 13 candies.
If n = 4, then 3n + 4 = 16 candies.
If m = 1, then 5m - 2 = 3 candies.
If m = 2, then 5m - 2 = 8 candies.
If m = 3, then 5m - 2 = 13 candies.
Since Mr. Gan has fewer than 20 candies, the only possible values for the number of candies he has are 7, 10, 13, and 16.
Kaylee cut half of a loaf of bread into four equal parts. What fraction of the whole loaf does each of the four parts represent?
1 whole divided by 4 parts is the same as saying each part is 1/4 or 25% of the whole.
Which of the following shows the table representation of the exponential function f(x)=5*2^x
0-5
1-7
2-9
3-11
0-1
1-10
2-100
3-1000
0-10
1-20
2-40
3-60
0-5
1-10
2-20
3-40
Answer:
The correct option is 4.
Step-by-step explanation:
The given function is
[tex]f(x)=5(2)^x[/tex]
Put x=0,
[tex]f(0)=5(2)^0=5\times 1=5[/tex]
Put x=1,
[tex]f(1)=5(2)^1=5\times 2=10[/tex]
Put x=2,
[tex]f(2)=5(2)^2=5\times 4=20[/tex]
Put x=3,
[tex]f(3)=5(2)^3=5\times 8=40[/tex]
Only table 4 represents the correct value of the given function, therefore the correct option is 4.
The table representation of the exponential function f(x)=5*2^x is: for x=0, f(x)=5; for x=1, f(x)=10; for x=2, f(x)=20; for x=3, f(x)=40.
Explanation:To find the table representation of the exponential function f(x)=5*2^x, we need to calculate the values of f(x) for different values of x. Remember, any number raised to the power of 2 is being squared, but in this case, x can be any integer, and we're multiplying the result of 2 raised to that power by 5. Here's how you calculate the first few values:
For x=0: f(0) = 5*2^0 = 5*1 = 5 For x=1: f(1) = 5*2^1 = 5*2 = 10 For x=2: f(2) = 5*2^2 = 5*4 = 20 For x=3: f(3) = 5*2^3 = 5*8 = 40
Therefore, the correct table representation of the function f(x)=5*2^x is:
0 - 5 1 - 10 2 - 20 3 - 40
What is the quotient?
Answer:
The answer is 1/9.
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Hope this helps. :D
For this case we have that by definition, any number raised to zero results in "1".
That is to say:
[tex]a ^ 0 = 1[/tex]
Then, given the following expression:
[tex]\frac {(- 3) ^ 0} {(- 3) ^ 2} = \frac {1} {(- 3) (- 3)} =[/tex]
Taking into account that:
[tex]- * - = +\\\frac {1} {(- 3) (- 3)} = \frac {1} {9}[/tex]
Answer:
[tex]\frac {1} {(- 3) (- 3)} = \frac {1} {9}[/tex]
Option c
may somebody help me please and thank you.
x^2+3x-8-2x^2+x-5
Collect Like Terms and Simplify
-x^2+4x-13
Therefore D is the correct answer
The first five multiples for the numbers 4 and 6 are shown below. Multiples of 4: 4, 8, 12, 16, 20, . . . Multiples of 6: 6, 12, 18, 24, 30, . . . What is the least common multiple of 4 and 6? 2 4 12 24
Answer:
12
Step-by-step explanation:
We are given first five multiples of 4 and 6 as shown below and we are to find their least common multiple.
Multiples of 4: 4, 8, 12, 16, 20, . . .
Multiples of 6: 6, 12, 18, 24, 30, . . .
From the given multiples, we can see that the number 12 and 24 are the common multiples which means that these numbers are multiples of both 4 and 6.
So the least common multiple will be 12.
The least common multiple (LCM) of 4 and 6 is 12. This is the smallest multiple that both numbers share.
Explanation:The least common multiple (LCM) of two numbers is the smallest number that is evenly divisible by both of those numbers. In this case, we are looking for the LCM of 4 and 6.
To find the LCM, we can list the multiples of both numbers and look for the smallest common multiple.
Multiples of 4: 4, 8, 12, 16, 20, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
From the lists, we can see that 12 is the smallest number that appears in both lists. Therefore, the LCM of 4 and 6 is 12.
So, the correct answer is 12. The LCM of 4 and 6 is 12 because it is the smallest number that is evenly divisible by both 4 and 6, as it appears in the list of multiples for both numbers.
Learn more about Least Common Multiple here:https://brainly.com/question/30060162
#SPJ6
What is the solution to this equation? 5x - 4 + 3x = 36 A. x = 5 B. x = 16 C. x = 20 D. x = 4
Let's do this in steps, show your work! | Make sure to ask questions!
#1. Simplify 5x - 4 + 3 to 8x - 4.
8x - 4 = 36.
#2. Add 4 to both sides.
8x = 36 + 4.
#3. Simplify 36 + 4 to 40.
8x = 40.
#4. Divide both sides by 8.
x = 40/8. <------ It turned into a fraction because it's easier to not divide a decimal.
#5. Simplify 40/8 to 5.
x = 5.
Therefore, x = 5.
If we know that p → q is true and p is true, what do we know about q?
a. q is false
b. q is true
c. q must be negated
d. q could be either true or false
Answer:
B
Step-by-step explanation:
If p and q are both true, then p→q is true.
If p is true, q is false, then p→q is false.
If p is false, q is true, then p→q is true.
If p and q are both false, then p→q is true.
So if you know that p→q and p are both true, then q must be true (because if q is false, then p→q must be false).
Evaluate: 5P5.
it's for permutations.
someone help pls
Answer:
120
Step-by-step explanation:
Using the definition
n[tex]P_{r}[/tex] = n! / (n - r ) !
where n! = n(n - 1)(n - 2) ....... × 3 × 2 × 1
Hence
5[tex]P_{5}[/tex] = 5! / 0! = 5! ← 0! = 1
5[tex]P_{5}[/tex] = 5! = 5 × 4 × 3 × 2 × 1 = 120
In mathematics, the permutation '5P5' equals 1 because there is exactly one way to arrange 5 items in 5 spots.
Explanation:The problem you are asked to solve involves understanding permutations, which in mathematics, is a way to calculate the number of possible arrangements of a set of items. Specifically, the permutation you are asked to evaluate is written as '5P5'.
In permutation notation, the expression 'nPn' always equals 1, because there are exactly 1 ways you can arrange 'n' items in 'n' spots.
Therefore, the solution to '5P5' is 1.
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ3
what is the area of the actual playground=_____
[tex]ft {}^{2} [/tex]
Answer:
a: 162 ft^2
Step-by-step explanation:
Lets turn the inches into feet. Every one inch is 3 feet so 3 inches is 9 feet and 6 inches is 18 feet. 9*18=162. The area of the playground is 162 ft^2
What is the probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube? Assume the number cubes are fair and have six sides. Express your answer as a fraction in simplest form.
Answer:
The probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube is 1/36
Step-by-step explanation:
There are total 6 possible outcomes of rolling a six sided fair cube. Therefore, the probability of rolling each number (1,2,3,4,5,6) is fair = 1/6
In this way,
The probability of rolling a 5 on the first number cube = p(A) = 1/6
The probability of rolling a 6 on the second number cube = p(B) = 1/6
The probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube is = p(A) * p(B) = 1/6*1/6 = 1/36
Answer:
1/36
Step-by-step explanation:
The probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube is 1/36
Step-by-step explanation:
There are total 6 possible outcomes of rolling a six sided fair cube. Therefore, the probability of rolling each number (1,2,3,4,5,6) is fair = 1/6
In this way,
The probability of rolling a 5 on the first number cube = p(A) = 1/6
The probability of rolling a 6 on the second number cube = p(B) = 1/6
The probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube is = p(A) * p(B) = 1/6*1/6 = 1/36
please answer it is math
Answer:
The maximum number of points is [tex]140\ points[/tex]
Step-by-step explanation:
we know that
Essay question represent the 10% on Mrs. Moore's English final exam
so
To find the number of points in Essay questions multiply the percent by total questions and then multiply by the value of 10 points each
[tex]10\%=10/100=0.10[/tex]
[tex]0.10*50=5\ Essay\ questions[/tex]
[tex]5*10=50\ points[/tex]
The remaining questions are
[tex]50-5=45\ questions[/tex]
To find the number of points in the remaining questions multiply the number of remaining questions by the value of 2 points each
[tex]45*2=90\ points[/tex]
therefore
The maximum number of points is
[tex]50\ points+90\ points=140\ points[/tex]
I’m very confused on how to solve this question help will be nice.
Answer:
see below
Step-by-step explanation:
Let q = number of quarters
Each quarter is worth .25
The total is 9.50
.25q = 9.50
Divide each side by .25
.25q/.25 = 9.50/.25
q =38
she has 38 quarters
Which expression is equivalent to
Answer:
1/81
Step-by-step explanation:
Remember:
b^-n = 1/b^n
Then
[(3^2)]^-2 = 1/[9^2]
1/81
Best regards
Answer:
The correct answer option is [tex]\frac { 1 } { 81 } [/tex].
Step-by-step explanation:
We are given the following expression and we are to find out whether which of the given answer options is equivalent to this expression:
[tex] ( 3 ^ 2 ) ^ { - 2 } [/tex]
We know the rule for solving the exponents:
[tex] ( b ^ n ) ^ { m } = b ^ { n \cdot m} [/tex]
This means that the exponents are multiplied with each other.
So, if we multiply them, for the given expression we get:
[tex] ( 3 ) ^ { - 4 } [/tex] = [tex] \frac { 1 } { 3 ^ 4 } = \frac { 1 } { 81 } [/tex]
Kevin and Randy Muise have a jar containing 70 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.50. How many of each type of coin do they have.
Answer:
50 nickels, 20 quarters.
Step-by-step explanation:
System of equations (q = # of quarters, n = # of nickels):
q + n = 70, 0.25q + 0.05n = 7.50
the first equation can be changed to q = 70 - n, so we are able to substitute q with 70 - n.
So, it will look like 0.25*70 - 0.25n + 0.05n = 7.50. This can be simplified to 0.2n = 10, which means that n = 50.
Knowing that we can solve q + 50 = 70, which means that q = 20.
By applying algebraic principles, it's determined that Kevin and Randy Muise have 20 quarters and 50 nickels. We've used two equations to solve this two-variable problem. The first equation comes from the total number of coins, and the second comes from the total value of the coins
Explanation:The subject of this question is a classic two-variable algebra problem. We have two unknowns here: the number of quarters (which we'll call Q) and the number of nickels (which we'll call N).
From the given information in the question, we can create the following equations:
Q + N = 700.25Q + 0.05N = 7.50Essentially, the first equation states that the total number of coins is 70, and the second equation is representative of the total value in dollars of the coins.
From the first equation, we can isolate one variable: N = 70 - Q.
Substituting this value into the second equation gives us
0.25Q + 0.05(70 - Q) = 7.50
⇒0.20Q +3.50 =7.50
⇒0.20Q= 4
⇒Q= 20
Solving this equation gives us the value of Q (number of quarters) = 20.
Substituting Q = 20 into our first equation: 20 + N = 70, we can find the value of N (number of nickels) = 50.
So, Kevin and Randy Muise have 20 quarters and 50 nickels.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ2
What is the area, in square meters, of a right triangle with sides of length 8 meters, 15 meters and 17 meters?
Answer:
60 square meters
Step-by-step explanation:
The area of a triangle is with the formula A = 1/2 b*h. The base and height are the measurements of the sides of a triangle which form a 90 degree angle. When all three measurements are given, the base and height are the smallest since the largest is the hypotenuse. Here b = 8 and h = 15.
So the area is A = 1/2 * 8 * 15 = 60.
A rectangle is 2/5 inches long and 1/3 inches wide.
What is the area of the rectangle?
Enter your answer in the box as a fraction in simplest form.
Answer:
The area of the rectangle is 2/15
Step-by-step explanation:
To figure this out you have to multiply the length and the width
2/5×1/3 = 2/15
This is the simplified answer
The answer is B. ( that’s why it has the 1 in front of it) but I need help showing how I got that as an answer
Answer: The area is 221.558, with the explanation below.
Step-by-step explanation: The area of a circle is solved by the equation
π x r². You are given the diameter of 16.8, and the radius is half of it, so the radius = 16.8/2 = 8.4
Next, you need to plug your numbers into the equation:
Area = 3.14 x 8.4²
Area = 3.14 x 70.56
Area = 221.558
Here is a picture of a cube, and the net of this cube. What is the surface area of this cube? Enter your answer in the box. cm² A cube and a net of the cube are shown. The edge length of the cube is labeled 13 centimeters. The net consists of 4 squares connected vertically, and 1 square is attached to the left of the third square and 1 square is attached to the right of the third square. One square in the net is labeled with a side labeled 13 centimeters.
Answer:
78 cm²
Step-by-step explanation:
since all sides are congruent you multiply the one measurement 6 times,so you do 13 × 6 equals 78
My favorite songdress
Answer:
I'm sorry but is this a question? I don't mean to be rude.
Step-by-step explanation:
the volume of a cylinder with a height of 25cm and a radius of 20cm
Answer:
5652 cm³
Step-by-step explanation:
V = 2πr² + 2πrh
= (2 × 3.14 × 3.14 × 20 ×20) + (2 × 3.14 × 20 × 25)
= 2512 + 3140
= 5652 cm³
PLEASE PLEASE HELP ASAP
Answer:
I GOT U ITS C DIDN'T HAVE TIME TO WRITE EXPLANATION SEEMS U IN A HURRY
Step-by-step explanation:
The sum of two numbers is 21. Their difference is 7. What are the numbers?
Answer:
The numbers are
14
and
7
.
Explanation:
Let the numbers be
x
and
y
.
x
+
y
=
21
x
−
y
=
7
y
=
21
−
x
x
−
(
21
−
x
)
=
7
x
−
21
+
x
=
7
2
x
=
28
x
=
14
∴
14
+
y
=
21
y
=
7
Answer: The required numbers are 14 and 7.
Step-by-step explanation: Given that the sum of two numbers is 21 and their difference is 7.
We are to find the numbers.
Let x and y represents the two numbers.
Then, according to the given information, we have
[tex]x+y=21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Adding equations (i) and (ii), we get
[tex](x+y)+(x-y)=21+7\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.[/tex]
From equation (i), we get
[tex]x+y=21\\\\\Rightarrow 14+y=21\\\\\Rightarrow y=21-14\\\\\Rightarrow y=7.[/tex]
Thus, the required numbers are 14 and 7.
Which function is represented by this graph?
The last option is not even a function, because it ambiguously defines the endpoints.
The first option doesn't define the endpoint, because they are always excluded.
So, the correct option is the second one, because it includes the left endpoint and excludes the right one.
The function d(x) is given by:
d(x)= 1 if 1≤x<4
2 if 4≤x<6
3.5 if 6≤x<11
and 5 if 11≤x<13
Step-by-step explanation:By looking at the graph of the function we observe that the function takes the value :1 when 1≤x<4
( because the graph is a straight horizontal line i.e. y=1 and the line has a closed circle at x=1 and open circle at x=4 )
also the function takes the value: 2 when 4≤x<6( because the graph is a straight horizontal line i.e. y=2 and the line has a closed circle at x=4 and open circle at x=6 )
also the function takes the value: 3.5 when 6≤x<11( because the graph is a straight horizontal line i.e. y=3.5 and the line has a closed circle at x=6 and open circle at x=11 )
also the function takes the value: 5 when 11≤x<13( because the graph is a straight horizontal line i.e. y=5 and the line has a closed circle at x=11 and open circle at x=13 )
PLEASE I REALLY NEED HELP
I believe the correct answer is 36
The slope of the tangent to a curve at any point (x, y) on the curve is x divided by y. Find the equation of the curve if the point (2, −3) is on the curve. x2 + y2 = 13 x2 + y2 = 25 x2 − y2 = −5 x2 − y2 = 5
[tex]x^2-y^2=-5[/tex]
Step-by-step explanation:The problem tells us that the slope of the tangent to a curve at any point [tex](x, y)[/tex] on the curve is x divided by y, that is:
[tex]m=\frac{x}{y}[/tex]
We also know that the point [tex](2,-3)[/tex] is on the curve. By taking a look on the options this point lies on both equations, namely:
[tex]x^2+y^2=13 \ because \ (2)^2+(-3)^2=13 \\ \\ x^2-y^2=-5 \ because \ (2)^2-(-3)^2=-5[/tex]
We know that the derivative is the slope of the tangent line to the graph of the function at a given point. So taking the derivative of both equations we have:
[tex]\frac{d}{dx}(x^2+y^2)=\frac{d}{dx}(13) \\ \\ \therefore 2x+2y\frac{dy}{dx}=0 \\ \\ \therefore m=\frac{dy}{dx}=-\frac{x}{y}[/tex]
And:
[tex]\frac{d}{dx}(x^2-y^2)=\frac{d}{dx}(-5) \\ \\ \therefore 2x-2y\frac{dy}{dx}=0 \\ \\ \therefore m=\frac{dy}{dx}=\frac{x}{y}[/tex]
So [tex]x^2-y^2=-5[/tex] also meets the requirement of the condition the slope of the tangent to a curve at any point (x, y) on the curve is x divided by y. Therefore this is the correct option.
Answer:
The correct option is D
Step-by-step explanation:
Edge2020
Carl earned $40 for 5 hours of mowing lawns. He earned $35 for 7 hours of babysitting.
Which statement correctly compares Carl’s earnings per hour for mowing lawns and
babysitting?
Answer:49,000
Step-by-step explanation:you just multiply it
Answer:
He earned $3 per hour for mowing lawns.
Step-by-step explanation:
I did the assignment
Determine the mean of 28,40,53,39,45
Answer:
41
Step-by-step explanation:
Add the numbers together and divide by 5. 5 is the amount of numbers in the example.
Answer: The mean of all the numbers is 41.
Step-by-step explanation:
To find the mean of a set of numbers you must first add them all together. In this case, all of the numbers added together equaled 205. Then, you divide what ever your previous number was by how many numbers are in the original set all total. In this case, there was 5. So my last step would be dividing 205 / 5 = 41. 41 is my final answer.
Determine the total number of roots of each polynomial function using the factores form? F(x) = (x-6)^2(x+2)^2
Answer:
4
Step-by-step explanation:
If we perform the indicated multiplication, the highest powered x term will be 4 (as in x^4). Thus, the total number of roots of this polynomial will be 4.
Answer:
total number of roots =4
Step-by-step explanation:
the total number of roots of each polynomial function using the factored form
[tex]F(x) = (x-6)^2(x+2)^2[/tex]
Given f(x) is in factored form, to get the roots we look at the factors and the exponents.
[tex](x-6)^2[/tex] has exponent 2, so we have two roots 6 and 6
like that [tex](x+2)^2[/tex] gives us two roots because it has exponent 2
So total number of roots for this polynomial function is 4
A cylinder has a radius of 10 m and a height of 8 m what is the exact volume of he cylinder
[tex]\bf \textit{volume of a cylinder}\\\\ V = \pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=10\\ h=8 \end{cases}\implies V=\pi (10)^2(8) \\\\\\ V=800\pi \implies V\approx 2513.27[/tex]
Answer:
V = 800π
Step-by-step explanation:
The formula for volume of a cylinder is V = πr²h where r is the radius of the base circle, and h is the height of the cylinder
We are given r = 10, and h = 8. Plug them in and solve for V...
V = π(10²)(8)
V = π(100)(8)
V = 800π
This is the EXACT answer. Leave it in terms of pi. If you multiply out pi, you have to round, then you have an estimated answer.