Answer:
Right 3, Down 4
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
[tex]g(x) = (x + 3)^2 - 4[/tex]
Required
The transformation from f(x) to g(x)
When a function is translated up by h units, the rule is:
[tex](x,y) \to (x + h,y)[/tex]
So, we have:
[tex]f'(x) = (x + h)^2[/tex]
By comparison, h = 3. So:
[tex]f'(x) = (x + 3)^2[/tex]
When a function is translated down by h units, the rule is:
[tex](x,y) \to (x,y - h)[/tex]
So, we have:
[tex]g(x) = f'(x) -h[/tex]
By comparison, h = 4. So:
[tex]g(x) = (x + 3)^2 - 4[/tex]
Hence, the transformation is: 3 units right and 4 units down
Is the answer option b?
Answer:
yes, it is B
Step-by-step explanation:
every input value of x has an unique result value y.
there are no 2 values for x that produce the same result value y.
and there are no multiple result values possible for a subject x value.
bottom line, yes, it is a function, and a 1:1 function at that.
Find the amount and the compound interest on rupees 5000 for 2 years at 6% per annum, Interest payable yearly. Answer with full steps and formula NO BAD ANSWERS REQUIRED :D
Answer:
I. Amount = 5618 Rupees
II. Compound interest = 618 Rupees
Step-by-step explanation:
Given the following data;Principal = 5000 RupeesTime = 2 yearsInterest rate = 6%To find the compound interest;
Mathematically, compound interest is calculated using the formula;
A = P(1 + r)^t
Where;
A is the future value.P is the principal or starting amount.r is annual interest rate.t is the number of years for the compound interest.Substituting into the formula, we have;
A = 5000(1 + 0.06)^2
A = 5000(1.06)^2
A = 5000 * 1.1236
A = 5618 Rupees
Next, we would determine the compound interest using the formula;
C.I = A - P
C.I = 5618 - 5000
Compound interest (C.I) = 618 Rupees
please tell me what x =?
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from angle x, we know the opposite side and the adjacent side. Therefore, we should use the tangent function to solve.
tan(x) = 8/10
x = tan^-1(8/10)
x = 38.7 degrees
Hope this helps!
Find the distance across the lake. Assume the triangles are similar.
Answer:
202.5
Step-by-step explanation:
[tex]\frac{L}{45}[/tex] = [tex]\frac{90}{20}[/tex] → [tex]\frac{L}{45}[/tex] = [tex]\frac{9}{2}[/tex]
9 x 45 = 405 → 2L=405
L=[tex]\frac{405}{2}[/tex] → L = 202.5
PLEASE HELP ASAP
Solve the triangle. Round your answers to the nearest tenth.
Answer Options:
A. m∠A=41, b=11, c=29
B. m∠A=41, b=13, c=29
C. m∠A=41, b=10, c=29
D. m∠A=41, b=13, c=25.9
Answer:
Optiom B
Step-by-step explanation:
If you use sine rule here, you'll find the other two sides
for the angle, do 180-24-115 = 41
Answered by GAUTHMATH
Find the measure of the numbered angles.
Angle 1 =
Angle 2 =
Angle 3 =
Angle 4 =
Angle 5 =
Angle 6 =
Angle 7 =
Angle 8 =
Explanation in pictures.
Hope this helps!! Have a good day!
Square Root of 9801
With Steps Please
Answer:
99
Step-by-step explanation:
First give it as a product of prime factors. Divide 9801 with prime numbers. The first picture divides 9801 fron prime numbers. Prime numbers are 2,3,5,7, 11. We can only divide using 3 and 11. So we get 3⁴ and 11². The second picture shows how I got the square root of 9801. Square root is ½. So we multiply each power with ½ so we finally get 99. You can recheck for yourself using a calculator. It is 99.
The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 2. What was the size of the original rectangle?
Answer:
Size of the original rectangle is 30*20=600
Step-by-step explanation:
Let the length and width of rectangle be x+10 and x. After increasing the dimensions, the new length and width are x+20 and x+10
ATQ, (x+20)(x+10)=2(x+10)(x), x=20.
A group has more than $120 to spend. The inequality 5x + 20 > 120 represents the cost to rent a hall for a conference, where x represents the number of hours the group can rent the hall. Which of the following is the solution for this situation?
Answer:
x>20
Step-by-step explanation:
You want to try and get the x alone so
5x + 20 > 120
-20 -20 Subtract 20 from each side
5x > 100
5x/5 > 100/5 Divide 5 from each side
x > 20
Is 392 a perfect cube? If not, find the smallest natural number by which
392 must be multiplied so that the product will be a perfect cube.
Answer:
no its not a perfect cube, we need to multiply a seven to make it perfect cube
Step-by-step explanation:
answer from GAUTHMATH
One dozen cookies cost $5.50. At that rate, how much does one cookie cost?
Answer:
0,458$
Step-by-step explanation:
PLSSS HELPPP
give me the answers and explain
Find the slope of the line that passes through (26, 15) and (1, 86).
Answer:
-71/25
Step-by-step explanation:
We can use the slope formula when given two points
m = (y2-y1)/(x2-x1)
m = (86-15)/(1 -26)
= 71/-25
= -71/25
Answer:
[tex]\displaystyle m = \frac{-71}{25}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (26, 15)
Point (1, 86)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{86 - 15}{1 - 26}[/tex]Subtract: [tex]\displaystyle m = \frac{71}{-25}[/tex]What is 21+x=70 what is X?
this is me
Answer:
Simplifying
Simplifying
21 + x = 70
Solving
21 + x = 70
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-21' to each side of the equation.
21 + -21 + x = 70 + -21
Combine like terms: 21 + -21 = 0
0 + x = 70 + -21
x = 70 + -21
Combine like terms: 70 + -21 = 49
x = 49
Simplifying
x = 49
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{21 + x = 70}[/tex]
[tex]\large\textsf{x + 21 = 70}[/tex]
[tex]\large\text{SUBTRACT 21 to BOTH SIDES}[/tex]
[tex]\large\textsf{x + 21 - 21 = 70 - 21}[/tex]
[tex]\large\text{CANCEL out: 21 - 21 because that gives you 0}[/tex]
[tex]\large\text{KEEP: 70 - 21 because that helps solve for the x-value}[/tex]
[tex]\large\textsf{x = 70 - 21}[/tex]
[tex]\large\textsf{\bf x = 49}[/tex]
[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 49}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
As James bought his textbooks for classes one semester, he estimated the cost to the nearest ten dollars. He knew he could cover the cost up to $315. His math book cost $68.41, biology text was $105.35, literature text cost $72.49, and the AutoCAD text was $59.91. What rounded sum did James determine
Answer:
$310
Step-by-step explanation:
The first step is to add the costs of the textbook together :
$68.41 + $105.35 + $72.49 + $59.91 = $306.16
In order to round off to the nearest ten dollars, look at the units figure, if the number is greater or equal to 5, add 1 to the ten figure. If this is not the case, add zero. Replace the unit digit with zero
The unit digit is greater than 6, so 1 is added to the tens digit. The amount becomes $310
what is this please tell answer
Answer:
x=6, y=4, z=8
(c) 6I hope this is helpful!
Evaluate the expression when a=3.
a^2 - 6a -5
Answer:
- 14
Step-by-step explanation:
a = 3
a^2 - 6a - 5
= 3^2 - 6 ( 3 ) - 5
= 9 - 18 - 5
= 9 - 23
= - 14
Consider the piecewise function shown on the graph. Over which interval of the domain does the graph represent an exponential function?
I think the answer is c in which graph shown in the above
Answer:
see attached, x>=1
Step-by-step explanation:
plsssssssssssssss help meeee
Answer:
64 vs. 4 so 60 extra people
Step-by-step explanation:
Answer:
I think 60 more people
Step-by-step explanation:
You just plug in p for period 4 and period 2 then solve for N. Then it's asking for how many more in pd 4 then 2 which is 60, I think..
Combine and simplify these radicals.
Answer:
4 sqrt(3)
Step-by-step explanation:
sqrt(3) * sqrt(16)
sqrt(3) *4
4 sqrt(3)
Answer: d
Step-by-step explanation: I took the test
If cos(27) =p, express sin(27) in terms of p
Answer:
√(p²-1)
Step-by-step explanation:
sin (27°) = √(p²-1) / 1
= √(p²-1)
Given the functions below, find f(x) + g(x)
f(x) = 3x - 1
g(x) = x2 + 4
Answer:
x^2+3x+3
Step-by-step explanation:
f(x) = 3x - 1
g(x) = x^2 + 4
f(x) + g(x) = 3x-1+ x^2 +4
Combine like terms
= x^2+3x+3
What is the length of BD?
Answer:
BD = 10 √3
Step-by-step explanation:
ABC ∆ ,
BD ÷ 20 = sin 60
BD = 20 sin 60
BD = (20 √3) / 2
= 10 √3
-2 (x+5):4
Pliss es para hoy
I don't know how you want it solved but, I am giving u -2 I hope this helps
Abby made the following conjecture: The sum of a multiple of 7 and a multiple of 8 will be an
odd number. Do you agree or disagree? Briefly justify your decision with a counterexample if
possible.
Answer:
Disagree. As long as the odd number (7) is multiplied by an even number, the sum of multiples of an odd and even number in general will add to be even.
Step-by-step explanation:
Assume you have a=7 and b=8.
Now there are 4 combinations since there are only two types of numbers: even and odd.
Combination 1 would consist of an ODD amount of multiples of a, and and ODD amount of multiples of b.
See: 3a + 3b
3(7) + 3(8) = 45
*Combination 2 would be an EVEN amount of a and an EVEN amount of b.
2a + 2b
14 + 16 = 30
HERE, in combination 2, the claim is already debunked.
Combination 3 is an ODD amount of a and an EVEN amount of b
1a + 2b
7 + 16 = 21
*Combination 4 is an EVEN amount of a and an ODD amount of b
2a + 1b
14 + 8 = 24
HERE, in combination 4, the claim is justified again
2. The lines shown in the figure are parallel lines cut by a transversal. Angles a and e are:
b
a
d
8
h
Answer:
Corresponding AnglesStep-by-step explanation:
Angles a and e are corresponding angles and they are also congruent.tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
HURRY QUICKLY Ashley is preparing for a horse riding competition. She has trained her horse for 4 hours and has completed 172 rounds. At what rate has Ashley ridden her horse in rounds per hour?
A.
42 rounds per hour
B.
44 rounds per hour
C.
45 rounds per hour
D.
43 rounds per hour
Step-by-step explanation:
C. 45 rounds per hour. is the answer
Answer:
D (43 Rounds Per Hour)
Step-by-step explanation:
Ashley has completed 172 rounds and trained her horse for 4 hours. Supposing she riding is training her horse, we can divide 172 by 4, showing how much rounds is completed in an hour. If you think about it, dividing by four is making it four times less. And since Ashley have ridden it for four hours, dividing it by four makes one hour. Now, for the math, we do 172/4 (172 divided by 4), and get 43, which is D.
Which expression is equivalent to (3^2)^-2
Answer:
1/3^4
1/81
Step-by-step explanation:
(3^2)^-2
We know that a^b^c = a^(b*c)
3 ^(2*-2)
3^-4
We know that a^-b = 1/a^b
1/3^4
1/81
The chart shows pricing and payment options for two big-ticket items.
If someone were unable to pay cash right now, which financing option would be best for the laptop and for the refrigerator?
a. rent-to-own; installment
b. installment; rent-to-own
c. rent-to-own; rent-to-own
d. save up and pay cash
Answer:its C rent-to-own ; rent-to-own
Step-by-step explanation:
I got a 100 on my test
Solve the compound inequality 7x > –35 and 3x ≤ 30.
Answer:
x>-5 x ≤10
Step-by-step explanation:
-35/7=-5
7x/7=x
3x/3=x
30/3=10
Answer: -5 < x _< 10
Step-by-step explanation:
