The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.
What is the equation of g(x)?
A. g(x) = 5x – 9
B. g(x) = 5x – 10
C.g(x) = 5x – 9
D. g(x) = 5x – 10
Answers
Your function f(x) should be 5^x, instead of 5x
Answer should be g(x) = 5^x - 10, since it shifts f(x) downward by 10 units
The equation of the function is , g(x) = 5x -10 , Option B is the right answer.
What is a Function ?A function is a mathematical representation of an independent variable and a dependent variable.
The given function is
f(x) = 5x
As the y intercept is shifting from (0 ,1) to (0,-9)
therefore the function is translating 10 points down
therefore the equation of the function is
g(x) = 5x -10
Therefore Option B is the right answer.
To know more about Function
https://brainly.com/question/12431044
#SPJ5
Related Questions
What is the factored form of the expression k^2 - 9h^2
Answers
a^2 - b^2 = (a+b) (a-b)
So, what we need to do here is apply this equation:
k^2 - 9h^2 =
k * k - (3h)^2 =
(k + 3h) (k - 3h)
During one year about 163 million adults over 18 years old in the United States spent a total of about 93 billion hours online at home. On average, how many hours per day did each adult spent online at home?
1. How do you write each number in scientific notation?
2 How do you convert the units to hours per day.
Answers
[tex]\bf 163,000,000\implies 163\times 10^6 \\\\\\ 93,000,000,000\implies 93\times 10^9\\\\ \cfrac{93\times 10^9}{163\times 10^6}\impliedby \textit{hours per year for one adult} \\\\\\ \cfrac{93\times 10^9\times 10^{-6}}{163}\implie
s \cfrac{93\times 10^{9-6}}{163}\implies \cfrac{93\times 10^3}{163}[/tex]
that's how many hours each adult spent a year... now, how many hours is that per day? well, there are 365 days a year, so, we simply divide it by 365
[tex]\bf \cfrac{\frac{93\times 10^3}{163}}{365}\implies \cfrac{\frac{93\times 10^3}{163}}{\frac{365}{1}}\implies \cfrac{93\times 10^3}{163}\cdot \cfrac{1}{365}\implies \cfrac{93\times 10^3}{163\cdot 365}\quad \cfrac{hours}{day}[/tex]
Final answer:
To write each number in scientific notation, express it as a product between 1 and 10 and a power of 10. Each adult spent an average of 570.55 hours per day online at home.
Explanation:
To write each number in scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10.
163 million can be written as 1.63 x 10⁸
93 billion can be written as 9.3 x 10¹⁰
To convert the units to hours per day, we need to divide the total number of hours by the number of adults.
So, each adult spent an average of (93 x 10¹⁰) / (163 x 10⁸) = 570.55 hours per day online at home. Scientific notation simplifies large numbers, facilitating computations and providing a concise representation of quantities in mathematical contexts.
Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?
A He showed that an explicit formula could be created.
B He showed that a recursive formula could be created.
C He showed that f(n) ÷ f(n − 1) was a constant ratio.
D He showed that f(n) − f(n − 1) was a constant difference.
Answers
C. He showed that f(n)/(f(n-1) was a constant ratio.
Line LJ is a diameter of circle K. If tangents to circle K are constructed through points L and J, what relationship would exist between the two tangents? Explain.
Answers
If tangents are constructed through points L and J, then the tangents are perpendicular to the diameter and parallel to each other.
Find the probability of at least 2 girls in births. Assume that male and female births are equally likely and that the births are independent events. Round to three decimal places.
Answers
Male and FemaleMale and Male Female and Male Female and Female
All four variants are equally likely.Probability of each one is 1/4 = 0.25.So, Result "Female and Female"
are probability = 0.250 --- if round to three decimal places.
A model for a company's revenue is R=-15p^2+300p+12,000, where p is the price in dollars of the company's product. What prize will maximize revenue?
Answers
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} R = &{{ -15}}p^2&{{ +300}}p&{{ +12,000}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so the Revenue will be the highest at [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex] and that will happen at the price of [tex]\bf -\cfrac{{{ b}}}{2{{ a}}}[/tex]
[tex]R(p)=-15 p^{2}+300p+12,000[/tex]
Move the 12,000 over to the other side and set the equation equal to 0:
[tex]-15 p^{2}+300p=-12,000[/tex]
In order to complete the square, the leading coefficient on the squared term has to be a 1 and it's a -15, so we have to factor that out:
[tex]-15( p^{2}-20p)=-12,000 [/tex]
Now it's ready to complete the square on it. Do this by taking half the linear term, squaring it, and then adding it in. Our linear term is 20p. Half of 20 is 10 and 10 squared is 100, so we will add in 100 on the left. Let's do this next step in two parts:
[tex]-15( p^{2}-20p+100)=-12,000 [/tex]
That's not quite complete yet because if we add in 100 inside the parethesis on the left we have to add in that same amount on the right. But on the left, we didn't just add in 100, we added in -15 TIMES 100 cuz we can't just forget about the -15 we factored out. That looks like this then:
[tex]-15( p^{2}-20p+100)=-12,000-1,500 [/tex]
The whole reason for doing this is to create a perfect square binomial on the left which is what we have done. The perfect square binomial is this (and we are going to do the subtraction on the right at the same time):
[tex]-15(p-10)^{2}=-13,500[/tex]
If we move the right side over to the left we get this:
[tex]-15(p-10) ^{2}+13,500=0 [/tex]
which gives us a vertex of (10, 13,500). That means that at a price of $10, the max revenue will be $13,500. See how beautifully that works out!??
What kind of transformation is illustrated in this figure ?
Answers
5⁄6 · n = 10 (solve for n)
Answers
When you divide 5/6 and 10 you get 12.
To check your answer multiply 5/6 and 12 and you will get 10.
N=12
PLEASE CAN SOMEONE HELP!!!????
Use elimination to solve for x and y:
−2x−y=9
2x−9y=1
My Choices are....
a. (−4,−1)
b. (−1,−4)
c. (5,1)
d. (−1,−7)
Answers
-2x-y=9
2x-9y=1 +
0x-10y=10
-10y=10
divide by -10
y=-1
sub back
-2x-y=9
-2x-(-1)=9
-2x+1=9
-2x=8
divide by -2
x=-4
y=-1
(x,y)
(-4,-1)
A
The values of x and y after solving both the equations by the elimination method are -4 and -1. So option A is correct
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Two linear equations
−2x − y = 9
2x − 9y = 1
by using elimination method,
−2x − y = 9
2x − 9y = 1
0 - 10y = 10
y = -1
2x − 9× -1 = 1
2x = -8
x = -4
Hence, the values are, -4 and -1
To know more about Equation check:
https://brainly.com/question/1529522
#SPJ2
A ship travels 10 miles from Point A to Point B, makes a turn of 112, and travels 16 miles to Point C. If the ship travels directly from Point C back to Point A, how many miles will it travel on the last leg of the trip (from Point C to Point A)? Round your answer to the nearest tenth of a mile.
Answers
[tex] 10^{2} + b^{2} = 16^{2} [/tex]
and [tex]100+ b^{2} =256[/tex]
and [tex] b^{2} =256-100[/tex]
so [tex] b^{2} =156[/tex]
Take the square root of both sides to find that b = 12.5
Explain what needs to happen to the inequality sign when dividing or multiplying by a negative number. a. nothing happens c. change the inequality sign to an equals sign b. flip the inequality sign d. the inequality needs to be graphed on a number line
Answers
so the answer is B
Answer:
(B) flip the inequality sign.
Step-by-step explanation:
If we consider an inequality such that [tex]-x\leq7[/tex], then if we multiply the inequality with a negative number such as [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Also, if we divide the above inequality [tex]-x\leq7[/tex], by a negative number that is [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Therefore, if we multiply or divide an inequality by a negative number, then it flips the inequality sign.
Hence, option (B) is correct.
Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?
Answers
52% = 0.52
78/0.52 =150
150 students voted
Which expression is equivalent to (cos x)(tan(–x))?
A. -sin x
B. sin x
C. -csc x
D. csc x
Answers
[tex][cos(x)][tan(-x)][/tex] is the same as [tex][cos(x)][ -\frac{sin(x)}{cos(x)}] [/tex]
We can now cancel out the cos(x), which leaves us only with -sin(x) remaining. So your answer is A.
Sophie has a hard rubber ball whose circumference measures 13 inches. she wants to store it in a box. what is the number of cubic inches in the volume of the smallest cube- shaped box with integer dimensions that she can use?
Answers
Because the circumference of the ball is 13 inches, therefore
2πr = 13
r = 13/(2π) = 2.069 in
In order to fit the ball into a cube-shaped box with integer dimensions, each side of the box should measure 3 inches (the next integer greater than 2.069).
The volume of the cube-shaped box is 3³ = 27 in³.
Answer: The volume is 27 in³.
What is the prime factorization of -96? tell me how do u get the answer
Answers
the prime factorization of -96 is : - 3×2^5
Answer: -1 x 2^5 x 3
Step-by-step explanation: To find the prime factorization of -96, we need to first factor out -1, which gives us 1 x (-1) x 2 x 2 x 2 x 2 x 2 x 3. Then, we can rewrite -1 as -1^1, and combine the 2's to get 2^5. So the prime factorization of -96 is -1^1 x 2^5 x 3.
Remember, negative numbers can also have prime factorizations.
Find the volume of revolution bounded by the curves y = 4 – x2 , y = x, and x = 0, and is revolved about the vertical axis.
Answers
The rest of solution in the attachment.
There's a mistake in the picture
It shoud be
[tex]V=\pi\left(\dfrac{289\sqrt{17}-521}{60}\right)\approx35[/tex]
Factor completely 36x2− 121.
Answers
Factorising (a² - b²) gives (a+b)(a-b)
Factorising 36x² - 121 gives (6x+11)(6x-11)
what is the slope of a line that passes through (-4,-13) and (19,11)
Answers
m (gradient) = (y1 - y2) / (x1 - x2)
where (x1, y1) is the coordinate of the first point, and (x2, x2) is the coordinate of the second point
in your question:
x1 = -4
x2 = 19
y1 = -13
y2 = 11
m = (-13 -11) / (-4 -19) = -24 / -23 = 24/23 or 1.04 (2d.p.)
hope that helps :)
Answer:
24/23
Step-by-step explanation:
- vs - = + after -24,-23 =
Answer = 24, 23
in a certain county, the number of charter schools is 4 less than twice the number of alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?
Answers
Answer:
There are [tex]26[/tex] alternative schools in the country
Step-by-step explanation:
Let
x------> the number of charter schools
y-----> the number of alternative schools
we know that
[tex]x=48[/tex]
[tex]x=2y-4[/tex] -----> equation A
substitute the value of x in the equation A and solve for y
[tex]48=2y-4[/tex]
[tex]2y=48+4[/tex]
[tex]2y=52[/tex]
[tex]y=26[/tex]
How do I solve this
Answers
so, hmm which are those? let's check, let's set the denominator to 0, and solve for "x".
[tex]\bf x^2+6x-7=0\implies (x+7)(x-1)=0\implies x= \begin{cases} -7\\ 1 \end{cases} \\\\\\ \textit{let's check, } x=-7\quad \cfrac{(-7)+2}{(-7)^2+6(-7)-7}\implies \cfrac{-5}{49-42-7}\implies \cfrac{-5}{0} \\\\\\ x=1\quad \cfrac{(1)+2}{(1)^2+6(1)-7}\implies \cfrac{3}{1+6-7}\implies \cfrac{-3}{0}[/tex]
Permutations!!
If 9 actors must sit together how many ways are there to seat 13 people around the table?
Answers
To calculate the number of ways to seat 13 people around a table with 9 actors sitting together, we treat the 9 actors as one unit and then arrange the five units around the table, resulting in (4! * 9!) different possible arrangements.
Explanation:The question asks us to calculate the number of ways to seat 13 people around a table if 9 actors must sit together. This can be approached as a permutations problem in combinatorics.
Firstly, treat the 9 actors as one unit since they must sit together. With this in mind, we effectively have 5 units to arrange: the group of 9 actors and the remaining 4 individuals. As the seating arrangement is around a circular table, we can fix one person's seat and arrange the remaining units. As a result, there are (5-1)! ways to arrange these units since circular permutations eliminate the concept of a distinct 'starting' point that linear permutations have.
Now we need to consider the arrangements of the 9 actors within their group. Since their relative positions to each other matter, they can be permuted in 9! ways.
Therefore, the total number of seating arrangements would be the product of the two permutations: (5-1)! * 9!.
Calculating this gives us (4!) * 9! = (4*3*2*1) * (9*8*7*6*5*4*3*2*1) different possible arrangements.
It costs $35$35 per hour to rent a boat at the lake. You also need to pay a $25$25 fee for safety equipment. You have $200$200. For how long can you rent the boat?
Answers
Accuracy is a measure of how close an answer is to the actual or expected value
Answers
:)
How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?
Answers
Solve the following system by graphing.
x - y = 4
x + y = 2
What is the solution of the system?
(3, -1)
(3, 1)
(-1, 3)
Answers
the solution is : (3, -1)
put x= 3 and y = -1
you have : 3-(-1) = 4 and 3+(-1) = 2 ..... right
The solution for the system of equation x - y = 4 and x + y = 2 is (3, -1).
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of equations,
x - y = 4 (1)
And x + y = 2 (2)
To find the solution of the equations,
Add both the equations,
x - y + x + y = 4 + 2
2x = 6
x = 3,
Substitute the value of x = 3 in equation (1),
3 - y = 4
y = -1
The values of x and y are 3 and -1 respectively.
Hence, option (A) is correct.
To know more about Equation on:
brainly.com/question/187506
#SPJ2
A comic-strip writer churns out a different number of comic strips each day. For 16 days, the writer logged the number of comic strips written each day (sorted low to high): {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7}. What type of skew can be observed in this distribution?
positive skew
negative skew
zero skew
skew cannot be observed
Answers
We have the data set already in ascending order, so finding the quartiles is quite straight forward.
We have Q₁ = 2, Q₂ = 3, Q₃ = 5 (refer to the first picture below)
The box plot is given in the second picture and from this plot, we can see that the data tail slightly on the right, and this shows a positive skew.
Find the area of a square with apothem 9 in. Round to the nearest whole number.
281 in2
305 in2
458 in2
324 in2
Answers
So, if the apothem is 9in, the length of the side is 2 * 9in = 18 in.
And, the area of the square is (length of the side)^2 = (18 in)^2 = 324 in^2
Answer: 324 n^2
Answer:
The area of the square is 324 square inches.
Step-by-step explanation:
The apothem of the square is 9 inches.
The side of the square is twice the length of the apothem.
Hence, the side of the square is given by
[tex]a=2\times 9=18\text{ in}[/tex]
The area of a square is the given by
[tex]A=a^2\\A=18^2\\A=324\text{ in}^2[/tex]
Therefore, the area of the square is 324 square inches.
Write 5000 = 12 as an order pair
Answers
If XYZ measures 75, what is the measure of XWZ ? A. 285 B. 210 C. 75 D. 150
(Its a circle, and its saying that the arc is 775 and wants to know what the rest of the circle is)
Answers
The measure of XWZ is 285
what is arc?The arc of a circle is defined as the part or segment of the circumference of a circle.
Given:
<XYZ = 75
As, we know central angle of 360
So, arc(XWZ) + <XYZ = 360
arc (XWZ) = 360 - 75
arc(XWZ) = 285
Learn more about arc here:
https://brainly.com/question/15359030
#SPJ5
If you guess an answer on two multiple choice questions with the options a, b, or c, what is the probability of you guessing the answer to both questions correctly?
Answers
(1/3) x (1/3) = 1/9