The graph of the cube root of X is shifted one unit down in seven units to the left. What is the equation of the resulting graph? Explain
Using translation concepts, it is found that the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 7} - 1[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The cube root function is given by:
[tex]y = \sqrt[3]{x}[/tex]
The changes are as follows:
Shifted one unit down, hence 1 is subtracted from the function.Shifted seven units to the left, hence [tex]x \rightarrow x + 7[/tex] in the domain of the function.Hence, the equation is given by:
[tex]y = \sqrt[3]{x + 7} - 1[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
What’s the constant of proportionality of the relationship shown in the graph?
Answer: It's 3
Step-by-step explanation:
Is this congruent by SSS, SAS, AAS, ASA? Hurry please ASAP! Only if you know!
Answer:
Side-Side-Side (SSS)
Step-by-step explanation:
I believe these triangles are congruent by the postulate SSS because both triangles have all three sides equal.
what is 4(2×-7)+3(3×-1)=3(2-×)
Answer:
x=37/20
Step-by-step explanation:
4(2x-7)+3(3x-1)=3(2-x)
8x-28+9x-3=6-3x
17x+3x=6+31
20x=37
Answer:
x = [tex]\frac{71}{3}[/tex]
Step-by-step explanation:
1. Simplify/distribute each side.
[tex]4(2)(-7)+3(3)(-1)=3(2-x)[/tex]
[tex]4(2)(-7)+3(3)(-1)=(3)(2)+(3)(-x)[/tex]
[tex]-56+-9=6+-3x[/tex]
2. Flip the equation around.
[tex]-3x+6=-65[/tex]
3. Subtract 6 to balance the equation.
[tex]-3x+6-6=-65-6[/tex]
[tex]-3x=-71[/tex]
4. Divide each side by 3. We know they are in the same fact family.
[tex]\frac{-3x}{-3} = \frac{-71}{3}[/tex]
Deena deposited $48 in a new bank account. After buying groceries, she had $19 left in the account. Then she paid her cell phone bill, which was $31. Select all the true statements about Deena’s account.
To start, Deena had a positive balance.
In this situation, 0 represents an empty bank account.
After paying for groceries, Deena had a negative balance.
After paying her cell phone bill, Deena had –$12 in the account.
The smallest balance in the account was $19.
Step-by-step explanation:
Step one:
given data
amount deposited=$48
after the purchase of groceries
account balance= $19
cell phone bill, which= $31
Step two:
The account balance after paying for groceries will be
=19-31= $-12
she will have a deficit of $12, hence a negative account balance
To start, Deena had a positive balance. -------True
In this situation, 0 represents an empty bank account. -----True
After paying for groceries, Deena had a negative balance. ---True
After paying her cell phone bill, Deena had –$12 in the account. ...True
The smallest balance in the account was $19. ....True
The m<1=4x-30 and the m<5=2x+50. Find m<1 and m<7.
A. M<1=130 and M<7=130
B. M<1=130 and M<7=50
C. M<1=50 and M<7=50
D. M<1=50 and M<7=130
Answer:
D) m<1 = 50 m<7 = 130
Step-by-step explanation:
Lets set up the equation!
We know m<4 is 4x-30 and the m<5 is 2x + 50 due to alternate interior angles they are congruent so we can forge an equation, all we do is set them equal to each other!
4x-30 = 2x+50
Add 30 to both sides
4x = 2x +80
Subtract 2x from both sides.
2x = 80
Divide both sides by 2
x = 40
Now that we know x we can just plug it into the expression of m<4 to find m<1
4x-30
4(40)-30
80 - 30
50
m<4 = 50
Because m<1 and m<4 are vertical angles they are congruent!
m<1 = 50
We also know m<4 and m<5 are congruent so m<5 = 50 as well.
Because <7 is supplementary to <5 we know that the sum of both angles amount to 180.
x represents m<7
50 + x = 180
Now we solve by subtraction 50 from both sides
x = 130
m<7 = 130
Brainliest is appreciated!
how many solutions does 6 -3x = 12 - 6x have?
A. two solutions.
B. no solutions.
C. one solution.
D. infinitely many solutions.
Answer:
Step-by-step explanation:
6-3x=12-6x
Only one solution of x=2
find the distance between PQ. P(3,4) and Q(6,8)
25
20
15
5
A farmer grows a particular plant that has a gene that can be manipulated to control the age t at which the plant matures. The number of seeds S(t) produced by a plant maturing at age t is S(t)=−0.3t2+30t+0.2 seeds per mature plant A farmer asks the geneticists to genetically engineer a plant line that accounts for the fact that on his farm, only P(t)=90000t+100, plants mature to age t. What age of maturity should the geneticist select for the plants to maximize the seed production of the farmer's crop?a. Between 130 and 140 days b. Between 120 and 130 days
Answer:
The correct option is;
Between 40 and 50 days
Step-by-step explanation:
The number of seeds that are produced by a plant maturing at age t, S(t), is given as follows;
S(t) = -0.3·t² + 30·t + 0.2
The proportion of plants maturing at age (t) in the plants to be engineered by the geneticist P(t) = 90000/(t + 100)
The number of seeds produced by the plants = S(t) × P(t) = (-0.3·t² + 30·t + 0.2)×(90000/(t + 100))
To find the maximum number of seeds, we differentiate using an online tool, and equate to zero to get;
d((-0.3·t² + 30·t + 0.2)×(90000/(t + 100)))/dt = (-27000·t² - 5400000·t + 269982000)/(t + 100)² = 0
(-27000·t² - 5400000·t + 269982000)/(t + 100)² = 27000(t - 41.419)(t + 241.419)/(t + 100)² = 0
t = 41.419 or t = -241.419
Therefore, in order to maximize the production of seed of the crops of the farmer, the geneticist should select between 40 and 50 days.
Find the slope of the line that passes through (5,8) and (2,3).
Answer:
(-5,-3)
Step-by-step explanation:
y values minus y values over x values minus x values
A package of 3 pairs of insulated costs $15.57. What is the unit price of the pairs of ?
Answer:
-3 pairs cost $15.57
15.57 divided by 3
$5.19 per pair unit rate
during migration , a butterfly can travel 30 miles in 1 hour . which graph best represents y , the number of miles a butterfly can travel in x hours ?
what is the domain of this scatter plot?
Answer:
this answer should be green
Use the given information to write the equation of the line.
slope 2, y-intercept - 4
HELP THIS IS THE 5TH TIME I POSTED THIS BRUH
Answer:
it's blurry all i see is pixels...
i'll help if you send me a picture...
Step-by-step explanation:
Select all of the points that are solutions to the linear equation 2x + 9y = 54
good luck
Step-by-step explanation:
Isabella has an allowance of $15.00 per week. you are in bowling league that costs $6.50 for each week, and you save at least $5.00 each week. write and solve an inequality to show how you have left to spend each week.
what's the answer to this question?
Answer:
6.5+5=11.5-15
3,5
Step-by-step explanation:
plz help me ;-;,i really need some help
Answer:
The building is taller than 12ft is b>12
The box contains more than 11 books is b>11
Answer:
b<11 is The board is shorter than 11 cm
b>11 is The box contains more than 11 books
b<12 is There are fewer than 12 beetles in a jar
b>12 is The building is taller than 12 ft.
Step-by-step explanation:
For the function f(x) = (x – 9)7, find f-1(x).
Answer:
Let y=x,
y=(x-9)7
(y+9) ÷7=x
f-1(x)=(y+9)÷7
9-(7-3x) = 4+x-(3-x) solve for x
Answer:
The answer is x= -1.
I need help with solving this problem please I will mark brainliest if correct
Answer:
both anges are 105
x = 128
Step-by-step explanation:
This is based on a theorem called F-angles.
If a and b are parallel, then these angles are equal.
So x = 105+23 = 128
How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
No Solution
Step-by-step explanation:
As the two lines have the identical slope (-1/2x), that means these two lines are parallel, and therefore they have no solution.
Please help! Only if you know though :))$
Answer:
180
Step-by-step explanation:
What is the retail price of a shirt that has a wholesale price of $12 and is marked up by 60 percent?
A. $7.20
B. $19.20
C. $31.20
D. $72.00
Answer:
Ium try b yup that's it I think but if not it's a
Answer:
it B i took the test
Step-by-step explanation:
Answer my math question I asked so many times I lost most of points by
Answer:
im sorry i wish i can help
Step-by-step explanation:
pls help i don't know what it is asking
Answer:
e=1
Step-by-step explanation:
Suppose AP = 2 cm and BQ = 7 cm. What is the length of PC?
Step-by-step explanation:
is this a quadrilateral? or polygon or triangle?
what are the angles (I believe there should be at least an angle given) else PC can be any value that is positive
A 245 inch board is cut into two pieces. One piece is four times the length of the other one. Find the length of the shorter piece
Answer:
30.625
Explanation:
Hope this helps.
Determine the range of the following graph
solve the equation by taking square roots
(x-3)^2 +8 = -10
Answer:
x = 3 ± 3i√2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Vertex Form: f(x) = a(bx - c)ⁿ + dCompleting the SquareSolving rootsAlgebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define equation
(x - 3)² + 8 = -10
Step 2: Solve for x
Subtract 8 on both sides: (x - 3)² = -18Square root both sides: x - 3 = ±√-18Factor: x - 3 = √-1 · ±√18Simplify: x - 3 = ±3i√2Add 3 to both sides: x = 3 ± 3i√2