Answer:
Domain: [tex]0\leq x\leq 6[/tex]
Range: [tex]\{0, 12, 24, 36, 48, 60, 72\}[/tex]
Step-by-step explanation:
Let [tex]y[/tex] or [tex]f(x)[/tex] be equal to the amount of plant food that remains after each day.
[tex]x[/tex] be the number of days that have passed.
Total amount of plant food used is 72 mm.
Number of days the experiment goes on is 6 days.
Plant food used each day is [tex]\dfrac{72}{6}=12\ \text{mm}[/tex].
So, the function will be
[tex]y=f(x)=72-12x[/tex]
at
[tex]x=0,y=72[/tex]
[tex]x=1,y=72-12\times 1=60[/tex]
[tex]x=2,y=72-12\times 2=48[/tex]
[tex]x=3,72-12\times 3=36[/tex]
[tex]x=4,72-12\times 4=24[/tex]
[tex]x=5,72-12\times 5=12[/tex]
[tex]x=6,72-12\times 6=0[/tex]
Value of [tex]x[/tex] is the domain which is [tex]0\leq x\leq 6[/tex].
Value of [tex]y=f(x)[/tex] is the range which is [tex]\{0, 12, 24, 36, 48, 60, 72\}[/tex].
there are 1,920fence posts used in a 12-killometer strech fence how many fence posts are used in one kilometer
Answer:
160
Step-by-step explanation:
Just divide 1920 into 12
Simply.
[tex] \frac{ab - a}{a} = [/tex]
[tex] \frac{2x + y}{y} = [/tex]
I mainly forgot how to do it. Do I divide -ab to get it alone? How do I do it?
Answer:
Required Answer:-First go to first equation[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac{ab-a}{a}}[/tex]
Take common[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {{\bcancel {a }}(b-1)}{{\bcancel {a}}}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]{\underline{\boxed{\bf b-1)}}}[/tex]
use the distributive property to expand this equation please2/3 (18x + 6z)
Answer:
12x + 4z
Step-by-step explanation:
Given: 2/3 (18x + 6z)
Multiply the fraction 2/3 into each term
([tex]\frac{2}{3}[/tex])*18x + ([tex]\frac{2}{3}[/tex])*6z
[tex]\frac{36}{3}[/tex]x + [tex]\frac{12}{3}[/tex]z
12x + 4z
What is the solution to the system of equations below?
y=-6x-10
and
y=-3x-21
(2, -22)
(2,48)
(-2, 2)
(-2, -20)
Answer:
Please check the explanation.
Step-by-step explanation:
Given the equations
[tex]y=-6x-10[/tex]
[tex]y=-3x-21[/tex]
solving the system of the equations
Arrange the equation variables for elimination
[tex]\begin{bmatrix}y+6x=-10\\ y+3x=-21\end{bmatrix}[/tex]
[tex]y+3x=-21[/tex]
[tex]-[/tex]
[tex]\underline{y+6x=-10}[/tex]
[tex]-3x=-11[/tex]
[tex]\begin{bmatrix}y+6x=-10\\ -3x=-11\end{bmatrix}[/tex]
solve
[tex]-3x=-11[/tex]
Divide both sides by -3
[tex]\frac{-3x}{-3}=\frac{-11}{-3}[/tex]
[tex]x=\frac{11}{3}[/tex]
[tex]\mathrm{For\:}y+6x=-10\mathrm{\:plug\:in\:}x=\frac{11}{3}[/tex]
[tex]y+6\cdot \frac{11}{3}=-10[/tex]
[tex]y+6\cdot \frac{11}{3}=-10[/tex]
[tex]y=-32[/tex]
Therefore, the solutions to the system of the equations are:
[tex]y=-32,\:x=\frac{11}{3}[/tex]
But, it seems none of the options is true.
Answer:
A. (2, -22)
Step-by-step explanation:
I just took the test and i got a one hundred! I really hope it helped!!!!
maria wanted to invest $10,000 at the bank. she invested part of her money in a cd account paying 2.1% simple interest and invest the rest of her money in a checking account paying 1.5% simple interest. After 1 year, her interest income was $195. How much did Maria invest in each account
Answer:I = ?, P = $500, r = 6%, t = 3 years
Step-by-step explanation:
Solve each equation. For each step. Identify the property used.
14 + 3n = 8n - 3(n-3)
22x + 11 = 4x - 7
(P.S. The properties that the problem is asking for are the properties of equality. Division property of equality, etc, etc.)
Answer:
Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2
Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1
Step-by-step explanation:
We will solve the equations one by one
So,
[tex]14 + 3n = 8n - 3(n-3)[/tex]
Applying Distributive property
[tex]14 + 3n = 8n - 3n+9\\14+3n = 5n+9[/tex]
Subtraction property of equality (Subtracting 14 from both sides)
[tex]14+3n-14 = 5n+9-14\\3n = 5n-5[/tex]
Subtraction property of equality (Subtracting 5n from both sides)
[tex]3n-5n = 5n-5-5n\\-2n = -5[/tex]
Division property of equality (Dividing both sides by -2)
[tex]\frac{-2n}{-2} = \frac{-5}{-2}\\n = \frac{5}{2}[/tex]
Second Equation:
[tex]22x + 11 = 4x - 7[/tex]
Subtraction property of equality (Subtracting 11 from both sides)
[tex]22x + 11-11 = 4x - 7-11\\22x = 4x-18[/tex]
Subtraction property of equality (Subtracting 4x from both sides)
[tex]22x-4x = 4x-18-4x\\18x = -18[/tex]
Division property of equality (Dividing both sides by 18)
[tex]\frac{18x}{18} = \frac{-18}{18}\\x = -1[/tex]
Hence
Solution of [tex]14 + 3n = 8n - 3(n-3)[/tex] => x = 5/2
Solution of [tex]22x + 11 = 4x - 7[/tex] => x=-1
Noah said, "Division always results in a smaller number. When you divide a number by a second number, the result will always be smaller than the first number."
Jada said, "I disagree. I think the result can be larger or smaller, depending on the number you are dividing by."
Do you agree with Noah or Jada?
LaTeX: 20\div420÷4 results in a number
[ Select ]
20.
LaTeX: 20\div\frac{1}{4}20÷14 results in a number
[ Select ]
20, so
[ Select ]
is correct.
Answer:
Step-by-step explanation:
Greater, provided the divisor is positive.
It would be more accurate and clearer to say that when dividing a number which is greater than zero by a number between 0 and 1, then the quotient is greater than the dividend.
If the divisor is negative and the dividend is positive, then the quotient is negative (and hence less than the dividend).
Solve for the variable
-3/4b = 2
Answer:
b = 2.666.......
Step-by-step explanation:
[tex]-\frac{3}{4} b = 2[/tex]
------ -----
[tex]-\frac{3}{4}[/tex] [tex]-\frac{3}{4}[/tex]
b = 2.666.....
Please Hurry! Due by tonight!
Step-by-step explanation:
the y-intercept is 1 because it's on the y(axis). the line from 1 goes down 1 over three so the slope is 1/3.
your equation would be y=1/3x+1
okay so i got (1,1) but it's not on here ;-;
please someone help me please??!!!
Answer:
how should I know?
Step-by-step explanation:
Answer:
a.)
x= -2 , -1, 0, 1, 2, 3
y=8 , 7, 6, 5, 4, 3
and for b just plot the point and then connect them. im not sure how i can show you
Step-by-step explanation:
What is the total number of servings the modified recipe will make?
9514 1404 393
Answer:
B. 4
Step-by-step explanation:
Equating exponents, we have ...
2x +7 = 15
2x = 8 . . . . . subtract 7
x = 4 . . . . . . divide by 2
The equation is true when the value of x is 4.
hope this helps enjoy.
A surveyor is surveying a street. The surveyor is standing at point Plooking down the street at a No Parking sign at point A and a stop sign at point R. Given PA=3x-4, PR=21 meters, AR=7 meters and point A is between point Rand point What is the value of x in meters?
Answer:
Step-by-step explanation:
If point A is between P and R, then;
PA+AR = PR
Given
PA=3x-4,
PR=21 meters,
AR=7 meters
Substitute
3x-4 +7 = 21
3x+3 = 21
3x = 21-3
3x =18
x =18/3
x = 6
Hence the value of x is 6m
The number of avocados ( a ) (a) a particular tree produces each year can be modeled by the function a ( y ) a(y). What does a ( 12 ) = 364 a(12)=364 mean?
Answer:
[tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.
Step-by-step explanation:
Let [tex]a[/tex] the number of avocados that a particular tree produces at a year. [tex]a(y)[/tex] is the number of avocados that a particular tree produces at y-th year. Hence, [tex]a(12) = 364[/tex] means that 364 avocados are produced by a particular tree at 12-th year.
Use the quadratic formula to solve the equation.
5x2-3x + 1 = 0
X=
Answer:
x= 11/3
Step-by-step explanation:
Name a ray with an endpoint of A.
Given: m || n and p is a traversal.
Prove: m<2=m<7
What is the missing reason in the proof?
Answer:
Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are congruent.
Haley bought 1.6 pounds of almonds for $13.20. How much did she pay per pound for the almonds? Record your answer and fill in the bubbles on your answer document. Be sure to use correct place value. +/- .
Answer:
She paid $8,25 per pound
Step-by-step explanation:
Given
[tex]Weight = 1.6\ lb[/tex]
[tex]Total= \$13.20[/tex]
Required
Determine the amount paid per pound
To do this, we simply divide the amount by the weight of Almonds.
[tex]Amount = \frac{Total}{Weight}[/tex]
[tex]Amount = \frac{\$13.20}{1.6\ lb}[/tex]
[tex]Amount = {\$8.25/\ lb[/tex]
Hence, she paid $8,25 per pound
Please quickly! Out of 5,500 people who attended the football game, fifty-six percent were rooting for the home team. How many people rooted for the home team?
Peter is painting his bedroom. His bedroom has four walls. Yesterday, he painted 1 2/5 walls. What fraction of the walls is left to paint?
Answer: 2 3/5ths are left or 13/5
Step-by-step explanation: 1 2/5 + 2 3/5 = 4 total walls
A 14 foot long ramp is being built to access a front door in a house. The door is 5 feet above the ground. How far away from the base of the house must the ramp be placed? What angle will the ramp make with the ground?
Answer:
The ramp must be placed 13.08 feet from the base of the house.
The angle the ramp will make with the ground is 20.92°.
Step-by-step explanation:
An illustrative diagram for the scenario is shown below.
In the diagram, d represents the distance of the door from the ground, r represents the length of the ramp and x represent the distance of the ramp from the base of the house.
To determine how far away from the base of the house the ramp must be placed, that is to determine x in the diagram.
The diagram is a right angle triangle and x can be determine using the Pythagorean theorem which states " the square of the hypotenuse equals sum of the squares of the other two sides"
In the diagram, the hypotenuse is r
∴ r² = d² + x²
r = 14 ft
d = 5 ft
∴ 14² = 5² + x²
196 = 25 + x²
Then, x² = 196 - 25
x² = 171
x = √171
x = 13.08
Hence, the ramp must be placed 13.08 feet from the base of the house.
Now, to determine what angle the ramp will make with the ground, that is θ in the diagram.
From the formula
Sinθ = Opposite / Hypotenuse
In the diagram, opposite = d = 5ft
and Hypotenuse = r = 14ft
∴ Sinθ = 5ft / 14ft
Sinθ = 0.3571
∴ θ = Sin⁻¹(0.3571)
θ = 20.92°
Hence, the angle the ramp will make with the ground is 20.92°.
Solve the following equation:
a/3.5 - 4.8 = 6.3
a= ______
Answer:
a= 38.85
Step-by-step explanation:
Answer:
[tex]\boxed {a = 38.85}[/tex]
Step-by-step explanation:
Solve for the value of [tex]a[/tex]:
[tex]\frac{a}{3.5} - 4.8 = 6.3[/tex]
-Add both sides by [tex]4.8[/tex]:
[tex]\frac{a}{3.5} - 4.8 + 4.8 = 6.3 + 4.8[/tex]
[tex]\frac{a}{3.5} = 11.1[/tex]
-Multiply both sides by [tex]3.5[/tex]:
[tex]a = 11.1 \times 3.5[/tex]
[tex]\boxed {a = 38.85}[/tex]
Therefore, the value of [tex]a[/tex] is [tex]38.85[/tex].
For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy???
Answer: 4 and a half
Step-by-step explanation:
Jamie tossed a coin 50 times. The coin landed on heads 27 times and landed on tails
23 times. What is the relative frequency of landing on heads?
Answer: 54%
Step-by-step explanation:
The relative frequency of landing on heads is 0.54 or 54%.
Given that Jamie tossed a coin 50 times.
Head showed for 27 times.
Tails showed for 23 times.
We need to find the relative frequency of landing on heads,
The relative frequency of an event is calculated by dividing the number of times the event occurred by the total number of trials or occurrences.
In this case, Jamie tossed a coin 50 times, and it landed on heads 27 times.
To find the relative frequency of landing on heads, we divide the number of times the coin landed on heads (27) by the total number of tosses (50):
Relative Frequency of landing on heads = Number of heads / Total number of tosses
Relative Frequency of landing on heads = 27 / 50
Simplifying this fraction, we get:
Relative Frequency of landing on heads = 0.54
This means that, based on the given data, the coin landed on heads approximately 54% of the time in the 50 tosses performed by Jamie.
Therefore, the relative frequency of landing on heads is 0.54 or 54%.
Learn more about Relative Frequency click;
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A circular garden has a diameter of 8 feet, and a rectangular garden has side lengths of 5 feet by 9 feet.
find the difference in square feet between the two gardens
Answer:
rectangular
Step-by-step explanation:
Answer:
The square of a number decreased by 8 times the number equals 9. Determine the two possible values of the number. X2-8x=9. +1-9 ... 9. Basic Area of Rectangles. 16 The length of a rectangular room is 5 less than ... 17 The total area of Jon's backyard is 144 square feet. ... the length of a side of the original square garden.
Step-by-step explanation:
i hope this helps!
How many bottles did eric buy for his friends
Answer: It depends on how many friends Eric had, and how many bottles they wanted. I would be able to answer more if your were a little more specific with the details
Step-by-step explanation:
due soon will give brainalist no fake answers!!
Answer:
90gr strawberry jelly
6 sponge fingers
315ml custard
135gr tinned fruit
Step-by-step explanation:
120/4 = 30 * 3 = 90
8/4 = 2 * 3 = 6
420/4 = 105 * 3 = 315
180/4 = 45 * 3 = 135
Felix can grow 6 plants with every seed packet. Write an equation that shows the relationship between the number of seed packets x and the total number of plants y. Write your answer as an equation with y first, followed by an equals sign.
Answer:
I believe it’s:
Y= 6x
Step-by-step explanation:
Need help in math ASAP
Answer:
B
Supplementary means they add to make 180 deg, so solve (4x-8)+(2x+2)=180
Answer:
angle a + angle b=180
4x-8+(2x+2)=180
6x-6=180
6x=180+6
x=186/6
{x=31°}
which of the following is an arithmetic sequence with common difference 2
A. 1, -3, 5, -7, 9
B. 2, 4, 8, 16, 32
C. 10, 8, 6, 4, 2
D. 13, 15, 17, 19, 21
Answer:
C is the answer.
C has a common difference of "2"
Step-by-step explanation:
You could say that the word "difference" also means Subtraction, so in a simpler way of saying "The common difference of 2" you could say, "Which one of the following is subtracting by 2?"
PLEASE MARK BRAINLIEST