Answer:
[tex]r\leq 10.8[/tex]
OR
[tex]r\leq 10[/tex]
Step-by-step explanation:
Given that:
Amount of water in the aquarium = 9 gallons
Weight of water in the aquarium = 85 pounds
Total weight that aquarium can hold = 112 pounds
Weight of each rock = 2.5 pounds
To find:
The inequality to find the number of rocks, [tex]r[/tex] that can put in her tank.
Solution:
First of all, let us find more weight that the aquarium can hold after putting the water in the aquarium.
Additional weight that can be put in the aquarium = Total weight - Weight of water = 112 - 85 = 27 pounds
This 27 pounds can be of rocks.
Let the number of rocks that can be put in the aquarium = [tex]r[/tex]
Total weight of [tex]r[/tex] number of rocks = Weight of one rock multiplied by [tex]r[/tex]=2.5[tex]r[/tex]
Now, this weight of rocks must be lesser than or equal to 27 pounds.
Therefore, the in equality is:
[tex]2.5r\leq =27\\\Rightarrow r \leq 10.8\\OR\\\Rightarrow r \leq 10[/tex]
Several friends compared their bank account balances. Current Account Balance Name Checking account balance Zöe $10.98 Yvette –$11.32 Xavier –$11.71 Wyatt $11.75 Vern $10.89 Which list shows the people in order of the least bank balance to the greatest bank balance? Vern, Zöe, Yvette, Xavier, Wyatt Xavier, Yvette, Vern, Zöe, Wyatt Yvette, Xavier, Vern, Zöe, Wyatt Wyatt, Zöe, Vern, Yvette, Xavier
Answer:
A. Vern, Zöe, Yvette, Xavier, Wyatt
Step-by-step explanation:
Zöe $10.98
Yvette –$11.32
Xavier –$11.71
Wyatt $11.75
Vern $10.89
Arrange from the least bank balance to the greatest bank balance
Vern $10.89
Zöe $10.98
Yvette –$11.32
Xavier –$11.71
Wyatt $11.75
Which list shows the people in order of the least bank balance to the greatest bank balance?
A. Vern, Zöe, Yvette, Xavier, Wyatt
B. Xavier, Yvette, Vern, Zöe, Wyatt
C. Yvette, Xavier, Vern, Zöe, Wyatt
D. Wyatt, Zöe, Vern, Yvette, Xavier
Answer:
Vern, Zöe, Yvette, Xavier, Wyatt A
Step-by-step explanation:
I took the test :)
Im not sure what to do
Answer:
[tex]h(-1)=\frac{-2}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
[tex]h(x)=\frac{2x-6}{4x^2+8}[/tex]
h(-1) is x = -1
Step 2: Evaluate
Substitute: [tex]h(-1)=\frac{2(-1)-6}{4(-1)^2+8}[/tex]Exponents: [tex]h(-1)=\frac{2(-1)-6}{4(1)+8}[/tex]Multiply: [tex]h(-1)=\frac{-2-6}{4+8}[/tex]Subtract: [tex]h(-1)=\frac{-8}{4+8}[/tex]Add: [tex]h(-1)=\frac{-8}{12}[/tex]Simplify: [tex]h(-1)=\frac{-2}{3}[/tex]What is an equation in standard form of the line that has x-intercept 1 and y-intercept 4?
A. x-4y=4
B. 4x-y=4
C. 4x+y=4
D. x-4y=-4
The equation of the straight line that has x-intercept 1 and y-intercept 4 is:
4x - y = 4
What is a straight line?"A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point."
Given, the line has a x-intercept of 1 and y-intercept of 4. T
Therefore, the line passes through the points (1, 0) and (0, 4).
Now, we can find the slope of the line 'm' that passes through those either points.
Therefore, (x₁ - x₂) = m(y₁ - y₂)
⇒ (1 - 0) = m(0 - 4)
⇒ m = [tex]\frac{1}{4}[/tex]
Now, the equation of the line that has x-intercept 1 and y-intercept 4 is:
(x - x₁) = m(y - y₁)
⇒ (x - 1) = [tex]\frac{1}{4}[/tex](y - 0)
⇒ 4(x - 1) = y
⇒ 4x - y = 4
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Quadratic
3p^2−7p−1=0
Answer:
[tex]x=\frac{7\pm\sqrt{61} }{6}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Step-by-step explanation:
Step 1: Define
3p² - 7p - 1 = 0
Step 2: Identify Variables
a = 3
b = -7
c = -1
Step 3: Find roots
Substitute [Quad Formula]: [tex]x=\frac{7\pm\sqrt{(-7)^2-4(3)(-1)} }{2(3)}[/tex]Evaluate Exponents: [tex]x=\frac{7\pm\sqrt{49-4(3)(-1)} }{2(3)}[/tex]Multiply: [tex]x=\frac{7\pm\sqrt{49+12} }{6}[/tex]Add: [tex]x=\frac{7\pm\sqrt{61} }{6}[/tex]Answer:
x = 7 + √61 ÷ 6
Step-by-step explanation:
3p² - 7p - 1 = 0 is a given equation
3p² - 7p - 1 = 0
Here,
a = 3
b = - 7
c = - 1
Now, Discriminant
D = b² - 4ac
= (- 7)² - 4 (3)(- 1)
= 49 + 12
D = 61 > 0
So, Quadratic Equation
ax² + bx + c = 0
x = - b ± √b² - 4ac ÷ 2a
x = - (- 7) ± √(- 7)² - 4 (3)(- 1) ÷ 2(3)
x = 7 ± √61 ÷ 6
x = 7 ± √61 ÷ 6
x = 7 + √61 ÷ 6 or x = 7 - √61 ÷ 6
∴ Not real Value
Thus, The real value of x is 7 + √61 ÷ 6
-TheUnknownScientist
There are 2.54 centimeters in 1 inch. If a pencil is 18 cm long, how many inches is it? Round to the nearest whole number.
Answer:
7 Inches
Explanation:
2.54 Cm. In One Inch.Pencil Is 18 Cm LongDivide:
18 ÷ 2.54 = 7.08661417323
Round:
7
- PNW
HELP ME PLZ. 2. Mrs. Wilson's dad is looking for a new fishing pole for an upcoming trip to the Grand
Canyon. He found the model he likes at a local sporting goods store. The price of the pole is
$59.50 with a sales tax of 6%. However, he can purchase the pole on a website for $62.50 with
no sales tax added on the price. What is the difference in the price between the store and the
website? Which is more expensive?
At one time the aircraft is 200 m above the surface the submarine is 55 m below the surface and the underwater robotic vehicle is 127 m below the surface what is the distance between the submarine and the aircraft
Answer:
The aircraft and the submarine are 255 m apart
Step-by-step explanation:
Here, we want to calculate the distance between the submarine and the aircraft
From the question;
The aircraft is 200 m above the surface and the submarine is 55 m below ( this is same as an altitude of -55)
So the distance between the two will be;
200-(-55) = 255 m
Answer:
255m
Step-by-step explanation:
4x-5=x-1+3x I need help
Answer:
x = no solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define equation
4x - 5 = x - 1 + 3x
Step 2: Solve for x
Combine like terms: 4x - 5 = 4x - 1Subtract 4x on both sides: -5 ≠ -1Here we see that -5 does not equal -1.
∴ This equation has no solutions.
Plssssss help me I don’t understand this!!!
Answer:
D. 375
Step-by-step explanation:
this is the answer because the distance you need to travel doesn't change based off the amount of gas you have
Carson invested $850 in an account paying an interest rate of 5.7% compounded
daily. Assuming no deposits or withdrawals are made, how much money, to the
nearest dollar, would be in the account after 6 years?
Answer:
$850×5.7/100=48.45
850+48.45=898.45
898
Answer: 1197
Step-by-step explanation:
PLEASE ANSWERR CORRECTLY!!!!!!!!
WILL MARK BRAINLIEST FOR CORRECT ANSWER!!!!!!!!
At the beginning of the week, Naveen has 87 trading cards. On Monday, he gets 9 more. On Tuesday, he gives 16 away. On Wednesday, he is given 3 by a friend. On Thursday, he sells all of his cards to a collector. The collector pays him a rate of c for every card that Naveen has. If Naveen earns $124.50 from the sale, what is c, the rate that the collector pays for each card?
A) $1.08
B) $1.50
C) $41.50
D) $83.00
PLEASE ANSWER CORRECTLY!!!!!!!!
HURRY!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B) $1..50
Step-by-step explanation:
First, how many trading cards did Naveen have?
87 + 9 - 16 + 3 = 83
$124.50 / 83 = $1.50
The total cost of gas and the price paid per gallon have a proportional relationship. Five gallons of gas cost $13.35.
How many gallons of gas is purchased for $34.71?
Answer:
thank you for the free points
Step-by-step explanation:
Answer:
13 gallons
Step-by-step explanation:
13.35 = 5 gallons of gas
1 gallon = 2.67
y = 2.67x
34.71 = 2.67x
[tex]\frac{34.71}{2.67} = \frac{2.67x}{2.67}[/tex]
x = 13
What is the slope of the line ?
O 1/4
O 8/17
O 4
O 6
30 P O I N T S H U R R Y
Answer:
1 1/2
Step-by-step explanation:
I think
Answer:
1 1/14
Step-by-step explanation:
same denominator so, 10+11 = 21,
simplified, 1 1/14
what is the solution for a^3+3a^2b-4b-11b+7
The expression a³ + 3 a² b - 4 a b - 11 b + 7 will have 5 terms in it.
We are given the expression:
a³ + 3 a² b - 4 a b - 11 b + 7
We need to find the number of terms this expression has.
We can see that, this expression has 5 terms.
The first term will be a³.
The second one will be 3 a² b.
The third one will be 4 a b.
The fourth one will be 11 b.
And the fifth one will be 7.
Therefore, we get that, the expression a³ + 3 a² b - 4 a b - 11 b + 7 will have 5 terms in it.
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Your question was incomplete, Please refer the content below:
How many terms are in the expression a³ + 3 a² b - 4 a b - 11 b + 7?
A 100 g ball and a 50 g ball are dropped from a tower. both balls are the same size and there is no air resistance. which answer best describes how they fall? responses both balls hit the ground at the same time. both balls hit the ground at the same time. the 100 g ball hits the ground first. the 100 g ball hits the ground first. the 50 g ball hits the ground first.
When the 100 g ball and a 50 g ball are dropped from a tower. both balls are the same size and there is no air resistance, B. both balls hit the ground at the same time.
How to illustrate the information?When an object moves through the air, air resistance acts as a force. When a body is moving through the air, this force works in the opposite direction. A frictional force is applied to the moving body by air resistance. Air resistance causes a body's speed to slow down as it moves.
Because air resistance slows down the motion of the falling object, it impacts acceleration during a fall to a lesser extent than gravity (g). The object's surface area and speed both influence how much it slows down.
Therefore, when the 100 g ball and a 50 g ball are dropped from a tower. both balls are the same size and there is no air resistance, both balls hit the ground at the same time.
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Answer: Both balls hit the ground at the same time.
Step-by-step explanation: I took the test
Explain why f(x) = x^2-x-6/x^2-9 is continuous at x = 2.
a. f is defined at x = 3
b. f is not defined at x = 2
c. f is defined at x = -3
d. f is defined at x = 2
The correct answer is option D. ([tex]f[/tex] is defined at [tex]x = 2[/tex])
The rational Function is continuous at a given value if its Denominator is not zero. In this exercise, we proceed to Factor the expression by check the value Denominator for each value of [tex]x[/tex].
[tex]f(x) = \frac{x^{2}-x-6}{x^{2}-9}[/tex]
[tex]f(x) = \frac{(x-3)\cdot (x+2)}{(x+3)\cdot (x-3)}[/tex]
As we can see, [tex]f[/tex] is not defined for [tex]x = -3[/tex] and [tex]x = 3[/tex]. Hence, we conclude that right answer is D.
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Which number below is a prime number? O A. 61 OB. 102 O C. 75 O D. 64
Answer:
Step-by-step explanation:
61 is divisible by itself and 1. It's prime.
102 ends in a 2. Therefore it is not prime because it can be divided by 2,
75 = 3*5*5 not prime.
64 = 2 * 2 * 2 *2 * 2*2 Not prime.
Both pyramids in the figure have the same base area as the prisme
The ratio of the combined volume of the pyramids to the volume of the prism,expressed as a fraction in simplest form,is 1/3.
How to calculate the ratio?The volume of a pyramid is (1/3) (base area) (height)
Volume of the lower pyramid = (1/3) (base area) (height) Volume of the upper pyramid = (1/3) (basearea × height)
The combined volume of both pyramids = (2/3) × (base area) (height) .
Their base area is (length x width) of the prism, and their height is (1/2 the height) of the prism.
From here, we'll work with the dimensions of the prism ... L, W, and H .
Combined volume of the pyramids = (2/3) (L x W) (1/2 H)
= (1/3) (L x W x H) .
Volume of the prism = (L x W x H)
The pyramids occupy 1/3 the volume of the prism.
The ratio is 1/3 .
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Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the prism,expressed as a fraction in simplest form,is
Mrs. Drew wants to build a square sandbox with an area of 49 square feet. What is the total length of wood Mrs. Drew needs to make the sides of the sandbox?
Answer:
52 feet of wood is required to make the sides of the square sandbox.
Step-by-step explanation:
Answer:
get one side of the square by getting the square root of 49.
Step-by-step explanation:
S*S=area.
[tex] \sqrt{49} [/tex]
=7. 7*4=28feet
15 points!
identify the slope of the line given in the table: __ identify the slope of the line given in the graph: __ which linear function has a negative slope? ___ which linear function has the steeper slope? ___
Are you sure you didn't have an image to go along with this? Cause this is very unclear...
Answer:
a) -3/2
b) 2/3
c) table
d) table
Step-by-step explanation:
which equation represents the line shown on the
Answer:
A
Step-by-step explanation:
y-int = -2
so the line should cross (0, -2)
Rise over run is 2/5 so go up 2, over 5 and put your dot etc...
9x(10-10x) simplify
i put 90x-90x^2 but it's wrong so i kinda need help
Answer:
Step-by-step explanation:
I hope this helps:)
How do I solve and respond to this question?
Answer:
i think its 6 and 8
Step-by-step explanation:
sorry if i get it wrong
can you tell me if it is right or wrong
5 = 2m − 5
How do you solve for M
a dozen cookies shared among 15 children. If each child receives the same amount of pizza, how much will each child get?
I need help with this, plz help
Answer:
<AFB
Step-by-step explanation:
5 cupcakes cost $8.75. At this rate, how much would 3 cupcakes cost
Answer:
$5.25
Step-by-step explanation:
8.75/5=1.75
1.75 x 3=5.25
Answer:
$5.25
Step-by-step explanation:
8.75 devided by 5 is 1.75 so for 1 cupcake it is $1.75. $1.75 X 3= $5.25
A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the accompanying
table. Write the linear regression equation that represents this set of data, rounding
all coefficients to the nearest hundredth. Using this equation, find the projected test
grade, to the nearest integer, for a student with a homework grade of 49.
The linear regression equation that represents this set of data is Y = -12.41 + 1.15x and the projected test grade for a student with a homework grade of 49 is 44 and this can be determined by using the generalized equation of regression.
Given :
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table.The generalized regression equation is given below:
Y = a + bX --- (1)
where b is given by the formula:
[tex]\rm b = \dfrac{N\sum XY-\sum X \sum Y}{N\sum X^2-(\sum X)^2}[/tex]
Now, substitute the values of the known terms in the above formula in order to determine the value of 'b'.
b = 1.15
and the formula of a is given below:
[tex]\rm a = \dfrac{\sum Y - b \sum X}{N}[/tex]
Now, substitute the values of the known terms in the above formula in order to determine the value of 'a'.
a = -12.41
Now, substitute the values of a and b in the equation (1).
Y = -12.41 + 1.15x
Now, at x = 49 the value of Y becomes:
Y = -12.41 + 1.15(49)
Y = 43.94
Y [tex]\approx[/tex] 44
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The school is 4000 meters from Jim house how many kilometers is this
Answer:
A
Step-by-step explanation: