Jake needs to buy 120 beverages for a party. What equation, in standard form, determines the number x of 8-packs of juice and the number y of 12-packs of water that Jake can buy?
___ x + ___y = ____
Answer:
8x+12y=120
Step-by-step explanation:
i took the test
The difference between the areas of the figures is less than 4.
An absolute value inequality that represents this situation is ___
The solution of the inequality is ___
Answer:
1. |40 – 4x| < 4
2. 9 < x < 11
Step-by-step explanation:
We'll begin by calculating the area of each figure. This can be obtained as follow:
For triangle:
Area = ½ × base × height
Base = 8
Height = 6
Area =?
Area = ½ × 8 × 6
Area = 4 × 6
Area = 24
For Rectangle:
Area = length × breadth
Length = x – 4
Breadth = 4
Area =?
Area = (x – 4) × 4
Area = 4x – 16
Summary:
Area of triangle (Aₜ) = 24
Area of rectangle (Aᵣ) = 4x – 16
1. Writing an absolute value for the inequality.
From the question given above, we were told that the difference between the areas of the figures is less than 4. This can be written as:
Aₜ – Aᵣ < 4
Area of triangle (Aₜ) = 24
Area of rectangle (Aᵣ) = 4x – 16
24 – (4x – 16) < 4
Simplify
24 – (4x – 16) < 4
Clear bracket
24 – 4x + 16 < 4
24 + 16 – 4x < 4
40 – 4x < 4
Thus, we can write the absolute value for the above inequality as:
|40 – 4x| < 4
2. Determination of the solution of the inequality.
This is illustrated below:
|40 – 4x| < 4
Thus the above equation can be written as
– 4 < 40 – 4x < 4
Subtract 40 from both side
– 4 – 40 < 40 – 4x – 40 < 4 –40
– 44 < – 4x < – 36
Divide through by –4
– 44/–4 < x < – 36/–4
11 > x > 9
Note: the inequality sign changed because we divided by a negative number
Thus, 11 > x > 9 becomes 9 < x < 11
Therefore, the solution to the inequality is 9 < x < 11
The double number line shows that 4 pounds of tomatoes cost $14. Draw tick marks and write labels to show the prices of 1, 2, and 3 pounds of tomatoes.
Answer:
every tick is 3.50
Step-by-step explanation:
14/4=3.5
The price of one, two, and three pounds of tomatoes is $10.5. Each quantity is represented by its own number line in a double number line, with corresponding pairs of values lined up.
How are double number lines created?Equal ratios are represented by two parallel number lines in a double number line diagram. The tick marks are in the same places on both number lines.Despite the fact that the other numbers change frequently, the tick marks labeled with 0 always line up.Diagrams with a double number line can show you how two quantities are related in terms of their ratios.They work best when the quantities have different units. (The unit rate is represented by the number 1) Students can more easily "see" that the same ratio can take many different comparable shapes when using double number line diagrams.Therefore,
Given,
4 pounds of tomatoes cost = $14
We find the prices of 1, 2, and 3 pounds of tomatoes
14/4 = 3.5
So,
1 lb = 3.5
2 lbs = 2× 3.5 = 7
3 lbs= 3 × 3.5 = 10.5
Hence, The price of one, two, and three pounds of tomatoes is $10.5.
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Lee can type 1 1/3 pages every 15 minutes. How many hours does it take him to to type 10 2/3 pages? Complete the rate table to solve the proportion
Answer:
The answer is 8 because you need to add 1 1/3 eight times to get 10 2/3
Answer:
It takes two hours
Step-by-step explanation:
Rotation is a ______?
A. Spin or turn
B.slide
C.mirror or flip
D.move
HURRY PLEASE
Answer:
A) Spin or turn
Step-by-step explanation:
How would you find the quadratic that goes through the point (4,0), the axis of symmetry is x=7, and it also goes through the point (1,5)?
9514 1404 393
Answer:
y = (5/27)(x -7)^2 -5/3
Step-by-step explanation:
Use the given points to find the unknowns in the equation.
If the axis of symmetry is x=7, then the equation can be written in the form ...
y = a(x -7)^2 +b
Filling in the two point values, we have two equations:
0 = a(4 -7)^2 +b ⇒ 9a +b = 0
5 = a(1 -7)^2 +b ⇒ 36a +b = 5
__
Subtracting the first equation from the second, we have ...
(36a +b) -(9a +b) = (5) -(0)
27a = 5
a = 5/27
Substituting that value into the first equation gives ...
9(5/27) +b = 0
5/3 +b = 0
b = -5/3
So, the quadratic can be written in vertex form as ...
y = (5/27)(x -7)^2 -5/3
A worker package 150 games in 15 minutes. how many games can he package per minute?
Answer:
600 games
Step-by-step explanation:
60/15=4
150*4=600
what is a polynomial
A polynomial is an expression that contains several terms.
Examples include...
5x +1
5x^(-2) +1
Examine this algebraic expression:
3x
4
− 2y +
3
7
What are the variables?
What are the coefficients?
3x/4 and –2y
What is the constant?
Answer:
C/ x and y
A/-2 and 3/4
B/ 3/7
Step-by-step explanation:
i got it right
The variables are x and y, the coefficients are -2 and 3/4, and the constant is 3/7 in the given algebraic expression 3x/4 − 2y + 3/7.
What is the algebraic expression?Algebraic expressions are mathematical statements that comprise at least two variables or integers.
What are arithmetic operations?Arithmetic operations can also be described via subtracting, dividing, and multiplying built-in functions.
We have been the given algebraic expression as :
⇒ 3x/4 − 2y + 3/7
Here variables are x and y
The coefficients are -2 and 3/4
The constant is 3/7
Therefore, the variables are x and y, the coefficients are -2 and 3/4, and the constant is 3/7 in the given algebraic expression 3x/4 − 2y + 3/7.
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is 5.8 greater then fifty eight hundreths
Answer:
no
Step-by-step explanation:
fifty eight hundreths= 5,800
5.8<5,800
Pls help me with number 6 and 7 choose 2 answers for number 6 and 3 for 7 !! ILL MARK BRAINLIST !!
Answer:
You cant make him brainiest unless more than one person answers so I'm just "answering" so you can give him brainiest
Step-by-step explanation:
Can someone help me with these 2 please thank you :)
Answer:
11. -0.250
12. 0
PLEASE HELP ASAP!!!
A cone has a volume of 200 in^3 and a
height of 10 in. Find the radius of this cone.
Answer:
The radius is 4.37 in approximately
Step-by-step explanation:
What is the equation, in slope-intercept form, of the line that passes through (0, 6) and has a slope of 4 (5 points)
Answer: y=4x+6
Step-by-step explanation: you replace the variables in the equation with the variables in the point given to find b.
Answer:
[tex]y = 4x+6[/tex]
Step-by-step explanation:
Equation of a line
The equation of a line can be written in the form:
[tex]y = mx+b[/tex]
Where m is the slope of the line and b is the y-intercept. We are given the value of m=4, thus the equation becomes:
[tex]y = 4x+b[/tex]
To find the value of b, we use the point (0,6):
[tex]6=4*0+b[/tex]
Solving:
[tex]b=6[/tex]
Thus, the equation in slope-intercept form of the required line is
[tex]\boxed{y = 4x+6}[/tex]
When a number, half of the number, and a third of the number are added together, the
sum is 275. Find the three numbers.
Step-by-step explanation:
Let the number be x.
Half of a number is x/2 and a third of the number is x/3
ATQ,
[tex]x+\dfrac{x}{2}+\dfrac{x}{3}=275\\\\\dfrac{6x+3x+2x}{6}=275\\\\\dfrac{11x}{6}=275\\\\x=\dfrac{275\times 6}{11}\\\\x=150[/tex]
Frist no is 150
Second no is 150/2 = 75
Third no is 50
Help!!!!!! I need to know if it's right!
Answer:
I think it's right
Step-by-step explanation:
as -1×-1=+1 (positive 1)
which is different from the answer in step 1 because you needs to get -1 for the correct answer.
-1(x-1)= -x+1
the real answer is -1(x+1)= -x-1
Julian factored -1 incorrectly in the second step. The correct option is B.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given polynomial 2x⁴ + 2x³ - x² - x will be solved as below:-
P = 2x⁴ + 2x³ - x² - x
P = x ( 2x³ + 2x - x - 1 )
P = x ( 2x² [ x + 1 ] -1 ( x + 1 )
P = x ( 2x² - 1 ) ( x + 1 )
Therefore, Julian factored -1 incorrectly in the second step. The correct option is B.
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I want to find the value of x
Answer:
WALA NG VALUE ANG X DAHIL INIWAN KA NA NIYA
Can someone help me please
Answer:
i cant see the picture
Step-by-step explanation:
WILL GIVE BRAINLIEST!
The estimated total cost, y, of a child's toy is partially based on the number of batteries used, x. The cost per battery is $0.50. They toy itself costs $15. Which equation represent the situation?
a
y = 0.50x - 15
b
y = 15x - 0.50
c
y = 15x + 0.50
d
y = 0.50x + 15
Answer:
D: 0.50x+15
Step-by-step explanation:
batteries used(each)- x, so you add the x in front of 0.50 representing multiplication between the #
you are doing total cost so you are doing addition (obvously) then its a plain $15 for the toy itself therefore,
y=0.50x+15 (hope this made sense)
pls help jwjwkwkwwkwkwkwkwkkwwkkwkwwkkwkw
Answer:
o,-3 and 1.5,0
Step-by-step explanation:
You can find a calculator on a website called Desmos that might help answer related questions.
Which of the following angles are congruent?
Answer:
angle B and angle f
Step-by-step explanation:
im not all that smart but goodluck
4 yards per week in feet per day
Answer:
1,71429...
Step-by-step explanation:
4yd = 3ft
→12ft per week
12 ÷ 7 = 1,71429
One class is selling tickets for $2.50 each and has already raised $350.
• The other class is selling tickets for $3.00 each and has already raised $225.
Which equation can be used to find t, the number of tickets each class needs to sell so that the total amount raised is the same for both classes?
Answer: 2.5t + 350 = 3t + 225
t = 250 btw
Answer:
b
Step-by-step explanation:
b
The work that Ryan did to find the greatest common factor of 48 and 72 is shown below.
Answer:
D. Ryan found the Least Common Multiple
Answer :
D - Ryan found the least common multiple.
Evaluate y 2 -y 1 x 2 -x 1 given the following values x 1 =10,x 2 =0,y 1 =14 and y 2 =6
Answer: the answer is 2
Step-by-step explanation:
y = -4x - 12
What is the slope(m) and the y-intercept (b)
Answer:
x=6.0
Step-by-step explanation:
the slope (m) is -4, indicating a downward slope, and the y-intercept (b) is -12,
In the equation y = -4x - 12, the coefficient of x, -4, represents the slope of the line. The slope (m) is the ratio of the vertical change to the horizontal change between any two points on the line. In this case, the slope is -4, indicating that for every unit increase in x, the y-value decreases by 4.
The constant term, -12, represents the y-intercept (b). The y-intercept is the point where the line intersects the y-axis. In this equation, the y-intercept is -12, which means that the line crosses the y-axis at the point (0, -12).
To summarize, the slope (m) is -4, indicating a downward slope, and the y-intercept (b) is -12, representing the point where the line crosses the y-axis.
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There is a proportional relationship between a volume measured in cups, c and the same volume measured in tablespoons, t.
3 cups are equivalent to 48 tablespoons.
What is the constant of proportionality for this relationship? What does this mean in terms of volume measured in cups, c and the same volume measured in tablespoons, t?
Answer:
We really need help someone please help us
Step-by-step explanation:
Is the equation true or false when x = 4?
(3−x28)⋅12=3x
true
false
Answer:
false
Step-by-step explanation:
the equation x would be -1.04 or 1.03 so it would be false
Answer:
the actual answer is true
Step-by-step explanation:
The model below is used to represent the area of a
square with a side length of /64 units.
Answer:
8
Step-by-step explanation:
Because you can count the squares on the side or you can just do the square root of 64.
4/5 + 3 1/10
Please answer quick (◍•ᴗ•◍)❤
Answer:
3 9/10
Step-by-step explanation:
Find the common factor
8/10+3 1/10
3 9/10