The container with a volume of 2 cubic yards, which is equivalent to 54 cubic feet, would require 3 barrels of sand to fill it up, as the volume of each barrel is 18 cubic feet.
Explanation:To find out how many barrels of sand will be needed to fill a container with a volume of 2 cubic yards, we first need to convert cubic yards to cubic feet, as the measurement of the barrel volume is given in cubic feet. Since 1 cubic yard is equivalent to 27 cubic feet, 2 cubic yards will be 2 * 27 = 54 cubic feet.
Next, we divide the volume of the container by the volume of one barrel of sand. Hence, the number of barrels needed = 54 cubic feet / 18 cubic feet per barrel = 3 barrels.
So, it will take 3 barrels of sand to fill a container with a volume of 2 cubic yards.
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Simon used these steps to solve an equation:
Step 1: -6(x + 7) = 2(x − 11)
Step 2: -6x − 42 = 2x − 22
Step 3: -8x − 42 = -22
Step 4: -8x = 20
Which property did he use to get from step 3 to step 4?
A. addition property of equality
B. distributive property
C. subtraction property of equality
D. transitive property
A. Addition Property of Equality. The property that states that if you add the same number to both sides of an equation, the sides remain equal. Which as we see the equation still remains equal.
To go through Step 3 to Step 4 he used the addition property of equality. Option A is correct.
Given that,
Simion used steps to solve the equation,
To determine which property did he use to get from step 3 to step 4.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Step 1: -6(x + 7) = 2(x − 11)
Distributive property
Step 2: -6x − 42 = 2x − 22
Addition property of equality
Adding 2x on both side
Step 3: -8x − 42 = -22
Addition property of equality
Adding 42 on both sides
Step 4: -8x = 20
Thus, to go through Step 3 to Step 4 he used the addition property of equality. Option A is correct.
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Consider the equation 5y = 2x +4. Select all the equations that are perpendicular to the given equation.
None of the given equations are perpendicular to the equation '5y = 2x +4'. This is because perpendicular lines have reciprocal, negative slopes and none of the given lines meet this criteria.
Explanation:To find the equations that are "perpendicular" to the given equation 5y = 2x +4, we first need to find out the slope of the given equation. The slope of the equation is obtained by rearranging it into the y=mx+b form where m stands for the slope. Thus, y=(2/5)x+4/5, which gives us a slope (m) of 2/5.
Perpendicular lines have slopes that are negative reciprocals of each other. So, for a line to be perpendicular to the given line, it should have a slope of -5/2.
Given the equations 7 y = 6x + 8, 4y = 8, and y + 7 = 3x, let's find out their slopes. The slope for the first equation is 6/7, for the second equation is undefined as it's a horizontal line, and for the third equation is 3. Hence, none of these lines are perpendicular to the given line. Similarly, none of the lines Y2 = -173.5+ 4.83x − 2(16.4) and line Y3 = -173.5+ 4.83x + 2(16.4) don't have a slope of -5/2 and hence, are not perpendicular to the given line.
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A line has a slope of 2/3 and a y-intercept of 4.
Which of the following is the equation of the line?
The equation of the line with a slope of 2/3 and y-intercept of 4 is y = 2/3x + 4.
Explanation:The equation of a line in slope-intercept form (which is the most common form we deal with in algebra) is y = mx + b, where m is the slope and b is the y-intercept.
In this case, you're given that the slope (m) is 2/3 and the y-intercept (b) is 4. Substituting these values into the equation gives you the equation of the line: y = 2/3x + 4.
This is the equation that represents the given line
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Final answer:
The equation of the line with a slope of 2/3 and a y-intercept of 4 is y = 2/3x + 4.
Explanation:
To find the equation of a line with a slope of ⅓ and a y-intercept of 4, we can use the slope-intercept form of a line, which is y = mx + b where m is the slope and b is the y-intercept.
The given slope is ⅓, so m = ⅓. Given that the y-intercept is 4, b = 4.
Plugging these values into the slope-intercept equation, we get y = ⅓x + 4, which is the equation of the desired line.
The equation of a line is a mathematical expression that describes the relationship between the independent variable (x) and the dependent variable (y) for points on that line in a Cartesian coordinate system. It allows you to represent a straight line graphically on a two-dimensional plane.
for #3 find the x and y-intercept and graph
Answer:
The x-intercept is at -8 and the y-intercept is at -5.
Step-by-step explanation:
When you simplify 5x + 8y = 40 into y = mx + b form, you get y = -5/8x - 5.
Answer: x-intercept is (-8,0) and y-intercept is (0,-5)
Step-by-step explanation:
5x+8y=-40
To find the x-intercept, you plug in 0 in for y.
5x+8(0)=-40
5x=-40
Then solve for x
5x/5=-40/5
x=-8
The x-intercept is (-8,0)
To find the y-intercept, you plug in 0 in for x
5(0)+8y=-40
8y=-40
Solve for y
8y/8=-40/8
y=-5
y-intercept is (0,-5)
Which of the following is(are)the solution(s) to |x+3|=12?
Can someone help me, I have no idea how to do this :(
Dan wrote (2x10^6)+(3x10^4)+(5x10^3)+4 for the expanded form of two millions , three hundred fifty thousand, four. What error did he make in the expanded form? What is the standard form of the number?
Answer:
Part 1) Dan wrote in expanded form two millions thirty five thousand, four instead of two millions , three hundred fifty thousand, four
Part 2) The standard for of the number is [tex]2,350,004[/tex]
Step-by-step explanation:
we have
The number two millions , three hundred fifty thousand, four
we know that
Dan Wrote
[tex](2*10^6)+(3*10^4)+(5*10^3)+4=2,000,000+30,000+5,000+4=2,035,004[/tex]
The number that Dan wrote is two millions thirty five thousand, four
The correct number in expanded form is
[tex](2*10^6)+(3*10^5)+(5*10^4)+4=2,000,000+300,000+50,000+4=2,350,004[/tex]
The standard for of the number is [tex]2,350,004[/tex]
Explain how you could write the mixed number 45 3/8 in
scientific notation.
Answer:
[tex]4.5375*10^1[/tex]
Step-by-step explanation:
we know that
[tex]45\frac{3}{8}=45+\frac{3}{8}=45+0.375=45.375[/tex]
Convert decimal number in scientific notation
A number expressed in scientific notation has the form
[tex]a*10^{n}[/tex]
where
[tex]1\leq a < 10[/tex]
n is a integer
Expressing 45.375 in this form means writing the number as a value between 1 and 10
so
For a=4.5375,n=1
[tex]45.375=4.5375*10^1[/tex]
Final answer:
The mixed number 45 3/8 can be expressed in scientific notation as 4.5375 *[tex]10^2[/tex] by first converting it to an improper fraction, then to a decimal, and finally moving the decimal point two places to the left.
Explanation:
To write the mixed number 45 3/8 in scientific notation, let's first convert it into an improper fraction and then into a decimal. The mixed number 45 3/8 is equivalent to (45 * 8 + 3) / 8, which simplifies to 363/8 or 45.375 as a decimal.
Now, to express this in scientific notation, we move the decimal point two places to the left so that the number falls between 1 and 10. As a result, we get 4.5375. Since we moved the decimal two places to the right, we multiplied by 10 to the power of 2([tex]10^2[/tex])
Finally, 45 3/8 in scientific notation is 4.5375 *( [tex]10^2[/tex] ).
the line of the line below is -4 use the coordinates of the labeled point to find a point slope equation of the line(4,-9)
a. y - 9 = -4(x + 4)
b. y + 9 = 4(x - 4)
c. y + 9 = -4(x - 4)
d. y - 9 = 4(x + 4)
Answer:
c. y + 9 = -4(x - 4)
Step-by-step explanation:
According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful.
I am joyous to assist you anytime.
What is the value of y if 6y-2=34
Answer:
6
Step-by-step explanation:
6y - 2 = 34
6y = 36
y = 6
Answer:
y = 6
Step-by-step explanation:
6y - 2 = 34
+2 +2
6y = 36
[tex]\frac{6y}{6} = \frac{36}{6}[/tex]
y = 6
X^2- 4y² = 9
3x + 4y = 7
Answer:
[3⅖, -⅘], [5, -2]
Step-by-step explanation:
I could not do any more, but I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
15-(0.7 x3) please help meeeeee
Answer:
129/10 or 12.9
Step-by-step explanation:
Multiply 0.7 by 3 and subtract that answer by 15
Answer:
12.9 dat was easy
What is the first step in simplifying
Answer: PEMDAS
parenthesis, exponents, multiplication, division, addition, subtraction
Step-by-step explanation:
Answer:
Collect like terms or reduce or using PEMDAS METHOD.
What is 240 divided by 6
Answer:
40
explanation:
240 ÷ 6 = 40
The value of expression 240 divided by 6 would be equal to 40
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the expression of 240 divided by 6
A negative divided by a negative is positive
240 ÷ 6 = 40
Therefore, The value of 240 divided by 6 is; 40
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Find n 5|6n+15|+2=-43
Answer:
No solutionStep-by-step explanation:
[tex]5|6n+15|+2=-43\qquad\text{subtract 2 from both sides}\\\\5|6n+15|+2-2=-43-2\\\\5|6n+15|=-45\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup^1|6n+15|}{5\!\!\!\!\diagup_1}=\dfrac{-45\!\!\!\!\!\diagup^9}{5\!\!\!\!\diagup_1}\\\\|6n+15|=-9\qquad\bold{FALSE}\to\text{no solution}\\\\\text{because}\ |a|\geq0\ \text{for any real value of}\ a.[/tex]
Which compound inequality is represented by the graph?
x<-40x2>3
x<-4 and 2>3
x<-4 or x <3
x<-4 and x <3
1/5 x 6/7 ?
A. 6/12
B.7/30
C.6/35
D.7/35
In order to get the answer to this question you must multiply the numerators then multiply the denominators and reduce if needed.
[tex]\frac{1}{5} \times\frac{6}{7}[/tex]
[tex]1\times6=6[/tex]
[tex]5\times7=35[/tex]
[tex]=\frac{6}{35}[/tex]
Therefore your answer is option C "6/35."
Hope this helps.
Which describes the transformation? Select three options,
Answer:
There are four kind of transformation that can take place in any Geometrical shape
1. Reflection----Congruent Image
2. Rotation---Congruent Image
3. Translation---Congruent Image
4. Dilation -----Similar Image
The Correct three options which Describes Transformation are
→ It is rigid.----( Reflection, Translation, Rotation)
→ It is non-rigid.-----(Dilation)
→ It is isometric.------Length remain Preserved that is Reflection, Translation, and Rotation
→The size is preserved.-------Reflection, Translation, and Rotation.
I Hope It's Helpful:)
10. 4(x - 1) - 5 = 3x + 7
how do i Distribute
Answer:
x=16
Step-by-step explanation:
The Distributive property says a(b+c) = ab+ac
1) You have 4(x-1)... This can be simplified to 4x-4
4x-4-5=3x+7
2) Combine alike terms:
4x-9=3x+7
3) add a 9 to both sides:
4x=3x+16
4) subtract a 3x from both sides:
x=16
I am thinking of a number. If you triple my number and subtract 11, you get my number plus 33. What's my number?"
Answer:
22
Step-by-step explanation:
22 x 3 = 66
66- 11 = 55
55-33 = 22
For each of the hypothetical data sets, determine whether a bar graph or a pie chart would be an appropriate way to display the data. In some cases, both types of graphs may be appropriate.
the percent of individuals with each of the following natural eye colors:
brown, blue, green, hazel, and other
the population density of each of the 50 states in the United States
the number of college students who play basketball, baseball, or soccer
the proportion of traditional public schools in a region compared to
the proportion of charter and private K–12 schools in that region.
choices: Bar graph Pie chart
The final answers of four different parts of the question can be concluded in the following bulletin points.
Both the charts can be used to represent the above condition but the better way to represent it is Pie chart.Bar Graph is the better way to represent the above scenario, because the higher data entry may result in a very huge pie chart to understand it properly.The pie chart is the better way to represent the above situation.The pie chart is the better way to represent the above situation.1). The percent of individuals with each of the following natural eye colors:
brown, blue, green, hazel, and others.
Both the charts can be used to represent the above condition but the better way to represent it is Pie chart.2). The population density of each of the 50 states in the United States.
Bar Graph is the better way to represent the above scenario, because the higher data entry may result in a very huge pie chart to understand it properly.3). The number of college students who play basketball, baseball, or soccer.
The pie chart is the better way to represent the above situation.4). The proportion of traditional public schools in a region compared to
the proportion of charter and private K–12 schools in that region.
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For the percent of individuals with each natural eye color and the population density of each state in the United States, a bar graph is appropriate. For the number of college students who play different sports, a bar graph is also appropriate.
Explanation:A bar graph would be an appropriate way to display the percent of individuals with each natural eye color. Each bar in the graph would represent a different eye color, and the length of the bar would represent the percentage of individuals with that eye color. This would allow for easy comparison of the different eye colors.
For the population density of each state in the United States, a bar graph would also be appropriate. Each bar in the graph would represent a different state, and the height of the bar would represent the population density of that state. This would allow for easy comparison of the population densities between states.
For the number of college students who play basketball, baseball, or soccer, a bar graph would be the most appropriate choice. Each bar in the graph would represent a different sport, and the height of the bar would represent the number of students who play that sport. This would allow for easy comparison of the number of students playing each sport.
what is 3w + 5 =23 it's a two step equation
Answer:
w=6
Step-by-step explanation:
3w+5=23
3w=23-5
3w=18
w=6
The solution to the equation 3w + 5 = 23 is w = 6.
The given equation is 3w + 5 = 23.
We need to solve for w.
Subtract 5 from both sides of the equation to isolate the term with 3w:
3w + 5 - 5 = 23 - 5
3w = 18
Divide both sides of the equation by 3 to solve for w:
(3w) / 3 = 18 / 3
This simplifies to:
w = 6
Therefore, the solution to the equation 3w + 5 = 23 is w = 6.
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The number of boys in the tennis club is 10 more than half the number of girls. There are 30 boys in the tennis club. All together, how many boys and girls are in the club.
Answer:
36
Step-by-step explanation:
Number of boys = 30
also, Number of boys = 10(number of girls/2)
∴ 30 = 10(number of girls/2)
30×2 = 10(number of girls)
⇒ number of girls = [tex]\frac{60}{10}[/tex]
⇒ number of girls = 6
Total number of girls and boys = 30 + 6 = 36
5x+34=-2+14x i need the individual steps
Answer: x = 4
Step-by-step explanation:
5x + 34 = -2 + 14x
5x - 5x + 34 = -2 + 14x -5x Remove 5x from both sides
34 = -2 +9x
34 + 2 = -2 + 2 + 9x Add 2 to both sides (remove constant)
36 = 9x
36/9 = 9x/9 Divide both sides by 9 to isolate the variable
4 = x
or
x = 4
Steven is cutting an 11 ft piece of lumber into three pieces to build a triangular garden. Which diagram shows a way i
which he can cut the wood to create three pieces that can form a triangle?
Answer:
The correct answer is 3ft | 4ft | 4ft
Step-by-step explanation:
Got it correct on edge
The dimensions of the lumber that can be used to build the triangular garden are 3ft, 4 ft and 4ft.
What are the pieces that can be used to build the triangular garden?A triangle is a three-sided polygon with three edges and three vertices. The sum of angles in a triangle is 180 degrees
In order to determine the pieces that can be used to build the triangular garden, the sum of the two sides must be greater than the length of the third side
2 + 2 < 7
1 + 4 < 6
3 + 2 < 6
3 + 4 > 4
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3. What is the name of a symbol that is used to
represent a quantity that can change?
Answer:
Variable
Step-by-step explanation:
A Variable is a letter or symbol used to represent a quantity that can change.
The symbol used to represent a quantity that can change is called a variable.
We have,
The symbol that is commonly used to represent a quantity that can change is called a variable.
In mathematics and algebraic equations, variables are often represented by letters such as x, y, or z.
Variables are placeholders for unknown or changing values that can be assigned different numerical or algebraic values during calculations or problem-solving.
They allow for the generalization and manipulation of mathematical expressions and equations.
Thus,
The symbol used to represent a quantity that can change is called a variable.
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Jenna calculated several numbers in her calculator. The result displayed -1.7E-4 on the calculator screen. Which equivalent number(s) does this represent? Select all that apply.
1. -1.7 x 10^-4
2. 1.7 x 10^-4
3. 0.00017
4. -0.00017
5. -1,700
Answer:
1, 4
Step-by-step explanation:
e is the exponent of the number, therefore it is the number which 10 is raised by, so -4.
Which means -1.7 will be multipled by 10 raised to the -4 power, so 1 is obviously correct.
Additionally, This is in scientific form. You can also write this in standard form in decimals, 10^-4 means it is 4 decimal places ahead the original number so you can move the decimal point back 4 places and add 0s, you will see that -0.00017 is also in fact correct.
Answer:
1 and 4.
Step-by-step explanation:
That would be -1.7 * 10^-4.
Also it can be written as -0.00017.
sam is 5 feet tall and casts a shadow 4 feet long. at the same time, a nearby tree casts a shadow 12 feet long. what is the height of the tree
Answer:
15
Step-by-step explanation:
We can just make a ratio. 5:4 = x:12. We see x=15
The height of the tree = 15m.
let us say the height of the tree=h
in this problem,
the height of the sam can be treated as perpendicular of a right-angle triangle.
while his shadow can be treated as the base of the same triangle.
now, we need to calculate the angle of elevation α
what is the angle of elevation?it is the angle between the line of sight and the horizon.
hence,
the tangent of the angle of elevation α= height/length of the shadow
tanα= 5/4
tan α = height of the tree/length of the shadow of the tree
5/4 = h/12
h=15m
therefore, the height of the tree = 15m
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5. Margaret is making fudge for a
party. The recipe calls for
| 1 1/4 cups of sugar and 1 1/4cups of
chocolate chips. How many cups
of sugar and chocolate chips does
Margaret need to make the
fudge?
Margaret needs 2 1/2 cups of sugar and chocolate chips to make the fudge.
Explanation:To make the fudge, Margaret needs 1 1/4 cups of sugar and 1 1/4 cups of chocolate chips.
To find the total number of cups needed, add the amounts of sugar and chocolate chips: 1 1/4 + 1 1/4 = 2 1/2 cups.
Therefore, Margaret needs 2 1/2 cups of sugar and chocolate chips to make the fudge.
What is the answer to 10h - 4h
Answer:
Step-by-step explanation:6 hours because 10-4=6