Graded Assignment
Unit 2 End of Unit 2 Assignment: Adding and Subtracting Rational Numbers
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 4 points)
1. Use both methods to find the distance between the points on the number line.
Method A: Count the number of units between the points.
Method B: Take the absolute value of the difference of the two numbers.
When taking the absolute value, show the larger number first, then show the lesser number first when finding the difference.
Answer:
A.
B.
(Score for Question 2: ___ of 5 points)
2. The table shows several animals that live in or below a tree. The table also shows the elevation of their dwellings, relative to ground level.
Dwellings Elevation (m)
Groundhog burrow -1.2
Red squirrel den 0.3
Robin’s nest 3.6
(a) Plot and label the elevation of each dwelling on a vertical number line.
(b) Calculate the vertical distance between each pair of dwellings. Organize your results in a table.
Answer:
a) Plot and label the elevation of each dwelling on a vertical number line. (2 pts)
b) Calculate the vertical distance between each pair of dwellings. (3 pts)
Groundhog burrow to Red squirrel den
Red squirrel den to Robin’s nest
Groundhog burrow to Robin’s nest
(Score for Question 3: ___ of 6 points)
3. A recipe calls for cups of flour, cup of white sugar, and cup of brown sugar.
(a) How many total cups of ingredients are there? Find a common denominator and then show your work using a number line.
(b) Which of the following mixing bowls should you use to make the recipe: 2-cup, 3-cup, or 4-cup? Explain why you choose this mixing bowl.
Answer:
a) How many total cups of ingredients are there? Find a common denominator and then show your work using a number line. (4 pts)
b) Which of the following mixing bowls should you use to make the recipe: 2-cup, 3-cup, or 4-cup? Explain why you choose this mixing bowl. (2 pts)
Answers
Answer:
Okay Im going off of my work because we did some in class and then the rest by ourselves but i turned mine in yesterday but didnt recieve a grade yet but i hope these help you...
The number number line it is seven units apart.
The absolute value larger number smaller number would be 2 - (-5). So what you do with that is keep the 2 change the subtraction sign to plus sign and change the negative 5 to positive 5. So your answer would be 7.
And smaller number to larger number would be -5 - 2. And then you do the same steps as the last one. Keep the negative five, change the subtraction sign to addition sign and make the two negative. And that answer would be -7
2. For the number two problem you would plot the robins nest just below the top of the verticle line. the red squirrel den would be right next to the zero but a tad up. And the groundhog burrow would be below the zero mark and a little before the end of the verticle line.
Next, for groundhog burrow to red squirrel den you put the number 0.3-(-1.2)=1.5 Red squirrel den to Robin’s nest 3.6 – 0.3 = 3.3. And for the last one Groundhog burrow to Robin’s nest 3.6 – (-1.2) = 4.8.
3. you have to turn the 1 1/2 and 3/4 into 8ths. 1/2= 3*4 = 12 and for the denominator 2*4 = 8. So 12/8.
The next one is 3*2 which is 6 and 4*2=8
so now you have 12/8, 6/8, and 1/8
you have to add the points on the chart (i cant really help you on this part because i do not know how to upload picture) but you would make 24 and then you find where 12/8 would go and draw the hops but on mine the hop looks like how you would draw a rainbow but just one for the 12. Then do the same for the 6 and add 1 for the last one to make 19.
On mine I add the 12 + 6 + 1 = 19 so that is how i got mine. (sry if this a bad explination)
it should kinda look like this on the chart.
| | | | | | | | | | | | | | | | | | | | | | | | they should be spaced apart like this.
and for the last one i put cup 3 because it bigger than the amount of ingrident in the recipe. (im not sure if that one was the answer this is the only part we didnt get help on in class)
Related Questions
Which picture shows the correct graph of |x|=5?
Answers
|x| = 5
x = 5 or x = -5
You need a graph that has a closed dot on -5 and a closed dot on 5.
Answer: B. Picture B
the recipe for an omelet says 5 eggs make 2 serving. how many eggs are required to make 8 serving?
Answers
find the product 0.9×079=
Answers
Answer is 71.1 because 0.9 x 079 in a calculator is 71.1
The speed limit on the highway is 55 mph which equality best describes this me assuming the variable S represents be help ASAP
Answers
The answer is the speed is less than or equal to 55 mph.
S≤55
As line becomes the value of its slope get bigger
Answers
What is your question exactly??
what polynomial could you subtract from 5x^3-12x-x^2+9-12x^5-6x^4 to give a difference of 19+8x^3-18x-19x^5-2x^2-8x^4 ???
Answers
Given polynomial is:
[tex]-12x^{5}-6 x^{4}+5 x^{3}-x^{2}-12x+9[/tex] ..... Lets say it is "a"
We have to subtract a polynomial from this above one, to get the answer as:
[tex]-19x^{5}-8x^{4}+8x^{3}-2x^{2}-18x+19[/tex] ..... Lets say it is "c"
Lets say we have to subtract "b" so we have : [tex]a-b=c[/tex] or we can say [tex]a-c=b[/tex]
So, we will subtract "c" from "a" and get:
[tex]7x^{5}+2x^{4}-3x^{3}+x^{2}+6x-10[/tex]
Hence, this is the answer.
What is the answer???♀️♀️♀️
Answers
5-(-8) = 5 + 8 =13
As multiplication of two negatives is positive
oint) Solve the following inequality. Enter the answer in interval notation. 10x - 5 < -10(8x - 2)+3 Answer: Note: If the answer includes more than one interval, write the intervals separated by the "union" symbol, U. If needed, enter \infty as infinity and -\infty as -infinity.
Answers
Zoe has 1500 beads. She wants to make 6 friendship bracelets. She needs 215 beads for each bracelet. How many beads will Zoe have left after making all six of the bracelets? explain
Answers
215 beads per bracelet x 6 bracelets = 1290 beads
This tells us that to make all 6 bracelets, it will use up 1290 beads, now subtract that from your total number of beads.
1500-1290= 210
So Zoe will have 210 beads left over. Since this is a word problem, it is best to answer it in the same format:
Zoe will use 1290 beads to make 6 friendship bracelets. After all of the bracelets are made, she will have 210 beads left over.
hope this helps!
Zoe will have 210 beads left after making all six of the friendship bracelets.
Explanation:Zoe has 1500 beads and wants to make 6 friendship bracelets, with 215 beads needed for each bracelet. To find the total number of beads needed for all the bracelets, multiply the beads required for one bracelet (215) by the number of bracelets (6). This equals 1290 beads. To find the number of beads Zoe will have left after making all the bracelets, subtract the total number of beads needed (1290) from the initial number of beads (1500). Therefore, Zoe will have 210 beads left.
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Evaluate 3⋅(1−21/0−^3)+12
A.−3,012
B. −2,988
C.2,600
D.3,066
Answers
At a summertime poolside snack bar, 200 ice cream scoops were sold in one day. Double scoops were sold for $1.25 each and single scoops were sold for $1 each. If the proceeds from the sale of the cones were $221.75, how many of each kinds of cone were sold? In all, how many scoops of ice cream were sold?
Answers
Answer:
a) 87 double scoops and 113 single scoops.
b) 287 scoops of ice cream.
Step-by-step explanation:
1. You need to make a system of equations, where double scoops are represented by [tex]x[/tex] and the single scoops are represented by [tex]y[/tex]:
[tex]\left \{ {{x+y=200} \atop {1.25x+y=221.75}} \right.[/tex]
2. You can apply the Elimination Method:
- Multiply the first equation by -1 to cancel the variable [tex]y[/tex] from the system. Add both equations:
[tex]0.25x=21.75[/tex]
- Solve for [tex]x[/tex]:
[tex]x=\frac{21.75}{0.25}\\x=87[/tex]
- Substitute the value of [tex]x[/tex] into one of the original equations and solve for [tex]y[/tex]:
[tex]87+y=200\\y=113[/tex]
3. You can calculate the total number of scoops of ice cream that where sold as below:
[tex]2x+y[/tex]
4. Substitute values:
[tex]2(87)+113=287[/tex] scoops of ice cream
Answer: The number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.
Step-by-step explanation: Given that at a a summertime poolside snack bar, 200 ice cream scoops were sold in one day.
Double scoops were sold for $1.25 each and single scoops were sold for $1 each. The proceeds from the sale of the cones were $221.75.
We are to find the number of single scoop cones, double scoop cones and the number of scoops of ice cream that sold.
We Let x and y represents the number of cones of single scoop and double scoop ice cream that sold.
Then, according to the given information, we have
[tex]x+y=200\\\\\Rightarrow x=200-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]1\times x+1.25y=221.75\\\\\Rightarrow x=221.75-1.25y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Comparing equations (i) and (ii), we get
[tex]200-y=221.75-1.25y\\\\\Rightarrow 1.25y-y=221.75-200\\\\\Rightarrow 0.25y=21.75\\\\\Rightarrow y=\dfrac{21.75}{0.25}\\\\\Rightarrow y=87.[/tex]
From equation (i), we get
[tex]x=200-87=113.[/tex]
Therefore, total number of scoops that were sold is
[tex]113+2\times87=113+174=287.[/tex]
Thus, the number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.
A report prepared by a credit bureau which shows details of an individual’s credit history is a _____.
Answers
The answer is Credit Report
Answer:
Credit Report fellas!
Step-by-step explanation:
Calcule:
a) (+9) + (-5) =
b) (+3) + (-4) =
c) (-8) + (+6) =
Answers
a) 9 + -5 = 9-5 = 4
b) 3 +-4 = 3 -4 = -1
c) -8 + 6 = -2
identify the initial amount,a,and the growth factor,b,in each exponential function.Break b into (1+r)where r is the rate of growth. Give r as a percentage. y=1.05(1.46)^x
Answers
Given function : [tex]y=1.05(1.46)^x[/tex]
We need to identify a " initial amount", b "growth factor", r " rate of growth".
We know, exponential growth formula
[tex]y=a(b)^x[/tex], where a is initial amount, b is growth factor. On comparing with given function let us find values of a and b.
[tex]y=1.05(1.46)^x[/tex] ⇔ [tex]y=a(b)^x[/tex].
We can see a= 1.05 and b = 1.46.
Now, b=1+r.
Therefore, 1+r =1.46.
Subtracting 1 from both sides, we get
1+r-1 =1.46-1
r = 0.46.
On converting 0.46 into percentage, we get
0.46 × 100 = 46.
Therefore, intial amount a = a= 1.05 , growth factor b = 1.46, and the rate of growth r= 46%.
Final answer:
The initial amount, a, is 1.05, and the growth factor, b, is 1.46 in the exponential function y=1.05(1.46)ˣ. The growth rate, r, when expressed as (1+r), is 46%.
Explanation:
To identify the initial amount a and the growth factor b in the exponential function y=1.05(1.46)ˣ, we look at the standard form of an exponential function, which is y=a×bˣ. Comparing this with the given function, we can see that the initial amount a is 1.05 and the growth factor b is 1.46.
To express the growth factor in the form of (1+r), where r is the rate of growth, we can set b = 1 + r. This means that r would be b - 1, which is 1.46 - 1 = 0.46. To express r as a percentage, we multiply by 100, resulting in a growth rate of 46%.
If length of one side of cube is 20 cm, then volume of cube must be...
A: 4000 cm 3
B: 6000 cm 3
C: 800 cm 3
D: 8000 cm 3
Answers
All sides of a cube are congruent
20*20*20=8000
Answer: d) 8000 cm^3
Hope this helps :)
D
the volume (V ) of a cube = s³ ( where s is the length of the side )
here s = 20, hence
V = 20³ = 8000 cm³
Five-hundred twenty-one million, three hundred four thousand, six hundred two and three tenths. In standard form
Answers
Find the number that makes the ratio equivalent to 2:8.
Answers
A ratio is used to describe how two or more quantities are related. For example, we might say that a fruit drink calls for sugar crystals to be mixed with water in a ratio of 2:8. This means that for every 2 scoops sugar crystals, there will need to be 8 ounces of water. If there were 200 scoops of sugar crystals, there would need to be 800 ounces of water.
Sure, we'll start off by simplifying the ratio 2:8. Simplifying it gives us 1:4.
Our aim is to find a number, let's denote it by x, such that the ratio 2:x will be the same as 1:4.
To find such an x, we need to set up an equation using the principle of equivalence of ratios. This gives us 2/x = 1/4.
Now we proceed to solve this equation for x. We do this by cross-multiplying the fractions in the equation.
Cross-multiplication gives us 2*4 = x*1. Simplifying this yields 8 = x.
Hence, we can conclude that the number x that makes the ratio 2:x equivalent to 2:8 is 8.
Which ordered pair is a solution of the equation?
x+7y=17
Choose 1 answer:
(Choice A)
A
Only (10,1)
(Choice B)
B
Only (-4,3)
(Choice C)
C
Both (10,1) and (-4,3)
(Choice D)
D
Neither
Answers
The ordered pair is a solution of the equation is option C) Both (10, 1) and (-4, 3)
Which ordered pair is a solution of the equation?To know which ordered pair is a solution of the equation x + 7y = 17, we can substitute the values of x and y from each option into the equation and see if it holds true:
A) (10, 1)
Substitute x = 10 and y = 1 into the equation:
10 + 7(1) = 10 + 7 = 17
So, (10, 1) is a solution.
B) (-4, 3)
Substitute x = -4 and y = 3 into the equation:
-4 + 7(3) = -4 + 21 = 17
So, (-4, 3) is also a solution.
So, both (10, 1) and (-4, 3) satisfy the equation x + 7y = 17, the correct answer is: option C) Both (10, 1) and (-4, 3)
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Please help me with this
Answers
The perimeter of the rectangle:
[tex]P_R=2(4x+2+2x)=2(6x+2)=(2)(6x)+(2)(2)=12x+4[/tex]
The perimeter of the square:
[tex]P_S=2(5x-3+3x+1)=2(8x-2)=(2)(8x)+(2)(-2)=16x-4[/tex]
The perimeter of the rectangle is equal to the perimeter of the square. We have the equation:
[tex]12x+4=16x-4\qquad|\text{subtract 4 from both sides}\\\\12x=16x-8\qquad|\text{subtract 16x from both sides}\\\\-4x=-8\qquad|\text{divide both sides by (-4)}\\\\x=2[/tex]
The side lengths of the square:
[tex]5x-3\to5(2)-3=10-3=7[/tex]
The side lenghts of the rectangle:
[tex]4x+2\to4(2)+2=8+2=10\\2x\to2(2)=4[/tex]
Other method.
If the first figure is a square, then the length of the sides are equal.
Therefore
[tex]5x-3=3x+1\qquad|\text{add 3 to both sides}\\\\5x=3x+4\qquad|\text{subtract 3x from both sides}\\\\2x=4\qquad|\text{divide both sides by 2}\\\\x=2[/tex]
Further part of the solution as above.
Comb someone help me
Answers
C is the correct statement
∠CBE and ∠DEB are same side interior angles
Javier has 4 boxes of comic books. The mean number of books in each box is 25 . Which number line shows what could happen to the mean if he fills two more boxes, one with 26 comic books and one with 30 comic books?
Answers
The mean could increase from 25 to 27.
Explanation:The mean number of books in each box is 25. If Javier fills two more boxes, one with 26 comic books and one with 30 comic books, the mean could increase or stay the same. Let's calculate the mean with and without the additional boxes:
Mean without additional boxes: (4 boxes * 25 books per box) / 4 = 25
Mean with additional boxes: (6 boxes * 25 books per box + 26 books + 30 books) / 8 = (150 + 26 + 30) / 8 = 27
Therefore, the mean could increase from 25 to 27 if Javier fills two more boxes with 26 and 30 comic books.
Tom saves $5 each month, how many months will he need to save $20?
Answers
4 months because:
1 month = 5 dollars
so you add 5 until you get to 20 dollars. And as many times as you added 5 is how
many months. So:
5= 5
5 + 5 = 10
5+5+5= 15
5+5+5+5= 20
^ ^ ^ ^
1 2 3 4
your answer is 4 months ^^
What is the GCF of two prime numbers
Answers
It must be 1.
Factors of prime numbers are 1 or themselves, the only factor common to all prime numbers is 1.
Echy~
The Greatest Common Factor (GCF) of two prime numbers is always 1.
The Greatest Common Factor (GCF) of two prime numbers is always 1 because prime numbers are numbers with only two factors: 1 and themselves.
For example, the GCF of 3 and 5, both prime numbers, is 1 because they do not have any common factors other than 1.
Therefore, when dealing with two prime numbers, the GCF will always be 1.
The length of a rectangle is 12 units longer than the width. The perimeter is 7 times the width. Find the length and the width of the rectangle?
Answers
Log explanation below; answer is at bottom.
If the length, l, is 12 units longer than the width, w, then w = l - 12. If the perimeter, p,
p = 2l +2w,
is 7 x w, then
w = p/7
When two things are set equal to the same variable, they are equal to each other, so,
l - 12 = p/7
Now you need to get rid of the p so you are only working with one variable. To do this you plug in whatever p is equal to for p, so,
l - 12 = (2l + 2w)/7 now to get rid of the w do the same thing we did with p just for w. So,
l - 12 = (2l + 2(l - 12))/7
To solve this you want to multiply both sides by 7 first to get rid of the fraction.
7l - 84 = 2l + 2(l - 12)
Next you want to distribute the 2 over the l and the 12.
7l - 84 = 2l + 2l - 24
Next you want to combine like terms on each side.
7l - 84 = 4l - 24
Next add 84 and subtract 4l from sides to isolate the variable.
3l = 60
Now divide each side by 11 to get your answer.
l = 20.
To find the width,
w = l - 12
Just plug in and solve.
w = 20 - 12
w = 8
So your length and width are 20 and 8.
l = 20
w = 8
The width of the given rectangle is 8 units and the length is 20 units.
To find the length and the width of a rectangle when given that the length is 12 units longer than the width and the perimeter is 7 times the width, we can set up two equations. Let's denote the width as w and the length as l. According to the problem, l = w + 12 and the perimeter P = 2l + 2w is equal to 7w.
Set up the equations
l = w + 12
P = 2l + 2w
P = 7w
Substitute the value of l into the perimeter equation
7w = 2(w + 12) + 2w
Solve for w
7w = 2w + 24 + 2w
7w = 4w + 24
3w = 24
w = 8
Find the length using the width
l = w + 12
l = 8 + 12
l = 20
Find the distance CD rounded to the nearest tenth.
C=(5,6) and D (2,2)
CD=
Answers
Use the distance formula to find the distance between points C (5,6) and D (2,2).
d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
Plug the corresponding values in to the equation.
d=[tex]\sqrt{(2-5)^2+(2-6)^2}[/tex]
Then simplify the rest of the equation.
d=[tex]\sqrt{(-3)^2+(-4)^2}[/tex]
d=[tex]\sqrt{9+16}[/tex]
d=[tex]\sqrt{25}[/tex]
d=[tex]5[/tex]
The distance of the two points CD is 5.
To find the distance between point C=(5,6) and point D=(2,2), we use the distance formula which results in d=5.0 units rounded to the nearest tenth.
To calculate the distance between point C and point D, we use the distance formula derived from the Pythagorean theorem. The coordinates given are C=(5,6) and D=(2,2). The distance formula is:
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
Substituting the coordinates of points C and D into the formula gives us:
d = √{(2 - 5)² + (2 - 6)²}
This simplifies to:
d = √{(-3)² + (-4)²}
Further simplifying:
d = √{9 + 16}
d = √{25}
Finally, taking the square root of 25:
d = 5
Therefore, the distance between point C and point D, rounded to the nearest tenth, is 5.0 units.
emily earns $75 per day plus a commission. her commission is 15%. she sells $600 worth of furniture. how much does she earn for the day
Answers
It would be $165. If she earns $75 a day, plus what she make from selling the furniture. That 15% of $600 is $90. Simply add $90+$75 and your answer is $165.
Simplify
9 – 5(–7x + 5)
Answers
9-5(-7x+5)
------------------
9+35x-25
35x+9-25
35x-16
Hello!
[tex]9 - 5(-7x + 5)[/tex]
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓
First you had to expand.
[tex]-5(-7x+5):35x-25[/tex]
[tex]9+35x-25[/tex]
Then simplify it should be the correct answer.
[tex]9+35x-25:35x-16[/tex]
[tex]=35x-16[/tex]
Answer⇒⇒⇒⇒35x-16
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
20x^2-30=4x solve for x
Answers
Answer:
x=1.3288 or -1.1288
Step-by-step explanation:
Given [tex]20x^{2}-30=4x[/tex]
Subtract 4x from both sides
[tex]20x^{2}-4x-30=0[/tex]
Since we can factor out 2 from whole equation, let's factor out 2.
[tex]2(10x^{2}-2x-15)=0[/tex]
Divide with 2 on both sides
[tex]10x^{2}-2x-15=0[/tex]
We got the quadratic equation, we can solve for x using quadratic formula.
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac} } {2a}[/tex]
[tex]x=\frac{2\pm\sqrt{2^{2}-4X10X(-15)} } {2X10}[/tex]
[tex]x=\frac{2\pm\sqrt{604} }{20}[/tex]
[tex]x=\frac{2\pm2\sqrt{151}}{20}[/tex]
[tex]x=1.3288or-1.1288[/tex]
the parent function of a quadratic equation is vertically stretched by a factor of 2, then translated 5 units to the right and 1 unit down. write the equation of the new function in vertex form
Answers
A vertical stretch appears as a multiplier for the function value. Translation right appears as a value subtracted from the independent variable. Translation up appears as a value added to the function value.
For function f(x), stretching by a factor of 2, then translation 5 right and -1 up will give the function
... g(x) = 2f(x-5) -1
When f(x) = x², this becomes ...
... g(x) = 2(x -5)² -1
... g(x) = 2x² -20x +49
The equation of the new function in vertex form after the parent function of a quadratic equation is vertically stretched by 2, translated 5 units to the right and 1 unit down is y = 2(x - 5)^2 - 1.
Explanation:The parent function of a quadratic equation is given by f(x) = x^2. When it is vertically stretched by a factor of 2, it becomes 2f(x) = 2x^2. 5 units translation to the right will give f(x - 5) = 2(x - 5)^2 and a 1 unit downward shift gives f(x) = 2(x - 5)^2 - 1. Therefore, the equation of the new function in vertex form is y = 2(x - 5)^2 - 1.
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Which equations show how to find 16-9?
A. 9+1=10 , 10 +5 =15
B. 9+1=10 , 10+6=16
C. 9+2=11 , 11+6=17
D. 9+1=10 , 10+9=19
Answers
The option B, [tex]\(9 + 1 = 10\)[/tex] and [tex]\(10 + 6 = 16\)[/tex], correctly shows how to find [tex]\(16 - 9\)[/tex], as it demonstrates that starting with 9 and adding 1 to it and then adding 6 more yield the result of 16. Option b is the correct answer.
The equation to find [tex]\(16 - 9\)[/tex] should involve subtracting 9 from a number and getting a result of 16. Among the provided options:
A. 9+1=10 , 10 +5 =15: This equation does not result in 16.
B. 9+1=10 , 10+6=16 : This equation satisfies the condition [tex]\(16 - 9 = 16\)[/tex], so it's the correct answer.
C. 9+2=11 , 11+6=17 : This equation does not result in 16.
D. 9+1=10 , 10+9=19 : This equation results in 19, not 16.
So, option B, [tex]\(9 + 1 = 10\)[/tex] and [tex]\(10 + 6 = 16\)[/tex], correctly shows how to find [tex]\(16 - 9\)[/tex], as it demonstrates that starting with 9 and adding 1 to it and then adding 6 more yields the result of 16.
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