Question 1-5
Sarah is demonstraing the idea that polynomials are closed under addition. Her work and explanation are shown.
Select an equation and phrases to complete the statement.
Part A:
Add 3x4 + 6x - 7 to
Equation A 2x - (2x)2 + 4x-1
Equation B (2x)2 + 4.4x - 9
Equation C (-8x)-2 - (3x)3 +7
Part B:
This is closed because
of the sum are
and the sum is a polynomial.
Answers
This is closed under addition because the sum of the polynomial produces another polynomial.
What is a polynomial?A polynomial is an expression that involves the addition, subtraction and multiplication of variables.
Polynomials will be closed under an operation if the operation produces another polynomial.
(3x⁴ + 5x - 7) + (2x - (2x)² + 4x - 1) + [(-8x)⁻² - (3x)³ + 7]
= 3x⁴ - 27x³ - 4x² + 9x - 1 + (-8x)⁻²
This is closed under addition because the sum of the polynomial produces another polynomial.
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Related Questions
Help please I would appreciate
Answers
Answer:
66 (no other answer)
Step-by-step explanation:
The number can be divided by 2 so its even. Its a multiple of 11. It is between 20 and 79. it is a multiple of 3.
L1S2
Area - Compound Shapes
Find the area of the shaded region in each figure. Round your answer to 2 decimal
places if required. (Use = 3.14)
PLEASE HELP I WILL MARK BRAINLIEST!
Answers
Answer:
just trust yourself
Step-by-step explanation:
If one side of a square is 12 inches, what is the perimeter and area of the parallelogram?
Answers
Answer:
P = 48in
Step-by-step explanation:
P=4a=4·12=48in
What property of operations is used to show that 12x + 6y is equivalent to(2x + y)?
Answers
Answer:
Distributive property. When you factor out a GCF, from 12x + 6y, you would get 6(2x+y).
Step-by-step explanation:
12x + 6y is equivalent to 2x + y using the distributive property of multiplication over addition.
What is Number system?A number system is defined as a system of writing to express numbers.
The distributive property states that a(b + c) = ab + ac, where a, b, and c are any real numbers.
We can apply this property to the expression 2x + y by multiplying 2x by 6 and y by 6, giving:
12x + 6y = 6(2x) + 6(y)
Then, we can use the distributive property again to simplify the expression inside the parentheses:
6(2x) + 6(y) = 6(2x + y)
Substituting this expression back into the original equation, we get:
12x + 6y = 6(2x + y)
Simplifying further by dividing both sides by 6, we obtain:
2x + y = 12x/6 + 6y/6
2x + y = 2x + y
Therefore, we have shown that 12x + 6y is equivalent to 2x + y using the distributive property of multiplication over addition.
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For a project in her Geometry class, Naomi uses a mirror on the ground to measure
the height of her school building. She walks a distance of 12.25 meters from the
school, then places a mirror on flat on the ground, marked with an X at the center.
She then steps 1.7 meters to the other side of the mirror, until she can see the top of
the school clearly marked in the X. Her partner measures the distance from her eyes
to the ground to be 1.15 meters. How tall is the school? Round your answer to the
nearest hundredth of a meter.
Answers
Answer:
8.28
Step-by-step explanation:
we can express this question as
12.25/1.7=x/1.15
this can be simplified to
x=8.28
The height of Naomi's school building is 8.29 meters
Concept of similar triangles:
Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.
In the given question and attached figure we have,
BC = 12.25 metersCD = 1.7 metersDE = 1.15 metersNow we have to find the height(AB) of the building,
By the properties of similar triangles, we can write,
AB / BC = DE / CD
Putting all the values we get,
AB / 12.25 = 1.15 / 1.7
Simplifying we get,
AB = (1.15 / 1.7) × 12.25
By further simplifying,
AB = 8.29 meters
Therefore, the height of Naomi's school building is 8.29 meters.
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There are 10 students in Class 1 and 40 students in Class 2.
All 50 students sit a test.
The mean score for the students in Class 1 was 80%
The mean score for the students in Class 2 was 70%
Find the mean score of all the students.
Answers
Answer:
72%
Step-by-step explanation:
We have 10 sudents in class 1 and 40 in the other for a total of 50 students.
The 10 in class 1 had a mean of 80 so we do 80x10=800
The mean of the class of 40 is 70, so we do 40x70=2800
we add both of those together to get 3600 then we divide that by 50 because there are 50 students in total.
3600/50=72.
Ashley is riding her bike to train for a triathlon and so far has traveled 96 miles.
She is riding at an average rate of 15 miles per hour.
Calculate the time that she has been riding her bike in hours.
Answer:
hours
Note: Write the answer in decimal form.
Answers
Answer:
6.4
Step-by-step explanation:
she has been riding her bike for 6.4 hours.
у
6
2 Look at the coordinate plane at the right.
Choose True or False for each statement about the points in the
coordinate plane.
5
4
L
a.
3
Point J and point Khave the same
y-coordinate.
True
False
2.
1
K
b. Point K and point L have the same
x-coordinate.
True
False
O
► X
6
1
2
3
4
5
c. Point J and point L are the same
distance up from the origin.
True
False
True
False
d. The y-coordinate of point L is 5.
e.
Point is the nearest point to the
right of the origin.
True
False
Answers
Answer:
A. False
B. True
C. False
D. True
E. False
the dimensions of a rectangular dining room are 18 feet by 16 feet long if a scale factor 1/4 is used to make a scale model of the dining room what is the area of the dining room in the scale model.
Answers
calculate the sides of the rectangle in scale factor model
Length: 18 * 1/4 = 4.5 feet
Width: 16 * 1/4 = 4 feet
Rectangle area in scale factor model:
Length * Width
4.5 * 4
18 feet²
Answer:
Given dimensions of a rectangular dining table:
width = 18 ftlength = 16 ftIf a scale factor of [tex]\dfrac14[/tex] is used, then we need to multiply each measurement by [tex]\dfrac14[/tex]:
[tex]\implies \textsf{width}=18 \times \dfrac14[/tex]
[tex]=4.5 \textsf{ units}[/tex]
[tex]\implies \textsf{length}=16 \times \dfrac14[/tex]
[tex]=4 \textsf{ units}[/tex]
Therefore, the scale model of the dining room will be 4.5 by 4 units.
Exactly 150 years ago, students planted a tree in front of their school. Since then, the tree has grown 21 meters taller and the distance around the trunk has increased by 3 meters. Use pencil and paper. Describe how you can use this information to find at least two different unit rates. Then find these unit rates.
Answers
Answer: There are 2 different unit rates here:
The increase of the tree's height per year
The increase of the tree's trunk per year
Rate of tree's height per year
= 33m / 150 years = 0.22m per year.
Rate of tree's trunk per year
= 3m / 150 years = 0.02m per year.
If you have 19 cups full of water and 45 gallons of water. what does the gallon equals to how many cups of water?
Answers
Answer:
45 divide by 19 =2 r 7 thanks
The measures of heights (in inches) of a class of students are shown. 60, 60,54, 62, 62, 57,58, 65, 54,67, 63,57, 62, 54, 72, 66, 54, 69, 55, 61 Find the mean, median, mode, range, and standard deviation of the heights.b. A new student who is 7 feet tall joins your class. How would you expect this student’s height to affect the measures in part (a)?
Answers
Answer:Compute the variance: 49+25+16+9+1+16+36+648=27.
The variance is a measure of the dispersion and its value is lower for tightly grouped data than for widely spread data. In the example above, the variance is 27. What does it mean to say that tightly grouped data will have a low variance? You can probably already imagine that the size of the variance also depends on the size of the data itself. Below we see ways that mathematicians have tried to standardize the variance.
Step-by-step explanation:
Anona poured 5.6 cups of
water into her dog's water bowl
this morning. If her dog drinks 27 fluid ounces of the water,
how many fluid ounces of water
will be left in the bowl?
Answers
Answer:
Step-by-step explanation: 5.6 would be the add on to 27 so since it included the key word '' left'' you'd substract the two and you'd get your answer, just use calculator. You got this!!!
Go sub to clan fbib !!!!!
HELP GUYS ASAP THIS QUESTION IS DUE SOLVE
The diameter of a cylinder is 1 yd. The height is 12 ydof the cylinder? Find the volume of the cylinder.
Answers
Answer:
the volume should be 9.42
Please help me on all of these problems i am confused how they correlate
Answers
Answer:
Step-by-step explanation:
a) Area is multiplied by the square of the scale factor, so it is (3.1)^2 = 9.61 times larger.
b) Same logic, (1/6)^2 = 1/36
c) correct
d) 3
I need help please provide the steps
Answers
Answer:
1/[tex]\sqrt{2}[/tex] - 1/4
Step-by-step explanation:
We can write 2[tex]\sqrt{8}[/tex] as 2*[tex]\sqrt{4}[/tex]*[tex]\sqrt{2}[/tex]
That becomes 4[tex]\sqrt{2}[/tex], since the square root of 4 is 2 (±2, to be exact)
(4/(4[tex]\sqrt{2}[/tex]) - ( [tex]\sqrt{2}[/tex]/4[tex]\sqrt{2}[/tex])
1/[tex]\sqrt{2}[/tex] - 1/4
The length of a rectangle is 4 cm less than twice its width. The perimeter of the
rectangle is 58 cm. What are the dimensions of the rectangle?
Answers
Step-by-step explanation:
Let width be x
according to question
length = 2x-4
perimeter = 58
now,
perimeter = 2(length + width)
58 = 2(x+2x-4)
58 = 6x-8
6x = 66
x = 11
putting value of x in length
2x-4
= 2 X 11 -5
= 18
hence the dimensions of the rectangle is 18 and 11
I NEED HELP PLEASEEEEEEEEEEE
Answers
#6) 2,4,6 and 8 is 152 degrees 1,3,5 and 7 are 28 degrees.
If A=615.44 ft sq, what is the radius
Answers
I think the radius would be 13.9 ft
16% of 250 is equal to 250% of 16. True or false
Answers
Answer:
TrueStep-by-step explanation:
16% of 250
250*16/100 = 40250% of 16
16*260/100 = 40Both outcomes are same so the answer is True
Let's check
16% of 250
0.16(250)40250% of 16
2.5(16)40Yes true
Which expression is equivalent to 3 square root of x^5 y
Answers
[tex] \sqrt[3]{ {x}^{5}y } = {x}^{ \frac{5}{3} } {y}^{ \frac{1}{3} } \\ [/tex]
Thus the second option is the correct answer
Kalel says that 24 divided by 5 equals 36 divided by 8 because both are "4R4". Show his mistake using decimal division.
Answers
Answer: 24/5=4.8 36/8=4.5
Step-by-step explanation: First, let's start off by dividing 24 by 5. We can turn this into 24.0 divided by 5 to make it a bit simpler. We know that 240 by 5 = 48, then since there is a decimal 1 digit to the left in 24.0, we apply that decimal 1 digit to the left in 48, making it 4.8! Now let's do 36 by 8. We can do what we did for problem 1 and turn 36 into 36.0, 360 by 8 = 45 and applying the same logic we used before, 360 turns into 36.0, and 45 turns into 4.5! Therefore, Kalel is wrong, and the two equation is not equal.
P.S. Using long division, Kalel is technically kind of right, but there's still that unaccounted for '4' that we still need to divide.
HELP!! I’m in class I just need help with the fill in blanks segment help me please
Answers
Answer:
First Blank: “controlled” Second Blank: "a Different" Third Blank: "the same" Last Blank: "Height of the ramp"
Step-by-step explanation:
Use the data below.
22, 16, 18, 14, 16, 34, 20
Mean:
Median:
Mode:
Range:
Answers
Step-by-step explanation:
mean = sum of all data points / number of data points
(22+16+18+14+16+34+20)/7 = 140/7 = 20
median is the number, where half of the data points are smaller, and the other half are larger.
first we need to sort the data points
14, 16, 16, 18, 20, 22, 34
median = 18
mode is the data point occurring most often.
mode = 16 (occurring 2 times, while the others occur only once).
range is the difference between the largest and the smallest data point.
range = 34 - 14 = 20
-9 more than a number results in -20
Answers
Answer:
-9+x=-20
Step-by-step explanation:
I am not so positive on this one, but if you are not doing inequalities, then this should be correct.
"More than" would insinuate that you are adding. In this class, you would have a number to replace that x, but since no number was given, you place the x in its place. x=-11, because when you "add" -9 with something to get -20, it would have to be -11. Negative numbers can be confusing because when you subtract a negative number by another negative, you end up with a negative. Like in this case. Normally, you would just put -11, so it would look like -9 - 11 = -20. But since this says "more than", unless you are doing inequalities, you add.
If you are doing inequalities, then your answer should be this:
-9 > x = -20
I hope this helps!
-No one
Find f(2) if f(x)=2x+1
Answers
[tex]f(x) =2 x+1 \\\\ \text{If x = 2,}\\\\f(2) = 2(2) +1 = 4+1 = 5[/tex]
Answer:
5
Step-by-step explanation:
plug 2 in for x
f(2) = 2(2) + 1
f(2) = 5 [Asnwer]
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Please help!
consider the function f(x)=-(x+2)^2+4
2 + 4.
a) in what form is this quadratic function written? _________________________
b) list the values of the following parameters
a = ______
h = ______
k = ______
vertex = ___________
c) what will the a parameter do to this function?
Answers
Answer:
Below,
Step-by-step explanation:
f(x)=-(x+2)^2+4
(a) Vertex form
(b) a = -1 , h = -2 and k = 4.
vertex = (-2, 4)
(c) The value of a, -1 will invert it vertically or we can describe it as a reflection in the line y = 4. The graph will change from a U shape to a ∩ shape.
Which of the following is not a parallelogram? A. Square B. Rhombus C. Rectangle D. Right Triangle
Answers
Pleas help me (and pls don't ban my question this time Brainly)
Answers
Answer:
d = 7.2
Step-by-step explanation:
12 + d = -4.8
subtract 12 from both sides and you get
d = 7.2
Answer:
-16.8
Step-by-step explanation:
The equation can be solved by performing the inverse of the operation that is done to the variable. Here, 12 is added to the variable. The inverse of that operation is addition of the "additive inverse", or "opposite" of 12:
12 + d = -4.8 . . . . . . given equation
12 -12 +d = -4.8 -12 . . . . . the same operation is done to both sides
d = -16.8
The value of d that makes the equation true is -16.8.
_____
The addition (subtraction) property of equality tells you that adding (subtracting) the same number from both sides of an equation will not change the value of the variable.
A mom shared $490 between her 2 daughters in the ratio of 4 : 3 respectively. Calculate how much money is the larger share?
Answers
Step-by-step explanation:
let ratio be 4x and 3x
sum : 490$
4x+3x = 490
7x=490
x=490/7
Hence x = 70
first daughter gets = 4x =4 x 70 = 280
second daughter gets =3x = 3x 70 = 210
first daugter gets the larger share