We can use the number line as a model to help us visualize adding and subtracting of signed integers. Just think of addition and subtraction as directions on the number line. There are also several rules and properties that define how to perform these basic operations.
To add integers having the same sign, keep the same sign and add the absolute value of each number.
To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest.
Subtract an integer by adding its opposite.
answer: well i thing subtracting and adding integers are related because they both can be solved using an number line
what is the simplified form of
[tex] \sqrt[7]{x ^{5} } \times \sqrt[7]{ {x}^{5} } [/tex]
A.
[tex] \sqrt{x} [/tex]
B.
[tex] x\frac{4}{9} [/tex]
C.
[tex]x[/tex]
D.
[tex]x \sqrt[7]{ {x}^{3} } [/tex]
To simplify the expression √7{x 5} × √7{x 5}, you can multiply the radicands together and simplify the result.
Explanation:To simplify the expression √7{x 5} × √7{x 5}
We can use the properties of radicals to simplify the expression. When multiplying radicals with the same index, we can simplify by multiplying the radicands together. In this case, the radicands are both x5, so the simplified form will be:
√7{x 5} × √7{x 5} = √7{x 5 × x 5} = √7{x10}
Therefore, the simplified form of the expression is √7{x10}.
For every $50.00, Michael earns, he saves $5.. for the future. what is the constant of proportionality (k)?
Constant of proportionality is given by: y=kx oy [tex]k=\frac{y}{x}[/tex]
So lets suppose y = 50 and x = 5 so k will be [tex]\frac{50}{5}=10[/tex]
This 10 will remain constant. For every $50 Michael saves $5, for $100 he will save $10 , for $150 he will save $15 and so on.
So this 'k' will be same for each value of x and y.
The volume of a rectangular prism is given by the formula V=lwh, where I is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?
Answer:
The answer is [tex]6x^{3} +39x^{2}+54x[/tex]
Step-by-step explanation:
Volume of the rectangular prism = Length * Width * Height
Length (l) = [tex]x+2[/tex]
Width (w) = [tex]3x[/tex]
Height (h) = [tex]2x+9[/tex]
By substituting these values to the equation above,
Volume of the rectangular prism = [tex](x+2)*3x*(2x+9)[/tex]
=[tex](3x^{2} +6x)*(2x+9)[/tex]
=[tex]6x^{3} +27x^{2} +12x^{2} +54x[/tex]
=[tex]6x^{3} +39x^{2}+54x[/tex]
Therefore,
The answer is [tex]6x^{3} +39x^{2}+54x[/tex]
Answer:
Volume = [tex]6x^3+39x^2+54x[/tex]
Step-by-step explanation:
Prism is an object which has two bases which are parallel to each other and other faces are parallelograms .
Rectangular prism is a three dimensional figure which has 6 faces which are all rectangles .
Let l be the length of rectangular prism , w be the width of prism and h be the height of prism .
Then volume of rectangular prism is equal to [tex]lwh[/tex] .
We will also use formula: [tex]a(b+c)=ab+ac[/tex]
Here,
[tex]l=x+2\\w=3x\\h=2x+9[/tex]
Therefore,
volume of rectangular prism is calculated as follows:
[tex]V=\left ( x+2 \right )\left ( 3x \right )\left ( 2x+9 \right )\\=\left ( 3x^2+6x \right )\left ( 2x+9 \right )\\=3x^2\left ( 2x+9 \right )+6x\left ( 2x+9 \right )\\=6x^3+27x^2+12x^2+54x\\=6x^3+39x^2+54x[/tex]
PLEASE ANSWER
A map has a scale of 1/3 inch to 2 miles. The shortest distance between 2 cities on the map measures 7 inches. If d represents the shortest distance between the 2 cities, what is d?
A) 14 mi
B) 21 mi
C) 36 mi
D) 42 mi
1/3 = 7
------ ---------
2 miles ? miles
using cross products
1/3 * ? = 2 * 7
1/3 ? =14
? = 42 miles
Answer:
42
Step-by-step explanation:
Reggie Lost 4 spaceships in level 3 of a video game he lost 50 points for each spaceship when he completed level 3 he earned a bonus of 550 points by how much to his score change?
Reggie's score changed by 350 points.
Explanation:Reggie lost 4 spaceships in level 3 of a video game, and he lost 50 points for each spaceship. So, the total points lost would be 4 multiplied by 50, which is 200 points. However, when Reggie completed level 3, he earned a bonus of 550 points. To find out how much his score changed, we need to consider both the points lost and the bonus earned.
Points lost: 4 spaceships x 50 points/spaceship = 200 points
Bonus earned: 550 points
Score change: Bonus earned - Points lost = 550 points - 200 points = 350 points
Therefore, Reggie's score changed by 350 points.
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Examine each number. What number can you add to this number to make a number that has a whole-number square root?
a) 42 c) 470
b) 101 d) 1000
9514 1404 393
Answer:
a) 7
b) 20
c) 14
d) 24
Step-by-step explanation:
The desired number is found by subtracting the given number from the square of the integer just higher than the root of the given number.
a) √42 ≈ 6.5, so the desired number is 7² -42 = 49 -42 = 7
__
b) √101 ≈ 10.05, so the desired number is 11² -101 = 121 -101 = 20
__
c) √470 ≈ 21.7, so the desired number is 22² -470 = 484 -470 = 14
__
d) √1000 ≈ 31.6, so the desired number is 32² -1000 = 1024 -1000 = 24
What is the inflation rate if the price of a chocolate milkshake was $5 dollars last year but $15 this year
Solve for number eight please ! I really need help with this !!!
Answer:
x + (x+1) + (x+2) = 90
3x + 3 = 90
3x = 87
x = 29 (which is the smallest of the 3 numbers).
Step-by-step explanation:
Consider the polynomials A=4x2−10 and B=−6x2−5 . Determine the sum and difference of these polynomials. A+B=
A−B=
A + B = - 2x² - 15 , A - B = 10x² - 5
A + B = 4x² - 10 - 6x² - 5 = - 2x² - 15
A - B = 4x² - 10 ) - ( - 6x² - 5 ) = 4x² - 10 + 6x² + 5 = 10x² - 5
You are playing a game. You start at 0 then you score -8 points on each 4 turns what is your score after those 4 turns
A line segment is drawn between the points (5,8) and (-1,6). What are the coordinates of the midpoint of the segment?
Hello!
To find the midpoint of the line segment, use the formula: [tex](\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]. In simpler terms, we are finding the average of the two points.
We can assign [tex]x_{1}[/tex] and [tex]y_{1}[/tex] to the point (5, 8), and (-1, 6) to [tex]x_{2}[/tex] and [tex]y_{2}[/tex].
[tex](\frac{5+(-1)}{2}, \frac{8+6}{2}) = (\frac{4}{2}, \frac{14}{2}) = (2, 7)[/tex]
Therefore, the coordinates of the midpoint of the line segment is (2, 7).
Final answer:
The coordinates of the midpoint of the line segment with endpoints (5,8) and (-1,6) are (2,7).
Explanation:
To find the coordinates of the midpoint of a line segment, we can use the midpoint formula which states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
Using the formula, we can find the midpoint of the line segment with endpoints (5,8) and (-1,6).
x-coordinate: (5 + (-1)) / 2 = 4 / 2 = 2
y-coordinate: (8 + 6) / 2 = 14 / 2 = 7
Therefore, the coordinates of the midpoint of the line segment are (2,7).
Name the operation you would do first: -8 + 13 + (-24) + 6(-4)
You would just start from the beginning because it is all addition (Pemdas) Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
90998.0014483 rounded to the nearest ten
Answer:
91000 or 9.100 * 10^4
Step-by-step explanation:
This mean that a lot of things are going to change. The decimal will disappear. If that happens what you have is
90998
Now many other things will disappear as well because you are rounding
The easiest way to show this is just to round which will give you
91000
If you know scientific notation then the answer becomes
9.100 * 10^4
What is the value of each number in 1,567.209?
The value of one (1) is one-thousand (1,000)
The value of five (5) is five-hundred (500)
The value of six (6) is sixty (60)
The value of seven (7) is seven (7)
The value of two (2) is two-tenths (0.2)
The value of zero (0) is zero hundredths (0.00)
The value of nine (9) is nine thousandths (0.009
FND THE SUM OR DIFFERENCE! 3 QUESTIONS!! MATHMATICS
1. 7/8 - 5/12
a.11/24
b. 2/24
c. 2/8
d. 2/12
2. 1/6 + 3/8
a. 4/6
b. 4/8
c. 4/14
d. 13/24
3. the sum of two numbers 7/8 one addend is 3/4 what is the other?
a. 4/4
b.1/8
c. 1/4
d 2/8
What is 0.96 rounded to the nearest tenth
Your answer would be 1. Hope this helps :)
0.96 rounded to the nearest tenth is:
1
Because 6 is greater than 4. The number has to be greater than 4 for it to be rounded up, but if it's not, then the number only gets rid of the number behind the tenth.
Hope this helped! :D
calculate midpoint of (8,4) and (12,2)
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have:
[tex]A(8,\ 4)\to x_A=8,\ y_A=4\\B(12,\ 2)\to x_B=12,\ y_B=2[/tex]
Substitute:
[tex]\dfrac{8+12}{2}=\dfrac{20}{2}=10\\\\\dfrac{4+2}{2}=\dfrac{6}{2}=3[/tex]
Answer: (10, 3).Let's first recall what is known as the Midpoint formula we have, so by the Midpoint formula, we know that, the midpoint of any line segment joining the points [tex]{\bf{A(x_{1},y_{1})}}[/tex] and [tex]{\bf{B(x_{2},y_{2})}}[/tex] is given by
[tex]{\boxed{\bf{M(x,y)=\bigg(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\bigg)}}}[/tex]Now, if we assume our points to be A(8,4) and B(12,2) and the midpoint being M, then we will be having :
[tex]{:\implies \quad \sf M=\bigg(\dfrac{8+12}{2},\dfrac{4+2}{2}\bigg)}[/tex]
[tex]{:\implies \quad \sf M=\bigg(\dfrac{20}{2},\dfrac{6}{2}\bigg)}[/tex]
[tex]{:\implies \quad \boxed{\bf{M=(10,3)}}}[/tex]
Hence, the required Midpoint is (10,3)
How to write 0.0306 in words
a random selection of plants receiving two different types of treatments
Please help with the question ASAP
Nathan stated that any number (except 0) raised to the zeroth power is equal to 1. Is Nathan correct or incorrect? If Nathan is correct, create an example to back him up. You will need to explain your example thoroughly so that another student would be able to understand your reasoning. If Nathan is incorrect, create an example that shows his error in thinking. You will need to explain your example thoroughly so that another student would be able to understand your reasoning.
Nathan is incorrect. Any number times 0 is equal to 0!
-Abha
Lily takes a train each day to work that averages 35miles per hour. On her way home, her train ride follows the same path and averages 45miles per hour. If the total trip takes 2.5 hours, which equation can be used to find n, the number of miles lilly’s Home is from her work?
Answer:
distance distance
--------------- + ----------------- = 2.5 hrs
35 mph 45 mph
The distance is 49.22 miles.
Step-by-step explanation:
The time spent on the outward trip PLUS the time spent on the return trip add up to 2.5 hrs. Thus,
distance distance
--------------- + ----------------- = 2.5 hrs
35 mph 45 mph
Then 45d + 35d = 2.5(35)(45) = 3937.5. Adding 45d and 35d, we get 80d. Dividing 3937.5 by 80 results in 49.22 (miles).
The home to work distance is 49.22 miles.
Answer:
49.22
Step-by-step explanation:
The equation to your answer is n/35+n/45=2.5
I need help with math -4+a=15
Note the equal sign. What you do to one side, you do to the other. Isolate the a.
Add 4 to both sides
a- 4 (+4) = 15 (+4)
a = 15 + 4
a = 19
19 is your answer for a
hope this helps
The answer is 19.
-4 + a = 15
4 + -4 + a = 15 + 4 -Add 4 to both sides
a = 19
Is the following sequence arithmetic? If so, identify the common difference.
-0.3, 0.1, 0.5, 0.9, …
A) Yes; -0.2
B) No
C) Yes; -0.4
D) Yes; 0.4
Answer:
Option D
Yes 0.4
Step-by-step explanation:
A sequence is said to be arithmetic if there is a pattern as
nth term is got by adding d to n-1th term.
d = common difference
The sequence will look like
a, a+d,a+2d, a+3d,......
where I term= a and each time d is added to get the next term.
Our given sequence is
-0.3, 0.1, 0.5, 0.9, …
Let us find difference between Ii and I term
=0.1-(-0.3) = 0.4
Similarly iii term - ii term
=0.5-0.1 =0.4
and iv term - iii term = 0.9-0.5 = 0.4
Hence confirmed that this is an arithmetic sequence with I term =-0.3 and common difference = 0.4
A pet store has nine dog leashes. It has a few were dog leashes then dog collars. How many dog collars does the store have
Does it say how many less leashes the store has compared to X collars? Cause if it doesn't you'll just have to estimate the answer between I would say 5 and 7.
HELP PLZ SHOW WHORK THXS YALL ^_^ luv yall
Answer:
Tony pays $6.75 for his item, & Tanya pays $9 for her items
Step-by-step explanation:
Let Tanya's item be x, and Tony's be y. Set the system of equality:
3x = 4y
y = x - 2.25
Plug in x - 2.25 for y in the first equation
3x = 4(x - 2.25)
Distribute 4 to all terms within the parenthesis
3x = 4x - 9
Isolate the x. Subtract 4x from both sides
3x (-4x) = 4x (-4x) - 9
3x - 4x = -9
-x = -9
Isolate the x. Divide -1 from both sides
(-x)/-1 = (-9)/-1
x = 9
-------------------------------------------------------------------------------------------------------------------
Plug in 9 for x in the equation
y = x - 2.25
y = (9) - 2.25
y = 6.75
--------------------------------------------------------------------------------------------------------------------
Tony pays $6.75 for his item, & Tanya pays $9 for her items
--------------------------------------------------------------------------------------------------------------------
~Rise Above the Ordinary
a group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the survey are: 60 students like building snowmen; 10 students like building snowmen, but don't like skiing; 80 students like skiing; 5 students don't like building snowmen. Part B: What is the probability that a student who does not like building snowmen also does not like skiing?
Answer:
2/5 or 0.4
Step-by-step explanation:
10 students like building snowmen but do not like skiing
so students who like both building snowman and skiing = 60 - 10 = 50
Total number of students who does not like building snowman and also does not like skiing = 80 - 60 = 20
Therefore, the probability that a student who does not like building snowmen also does not like skiing = 20/50 = 0.4
Linda goes to a spinning class at the health and fitness club there are five classes a week in the table above shows the number of people in each class last week what is the mean number of people in each class mon 13 Tue 23 wed24 thor 31 fri14
The mean number of people in each spinning class last week is calculated by summing up the total number of attendees and dividing by the number of classes. The mean attendance for last week was 21.
Explanation:To calculate the mean number of people attending the spinning class each day, you would add up the total number of people for the week and then divide by the number of classes.
The given numbers are:
Mon: 13 Tue: 23 Wed: 24 Thu: 31 Fri: 14
So the sum of the attendees is: 13 + 23 + 24 + 31 + 14 = 105
The mean is then calculated by dividing the total by the number of days, which is 5 in this case:
Mean = Total ÷ Number of Days = 105 ÷ 5 = 21
So, the mean number of people in each class last week was 21.
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A basketball team scored an average of 52 points in each of 15 games. Based on the average, how many points did the team score in all? Please help it’s for my son homework
The basketball team, based on their average score of 52 points a game, would score a total of 780 points in 15 games.
Explanation:
To compute the total number of points a team scores in all games, based on their average score, the formula to use is: Total Score = (Average Score) × (Number of Games). The question states that the basketball team scored an average of 52 points in each of 15 games. So, we have:
Total Score = 52 points per game × 15 games
Calculating the above gives Total Score = 780 points.
This means that, based on their average of 52 points per game, the basketball team would score a total of 780 points in 15 games.
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The table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward.
Which statements are true? Check all that apply.
The ball is at the same height as the building between 8 and 10 seconds after it is thrown.The height of the ball decreases and then increases.The ball reaches its maximum height about 4 seconds after it is thrownThe ball hits the ground between 8 and 10 seconds after it is thrown.The height of the building is 81.6 meters.
* First is correct - the height crosses the 0 point between 8 and 10 secs
* Third is correct - 81.6 m is max at 4 secs
all others incorrect