Answer:
Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers. They are different because Integers include all whole numbers and their negative counterpart e.g. … -4, -3, -2, -1, 0,1, 2, 3, 4,… is a rational number but not an integer. All rational numbers belong to the real numbers. If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called opposites.
Step-by-step explanation:
Find the distance between (-3, 11) and (-6,4).Round to the nearest then the
Answer:
d =7.6
Step-by-step explanation:
[tex](-3,11) =(x_1,y_1)\\(-6,4)=(x_2,y_2)\\\\\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\\\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\\=\sqrt{\left(-6-\left(-3\right)\right)^2+\left(4-11\right)^2}\\= \sqrt{(-6+3)^2+(4-11)^2}\\ \\d= \sqrt{(-3)^2+(-7)^2} \\\\d = \sqrt{9+49}\\ \\d = \sqrt{58}\\\\d = 7.61577\\\\d =7.6[/tex]
If a car travels 600 meter in 20 seconds how fast is it going
Answer:
30 meters per second
Step-by-step explanation:
Step 1:
600 ÷ 20 = 30
Answer:
30 meters per second
Hope This Helps :)
Answer:
30 m /s
Step-by-step explanation:
We are looking for the speed
d/t = speed
600m / 20 second
30 m /s
what is -21.6 simplified?
Answer:
108/5
Step-by-step explanation:
Answer:
-22
Step-by-step explanation:
because -21.6 rounded to the next whole number is rounded to -22 because of the 6 in the number, which is larger than 5 so it passes to the next highest number.
If Hannah weights 29 pounds and her medicine says dosage of child weight 10-15 mg/kg what is Hannah weight in kilograms? Round to the nearest hundredth
Answer:
13.16
Step-by-step explanation:
Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of each kind does he have?
Find the distribution of responses about whether there was broken glass at the accident for the subjects in this study using relative frequencies
Answer:
Probability of having broken glass = 0.1933
Probability of not having broken glass = 0.8067
Step-by-step explanation:
The Treatment table in the file attached to the given question is written out and completed below;
Treatment
Response Smashed into Hit Control Total
Yes 16 7 6 29
No 34 43 44 121
Total: 50 50 50 150
Using relative frequencies,
the distribution of responses about whether there was broken glass at the accident for the subjects in this study can be computed as follows:
Probability of having broken glass = [tex]\dfrac{29}{150}[/tex]
Probability of having broken glass = 0.1933
Probability of not having broken glass = [tex]\dfrac{121}{150 }[/tex]
Probability of not having broken glass = 0.8067
Sort the following objects by length. Place the shortest object at the top.
Answer:
Ok, here we have two points A and B.
The shorter object will be the second option, AB with a line on top, this is a segment, so the length of this object is equal to the distance between A and B.
The next one is AB with an arrow pointing to the right, this is ray, is a line that starts in A and passes through B, and continues infinitely.
The third will be the bottom option, AB with a double-arrow on top, this is the notation for a line that passes through A and B, and it extends to infinity in both directions.
A rock is thrown upward with a velocity of
22 meters per second from the top of a
45 meter high cliff, and it misses the cliff on the way back down. When will the rock be
9 meters from ground level? Round your answer to two decimal places.
Answer:
5.76 seconds
Step-by-step explanation:
We are given;
Position of rock from ground level; h(t) = 9 m
Height of cliff;h_0 = 45 m
Velocity;v_0 = 22 m/s
To solve for the time, we will use the gravity formula which is;
h(t) = (-1/2)gt² + (v_0)t + h_0
Plugging in the relevant values to get;
9 = (-1/2)(9.81)t² + 22t + 45
Subtract 9 from both sides to get;
-4.905t² + 22t + 45 - 9 = 0
-4.905t² + 22t + 36 = 0
Finding the roots of the equation through quadratic formula gives;
t = 5.76 or -1.27
t cannot be negative, so we will use the positive value to get;
t = 5.76 s
Thus, the rock will be 9m from the ground level after 5.76 seconds
What is the least common denominater of 3/4 and 7/10
Answer:
Least Common Multiple of 3 , 4 and 7 is 84 .
Step-by-step explanation:
Answer:
your answer is 20
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Michael has a substantial student debt, but he recently got a new job, which came with a signing bonus. He calculates that with his new job, he can put aside a fixed amount of money every month to pay off his debt. He also puts the entirety of his bonus towards paying off his debt. He constructs the expression 36,700-(5,000+500m) to represent the size of his debt after m months. Which number describes the value of his signing bonus?
Answer:
5000
Step-by-step explanation:
Given the following :
Constructed expression used to express size of debt after m, months :
36,700 - (5000 + 500m)
Since it was stated that he his whole signing bonus was dedicated towards paying his debt, then this will be a constant figure or digit.
Then a fixed amount from his monthly pay is also dedicated towards offsetting the loan:
Thus the fixed amount will be the Coefficient of m, where m is the number of months.
Thus total amount paid after m months can be deduced from the expression to be :
(5000 + 500m); where
5000 constant fee is the signing bonus.
Answer:
5000
Step-by-step explanation:
the sum of twice a
number and 31
Answer:
Let the unknown number be x ;
[tex]2(x) +31\\=2x+31[/tex]
Step-by-step explanation:
Evaluate each expression. 12k − h 2; use h = 2, and k = 3
Please help me solve these questions
Evaluate step by step
g(-2)=x^2+3X+2
And
g(3.14)=x^2+3X+2
Answer:
g(-2) = 0
g(3.14) = 21.2796
Step-by-step explanation:
Simply substitute the values for x.
Step 1: Find g(-2)
g(-2) = (-2)² + 3(-2) + 2
g(-2) = 4 - 6 + 2
g(-2) = -2 + 2
g(-2) = 0
Step 2: Find g(3.14)
g(3.14) = (3.14)² + 3(3.14) + 2
g(3.14) = 9.8596 + 9.42 + 2
g(3.14) = 19.2796 + 2
g(3.14) = 21.2796
-|(-12) + 20 + (-5) + (-7)| = ?
Answer:
-4
Step-by-step explanation:
=> -|-12+20-5-7|
=> -|-4|
=> -4
(+8)-(+7)=(+8)+(+7)=(+8)+(-7) what the answer
Answer:
it wouldn't be equal
Step-by-step explanation:
Answer:
(+8)-(+7) = (+8)+(-7) = 1
Step-by-step explanation:
The given statement ...
(+8)-(+7)=(+8)+(+7)=(+8)+(-7)
is false. The middle sum is not equal to the other two.
__
In general, subtracting a number is the same as adding it opposite:
(+8)-(+7) = (+8)+(-7) = 1
An airplane descends 300 feet every 6 seconds. By how many feet does the airplane descend in 1 second?
Answer- 50 feet
Step-by-step explanation:
1 times 6 equals 6
n times 6 equals 300
solve for n
A square rug has an area 94 ft. Write the side length as a square root. Then decide if the side length is a rational number.
Hey there! I'm happy to help!
All of the sides of a square are the same. Therefore, to find the area, you multiply the side by itself. Multiplying a number by itself is conveniently called squaring.
Doing this backwards is called finding the square root. If you have an area of 64, you square root it, showing you that the sides are 8.
Therefore, the side length here is √94.
If we put √94 into the calculator, we see that it is 9.895359715.....
That number never ends and it goes on in no particular order, so it cannot be written as a fraction of two integers and therefore is not a rational number.
Have a wonderful day! :D
The equivalent of 3/8 inch is _____ /64 inch.
Answer:
24/68 inches
Step-by-step explanation:
Multiply 3 times 8 to get 24. The denominator was multiplied by 8 so you have to do the same thing to the numerator.
Hope This Helps :)
The equivalent of the quantity [tex]\frac{3}{8}[/tex] inch is [tex]\frac{24}{64}[/tex] inch.
The given quantity is [tex]\frac{3}{8}[/tex] inch.
Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.
Here, in equivalent given fraction denominator is 64.
Let the numerator be x.
Now, [tex]\frac{3}{8}[/tex] inch = [tex]\frac{x}{64}[/tex] inch
3×64=x×8
x=3×8
x=24
So, the numerator of the fraction is 24.
Hence, the equivalent of the quantity [tex]\frac{3}{8}[/tex] inch is [tex]\frac{24}{64}[/tex] inch.
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what is x in the problem
x(2x-5)=12
Answer:
x€(4, -1.5)
Hope this answer is helpful...
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jorge bought 3 shirts and 2 pairs of pants. each shirt cost $21.50 and each pair of pants cost $34.45. if he had $145 in his wallet, how much money will he have left after paying for his clothes?
Answer: he will have $11.60 left
A line passes through the point , 9,−2 and has a slope of 4/3. Write an equation in point-slope form for this line.
Answer:
y + 2 = [tex]\frac{4}{3}[/tex] (x - 9)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = [tex]\frac{4}{3}[/tex] and (a, b) = (9, - 2) , thus
y - (- 2) = [tex]\frac{4}{3}[/tex] (x - 9) , that is
y + 2 = [tex]\frac{4}{3}[/tex] (x - 9)
Answer:
y+2 = 4/3( x-9)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point on the line
y - -2 = 4/3( x-9)
y+2 = 4/3( x-9)
if a circle's circumference is 15 inches what is its radious? leave the symbol pi in your answer
Answer:
the radius is 2.38
Step-by-step explanation:
use the formula c=2pi r
Answer:
15/2π
Step-by-step explanation:
If the circumference is 15 inches, we can create an equation using the following formula:
Circumference of circle = 2 x π x radius
which is C = 2πr
Now, substituting our value of the circumference (15) into the equation, we get:
15 = 2πr
In order to find r, the radius, we must divide both sides by 2π, which makes r the subject. This cancels out the 2π on the right side, leaving us with:
15/2π = r
So the radius is 15/2π.
How do i find the perimeter and area of the triangle with these points? The directions say to round to the nearest tenth. A (‐1, 3 ), B( 8, 3), C( ‐1, 5).
Maria brought 17 packs of cola to a party, and each pack had 6 cans. Kira brought 9 cans of juice. How many cans did they bring in all?
Answer:
In total they brought 111 cans
Step-by-step explanation:
17*6=102
102+9=111
Maria:
No. of cans in a pack = 6
No.of cans in 17 pack = 6 * 17 = 102 cans
No. of cans bought by Heather = 9 cans
Total cans = 102 + 9 = 111 cans
A factory uses 1/3 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 2/3 of a barrel of raisins. How many batches of granola bars did the factory make yesterday?
Answer:
2
Step-by-step explanation:
since it takes 1/3 to make one batch then you have 2/3 it means yesterday they made 2 batches
Solve for x in the equation x2 + 2x + 1 = 17.
O x=-11 15
O x=-14 17
O x=-2+2V5
O x=-1:13
Answer:
x = sqrt(17) - 1 or x = -1 - sqrt(17)
Step-by-step explanation:
Solve for x:
x^2 + 2 x + 1 = 17
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x + 1)^2 = 17
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x + 1 = sqrt(17) or x + 1 = -sqrt(17)
Hint: | Look at the first equation: Solve for x.
Subtract 1 from both sides:
x = sqrt(17) - 1 or x + 1 = -sqrt(17)
Hint: | Look at the second equation: Solve for x.
Subtract 1 from both sides:
Answer: x = sqrt(17) - 1 or x = -1 - sqrt(17)
the expression as an inequality for the statement above is....
Answer:
See below.
Step-by-step explanation:
"The cost, c, to have dinner at Jack's Cafe is at most $25."
In other words, the cost can not go above $25.
This means that the cost c will always be less than or equal to $25.
So, our answer is:
[tex]c\leq 25[/tex]
Or the second choice.
And we're done!
Convert the given amount to the given unit.
6.5 lb; ounces
6.5 lb =
ounces
Answer:
12.10on zas
Step-by-step explanation:
Esun as uma
simplify the expresssion 2x^2+8+3x^2+4x-10
Answer:
x= 0.348 OR X= -1.148
Step-by-step explanation:
Given that:
2x^2+8+3x^2+4x-10
The first step is to rearrange the parameters given, by doing so, we have:
= 2x^2 +3x^2 +4x -10+8
= 5x^2 +4x - 2
The above equation forms the basis of a quadratic equation;
So using quadratic formula
= (-b +/- (√b^2-4ac))/2a
= (-4 +/- (√4^2 -4*5*(-2))/2*5
= -4 +/- (√ 16 - (-40))/10
=( -4 +/- √ 56 ) / 10
=( -4 +√ 56 ) / 10 OR =( -4 - √ 56 ) / 10
= (-4 + 7.48)/10 OR (-4 -7.48)/10
= 3.48/10 OR -11.48/10
= 0.348 OR. -1.148
SO, x= 0.348 OR X= -1.148
Logan and Lily mix blue and red paint to make batches of purple paint as shown in the tables. 2 tables. The first table is a 2-column table with 4 rows titled Logan. Column 1 is labeled Blue with entries 3, 4, 5, 6. Column 2 is labeled Red with entries 9, 12, 15, 18. The second table is a 2-column table with 4 rows labeled Lily. Column 1 is labeled blue with entries 4, 6, 12, 14. Column 2 is labeled Red with entries 10, 15, 30, 35. Compare the ratios of blue paint to red paint. Which statement is true? Logan has a higher ratio than Lily. Lily has a higher ratio than Logan. Only some of Logan’s ratios are greater than Lily’s ratios. Logan and Lily’s ratios are equal.
Answer:
Lily has a higher ratio than Logan
Step-by-step explanation:
The True statement is Lily has a higher ratio than Logan
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
Column 1 Column 2
3 9
4 12
5 15
6 18
Second table
Column 1 Column 2
4 10
6 15
12 30
14 35
The ratio from the first table is = 3/9 = 1:3 = 5/15
and, the ratio from the second table is = 4/10 = 2:5= 6/15
Hence, Lily has a higher ratio than Logan.
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