Yes
For Example :If the rectangle has sides of Square root 8 and square root 2 which are two irrational numbers but when multiplied it gives an area of 4 square units which is a rational number.
No, it is not possible for a rectangle to have rational side lengths and an irrational area, because two rational numbers are always rational.
Given that,
To figure out, is it possible for a rectangle to have rational side lengths and an irrational area.
Rational numbers can be structured in the form of the fraction of integers. Eg- 5/6, 2/3, etc.
Here,
in a rectangle, two sides have rational length and the area of the rectangle is a product of the sides of the rectangle.
Since there is a property of the rational numbers that, when two rational numbers are multiplied together the product of the rational number is always rational.
So the area of the rectangle also would be rational.
Thus, it is not possible for a rectangle to have rational side lengths and an irrational area.
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Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet. How many ducks and how many cows does Old Mc Donald have?
Answer:
The number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.
Step-by-step explanation:
We are given that Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet.
Let the number of ducks Old Mc Donald raises be 'x' and the number of cows Old Mc Donald raises be 'y'.
So, according to the question;
The first condition states that the animals have a total of 100 heads, that means;[tex]x+y=100[/tex]
[tex]x=100-y[/tex] -------------------- [equation 1]
{because one head of a duck and one head of cow}
The second condition states that the animals have a total of 354 feet, that means;[tex]2x+4y=354[/tex]
[tex]x+2y=177[/tex] --------------- [equation 2]
{because there are two feet of a duck and four feet of cow}
Now, putting the value of x in equation 2 we get;
[tex]100-y+2y=177[/tex]
[tex]y=177-100[/tex]
y = 77 cows
Putting this value of y in equation 1 we get;
x = 100 - y
x = 100 - 77 = 23 ducks
Hence, the number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.
Rita has 1 3/4 yards of red material, 3 1/3 yards of blue material, and 4 1/2 yards of striped material. Altogether, how much material does Rita have?
Answer:
9 7/12
Step-by-step explanation:
1 3/4 + 3 1/3 + 4 1/2
1 + 3 + 4 = 8
8 + 3/4 + 1/3 + 1/2
8 + 9/12 + 4/12 + 6/12
8 + 19/12
8+ 1 7/12
9 + 7/12
9 7/12
What is the solution for this inequality? 8x ≤ -32
Answer:
x≤-4
Step-by-step explanation:
There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.
8x≤-32
1. Divide both sides by 8
How do I express 32 kilometeters in miles?
Answer:
19.84 Miles
give or take
Step-by-step explanation:
1 km is .62 miles
.62 x 32 = 19.84
Answer:
19.88 miles
Step-by-step explanation:
The city of Atlanta plans to hold a parade after the Atlanta Falcons win the Super Bowl. They intend to allow fans to watch from the sidewalk on both sides of Peachtree Street. The parade route will be 1 mile long (5,280 feet are in a mile) and the sidewalks are 10 feet deep. If the average person takes up 3 square feet of space, what is the estimate for the number of people who can attend the parade?
Answer:
17600 people.
Step-by-step explanation:
Given that The parade route will be 1 mile long (5,280 feet are in a mile) and the sidewalks are 10 feet deep.
The area of the parade route will be
5280 × 10 = 52800 ft^2
If the average person takes up 3 square feet of space, then, divide the area by 3. That is,
52800 / 3 = 17600 people.
Therefore, the estimate for the number of people who can attend the parade will be 17600 people.
The amount of a certain medication remaining in the bloodstreamt
hours after taking the medicine is modeled by the equation M(t) = -4**
5x2 + 3x +18. Package directions recommend taking a second dose 4-6
hours after the initial dose,
Answer:
45, 46, 33, 0, 6
Step-by-step explanation:
Can someone help me with these word problems?
Help ASAP it’s either
68degrees
110 degrees
136 degrees
or 112 degrees
Answer:112
Step-by-step explanation: Line SW is 180 degrees since it is a straight line. Subtract angle TBU 18 and angle UBW 50 from line SW 180 to get angle SBU which is 112.
Find the midpoint of R(2,2) and S(-3,6)
Answer: (-0.5, 4)
Step-by-step explanation:
Midpoint formula: [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
(x1, x2)=(2, -3)
(y1, y2)=(2, 6)
-----------------------------------------------
[tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
=[tex](\frac{2-3}{2} ,\frac{2+6}{2} )[/tex]
=[tex](\frac{-1}{2} ,\frac{8}{2} )[/tex]
=[tex](-0.5, 4)[/tex]
Hope this helps!! :)
Please let me know if you have any question or need further explanation
Answer:
[tex]M=(-\frac{1}{2},4)[/tex]
Step-by-step explanation:
The midpoint formula is given by:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Let (2,2) be x₁ and y₁ and let (-3,6) be x₂ and y₂. Therefore:
[tex]M=(\frac{2+-3}{2},\frac{2+6}{2})[/tex]
Simplify:
[tex]M=(-\frac{1}{2},\frac{8}{2})\\M=(-\frac{1}{2},4)[/tex]
Chicken eggs can be categorized as large if they weigh at least 2 ounces. Clare weighs 48 large eggs and finds that they have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces. Interpret 0.08 ounces in this situation.
Answer: The average difference of weights of all 48 eggs from mean eight is 0.08.
Step-by-step explanation:
The mean absolute deviation of a data interprets the mean distance between each data point and the mean.
When this distance goes larger it means data has greater variability
Given, 48 large eggs have a mean weight of 2.1 ounces and a mean absolute deviation of 0.08 ounces.
It means that the average difference of weights of all 48 eggs from mean eight is 0.08.
i need help , what’s the answer ?
Answer:
D,
Step-by-step explanation:
that's because you only factorise when you have a common factor, ax-3b cannot be factorised because they have nothing in common so it is wrong to use x to factorise it. If you want to be sure that it is not factorisable, try expanding it and you'll see that you will not get the same answer.
Answer as a decimal with four decimal places.
Answer:
Answer as a fraction. Do not include spaces in your answer.
1st question
-31/15
2nd question
19/40
3rd = Answer as a decimal with four decimal places
0.8333…
4th = fraction
5th =rational
6th =rational
Step-by-step explanation:
edge 2021
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression can be reduced to 0.8333.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be written as shown below,
[tex]2.5 \times 0.\bar3[/tex]
= (25/10) × (1/3)
= 25/30
= 5/6
= 0.8333....
Hence, the given expression can be reduced to 0.8333.
Learn more about Expression:
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The line y= -x + 3 best models which of the following scatter plots?
Answer:
a
Step-by-step explanation:
Since we have a negative slope, that means the correlation for the scatter plot also has to be negative.
Since the only scatter plot that has a negative correlation is graph A, a is our answer.
A city council consists of 8 members. Of the 3 men on the committee, 1 has a bachelor's degree and the other 2 have master's degrees. Of the 5 women on the committee, 4 have bachelor's degrees and 1 has a master's degree. A member is chosen at random to take notes at a meeting. What is the probability that the committee member has a bachelor's degree?
Answer:
5/8
Step-by-step explanation:
1 man, 4 women out of 8 people total
Given h(x) = -2x + 5, solve for a when h(x) = 3.
Answer:
Step-by-step explanation:
-2x + 5 = 3
-2x = -2
x = 1
Multiplying a number by which of the following would result in a smaller number?
O 100
O 101
O 102
10-1
Answer:
10^(-1)
Step-by-step explanation:
Recall that a value that is multiplied by a number that is between 0 and 1 will result in a number that is smaller than the original number.
the first 3 are all greater than 1, hence will result in a greater value if when multiplied with another number.
The last one is 10^(-1) = 0.1
Anything multiplied by 0.1 will result in a value that is 1/10th of the original value.
Hence this is the answer.
Answer:
10/\-1 is correct
Step-by-step explanation:
A comparison of two quantities with similar units, by division is called: *
1.ratio table
2.rate
3.ratio
4.origin
If 3x - 8= -2, find the value of x - 6.
Answer:
x-6 = -4
Step-by-step explanation:
3x - 8= -2
Add 8 to each side
3x - 8+8= -2+8
3x = 6
Divide by 3
3x/3 = 6/2
x =2
We want to find x-6
2-6 = -4
Answer: - 4
Step-by-step explanation:
3x - 8 = -2
3x = -2 + 8
3x = 6
x = 6/3
x = 2
so, therefore x - 6 => 2 - 6 = -4
Why is the sum of a rational number and a irrational number always irrational
Answer:
A rational number is a number able to be put into a fraction, an irrational number is not able to be. Therefore, when adding the two, the rational and the irrational will be irrational. For example, 2 is a rational number, and 1.8903 is irrational. If you add the two, you will get 3.18903, which is unable to be put into a fraction.
3 + root 3 *2 +root 2
Answer:
6 + 3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
(3 + [tex]\sqrt{3}[/tex] )(2 + [tex]\sqrt{2}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
3(2 + [tex]\sqrt{2}[/tex] ) + [tex]\sqrt{3}[/tex] (2 + [tex]\sqrt{2}[/tex] ) ← distribute both parenthesis
= 6 + 3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex]
The following list details the numbers of tickets sold for a talent show grade 9:22; grade 10:32; grade 11: 41; and grade 12:30. What are the
domain and range of this relation?
A domain: (22, 32, 41, 30); range: {9, 10, 11, 12}
B. domain: {9, 22, 10, 32); range: {11, 41, 12, 30}
C. domain: {9, 10, 11, 12); range: (22, 32, 41, 30)
D
domain: {11, 41, 12, 30}; range: {9, 22, 10, 32)
Answer: C. domain: {9, 10, 11, 12); range: (22, 32, 41, 30)
Step-by-step explanation:
The data set is:
(9, 22)
(10,32)
(11, 41)
(12, 30).
In the usual notation, the number at the left is the input (belons to the domain) and the number in the right is the output (belongs to the range).
Then the domain would be:
{9, 10, 11, 12}
and the range:
{22, 32, 41, 30}
The correct option is C
25=19+k. What’s the answer?
Answer:
k=6
Step-by-step explanation:
25=19+k
Subtract 19 from each side
25-19=19-19+k
6 = k
Answer:
k = 6
Explanation:
to find the value of k in the equation provided, you must subtract nineteen from both sides. this will isolate the variable.
25 = 19 + k
25 - 19 = 19 - 19 + k
6 = k
k = 6
therefore, the value of the variable k in 25 = 19 + k is 6.
Help please functions problem
Answer:
f(3) = 24
Step-by-step explanation:
substitute X for 3.
F(3) = 3 * (2) ^3
= 24
1.) A boy has $12 saved. He decides to start saving on a regular basis. He figures out that he
can
save $1.50 per day. What is the total amount he will have saved after 1 day? 2 days? 3 days?
17days? X days?
Answer:
12 + (1.50 multiplied by x)
Step-by-step explanation:
You have 12 dollars as the base. For every x days (x is the amount of how many days) he'd save $1.50. For one day, he'd save 1.50 plus his 12 dollars. Two days, he'd save 12 + (1.50 x x). Three, it'll be 12 + (1.50 x x) and so on.
I hope this helped. :)
Solve the following simultaneous equations : with the help of steps
1. x + 2y = 1, 3x - y = 17
Answer:
x = 5, y = -2
Step-by-step explanation:
Given equations:
x + 2y = 13x - y = 17From the first equation we get:
x = 1 -2ySubstitute x in the second equation, find y:
3x - y = 173*(1-2y) - y = 173 - 6y - y = 17-7y = 17 - 3-7y = 14y = -14/7y = -2Find x:
x = 1 - 2y x = 1 - 2*(-2)x = 1 + 4x = 5Determine whether each ordered pair is a solution of y = x+3. (2,5) (4,6) (5,8) (3,7)
Answer:
(2,5) and (5,8)
Step-by-step explanation:
you can just plug in the numbers to get your answer and if two numbers aren't the same then its not a solution
example: (2,5)
5 = 2 + 3
5 = 5
5 does equal 5 making it a solution because it makes sense right?
example: (4,6)
6 = 4 + 3
6 = 7
this isn't a solution because six doesn't equal 7
Answer:
[see below]
Step-by-step explanation:
[tex]y=x+3[/tex]
(2,5):[tex]5=2+3\\\\\boxed{5=5}[/tex]
The ordered pair is a solution.
(4,6):[tex]6=4+3\\\\\boxed{6\neq7}[/tex]The ordered pair is not a solution.
(5,8):[tex]8=5+3\\\\\boxed{8=8}[/tex]The ordered pair is a solution.
(3,7):[tex]7=3+3\\\\\boxed{7\neq 6}[/tex]
The ordered pair is not a solution.
Hope this helps.
Given the formula C= 1/2t(c1-c2), solve for t.
Answer:
[tex]t=\frac{2C}{c1-c2}[/tex]
Step-by-step explanation:
[tex]C=\frac{1}{2}t(c1-c2)\\2(C)=2(\frac{1}{2}t(c1-c2))\\2C=t(c1-c2)\\\frac{2C}{c1-c2}=\frac{t(c1-c2)}{c1-c2}\\t=\frac{2C}{c1-c2}[/tex]
Answer:
[tex]t=\frac{2C}{c_{1}-c_{2}}[/tex]
Step-by-step explanation:
[tex]C=\frac{1}{2}*t(c_{1}-C_{2})\\\\[/tex]
Multiply both sides by 2,
[tex]2*C=2*\frac{1}{2}*t*(c_{1}-c_{2})\\\\2C=t*(c_{1}-c_{2})\\\\\frac{2C}{(c_{1}-c_{2})}=t\\\\\\t=\frac{2C}{c_{1}-c_{2}}[/tex]
Perimeter of square = 12 1/2 in
Side length of square=
Find the value of x in the triangle shown below.
Answer:
55
Step-by-step explanation:
98+27+x=180
Answer:
Step-by-step explanation:
x + 98° + 27° = 180
x + 125° = 180°
x = 55°
Marie goes to the clothing store. Her purchases equal $89.25. The sales tax is 8%. How much tax does she pay?
A $7.14
B $7.86
C S71.40
D S78.60
Answer: A. $7.14
Step-by-step explanation:
price × percentage of sales tax=amount of tax
89.25 × 8%=$7.14
Hope this helps!! :)
Please let me know if you have any question