Answer: A rational number is any value that can be expressed as a ratio of two integers. An irrational number is any value that cannot be expressed as a ratio of two integers.
Rational 4 and 1/4
Irrational π and √3
If a number can be written in the form of the fraction of p and q then that number is known as the rational number whereas a number is not written in the form of the fraction p and q then that number is known as the irrational number.
Rational Number - If a number can be written in the form of the fraction of p and q then that number is known as the rational number, that is:
[tex]\rm Rational \;Number = \dfrac{p}{q}[/tex]
Where q is the denominator and p is the numerator.
For example - [tex]\dfrac{4}{3}[/tex] , [tex]\dfrac{1}{4}[/tex] , etc
Irrational Number - If a number is not written in the form of the fraction p and q then that number is known as the irrational number, that is:
[tex]\rm Irrational \;Number \neq \dfrac{p}{q}[/tex]
Where p is the numerator and q is the denominator.
For example - [tex]\pi, \sqrt{3}[/tex], etc
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What is the range of the given function?
{(-2.0), (-4,-3), (2, -9), (0.5), (-5, 7)}
The range is the y-values.
Let r = range
r = {0, -3, -9, 5, 7}
simplify
[tex]3 (3w - 4x) + \frac{25x - 5}{ 5 } [/tex]
Answer:
9w−7x−1
Step-by-step explanation:
Simplify the expression.
What is the solution to 2(3x + 6) = 3(2x - 6)?
Answer:
The statement is false. 12 ≠ -18
Step-by-step explanation:
2(3x + 6) = 3(2x - 6)
6x + 12 = 6x - 18
-6x -6x
12 ≠ -18
If u varies directly with v, with k=0.6, what is the value of u when v=7.8?
a. u = 13
b. u = 0.77
c. u = 0.468
d. u = 4.68
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{"u" varies directly with "v"}}{u=kv}\qquad \textit{we know that } \begin{cases} k=0.6\\ v=7.8 \end{cases} \\\\\\ u=(0.6)(7.8)\implies u=4.68[/tex]
What is the value of a in the equation 3 a plus b equals 54, when b equals 9?
Answer:
a = 15
Step-by-step explanation:
Given
3a + b = 54 ← substitute b = 9
3a + 9 = 54 ( subtract 9 from both sides )
3a = 45 ( divide both sides by 3 )
a = 15
An equation is formed when two equal expressions. The value of a in the equation 3a+b=54, when b equals 9 is 15.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given statement "3 a plus b equals 54" in terms of the equation can be written as,
3a + b = 54
Given an equation 3a+b=54. Also, the value of b in the given equation is 9. Therefore, the value of a in the given equation can be written as,
3a + 9 = 54
Subtract 9 from both sides of the equation,
3a + 9 - 9 = 54 - 9
3a = 45
Divide both the sides of the equation by a,
3a/3 = 45/3
a = 15
Hence, the value of a in the equation 3a+b=54, when b equals 9 is 15.
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If my bill is $160 and they’re going to takeoff 25% of the total bill how much money will I give them
$40 will be taken off the bill and you will be paying a total of $120.
Multiply 160 by .25 to find the amount taken off ($40), and then subtract from the total to find the amount that you will be paying ($120).
Have a great day!
Answer:
You will pay $120
Step-by-step explanation:
There are many methods in solving this percentage equation, but this is by far my favorite. Here is how it works.
1.Take 160, the original amount. 160
2.Then take the percent amount .25
and convert into decimal. ---------------------
3. Multiply the numbers 40.00
4. Subtract the product from 160
original amount, 160. - 40
--------------------
$120
That is how I would get my answer. I am very sorry if the formatting messes up, but it is this basic problem: 160*.25=40.00 then 160-40=120
A lemonade recipe calls for 2 caps of sugar and 3 caps of water.how many cups of sugar are needed when using 12 cups of water
Answer:
8 Cups of Sugar.
Step-by-step explanation:
3x4=12 cups of water.
2x4=8 cups of sugar
Dr.Imos plants a vegetable garden each year.He plants one fourth of his garden in corn.and one half of his garden in tomatoes,He buys 240 seeds.If he pays $0.05 per seed for all vegetables he plants, how much does he spend on seeds? use S.O.L.V.E
Answer: $12
Step-by-step explanation:
0.05 x 240 = $12
Hope this helps!
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
X measures 30°, Y measures 67°, and Z measures 83°.
Since the sum of the measures of the angles of a triangle is 180, and the sum of the measures of the second and third angles is five times the measure of the first angle, and the third angle is 16 more than the second, for find the measures of the three angles, the following calculation must be performed, posing linear equations:
X + Y + Z = 180 Y + Z = 5X Z = Y + 16
X + 5X = 180 6X = 180 X = 180/6 X = 30
Y + Y + 16 = 5 x 30 2Y + 16 = 150 2Y = 150 - 16 Y = 134/2 Y = 67
Z = 67 + 16 Z = 83
Therefore, X measures 30 °, Y measures 67 °, and Z measures 83 °.
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Let x, y, and z represent the measures of the first, second, and third angles of the triangle. We can create a system of equations to find the values of x, y, and z. Solving this system, we find that x = 28, y = 32, and z = 48.
Explanation:Let's use x, y, and z to represent the measures of the first, second, and third angles, respectively.
The sum of the measures of the second and third angles is five times the measure of the first angle, so we have the equation y + z = 5x.
The third angle is 16 more than the second, so z = y + 16.
Since the sum of the measures of the angles of a triangle is 180, we have the equation x + y + z = 180.
Now we can solve these equations to find the measures of the three angles.
Substituting z = y + 16 into the equation y + z = 5x, we get y + y + 16 = 5x, which simplifies to 2y + 16 = 5x.
Substituting z = y + 16 into the equation x + y + z = 180, we get x + y + y + 16 = 180, which simplifies to x + 2y + 16 = 180.
Now we have a system of equations:
2y + 16 = 5x
x + 2y + 16 = 180
Solving this system, we find that x = 28, y = 32, and z = 48.
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5. Adair suggests that they package together the fries and soda in a combo for a $0.75
discount. If the student council pays $0.85 per french fry and $1.20 per soda, then how much
money will they make if they sell 45 combos?
Answer:
$58.50
Step-by-step explanation:
It is given that the the student council pays
For per french fry = $0.85
For per soda fry = $1.20
Discount on the combo of fries and soda = $0.75
Total revenue for one combo = $0.85 + $1.20 - $0.75 = $1.30
Since the total revenue for one combo is $1.30, therefore the total revenue for 45 combo is
Total revenue for 45 combo = 45 × $1.30 = $58.50
Therefore, they will make $58.50 if they sell 45 combos.
What is the polynomial function of least degree whose only zeros are -2, 3, and 4
Answer:
[tex]x^3-5x^2-2x+24[/tex]
Step-by-step explanation:
the polynomial function of least degree whose only zeros are -2, 3, and 4
Factors are -2,3 and 4
First we write the polynomial in factor form
If 'a' is a zero of the polynomial then (x-a) is a factor
Factors are -2,3 and 4
Polynomial is [tex](x-(-2))(x-3)(x-4)[/tex]
[tex](x+2)(x-3)(x-4)[/tex]
Now we multiply all the parenthesis
[tex](x+2)(x-3)(x-4)[/tex]
[tex](x^2-3x+2x-6)(x-4)[/tex]
[tex](x^2-x-6)(x-4)[/tex]
[tex]x^3-4x^2-x^2+4x-6x+24[/tex]
[tex]x^3-5x^2-2x+24[/tex]
The number 392 is what percent of 560? I need help with this math problem
Its 70%
392/560 = 0.7
0.7 * 100 = 70%
Solve for x..
12x + 7 < -11 OR
5x – 8 > 40
Answer:
x>48/5 or x<-3/2
Step-by-step explanation:
Solve for x
a) 12x + 7 < -11
12x < -11-7
12x < -18
x < -18/12
⇒ Simplify: divide the numerator by 6
x < -3/2
b) 5x – 8 > 40
5x > 40+8
5x > 48
x > 48/5
Therefore, x>48/5 or x<-3/2.
Find Each Difference 125 - ( -114 )
Answer:
125-(-114)=239
Step-by-step explanation:
Change the subtraction to addition and change the negative in the second number to a positive (it's the opposite). Then add them. 125+114=239
CAN EXPLAIN FURTHER
Annette, Barb, and Carlita work in a clothing shop. One day the three had combined sales of $1480. Annette sold $120 more than Barb. Barb and Carlita combined sold $280 more than Annette. Write and solve a linear system to find out how much did each person sold.
Answer:
The quantity sold by Annette was $600
The quantity sold by Barb was $480
The quantity sold by Carlita was $400
Step-by-step explanation:
Let
x ----> quantity sold by Annette
y ---> quantity sold by Barb
z ---> quantity sold by Carlita
we know that
[tex]x+y+z=1,480[/tex] ----> equation A
[tex]x=y+120[/tex] ----> equation B
[tex]y+z=x+280[/tex] ----> equation C
substitute equation C in equation A and solve for x
[tex]x+(x+280)=1,480[/tex]
[tex]2x=1,480-280[/tex]
[tex]2x=1,200[/tex]
[tex]x=\$600[/tex]
Find the value of y
[tex]x=y+120[/tex]
[tex]600=y+120[/tex]
[tex]y=600-120=\$480[/tex]
Find the value of z
[tex]x+y+z=1,480[/tex]
[tex]600+480+z=1,480[/tex]
[tex]1,080+z=1,480[/tex]
[tex]z=\$400[/tex]
therefore
The quantity sold by Annette was $600
The quantity sold by Barb was $480
The quantity sold by Carlita was $400
The solution involves setting up a system of three linear equations based on the given problem. By solving these equations methodically, we find that Barb, Annette, and Carlita sold $400, $520, and $560 of clothing respectively.
Explanation:The problem involves setting up and solving a system of linear equations. Here's how we approach it:
Let's denote Barb's sales as B, Annette's sales as A, and Carlita's sales as C.The total sales are given to be $1480, so we have our first equation as A + B + C = 1480.The problem states that Annette sold $120 more than Barb. This gives us another equation: A = B + 120.It is also said that Barb and Carlita combined sold $280 more than Annette, hence the third equation: B + C = A + 280.Now we have a system of three equations which we can solve step-by-step. Firstly, substitute A from the second equation into the first and third one, providing us with two new equations: B + 120 + B + C = 1480 and B + C = B + 120 + 280. These simplify to 2B + C = 1360 and B = 400. Substituting B = 400 into the equation 2B + C = 1360 gives C = 560.Last, we substitute B = 400 into the second equation A = B + 120, which simplifies to A = 520.So, Barb sold $400 of clothing, Carlita sold $560, and Annette sold $520.
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how do you solve -2/5x -9<9/10
Answer:
x > -99/4
Step-by-step explanation:
I must assume that you meant (-2/5)x -9<9/10.
This inequality has 3 terms. The LCD is 10. Multiply each term by 10 and reduce the result:
10(-2/5)x - 10(9) < 10(9/10), or:
-4x - 90 < 9
Adding 90 to both sides results in:
-4x < 99
Here we must divide by a negative number (that is, by -4). This requires reversing the direction of the inequality sign:
x > -99/4 is the final solution.
dachelle does pushups every morning. she does 3 sets of pushups, 7 days a week. How many pushups does dachelle do in one week?
Answer:
21
Step-by-step explanation:
If she does 3 pushups every morning, than you need to multiply 3x7
3 sets of 8 pushups a day (can't forget that information!! its critical the the problem!!!) 7 days a week
3*8 = 24
24*7 = 168
168 pushups a week
If a ball dropped from a tower reaches the ground after 3.5 seconds, what is the height of the tower? Given: g = –9.8 meters/second2 A. 56.00 meters B. 60.03 meters C. 62.08 meters D. 62.50 meters
Answer:
B. 60.03 meters.
Step-by-step explanation:
We use the equation of motion under gravity:
h = ut - 0.5gt^2 where h = height, t = time and u = initial velocity.
h = (0)(3.5) - 0.5 * -9.8 * 3.5^2
= 60.025 m.
The height of the tower is found by utilizing the equation of motion for free fall. When the given values are input into the equation, the result is 60.03 meters. Hence, the correct answer is option B (60.03 meters).
Explanation:This is a question about the physics of free fall motion. In problems of free fall, we consider the motion under the gravitational force alone. We disregard air resistance to simplify our calculations. The height (h) of the tower can be calculated using the equation of motion: h = 0.5 * g * t^2, where g is the acceleration due to gravity and t is the time taken for the ball to reach the ground.
Plugging the values into the formula, h = 0.5 * -9.8 m/s^2 * (3.5 s)^2 = -0.5 * -9.8 * 12.25 = 60.03 meters. The distance is positive, because we are considering the magnitude of the height, rather than the directional displacement. So, option B (60.03 meters) is the correct answer.
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i need help with math You reflect triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1), across the x-axis, across the y-axis, and across the x-axis again to form triangle P′Q′R′.
Answer:
After these reflections, the coordinates of P' will be P'(4,-4)
Step-by-step explanation:
The question is
After these reflections, the coordinates of P' will be?
we have
Triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1)
Part 1) Reflect triangle PQR across the x-axis
we know that
The rule of the reflection of a point across the x-axis is
(x,y) -----> (x,-y)
Applying the rule of the reflection across the x-axis at the coordinates of triangle PQR
P(-4, -4) -----> P'''(-4,4)
Q(-1, -3) -----> Q'''(-1, 3)
R(-3, -1) ----> R'''(-3, 1)
Part 2) Reflect triangle P'''Q'''R''' across the y-axis
we know that
The rule of the reflection of a point across the y-axis is
(x,y) -----> (-x,y)
Applying the rule of the reflection across the y-axis at the coordinates of triangle P'''Q'''R'''
P'''(-4,4) -----> P''(4,4)
Q'''(-1, 3) ---> Q''(1, 3)
R'''(-3, 1) ---> R''(3, 1)
Part 3) Reflect triangle P''Q''R'' across the x-axis again
we know that
The rule of the reflection of a point across the x-axis is
(x,y) -----> (x,-y)
Applying the rule of the reflection across the x-axis at the coordinates of triangle P''Q''R''
P''(4,4) ----> P'(4,-4)
Q''(1, 3) ----> Q'(1, -3)
R''(3, 1) ----> R'(3, -1)
therefore
After these reflections, the coordinates of P' will be P'(4,-4)
8. Which animal is closest to sea level?
Shark -7
Sea Lion -10
Seagull 24
Turtle -6
Turtle is closest to the sea level.
What is number line ?In which horizontal straight line, we represent integer numbers from low value to high, from left to right, is called number line.
Zero is in the middle of that line.
If we consider the number line, then in the left side of zero, we have all the negative values, where .... < -5< -4< -3< -2< -1< 0
And in the right side of zero, we have all the positive values, where 0<1<2<3<4<5 and so on....
Which animal is closest to sea level ?We know that, Level zero is called the sea level.
So, if we assume number line in vertical way, then the zero will be the sea level.
Here, if we arrange levels of animals from low to high, we get,
Sea lion(-10)<Shark(-7)<Turtle(-6)<0 <Seagull(+24)
We see that, zero is in between -6 & 24
The distance between 0 & -6 is 6 units whereas between 0 & 24 is 24 units.
So, Turtle is closest to sea level.
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Sea Lion has the lowest value indicating its proximity to sea level. Hence, the correct option is second.
Sea Lion is the animal closest to sea level with a value of -10. This means it is approximately 10 meters below sea level. In comparison, the Shark has a value of -7, the Turtle has a value of -6, and the Seagull has a value of 24, making the Sea Lion the closest to sea level.
Add 5/8+7/8 . Simplify the answer and write as a mixed number.
Answer: 1 1/2
Step-by-step explanation: 5/8 + 7/8
= 12/8
simplifies to 1 1/2
solve 10m -28 = 6 -7m
Answer:
Step-by-step explanation:
Answer:
The solution to 10m -28 = 6 -7m is m = 2.
Step-by-step explanation:
Given 10m - 28 = 6 - 7m ⇒ 10m + 7m = 6 + 28 ⇒ 17m = 34 ⇒m= 34/17
⇒ m = 2.
what is the value of x?
enter your answer in the box
Hey!
--------------------------------
Polygon: Heptagon
Vertices: 7
Sum of angles: 900°
--------------------------------
Solution:
158 + 120 + 139 + 121 + 125 + 126 = 789
900 - 789 = 111°
--------------------------------
Answer:
x = 111°
--------------------------------
Hope This Helped! Good Luck!
if you have $18 and you spend $11 on movie tickets , what fraction of your money did you spend?
Answer:
11/18
Step-by-step explanation:
The fraction you spent is the ratio of the amount you spent to the amount you started with:
__
$11/$18 = 11/18 . . . . fraction spent on movie tickets
Can you help me with number 10
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{(3^{-2})^2}{3^{-3}}\implies \cfrac{3^{-2\cdot 2}}{3^{-3}}\implies \cfrac{3^{-4}}{3^{-3}}\implies \cfrac{1}{3^{-3}\cdot 3^4}\implies \cfrac{1}{3^{-3+4}}\implies \cfrac{1}{3^1}\implies \cfrac{1}{3}[/tex]
How do I solve an equation like this, one with a negative in front of parentheses?
2-(4-x) = 7x-5x
The factor outside the parentheses is -1. Distribute using that factor.
2 - (4 - x) = 7x - 5x
-1 * 4 = -4 and -1 * -x = x
2 - 4 + x = 7x - 5x
Simplify.
-2 + x = 2x
x = 2x + 2
-x = 2
x = -2
Answer:x = -2
Simplify the expression 5^22/5^13
To solve, multiply 5 by 5 twenty-two times. It will equal 2384185791015625. Then, multiply 5 by 5 thirteen times. It will equal 1220703125. Finally, simplify 2384185791015625/1220703125. You should get 1953125 as your answer. Therefore, 1953125 is the answer.
Edit: 5^22 means 5²² which means to multiply 5 by 5 by 5... for 22 times. It means the exponents. (Power of)
The expression 5^22/5^13 simplifies to 5^(22-13) which equals 5^9. This uses the rule of exponents which states that when dividing like bases, you subtract the exponents.
Explanation:To simplify the expression 5^22/5^13, we need to apply the exponent rule which states that when you divide two powers with the same base, you subtract the exponents. In this case, we subtract the exponent of 5^13 from the exponent of 5^22. So, 5^22/5^13 = 5^(22-13) = 5^9.
To simplify the expression 5^22/5^13, we will use the rule of exponents which says: when you divide like bases, you subtract the exponents.
Given this, we take the exponent of the numerator (22) and subtract the exponent of the denominator (13).
Therefore, 5^22/5^13 simplifies to 5^(22-13), which equals 5^9.
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Help me thank you!!!!
Answer:
Step-by-step explanation:
<1 = <5 Corresponding angles.
<5 + <6 = 180° Angles making up the same straight line are supplementary.
<1 + <6 = 180° <1 and <5 are equal.
<6 = 180° - <1 If we know <1 we can easily find six. It is <1s supplement.
What is the decimal equivalent of 8/32
Answer:
.25
Step-by-step explanation:
8/32 = 1/4
1/4 = .25
Answer:
0.25
Step-by-step explanation:
Polygon ABCD is translated to create polygon A'B'CD'. Point A is located at(1,
5), and point A'is located at (-2, 3). Which expression defines the
transformation of any point (x, y) to (x,y) on the polygons?
x'= x-3
y'= y - 2
X'=x-2
y'=y-3
Ox'= x-1
y'=y-8
x = x + 3
y = y'+2
Answer:
the answer is
x′ = x − 3
y′ = y − 2
Step-by-step explanation:
Answer:
x′ = x − 3
y′ = y − 2
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