The product of 576 and 684 is a rational number since it results in an integer, which is a subset of rational numbers.
Explanation:The product of 576 and 684 is asked to be classified as rational or irrational. The multiplication of two integers will always produce another integer, as is the case with 576 multiplied by 684. Since all integers are rational numbers (they can be expressed as the ratio of two integers), the product, in this case, is also a rational number.
Therefore, the product of 576 and 684 is rational because it can be expressed as a ratio of the two integers (the product itself over 1), fitting the definition of a rational number which includes integers, fractions, finite decimals, and repeating decimals.
Final answer:
The product of 576 and 684 is a rational number because the multiplication of two integers always results in another integer.
Explanation:
The question asks whether the product of 576 and 684 is rational or irrational. A rational number is a number that can be expressed as a ratio of two integers. Since both 576 and 684 are integers, their product will also be an integer, as the multiplication of two integers always results in another integer. Therefore, this product is definitely a rational number. An irrational number, by contrast, cannot be expressed as such a ratio, and is typically found with non-repeating, non-terminating decimal expansions or with numbers like the square root of a non-square number. However, as there is no square root or any other irrational operation involved in multiplying 576 and 684, the result is rational.
If 8 cases of merchandise cost 60$, what would a dozen cases cost?
Answer: $90
Step-by-step explanation: First, we can change "one dozen" to 12 since it represents the same value.
To find out how much 12 cases of merchandise will cost, we will need to find the unit price per case of merchandise.
Unit price means the cost per unit in this case, the cost per case of merchandise.
Since we know that it costs $60 for 8 cases of merchandise, to find the cost for 1 case of merchandise, we need to divide 8 into $60 or $60 ÷ 8.
60 ÷ 8 = 7.50
Now, we know that it costs $7.50 for 1 case of merchandise.
To find the cost for 12 cases of merchandise, we will multiply the cost for 1 case of merchandise by the number of cases of merchandise we have.
In this case, we will multiply 7.50 by 12 which gives us 90.
Therefore, a dozen cases of merchandise will cost $90.
Leon’s older brother is 4 3/4 feet tall . Leon is 1/3 foot shorter than his brother . How tall is Leon ?
Answer:
4 5/12
Step-by-step explanation:
4 3/4 = 19/4
19/4 = 57/12
1/3 = 4/12
57/12 - 4/12 = 53/12 = 4 5/12
2 FUIILS
A clothing store sells T-shirts, t, for $8 a shirt, and shorts, s, for $12 each. The
store earned $180 revenue last month. The store sold three times as many T-
shirts as shorts. Which system of equations represents this scenario?
8t+12s=180 and t=3s is the system of equations that represents the given scenario.
Step-by-step explanation:
Given,
Cost of a t-shirt = $8
Cost of a shorts = $12
t-shirt = t
shorts = s
Revenue earned = $180
According to given statement;
8t+12s=180
The store sold three times as many T- shirts as shorts.
t = 3s
8t+12s=180 and t=3s is the system of equations that represents the given scenario.
Keywords: linear equation, revenue
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Answer: 8t+12s=180;t=3s APEX
45.6379 rounded to the nearest hundread
Answer:
45.64
Step-by-step explanation:
thats the answer
To round 45.6379 to the nearest hundred, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros.
Explanation:To round 45.6379 to the nearest hundred, we look at the digit in the hundredth place, which is 5. Since 5 is greater than or equal to 5, we round up. Therefore, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros. The rounded number to the nearest hundred is 45.6400.
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The manager at Gabriela's Furniture Store is trying to figure out how much to charge for a book shelf that just arrived. The book shelf was bought at a wholesale price of $147.00 and Gabriela's Furniture Store marks up all furniture by 60 percent.
At what price should the manager sell the book shelf?
The manager should sale the bookshelf for $235.20
Step-by-step explanation:
Wholesale price of book shelf = $147.00
Mark up = 60% of original price
[tex]Mark\ up=\frac{60}{100}*147.00\\\\ Mark\ up=\frac{8820}{100}\\Mark\ up=\$88.20[/tex]
Total = Wholesale price + Mark up
[tex]Total= 147.00+88.20\\Total=\$235.20[/tex]
The manager should sale the bookshelf for $235.20
Keywords: mark up, percentage
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if a= -0.5 and b=5, find the value of 4a+b
When [tex]\(a = -0.5\) and \(b = 5\), the value of \(4a + b\) is \(3\).[/tex]
To find the value of [tex]\(4a + b\) when \(a = -0.5\) and \(b = 5\)[/tex], we simply substitute the values of a and b into the expression 4a+b and then perform the arithmetic.
Given that [tex]\(a = -0.5\) and \(b = 5\)[/tex], we have:
[tex]\[4a + b = 4(-0.5) + 5\][/tex]
Now, let's calculate:
[tex]\[4a + b = -2 + 5\]\[4a + b = 3\][/tex]
in the function f(x)=x^2 has the domain of {-2,4,8,9} what is the range
For the function f(x) = x^2 range will be { 4 , 16 , 68 , 81 }
Solution:Given that:
[tex]\text {Function is } f(x)=x^{2}[/tex]
Domain of the function is {-2, 4, 8, 9}
Need to determine range of the function.
Domain of the function is possible input of the function that is x and range of the function is possible output of the function that is f(x)
As there are only four input values for x that are -2,4,8,9 we can determine the range by calculating value of f(x) for each of the x
[tex]\begin{array}{l}{\text {At } x=-2:} \\\\ {f(x)=f(-2)=-2^{2}=4}\end{array}[/tex]
[tex]\begin{array}{l}{\text {At } x=4:} \\\\ {f(x)=f(4)=4^{2}=16}\end{array}[/tex]
[tex]\begin{array}{l}{\text {At } x=8:} \\\\ {f(x)=f(8)=8^{2}=64} \\\\ {\text {At } x=9:} \\\\ {f(x)=f(9)=9^{2}=81}\end{array}[/tex]
Thus the range of given function is { 4 , 16 , 68 , 81 }
Which are solutions of the equation (x+5)(x - 3) = 0? Check all that apply.
x= -15
x=-5
X=-3
x= 2
x=3
x=5
ای
Answer:
x=-5, 3
Step-by-step explanation:
(x+5)(x-3)=0
Apply the zero property,
set x+5=0 and x-3=0.
x=0-5=-5
x=0+3=3
x=-5, 3
Answer:
b&e
Step-by-step explanation:
our class voted for treasurer.there are 20 students.after voting billy received 3 times more votes then keeton.how many votes did billy receive?
Answer:
Votes received by Billy =15
Step-by-step explanation:
Given:
Total students in the class = 20
Billy receives 3 times more vote than Keeton.
To find the number of votes Billy receives.
Solution:
Let number of votes Keeton gets [tex]=x[/tex]
∴ Billy received [tex]=3x[/tex] votes
Expression for total votes can be given by ⇒ [tex]x+3x[/tex]
Total votes =20 as number of students is 20.
So, the equation to find [tex]x[/tex] is:
[tex]x+3x=20[/tex]
Solving for [tex]x[/tex]
⇒ [tex]4x=20[/tex]
Dividing both sides by 4.
[tex]\frac{4x}{4}=\frac{20}{4}[/tex]
∴ [tex]x=5[/tex]
∴ Votes received by Keeton = 5
Votes received by Billy = [tex]3\times 5[/tex] = 15
Factor using the distributive property using the GCF
10x-35
Answer:
5(2x-7)
Step-by-step explanation:
Find the differential for P=0.2x^(2)-17x-10
The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17
Step-by-step explanation:
Let us revise how to differentiate an equation with respect to x
If the equation is [tex]y = ax^{n}+b[/tex] , where a , b are constant
The differentiation of the term [tex]ax^{n}[/tex] is [tex]a(n)x^{(n-1)}[/tex] (multiply the coefficient of x by the power"n" and subtract 1 from the power)The differentiation of the term b is 0, because b is a constantThe differentiation of y is [tex]\frac{dy}{dx}=a(n)x^{(n-1)}+0=a(n)x^{(n-1)}[/tex]You can write [tex]\frac{dy}{dx}[/tex] as y'∵ P = 0.2x² - 17x - 10
- Let us differentiate each term
∵ The differentiation of 0.2x² is [tex]0.2(2)x^{2-1}=0.4x^{1}=0.4x[/tex]
∵ The differentiation of -17x is [tex]-17(1)x^{1-1}=-17x^{0}=-17(1)=-17[/tex]
∵ The differentiation of -10 is zero because the differentiation
of the numerical term is 0
∴ The differentiation of P is P' = 0.4x - 17
The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17
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What is the value of x in the equation? 5 1 10 x − 6 4 5 = 3 1 4 A) 1 1 9 B) 1 1 5 C) 1 3 20 D) 1 33 34
The value of x in the equation is 11/15.
Explanation:To find the value of x in the equation 5 1 10 x - 6 4 5 = 3 1 4, we need to isolate x on one side of the equation. Here's how you can solve it:
Step 1: Add 645 to both sides of the equation.
Step 2: Subtract 314 from both sides of the equation.
Step 3: Simplify the equation.
Step 4: Divide both sides of the equation by 510.
Step 5: Simplify the fraction.
Therefore, the value of x in the equation is 11/15, which is option B) 11/15.
What does control for eximerment mean
.
Answer:
The definition of a control experiment is a test where the person conducting the test only changes one variable at a time in order to isolate the results. An experiment where all subjects involved in the experiment are treated exactly the same except for one deviation is an example of a control experiment.
Step-by-step explanation:
Answer/Explanation:
You need a control to show how 1 changed variable will change to result.
The volume of one cube is 1/216 times the volume of the second cube. How many more times
is the length measurement of the second cube?
A 21 times
B 16 times
C 6 times
D 4 times
Answer:
c 6 times that the answer
Final answer:
The second cube's side length is 6 times that of the first cube because the volume of a cube is a cubic function of its side length, and taking the cube root of 1/216 gives us 1/6.
Explanation:
The student's question is asking to determine how many times larger the side length of the second cube is compared to the first cube, given that the volume of the first cube is 1⁄216 times the volume of the second cube. The volume of a cube is calculated by raising the side length to the third power (V = s3). Therefore, if we denote the side length of the first cube as s and that of the second cube as S, we have s3 = 1⁄216S3. To find the side length ratio, we take the cube root on both sides of the equation, yielding s = 1⁄6S, which means the second cube's side length is 6 times that of the first cube.
The correct answer to the question is C, 6 times
Which is the Graph of 4x + 2y < 3 ?
Answer:
2nd graph on edge 2020
Step-by-step explanation:
the line will cross the y-axis at y = 1.5 and the line will be a broken line
Inequality graphs
The inequality functions are not separated by an equal sign.
For the inequality 4x + 2y < 3, the lower portion of the graph will be shaded
Determine the y-intercept. If x = 0
4(0) + 2y < 3
2y < 3
y < 1.5
This shows that the line will cross the y-axis at y = 1.5 and the line will be a broken line as shown:
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Lisa runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
Answer:
6/55 = x/44
55x = 6(44)
55x = 264
x = 264/55 = 4.8 miles
hope this helps<3
Step-by-step explanation:
what grade is a 259 out of 360 plz help
Answer:
Convert fraction (ratio) 259 / 300 Answer:86.3%
Find the slope intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x-3y=10
Answer:
y=4x+23
Step-by-step explanation:
The slope-intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x-3y=10 is y = 4x + 23.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.
And we have the given equation:
12x - 3y = 10
Arranging the equation as slope-intercept form.
3y = 12x - 10
Divide by 3,
y = 4x - 10/3.
And this line is parallel to the required line.
So, the slope of the required line;
m = 4
Hence, the slope-intercept form,
y = 4x+b equation 1
To find y-intercept:
We substitute the value of x and y from the point (-5,3) to the slope-intercept form,
y = 4x + b
(3) = 4(-5) + b
b = 20 +3
b = 23
Now, the equation 1
y = 4x + 23
Therefore, y = 4x + 23 is the required slope-intercept form.
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A rectangle is 19 feet long and 42 feet wide. What is the area of the rectangle, in square yards? Express your answer as a mixed number in lowest terms.
Answer:
[tex]86\frac{2}{3}[/tex] yards²
Step-by-step explanation:
19 feet = [tex]\frac{19}{3}[/tex] yards
42 feet = 14 yards
14 × [tex]\frac{19}{3}[/tex] = [tex]\frac{266}{3}[/tex] = [tex]86\frac{2}{3}[/tex]
The circumference of a circle is 35 pi. What is the diameter?
Answer:
Diameter is 11.14
Step-by-step explanation:
c=dπ
so... 35=dπ
solve for d:
35/π=d
11.14=d
Answer:
11.14
Step-by-step explanation:
/calculators/circumference-calculator/
A coin is tossed.
What is the probability of the coin landing heads up?
A. 1/2
B. 1/4
C. 1/6
D. 1/3
Answer: 1/2
Step-by-step explanation: In this problem, we're tossing a coin and we want to find the probability of tossing a heads.
Now, let's find the probability of tossing a heads.
Remember that a coin has two sides which are heads and tails. When you flip a coin, each side is as likely to come up as the other. This means that the probability of flipping heads is the fraction 1/2.
Since the probability of flipping a heads is 1/2, we can also say that the probability of flipping a heads is 50%.
Therefore, the probability of flipping a heads on a fair coin is 1/2.
What is the equation of the line that has a slope of -4 and goes through (-1,6)?
A. y + 6 = -4(x + 1)
B.
y + 6 = -4(x - 1)
C.
D.
y-6 = -4(x + 1)
y - 6 = -4(x - 1)
Answer:
y-6=-4(x+1)
Step-by-step explanation:
y-y1=m(x-x1)
Where m=slope and (x1, y1) is a point on the line.
m=-4
y-6=-4(x-(-1))
y-6=-4(x+1)
Answer:
y-6=-4(x+1)
Step-by-step explanation:
Plato
solve the equation for y
[tex] - 3x + 8y = - 48[/tex]
-3x +8y = -48
Add 3x to both sides:
8y = 3x -48
Divide each term by 8:
y = 3x/8 - 6
Answer Y=-45/8
Step-by-step explanation:
-3+8y=-48
-3+8y+3=-48+3
8y=-45
8y/8=-45/8
y=-45/8
A ball is thrown and it follows a parabolic path. At each horizontal distance (x) the following equation models the ball’s height (y).
Y=-0.02x^2+0.8x+3
What will the height of the ball be at a distance of 10 feet?
A. 6
B. 7
C. 8
D. 9
Answer D). 9 ft is correct
Height of the ball at a horizontal distance of 10 feet is 9 ft
Step-by-step explanation:
A ball is thrown and it follows a parabolic path. At each horizontal distance (x) the following equation models the ball’s height (y).
Y(x) = [tex]-0.02x^{2} +0.8x+3[/tex]
Question asked is " What will be height (Y) of the ball when X=10 ft "
Simply putting value of X in given equation
we get,
Y(x) = [tex]-0.02x^{2} +0.8x+3[/tex]
Y(x) = [tex]-0.02(10)^{2} +0.8(10)+3[/tex]
Y(x) = [tex]-0.02(100)} +8+3[/tex]
Y(x) = [tex]-2 +8+3[/tex]
Y(x) = [tex]9[/tex]
Therefore, Height of the ball at a horizontal distance of 10 feet is 9 ft
Answer D. 9 ft is correct
The height of the ball at a distance of 10 feet according to the given equation is 9 feet (option D). This was achieved by substituting the value of 10 into the equation.
Explanation:To find the height of the ball at a distance of 10 feet, you need to substitute the value for the horizontal distance (x) in the given equation. The equation modeling the ball's height is: Y=-0.02x^2+0.8x+3. So, we replace x with 10 in this equation, as follows:
Y=-0.02(10)^2+0.8(10)+3 Y=-0.02(100)+8+3 Y=-2+8+3 Y=9
Therefore, the height of the ball at a distance of 10 feet is 9 feet, so option D is correct.
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Which algebraic expression is equivalent to this expression? 3(2x − 8) – 11x A. -5x – 8 B. -5x – 24 C. -17x – 24 D. -17x – 24
Answer:
B
Step-by-step explanation:
Given
3(2x - 8) - 11x ← distribute parenthesis
= 6x - 24 - 11x ← collect like terms
= - 5x - 24 → B
if x is 5 x 15 and b is 11 x 189 what is b - x + 56?
please help it’s due in 2 days and idk how to do it
Answer:
2060
Step-by-step explanation:
x=5*15
b=11*189
-------------
x=75
b=2079
b-x+56=2079-75+56=2060
Answer:
i just want points
Step-by-step explanation:
The height of trapezoid VWXZ is 8 StartRoot 3 EndRoot units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX. Trapezoid V W X Z is shown. A line is drawn from point W to point Y on side Z X, forming a right angle. Angles W V Z and V Z Y are right angles. The length of V W is 10 and the length of W Y is 8 StartRoot 3 EndRoot. Angle YW X is 30 degrees, and angle W X Y is 60 degrees. Once you you know the length of YX, find the length of the lower base, ZX. 14 units 10 + 4 StartRoot 3 EndRoot units 18 units 10 + 8 StartRoot 3 EndRoot units
Answer:
18
Step-by-step explanation:
The lower base will 18units.
What is trapezoid?quadrilatral whose one opposite sides are parallel.
What is tangent of an angle?The tangent of an angle is the ratio between the opposite side of the angle and the adjacent side of the angle.
tanθ=opposite side/adjacent side
So according to asked question
in the trpezoid VWXZ,
VW || XZ
Height of trapezoid= VZ =WY=8√3
VW=10
∠YWX=30°
∠WXY=60°
In triangle ΔWYX,
∠WYX=90°
ΔWYX is a right angle triangle
so, tan∠YWX= XY/WY
⇒tan30°=XY/8√3
⇒1/√3=XY/8√3
⇒XY=8√3/√3
⇒XY=8 units
the length of the lower base ZX= ZY+XY = VW+XY = 10+8=18units
Therefore the lower base will 18units.
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For f(x) = 7
, substitute 3 for x in the function to solve for f(3)
Answer:
f(3)=7
Step-by-step explanation:
f(x)=7
f(3)=7
210000000 in standard form
Answer:
2.1 x 10^8
Step-by-step explanation:
2.1*10^8
The first number can not exceed ten so just count how many decimal place it would be and that should be the power.
there are 31 days in the month of may. what fraction of the month does 10 days represent
Answer:
10/31
Step-by-step explanation:
I'm pretty certain this is the answer, since 10/31 cannot be simplified any further; 31 being the total days in the month of May
A 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.
To find the fraction of the month that 10 days represent, we can divide the number of days represented by 10 by the total number of days in the month, which is 31.
Fraction = (Number of days represented) / (Total number of days in the month)
Fraction = 10 / 31
Therefore, 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.
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