Answer:
A unit rate is the answer which you get when you divide one of the numbers by the other. This is how much one would be. Here is a video:
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Just remove the spaces in between and you should be alright.
Final answer:
A unit rate is a comparison of two measurements with one unit having a value of 1, such as 55 miles per hour (55/1 miles/hour). Unit rates are useful in mathematics and science to understand how quantities relate on a per-unit basis, which is essential for dimensional analysis and unit conversions.
Explanation:
A unit rate is a type of rate that compares a quantity to one unit of another quantity, essentially telling us how much of one thing is present per one unit of another thing. A common example of a unit rate is speed, such as 55 miles per hour, which is written as 55 miles/1 hour. Here we are comparing the distance traveled to the time taken to travel that distance, indicating how many miles are covered in one hour.
Unit rates are related to proportions, which are equations that state that two ratios are equivalent. For example, 1/2=3/6 is a proportion. However, a unit rate always has a denominator of one, making it a special kind of ratio that is easily comparable across different scenarios.
Using unit scales is similar in concept to unit rates, but involves comparing two measurements where none necessarily equals one. For example, a unit scale on a map may be represented as 1 inch = 100 feet, showing the ratio of the size of the map to the actual size of the territory covered.
Understanding unit rates is also essential for dimensional analysis in science and unit conversions. Dimensional analysis is a process used in physics to ensure that the units in calculations cancel out or match up properly, indicating correct use of units in formulas and computations.
Bred has to paint a wall with 8 horizontal stripes. He has enough paint only for 5 blue, 5 red and 5 white stripes. If he can use at most 2 colors, how many different ways he can paint the wall.
Bred has a total of 771 ways to paint the wall, taking into account that he can use at most two colors for the stripes or just one.
Explanation:The subject matter pertains to the field of combinatorics, a branch of mathematics dealing with combinations and permutations. The task requires finding the number of ways to paint 8 stripes on a wall using up to 2 colors from a selection of 3 colors, namely: blue, red, and white. Since we have more paint than stripes, the limiting factor in this problem is the number of stripes, not the quantity of paint.
As Bred can use at most two colors for the stripes, the combinations we can have with two colors are: blue and red, blue and white, red and white. In each of these combinations, there are 2^8 (or 256) ways to paint 8 stripes (exploration of all binary possibilities). So, for three combinations, it will be 3*256 = 768 ways.
Now, let's look at the single color options. He can also paint the stripes all in one color, but since he has only three colors, he has three ways for this.
Hence, in total, Bred has 768 (from two-color combinations) + 3 (from single color option) = 771 ways to paint a wall.
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Ms. Chen is planning to take her camp group on a field trip to Pottery Bayou where each person will create her own piece of art pottery. The regular cost is $22 per person. There is a group special that costs $18 per person with an additional $24 fee for a private room. Ms. Chen is trying to decide if she should use the regular price or the group special.
1. Write an equation to show the total cost of the regular price with x people
2. Write an equation to show the total cost of the group special with x people
have a good day!!!!!!!!!
The total cost of the regular price for a group of x people is represented by the equation C = 22x, while the total cost of the group special is represented by C = 18x + 24.
Explanation:Equations for Total Cost
1. Total Cost of Regular Price: Ms. Chen can calculate the total cost for x people with the regular price by using the equation C = 22x. Here, C represents the total cost, and x is the number of people in the group.
2. Total Cost of Group Special: To calculate the total cost for x people with the group special, Ms. Chen would use the equation C = 18x + 24. C is still the total cost, x is the number of people, and 24 represents the additional fee for the private room.
By comparing the results of both equations for a specific number of people, Ms. Chen can determine which option is more cost-effective.
For what value of x does 3^4x=27^x-3?
x=4.80989686
by simplifying both sides of the equation, then isolating the variable.
Answer:
x= - 9
Step-by-step explanation:
This problem bothers on the law of indices
Given the expression
3^4x=27^x-3
We can also simplify it using the law
3^4x= 3^3(x-3)
Equating the powers we have
4x= 3(x-3)
Opening bracket
4x= 3x-9
Collecting like terms we have
4x-3x=-9
x=-9
Indices are used to show numbers that have been multiplied by themselves. They can also be used to represent roots, such as the square root, and some fractions. The laws of indices enable expressions involving powers to be manipulated more efficiently than writing them out in full.
what is the area of pentagon ABCDE? 16 square units, 20 square units, 24 square units, or 36 square units?
Answer:
its A i just took the test
Step-by-step explanation:
Answer: The correct answer is 24 square units.
Step-by-step explanation:
What is the value of X? show all of your work
Answer:
11
Step-by-step explanation:
you need to divide 89 by 8 then round and you get 11
2 7/8 plus 3 2/8 plus 1 1/8
Answer:
7.25
Step-by-step explanation:
2 7/8 + 3 2/8 * 1 1/8 = 7.25
Answer:
7 1/4
Step-by-step explanation:
exact form is 29/4 but if you wanted to simplify it the mixed number form is 7 1/4
The perimeter of a rectangular rug is 24 ft. The length of the rug is 1 2/5 its width. What is the area of the rug?
Answer:
35 ft²
Step-by-step explanation:
We set up a system of linear equations describing this rug and then solve it:
Perimeter: P = 2L + 2W
L = (1 2/5)W = 1.4W
Going back to the Perimeter equation, and knowing that P here is 24 ft, we have:
24 ft = 2(1.4W) + 2W, or 2.8W + 2W, or 4.8W.
Solve for W (width) by dividing both sides of this equation by 4.8:
W = 24 ft / 4.8 = 5
The width of the rug is 5 ft; the length is 1.4(5 ft), or 7 ft.
Thus the area of the rug is A = L * W, or A = (7 ft)(5 ft) = 35 ft²
neal uses 1 1/4 gallons of water and 8 cups of apple cider in a recipie how many combined gallons of water and apple cider does neal use in the recipe show work
Answer: 1 3/4 gallons
Step-by-step explanation: In order to determine the total number of gallons in the recipe you need to convert 8 cups to gallons. There are 16 cups in 1 gallon. In order to determine how many gallons 8 cups is you need to divide 8/16 = 1/2 gallon.
The total number of gallons is 1 1/4 + 1/2.
1 1/4 + 1/2 = 1 3/4 gallons.
If 2a+ 2/a =4, what is the value of 2a^2− 2/a^2 ?
ANSWER
0
EXPLANATION
Given :
[tex] \frac{2a + 2}{a} = 4[/tex]
We solve for 'a' to obtain,
[tex]2a + 2 = 4a[/tex]
This implies that,
[tex]2 = 4a - 2a[/tex]
[tex]2 = 2a[/tex]
This implies that,
[tex]a = 1[/tex]
We substitute a=1 into
[tex] \frac{ 2{a}^{2} - 2}{ {a}^{2} } [/tex]
This gives us,
[tex]\frac{ 2{(1)}^{2} - 2}{ {(1)}^{2} } = \frac{2 - 2}{2} = \frac{0}{2} = 0[/tex]
How many triangles can you make from straws with the lengths 2,1,2 inches?
Answer:
You can make one triangle with these lengths
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Verify if the lengths satisfy the triangle inequality theorem
1) 2+1 > 2
3 > 2 ------> is true
2)2+2 > 1
4 > 1 -----> is true
so
The lengths satisfy the triangle inequality theorem
therefore
You can make one triangle with these lengths
please help!!!!!
The price tags at a clothing store do not include the
sales tax in the prices. Chase buys $210 worth of
clothing at the store. He hands the cashier $250
and receives $15.89 in change. How much sales
tax does Chase pay on his purchase?
A $24.11
B $15.89
C $40
D $210
Answer:
A. $24.11
Step-by-step explanation:
Take $210 out of the $250 he gave the cashier
250 - 210 = 40
So you have his exact change without the tax though. so take what he RECIVED away from what he was suppose to recive which is 40. So.....
40 - 15.89 = 24.11
$24.11
Hope this helps!
what is the slope of the line (1,6) and (-5, -7)
[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-7-6}{-5-1}\implies \cfrac{-13}{-6}\implies \cfrac{13}{6}[/tex]
The slope of the line is [tex]\frac{13}{6}[/tex].
What is the slope of line?A slope of a line is the change in y coordinate with respect to the change in x coordinate.
What is slope formula?If [tex]P(x_{1} ,y_{1} )[/tex] and [tex]Q(x_{2} ,y_{2} )[/tex] are the two points on a straight line, then the slope formula is given by:
Slope, m = Change in y-coordinates/Change in x-coordinates
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
According to the given question.
We have a two points (1, 6) and (-5,-7).
Therefore, the slope of the line from these points is given by
[tex]slope = \frac{-7-6}{-5-1} = \frac{-13}{-6} =\frac{13}{6}[/tex]
Hence, the slope of the line is [tex]\frac{13}{6}[/tex].
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Wendy is making lemonade. As shown below, Wendy mixes water and lemon juice . Which equation shows how much lemon juice is needed for 10 ounces of water
Answer:
3 times 10
Step-by-step explanation:
0.034 is 1/10 of 0.0034
False, .0034 is 1/10 of .034
The statement that 0.034 is 1/10 of 0.0034 is incorrect. In fact, 0.034 is 10 times larger than 0.0034. Thus, it's correct to say 0.0034 is 1/10 of 0.034.
Explanation:No, the statement that 0.034 is 1/10 of 0.0034 is not correct. When comparing the two numbers, we can see that 0.034 is actually 10 times larger than 0.0034, not 1/10. To confirm this, we can perform the division operation: 0.034 ÷ 0.0034 = 10. Therefore, we can say that 0.0034 is 1/10 of 0.034, but not the other way around.
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Find the missing number: 8.4(1.5 + 2.3) = 12.6 +
Answer:
19.32
Step-by-step explanation:
To find the missing number, we need to solve for the total of the left side of the equation.
Total = 8.4(1.5 + 2.3)
Total = 8.4(3.8)
Total = 31.92
Now we subtract the total to the only value on the right side.
Missing number = 31.9-12.6
Missing number = 19.32
8.4(1.5+2.3) = 12.6 + 19.32
A baker is making bread. The recipe uses2/3 cup of walnuts for each bread recipe. The baker has 7 1/2 cups of walnuts. What's the number of full recipes of walnuts bread the baker can make?
Answer:
You can make 11 recipes with 7 1/2 cups of walnuts
Answer:
Step-by-step explanation:
11 1/4 but it says the number of full recipes so it would be 11
A give line has the equation 10x+2y=-2. What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? Y=(________)x + 12
first off, let's solve the "given" line for "y", that way we can put it in slope-intercept form to see what its slope might be.
[tex]\bf 10x+2y=-2\implies 2y=-10x-2\implies y=\cfrac{-10x-2}{2} \\\\\\ y=\cfrac{-10x}{2}-\cfrac{2}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-5}x-1\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
well, a parallel line to that one, will have the same exact slope, so then, we're really looking for the equation of a line whose slope is -5 and runs through (0 , 12)
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{12})~\hspace{10em} slope = m\implies -5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-12=-5(x-0) \\\\\\ y-12=-5x\implies y=-5x+12[/tex]
Solve for X.
x2= -63
Write your answer in simplified, rationalized form.
this is the answer to your equation
The solutions to the equation x² = -63 in simplified, rationalized form are:
x = 3√7 * i
x = -3√7 * i
Isolate x²: In this case, x² is already isolated on one side of the equation.
Apply the Square Root Property: Take the square root of both sides of the equation to eliminate the exponent on x²:
√(x²) = √(-63)
Simplify and Introduce Imaginary Unit: Recall that the square root of a negative number is an imaginary number. We introduce the imaginary unit 'i,' defined as √(-1):
x = ±√(63) * √(-1)
x = ±√63 * i
Simplify and Rationalize: √63 cannot be simplified further, but we can rationalize it by multiplying both the numerator and denominator by √3:
x = ±√63 * i * √3 / √3
x = ±3√7 * i
Please help solve this problem
Answer: OPTION C
Step-by-step explanation:
By definition you know that:
[tex]\sqrt[n]{a^n}=a[/tex]
and by the exponents properties you also know that:
[tex]a^n*a^m=a^{(n+m)}[/tex]
Now, descompose 18 into its prime factors:
18=2*3*3=2*3²
Rewrite the expression and simplify (Keep on mind that: [tex]\sqrt{x^4}=x^{(\frac{4}{2})}=x^{2}[/tex]). Then, you obtain:
[tex]\sqrt{2*3^2*x^4*y*y^2}=3x^2y\sqrt{2y}[/tex]
Answer:
C. [tex]3x^2y\sqrt{2y}[/tex].
Step-by-step explanation:
The given radical expression is [tex]\sqrt{18x^4y^3}[/tex].
We can rewrite this radical expression to obtain;
[tex]\sqrt{2\times9 \times (x^2)^2\times y^2\times y}[/tex].
This will give us;
[tex]\sqrt{2y} \times \sqrt{9(x^2)^2 y^2}[/tex].
[tex]3x^2y\sqrt{2y}[/tex].
The correct choice is C
PLZ HELP I REALLY NEED IT PLZ
Answer:
number 16 is correct nice job! number 17 is J=PM/300
Step-by-step explanation:
For 16 the answer is option D
For 17 the correct option is D
Step-by-step explanation:See the attached figure
Help...!!???!!??!!??!??
Answer:
[tex]\large\boxed{b)\ y=\dfrac{3}{4}x-1}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b = y-intercpt → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (4, 2) and (0, -1) - y-intercept → b = -1.
(we see this already which equation. Only in b) y-intercept is b = -1).
Anyway, calculate the slope:
[tex]m=\dfrac{-1-2}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}[/tex]
Finally we have the equation:
[tex]y=\dfrac{3}{4}x-1[/tex]
When rolling a number cube what is the probability of rolling a number greater than two
Answer:
it is 5/6
Step-by-step explanation:
it's easy. There are 5 numbers that are greater than 2.
Answer: the answer is 2/3 i took the test
Steve drove at a constant rate to the beach for a vacation. In the equation below, t is the time in hours it took Steve to drive to the beach.
64t = 384
What is the unit rate in the equation above?
The unit rate in the equation 64t = 384 is 64.
Explanation:The unit rate in the equation 64t = 384 is 64.
To find the unit rate, we divide the total value by the number of units. In this case, the total value is 384 and the number of units is 64. When we divide 384 by 64, we get the unit rate of 6.
Therefore, the unit rate in the equation is 64.
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The unit rate in the equation 64t = 384 is 6.
Explanation:The unit rate in the equation 64t = 384 is 6.
To find the unit rate, divide both sides of the equation by 64:
t = 384/64 = 6.
Therefore, the unit rate is 6, which means that Steve drove at a constant rate of 6 hours to reach the beach.
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Study the image. Find the pair of vertical angles.
Answer:
<3 and <6 are Vertical angle and is the correct answer
Step-by-step explanation:
1) Vertical angle is The angles opposite each other when two or more line intersect each other or crosses each other.
Hopes this helps.
Answer:
∡3 and ∡6Step-by-step explanation:
Vertical angles: each of the pairs of opposite angles made by two intersecting lines.
The vertical angles from the picture:
∡1 and ∡4
∡2 and ∡5
∡3 and ∡6
2. Two linear functions in a coordinate plane have no points
of intersection. Which pair of functions does not intersect?
A:6x + 2y = 12 and 20x + 10y = 14. B:4x + 2y = 12 and 20x + 10y = 30
C:6x +2y = 12 and y = 0.5x -0.6
D:10x + 10y = 6 and y = 0.5x - 0.6
Option B is correct since both the lines given in option B have same slope so both the lines do not intersect each other and hence have no common solution.
The given equations are of the form
ax + by = c ......(1)
Slope for the equation of line is given by [tex](\dfrac{-a}{b} )[/tex]
We can clearly see that in option B the lines given are
4x + 2y = 12 .......(2)
20x + 10y = 30....... (3)
Slope of equation (2)
[tex](\dfrac{-4}{2} )= -2[/tex]
Similarly slope of equation (3)
[tex](\dfrac{-20}{10} )= -2[/tex]
Which concludes that both are parallel to each other.
Since parallel lines can not have any common solution so they never intersect each other. Hence option B is correct.
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What is the factored form of the following expression?
x^2 - x - 42
Answer:
(x - 7)(x + 6)
Step-by-step explanation:
Consider the factors of the constant term ( - 42) which sum to give the coefficient of the x- term ( - 1)
The factors are - 7 and + 6, since
- 7 × 6 = - 42 and - 7 + 6 = - 1
x² - x - 42 = (x - 7)(x + 6)
Answer:
Factor x²−x−42 using the AC method.
(x+6)(x-7)Step-by-step explanation:
What is the factored form of the following expression?
x^2 - x - 42
STEPS:
x²-x-42
Break the expression into groups:
=(x²+6x)+(-7x-42)
Factor out x from x²+6x: x(x+6)
Factor out -7 from -7-42: -7(x+6)
=x(x+6)-7(x+6)
Factor out common term x+6
ANSWER=(x+6)(x-7)
what is the degree angle of sircle
Answer: there are 360 degrees in a circle, that there are 90 degrees in a right angle, and that the angle of an equilateral triangle contains 60 degrees.
Step-by-step explanation:
There are 360 degrees in a circle
10............................
No, they do not represent the same quantity. Explained in attached sheet.
g=-4x/3, solve for x
Answer:
-3/4 g =x
Step-by-step explanation:
g=-4x/3
Multiply each side by 3
3g = -4/3 x *3
3g = -4x
Divide each side by -4
3/-4 g = -4x/-4
-3/4 g =x
Some one help please hurry.
this is an example, but it's not drawn accurately and not to scale
use a protractor and ruler for yours