Answer:
constant of proportionality = 10
Step-by-step explanation:
the equation to find the constant of proportionality is,
y = kx
where k is the constant of proportionality
by substituting any value of y and x from the table,
30 = k3
thus, k = 10
for any given number of counselor the children will be it's ten times.
Tim purchased a pair of running shoes for $79.20, which included 10% sales tax. If the shoes were on sale for 40% off the original price, what was the original price of the running shoes?
The original price of the shoes was $108.85.
What is the original price?
The price that was established by the MSRP (manufacturer's suggested retail price) is known as the original pricing.
The original price was often always less expensive than the current price, though original and current prices occasionally coincide.
The cost price of an item is always used to determine the sales tax, which is then applied to the total of the bill.
Tim purchased a pair of running shoes = $79.20
sales tax =10%
shoes were on sale for 40% off the original price,
Let the original price of the running shoes be x.
Converting a given problem into an equation and solving for variable x.
(X-0.4X)+0.1X=79.20
X-0.4X+0.1X=79.2
7X=792
X=108.85
The original price of the shoes was $108.85.
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Graph the line with slope of 5/3 and goes through the point (2, 1).
Answer:
Point 1: (2, 1)
Point 2: (5, 6)
Step-by-step explanation:
In order to graph the line, we need to know where to start. Luckily, we have our first point given. (2, 1)
Point 1: (2, 1)
A trick I know to find point 2 is:
1. rise up the y-axis by 5 points then move to the right 3
or
2. (2, 1)
+ (3, 5)
----------
Point 2: (5, 6)
I hope this helps!
Answer:
y= 5/3x + -7/3
Step-by-step explanation:
plug in the values into y-mx+b
1=5/3 (2) + b
solve for b
The distance between City A and City B is 200 miles. A length of 1.7 feet represents this distance on a certain wall map. City C and City D are 4.25 feet apart on this map. What is the actual distance between City C and City D?
The actual distance between City C and City D is
The actual distance between City C and City D is 500 miles .
In the question ,
it is given that ,
the distance of 200 miles between City A and City B is represented by 1.7feet on the map .
the scale factor of map is 1.7 feet = 200 miles
So , 1 feet = 200/1.7 miles
= 117.64 miles
So , on map, 1 feet is 117.64 miles of actual distance .
Given that the distance between City C and City D on the map is 4.25 feet .
So , in actual
4.25 feet = 4.25*117.64
= 499.97
≈ 500
we get , 4.25 feet = 500 miles .
Therefore , The actual distance between City C and City D is 500 miles .
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A photo taken with a smartphone has 1,227,104 pixels. A photo taken with a camera has 11,943,936 pixels. Approximately how many times more pixels are in the photo taken with the camera?
Answer:
about 10 times more
Step-by-step explanation:
I popped it in a calculator and divided the 2 numbers and just rounded to the nearest whole number
AX'Y'Z' is a translation of AXYZ. Write the translation rule
Rule of Mapping The coordinates for (x,y) are translated to (x7,y+5) via a mapping rule that has the following form: (x,y) (x7,y+5). Translation A transformation that moves every point on a shape by the same amount is called a translation
Initially, label the graph AXYZ. Translate "XYZ" into "AX'Y'Z" by adding 3 to the x value and taking away 2 from the y value.
What is the formula for translation?
If we are aware of the direction and magnitude of the figure's movement, we may draw the translation in the coordinate plane. Use P'(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up.
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If the divisor is a decimal then you must multiply by a power of 10 to make it a whole number. Why is it important to multiply the dividend and the divisor by the same power of 10? NEED HELP ASAP WILL GIVE BRAINLIST ALSO NO SAMPLE RESPONSE
In this example, the number being divided (15) is known as the dividend, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how 15 x 3 = 5 is a correct equation even if you change the quotient and divisor.
Explain about the divisor and dividend?The dividend appears to the right, or underneath, the division bracket, while the divisor is the number that appears to the left, or outside, of the division bracket.
An integer that divides another integer to obtain a result is called a divisor. The result of this division, or quotient, is the dividend, which is the original number that was divided. Quotient = Dividend Divisor.
To keep the divisor and dividend in the same proportion to one another, you multiply them by the same power.
This is true for division that is not decimal.
10 / 5 = 2.
Multiplying both sides by ten results in 100/50, which is still two.
If you merely divided by 10, you would get 100/5, which is equal to 20, or 10/50, which is equal to 1/5. Both of these throw off the ratio.
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In one year, the total amount of water used in a certain town was 5.342 x 10¹⁸ gallons. In the same year, the town's population was 2.34 x 10¹⁵ people. Determine the approximate amount of gallons used per person in that town in one year.
The approximate amount of gallons used per person with the population of 2.34 x 10¹⁵ people is 2283 gallons.
How can the number of gallons be calculated?We were given the total amount of water used in a the town as 5.342 x 10¹⁸
We were also told that the total number of the people in that town is 2.34 x 10¹⁵ people.
Then we can determine the amount of gallons used per person by making the division of the total amount of the water used by the total number of the people in the town as :
( 5.342 x 10¹⁸)/(2.34 x 10¹⁵ )
= 2283 gallons.
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What is the gradient of a line perpendicular to a line with a gradient of 1/3?
1234567890 + 0987654321
Answer:
Step-by-step explanation:
2222222211
What is the solution set to the equation (2x−4)(4x−5)=0? {5/4,2}{2}{−2,−5/4}{4/5,5/4}
Since the equation is written as factors, we can equate each factor to zero in order to find the solutions of the equation:
[tex]\begin{gathered} (2x-4)(4x-5)=0\\ \\ \begin{cases}2x-4=0\rightarrow2x=4\rightarrow x=2 \\ 4x-5=0\rightarrow4x=5\rightarrow x=\frac{5}{4}{}\end{cases} \end{gathered}[/tex]The solution set is {5/4, 2}, therefore the correct option is the first one.
Need help with number 8
For the given equation, y = -1.5x + 3.5, graph is sketched below.
What is an equation?A mathematical equation is a calculation that shows the equivalence of two expressions by using the matching sign. When solving a variable equation, the first step is to identify the values of the variables that lead to the equivalency. The unknown variable values that satisfy the equivalence are known as the equation's solutions, while the unidentified variables are defined as the parameters for which the equation must be answered. Equations come in two varieties: identity equations and conditioned equations.
Given equation, y = -1.5x + 3.5
for x = 1, y = 2
for x = 2, y = 0.5
The graph of the equation is attached
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Marco needs to buy some cat food. At the nearest store, bags of 2 food cost $9.50 How much would Marco spend on 3 bags of cat food?
Marco will have to spend $ 14.25 on 3 bags of cat food.
What is an example of a unitary method?A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel. The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given:
Bags of 2 cat food cost $9.50
Therefore bags of 1 cat food cost $9.50 /2
=$ 4.75
Therefore bags of 3 cat food cost $ 4.75 x 3
= $ 14.25
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Using the answer choices provided, complete the proof.
Since two lines AC and BD intersect at point E
we have proved
∠DEC = ∠AEB
Proof:Given,
The straight line has a 180-degree angle.
The two lines AC and BD intersect at E.
consider AEB : BEC = 9: 11.
If BEC is x, then AEB is 9x / 11 and AEC + BEC
= 180 degree (9 x /11) + x = 180.
9x + 11x = 11 * 180
20x = 11 * 180 x = 99
BEC is 99 degrees and AEB is 81 degrees.
Because angle AED is vertically opposite angle BEC, angle AED = 99 degrees.
Because angle DEC is vertically opposite angle AEB, angle DEC equals 81 degrees.
Hence ∠DEC = ∠AEB.
Hence proved
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What is the value of x?
0.2x(4.5-2.5x) = 7.5 +1.7x
14x + 1 = 10x - 19 solve for x
Answer:
x = -5
Step-by-step explanation:
The image has the explanation.
(Source: Algebra Calculator, MathPapa, I suggest using it.)
Btw, could I get Brainliest? Thanks!
9(c-1) + 7c please I need this
Answer:
16c-9
Step-by-step explanation:
9(c-1)+7c
9c-9+7c
The given table of values represents a linear equation. What is the slope?
X: 3 4 5 6
Y: 1 5 9 13
A. 3
B. 2
C. 4
D. 5
Answer: C
Step-by-step explanation:
y2 - y1/x2 - x1 = M
For example: Take the coordinates ( 3,1) and (4,5)
5-1 = 4
4-3 = 1 4/1 = 4
M=4
1 + 1
I’ll mark brainliest if explanation included!!
Answer: 1+1=1
Step-by-step explanation: because just like in multiplication for infinity
1x1 will always equal one and if you flip the x sign it will be a plus sign so 1+1=1
I'm so smart :)
whats the same as 2/9
Answer:4/18
Step-by-step explanation:
Which pair of radicals is a pair of like radicals?
O 5√6 and 6√5
O 9√2 and -9√/3
O 3√7 and 11√7
O 7√5 and 7√3
Correct option is C. The pair of radical is 3√7 and 11√7
A number system is what?
A way to express or represent numbers is through the number system.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
From all the pairs,
5√6 and 6√5
9√2 and -9√/3
3√7 and 11√7
7√5 and 7√3
Only 3√7 and 11√7 is a radical as it has same value of under root.
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6) A ferris wheel can accommodate 45 people in 30 minutes. How many peoplecould ride the ferris wheel in 3 hours? What was that rate per hour?
The ferris well can accomodate 45 people in 30 minutes.
You need to calculate how many people you can accomodate in 3 hours.
To do so the first step is to express the 3 hours in minutes:
You know that 1 hour has 60 minutes, multiply 60 by 3 to determine how many minutes there are in 3 hours:
[tex]60\cdot3=180[/tex]3 hours equal to 180 minutes
Now you can use cross multiplication to determine the number of people that can ride the ferris well in three hours.
30 min_____45 people
180min_____x people
[tex]\begin{gathered} \frac{45}{30}=\frac{x}{180} \\ x=(\frac{45}{30})180 \\ x=270 \end{gathered}[/tex]The ferris well can accomodate 270 persons in 3 hours.
Here is a diagram of a person standing next to a lorry.
The diagram shows two centimetre rulers.
The person and the lorry are drawn to the same scale.
The lorry is approximately 12.8 m in length.
Using the scale diagram, estimate the height of the person in metres.
from the diagram, we can see the Lorry is 12 cm in the model drawing, whilst in actual length is 12.8 metres, now the person on the model drawing shows as 1.5 cm, so
[tex]\begin{array}{ccll} \stackrel{cm}{model}&\stackrel{metre}{actual}\\ \cline{1-2} 12 & 12.8\\ 1.5& x \end{array} \implies \cfrac{12}{1.5}~~=~~\cfrac{12.8}{x} \\\\\\ 12x=(1.5)(12.8)\implies x=\cfrac{(1.5)(12.8)}{12}\implies x=\stackrel{metres}{1.6}[/tex]
Find area and perimeter
The perimeter and area of the given polygon is 24 inches and 20 square inches respectively.
According to the question,
We have a figure with each side being 2 inches.
We know that the perimeter of a figure is sum of all of its sides.
Now, the total number of sides we have are 12.
So, we have:
Perimeter of the polygon = sum of all 12 sides
Perimeter of the polygon = 12*2 (because each side is equal)
Perimeter of the polygon = 24 inches
Now, we know that in a square all four sides are equal. If we observe the given polynomial then we notice that there are 5 squares in it. Out of these 5 squares, 4 are formed with real lines and 1 imaginary line and there is 1 imaginary square in the center with its sides as 2 inches.
We know that the area of square is (side*side).
Area of 5 squares = 5*(side*side)
Area of 5 squares = 5*(2*2) square inches
Area of 5 squares = 5*4 square inches
Area of 5 squares = 20 square inches
Hence, the correct option is A (the first one with 24 inches of perimeter and 20 square inches of square).
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solve for x. A= x-y-6z
Answer: x = a + y + 6 z
Answer:
x = y + 6z + a
Please:
Please Give Brainlist
What is the value of 21 + 62 – (35 – 8) • 3?
Answer:
Step-by-step explanation:
21+62-(35-8)x3
=83−(35−8)(3)
=83−(27)(3)
=83−81
=2
Answer: 56
Step-by-step explanation:
21+62=83 -(36-8) =56
A polynomial function has zeros at -4 (multiplicity 3), -1 (multiplicity 8) and 2 (multiplicity 1). Which equation couldrepresent this function?Ax)Ax)A.B.C.D.WSelect one:O a. AO b. Bос. СO d. D
When a function has a zero with an even multiplicity, there is no sign shift for the function at that zero.
If the zero has odd multiplicity, the function shifts its sign at that point.
Since the function has zeros at -4, -1 and 2, those must be the points where the function touches the X-axis. Options A and C display this feature.
Nevertheless, the only even multiplicity is for the zero x=-1, so the function must have sign shifts at x=-4 and x=2, but no sign shift at x=-1. This is correctly displayed on option C.
Therefore, the graph that correctly represents the described function is that from option C.
I need the answers to the question
Given
we have
[tex]P(x)=x^3+2x^2+x+2[/tex]Required
we need to write it in terms of linear factors.
Explanation
Here
[tex]\begin{gathered} P(x)=x^3+2x^2+x+2 \\ =x^2(x+2)+x+2 \\ =(x+2)(x^2+1) \\ =(x+2)(x+i)(x-i) \\ so\text{ }P(x)=(x+2)(x+i)(x-i) \\ so\text{ }P(x)=(x+2)(x+\sqrt{-1})(x-\sqrt{-1}) \\ \end{gathered}[/tex]the answer is (x+2)(x+i)(x-i)
A red candle is 8 inches tall and burns at a rate of 7
10 inch per hour.
A blue candle is 6 inches tall and burns at a rate of 1
5 inch per hour.
After how many hours will both candles be the same height?
After four hours, the height of the candles will be the same.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.
Let x be the number of hours and y be the height.
y = -0.70x + 8 ...1
y = -0.20x + 6 ...2
From equations 1 and 2, then we have
- 0.20x + 6 = - 0.70x + 8
(0.70 - 0.20)x = 8 - 6
0.50x = 2
x = 4 hours
After four hours, the height of the candles will be the same.
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while playing lawn darts with his friend, jack notices that when he throws a dart up at 60 degrees it travels 11 meters. how high did the dart travel?
Answer: Approximately 9.526279 meters
======================================================
Explanation:
See the diagram below.
Draw a horizontal line to mark points A, B and C on it
A = dartboard
B = Jack's location
C = midpoint of A and B
Segment AB is the 11 meter horizontal distance from Jack to the dartboard. Half of this is BC = 11/2 = 5.5 meters.
Then just above point C, we'll have a fourth point D. Segment CD is the unknown max height of the dart. Let's call this x.
The dart will begin at point B, go upward in a parabolic arc to get to point D (the peak of the mountain), then come back down to arrive at point A.
------------------------------------
Focus on triangle BCD. Angle B = 60 degrees is the angle of elevation that Jack uses to throw the dart.
We'll use the tangent ratio to connect the opposite side x to the adjacent side 5.5
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\text{B}) = \frac{\text{CD}}{\text{BC}}\\\\\tan(60) = \frac{\text{x}}{5.5}\\\\\text{x} = 5.5*\tan(60)\\\\\text{x} \approx 9.526279\\\\[/tex]
Make sure your calculator is in degree mode.
Segment CD is approximately 9.526279 meters which is the max height the dart reaches.
See the diagram below.
Is this a valid argument?
Given: If I drive over 60 miles an hour, then I am breaking the law.
If I am breaking the law, then I could go to jail.
Conclusion: If I drive over 60 miles an hour, then I could go to jail.
1. No. This is an improper use of the Law of Syllogism
2. No. This is an improper use of the Law of Detachment.
3. Yes. This argument uses the Law of Detachment.
4. Yes. This argument uses the Law of Syllogism.
Answer:
4. Yes. This argument uses the Law of Syllogism.
Step-by-step explanation:
Law of Syllogism:
Statement 1: If p, then q.
Statement 2: If q, then r.
Statement 3: If p, then r.
p = "If I drive over 60 miles an hour"
q = "I am breaking the law"
r = "I could go to jail"