Answer:
Therefore the required Equations are
[tex]y =2(x+3)\ \textrm{is the required expression for First condition.}\\y = 3x-2\ \textrm{is the required expression for Second condition.}[/tex]
Step-by-step explanation:
Given:
'y' represents the larger number and
'x' represents the smaller number
Then, a larger number is double the sum of 3 and a smaller number will be
Larger no = double of ( 3 and smaller number)
∴ [tex]y=2(x+3)\ \textrm{is the required expression for First condition.}[/tex]
Now,
The larger number is 2 less than 3 times the smaller number.
Larger number = 3 times smaller number and 2 less
∴ [tex]y=3x-2\ \textrm{is the required expression for Second condition.}[/tex]
Therefore the required Equations are
[tex]y =2(x+3)\ \textrm{is the required expression for First condition.}\\y = 3x-2\ \textrm{is the required expression for Second condition.}[/tex]
Final answer:
The correct equations that model the situation are y = 3x - 2 and y = 2(x + 3), as they reflect the two conditions given in the problem description.
Explanation:
To determine which equations model the situation described, we should translate the worded statements into algebraic equations. The first statement tells us that a larger number 'y' is double the sum of 3 and a smaller number 'x'. This can be written as y = 2(x + 3). The second statement tells us that the larger number is 2 less than 3 times the smaller number, which can be written as y = 3x - 2.
Now, we need to verify the provided choices against these two derived equations:
y = 3x - 2 (Correct, it matches the second statement we translated from the problem description.)
3x - y = 3 (Incorrect, because rearranging this gives y = 3x - 3, which does not match either of our derived equations.)
3x - y = -2 (Incorrect, because rearranging this gives y = 3x + 2, which does not match either of our derived equations.)
y = 2 - 3x (Incorrect, this does not match the format of either derived equation.)
y=2(x + 3) (Correct, it matches the first statement we translated from the problem description.)
The cost y (in dollars) for x ounces of peanuts is
represented by the equation y = 0.23x. The cost y
(in dollars) for x ounces of pecans is represented by
the equation y = 0.45x. Which statement is true?
Select all that apply.
A The cost for peanuts is $0.22 per ounce less than
the cost for pecans.
B The cost for peanuts is greater than the cost
for pecans.
C The cost for 8 ounces of peanuts is $3.60.
D The cost for 8 ounces of pecans is $3.60.
Answer:
Options A and D are correct.
Step-by-step explanation:
The cost y (in dollars) for x ounces of peanuts is represented by the equation
[tex]y=0.23x[/tex] .... (1)
It means the cost of each ounce of peanuts is $0.23.
The cost y (in dollars) for x ounces of pecans is represented by the equation
[tex]y=0.45x[/tex] .... (2)
It means the cost of each ounce of pecans is $0.45.
$0.45 > $0.23
It means the cost for pecans is greater than the cost of peanuts. Option B is incorrect.
[tex]\$0.45-\ $0.23=\$0.22[/tex]
The cost for peanuts is $0.22 per ounce less than the cost for pecans. Option A is correct.
Substitute x=8 in equation (1).
[tex]y=0.23(8)=1.84[/tex]
The cost for 8 ounces of peanuts is $1.84. Option C is incorrect.
Substitute x=8 in equation (2).
[tex]y=0.45(8)=3.6[/tex]
he cost for 8 ounces of pecans is $3.60.. Option D is correct.
Pia uses 6 cups of sugar to make 8 pies
At that rate , how much sugar will it take to make 12 pies
3 cups + the original 6 = 9 cups.
Answer:
The answer is 9 cups of water
Step-by-step explanation:
Jill has four bags of marbles there are three red five green to yellow and 6 black marbles in each bag how many marbles does Jill have show how you found the answer...Helppp
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3 x 4 = 12
5 x 4 = 20
2 x 4 = 8
6 x 4 = 24
12 + 20 + 8 + 24 = 64
She has 64 marbles
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a pair of shoes with cost rupees 320 was sold at a loss of 5% what was the selling price if it is sold at profit of 20% find the gain percent if it were sold for Rs360
Answer:
Please see the answer below:
Step-by-step explanation:
1. Loss 5%
Cost = Rs.320
Loss % = 5% = 0.05
Sale Price = Rs.320 - (Rs.320 x 0.05) = Rs.320 - Rs.16 = Rs.304
2. Profit 20%
Cost = Rs.320
Profit % = 20% = 0.20
Sale Price = Rs.320 + (Rs.320 x 0.2) = Rs.320 + Rs.64 = Rs.384
3. Sold for Rs.360
Cost = Rs.320
Sale Price = Rs.360
Gain % = (Rs.360 - Rs.320) / Rs.320 = Rs.40 / Rs.320 = 0.125
or
Gain % = 12.5%
Answer:
If sold at a loss of 5%, the selling price would be Rupee 304
If sold at a Profit of 20% the selling price would be Rupee 384
Step-by-step explanation:
Cost of shoes = Rupees 320
Loss incurred (5% x 320) = Rupees 16
Price of shoe = (320 - 16) = 304
The selling price if sold at a loss of 5% would be Rupees 304
IF SOLD AT A PROFIT OF 20%
Cost of shoes = Rupees 320
Loss incurred (20% x 320) = Rupees 64
Price of shoe = (320 + 64) = 384
The selling price if sold at a loss of 5% would be Rupees 384
Francis is constructing a line parallel to EF through point G.
What step should be his next step?
With the compass point on G and a wider opening
.than was used to construct the first arc, construct
an arc that intersects GD and EF.
o
With the compass point on G and the same
opening that was used to construct the first arc,
construct an arc that intersects GD on the
opposite side of point A and extends to the right of
point G.
With the compass point on A and the same
opening that was used to construct the first arc,
construct an arc that intersects GD on the same
side of point A as point G and extends to the right
of point G.
With the compass point on G and a wider opening
than was used to construct the first arc, construct
an arc that intersects EF twice
Answer:
Hope I helped!
Step-by-step explanation:
To construct a parallel line, set the compass to the same opening used for the first arc and draw an arc from point G that intersects line GD. This creates a parallel line to line EF through G.
Explanation:To construct a line parallel to EF through point G, Francis should set the compass point on G and adjust the compass to the same opening that was used to construct the first arc. He then needs to create an arc that intersects GD on the opposite side of point A and extends to the right of point G. This step ensures that the line through G will have the same angle with GD as EF does with GD, allowing it to be parallel to EF.
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Given: ΔABC is a right triangle. AC = 20 BC = 5 Determine the length of the missing side of ΔABC. When applicable, simplify radicals and show all of your work.
Answer:
[tex]AB=5\sqrt{15}\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
we have
[tex]AC=20\ units[/tex] ----> is the hypotenuse
[tex]BC=5\ units[/tex] ----> is a leg
[tex]AB=?\ units[/tex] ----> is a leg
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
substitute the given values
[tex]20^2=AB^2+5^2[/tex]
solve for AB
[tex]AB^2=20^2-5^2[/tex]
[tex]AB^2=375[/tex]
[tex]AB=\sqrt{375}\ units[/tex]
simplify
we know that
[tex]375=(25)(15)=5^2(15)[/tex]
substitute
[tex]AB=\sqrt{5^2(15)}\ units[/tex]
[tex]AB=5\sqrt{15}\ units[/tex]
The circumference of a circle is 3.2mm.
Find the length of the diameter.
Give your answer rounded to 3 SF.
The diameter of circle is 1.018 mm.
Step-by-step explanation:
Given,
Circumference of circle = 3.2 mm
We know that;
Circumference = 2πr
[tex]3.2=2\pi r\\[/tex]
Putting π=22/7
[tex]3.2=2*\frac{22}{7}*r\\3.2=\frac{44}{7}r[/tex]
Multiplying both sides by 7/44
[tex]\frac{7}{44}*3.2=\frac{7}{44}*\frac{44}{7}r\\\\\frac{22.4}{44}=r\\\\r=0.509[/tex]
Diameter = 2r
Diameter = 2*0.509
Diameter = 1.018 mm
The diameter of circle is 1.018 mm.
Keywords: circle, circumference
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Find the factorization of 180
Answer:
180=2^2×3^2×5
Step-by-step explanation:
We have to obtain the factors of 180 which are prime numbers
A prime number being a number with only 2 factors.That is 1 and the number itself.
For example 5 only has 2 factors 1 and 5⇒5=1×5
Here are the first few prime numbers
2,3,5,7,11,13,.....
A number which is not prime is a composite number. Composite numbers have more than 2 factors. All composite numbers can be expressed as a product of prime factors.
Answer:
5 x 2 x 2 x 3 x 3
Step-by-step explanation:
I basically did the prime factors of 18 which is 1, 2, 3, 6, 9, 18. I broke it down elminated any other numbers not referring to the prime factor. Thats how you get your answer sorry if it's not a good explantion
a cyclist rides his bike at a rate of 10 kilometers per hour.what is this rate in miles per hour? how many miles will the cyclist travel in 4 hours? in your computations assume that 1 mile is equal to 1.6 kiolmeters. Do not round your answers
Answer:
Step-by-step explanation:
A cyclist moving at 10 kilometers per hour is traveling at a rate of 6.25 miles per hour. Over 4 hours, the cyclist will travel a total distance of 25 miles.
Explanation:To convert kilometers per hour to miles per hour, you have to divide the kilometers value by 1.6 (because it's given that 1 mile = 1.6 kilometers). So, if the cyclist is cycling at 10 kilometers per hour, this translates to 10 / 1.6 = 6.25 miles per hour.
Next, to find out how many miles the cyclist will travel in 4 hours, we'll simply multiply this rate by the time. So, 6.25 (miles per hour) * 4 (hours) = 25 miles.
Therefore, the cyclist, if maintaining a speed of 10km per hour, will travel 25 miles in a 4 hour time span.
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A pair of jeans is regularly $129.99, on sale for $90.99 before tax. What is the percent markdown?
The percent markdown is 30%
Step-by-step explanation:
Given
Regular price of jeans = r = $129.99
Sale price = s = $90.99
The percent markdown can be given by the formula:
[tex]percent\ markdown = \frac{Markdown}{Regular\ price}*100[/tex]
Where markdown = Regular price - Sale price
So,
[tex]Markdown = r -s\\= 129.99 - 90.99\\=39[/tex]
Putting the values in the formula
[tex]Percent\ Markdown = \frac{39}{129.99} * 100\\=0.300 * 100\\=30\%[/tex]
Hence,
The percent markdown is 30%
Keywords: Percentage, markdown
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Fred is a server at a restaurant. On average, he can serve 6 tables per hour. Fred earns between $3.08 and $5.23 in gratuity per table. Which is a reasonable amount of gratuity that Fred earned in a 33 hour work week? A. $1,584.00 B. $24.00 C. $792.00 D. $132.00
Answer:
C. $792.00
Step-by-step explanation:
33 hours Fred can serve 33 x 6 = 198 tables
minimum gratuity : 3.08 x 198 = 609.8
maximum : 5.23 x 198 = 1035.5
Therefore $792.00 is a reasonable amount
What is the solution of square 2x+4=16?
A)x=6
B)x=72
C)x=126
D)no solution
Answer:
Its 126 i think
Step-by-step explanation:
Answer:
C) x=126
Step-by-step explanation:
What is 3(1+6r)=14-12
Answer:
r = 0.055555.....
Step-by-step explanation:
3(1+6r)=14-12 Write out formula.
3+18r=2 Distributive Property Form.
(3-3)+18r=2-3 Subtract 3 to both sides.
(18/18)r=-1/18 Divide both sides by 18
r=0.055555..... or -1/18.
Negative 3 is twice as large as a number,h
Answer:
negative 6 is the answer
Step-by-step explanation:
ILL GIVE BRAINLEST AND POINTS
Answer:
P'(2, - 2 )
Step-by-step explanation:
The translation rule
(x, y ) → (x + 9, y - 3 )
Means add 9 to the original x- coordinate and subtract 3 from the original y- coordinate, thus
P(- 7, 1 ) → P'(- 7 + 9, 1 - 3 ) → P'(2, - 2 )
Answer:
2,-2
Step-by-step explanation:
What is the absolute value of the expression of negative 5X +12 when X equals five
Answer: 13
Step-by-step explanation:
x = 5
-5 (5) + 12
-25 + 12
-13
abs(-13) = 13
To find absolute value, solve the equation as is and then make the answer positive.
Jacob has $1,000 in a checking account and withdraws $40 each week. His account requires a minimum balance of more than $400. Write and inequality to model the number of weeks,x, that he can withdraw $40 to maintain the minimum balance requirement.
Answer:
x is less than or equal to 24Step-by-step explanation:
If 1000 divided by 40 equals 25, then you would want to stay under that.
so your next best bet is 24
then we just input our variable and sign
[tex]x \leqslant 24[/tex]
CAN SOMEONE PLEASE HELP ME
Answer:
3* 10⁵
Step-by-step explanation:
6* 10⁸ / 2 * 10³ = 3 * 10⁸⁻³ = 3* 10⁵
12-2/3x=x-18 so how do you answer this question
Answer:
x=18
Step-by-step explanation:
12-2/3x=x-18
12-2/3x-x=-18
12-2/3x-3/3x=-18
12-5/3x=-18
5/3x=12-(-18)
5/3x=12+18
5/3x=30
x=30/(5/3)
x=(30/1)(3/5)
x=90/5
x=18
Answer:
x = 18Step-by-step explanation:
[tex]12-\dfrac{2}{3}x=x-18\qquad\text{subtract 12 from both sides}\\\\12-12-\dfrac{2}{3}x=x-18-12\\\\-\dfrac{2}{3}x=x-30\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup\cdot\left(-\dfrac{2}{3\!\!\!\!\diagup_1}x\right)=3\cdot x-3\cdot30\\\\-2x=3x-90\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-2x-3x=3x-3x-90\\\\-5x=-90\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5x}{-5}=\dfrac{-90}{-5}\\\\x=18[/tex]
Draw an angle for each measurement
in this way ,u can do other as well with the help of protractor...
The largest sandwich ever made weighed 5440 pounds. If everyone on Earth shares the sandwich equally, how much would you get? what fraction of a regular sandwich does this represent?
Final answer:
If everyone on Earth shared the largest sandwich ever made equally, each person would get approximately 0.00000069 pounds of the sandwich. This represents a fraction of 69/1,000,000,000 of a regular sandwich.
Explanation:
To find out how much each person would get if everyone on Earth shared the largest sandwich ever made equally, we can divide the weight of the sandwich by the population of the Earth. According to the most recent estimates, the population of the Earth is approximately 7.9 billion people.
So, if we divide the weight of the sandwich (5440 pounds) by the population of the Earth (7.9 billion), each person would get approximately 0.00000069 pounds or 0.00000031 kilograms of the sandwich.
To express this as a fraction of a regular sandwich, we need to compare it to the weight of a regular sandwich. Let's say a regular sandwich weighs 1 pound. In that case, the amount each person would get from the largest sandwich ever made represents a fraction of 0.00000069/1 or simply 69/1,000,000,000 of a regular sandwich.
What is 8,147 ÷ 24 with a remainder
Answer:
339 R11
Step-by-step explanation:
8,147 ÷ 24 = 339 R11
The sales tax in your city is 8.8%, point, 8, percent, and an item costs $63$, before tax.
How much tax would you pay on that item?
Round to the nearest hundredth or cent.
You would pay $5.54 on that item.
Step-by-step explanation:
Given,
Cost of item = $63
Sales tax rate = 8.8%
Amount of sales tax = 8.8% of cost of item
Amount of sales tax = [tex]\frac{8.8}{100}*63[/tex]
Amount of sales tax = [tex]\frac{554.4}{100}[/tex]
Amount of sales tax = $5.54
You would pay $5.54 on that item.
Keywords: percentage, division
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what is 1000 times 0.072 I need help
Answer:
72
Step-by-step explanation:
If you move the decimal point 3 times, you get 72!
Answer:
72. the decimal point will move. (promise not copying) (the other person can get the credit though)
Step-by-step explanation:
a rocking horse has a weight of 60 pounds. what percentage of the weight is 114 pounds?
Answer:
190% I believe, I hope this helped!
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The ordered pairs of A and C are not functions
Step-by-step explanation:
To determine if the ordered pairs are a function you look at the x values to see if they repeat. You don't want one input(x values) to lead to two outputs(y values). This would mean that you are never sure which output you will get.
In the answer A the x value "2" repeats, in the answer C the x value "1" repeats thus not making them functions.
Find three different pairs of fractions which multiply to 25/32.
Answer:
Step-by-step explanation:
5/8*5/4=25/32
1/16*25/2=25/32
25/16*1/2=25/32
To find three different pairs of fractions that multiply to 25/32, start by factoring the numerator and denominator. Then pair up the factors to form fractions.
Explanation:To find three different pairs of fractions that multiply to 25/32, we can start by factoring the numerator and denominator of 25/32. 25 can be factored as 5 * 5 and 32 can be factored as 2 * 2 * 2 * 2 * 2. We can then pair up the factors to form fractions:
5/2 * 5/2 = 25/45/2 * 5/32 = 25/645/2 * 1/4 = 5/8So, three different pairs of fractions that multiply to 25/32 are 5/2 * 5/2 = 25/4, 5/2 * 5/32 = 25/64, and 5/2 * 1/4 = 5/8.
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Lily bought 25.29 pounds of grapefruit. The lightest grapefruit weighed 1.4 pounds. The heaviest grapefruit weighed 1.6 pounds. Which is the best estimate of how many grapefruits she purchased? A. 19 B. 17 C. 10 D. 50
Answer:
B
Step-by-step explanation:
GIven that the lightest is 1.4 and the heaviest is 1.6, this implies that ALL the fruit must weigh between 1.4 and 1.6.
This also implies that the average weight of the fruit must also be between 1.4 lb and 1.6 lb.
recall that : average weight = total weight / number of fruit
we are given than total weight = 25.29 lb, so
average weight = 25.29 / number of fruit
Just go down the choices and test which choice gives an average weight between 1.4 and 1.6 lbs.
Choice A: number of fruit = 19
average = 25.29 / 19 = 1.33 (outside of range, not the answer)
Choice B: number of fruit = 17
average = 25.29 / 17 =1.49 (within range , possible answer)
Choice C: number of fruit = 10
average = 25.29 / 10 = 2.529 (outside of range, not the answer)
Choice D: number of fruit = 50
average = 25.29 / 50 = 0.5058 (outside of range, not the answer)
From the above, we can see that only B gives an average between 1.4 and 1.6 lb.
Answer:
B
Step-by-step explanation:
GIven that the lightest is 1.4 and the heaviest is 1.6, this implies that ALL the fruit must weigh between 1.4 and 1.6.
This also implies that the average weight of the fruit must also be between 1.4 lb and 1.6 lb.
recall that : average weight = total weight / number of fruit
we are given than total weight = 25.29 lb, so
average weight = 25.29 / number of fruit
Just go down the choices and test which choice gives an average weight between 1.4 and 1.6 lbs.
Choice A: number of fruit = 19
average = 25.29 / 19 = 1.33 (outside of range, not the answer)
Choice B: number of fruit = 17
average = 25.29 / 17 =1.49 (within range , possible answer)
Choice C: number of fruit = 10
average = 25.29 / 10 = 2.529 (outside of range, not the answer)
Choice D: number of fruit = 50
average = 25.29 / 50 = 0.5058 (outside of range, not the answer)
From the above, we can see that only B gives an average between 1.4 and 1.6 lb.
Please solve question 75
Good evening ,
Answer:
(C) 36
Step-by-step explanation:
The length of the continuous solid path from P To Q = 3×(Length of the dashed line) = 3×(12) = 36 in.
:)
=========================================
Explanation:
Check out the attached image below. Basically I drew out the given diagram and then I added the variables a,b,c,d,e,f,g. Those variables represent the side lengths of the 7 squares. Each square has a perimeter of 4*s where s is the side length, but we dont consider the side that is running along the dashed line (that connects P directly to Q). So we have 3 sides per square added up.
The first square has us travel a distance of 3*a, then the second square a distance of 3*b and so on. Overall, the total distance traveled is
3a+3b+3c+3d+3e+3f+3g = 3(a+b+c+d+e+f+g)
The goal is to figure out what a+b+c+d+e+f+g is equal to. This is equal to the length of segment PQ since the 7 letters are pieces of segment PQ (i.e., I'm using the segment addition postulate).
In other words,
a+b+c+d+e+f+g = 12
3(a+b+c+d+e+f+g) = 3*12
3(a+b+c+d+e+f+g) = 36
Total distance traveled = 36
The ratio of the number of hours it takes the three pipes A, B and C to fill an olympic pool is 4:9:12. Answer each of the following questions if it is known that the second pipe takes 72 hours to fill the pool.
b
How long would it take to fill the pool if pipes A and C work to fill the pool and pipe B drains the pool at the same rate as it would be filling it?
Answer:
36 hours
Step-by-step explanation: