Final answer:
Using a system of equations, we established that there are 8 pigs and 11 ducks among the 19 animals with a total of 54 legs.
Explanation:
To solve the problem of determining how many pigs and ducks there are when there are 19 animals in total and 54 legs, we set up two equations. Let's assume the number of pigs is x and the number of ducks is y. Pigs have 4 legs, and ducks have 2 legs. We can summarize this information in the following system of equations:
Equation 1: x + y = 19 (because there are 19 animals total)
Equation 2: 4x + 2y = 54 (because the total number of legs is 54)
We can solve this system using the substitution or elimination method. Simplifying Equation 2 by dividing every term by 2 gives us 2x + y = 27, which we'll call Equation 3.
Equation 3: 2x + y = 27
We can now subtract Equation 1 from Equation 3 to find the value of x:
(2x + y) - (x + y) = 27 - 19
(2x - x) + (y - y) = 8
x = 8 (number of pigs)
Substitute x back into Equation 1:
x + y = 19
8 + y = 19
y = 19 - 8
y = 11 (number of ducks)
Therefore, there are 8 pigs and 11 ducks among the 19 animals.
Will earns $98 a week bagging groceries. He saves 80% of what he makes per week and spends the rest on lunches. How much does Will spend each week on lunches
Answer:
$19.60
Step-by-step explanation:
$98 is made each week.
80% is saved, and the rest is spend on lunch, so 20% is spent on lunch.
20%=.20
98•.20=19.6
$19.60 is spend on lunches each week.
Janet can read 3.6 pages of a book in a minute. If she read for 2.71 minutes. How much would have she had read
Final answer:
It would have taken Janet about 9.7536 pages to read..
Explanation:
To determine Janet's reading progress, her reading speed is multiplied by the duration she read. With a reading speed of 3.6 pages per minute, if Janet read for 2.71 minutes, the calculation is 3.6 multiplied by 2.71, resulting in 9.7536. Hence, Janet would have read approximately 9.7536 pages. This calculation showcases how the product of reading speed and time provides a quantitative measure of reading accomplishment. It's a straightforward way to estimate the amount of material covered within a specific timeframe, offering insights into reading efficiency and progress.
Brain May, guitarist for Queen, does not know how to price his signature Antique Cherry Special that cost £280 to make. He know he wants 85% markup on cost. What price should Brian May ask for the guitar?
Answer:
£518
Step-by-step explanation:
Asking price = original cost × markup%
A = 280(1.85) = 518
Brian May needs to price his Antique Cherry Special guitar at £518. This price is determined by the original cost, £280, and a 85% markup, £238, on this cost.
Explanation:Brian May needs to define a price for his signature Antique Cherry Special guitar that was costed at £280 and he wants an 85% markup on this cost. Markup is calculated by multiplying the cost by the markup percentage. In this case, the markup is £280 * 85/100 = £238. Therefore, to determine the final price Brian needs to add the original cost and the markup, which is £280 + £238 = £518. So the price Brian should ask for the guitar is £518.
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The distance between Quebec City and New York City is 520 miles if Kate leaves Quebec and will leaves New York at 9:09 a.m. And they tried toward each other at 55 miles per hour and 75 miles per hour respectively at what time will they meet?
Kate and Will meet at 1 : 09 pm
Solution:
The distance between Quebec City and New York City is 520 miles.
At the point where Kate and Will meet, they would have traveled 520 miles.
Let "t" represent the time it takes Kate to travel a certain distance before they met.
[tex]Distance = speed \times time[/tex]
If Kate drives at 55 mph, the distance covered would be
[tex]Distance = 55 \times t = 55t[/tex]
If Will drives at 75 miles per hour, then the distance covered will be
[tex]Distance = 75 \times t = 75t[/tex]
Since the total distance covered is 520 miles
Which means,
[tex]55t + 75t = 520\\\\130t = 520\\\\t = \frac{520}{130}\\\\t = 4[/tex]
Given that in question,
If Kate leaves Quebec and will leaves New York at 9:09 a.m
4 hours after 9: 09 am, Kate and Will will meet
9: 09 am + 4 hours = 1: 09 pm
Thus they would meet at 1 : 09 pm
how can you determine if a polygon is a convex?
Answer:
You can determine if a polygon is a convex, by which way the edges points out
Convex is when all the points are facing out, so a polygon is a convex if all the edges are pointing out.
Answer:
No side of the polygon crosses any other, even when extended indefinitely.
Step-by-step explanation:
If no sides of the polygon cross each other, it is convex when it has no internal reflex angles (angles measuring more than 180°). If sides of the polygon cross each other, it is not convex.
Another way to describe a convex polygon is that extending any one side indefinitely will not cause it to cross any other side.
The surface area of a cell phone screen is 6800 mm2. Use the fact that 10 mm = 1 cm to convert this area to cm2. Round your answer to the nearest whole number. Do not type the units in the space below.
Answer:
[tex]68 \: {cm}^{2} [/tex]
Step-by-step explanation:
You can use 1 cm = 10 mm very well to help you with this.
The small two at the end of the unit (cm^2) refers, that the shape of an object is two dimensional. If we make 1 cm two dimensional by multiplying it with the original 1 cm, we get a total area of
[tex]1 \: {cm} \times 1 \: {cm} \: = 1 \: {cm}^{2} [/tex]
We have created an equation. Since we know 1 cm = 10 mm, we can replace the centimetres in the equation with the millimetres, like so:
[tex]10 \: mm \times 10 \: mm = 1 \: {cm}^{2} \\ 100 \: {mm}^{2} = 1 \: {cm}^{2} [/tex]
From there, its just a simple matter of calculation:
[tex]6800 \: {mm}^{2} \times \frac{1 \: {cm}^{2} }{100 \: {mm}^{2} } = 68 \: \: {cm}^{2} [/tex]
If the equipment is 30% off and the sale price is $315 what percent of the original price are you paying?
Answer:
Step-by-step explanation:
94 dollars
Answer:
The discount would be $94.50 but the final price would be $220.25.
Hope this helps!
A concert hall has three sections: the main floor, the balcony, and the gallery. For a recent concert, 1020 tickets were sold. There were twice as many balcony tickets sold as gallery tickets, and 225 more main floor tickets than balcony tickets. If g represents the number of gallery tickets sold, which expressions represents this situation?
A. Gallery: g Balcony: g Main Floor: g + 225
B. Gallery: g + g + 225 Balcony: 2g Main Floor: g
C. Gallery: g Balcony: g + 225 Main Floor: 2g + 225
D.Gallery: g Balcony: 2g Main Floor: 2g + 225
Answer:
c is the answer i am preety sure
Step-by-step explanation:
Gallery = g
Balcony = 2g (twice as many gallery)
Main floor = 2g + 225 ( 225 more than balcony)
The answer would be D.
In September there were 16 members in the music club. In October the member of members was 24. What was the percent increase?
Answer:
9%
Step-by-step explanation:
It is simple because you just count to get to 24 and that is the percentage.
2, -10, 50, -250,...
Answer:
Multiply by 5
-250, 1250
Step-by-step explanation:
2 x -5 = -10
-10 x -5 = 50
50 x -5 = -250
-250 x -5 = 1250
Is 3/9 a function of y Equals 6X
Answer:
yes
Step-by-step explanation:
well plug it in: y=6x -> y=6(3/9) and solve, yes if theres a slope of 1
If 80 inches is equivalent to 44 inches, then 28 inches would be equivalent to what?
Answer:
Well no cheating not from me
Step-by-step explanation:
Wayne's savings to Stef's savings were in the ratio 5:6
After spending $28 each the ratio became 1:4
I need to find wayne's savings BEFORE he spent 28 and Stef's savings AFTER she spent 28
HELP PLEASE TY
Answer:
a) $30
b) $8
Step-by-step explanation:
Wayne's savings to Stef's savings were in the ratio 5:6.
Let, Wayne's saving is 5x and Stef's saving is 6x.
Now, given that after spending $28 each the ratio became 1:4.
So, we can write the equation as
[tex]\frac{5x - 28}{6x - 28} = \frac{1}{4}[/tex]
⇒ 20x - 112 = 6x - 28
⇒ 14x = 84
⇒ x = 6
a) Therefore, Wayne's savings before he spends $28 is $(5 × 6) = $30
b) And, Stef's savings after she spends $28 will be $(6x - 28) = $(6 × 6 - 28) = $8 (Answer)
5. People get energy from the food they eat. This energy is measured
in calories. When you exercise, you use up or burn calories. The
picture at the right shows about how many calories a 125-pound
person burns each minute bowling. How many calories does a
125-pound person burn in 2 hours of bowling?
ASAP! please help!
Answer:
Step-by-step explanation:
I don't have all the information, but all you need to do it convert 2 hours to minutes (which would be 120 minutes) and setup a proportion.
amount of calories burnt per minute x (total amount of calories burnt)
____________________________ = ________________
1 minute 120 minutes
Hope this helps!
They would burn 360 calories doing 2 hr of bowling.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that this energy is measured in calories. When you exercise, you use up or burn calories.
The information shows about how many calories a 125-pound person burns each minute bowling.
We need to do it convert 2 hours to minutes which would be 120 minutes and setup a proportion.
The amount of calories burnt per minute x (total amount of calories burnt)
1 minute = 120 minutes
Multiply 120 x 3 = 360.
Hence, they would burn 360 calories doing 2 hours of bowling.
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25 kids took a math test. If 20 kids passed the test, what percent of kids did not pass the test?
Answer: 20%
Step-by-step explanation:
25 = 100%
25/5 = 5
100/5 = 20
That means 80% passed and 20% didnt.
Answer:
20%
Step-by-step explanation:
If 20 kids passed, that means 5 did not. 5/20 is 0.2. Write that in percentage is 20%.
State the quadratic formula
Answer:
Step-by-step explanation:
I do not deed the answers for 11, or 12 just 13
13.
A
B
C
D
E
F
G
a) ASA congruency
b)SAS congruency
c)SSS congruency
d) Not congruent
Step-by-step explanation:
Step 1:
a)
Angle PRQ = Angle RQS
Angle PRQ = Angle QRS (since PQ is parallel to RS , these form corresponding angles and hence are equal.
QR is the common Side
Hence 2 angles are same and the side which is included are same.Hence the 2 given triangles are congruent.
Step 2 :
b)
Angle IGH = Angle EDF
Side IG = DF and Side GH = DE
Here 2 of the sides of the triangle are same and the Angle which is included are same.
Hence the given triangles are equal
Step 3:
c)
In the given triangles the three sides re equal. Hence as per the side Side Side postulate the triangles are equal.
Step 4:
d) 2 angles are equal but the equal Side is not included and hence the two triangles are not congruent
Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the chair free including the bottom
Answer:
Akira needs 45 square inches of gold foil to cover the chair free including the bottom
Step-by-step explanation:
Total surface = surface area of the base square + area of 4 triangles
Step 1: The surface area of the base square
surface area of the base = surface area of the square = [tex]s^2[/tex]
where s is the side length
The the surface area of the base = [tex]3^2[/tex] = 9 square inches
Step 2: The surface area of the side triangles
The area of the triangle = [tex]\frac{1}{2}\times \text{side length} \times \text{slant height}[/tex]
On substituting the values,
The area of the triangle =[tex]\frac{1}{2} \times 3 \times 6[/tex]
The area of the triangle = [tex]\frac{18}{2}[/tex]
The area of the triangle = 9 square inches
Now the area of 4 triangles = 4 x 9 = 36 square inches
Thus the total surface area = 9 + 36 = 45 square inches
The amount of gold foil needed to cover a trophy in the shape of a square pyramid can be calculated using the surface area formula for square pyramids, which considers the base area and the slant height.
Explanation:To calculate the amount of gold foil needed to cover the trophy, we need to find the surface area of the square pyramid trophy. The surface area of a square pyramid is calculated by the formula: Surface Area = base area + 1/2 * Perimeter of base * slant height. If we know the length of the base (which is a square here), the slant height, we can substitute them into this formula to get the surface area. This is the amount of gold foil Akira used to cover her trophy, assuming the gold foil perfectly fits the trophy shape with no overlap.
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When a number is decreased by 79%, the result is 13. What is the original number to the nearest tenth?
If a number is decreased by 79%, we are left with 21%.
so let's devide by 21 to get down to 1%, then multiply by 100 to get to the origininal number:
13 / 21 * 100 = 61.9047619048
To the nearest tenth it's 61.9
Final answer:
To find the original number when decreased by 79% to result in 13, we solve the equation 0.21x = 13, which gives us 61.9047619. Rounding this to the nearest tenth gives us 61.9.
Explanation:
To find the original number, we need to translate the percentage decrease back into the original number. Here's the step-by-step calculation:
We understand that after decreasing the original number by 79%, we have 21% of it left, which is equivalent to the number 13.So to find the original number (let's call it x), we set up the equation 0.21x = 13.Divide both sides by 0.21 to solve for x: x = 13 / 0.21 which equals 61.9047619.Round to the nearest tenth. We look at the hundredth's digit, which is 0, we round down the tenth's place to get the final answer, 61.9.So the original number to the nearest tenth is 61.9.
E=IZ
Where E=(5+9i) and I=(8+7i)
How do I solve for Z?
Answer:
[tex]Z = \frac{37i }{113 } - \frac{23}{113} [/tex]
Step-by-step explanation:
We have the complex number relationship as:
E=IZ
Where E=(5+9i) and I=(8+7i)
We solve for Z to get;
Z=E/L
We then substitute the expressions to get:
[tex]Z = \frac{5 + 9i}{8 + 7i} [/tex]
We rationalize to get:
[tex]Z = \frac{5 + 9i}{8 + 7i} \times \frac{8 - 7i}{8 - 7i} [/tex]
We simplify to obtain:
[tex]Z = \frac{40 - 35i + 72i - 63}{ {8}^{2} + {7}^{2} } [/tex]
This gives
[tex]Z = \frac{37i - 23}{113 } [/tex]
Or
[tex]Z = \frac{37i }{113 } - \frac{23}{113} [/tex]
If log4(x) = –2 , which of the following is the correct value of X?
a. x = -16
b. x =
c.x = -8
d.x=1
Answer:
c
Step-by-step explanation:
4*-8=-2
9. Four increased by half of a
number is equal to six.
How do u write it??
Answer:
4+ x/2 =6
Step-by-step explanation:
Let the number be X
half of the number is 1/2 multiply X= X/2
Four increased by half the number is 4+X/2
Therefore, Four increased by half of anumber is equal to six is written as
4+ x/2 =6
Kristin spent 40$ on pampers. If they cost 8$ / package , how many packages did she buy
Answer:
5 Packages
Step-by-step explanation:
40 / 8 = 5
7/12 times 7. Note: the answer is a mixed number :)
Answer:
[tex]4\frac{1}{12}[/tex]
Step-by-step explanation:
7/12 * 7
7 = 7/1
7/12 * 7/1
49/12
12 goes into 49 four times, with a remainder of 1
[tex]4\frac{1}{12}[/tex]
Hope this helps :)
Answer:
4 1/12
Step-by-step explanation:
7/12 X 7
7/12 which is 7/12
do 7/12 times 7 which is 49/12
12 goes 4 times into 49 (up to 48)
there's one remaining
and its over 12
4 1/12
given f (x) = 5x + 1 find f(-3)
Answer:
x=-4/5
Step-by-step explanation:
So first, since it says find f(-3) put -3 in the place of x in F(x)
So, f(-3)=5x+1
-3=5x+1
-4=5x
x=-4/5
or
x=-.8
What is the least common multiple of 30 and 13
Answer: it would be 390
Just keep counting how many times one number goes into the other, start with the smallest
write an equation in slope intercept form of the line that passes through (-1 5) and is parallel to the graph of 2y+4x= -8
Answer:
Therefore, equation of the line that passes through (-1,5) and is parallel to the line
[tex]2y+4x=-8[/tex]
is
[tex]y=-2x+3[/tex]
Step-by-step explanation:
Given:
[tex]2y+4x=-8[/tex] .Equation of line
can be written as
[tex]y=-2x-8[/tex] ...which is in Slope intercept form
To Find:
Equation of line passing through ( -1, 5) and is parallel to the line 2y+4x=-8
Solution:
[tex]y=-2x-8[/tex] ...........Given
Comparing with,
[tex]y=mx+c[/tex] ....general form in slope intercept
Where m =slope
We get
[tex]Slope = m = -2[/tex]
We know that parallel lines have Equal slopes.
Therefore the slope of the required line passing through (-1 , 5) will also have the slope = m = -2.
Now the equation of line in slope point form given by
[tex](y-y_{1})=m(x-x_{1})[/tex]
Substituting the points and so we will get the required equation of the line,
[tex](y-5)=-2(x-(-1))=-2(x+1)\\\\y-5=-2x-2\\y=-2x+3......Equation\ of\ line[/tex]
Therefore, equation of the line that passes through (-1,5) and is parallel to the line
[tex]2y+4x=-8[/tex]
is
[tex]y=-2x+3[/tex]
what is the quotient when (x+3) is divided into the polnomial 2x^2+x-15
Answer:
2x-5
remainder of 0
Step-by-step explanation:
Check the image
Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of blank
The blank is -8
Step-by-step explanation:
Let us revise some rules of indices:
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex] [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] [tex]a^{m}[/tex] = [tex]a^{n}[/tex] , them m = n∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]
∵ All bases are equal
∴ Use the first and third rule above to find x
∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]
∴ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S
∵ [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S
Equate L.H.S and R.H.S
∴ [tex]4^{-3}[/tex] = [tex]4^{5+x}[/tex]
Equate the indices of the two sides
∴ -3 = 5 + x
- Subtract 5 from both sides
∴ -8 = x
∵ x represents the blank
∴ The blank = -8
The blank is -8
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Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of negative eight.
To solve for the missing exponent, we can use the following properties of exponents:
Multiplying exponents with the same base: When multiplying powers with the same base, we add their exponents.
Negative exponents: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
Applying these properties:
4^3 * 4^-6 = 4^(3 - 6) = 4^-3 (since 4^-6 = 1/4^6)
4^5 * 4^x = 4^(5 + x)
Setting these equal to find x:
4^-3 = 4^(5 + x)
Therefore, x = -3 - 5 = -8.
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood. What is the total number of fliers they gave out
Answer:
The total number of fliers they gave out is 1368.
Step-by-step explanation:
Given:
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood.
Now, to find the total number of fliers they gave out.
Let the total number of fliers be [tex]x.[/tex]
Number of fliers they gave out for a political campaign:
[tex]\frac{21}{38}\ of\ x[/tex]
[tex]=\frac{21}{38} \times x[/tex]
[tex]=\frac{21x}{38}[/tex]
Number of fliers remaining they gave out in another neighborhood = 612.
Now, to get the total number of fliers by putting an equation:
[tex]x-\frac{21x}{38} =612[/tex]
[tex]\frac{38x-21x}{38} =612[/tex]
[tex]\frac{17x}{38} =612[/tex]
Multiplying both sides by 38 we get:
[tex]17x=23256[/tex]
Dividing both sides by 17 we get:
[tex]x=1368.[/tex]
Therefore, the total number of fliers they gave out is 1368.