Answer:
12 geese
10 dogs
Step-by-step explanation:
We are given;
Total number of animals (dogs and geese) is 22 Total number of legs of animals is 64We are required to determine the number of geese and dogs that Alex counted;
We need to know that;
a dog has 4 legs while, a geese has 2 legs Therefore;Assuming he counted x number of geese and y number of dogs;
Then;
x + y = 22, and
2x + 4y = 64
Thus, solving the equation simultaneously;
we can multiply the first equation by 2, to get
2x + 2y = 44
2x + 4y = 64
Eliminating x (by subtracting the second eqn from the first eqn), we get;
-2y = -20
y = 10
Solving for x;
x = 22 - y
= 22 - 10
x = 12
Therefore; he counted 12 geese and 10 dogs
The width of a photograph is 4 centimeters more than three tenths of the length. If the width is 13 centimeters, what’s the length?
Answer:
30 centimeters
Step-by-step explanation:
since the width is 4 centimeters more than 3/10 of the length, then 13 is 4 centimeters more than 3/10 of the length. 4 less than 13 is 9, so nine is 3/10 of the length. if 9 is 3/10, then 3 is 1/10 because 3/10 is three times 1/10. If 3 is 1/10, that means that 30 is the length because 1/10 multiplied by 10 is 10 tenths, or 1.
Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $24.80. The oil change for the other car required 7 quarts of oil and cost $29.30. How much is the labor fee and how much is each quart of oil?
The labor fee is $13.55 and each quart of oil is $2.25
Step-by-step explanation:
Let,
x be the amount of each quart of oil
y be the amount of labor fee
According to given statement;
5x+y=24.80 Eqn 1
7x+y=29.30 Eqn 2
Subtracting Eqn 1 from Eqn 2
[tex](7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{4.50}{2}\\x=2.25[/tex]
Putting x=2.25 in Eqn 1
[tex]5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55[/tex]
The labor fee is $13.55 and each quart of oil is $2.25
Keywords: linear equation, subtraction
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Mary just got a new job at Justice. She makes $10 an hour plus 4% commission on her sales. If she worked 6 hours
on Saturday and did $350 in sales how much did she make for the day?
Answer: $74
Step-by-step explanation:
cost for an hour = $10
since she worked for 6 hours , this means that she made $(6x10) = $60
Also , she made 4% commission on her sale and she sold $350 , this means that she made 4% of 350 =$14
Therefore: she made $ 60 + $14 for the day. Thai is , she made $74 for the day
A total of $30,000 is invested in two corporate bonds that pay 5.5% and 6.25% simple interest. the investor wants an annual interest income of %1800 from the investments. what is the most that can be invested in the 5,5% bond?
Answer:
$10,000
Step-by-step explanation:
Let x represent the amount invested in the 5.5% bond.
For an annual income of $1800, we want ...
(5.5%)x + (6.25%)(30,000-x) = 1800
(-0.75%)x + 1875 = 1800
-0.0075x = -75 . . . . . . . . . subtract 1875
x = 10,000 . . . . . . . . . . . . . divide by -0.0075
At most $10,000 should be invested at 5.5% to obtain at least $1800 in interest.
Alex wants to buy 4 pounds of peaches.They cost $1.20 per pound.How much will Alex need to spend for the peaches?
Simplify: 18³×18²×18³
Answer:
18 to the 8th power
Step-by-step explanation:
18 + 2 + 3 + 34/5 is greater than less then or equal to 1/2
Greater Than!
First make the denominator (the bottom number) the same for both fractions. So you can multiply the 1/2 by 5 and the 4/5 by 2.
This will make them 5/10 and 8/10.
Then, you see that 8/10 (4/5) is greater than 5/10 (1/2)
Hope that’s makes sense! :)
The fraction 4/5 is greater than 1/2. This conclusion can be reached by converting the fractions to decimal form, where 4/5 becomes 0.8 and 1/2 becomes 0.5, highlighting that 0.8 is indeed greater than 0.5.
Explanation:The question is whether the fractional value of 4/5 is greater than, less than, or equal to 1/2. To compare these fractions, it may be helpful to first convert them to decimal form, as this is often easier to understand than comparing fractions directly. 4/5 as a decimal is 0.8 and 1/2 as a decimal is 0.5. Hence, 0.8 is greater than 0.5. Therefore, 4/5 is greater than 1/2.
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the sum of the 5th term of the 7th term of an ap is 52 and the 10th term is 46 find the AP
Answer:
The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................
Step-by-step explanation:
From the question;
Sum of fifth term and 7th term is 52 That is; 5th term + 7th term = 5210th term is 46We are required to find the AP;
We need to know that in an AP ;nth term = a + (n-1) d , where a is the first term and d is the common difference
Therefore, In this case;5th term = a + 4d
7th term = a + 6d
Therefore;5th term + 7th term = 2a + 10d = 52 ..........eqn 1
10th term = a + 9d
Thus, a + 9d = 46 ............. eqn 2We can solve eqn 1 and eqn 2 simultaneously to get the value of a and d2a + 10d = 52
a + 9d = 46
Multiplying the second equation by 2, we get;
2a + 10d = 52
2a + 18d = 92
Eliminating a by subtracting the two equations; we get;
-8d = -40
d = 5
Solving for a
a + 9d = 46
a = 46 - 9d
= 46 - 9(5)
= 46 - 45
a = 1
Thus, the first term, a= 1 and the common difference, d= 5
Therefore;
First term = a = 1
Second term = a + d = 1 + 5 = 6
Third term = a + 2d = 1 + 2(5) = 11
Fourth term = a + 3d = 1 + 3(5) =16
Fifth term = a + 4d = 1 + 4(5) = 21
Sixth term = 1 + 5d = 1 + 5(5) = 26
Seventh term = 1 + 6d = 1 + 6(5) = 31
Thus,
The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................
what is the equation of the line that passes through (1,5) and (-2,14) in slope intercept form
Answer: y = -3x + 8
Step-by-step explanation:
The formula for finding equation of line when two points are given is :
[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 1
[tex]x_{2}[/tex] = -2
[tex]y_{1}[/tex] = 5
[tex]y_{2}[/tex] = 14
Substituting the values , we have
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{14-5}{-2-1}[/tex]
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{9}{-3}[/tex]
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{-3}{1}[/tex]
y-5 = -3(x-1)
y -5 = -3x + 3
writing the equation in slope - intercept form , we will make y the subject of the formula:
y = -3x + 3 + 5
y = -3x + 8
Stefan sells Jin a bicycle for $140 and a helmet for $16. The total cost for Jin is 130% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Final answer:
Stefan spent $120 originally to buy the bike and helmet and made $36 by selling them to Jin.
Explanation:
To find out how much Stefan spent originally, we need to divide the total cost for Jin by 130%.
Let's call the original amount x.
Jin's total cost is 130% of x, which can be expressed as 1.3x.
We know that the total cost for Jin is $140 for the bike + $16 for the helmet = $156.
So we have the equation 1.3x = $156. To solve for x, divide both sides of the equation by 1.3. x = $156 / 1.3 = $120.
Therefore, Stefan spent $120 originally to buy the bike and helmet.
To find out how much money Stefan made by selling the bike and helmet, we subtract the original amount spent from the total cost for Jin.
Money made = $156 - $120 = $36.
when Elena 's car moves forward such that each tire make one full rotation ,the car has traveled 72 inches .how many full rotations will the tire need to make for Elena's car to travel 10 yards
Write 6,219 in expanded
form.
Answer: 6000+200+10+9
Step-by-step explanation:
The ones place multiplies by 1 so 9*1=9
The tens place multiplies by 10 so 10*1=10
The hundreds place multiply by 100 so 100+2=100
The thousands place multiply by 1000 so 1000*6=6000
Hope This Helps!!!
YOU WILL BRAINLIST ALSO 47 POINTS!!!
1. It takes 1 banana and 3 scoops of ice cream to make a banana split. If an ice cream shop scooped 42 scoops of ice cream into banana splits, how many bananas did they use? [Type your answer as a number.]
a0 bananas ___
2. At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
a0 minutes __
3. A zoo has 3 mammals for every 5 reptiles. If the zoo has 72 mammals, how many reptiles does it have? [Type your answer as a number.] __
Answer:
Please Mark Brainliest!
Step-by-step explanation:
i think it would be 14 bananas if u take 3 divided by 42
hope that is right.
he rides for 7 min and waits in line for 20 min, if he was to wait in line for 60 min then he would ride for 21 min, if you divide 20/60 then you'll get 3. Multiply the 7 with that 3 and you'll get "21".
120
round 7,834 to the nearest hundred
Answer:
7,800
Step-by-step explanation:
Because the 3 goes down.
I will mark free Brainlyest and free point if answered correctly.
How good is Pizza to you? And what is 8/2?
Answer:
Pizza is pretty good tbh. Also the answer is 4.
Answer:
Pizza is great
Step-by-step explanation:
And 8/2 is 4. Pls mark brainliest thx! :)
what is 1 1/2 divided by 3/4
The answer to this one would be 2.
Answer: 2
Step-by-step explanation:
1 1/2 divided 3/4
First make all a fraction
3/2 divided 3/4
3/2*4/3 inverted
2
If Damian is able to read 80 pages in 2 hours how long does it take for him to reach each page
Answer:
Step-by-step explanation:
If he reads 80 pages in 2 hours, that means he reads 80 pages in 120 minutes. 80 pages/120 minutes simplifies to 2 pages/3 minutes. It also means it takes him 1 and a half minutes to read each page.
what fractions are less than and greater than 1/2
Answer:
Less than: 1/4, 1/8, 1/16,...
Greater than: 5/8, 3/4, 1,...
Hope this helps :)
Read the pic boiiiiiiiiiiiiiiiii
Answer:
a is the answer or 320 ft
Step-by-step explanation:
95*65=6175 ft^ for area
95+95+65+65=320 ft
What is 321 in standard and expanded form
Answer:
321 300 20 1
Step-by-step explanation:
In written for: Three hundred twenty-one
Expanded form: 300 + 20 + 1
Standard form: 321
Fraction form: 321/1
Decimal form: 321.00
Write the equation of a line that contains (2,-4) and that is perpendicular to y=2/3x+2
Answer:
y = - [tex]\frac{3}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{2}{3}[/tex] x + 2 ← is in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex], thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 4) into the partial equation
- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1
y = - [tex]\frac{3}{2}[/tex] x - 1 ← equation of perpendicular line
Please help me with these answers!!!
Answer:
Step-by-step explanation:
5) D 2000/200 = 10
6) C 90/9 = 10
7) B 80/8 = 10
8) A) 10 times 2 =10*2 = 20
When 238 is divided by the natural number n, the quotient is 3 more than n, and there is no remainder. What is n?
Answer:
n = 14
Step-by-step explanation:
Write the equation in algebraic (numbers and symbols) form
[tex]\frac{238}{n}[/tex] = n + 3 Rearrange the equation
[tex]n\frac{238}{n}[/tex] = n(n + 3) Multiply both sides by 'n'
238 = n(n + 3) On the left, multiplying and dividing by 'n' cancels out
238 = n² + 3n Distributed right side
0 = n² + 3n - 238 Rearranged to standard form for quadratic equations
Remember standard form for quadratic equations is: ax² + bx + c = 0
State the variables a, b and c:
a = 1; b = 3; c = -238
When a quadratic equation is in standard form, you can use the quadratic formula to solve for 'n'. (Usually, you see the variable 'x', but the quadratic formula can solve for 'n' as if it is 'x', as long as it's in standard form.)
[tex]n = \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex] (ignore the Â, it's a formatting error)
[tex]n = \frac{-(3)±\sqrt{(3)^{2}-4(1)(-238)}}{2(1)}[/tex] Substitute the values for 'a', 'b' and 'c' from the equation
[tex]n = \frac{-3±\sqrt{9-(-952)}}{2}[/tex] In the root, two negatives make a positive
[tex]n = \frac{-3±\sqrt{9+952}}{2}[/tex] Add inside the root
[tex]n = \frac{-3±\sqrt{961}}{2}[/tex] Find the square root of 961
[tex]n = \frac{-3±{31}{2}[/tex] Split the equation at the ±
Split for adding:
[tex]n = \frac{-3+31}{2}[/tex] Simplify
n = 14
Split for subtracting:
[tex]n = \frac{-3-31}{2}[/tex] Simplify
n = -17
You get the answers 14 and -17 for 'n'. Decide which one is 'inadmissible', meaning it can't be right even if it solves the equation.
The problem says 'n' is a natural number. Natural numbers are all non-partial numbers count up from 1. (Non-partial means as a fraction, they are reduced to a number over 1). Since -17 is less than 1, it is inadmissible because it is not a natural number.
Therefore, 'n' is 14.
what is 9/20 times 4/5 in simplest form ?
Answer:
0.36 or [tex]\frac{9}{25}[/tex]
Step-by-step explanation:
9/20=.45
4/5=.8
Answer: .36
How do we solve for “p”, when
P= 75 + 45h
Answer:
See below.
Step-by-step explanation:
The equation is already solved for p.
p = 75 + 45h
Final answer:
To solve for the fluid density 'p', use the hydrostatic pressure formula P = pgh. By rearranging the formula to p = P / (gh) and inputting the known values for P (atmospheric pressure) and h (height of the water column), the density can be calculated.
Explanation:
To solve for density 'p' when given the equation P = 75 + 45h, where P represents atmospheric pressure and h is the height of a column of fluid, we need to incorporate the concept of hydrostatic pressure. The formula for hydrostatic pressure is P = pgh, where 'p' is the fluid density, 'g' is the acceleration due to gravity, and 'h' is the height of the fluid column. If we know the value of 'P' and the value of 'h', we can isolate 'p' by rearranging the equation to p = P / (gh). This calculation assumes that 'g', the acceleration due to gravity, is a known constant.
Let's assume 'P' is given as 1.00 atm (standard atmospheric pressure) for a water column which is the fluid we're working with. The density 'p' of water that creates this pressure can be calculated by inserting the known values into the expression for 'h'. For instance, if 'h' is 10 meters, the equation would be p = 1.00 atm / (9.81 m/s² × 10 m). To get 'p' in appropriate units, we would convert atm to pascals, and the result will provide the density in kg/m³.
Hey yall It's been a while Wassup but da question is : What term best describes 3x+5 . If u dont know da answer dont waste my time typin junk dat dont make sense
25. Belle had the choice of taking out a 4-year car loan at
8.5% simple interest or a 5-year car loan at 7.75%
simple interest. If she borrows $15,000, how much
interest would she pay for each loan? Which option
will require less interest?
Answer:
the first loan is cheaper
Step-by-step explanation:
convert percent values to decimals
8.5/100=.085
7.75/100=.0775
find the value for the first loan
1550*.085*4=527
find the value for the first loan
1550*.0775*5=600.625
compare
Belle would pay $5100 in interest for the 4-year loan at 8.5% and $5812.50 for the 5-year loan at 7.75%. Therefore, less interest would be paid with the 4-year loan.
Explanation:To calculate the simple interest, we use the formula I = P*R*T, where P is the principal amount, R is the interest rate, and T is the time in years.
For the 4-year loan at 8.5%, interest would be: I = $15,000 * 8.5/100 * 4 = $5100
For the 5-year loan at 7.75%, interest would be: I = $15,000 * 7.75/100 * 5 = $5,812.50.
So, the 4-year loan at 8.5% will require less interest payment.
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Please help! Also, show work, please!
if each person had to run 1/25 of a mile then you would need to have 5 people per team. it takes 5/25 to equal 1/5. So your answer is 5!!
Hope this helps! :)
A submarine hovers at 66 and two-thirds yards below sea level. If it ascends 24 and StartFraction 1 over 8 EndFraction yards and then descends 78 and three-fourths yards, what is the submarine’s new position, in yards, with respect to sea level? Negative 169 and StartFraction 13 over 24 EndFraction Negative 121 and StartFraction 7 over 24 EndFraction Negative 12 and StartFraction 1 over 24 EndFraction 12 and StartFraction 1 over 24 EndFraction
A submarine hovers at 66 and 2/3 yards below sea level. If it ascends 24 and 1/8 yards and then descends again 78 and 3/4 yards, what is the submarine’s new position, in yards, below sea level?
Answer:
The submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.
Solution:
Given that a submarine hovers at [tex]66\frac{2}{3}[/tex] yards below sea level. This means that the position of submarine is negative
Therefore, we get [tex]-66\frac{2}{3}[/tex]
Also given that it ascend [tex]24\frac{1}{8}[/tex] yards
So we have to add [tex]-66\frac{2}{3}[/tex] and [tex]24\frac{1}{8}[/tex]
[tex]\rightarrow -66\frac{2}{3} + 24\frac{1}{8}\\\\\text{Convert mixed fractions to improper fractions }\\\\\rightarrow -\frac{66 \times 3+2}{3} + \frac{24 \times 8+1}{8} = \frac{-200}{3} + \frac{193}{8}\\\\\rightarrow \frac{-200 \times 8}{3 \times 8} + \frac{193 \times 3}{8 \times 3}\\\\\text{Simplify the above expression }\\\\\rightarrow \frac{-1600}{24} + \frac{579}{24} = \frac{-1021}{24}[/tex]
The submarine descends again 78 and 3/4 yards
This means we need to subtract [tex]-78\frac{3}{4}\text{ yards from } -\frac{1021}{24}\text{ yards}[/tex]
[tex]\rightarrow \frac{-1021}{24} -(78\frac{3}{4})\\\\\rightarrow \frac{-1021}{24} - \frac{78 \times 4 + 3}{4}\\\\\rightarrow \frac{-1021}{24} - \frac{315}{4} = \frac{-1021}{24} - \frac{315 \times 6}{4 \times 6}\\\\\rightarrow \frac{-1021 -1890}{24} = \frac{-2911}{24}\\\\\text{Simplify the expression }\\\\\rightarrow \frac{-2911}{24} = -121\frac{7}{24}[/tex]
Therefore, the submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.
Answer:
The answer-121 and 7/24
Hope this helps
:D
If I'm wrong sorry
And sorry that I'm super late
sahil is putting together supply kits and has 36 packs of x pencil, 12 packs of y crayons, and 24 erasers. Write an expression to show the total number of items.
Answer:
36x + 12y + 24 = T
Step-by-step explanation:
If Sahil has 36 packs of x pencils, then x would equal the number of pencils in each pack. Same thing goes for y. 12 packs of y pencils and y will be the number of crayons in each pack.
36(x) = Total number of pencils.
12(y) = Total number of crayons.
24 = The numbers of erasers which is given.
36x + 12y + 24 = Total numbers of items.