Answer:
2 cups of flour
Step-by-step explanation:
To make 5 batches of cookies, 10 cups of flour are required.
To make 1 batch of cookies:
10 cups ÷ 5 cups = 2 cups of flour.
To find out how many cups of flour are required for each batch of cookies, divide the total cups of flour (10 cups) by the number of batches (5 batches), which equals 2 cups of flour per batch.
Explanation:To determine how many cups of flour are needed for each batch, we can set up a simple division equation where we divide the total amount of flour by the number of batches. The student is given that 10 cups of flour make 5 batches of cookies. Using this information, we calculate the amount of flour per batch as follows:
Amount of flour per batch = Total cups of flour ÷ Number of batches
Amount of flour per batch = 10 cups ÷ 5 batches
Thus, the amount of flour required for each batch is:
Amount of flour per batch = 2 cups
Divide - 2x3 – 4x2 + 3x + 2 by x – 3.
To divide the given polynomial by a binomial, use polynomial long division, resulting in a quotient of -2x² - 10x - 30 and a remainder of 92.
Dividing a Polynomial by a Binomial
To divide the polynomial -2x³ – 4x² + 3x + 2 by the binomial x - 3, we will use polynomial long division, which is a process similar to long division with numbers. It involves subtracting multiples of the divisor from the dividend to get a quotient and possibly a remainder.
First, divide the first term of the dividend, -2x³, by the first term of the divisor, x, to get -2x².
Multiply the divisor x - 3 by the first term of the quotient, -2x², to get -2x³ + 6x².
Subtract this result from the dividend to obtain the new dividend -4x2 (adjusting the original terms), which becomes -10x².
Repeat this process with the remaining terms of the new dividend.
Continue until all terms of the dividend have been divided.
This process results in the quotient -2x² - 10x - 30 and a remainder of 92. The complete division statement is -2x³ – 4x² + 3x + 2 = (x - 3)(-2x² - 10x - 30) + 92.
Solve the system:
5x-7y=-41
-3x-5y=-3
Answer:
x = -4 , y = 3
Step-by-step explanation:
5x - 7y = -41 ... (i)
-3x - 5y = -3 ... (ii)
Multiplying (i) by -3 and (ii) by 5 ;
-15x + 21y = 123 ... (i)
-15x - 25y = -15 ... (ii)
Subtracting (i) by (ii) ;
0 + 46y = 138
46y = 138
y = 138 ÷ 46 = 3
Returning to equation (ii) ;
-3x - 5(3) = -3
-3x = -3 + 15
-3x = 12
x = -4
Answer: The values of x and y in the given equations are [tex]x=-4[/tex] and [tex]y=3[/tex]
Step by step explanation:
Given system of equations are
[tex]5x-7y=-41\hfill (1)[/tex]
[tex]-3x-5y=-3\hfill (2)[/tex]
To find the values of x and y :
by using Elimination method
Now multiplying the equation (1) into 3 we get
[tex]15x-21y=-123[/tex]
Now multiplying the equation (2) into 5 we get
[tex]-15x-25y=-15[/tex]
Adding the above two equations
[tex]15x-21y=-123[/tex]
[tex]-15x-25y=-15[/tex]
_________________
[tex]-46y=-138[/tex]
_________________
[tex]46y=138[/tex]
[tex]y=\frac{138}{46}[/tex]
[tex]y=3[/tex]
Therefore [tex]y=3[/tex]
Substitute y value in equation (1)
[tex]5x-7y=-41[/tex]
[tex]5x-(7\times 3)=-41[/tex]
[tex]5x-21=-41[/tex]
[tex]5x=21-41[/tex]
[tex]5x=-20[/tex]
[tex]x=-\frac{20}{5}[/tex]
[tex]x=-4[/tex]
Therefore [tex]x=-4[/tex]
The values of x and y are [tex]x=-4[/tex] and [tex]y=3[/tex]
HELP ASAP NEED THIS ANSWER
A cruise ship can cover 18 nautical miles in 342 minutes. How many nautical miles will it travel in 152 minutes?
A. 8
B. 10
C. 12
D.6
Answer:
A.
The cruise ship will travel 8 nautical miles in 152 minutes.
Step-by-step explanation:
Distance covered by the cruise ship in 342 minutes = 18 nautical miles
Distance covered in 1 minute = [tex]\frac{18}{342}[/tex] nautical miles
= [tex]\frac{1}{19}[/tex] nautical miles
Distance covered in 152 minutes = [tex]\frac{1}{19}\times152[/tex] nautical miles
= 8 nautical miles
So, distance covered by cruise ship in 152 minutes is 8 nautical miles.
∴ The correct answer is option A.
The average 12 to 17 year or spends 645 minutes per month on a personal computer this is 732 fewer minutes per month than the average 18 to 24 year old spends how many minutes per month does the average 18 to 24 year old spend on a personal computer
Answer:
1377 minutes
Step-by-step explanation:
645 + 732 = 1377 min
Use the graph to find estimates for the solutions of
[tex]3x {}^{2} - 3x - 1 = x + 1[/tex]
Answer:
x = - 0.25, x = 1.25
Step-by-step explanation:
The solutions to the equation are the values of x where the graph crosses the x- axis, that is as an estimate
x ≈ - 0.25 and x ≈ 1.25
Answer:
[tex]x=-0.4[/tex]
[tex]x=1.7[/tex]
Hopefully the answers are accepted to the nearest tenths.
Step-by-step explanation:
Since the left hand side was already graphed, we just need to graph the right hand side which is [tex]x+1[/tex].
We are going to still let [tex]y[/tex] represent the outputs of [tex]x+1[/tex].
So we want to graph the equation [tex]y=x+1[/tex] on the same graph as the parabola, the almost U shaped graph.
You could make a table to plot the equation.
[tex]y=x+1[/tex]
[tex]x[/tex] | [tex]y[/tex] | ordered pair to graph [tex](x,y)[/tex]
-------------------------------------------------------------------------------------------------------
-2 -2+1=-1 (-2,-1)
-1 -1+1=0 (-1,0)
0 0+1=1 (0,1)
1 1+1=2 (1,2)
2 2+1=3 (2,3)
The purple line I made is the line formed from these points which was generated from the equation [tex]y=x+1[/tex].
Now where the blue curve touches the purple line is our solutions. I put those in orange.
The solutions are approximately, [tex]x=-0.4[/tex] or [tex]x=1.7[/tex].
Hopefully, it accepts solutions to the nearest tenths.
We are trying to approximate where those orange dots are on the number line. Please see attachment 2.
18. Elena wants to estimate 197.6 = 5.48.
Which number sentence shows the best
way to estimate this quotient?
A - 100 =5= 20
B - 100 = 10 = 10
C - 200 = 5 = 40
D- 200 = 10 = 20
Answer:
Step-by-step explanation:
the only way I knew this was division was because of the word quotient. Before u post, please check ur question to see if it is worded correctly....equals does not mean division.
197.6 / 5.48.....estimate
197.6 rounds to 200
5.48 rounds to 5
so the best way would be : C. 200 / 5 = 40 <===
the real answer is : 197.6 / 5.48 = 36.058.......so an estimate is not exact...but it can be close
The best way for Elena to estimate the quotient of 197.6 divided by 5.48 is to round 197.6 to 200 and 5.48 to 5, and then calculate 200 divided by 5, which gives 40 as the estimated result. This corresponds to Option C: 200 ÷ 5 = 40.
Elena wants to estimate the quotient of 197.6 divided by 5.48. Estimation involves rounding numbers to make calculations easier while still getting a number that is close enough to the actual answer for practical purposes. The ideal way to estimate is to round each number to a convenient figure that is easy to divide mentally.
In our case, 197.6 can be rounded to 200 since it is very close to it, and 5.48 can be rounded to 5 or 10. The options provided suggest rounding to the nearest whole number or to the nearest ten. Thus:
Option C (200 ÷ 5 = 40) uses rounding to the nearest fifth, which provides an estimate that is most accurate.
Option D (200 ÷ 10 = 20) also provides a reasonable estimate, but it rounds the divisor to the nearest ten, which might lead to a less accurate estimate.
Therefore, the number sentence that shows the best way to estimate this quotient is Option C: 200 ÷ 5 = 40.
The price of a video game was reduced from $70 To $40. By what percent what is the price of the video game reduced.
Answer:
Step-by-step explanation:
reduced amount = 70 - 40 = $30
Percent of reduction = [tex]\frac{30}{70}*100\\=\frac{300}{7} \\=42\frac{6}{7}[/tex]%
0r 42.86%
Answer:
Step-by-step explanation:
percent decrease = (original number - new number) / (original number) * 100
= (70 - 40) / 70 * 100
= 30/70 * 100
= 0.42857 * 100
= 42.857 % decrease....if u need it rounded, 42.86%....or if u
need it rounded to the nearest whole percent, its 43%
The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the greater number?
The greater number is 121
Step-by-step explanation:
The given is:
The sum of 2 positive numbers is 151The lesser number is 19 more than the square root of the greater numberWe need to find the greater number
Assume that the smaller number x and the greater number is y
∵ The smaller number is x and the greater number is y
∵ Their sum is 151
∴ x + y = 151 ⇒ (1)
∵ The lesser number is 19 more than the square root of the greater
number
∴ x = 19 + √y ⇒ (2)
- Substitute x in equation (1) by equation (2)
∵ (19 + √y) + y = 151
- Subtract 151 from both sides and re-arrange the terms from
the greatest power y
∴ y + √y - 132 = 0
Chang [tex]\sqrt{y}[/tex] to [tex]y^{\frac{1}{2}}[/tex] and substitute [tex]y^{\frac{1}{2}}[/tex] by h
∵ [tex]y^{\frac{1}{2}}[/tex] = h
∴ y = h²
- Substitute each y by h
∴ h² + h - 132 = 0
- Factorize it into two factors
∴ (h - 11) (h + 12) = 0
- Equate each factor by 0 to find h
∵ h - 11 = 0
- Add 11 to both sides
∴ h = 11
∵ h + 12 = 0
- subtract 12 from both sides
∴ h = -12
∵ h = [tex]y^{\frac{1}{2}}[/tex]
∴ [tex]y^{\frac{1}{2}}[/tex] = 11 and -12
∵ [tex]y^{\frac{1}{2}}[/tex] = √y
∴ √y = 11
∴ √y = -12 ⇒ rejected square root can't give -ve number
∴ √y = 11 only
- To find y square the both sides
∴ y = 121
The greater number is 121
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The solution involves setting up two equations from the given information and then substituting one into the other to create a quadratic equation in terms of the greater number, x, and solving for x.
Explanation:The question involves finding two positive numbers given that their sum is 151 and that the lesser number is 19 more than the square root of the greater number. To find the greater number, let's denote the greater number as x and the lesser number as y. The two conditions given are:
x + y = 151 (The sum of the numbers is 151.)y = √x + 19 (The lesser number is 19 more than the square root of the greater number.)We can substitute the second condition into the first:
x + (√x + 19) = 151x + √x + 19 = 151√x + 19 = 151 - x(√x + 19)2 = (151 - x)2x + 2 * 19 * √x + 19^2 = [tex]151^2[/tex]- 2 * 151 * x + [tex]x^2[/tex]Subtract x from both sides and simplify:2 * 19 * √x +[tex]19^2[/tex] =[tex]151^2[/tex]- 2 * 151 * xThis equation can then be solved for x to find the greater number.After simplifying the quadratic equation and solving for x, we will find the value for the greater number.
When 3x+2_<5(x-4) is solved for x, the solution is
Answer:
x ≤ 11
Step-by-step explanation:
Simplify the equation, then isolate "x" by using reverse operations in reverse BEDMAS order.
3x + 2 ≤ 5(x-4) Distribute over the bracket by multiplying.
= 3x + 2 ≤ 5x - 20 Start isolating "x" on the left side.
= 3x + 2 - 2 ≤ 5x - 20 - 2 Subtract 2 from both sides.
= 3x ≤ 5x - 22
= 3x - 5x ≤ 5x - 22 - 5x Subtract 5x from both sides to move x to left side
= -2x ≤ -22
= -2x/-2 ≤ -22/-2 Divide both sides by -2 to isolate x
= x ≤ 11 Final answer
Write an equation for the nth term of the arithmetic sequence. Then find a30.
11, 10, 9, 8, ...
Answer:
Therefore the equation dor nth term is,
[tex]a_{n} =a_{1} + (n-1)\times d[/tex] and
[tex]a_{30} =-18[/tex]
Step-by-step explanation:
Given:
Arithmetic Sequence as
11 , 10 , 9 , 8 , ..........
∴ First term = a₁ = 11
Second term = a₂ = 10
∴ Common Difference = d = a₂ - a₁ = 10 - 11 = -1
∴ d = -1
To Find:
[tex]a_{n} = ?\\and\\a_{30} = ?[/tex]
Solution:
An equation for the nth term of the arithmetic sequence is given by
[tex]a_{n} =a_{1} + (n-1)\times d[/tex]
Substitute n= 30 for [tex]a_{30}[/tex] and a₁ and d we get
[tex]a_{30} =11 + (30-1)\times -1\\\\a_{30} =11+29\times -1\\\\a_{30} =11-29\\\\a_{30} =-18\\\\\therefore a_{30} =-18\ \textrm{as required}[/tex]
Therefore,
[tex]a_{30} =-18[/tex]
The nth term of the given arithmetic sequence can be represented by the equation an = 12 - n. The 30th term of this sequence is -18.
Explanation:In order to write an equation for the nth term of an arithmetic sequence, we need to know the first term (a1) and the common difference (d). In the given arithmetic sequence 11, 10, 9, 8, ..., the first term a1 is 11 and the common difference d is -1 (because each term reduces by 1).
The general formula for the nth term (an) of an arithmetic sequence is: an = a1 + (n-1) * d. Substituting the values of a1 and d in the equation, we get: an = 11 + (n-1) * -1 = 12 - n.
To find a30, substitute n = 30 in the equation, we get a30 = 12 - 30 = -18.
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which if the following describes the transformation of the graph y=x^2 in graphing y=-x^2-5
Answer:
Step-by-step explanation:
f: y=x^2
g: y= -x^2
h: y= -x^2-5
first we transform the graph of f to the graph of g using the reflexion across y-axis .
then we transform of g to the graph of h using the translation -5( vector j )
look at the photo below for the graphics.
:)
Answer: a translation 5 units to the left
rachel received a $70 gift card for a coffee store. she used it in buying some coffee that cost $7.44 per pound. after buying the coffee, she had $25.36 left on her card. how many pounds of coffee did she buy?
Answer:
6 pounds.
Step-by-step explanation:
70-25.36= 44.64 (the amount of money she spent)
44.64/7.44 (per pound cost)= 6
Answer:
Rachel bought 6 pounds of coffee.
Step-by-step explanation:
First, do $70-$25.36, because that will give you the total amount of money she spent on coffee.
$70-$25.36= $44.64.
Rachel spent $44.64 on coffee.
Next, you know that every pound of coffee costs $7.44.
So, $7.44x = $44.64
x= the number of pounds of coffee Rachel purchased.
So, we have to now isolate x.
$7.44x / $7.44 = $44.64 / $7.44
x= 6
Therefore, Rachel purchased 6 pounds of coffee.
If you need anymore help on any math problems, email me at: icecreamforest7@aol.com
I also tutor.
Hope this helps:)
Plz help I’ve been struggling on this for a long time
Answer:
Step-by-step explanation:
the easiest way is to convert these fraction to decimals because as you can see on the number line the numbers are whole and decimals on the small tik mark
-3 3/4 would convert to as -3.75
1/2 would convert into 0.5
now plot those on a number line
*remember the small tiks are worth .25*
how do I solve for y: 2 + y = -7 + 2y
Answer:
y=9
Step-by-step explanation:
2+y=-7+2y
2=-7+2y-y
2=-7+y
y=2-(-7)
y=2+7
y=9
Answer:
2 + y = -7 + 2y
collect like terms
y-2y=-7-2
-y=-9
y=9
Step-by-step explanation:
High grade steel consists of 85% iron and 15% magnese. Low grade steel consists of 67% iron and 33% mag ese. NASA orders 500 tons of steel and specifies that it must be in the proportion 80% iron and 20% steel. How many tons of high grade and low grade steel must you melt together to create steel that matches NASA’s requirements?
Answer:
[tex]361\dfrac{1}{9}[/tex] tons of high steel and [tex]138\dfrac{8}{9}[/tex] tons of low steel
Step-by-step explanation:
Let x be the number of tons of high grade steel and y be the number of tons ow low grade steel needed.
In x tons of high grade steel there are
[tex]0.85x[/tex] tons of iron
[tex]0.15x[/tex] tons of magnese
In y tons of low grade steel there are
[tex]0.67y[/tex] tons of iron
[tex]0.33y[/tex] tons of magnese
NASA orders 500 tons of steel, so
[tex]x+y=500[/tex]
and specifies that it must be in the proportion 80% iron and 20% magnese, so
[tex]0.85x+0.67y=500\cdot 0.8\\ \\0.85x+0.67y=400[/tex]
From the first equation,
[tex]x=500-y[/tex]
Substitute it into the second equation:
[tex]0.85(500-y)+0.67y=400\\ \\425-0.85y+0.67y=400\\ \\-0.18y=-25\\ \\y=\dfrac{2,500}{18}=138\dfrac{8}{9}\ tons\\ \\x=361\dfrac{1}{9}\ tons[/tex]
122.55 is 47 1/2 of what number???
Answer:
2.58
Step-by-step explanation:
47 1/2=95/2
122.55/(95/2)=(122.55/1)(2/95)=245.1/95=2.58
A wooden block immersed partially into water. There were 15% of the total volume of the block
exposed and 85% of the total volume immersed in water. Calculate a. the density of the wooden block
Density of wooden block is 850 kilogram per cubic meter
Solution:
Given that wooden block immersed partially into water
There were 15% of the total volume of the block exposed and 85% of the total volume immersed in water
To find: density of the wooden block
The upward force exerted by any fluid upon a body placed in it is called buoyant force
Buoyant force is balanced by weight force of block
Buoyant force is weight of water displaced by block
Buoyant force = [tex]\rho_{w} V_{2} g[/tex]
Density of water = [tex]\rho_w[/tex] = 1000 kg/m3
[tex]V_2[/tex] = volume of block in water = 0.85 V
[tex]V_1[/tex] = Volume of block in air = 0.15 V
Weight of block = [tex]\rho V g[/tex]
Therefore,
[tex]\rho V g = \rho_{w} V_{2} g\\\\\rho V = \rho_{w} V_{2}\\\\ \rho V = 1000 \times 0.85V\\\\\rho = 1000 \times 0.85\\\\\rho = 850[/tex]
Thus density of wooden block is 850 kilogram per cubic meter
Describe how to interpret the solution of the system of
equations to solve a problem.
Graphing is a very useful tool to solve a system of equations but the only major disadvantage is that it is very time-consuming. So, we can solve the system of equations quickly by isolation one variable in one equation and then we get the answer by substituting the resulting expression for the variable in the other equation.
Step-by-step explanation :
Step 1:
Consider the system of equations:
5x + y =13
3x=15 - 3y
Step 2 :
y is the easiest variable to isolate in the first equation, because it has no coefficient:
y = 13 - 5x
Step 3 :
In the second equation, substituting for y :
3x = 15 - 3(13 - 5x)
Step 4 :
Solve the equation:
3x = 15 - 39 + 15x
3x = 15x - 24
-12x = - 24
x = 2
substituting this x-value into the "isolated equation" to find y:
y = 13 - 5x = 13 - 5(2) = 13 - 10 = 3
The solution to the system is (2, 3). This point is used to check for solutions in both equations.
Interpreting the solution of a system of equations involves determining the type of solution (unique, infinitely many, or no solution) and understanding how it relates to the problem being solved. It allows us to find the specific values for the variables that satisfy all the equations and provides insights into the relationships between the variables.
Interpreting the solution of a system of equations is a crucial step in solving a problem. It allows us to understand the relationship between the variables and determine the values that satisfy all the equations in the system. Here's how you can interpret the solution:
1. Determine the type of solution: A system of equations can have three types of solutions: a unique solution, infinitely many solutions, or no solution. To determine the type of solution, solve the system of equations using methods such as substitution, elimination, or matrices.
2. Unique solution: If the system of equations has a unique solution, it means that there is only one set of values for the variables that satisfies all the equations. This solution represents the point where all the equations intersect. In practical terms, this means that there is a specific answer to the problem being solved.
3. Infinitely many solutions: If the system of equations has infinitely many solutions, it means that there are multiple sets of values for the variables that satisfy all the equations. This usually occurs when the equations represent the same line or planes that overlap. In practical terms, this may indicate that there are multiple valid solutions to the problem.
4. No solution: If the system of equations has no solution, it means that there are no values for the variables that satisfy all the equations simultaneously. This usually occurs when the equations represent parallel lines or planes that do not intersect. In practical terms, this may indicate that the problem being solved is not feasible or does not have a valid solution.
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Janice has a summer job giving tours at the zoo. she earns 62.50 for 5 hours a day. she is trying to earn 500 by the end of the summer. how many tours will she need to give the zoo? (I need unit rate per tour and how many she needs)
Janice earns $12.50 per hour. If her tours last 1 hour each, that's also her rate per tour. She needs to give 40 tours to reach her goal of $500.
Explanation:First, we need to find out how much Janice earns per hour. She earns $62.50 for 5 hours of work, so we divide $62.50 by 5 to find her hourly rate. This gives us $12.50 per hour. If Janice's goal is to earn $500 by the end of the summer, we divide $500 by her hourly rate of $12.50 to find out how many hours she needs to work. This equals 40 hours total.
However, to fully answer this question, we also need to know the duration of a single tour. Without knowing how long each tour lasts, it's impossible to calculate how many tours Janice needs to give. Let's imagine each tour lasts 1 hour for simplicity. In that case, Janice would need to give 40 tours to reach her goal of $500.
So, Janice's unit rate per tour (assuming each tour is 1 hour long) is $12.50, and she needs to give 40 tours to reach her summer earnings goal of $500.
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Carter lives on a street where all the house numbers are a multiple of 6. Name two house numbers between 601 and 650
Answer:
606 and 612
Step-by-step explanation:
A number is a multiple of 6 if:
1. the sum of its integers can be divided by 3
2. The number is even (ending in 0, 2, 4, 6, 8
With this rule in mind, you have to play around with the numbers. Of course, all odd numbers are out.
606:
6 is even
6 + 6 = 12
12 divided by 4 is 3
612:
2 is even
6 + 1 + 2= 9
9 divided by 3 is 3
Step-by-step explanation:Given that Carter lives on a street where all the house numbers are multiples of 6. We are given to name any two possible house numbers between 601 and 650.The numbers lying between 601 and 650 are602, 603, 604, 605, . . . ,648, 649.And the numbers among these which are multiples of 6 are606, 612, 618, 624, 630, 636, 642, 648.So, any two of these eight numbers can be possible.Thus, the numbers are 606 and 650.
What is the degree of 24x?
Answer:
5
Step-by-step explanation:
Find all the zeros of F(x)= 4x^4-4x^3-11x^2+6x+9 given that -1 is a zero with a multiplicity of 2
Answer:
The zeros are:
[tex]x=-1,\:x=\frac{3}{2}[/tex]
Step-by-step explanation:
As the function is given by
[tex]F(x)=4x^4-4x^3-11x^2+6x+9[/tex]
We have to find the zeros of [tex]4x^4-4x^3-11x^2+6x+9[/tex].
So,
[tex]4x^4-4x^3-11x^2+6x+9=0[/tex]
Factor left side of equation.
[tex]\left(x+1\right)^2\left(2x-3\right)^2=0[/tex]
[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]Solving\:x+1=0[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]
[tex]x+1-1=0-1[/tex]
[tex]x=-1[/tex]
[tex]Solving\:2x-3=0[/tex]
[tex]x=\frac{3}{2}[/tex]
So, the zeros are:
[tex]x=-1,\:x=\frac{3}{2}[/tex]
Keywords: zeros, equation
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Asa saves dimes and quarters so that he will have exact change for he bus. He dabs and then dumps the container that he has been using for collecting his coins and finds he has 47 coins that are worth $9.50. How many of each coin does he have?
Asa has 15 dimes and 32 quarters.
Step-by-step explanation:
Given,
Total coins = 47
Worth of coins = $9.50 = 9.50*100 = 950 cents
1 dime = 10 cents
1 quarter = 25 cents
Let,
Number of dimes = x
Number of quarters = y
According to given statement;
x+y=47 Eqn 1
10x+25y=950 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=47)\\10x+10y=470\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](10x+25y)-(10x+10y)=950-470\\10x+25y-10x-10y=480\\15y=480[/tex]
Dividing both sides by 15
[tex]\frac{15y}{15}=\frac{480}{15}\\y=32[/tex]
Putting y=32 in Eqn 1
[tex]x+32=47\\x=47-32\\x=15[/tex]
Asa has 15 dimes and 32 quarters.
Keywords: linear equation, elimination method
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The question involves setting up and solving a system of linear equations based on the total number and value of the coins. It's a high school level mathematics question about algebra.
Explanation:The subject of this question falls into the field of Mathematics, specifically algebra. We need to find the number of dimes (let's denote it as D) and quarters (Q) Asa has saved, knowing their total amount and value. We can set up a system of equations based on the information provided:
The total number of coins (dimes and quarters) is 47, so we can create an equation: D + Q = 47. The total value of all coins is $9.50, but to simplify the equation we will use cents instead of dollars: 10D + 25Q = 950.
Solving this system of equations will give us the precise numbers of each coin that Asa has saved.
Learn more about Solving System of Equations here:https://brainly.com/question/29050831
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Determine if lines JK and LM are parallel, perpendicular, or neither.
J(1,9), K(7,4), L(8,13), M(-2,1)
A. Parallel
B. Perpendicular
C. Neither
Determine if the lines are parallel, perpendicular, or neither.
4x +5y = 10 and 5x -4y =28
Hint: Solve for y
A. Parallel
B. Perpendicular
C. Neither
Answer:
the first one is "perpendicular"
the second one is also "perpendicular"
Step-by-step explanation:
Answer:
1. Perpendicular; 2, perpendicular
Step-by-step explanation:
1. Segments JK and LM
(a) Calculate the slopes of the segments
(i) Segment JK
[tex]m_{1} = \dfrac{4 - 9 }{7 - 1} = -\dfrac{5}{6}[/tex]
(ii) Segment LM
[tex]m_{2} = \dfrac{13 - 1 }{8 - (-2)} = \dfrac{12}{8 + 2} = \dfrac{12}{10 } = \dfrac{6}{5}[/tex]
(b) Compare their slopes
[tex]m_{2} =\dfrac{6}{5} = -\dfrac{1}{m_{1}}[/tex]
The two segments are perpendicular.
Their graphs are shown in Figure 1.
2. Equations
(a) Calculate the slopes of the segments
(i) First equation
4x + 5y = 10
5y = 10 - 4x
y = 2 - ⅘x
m₁ = -⅘
(ii) Second equation
5x - 4y = -28
-4y = -28 - 5x
y = 7 + ⁵/₄x
m₂ = ⁵/₄
(b) Compare the slopes
m₂ = ⁵/₄ = -1/m₁
[tex]m_{2} =\dfrac{5}{4} = -\dfrac{1}{m_{1}}[/tex]
The two lines are perpendicular.
The graphs are shown in Figure 2.
b. When she is done exploring the reef, she ascends at a rate of 5 feet per minute. Once she reaches
a height of -30 feet, she must rest for 15 minutes to allow her body to adapt to the changing water
pressure. She then continues to the surface at the same rate. How long will it take the diver to reach
the surface?
Answer:
6 minutes.
Step-by-step explanation:
She ascends at a rate of 5 feet per minute from the reef.
Once she reaches a height of -30 feet, she must rest for 15 minutes and she then continues to the surface at the same rate.
So, she dives from - 30 feet height to water surface i.e. 0 feet height with a rate of 5 feet per minute.
Therefore, she will take [tex]\frac{30}{5} = 6[/tex] minutes to reach the surface.
(Answer)
Answer:
6 min
Step-by-step explanation:
Which relationship between x and y in the equation shows a proportional relationship?
A. y = 4x + 2
B. y = 8x
C. y = x - 2
D. y = x/2 + 2
Answer:
B. [tex]y=8x[/tex]
Step-by-step explanation:
A proportional relationship in 'x' and 'y' is given as:
[tex]y=kx[/tex]
Where, 'k' is called as the constant of proportionality.
So, the graph of a proportional relationship always crosses the origin.
This means that the 'x' and 'y' intercepts of a proportional relationship is always at the origin (0, 0).
From among all the options, the option that matches the definition of a proportional relationship is option B. [tex]y=8x[/tex]
Here, [tex]k=8[/tex].
Therefore, the correct option is option B.
find the sum of first 51term of an AP whose second and third term are 14 and 18 respectively
Answer:
Step-by-step explanation:
a₂ = 14
a₃ = 18
d = a₃ -a₂ = 18 - 14 = 4
a₁ = 14 - 4 = 10
nth term = a + (n-1)d
a₅₁ = 10 + 50 * 4
= 10 + 200
= 210
Everyone in a class of 35 students takes math and history. 8 students received an A in history, 15 received an A in math and 3 received an A in both courses. How many students did not receive an A in either course?
Answer:
15Step-by-step explanation:
When you add the numbers of students with A's in history and math, you get 8+15 = 23. However, this counts the 3 kids who got A's in both subject two times! So, there are 23-3=20 (20 students) different students who got an A in at least one of the courses. That gives us 35-20=15 who didn't get an A in either.
So, the answer is 15!!
Hope this helped, have a great day! :D
ignore my working out
Can someone help me and explain the answer please
Answer:
A = (90°, 1)
B = (270°,-1)
Step-by-step explanation:
if we don't use a calculator, we can explain by reasoning.
Observation 1:
recall y=sin x and y=cos x take values between -1 ≤ y ≤ 1, hence we know that the largest possible value for both functions is 1 and the smallest possible value is -1.
Observation 2:
we also know that both sin and cos functions are cyclic, which means that at some point, the function repeats itself every 360 degrees.
in question 1, we see that point A is located at the top most part of the curve, by observation 1, we can conclude that the y-value must be the maximum value of 1.
We also see that point A is 1/4 of the distance between the starting point of the curve at x=0 and to the end of the curve at x=360 before the curve begins to repeat itself,
hence the x - value is 1/4 of 360 = 90 degrees
Similarly, for point B, we see that B is at the lowest point of the curve, hence by observation 1, we can say that at B, y = -1.
B is also 3/4 of the distance between the start point and the end of the curve before it repeats itself,
hence the x-value of B is 3/4 x 360 = 270 degrees
Which number completes the square? x2 − 4x + _____
Answer:
[tex]x^2-4x+4[/tex]
Step-by-step explanation:
In order to complete the square, we need to half b and then square it. This allows us to find c.
In this case, the coefficient of x is b and the unknown term is c
From this, we can see that b = -4
First, we need to half it
[tex]-\frac{4}{2} \\\\-2[/tex]
Next we need to square it
[tex](-2)^2\\\\4[/tex]
This gives us our answer of 4.
To complete the square, we want to form a perfect square trinomial from the given quadratic expression, x^2 - 4x + _____.
A perfect square trinomial is an expression that can be factored into (x - p)^2, which when expanded, is x^2 - 2px + p^2.
This means we're looking for a value that will allow us to write our given expression in the form of (x - p)^2 where -2p will be the coefficient of x, which in our case is -4.
Now, go through the steps to find the value needed to complete the square:
1. We start with the coefficient of x, which is -4.
2. To find p, we divide this coefficient by 2: -4 / 2 = -2.
3. Finally, we square this result to find the number that completes the square: (-2)^2 = 4.
Therefore, the number needed to complete the square in the expression x^2 - 4x + _____ is 4.
When you add 4, the expression becomes x^2 - 4x + 4, which is equivalent to (x - 2)^2, thus completing the square.