Answer: (x + 1 )(x+5)
Step-by-step explanation:
Given :
[tex]x^{2}[/tex] + 6x + 5
Compare with the general quadratic equation:
a[tex]x^{2}[/tex] + bx + c
To factorize , you are to find two numbers that multiply to give ac , and add to give b.
After which you will re - write the middle number with those numbers.
From the given question , ac = 5[tex]x^{2}[/tex] , we are to find two numbers that will multiply to give 5[tex]x^{2}[/tex] and add to give 6x.
The numbers are 1x and 5x.
We will then replace the middle number by the two numbers , that is
[tex]x^{2}[/tex] + x + 5x + 5
x(x+1) +5( x +1)
(x+1)(x+5)
7: Maribel blinks her eyes 105 times in 5 minutes. If b represents the number of times Maribel blinks in m minutes, what is a linear equation that represents this situation? Assume that Maribel blinks her eyes at a constant rate
Answer:
Step-by-step explanation:
105/5= 21
21m=b
feel free to ask any question
[tex]\[b = 21m\][/tex] This equation indicates that the number of blinks [tex]\( b \)[/tex] is equal to [tex]21[/tex]times the number of minutes [tex]\( m \)[/tex]
To find a linear equation that represents the number of times Maribel blinks in a given number of minutes, we can use the information provided and assume a constant rate of blinking.
Given:
Maribel blinks [tex]105[/tex] times in [tex]5[/tex] minutes.
To find the rate of blinking per minute, we divide the total number of blinks by the total number of minutes:
[tex]\[\text{Rate of blinking} = \frac{105 \text{ blinks}}{5 \text{ minutes}} = 21 \text{ blinks per minute}\][/tex]
Let [tex]\( b \)[/tex] represent the number of blinks, and let [tex]\( m \)[/tex] represent the number of minutes. Since Maribel blinks at a constant rate, the relationship between [tex]\( b \)[/tex] and [tex]\( m \)[/tex] is linear and can be described by the equation:
[tex]\[b = 21m\][/tex]
Dave buys a basketball for $20 plus an 8% tax. Mel bought a football for $28 plus an 8% tax. Enter the difference that Dave and Mel paid, including tax. Round your answer to the nearest cent.
Answer:
Dave:
$20 + 8% of 20 = $21.6
Dave payed a total of $21.6 for the basketball.
Mel
$28 + 8% of 28 = $30.2
Mel payed a total of $30.2 for the football.
$30.2 - $21.6 = $8.6
The difference is $8.6.
One woman is able to buy 5 hat and 4 pairs of mittens for $30 another woman purchase 5 pairs ovens and 2 hats for 19 what are the prices
Answer:
The cost of 1 hat = $2.24
The coat of 1 pair of oven mitten = $2.06
Step-by-step explanation:
Let us assume the cost of 1 hat = $ x
The cost of 1 pair of oven mitten = $y
Case 1: 5 hat and 4 pairs of mittens for $30
Cost of 5 hats =5 x ( cost of 1 hat) = 5 x = $ (5 x)
Cost of 4 mittens =4 x ( cost of 1 mittens) = 4 (y) = $ (4 y)
Total cost of 5 hats + 4 mittens = 5x + 4 y
⇒ 5 x + 4 y = $30 ....... (1)
Case 2: 2 hat and 5 pairs of mittens for $30
Cost of 2 hats =2 x ( cost of 1 hat) = 2 x = $ (2 x)
Cost of 5 mittens =5 x ( cost of 1 mittens) = 5 (y) = $ (5 y)
Total cost of 2 hats + 5 mittens = 2 x + 5 y
⇒2 x + 5 y = $19 ....... (2)
Now, solving (1) and (2) , we get:
5 x + 4 y = $30 (multiply by -2)
2 x + 5 y = $19 (multiply by 5)
Add both equations, we get:
-10 x - 8 y + 10 x + 25 y = -60 + 95
or, 17 y = 35
or, y = 35/17 = 2.05
or, y = $2.06
Now, 5 x + 4y = 30
⇒ 5 x + 4 (2.06) = 30
or, 5 x = 30 - 8.24 = 21.76
so, x = 21.76/5 = 2.24
or, x = $2.24
Hence, the cost of 1 hat = $2.24
And the coat of 1 pair of oven mitten = $2.06
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.
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.
Multiply.
24.41
x 2.2
explain how u did it
________
Answer:
53.702
Step-by-step explanation:
You split the two numbers into two.
24, 0.41, 2, and 0,2
Then multiply each one by each other
2 x 24
2 x 0.41
0.2 x 24
0.2 x 24
24 x 2
24 x 0.2
0.41 x 2
then add all of them together and you get your answer
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%
solve q=r/2 (s+t) for t
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
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.
How many times does 6 go into 24?
Answer:
4
Step-by-step explanation:
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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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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Write an equation for the line that
passes through the point (5, -4) and
is parallel to the line y = 2x + 3.
Answer:
y = 2x - 14
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 = 2x + 3 ← is in slope- intercept form
with slope m = 2
Parallel lines have equal slopes, thus
y = 2x + c ← is the partial equation
To fid c substitute (5, - 4) into the partial equation
- 4 = 10 + c ⇒ c = - 4 - 10 = - 14
y = 2x - 14 ← equation of parallel line
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
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]
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
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.
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.
What is the degree of 24x?
Answer:
5
Step-by-step explanation:
Find the distance between these points.
A (5,8), B(-3, 4)
AB =
Answer:
8.9 thats rounded if it wasnt rounded it'll be 8.944
Step-by-step explanation
AB = 14.42
If you plot these points on a graph, they will not be in a straight line, so we'll need to do a little more math here. Draw a diagonal line connecting both points, and use this line as the hypotenuse, so you can draw a right triangle. Count the lengths of each side (except the long, diagonal line called the hypotenuse). Use the equation a^2 + b^2 = c^2 to find the length of side c.
Since side a is 8 units long, square it to get 64.
And side b is 12 units long, and if we square it we get 144.
64 + 144 = 208.
One last step. Now we need to find the square root of 208.
It is 14.42.
So, the distance between points a and b is 14.42 units.
what is 2 divide by 36
Answer:
0.0555555556
Step-by-step explanation:
Answer:
1/18 or 0.055...
Step-by-step explanation:
2/36=1/18
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
PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!! EXTRA POINTS!!!
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.
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.
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]
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
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
Learn more about elimination method at:
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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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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