Answer: 26
Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.
Consecutive even numbers can be represented as x, x + 2, and x + 4.
Since the sum of these is 84, our equation reads
x + (x + 2) + (x + 4) = 84.
Simplifying on the left we get 3x + 6 = 84.
Subtract 6 from both sides and we have 3x = 78.
Divide both sides by 3 and x = 26.
So our smallest number is 26.
To find the smallest of three consecutive even numbers that sum up to 84, we set up an equation and solve for 'x', where 'x', 'x+2', and 'x+4' represent the numbers. Solving this gives us the smallest number, which is 26.
Explanation:Finding the Smallest of Three Consecutive Even NumbersIf the sum of three consecutive even numbers is 84, we can find the smallest number by setting up an equation. Let's denote the smallest even number as 'x'. The next consecutive even number would be 'x + 2', and the one after that would be 'x + 4'. The sum of these three numbers should equal 84:
x + (x + 2) + (x + 4) = 84
Simplifying this equation, we get:
3x + 6 = 84
Subtracting 6 from both sides, we have:
3x = 78
Now, dividing both sides by 3 gives us:
x = 26
Therefore, the smallest of the three consecutive even numbers is 26.
Seven tenths minus one half
Answer:
7/10 - 1/2 = 7/10 - 5/10 = 2/10 = 1/5 (one fifth)
Step-by-step explanation:
A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2730 in^3, what were the original dimensions of the piece of metal?
Answer:24 oringal width
49 original length
Step-by-step explanation:
The original dimensions of the rectangular piece of metal were 30 inches by 55 inches, based on the given conditions of making an open box and its volume.
Explanation:In this problem, we have a rectangular piece of metal that is being converted into an open box. Note that the length of the rectangular piece is 25 in longer than its width.
When squares with side 5 in are cut from the corners and the sides are folded up to make the open box, the dimensions of the box formed become length = w+25-10, width = w-10, and height = 5, where w is the width of the original rectangular piece.
The volume of a box is given by the product of length, width, and height. So if the volume of this box is given as 2730 cubic inches, we can write the equation (w-10)(w+15)(5)=2730.
This can be solved to give w=30 (excluding the negative solution as unrealistic for this context). Therefore, the original dimensions of the metal piece were 30 in (width) by 55 in (length).
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What are the values of a, and r of the geometric series?
2-2+2-2+2
a = 2 and r=-2
a = -2 and r = 2
aq=-1 and r = 2
az = 2 and r=-1
Answer:
a = 2; r = -1
Step-by-step explanation:
a is the first term: 2
r is the ratio of successive terms: -2/2 = 2/-2 = -1.
Answer:
a = 2; r = -1
Step-by-step explanation:
a is the first term: 2
r is the ratio of successive terms: -2/2 = 2/-2 = -1.
Joe is going to rent a truck for one day.company A has no initial fee but charges 80 cents for every mile driven. Company B charges an initial fee of $50 and an additional 60 cents for every mile driven.for what mileage will company A charge more than company B?
Answer:
Therefore the minimum mileage for which Company A will charge more than Company B is 251 miles.
Step-by-step explanation:
i) let x be the number of miles driven
ii) If Joe rents the truck from Company A the Joe will pay Company A
= $0.8x
iii) If Joe rents the truck from Company B then Joe will pay Company B
= $50 + $0.6x
iv) the mileage for which the rents of both companies will be equal is given by
$0.8x = $50 + 0.6x
Therefore 0.2x = $50
Therefore x = [tex]\frac{50}{0.2} = \frac{500}{2} = 250[/tex] miles.
Therefore the minimum mileage for which Company A will charge more than Company B is 251 miles.
Is 120 of 100 larger than 100
Answer:
No
Step-by-step explanation:
120/100 is the same as 1 20/100 or 1 2/10. 1 2/10 is not greater than 100
Answer:
Step-by-step explanation:
nop
Find the product
729 x 82
Answer:
59,778
Step-by-step explanation:
The product of 729 and 82 is calculated through standard multiplication, resulting in a final product of 59,778.
Explanation:The student is asking to calculate the product of two numbers, 729 and 82. To find the product, we can use basic multiplication skills. Here is the step-by-step calculation:
First, set up the multiplication:
Next, multiply 2 by each digit of 729 and write the result below the line.
Then, multiply 8 by each digit of 729, remember to shift one place to the left.
Now, add both results to get the final
product
.
The final product of 729 multiplied by 82 is 59,778.
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Find 6 times as many as,2plus 9
Answer:
The answer is 21.
Step-by-step explanation:
6 * 2 = 12 + 9 = 21
Answer:
66
Step-by-step explanation:
The equation would go like this:
6(2+9)
Next you solve for parenthesis:
6(11)
Lastly multiply:
6(11)=66
Sarah has a collection of nickels, dimes, and quarters worth $9.25. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?
Answer:
See image attached.
Step-by-step explanation:
Final answer:
The initial setup for the equation based on the coin values and the total amount led to an incorrect result with a negative number of nickels. This suggests there was an error in the calculations or assumptions, and the equation should be revisited and the numbers checked to find the correct number of each type of coin.
Explanation:
Let's call the number of nickels Sarah has n. According to the problem, Sarah has 10 more dimes than nickels, which means she has n+10 dimes. It is also given that she has twice as many quarters as dimes, making it 2(n+10) quarters. In terms of their values, nickels are worth 5 cents, dimes are worth 10 cents, and quarters are worth 25 cents. The total value of Sarah’s coins is $9.25, which is equivalent to 925 cents.
To find the number of each coin, we can set up the following equation:
5n + 10(n+10) + 25(2(n+10)) = 925
Simplifying the equation:
5n + 10n + 100 + 50n + 1000 = 925
65n + 1100 = 925
65n = 925 – 1100
65n = -175
n = -175 / 65
n = -2.6923
This result is not possible since we cannot have a negative number of coins. It seems there was an error in the calculations or assumptions. It is important to check the equation and numbers we're using to ensure they properly represent the coin values and the total amount.
A dollar store sells items for $1 and $2. You plan to go there and spend at least $20. Let eggs stand for the number of one dollar items and Y stand for the number of two dollar items. Right and gravity linear any quality that models the solution.
Answer:
Step-by-step explanation:
y=5x=10
A campus apartment has two bedrooms and two attached bathrooms and rents for $1,025 per month plus an average of $60 per month for electricity. You are a student and would have the option of splitting the rent with a fellow student 60/40. You pay 40% as your name is on the lease. Your scholarship gives you $700 per month for housing. What can you save above your out of pocket housing cost with your scholarship and your roommate's contribution in an Academic Year (8 months).
I can save $2,128 in my academic year and my roommate can save $392 in their academic year.
Step-by-step explanation:
Total housing amount= rent + electricity= $1,025 + $60= $1,085 per month
My rent is 40% of $1,085 which equals $434 a month while my roommate’s rent would be 60% of $1,085 which equals $651 a month.
The scholarship gives me $700 a month for housing out of which I spend $434 and my roommate spends $651.
I save; $700 - $434 = $266 a month
My roommate saves; $700 - $651 = $49 a month.
An academic year lasts for 8 months so my savings= $266 x 8 = $2,128
My roommate’s savings= $49 x 8 = $392
Answer:
$2,128
Step-by-step explanation:
Expenses is allocated based on the decided ratios. Expenses and Inflows
Expenses will be calculated for 8 Months time period.
Rent = 1,025 x 8 months = $8,200
Electricity Expense = $60 x 8 = $480
Total Expense = $8,200 + $480 = $8,680
Total Scholarship = $700 x 8 = $5,600
Out of Pocket Cost = $8,680 x 40% = $3,472
Saving is the difference between The scholarship received and the Expenses made from pocket.
Saving = $5,600 - $3,472 = $2,128
The numbers 19 and 28 are rounded to the nearest ten and then multiplied to estimate the product. What is the best estimate of 19 × 28 based on this method?
200
300
600
900
Answer:
600
Step-by-step explanation:
you round up 19 to 20 then you round up 28 to 30 and multiply 20 and 30
Answer:
20*30
= 600
About 600
C
Montell gets $10.50 each week for doing yard work for his neighbors. He has earned $63 so far. Write and solve an equation to find how many weeks it took for him to earn that amounts.
Answer:
10.50x = 63
You'll divide 63 by 10.50 to get 6 weeks.
PLEASE HELP! WILL GIVE 70 POINTS!!
What is the surface area of the right triangular prism below?
Answer:
[tex]A=189\ mm^2[/tex]
Step-by-step explanation:
Surface Areas
Is the sum of all the lateral areas of a given solid. We need to compute the total surface area of the given prism. It has 5 sides, two of them are equal (top and bottom areas) and the rest are rectangles.
Computing the top and bottom areas. They form a right triangle whose legs are 4.5 mm and 6 mm. The area of both triangles is
[tex]\displaystyle A_t=2*\frac{b.h}{2}=b.h=(4.5)(6)=27 mm^2[/tex]
The front area is a rectangle of dimensions 7.7 mm and 9 mm, thus
[tex]A_f=b.h=(7.5)(9)=67.5 \ mm^2[/tex]
The back left area is another rectangle of 4.5 mm by 9 mm
[tex]A_l=b.h=(4.5)(9)=40.5 \ mm^2[/tex]
Finally, the back right area is a rectangle of 6 mm by 9 mm
[tex]A_r=b.h=(6)(9)=54 \ mm^2[/tex]
Thus, the total surface area of the prism is
[tex]A=A_t+A_f+A_l+A_r=27+67.5+40.5+54=189\ mm^2[/tex]
[tex]\boxed{A=189\ mm^2}[/tex]
If the entries of A + B are represented by Xij and the entries of A − B are represented by yij the value represented by x24 is and the value represented by y13 is .
Answer:
[tex]x_{24} = a_{2} +b_{4} \\y_{13} = a_{1} - b_{3}[/tex]
:)
Answer:
it -3 and 7
Step-by-step explanation:
Set up a percent ratio to help find the part given the percent and the whole. On a 50-point quiz, Jenna earned 82% of the points. How many points did she earn?
Wang Xiu Ying has
109
109109 dollars in her savings account. She has
−
21
−21minus, 21 dollars in her checking account.
Write an inequality that correctly compares the account values.
Which one of the following descriptions is correct?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Wang Xiu Ying's checking account has a lower account value than her savings account.
(Choice B)
B
Wang Xiu Ying's savings account has a lower account value than her checking account.
Answer:
109>21
Answer is A.
Step-by-step explanation:
When we read this example. We can conclude :
Saving account : $109
Checking : $21
So:
Wang Xiu Ying's checking account has a lower account value than her savings account.
Answer: 109>-21
B
Step-by-step explanation:
for what value of x is the rational expression below undefined? x-4 / 4+x a. 0 b. -4 c. -1 d. 4
Answer:
The answer is option b. -4
Step-by-step explanation:
Given: [tex]\frac{x-4}{4+x}[/tex]
the rational expression will be undefined at the zeros of the denominator
To find the zeros of the denominator
the denominator = 0
∴ 4 + x = 0
∴ x = -4
So, the rational expression will be undefined at x = -4
The answer is option b. -4
Answer:
b)
Step-by-step explanation:
[tex]\frac{x-4}{4+x}\ and\ 4+x\neq 0\ (we\ can't\ divide\ by\ 0)[/tex]
[tex]4+x\neq 0\\x\neq -4[/tex]
Your phones service plan costs $10 per month and .15 cents per minute to make a call. Write an equation that represents the cost to use your phone per month
Answer:
an equation for how much your phone costs per month=
.15x+10
The sum of 5 times a number and 4 is equal to 6
Answer:
5(x+4)=6
5 times a number and (+) 4 is equal to 6.
#14 Lia spend $4 more on
her backpack than Kiera.
Write an algebraic
expression that represents
the situation.
Answer:
x=y+4
Step-by-step explanation:
Amount spent by Lia=x
Amount spent by Kiera=y
x=y+4
Answer: [tex]k+4[/tex]
Step-by-step explanation:
You need to analize the data given in order to solve the exercise.
First, it is important to remember that, in Word problems the word "more" indicates Addition.
In this case, let "k" represents the amount of money (in dollars) that Kiera spends on her backyard.
Accordding to the information provided in the exercise, you know that Lia spends $4 dollars more on her backyard than Kiera spends on her backyard.
Therefore, you can identify that the amount of money that Lia spends can be found by adding the amount of money Kiera spends and $4.
Based on the above, you can determine that this situation can be represented with the following expression:
[tex]k+4[/tex]
A recipe for 5 batches of bagels uses 15 cups of flour. Ciro wants to know how many cups are needed for 1 batch. Johanna wants to know how many cups she will need to make 20 batches. Drag an expression to answer each question.
Expressions:
15 × 4
5 × 4
20 ÷ 5
15 ÷ 5
20 – 15
20 + 5
Any help? Sorry, I'm dumb. Free 10 points I guess?
ciro needs 3 cups of flour johanna needs 20 x 15 cups
So, I think I had this for my Imagine math, so I'll help you :D
Ciro (How many cups in 1 batch):; 15 / 5 = 15 divided by 5
Johanna (How many cups for 20 batches):; 15 x 4 = 15 multiplied by 4
I hope this helps :)
What is the slope of the line that is perpendicular to the line that passes through (-2, 7) and (4, 9)? Type a numerical answer in the space provided.
Answer:
Therefore [tex]m_{2}[/tex] = -3.
Step-by-step explanation:
i) let us say the slope of the line passing through (-2,7) and (4,9) is [tex]m_{1}[/tex].
ii) to find the slope of the line passing through two points ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) we use the formula m = [tex]\dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]. Therefore we can say that [tex]m_{1}[/tex] = [tex]\dfrac{9 - 7}{4 - (-2)}[/tex] = [tex]\dfrac{1}{3}[/tex].
iii) let us say the slope of the perpendicular line to the line passing through (-2,7) and (4,9) is [tex]m_{2}[/tex]
iv) from the formula for the slopes of a line and the line perpendicular to it which is given by [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = -1, therefore [tex]m_{2}[/tex] = -1 ÷ [tex]m_{1}[/tex] = -3. Therefore [tex]m_{2}[/tex] = -3
Choose a method to solve the following system of equations. Explain why you chose that method.
Solve.
y = 2x + 7
y = -2x - 5
I have been trying to figure it out but idk.
Answer:
The values for the two equations are x=-3 and y=1
Therefore the solution is (-3,1)
Step-by-step explanation:
Given equations are [tex]y=2x+7\hfill (1)[/tex]
[tex]y=-2x+5\hfill (2)[/tex]
To solve the given equations by Substitution method :
We are using here to solve the given equations by Substitution method because equations (1) and (2) are equivalent ( it has same solution )
Therefore we can equate the two given equations or substitute the y value equation (1) in (2) we get
2x+7=-2x-5
Subtracting with -(2x-5) on both sides we get
2x+7-(-2x-5)=-2x-5-(-2x-5)
2x+7+2x+5=-2x-5+2x+5
4x+12=0 ( adding the like terms )
4x=-12
[tex]x=-\frac{12}{4}[/tex]
Therefore x=-3
Now substitute the value x=-3 in equation (1) we get
y=2(-3)+7
y=-6+7
Therefore y=1
The values are x=-3 and y=1
The solution is (-3,1)
A new notebook computer with DVD player cost $808 Derek muller has $969 in his checking account how much will be left in his checking account after he buys the notebook computer
Answer: $161
Step-by-step explanation: Subtract $808 from $969
Answer: he will have $161 in his account after he buys the computer and dvd player.
Step-by-step explanation:
First, do 969-808 and you simply get 161 as your answer
So, for this problem you are simply subtracting
* brainliest answer this plz....
4/9 is it equivalent to 20/36
Answer: No
Step-by-step explanation: In order to decide whether the given fractions are equivalent, first write each fraction in lowest terms.
A fraction is written in lowest terms if the greatest common factor of the numerator and the denominator is 1.
So for our first fraction, 4/9, since the greatest common factor of 4 and 9 is 1, we know that are fraction is already written in lowest terms.
For our second fraction however, since the greatest common factor of 20 and 36 is 4, we must divide both the numerator and the denominator by 4 to write our fraction in lowest terms. This gives us 5/9.
Since 5/9 is bigger than 4/9, te fractions are not equivalent so no, 4/9 is not equivalent to 20/36.
What is the answer to 5% of $30
Answer: $1.50
Step-by-step explanation: To find 5% of $30, first write 5% as a decimal by moving the decimal point 2 places to the left to get .05. Next, "of $30" means times 30 so we multiply .05 times 30 which gives us 1.5.
Finally, remember that we want to write our answer in terms of dollars so 1.5 dollars is the same thing as $1.50.
So 5% of $30 is $1.50.
Factor the following trinomials:
a) x^2 -2x -1
b) x^2 -3x+1
Final answer:
To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, you can use the quadratic formula or factoring by grouping.
Explanation:
To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, we can use the quadratic formula or factoring by grouping.
a) For x^2 - 2x - 1, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac))/(2a)
Plugging in the values, we have:
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-1)))/(2(1))
x = (2 ± sqrt(4 + 4))/(2)
x = (2 ± sqrt(8))/(2)
x = (2 ± 2sqrt(2))/(2)
x = 1 ± sqrt(2)
Therefore, the factored form is: x^2 - 2x - 1 = (x - (1 + sqrt(2)))(x - (1 - sqrt(2)))
b) For x^2 - 3x + 1, we can also use the quadratic formula:
x = (3 ± sqrt(3^2 - 4(1)(1)))/(2(1))
x = (3 ± sqrt(5))/(2)
Therefore, the factored form is: x^2 - 3x + 1 = (x - (3 + sqrt(5))/(2))(x - (3 - sqrt(5))/(2))
a) x^2 - 2x - 1 = (x - 1)(x + 1)
b) x^2 - 3x + 1 = (x - 1)^2
a) x^2 - 2x - 1:
This trinomial is in the form ax^2 + bx + c. To factor it, we need to find two numbers that:
Multiply to ac (in this case, 1 * -1 = -1).
Add up to b (in this case, -2).
These two numbers are -1 and 1.
So, we can rewrite the trinomial as:
(x - 1)(x + 1)
Therefore, the factored form of x^2 - 2x - 1 is (x - 1)(x + 1).
b) x^2 - 3x + 1:
This trinomial is also in the form ax^2 + bx + c. To factor it, we need to find two numbers that:
Multiply to ac (in this case, 1 * 1 = 1).
Add up to b (in this case, -3).
These two numbers are -1 and -1.
So, we can rewrite the trinomial as:
(x - 1)(x - 1)
However, it is common practice to simplify repeated factors, so the fully factored form of x^2 - 3x + 1 is (x - 1)^2.
help please there is also another question i asked like 7 hours ago that was NEVER ANSWERED but please answer ILL MARK BRAINLIEST
Answer:
the first one would be m<EOF+m<FOB=180°,
and the second one would be 76ft
Step-by-step explanation:
supplementary angle means the angle that would make it equal 180°. if m<EOF is an acute angle then the angle that is supplementary to EOF would be obtuse, so FOB.
then for the second question, the midpoint splits the angle in HALF, so that means in order to find RT you multiply 38×2.
does 490/10 equel to 4.9
Answer:
No it equals to 49
Step-by-step explanation:
490÷10=49
Find the sum: 2 1/3+1 3/4
Answer:
2 1/3 + 1 3/4
Step-by-step explanation:
First, find a common denominator which is 12.
2 4/12 + 1 9/12
= 4 1/12 or 37/12