Use algebra tiles to model and solve x+5=3x-1
Answers
x - 3x = -1 -5
-2x = -6
2x = 6
x= 6÷ 2
x = 3
Whatever blocks you have on both sides you can cancel. So we cancel one [tex]x[/tex]-block, and to take away the [tex]-1[/tex]-block, we balance the equation by putting a [tex]+1[/tex]-block on the other side. We are left with 2 [tex]x[/tex]-blocks equal to 6 [tex]+1[/tex]-blocks. This is equivalent to 1 [tex]x[/tex]-bock equal to 3 [tex]+1[/tex] blocks, so [tex]x=3[/tex].
Algebraically, you can write
[tex]x+5=3x-1 \\ 5=2x-1 \\ 6=2x \\ x=3[/tex].
I personally find the latter approach much easier, but I think the tiles are a nice way to conceptualize what you're doing.
Related Questions
how do you compare y intercepts and rates of change
Answers
87.5% of what number is 49?
Answers
87.5%*y=49
.875y=49
____ ___
.875 .875
divide both sides by .875
y=56
Owen settled on a price of $7,870 for a new car. The dealer had to add 4.5% sales tax to this price, but allowed a $1,200 trade-in for Owen's old car. Although not a universal practice, please add the sales tax to the price of the new car first and then deduct the trade- in value. If the dealer required a 15% down payment, calculate the amount of the purchase price that Owen financed.
Answers
To find the amount that Owen financed, we first calculate the sales tax, add it to the initial price, deduct the trade-in value, and then calculate the percent of the final price that Owen needs to finance.
Explanation:To solve the problem, we first need to calculate the total cost of the car by adding the sales tax to the original price. Sales tax is calculated as follows: $7,870 * 4.5/100 = $354.15. So, the total cost before the trade-in is $7,870 + $354.15 = $8,224.15.
Next, we deduct the trade-in value of the old car, which is $1,200. The price after trade-in is, therefore, $8,224.15 - $1,200 = $7,024.15.
Finally, the dealer requires a 15% down payment. The amount Owen needs to finance is therefore 85% of the final price (100% - 15% = 85%). The financed amount is: $7,024.15 * 85/100 = $5,970.53.
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The cost of 3 pounds of grapes is $6.57 what is the constant of proportionality that relates that cost in dollars,y,to the number of pounds of grapes,x?
Answers
for one pound of grapes it would cost $2.19,
for two pounds of grapes it would be $4.38,
and for three pounds of grapes would be $6.57.
Using the given points, determine the slope. (5,-6)and(2,15)
Answers
Subtract the x-coordinates in the same order. This is the run.
Slope = rise/run.
Subtract the y-coordinates: -6 - 15 = -21. rise = -21
Subtract the x-coordinates in the same order:5 - 2 = 3. run = 3
slope = rise/run = -21/3 = -7
ax+z=aw-y solve for a
Answers
I need help for 2, 4,7 and 9 !! SOLVE FOR X !!! Thank you
Answers
Lorenzo plans to purchase three identical shirts. The shirts are on sale for 20% off. Let c represent the cost of each shirt. Which expressions can Lorenzo use to calculate his total cost for the three shirts after the discount?
Select each correct answer.
A. 0.80(3c)
B. 3c−0.20(3c)
C. 3(c−0.20c)
D. 1.20(3c)
please help
Answers
B. 2c-0.20(3c)
C. 3(c-0.20c)
I'm 100% sure that these are the answers. ♡
Answer:
Options A, B and C are correct choices.
Step-by-step explanation:
Let c represent the cost of each shirt.
As Lorenzo bought 3 shirts, so the cost of 3 shirts will be 3c.
We have been given that the shirts are on sale for 20% off, so the total cost of three shirts after discount will be 3c minus 20% of 3c.
We can represent this information in an equation as:
[tex]\text{Total cost for the three shirts after the discount}=3c-(\frac{20}{100}\times 3c)[/tex]
[tex]\text{Total cost for the three shirts after the discount}=3c-(0.20\times 3c)[/tex]
[tex]\text{Total cost for the three shirts after the discount}=3c-0.60c[/tex]
[tex]\text{Total cost for the three shirts after the discount}=2.40c[/tex]
Let us see our given choices one by one.
A. 0.80(3c)
Upon simplifying our given expression we will get,
[tex]0.80(3c)=2.40c[/tex]
Therefore, option A is a correct choice.
B. 3c−0.20(3c)
We have already seen that total cost of 3 shirts after discount will be 3c minus 20% of 3c and after simplifying our expression we will get,
[tex]3c-0.20(3c)=3c-0.60c=2.40c[/tex]
Therefore, option B is a correct choice as well.
C. 3(c−0.20c)
Upon simplifying our given expression we will get,
[tex]3(c-0.20c)=3c-0.60c=2.40c[/tex]
Therefore, option C is a correct choice as well.
D. 1.20(3c)
Upon simplifying our given expression we will get,
[tex]1.20(3c)=3.60c[/tex]
Since total cost of 3 shirts after discount is 2.40c, therefore, option D is not a correct choice.
Lee baked 50 cookies. He gave some to a friend and ate 50% of the remaining cookies. He had 15 cookies left. What percentage of the cookies did he give to his friend?
Answers
He ate 50% of the remaining cookies.
He had 15 cookies left
15 = 50% so 30 = 100%
He had 30 left after giving cookies to his friend.
50 - 30 = 20
He gave 20 cookies to his friend.
20 is 40% of the total amount of cookies.
He gave his friend 40% of the cookies
Find the missing value to the nearest hundredth of a degree. Help!!
Answers
cos(alfa)=0.2546
arc cos (0.2546)=75.2501---------- > 75.25°
the answer is 75.25°
Answer:
The answer above for question 7 is also correct its B. 30 degrees. Because that anser is hard to find on here.
Step-by-step explanation:
Using the variables 'x' and 'y', write an equation for the situation. Your school sold adult and student tickets for a high school play. They sold a total of 782 tickets.
Answers
Is there any other info given or no?
Step 1: Assign variable for the unknown that we need to find
Let ' x ' be the number of adult tickets
and Let ' y ' be the number of student tickets
Step 2: Use the given sentence to write an equation.
Sentence: "Your school sold adult and student tickets for a high school play. They sold a total of 782 tickets."
[tex] Number \; of\; adult\; tickets + \; Number \; of\; student\; tickets\; =\; Total\; number\; of\; tickets\\ \\ x + y = 782 [/tex]
Which of the sets of ordered data represents this box-and-whisker plot?
65, 65, 70, 75, 80, 80, 85, 90, 95, 100
65, 70, 75, 80, 80, 85, 90, 95, 100
65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100
65, 70, 75, 80, 85, 90, 95, 100
Answers
the calculated five-number summaries with the given box-and-whisker plot, the set of ordered data that matches the plot is: 65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100
To determine which set of ordered data represents a given box-and-whisker plot, we need to understand how a box-and-whisker plot is constructed.
A box-and-whisker plot shows the distribution of a dataset by displaying the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Here's how these values are calculated:
1. Arrange the data in ascending order.
2. Find the median (Q2), which is the middle value of the dataset.
3. Find the first quartile (Q1), which is the median of the lower half of the dataset (excluding the median itself).
4. Find the third quartile (Q3), which is the median of the upper half of the dataset (excluding the median itself).
5. Determine the minimum and maximum values.
Let's calculate the five-number summary for each set of ordered data:
1. For the dataset: 65, 65, 70, 75, 80, 80, 85, 90, 95, 100
- Minimum: 65
- Q1: 70
- Median: 80
- Q3: 90
- Maximum: 100
2. For the dataset: 65, 70, 75, 80, 80, 85, 90, 95, 100
- Minimum: 65
- Q1: 75
- Median: 80
- Q3: 90
- Maximum: 100
3. For the dataset: 65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100
- Minimum: 65
- Q1: 70
- Median: 77.5 (average of 75 and 80)
- Q3: 85
- Maximum: 100
4. For the dataset: 65, 70, 75, 80, 85, 90, 95, 100
- Minimum: 65
- Q1: 72.5 (average of 70 and 75)
- Median: 82.5 (average of 80 and 85)
- Q3: 92.5 (average of 90 and 95)
- Maximum: 100
Comparing the calculated five-number summaries with the given box-and-whisker plot, the set of ordered data that matches the plot is: 65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100.
Which trinomials are perfect square trinomials? Select each correct answer.
A) m^2+10m+100
B) m^2+10m+25
C) m^2+24m+144
D) m^2+36m+60
Answers
[tex](a+b)^2[/tex]
the expansion is
[tex]a^2+2ab+b^2[/tex]
so if we say that a=m then
[tex](m+b)^2=m^2+2mb+b^2[/tex]
basically, if you take the coefient (number part) of the 2mb term and divide it by 2 and square it, you should get the last term
(coefient is the number part, like in 4m, 4 is the coefient)
A.
[tex]m^2+10m+100[/tex]
10m is the 2mb term
10 is the coefient, 10/2=5, 5^2=25, 25≠100, so not a perfect square trinomial
B.
[tex]m^2+10m+25[/tex]
as from before, 10 is coefient, 10/2=5, 5^2=25, 25=25, yep, this is perfect square trinomial
C.
[tex]m^2+24m+144[/tex]
24m is the 2mb term, 24 is coefient, 24/2=12, 12^2=144, 144=144, yep this is a perfect square trinomail
D.
[tex]m^2+36m+60[/tex]
36m is the 2mb term, 36 is the coefient, 36/2=18, 18^2=324, 324≠60, so not a perfect square trinomial
answers are B and C
What is the area of this circle
Answers
[tex]\pi \times {r}^{2} [/tex]
We can follow this formula to find the area of a circle.
Area of the circle:
153.94
(Approximate)
7in*7in=49square in
than multiply by pi
hope this helps
what is the length of line segment ab
Answers
Distance Formula:
√((x₂ - x₁)² + (y₂ - y₁))
√((5 - 0)² + (0 - 12)²) = 13
Answer:
The length of line segment is 13 units
Step-by-step explanation:
Given the line segment AB.
we have to find the length of line segment.
The coordinates of A and B are (0, 12) and (5, 0) respectively.
By distance formula,
[tex]\text{The distance between the points }A(x_1,y_1)\text{ and } B(x_2, y_2)[/tex]
[tex]AB=\sqrt{(x_2-x_1)^2+y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(5-0)^2+(0-12)^2}[/tex]
[tex]AB=\sqrt{25+144}=\sqrt{169}=13 units[/tex]
Hence, the length of line segment is 13 units.
A bird picks up a golf ball and drops it while flying 81 feet above the ground. The ball hits the top of a 32-foot-tall pine tree then bounces down to the ground. After how many seconds does the ball hit the tree?
Answers
A bird picks up a golf ball and drops it while flying 81 feet above the ground
The ball hits the top of 32 foot - tall pine tree
Now distance travelled by the ball till hitting the pine tree = 81 - 32
= 49 feet
now we have to convert feet into metre
49 feet = 14.93 metre
By applying formula s = ut + 1/2at^2
here initial velocity u = 0
And acceleration is g
therefore, 14.93 = 1/2*9.8*t^2
i.e. 14.93 = 4.9*t^2
i.e. t^2 = 14.93/4.9 = 3.047
i.e. t = 1.75 secs
Therefore ball hits the tree after 1.75 secs
Ryan made 65 ounces if apple jelly. He put the same amount of jelly into 6 jars. How much jelly is in each jar?
Answers
65 oz / 6 jars
And now we solve:
65 / 6 = 10.83 oz
The answer is: There are 10.83 oz in each jar.
A rectangular field is 0.45 kilometers long and 0.4 kilometers wide. What is the area of the field in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
Answers
area of rectangle = l * w
here l=0.45 km
w=0.4 km
area = 0.45 * 0.4 = 0.18 sq. km
Answer : Area = 0.18 km²
4 points: A,B,C and D are marked in order on a line such that AB:AC = 3:7 and BD:CD= 9:2. If CD is 100cm long, find the length of AB.
Answers
The line is in order of A-B-C-D
Both ratios share BC so we can use that to transfer from one ratio to the next.
AB =3x AC=7x
subtract them to find the measurement of BC
AC- AB = BC
7x-3x = 4x . BC = 4x
BD= 9y CD=2y
Subtract them to find the measurement of BC
BD - CD = BC
9y-2y =7y BC =7y
CD is 100cm so 2y= 100 or y=50
substitute y for bc
7(50)=350
substitute BC for terms of x
350 = 4x
divide both sides by 4
X= 87.5
Substitute for AB
AB = 3x
AB = 3(87.5) = 262.5cm
Mrs. Jackson earned a $500 bonus s for signing a one-year contract to work as a nurse. Her salary is $22 per hour. If her first weeks checks including the bonus is $1,204, how mqny hours did Mrs. Jackson work?
Answers
To find the number of hours Mrs. Jackson worked, subtract the bonus from her total earnings and divide the result by her hourly rate. Mrs. Jackson worked 32 hours.
Explanation:To find the number of hours Mrs. Jackson worked, we need to subtract the bonus from her total earnings and divide the result by her hourly rate. Let's set up an equation:
Total earnings - Bonus = Hourly rate * Number of hours worked
$1204 - $500 = $22 * ">Number of hours worked
$704 = $22 * Number of hours worked
Divide both sides of the equation by $22:
Number of hours worked = $704/$22 = 32 hours
Therefore, Mrs. Jackson worked 32 hours.
Mrs. Jackson worked 32 hours in total.
Explanation:To calculate the number of hours Mrs. Jackson worked, we need to subtract the bonus from her total earnings and then divide the result by her hourly rate.
Let's set up an equation for this:
Total earnings - Bonus = Hourly rate * Hours worked
Substituting in the given values:
1204 - 500 = 22 * Hours worked
Simplifying the equation:
704 = 22 * Hours worked
Dividing both sides by 22 gives:
Hours worked = 704 / 22 = 32
Therefore, Mrs. Jackson worked 32 hours in total.
112=7x+7(-4x-17)
So i need help with this and a worksheet that relates to these types of problems i got a 10% on it please helpppp
Answers
multiply the 7 by everything in parentheses
112=7x+(7*-4x)+(7*-17)
Positive multiplied by a negative is negative
112=7x-28x-119
combine like terms
112= -21x-119
add 119 to both sides
231= -21x
divide both sides by -21
-11= x
Check:
Substitute answer in equation
112= 7x + 7(-4x-17)
112= 7(-11)+7[(-4)(-11)-17]
112= -77 + 7(44-17)
112= -77 + 7(27)
112= -77 + 189
112=112
Hope this helps! :) Good luck with math!!
A piece of wood is 3/4 meter long is being cut into smaller pieces that are each 1/10 meter long. Which expression is one of the steps in determining how many pieces can be cut?
A. 3/4 • 1/10
B. 3/4 • 10/1
C. 10/1 • 4/3
D. 1/10 • 3/4
Answers
The expression that is one of the steps in determining how many pieces can be cut is B. 3/4 • 10/1
how to find the height of a cylinder knowing the volume
Answers
The formula for volume of a cylinder is:
V = pi × r^2 × h
You'll do the opposite to find the height:
H = V ÷ pi × r^2
As you can see, you need the volume and the radius to find the height.
11 + 5 + 22 × 12 − 10
Answers
22 x 12 = 264
11 + 5 = 16
264 + 16 = 280
280 - 10 = 270
270 is your answer
hope this helps
Which civilization was known to use geometry to construct canals for the transportation of water?
A.
Greeks
B.
Egyptians
C.
Maya
D.
Babylonians
Answers
how many minutes are in the time interval from 7:09 a.m. to 10:36 a.m.
Answers
In-between these two times, there are 3 hours and 27 minutes.
This calculates to 207 minutes.
The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?
Answers
HELP
How many pieces 3/7 of a foot each can I make out of 7/2 feet of rope?
Answers
Bill is shopping for folder, notebook, and pencils for the first day of school. a notebook costs 4 times as much as a folder. a notebook costs 2 times as much as a set of pencils. each folder costs $ 2 . determine the costs for 1 folder, 1 notebook, and 1 set of pencils.
Answers
Amir is operating a machine that adds sand to a concrete mixture. The machine adds 1/10 ton of sand to the mixture in 4/5 minute. Enter a number in each box to complete the statements. Write the ratio that compares 1/10 ton of sand to 4/5 minute. The ratio in ton(s) per minute(s) is $$ . Simplify the ratio to find the amount of sand added in one minute. ton(s) per minute
Answers
for the above question, we can first convert the fractions to decimals to make it easier to work with
1/10 of sand - 0.1 ton
4/5 minute - 0.8 minute
Q1 -
ratio
0.1:0.8
since the ratio is in decimals we can convert it to whole numbers by multiplying by 10
1:8
Q2. amount of sand added in 0.8 minutes - 0.1 ton
amount of sand added in 1 minute - 0.1/0.8 = 0.125 tons