The solution to the inequality 2x<8 is x<4.
Step-by-step explanation:
Given inequality is;
2x < 8
For solving this inequality, we will divide both sides by 2 to find the value of x, therefore;
Dividing both sides by 2
[tex]\frac{2x}{2}<\frac{8}{2}\\x<4[/tex]
It means that x is less than four.
Thus,
The solution to the inequality 2x<8 is x<4.
Keywords: inequality, division
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Julian bought 8 books this year. He gets a free book every time he buys 1. How many books altogether did he get this year
Answer:16 books
Step-by-step explanation:
Final answer:
Julian bought 8 books and received a free book with each purchase, resulting in 16 books altogether by the end of the year.
Explanation:
The question is asking how many books Julian would have altogether if he bought 8 books and received a free book with each purchase this year. To solve this, we need to consider that for every book purchased, he gets an additional book without cost. Therefore, Julian gets 2 books each time he makes a purchase for one book. As he bought 8 books, we simply need to double that amount to account for the free books he received.
To calculate: 8 books purchased × 2 = 16 books altogether.
Julian would have a total of 16 books by the end of the year after his purchases and receiving the complementary books.
Which day had the greatest decrease in value from the previous day?
A.monday
B.tuesday
C.wensday
D.friday
Answer:
B. Tuesday
Step-by-step explanation:
It is the only decrease in price going by the graph
Answer:
Tuesday
Step-by-step explanation:
It went down by the most that day, i.e. from $3.25 to $3.00.
Other days, it did not decrease by as much.
The width of a rectangle is 4 1/6 feet, and its area is 35 square feet. What is the perimeter of this rectangle?
Answer:
25 2/15
Step-by-step explanation:
A = length x width
width is 4 1/6
35 = 4 1/6 x length
solve for length
divide both sides by 4 1/6
35 divided by 4 1/6 or multiply 35 x 6/25 (reciprocal)
210/25
8 10/25 = 8 2/5 is the length
to find perimeter 2xlength + 2xwidth
2 x 4 1/6 + 2 x 8 2/5 = 2 x 25/6 + 2 x 42/5 = 50/6 + 84/5
convert to common denominator and add
use 30 as common denominator
250/30 + 504/30= 754/30
25 4/30 or 25 2/15
Final answer:
To find the perimeter of the rectangle, calculate the length using the given area and width. Then, apply the perimeter formula P = 2l + 2w. The perimeter is approximately 25.1 feet.
Explanation:
Calculating the Perimeter of a Rectangle
To find the perimeter of a rectangle, you need to know both the width and the length of the rectangle. The perimeter is the total distance around the rectangle, which is the sum of twice the width and twice the length: P = 2l + 2w.
The width of the rectangle is given as 4 1/6 feet. To find the length, we can use the provided area of the rectangle which is 35 square feet. The area of a rectangle is found by multiplying the length by the width: A = l × w. Let's call the length 'l'.
First, convert the width to an improper fraction: 4 1/6 = (4 × 6 + 1)/6 = 25/6 feet. Now set up the equation using the area: 35 = (25/6) × l. Solving for 'l' gives us l = (35 × 6)/25 = 210/25 = 8.4 feet.
Now that we have the length, calculate the perimeter using the equation P = 2l + 2w:
P = 2 × 8.4 + 2 × 4 1/6
P = 16.8 + 2 × 25/6
P = 16.8 + 50/6
P = 16.8 + 8.333...
P = 25.133... feet
Therefore, the perimeter of the rectangle is approximately 25.1 feet when rounded to one decimal place.
To make circular cake boards, a company cuts circles out of plastic squares. The circles are cut as wide as the squares to lessen the amount of wasted material. Use the drop-down menus below to complete statements about the amount of wasted material for circular cake boards with a diameter of d.
The area of the wasted material is given by the difference:____-______
d^2
4d
π(d/2)^2
Answer:
d^2 - π(d/2)^2
Step-by-step explanation:
Since the diameter of the circle is equal to the side of a square (d), that means that we have a circle inscribed in square.
If we draw a square and inscribe a circle in it, all parts of the square outside the circle will be waste, in this particular case.
If we want to find the area of the wasted material we need to subtract the area of the circle from the area of the square.
Area of the circle is:
P1 = πr^2, r being the radius
Since radius is half the diameter, that means that:
P1 = π • (d/2)^2
Area of the square whose side is d is:
P2 = d^2
So, the area of wasted material is:
P = P2 - P1
P = d^2 - π(d/2)^2
Round 5 9/17 to the nearest whole number
Answer:
6
Step-by-step explanation:
Which of the following is the correct factorization of the trinomial below?
-7x² - 5x+18
Answer:
-1(7x-9)(x-2)
Step-by-step explanation:
Because I'm right you're wrong, I'm big, you're small, and there's nothing you can do about it!!!
which scenario best matches the linear relationship expressed in the equation y=-14+1700
1) Kent has $1,700 in his bank account and spends $14 each week.
2) Kent has $1,700 in his bank account and deposits $14 each week.
3) Kent had $1,700 in his bank account and deposited another $14.
4) Kent has $14 in his bank account and spent $1,700.
Question:
Which scenario best matches the linear relationship expressed in the equation y = –14x + 1,700?
1) Kent has $1,700 in his bank account and spends $14 each week.
2) Kent has $1,700 in his bank account and deposits $14 each week.
3) Kent had $1,700 in his bank account and deposited another $14.
4) Kent has $14 in his bank account and spent $1,700.
Answer:
Option 1) Kent has $1,700 in his bank account and spends $14 each week.
Step-by-step explanation:
Let x denote the number of weeks.
Option 1: Kent has $1,700 in his bank account and -14x as the negative sign denotes how much amount he spend each week.
Thus, Option 1 is the correct answer.
Option 2: Kent has $1,700 in his bank account and deposits $14 each week.
Writing it as equation, we have, [tex]y=14x+1700[/tex] which is not the expressed linear equation.
Hence, Option 2 is not the correct answer.
Option 3: Kent had $1,700 in his bank account and deposited another $14.
Writing it as equation, we have, [tex]y=14+1700[/tex] which is not the expressed linear equation.
Hence, Option 3 is not the correct answer.
Option 4: Kent has $14 in his bank account and spent $1,700.
Writing it as equation, we have, [tex]y=14-1700[/tex] which is not the expressed linear equation.
Hence, Option 4 is not the correct answer.
Thus, the scenario that matches the linear equation relationship expressed in the equation is Option 1.
The answer is Kent has $1,700 in his bank account and spends $14 each week.
Answer:
A
Step-by-step explanation:
All of the 4th grade teachers and students from Cambridge went on a field trip to an art museum. Tickets were $5.50 per teacher and $3.00 for each student. This group paid $29.00 in total. The next month, the same group visited a science museum where the tickets were $22.00 for teachers and $11.50 for students. The group paid $113.00 in total. Find the number of teachers and students on the field trips.
Answer:
Students= 6
Teachers= 2
Step-by-step explanation:
Given: Art museum trip:
Cost of ticket= $5.5 per teacher and $3 per student.
Total amount paid= $29.
Science trip:
Cost of ticket= $22 per teacher and $11.5 per student.
Total amount paid= $113.
Lets assume number of teacher be "x" and number of students be "y".
Now, forming an equation for cost of each trip.
we know, total cost= [tex]cost\ of \ each\ ticket \times numbers\ of\ tickets[/tex]
∴Art museum trip, [tex]5.5x+3y= 29[/tex] ---- 1st equation
Science museum trip, [tex]22x+11.5y= 113[/tex] ---- 2nd equation
Next using elimination method to find number teacher and students
[tex]5.5x+3y= 29\\22x+11.5y= 113[/tex]
Multiplying both side of 1st equation by 4
∴ [tex]22x+12y= 116\\22x+11.5y= 113[/tex]
changing sign of 2nd equation on both side and solving it.
∴ [tex]0.5y= 3[/tex]
Dividing both side by 0.5
[tex]y= \frac{3}{0.5}= 6[/tex]
Hence, number of students on field trip was 6.
Subtituting the value of y in 1st equation to find the number of teachers in field trip.
[tex]5.5x+3y= 29[/tex]
⇒ [tex]5.5x+3\times 6= 29[/tex]
⇒ [tex]5.5x+18= 29[/tex]
Subtracting both side by 18
⇒ [tex]5.5x= 11[/tex]
Dividing both side by 5.5
⇒ [tex]x= \frac{11}{5.5}= 2[/tex]
Hence, there were 2 teachers on field trips.
Julio sold candles for three weeks. Let x represent the number of candles he sold the first week. He sold twice the number of candles the second week as he did the first week. In the third week, Julio sold 4 less than the number he sold the first week. Which expression represents the total number of candles Julio sold in the three weeks?
The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.
Step-by-step explanation:
Let,
x be the number of candles sold by Julio in first week.
According to given statement;
Candles sold in first week = x
He sold twice the number of candles the second week as he did the first week.
Candles sold in second week = 2x
In the third week, Julio sold 4 less than the number he sold the first week.
Candles sold in third week = x-4
Total candles sold = First week + Second week + Third week
Total candles sold = x+2x+(x-4)
The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.
Keywords: addition, variable
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WILL MARK BRAINLIEST 25 POINTS
The graph shows f(x) and its transformation g(x) .
Enter the equation for g(x) in the box.
Answer:
g (x) = 2 ^ (x + 2)
Step-by-step explanation:
For this case the transformation of f (x) is given by
g (x) = 2 ^ (x + 2)
To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)
For (-2,1)
g (-2) = 2 ^ ( -2 + 2)
g(-2)=1
For (-1,2)
g (-1) = 2 ^ ( -1+ 2)
g(-1)=2
For (0,4)
g (0) = 2 ^ ( 0+ 2)
g(0)=4
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A medication is administered to a patient and the
concentration of the medication in the
bloodstream is monitored. At time t> 0 (in hours
since giving the medication) the concentration, in
mg/L. is modeled by the graph of the rational
function on the right. Approximately when does
the medication reach half of its highest
concentration in the patient's bloodstream?
1 hour
1 hour, 15 minutes
3 hours
3 hours, 45 minutes
The medication reach half of its highest concentration in the patient's bloodstream in 3 hours 45 minutes, the correct option is D.
What is the meaning of concentration of a solution?Concentration of a solution is the milligrams of the solvent dissolved in a liter of solution.
The graph shows the variation of the concentration of the solution with time.
The highest concentration of the medicine is 2.5 mg/L.
The half of the highest concentration is 1.25 mg/L.
The graph can be seen for the time corresponding to the concentration 1.25 mg/ L.
The time taken is 3.75 hours = 3 hours 45 minutes.
The missing diagram is attached with the answer.
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Answer:
D on Edge
Step-by-step explanation:
Just got it right.
Justin saves $8 every week. Which equation represents the amount of money Justin has,y, after x number of week?
If Justin saves $8 every week, and x represents the number of weeks, this can be set up as 8x. We are trying to find the amount of money Justin has after x weeks, so y = 8x.
Can someone please help me :) !!!!
In the diagram, PCG and CGR are supplementary, the measure of AGK =10x° and the measure of PCG=(6x100)°
Based on this information , which equation can be used to the find the value of x?
A. 6x +100 + 10x =180
B. 6x+ 100 -10x =90
C. 6x+100+10x=90
D. 10x=6x+100
Answer:
A
Step-by-step explanation:
supplementary angles add up to 180
angle cgr and kga are vertical angles so they are equal
that makes the two angles in question add up to 180
how do you estimate 175.32 ÷ 3 =
Answer:
≈ 58
Step-by-step explanation:
Estimation usually means you want an answer good to one or maybe two significant figures. That usually means you want to round the numbers involved to one or two significant figures.
Doing that here transforms the problem to 180/3 = 60, an answer with one significant figure.
You can improve the estimate a bit by recognizing that it is a little high (the numerator is higher than 175.32, but the denominator is the same). Since the numerator is high by about 5, the estimate is high by about 5/3 or a little less than 2. A closer estimate will be 60 - 2 = 58.
_____
The degree to which you refine the estimate will depend on the error requirements you have. Certainly an estimate of 60 is within 10% of the true value, so is "close enough" for many purposes.
To estimate 175.32 by 3, round 175.32 to 175, and divide by 3 to get 58. Since 175 is just under 180, which divides evenly by 3 to give 60, an estimate of 58 is reasonable.
To estimate the division of 175.32 by 3, we can round the numbers to make the calculation easier. First, we round 175.32 to 175 which is very close in value, and 3 remains as it is because it is already a whole number. So, our estimation becomes 175 / 3.
Dividing 175 by 3 gives us 58 as 3 times 58 is 174. We can see that this approximation is just 1 less than our rounded number, so it is a reasonable estimate. Therefore, 175.32 / 3 is approximately 58 when we estimate it without a calculator.
To check our estimation, we can compare it to similar, simple calculations. For example, if we divide 180 by 3, we get 60. Since 175 is slightly less than 180, our estimation of 58 is likely a good approximation for the division of 175.32 by 3.
Calculate the premiums indicated in the chart below on $30,000 policies. Don Cole is forty years old. Type of Policy Annual Premium Semiannual @ 51% Quarterly @ 26% Monthly @ 9% 10-year term $240.00 $ $ $ Whole Life $652.50 $ $ $ 20-Payment Life $945.00 $ $ $ 20-year Endowment $1,346.10 $ $ $
The premiums indicated in the chart below on $30,000 policies are $240.00, $122.40, $62.40, $21.60, $652.50, $332.775, $169.50, $58.725 , $945.00, $482.475, $245.70, $85.05, $1,346.10, $686.761, $350.286 and $121.15.
To calculate the premiums for a $30,000 policy, first, we need to find the appropriate premium amount based on the given percentages for different payment frequencies (annual, semiannual, quarterly, and monthly).
**10-year Term Policy:**
- Annual premium: $240.00
- Semiannual premium (51% of annual): $240.00 * 51% = $122.40
- Quarterly premium (26% of annual): $240.00 * 26% = $62.40
- Monthly premium (9% of annual): $240.00 * 9% = $21.60
**Whole Life Policy:**
- Annual premium: $652.50
- Semiannual premium (51% of annual): $652.50 * 51% = $332.775 (approximately $332.78)
- Quarterly premium (26% of annual): $652.50 * 26% = $169.50
- Monthly premium (9% of annual): $652.50 * 9% = $58.725 (approximately $58.73)
**20-Payment Life Policy:**
- Annual premium: $945.00
- Semiannual premium (51% of annual): $945.00 * 51% = $482.475 (approximately $482.48)
- Quarterly premium (26% of annual): $945.00 * 26% = $245.70
- Monthly premium (9% of annual): $945.00 * 9% = $85.05
**20-year Endowment Policy:**
- Annual premium: $1,346.10
- Semiannual premium (51% of annual): $1,346.10 * 51% = $686.761 (approximately $686.76)
- Quarterly premium (26% of annual): $1,346.10 * 26% = $350.286 (approximately $350.29)
- Monthly premium (9% of annual): $1,346.10 * 9% = $121.15
Please note that the semiannual, quarterly, and monthly premiums are rounded to the nearest cent.
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A piece of paper is 0.01 centimeters thick When you fold it once it becomes 0.02 cm thick. If you fold it again it doubles again to 0.04 cm thick each fold doubles thickness of the paper. how thick is the paper?
Answer: Should Be 0.01
Step-by-step explanation: It’s Asking How Thick it is and never asked when So it would automatically mean from the start therefore it’s 0.01 cm thick
The 4th term of an arithmetic sequence is 12 and the 8th term is 36. Find the 17th term of the sequence.
How do you work it out?
Answer: 90
Step-by-step explanation:
The formula for calculating the nth term of a sequence is given as :
[tex]t_{n}[/tex] = a + ( n - d )
Where a is the first term
d is the common difference and
n is the number of terms
This means that the 4th term of an arithmetic sequence will have the formula :
[tex]t_{4}[/tex] = a + 3d
And the 4th term has been given to be , 12 ,substituting into the formula we have
12 = a + 3d .............................. equation 1
Also substituting for the 8th term , we have
36 = a + 7d .............................. equation 2
Combining the two equations , we have
a + 3d = 12 ................... equation 1
a + 7d = 36 ------------ equation 2
Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is
a = 12 - 3d ................... equation 3
substitute a = 12 - 3d into equation 2 , equation 2 then becomes
12 - 3d + 7d = 36
12 + 4d = 36
subtract 12 from both sides
4d = 36 - 12
4d = 24
divide through by 4
d = 6
substitute d = 6 into equation 3 to find the value of a, we have
a = 12 - 3d
a = 12 - 3 ( 6)
a = 12 - 18
a = -6
Therefore , the 17th term of the sequence will be :
[tex]t_{17}[/tex] = a + 16d
[tex]t_{17}[/tex] = -6 + 16 (6)
[tex]t_{17}[/tex] = -6 + 96
[tex]t_{17}[/tex] = 90
Therefore : the 17th term of the sequence is 90
its was taylor's 8th birthday and there were 47 presents. Each kid brought 10 presents, except for three kids who brought five presents each and two kids who bought one present each. How many kids came to Taylor's party
Total of 8 kids came to Taylor's party.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
Given is Taylor's 8th birthday and there were 47 presents. Each kid brought 10 presents, except for three kids who brought five presents each and two kids who bought one present each.
Assume that [n] students bought 10 presents. Then, we can write -
3 x 5 + 2 x 1 + 10n = 47
15 + 2 + 10n = 47
10n = 30
n = 3
Total kids = 3 + 3 + 2 = 8
Therefore, total of 8 kids came to Taylor's party.
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The vertex of a parabola is at (8,-1)and its y-interpret is-17. Which function represents the parabola
Answer:
D
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (8, - 1), thus
y = a(x - 8)² - 1
To find a substitute (0, - 17), the coordinates of the y- intercept into the equation.
- 17 = a(0 - 8)² - 1
- 17 = 64a - 1 ( add 1 to both sides )
- 16 = 64a ( divide both sides by 64 )
a = [tex]\frac{-16}{64}[/tex] = - [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex](x - 8)² - 1 → D
A woman traveled 2445.9 miles in 18 hours five minutes what is the average speed of her flight in miles per hour
The average speed is 135.26 miles per hour
Solution:
Given that, woman traveled 2445.9 miles in 18 hours five minutes
To find: Average speed of her flight in miles per hour
Let us first convert 18 hours 5 minutes to hours
We know that,
[tex]1 \text{ minute } = \frac{1}{60} \text{ hour }[/tex]
Therefore,
[tex]5 \text{ minute } = \frac{5}{60} \text{ hour } = 0.083 \text{ hour }[/tex]
Thus we get,
18 hours five minutes = 18 hour + 0.083 hour = 18.083 hour
Given that, distance = 2445.9 miles
Average speed is given by formula:
[tex]Average\ speed = \frac{distance}{time}\\\\Average\ speed = \frac{2445.9}{18.083}\\\\Average\ speed = 135.26[/tex]
Thus average speed is 135.26 miles per hour
What’s -3 + 6k + 11k - 10 (combining like terms)
Answer:
17k + -13
Step-by-step explanation:
6k + 11k take the + next to the 6k making it say 6k+11
-3 - 10 take the - next to the 10 making it say -3 - 10
Please help ASAP! Thanks! For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
Part 1) [tex]A=36(\pi-2)\ cm^2[/tex]
Part 2) [tex]P=6(\pi+2\sqrt{2})\ cm[/tex]
Step-by-step explanation:
Part 1) Find the area
we know that
The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle
so
[tex]A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)[/tex]
we have that the base and the height of triangle is equal to the radius of the circle
[tex]r=12\ cm\\b=12\ cm\\h=12\ cm[/tex]
substitute
[tex]A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)[/tex]
[tex]A=(36\pi-72)\ cm^2[/tex]
simplify
Factor 36
[tex]A=36(\pi-2)\ cm^2[/tex]
Part 2) Find the perimeter
The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle
The circumference of a quarter of circle is equal to
[tex]C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r[/tex]
substitute the given values
[tex]C=\frac{1}{2}\pi (12)[/tex]
[tex]C=6\pi\ cm[/tex]
The hypotenuse of right triangle is equal to (applying the Pythagorean Theorem)
[tex]AC=\sqrt{12^2+12^2}[/tex]
[tex]AC=\sqrt{288}\ cm[/tex]
simplify
[tex]AC=12\sqrt{2}\ cm[/tex]
Find the perimeter
[tex]P=(6\pi+12\sqrt{2})\ cm[/tex]
simplify
Factor 6
[tex]P=6(\pi+2\sqrt{2})\ cm[/tex]
Answer:
36(π-2)cm^2 is area
Perimeter is 6(π+2√2)
Step-by-step explanation:
100 points
the prime factors of a number are 2 2 2 and 5. what is the number
Answer:
The number is 40
Step-by-step explanation:
Step 1: To find the number, multiply all of the numbers together
2 * 2 * 2 * 5
40
Answer: The number is 40
Answer:
40
Step-by-step explanation:
2×2×2×5 = 40
Someone please help. Please give me a step by step answer for this mathematical equation
18-6.3x = 49.5
Answer:
When solving equations you goal is to get x by itself so
18-6.3x=49.5 (first step would be to minus 18 from each side)
-6.3x=31.5 (18-18=0, 49.5-18=31.5) (now you want to divide each side by -6.3)
x=-5 (-6.3/-6.3=1, 31.5/-6.3=-5)
Your final answer is
x=-5
Hope this helps ;)
DEFINE ALL OF THESE, ONE SENTENCE EACH, PLEASE
The Kissing Number Problem. ...
The Unknotting Problem. ...
The Large Cardinal Project.
Answers:
These are the three major and pure mathematical problems that are unsolved when it comes to large numbers.
The Kissing Number Problem: It is a sphere packing problem that includes spheres. Group spheres are packed in space or region has kissing numbers. The kissing numbers are the number of spheres touched by a sphere.
The Unknotting Problem: It the algorithmic recognition of the unknot that can be achieved from a knot. It defined the algorithm that can be used between the unknot and knot representation of a closely looped rope.
The Large Cardinal Project: it says that infinite sets come in different sizes and they are represented with Hebrew letter aleph. Also, these sets are named based on their sizes. Naming starts from small-0 and further, prefixed aleph before them. eg: aleph-zero.
Which is the graph of f(x) = 2(3)x?
Answer:
a
Step-by-step explanation:
if f(x)=y then when x is 1 2(3)^X= 6
Answer:
first graph
Step-by-step explanation:
given: [tex]f(x) = 2(3)^{x}[/tex]
substitute some values for x and see which curves accurately reflect the corresponding y-values:
when x = 0, f(0) = 2(3)^0 = 2(1) = 2
hence the graph must pass through the point (0,2)
We can see from the choices that the 2nd and 4th graphs do not pass through (0,2), so we can eliminate these 2 from consideration
when x = 1, f(1) = 2(3)^1= 2(3) = 6
hence the graph must pass through the point (1,6)
We can see that the 3rd graph does not pass through this point so we can eliminate the 3rd graph also.
Only the 1st graph gives points consistent with the 2 cases above.
did i do this right?
find the equation of the axis of symmetry for the parabola
y=x^2-8x+5
used y=ax^2+bx+c and got a=1 b=-8 and c=5
then used the formula x=-b/2a and plugged that in and got x=- -8/2(1) and simplified to get x=4 as the axis of symmetry.
Help me thank you, and explain!
Answer:
The total area of the shape = 4 + 4 + 2 = 10 square units
Step-by-step explanation:
This shape consists of three shape parts.
A right triangle with base 4 units and perpendicular 2 units at the right side.A square with the equal length and width i.e. 2 units. at the middleA right triangle with base 2 units and perpendicular 2 units at the left sideSo, the total area of this shape is the sum of the areas of these shape parts.
1st Part) Finding the area of Right Triangle with base 4 units and perpendicular 2 units
A right triangle with base 4 units and perpendicular 2 units.
Let
'a' be perpendicular side = 2 units
'b' be the base side = 4 units
As
The area of right triangle
[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(4)(2)}{(2)}[/tex] = 4 square units
2nd Part) Finding the area of Square with the equal length and width i.e. 2 units
Let a be the length of any side = 2 units
As the area of square
[tex]A=a^{2} }[/tex]
[tex]A = (2)^{2}=4[/tex] square units
3rd Part) Finding the area of Right Triangle with base 2 units and perpendicular 2 units
A right triangle with base 2 units and perpendicular 2 units.
Let
'a' be perpendicular side = 2 units
'b' be the base side = 2 units
As
The area of right triangle
[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(2)(2)}{(2)}[/tex]= 2 square units
Therefore the total area of the shape will be the sum of area of Right Triangle with base 4 units and perpendicular 2 units, area of Square with the equal length and width i.e. 2 and area of Right Triangle with base 2 units and perpendicular 2 units
So,
The total area of the shape = 4 + 4 + 2 = 10 square units
Keywords: area of a shape, area of triangle, area of square
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The model builder has 4 pieces of balsa wood that are 4 cm, 5 cm, 6 cm, and 7 cm in length. How many different combinations of 3 pieces can be used to make triangles without breaking or cutting the pieces? List the combinations as inequalities.
Answer:
4<5<6
4<5<7
4<6<7
5<6<7
since there are 4 pieces of wood, you will have 4 combinations. since the sum of the 2 shortest sides need to be more than the longest side the inequalities above are valid.
Hope this helps!!
Final answer:
Out of the four lengths of wood provided, there are three valid combinations that can form triangles: 4 cm, 5 cm, 6 cm; 4 cm, 6 cm, 7 cm; and 5 cm, 6 cm, 7 cm. These combinations satisfy the Triangle Inequality Theorem, which is necessary for forming triangles.
Explanation:
To determine how many different combinations of 3 pieces of balsa wood can be used to make triangles, we must recall the Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For the pieces of lengths 4 cm, 5 cm, 6 cm, and 7 cm, we can form the following combinations that satisfy the Triangle Inequality Theorem:
4 cm, 5 cm, 6 cm
4 cm, 6 cm, 7 cm
5 cm, 6 cm, 7 cm
The inequalities for these combinations are as follows:
4 cm + 5 cm > 6 cm
4 cm + 6 cm > 5 cm
5 cm + 6 cm > 4 cm
4 cm + 7 cm > 6 cm
6 cm + 7 cm > 4 cm
5 cm + 7 cm > 6 cm
Each of these combinations is valid as the sum of the lengths of any two pieces is greater than the length of the third piece.
Which of the following are like terms in this expression? 12a-7+7a+12b
Answer:
Step-by-step explanation:
in order to be like terms, they have to have the same variable (and exponent, if there is any).....or be just a constant with no variables (just a number)
like terms in 12a - 7 + 7a + 12b are :
12a and 7a....because they have the exact same variable (a)
12b....no like terms
-7...no like terms
so ur answer is : 12a and 7a