A rhombus, COAL is centered at the origin. The longer diagonal is on the y-axis and has a
length of 27m. The shorter diagonal is on the x-axis and has a length of has diagonals with
length 19m. Determine the coordinates of the vertices.
Answers
Answer with Step-by-step explanation:
We are given that
COAL is a rhombus .
CA and LO are the diagonals of rhombus COAL.
CA=27 m
OL=19 m
We know that
Diagonals of rhombus are bisect to each other.
Let P(0,0) be the intersecting point of diagonals
Therefore, CP=PA
LP=PO
Length PO=[tex]\frac{1}{2}LO=\frac{19}{2}=9.5 m[/tex]
Length of CP=[tex]\frac{1}{2}PA=\farc{1}{2}(27)=13.5 m[/tex]
Let C([tex]0,y_2),O(x_1,0),A(0,y_1) \;and\;L(x_2,0)[/tex].
Distance formula:[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
[tex]CP=\sqrt{(0-0)^2+(0-y_2)^2}=13.5[/tex]
[tex]\sqrt{y^2_2}=13.5[/tex]
[tex]y_2=\pm 13.5[/tex]
C(0,13.5) or (0,-13.5)
[tex]\sqrt{(y_2-y_1)^2}=27[/tex]
Substitute the value [tex]y_2=13.5[/tex]
[tex]\sqrt{13.5-y_1}=27[/tex]
[tex]13.5-y_1=\pm 27[/tex]
[tex]y_1=13.5-27=-13.5[/tex]
A(0,-13.5)
[tex]13.5-y_1=-27[/tex]
[tex]y_1=13.5+27=40.5[/tex]
A(0,40.5)
Substitute [tex]y_2=-13.5[/tex]
[tex]\sqrt{(-13.5-y_1)^2}=27[/tex]
[tex]-13.5-y_1=\pm 27[/tex]
[tex]-13.5-y_1=27[/tex]
[tex]y_1=-13.5-27=-40.5[/tex]
A(0,-40.5)
[tex]-13.5-y_1=-27[/tex]
[tex]y_1=-13.5+27=13.5[/tex]
A(0,13.5)
[tex]LP=\sqrt{(x_2-0)^2}=9.5[/tex]
[tex]\sqrt{x^2_2}=9.5[/tex]
[tex]x_2=\pm 9.5[/tex]
L(9.5,0) or L(-9.5,0)
[tex]\sqrt{x_2-x_1)^2}=19[/tex]
[tex](9.5-x_1)^2}=19[/tex]
[tex]9.5-x_1=\pm 19[/tex]
[tex]9.5-x_1=19[/tex]
[tex]x_1=9.5-19=-9.5[/tex]
[tex]9.5-x_1=-19[/tex]
[tex]x_1=9.5+19=28.5[/tex]
[tex](-9.5-x_1)=19[/tex]
[tex]-9.5-x_1=\pm 19[/tex]
[tex]-9.5-x_1=19[/tex]
[tex]x_1=-9.5-19=-28.5[/tex]
[tex]-9.5-x_1=-19[/tex]
[tex]-9.5+19=x_1[/tex]
[tex]x_1=9.5[/tex]
O(-9.5,0) or O(28.5,0) or (-28.5,0) or (9.5,0)
Related Questions
In his free time Gary spends 10 hours per week on the internet and 9 hours per week on video games. If Gary has 5 hours of free time per day what percent of free time is he using to play video games and use the internet
Answers
Final answer:
Gary spends approximately 54.29% of his free time on video games and the internet.
Explanation:
To find the percentage of free time that Gary spends on video games and the internet, we need to calculate the total number of hours he spends on these activities and divide it by the total number of hours of free time he has.
First, calculate the total number of hours Gary spends on video games and the internet: 10 + 9 = 19 hours.
Next, calculate the total number of hours Gary has for free time in a week: 5 hours per day x 7 days = 35 hours.
To find the percentage, divide the total number of hours spent on video games and the internet by the total number of hours of free time and multiply by 100: (19 / 35) x 100 = 54.29%.
Therefore, Gary spends approximately 54.29% of his free time on video games and the internet.
To find the percentage of free time that Gary is using to play video games and use the internet, calculate the total free time and the proportion of time spent on video games and internet use.
Explanation:To find the percentage of free time that Gary is using to play video games and use the internet, we need to calculate the total amount of free time Gary has and then determine the proportion of that time spent on video games and internet use.
Gary spends 10 hours per week on the internet and 9 hours per week on video games. This is a total of 10 + 9 = 19 hours per week.
Since Gary has 5 hours of free time per day, he has a total of 5 * 7 = 35 hours of free time per week.
To find the percentage, we divide the time spent on video games and internet use (19 hours) by the total free time (35 hours) and then multiply by 100. So, the percentage is (19/35) * 100 = 54.28% (rounded to two decimal places).
Expand.
Your answer should be a polynomial in standard form.
(9h+3)(-h-1)
Answers
Answer:
Step-by-step explanation:
Determine whether the given equation has one solution, no solution, or infinitely many solutions.
2 - 3(x + 4) = 3(3 - x)
one solution
no solution
infinitely many solutions
cannot be determined
Please show me how you get your answer, I really need to know how to do this
Answers
Answer:
No Solution.
Step-by-step explanation:
2 - 3(x + 4) = 3(3 - x)
2 - 3x - 12 = 9 - 3x
Move the terms in x to one side and the numbers to the other
-3x + 3x = 9 - 2 + 12
0 = 19.
This is absurd so there is No Solution.
Find the greatest common factor.
4z, 6z3
Write your answer as a constant times a product of single variables raised to exponents.
Answers
The GCF of given terms is: 2z
Step-by-step explanation:
A largest factor that is shared by all given terms is called greatest common factor.
So,
Given terms are:
4z , 6z^3
Factoring the terms
[tex]4z = 2.2.z\\6z^3 = 2.3.z.z.z[/tex]
The common factors in both terms are: 2 and z
So,
The GCF of given terms is: 2z
Keywords: GCF, factors
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If 3(d+1)=4(d–2), then what is the value of 5(d–2)?
Answers
Answer:
Ans => 45
Step-by-step explanation:
3(d+1) = 4(d-2)
Expanding the brackets we have:
3d + 3 = 4d - 8
our aim now is to solve for d
3d - 4d = -8 - 3
-d = -11
=> d = 11
we can now get 5(d-2)
substituting d = 11
5(11-2)
5(9)
= 45
The value of 5(d-2) is 45.
3(d+1)=4(d–2)
3d + 3 = 4d - 8.
3d - 4d = -8 - 3.
-d = -11
d = 11
Substitute d = 11 into 5(d–2):
5(d-2)=5(11-2)
= 5(9)
= 45.
What polynomial should be subtracted from 7x^2−6x+5 to get the difference equal to x^2−x.
Answers
Answer: 6x^2-5x+5
Step-by-step explanation:
Answer:
6x^2-5x+5
Step-by-step explanation:
Essentially, you just put the two in a column:
7x^2−6x+5
- y
=x^2-x
("y" represents answer)
A history Club sold rolls of wrapping paper as a fundraiser. The wrapping paper was sold in small rolls and large rolls. The club earned $3 for every small roll sold. The club earned $4.50 for every large roll sold. The club sold 10 more large rolls than small rolls. The club collected $135 more from sales of large rolls than from sales of small rolls. The equation 3 S + 135 = 4.5( s + 10) can be used to represent this situation, where s represents the number of small rose the club sold. How many small roles did the history Club sell? Of wrapping paper as a fundraiser. The wrapping paper was sold and small rose and large Rose. The club earn $3 for every small role sold. The club sold 10 more large rolls than small rolls. The club collected $135 a more from sales of large rolls than from sales of small rolls. The equation 3x + 135 = 4.5(s + 10) can be used to represent this situation, where s represents the number of small rolls the club sold. How many small rolls did the history Club sell?
Answers
Answer:
hence small rolls 60 and large rolls 70
Step-by-step explanation:
let club sold s small rolls
hence club sold s+10 large rolls
earning from small roll 3s
earning from large rolls 4.5(s+10)
hence
4.5(s+10) - 3s = 135
or 4.5(s+10) = 3s +135
3s +135 = 4.5(s+10)
3s +135 = 4.5s +45
4.5s +45 = 3s +135
4.5s -3s = 135-45
1.5s = 90
s = 90/1.5
s= 60
s+10 = 70
hence small rolls 60 and large rolls 70
The history club sold 60 small rolls of wrapping paper according to the given equation.
Explanation:The subject here is Mathematics, specifically algebra. The equation given by the problem, 3S + 135 = 4.5(S + 10), can be solved to find 'S', which represents the number of small rolls sold by the history club. Start by distributing the 4.5 across the (S + 10) on the right side of the equation. This gives 3S + 135 = 4.5S + 45. Subtract 3S from both sides of the equation to get 135 = 1.5S + 45. Subtracting 45 from both sides then gives 90 = 1.5S. Finally, divide each side of the equation by 1.5 to get S = 60. So, the history club sold 60 small rolls.
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The inequality x + 12x + 35 has two critical points and three possible intervals for solutions. Choose
each set of possible test points for the three intervals.
-8,-6,4
-10, -6,0
-6,0,6
-6,0, 10
Answers
Answer:
Option 1 and 2.
Step-by-step explanation:
Consider he given inequality is
[tex]x^2 + 12 x+35\ge0[/tex]
Splitting the middle term we get
[tex]x^2 +7x+5x+35\ge0[/tex]
[tex]x(x+7)+5(x+7)\ge0[/tex]
[tex](x+5)(x+7)\ge0[/tex]
The related equation is
[tex](x+5)(x+7)=0[/tex]
Using zero product property we get
[tex]x+5=0\Rightarrow x=-5[/tex]
[tex]x+7=0\Rightarrow x=-7[/tex]
Draw number line and mark -5 and -7 on it.
Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).
The set of possible test points for
⇒ (-∞ , -7] → -8, -10
⇒ [-7,-5] → -6
⇒ [-5,∞) → -4, 0, 4, 6
-8,-6,-4 and -10,-6,0 satisfies the given condition.
Therefore, the correct options are 1 and 2.
Carl's age, 32, is 25 less than one-third his weight. How much does
Carl weigh?
Answers
Answer:
21
Step-by-step explanation:
32-25<1/3x
7*3=x
21=x
Answer:
171
Step-by-step explanation:
Carl’s age, 32 + 25 = 57
57 x 3 = 171
5) Devon has 2 equal stacks of Post-Its in his locker. He used 14 of them last week and has
22 left over. How many Post-Its were in each stack?
Answers
Answer: 18
Step-by-step explanation:
1.We must total 14 and 22 (14+22) that brings the number of post which is 36.
2.The we must divide 36 by 2 (36÷2). It said two stacks that is why the division by 2 comes in place and it gives us our answer 18
What is the percentage of increase from the least expensive policy to the most expensive policy? To the
nearest tenth of a percentage.
Answers
7.8 6.8 and 5.8
Is what they forgot to put
Answer is 7.8
Company charges $80 per hour fee for computer repair plus a 1 time service fee. The total for 3 hours was $290. Write the point slope form of an equation to find the total fee y for any number of hours x
Answers
Answer:
y=80x+50 for the one time service fee.
Anytime after that would be y=80x
Step-by-step explanation:
Y is how much the total is and 80 is how much it is an hour. X is the number of hours worked. With the first time fee of $50, your equation would be y=80x+50. Anytime after that, excluding the “one time fee,” the equation would be y=80x.
PLEASE HELP ASAP
Which pairs of rectangles are similar polygons?
Select Similar or Not Similar for each pair of rectangles.
Answers
Answer:
A & B Not Similar B & C Not Similar A & C Similar
Step-by-step explanation:
i just took the test and these are the correct answers that they gave on review of test, Youre welcome :)
A cell phone company charges a $20 flat fee plus 5 cents for every minute used for calls.
Which algebraic equation that could be used to represent the situation?
A.
Y= 0.05x + 20
B.
Y = 5x + 20
C.
Y = 20x + 0.5
D.
Y = 20x + 5
Answers
Barney has
[tex]16 \frac{1}{5} [/tex]
yards of fabric. To make an elf costume, he needs
[tex]5 \frac{2}{5} [/tex]
yards of fabric. How many costumes can Barney make?
Answers
Barney can make 3 costumes from the total fabric.
Step-by-step explanation:
Given,
Amount of fabric Barney has = [tex]16\frac{1}{5}=\frac{81}{5}\ yards[/tex]
Amount of fabric required for an elf costume = [tex]5\frac{2}{5}=\frac{27}{5}\ yards[/tex]
Let,
x represent the number of costumes that can be make from total fabric.
[tex]\frac{27}{5}x=\frac{81}{5}[/tex]
Multiplying both sides by 5/27
[tex]\frac{5}{27}*\frac{27}{5}x=\frac{81}{5}*\frac{5}{27}\\\\x=\frac{81}{27}\\\\x=3[/tex]
Barney can make 3 costumes from the total fabric.
Keywords: fraction, multiplication
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A conical tent has a radius of 10.4 ft and a height of 8.4 ft. Doubling which dimensions will quadruple the volume of the tent?
Answers
Answer: Doubling the radius.
Step-by-step explanation:
The volume of a cone can be found with the following formula:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cone.
Let's find the volume of the conical tent with a radius of 10.4 feet and a height of 8.4 feet.
Identifiying that:
[tex]r=10.4\ ft\\\\h=8.4\ ft[/tex]
You get this volume:
[tex]V_1=\frac{1}{3}\pi (10.4\ ft)^2(8.4\ ft)\\\\V_1=951.43\ ft^3[/tex]
If you double the radius, the volume of the conical tent will be:
[tex]V_2=\frac{1}{3}\pi (2*10.4\ ft)^2(8.4\ ft)\\\\V_2=3,805.70\ ft^3[/tex]
When you divide both volumes, you get:
[tex]\frac{3,805.70\ ft^3}{951.43\ ft^3}=4[/tex]
Therefore, doubling the radius will quadruple the volume of the tent.
The bracelet Lily would like to buy costs $5 less than 5 times the amount she has saved . The bracelet costs $30. How much money does Lily have saved?
Answers
Lily has saved $ 7
Solution:
Given that bracelet costs $30
The bracelet Lily would like to buy costs $5 less than 5 times the amount she has saved
Cost of bracelet = $ 30
From given statement,
Cost of bracelet = 5 times the amount she has saved - 5
Let "x" be the amount saved by lily
Cost of bracelet = 5 times x - 5
Here "times" represents multiplication
30 = 5(x) - 5
30 = 5x - 5
30 + 5 = 5x
5x = 35
On dividing 35 by 5 we get 7
x = 7
Thus Lily saved $ 7
Answer:
1. Start with the cost of the bracelet: 30.
2. Add 5: 30 + 5 = 35.
3. Divide by 5: 35 / 5 = 7
So, Lily has $7 saved
Step-by-step explanation:
Hope it helpss ! :D
For what value of x is line m parallel to line n? This is quite urgent.
Answers
Answer:
20
Step-by-step explanation:
Line m and n are parallel lines cut by the transversal (without name). So, angles with measures [tex]65^{\circ}[/tex] and [tex](3x+5)^{\circ}[/tex] are corresponding angles.
The Corresponding Angles Theorem states if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Hence,
[tex]3x+5=65\\ \\3x+5-5=65-5\\ \\3x=60\\ \\x=\dfrac{60}{3}\\ \\x=20[/tex]
HELP ME 15 POINTS!!!!
Which is the MOST REASONABLE approach for the company to take to lessen the number of latecomers to work?
A) Relocate the company to an area with less traffic.
B) Deduct the lost time for any reason from vacation time.
C) Delay the start time of work days when there is bad weather.
D) Implement better procedures at the security gate.
Answers
Answer:
D) Implement better procedures at the security gate.
Step-by-step explanation:
Given no other restrictions what are the domain and range of the following function f(x)=x^2-2x+2
Answers
Answer:
R= {y|y>=1}
Step-by-step explanation:
D = all real numbers R= {y|y>=1}.
All polynomials have domain of all real numbers.
For the range, the vertex format is useful;
Y= (X-1)^2 + 1
Since (X-1) is never less than zero, Y>=1.
That is where the vertex is, at Y=1
647 divided by 3 step by step. thanks.
Answers
Answer:
215
Step-by-step explanation:
215
3
647
6
04
3
17
15
2
hope this helped
You have budgeted $100 to improve your swimming over the summer. At your local pool, it costs $50 to join the swim association and $5 for each swim class. Write and solve an inequality to find the possible numbers of swim classes you can attend with
Answers
Answer:
[tex]50+5x\le 100[/tex]
[tex]x\le 10[/tex]
You can visit at most 10 swim classes.
Step-by-step explanation:
Let x be the number of swim classes you can attend with.
At your local pool, it costs $50 to join the swim association and $5 for each swim class. then x classes cost $5x and the total cost is $(50 + 5x).
You have budgeted $100 to improve your swimming over the summer. Hence,
[tex]50+5x\le 100[/tex]
Solve this inequality:
[tex]50+5x-50\le 100-50\\ \\5x\le 50\\ \\x\le 10[/tex]
You can visit at most 10 swim classes.
The student can join the swim association and attend up to 10 swim classes within the $100 budget.
Explanation:This question is asking for the creation and solution of an inequality based on a budgeting scenario. The student has budgeted $100 and needs to spend $50 to join the swim association, leaving $50 for swim classes at $5 each. The problem can be represented by the inequality 5c ≤ 50, where c is the number of swim classes.
To solve the inequality, you would divide both sides by 5. The solution of this inequality is c ≤ 10. So, the student can attend up to 10 swim classes within the budget.
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what is $750x+150<1000
Answers
For this case we must resolve the following inequality:
[tex]750x + 150 <1000[/tex]
Subtracting 150 from both sides of the inequality we have:
[tex]750x <1000-150\\750x <850[/tex]
We divide between 750 on both sides of the equation:
[tex]x <\frac {850} {750}[/tex]
We simplify, dividing by 5 numerator and denominator:
[tex]x <\frac {170} {150}[/tex]
We simplify, dividing by 5 numerator and denominator:
[tex]x <\frac {34} {30}[/tex]
We simplify, dividing by 2 numerator and denominator:
[tex]x <\frac {17} {15}[/tex]
Thus, the solution is given by all values of x less strict than[tex]\frac {17} {15}[/tex]
Answer:
[tex]x <\frac {17} {15}[/tex]
Which values of x are solutions to the inequality?
x < -200. select each correct answer
A. x = - 120
B. x = - 210
C. x = -200
D. x = -201
Answers
Answer:
B. [tex]x=-210[/tex]
D. [tex]x=-201[/tex]
Step-by-step explanation:
Given:
The inequality for 'x' is given as:
[tex]x<-200[/tex]
The above inequality tells us that, the value of the variable 'x' is less than -200.
-200 is a negative number. So, for a negative number, the larger the value of the number, the smaller the number is.
Example: -2 is less than -1 although 2 has a greater magnitude than 1.
Therefore, the numbers that are less than -200 are -210 and -201.
So, the values of 'x' that satisfy the given inequality are -201 and -210
Thus, the correct options are (B) and (D).
what is .41 as a fraction
Answers
Answer: 41/100
Step-by-step explanation: First, we can change .41 to 0.41 by putting a zero in front of the decimal point.
Using the place value chart, we can see that 0.41 means 0 units, 4 tenths a 1 hundreth. Think of 4 tenths and 1 hundredth as 41/100 so we have 41/100.
Since the fraction 41/100 is in lowest terms, this is our final answer.
Sam and Odel have been selling frozen pizzas for a class fundraiser. Sam has sold half as many pizzas as Odel. Together they have sold a total of 126 pizzas. How many pizzas did Sam sell
Answers
Answer:
Step-by-step explanation:
Sam has sold 63 pizzas, because the problem is asking what is the half of 126 basically, which is 63 and is also saying that sam sold HALF as many pizzas.
Diego pours 6.8 ounces of water from a full bottle. He estimates that he poured out 20% of the water in the bottle. About how much water was in the full bottle?
Answers
Answer:
Full bottle can fill 34 ounces water and 27.2 ounces left in the bottle
Step-by-step explanation:
Full bottle : 100%
6.8 ounces: 20%
100% / 20% = 5
Full bottle = 6.8 x 5 = 34 ounces
water remain in bottle = 34 -6.8 = 27.2 ounces
There is 34 ounces of water in the bottle initially and this can be determined by using the unitary method.
Given :
Diego pours 6.8 ounces of water from a full bottle.He estimates that he poured out 20% of the water in the bottle.The following steps can be used in order to determine the total amount of water in the full bottle:
Step 1 - The unitary method can be used in order to determine the total amount of water in the full bottle.
Step 2 - According to the given data, Diego pours 6.8 ounces of water from a full bottle which is the 20% of the water in the bottle.
Step 3 - If 20% is 6.8 ounces of water than the 100% is given by:
[tex]=\dfrac{6.8}{20}\times 100[/tex]
Multiply 6.8 by 100 in the above expression.
[tex]=\dfrac{680}{20}[/tex]
Divide 680 by 20 in the above expression.
= 34 ounces
So, there is 34 ounces of water in the bottle initially.
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I don’t understand what it is asking so I need help with the work
Answers
Answer: The diver is 23 feet under sea level
Step-by-step explanation:
If we draw a vertical number line (image attached), where point 0 is sea level (the diver's initial position), the first point under sea level is -20, since we are told it dives a distance of 20 ft (the negative sign is only to indicate the direction, since a distance cannot be negative).
Then, the diver goes 10 ft deep. This means now it is 30 ft under sea level and the second point is -30.
After that the diver swims up 12 ft, hence we have to count 12 points up in our number line and the corresponding point is -18.
Finally, the diver swims 5 ft lower and keep that position. Hence, we have to count 5 points below point -18 in the number line, resulting in the last point: -23.
This means the diver's final position is 23 feet under sea level.
If we want to prove it with numbers, we can do it as follows:
20 ft (down)+10 ft (down)-12 ft (up)+5 ft (down)=23 ft
HLEP PLEASE!!!!!!!!!!!!!!!!!Add. State the sum in simplest form.
Answers
Answer: the answer would be B. ( 18y+35x over 15xy
Find the zero(s) of the following functions algebraically: f(x)=3x-21
Answers
Answer:
x=7
Step-by-step explanation:
The function is:
f(x)=3x-21.
The zero(s) is/are any value(s) that make(s) the function equal(s) to zero.
This implies that, to find the zero(s), we equate the function to 0 and solve for x
This implies that:
3x-21=0
3x=21
Dividing through by 3, we obtain
x=7