find the area A of JKL with vertices J(-5,5) K(0,9) L(3,5)
Answers
Answer:
Now suppose that x1,y1 , x2,y2 , , xn,yn are the vertices of a polygon (with positive orientation). The area of the polygon is A 1 2 C xdy ydx 1 2 x1y2 x2y1 x2y3 x3y2 xny1 x1yn . The problem asks us to find the area of the pentagon with vertices 0,0 , 2,1 , 1,3 , 0,2 , and 1,1 .
Step-by-step explanation:
The area of the given triangle JKL is 16 units square.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
Given vertices form a triangle in the coordinate plane ;
Base = 3 + 5 = 8 units
Height = 9 - 5 = 4 units.
Since the area of a triangle is given as (1/2) × base × height.
So,
Area = (1/2) × 8 × 4 = 16 unit square.
Hence "The area of the given triangle JKL is 16 units square".
For more about triangles,
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Related Questions
f 5y - 8 < 12, what is the maximum possible value of 10y ?
Answers
Answer: 30 is the maximum possible value of y
a triangle has vertices d(6,1), e(2,3) and f(-1,-3). show that triangle DEF is a right angle triangle and identify the right angle triangle
Answers
We'll need the slope formula which is
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\[/tex]
We subtract the y values together, and divide that over the difference in the x values when subtracted in the same order.
Let's find the slope of line DE
[tex]D = (x_1,y_1) = (6,1) \text{ and } E = (x_2,y_2) = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 1}{2 - 6}\\\\m = \frac{2}{-4}\\\\m = -\frac{1}{2}\\\\[/tex]
The slope of line DE is -1/2.
Next, compute the slope of line EF
[tex]E = (x_1,y_1) = (2,3) \text{ and } F = (x_2,y_2) = (-1,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - 3}{-1 - 2}\\\\m = \frac{-6}{-3}\\\\m = 2\\\\[/tex]
The slope of line EF is 2.
Lastly, compute the slope of line FD
[tex]F = (x_1,y_1) = (-1,-3) \text{ and } D = (x_2,y_2) = (6,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-3)}{6 - (-1)}\\\\m = \frac{1 + 3}{6 + 1}\\\\m = \frac{4}{7}\\\\[/tex]
The slope of line FD is 4/7.
--------------------------
To recap everything so far, we found the following:
slope of DE = -1/2slope of EF = 2slope of FD = 4/7The product of the first two slopes gets us (-1/2)*(2) = -1 showing that DE is perpendicular to EF.
Perpendicular slopes multiply to -1 as long as neither line is vertical nor horizontal.
Since DE is perpendicular to EF, this proves we have a 90 degree angle at point E.
Therefore triangle DEF is a right triangle.
100 POINTS!!!
What is the square root of -2?
Answers
Answer:
± i [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the result that [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-2}[/tex]
= ± [tex]\sqrt{2(-1)}[/tex]
= ± [tex]\sqrt{2}[/tex] × [tex]\sqrt{-1}[/tex]
= ± [tex]\sqrt{2}[/tex] × i
= ± i [tex]\sqrt{2}[/tex]
Is the open sentence 3z = 2z + 5 true or false when z = 5?
Answers
Answer:
Your answer to your question is FALSE!!!!!!
Answer:
True
Step-by-step explanation:
Plug the value of z in: 3(5) = 2(5) + 5Simplify: 15 = 10 + 510 + 5 = 15So, the open sentence is true.I hope this helps!
7/8 divided by 1/4 simplest form
Answers
[tex] = \frac{7}{8} \div \frac{1}{4} [/tex]
[tex] = \frac{7}{8} \times \frac{4}{1} [/tex]
[tex] = \frac{(7 \times 8)}{4} [/tex]
[tex] = \frac{56}{4} [/tex]
[tex] = \frac{56 \div 4}{4 \div 4} [/tex]
[tex] = \frac{14}{1} [/tex]
[tex] = 14[/tex]
Therefore :-
[tex] \frac{7}{8} \div \frac{1}{4} = 14[/tex]
What is an equation of the line that passes through the point (-6,-6) and is parallel to the line x-3y=18
Answers
y = (1/3)x - 4
Explanation:
The general form for a line in slope-intercept form is
y = mx + b
where:
“m” is the slope,
“b” is the y-intercept,
“x” and “y” are points on the graph.
A line parallel to x - 3y = 18 will have the same slope, or “m” in slope-intercept form.
Isolate “y” to find the slope:
x - 3y = 18
-3y = -x + 18
y = (1/3)x - 6
m = 1/3
Note that ordered pairs are written (x, y).
Substitute (-6, -6) and m = 1/3 into the general form.
y = mx + b
-6 = (1/3)(-6) + b
Simplify and isolate “b”.
-6 = -2 + b
b = -4
Write the equation of the line using “m” and “b”.
y = (1/3)x - 4
the scale of a map is 1cm : 2km. if the length of Alfreda creek on this map is about 2.85 cm, calculate the actual length of the creek
Answers
1 cm..............2 km = scale of the map
2,85 cm....... n km = to be calculated
n x 1 = 2 x 2,85
n = 5,7 km
Step-by-step explanation:
1cm rep 2km
2.85x2
=5.7
=5.7km
At a recent marathon, spectators lined the street near the starting line to cheer for the runners. The crowd lined up 5 feet deep on both sides of the street for the first mile. You estimate that 14 people can comfortably fit in a square that measures 5 feet by 5 feet. Using this information, how many people cheered for the runners at the start of the race? 1mile=5280 feet
Answers
Answer:
29568 people cheered for the runners at the start of the race
Step-by-step explanation:
From the question, the crowd lined up 5 feet deep on both sides of the street for the first mile.
This lined up crowd could be related to a rectangle that is 1 mile long and 5 feet wide.
First, Convert 1 mile to feet
1 mile = 5280 feet
Hence, the length of the rectangle is 5280 feet and the width is 5 feet.
Now, we will determine how many 5 feet by 5 feet square we can get from the 5280 feet by 5 feet rectangle. To do that, we will divide 5280 feet by 5 feet
5280 feet ÷ 5 feet = 1056
Hence, from the rectangle, we can get 1056 5 feet by 5 feet square.
From the question, you estimate that 14 people can comfortably fit in a square that measures 5 feet by 5 feet,
∴ 14 × 1056 people will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.
14 × 1056 = 14784 people
This is the amount of people that will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.
Since the crowd lined up on both sides of the street, then
2 × 14784 people will comfortably fit in the crowed lined up 5 feet deep on both sides of the street for the first mile
2 × 14784 = 29568 people
Hence, 29568 people cheered for the runners at the start of the race.
6.
Using the incenter P, find the measure of Angle XZY
Answers
Answer: 62
Step-by-step explanation:
A triangular garden has an area of 112 ft2. Its height is 2 ft more than its base. Find the measure of the base.
Answers
Answer:
14 ft.
Step-by-step explanation:
First, we will assign variables to each value. If height is h, and base is b, then
1/2bh = 112 and h=b+2.
We will use substitution in this system of equations. first, we will isolate the b in bh/2=112. To do this we will multiply both sides by 2 to isolate the variables, so bh=224. Then, to isolate just one variable, in this case, b, we will divide 224 by h, getting us b=224/h.
Then, we will substitute b for this value in h+2=b, leaving us with h+2=224/h
Then isolate the variable. h will equal either -14 or 16. Because this is a geometric shape, the value of its sides cannot be negative, so it has a height of 16.
Then, plug this into the second equation. If the height is 2 ft more than the base, then the base will be 14 ft.
The diagram shows a rectangle with its side.
a) Find an expression, in terms of x, for the perimeter of the rectangle.
b) The perimeter of the rectangle is 56 cm. Find the value of x. 1
Answers
Answer:
Ans of a = 18x
Ans of b = 3.111
find the three consecutive even intergers such that the sum of twice the smallest number and three times the largest is 42
Answers
Answer:
6, 8, 10.
Step-by-step explanation:
Let n be any integer.
Then our first even integer will be [tex]2n[/tex]
And the consecutive integers will be [tex]2n+2[/tex] and [tex]2n+4[/tex]
We want to find the integers such that the sum of twice the smallest number (2n) and three times the largest number (2n+4) is 42. In other words:
[tex]2(2n)+3(2n+4)=42[/tex]
Solve for n. Distribute:
[tex]4n+6n+12=42[/tex]
Combine like terms:
[tex]10n+12=42[/tex]
Subtract 12 from both sides:
[tex]10n=30[/tex]
Divide both sides by 10:
[tex]n=3[/tex]
So, the value of n is 3.
This means that our first even integer is 2(3) or 6.
So, our sequence of integers is: 6, 8, 10.
And we're done!
Notes:
We use 2n because anything integer multiplied by 2 ensures that the resulting number is even. Starting out, n can be either even or odd, but by multiplying it by 2, we will get an even number.
What is the slope of the line that contains (-3,5) and (-3, 6)?
Answers
Answer:
1
Step-by-step explanation:
You can find slope by the formula
y2-y1 over x2-x1
In this case, 6-5 over -3-(-3) or -3=3
This is equal to 1 over 0 which is 1
What select factor was applied to the first rectangle to get the result image
Answers
Answer:
A factor of 0.2
Step-by-step explanation:
If we multiply 2.5 by 0.2, we get 0.5, the width of the smaller rectangle.
I need help finding the measure of the missing angles
Answers
Answer:
x = 61°
y = 29°
Step-by-step explanation:
Since x°+29° is a right angle (90°), you would have to subtract 29 from 90 to get x.
90 - 29 = x
90 - 29 = 61
x = 61°
For y: You can infer that y°+x°=90° as well because the angles are corresponding angles. So to find y°, you would do the same thing as finding x.
90 - x = y
90 - 61 = 29
y = 29°
Hope this helps :)
3.2, 3 ⅔, 3.25, 3 ½ greatest to least
Answers
Answer:
3.2, 3.25, 3 1/2, 3 2/3
Step-by-step explanation:
You can put them on a number line and find out the order. Or, convert to decimals or fractions.
Calculator
What is the slope of the line passing through the points (1, 2) and (5, 4)?
N
O 2
O-2
0 1
Answers
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}[/tex]
5x-6=3
find the value for x
Answers
Answer:
x = 9/5 = 1 4/5
Step-by-step explanation:
5x - 6 = 3
+6 +6
(add positive 6 to the negative 6 = - 6 + 6 = 0, and to the answer = 3 = 3 + 6 = 9)
5x = 9
÷5 ÷5
x = 9/5 (improper fraction)
= 1 4/5 (mixed numeral)
Hello.
First, let's add 6 to both sides:
[tex]\tt{5x-6+6=3+6}[/tex]
[tex]\tt{5x=9}[/tex]
The next step is to divide both sides by 5:
[tex]\tt{x=\displaystyle\frac{9}{5}[/tex] (Improper fraction)
[tex]\tt{x=\displaystyle1\frac{4}{5}[/tex] (Mixed number)
I hope it helps.
Have a great day.
[tex]\boxed{imperturbability}[/tex]
Abbey has $25. She plans on saving $10 a week. Which inequality shows how many weeks, w, she must save to have at least $250?
Answers
Answer:
22.5 weeks
Step-by-step explanation:
can anyone show how to do this....6840 ÷ 7
Answers
6840 ÷ 7 = ?
6840 | 7
63 977
=54
49
=50
49
=1
⇒ 6840 ÷ 7 = 977 remainder 1
Simplify the expression
a/3+3a/4
Answers
Answer:
[tex]\frac{13}{12}a\\[/tex]
Step-by-step explanation:
[tex]\frac{a}{3} + \frac{3a}{4}= \frac{13}{12}a[/tex]
Answer:
the answer is 13a/12 simplified
Can anybody help me?
I'm on a time crunch.
x + 3= 8x -11
Question 1 options:
x=-1
x=1
x=2
x=4
Answers
Answer: x = 2
Steps: x + 3= 8x - 11
Subtract three form both sides: x + 3 - 3 = 8x - 11 - 3
Simplify: x = 8x - 14
Subtract 8x from both sides: x - 8x = 8x - 14 - 8x
Simplify: -7x = -14
Divide both sides by negative seven: -7x ÷ -7 = -14 ÷ -7
Simplify: x = 2
CAN SOMEONE HELP ME OUT PLEASE AND THANK YOU
Answers
answer? what is it?
7(3+5)+9
Answers
Answer:
65
Step-by-step explanation:
3+5=8
7x8+9
56+9
=65
Please give brainliest!
Answer:
=> 65
Step-by-step explanation:
=> 7(3+5)+9
=> 7(8)+9
=> 56+9
=> 65
Omar grouped the terms and factored the gcf out of the groups of the polynomial 3x3 – 15x2 – 4x 20. his work is shown. step 1: (3x3 – 15x2) (–4x 20) step 2: 3x2(x – 5) 4(–x 5) omar noticed that he does not have a common factor. which accurately describes what omar should do next? omar should realize that his work shows that the polynomial is prime. omar should go back and regroup the terms in step 1 as (3x3 – 15x2) – (4x 20). in step 2, omar should factor only out of the first expression. omar should factor out a negative from one of the groups so the binomials will be the same.
Answers
The step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.
What are prime polynomials?Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomials.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
The polynomial that Omar is dealing with is:
[tex]3x^3 - 15x^2 -4x + 20[/tex]
We see that 3 times 5 = 15 and 4 times 5 = 20, so trying in that way:
[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5)[/tex]
Taking out a negative factor from second term would make the binomials same, after which we can take that common out, as shown below:
[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5) \\3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) -4(x-5) \\3x^3 - 15x^2 -4x + 20 = (x-5)(3x^2-4)[/tex]
It successfully got factored, thus not a polynomial.
Thus,the step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.
Learn more about prime polynomials here:
https://brainly.com/question/10717989
Answer: Omar should factor out a negative from one of the groups so the binomials will be the same.
Step-by-step explanation: Answer on edge
Work out area of the triangle and give answer to 1.dp
Answers
Answer:
A ≈ 62.8 cm²
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] ab sinC
where a = 10, b = 13 and C = 105° , then
A = [tex]\frac{1}{2}[/tex] × 10 × 13 × sin105° = 65 × sin105° ≈ 62.8 cm² ( to 1 dec. place )
Plz help! ASAP! Will mark Brainliest
Answers
Answer:
7/8 quart
Step-by-step explanation:
which sequence of transformations can be preformed on figure qrstu to show that the fugures are congruents
Answers
Answer:
Reflections, rotations, and translations produce an image that is congruent to the pre-image. Sequences of those transformations produce congruent images.
Ariel spends $330 on 3 gold rings. The rings all cost the same amount. What is the cost of each ring?
Answers
Answer:
$110
Step-by-step explanation:
divide 330 by 3
$115 i think..........................
Some steps are shown in converting the following conic inequality from general form to standard form. Complete the conversion and identify the shape, key feature, and which ordered pair is part of the solution set. 9x2 – 18x 4y2 16y – 11 > 0 9x2 – 18x 4y2 16y > 11 9(x2 – 2x) 4(y2 4y) > 11 9(x2 – 2x 1) 4(y2 4y 4) > 11 9 16 The conic represented in this inequality is a(n). The center is at. The ordered pair, , is a solution to the inequality.
Answers
The given inequality shows an ellipse with a center at (1,-2)
The major axis will be [tex]a=\sqrt{\dfrac{26}{9} }[/tex]
The minor axis will be [tex]b=\sqrt{\dfrac{26}{4} }[/tex]
What is an ellipse?The equation of an ellipse is written in the form
[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.
Now the given inequality is
[tex]9x^2+18x+4y^2+16y-11 > 0[/tex]
[tex]9x^2+18x+4y^2+16y > 11[/tex]
[tex]9(x^2-2x)+4(y^2+4y) > 11[/tex]
[tex]9(x^2-2x+1)+4(y^2+4y+4) > 11+9+16[/tex]
[tex]9(x^2-2x+1)+4(y^2+4y+4) > 26[/tex]
On further solving
[tex]9(x-1)^2+4(y+2)^2 > 26[/tex]
[tex]\dfrac{(x-1)^2}{\dfrac{26}{9} } + \dfrac{(y+2)^2}{\dfrac{26}{4} } > 1[/tex]
Thus by comparing the equation with the standard form
[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
Thus we can see that the center (h,k) is (1,-2)
The major axis will be [tex]a=\sqrt{\dfrac{26}{9} }[/tex]
The minor axis will be[tex]a=\sqrt{\dfrac{26}{4} }[/tex]
To know more about ellipse follow
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Answer:
ellipse with a dashed line boundary
(1,-2)
(-2,0)
Step-by-step explanation:
assignment