In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=71°, and JH = 2 feet. Find the length of IJ to the nearest tenth of a foot.
Answers
Answer:
IJ is 5.8 ft
Step-by-step explanation:
Here, we want to calculate the length of IJ
to Find IJ, we need the appropriate trigonometric ratio
The trigonometric ratio to use in this case is the one that connects the opposite and the adjacent
from the question, IJ is the opposite
This is the side facing the given angle
HI is the hypotenuse which is the side facing the right-angle
HJ is the third side which is the adjacent
Mathematically;
That is the Tan
Tan 71 = IJ/2
IJ = 2 Tan 71
IJ = 5.8
Related Questions
Write as a decimal. Use bar notation if necessary.
Answers
Find the missing angle in the triangle below
Answers
Answer:
120
Step-by-step explanation:
Exterior angle theorem
50 + 70 = 120
Answer:
120
Step-by-step explanation:
the insides of a triangle add up to 180 degrees. You're given 70 and 50 degrees which add to 120 and that means the other angle is 60 degrees. Since you're trying to find an outside angle, you need to do subtract the 60 degrees we just found from 180 (because its a supplementary angle). 180-60 is 120 and thats the answer
Helpppppppppppppppp ill mark you brainlist write in y=mx+b form
Answers
Answer:
The equation of the line in slope-intercept form is:
[tex]y\:=\:\frac{-10}{7}x-\frac{45}{7}[/tex]Step-by-step explanation:
Given the points
(-8, 5)(-1, -5)Finding the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-8,\:5\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-5\right)[/tex]
[tex]m=\frac{-5-5}{-1-\left(-8\right)}[/tex]
[tex]m=-\frac{10}{7}[/tex]
We know the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
substituting m = -10/7 and (-8, 5) in the slope-intercept form to determine the y-intercept
[tex]5\:=\:\frac{-10}{7}\left(-8\right)+b[/tex]
[tex]\frac{80}{7}+b=5[/tex]
[tex]b=-\frac{45}{7}[/tex]
now substituting m = -10/7 and b = -45/7 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{-10}{7}x+\left(-\frac{45}{7}\right)[/tex]
[tex]y\:=\:\frac{-10}{7}x-\frac{45}{7}[/tex]
Thus, the equation of the line in slope-intercept form is:
[tex]y\:=\:\frac{-10}{7}x-\frac{45}{7}[/tex]an island has three towns located at points with the coordinates a (15,3) b (25,10) and c (0,20) where the coordinates have units of Km the government wants to locate a toxic waste dump at a position as far as possible away from each town you may assume that this location is not on the edge of the island find the coordinates at the point where the toxic waste dump should be located
Answers
9514 1404 393
Answer:
(13.06, 16.41)
Step-by-step explanation:
Any point not on a perpendicular bisector of the line between towns will be closer to one town than the other. So, the intersection of perpendicular bisectors will be the equidistant from all towns. That point is the circumcenter of the circle circumscribing the triangle with the towns as its vertices. This can be found as the intersection of two perpendicular bisectors of the segments between the towns.
The midpoint of AB is ...
(A +B)/2 = ((15, 3) +(25, 10))/2 = (40, 13)/2 = (20, 6.5)
The midpoint of AC is ...
(A +C)/2 = ((15, 3) +(0, 20))/2 = (15, 23)/2 = (7.5, 11.5)
__
The differences between points are ...
B -A = (25, 10) -(15, 3) = (10, 7)
C -A = (0, 20) -(15, 3) = (-15, 17)
Then the perpendicular bisector equations can be written as ...
bisector of AB ⇒ 10(x -20) +7(y -6.5) = 0
10x +7x -245.5 = 0
bisector of AC ⇒ -15(x -7.5) +17(y -11.5) = 0
-15x +17y -83 = 0
These have coefficients that aren't particularly nice, so a method similar to Cramer's Rule is suitable for solving this pair of equations. Using the "cross multiplication method", we have ...
x = (7(-83) -17(-245.5))/(10(17) -(-15)(7)) = 3592.5/275 = 13 7/110 ≈ 13.06
y = (-245.5(-15) -(-83)(10))/275 = 4512.5/275 = 16 9/22 ≈ 16.41
The point as far as possible from each town within the boundary of the island has coordinates (13.06, 16.41).
_____
Further detail regarding the solution
Here, we have written the equation for the perpendicular bisector this way. The difference in coordinates between points R and S can be called ...
R -S = (∆x, ∆y)
The midpoint of segment RS can be called ...
(R +S)/2 = (h, k)
Then the line that is a perpendicular bisector of RS can be written as ...
∆x(x -h) +∆y(y -k) = 0
This is the form that is used above.
__
The "cross multiplication method" for solving a pair of general-form linear equations ...
ax +by +c = 0
dx +ey +g = 0
will give the solution as ...
1/(ae -db) = x/(bg -ec) = y/(cd -ga)
If you write the coefficients in two rows of four, the pattern of products and differences is easy to see.
[tex]\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right][/tex]
2. Suppose you are making some soup. You have 7 types vegetables in front of you (one serving of each) and you want to include 4 of them in your soup (each being different). How many ways are there to do this?
Answers
3 different ways to do it.
Using the combination formula, it is found that there are 35 ways to do this.
The order in which the vegetables are included is not important, thus, the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given as follows:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 vegetables from a set of 7, thus:
[tex]C_{7,4} = \frac{7!}{4!(7-4)!} = 35[/tex]
There are 35 ways to do this.
A similar problem is given at https://brainly.com/question/24278448
Name the side included by ∠A and ∠B
Answers
Answer:
I think may be it is Option 2 (AB)
someone please help??????
Answers
Answer:
[tex]a) x=15\\b) AD\ is\ not\ parallel\ tp BC[/tex]
Step-by-step explanation:
[tex]As\ we\ know\ that,\\Angle\ D=3x\\Angle\ A=2x\\Angle\ B=90\\Angle\ C=x\\The\ Angle\ Sum\ Property\ Of\ A\ Quadrilateral\ states\ that\ the\ sum\ of\ all\\ the\ interior\ angles\ of\ a\ quadrilateral\ is\ 180.\\Hence,\\ \angle D+ \angle A + \angle B + \angle C=360\\3x+2x+90+x=180\\3x+2x+x=180-90\\6x=90\\x=15\\Hence, x=15[/tex]
[tex]Hence,\\As\ Angle\ A\ and\ Angle\ B\ are\ co-interior\ angles, if\ they\ are\\ supplementary\ then\ AD \parallel BC.\ Lets\ check\ that\ out.\\Hence,\\Angle\ A=2x=2*15=30\\Angle\ B=90\ [Given]\\Hence,\\As\ 90+30\neq 180,\\Angle\ A +Angle\ B\neq 180\\Hence,\\As\ Angle\ A and\ Angle\ B\ are\ not\ supplementary, AD\ will\ not\ be\ parallel\ to\ CB.[/tex]
C
15 mm
8 mm
Pythagorean theorem
Answers
Explanation:
•8^2 + 15^2 = C^2
•64 + 225 = C^2
•289 = C^2
•Then square root both of them to get 17 = C.
Plz help 50 points
Help on number 2 and 3 please. What if you can’t read number 3’s answer it is;
A.8
B. 1/8
C.2/9
D. 9/2
Plz help on number 2 and 3
Answers
Answer: So the answer to number 2 is D! And the answer to number 3 is C I think I am not pretty sure about #3 but I am sure its D for 2 and pretty sure for #3 is C!
6 (4x6) x 9 (5x9) judjsjdjdjddjdnnddnfndndndndndndndndn
Answers
Answer:
48 600
Step-by-step explanation:
6(4×6) × 9(5×9)
Solve the numbers in brackets first
6(20) × 9(45)= 120 × 405
= 4 8 600
Answer:
6(20) × 9(45)= 120 × 405
= 4 8 600
Whats The Answer Marking Brainliest, Please explain your answer:D..............................Please HELP!!!!
Answers
Answer:
A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Select the correct answer.
Which expression represents a difference of squares?
A.
81 − 49y2
B.
t2 + 100
C.
4x2 − 16x
D.
25k − 64
Answers
Answer:
The answer is A I'm not 100 percent sure
Answer:
A.
81 − 49y2
Step-by-step explanation:
edmentum answer---
50 points! i honestly forgot how to do algebra lol can someone help me and explain the steps for me?
2x + 14 = 18 x=?
Answers
Answer: x=2
Step-by-step explanation: Plug 2 in the equation. 2 x 2 is 4. 4 + 14 is 18.
Help! I’m awful at graphs and stuff
Answers
Answer: for b: function one has a greater rate of change
Step-by-step explanation: sorry i don't know the first one
Answer:
a) -2 and 4, b) function 2
Step-by-step explanation:
Rate of change is the same thing as slope. For the first function, the table, we can use two of the points and the slope formula. I'll use (-1,3) and (-2,5). Remember the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Plug the points in:
[tex]m=\frac{5-3}{-2-(-1)}\\m=\frac{2}{-1}\\m=-2[/tex]
(Remember that subtracting a negative = adding. I look at it like the two 'minus' signs form one plus sign, if that helps)
So the slope of function 1 is -2.
We can do the same thing with the second function. Two points that I notice on the graph are (-1,0) and (0,4). Let's use the same slope formula.
[tex]m=\frac{4-0}{0-(-1)}\\m=\frac{4}{1}\\m=4[/tex]
And the slope of function 2 is 4. That answers the first part. The second part asks about rate of change.
Function 2 has a greater rate of change, since 4>-2.
Hope this helps!
A machine produces 264 bolts in 42 minutes. At the same rate, how many minutes would it take to produce 308 bolts?
minutes
Answers
Answer:
49.6 minutes to create 308 bolts
Step-by-step explanation:
hope this helps :)
Reuben bought 5CDS that were each the same priceIncluding sales tax, he paid a total of \$81.50. Each CD had a tax of $0.60. what was the price of each cs before tax ?
Answers
Answer:
The price of each CD before tax is $15.70
Step-by-step explanation:
Given that:
Number of CDs bought by Reuben = 5
Cost of five CDs = $81.50
Sales tax on each CD = $0.60
Sales tax on 5 CDs = 0.60*5 = $3.00
Price of CDs without tax = 81.50 - 3.00 = $78.50
Price of each CD = [tex]\frac{Cost\ of\ CDs}{No.\ of\ CDs}[/tex]
Price of each CD = [tex]\frac{78.50}{5}[/tex]
Price of each CD = $15.70
Hence,
The price of each CD before sales tax is $15.70
The senior class plans a school trip to Washington DC. Students should bring money for meals and
souvenirs. They are told to bring at least $60 but no more than $135. Write a compound inequality that
represents the amounts of money a student can bring.
Answers
Answer:
The required inequality is:
[tex]\mathbf{x >60\: and\: x<135}[/tex]
Step-by-step explanation:
Minimum Money students should bring = $60
Maximum Money students should bring= $135
We need to write compound inequality that represents the amounts of money a student can bring.
Compound inequalities are combination of two inequalities combined with "and" , and "or"
And is used, when both inequalities should be true.
Or is used when one of the inequality should be true.
In our case we would use and because we need both inequalities to be true.
The required inequality is:
[tex]\mathbf{x >60\: and\: x<135}[/tex]
(picture included) brainliest
Answers
Answer:
A. y = -1/4x + 1 1/2
B. The rate of change is losing/decreasing -1/4 (y axis unit) per (x axis unit)
Step-by-step explanation:
A. Your equation is 2x + 8y = 12
so solve this for y like any other other question. Start by subtracting 2x from both sides: 8y = -2x + 12
then divide both sides by 8 to isolate y: y = -2/8x + 12/8
simplify your equation: y = -1/4x + 3/2
turn 3/2 into a mixed fraction: y = -1/4x + 1 1/2
B. The rate of change is the same thing as the slope but you say it with units. I cant see a scenario but you can say something like:
The rate of change is losing/decreasing -1/4 (y axis unit) per (x axis unit)
Please help its math...I will give brainliest!
For a holiday sale, all items at Marty’s Electronics are discounted by 25%. Paula bought a laptop that had an original list price of $1,700. If 8% tax was applied to the sale after the discount was taken off, how much did Paula pay for her new computer? SHOW YOUR WORK! Thank you
Answers
Answer:
$1,377
Step-by-step explanation:
the way that I did it-
100-25=75
1700x0.75=1275
8%=0.08, just add a 1 to the sales tax whenever you are calculating that.
1275x1.08=1377
therefore it is $1,377
brainliest would be appreciated :)
do videos give mastary on khan?????????????????
Answers
Answer:
No they are only there so u can understand and answer the questions
Which best explains how you know that A(-1,6) is on the same line as a B( -3,10) and C (-5,14)
Answers
Answer:
To get from A to B and from B to C, you move left 2 units and then up 4 units.
Step-by-step explanation:
hope this helps :)
Which expression is equivalent to StartFraction RootIndex 4 StartRoot 6 EndRoot Over RootIndex 3 StartRoot 2 EndRoot?
Answers
Answer:
C
Step-by-step explanation:
used a calc and took test
HELP!!!! WILL MARK BRAINLIEST!!!!
Answers
Answer:
j
Step-by-step explanation:
-14=6x-8(x+3)
use the distributive property And show the steps that you did
Answers
Answer:
x=-5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
PLEASEEEEE HELPPPPP !!!!!!!!!!! I will mark Brianliesttttt !!!!!!!!!!!!!!!
Answers
Answer:
D. m<RST = 2(m<TSU)
Step-by-step explanation:
Given that m<RST = 76°, m<RSU = 48°, and m<TSU = 38°, this implies that:
SU is an angle bisector of angle RST. Thus,
m<RST is twice the measure of <RSU or <TSU.
Therefore, the only option that is correct is:
D. m<RST = 2(m<TSU)
Solve the system given:
y = -6
y = -2x - 2
A(-3,1)
B (-6,2)
C (1,3)
D (2,-6)
Answers
the answer to your question is:
D (2, -6)
i hope this was helpful ;)
Help me with question 3
Answers
The input x = 1 leads to multiple outputs y = 1 and y = 2 simultaneously, which is why choice D isn't a function.
A function is only possible if any input leads to exactly one output only. Choices A,B and C are all functions for this reason.
Answer:
I believe it would be C.
What is the equation for the
following table:
X Y
1 -5
2 -7
3 -9
4 -11
Answers
y= mx+b
-5= -2(1) + b
-5 = -2 + b
b = -3
equation: y= -2x-3
Plainfield Community Center is buying new seating for their building. They want to purchase a combination of stools and chairs. Stools cost $50 and chairs cost $65. The center cannot spend more than $3000.
Which inequality represents all possible combinations of s stools and c chairs?
50s+65c≤3000
50c+65s≥3000
50s+65c<3000
50c+65s≤3000
Answers
Answer:
D) 50s + 65c ≤ 3000
Step-by-step explanation:
50s represents the stools and 65c represents the chairs
you can't go over 3000 and so this is the only answer that makes sense.
Answer:
The answer is D) 50s + 65c ≤ 3000!
Step-by-step explanation:
I just took the test and i got 100%. Hope this helps! :]
Ms portillo cat weighs 6 kilograms her dog ways 22 more killergrams how much does the dog way
Answers
Answer:
28 kilograms
Step-by-step explanation:
All you have to do is 22+6