Solved previously.The altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units. What is the area of the triangle, in square units
Answers
Answer:
6√3 square units
Step-by-step explanation:
The ratios of side lengths in a 30°-60°-90° triangle are 1 : √3 : 2. Using this fact, we can find the lengths of the orthogonal sides of the triangle to be ...
3(2/√3) = 2√3 . . . . side AB in the attached figure
and
2·3 = 6 . . . . . . . . . . side AC in the attached figure
Then the area of the triangle is ...
A = 1/2bh
A = 1/2(6)(2√3) = 6√3 . . . . square units
Related Questions
All the workers in a company were asked a survey question. The two-way frequency table shows the responses from the workers in the day shift and night shift. Complete parts a and b.
Please don't ask me to download the answer
Answers
A two-way relative frequency table consists of two types of data or data in two categories one relating to the columns and the other relating to the rows.
Shift Response
Yes No Total
Day
67% 33% 100%
Night
23% 77% 100%
Total
45% 55% 200%
In this table there is data relating to two categories day/ night and yes/no.
Along the rows the percentages of the day/night data are calculated.
Along the columns the percentages of the yes/no data are calculated.
Shift Response
Yes No Total
Day 67/100*100 33/100 *100 100
= 67% =33% 100%
Night 23/100*100 77/100*100 100
= 23% =77% 100%
Total 90/200 *100 110/200*100 200
= 45% = 55% 200%
These calculations are done by dividing the row cells by their respective row totals.
Similarly the columns cells are filled by dividing the column cells with their respective column totals.
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60 Point Question Answer ASAP! Brainliest to best/first answer
Answers
Step-by-step explanation:
the change rate between the data points gives us the print rate.
so,
(f(x2) - f(x1)) / (x2 - x1)
starting with x1 = 10 and x2 = 15 we see
(133 - 98) / (15 - 10) = 35/5 = 7
that means he is printing 7 pages per minute.
we see that we have the same difference (35 prints) for every following 5-minute interval.
so, that is the confirmed print rate.
and yes, the amount is increasing, of course.
after 10 minutes he has 98 flyers but we know he could have printed only 7×10 = 70 flyers in that time.
so, he started with 98-70 = 28 flyers before actually printing new ones.
Mr Brown bought TV for a total money of 20000 including VAT of VAT is 15% then find the original price of the tv
Answers
Answer:
17,391.30
Step-by-step explanation:
original is always 100%.
if 115% = 20000
wat of 100%= ?
crossmultiply to obtain 17,391.30 as the original price.
Drag and drop the answers to the boxes to correctly complete the proof.
Given: Rhombus JKMH with diagonals intersecting at point P
Rhombus J K M H with diagonals J M and H K intersecting at P
Prove: JM⎯⎯⎯⎯⎯⊥HK⎯⎯⎯⎯⎯⎯
By the definition of Response area, JK⎯⎯⎯⎯⎯≅KM⎯⎯⎯⎯⎯⎯ and by the reflexive property of congruence, KP⎯⎯⎯⎯⎯≅KP⎯⎯⎯⎯⎯ . Because the diagonals of a rhombus bisect a pair of opposite angles, ∠JKP≅∠MKP , making △JKP≅△MKP by the Response area. Because Response area, ∠JPK≅∠MPK, and these angles are right angles because two angles that form a linear pair are congruent, thereby making JM⎯⎯⎯⎯⎯⊥HK⎯⎯⎯⎯⎯⎯ by the definition of perpendicular segments.
Response area means blank
The answers are Congruent segments, a rhombus, a parallelogram, SSS congruence postulate, ASA congruence postulate, SAS congruence postulate, CPCTC, they are adjacent, and vertical angles are congruent
Answers
The completed proof is presented as follows;
By definition of a rhombus [tex]\overline{JK} \cong \overline{KM}[/tex] and by the reflexive property of
congruence [tex]\overline{KP} \cong \overline{KP}[/tex], because the diagonals of a rhombus bisect a pair
of opposite angles, ∠JKP ≅ ∠MKP, making ΔJKP ≅ ΔMKP by the SAS
congruency postulate, because CPCTC, ∠JPK ≅ ∠MPK, and these angles
are right angles because two angles that form a linear pair are congruent,
thereby making, [tex]\overline{JK} \perp \overline{KM}[/tex] by definition of perpendicular segments.
Reasons:
Please find attached the drawing of the given rhombus JKMH, that show
the point of intersection of the diagonals JM and HK at point P.
A rhombus is an equilateral quadrilateral, therefore, the adjacent sides [tex]\overline{JK} \ and \ \overline{KM}[/tex] are congruent.The SAS congruency postulate states that if a triangle has two sides and an included angle that are congruent to two sides and an included angle of another triangle, then the two triangles are congruent.CPCTC is an acronym for Congruent Parts of Congruent Triangles are Congruent.Learn more about the properties of a rhombus here:
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What is the solution to the 2nd degree equation below?x² + 2x + 4 = 0
Answers
Answer:
x = (−2 ± √−12)/2
Step-by-step explanation:
Using the quadratic formula (search it up if you don't know what it is, but it's basically the first thing in the pic):
The graph shows the amount of rain that falls over time. Does the rain fall at a constant or variable rate? How much rain falls per hour?
thanks!
Answers
Answer: yes, it does fall at a constant rate. for each hour there is one inch of rainfall.
Step-by-step explanation:
if the line goes the the origin (0,0) then that means that it is a constant rate. if you look at the chart, there is number on every other line. This means that there is an odd number on the other lines. If you then go up the line for 1 hour, then you will meet at lines intersecting to get 1 inch of rainfall per hour
An artist spends $80 on brushes and paint. For canvas and
frames, she has to spend an additional $20 per painting.
Write an equation in slope-intercept form(y=mx+b) that shows
the relationship between the artist's total expenses(y) and the
number of paintings(x) that she makes.
Answers
Answer:
y = 20x + 80
Step-by-step explanation:
Which of the following is the ratio of 5 cm to 10 km
Answers
Answer:
1/200000
Step-by-step explanation:
first 10 km equals to 1000000cm
so 5/1000000cm
equals to 1/200000
5. Name a pair of supplementary angles.
6.Name a pair of vertical angles
7.Name a pair of adjacent angles
(Please answer if u can!)
Answers
Answer:
5. Angles FGE and CGE are supplementary
6. Angles FGE and BGC are vertical
7. Angles FGE and GED are adjacent
Step-by-step explanation:
Problem 5
Answer: Angle EGF and angle FGBExplanation:
The straight line EGB can be decomposed into the angle pieces of angle EGF and angle FGB. Another way we can break this straight angle down is to break it into angle EGA and angle AGB. Whichever route you go for, the smaller angles add back to 180 degrees. There are other possible answers you could go for. Check out the diagram below for a visual of these angles (shown in red)
========================================================
Problem 6
Answer: Angle AGB and angle EGD
Explanation:
Focus on lines AD and EB. They intersect at point G. The two lines form the opposite angles AGD and EGD which are considered vertical angles. Whenever we have an X shape like this, we'll have vertical angles in the opposite positions like this. Vertical angles are always congruent. There are other pairs of vertical angles shown in this diagram. Check out the diagram below for a visual of these angles (shown in blue)
========================================================
Problem 7
Answer: Angle BGC and Angle CGDExplanation:
The angles BGC and CGD are right next to each other, so we consider them adjacent. They share the common ray GC. Think of it like two neighbors sharing a common wall in an apartment building. There are other possible answers you could go with as long as the two angles share a common ray or line, and also share a common vertex as well. Check out the diagram below for a visual of these angles (shown in green)
Jasmine bought 32 kiwi fruit for $16. How many kiwi can Lisa buy if she has $4?
Answers
Answer:
8 kiwis
Step-by-step explanation:
32/16= 2
2 kiwi for $1
4*2= 8
Answer:
8
Step-by-step explanation:
Method 1:
32 kiwi = $16
(÷4)
8 kiwi = $4
(take $16 divided by $4 to find the number of sets of 8 kiwis. hope this helps.)
Ans: 8
Method 2:
$16 ÷ 32 = $0.50 (cost of 1 kiwi)
$4÷$0.50=8
Patrica earns $12.50 per hour. She saves $3.25 of her hourly pay. What percentage of her hourly salary does she save?
Answers
Answer:
26%
Step-by-step explanation:
Well, we need to find what percent 3.25 is of 12.50.
12.50*x=3.25
3.25/12.50=.26
26% is saved.
mikah bought a dozen cupcakes for her friends birthday. if she paid 3.48 dollars for the cupcakes what was the cost per cupcake. explain please
Answers
1 cupcake = $3.48/12 = $0.29
Each cupcake must equal $0.29. To prove this, if we multiply 0.29 by 12, we should get her original cost of $3.48.
geometry - please help
solve for x & y
Answers
Hope it helps.
Don't forget to click the Brainliest button if you like my answer and if you have any query, feel free to ask in the comment section.
Bob's Gift Shop sold 350 cards for Mother's Day. One salesman, Bentley, sold 2% of the cards sold for Mother's Day. How many cards did Bentley sell?
Answers
2% of 350 is 7, so Bentley sold 7 cards on Mother's Day
One bunch of seedless black grapes cost $2. How many bunches can you buy for $20?
Answers
Answer:
If one bunch is two dollars even, then you could buy 10 bunches.
Step-by-step explanation:
20 divided by 2 = 10
So, you could buy ten bunches of grapes.
Answer:
the answer is 10 because 2 goes into 20 10 times.
Step-by-step explanation:
What factoring pattern can you use to solve x^2+14x+49=0
A (ax+√c)^2=0
B (√a*x+√c)^2=0
C (√a*x+c)(√a*x-c)=0
D (ax+√c)(ax-√c)=c
Answers
Answer:
B (√a*x+√c)^2=0
Step-by-step explanation:
It can be helpful to look a the expanded form of each of these factoring patterns.
A (ax+√c)^2=0 ⇒ a^2x^2 +2a√c*x +c = 0
B (√a*x+√c)^2=0 ⇒ ax^2 +2√(ac)*x +c = 0
C (√a*x+c)(√a*x-c)=0 ⇒ ax^2 -c^2 = 0
D (ax+√c)(ax-√c)=c ⇒ a^2x^2 -c = c
If 'a' and 'c' represent the coefficients in the given equation, then choices A, C, and D can be eliminated. The expanded forms of those end up with a^2 and/or c^2 as coefficients, not 'a' and 'c'.
Choice B is the only sensible one, and fits the given equation.
a = 1, c = 49 ⇒ √a = 1, √c = 7
x^2 +14x +49 = (x +7)^2 = 0 . . . . . factored using Pattern B
A man has a collection of 19 coins worth $2.55. There are twice as many nickels as dimes. If the rest are quarters, how many quarters are there?
Answers
Answer:
7 quarters
Step-by-step explanation:
At a football stadium, 10% of the fans in attendance were teenagers. If there were 30 teenagers at the football stadium, what was the total number of people at the stadium?
Insert the values given in the problem then scale up or down to find the missing value.
Answers
Answer:
i believe the answer to this is a total of 300 people because you multiply the ten percent into the 30 people which factors out some numerical values, so then your answer as i just said is 300 people in total attended the game.
Step-by-step explanation:
what is 3 3/5 - 6 1/7
Answers
3 3/5 - 6 1/7
18/5 - 43/7
= -89/35
= -2 19/35
Fill with possible values to make the statement true in 2 diffrent ways:
35 is _% of _
Answers
Answer:
35 is 35% of 100 and 35 is 17.5% out of 200
Step-by-step explanation:
1/3 + 3/5 in fraction form
Answers
Solution: 1/3 + 3/5
Take the LCM of 3 and 5 is 15.
⇛(5+9)/15
⇛14/15 in fractional form.
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-1 5/6 ÷ -3 1/3 in fraction form...
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Answer:
14/15
Step-by-step explanation:
When you simplify a fraction, you have to divide or multiply the numerator(the top number) and the denominator(the bottom number) by the same number. In order to add or subtract two fractions, both have to have the same denominator. The LCD, or least common denominator, of 3 and 5 is 15. 15÷3=5, so you multiply 1/3 by 5 and and 5 to get 5/15. 15÷3=5, so you multiply 3/5 by 3 and 3 to get 9/15. The denominator stays the same when adding or subtracting fractions, and 5+9=14, so the answer is 14/15.
In ΔFGH, f = 830 inches, g = 460 inches and h=500 inches. Find the measure of ∠H to the nearest degree.
Answers
Answer:
32 degrees
Step-by-step explanation:
The law of cosines can be used for this:
h^2 = f^2 +g^2 -2fg·cos(H)
cos(H) = (f^2 +g^2 -h^2)/(2fg)
cos(H) = (650,500/763,600)
H = arccos(6505/7636) ≈ 31.5826°
10-4/4x89-1/2+43992/69x174
Answers
10.127781530000000000
What is the equation to find the slope
m=
Answers
Answer:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Step-by-step explanation:
Answer:
[tex]\huge\boxed{m=\frac{y_2-y_1}{x_2-x_1} }[/tex]
Step-by-step explanation:
The equation for slope is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], when given two points,
[tex](x_1,y_1), and (x_2,y_2)[/tex].
Hope it helps :) and let me know if you want me to elaborate.
In a survey, 3 out of 20 students were left-handed. Based on this information, if 300 students were interviewed, how many of them could be expected to be left-handed?
Answers
Based on the information given, from the fraction, it can be noted that the number of left-handed people will be 45.
From the information given, it was stated that in the survey, 3 out of 20 students were left-handed.
Therefore, in a population of 300 people, the number of left handed people will be:
= 3/20 × 300.
= 3 × 15
= 45
There are 45 left handed people.
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if p(q) = q^2 + 4q − 12,then what is p(−1)?
Answers
Step-by-step:
Plug -1 into the equation in place of q.
p(-1) = (-1)^2 + 4(-1) - 12
p(-1) = (-1)^2 - 4 - 12
p(-1) = (-1)^2 -16
p(-1) = 1 - 16
p(-1) = -15
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring q2-4q-12
The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .
-12 + 1 = -11
-6 + 2 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
q2 - 6q + 2q - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
2 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q+2) • (q-6)
Which is the desired factorization
Equation at the end of step
1
:
(q + 2) • (q - 6) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : q+2 = 0
Subtract 2 from both sides of the equation :
q = -2
Solving a Single Variable Equation:
2.3 Solve : q-6 = 0
Add 6 to both sides of the equation :
q = 6
Supplement : Solving Quadratic Equation Directly
Solving q2-4q-12 = 0 directly
12 times 3/8 and simplified
Answers
Answer:
4 1/2
Step-by-step explanation:
[tex]12*\frac{3}{8} \\=3*\frac{3}{2} \\=9/2= 4 \frac{1}{2}[/tex]
The graph of a proportional relationship passes through the given point and (1, y). Find y.
Given point: (19, 342)
Answers
Answer: 4/3
Step-by-step explanation:
PLEASE HELP. I'LL GIVE BRAINLIEST.
Find the missing value to complete the square. So what is the value of the question mark that would make the equation true.
x² + 8x + ?
Answers
Answer:
16
Step-by-step explanation:
(x+4)(x+4)
Answer:
The answer is 16.
Step-by-step explanation:
Since the 8x is positive, the equation [tex](x+y)^2[/tex] must have y as a positive number.
Let's see this!
An easy way to complete the square if you have the constants for x2 and
But not the non-variable number is to divide the x constant, and then square it.
Example:
[tex]\frac{8x}{2} \\\\4^2=16[/tex]
The last number must be 16. Let's check it.
[tex](x+4)^2=x^2+8x+16[/tex]
What is the length of DE?
А. 8
В. 7
С. 6
D. 5