the diagram shows a right-angle triangle.
Answer:
Step-by-step explanation
The shortest length of the right-angled triangle is 4 cm.
What is a right-angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angles is a right angle.
Given is, the diagram shows a right-angle triangle.
We have area of the right-angle triangle = 18 cm²
We know that area of a right-angle triangle = 1/2(base)(height)
18 = 1/2(x - 1)(x + 4)
36 = (x - 1)(x + 4)
x² + 4x - x - 4 = 36
x² + 3x - 4 = 36
x² + 3x - 4 - 36 = 0
x² + 3x - 40 = 0
x² - 5x + 8x - 40 = 0
x(x - 5) + 8(x - 5) = 0
x + 8)(x - 5) = 0
x = -8 or 5
we can only use positive numbers because length can't be negative,
Thus, x = 5
The shortest side is definitely one of the 2 legs. The hypotenuse of a triangle is the longest side.
Therefore,
height = x - 1 = 5 - 1 = 4 cm
base = x + 4 = 5 + 4 = 9 cm
Hence, the shortest length of the right-angled triangle is 4 cm.
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Select all the correct answers.
Which relations represent functions?
Answer:
First and third relations represent functions.
Step-by-step explanation:
First and third relations are one-to-one and many-to-one respectively, therefore these are functions.
Second and fourth relations are one - to - many, thus they are not functions.
Answer:
first and third
Step-by-step explanation: just took the test like 5 secs ago
The info is in the picture
Answer:
no it isn't the inverse.
solve the equation:
6= k/9
k=
PLSSSSSSSSSSSSSSSSSS HELP MEEEE
PLZZZZ HELP!!! what is y = 2/3x - 6 in standard form
Answer:
2
x
−
3
y
=
18
Step-by-step explanation:
Hope I helped
Please help!! I’m stuck on this one haha
Answer:
Ready to help soon as we know what that "one" is
Answer:
hahaha where is the pic
Step-by-step explanation:
please help me in math
EASY PLEASE HELP PLEASE HELP 15 POINTS...PLEASE HELP
Answer: its is 3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Lara measured a swimming pool MAD scale drawing scale used what is 9 mm: 4 m in the drawing the pools 99 mm long what is the length of the actual pool
Answer: The actual pool is 44 m long.
Step-by-step explanation:
Given : The scale used for drawing :
9 mm: 4 m
i.e. for each 1 mm of drawing we have [tex]\dfrac{4}{9}\ \text{m}[/tex] of actual pool.
If the pool is 909 m long , then the actual pool will be [tex]\dfrac49\times99= 4\times11=44\text{ m long.}[/tex]
hence, the actual pool is 44 m long.
what is the interior of a decagon
Answer:
Decagon Definitions A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° 144 ° and they all add up to 1,440° 1,440 °.
Step-by-step explanation:
really hope this helps, Good luck ^w
help me please , the question is in the picture .
Answer: 4.2x10^5=420000
Step-by-step explanation: its a positive five so you go in the positive direction from the decimal but if it was a negative you could go the other way (hope this helps)
1) a verify : x² + 4x+3 = (x+2) ²)
Answer:
NO
Step-by-step explanation:
X^2+4X+3=(X+2)(X+2)
X^2+4X+3=X^2+2X+2X+4
X^2+4X+3=X^2+4X+4
Answer:
undefined
Step-by-step explanation:
x²+4x+3 = (x+2)²
first of all you open the bracket on the Right hand side..
(x+2)² = (x+2)(x+2)
= x(x+2)+ 2(x+2)
=x²+2x+ 2x+4
= x²+4x+4
therefore,
x²+4x+3 = x²+4x+4
next, we collect all like terms together,
x²-x²+4x-4x = 4-3
0+0 = 1
the answer is undefined
because 0 cannot be equal to 1
Find the slope of line
Answer:
2/4
Step-by-step explanation:
rise/run
go up (rise) 2, run 4
2/4
Robert found a game spinner that was not completely labeled. The spinner is shown at right. Help Robert figure out what fraction of the spinner is missing.
Circle with four unequal sections, labeled: 1 third, blank, 1 sixth, 3 eighths.
Step-by-step explanation:
Where is the image of the spinner shown?
Suppose a system of two linear equations has one solution. What must be true about the graphs of the two equations?
They intersect at one point.
They intersect at two points.
They have the same slope.
They have the same y-intercept.
Answer:
They intersect at one point
Step-by-step explanation:
I took the test and got 100%
Answer:
They have to intersect at one point
Step-by-step explanation:
Pls find m<1 TYSM! **the answer is not 40**
Step-by-step explanation:
Does that make sense to u??
write the polynomial in standard form 3-3m+4m^{2} -1/2m^{6}
Answer:
[tex]3-3m+4m^2-\frac{1}{2} m^6[/tex]
Step-by-step explanation:
Write each fraction in simplest form.
1) 4/8
2) 3/9
??
22
3) 9/12
??
4) 3/6
??
Step-by-step explanation:
1. 4/8=1/2
2.3/9=1/3
3.9/12=3/4
4.3/6=1/2
I NEED HELP ON 4 and 5 PLEASE HELP
Answer:
#4 See attachments
#5 See attachments
Step-by-step explanation:
Please help me i'm not very good at math :))
Answer: (1, 5)
Explanation:
You really just have to input all the variables into the inequality and see if it is accurate.
(2, 4)
4 > 2(2) 4 > 4 no, it is equal to, not greater than
4 > 3 yes
(0, 3)
3 > 2(0) 3 > 0 yes
3 > 3 no, again, equal to
(4, 6)
6 > 2(4) 6 > 8 no
6 > 3 yes
(1, 5)
5 > 2(1) 5 > 2 yes
5 > 3 yes
Notice that two line segments are formed on each transversal between the central parallel line and the outer parallel lines. Measure the lengths of the four line segments.
Answer:
Picture?
Step-by-step explanation:
Answer:
heres the picture
Step-by-step explanation:
a(b + c) = a • b + a • c, where a, b, and c are real numbers
Use the distributive property to simplify the expression.
8(3 + 4) = 24 +
Answer:
a(b + c) = a • b + a • c
=> 8(3 + 4) = 8.3 + 8.4 = 24 + 32
Step-by-step explanation:
Answer:
The answer for the blank is 32
Step-by-step explanation:
8x - 9 - 5x = 3x - 36 - 18x
Answer:
[tex]8x - 9 - 5x = 3x - 36 - 18x \\ 8x - 5x - 9 = 3x - 18x - 36 \\ 3x - 9 = - 15x - 36 \\ 3x = - 15x - 36 + 9 \\ 3x = - 15x - 27 \\ 3x + - 15x = - 27 \\ - 12x = - 27 \\ x = \frac{ 27}{12} [/tex]
How much will you get paid if you work 28.5 hours for $7.75 per hour?
Answer:
you will get $220.87 hope this helps :) .
Select the correct answer. Which equation, when solved, gives 8 for the value of x?
The 3rd equation, as if you solve for x as shown, you will end up with equation x=8.
[tex]\frac{5}{4}x-\frac{3}{2}x=-4+2[/tex]
[tex]\frac{5}{4}x-\frac{6}{4}x=-2[/tex]
[tex]-\frac{1}{4}x=-2[/tex]
[tex]x=8[/tex]
The manager of a garden store decides to hold a Buy 3, Get 1 Free sale on vegetable plants. The sale is held for one week and a total of 636
vegetable plants were sold (not including the ones given away for free). If each plant cost the store $2.90, how much money did the store lose
by giving away the free plants?
Answer:
the shop lost $922.20 by giving away free vegetable plants.
Step-by-step explanation:
you would start by dividing 636 by two to see how many free vegetable plants were given away.
636 / 2 = 318
this shows us how many free vegetable plants were given for free, so then to find how much money the store lost giving them away for free, you would multiply 318 by 2.9
318 x 2.9 = 922.2
Therefore the shop lost $922.20 by giving away free vegetable plants.
Rewrite the rational exponent as a radical
Answer:
C OR D
Step-by-step explanation:
Radio signals travel at a rate of 3 × 10^8 meters per second. How many seconds will it take for a radio signal to travel from a satellite to the surface of the Earth if the satellite is orbiting at a height of 3.6 × 10^7 meters?
10.8 × 10^15 seconds
1.2 × 10^–1 seconds
1.08 × 10^16 seconds
8.3 seconds
Answer:
b or 1.2*10⁻1
Step-by-step explanation:
10^8=one hundred million and that *3=three hundred million
10^7=ten million*3.6=36 million.
it has to be about 0.1 seconds so b
Answer:
1.2 × [tex]10^{-1}[/tex] of a second
Step-by-step explanation:
d = vt , t = d / v
t = ( 3.6 × [tex]10^{7}[/tex] )( 3 × [tex]10^{8}[/tex] ) = (3.6 ÷ 3) × ( [tex]10^{7}[/tex] ÷ [tex]10^{8}[/tex] ) = 1.2 × [tex]10^{7 - 8}[/tex] = 0.12 of second
t = 1.2 × [tex]10^{-1}[/tex] of a second
A circle has a circumference of 452.16 units. what is the radius
Answer:
Circumference = 2*r*pi
452.16 = 2*r*pi
226.08 = r*pi
226.08 = r*(3.14)
72 = r
The radius is 72
Step-by-step explanation:
the amount of sleep that elementary school children get per night follows a normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours. is it unusual for an elementary student to get at least 12 hours of sleep?
Answer:
Yes, that is unusual as the problem is given.
Step-by-step explanation:
If the mean is 9.5 and the standard deviation is 0.55, then anything within the normal curve of 10.05 on the high end and 8.45 on the low end is normal. 12 is more than several standard deviations or an outlier if this makes sense.
So, it is unusual as the problem is stated, but if it's a weekend, 12 hours is normal. LOL
Good luck!
Based on the normal distribution parameters given, the probability of a student getting atleast 12 hours of sleep ls 0. Hence, it is abnormal.
Given the Parameters :
Mean = 9.5 Standard deviation = 0.55Using the Zscore formula, the probability of getting a atleast 12 hours of sleep can be expressed thus :
Zscore = (Score - Mean) / standard deviation
For X ≥ 12 :
Z = (12 - 9.5) / 0.55 = 4.545The probability using a normal distribution table :
P(Z ≥ 4.54) = 1 - P(Z ≤ 4.54)
P(Z ≤ 4.54) = 1 ( normal distribution table)
P(Z ≥ 4.54) = 1 - 1 = 0
Since, the probability is 0 ; hence, it is unlikely and therefore, abnormal.
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