The longer leg of a right triangle is 4 inches longer than the shorter leg. The hypotenuse is 8 inches longer than the shorter leg. Find the side lengths of the
triangle.
Answers
Answer:
lengths are 12, 16, and 20
Step-by-step explanation:
let 's' = length of smaller leg
let '4+s' = length of second leg
let '8+s' = length of hypotenuse
Now use the Pythagorean Theorem: a² + b² = c²
s² + (4+s)² = (8+s)²
s² + 16 + 8s + s² = 64 + 16s + s²
2s² + 8s + 16 = 64 + 16s + s²
subtract s² from each side:
s² + 8s + 16 = 64 + 16s
subtract '16s' from each side:
s² - 8s + 16 = 64
subtract 64 from each side:
s² -8s - 48 = 0
factor:
(s+4)(s-12) = 0
's equals -4 and 12 but -4 is discarded as a length so smallest side is 12
Related Questions
tell whether the sequence is arithmetic if it is what is the common difference?
19, 12, 5, -2
no
yes; 1/7
yes;7
yes;-7
Answers
Answer:
(d) yes; -7
Step-by-step explanation:
The differences between terms are ...
12 -19 = -7
5 -12 = -7
-2 -5 = -7
These are all the same, so this difference is "common". A sequence in which terms have a common difference is an arithmetic sequence.
This sequence is arithmetic, with a common difference of -7.
can I have help pls
Answers
What is the value of the expression n(8n/10) when n =
5?
Answers
Answer:
(8n/10)
8 × 5 = 40
40 ÷ 10 = 4
Solve for x in the triangle.
Answers
Answer:
A. 1.7
Step-by-step explanation:
x = 1.74303
If rounded, 1.7
Answer: 100% correct
1. A. 1.7
2. D. 64.4
3. A= 140, E= 24, and F= 16
4. 106 mi
Step-by-step explanation:
There is a picture inside the question pls help asap!!
Answers
Explanation:
Could I get brainliest for my amazing efforts.
Find the area of quadrilateral ABCD.
A. 20.2 units²
B. 20.4 units²
C. 37.66 units²
D. 46.66 units²
Answers
HELP PLEASE, IF YOU GET IT RIGHT YOU WILL RECEIVE BRAINIEST !!!!
Answers
Answer:
ok it is very hardest app
I need this answered ASAP. A baseball hit by
a player in the major leagues
can leave the bat at a speed
of 110 miles per hour.
Suppose a batter hits a ball
at that speed directly back
to the pitcher’s mound,
about 61 feet from home
plate. To the nearest tenth of
a second, how long does it
take the ball to reach the mound?
Answers
Consider the polynomial p(x) = 16x4 - 81y4. Which of the following are equivalent expressions?
Select all that apply.
Answers
Answer:
Second expression and Last expression
Step-by-step explanation:
Second expression and Last expression
1. [tex](4x^2-9y^2)(4x^2-9y^2)[/tex]
[tex]4x^2(4x^2-9y^2)-9y^2(4x^2-9y^2)[/tex]
[tex]16x^4 -36x^2y^2 -36x^2y^2+81y^4[/tex]
[tex]16x^4 -72x^2y^2+81y^4[/tex]
2. [tex](4x^2-9y^2)(4x^2+9y^2)[/tex]
[tex]4x^2(4x^2+9y^2)-9y^2(4x^2+9y^2)[/tex]
[tex]16x^4+36x^2y^2-36x^2y^2-81y^4[/tex]
[tex]16x^4-36y^4[/tex]
3. [tex](4x^2+9y^2)(2x-3y)(2x-3y)[/tex]
[tex](4x^2+9y^2)(4x^2-6xy-6xy+9y^2)[/tex]
[tex](4x^2+9y^2)(4x^2-12xy+9y^2)[/tex]
[tex]16x^4-48x^3y+36x^2y^2+36x^2y^2-108xy^3+81y^4[/tex]
[tex]16x^4 -48x^3y+72x^2y^2-108y^3+81y^4[/tex]
4. [tex](4x^2+9y^2)(2x+3y)(2x+3y)[/tex]
[tex](4x^2+9y^2)(4x^2+6xy+6xy+9y^2)[/tex]
[tex](4x^2+9y^2)(4x^2+12xy+9y^2)[/tex]
[tex]16x^4+48x^3y+36x^2y^2+36x^2y^2+108xy^3+81y^4[/tex]
[tex]16x^4+48x^3y+72x^2^2+108xy^3+81y^4[/tex]
5. [tex](4x^2+9y^2)(2x+3y)(2x-3y)[/tex]
[tex](4x^2+9y^2)(4x^2-6xy+6xy-9y^2)[/tex]
[tex](4x^2+9y^2)(4x^2-9y^2)[/tex]
[tex]16x^4-36x^2y^2+36x^2y^2-81y^4[/tex]
[tex]16x^4-81y^4[/tex]
Hope this helps!
F(x)=2x+6, g(x)=4x^2+1; find (g • f)(1)
Answers
Answer:
257
Step-by-step explanation:
[tex]g\cdot{f}=4(2x+6)^2+1\\(g\cdot{f})(1)=4(2*1+6)^2+1=4\times64+1=257[/tex]
If each of the numbers in the following data set were multiplied by 18, what
would be the new median of the data set?
14, 20, 18, 58, 71, 36, 28
what would be the new median of the data set ?
Answers
The answer is 28 or 504. My explanation....
ALRIGHT! So, it took me a little while to do it all.... since I wasn't really sure if it was already multiplied by 18 or not.
So the normal numbers in order from least to greatest,(because that's easier)
14, 18, 20, 28, 36, 58, 71.
The new numbers I multiplied by 18 are...
252, 324, 360, 504, 648, 1044, 1268.
When I put it like that you can clearly see the new median. 28 and 504!
let’s decide whether the following points are on the line 2x=y - 7
(-8.6, -10.2)
Answers
Answer:
14.997
Step-by-step explanation:
yea yeaaa i knowwww
what is 4,357.25 rounded to the second decimal
Answers
what is 4,357.25 rounded to the second decimal
A:4,400
If you only have a 1 3 cup measuring cup and a recipe calls for 5 1 3 cups of flour, how many 1/3 cups would you need to use?
Answers
Answer:
You would need 16 1/3 cups!
Step-by-step explanation:
I used an equation, but you could also use mental conversions! :
1/3c = 5 1/3
(1/3c)3 = (5 1/3)3 (multiply each side by 3 (3/1))
3c /3 = (48) /3 (divide each side by 3)
c = 16
:)
(c = cups!)
The requried number of 1/3 cups to make the recipe is 16.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Measuring cup = 1/3
Recipe required number of cups = 5 1/3 of flour,
Let the number of 1/3 cups = x
1/3x = 5 1 / 3
x/3 = 16 / 3
x = 16
Thus, the requried number of 1/3 cups to make the recipe is 16.
Learn more about models here:
https://brainly.com/question/22591166
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Pls help rn i need help quickly
Answers
Answer:
800 mm^2
Step-by-step explanation:
(25+7)*(23+8) - 8*10 - 7*5 - 7*11
= 800 mm^2
A class has 7 boys and 10 girls. Select all associated ratios for this class.
10:3
7:3
17:5
7:17
10:7
10:17
7:10
3:7
Answers
Answer:
7:10
Step-by-step explanation:
…..
because boys number is 7 and girl number is 10 so
Write the standard form of the line that contains a slope of 12 and y-intercept of 3. Include your work in your final answer.
Answers
Answer:
y = 12x+3
Step-by-step explanation:
y = mx+c
m is the gradient/slope
c is the y intercept
so m is 12 and c is 3
Find the area of the regular 18-gon with radius 11 mm
Answers
Answer:
36
Step-by-step explanation:
When a number is decreased by 40% of itself, the result is 90. What is the number?
Answers
• Let the number be 'x'.
• Then, 40% of x -
= 40/100 × x
= 2/5 × x
= 2x/5
• Now, decreased number -
= x - 2x/5
= (5x - 2x)/5
= 3x/5
• But, according to the question, decreased number = 90
=> 3x/5 = 90
=> x = 90 × 5/3
=> x = 450/3
=> x = 150
• Hence, the number is 150
• Now, if 150 is increased by 40% -
= 150 + 40% of 150
= 150 + 40/100 × 150
= 150 + 4 × 15
= 150 + 60
= 210
__________________
DefinitionsPercentage - In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Solvewe can substitute 40% for 0.4x and make an equation
[tex]x-0.4=90[/tex]
simplify
[tex]0.6x=90[/tex]
divide both sides by 0.6
[tex]x=150[/tex]
Amelia has $25 to spend on makeup this week she loves lipstick each lipstick tube cost $4 what is the maximum number of lipsticks that she can purchase
one step inequality word problems
Answers
Answer:
ok so x is how many she can buy so
4x≤25
x=6.26
so she can buy 6
Hope This Helps!!!
Draw a picture of 3 5/7 as a fraction.
Answers
If you would do this in whole number form, it'll be 40/7.
Answer:
3 5/7
Step-by-step explanation:
picture
Incorrect
Question 6
VNIA.
The figure is a trapezoid. Solve for the measure of angle Hand the measure of angle K.
1
439
H
a
104°
K
76
measure of angle H =
measure of angle K = 137
Answers
Answer:
∠H = 137°
∠K = 76°
Step-by-step explanation:
The sum of the interior angles of a trapezoid = 360°
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180°
The legs are the non-parallel sides: JK and HI
Therefore, 104 + ∠K = 180
⇒ ∠K = 180 - 104 = 76°
And, ∠H + 43 = 180
⇒ ∠H = 180 - 43 = 137°
Sum of two adjacent angles in trapezium equals 180°
[tex]\\ \tt\hookrightarrow <H+43=180[/tex]
[tex]\\ \tt\hookrightarrow <H=180-43[/tex]
[tex]\\ \tt\hookrightarrow <H=137[/tex]
And
[tex]\\ \tt\hookrightarrow <K+104=180[/tex]
[tex]\\ \tt\hookrightarrow <K=180-104[/tex]
[tex]\\ \tt\hookrightarrow <K=76°[/tex]
Determine which point is the solution to the given system.
y= -7/2 x + 32
y= 4/5 x -11
A. (10,-3)
B. (8,4)
C. (15, 1)
D. (12,-10)
Answers
Answer:
WHAT UP
Step-by-step explanation:
DO THIS AND THAT LOL
Find the dimensions of a rectangle
having a perimeter of 38 meters
and an area of 84 square meters.
What is the length of the shorter side?
Answers
Find the value of x and y in parallelogram ABCD.
A) x = 13, y = 7
B) x = 15, y = 6
C) x = 1, y = 1
D) x = 6, y = 8
E) None of the answers are correct
Answers
Step-by-step explanation:
х-7=6 , х=13
2у-6=8 у= 7
А)
HELP ME FIND MIDPOINT
Answers
Answer: (-1/2, 0) which is the same as saying (-0.5, 0)
================================================
Explanation:
The x coordinates of A and B are -2 and 1 respectively.
Add up those values to get -2+1 = -1
Then cut that result in half: -1/2 = -0.5
This is the x coordinate of the midpoint.
--------
Repeat for the y coordinates:
Add: 1 + (-1) = 0
Cut in half: 0/2 = 0
The y coordinate of the midpoint is 0
-------
Overall, the midpoint is located at (-1/2, 0) which is the same as writing (-0.5, 0). This is where the segment AB crosses the x axis.
Need help!!!
Select the correct answer.
Which table represents a quadratic relationship?
Answers
stay safe!
The table which represents a quadratic relationship is in option [tex]D[/tex].
What is quadratic relationship ?A quadratic relationship is a mathematical relation between two variables that follows the form of a quadratic equation.
Quadratic sequence [tex]=an^2 +bn+c[/tex]
So, According to the definition mentioned above if table follows the form of a quadratic equation then it is in quadratic relationship.
So,
To find out quadratic relationship,
We will find first difference in every table and then second difference (Second difference is the difference between the first difference).
We have,
Table A;
[tex]\left \begin{array}{ccccc}x& \ &f(x)&First\ Difference & Second\ Difference \\-2& &4&2-4=-2\\-1& &2&1-2=-1&-1+2=1\\0& \ &1&0.5-1=-0.5&-0.5+1=0.5\\1& &0.5&0.25-0.5=-0.25&-0.25+0.5=0.25\\2& &0.25&0.125-0.25=-0.125\\3& &0.125\end{array}\right[/tex]
So, In the above table we can see that second difference is not equal that means it is not in quadratic relationship.
Now,
Let Table D;
[tex]\left \begin{array}{ccccc}x& \ &f(x)&First\ Difference & Second\ Difference \\-2& &-23.4&\\-1& &-23.2&-23.2+23.4=-0.2&0.2-0.2=0\\0& \ &-23&-23+23.2=-0.2&0.2-0.2=0\\1& &-22.8&-22.8+23=-0.2&0.2-0.2=0\\2& &-22.6&-22.6+22.8=-0.2\\3& &-22.4&-22.4+22.6=-0.2\end{array}\right[/tex]
So, here in this table, we can see that second difference is equal that means it is in quadratic relationship.
Hence, we can say that the table which represents a quadratic relationship is in option [tex]D[/tex].
To know more about quadratic relationship click here
https://brainly.com/question/17109031
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Quadrilaterals are formed on the side of a fishing tackle box by the adjustable shelves and connecting pieces. Explain why the shelves are always parallel to each other no matter what their position is.
Answers
If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram
10
Find the area of the semicircle.
Either enter an exact answer terms of ar or use 3.14 for at and enter your answer as a decimal.
units2
Answers
Answer: 39.25
========================================
Work Shown:
d = diameter = 10
r = radius = d/2 = 10/2 = 5
A = area of a full circle
A = pi*r^2 = 3.14*5^2 = 78.5
Cut this in half to get the area of a semicircle (aka half circle)
(78.5)/2 = 39.25
This result is approximate.
4. Find the length of the hypotenuse of a triangle with the coordinates (1, —2), (1, 7), and (13, —2)
help pls brainliest gib
Answers
Answer:
answer attached
Step-by-step explanation:
answer attached
hope this helps!