By verbal reasoning, the pair of words required can be obtained from the
synonyms of the given pair.
Correct response:
- <u>Variable</u>; <u>supposition</u>
<h3>Analysis used for making the above selection</h3>
Prediction: A prediction is a statement indicating the result to be
expected from a trial or test, based on deductive reasoning from a
theory or hypothesis.
An explanation is a statement describing a phenomenon and is taken as
an hypothesis.
A variable is an outcome of a test or trial, or observation.
A supposition is a held notion or belief that is similar to a hypothesis.
Therefore;
Prediction is to explanation as <u>variable</u> is to <u>supposition</u>.
Learn more about prediction and variables here:
brainly.com/question/17372552
This is just simple Pythagorean’s theorem. a^2 + b^2 = c^2
Number 2:
5^2 + x^2 = 10^2
25 + x^2 = 100
x^2 = 75
x = sqrt 75 = 5*sqrt(3)
Number 3:
4^2 + x^2 = 7^2
16 + x^2 = 49
x^2 = 33
x = sqrt 33
Answer:
Amount of Winter sealer for 2 coats[in square feet] = 576 square feet
Step-by-step explanation:
Given:
Length of drive way at garage door = 12 feet
Length of drive way at street = 20 feet
Length of total driveway = 18 feet
Find:
Amount of Winter sealer for 2 coats[in square feet]
Computation:
Amount of Winter sealer for 2 coats[in square feet] = 2[Area of trapezoid]
Amount of Winter sealer for 2 coats[in square feet] = 2[(1/2)(Sum of parallel side)(Height)]
Amount of Winter sealer for 2 coats[in square feet] = 2[(1/2)(12 + 20)(18)]
Amount of Winter sealer for 2 coats[in square feet] = 2[(1/2)(32)(18)]
Amount of Winter sealer for 2 coats[in square feet] = 32 x 18
Amount of Winter sealer for 2 coats[in square feet] = 576 square feet
Answer:
Step-by-step explanation:
If the ratio of triangle = 3:5:7
Total ratio = 3+5+7 = 15
The sum of angle in a triangle is 180°
1st angle= 3/15× 180 = 3 × 12 = 36°
2nd angle= 5/15 × 180 = 5 × 12 = 60°
3rd angle= 7/15 × 180 = 7 × 12 = 84°
shortest side: 851
middle side:927
longest side : 1306
Explanation
Step 1
Let
x represents the shortest side
y represents the middle side
z represents the longest side
so, set the equations
a) the perimeter of a rectangle is the sum of the sides, so
![\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BPerimeter%3D%20side1%2Bside2%2Bside3%7D%20%5C%5C%20replace%20%5C%5C%203084%3Dx%2By%2Bz%20%5C%5C%20x%2By%2Bz%3D3084%5CRightarrow%5Ctext%7B%20Equation%281%29%7D%20%5Cend%7Bgathered%7D)
b) The shortest side measures 76 mi less than the middle side( in other words, you have to subtract 76 from middle side to get the shortest side)
![x=y-76\Rightarrow equation(2)](https://tex.z-dn.net/?f=x%3Dy-76%5CRightarrow%20equation%282%29)
c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)
![z=y+379\Rightarrow equation(3)](https://tex.z-dn.net/?f=z%3Dy%2B379%5CRightarrow%20equation%283%29)
Step 2
solve the equations
a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)
![\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\ \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%2By%2Bz%3D3084%5CRightarrow%5Ctext%7B%20Equation%281%29%7D%20%5C%5C%20%28y-76%29%2By%2B%28y%2B379%29%3D3084%20%5C%5C%20-76%2B3y%2B379%3D3084%20%5C%5C%20303%2B3y%3D3084%20%5C%5C%203y%3D3084-303%20%5C%5C%20%20%5C%5C%203y%3D2781%20%5C%5C%20%5Ctext%7Bdivide%20both%20sides%20by%203%7D%20%5C%5C%20%5Cfrac%7B3y%7D%7B3%7D%3D%5Cfrac%7B2781%7D%7B3%7D%20%5C%5C%20y%3D927%20%5Cend%7Bgathered%7D)
now, replace the y value in equatino (2) to find x
b)
![\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3Dy-76%5CRightarrow%20equation%282%29%20%5C%5C%20x%3D927-76%20%5C%5C%20x%3D851%20%5Cend%7Bgathered%7D)
c) finally, prelace x and y value in equation (1) to find z
![\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%2By%2Bz%3D3084%5CRightarrow%5Ctext%7B%20Equation%281%29%7D%20%5C%5C%20851%2B927%2Bz%3D3084%20%5C%5C%20%5Ctext%7Badd%20like%20terms%7D%20%5C%5C%201778%2Bz%3D3084%20%5C%5C%20%5Ctext%7Bsubtract%201778%20in%20both%20sides%7D%20%5C%5C%201778%2Bz-1778%3D3084-1778%20%5C%5C%20z%3D1306%20%5Cend%7Bgathered%7D)
so
shortest side: 851
middle side:927
longest side : 1306
I hope this helps you