Answer:
A) 25
Step-by-step explanation:
I am assuming that you mean: 2x² - 7.
Kathy worked 25.75 hours + 18.25 hours = 44 hours these two weeks.
well for a line, to get its slope all we need is two points, so let's use (-6, 5) and (0, 1), and get the equation of it.
![\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=-\cfrac{5}{6}[x-(-6)]\implies y-5=-\cfrac{5}{6}(x+6) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{to get the x-intercept, we set y = 0, solve for \underline{x}} \\\\\\ 0-5=-\cfrac{5}{6}(x+6)\implies -30=5x+30\implies -60=5x \\\\\\ \cfrac{-60}{5}=x\implies -12=x~\hfill \boxed{\stackrel{x-intercept}{(-12,0)}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%0A%5Ccline%7B1-1%7D%0A%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%0A%5Ccline%7B1-1%7D%0A%5C%5C%0Ay-y_1%3Dm%28x-x_1%29%0A%5C%5C%5C%5C%0A%5Ccline%7B1-1%7D%0A%5Cend%7Barray%7D%5Cimplies%20y-5%3D-%5Ccfrac%7B5%7D%7B6%7D%5Bx-%28-6%29%5D%5Cimplies%20y-5%3D-%5Ccfrac%7B5%7D%7B6%7D%28x%2B6%29%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Ctextit%7Bto%20get%20the%20x-intercept%2C%20we%20set%20y%20%3D%200%2C%20solve%20for%20%5Cunderline%7Bx%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A0-5%3D-%5Ccfrac%7B5%7D%7B6%7D%28x%2B6%29%5Cimplies%20-30%3D5x%2B30%5Cimplies%20-60%3D5x%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B-60%7D%7B5%7D%3Dx%5Cimplies%20-12%3Dx~%5Chfill%20%5Cboxed%7B%5Cstackrel%7Bx-intercept%7D%7B%28-12%2C0%29%7D%7D)
now, where's the y-intercept of that line? well, to get the y-intercept, we set x = 0 and solve for "y"....hmmmm wait a second, notice (0, 1), x = 0, y = 1, that's the y-intercept already.
a. The volume of prism 1 is 8346.562 ft³
b. The surface area of the white eraser is 13 cm²
The question has to do with scale factor
<h3>What is scale factor?</h3>
Scale factor is the ratio of two similar quantities
<h3>a. How to find the volume of Prism 1.</h3>
Since
- Prism 1 has a surface area of A = 289 ft² and
- Prism 2 has a surface area of A' = 529 ft².
Let
- L be the length of side of prism 1 and
- L' the length of side of prism 2
We have that scale factor = A/A'
Also,
A/A' = (L/L')²
L/L = √(A/A') = √( 289 ft²/ 529 ft²) = √0.49 = 0.7
Since
- prism 1 has a volume of V and
- prism 2 has a volume of V' = 24334 ft³. We have that
V/V' = (L/L')³
So, V = (L/L')³V'
So, substituting the values of the variables into the equation, we have
V = (L/L')³V'
V = (0.7)³24334 ft³
V = 0.343 × 24334 ft³
V = 8346.562 ft³
So, the volume of prism 1 is 8346.562 ft³
<h3>b. How to find the surface area of the white eraser?.</h3>
Since
- The white eraser has volume of V = 2 cm³ and
- The yellow eraser has volume of V' = 16 cm³.
Let
- L be the length of side of white eraser and
- L' the length of side of yellow eraser
We have that scale factor = V/V'
Also, V/V' = (L/L')³
L/L = ∛(V/V')
= ∛( 2 cm³/16 cm³)
= ∛(1/8)
= 1/2
Since
- White eraser has a surface area of A and
- Yellow eraser has a surface area of A = 52 cm² . We have that
A/A' = (L/L')²
So, A = (L/L')²A'
So, substituting the values of the variables into the equation, we have
A = (L/L')²A'
A = (1/2)²52 cm²
A = 1/4 × 52 cm²
A = 13 cm²
So, the surface area of the white eraser is 13 cm²
Learn more about scale factor and surface area here:
brainly.com/question/26161002
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Answer:
liar
Step-by-step explanation:
