namely, how many times does 0.4 go into 6⅓? or 6⅓ ÷ 0.4.
first off, let's convert the mixed fraction to improper, and the decimal to a fraction . We can always convert the decimal to a fraction by simply <u>adding as many zeros on the denominator as there are decimals and lose the dot atop</u>, let's do so.
![\bf 0.\underline{4}\implies \cfrac{04}{1\underline{0}}\implies \cfrac{4}{10}\implies \cfrac{2}{5}~\hfill \stackrel{mixed}{6\frac{1}{3}}\implies \cfrac{6\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{19}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{How many servings of pasta were in the dish?}}{6\frac{1}{3}\div 0.4\implies \cfrac{19}{3}\div \cfrac{2}{5}}\implies \cfrac{19}{3}\cdot \cfrac{5}{2}\implies \cfrac{95}{6}\implies 15\frac{5}{6}](https://tex.z-dn.net/?f=%5Cbf%200.%5Cunderline%7B4%7D%5Cimplies%20%5Ccfrac%7B04%7D%7B1%5Cunderline%7B0%7D%7D%5Cimplies%20%5Ccfrac%7B4%7D%7B10%7D%5Cimplies%20%5Ccfrac%7B2%7D%7B5%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B6%5Cfrac%7B1%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B6%5Ccdot%203%2B1%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B19%7D%7B3%7D%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Cstackrel%7B%5Ctextit%7BHow%20many%20servings%20of%20pasta%20were%20in%20the%20dish%3F%7D%7D%7B6%5Cfrac%7B1%7D%7B3%7D%5Cdiv%200.4%5Cimplies%20%5Ccfrac%7B19%7D%7B3%7D%5Cdiv%20%5Ccfrac%7B2%7D%7B5%7D%7D%5Cimplies%20%5Ccfrac%7B19%7D%7B3%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B2%7D%5Cimplies%20%5Ccfrac%7B95%7D%7B6%7D%5Cimplies%2015%5Cfrac%7B5%7D%7B6%7D)
The answer is 30 for all the dimensions
Answer:
128degrees
Step-by-step explanation:
Note that the given triangle ABC is an isosceles triangle with base angles equal, hence;
m∠BAC = m∠BCA
7x+1 = 5x+9
7x - 5x = 9-1
2x = 8
x = 8/2
x = 4
m∠BAC = 5x+6
m∠BAC = 5(4)+6
m∠BAC = 26 degrees
The vertex angle = 180 - (26+26)
The vertex angle = 180 - 52
The vertex angle = 128degrees
Answer:
x = 5
Step-by-step explanation:
You have a right triangle, so you can use the Pythagorean Theorem.
a^2 + b^2 = c^2
x^2 + 12^2 = 13^2
x^2 + 144 = 169
x^2 = 25
x = 5
Answer: x = 5
