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3 years ago

Solve the inequality 12(1/2 x - 1/3) > 8 - 2x

Mathematics

1 answer:

pentagon [3]3 years ago

3 0

Answer:

$D. \\x>\frac{3}{2}$

Step-by-step explanation:

12(1/2x - 1/3) > 8 - 2x

6x - 4 > 8 - 2x

6x + 2x - 4 > 8 - 2x + 2x

8x - 4 > 8

8x - 4 + 4 > 8 + 4

8x > 12

8x ÷ 8 > 12 ÷ 8

x > 1.5

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Read 2 more answers

Plz help, I need help on these couple questions for home work

sveta [45]

$5\frac{3}{8}= \frac{43}{8}$

1c = 8 fl oz

$\frac{43}{8}= \frac{43}{8}\times8=43$

Hence, a: 43 fl oz is correct

1 inch = 0.0833 foot

43 inch = $43\times0.0833=3.581$

Hence, option D $3\frac{7}{12}$ is correct.

Length of material Mili has = $7\frac{1}{2}= \frac{15}{2}$

Length needed for her skirt = $4\frac{5}{8}= \frac{37}{8}$

Material left will be = $\frac{15}{2}- \frac{37}{8}$

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3 years ago

What is the first term in a geometric sequence if the common ratio is − 2 and the sum of the first six terms is −105?

Serggg [28]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-2\\
n=6\\
S_6=-105
\end{cases}$

$\bf -105=a_1\left( \cfrac{1-(-2)^6}{1-(-2)} \right)\implies -105=a_1\left( \cfrac{1-(64)}{1+2} \right)
\\\\\\
-105=a_1\left( \cfrac{-63}{3} \right)\implies -105=a_1(-21)
\\\\\\
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3 years ago

In rhombus MOTH, angle HTM=(5x+6) degrees. If angle HMO=(12x-6)degrees, what is angle HMO?

forsale [732]

Answer:

m∠HMO=102°

Step-by-step explanation:

we know that

In a Rhombus the diagonals bisect the angles and opposite angles are equal

In this problem

Angles HMO and HTO are opposite angles

m∠HMO=m∠HTO

m∠HTM=(1/2)m∠HMO ----> because the diagonals bisect the angles and opposite angles are congruent

substitute the values

$(5x+6)\°=(1/2)(12x-6)\°$

solve for x

$10x+12=12x-6\\12x-10x=12+6\\2x=18\\x=9$

<em>Find the measure of angle HMO</em>

m∠HMO=(12x-6)°

substitute the value of x

m∠HMO=(12(9)-6)=102°

see the attached figure to better understand the problem

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4 years ago