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Digiron [165]
3 years ago
6

Solve the inequality. Write the solution in interval notation. Choose the correct solution. 6x > – 24

Mathematics
1 answer:
Phoenix [80]3 years ago
5 0
Divide by 6.
  -4 < x

The appropriate solution is (-4, ∞).

_____
No value is equal to ∞, so (-4, ∞] seems inappropriate. Since the comparison symbol is < rather than ≤, [-4, ∞) is definitely inappropriate.
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What is the value of X
Volgvan

Answer:

Step-by-step explanation:

it's another one of those similar triangles

it's easier to see this one.

t /c = u / b

where

t = 7x + 3

c = 27

u = 35

b = 21

plug in the knowns

7x + 3 / 27 = 35 / 21

7x + 3  = 27 ( 35 / 21 )

7x + 3 = 9 ( 35 / 7 )     ( divided by 3 )

7x  + 3  = 9 ( 5)     ( 7 into 35 =5 )

7x  + 3  = 45

7x = 45 - 3

7x = 42  

x = 6

I checked it, the ratio is 1_2/3  :) for both, but you can check it too

7 0
3 years ago
the sum of the first nine terms of an arithmetic series is 162, and the sum of the first 12 terms is 288. Determine the first fi
Natali5045456 [20]

Answer:

\boxed{\pink{\tt \leadsto Sum \ of \ first \ five \ terms \ is \ 50 . }}

Step-by-step explanation:

Given that , the sum of the first nine terms of an arithmetic series is 162 and the sum of the first 12 terms is 288.

\boxed{\red{\bf \bigg\lgroup For \ answer \ refer \ to \ attachment \bigg\rgroup  }}

<h3><u>Related</u><u> </u><u>Infor</u><u>mation</u><u> </u><u>:</u><u>-</u><u> </u></h3>

• The sum of n terms of an AP is

\boxed{\orange{\sf S_n = \dfrac{n}{2}[2a+(n-1)d] }}

• nth term of an AP is given by ,

\boxed{\blue{\sf T_n = a+(n-1)d }}

8 0
2 years ago
Please help solve for x..
aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

x^{100}-4^x \cdot x^{98}-x^2+4^x=0

Factor out -1:

\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0

Divide both sides by -1:

\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0

Rearrange the terms:

\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0

\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:

\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0

Factor the first two terms and the last two terms separately:

\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0

Factor out the common term (x^{98}-1) :

\implies (4^x-x^2)(x^{98}-1)=0

<u>Zero Product Property</u>:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}

Therefore, the solutions to the given equation are: x = 1 or x = -1

Learn more here:

brainly.com/question/27751281

brainly.com/question/21186424

3 0
2 years ago
In a certain county, the number of Charter Schools is eleven less than twice the number of Alternative Schools. There are 35 Cha
vitfil [10]
Id have to say 2a-11=35 

5 0
3 years ago
PLEASE HELP!!! Find the equation , in the standard form of the line passing through the points (3,-4) and (5,1)
ExtremeBDS [4]
\bf \begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&&(~ 3 &,& -4~) &#10;%  (c,d)&#10;&&(~ 5 &,& 1~)&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope =  m\implies &#10;\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-3}\implies \cfrac{1+4}{5-3}\implies \cfrac{5}{2}&#10;\\\\\\&#10;% point-slope intercept&#10;\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-4)=\cfrac{5}{2}(x-3)\implies y+4=\cfrac{5}{2}x-\cfrac{15}{2}

\bf y=\cfrac{5}{2}x-\cfrac{15}{2}-4\implies y=\cfrac{5}{2}x-\cfrac{23}{2}\impliedby &#10;\begin{array}{llll}&#10;\textit{now let's multiply both}\\&#10;\textit{sides by }\stackrel{LCD}{2}&#10;\end{array}&#10;\\\\\\&#10;2(y)=2\left( \cfrac{5}{2}x-\cfrac{23}{2} \right)\implies 2y=5x-23\implies \stackrel{standard~form}{-5x+2y=-23}&#10;\\\\\\&#10;\textit{and if we multiply both sides by -1}\qquad 5x-2y=23

side note:  multiplying by the LCD of both sides is just to get rid of the denominators
5 0
3 years ago
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