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3 years ago

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

1 answer:

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.

You might be interested in

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>Related Information :- </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 $(x^{98}-1)$ :

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

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

Using the Zero Product Property, 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]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 3 &,& -4~) 
% (c,d)
&&(~ 5 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-3}\implies \cfrac{1+4}{5-3}\implies \cfrac{5}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-4)=\cfrac{5}{2}(x-3)\implies y+4=\cfrac{5}{2}x-\cfrac{15}{2}$

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

side note: multiplying by the LCD of both sides is just to get rid of the denominators

5 0

3 years ago