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3 years ago

Find the y-intercept and x-intercept of the line. – 3x+9y= 14

Mathematics

1 answer:

pickupchik [31]3 years ago

3 0

Answer:

$\huge\boxed{x-intercept=-\dfrac{14}{3}=-4\dfrac{2}{3}}\\\boxed{y-intercept=\dfrac{14}{9}=1\dfrac{5}{9}}$

Step-by-step explanation:

$-3x+9y=14\\\\x-intercept\ \text{for}\ y=0:\\\\-3x+9(0)=14\\-3x+0=14\\-3x=14\qquad\text{divide both sides by (-3)}\\\boxed{x=-\dfrac{14}{3}=-4\dfrac{2}{3}}}$

$y-intercept\ \text{for}\ x=0:\\\\-3(0)+9y=14\\0+9y=14\\9y=14\qquad\text{divide both sides by 9}\\\boxed{y=\dfrac{14}{9}=1\dfrac{5}{9}}$

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Solve 4(2x - 3) = 6x + 2

vaieri [72.5K]

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4(2x - 3) = 6x + 2

Expand it:

8x - 12 = 6x + 2

+ 12 to both sides

8x = 6x + 14

- 6x from both sides

2x = 14

Divide both sides by 2:

x = 7

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4 0

3 years ago

The common difference in an arithmetic sequence is –2 and the first term is 47. What is the 29th term?

BlackZzzverrR [31]

An arithmetic sequence is an ordered list of numbers where the next number is found by adding on to the last number (ex: 2,5,8,11... is a sequence where 3 is added on to find the next number).

The equation for an arithmetic sequence is
$A_{n}=A_{1}+(n-1)d$

$A_{n}$ is the "n-th" number in the sequence (ex: is the first term in the sequence)
d is the number you add (common difference) to find the next number
The first number in the sequence is 47 so $A_{1}=47$
d=-2 because the question gives you that

$A_{n}=A_{1}+(n-1)d$
 $A_{29}=47+(29-1)(-2)$
 $A_{29}=47+(28)(-2)$
 $A_{29}=47+-56$
 $A_{29}=-9$

The answer is A. -9.

 

The answer is C. 158

For the second one, it gives you $A_{1}=4$ and $A_{}=18$
You can use this to find d

 $A_{n}=A_{1}+(n-1)d$
 $A_{3}=4+(3-1)d$
 $18=4+(3-1)d$
 $18=4+2d$
 $14=2d$
 $7=d$

Now you can just solve using the equation normally.
 $A_{n}=A_{1}+(n-1)d$
 $A_{23}=4+(23-1)(7)$
 $A_{23}=4+(22)(7)$
 $A_{23}=4+154$
 $A_{23}=158$

The answer is C. 158

8 0

3 years ago

Read 2 more answers

Please help ASAP for 10 points!!

Orlov [11]

Answer:

Step-by-step explanation:

(2x²+3x-4) +(8-3x) +(-5x²+2)= 2x²+3x-4 +8-3x-5x²+2 = - 3x²+6

5 0

3 years ago

URGENT! WILL GIVE BRAINLY FOR CORRECT ANSWER

Minchanka [31]

Answer:

sorry if im wrong i think wrong numbers. plz check

Step-by-step explanation:

The center of dilation of the question is (-4,-3) .

let say that

x0=-4

y0=-3

Label the image A'B'C'

The new coordinate would be

A(-4,-1)

x=4

y=-1

x'=x0+ 2(x - x0)

x'= -4+ 2(-4 +4)

x'=-4

y'=y0+ 2(y - y0)

y'= -3+ 2(-1 +3)

y'=-3 +4= 1

______________________________

B(-4,-3)

x=-4

y=-3

x'=x0+ 2(x - x0)

x'= -4+ 2(-4 +4)

x'=-4

y'=y0+ 2(y - y0)

y'= -3+ 2(-3 +3)

y'=-3

______________________________

C(-1,-3)

x=-1

y=-3

x'=x0+ 2(x - x0)

x'= -4+ 2(-1 +4)

x'=-4 +6= 2

y'=y0+ 2(y - y0)

y'= -3+ 2(-3 +3)

y'=-3

A'(-4,1)

B'(-4,-3)

C'(2,-3)

3 0

2 years ago

La funcion que representa el beneficio obtenido por una empresa si vende x unidades de uno de sus productos es f(x)= -70x^2+2800

DerKrebs [107]

Answer:

$20$

Step-by-step explanation:

La función es

$f(x)=-70x^2+2800x-45000$

Diferenciando con respecto a $x$ obtenemos

$f'(x)=-140x+2800$

Igualar con cero

$0=-140x+2800\\\Rightarrow x=\dfrac{2800}{140}\\\Rightarrow x=20$

Doble derivada de la función

$f''(x)=-140$

Entonces, la función es máxima cuando el número de unidades vendidas, $x=20$ ,

3 0

3 years ago