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kondaur [170]
3 years ago
12

Solve 5a - 4a = -9 - 8a

Mathematics
2 answers:
Gnoma [55]3 years ago
6 0
The answer you should get is a=-1
Elena-2011 [213]3 years ago
3 0
5a - 4a = -9 - 8a
a = -9 - 8a
9a = -9
a = -1
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The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which order
Gekata [30.6K]

The ordered pair (-3 , \frac{4}{375} ) is on g(x) ⇒ 1st answer

Step-by-step explanation:

Let us revise the reflection across the axes

  • If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)  (change the sign of y)
  • If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)  (change the sign of x)

∵ f(x)=\frac{1}{6}(\frac{2}{5})^{x}

∵ f(x) is reflected across the y-axis to create the function g(x)

- Change the sign of x

∴ g(x)=\frac{1}{6}(\frac{2}{5})^{-x}

To find the point that lies on g(x) substitute x in g(x) by the x-coordinate of the point if the answer equal to the y-coordinate of the point, then the point lies on it if not then the point does not lie on it

∵ The coordinates of the point are (-3 , \frac{4}{375} )

∴ x = -3 and y = \frac{4}{375}

- Substitute x by -3 in g(x)

∵ g(x)=\frac{1}{6}(\frac{2}{5})^{-x}

∴ g(x)=\frac{1}{6}(\frac{2}{5})^{-(-3)}

∴ g(x)=\frac{1}{6}(\frac{2}{5})^{3}

∵ (\frac{2}{5})^{3}=\frac{2^{3}}{5^{3}}=\frac{8}{125}

∴ g(x)=\frac{1}{6}(\frac{8}{125})

∴ g(x)=\frac{8}{750}

- Divide up and down by 2

∴ g(x)=\frac{4}{375}

∵ The value of g(x) equal to the y-coordinate of the point

∴ The point (-3 , \frac{4}{375} ) lies on g(x)

The ordered pair (-3 , \frac{4}{375} ) is on g(x)

Learn more:

You can learn more about the reflection in brainly.com/question/5017530

#LearnwithBrainly

9 0
3 years ago
Read 2 more answers
P=−4b 2 +6b−9 <br> Q=7b 2 −2b−5<br> ​P−Q=<br> Your answer should be a polynomial in standard form.
shepuryov [24]

Answer:

−11b^2+8b−4

Step-by-step explanation:

−4b2+6b−9−7b2+2b+5

Simplify by adding terms.

11b2+8b−4

3 0
3 years ago
Work out the formula of the nth term in the following quadratic sequence:<br> 19, 15, 9, 1...
Butoxors [25]

In a quadratic sequence we'll get a linear first difference and a constant second difference.  Let's verify that.

n          1   2   3   4

f(n)       19  15  9   1

1st diff   -4  -6  -8

2nd diff     2   2

We see that we got a constant second difference.  We could just extend that and work back up to get more values.

n          1   2   3   4       5    6      7

f(n)       19  15  9   1      -9   -21   -35

1st diff   -4  -6  -8   -10  -12   -14

2nd diff     2   2    2     2    2

That's just an aside; we're after the general formula.  We have

f(1)=19, f(2)=15, f(3)=9

In general we can assume

f(n) = an²  + bn + c

We get three equations in three unknowns,

19 = a(1²)+b(1)+c = a+b+c

15 = a(2²) + b(2) + c = 4a + 2b + c

9 = a(3²) + b(3) + c =  9a + 3b + c

That's a 3x3 linear system; it's easy to solve directly.  Subtracting pairs,

4 = -3a - b

6 = -5a - b

Subtracting those,

-2 = 2a

a = -1

b = -3a -4 = -1

c = 19-a-b = 21

Answer: f(n) = -n² - n + 21

Check:

f(1) = -1 - 1 + 21 = 19, good

f(2) = -4 - 2 + 21 = 15, good

f(3) = -9 - 3 + 21 = 9, good

f(4) = -16 - 4 + 21 = 1, good

Let's check our extended table, how about

f(7)= -49 - 7 + 21 = -35, good

6 0
3 years ago
Maria has 180 pieces of chocolate candy and 144 pieces of fruity candy. She wants to give each child the same amount of candy so
ValentinkaMS [17]
144, cause each child gets a chocolate and a fruit candy
7 0
3 years ago
He length of a rectangle is three times its width. The perimeter of the rectangle is at most 112 cm.
g100num [7]
The equation relating length to width
L = 3W
The inequality stating the boundaries of the perimeter
LW <= 112
When you plug in what L equals in the first equation into the second equation, you get
3W * W <= 112
evaluate
3W^2 <= 112
3W <= 4 \sqrt{7}
W <= \frac{4 \sqrt{7} }{3} cm
8 0
3 years ago
Read 2 more answers
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