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2 years ago

Solving Exponential Equations (lacking a common base) (0.66)^k=9

Mathematics

1 answer:

Alexandra [31]2 years ago

3 0

Answer:

k = log9 / log 0.66

k = 5.3

Step-by-step explanation:

Please always remember that, when an exponential equation is given with different bases, the best approach is to take log of both sides.

If you have a calculator handy, that would be pretty fast and easy.

0.66 ^ k = 9

Take log of both sides:

klog 0.66 = log 9

k = log 9 / log 0.66

k = 0.954 / - 0.18

k = -5.3

Maths is fun, let's keep learning

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Write the equation in slope intercept form. what are the slope and y-intercept?

Leno4ka [110]

Slope intercept is basically solve for y
y=mx+b
m=slope
b=yintercept

-3x-10y=7
add 3x to both sides
-10y=3x+7
divide both sides by -10
y=-3/10x-7/10

slope is -3/10
yintercept is -7/10 or at point (0,-7/10)

5 0

2 years ago

What is the equation in slope-intercept from of the line that passes through the points (-4,47) and (2,-16

Harrizon [31]

Answer:

Step-by-step explanation:

SLOPE FORMULA:

y₂-y₁/x₂-x₁=rise/run

SLOPE-INTERCEPT FORM:

y=mx+b

m represents the slope.

b represents the y-intercept.

y₂=(-16)

y₁=47

x₂=2

y₁=(-4)

Solve.

$\displaystyle \mathsf{\frac{(-16)-47}{2-(-4)}=\frac{21}{6}=\frac{21}{2}=-\frac{21}{2} }}$

Furthermore, the y-intercept is 5.

y=-21/2x+5

The correct answer is y=-21/2x+5.

6 0

3 years ago

) Picture frames are produced such that the four sides of a picture frame consist of two pieces from a population whose mean len

Natali [406]

Answer:

The mean perimeter of frame = 38 cm

Step-by-step explanation:

By perimeter of a rectangle, the formula is given as:

Perimeter of rectangle = 2(A + B)

Going by the illustration in the question, the perimeter is

==> 2(32 + 44) = 152 cm.

However, we a given the mean perimeter of the frame which are:

32 and 44. We can either choose to say; each sides is (32 by 32) and (44 by 44). Or we consider it in mean/average term as given: (32 by 44).

Case 1: To obtain the mean perimeter of the frame using the first scenario, we say:

Mean perimeter = (32+32+44+44)/4 = 38 cm.

Case 2: We can simply say:

Mean perimeter = (32 + 44)/2 = 38 cm.

Graphically: Assuming that the frame is given below

32 cm

---------------------------------

| |

44 cm| | 44 cm

| |

----------------------------------

32 cm

The mean of upper frame/bars = 32 cm

The mean of side frame/bars = 44 cm

Hence, the mean of the perimeter = (32 + 44)/2 = 38 cm

OR,

we take the sum of all the sides (32 + 44 + 32 + 44) and divide by total number of sides (4). That is;

The mean of the perimeter = (32 + 44 + 32 + 44)/4 = 38 cm

3 0

3 years ago

Find the values of k so that each remainder is three. 10. (x^2+ 5x + 7) = (x + k)

Goryan [66]

Answer:

$k=1\text{ or } k=4$

Step-by-step explanation:

We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a binomial in the form (x - a), then our remainder will be P(a).

We are dividing:

$(x^2+5x+7)\div(x+k)$

So, a polynomial by a binomial factor.

Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.

We want our remainder to be 3. So, P(a)=P(-k)=3.

Therefore:

$(-k)^2+5(-k)+7=3$

Simplify:

$k^2-5k+7=3$

Solve for k. Subtract 3 from both sides:

$k^2-5k+4=0$

Factor:

$(k-1)(k-4)=0$

Zero Product Property:

$k-1=0\text{ or } k-4=0$

Solve:

$k=1\text{ or } k=4$

So, either of the two expressions:

$(x^2+5x+7)\div(x+1)\text{ or } (x^2+5x+7)\div(x+4)$

Will yield 3 as the remainder.

5 0

3 years ago

A) If it takes 125 chinchillas to make a coat and he needs to make 10 coats, how many chinchillas must Barton have by the end of

Nesterboy [21]

So one coat uses 125 chinchillas . So, 10 * 125 will give you how many will give you 1250 chinchillas.. this is the number of chinchillas needed for 10 coats. So for 2 years you would have to multiply it by two so, 1250 * 2 = 2500.

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3 years ago