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3 years ago

13

Barbara has $70.00 in her pocket and a $20 gift card. Which purchase will she be able to make without having to use her credit c

ard?

1 answer:

suter [353]3 years ago

3 0

Yes depending on her purchase. If it is over 90.00 dollars then no she will not.

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If f(x)= 9^x then prove that f(m+n+p) = f(m).f(n).f(p)

kakasveta [241]

Answer:

f(x)=9^(x)

Plugging in m+n+p=x, we have

f(m+n+p) = 9^(m+n+p)

Using the properties of exponential a^(b+c) = a^b*a^c, we have

f(m+n+p) = 9^(m)*9^(n)*9^(p)

f(m+n+p) = f(m)*f(n)*f(p)

4 0

3 years ago

Let C(n) be the constant term in the expansion of (x + 4)n. Prove by induction that C(n) = 4n for all n is in N. (Induction on n

stiks02 [169]

Answer:

C(n) = 4 n for all possible integers n in N. This statement is true when n=1 and proving that the statement is true for n=k when given that statement is true for n= k-1

Step-by-step explanation:

Lets P (n) be the statement

C (n) = 4 n

if n =1

(x+4)n = (x+4)(1)=x+4

As we note that constant term is 4 C(n) = 4

4 n= 4 (1) =4

P(1) is true as C(n) = 4 n

when n=1

Let P (k-1)

C(k-1)=4(k-1)

we need to proof that p(k) is true

C(k) = C(k-1) +1)

=C(k-1)+C(1) x+4)n is linear

=4(k-1)+ C(1) P(k-1) is true

=4 k-4 +4 f(1)=4

=4 k

So p(k) is true

By the principle of mathematical induction, p(n) is true for all positive integers n

3 0

3 years ago

Addison earn $25 Mowing her neighbors lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday sh

larisa [96]

$29. 25-18+50=57. 86-57=29

8 0

4 years ago

What is the equation of a line (in standard form) that passes through point A(1,-4) and has a slope of 3/4?

Anna35 [415]

Answer:

3x-4y=19

Step-by-step explanation:

Hi there!

We want to write the equation of the line in standard form that passes through the point (1, -4) and has the slope of 3/4

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative

First, in order to find ax+by=c, we'll need to get slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Since we already know the slope (3/4), we can substitute it into the formula for y=mx+b.

y=3/4x+b

Now we need to solve for b

Since the equation passes through the point (1, -4), we can use it to solve for b

Substitute 1 as x and -4 as y.

-4=3/4(1)+b

Multiply

-4=3/4+b

Subtract 3/4 from both sides

-19/4=b

Now substitute -19/4 as b into the equation

y=3/4x-19/4

Now we have the equation in slope-intercept form, but remember, we want it in standard form

Since x and y are on the same side in standard form, subtract 3/4x from both sides

-3/4x+y=-19/4

Remember that a cannot be negative, and the coefficients are integers (they cannot be fractions)

So in order to clear the fractions and change the sign of the equation, multiply both sides by -4

-4(-3/4x+y)=-4(-19/4)

Multiply

3x-4y=19

Hope this helps!

8 0

3 years ago

If y= 1/5 when x=3, find y when x=4, given that y varies directly with x

lisov135 [29]

Answer:

<h2> $y = \frac{4}{15}$ </h2>

Step-by-step explanation:

To find y when x=4, we must first find the relationship between them

The statement

y varies directly with x is written as

<h3> $y \: \: \: \alpha \: \: \: kx$ </h3>

where k is the constant of proportionality

From the question

when y = 1/5

x = 3

Substitute the values into the above formula and solve

That's

<h3> $\frac{1}{5} = 3k \\ 15k = 1 \\ k = \frac{1}{15}$ </h3>

So the formula for the variation is

<h3> $y = \frac{x}{15}$ </h3>

From the question

when x = 4

<h3> $y = \frac{4}{15}$ </h3>

Hope this helps you

5 0

3 years ago