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ANTONII [103]
3 years ago
7

7+ X -9= -15 solve the equation

Mathematics
2 answers:
Aleksandr-060686 [28]3 years ago
6 0
I believe the answer is x=24
Andrews [41]3 years ago
6 0
X=-15+9-7
x= -6-7
x= - 13
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What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brot
Nat2105 [25]

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

a = 500 --- starting balance

m = 10 --- monthly rate

Her brother

a = 100 ---- starting balance

r = 10\% --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

y = ab^x

Where b = 1 + r

So, we have:

y = ab^x

y = 100 *(1 + 10\%) ^x

y = 100 *(1 + 0.10) ^x

y = 100 *(1.10) ^x

Hence:

g(x) = 100 *(1.10) ^x

Next, we calculate Molly's function (a linear function)

The monthly function is:

y = mx + a

So, we have:

y = 10x + 500

Annually, the function will be:

y = 10x*12 + 500

y = 120x + 500

So, we have:

f(x) = 120x + 500

At this point, we have:

f(x) = 120x + 500 ---- Molly

g(x) = 100 *(1.10) ^x ---- Her brother

<u>Next, we test each option</u>

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

y = 120x + 500

The slope of a linear function with the form: y = mx + b is m

By comparison:

m = 120

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

m = 120

For his brother:

Rate of change is calculated using:

m = \frac{g(b) - g(a)}{b - a}

m = \frac{g(40) - g(32)}{40 - 32}

m = \frac{g(40) - g(32)}{8}

Calculate g(40) and g(32)

g(x) = 100 *(1.10) ^x

g(40) = 100 * 1.10^{40} =4526

g(32) = 100 * 1.10^{32} = 2111

So, we have:

m = \frac{4526 - 2111}{8}

m = \frac{2415}{8}

m = 302

By comparison: 302 > 120

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

m = 120 --- Molly's rate of change

For his brother:

m = \frac{g(b) - g(a)}{b - a}

m = \frac{g(30) - g(24)}{30 - 24}

m = \frac{g(30) - g(24)}{6}

Calculate g(30) and g(24)

g(x) = 100 *(1.10) ^x

g(40) = 100 * 1.10^{30} =1745

g(32) = 100 * 1.10^{24} = 985

So, we have:

m = \frac{g(30) - g(24)}{6}

m = \frac{1745 - 985}{6}

m = \frac{760}{6}

m = 127

By comparison: 127 > 120

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

m = 120 --- Molly's rate of change

For his brother:

m = \frac{g(b) - g(a)}{b - a}

m = \frac{g(4) - g(0)}{4 - 0}

m = \frac{g(4) - g(0)}{4}

Calculate g(4) and g(0)

g(x) = 100 *(1.10) ^x

g(4) = 100 * 1.10^4 =146

g(0) = 100 * 1.10^{0} = 100

So, we have:

m = \frac{g(4) - g(0)}{4}

m = \frac{146 - 100}{4}

m = \frac{46}{4}

m = 11.5

By comparison: 120>11.5

Hence, Molly's account has a faster rate over [0,4]

(c) is false

4 0
3 years ago
If the sum of two prime numbers is divisible by seven and is a perfect square what is the possible product of these numbers
disa [49]
The possible product can be 94.
You need the sum of two prime numbers that is divisible by seven and is a perfect square.
A number that is a perfect square and divisible by 7 is number 49 (7^2=49).
A prime number is a number that is divisible only by 1 and itself.
49 = 47 + 2 (47 and 2 are prime)
47 × 2 = 94.
3 0
3 years ago
Is 976 -522 more or less than 400? Explain how you can tell without actually subtracting.
liq [111]
You can round 976 to 1000 and 522 to 500. So it would be
1000 - 500 = 500. The answer you would get after subtracting 976-522 would be more than 400 if you round it.
3 0
3 years ago
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Eddie is fishing. He has 1 and one fourth ounces of weight on his line, but his bait isn't getting to the bottom of the lake. Ed
vladimir1956 [14]
1 1/4 + 1/2 + 3/4 = 
5/4 + 1/2 + 3/4 =
5/4 + 2/4 + 3/4 =
10/4 = 2 1/2 (or 2.5) oz's <

4 0
3 years ago
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A bed is 6 1/2 feet long.the material to make a sheet for the bed is to be 1 1/2 times as long to allow for hems and tucking und
Svetllana [295]
Answer:  9 3/4 feet long

Explanation:

1 1/2 x 6 1/2 = 3/2 x 13/2 = 39/4 = 9 3/4 feet long
4 0
3 years ago
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