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3 years ago

Please help me- pt. 4

Mathematics

1 answer:

nignag [31]3 years ago

6 0

11/30 bags of mulch is needed.

Step-by-step explanation:

We have to find the number of bags of mulch.

7 (1/2) sq. yards need 2(3/4) bags of mulch.

So one sq. yd need 2(3/4) / 7(1/2)

We have to change the mixed fraction into improper fraction and then dividing them we will get the answer.

2(3/4) = ((2×4)+ 3)/4 = (8+ 3)/4 = 11/4

7(1/2) = ((7×2)+1)/2 = (14+1)/2 = 15/2

11/4 ÷ 15/2

It change into multiplication as,

11/4 × 2/15 = 11/30 bags of mulch is needed.

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Answer:

1.3223 is the answer for y

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3 years ago

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What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9

skelet666 [1.2K]

Answer:

Step-by-step explanation:

Let $u^2=x^4\\u = x^2$

Subbing in:

$9u^2-2u-7=0$

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:

$9u^2-9u+7u-7=0$

Group together in groups of 2:

$(9u^2-9u)+(7u-7)=0$

Now factor out what's common within each set of parenthesis:

$9u(u-1)+7(u-1)=0$

We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:

$(u-1)(9u+7)=0$

Remember that $u=x^2$

so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.

$(x^2-1)(9x^2+7)=0$

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring $(x^2-1)$ gives us that x = 1 and -1. The other set is a bit more tricky. If

$9x^2+7=0$ then

$9x^2=-7$ and

$x^2=-\frac{7}{9}$

You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:

$x=$ ± $\sqrt{-\frac{7}{9} }$

which will simplify down to

$x=$ ± $\frac{\sqrt{7} }{3}i$

Those are the 4 solutions to the quartic equation.

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3 years ago

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julsineya [31]

Answer:

After 1 years: 20235.396, which can be rounded to 20235.40

After 2 years: 21523.79

After 5 years: 25388.98

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What he said bro and it right Ik

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3 years ago

At 7:00 a.m., Alicia pours a cup of tea whose temperature is 200°F. The tea starts

soldier1979 [14.2K]

Answer:

Step-by-step explanation:

Here we have the temperature variation with time given in an exponential equation as follows;

Let the temperature at time x (in minutes) = y

Therefore, y = a × mˣ + b

Where:

b = Shift of the curve or the limit value of the decreasing exponential function as x → ∞

When y = 200, x = 0

Therefore. 200 = a × m⁰ + c = a + c

We note that c is the shift of the graph, the value upon which temperature increases = final temperature = 72°F

Hence a = 200 - 72 = 128°F

When y = 197, x = 2 minutes

Therefore, 197 = 128·m² + 72 =

m² = (197 - 72)/128 = 125/128

m = √(125/128) = 0.98821

Hence the exponential equation of cooling is presented in the following equation;

y = 128 × (0.98821)ˣ + 72

Therefore, y = 128(0.989)x + 72

When the temperature is 172°F we have;

170 = 128 × (0.989)ˣ + 72

∴ (0.989)ˣ = (170 - 72)/128

= 98/128

= 0.7656

log(0.989)ˣ = log(0.7656)

x·log(0.989) = log(0.7656)

x = log(0.7656)/log(0.989)

= 24.15 minutes

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3 years ago