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3 years ago

Which diagram matches the following situation?

Mathematics

1 answer:

Alika [10]3 years ago

7 0

Answer:

the second one. AKA the right top one

Step-by-step explanation:

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55x^2 + 62y^2 + 38 − 63x^2 + 8 Combine like terms

Cerrena [4.2K]

Answer: -8x^2 + 62y^2 + 46

6 0

3 years ago

Y is directly related to x and y is 81 when x is 27 the constant of.variation is

s2008m [1.1K]

Answer:

k = 3

Step-by-step explanation:

Given that y and x are directly related then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 81 when x = 27

k = $\frac{y}{x}$ = $\frac{81}{27}$ = 3

8 0

3 years ago

Meg is 6 years older than Victor. Meg's age is 2 years less than five times Victor's age. The equations below model the relation

Verdich [7]

Since no possible correct method is posted, I will suggest a couple.

Method 1: guess and check

Works well for simple problems involving integers like this one.

Victor's age must be zero or greater than one, say one.

Guess v=1, find m=v+6=7, check m=5v-2=5-2=3 no good.

we need to make v bigger

Guess v=2, find m=v+6=2+6=8, check m=5v-2=5*2-2=8 ✔

So v=2, m=8.

Method 2:

Solve the system of two equations.

since the left-hand sides is m in both equations, and since m=m, we just have to equate the right-hand sides to solve for v.

5v-2=v+6

Solve for v

5v-v = 6+2

4v=8

v=2,

so again, v=2, m=v+6=2+6=8.

6 0

4 years ago

Part A: Find the LCM of 7 and 12. Show your work. (3 points)

inna [77]

Answer:

A. 84; B. 8; C. 8 × 19

Step-by-step explanation:

Part A. Least common multiple

Step 1. List the prime factors of each.

7 = 7

12 = 2 × 2 × 3

Step 2: Multiply each factor the greatest number of times it occurs in either number.

7 has one 7; 12 has two 2s and one 3.

LCM = 7 × 2 × 2 × 3

LCM = 7 × 12

LCM = 84

Part B. Highest common factor

Find all the factors of 56 and 96.

Factors of 56: 1, 2, 4, 7, 8, 14, 28

Factors of 96: 1, 2, 4, 6, 8, 12, 16, 24, 32, 48

The highest factor that in both 56 and 96 is 8.

Part C. Factoring

56 + 96 = 8(7 + 12) = 8 × 19

The GCF is 8.

19 = 7 + 12 is the sum of two numbers that do not have a common factor.

4 0

4 years ago

1 х Given g(x)=

yarga [219]

(a) Since $g(x)=\sqrt[3]{x}$ and $h(x) = \frac1{x^3}$ , we have

$(g\circ h)(x) = g(h(x)) = g\left(\dfrac1{x^3}\right) = \sqrt{3}{\dfrac1{x^3}} = \dfrac1x$

We're given that

$(f \circ g \circ h)(x) = f(g(h(x))) = f\left(\dfrac1x\right) = \dfrac x{x+1}$

but we can rewrite this as

$\dfrac x{x+1} = \dfrac{\frac xx}{\frac xx + \frac1x} = \dfrac1{1+\frac1x}$

(bear in mind that we can only do this so long as x ≠ 0) so it follows that

$f\left(\dfrac1x\right) = \dfrac1{1+\frac1x} \implies \boxed{f(x) = \dfrac1{1+x}}$

(b) On its own, we may be tempted to conclude that the domain of $(f\circ g\circ h)(x) = \frac1{1+x}$ is simply x ≠ -1. But we should be more careful. The domain of a composite depends on each of the component functions involved.

$g(x) = \sqrt[3]{x}$ is defined for all x - no issue here.

$h(x) = \frac1{x^3}$ is defined for all x ≠ 0. Then $(g\circ h)(x) = \frac1x$ also has a domain of x ≠ 0.

$f(x) = \frac1{1+x}$ is defined for all x ≠ -1, but

$(f\circ g\circ h)(x)=f\left(\frac1x\right) = \dfrac1{1+\frac1x}$

is undefined not only at x = -1, but also at x = 0. So the domain of $(f\circ g\circ h)(x)$ is

$\left\{x\in\mathbb R \mid x\neq-1 \text{ and }x\neq0\right\}$

7 0

3 years ago