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2 years ago

What is YZ ? Enter your answer as a decimal in the box.

Mathematics

2 answers:

Jobisdone [24]2 years ago

7 0

If you look at the figure, triangles XVW and ZYW are similar. So, you can use ratio and proportion to solve this problem. Notice that there are tick marks on th other two sides of the bigger triangles. That indicates that the like signs of ticks are equal. For example, that means XZ = ZW and that XW = 2XZ = 2ZW.

24.4/YZ = XW/ZW
24.4/YZ = 2ZW/ZW
24.4/YZ = 2
Solving for YZ,
<em>YZ = 12.2</em>

murzikaleks [220]2 years ago

3 0

Answer:

12.2

Step-by-step explanation:

you break it down till you get 12.2

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10 x 3 tens - unit form and standard form

vfiekz [6]

<span>10X3 tens in unit form is written:
10*3 tens = 30 tens = 300 units

10X3 tens in standard form:
10 x 3 tens = 10 x 30 = 300</span>

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2 years ago

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A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

madreJ [45]

It would be 4x < h < 10x
the difference between 3x - 7x =4
and the sum would be 3x + 7x =10

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2 years ago

A tanker that ran aground is leaking oil that forms a circular slick about 0.2 foot thick. To estimate the rate dV/dt (in cubic

blondinia [14]

Answer:

dV/dt = 155.74 ft^3/minute

Step-by-step explanation:

Volume V = Area × thickness

Area A= πr ^2

Thickness = 0.2 ft

Volume V = 0.2A = 0.2πr^2

V = 0.2πr^2

Differentiating both sides;

dV/dt = 0.2π × 2r dr/dt = 0.4πr.dr/dt

Given;

r = 400 ft

dr/dt = 0.31 ft/minute

π = 3.14

Substituting the values

dV/dt = 0.4πr.dr/dt = 0.4 × 3.14 × 400 × 0.31

dV/dt = 155.74 ft^3/minute

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2 years ago

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Function f is a linear function with an initial value of 17 and a rate of change of –3. Some values for the linear function g ar

tia_tia [17]

Answer:

g(x) exceed f(x) by $10$ when $x=5$

Step-by-step explanation:

step 1

Find the equation of function f(x)

we know that

The initial value is the y-intercept of the linear function (value of y when the value of x is equal to zero)

$b=17$

The rate of change is equal to the slope

$m=-3$

therefore

$f(x)=-3x+17$

step 2

Find the equation of function g(x)

Let

$A(0,-8),B(2,0)$

Find the slope

$m=(0+8)/(2-0)=4$

$b=-8$ ----> point A

therefore

$g(x)=4x-8$

step 3

Find the value of f(x) and g(x) for $x=5$

$f(5)=-3(5)+17=2$

$g(5)=4(5)-8=12$

Find the difference

$g(5)-f(5)=12-2=10$

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2 years ago

Let f(x)=4x-1 and g(x)=2x^2+3. Perform each function operations and then find the domain.

Triss [41]

F(x) = 4x - 1
g(x) = 2x² + 3

1. (f + g)(x) = (4x - 1) + (2x² + 3)
(f + g)(x) = 2x² + 4x + (-1 + 3)
(f + g)(x) = 2x² + 4x + 2
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

2. (f - g)(x) = (4x + 1) - (2x² + 3)
  (f - g)(x) = 4x + 1 - 2x² - 3
(f - g)(x) = -2x² + 4x + 1 - 3
(f - g)(x) = -2x² + 4x - 2
Domain: {x|-∞ < x < ∞}, (-∞, ∞)
3. (g - f)(x) = (2x² + 3) - (4x - 1)
(g - f)(x) = 2x² + 3 - 4x + 1
(g - f)(x) = 2x² - 4x + 3 + 1
(g - f)(x) = 2x² - 4x + 4
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

4. (f · g)(x) = (4x + 1)(2x² + 3)
(f · g)(x) = 4x(2x² + 3) + 1(2x² + 3)
(f · g)(x) = 4x(2x²) + 4x(3) + 1(2x²) + 1(3)
(f · g)(x) = 8x³ + 12x + 2x² + 3
(f · g)(x) = 8x³ + 2x² + 12x + 3
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

5. $(\frac{f}{g})(x) = \frac{4x - 1}{2x^{2} + 3}$
Domain: 2x² + 3 ≠ 0
- 3 - 3
2x² ≠ 0
2 2
  x² ≠ 0
x ≠ 0
(-∞, 0) ∨ (0, ∞)

6. $(\frac{g}{f})(x) = \frac{2x^{2} + 3}{4x - 1}$
Domain: 4x - 1 ≠ 0
+ 1 + 1
4x ≠ 0
4   4
x ≠ 0
  (-∞, 0) ∨ (0, ∞)

6 0

2 years ago