Mathematics, 12.04.2021 07:30 aa010002

A shadow 15 feet long is cast by a street sign that is 8 feet tall. If an outdoor sculpture close by casts a shadow 30 feet long, how tall is the outdoor sculpture?
Write your answer as a whole number or a decimal. Do not round.

A shadow 15 feet long is cast by a street sign that is 8 feet tall. If an outdoor sculpture close b

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Answer from: Quest

oof

step-by-step explanation:

Answer from: Quest

answer:

given the linear inequality : $x-2y\geq -12$

add 2y to both sides we get;

$x-2y+2y\geq -12+2y$

simplify:

$x\geq -12+2y$

add 12 to both sides of an equation;

$x+12\geq -12+2y+12$

simplify:

$x+12\geq 2y$

divide both sides by 2 we get;

$\frac{x}{2} + 6 \geq y$

$y\leq \frac{x}{2} + 6$

the related equation for the inequality equation [1] is;

$y =\frac{x}{2} +6$

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

$y =\frac{0}{2} +6$

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

$0 =\frac{x}{2} +6$

subtract 6 from both sides we get

$0-6 =\frac{x}{2} +6-6$

$-6 =\frac{x}{2}$

multiply both sides by 2 we get;

$-6 \times 2=x$

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

Answer from: Quest

a) 40 more; b) old factory: 10%, new factory: 16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.

using the function, substituting 0 in for w,

$p(w)=230(1.1)^w\\\\p(0)=230(1.1)^0\\\\p(0)=230(1)=230$

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate. the equation for the old factory is $p(w)=230(1.1)^w$ ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1. this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

$\text{percent of change}=\frac{\text{amount of change}}{\text{original amount}}$

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337. this is the first week that the new factory surpasses the old.

Answer from: Quest

answer: c

step-by-step explanation

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