Answer:
a) J':(-7,7) K':(-5,2) L':(-2,3)
b) The x coordinates remained the same, the y coordinates swapped from negative to positive.
Step-by-step explanation:
Aside: I'm using J', K', and L' to denote the new locations of J,K,L after the reflection.
When an object is reflected over the x-axis, it means it's positive points will flip to negative y space, and negative points will flip to positive y space.
That said, J, for instance, will have the same X-coordinate, but its Y-coordinate will flip from negative to positive. Doing this with every vertex mirrors the triangle over the X-axis.
Therefore, J:(-7,-7) will become J':(-7,7), and likewise with K and L becoming K':(-5,2) and L':(-2,3).
Answer: 23.7 lb
Step-by-step explanation:
Mean m = 15 lb
Standard deviation d = 3.3 lb
To determine the surcharge weight, we need to know the highest weight of 99% of the parcels.
P(z<x) = 0.99 = ¢(Z)
Z = 2.33
Since Z = (x - m)/d
x = dZ + m
x = 3.3*2.33 + 15
x = 22.689 lb approximately
x = 22.7 lb
Therefore, the highest weight for 99% if the parcels is 22.7 lb.
That is, the surcharge weight = 22.7 + 1 = 23.7 lb
a. The value of x is 7
b. The measure of ∠1 is 99°
<h3>Calculating angles </h3>
From the question, we are to solve for x
From the given diagram, we can write that
m∠NMQ + m∠MQN + m∠QNM = 180° (<em>Sum of angles in a triangle</em>)
From the given information,
m∠NMQ = 5x +19
m∠MQN = 8x -11
m∠QNM = 11x + 4
Then,
5x + 19 + 8x -11 + 11x + 4 = 180
Collect like terms
5x + 8x + 11x = 180 - 19 + 11 - 4
24x = 168
∴ x = 168/24
x = 7
Hence, the value of x is 7
b.
Measure of ∠1 + m∠QNM = 180° (<em>Sum of angles on a straight line</em>)
∴ Measure of ∠1 = 180° - m∠QNM
But m∠QNM = 11x + 4
∴ m∠QNM = 11(7) + 4
m∠QNM = 77 + 4
m∠QNM = 81°
Then,
Measure of ∠1 = 180° - 81°
Measure of ∠1 = 99°
Hence, the measure of ∠1 is 99°
Learn more on Calculating angles here: brainly.com/question/25716982
#SPJ1
Answer:
A. −2(x − 7)2 + 118; x = $7
Step-by-step explanation:
The expression −2x² + 28x + 20 represent the store weekly profit in dollars, where x represents the price of a new video game.
let f(x) = −2x² + 28x + 20
We need to rewrite this quadratic function in the vertex form.
f(x) = −2(x² - 14x) + 20
f(x) = −2(x² - 14x +49) - {-2(49) + 20}
f(x) = −2(x² - 14x +49) + 98 + 20
f(x) = −2(x² - 7)² + 118
The equivalent expression that reveals the video game price that produces the highest weekly profit is -2(x-7)^2+118 and the price is $7