Answer:
<h2>m∠ABD = 20°</h2>
Step-by-step explanation:
If m∠ABC = 40° and BD is the bisector of ∠ABC, then
(1) m∠ABD = m∠DBC
(2) m∠ABC = m∠ABD + m∠DBC
From (1) and (2) we have:
m∠ABC = 2m∠ABD
Therefore
2m∠ABD = 40° <em>divide both sides by 2</em>
m∠ABD = 20°
Answer:
GCF: (x - 2)
4 / (x + 5)
Step-by-step explanation:
The expression given is:
(4x - 8) / (x² + 3x - 10)
To find the greatest common factor, we have to factorise the numerator and denominator individually.
NUMERATOR:
4x - 8 = 4(x - 2)
DENOMINATOR:
x² + 3x - 10 = x² + 5x - 2x - 10
x² + 3x - 10 = x(x + 5) - 2(x + 5)
x² + 3x - 10 = (x - 2) ( x + 5)
So, the expression becomes:
4(x - 2) / [(x - 2) ( x + 5)]
We observe that the common factor in both numerator ad denominator is (x - 2).
This is the greatest common factor (GCF).
Factoring out (x - 2), the expression can be rewritten as:
4 / (x + 5)
<span>f you can't plausibly put a line through the dots, if the dots are just an ... the following scatterplots appear to have positive, negative, or no correlation. ... asked about "outliers", which are the dots that don't seem to fit with the rest of ... Tell which sort of equation you think would best model the data in the following <span>scatterplots</span></span>
Answer:
-4
Step-by-step explanation:
-5x-10=10
add 10 to -10 to get rid of it, and to 10 because whatever you do to one side, you have to do to the other
-5x=20
divide -5 into 20
x = -4
Answer:
83.045( decreasing demand per unit time)
Step-by-step explanation:
let p be the price per product and q the number of units sold.
Given that p=$3.40 and q rate is 12%
-We are given that:
![pq=8000\\\\p=3.4\\\\\frac{dp}{dt}=0.12](https://tex.z-dn.net/?f=pq%3D8000%5C%5C%5C%5Cp%3D3.4%5C%5C%5C%5C%5Cfrac%7Bdp%7D%7Bdt%7D%3D0.12)
#We differentiate using product rule to get the rate at which demand changes over time:
![p\frac{dq}{dt}+q\frac{dp}{dt}=0\\\\\frac{dq}{dt}=\frac{-q\frac{dp}{dt}}{p}\\\\=-\frac{(8000/3.4)(0.12)}{3.5}\\\\=-83.045](https://tex.z-dn.net/?f=p%5Cfrac%7Bdq%7D%7Bdt%7D%2Bq%5Cfrac%7Bdp%7D%7Bdt%7D%3D0%5C%5C%5C%5C%5Cfrac%7Bdq%7D%7Bdt%7D%3D%5Cfrac%7B-q%5Cfrac%7Bdp%7D%7Bdt%7D%7D%7Bp%7D%5C%5C%5C%5C%3D-%5Cfrac%7B%288000%2F3.4%29%280.12%29%7D%7B3.5%7D%5C%5C%5C%5C%3D-83.045)
Hence, demand is decreasing at a rate of 83.045 units per unit time.