Answer:
in triangle ACD and BCE
AC = EC
angle ACD = angle ECB ( COMMON ANGLE).
CB = CD
BY side and side criteria
triangle ACD is congruent to triangle BCE
so angle a is congruent to angle E
hence, proved
Answer:
The solution set is (-20/9, -95/9)
Step-by-step explanation:
To solve using the substitution method, start by solving the second equation for y.
1/3y = 7/3x + 5/3
y = 7x + 5
Now that we have this, we can plug it in for y in the first equation. Then we can solve for x.
-4x - 2(7x + 5) = 30
-4x - 14x - 10 = 30
-18x - 10 = 30
-18x = 40
x = -20/9
Now that we have the value of x, we can solve for y by inputting the x value into either equation.
-4x - 2y = 30
-4(-20/9) - 2y = 30
80/9 - 2y = 30
80/9 - 2y = 270/9
-2y = 190/9
y = -95/9
Answer:
The answer is C
Step-by-step explanation:
Answer:
D. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
Step-by-step explanation:
The population mean, μ is given as 87
This population value is used to state the Null hypothesis ;
H0 : μ = 87
The alternative hypothesis is the opposite of the Null ; and hence, claims that the mean is different from the population mean, μ ≠ 87
H1: μ ≠ 87
The Decison level :
When Pvalue < α ; We reject the Null otherwise we fail to reject the null
The given p and α value :
P-value = 0.0752
α = 0.05
0.075 > 0.05 ; Hence ;
Pvalue > α ; We fail to reject the Null
We can thus conclude that there is not enough evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
Step-by-step explanation:
complementary angles are 90°,supplementary are 180°
(3x+25)+2x=180(supplementary angles)
2x +3x is 5x
5x=180-25=155
5x=155÷5=31
x=31
