The vertex angle of on isosceles triangle measures 42 a base angle in the triangle has a measure given by 2x+3

Step-by-step explanation:

I take it that the question is What is the value of x.

... Every triangle has a measure of 180o so that is what is on the right side of the equation.

... the Vertex of an isosceles triangle has a unique value. There is only one angle with a measure of 42.

... The Base angles are equal. And there are 2 of them.

Equation

2x + 3 + 2x + 3 + 42 = 180o      

Solution

Combine like terms

2x + 2x + 3 + 3 + 42 = 180  Show the like terms as 1 term for the xs and 1 for the pure numbers on the left.

4x + 48 = 180   Subtract 48 from both sides

4x = 180 - 48    combine

4x = 132            Divide by 4

4x/4 = 132/4

x = 33

Answer

x = 33

2x + 3 = 2*33 + 3 = 69

So the three angles are

69 + 69 + 42

Check

69 + 69 + 42

138 + 42

180 as it should.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;