The value of the expression 18 - (16 • 12) is -174.
Explanation:
To evaluate the expression 18 - (16 • 12), we need to follow the order of operations, also known as PEMDAS. According to PEMDAS, we first perform any calculations inside parentheses, then evaluate exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.
In this expression, we have the operation of multiplication inside parentheses. So, we start by evaluating 16 • 12, which equals 192.
Now, we can rewrite the expression as 18 - 192.
Next, we perform the subtraction, which gives us -174.
Therefore, the value of the expression 18 - (16 • 12) is -174.
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The following two triangles are similar.
a) What scale factor is applied to triangle A to create triangle B?
b) Find the values of x and y.
c) Are these right triangles?(yes or no)
Step-by-step explanation:
all pairs of corresponding sides have the same scale factor.
so, we only need to find one to know it for all.
a)
we know 2 corresponding sides : 6 and 12.
that means
12 × s = 6
s = 6/12 = 1/2
b)
x = 5 × s = 5 × 1/2 = 2.5 = 2 1/2
y = 13 × s = 13 × 1/2 = 6.5 = 6 1/2
c)
to be right-angled triangles they need to fulfill the Pythagoras criteria :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle).
a and b are the legs.
so, for the larger triangle we have
13² = 12² + 5²
169 = 144 + 25 = 169
correct. it is right-angled.
for the smaller triangle :
6.5² = 6² + 2.5²
42.25 = 36 + 6.25 = 42.25
as expected : also correct. so, yes, they are both right-angled.
The table of values represents a function f(x) How much greater is the average ra
The average rate of change over the interval [9,10] is greater by 6490.
The average rate of change of a polynomial is the slope of the function.
The average rate of change over the interval [7, 9] is the slope between ( 7, f(7) ) and ( 9, f(9) )
where f(7) and f(9) is the value of the function at 7 and 9.
So, the slope between ( 7, 1852 ) and ( 9, 3878 )
= (3878-1852)/(9-7)
= 2026/2
= 1013
Similarly,
The average rate of change over the interval [4, 6]
i.e. slope between ( 4, f(4) ) and ( 6, f(6) )
So, the slope between ( 4, 358 ) and ( 6, 1178 )
= (1178-358)/(6-4)
= 820/2
= 410
and
1013-410 = 603
So, the polynomial is 603 greater than the average rate of change over the interval [7, 9] than the interval [4, 6]
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what are significant digits in a quantity?
Significant digits, also known as significant figures, refer to the digits in a quantity that are considered to be reliable and meaningful based on the precision of the measurement.
The significant digits in a given quantity include all the digits that are known with certainty, as well as one uncertain digit that is estimated based on the measurement's precision.
For example, if the length of a table is 1.23 metres, the digits "1," "2," and "3" are all significant, whereas the digit "0" is not significant because it is just a placeholder.
The number of significant digits in a number is determined by the measurement instrument or method used.
For example, if you use a centimeter-marked ruler to measure the length of a table, you can estimate the length to the nearest millimetre, implying that the last digit is uncertain and estimated. Because you have three certain digits and one estimated digit, the number of significant digits in this case is three.
When performing mathematical operations on numbers with varying numbers of significant digits, the result should be rounded to the same number of significant digits as the least precise measurement. This is necessary to maintain the calculation's accuracy and precision.
Understanding significant digits is essential for precise scientific measurements and calculations. It can aid in the prevention of errors and the production of reliable and meaningful results.
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how many different triangles can be constructed with angles that measure 120, 40, and 60
Answer:
It would be zero
Step-by-step explanation:
how many millions are in billions
Answer:
1000 millions are in a billion
Step-by-step explanation:
1 million can be written as 1000000 (6 zeros)
1 billion can be written as 1000000000 (9 zeros)
the difference in the zeros is three and 1000 has three zeros so we can say,
1000000 x 1000 = 1000000000
their zeros are basically added together.
A 19 ft rope is tied from the top of a tent pole to a stake 11 ft away. To the nearest degree, what is the angle of elevation from the stake up to the tent pole?
The angle of elevation from the stake up to the tent pole is, 54.55°.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, A 19 ft rope is tied from the top of a tent pole, It is the hypotenuse length.
Also, The state is 11 feet away and it is the adjacent length.
We know, cos = adjacent/hypotenuse.
cos = 11/19.
Ф = cos⁻¹(0.58).
Ф = 54.55°.
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Use the series formula to find the sum of the geometric sequence -5,15,45,135 Use the series formula to find the sum of the geometric sequence. Find the sum of the first 10 terms.
The sum of the first 10 terms of the sequence -5, 15, 45, 135 is 295240.
We can use the following formula to determine the sum of a geometric sequence:
S = a(1 - r^n) / (1 - r) (1 - r)
where an is the first term, r is the common ratio, and n is the total number of terms, S is the sum of the sequence.
We can see that the first term in the series -5, 15, 45, 135 is -5, and the common ratio is 3. (since each term is obtained by multiplying the previous term by 3). The series contains 4 terms, hence n is equal to 4. Adding these values to the formula yields the following results:
S = -5(1 - 3^4) / (1 - 3) (1 - 3)
S = -5(1 - 81) / (-2) (-2)
S = 5(80) (80)
S = 400
The total of the numbers 5, 15, 45, and 135 equals 400.
We may once more use the following formula to determine the sum of the first 10 entries in the same sequence:
S = a(1 - r^n) / (1 - r) (1 - r)
Instead, we will use a = -5, r = 3, and n = 10 this time. By replacing these values, we obtain:
S = -5(1 - 3^10) / (1 - 3) (1 - 3)
S = -5(1 - 59049) / (-2) (-2)
S = 5(59048) (59048)
S = 295240
The result is 295240 for the first 10 terms in the series, which are -5, 15, 45, and 135.
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An angle measures 120.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.
Step-by-step explanation:
Let x be the measure of the angle we are trying to find.
By definition of supplementary angles, we know that the angle's supplementary angle measures 180° - x.
We are also given that the angle measures 120.2° less than its supplementary angle. This can be written as:
x = (180° - x) - 120.2°
Simplifying the equation, we get:
x = 59.9°
Therefore, the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.
To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted
the number of trees with diameters exceeding 12 inches in each square. The data are listed here.
O
Relative Frequency
Relative Frequency
7
9
2
11
9
7
X+S
9
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
8
x + 2s
9
x + 3s
H
Need Help?
7 4 8 10
1
6
5
10
8
748
10 8
USE SALT
5. 526
8
4
9
8
7
(a) Construct a relative frequency histogram to describe the data.
Frequency of lumber
5
Interval
Read It
3. 382 to 11. 961
6
06 9
11 10 11 8 8 10 8 8 12
1. 237 to 14. 106
7
7
11
8 8 10
9
9560
Frequency of lumber
L
77
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
7 8
to 9. 816
7 7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
7 7
10 10 7 4 8 7
(c) Calculates for the data. (Round your answer to three decimal places. )
S = 2. 145
✔timber trees
(b) Calculate the sample mean x as an estimate of μ, the mean number of trees for all 50-by-50-foot squares in the tract.
(Round your answer to three decimal places. )
X = 7. 671
timber trees
Construct the intervals x ±s, x ± 2s, and X + 3s. Calculate the percentage of squares falling into each of the three intervals,
and compare with the corresponding percentages given by the Empirical Rule and Tchebysheff's Theorem. (Round your
interval values to three decimal places. Round actual percentages to two decimal places. )
Actual Percentage
Relative Frequency
X %
Relative Frequency
X %
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
X %
0. 40
0. 35
0. 30
0. 25
0. 20
0. 15
0. 10
0. 05
Frequency of lumber
7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
Frequency of lumber
at least 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
amount of lumber
Tchebysheff
at least 75%
at least 89%
%
95
Empirical
≈ 68%
≈ 99. 7%
%
The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67
In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.
By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.
In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:
=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).
If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.
If the owner counted 7 trees in the first square, the formula would be
=> (7 / 70) x (2500 / 12) = 16.67.
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Complete Question:
To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.
7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5
How to convert convert meters to miles?
To convert any number of meters to miles, you simply need to multiply the number of meters by this conversion factor 0.000621371192
The conversion factor from meter to miles is 0.000621371192
1 meter = 0.000621371192 miles
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
So, to convert meter to miles you can multiply the number of kilometers by 0.000621371192
The distance in miles = conversion factor × The distance in meters
Therefore, the steps to convert meter to miles has been explained
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pls help with this homework question
Answer:
h = 12 feet
Step-by-step explanation:
using the right triangle shown in the diagram.
the base of the triangle is half the measure of the base of the square side.
then base of triangle = [tex]\frac{1}{2}[/tex] × 32 = 16 feet and hypotenuse = 20 feet
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
h² + 16² = 20²
h² + 256 = 400 ( subtract 256 from both sides )
h² = 144 ( take square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
the height h of the pyramid is 12 feet
A file that is 228 megabytes is being downloaded. If the download is 15.4% complete, how many megabytes have been downloaded?
Answer:
35.112
Step-by-step explanation:
15.4% = 0.154. 228*0.154=35.112.
one condition of a well-defined probability density function of a continuous random variable x is that f(x) is multiple choice question. greater than zero for all values of x. not greater than zero for all values of x. less than zero for all values of x. greater than four for all values of x.
The correct answer is:
greater than zero for all values of x.
What is Probability ?Probability is a way of evaluating how likely something is to happen. Several things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. One is the probability of every event in a sample space.
Now in the given question ,
A probability density function (PDF) of a continuous random variable x is a function that describes the relative likelihood of x taking on different values in a continuous range. The PDF is defined such that the area under the curve between any two values a and b represents the probability of x being in that range, i.e., P(a ≤ x ≤ b).
Since probabilities are non-negative, the PDF of a continuous random variable must also be non-negative. That is, f(x) > 0 for all values of x. This condition ensures that the area under the curve is non-negative, which is necessary for it to represent a valid probability distribution.
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what is the 95 % conversion in decimal ?
The 95 % conversion in decimal is 0.95.
To convert a percentage to a decimal, you divide the percentage by 100.
Therefore, to convert 95% to a decimal, you divide 95 by 100:
95 ÷ 100 = 0.95
So, 95% as a decimal is 0.95.
A percentage is a fraction expressed as a fraction of 100 in mathematics. It is frequently used to express percentages, rates, or frequencies in terms of 100. For example, if 95 out of 100 people agree on something, we can express this as a 95% probability.
To convert a percentage to a decimal, simply divide it by 100. The outcome is a number between 0 and 1, with 1 representing the entire (or 100%). In the case of 95%, dividing by 100 yields 0.95 as the decimal equivalent.
Simply multiply a decimal by 100 to convert it to a percentage. To convert 0.95 to a percentage, multiply it by 100 to get:
0.95 x 100 = 95%
As a result, percentages and decimals are two different ways of representing the same value. While percentages are frequently used to express proportions or rates, decimals are frequently used in mathematical computations or scientific notation.
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the radius of a sphere was measured and found to be 21 cm with a possible error in measurement of at most 0.03 cm. what is the maximum error in using this value of the radius to compute the volume of the sphere?
The maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.
What is sphere ?
A sphere is a three-dimensional shape that is perfectly round, with all points on the surface at an equal distance from the center.
The formula for the volume of a sphere is given by V = (4/3)πr³, where r is the radius of the sphere.
The maximum error in the measurement of the radius is given as 0.03 cm. Therefore, the actual radius of the sphere can be anywhere between 20.97 cm (21 - 0.03) and 21.03 cm (21 + 0.03).
To find the maximum error in using this value of the radius to compute the volume of the sphere, we need to find the maximum possible difference in the volumes calculated using these two values.
So, we can calculate the volume of the sphere using the maximum and minimum values of the radius as follows:
V_max = (4/3)π(21.03)³
V_min = (4/3)π(20.97)³
Now, we can find the difference between these two values to get the maximum possible error:
Max error = V_max - V_min
Max error = (4/3)π(21.03)³ - (4/3)π(20.97)³
Max error ≈ 554.86 cubic centimeters
Therefore, the maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.
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Mr. shaw graphs the function f(x) = –5x 2 for his class. the line contains the point (-2, 12). what is the point-slope form of the equation of the line he graphed? y – 12 = –5(x 2) y – 12 = 2(x 2) y 12 = 2(x – 2) y 12 = –5(x – 2)
Answer:
y - 12 = -5(x + 2)
Step-by-step explanation:
Explain how to use the regression calculator to make a reasonable prediction
The regression calculator is a useful tool for making predictions based on historical data. This calculator is used to predict future outcomes based on past patterns.
To use the regression calculator, you must first collect the historical data that you want to use to predict the future. This can be anything from the number of sales of a product to the number of visitors to a website.
Once the data has been collected, you need to enter the regression calculator. This calculator will allow you to enter the data and then generate a regression model. This will give you a trend line that will fit the data you have entered. This trend line will allow you to predict the future outcome with some accuracy.
To make a reasonable prediction, you will need to adjust the model to ensure that the results are as accurate as possible. This is achieved by varying the parameters of the model, such as the type of regression (linear, polynomial, etc.), the number of variables and the variable boundaries. These parameters will influence the accuracy of the prediction.
Once the model is ready, predictions can be made using the trend line. The trend line will give you a prediction for the future based on the historical data entered. This will help you make informed decisions about the future.
In summary, the regression calculator is a useful tool for predicting the future based on past patterns. For best results, you should carefully adjust the model parameters to obtain an accurate trend line. This will allow you to make reasonable predictions regarding the future.
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Enter a range of values for x. + 42° 3x+15 3x+15° 23 21 [ ? ]
The value of x is given as follows:
x = 9.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Similar triangles have congruent angle measures, and the angles of 3x + 15º and 42º are congruent, hence the value of x is obtained as follows:
3x + 15 = 42
3x = 27
x = 9.
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what is standard error of mean
The standard error of mean is a technique for calculating the sampling distribution's standard deviation.
A technique for assessing the standard deviation of a sampling distribution is standard error of the mean. The acronym SEM stands for standard error of the mean, which is another name for it. For instance, in a sample space, the sample mean is often the projected population mean value. But, if we choose another sample from the same population, the result can be different.
As a result, a population of the sampled means with unique variance and means will emerge. The standard deviation of such a sample mean, which includes all feasible samples taken from the same specified population, could be referred to as the standard error of mean. SEM is an approximation of standard deviation that was determined from the sample.
The standard error of the mean (SEM) demonstrates how the mean changes when the same quantity is evaluated in various tests. Consequently, the SEM will be higher if the outcome of random fluctuations is crucial. Yet if repeated attempts fail to reveal any change in the data points, the standard error of the mean will be equal to zero.
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y=80(1.3)^x growth or decay
The +equation represents exponential growth
What is the exponential functions?
An exponential function is a mathematical function that has the form f(x) = a*b^x, where a and b are constants, and x is the independent variable.
The equation y = 80(1.3)^x represents exponential growth.
In this equation, "y" represents the value of the function at a given time or input, "x" represents the time or input, and "1.3" is the growth factor, which is greater than 1.
As "x" increases, the value of the function "y" grows at an increasing rate. This is because the growth factor is greater than 1, which means that each input value results in a larger output value than the previous one.
Hence, this equation represents exponential growth.
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The bacteria took 1 hour and 40 minutes to fill the initial bottle explain how it only took 10 minutes to fill 3 additional empty bottles
Due to the exponential growth of bacteria it only took 10 minutes to fill 3 additional empty bottles.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes.
Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.
The answer needed is -
The full bottle doubled after 5 minutes.
The 2 full bottles doubled after 5 minutes.
Exponential growth is a multiplicative rate of change.
Therefore, due to exponential growth bacteria filled the bottle fast.
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Answer:
The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.
what is 21% of .31 with work shown
Answer:
0.0651
Step-by-step explanation:
To find 21% of 0.31, we can use the following formula:
21% × 0.31
We can convert the percentage to a decimal by dividing by 100:
0.21 × 0.31
Multiplying these two numbers, we get:
0.0651
Therefore, 21% of 0.31 is 0.0651.
Are the two triangles similar?
Yes or no?
How do you know?
Step-by-step explanation:
yes, they are, because both triangles have the same 3 angles :
the right angle = 90°
65°
25°
now, the side lengths can be different, but because of the same angles, the ratio between the corresponding side lengths will be the same for all sides (e.g. if one pair of sides has the scaling factor of 3 from the smaller to the larger triangle, then the other pairs will also have the same scaling factor 3).
that is the difference between equivalent and similar : for "equivalent" also the side lengths must be the same.
for "similar" only the angles need to be the same.
Write the standard form of the equation of each line.
1) y=3x+1
2) y=-9/5x+3
helppppp plsssss
Answer:
Step-by-step explanation:
(1)To write this in standard form, we want the x and y terms on the same side of the equation and the constant on the other side. To do this, we can subtract 3x from both sides:
-3x + y = 1
So the standard form of the equation is:
-3x + y = 1
(2)y = -9/5x + 3
To write this in standard form, we want to eliminate the fraction by multiplying both sides by the denominator (5):
5y = -9x + 15
Next, we can move the x term to the left side by adding 9x to both sides:
9x + 5y = 15
So the standard form of the equation is:
9x + 5y = 15
What is the conversion of 175 cm to inches ?
The conversion factor for converting centimetres to inches (in.) is 0.3937. Thus, the conversion of 167 centimetres to inches is equals to the 68.89 inches.
To convert from one unit to another, multiply by a conversion factor. The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and is approximately equal to 39.37 inches. An inch is a unit of length or distance in measurement system of common American units and British Imperial units. One inch is defined as 1/12 of a feet. To convert a centimeter value to its equivalent inch value, simply multiply the centimeter value by 0.39370078740 (the conversion factor). The formula to convert centimeters to inches is: Inches
= Centimeters × 0.39370078740.
The factor 0.39370078740 is the result of dividing 1/2. So the best formula is inches = centimeters / 2.54. Now we need to convert 175 cm to inches. So, according to the formula, inches = 175 cm / 2.54
= 68.8976377953 ~ 68.89
Hence, required value is 68.89 inches.
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when multiplying matrices, multiply the elements in each of the first matrix times the corresponding elements in each. is it true?
False, every component of the matrix is multiplied by the same amount when you multiply a matrix by a number. A new matrix is created by this operation; it is known as a scalar multiple.
A rectangular matrix is a grouping of numbers in rows and columns. A matrix element/entry is the term used to describe each number in the matrix. The combination of a real number and a matrix is referred to as scalar multiplication.
Each entry/element of the matrix is multiplied by the specified scalar in scalar multiplication. Comparatively, matrix multiplication describes the result of two matrices. This operation is totally different. We can't just multiply the corresponding entries in two matrices to multiply them.
The first matrix must have exactly as many columns as the second matrix has rows in order to perform matrix multiplication. The resulting matrix has the same number of columns and rows as the second matrix, and its number of columns matches the number of rows in the first matrix.
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Find the rate of change between:
(-2/3,-4)
(-3,4)
Would appreciate some help I don’t understand this at all.
Answer:
The rate of change between (-2/3, -4) and (-3, 4) is:
(change in y) / (change in x) = (4 - (-4)) / (-3 - (-2/3))
= 8 / (-2/3)
= -12
Therefore, the rate of change is -12.
Step-by-step explanation:
=]
Considerthecircularfaceintheaccompanyingfigure. For each of the matrices a in exercises 24 through 30, draw a sketch showing the effect of the linear transformation t(x⃗) = ax⃗ on this face
Linear transformation of a matrix is discussed below.
What is matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Given is to discuss the linear transformation of a matrix.
The matrix of a linear transformation is a matrix for which T(x) = A(x) for a vector (x) in the domain of T. This means that applying the transformation T to a vector is the same as multiplying by this matrix. Such a matrix can be found for any linear transformation T from [tex]R^{n}[/tex] to [tex]R^{m}[/tex] for fixed value of n and m, and is unique to the transformation.Therefore, linear transformation of a matrix is discussed above.
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What is the conversion of 720 minutes to hours?
The conversion of 720 minutes to hours is equal to 12 hours.
The units involved in this conversion are minutes and hours.The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. An hour (symbol: h; also abbreviated hr.) is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions.The conversion factor from minutes to hours is 0.0166667, which means that 1 minutes is equal to 0.0166667 hours:1 min = 0.0166667 hr, There are 60 minutes in one hour. To convert 720 minutes to hours, you can divide 720 by 60:
720 minutes ÷ 60 minutes/hour = 12 hours
So, 720 minutes is equal to 12 hours.
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Mathematics word problem. Working out would be really helpful. 20 points
Answer:
d = 86e = 94Step-by-step explanation:
You want the measures of angles d° and e° in the given figure.
AssumptionsUsually, geometry problems tell you not to assume anything that isn't marked or stated regarding the figure. In order to answer this question, we need to assume ...
∆ACD is isosceles∆ABE ~ ∆ACDIsosceles triangleThe base angles in an isosceles triangle are congruent. That means each of them is the complement of half the vertex angle.
∠D = 90° -1/2∠A = 90° -8°/2 = 86°
The segments CD and BE are parallel, so angle E is the supplement of angle D:
∠E = 180° -86° = 94°
The angle measures are d° = 86° and e° = 94°.
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Additional comment
This is not a "word problem." All of the relations necessary for answering the question are shown in the diagram, not stated in words. (The question is necessarily written in words—for any problem.)
If b is a base angle and v is the vertex angle of an isosceles triangle, then the sum of angles is ...
b + b + v = 180°
2b = 180° -v . . . . . . subtract v
b = 90° -v/2 . . . . . . divide by 2
Effectively, the altitude of an isosceles triangle bisects the vertex angle and creates two congruent right triangles. The acute angles in that triangle are the original base angle and half the vertex angle. They are complementary.
