Answer: $72.96
Step-by-step explanation:
7.6% = 0.076
Take 960.00 times 0.076 = $72.96
please help will give brainliest
The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.
Given that, the polygon IJKL if IJ≅KL, JK≅LI, IJ⊥JK, JK⊥KL, KL⊥LI and LI⊥IJ.
What is a rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Here, the opposite sides IJ and KL are equal and the opposite sides JK and LI are equal.
Since, all the sides are perpendicular to each other makes an angle 90°
The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.
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What is the domain of this function?
f(x) = ²x - 3| + 1 ?
Answer: A.
Step-by-step explanation:
Most of the function f(x) has a domain (- infinity, positive infinity), and the function in the picture is the same. So, the answer is A
sum of two numbers is -11/12 ,one of them is 9/2, find the other
pls answer fasttttttt!!!!
plssssssssssssssssssssssssssssss.
step by step
Answer:
- [tex]\frac{65}{12}[/tex]
Step-by-step explanation:
let the number to be found be n , then
n + [tex]\frac{9}{2}[/tex] = - [tex]\frac{11}{12}[/tex]
multiply through by 12 ( the LCM of 2 and 12 ) to clear rhe fractions
12n + 54 = - 11 ( subtract 54 from both sides )
12n = - 65 ( divide both sides by 12 )
n = - [tex]\frac{65}{12}[/tex]
Calculate the magnitude of y. trapezium
K = 123°
L = 71°
M = 39°
N = y
Explanation:
A trapezium has four sides, so it is a quadrilateral.
Any quadrilateral has all four interior angles add to 360 degrees.
K+L+M+N = 360
123+71+39+y = 360
233+y = 360
y = 360-233
y = 127
Which are irrational numbers?
Answer:
A is the only irrational number present.
Step-by-step explanation:
The bottom two numbers can be simplified into 7 and 5. Meanwhile, B is a repeating number. A is a non-repeating and non terminating number.
Answer:
A.
Step-by-step explanation:
An irrational number is any real number that cannot be equally divided by 2 integers. (It's not a perfect square.)
No whole number multiplied by itself equals 27.
Find the radius of the circle which circumference is 22 cm.
Answer:
3.5 cm
Step-by-step explanation:
Circumference: C = 2πr
so radius r = C/2π = 22/2π = 3.5 cm
tom and addison made plans to meet up in the state park to spend some time hiking together. tom arrived early and started wandering up the trail, snapping some photos along the way. his speed was 4 kilometers per hour. addison arrived later, when tom was already 6 kilometers ahead, and started hiking up the trail at 10 kilometers per hour to catch up. how much time did it take addison to catch up to tom?
Answer:
Math Expert Answer
Step-by-step explanation:
So toms equation is y= 4x + 6 and addisons equation is y=10x so they will meet eachother in 1 hour. You can use a desmos calculator to input the equations for the answer
Answer:
1 hour
Step-by-step explanation:
Let's set up an equation for Tom's and Addison's distances: T(x) = 4x + 6, A(x) = 10x, where x is the amount of time since Addison started (in hours).
We solve for A(x) = T(x) and get:
10x = 4x + 6 → subtract 4x from both sides
6x = 6 → divide both sides by 6
x = 1
Therefore, it took Addison 1 hour to catch up with Tom
Chocolate bars cost $2.50 each.
The more chocolate bars Terri buys, the more
money she will have to pay.
Identify the dependent variable.
Answer:
The dependent variable is the cost
Step-by-step explanation:
The dependent variable is the variable that depends on the independent variable to either increase or decrease.
In this case, the dependent variable is the cost, and the independent variable is the number of chocolate bars.
for conducting a two-tailed hypothesis test with a certain data set, using the smaller of n11 and n21 for the degrees of freedom results in df11, and the corresponding critical values are t2.201. using the formula for the exact degrees of freedom results in df19.063, and the corresponding critical values are t2.093. how is using the critical values of t2.201 more conservative than using the critical values of 2.093?
Using the critical values of t=+/-2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of +/-2.093.
Critical Value Definition -
Critical value can be defined as a value that is compared to a test statistic in hypothesis testing to determine whether the null hypothesis is to be rejected or not.
If the value of the test statistic is less extreme than the critical value, then the null hypothesis cannot be rejected.
Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie; for example, a region where the critical value is exceeded with probability \alpha if the null hypothesis is true.
Using the critical values of t=±2.201 is more "conservative" than using the critical value of ±2.093 because it is more likely to reject the null hypothesis using the greater value i-e t=±2.201.
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show that if a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.
If a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.
In this question we need to prove if a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.
We know that the definition of divisibility i.e., m divides n if there exists an integer p such that n = mp
If a | c and b | d, then there exist integers x and y such that c = ax and d = by.
Consider a multiplication c * d
= (ax) * (by)
= axby
= (ab)xy
= ab(xy)
Let k be equal to the integer xy
So, cd = ab(k)
Using the definition of divisibility, cd is divisible by ab.
Therefore, if a | c and b | d, then ab | cd.
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2: Angle 1 and Angle 4 are vertical angles. If the measure of angle 1 equals 3x + 14 and the
measure of angle 4 equals 5x − 52, what is the measure of Angle 1?
3: Suppose that ∠ = 3x + 8 and ∠ = 2/3x + 62
If ∠ and ∠ are supplementary
angles, what is the measure of ∠?
4:Angle 2 and Angle 3 are vertical angles. If the measure of angle 2 equals 13x + 27 and the
measure of angle 3 equals 9x + 59, find the value of .
5: Suppose that m∠ABC = 163° and ∠XYZ = 5x + 2. If ∠ABC and ∠XYZ are supplementary
angles, determine the value of x
2. The measurement of angle 1 is 113°
3. The measure of ∠1 = 98° and ∠2 = 82°
4. The value of x is 8.
5. The value of x is 3.
What is the supplementary angle?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.
2.
Given that, ∠1 and ∠4 are vertical angle.
According to the vertical angle theorem, if two angles are vertical then they are congruent.
Therefore,
∠1 = ∠4
3x + 14 = 5x − 52
Subtract 5x from both sides:
3x - 5x + 14 = -52
-2x + 14 = -52
Subtract 14 from both sides:
-2x = -66
x = -33
Putting x = -33 in ∠1 = 3x + 14
∠1 = 3× 33 + 14 = 113°
3.
Given that, ∠1 = 3x + 8 and ∠2 = 2/3x + 62 are supplementary angles.
Therefore ∠1 + ∠2 = 180°
3x + 8 + 2/3x + 62 = 180°
11/3 x + 70 = 180°
Subtract 70 from both sides:
11/3 x = 110
x = 110 × (3/11)
x = 30
Putting x = 30 in ∠1 = 3x + 8 and ∠2 = 2/3x + 62
∠1 = 3x + 8 = 3×30 + 8 = 98°
∠2 = 2/3x + 62 = (2/3)×30 + 62 = 82°
4.
Given that, Angle 2 and Angle 3 are vertical angles. If the measure of angle 2 equals 13x + 27 and the measure of angle 3 equals 9x + 59.
Therefore,
∠2 = ∠3
13x + 27 = 9x + 59
Subtract 9x from both sides:
13x - 9x + 27 = 9x -9x +59
4x +27 = 59
Subtract 27 from both sides:
4x = 32
x = 8
5. Given that m∠ABC = 163° and ∠XYZ = 5x + 2 are supplementary angles.
m∠ABC + m∠XYZ =180°
163° + 5x + 2 =180°
165 + 5x = 180
Subtract 165 from both sides:
5x = 15
x = 3
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Answer:
2) m∠1 = 113°
3) 98° and 82°
4) x = 8
Angles = 131°
5) x = 3
Step-by-step explanation:
Question 2If Angle 1 and Angle 4 are vertical angles, then according the Vertical Angles Theorem they are congruent.
Therefore:
⇒ m∠1 = m∠4
⇒ 3x + 14 = 5x - 52
⇒ -2x + 14 = -52
⇒ -2x = -66
⇒ x = 33
To find the measure of Angle 1, substitute the found value of x into the expression for the angle:
⇒ m∠1 = 3x + 14
⇒ m∠1 = 3(33) + 14
⇒ m∠1 = 99 + 14
⇒ m∠1 = 113°
Question 3Given:
∠ = 3x + 8∠ = ²/₃x + 62If the angles are supplementary, they sum to 180°:
⇒ 3x + 8 + ²/₃x + 62 = 180
⇒ ¹¹/₃x + 70 = 180
⇒ ¹¹/₃x = 110
⇒ 11x = 330
⇒ x = 30
Substitute the found value of x into the expressions for the angles:
⇒ ∠ = 3x + 8
⇒ ∠ = 3(30) + 8
⇒ ∠ = 98°
⇒ ∠ = ²/₃x + 62
⇒ ∠ = ²/₃(30) + 62
⇒ ∠ = 82°
Question 4If Angle 2 and Angle 3 are vertical angles, then according the Vertical Angles Theorem they are congruent.
Therefore:
⇒ m∠2 = m∠3
⇒ 13x + 27 = 9x + 59
⇒ 4x + 27 = 59
⇒ 4x = 32
⇒ x = 8
Substitute the found value of x into the expressions for the angles:
⇒ m∠2 = 13x + 27
⇒ m∠2 = 13(8) + 27
⇒ m∠2 = 104 + 27
⇒ m∠2 = 131°
⇒ m∠3 = 9x + 59
⇒ m∠3 = 9(8) + 59
⇒ m∠3 = 72 + 59
⇒ m∠3 = 131°
Question 5Given:
m∠ABC = 163° m∠XYZ = 5x + 2If ∠ABC and ∠XYZ are supplementary, they sum to 180°:
⇒ m∠ABC + m∠XYZ = 180°
⇒ 163 + 5x + 2 = 180
⇒ 5x + 165 = 180
⇒ 5x = 15
⇒ x = 3
Figure A ha an area of 18 quare feet. Figure B ha an area of 98 quare feet and one of the ide length i 14 feet. Find the miing correponding ide length if figure A i imilar to Figure B
The side length of Figure A can be determined using the ratio of areas and the known side length of Figure B. The area of Figure A is 18 square feet and the area of Figure B is 98 square feet. The side length of Figure B is 14 feet. Using these values, the corresponding side length of Figure A can be calculated to be 7 feet.
The missing corresponding side length of Figure A can be determined using the ratio of areas and the known side length of Figure B. If two shapes are similar, then their corresponding sides are in the same ratio as their areas. Since the area of Figure A is 18 square feet and the area of Figure B is 98 square feet, the ratio of their areas is 18/98. Since the side length of Figure B is 14 feet, the corresponding side length of Figure A can be calculated by multiplying 14 feet by the ratio of 18/98, which is 0.1837. This value can be rounded to 7 feet. Therefore, the missing corresponding side length of Figure A is 7 feet. This result can be verified by calculating the area of Figure A using the known side length and the missing side length. If the two side lengths are multiplied together, the product should be equal to the area of Figure A, which is 18 square feet.
7 feet x 11 feet = 77 feet^2
77 feet^2 = 18 feet^2 (Area of Figure A)
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5(x-9)=55
What would you do to both ide firt?
A. Subtract 5
B. Divide by 5
C. Add 9
D. Subtract 55
Answer:
b
Step-by-step explanation:
we first make
1.Subtraction/Adding
2.Mutiply/Division
f(x)=x^4+8x^3+11x^2-9x+28=0
The roots of the quartic polynomial f(x) = x⁴ + 8x³ + 11x² - 9x + 28 are ±1, ±2, ±3, ±4, ±7, ±14, ±28
Roots of a PolynomialIn the given problem, we have to find the roots of the fourth degree polynomial and factorize the given polynomial equation first in order to obtain three equations which are linear and quadratic equation. We can easily determine the zeros of the fourth degree polynomial.
Generally, polynomials of fourth degrees are called quartic polynomials.
f(x) = x⁴ + 8x³ + 11x² - 9x + 28
When we factorize this, we wouldn't get a lower value because this quartic polynomial cannot be factorized.
However, we can still find the roots which are the solution to the polynomial and are
x = ±1, ±2, ±3, ±4, ±7, ±14, ±28
These values are the solution to the polynomial.
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complete question : What are the roots of f(x)=x^4+8x^3+11x^2-9x+28
Find u•v where theta is the angle between u and v
Answer:
88√2 = 124.5 (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}[/tex]
Given:
[tex]|u| = 8[/tex][tex]|v| = 22[/tex][tex]\theta =\dfrac{\pi}{4}[/tex]Substitute the given values into the dot product formula:
[tex]\begin{aligned}\implies u \cdot v &=|u||v| \cos \theta\\\\&=8 \cdot 22 \cdot \cos \left(\dfrac{\pi}{4}\right)\\\\&=176 \cdot \dfrac{\sqrt{2}}{2}\right)\\\\&=88\sqrt{2}\\\\&=124.5\; \sf (nearest\;tenth)\end{aligned}[/tex]
6th grade math IXL program
Answer:
1.5 groups.
Step-by-step explanation:
1 divided by 8/12 is 1.5
Answer:
1 1/2
Step-by-step explanation:
The figure shows a large rectangle that is divided into 12 parts of equal size.
Think of the entire rectangle as 1.
Each small rectangle is 1/12 of 1.
Now count 8 small rectangles starting at the left.
When you divide 1 by 8/12, you can fit 1 full 8/12 (8 small rectangles) and another half of 8/12 (another 4 small rectangles.
Since you can fit 1 1/2 groups of 8 small rectangles,the result is 1 1/2.
Answer: 1 ÷ 8/12 = 1 1/2
What is 10 percent of 75
Answer:
7.5
Step-by-step explanation:
100% = 75
100% divided by 10 is 10%
75 divided by 10 is 7.5
natalie is the creator of better brain, a new mindfulness app for teens. the app currently has 1,262 downloads, and natalie has set a goal of doubling the downloads every month. write an exponential equation in the form y
Answer:
1262(2)^x
Step-by-step explanation:
Pls helppp i dont get it at all
Answer:
Law of Sines
Step-by-step explanation:
a rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base.
The total cost is $245.31.
Given,
Volume = 10[tex]m^{3}[/tex]
Width = w
Length = 2w
Base area = Length x Width = [tex]2w^{2}[/tex]
Cost of base = $15
Cost of sides = $9
Since the volume is 10[tex]m^{3}[/tex],
Volume = Base Area x Height
Height = [tex]\frac{10}{2w^{2} }[/tex] = [tex]\frac{5}{w^{2} }[/tex]
Cost of making such a container:
Cost of base = [tex]2w^{2}[/tex] x 15 = $[tex]30w^{2}[/tex]
Cost of sides = [(2 x 2w x [tex]\frac{5}{w^{2} }[/tex]) + (2 x w x [tex]\frac{5}{w^{2} }[/tex])] x $9 = $[tex]\frac{270}{w}[/tex]
Overall Cost = Cost of Base + Cost of Sides
f(x) = [tex]30w^{2} + \frac{270}{w}[/tex] = [tex]30(w^{2} + \frac{9}{w})[/tex]
To get the minimum cost, we will have to find the derivative of f(x) and equate it to zero.
d(f(x))/dx = 0
[tex]2w - \frac{9}{w^{2} } = 0\\w^{3} = 4.5 \\w = 1.651m[/tex]
Putting the value of w in f(x),
f(x) = $245.31 (after calculations)
Therefore, the final answer is $245.31.
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Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 33 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Answer:330
Step-by-step explanation:
Set up cross multiplication:
33/x 10/100
Cross multiply
10*x 100*33
Divide sums
3,300/10x
Answer:
330 total cards
Statistics tree diagram word problem, select the correct tree diagram.
Each day mr brightside chooses one digit number from a random number table to decide if he will walk to work or drive that day. the numbers 0 through 3 indicate he will drive, 4 through 8 mean he will walk. if he drives, he has a probability of 0.1 of being late. if he walks, his probability of being late rises to 0.25. let 2=walk, d= drive, l=late, and nl= not late. which of the following tree diagrams summarizes these probabilities?
The tree diagram that summarizes these probabilities is Option (D).
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Here, N(S) = 10, The numbers from 0 - 9.
The probability of going to work by driving is (4/10) = 0.4.
If he drives, he has a probability of 0.1 of being late so P(NL) = 1 - 0.1 = 0.9.
The probability of going to work by walking is = 6/10 = 0.6.
if he walks, his probability of late rising to 0.25 so, P(NL) = 1 - 0.25 = 0.75.
Now we'll connect this information to the given options.
From the given options, Option (D) satisfies the given information.
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a man 6 feet tall walks at a rate of 5 ft / sec away from a light that is 15 feet above the ground. when he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?
On solving the provided question we can say that - rate is the tip of his shadow moving is [tex]d/dt ( s-x) = ds/dt - dx/dt = 25/3 - 5 = 25/3 - 15/3 = 10/3 ft/s = 10/3 ft/s[/tex]
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is what? A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
triangles and the ratios
15 ft s
-------- = --------------
6 ft s-x
Using cross products
[tex]15( s-x) = 6s\\15s -15x = 6s\\15s-6s = 15x\\9s = 15x\\s = 15/9 x\\s = 5/3 x[/tex]
Taking the derivative of each side with respect to time
[tex]ds/dt = 5/3 dx/dt\\We know dx/dt = 5 ft/s\\ds /dt = 5/3 * 5 = 25/3 ft/s\\a) ds/dt = 25/3 ft/s[/tex]
The length of the shadow is ( s-x)
[tex]d/dt ( s-x)\\ds/dt - dx/dt\\25/3 - 5\\25/3 - 15/3\\10/3 ft/s\\b) 10/3 ft/s[/tex]
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Write y+4=2(x-7) in standard form
[tex] \Large{\boxed{\sf 2x - y = 18}} [/tex]
[tex] \\ [/tex]
Explanation:We will try to write the given linear equation in standard form.
[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Standard \ Form \ of \ a \ linear \ equation \text{:}} \\ ~ \\ \tt Ax + By = C \end{array} \right] } [/tex]
Where:
A is a positive integer. (A ≠ 0)B and C are integers. (B ≠ 0)[tex] \\ [/tex]
Given linear equation:
[tex] \sf y + 4 = 2(x - 7) [/tex]
[tex] \\ [/tex]
First, expand the right side of the equation:
[tex] \sf y + 4 = 2 \cdot x + 2 \cdot (-7) \\ \\ \sf y + 4 = 2x - 14 [/tex]
[tex] \\ [/tex]
Subtract 2x from both sides of the equation:
[tex] \sf y + 4 - 2x = 2x - 14 - 2x \\ \\ \sf -2x + y + 4 = -14 [/tex]
[tex] \\ [/tex]
Subtract 4 from both sides of the equation:
[tex] \sf -2x + y + 4 - 4 = -14 - 4 \\ \\ \sf -2x + y = -18 [/tex]
[tex] \\ [/tex]
Since the coefficient of x (-2) has to be positive, multiply both sides of the equation by -1:
[tex] \sf -1 \cdot (-2x + y) = -1 \cdot (-18) \\ \\ \sf -1 \cdot (-2x) + (-1) \cdot y = 18 \\ \\ \boxed{\boxed{\sf 2x - y = 18 }} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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At her health clubs, Lauren uses a treadmill every 2 days and the weight machines every 8 days. She used a treadmill on march 2 and will use the weight machines on march 8. Lauren says that the first time she will use both a treadmill and the weight machines in march is march 16 because the lcm of 2 and 8 is 16. Does Lauren’s reasoning make sense? Use an example or a counterexample to explain your analysis
Lauren's reasoning does not make sense because the LCM of 2 and 8 is not 16, the LCM will be equal to 8.
What is LCM?The Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least frequent multiple (LCM) for two numbers.
It can also be computed for several different numbers.
As per the given information in the question,
Lauren says that the LCM of 2 and 8 is 16.
Now, let's check whether it is correct or not.
Let's make a factor of both numbers,
2 = 2 × 1
8 = 2 × 2 × 2
So, the LCM will be: 2 × 2 × 2 = 8
It means that the LCM of 2 and 8 is not 16, the LCM is 8.
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Jayden’s family has completed 90% percent of the trip. They have traveled 75 miles. How far is the trip?
Answer:
[tex]83\frac{1}{3} miles[/tex]
Step-by-step explanation:
90/100=75/x
90x=100(75)
90x=7500
/90. /90
x=83 1/3 miles
Hopes this helps
02.03 Focus Questions
What are linear equations and functions?
What are the different ways of representing a linear function?
How are key features of a linear function identified and interpreted from a graph?
How are key features of a linear function identified and interpreted from a table?
How are key features of a linear function identified and interpreted from an equation?
How are key features of a linear function identified and interpreted from a description?
Linear functions are those whose graph is a straight line and it has the following form. y = f(x) = a + bx.
There are several ways to represent a linear function such ad word form, function notation, tabular form, and graphical form.
The key features of a linear function identified and interpreted from a description as an increasing linear function results in a graph that slants upward from left to right and has a positive slope.
What is a linear function?A linear function can be expressed as a point slope or a line with a slope intercept. The ordered pairs will represent points on the line where a table of values representing the function is provided. According to the values in the table, the gradient of the line is a ratio of rise to run. The gradient and initial value of the function are shown in slope intercept form.
A graph with a positive slope and a left-to-right slope is produced by an increasing linear function. A graph with a negative slope and a left-to-right slant is produced by a decreasing linear function. A graph with a constant linear function looks like a horizontal line.
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all the sides of a triangle are integers, and the perimeter is 12. how many different possible triangles are there
3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
Given that,
The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).
We have to find how many such difference triangle are possible.
We know that,
Perimeter of the triangle is 12cm.
p=12
a+b+c=12
a+b≥c
b+c≥a
So,
a+b+c≥2c
12≥2c
c≤6
So,
a≤6,b≤6,c≤6
We get,
a=6,b=3,c=3
a=5,b=4,c=3
a=4,b=4,c=4
Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
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Jana purchase a jewelry making kit to make gifts for her friends.The kit includes Material to make 72 bracelets.Write and solve an equation to show how many more bracelets she can make from the kit.
WILL GIVE BRAINLIEST
Answer:
72 = b + 24
Step-by-step explanation:
b = 48 bracelets
what is the size of angle ADC
what is the size of angle ADB
Answer:
∠ADC = 58°∠ADB = 37° BD is a diameterStep-by-step explanation:
You want to know the measures of angles ADB and ADC given that inscribed angle BAC is 21° and exterior angle CBE is 58°.
Exterior angleAngle CBE is exterior to triangle CBA with remote interior angles BAC (21°) and ACB. The exterior angle is equal to the sum of the remote interior angles, so ...
∠CAB +∠ACB = ∠CBE
21° +∠ACB = 58°
∠ACB = 37° . . . . . . . . subtract 21°
a) ∠ADCThe measure of an inscribed angle is half the measure of the arc it intercepts. This means the measures of all inscribed angles that intercept the same arc are the same.
∠ADB = ∠ACB = 37°
∠BDC = ∠CAB = 21°
By the Angle Addition theorem, ...
∠ADC = ∠ADB +∠BDC = 37° +21°
∠ADC = 58°
b) ∠ADBAs we just saw, ...
∠ADB = 37°
c) BDFor angle CAD = 69°, the total of the inscribed angles with vertex A is ...
∠CAD +∠CAB = ∠BAD
69° +21° = 90° = ∠BAD
This means angle BAD intercepts an arc BD of 180°, hence segment BD is a diameter.
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The attached figure is accurately drawn.