Answers
Given the infromation about triangle ABC, we can use the law of cosines to find angles A and C:
\(\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ \Rightarrow\cos A=\frac{b^2+c^2-a^2}{2bc} \\ \text{then:} \\ \cos A=\frac{(12)^2+(16)^2-(14)^2}{2(12)(16)}=\frac{204}{384} \\ \Rightarrow A=\cos ^{-1}(\frac{204}{384})=57.9 \\ A=57.9 \end{gathered}\)then, for angle C, we have:
\(\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ \Rightarrow\cos C=\frac{a^2+b^2-c^2}{2ab} \\ \Rightarrow\cos C=\frac{(14)^2+(12)^2-(16)^2}{2(14)(12)}=\frac{84}{336} \\ \Rightarrow C=\cos ^{-1}(\frac{84}{336})=75.5 \\ C=75.5 \end{gathered}\)now, using the fact that the sum of interior triangles is 180, we have for angle B:
\(\begin{gathered} 57.9+\measuredangle B+75.5=180 \\ \Rightarrow\measuredangle B=180-57.9-75.5=46.6 \\ \measuredangle B=46.6 \end{gathered}\)therefore, the measure of each angle is:
A=57.9
B=46.6
C=75.5
Related Questions
Which expression shows 5 + 5 + 5 + 5 as multiplication?
5 × 2
5 × 4
5 × 5
5 × 10
Answers
Answer:
5 × 2= 10
5 × 4=20
5 × 5=25
5 × 10=50
5+5+5+5=20
there your answer
Step-by-step explanation:
you slow -_-
Answer : 5 x 4 (Option C)
Step-by-step explanation : 5 + 5 + 5 + 5 = 20
By trial & error method, we get
5 x 2 = 10 ≠ 20
5 x 4 = 20
5 x 5 = 25 ≠ 20
5 x 10 = 50 ≠ 20
Hence 5 x 4 is the right answer
You can either follow the trial & error method or the following method !!
5 + 5 + 5 + 5 has ' 4 ' fives
Hence, 5 + 5 + 5 + 5 = 5 (since it is the no) x 4 (since it is the no of times 5 is repeating)
Hence 5 x 4 is the right answer
{ You are requested to mark me the brainliest, if you can }
I GIVEEEE BRAINKLILSETR
Answers
Answer:
G) 5 hours
Step-by-step explanation:
120 / 2 = 60 mph, since the plane travels at 60 mph for it to travel 300 miles it will be: 300/60 which equals 5
Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account? a. A savings account provides security in tough financial times b. With a savings account, you can invest when the opportunity presents itself c. Having a savings account gives individuals the ability to borrow money from members in the community d. A savings account allows an individual to fulfill life long dream
Answers
Answer:
haveing a savings account give individuals the ability to borrow money from members in the community
the awnser is C
Step-by-step explanation:
Please help
will mark BRAINLIEST
Answers
The angle sum property of a triangle and the angle formed between a tangent and a radius of a circle indicates.
m∠ADC = 58°
What is a tangent to a circle?A tangent to a circle is a straight line which touches the circumference of a circle at only one point.
The vertical angles theorem indicates that we get;
∠1 ≅ ∠2
Therefore; m∠1 = m∠2
The tangent to a circle indicates that we get;
The angle formed at vertex B and Q are 90 degrees angles and the triangles ABP and AQP are right triangles, which indicates that the acute angles of each of the right triangles are complementary, therefore;
m∠1 + 26° = 90°
m∠1 = 90° - 26° = 64°
Therefore, m∠2 = m∠1 = 64°
m∠2 = m∠CAD = 64°
The segments AC and AD are radial lengths therefore, the triangle ΔACD is an isosceles triangle.
m∠ADC ≅ m∠ACD (Base angles of an isosceles triangle)
The angles ∠ADC and ∠ACD are therefore;
m∠CAD + m∠ADC + m∠ACD = 180° (Angle sum property of a triangle)
m∠CAD + m∠ADC + m∠ADC = 180°
m∠CAD + 2 × m∠ADC = 180°
64° + 2 × m∠ADC = 180°
m∠ADC = (180° - 64°)/2 = 58°
m∠ADC = 58°
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A certain prescription drug diminishes in the system at a rate of 25% per hour. If a person was administered 1450mg of the drug, how much will remain in 4 hours? How many hours will it take for the amount of the drug in their system to be less than 5mg?
Answers
9514 1404 393
Answer:
459 mgabout 20 hoursStep-by-step explanation:
The decay factor is 1 -25% = 0.75 per hour, so the exponential equation can be written ...
r(t) = 1450·0.75^t . . . . . milligrams remaining after t hours
__
a) After 4 hours, the amount remaining is ...
r(4) = 1450·0.75^4 ≈ 458.79 . . . mg
About 459 mg will remain after 4 hours.
__
b) To find the time it takes before the amount remaining is less than 5 mg, we need to solve ...
r(t) < 5
1450·0.75^t < 5 . . . . use the function definition
0.75^t < 5/1450 . . . . divide by 1450
t·log(0.75) < log(1/290) . . . . . take logarithms (reduce fraction)
t > log(1/290)/log(0.75) . . . . . divide by the (negative) coefficient of t
t > 19.708
It will take about 20 hours for the amount of the drug remaining to be less than 5 mg.
Katie just opened a checking account at the bank. Within the first month, she deposited three checks for $21.68, $42.09, and $65.44. She withdrew $4.64 for new pencils, $23.11 for earbuds, and $9.78 for movies from her account in the same month.
Answers
Complete question is;
Katie just opened a checking account at the bank. Within the first month, she deposited three checks for $21.68, $42.09, and $65.44. She withdrew $4.64 for new pencils, $23.11 for earbuds, and $9.78 for movies from her account in the same month.
Write Katie’s withdrawals as negative rational numbers and her deposits as positive rational numbers.
Answer:
Deposits are; +21.68, +42.09, and +65.44.
Withdrawals are; -4.64, -23.11, and -9.78
Step-by-step explanation:
We are told that the deposits are;
$21.68, $42.09, and $65.44.
Now, she withdrew $4.64 for new pencils, $23.11 for earbuds, and $9.78 for movies from her account in the same month.
We are told to write Katie’s withdrawals as negative rational numbers and her deposits as positive rational numbers.
A rational number is a number that can be expressed as the ratio of two integers. In this question, by inspection, all the given values for deposits and withdrawals can be expressed as the ratio of 2 integers.
Thus;
Deposits are; +21.68, +42.09, and +65.44.
Withdrawals are; -4.64, -23.11, and -9.78
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answers
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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Suppose a population contains 20,000 people. All else being equal, a study
based on a population sample that includes which of the following numbers
of respondents would be the most reliable?
A. 200
OB. 20
C. 2000
D. 2
Answers
A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.
In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.
A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.
Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.
Option A: 200 respondents
This represents only 1% of the population.
While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.
Option B: 20 respondents
This represents only 0.1% of the population.
With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.
Option C: 2000 respondents
This represents 10% of the population.
While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.
The study may provide reasonably reliable results, but there is room for potential sampling error.
Option D: 2 respondents
This represents an extremely small sample size, accounting for only 0.01% of the population.
With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.
Based on the options provided, option C with 2000 respondents would be the most reliable study.
Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.
However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.
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Find the domain and range of a function defined by a graph
Question
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Answers
Answer: domain (-2, 3] range [-2, 2)
These are the x-values left to right the paretheses ( ) indicates "not equal to" a bracket [ ]
Step-by-step explanation: Domains are the x-values left to right the parentheses ( ) indicates "not equal to" like the open circle on the graph; a bracket [ ] means "and equal to" like the solid circke on the graphed line.
Range means the y-values, bottom to top (least to greatest in math lingo)
The slope of a line is 1, and the y-intercept is -1. What is the equation of the line written in slope-intercept form?
Answers
Answer:
slope = 1
y-intercept - 1
slope intercept form: y = x - 1
Step-by-step explanation:
I am a rectangular prism.The volume is 360 cubic cm.My height is 12cm.My length is 6 cm.What is my width?
Answers
Answer:
5
Step-by-step explanation:
360/12/6=5
Double check: 5 x 6 x 12 = 360
Width = 5
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Is there any variable or constant that you could add to or subtract from both sides of 2=2
Answers
Yes, you could add to or subtract from both sides of 2=2.
What is a variable?
A characteristic that can be measured and given different values is known as a variable. Variables include things like height, age, income, province of birth, school grades, and type of housing. There are two main types of variables: categorical and numeric.
Equivalent equations are those that have the same sets of solutions. According to the equations' multiplication/division rule, all terms on both sides of an equation can be multiplied or divided by the same term, with the exception of zero, without changing the equation's solution set.
The equation is 2 = 2
Add x with both sides:
2 + x = 2 + x
The equation remains the same.
Add 3 with both sides:
2 + 3 = 2 + 3
5 = 5
The equation remains the same.
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A triangle has a base length of 3ac2 and a height 2 centimeters more than the base length. Find the area of the triangle if a = 2 and c = 3.
Answers
The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.
We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.
(1/2) * Base * Height = Area
We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.
Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters
Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).
Using these values as a substitute in the formula, we obtain:
Area =\((1/2) * 54 * 56 = 1512\) square centimeters
centimetres square
It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.
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HELP!!!!!A school is having a competition to see who can read the most books in one month (30 days). In the first 5 days, Jake reads 4 books. Meanwhile, Amy reads 5 books over 6 days. If they continue at these rates, who will win? By how many books?
Answers
is there a rate because im not understanding
Differentiate the following four levels of measurement and give an example of each: nominal, ordinal, interval and ratio.
-Nominal: a level of measurement describing a variable that has attributes that are merely different, as distinguished from ordinal, interval, or ratio measures. Gender is an example.
-Ordinal: a level of measurement describing a variable with attributes we can rank-order along some dimension. An example is socioeconomic status as composed of the attributes high, medium, and low.
-Interval: a level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes. There is however, no "true" zero point. Like the difference in temperature.
-Ratio: a level of measurement describing a variable with attributes that have all the qualities of nominal, ordinal, and interval measures and in addition are based on a "true zero" point. Ex. Number of children you have, makes sense to have a zero
Answers
The process of associating numbers with physical quantities and phenomena. Measurement is used in our day-to-day life
Nominal: A level of measurement describing a variable that has attributes that are merely different, as distinguished from ordinal, interval, or ratio measures.
Gender is an example.
Ordinal: A level of measurement describing a variable with attributes we can rank-order along some dimension.
An example is socioeconomic status as composed of the attributes high, medium, and low.
Interval: A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes. There is however, no "true" zero point. Like the difference in temperature. An example will be the measuring temperature.
Ratio: A level of measurement describing a variable with attributes that have all the qualities of nominal, ordinal, and interval measures and in addition are based on a true zero point. An example will be Number of children you have, makes sense to have a zero
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Subtract:14hours 20 minutes 40 second from 21 hours 15 minutes 20 second
Answers
Step-by-step explanation:
21. 15. 20
-. 14. 20. 40
equals to 8hrs1min20sec
pls gimme brainliest I need it
The larger of two numbers is 4 more than 2 times the smaller number. If the sum of the two numbers is 28, what is the larger number
Answers
Answer:
The larger number is 20.
Step-by-step explanation:
Let x and y be the two numbers.
y = 2x + 4
x + y = 28
So x + 2x + 4 = 28
3x = 24
x = 8
y = 20
Use the figure to answer the questions.
(a) Describe the relationship among the lengths of the segments formed by two secants. You may use words and/or and equation.
(b) Suppose CG = 3 in, CH = 2 in, and GE = 5 in, is it possible to find the length of DH? If so, show how to find the length. If not, explain why not.
Help would be appreciated!
Answers
Based on the intersecting secants theorem:
a. CG*CE = CH*CD
b. length of DH = 10 in.
What is the Intersecting Secants Theorem?When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.
a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:
CG*CE = CH*CD
b. Given the following lengths:
CG = 3 in, CH = 2 in, and GE = 5 in
CE = CG + GE = 3 + 5 = 8 in.
CD = CH + DH = 2 + DH
Substitute into CG*CE = CH*CD:
3*8 = 2*(2 + DH)
24 = 4 + 2DH
24 - 4 = 2DH
20 = 2DH
20/2 = DH
DH = 10 in.
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Need help on this please
Answers
Answer:
(x+8) ² + \(y^{2}\) = 64
find the volume of the rectangular prism?
Answers
Answer:
volume = 60 cm³
Step-by-step explanation:
volume = length × width × height
volume = 5 cm × 4 cm × 3 cm
volume = 60 cm³
What is an equation of the line that passes through the points (-6, 3)(−6,3)
Answers
Answer:
y = 3
Step-by-step explanation:
are you sure you typed this question in right?
3. The graph of a polynomial function fis
shown. Which statement about the
polynomial is true?
-3
A. The degree of the polynomial is even.
B. The degree of the polynomial is odd.
C. The constant term of the polynomial is even.
D. The constant term of the polynomial is odd.
Answers
The degree of the polynomial is even.
What is polynomial ?Algebraic expressions called polynomials include indeterminates and constants. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and \(x^{2}\) + 3x + 11. The "=" sign is absent from all of these samples, as you may have observed.
The polynomial's degree is even since the final behavior is the same in both directions (for -x and for +x, y→∞).
The y-intercept is the fixed term. Since it is not an integer, evenness and oddness cannot be determined.
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What is x. PLEASE HELP NEED ANSWERS NOW. M=
Answers
12x+16x+40-32=180
28x+8=180
X=180-8/28=6
I think so my calculation may be wrong )
Marcus was interested in whether the frequency that students check emails impacts their grades in the class. He categorized students into three groups. Those who checked email daily, those who checked email at least 2x a week (but not every day), and those who checked email less than 2x a week. Below are the GPAs for the students he studied. Conduct the steps of hypothesis testing on these data.
Table of data: GPAs for students separated by how often they check their email
Daily 2x a week Less than 2x a week
3.6 3.5 2.9
3.5 3.4 3.0
3.7 3.2 3.2
4.0 3.2 2.7
Answers
The steps to conduct the steps of hypothesis testing on these data are:
State the null hypothesis (H0) as well as the alternative hypothesis (H1):Select the significance level (alpha): Select the right test statistic:Formulate the decision rule:Compute the test statistic as well as the p-value:Decide on a decision.What is the hypothesis?The hypothesis will be:
H0: Email frequency does not affect grades.H1: Email frequency affects grades.Since we are comparing (GPAs) of three groups (students who check e-mail day by day, students who check mail at least 2x a week, and students who check mail less than 2x a week), one can be able to make use of one-way analysis of variance (ANOVA) as the fitting test measurement.
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Look at the picture you’ll understand 14 points!
Answers
Based on the number of hotdogs that Harry had when he came on Wednesday, the number he sold was 8 dozen hotdogs.
How many hotdogs did Harry sell on Wednesday?The graph shows the number of dozen hotdogs that remain at the beginning of each day.
The number of hotdogs sold on Wednesday can then be found as:
= Hotdogs started on Wednesday - Hotdogs remaining on Wednesday
= 38 - 30
= 8 dozen hotdogs
Question:
How many dozen hot dogs did Harry sell on Wednesday? How do you know?
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PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ANSWERRRRRRRRRRRRRRRRRRR WILL GIVE BRAINLISTTTTTTTTTTTT
Answers
Answer:
B
Step-by-step explanation:
B because you have to add. It says total amount and x represents the number of miles of the ride
Hey can anyone help me understand how to graph this?
Answers
Answer:
Step-by-step explanation:
?
Julian borrowed some money from his friend in order to help buy a new video game
system. Julian originally borrowed $100 and agreed to pay back his friend $20 per
week. Write an equation for L, in terms of t, representing the amount Julian owes
his friend after t weeks.
Answers
Answer:
L = 20t because the he needs to replenish his takings every week by 20.
20t
what is 900 * 158000
Answers
Answer:
142,200,000
Step-by-step explanation:
Used Calculator
Answer:
142200000
Step-by-step explanation:
It's a really long answer
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
Answers
The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).
1. Start by calculating the distance between the vertices of the original triangle ABC:
- Distance between A(4, 3) and B(3, -2):
Δx = 3 - 4 = -1
Δy = -2 - 3 = -5
Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26
- Distance between B(3, -2) and C(-3, 1):
Δx = -3 - 3 = -6
Δy = 1 - (-2) = 3
Distance = √((-6)² + 3²) = √45 = 3√5
- Distance between C(-3, 1) and A(4, 3):
Δx = 4 - (-3) = 7
Δy = 3 - 1 = 2
Distance = √(7² + 2²) = √53
2. Apply the scale factor of 1.5 to the distances calculated above:
- Distance between A' and B' = 1.5 * √26
- Distance between B' and C' = 1.5 * 3√5
- Distance between C' and A' = 1.5 * √53
3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):
- A' is located Δx units horizontally and Δy units vertically from A.
- Δx = 1.5 * (-1) = -1.5
- Δy = 1.5 * (-5) = -7.5
- Coordinates of A':
x-coordinate: 4 + (-1.5) = 2.5
y-coordinate: 3 + (-7.5) = -4.5
4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).
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