In ∆DEF, if m∠E is one more than three times m∠F and m∠D is three more than seven times m∠F, find the m∠D.
Answers
Answer: mD=115, mE=49, mF=16
Step-by-step explanation:
DEF is a triangle and were told to find angle measures.
If m∠E is (3F+1) and m∠D is (7F+3)
Use T-angle sum theorem and plug previous terms 7F+3+3F+1+F=180 which give F=16. Then substitute F=16 with angles D and E to find last results.
The measure of m∠D is 115 degrees
In the given triangle ∆DEF, if m∠E is one more than three times m∠F, hence;
m∠E = 3m∠F + 1
Similarly, if m∠D is three more than seven times m∠F, then;
m∠D = 7m∠F + 3
Taking the sum of the angles and equate it to 180 degrees
m∠D + m∠E + m∠F = 180
7m∠F + 3 + 3m∠F + 1 + m∠F = 180
11m∠F + 4 = 180
11m∠F = 180-4
11m∠F = 176
m∠F = 16
Since m∠D = 7m∠F + 3
m∠D = 7(16) + 3
m∠D = 115 degrees
Hence the measure of m∠D is 115 degrees
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Related Questions
discriminant of 2x2 - 4x + 7 = 0
Answers
Answer:
1
Step-by-step explanation:
The discriminant of the quadratic equation 2x2+4x-7=0 is 1
find the 16th term of the arithmetic sequence whose common difference is d=8 and whose first term is a↓1=3
Answers
Answer:
123
Step-by-step explanation:
3 + (16 - 1)8
3 + (15)8
3 + 120
123
The sales tax for an item was $18.60 and it cost $ 310 before tax. Find the sales tax rate. Write your answer as a percentage.
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HELP ME OUT REALL FAST PLEASEE
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Answer:
The answer is C because you have to multiply them both:)
Answer:
The answer is C
Step-by-step explanation:
What I'm about to write is overkill for this question, but it works for any common denominator. Factor the denominators.
10: 2 * 5
5 : 1 * 5
You need 1 five and 1 two. The answer is 10
The correct way to go about doing the question is to multiply the 5 by 2 and the 2 on top by 2
2*2/5*2 = 4/10
1/10 1 / 10
4/10 + 1/10
write a linear equation in slope intercept form for a line that passes through the point 6,-2 and has a slope of -2/3
Answers
y=0.625x+1.75 is the equation for your problem.
If an initial amount A0 of money is invested at an interest rate i compounded times a year, the value of the investment after t years is If we let n = 8, that is referred to as the continuous compounding of interest. Use L' Hospital's Rule to show that if interest is compounded continuously, then the amount after years is A=A0eit
Answers
Answer:
Following are the solution to the given point:
Step-by-step explanation:
Please find the comp[lete question in the attached file.
Given:
[tex]\bold{ \lim_{n \to \ \infty} (1+ \frac{r}{n})^{nt} =e^{rt}}[/tex]
In point 1:
[tex]\to y = (1+ \frac{r}{n})^{nt}[/tex]
In point 2:
[tex]\to \ln (y)= nt \ln(1+ \frac{r}{n})[/tex]
In point 3:
Its key thing to understand, which would be that you consider the limit n to[tex]\infty[/tex], in which r and t were constants!
[tex]=lim_{n \to \ \infty} \ln (y) = lim_{n \to \ \infty} nt \ln(1+\frac{r}{n})\\\\= lim_{n \to \ \infty} \frac{\ln(1+\frac{r}{n})}{\frac{1}{nt}}\\\\= lim_{n \to \ \infty} \frac{\frac{-r}{\frac{n^2}{(1+\frac{r}{n})}}}{- \frac{1}{n^2t}}\\\\= lim_{n \to \ \infty} \frac{\frac{rn^2t}{n^2}}{(1+\frac{r}{n})}\\\\= lim_{n \to \ \infty} \frac{rt}{(1+\frac{r}{n})}\\\\= \frac{rt}{(1+\frac{r}{0})}\\\\=rt[/tex]
In point 4:
[tex]\to \lim_{n \to \ \infty} = (1+\frac{r}{n})^{nt}[/tex] and
[tex]\to \lim_{n \to \ \infty} = A_0e^{rt}[/tex]
The table below represents equivalent ratios.
X y
6= 10
12 = 20
??= 45
Answers
Answer:
27
Step-by-step explanation:
6/10=12/20 because when you cross multiply, 120=120, so then you can do wither 6/10=x/45 and when you cross multiply you get 270=10x and 270/10=27.
Solve picture that I provided
Answers
Simplify 3x ^ 2 - 4 +2x -1 + x^ 2 then evaluate for x = - 1
Answers
Step-by-step explanation:
4x^2+2x-5
4(-1)^2+2(-1)-5
4-2-5
2-5= -3
1/x+x/2=11/6 transformable to quadratic equations
Answers
Note: Consider we need to find the solution of given equation.
Given:
The equation is
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
To find:
The solution of the equation.
Solution:
We have,
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
[tex]\dfrac{2+x^2}{2x}=\dfrac{11}{6}[/tex]
By cross multiplication, we get
[tex]6(2+x^2)=11(2x)[/tex]
[tex]12+6x^2=22x[/tex]
[tex]6x^2-22x+12=0[/tex]
[tex]2(3x^2-11x+6)=0[/tex]
Divide both sides by 2.
[tex]3x^2-11x+6=0[/tex]
Splitting the middle term, we get
[tex]3x^2-9x-2x+6=0[/tex]
[tex]3x(x-3)-2(x-3)=0[/tex]
[tex](x-3)(3x-2)=0[/tex]
Using zero product property, we get
[tex]x-3=0[/tex] and [tex]3x-2=0[/tex]
[tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex]
Therefore, the solutions of the given equation are [tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex].
Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).
Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
We are given the algebraic equation: 1/x+x/2=11/6
Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.
LCD(x,2,6) = 6x
Multiply all through the fractions by 6x
(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)
6 + 3x² = 11x
Rewriting the equation:
3x² - 11x + 6 = 0
Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
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here is a list of number 51 38 48 36 39 40 39 47
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Answers
Answer:
36
Step-by-step explanation:
Median is the Middle number in the sequence.
Hope this Helps!!
:D
36 38 39 40 47 48 51
So 40 is the median/middle number
If 39 twice is a typo and there are 8 numbers then average the two middle numbers (the 4th and 5th numbers)
The Buffalo Bills football team wanted to buy new footballs. what did the team have to pay per football? Be sure to explain all of your work.
Answers
Answer: I don't see the amount per football
Step-by-step explanation:
Look at image which graph shows T (ABC)?
Answers
Answer:
A.
Step-by-step explanation:
That is a translation of 3 units left and 6 units down.
Amaia purchased two blouses and a skirt for a total of $32. The sales tax rate is 8%. How much total sales tax will Amaia pay on these items?
Answers
Answer:
2.56
Step-by-step explanation:
8% of 32 is 2.56
A snowboard shop charges $10, plus an additional #3 per hour to rent a snowboard. Write the equation for the line in slope-intercept form.
HURRY HELP PLS!!
Answers
Answer:
y = 3x + 10
Step-by-step explanation:
Answer:
im pretty sure it is (0,5) or (10,0)
Step-by-step explanation:
8. Kim has a fever. Her temperature is 100.5 degrees Fahrenheit. Norr
temperature is 98.6 degrees Fahrenheit, How much above normal
temperature is Kim's fever?
Answers
Answer:
1.9 degrees above the normal temperture
Step-by-step explanation:
Normal temperture: 98.6 degrees Fahrenheit
100.5 - 98.6 = 1.9
A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 173 yellow peas.
Required:
a. Construct a 95â% confidence interval to estimate of the percentage of yellow peas.
b. It was expected thatâ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is notâ 25%, do the results contradictâ expectations?
Answers
Answer:
a
The 95% confidence interval is [tex] 0.2474 < p < 0.3188 [/tex]
b
The result obtained does not contradict expectation
Step-by-step explanation:
From the question we are told that
The number of green peas is k = 438
The number of yellow peas is u = 173
Generally the sample size is mathematically represented as
[tex]n = k + u[/tex]
=> [tex]n = 438 + 173[/tex]
=> [tex]n = 611[/tex]
Generally the sample proportion for yellow peas is
[tex]\^ p = \frac{u}{n}[/tex]
=> [tex]\^ p = \frac{173}{611 }[/tex]
=> [tex]\^ p = 0.2831[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.96 * \sqrt{\frac{ 0.2831 (1- 0.2831)}{611} } [/tex]
=> [tex]E = 0.0357 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex] 0.2831 -0.0357 <p< 0.2831 + 0.0357[/tex]
=> [tex] 0.2474 < p < 0.3188 [/tex]
From the question we are told that it was expected that 25% of the offspring peas will be yellow
Now from the 95% confidence interval obtained we see that the expected sample proportion(25% ) falls within it so it means that the result obtained does not contradict expectation
In Terrance County, 85% of eligible voters are registered to vote, and
government records from a recent gubernatorial election indicate that 60%
of registered voters actually voted in the election. If there are 21,800
eligible voters in Terrance County, how many people voted in the recent
qubernatorial election?
Answers
Answer:
11118 people voted
Step-by-step explanation:
Given
[tex]Eligible\ Voters = 21800[/tex]
[tex]Registered\ Voters = 85\%[/tex]
[tex]Voted\ Voters = 60\%[/tex]
Required
Determine the number of voters
First, we need to determine the number of registered voters.
[tex]Number = \%Registered\ Voters * Eligible\ Voters[/tex]
[tex]Number = 85\% * 21800[/tex]
[tex]Number = 18530[/tex]
Next, we determine the actual voters using
[tex]Voters = \%Voters * 18530[/tex]
[tex]Voters = 60\% * 18530[/tex]
[tex]Voters = 11118[/tex]
Hence, 11118 people voted
You want to earn an EAR of 12.682%. Therefore, you would pick an investment with a quoted interest rate of _________ APR with monthly compounding:
A) 12.30%
B) 12.68%
C) 12.00%
D) 12.28%
E) None of the above
Answers
Answer:
The correct option is C) 12.00%.
Step-by-step explanation:
This can be calculated using the formula for calculating the effective annual rate (EAR) as follows:
EAR = ((1 + (i / n))^n) - 1 .............................(1)
Where;
EAR = effective annual rate = 12.682%, or 0.12682
i = annual percentage rate (APR) = ?
n = Number of compounding periods or months = 12
Substituting the values into equation (1) and solve for i, we have:
0.12682 = ((1 + (i / 12))^12) - 1
0.12682 + 1 = (1 + (i / 12))^12
1.12682 = (1 + (i / 12))^12
(1.12682)^(1/12) = (1 + (i / 12))^(12/12)
1.12682^0.0833333333333333 = 1 + (i / 12)
1.00999962428035 - 1 = i / 12
0.00999962428035 = i / 12
i = 0.00999962428035 * 12
i = 0.119995491364199, or 11.9995491364199%
Approximating to 2 decimal places, we have:
i = 12.00%
Therefore, the correct option is C) 12.00%.
Tom is the custodian at the local highschool. He has a circular key ring with 9 keys on it. How many different arrangements of those keys can Tom make on his key ring?
Answers
tom will have his key 10
Answer:
40,320.. took the test on USA test prep
Step-by-step explanation:
Which statement describes the expression 9(8 + 25)?
1.9 times the quantity 8 times 25
2.9 times the quantity 8 plus 25
3. 25 more than 9 times s
4.25 more tha 9 plus s
Answers
Answer:
2
Step-by-step explanation:
ez any thing else just hit me up of so
TRUE OR FALSE?!?!?!!??!?!?!
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Answer:
False
Step-by-step explanation:
Cause the graphs show false instead of being true
Solve: 2x + 15 = -3x
Please help me out! I need to solve for X
Answers
Answer:
X=-3
Step-by-step explanation:
2x+15=-3x
15=-5x
x=15/-5
x=-3
Answer:
x = -3
Step-by-step explanation:
2x + 15 = -3x
15 = -5x
x = -3
What is the greatest number of baskets that Lisa can make?
Lisa is making fruit baskets.
• She has 12 pears, 30 apples, and 42 oranges.
• For each type of fruit, each basket must have the same number of pieces
of that fruit
• She must use all of the fruit.
A) 2
B 5
C)6
D)7
Answers
Answer: 5
Step-by-step explanation:
What is the multiplicative inverse of 1 2/3
Answers
Answer:
sorry if im wrong but im pretty sure -5/3
Step-by-step explanation:
Answer:
2/1
Step-by-step explanation:
A calculator showed me that this was the answer. I would give you the link but I would probably get deleted. I already got warned so yeah.
Hope this helps!
-2(b+5)= -6
What is b?
Answers
Answer:
-2
Step-by-step explanation:
It would be =
-2(-2 + 5) = -6
4 - 10 = -6
-10 and a positive four is a -6
What is the polynomial of least degree with the given zeroes -2 and 4?
Answers
Answer:
-2
Step-by-step explanation:
base on my stuck knowledge
a single serving of a cereal breakfast contains 18 grams of carbohydrates. this is 6% of the daily recommended allowance for 2000-calorie diet. how many grams of carbohydrates are recommended each day for a person on 2000 calorie diet.
Answers
Answer:
300g
Step-by-step explanation:
Given parameters:
Mass of carbohydrate in the cereal meal = 18g
Unknown:
Grams of carbohydrate recommended each day = ?
Solution:
The 18grams of the carbohydrate is just 6% of the total carbohydrate need per day;
6% x total carbohydrate recommendation = 18
[tex]\frac{6}{100}[/tex] x total carbohydrate = 18
Total carbohydrate = 18 x [tex]\frac{100}{6}[/tex] = 300g
Answer:
The answer is 300 grams of carbs on a 2000-calorie diet!
Step-by-step explanation:
Mass = 18g
daily allowance: ???
6% x total carbohydrate recommendation = 18
x total carbohydrate = 18
Total carbohydrate = 18 x = 300g on a 2000-calorie diet
A triangle has angles that measure 54.6° and 17.8°. Which equation can be used to find the value of x, the measure of the third angle in the triangle?
Answers
Answer:
58.6 + 17.8 + x = 180
Step-by-step explanation:
hope this helps
Does f(x)=|x|+5 go up or down
Answers
Answer:
up
Step-by-step explanation:
postive, up!
Answer:
..........UP..........