Answers
This will simplify to x=45.
In this case, these two angles are Alternate Interior Angles, which we know are congruent.
Because they are congruent, they will be the same angle. In other words, they will equal each other.
So we can set this problem up as an equation and solve for x:
3x-50 = 2x-5
3x-50+50 = 2x -5 + 50
3x = 2x + 45
3x - 2x = 2x -2x + 45
x = 45
ANSWER:
X= 45
Now find the angles accordingly.
3(45) - 50 = 85
2(45) - 5 = 85✔️
Everything checks out.
Related Questions
Please help! Need to pass a module test!
What is the equation of the line, in slope-intercept form, that contains the points (−1, 8) and (2, −1)?
y = −3x + 5
y = −x + 5
y = x + 5
y = −x + 3
Answers
-1 = -3(2) + b
-1 = -6 + b
Add 6 to both sides.
5 = b
y = -3x + 5
What are the coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) ? Enter your answer in the boxes.
Answers
[tex]distance \: xy \: = \sqrt{( { (3)}^{2} + {(4)}^{2} ) } \\ = \sqrt{(9 + 16)} = \sqrt{25} = 5[/tex]
[tex]distance \: xz \: = \sqrt{( {(2)}^{2} + {(6)}^{2} ) } \\ = \sqrt{(4 + 36)} = \sqrt{40} \\ = \sqrt{4} \times \sqrt{10} = 2 \sqrt{10} [/tex]
The centroid of a triangle is the point where the medians of the triangle meets.
The coordinates of the centroid is (-1,2)
The coordinates of the triangle are given as:
[tex]X = (-4,0)[/tex]
[tex]Y = (-1,4)[/tex]
[tex]Z = (2,2)[/tex]
The coordinates of the centroid is:
[tex]C = \frac 13(x_1 + x_2 + x_3,y_1+y_2+y_3)[/tex]
So, we have:
[tex]C = \frac 13(-4-1 + 2,0+4+2)[/tex]
[tex]C = \frac 13(-3,6)[/tex]
Expand
[tex]C = (\frac 13\times -3,\frac 13\times 6)[/tex]
[tex]C = (-1,2)[/tex]
Hence, the coordinates of the centroid is (-1,2)
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An employee contributes $75 each month to her 401(k). What will be the value of her 401(k) after the 240th deposit (20 years) if the per annum rate of return is assumed to be 12% compounded monthly?
Answers
To calculate the value of the 401(k) after 240 deposits (20 years), you can use the formula for compound interest. Using the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal investment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years, you can plug in the values to find the answer.
Explanation:To calculate the value of the 401(k) after the 240th deposit, we can use the formula for compound interest:
Formula: A = P(1 + r/n)^(nt)
Where:
A is the future value of the investmentP is the principal investment ($75 per month)r is the annual interest rate (12%)n is the number of times the interest is compounded per year (12 times for monthly compounding)t is the number of years (20 years)Using these values, the formula becomes:
A = 75(1 + 0.12/12)^(12*20)
Calculating this expression will give us the value of the 401(k) after 20 years.
Suppose you invest $2000 at an annual interest rate of 4.5%. how long will it take for it to earn $495?
Answers
100%:2090$=4.5%:x$, x=94.5$. After 2nd year I earned 94.5$ more, now I have 2184.05$.
100%:2184.05$=4.5%:x$, x=98.28$. After 3rd year I have 2282.33$.
100%:2282.33$=4.5%:x$, x=102.71$. After 4th year I have 2385.04$.
100%:2385.04$=4.5%:x$, x=107.33$. After 5th year I have 2492.37$.
So I need 6 years to earn 495$.
To calculate how long it takes for an investment to earn a certain amount in simple interest, use the formula T = I / (PR), where I is the interest, P is the principal, R is the rate of interest, and T is the time. For a $2000 investment at 4.5% interest to earn $495, it would take approximately 5.5 years.
Explanation:The subject of this question is Simple Interest. The formula for calculating simple interest is I = PRT, where I is the interest, P is the principal (the initial amount of money), R is the rate of interest per time period, and T is the time. In this case, we know the interest ($495), the principal ($2000), and the rate (4.5% or 0.045 as a decimal). We're trying to find out the time, so we rearrange the formula to T = I / (PR).
Substituting our known values, we get T = 495 / (2000 * 0.045). Doing the math, the time it takes for the investment to earn $495 is approximately 5.5 years.
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Why do two negatives equal a positive when adding?
Answers
Two negatives do equal a positive when you're multiplying them together though. This makes sense if you imagine multiplication as squishing or stretching a particular number on the number line. For example, imagine multiplying 2 x 1/2 as squishing the number 2 two times closer to 0. When you multiply 2 by a negative number, say, -1, you squish it so far down that you flip it to the negative side of the number line, bringing it to -2. You can imagine a similar thing happening if you multiply a number like -4 by -2. You squish -4 down to zero, and then flip it to the positive side and stretch it by a factor of 2, bringing it to 8.
I need help on this immediately. Please help me.
Answers
Reason A: Given
Reason B: Angle Addition Postulate
Reason C: Substitution Property
Reason D: Subtraction Property of Equality
----------------------------------------------------------
Further Explanation:
Reason A: At the very top of the problem, it states "given: ..." with the given angle property. All we do for the first line of any proof is repeat what is given to us. It seems silly and redundant, but it is important. Whenever you do a proof you always start with what you're given (some fact or theorem already proven earlier) and you somehow try to connect it to what you are trying to prove.
Reason B: The angle addition postulate is essentially the idea where we break up an angle into smaller pieces. This is probably better shown in a visual style instead of using words. Have a look at the attached image. Notice how the green angle ABD and the red angle DBE combine to form the purple angle ABE. Hopefully the image is clear enough. If not, then feel free to ask any questions.
Reason C: We're using the substitution property here. If x = a and x = b, then we can say that a = b. That's what is going on but on a more complicated level.
Reason D: We subtract the quantity "measure of angle DBE" from both sides. It is like going from x+2 = y+2 to x = y (subtract 2 from both sides). This is the subtraction property of equality in action. In general the rule is if a = b, then a-c = b-c
18 girls out of 32 students is what percent?
Answers
18 girls represent 56.25 percent of the total number of students.
To find what percent 18 girls out of 32 students represent, you can set up a proportion comparing the number of girls to the total number of students. This proportion is represented by the fraction 18/32. To convert this fraction into a percentage, multiply it by 100.
Here's the calculation step by step:
Divide 18 by 32 to get the decimal form.
Multiply the result by 100 to get the percentage.
Performing the calculation gives:
(18/32) x 100 = 56.25%
Therefore, 18 girls represent 56.25 percent of the total number of students.
What is the difference between -5 squared and -5 parenthesis squared?
Answers
Order of operations says to do exponents first, so without parentheses -5², you would square first then multiply by -1, leaving you with an answer of -25.
However, parentheses comes before exponents in order of operations, so with parenthesis (-5)² would be 25.
Ryan made 4 identical necklaces, each having beads and a pendant. the total cost of the beads and pendants for all 4 necklaces was $18.80 . if the beads cost a total of $9.20 , how much did each pendant cost?
Answers
Cost of 4 lots of b (beads) + cost of 4p (pendants) = $18.80
Put values in;
9.29 + 4p = 18.80
4p = 18.80 - 9.20
4p = 9.60
p = 2.40 cost of each pendant
2000 geometry question im i correct
Answers
Angle B is opposite the corresponding segment with a single tick mark.
This means angle B = angle F = 40 degrees
Side Note: we use SAS to prove the triangles congruent; then use CPCTC to find values of corresponding parts
Two cab rides cost the same amount for the same number of miles, m. Which situation can be represented by the equation 2.50 + 0.50m = 1.00 + 0.75m?
Answers
One cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.
The value of m is 6 in the equation 2.50 + 0.50m = 1.00 + 0.75m.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Two cab rides cost the same amount for the same number of miles, m.
The given equation is 2.50 + 0.50m = 1.00 + 0.75m.
Two point five zero plus zero point five zero times m equal to one point zero plus zero point seven five times m.
First cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.
2.50 + 0.50m = 1.00 + 0.75m
2.50-1.00=0.75m-0.50m
1.5=0.25m
Divide both sides by 0.25
m=6
Hence, the value of m is 6 in the equation 2.50 + 0.50m = 1.00 + 0.75m.
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To which place value is the number rounded 6.706 to 6.71
Answers
What's the intuition behind the equation 1+2+3+⋯=−1121+2+3+⋯=−112 ?
Answers
[tex]1+2+3+\cdots=-\dfrac1{12}[/tex]
is to demonstrate that a sum of infinitely many terms can be manipulated in a variety of ways to end up with a contradictory result. It's an artifact of trying to do computations with an infinite number of terms.
The mathematician Srinivasa Ramanujan famously demonstrated the above as follows: Suppose the series converges to some constant, call it [tex]C[/tex]. Then
[tex]\begin{matrix}C&=&1&+2&+3&+4&+5&+6&+\cdots\\4C&=&&+4&&+8&&+12&+\cdots\\-3C&=&1&-2&+3&-4&+5&-6&+\cdots\end{matrix}[/tex]
Now, recall the geometric power series
[tex]\displaystyle\sum_{n\ge0}x^n=1+x+x^2+x^3+\cdots=\dfrac1{1-x}[/tex]
which holds for any [tex]|x|<1[/tex]. It has derivative
[tex]\displaystyle\sum_{n\ge1}nx^{n-1}=1+2x+3x^2+4x^3+\cdots=\dfrac1{(1-x)^2}[/tex]
Taking [tex]x=-1[/tex], we end up with
[tex]1+2(-1)+3(-1)^2+4(-1)^3+\cdots=1-2+3-4+\cdots=\dfrac14[/tex]
and so
[tex]-3C=\dfrac14\implies C=-\dfrac1{12}[/tex]
But as mentioned above, neither power series converges unless [tex]|x|<1[/tex]. What Ramanujan did was to consider the sum [tex]1-2+3-4+\cdots[/tex] as a limit of the power series evaluated at [tex]x=-1[/tex]:
[tex]\displaystyle-3C=\lim_{x\to-1^+}\sum_{n\ge1}nx^{n-1}=\lim_{x\to-1^+}\frac1{(1-x)^2}=\frac14[/tex]
then arrived at the conclusion that [tex]C=-\dfrac1{12}[/tex].
But again, let's emphasize that this result is patently wrong, and only serves to demonstrate that one can't manipulate a sum of infinitely many terms like one would a sum of a finite number of terms.
PLEASE HELP!!!!!!!!!!
Whats the value of a?
a-2=3+6a/3
a=
Answers
a = -5
Answer:
a–2=3 6a/3
So I was told The answer was -5 but all the people r wrong its -3
proof
An urn contains 3 green balls, 2 blue balls, and 4 red balls. in a random sample of 5 balls, find the probability that at least one blue balls is selected.
Answers
Final answer:
To find the probability of at least one blue ball being selected from an urn with green, blue, and red balls in a sample of 5, calculate the probability of not selecting any blue balls and then subtract it from 1.
Explanation:
An urn contains 3 green balls, 2 blue balls, and 4 red balls. In a random sample of 5 balls, find the probability that at least one blue ball is selected.
Calculate the probability of not selecting any blue balls: P(no blue) = (7/9) * (6/8) * (5/7) * (4/6) * (3/5) = 0.167
Find the probability of at least one blue ball: P(at least one blue) = 1 - P(no blue) = 1 - 0.167 = 0.883
I don’t understand 9) PLEASE HELP!!! The line y=2.5x-7
Answers
For example, the observed Y value for -4 is -15. When you plug in -4 into the equation, you get this:
2.5x-7
2.5(-4) -7
-10 -7
=-17
The observed Y val. is -15, while the actual (equation) one is -17. -15 -(-17) is 2. 2^2 = 4
Do this process for all of the points, the add up the squared residuals, and you'll be done!
Hope this helped!
There are X giraffes at the zoo the number of elephants is 4 Less Than 3 times the number of giraffes and there are more than 23 elephants
Answers
the number of elephants is 3x -4
3X - 4 > 23
3X > 23 + 4
3X > 27
X > 9
there are more then 9 giraffes in the zoo.
There are 105 members of the high school band. Of these members, 1/5 play percussion instruments. How many members play percussion?
Answers
There are 4,315 pistachios in the bulk bin at the grocery store. Maria wants to split the pistachios into 40 packages so that each package has the same number of pistachios with none left over. Which explains whether or not it is possible?
Answers
divide total number by number of packages
4315 /40 = 107.875
it is not possible because it doesn't divide evenly
which graph shows the inequality b≤-7
Answers
b≤-7 mean b is "less than or equal to 7"
the arrow to the left of seven is the "less" part and the filled circle is the "equal to" part.
In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?
AB ≅ CD
AC ≅ BD
AB ⊥ BD
CD ⊥ BD
Answers
The answer is B AC ≅ BD Since you already know that ab ll cd, all you need to know is that ac is bd
Answer:
B. AC ≅ BD
Step-by-step explanation:
Since the definition of a parallelogram literally says that it's a quadrilateral with 2 parallel sides, we have AB || CD so the 2 other sides (AC and BD) need to be either similar or parallel (either works, due to that if they're similar we can prove that since AB || CD that they're parallel).
Round 35.78 to the nearest whole second
Answers
Answer: It is closer to 36 than it is to 35. So 36
Let f(x) = 2x2 − 2x + 7 and g(x) = x2 + 9x − 6. find f(x) − g(x). (1 point) x2 − 11x + 13 x2 − 11x + 1 x2 + 7x + 1 x2 + 7x + 13
Answers
=2x^2-2x+7-(x^2+9x-6)
=2x^2-2x+7-x^2-9x+6
=x^2-11x+13
First option
Answer:
[tex]x^2-11x + 13[/tex]
Step-by-step explanation:
Let [tex]f(x) = 2x^2 - 2x + 7[/tex] and [tex]g(x) = x^2 + 9x - 6[/tex]
We need to find f(x)- g(x)
Replace f(x) and g(x). then subtract the expressions
[tex]f(x)-g(x) =(2x^2 - 2x + 7)- (x^2 + 9x - 6)[/tex]
Remove the parenthesis and multiply negative sign inside second parenthesis
[tex]2x^2 - 2x + 7- x^2 - 9x + 6[/tex]
Combine like terms
[tex]x^2-11x + 13[/tex]
which type of triangle is best
Answers
Scalene triangle- A triangle where all angles are unequal.
Isosceles triangle- A triangle where two angles are equal.
Right triangle- A triangle with a right angle or 90° angle.
Now your question is what is the best triangle. That is an opinion question so I can't say. But out of the triangles above you could pick which one you think is the best :)
I need help with an Exponential Growth & Decay Word Problem. This is the problem: Mr. Jacobs won $1,000,000 in the lottery. He withdraws 10% of the money every year. How much money will he have left after 20 years? [Round your answer to the nearest dollar]
Answers
A=end amount
P=principal (initial) amount
R=rate
n=time (in this case, years)
For growth it is A=P(1+r/100)^n
Four students wrote statements about cosecant, secant, and cotangent values as shown below.
Anik
The cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1.
Isabella
The cosecant, secant, and cotangent of an acute angle are always greater than 1.
Kayla
The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.
Morris
The cosecant and secant of an acute angle may be greater than or equal to 1, but the cotangent of an acute angle is always less than 1.
Which student is correct?
Answers
Answer:
c Kayla is answer
Step-by-step explanation:
Since sine lies between-1 and +1 we have cosecant, reciprocal of sin lying always outside -1 and 1.
i.e. |cosec x|>1
For acute angle sine, cos , tan are positive
So cosec x >1 and similarly since cos x <1, sec x >1 always
But tanx varies between 0 and infinity for acute angles
Hence cot can take values from 0 to infinity
Hence the correct answer is that of Kayla
The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.
The statement about cosecant, secant, and cotangent values that is correct is Kayla's: The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.
What is the sine of an angle?In Trigonometry, the sine of an acute angle is a ratio of the length of an opposite side of a right-angled triangle to the length of its hypotenuse. Also, the sine of an angle generally lies between -1 and 1.
What is the cosecant (cosec) of an angle?In Trigonometry, the cosecant (cosec) of an acute angle is a ratio of the length of its hypotenuse to the length of an opposite side of a right-angled triangle. Thus, the cosecant of an angle is the reciprocal of the sine function and as such lies outside -1 and 1.
What is the cotangent of an angle?The cotangent of an acute angle is a ratio of the length of its adjacent side to the length of an opposite side of a right-angled triangle.
In conclusion, Kayla's statement about the values of cosecant, secant, and cotangent is correct.
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20 point to whoever answers first
What is the MEDIAN of may's temperatures
A. 72
B. 61
C. 71
D. 74
Answers
total the temperatures given
total = 497
divide by how many they gave (7)
497 / 7 = 71
answer is C 71 degrees
Answer:
c
Step-by-step explanation:
497 / 7 = 71
Given that line bd is both the median and altitude of triangle abc, congruence postulate sas is used to prove that triangle abc is what type of triangle
Answers
hope this helps :)
Answer:
Triangle ABC is an isosceles triangle.
Step-by-step explanation:
Let AD represent both the median and altitude of triangle ABC.
A median divides the side in two equal parts so BD=BC.
An altitude is a perpendicular drawn .A perpendicular makes an angle of 90°. Hence <ADB=<ADC=90°
AD is the side common to both the triangles ADB and ADC.
Hence Δ ADB≅ΔADC by SAS congruence postulate.
So AB=AC by c.p .c .t.c(congruent parts of congruent triangles are congruent)
Hence by definition of Isosceles triangle ΔABC is an isosceles triangle.
Does tis table represent a function ?
Answers
Answer: A function is so F(X) = Y where for every X exist only one Y, in this case you can see that F(3) = 4 and F(3) = 3, so the independent variable x = 3, has two solutions y.
So the solution is A, because a function cannot have two different y values for one x value.
Mario fills out an information card. His Zip code is 83628. His area code is 208. What is the value of the 2 in comparison in 83,628 and 208
Answers
The value of the digit 2 in both 83,628 and 208 is 200 because it is in the hundreds place in both numbers. The comparison shows that the absolute value of the digit 2 is the same in both cases despite being part of different overall numbers.
Explanation:The value of the digit 2 in the numbers 83,628 and 208 represents different values because of its position in each number, which is determined by the place value system. In the number 83,628, the digit 2 is in the hundreds place, which means it represents 200. In the number 208, the 2 is in the hundreds place as well, so it also represents 200.
However, to understand the value of the 2 in comparison between the two numbers, you must consider the whole numbers. While the value of 2 as an individual digit is the same in both cases (200), the overall values of the numbers are different. In a more complex mathematical context, when comparing values within different numbers like this, the absolute value of the digits may be the same, but their contributions to the numbers they are part of can vary based on the other digits in the number.
Nonetheless, in this comparison, the two-digit 2s both contribute the same absolute value of 200 to their respective numbers because they are both in the hundreds place.