In the diagram to the right three lines intersect at n.The measure of < GNF is 60, and the measure of < MNL is 47. What is the measure of < HNK?
Answers
< MNL = 47
< MNL and < GNH are vertical angles and are equal
so < GNH = 47
< GNL + < GNH + < HNK = 180....these angles form a straight line...so when added, they equal 180
60 + 47 + < HNK = 180
107 + < HNK = 180
< HNK = 180 - 107
< HNK = 73 <====
Measure of ∠HNK is equals to 73°.
What are linear pair angles?
" Linear angles are formed when the sum of pairs of adjacent angles is equals to 180°."
According to the question,
Measure of ∠GNF = 60°
Measure of ∠MNL = 47°
As per the linear pair angles definition ,
∠GNF, ∠FNM, ∠MNL forms linear pair angles .
Therefore,
∠GNF + ∠FNM + ∠MNL = 180°
Substitute the given values we get,
60° + ∠FNM + 47° = 180°
⇒ ∠FNM = 180° - 107
= 73°
As given three lines intersect at 'N'
∠FNM and ∠HNK are vertically opposite angles and are congruent.
Therefore,
Measure of ∠HNK = 73°
Hence, measure of ∠HNK is equals to 73°.
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Related Questions
Charles will babysit for up to 4 hours and charges $7 per hour. Write a function in function notation for this situation.
Answers
If I'm wrong please feel free to correct me.
Answer:
The function is [tex]C(x)=7x[/tex]
Step-by-step explanation:
Given : Charles will babysit for up to 4 hours and charges $7 per hour.
To find : Write a function in function notation for this situation ?
Solution :
Let the work done by Charles in 'x' hour.
The charges is $7 per hour.
To create a function of x,
The cost function of 'x' hour is [tex]C(x)=7x[/tex]
Charles will babysit for up to 4 hours.
So, The cost for 4 hour is [tex]C(x)=7\times 4[/tex]
[tex]C(x)=\$28[/tex]
It takes Henry 3 hours to paint someone’s portrait how many hours would it take for him to paint all 8 of his friends’ portraits
Answers
round the factors to estimate the products. 697 x 82=
Answers
700 x 80= 56,000
the sophomore class is selling pies as a fundraiser. it cost the class $4 for each pie and they plan to sell the pies for $12 each. Write and solve an equation to determine how many pies does the class have to sell in order to make at least $200
Answers
$12. $12
x 10. × 7
--------- ---------
$120 + $84
$204
what is square root of -36?
Answers
the square root of a negative number needs to end in I
so find the square root of 36 and add an I
sqrt(36) = 6
so sqrt(-36) = 6i
To the nearest hundred thousand, there were 700,000 visitors to an amusement park las year which could be the exact number of visitors?
Answers
11a+9=4a+30 what is the answer
Answers
11a-4a=30-9
7a=21
a=21/7
a=3
Carly has 2 more nickles than dimes in her pocket She has 40 cents How many nickels does carly have ? how many dimes does carly have?
Answers
Carly has 2 dimes and 4 nickels in her pocket.
Explanation:Let's assume Carly has x dimes in her pocket. Since Carly has 2 more nickels than dimes, she would have x + 2 nickels. The value of x dimes is 10x cents and the value of (x + 2) nickels is 5(x + 2) cents. Since Carly has 40 cents in total, we can set up the equation: 10x + 5(x + 2) = 40.
Simplifying the equation gives us: 10x + 5x + 10 = 40. Combining like terms gives us: 15x + 10 = 40. Subtracting 10 from both sides gives us: 15x = 30. Dividing both sides by 15 gives us:
x = 2.
Therefore, Carly has 2 dimes and 4 nickels.
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Affonso has 14 fewer dimes than nickels. He has 21 dimes.
Use the five-step problem-solving plan.
How many nickels does Affonso have?
Enter you answer in the box.
Answers
He has 21 dimes.
to find the nickels i believe you would add 14 and 21 so 14+21.
14+21=35
He has 35 nickels
What percent of 86 is 50 to the nearest whole percent
Answers
Answer:
58%
Step-by-step explanation:
Let us suppose x percent of 86 is 50.
Therefore, we have the below equation
x% of 86 = 50
Eliminating percentage, we get
0.0x × 86 = 50
Solve for x
[tex]0.0x\times86=50\\\\0.0x=\frac{50}{86}\\\\x=\frac{50}{86}\times100\\\\x=58.1[/tex]
Hence, in nearest whole percent, we have
x = 58%
Therefore, 58% of 86 is 50
what is the reciprocal of 60
Answers
In order to find the reciprocal of a number, we should just flop it over, like so:-
[tex]\sf{The~reciprocal~of~a~is~\frac{1}{a}}[/tex]
According to the formula, the reciprocal of 60 is:-
[tex]\bigstar{\boxed{\pmb{\frac{1}{60}} \longleftarrow\sf{reciprocal~of~60}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
The product of 5 and a number x is 14 .
What is the value of x?
x=194
x=120
x=54
x=434
Answers
none of them.
Product means multiplication, so the product of 5 and a number means 5 times a number which is 5x
so if 5x = 14
x = 14/5 = 2.8
x = 2.8 which isn't a choice.
Answer:
The answer is B 1/20
Step-by-step explanation:
The word "Product" means multiplication, and we need to find the value of "x" here's an equation:
5 times x = 1/4
5 times 1/20 = 1/4
Hope this helped! :3
Your digital camera has a 512 megabyte memory card. You take low resolution pictures requiring 4 megabytes of memory each and high resolution pictures requiring 8 megabytes of memory each. Write an equation for the number of low and high resolution pictures you can take.
Answers
The number of low and high resolution pictures that can be taken with a 512 megabyte memory card is determined by the equation 4L + 8H = 512, where L represents low resolution pictures and H represents high resolution pictures.
To determine the number of low and high resolution pictures that can be taken with a 512 megabyte memory card, we can set up an equation based on the storage requirements of each type of picture. Let's use L to represent the number of low resolution pictures and H to represent the number of high resolution pictures.
Because each low resolution picture requires 4 megabytes and each high resolution picture requires 8 megabytes, we can write the equation as:
4L + 8H = 512
This equation shows that the total memory used by L low resolution pictures and H high resolution pictures cannot exceed 512 megabytes, the capacity of the memory card.
what is the simplified form of 3abc divided by abc when abc does not equal zero
Answers
Simply put, the answer if you divide this equation by ABC, will quite literally transform into 3.
which of the following numbers that when divided by 1/2, give a result less than 1/2 ? select all that apply 3/8, 3/16,6/25,1/3
Answers
Answer:
theheckisthis thing
Step-by-step explanation:
What property is 0+91=91
Answers
2.5 repeating as a mixed number
Answers
If 20% of the science students at Central High study on physics, 25% study chemistry and the rest study only biology, what is the smallest number of science students who could be studying biology?
Answers
Given that 20% of students are studying Physics and 25% Chemistry, the rest, which is 55% are studying Biology. In the simplest case, where the total of students is 100, the smallest number of Biology students would be 55.
Explanation:The question asks us to identify the smallest possible number of students studying biology. Given that 20% of students study Physics and 25% study Chemistry, we can emphasize that the rest are studying Biology. In the simplest situation, the total number of science students could be 100 because percentages are based on 100. Therefore, for this case, 20 students are studying Physics, 25 are studying Chemistry, and the rest which is 55, are studying Biology. Thus, the smallest possible number of Biology students can be 55.
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What is the solution to the system of equations? { 4x−3y=26 3x+2y=11
Answers
4x - 3y = 26
3x + 2y = 11
Multiply 1st eqn by 2, second by 3.
That way the y term disappears when the equations are added.
8x - 6y = 52
9x + 6y = 33
Add
17x = 85
x = 5
Hope I could help :)
3x + 2y = 11
multiply by 2 for the first equation
8x - 6y = 52
9x + 6y= 33. multiply by 3 for the second equation
17x= 85.
x= 5
20-3y=26
-3y=-6
y=2
you are biking at a speed of 18mph. you are 3 miles behind your friend, who is biking at a speed of 12mph. write and solve an equation to find the amount of time it takes for you to catch up to your friend
Answers
Assume the distance moved by your friend is "d" and that the time taken for you to catch to him is "t"
you are moving with a velocity of 18 mph and your friend is moving with a velocity of 12 mph.
distance covered by your friend (d) = 12t miles ......> equation 1
If you add 3 to your rate, your distance will be the same as your friend's. This means that:
d+3 = 18t miles ......> equation 2
Substitute by 1 in 2:
12t + 3 = 18t
3 = 6t
t = 0.5 hours
This means that you will catch up to your friend in half an hour.
What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4? 4 32 128 512
Answers
Answer:- 512
Explanation:-
We know that [tex](m+1)^{th},\ (T_{m+1})[/tex] in the binomial expansion [tex](p+q)^n[/tex] is given by
[tex]T_{m+1}=^nC_m\ p^{n-m}q^m[/tex]
Assume that [tex]x^9y[/tex] occurs in the [tex](m+1)^{th}[/tex] term of the expansion of [tex](2y+4x^3)^4=(4x^3+2y)^4[/tex]
[tex]T_{m+1}=^4C_m\ (4x^3)^{4-m}(2y)^m[/tex]
Comparing power of x and y in [tex]x^9y[/tex] we get m=1
Thus term for m=1 [tex]=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y[/tex]
Thus the coefficient of [tex]x^9y[/tex] is 512.
What is the change in temperature from -8°F to 14°F?
Answers
Find an equation for the line with slope m through the point (a,c).
Answers
y-y1 = m(x-x1)
y-c = m(x-a)
---------------------------------------
If you want the answer in slope intercept form, then solve for y
y-c = m(x-a)
y-c = mx-ma
y-c+c = mx-ma+c
y = mx-ma+c
y = mx+c-ma
y = mx+(c-ma)
For this answer in slope intercept form the slope is m and the y intercept is c-ma
---------------------------------------
If you want the answer in standard form, then get the variable terms to the left side. Have the constant terms on the right side.
y = mx+c-ma
y-mx = mx+c-ma-mx
-mx+y = c-ma
Optionally you can multiply both sides by -1 to get mx-y = -c+ma but it will depend on your book if this step is carried out or not.
The equation of a line with a given slope and passing through a point can be found using the point-slope formula.
To find the equation of a line with a given slope (m) passing through a point (a, c), we can use the point-slope formula. The point-slope formula is given by:
y - c = m(x - a)
where (x, y) represents any point on the line. This equation represents a line with slope m passing through the point (a, c).
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HELP ME ASAP!!!
Ralph ate 1/2 of a pie before dinner. After dinner he ate 1/3 of what was left. What fraction of the pie did he eat after dinner?
Answers
Answer:
1/6
Step-by-step explanation:
1/2 * 1/3 = 1/6.
Do b. I will say thanks
Answers
For what values of y:is the value of the fraction 7−2y /6 greater than the value of the fraction 3y−7 /12 ?
Answers
Answer:
y<3
Step-by-step explanation:
Do you do rsm lol
y<3 is the value.
What is inequality?In mathematics, an inequality is a relation that makes a non-equal assessment between two numbers or different mathematical expressions. Its miles are used most often to evaluate numbers at the quantity line by means of their size. There are several unique notations used to represent exceptional types of inequalities:
The notation a < b means that a is less than b.
The notation a > b approach that a is greater than b.
The range of y which will satisfy this inequality will result in the first fraction of a larger value as compared to the second fraction.
Multiplying both sides of an inequality by 12, we get:
12×10>12×3y-7/12
2(7-2y)>3y-7
14-4y3y-7
14+7>3y+4y
21> 7y
3>9
y<3
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The perimeter of a rectangle is 24cm. If the length in y cm, what is the width?
Answers
if perimiter=24
24=2(L+W)
divide both sides by 2
12=L+W
if L=y then
12=y+W
minus y from both sides
12-y=W
the width is 12-y cm
Peyton is altering her new jacket to enter it into the Bodacious Bedazzling Contest. In order for a garment to be considered "bedazzled," it must contain an amount of gems that fall within the range of the following inequality 132 ≤ ½x + 8 ≤ 193. Find the range of gems Peyton must use to enter he jacket in the contest.
Answers
set up two equations
132=(1/2)x+8 x=248
193=(1/2)x+8 x=370
Answer:
the range will be 248 ≤ x ≤ 370
Step-by-step explanation:
The given inequality models the range of amount of gems.
132 ≤ 1/2x + 8 ≤ 193
So we have to solve the inequality for the value of x.
132 ≤ [tex]\frac{1}{2}x[/tex] + 8 ≤ 193
Now we subtract 8 from the inequality.
132 - 8 ≤ ([tex]\frac{1}{2}x[/tex] + 8) - 8 ≤ 193 - 8
124 ≤ [tex]\frac{x}{2}[/tex] ≤ 185
Now we multiply the inequality by 2
124 × 2 ≤ [tex](\frac{x}{2})[/tex] × 2 ≤ 185 × 2
248 ≤ x ≤ 370
So the range will be 248 ≤ x ≤ 370
3F equals -8.5 what does F equals
Answers
3F=-8.5
F = -8.5 / 3 =-2.8333333
round answer as needed
How many fourths are in two wholes? Use a fraction model to help you. Show two whole divided into four equal pieces. 2 dived by 1/4
Answers
Because there is 4 quarters in 1 whole. 4x2=8