Answer:
498 m
Step-by-step explanation:
The AAA theorem states that triangles are similar if all three corresponding angles are equal.
1. Compare triangles FHS and ILS
(a) Reason for similarity
∠F = ∠I = 90°
∠S is common.
∴ ∠H = ∠L
(b) Calculate SL
[tex]\begin{array}{rcl}\dfrac{SF}{SH} & = & \dfrac{SI}{SL}\\\\\dfrac{225}{380} & = & \dfrac{225 + 475}{SL}\\\\225SL & = & 380 \times 700\\& = & 266000\\SL & = & \textbf{1182 m}\\\end{array}[/tex]
2. Compare triangles ILS and GLE
(a) Reason for similarity
∠I = ∠G = 90°
∠L is common.
∴ ∠S = ∠E
(b) Calculate LE
[tex]\begin{array}{rcl}\dfrac{IS}{GE} & = & \dfrac{LS}{LE}\\\\\dfrac{700}{180} & = & \dfrac{1182}{LE}\\\\700LE & = & 180 \times 1182\\& = & 212800\\LE & = & \textbf{304.0 m}\\\end{array}[/tex]
3. Calculate EH
LE + EH + HS = LS
304.0 m + EH + 380 m = 1182 m
EH + 684 m = 1182 m
EH = 498 m
The distance from E to H is 498 m.
can I please get help?
Answer:
3x^2 -4
Step-by-step explanation:
f(x) = 2x^2 +3
g(x) = x^2 -7
(f+g) (x) = 2x^2 +3 + x^2 -7
Combine like terms
= 3x^2 -4
Answer:
[tex]\boxed{3x^2-4}[/tex]
Step-by-step explanation:
[tex](f+g)(x)[/tex]
Rewrite.
[tex]f(x)+g(x)[/tex]
[tex](2x^2 +3)+(x^2-7)[/tex]
Combine like terms and simplify.
[tex](2x^2 +x^2 )+(3-7)[/tex]
[tex](3x^2 )+(-4)[/tex]
[tex]3x^2 +-4[/tex]
A bicycle is on sale price for $300 it can be brought through a hire purchase with a deposit of $60 and 10%
interest the outstanding balance, to prepaid in 10 monthly installments calculate:
a)the amount of each monthly instalment
b)the total cost of buying the bicycle by hire purchase
Answer:
a) $26.4
b) $324
Step-by-step explanation:
Hire purchase is the purchase of an item which can be paid instalmentally.
The bicycle costs $300 for an instant purchase.
For a hire purchase, a $60 deposit must be made and the rest paid instalmentally over 10 months. An interest of 10% is included in the outstanding balance
The outstanding balance after paying deposit= $300 - $60 = $240
Hence, 10% of 240 = 10/100 × 240 = 24
An interest of $24 is added.
Therefore, a total of $240 + $24 = $264 will be paid for the next 10 months.
a) Hence, the amount to be paid in instalment each month is $264/10 = $26.4
b) the total cost of buying the bicycle by hire purchase= deposit amount + instalment price
= $60 + $264
= $324
Hence, a total of $324 will be paid for the bicycle by hire purchase.
N.B: $300 is the sale price + $24 interest
PLZ HELP ASAPPP!! I'M NOT 100% SURE ON HOW TO DO THIS
Answer:
1) 4a + 8
2) 12a² - 8a
3) 2a² + 8a
4) 4 - 6a
Step-by-step explanation:
The GCF of two numbers is the greatest common number each of the original two numbers can be divided by to get a whole number.
Hope it helps <3
Answer:
4 4a+8
4a [tex]12a^{2}[/tex]+8a
2a [tex]2a^{2} +8a[/tex]
2 4-6a
Step-by-step explanation:
Okay basicly you wand to find the biggest number that can go into both numbers
like the greatest common fact for 4a+8 would be 4 since only one of the numbers have an a you would just leave that out
Since you can take a 4 and an a out of [tex]12a^{2} \\[/tex] and out of 8a the greatest common factor would be 4a
Since you are able to take a 2 and an a out of [tex]2a^{2} +8a[/tex] your greatest common factor would be a
Since the largest number that can go into 4 and 6 is 2 your answer would be 2
Hope this helps you understand!
Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If
you get two solutions, are they both reasonable?
Answer:
n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n^2 + 2n + 4n + 8 = 143
n^2 + 6n - 135 = 0
(n + 15)(n - 9) = 0
n + 15 = 0
n = -15
n - 9 = 0
n = 9
I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.
Hope this helps!
Simplify the equation, and set it equal to zero to prepare for factoring.
Multiply the two factors in parentheses using the distributive property:
8(n2 + 2n + 4n + 8) = 1,144
Combine like terms inside the parentheses:
8(n2 + 6n + 8) = 1,144
Multiply the terms inside the parentheses by 8 using the distributive property:
8n2 + 48n + 64 = 1,144
Set the equation equal to zero by subtracting 1,144 from each side:
8n2 + 48n − 1,080 = 0
Factor out the GCF, which is 8:
8n2 + 48n − 1,080 = 0
8(n2 + 6n − 135) = 0
Divide both sides of the equation by 8:
n2 + 6n − 135 = 0
Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:
a = 1, b = 6, c = -135
The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:
6 = -9 + 15
-135 = -9 • 15
The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:
(n − 9)(n + 15) = 0
Use the zero product property, and solve for n:
n − 9 = 0 or n + 15 = 0
n = 9 or n = -15
There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9
Triangle T U V is shown. Side T U has a length of 5 units, side U V has a length of 8 units, and side T V has a length of 11 units. Which statement is true regarding triangle TUV? Angle T is the smallest angle. Angle V is the smallest angle. Angles U and V must be equal. Angles U and T must be equal.
Answer:
b
Step-by-step explanation:
edg 2020
The smallest measure of angle is angle ∠ V due to opposite angle of smallest side which is correct option(B).
What is a Triangle?A triangle is defined as simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol of Δ and consists of three connected vertices. Triangles can be categorized into a number of different varieties according on their sides and angles.
A triangle has three sides, three vertices, and three interior angles.
The angle sum property of a triangle states that the sum of the three interior angles of a triangle is always 180°
In ΔTUV,
Length of Side TU = 5 units
Length of Side UV = 8 units
Length of Side TV = 11 units
Side TU is opposite of angle ∠ V
Side UV is opposite of angle ∠ T
Side TV is opposite of angle ∠ U
The sides in order from longest to shortest : Side TV > Side UV = Side TU
The longest side is always opposite of the largest angle, and the smallest side is always opposite of the smallest angle.
Hence, the angle in order from longest to shortest : angle ∠ U > angle ∠ T > angle ∠ V
Thus, the smallest measure of angle is angle ∠ V.
Learn more about triangle here :
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Given: r || s, and t is a transversal that cuts both r and s. Prove: <1 = <5, <2 = <6, <3 = <7, and <4 = <8 Write a paragraph proof to prove that the corresponding angles shown are congruent.
Answer:
Lines r and s are parallel as Corresponding Angles given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.
Step-by-step explanation
answer from haven
Answer this please :(
Answer:
Part A: check B, E and F.
Part B: check E and G.
Step-by-step explanation:
The equation [tex]y = a(x - b)^2 + c[/tex] is the equation of a parabola written in the vertex form, where the vertex will be (b, c).
So, if the vertex is (2, -1), we have that b = 2 and c = -1
To find the c value, we use the information that the y-intercept is 3, so we have the point (0, 3). Using x = 0 and y = 3, we have:
[tex]3 = a(0 - 2)^2 - 1[/tex]
[tex]3 = 4a - 1[/tex]
[tex]4a = 4[/tex]
[tex]a = 1[/tex]
So we have a = 1, b = 2 and c = -1.
Part A: check B, E and F.
To find the x-intercepts, we need to find the values of x where y = 0:
[tex]0 = (x - 2)^2 - 1[/tex]
[tex]x^2 - 4x + 4 - 1 = 0[/tex]
[tex]x^2 - 4x + 3 = 0[/tex]
Solving using Bhaskara's formula (a = 1, b = -4 and c = 3), we have:
[tex]\Delta = b^2 - 4ac = 16 - 12 = 4[/tex]
[tex]x_1 = (-b + \sqrt{\Delta})/2a = (4 + 2)/2 = 3[/tex]
[tex]x_2 = (-b - \sqrt{\Delta})/2a = (4 - 2)/2 = 1[/tex]
So the x-intercepts are 1 and 3
Part B: check E and G.
Solve.
5x– 2y = 27
-3x +2y=-17
Enter your answer, in the form (x,y), in the boxes.
Answer:
x=5,y=-1
Step-by-step explanation:
5x– 2y = 27
-3x +2y=-17
Add the two equations together to eliminate y
5x– 2y = 27
-3x +2y=-17
----------------------
2x = 10
Divide by 2
2x/2 = 10/2
x = 5
Now find y
-3x +2y = -17
-3(5)+2y = -17
-15+2y =-17
Add 15 to each side
-15+15 +2y = -17+15
2y = -2
Divide by 2
2y/2 = -2/2
y =-1
Just need to know the elements of (A n B)
Answer:
{ 1,2}
Step-by-step explanation:
The ∩ means intersection, or what is in common for the two sets
The intersection of A and B is what is in the overlapping circles
The intersection of A and B is { 1,2}
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2). (–2, 0) (0, –2) (5, –7) (5, –2)
Answer:
(0, –2)
Step-by-step explanation:
I am assuming that point 'B' is (-5 , 0).
The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].
Apply the rule to point 'B':
[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]
B' should be (0, -2).
Answer:
Guy above me might be right but Im not sure. Im on the cumulative exam on edge.
Step-by-step explanation:
Tina had d dollars. She bought three cupcakes for her and her friends, which cost c dollars each. How much money does she have left after being so nice?
Answer: $(d-3c)
Step-by-step explanation:
Total amount Tina had = $d
Cost of cupcakes = $c
Number of cupcakes purchased = 3
Therefore,
Total cost of cupcakes = cost per cupcake × number of cupcakes
Total cost of cupcakes = $c × 3 = $3c
Amount left after cupcake purchase:
Total amount Tina had - total cost of cupcakes :
$d - $3c
evaluate the following using suitable identities : (102)^2
You answer is 10404 to get this answer multiply the 102 double time
What degree of rotation about the origin will cause the triangle below to map onto itself?
Answer:
=360
explanation:
When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.
Answer:
360
Step-by-step explanation:
6 (x - 5) = 5 (x - 4) i need it asap with steps pls
Step-by-step explanation:
[tex]6x - 30 = 5(x - 4)[/tex]
[tex]6x - 30 = 5x - 20[/tex]
[tex]6x - 30 - 5x = - 20[/tex]
[tex]x - 30 = - 20[/tex]
[tex]x = - 20 + 30[/tex]
[tex]x = 10[/tex]
Hope this is correct and helpful
HAVE A GOOD DAY!
A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5\text{ m}^213.5 m
2
13, point, 5, start text, space, m, end text, squared of material to build the cube.
What is the volume inside the giant sugar cube?
Give an exact answer (do not round).
Answer:
it is 3.375
Step-by-step explanation:
The volume inside the giant sugar cube is of 3.375m³.
To solve this question, we first find the side of the cube, given it's surface area, and with the side, we find the volume.
-----------------------------------
Finding the side:
Considering it took 13.5 m² of material to build the cube, we have that it's surface area is of 13.5m².
The surface area of a cube of side s is:
[tex]S_A = 6s^2[/tex]
In this question:
[tex]6s^2 = 13.5[/tex]
[tex]s^2 = \frac{13.5}{6}[/tex]
[tex]s = \sqrt{\frac{13.5}{6}}[/tex]
[tex]s = 1.5[/tex]
-----------------------------------
Volume:
The volume of a cube of side s is:
[tex]V = s^3[/tex]
In this question, [tex]s = 1.5[/tex], so:
[tex]V = 1.5^3 = 3.375[/tex]
The volume inside the giant sugar cube is of 3.375m³.
A similar question is found at https://brainly.com/question/11862932
What is the slope of the line through the points (4,2) and (-16,-6)
Answer:
2 / 5.
Step-by-step explanation:
The slope is the rise over the run.
In this case, the rise is 2 - (-6) = 2 + 6 = 8.
The run is 4 - (-16) = 4 + 16 = 20.
So, the slope is 8 / 20 = 4 / 10 = 2 / 5.
Hope this helps!
Answer:
the slope of the line that goes through (4,2) and (-16,-6) is 2/5
m= 2/5
Step-by-step explanation:
in order to find the slope we use the ∆y/∆x which is really the change in y over the change in x.
so all you have to do is find your y's and X's.
your y's are -6 and 2
your X's are -16 and 4
now in order to find the change in y and x you subtract your y's and x'x
the formula for this is:
∆y/∆x = y1-y2/x1-x2= (m aka the slope)
y1 is -6
and y2 is 2
-6 - 2 = -8
now do the X's
X1 is -16
and X2 is 4
-16 - 4 = -20
put that in fraction form and it's -8/-20
simplify that you get 2/5
Help with alll❤️ Please
Plz
Answer:
A, B, A
Step-by-step explanation:
(3)
Given
- 2x² + 10x + 12 ← factor out - 2 from each term
= - 2(x² - 5x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)
The factors are - 6 and + 1, since
- 6 × 1 = - 6 and - 6 + 1 = - 5, thus
x² - 5x - 6 = (x - 6)(x + 1) and
- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A
(4)
[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b), thus
[tex]x^{4}[/tex] - 81
= (x² )² - 9²
=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares
= (x - 3)(x + 3)(x² + 9) ← in factored form
x² - 3 is not a factor → B
(5)
Given
5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term
= 5([tex]x^{4}[/tex] - 64) ← difference of squares
= 5(x² - 8)(x² + 8) → A
There are 20 cars in my building’s parking lot. All of the cars are red or white. 12 of them are red, 15 of them are 4-door, and 4 of them are 2-door and white. How many of the cars are 4-door and red?
Answer:
11 cars
Step-by-step explanation:
There are 20 cars in my building's parking lot, 15 cars are 4-door, then
20 - 15 = 5 cars are 2-door.
5 cars are 2-door, 4 of them are 2-door and white, then
5 - 4 = 1 car is 2-door and red.
12 cars are red, 1 car is 2-door and red, then
12 - 1 = 11 cars are 4-door and red.
plz give me brianlist
The dimensions of a closed rectangular box are measured as 90 centimeters, 50centimeters, and 90 centimeters, respectively, with the error in each measurement at most .2.2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answer:
184 cm²
Step-by-step explanation:
Surface area of the rectangular box is expressed as S = 2(LW+LH+WH)
L is the length of the box = 90 cm
W is the width of the box = 50 cm
H is the height of the box= 90 cm
If there are error of at most 0.2 cm in each measurement, then the total surface area using differential estimate will be expressed as shown;
S = 2{(LdW+WdL) + (LdH+HdL) + (WdH+HdW)
Note that dL = dW = dH = 0.2 cm
Substituting the given values into the formula to estimate the maximum error in calculating the surface area of the box
S = 2{(90(0.2)+50(0.2)) + (90(0.2)+90(0.2)) + (50(0.2)+90(0.2))
S = 2{18+10+18+18+10+18}
S = 2(92)
S = 184 cm²
Hence, the maximum error in calculating the surface area of the box is 184cm²
6
R). Express 2x2 - 8x + 5 in the form a(x + b)² + c where a, b and
c are integers
Answer:
[tex]\large \boxed{\sf \ \ a = 2, \ b = -2, \ c = -3 \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]2x^2 - 8x + 5=2(x^2-4x)+5\\\\\text{*** We notice that *** }\\\\\text{*** } x^2-4x=(x-2)^2-2^2=(x-2)^2-4\\\\\text{*** So we can write ***}\\\\2x^2 - 8x + 5=2(x^2-4x)+5=2\left( (x-2)^2-4\right)+5\\\\=2\left(x-2\right)^2-8+5=\boxed{2\left(x-2\right)^2-3}[/tex]
So a = 2, b = -2, c = -3
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Determine the area under the standard normal curve that lies between â(a) Upper Z equals negative 0.12Z=â0.12 and Upper Z equals 0.12Z=0.12â, â(b) Upper Z equals negative 0.35Z=â0.35 and Upper Z equals 0Z=0â, and â(c) Upper Z equals 0.02Z=0.02 and Upper Z equals 0.82Z=0.82. â(a) The area that lies between Upper Z equals negative 0.12Z=â0.12 and Upper Z equals 0.12Z=0.12 is nothing. â(Round to four decimal places asâ needed.) â(b) The area that lies between Upper Z equals negative 0.35Z=â0.35 and Upper Z equals 0Z=0 is nothing. â(Round to four decimal places asâ needed.) â(c) The area that lies between Upper Z equals 0.02Z=0.02 and Upper Z equals 0.82Z=0.82 is nothing
Answer:
The answer is below
Step-by-step explanation:
The z score is a measure used in statistic to determine the number of standard deviations by which the raw score is above or below the mean. . The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}\\ where\ \mu \ is \ the\ mean, \sigma\ is\ the\ standard\ deviation\ and\ x \ is\ the\ raw\ score[/tex]
(a) Z = -0.12 and Z = 0.12
From the normal distribution table, Area between z equal -0.12 and z equal 0.12 = P(-0.12 < z < 0.12) = P(z < 0.12) - P(z < -0.12) = 0.5478 - 0.4522 = 0.0956 = 9.56%
b) The area that lies between Z = - 0.35 and Z=0
From the normal distribution table, Area between z equal -0.35 and z equal 0 = P(-0.35 < z < 0) = P(z < 0) - P(z < -0.35) = 0.5 - 0.3594 = 0.1406 = 14.06%
c) The area that lies between Z = 0.02 and Z = 0.82
From the normal distribution table, Area between z equal 0.02 and z equal 0.82 = P(0.02 < z < 0.82) = P(z < 0.82) - P(z < 0.02) = 0.7939 - 0.5080 = 0.2859 = 28.59%
A box contains 4 white ribbons and 8 pink ribbons. Determine whether the events of picking a white ribbon and then another white ribbon without replacement are independent or dependent. Then identify the indicated probability.
a. independent; 1/11
b. dependent; 1/12
c. dependent; 1/11
d. independent; 1/12
Answer:
dependent, 1/11
Step-by-step explanation:
the probability of picking a white ribbon at first is 1/3
the probability of picking a white ribbon next is 3/11
1/3 * 3/11 = 3/33 = 1/11
it is dependent because picking the first ribbon affects picking the second.
help me answer this question.
The midpoint of the diagonal of a square is 2 units from the vertex of the square. Calculate the area of the square
I will mark u as the brainliest.
Answer:
8 units²Step-by-step explanation:
Let side of the square = a
The , Area of square = a²
Now, Midpoint of Diagonal DB is E
And DE = 2 units
So, DB = 2 DE = 2 × 2 = 4 units
Now, using Pythagoras theorem in ∆ BCD
DB² = DC² + BC²
plug the values
[tex] {4}^{2} = {a}^{2} + {a}^{2} [/tex]
Collect like terms
[tex] {4}^{2} = 2 {a}^{2} [/tex]
Evaluate the power
[tex]16 = 2 {a}^{2} [/tex]
Swipe the side of the equation
[tex]2 {a}^{2} = 16[/tex]
Divide both sides of the equation by 2
[tex] \frac{2 {a}^{2} }{ 2 } = \frac{16}{2} [/tex]
Calculate
[tex] {a}^{2} = 8[/tex]
Therefore, The area of the square is 8 sq.units.
Hope this helps..
Best regards!!
The area of the square is 8 square units.
Let's assume that the side length of the square is "s". Since the midpoint of the diagonal is 2 units from the vertex of the square, the diagonal of the square is 4 units (twice the distance from the vertex to the midpoint).
We can use the Pythagorean theorem to find the side length "s" of the square:
[tex]s^2 + s^2 = 4^2\\2s^2 = 16[/tex]
Divide both sides by 2:
[tex]s^2 = 8[/tex]
Now, to find the area of the square, we use the formula:
[tex]Area = side length^2\\Area = s^2 = 8[/tex]
So, the area of the square is 8 square units.
To know more about area:
https://brainly.com/question/33403734
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x^2+8x=20 Solve by completing the square
Answer:
x = 2, x = -10
Step-by-step explanation:
(x+4)^2 = 36
(x+4) = 6, -6
x = 2, x = -10
PLEASSSSEEE HELP ! what number belongs in the box ? y=200+ ? x
Answer:
10
Step-by-step explanation:
It's the $10 that is to be added to the cost for each produced item.
When x is divided by 4, the remainder is 3. When r^2 is divided by
4, what must the remainder be?
Answer:
If x=7 that means that if 7 substitute r which is 7^2 and 7*7=49 and 49/4
=12 1/4
So the remainder is 1
Step-by-step explanation:
PLEASE HURRY! Use the diagram to answer the question. What is the measure of ∠A? Enter the correct value. Do not enter the degree symbol. (This is from Primavera. I've tried 60.07, and it is not correct.)
Answer: 60.1
Step-by-step explanation: If you did 13/15 and then took sin-1 and got 60.07356513, you did everything right.
But sometimes they want the answer rounded to one decimal point.
So try 60.1
Given: Circle k(O), m NM =65° ∠PNO≅∠PMO Find: m∠PNO, m∠ONM
Answer: m∠PNO =16.25° , m∠ONM=57.5°
Step-by-step explanation:
Given: Circle k(O), m NM =65° ∠PNO≅∠PMO
To find: m∠PNO, m∠ONM.
Since, central angle is equal to the measure of minor arc.
⇒∠MON = m NM =65°
In Δ MON , ON = OM [Radii of circle]
⇒ ∠ONM = ∠NMO (i) [Angle apposite to equal side of triangle are equal]
In Δ MON , ∠ONM + ∠NMO+∠MON =180°
⇒ ∠ONM + ∠ONM+65°=180° [from (i)]
⇒ 2∠ONM=115°
⇒ ∠ONM=57.5°
⇒ ∠ONM = ∠NMO =57.5°
Also, an inscribed angle is half of a central angle that subtends the same arc.
⇒∠MPN =half of∠MON
= [tex]\dfrac{65^{\circ}}{2}=32.5^{\circ}[/tex]
Also, ∠PNO≅∠PMO [Given]
⇒∠PNO =∠PMO
⇒ ∠PNO +∠ONM =∠PMO+∠NMO [∵∠ONM = ∠NMO]
⇒∠PNM=∠PMN
In ΔNPM
⇒ ∠MPN +∠PNM+∠PMN = 180°
⇒ 32.5° +∠PNM + ∠PNM= 180°
⇒ 2(∠PNM)= 147.5°
⇒ ∠PNM = 73.75°
Also, ∠PNM = ∠PNO+∠ONM
⇒73.75°= ∠PNO+57.5°
⇒ ∠PNO =16.25°
Hence, m∠PNO =16.25° , m∠ONM=57.5°
Answer:
Answer: m∠PNO =16.25° , m∠ONM=57.5°
Step-by-step explanation:
Given: Circle k(O), m NM =65° ∠PNO≅∠PMO
To find: m∠PNO, m∠ONM.
Since, central angle is equal to the measure of minor arc.
⇒∠MON = m NM =65°
In Δ MON , ON = OM [Radii of circle]
⇒ ∠ONM = ∠NMO (i) [Angle apposite to equal side of triangle are equal]
In Δ MON , ∠ONM + ∠NMO+∠MON =180°
⇒ ∠ONM + ∠ONM+65°=180° [from (i)]
⇒ 2∠ONM=115°
⇒ ∠ONM=57.5°
⇒ ∠ONM = ∠NMO =57.5°
Also, an inscribed angle is half of a central angle that subtends the same arc.
⇒∠MPN =half of∠MON
=
Also, ∠PNO≅∠PMO [Given]
⇒∠PNO =∠PMO
⇒ ∠PNO +∠ONM =∠PMO+∠NMO [∵∠ONM = ∠NMO]
⇒∠PNM=∠PMN
In ΔNPM
⇒ ∠MPN +∠PNM+∠PMN = 180°
⇒ 32.5° +∠PNM + ∠PNM= 180°
⇒ 2(∠PNM)= 147.5°
⇒ ∠PNM = 73.75°
Also, ∠PNM = ∠PNO+∠ONM
⇒73.75°= ∠PNO+57.5°
⇒ ∠PNO =16.25°
Hence, m∠PNO =16.25° , m∠ONM=57.5°
Step-by-step explanation:
Given the infirmation in the diagram, which theorem best justifies why lines j and k must be parallel
Answer:
Alternate Exterior Angles theorem
Answer:
alternate exterior angles
Step-by-step explanation:
alternate exterior angles are when two angles are on the far side of two lines and are not on the same side of the line cutting through the two parallel lines
Hope this is not redundunt or anything because I thought maybe I should just explain it so you would understand it next time :)
find the point of intersection between 2x - 6y = 12 and the line x = -2.
slope intercept: y = 1/3x - 2
Answer:
(-2, -8/3)
Step-by-step explanation:
2(-2) - 6y = 12
-4 -6y = 12
-6y = 16
y = -16/6 = -8/3