In the diagram, the measure of angle 6 is 98°.
A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
What is the measure of angle 7?
Answers
The measure of angle 7 is 82°.
What is transversal line?
A transversal is defined as a line that passes through two lines in the same plane at two distinct points in the geometry
Given:
angle 6= 98°
As, angle 6 and 7 forms a linear pair then
angle 6 + angle 7 = 180
98 + angle 7= 180
angle= 180-98
angle 7 = 82°
Hence, angle 7 is 82°.
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Related Questions
anwer this question with full method please
Answers
Step-by-step explanation:
Let simplify the identity
[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]
[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]
Combine Like Fractions
[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]
Multiply by reciprocals.
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]
Pythagorean Identity
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]
Double Angle Identity
[tex] \frac{ \cos(2x) }{1} [/tex]
[tex] \cos(2x) [/tex]
Now, we need to find cos 2x. Given that we have tan x.
Note that
[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]
So let find cos x and tan x.
We know that
[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]
We know that
[tex] \tan(x) = \frac{o}{a} [/tex]
[tex] \sin(x) = \frac{o}{h} [/tex]
[tex] \cos(x) = \frac{a}{h} [/tex]
So naturally,
[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]
So we need to find the hypotenuse,
remember Pythagorean theorem.
[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]
Here o is 1
h is root of 5.
So
[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]
[tex] {h}^{2} = 1 + 5[/tex]
[tex] {h}^{2} = 6[/tex]
[tex]h = \sqrt{6} [/tex]
Now, we know h, let plug in to find sin x and cos x.
[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]
[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]
Let's find these values squared
[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]
[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]
Finally, use the trig identity
[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]
So part I.= 2/3
ii. Use the definition of sine and cosine and Pythagorean theorem
Let sin x= o/h
Let cos x= a/h.
So
sin x squared is
[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]
[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]
By definition,
[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]
[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]
Remember that
[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]
So
[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]
[tex]1 = 1[/tex]
on a number line point D is at -6 and point E is at 8 point F lies between points D and E if DF:FE is 3:1 where does point F lie on the number line
Answers
The point F lies on 4.5 in the number line.
Number line is a One dimensional representation of point referring by a number only.
We know that if a point divides a line joining the points at x,y in the number line respectively in m:n ratio then that point lies on = (my+nx)/(m+n) in the number line.
Here in the give problem that,
Point D lies on -6 in number line
Point E lies on 8 in number line
And F lies between D and E points and DE:EF = 3:1
So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.
So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5
Hence the point F lies on 4.5 in the number line.
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Answer: 4.5
Step-by-step explanation:
Glass bottles are redeemed for 50 cents each. Plastic bottles are redeemed for 25 cents each and aluminum cans are .75 cents each. At the end of the event the collected a total of 35 glass bottles 50 plastic bottles and 22 aluminum cans. If there goal was $50 did they make enough money to save the condors
Answers
Answer:
no they did not make enough money
Step-by-step explanation:
Glass: 35 ×0.50 = 17.5
plastic: 50 × 0.25 = 12.5
aluminum: 22 × 0.75 = 16.5
17.5 + 12.5 + 16.5 = $46.5
9(x - 11) = 9 what is x
Answers
Answer:
x=12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
12-1 is 11 and than 9 times 1 is 9
HELP IM TIMED!!!!
X
-2
-1
0
1
2
3
f(x)
20
0
-6
-4
0
0
Which is an x-intercept of the continuous function in the
table?
O (-1,0)
O (0, -6)
O (-6,0)
O
(0, -1)
Answers
The difference of the product of 3 and 6 minus the quotant of 6 / 2
Answers
Answer:
Answer:
(3*6) - (6/2) = 15
Step-by-step explanation:
3 and 6 are being multiplied by them selves, and then subtracted by the answer of 6/2.
The answer of the equation is 15.
Step-by-Step Solution:
= (3 * 6) - 6/2
= 18 - 6/2
= 36/2 - 6/2
= (36 - 6)/2
= 30/2
=> 15
The Answer to this Expression is 15.
find the area occupied by the base of a cylindrical bowl if the base is 9 cm?
Answers
Answer:
is it radius or diameter?
If the bearing of p from y is 048degrees what is the bearing of y from p
Answers
Step-by-step explanation:
see photo for detailed analysis
Selena is preparing for her eighth-grade graduation party. she must keep within the budget set by her parents. which is the best price for her to purchase ice cream? a. $3.99/ 24 oz carton b. $4.80/ one-quart carton c. $11.00 / one gallon tub d. $49.60/ five gallon tub
Answers
Answer:
Basically find the unit rate by doing 3.99/24 = $0.16625/1oz
1 quart = 32 ounces so 4.8/32 = $0.15/1oz
1 gallon = 153.722 ounces so 11/153.722 = 0.07
49.6/768.61 = 0.06
Step-by-step explanation:
D.
look at the attachments
the last one at the bottomm c is200
please i really need help its khan
Answers
Answer:
all I know is the second on about world population in 2014 which was c
7•10⁹
Answer:
B
B
Step-by-step explanation:
there are 9 steps for the second question so it 10^9
and if you times the 1st population size by 20 you get very close to the second population size.
A bottle holds
5
55 milliliters of perfume.
How many bottles can we fill with
2
22 milliliters of perfume?
Answers
Answer:
0.4 bottles can be filled
Step-by-step explanation:
divide the amount that is present by the max amount
the bottle can only hold 5.55 millimeters; therefore the max amount would be 5.55 millimeters.
the amount that is present is 2.22 millimeters.
[tex]\frac{222 millimeters}{555 millimeters} = 0.4[/tex]
0.4 bottles
if the given values are 555 and 222 then the answer is still .4
Answer:
0.4 bottles can be filled
Which expression is the simplest form of - (4x³ + x²) + 2 (x³ - 3x²)?
OA.-223-5x²
B. -6x³6x²
OC.-6x³2x²
OD. -2x³-7x²
SUBMIT
Answers
-4x^3-x^2+2x^3-6x^2
Then combine like terms to get
-2x^3-7x^2
So your answer is D.
Hope this helped :)
Answer:
-2x³ - 7x².
Step-by-step explanation:
- (4x³ + x²) + 2(x³ - 3x²)
= - 4x³ - x² + 2x³ - 6x² Simplifying like terms:
= -2x³ - 7x².
william used 15 cm of tape to wrap 3 presents, Find the length of tape to wrap for 1 present?
Answers
A couple plans to have 4 children. The gender of each child is equally likely. Design a simulation involving 55 trials that you can use to model the genders of the children. Write your answer as number
Answers
Answer:
4x55x2
Step-by-step explanation:
4 kids 55trys 50 50 odds
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
A. F(x) = 3(x+4)2 +4
B. F(x)=3(x-4)2 - 4
C. F(x)=-3(x+4)² +4
D. F(x) = -3(x-4)² +4
Answers
The equation of the function is F(x) = -3(x-4)² +4 , the correct answer is Option D
The missing graph is attached with the answer
What is a function ?A function is a law that relate the independent variable and the dependent variable.
It is given that
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has been changed
From the graph, it is seen that,
G(x) when shifted by -4 on the negative x axis.
and graph shifted by +4 on the positive y axis.
F(x) is scaled by a factor of -⅓ of G(x)
it is reflected across the x-axis.
So the equation of the function is
F(x) = -3(x-4)² +4
Therefore , the correct answer is Option D.
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What is the missing reason in the proof? (Reason 9)
Answers
Answer:
transitive property
Step-by-step explanation:
Generally proofs flow naturally from one step to the next. Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.
From statement 8, note that [tex]90^{o}=m\angle{ABD}[/tex]
For statement 9, the proof asserts that [tex]m\angle{ABC}=m\angle{ABD}[/tex]
What changed between line 8 and 9? The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.
So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?
Recall from statement 3, that [tex]m\angle{ABC}=90^{o}[/tex].
The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).
Recall that the transitive property states:
[tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]
There are three parts,
1. the first part needs a=b
2. the second part needs b=c
3. the third part produces a=c
Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.
Statement 8 is like the second part, and statement 9 is like the third part.
Replacing "a" with [tex]m\angle{ABC}[/tex], replacing "b" with [tex]90^{o}[/tex], and replacing "c" with [tex]m\angle{ABD}[/tex], we can update the transitive property and see how it applies to our situation:
Original transitive property: [tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]
Updated transitive property: [tex]\text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}[/tex]
In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true. The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.
Find the length of segment AC if AB = 7.8 cm and BC = 25 mm. How many solutions are there in each case? Point B lies on line AC .
Answers
Answer:
103mm or 53mm
Step-by-step explanation:
--A------B------C--
AB=78mm BC=25mm AC=AB+BC=103mm
--A----C---B---
AB=78mm BC=25mm AC=AB-BC=53mm
-B---A---C-
is impossible because BA<BC but 78mm>25mm
Which term best describes the horizontal cross-sections of an oblique cone?
O A. Congruent discs
OB. Similar discs
OC. Similar polygons
O D. Congruent polygons
Answers
Answer:
B. Similar discs
Step-by-step explanation:
Definitions
Cone: A three-dimensional solid figure that has a circle at one end (the "base"), a point at the other end (the [tex]\sf a\:\!pex[/tex]), and a curved side.
Right Cone: A cone where the [tex]\sf a\:\!pex[/tex] is aligned on the center of the base.
Oblique Cone: A cone where the [tex]\sf a\:\!pex[/tex] is not centered over the base.
Horizontal Cross-section: The intersecting plane parallel to the base of the solid figure.
Congruent: The same shape and size.
Similar: When one shape can become the other after being resized, reflected, translated or rotated.
Disc: The region in a plane bounded by a circle.
Polygon: A two-dimensional closed shape with a minimum of 3 straight sides.
Therefore, the horizontal cross-sections of an oblique cone are similar discs.
Use the graphing calculator to graph the function f(x)=√x Which list contains three points that lie on the graph of
the function?
0(83) (42) (-11)
O (11 (42) (9. 3)
Answers
Answer:
The last option that starts with (1,-1)
what is the slope of the line that passes through the points (-9,0) and (-17 , 0 )
Answers
Answer:
[tex]\mathrm{Slope=== > 0}[/tex]
Step-by-step explanation:
Hi student, let me help you out!
.............................................................................................................
First, let's recall the slope formula: [tex]\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}}[/tex], where y2 and y1 are y-coordinates; x2 and x1 are x-coordinates.
Plugin the values: [tex]\mathrm{\cfrac{0-0}{-17-(-9)}}[/tex].
Upon simplifying, we obtain [tex]\mathrm{\cfrac{0}{-17+9}}[/tex].
Upon simplifying this further, we obtain [tex]\mathrm{\cfrac{0}{-9}}[/tex].
0 divided by anything results in 0.
✨ ∴, the slope of this particular line is 0, and this line looks something like this: [tex]\rule{200}{1}[/tex].
See, it's a horizontal line, with a rise of 0, meaning that it goes up 0 units.
Hope this helped you out! Ask in comments if even the slightest queries arise.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{5}}[/tex]
Which of the following did you include in your response? Check all of the boxes that apply. the range, or spread, of the salaries whether most people make a very low salary and one or two people make a high salary the minimum salary, and whether that is an entry level or starting salary the maximum salary whether the maximum salary is a lot higher than the average and other salaries are a lot lower than the mean
Answers
Answer:
to be honest i don't know
Step-by-step explanation:
uh
Answer: its all
Step-by-step explanation:
it does not matter which one you pic, you just have to pick one.
0.39 recurring as a fraction please [ 3 and 9 are both recurring]
Answers
Answer:
[tex]\frac{13}{33}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.3939.... (1) ← multiply both sides by 100
100x = 39.3939... (2)
subtract (1) from (2) thus eliminating the repeating digits
99x = 39 ( divide both sides by 99 )
x = [tex]\frac{39}{99}[/tex] = [tex]\frac{13}{33}[/tex] ← in simplest form
Step-by-step explanation:
0.39 repeating as a fraction
= 13/33
3/5x + 3 = 6 whats is x?
Answers
Answer:
X = 3/53/5x + 3 = 6
3/5x = 6 - 5
3/5x = 1
Multiplying both the sides with 5x3/5x (5x) = 1* 5x
3 = 5x
3/5 = X
Which point is on the graph of the inverse function h-¹(x)?
O (2,4)
0 (0)
O (0, 1)
O (-5, 1)
Answers
Answer: (0,1)
Step-by-step explanation:
If (x,y) lies on the graph of the original function, then (y,x) lies on the graph of the inverse.
Since (1,0) lies on the graph of h(x), (0,1) lies on the graph of its inverse.
(0, 1) point is on the graph of the inverse function h-¹(x).
What are inverse functions?Two functions f(x) and g(x) are inverses if their composition is equal to the identity.
Equation of line will be
y = -2x + 2 = h(x)
h⁻¹(x) will be calculated as:
x = -2y + 2
x - 2 = -2y
y = (2 - x)/2
So, y = h⁻¹(x) = (2 - x)/2
put x = 0 in the equation y = (2 - x)/2
y = 1
(0, 1) = (0, 1)
This, (0, 1) is the point on h⁻¹(x).
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It took for 4 butterflies to give birth to 4 larvae. how many larvae would 12 butterflies give birth to in 12 days
Answers
12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
It took 4 days for 4 butterflies to give birth to 4 larvae. After 4 days, each butterfly produces a larvae
Hence for 12 butterflies in 12 days:
number of larvae = 12 butterflies * (12 days /4 days per larvae) = 36 larvae
12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.
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How many grains of Fermiun will remain after 15 days? 50 25 12.5 6.25
Answers
Answer:
0.00305 (rounded)
Step-by-step explanation:
this is a geometric sequence so the formula is
an=a×r×n-1
Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate’s problem?
The shelter can house 15.6 cats because 15.6 < 28.
The shelter can house –8 cats because –8 < 28.
The shelter can house 17 cats because 17 < 28.
The shelter can house 28 cats because 28 < 28.
Answers
Answer:
The shelter can house 17 cats because
17 < 28.
Step-by-step explanation:
We cannot have fractions of cats, and we cannot have a negative number of cats. So the third statement is reasonable because c < 28.
(MARKING BRAINLIEST TO FIRST CORRECT ANSWER!) Which statement below is true?
A. All squares are rectangles because both are quadrilaterals, have 90 degree angles and the opposite sides are parallel.
B. All trapezoids are rectangles because the opposite sides are parallel.
C. All parallelograms are rhombus' because they have 4 congruent sides and the opposite sides are parallel.
D. All rectangles are trapezoids because all the sides are parallel.
Answers
Answer:
A. All squares are rectangles because both are quadrilaterals, have 90-degree angles and the opposite sides are parallel.
Step-by-step explanation:
This is the only true statement because all squares are rectangles just with equal sides, the angles will always be 90-degrees.
Hope this helps!
If not, I am sorry.
Instruction: draw a line perpendicular to line AB at point C.
I have followed the steps, please tell me what have I done wrong? :)
(picture included of my answer)
Answers
Answer:
it’s correct
Step-by-step explanation:
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
When taking the perpendicular of the line, it should be done at the midpoint of the line. Hence, by taking arcs from both endpoints, it should be done. This is why this is incorrect.
Can you translate that into slope intercept form
Answers
Answer:
y = (5/3)x + 4
Step-by-step explanation:
The general equation for slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. Since you have been given both of these values, you can plug them into the formula to find your answer.
slope (m) = 5/3
y-intercept (b) = 4
y = mx + b
y = (5/3)x + 4
