The required value of x of a triangle is 27°.
What is a triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Given, angle measurements of 2x, 4x+6, and x-15
Based on the definition of a triangle, the sum of all angles will be 180 degrees.
So, 2x + 4x+6 + x-15 = 180°
or, 7x - 9 = 180°
or, 7x = 189°
or, x = 189/7 = 27°
Hence, the required value of x of a triangle is 27°.
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a. Using parallel line relationships, find the value of
x. Use the relationship between the two marked
angles to set up your equation.
Show your work to support your answer. (4 pts)
x =
b. Find the measure of each of the angles. Don’t forget to label your answers.
Answer:
a and f are 14°
Angles b, c, d, and e are all 166°
Step-by-step explanation:
Alternate interior angles are congruent
x + 9 = 4x - 6 Subtract x from both sides
9 = 3x - 6 Add 6 to both sides
15 = 3x Divide both sides by 3
5 = x
Plug this back into the equation for find the angles measurements
x + 9
5 + 9
14
or
4x _ 6
4(5) -6
20 - 6
14
angles a and f are vertical angles so they are congruent and equal to 14
B ,c , d and e are all supplements to the found angles
180-14 = 166
The perpendicular biector of ide AB of triangle ABC interect ide AB at point D and BC at point E. If angle CAB = 82 degree and angle C = 68 degree, what i angle CAE
The angle of CAE is 22
What is perpendicular bisector ?A line known as a perpendicular bisector cuts a specified line segment precisely in half, creating a 90° angle at the junction. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.
Perpendicular bisector of ABC's side AB crosses BC at point E and side AB at point D. Additionally, m CAB = 82 and m C = 68.
Adopt A E.
In ABC, the triangle's angle sum property is A+B+C=180°.
82°+∠B+68°=180°
∠B= 180°-150°
∠B=30°
AD=B DDE is a perpendicular bisector in A DE and B DE.
If ADE=BDE=90°
DE is common.
Δ A DE ≅ Δ E DB→→[S AS]
∠DEB=∠D A E→→[CPCT]----(1)
In Δ DBE
∠EDB + ∠DBE+∠BED=180°→→Angle sum property of Triangle.
90° +30°+∠BED=180°
∠BED=180°-120°
∠BED=60°
So, ∠BAE=∠BED=60°------[using (1)]
∠CAE=∠CAB - ∠BAE
= 82°-60°
= 22°
Therefore the angle CAE is 22
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A full pond containing 625 gallons of water begins losing its water at a rate of 20% per week. If the pond now contains 320 gallons of water, how many weeks has it been since the pond was at full capacity?
(Use the digits 0 – 9 to enter a number. Use a decimal point only if necessary.)
If the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.
Given that, a full pond containing 625 gallons of water begins losing its water at a rate of 20% per week.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, number of gallons water being used for x weeks is
625-320=305 gallons
Now, number of gallons of water used in a week= 20% of 305
= 20/100 ×305
= 0.2 ×305
= 61 gallons
So, number of weeks = x=305/61
= 5
Therefore, if the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.
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Answer:
5
Step-by-step explanation:
Look that guys answer is better
What is the value of cosine (startfraction x over 2 endfraction) if tangent x = one-half and x is in quadrant iii? negative startstartroot startfraction 5 minus 2 startroot 5 endroot over 10 endfraction endendroot negative startstartroot startfraction 5 + 2 startroot 5 endroot over 10 endfraction endendroot startstartroot startfraction 5 minus 2 startroot 5 endroot over 10 endfraction endendroot startstartroot startfraction 5 + 2 startroot 5 endroot over 10 endfraction endendroot.
Given that x is in quadrant 3, its value for tan x=1/2 will be 206.565°, and its value for cos(206.565°) will be -0.894.
What is trigonometry?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.
Here,
Tan x=1/2
π<x<3π/2
x=tan⁻¹/²(1/2)
x=26.565°
As the x is in quadrant 3,
=180+26.565°
=206.565°
cos(206.565°)=-0.894
The value of x for tan x=1/2 will be 206.565° as x is in quadrant 3 and for the same value of x, cos(206.565°) will be -0.894.
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Answer:
-sqrt 5 - 2 sqrt 5/10
Step-by-step explanation:
Edge 2023
f(x) = 3x - 2 and g(x) = 2x
Find g(f(3))
Answer:
14
Step-by-step explanation:
To find g(f(3)), you will need to first find f(3) and then substitute that value into the function g(x).
To find f(3), substitute 3 for x in the equation for f(x):
f(3) = 3(3) - 2 = 9 - 2 = 7
Now substitute the value of f(3) into the equation for g(x):
g(f(3)) = g(7) = 2(7) = 14
Therefore, g(f(3)) = 14
Answer:
f(3)=7 g(3)=6
Step-by-step explanation:
f(x)=3x-2
f(3)=3(3)-2
f(3)=9-2
f(3)=7
g(x)=2x
g(3)=2(3)
g(3)=6
I NEED HELP ASAP
FIRST TI ANSWER GET BRAINLEST
Answer:
4.
y = -1/6 * x - 7/3
Step-by-step explanation:
We can just check:
1.
y = -1/6 * x
this doesn't work for x = -2 and y = -2 (first point) because we get
-2 = -1/6 * -2 = 1/3
this is nonsense
2.
y = -6x - 3/7
this doesn't work for x = -2 and y = -2 (first point) because we get
-2 = -6 * -2 - 3/7 = 12 - 3/7 = 11 + 4/7
this is nonsense
3.
y = -6x
this doesn't work for x = -2 and y = -2 (first point) because we get
-2 = -6 * -2 = 12
this is nonsense
4.
y = -1/6 * x - 7/3
this works for x = -2 and y = -2 because
-2 = -1/6 * -2 - 7/3 = 2/6 - 7/3 = 1/3 - 7/3 = -6/3 = -2
it also works for x = 4 and y = -3 because
-3 = -1/6 * 4 - 7/3 = -4/6 - 7/3 = -2/3 - 7/3 = -9/3 = -3
Simplify the expression |ab^3| if a>0 and b>0
The expression |ab^3| if a>0 and b>0 is even.
What is Parity Definition?
Even Function: A function is even if f(-x)=f(x) for all [tex]$x \in \mathbb{R}$[/tex] Odd Function: A function is odd if f(-x)=-f(x) for all [tex]$x \in \mathbb{R}$[/tex]
[tex]f(a): \quad|a|\left|b^3\right|[/tex]
[tex]f(-a): \quad|a|\left|b^3\right|[/tex]
[tex]-f(a):-|a|\left|b^3\right|[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
The expression |ab^3| if b>0
[tex]$$\begin{aligned}& f(a): \quad|a| b^3 \mid \\& f(-a): \quad|a|\left|b^3\right| \\& -f(a): \quad-|a| b^3 \mid\end{aligned}$$[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
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Line r has an equation of y=
6/7x+1. Line s includes the point (7,–7) and is perpendicular to line r. What is the equation of line s?
The equation of line s is y + 7 = -7/6(x - 7).
What is slope of a line?
A line's steepness and direction are measured by the line's slope. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, Δy, Δx respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx
Given equation of line r is y = 6/7x+1.
The slope of line r is m = 6/7
The slope of the line that is perpendicular to line r is -1/m = - 7/6.
The equation of line that passes through the point (x₁, y₁) with slope m is y - y₁ = m(x - x₁).
Putting m = - 7/6, x₁ = 7 and y₁ = -7 in y - y₁ = m(x - x₁):
y - (-7) = - 7/6(x - 7)
y + 7 = - 7/6(x - 7)
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Compare the function f(x)=3x-1/2 to the function shown in the graph. Which statements are
correct?
Please help me!! Help by finding the measure of angle 2
Answer:
Below
Step-by-step explanation:
Sum of interior angles for the uppr right triangle = 180
52 + 90 + '2' = 180
'2' =38°
Find the measure of angle f given the information below.
Answer:
53 degrees
Step-by-step explanation:
This is a transversal question (look at attached). Because the lines are parallel, g will equal to 180(a straight line is 180 degrees) - a. Then, because g + f + e = 180 (since it is a straight line), substitute the values that we know and solve. (61) + f +(66) = 180. f = 53
please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
EP = GP
GP = HP
angle EFH = 45
Think these 3 are the right answers, hope it helps.
A line with a lope of 1/6 pae through the point (0,-3) what i it equation in lope intercept form
An equation of line having slope 1/6 and passes through the point (0,-3) is y = 1/6x - 3
We know that the slope-point form of line is:
(y - y1) = m(x - x1)
Here, we need to find an equation of line having slope 1/6 and passes pae through the point (0,-3)
let (x1, y1) = (0, -3)
and m = 1/6
substitute values in above formula,
(y - (-3)) = 1/6 (x - 0)
y + 3 = 1/6 (x)
y = 1/6x - 3
which is slope-intercept form of line (y = mx + b)
Therefore, equation of line is y = 1/6x - 3
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Sun 4 Dec
vle.mathswatch.co.uk
In a class of 30 students, 13 of them are boys.
What percentage of the class are girls?
Give your answer to 1 decimal place.
Answer:56.6%
Step-by-step explanation:
30 - 13 = 17
17 /30 x 100 = 56.6 %
Multiply (-8.328)(15.99)
Answer:
-133.16472
Step-by-step explanation:
N/A
Answer:
-133.16472
Step-by-step explanation:
a project has the following projected outcomes in dollars: $210, $320, and $540. the probabilities of their outcomes are 25%, 55%, and 20% respectively. what is the expected value of these outcomes?
The expected value of these outcomes are $262.5, $496 and $648 respectively
How to calculate expected values?You should know that the expected value are the proportion of the values when valued with the percentages
The given values are $210, $320 and $540
The given percentages are 25%, 55% and 20%
The expected values are
0.25*210 = $52.5+210=$262.5
0.55*320=176+320=$496
0.20*540=108+540=$648
Therefore the projected values of the project are $262.5, $496 and $648 respectively
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f(x) = 2x³x² - 29x
What is the greatest possible number of turning points?
Answer:
4
Step-by-step explanation:
First we need to get some definitions out of the way
Definition of a turning point
A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising). A polynomial of degree n will have at most n−1 turning points.Definition of degree of polynomial
The degree of a polynomial is the degree of the term having the highest degree.The given polynomial is3. For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation
for the cost, C, after h hours of babysitting. What do you think the slope and the y-
intercept represent? How much money will she make if she baby-sits 5 hours? Graph
The price of the shirt was $38. It was reduced by 20% and then again by 10%. What was the final price of the shirt?
Answer:
Step-by-step explanation:
$38, 20% off = $30.40
$30.40, 10% off = $27.36
$27.36 is the final price of the shirt
What is inverse of the function f(x) = 4(x - 3)?
The inverse of the function f(x) = 4(x - 3) is f⁻¹(x)=(x+12)/4.
What is meant by inverse function?A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) generates y, then y entered into f's inverse creates x. x . Invertible refers to a function that has an inverse, which is represented by the symbol f1.
Inverse functions are functions that "reverse" one another in the broadest sense. If f, for instance, goes from a to b, then its inverse, f 1 f -1 f 1f, start superscript, minus 1, end superscript, must go from b to a.
Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F has an inverse if there are no horizontal lines that cross the graph of f more than once.
Let f(x)=y
f(x)=4(x-3)
f(x)=y
y=4(x-3)
x=4(y-3)
x=4y-12
4y=x+12
y=(x+12)/4
Therefore, f⁻¹(x)=(x+12)/4
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A new club sent out 250 coupons to boost sales for next year's memberships. They provided 4 times as many to potential members than to existing members. How many coupons did they send to existing members?
A.
4
B.
50
C.
5
D.
54
Answer: 50 existing members
A blueberry pie is made of 10 inch diameter pie pan.the pie is cut into 8 equal slides.what is the area of 1 slice
Cutting perfect slices of pie can be tricky. Crusts can crumble, bottoms can buckle and fillings can spill over, but there are a lot of tricks for a good slice.
What is diameter?In a circle, diameter is a line that passes through the center and meets the circumference at opposite ends. It is twice as long as that of the radius of the circle. In other words, the diameter of a circle is the line that passes through the center and divides the circle into two equal parts. Let us learn more about diameter definition and properties in this article.The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circumference of the circle. The diameter is also known as the longest chord of the circle.To learn more about diameter refer to:
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Shaun won 6 out of the 10 video games he played. What percent of the video games did Shaun win?
Answer:
60%
Step-by-step explanation:
Shaun won 60% percent of the games.
Answer:
Shaun won 60% out of the 10 video games he played.
Step-by-step explanation:
If Shaun played 10 video games and only won six out of all of them, he won 60% since we can count 10 as 100% and 6 as 60%.
Segment AB has point A located at (8, 9). If the distance from A to B is 10 units, which of the following could be used to calculate the coordinates for point B
O 10 √(x+8)2+(y+9)²
O10-√√(x+9)²+(y+8)²
O10-√√(x-8)2+(y-9)²
O10-√(x-9)2+(y-8)²
in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens. give a 95% confidence interval for percent of american adults who believe in aliens.
American adults believes in alien for the given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).
As given in the question,
Sample of American adults surveyed 'n' = 200
Percent of people believes in aliens are success 'p'= 72%
= 0.72
Percent of people who don't believes (failure) in aliens ' 1 - p' = 1 - 0.72
= 0.28
95% Confidence interval that represents Americans adults who believes in aliens
value of z - score for 95% confidence interval = ± 1.96
Margin of error 'MOE'= (z-score)√p ( 1- p) /n
= ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200
= 1.96 ( √0.2016 / 200)
= 1.96 ×√0.001008
= 0.063
Lower limit = p - MOE
= 0.72 - 0.063
= 0.66
Upper limit = p + Margin of error
= 0.72 + 0.063
= 0.78
Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).
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what value of k does the equation k + 4/x +3/x^2 =0. (I) two real and different roots. (Ii)coincident and real root. (iii) no roots
The value of k will be equal to 4/3 and there will be two real and different roots.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the equation is k + 4/x +3/x² =0. The value of k will be calculated as,
k + 4/x +3/x² =0.
kx² + 4x + 3 = 0
b² - 4ac =0
4² = 4 x k x 3
16 = 12k
k = 4/3
Therefore, the value of k will be equal to 4/3 and there will be two real and different roots.
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HELP MEEEEE PLEASEEEEEE
The bus is covering a distance of 42 miles in 1 hour 30 minutes then the speed of the bus will be 28 mph.
What is Average speed?
The overall distance the object covers in a given amount of time is its average speed. The scalar quantity represents the average speed. It does not have direction; it is represented by magnitude.
As per the given data provided in the question,
Total distance traveled by bus = 42 miles
Total time is taken by the bus = 1 hour 30 minutes = 1.5 hours.
Then the average speed of the bus will be,
[tex]Average\ Speed(S) = Total\ Distance/Total\ Time[/tex]
S = 42/1.5
S = 28 mph.
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The congruency theorem can be used to prove that △wut ≅ △vtu.
As per the congruency theorem, the two triangles are congruent.
Congruency theorem:
Congruency theorem states that "if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other."
Given,
Here we need to prove that congruency theorem can be used to prove that △wut ≅ △vtu.
Let us consider triangles WUT and VTU.
And in these triangles:
=> WU≅VT
And in those one, ∠T≅∠U,
Therefore, m∠T = m∠U = 90°
Here the side TU is common.
Now, we have to note that triangles WUT and VTU are right triangles, because m∠T = m∠U = 90°.
Then the side TU is common leg and sides WU and VT are hypotenuses.
Therefore, the HL theorem states: if the hypotenuse (WU) and one leg (TU) of a right triangle (ΔWUT) are congruent to the hypotenuse (VT) and one leg (TU) of another right triangle (ΔVTU), then the triangles are congruent.
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Answer: HL
Step-by-step explanation:
Hector spent 40. 15 for the dvds the sales tax was 2. 55 and he didnt have a coupon? How much would each dvd cost? please help fast
The cost of each DVD as per the given data will be 20.08 without tax. and 21.35 with sales tax.
Cost of DVD,
with sales tax
(40.15 + 2.55) / 2
= 42.70/2
= 21.35 per DVD
without sales tax
40.15 / 2
= 20.08 per DVD
Sales taxes are a type of tax that is paid to a governing body when goods and services are sold. Sales tax is an indirect tax that is often assessed at the time that certain taxable products are purchased or exchanged. It is assessed as a percentage of the item's retail price.
The government in power and the specific rules it enforces determine the sales tax, which is typically easy to calculate and collect. The sales tax can be thought of simply as an additional sum of money paid while buying products or services.
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You move left 7 units. You end at (-3, -5). Where did you start?
Answer:
[tex](4 , -5)[/tex]
Step-by-step explanation:
Note that when you move left or right any amount of units, you will be making the changes to the x-variable. If you move up or down any amount of units, you will be making the changes to the y-variable.
In this case, it is given that:
(x , y) = (-3 , -5)
You will want to move right 7 units, as you are trying to find your starting position. Add 7 from the x variable:
[tex](x , y) = (-3 , -5) = (-3 (+7) , -5)\\\\= (-3 (+7) , -5)\\= ((-3 +7) , -5)\\= (4 , -5)[/tex]
[tex](4 , -5)[/tex] is your starting position.
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