Here we can conjecture that :
The measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.
What is interior and exterior angle ?The exterior angle of any polygon is defined as the angle which is at the outside boundaries of that polygon. whereas, the interior angle is defined as the angle which is inside the polygon. In the other words if the polygon has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle.
What is Non adjacent interior angle ?Non adjacent angles are those angles which are not adjacent to each other. The non adjacent angles follow one of the properties which are listed below:
They do not share a common vertex or common side.They can share a side, but not share the common vertex.They share a common vertex, but not share the common side.In the given question,
taking a example say a triangle ABC with ∠A=64, ∠B = 45 and an external angle x to the side AC.
as sum of angles equal to 180
thus, ∠A + ∠B + ∠C = 180
64 + 45 + ∠C = 180
∠C = 180-109 = 71
now as x is external to ∠C,
therefore x = 180 - ∠C = 180 - 71
x = 109 = ∠A + ∠B
Hence we can make the conjecture that, the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.
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Solve for W
5 = 7w + 8w + 2
w = 5
Step-by-step explanation:
2+(7w)+(8w)=5
(7÷5)+(8÷5)+2
(1.4) (1.6) +2
+1.5
=3+2=5
consider inequality 12 < -3(x+4). The solution set of this inequality is x =
The solution set of this inequality is x = -8
What is inequality ?
A mathematical statement indicating an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.inequality
12 < -3(x+4)
12 < -3x - 12
12 + 12 < - 3x
24 < -3x
- 8 < x
The solution set of this inequality is x = -8
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Can please help me with this question
The possible coordinates of point G on the number line is -15 and 7.
How to find the coordinates on a number line?On the number line, point E has the coordinates of - 4, and EG = 11 .
The possible coordinates of point G are as follows:
A number line is a horizontal straight line with numbers placed at equal distances from each other along that line.
Negative numbers are on the left side while the positive numbers are on the right side.
Therefore, the possible coordinates of G is when we go left or right side of E on the number line.
Hence,
Let's go left E to G on the number line
-4 - 11 = -15Let's go right E to G on the number line
-4 + 11 = 7Therefore, the possible coordinates of point G on the number line is -15 and 7.
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Write a slope-intercept equation for a line passing through the given point that is parallel to the given line. Then write a second
equation for a line passing through the given point that is perpendicular to the given line.
(-7, 0), y=-0.9x + 4.4
The equation of the line parallel and perpendicular are y = -0.9(x+7) and y = 10/9(x+7) respectively
Equation of a lineThe equation of a line in point slope form is expressed as;
y - y₁ =m(x-x₁) (Parallel)
y - y₁ =-1/m(x-x₁) (Perpendicular)
Given the following
Point = (-7, 0)
Slope = -0.9
Substitute
y -0 = -0.9(x-(-7))
y = -0.9(x+7)
Similarly for the perpendicular line
y -0 = -1/-0.9(x-(-7))
y = 10/9(x+7)
Hence the equation of the line parallel and perpendicular are y = -0.9(x+7) and y = 10/9(x+7) respectively
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Sketch the solid that results when the region enclosed by the given equations is revolved about the y -axis.
y = x²
y = 2 x
y = x² , y = 2 x are the region enclosed by the given equations is revolved about the y -axis.
What exactly is a closed area?
All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.
What do you mean by the region that a closed curve encloses?
The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.
Whether contained or not?
Use enclosed at all times. No longer regarded as a regular variety, enclosed would even be mistaken for another word by many readers. Use enclose, encloses, and enclosing rather than inclose for other words that are similar to enclosed.The graph is attached in equation y = x² , y = 2 x
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nancy wants to vacation in austin texas. Hotel A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with 18% nightly room tax plus a one time $40 parking fee. After how many nights will Hotel B be less expesnsive?
The number of nights will be 8.62 when the Hotel B charge is less than A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that hotel, A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with 18% nightly room tax plus a one-time $40 parking fee. The number of the nights will be calculated as below:-
From the given data from the equations:-
A = 179 + ( 0.14 x 179 ) x
A = 204.06x
B = ( 169 + ( 0.18 x 169 )x + 40
B = 199.42x + 40
Equate the two equations:-
204.06x = 199.42x + 40
4.64x = 40
x = 40 / 4.64
x = 8.62 nights
Therefore, the number of nights will be 8.62 when the Hotel B charge is less than A.
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Find the arithmetic mean a n of the given terms. a n₋₁ = 0.3, a n₊₁ = 1.9
The arithmetic mean a n of the given terms a n₋₁ = 0.3, a n₊₁ = 1.9 is
a n = 1.6.
What is direct variation?
a n₋₁ = 0.3, a n₊₁ = 1.9
a n = a [tex]n_{+1}[/tex] - a[tex]n_{-1}[/tex]
a n = 1.9 - 0.3
a n = 1.6
Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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Use the given information to write an equation of the circle.
center (6,4) , through (2,1)
Using the given information, the equation of the circle with center located at point (6 , 4) and passes through the point (2 , 1) is (x - 6)^2 + (y - 4)^2 = 25.
Using the distance formula, get the radius of the circle by solving for the distance between the center (6 , 4) and the point (2 , 1).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(2 - 6)^2 + (1 - 4)^2
radius= √16 + 9
radius = √25
radius = 5
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (6 , 4)
r = 5
(x - 6)^2 + (y - 4)^2 = 5^2
(x - 6)^2 + (y - 4)^2 = 25
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a. Generate the first ten terms of the Fibonacci sequence.
The first ten terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on.
What is Fibonacci sequence and what are the first ten terms?The Fibonacci numbers, sometimes known as Fn in mathematics, are a series of numbers. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.
means
0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
Hence,the first ten terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on.
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[tex]\Large \boxed{\sf 0, 1, 1, 2, 3, 5, 8, 13, 21, 34}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
2. Find the domain and range of the function shown in the graph. Write the domain and range
using interval notation.
O domain: [-3,2)(3,7]
range: [-6,-1) [1,5)
O domain: (-6,-1](1,5]
range: (-3,2][3,7)
O domain: (-3,2][3,7)
range: (-6,-1](1.5]
O domain: [-6,-1) [1,5)
range: [-3,2)(3.7]
By looking at the graph:
Domain: (-6, 1] U (1, 5]
Range: (-3, 2] U [3, 7)
How to find the domain and range of the graphed function?
The domain is the set of inputs (horizontal axis) and the range is the set of the outputs (vertical axis).
By looking at the horizontal axis we can see that the first part goes from x = -6 to x = -1, this interval is (-6, 1]
(at x = -6 there is a open circle, so x = -6 does not belong to the domain)
Similarly, the second interval is (1, 5]
Then the domain is D: (-6, 1] U (1, 5]
To get the range we do the same thing, but we need to look at the vertical axis. The first interval goes from y = -3 to y = 2 and then y = 3 to y = 7, the range is:
R: (-3, 2] U [3, 7)
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Please help i'm stuck
Answer:
Decreases two times
Step-by-step explanation:
[tex].[/tex]
logarithmic differentiation Y=2^X
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
How to use logarithmic differentiation
Logarithmic differentiation is a combination of derivative rules and logarithm properties which is useful to derive power, exponential and power-exponential functions:
y = 2ˣ
㏑ y = ㏑ 2ˣ
㏑ y = x ㏑ 2
y' / y = ㏑ 2
y' = y · ㏑ 2
y' = 2ˣ · ㏑ 2
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
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For each equation, find the center and radius of the circle.
(x-1)²+(y-1)²=1
The equation of the circle (x - 1)^2 + (y - 1)^2 = 1 has a radius of 1 and a center located at (1 , 1).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x - 1)^2 + (y - 1)^2 = 1, is in standard form, then
h = 1
k = 1
r = 1
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How can you determine whether two variables x and y for a real-life situation are, correlated?
To determine if two variables, X and Y, are correlated, we can use the two simple ways. One is to create a scatter plot simply—a scatter plot plots X and Y pair values. A scatter plot shows a diagram of correlations. We can also identify if the correlation formed is positive, negative, or non-existent. Calculating the correlation coefficient R and determining its p-value associated with R is also possible.
Correlation coefficient values are always between -1 and 1.
Where
-1 indicates a perfect negative linear correlation between the two variables
0 shows a perfect positive linear correlation between the two variables
1 shows a perfect linear correlation between the two variables, indicates
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need help solving please
Answer: the answer is D
Both sides are equal to 5 radical 2
Step-by-step explanation:
Match each expression to the correct point
Answer:
Step-by-step explanation:
f = -3/2
d = -[tex]\pi[/tex]
e = - [tex]\sqrt{8}[/tex]
Answer:
56892 that's it hope it helps
12. A 500 N force is applied to a 25 m/s² object. The mass of the object is
A. 12,500 kg
B. 12,500 m/s
C. 20 kg
D. 20 m/s
Answer:
C is right 20kg
Step-by-step explanation:
bec
ause the formula of force=mass ×acceleration
to find mass= force/acceleration.
Draw a scale model of your classroom using any scale.
Answer: a scale model is a representation or copy of an object that is larger or smaller than the object being represented, (sorry if this wasnt what you were asking)
Step-by-step explanation:
What is the measure of n?
6
3
n
18
n = [?]√
In the triangle, The measure of side n is √ 108
What is a Triangle ?It belongs to the basic geometric forms. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a separate triangle and a distinct plane.
Identical sides have the same ratio since all of the triangles in the example are comparable.
Short side/long side:
n/6 = 18/n
n² = 6*18
n² = 108
n = √ 108
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Write a flow proof.
Given: ∠A and ∠C are right angles.
∠A B E ≅ ∠C B D, AE ≅ CD
Prove: BE ≅ BD
BE ≅ BD under corresponding parts of the congruent triangles.
What do we mean by a triangle's congruency?If all three corresponding sides and angles of two triangles are the same size, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are moved, they will coincide.When two triangles satisfy the five congruence conditions, congruence exists.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given:
∠A and ∠C are right angles.∠ABE ≅ ∠CBD, AE ≅ CDSo, we can say that △ABE ≅ △CBD is under AAS condition.
Then, we can conclude that BE and BD are identical. (Corresponding parts of the congruent triangles)So, BE ≅ BD.Therefore, BE ≅ BD under corresponding parts of the congruent triangles.
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Where did the formula for summing finite geometric series come from? Suppose the geometric series has first term a₁ and constant ratio r , so that S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹
a. Show that r S n = a₁r+ a₁ r²+ a₁ r³+ . . . . +a₁rⁿ .
The total of a geometric series is an unlimited number of terms with a fixed ratio between them.
If S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹ then rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ.
What is the formula for geometric series?
The sum of a geometric series Sn is given by:
[tex]$S_n=a(\frac{1-r^{n} }{1-r} )[/tex]
Given:
Sum of first n terms of the Geometric progression be
Sn = a₁ + a₁r + a₁ r² + . . + a₁ rⁿ⁻¹ ---(1)
On multiplying by r on both sides,
r Sn = a₁r + a₁ r² + . . + a₁ rⁿ⁻¹ + a₁ rⁿ ----(2)
So, (2) − (1) gives,
[tex]rS_n-S_n=ar^{n} -a[/tex]
[tex]S_n(r-1)=a(r^{n} -1)[/tex]
Therefore, the sum of n terms of a GP is:
[tex]$S_n=a(\frac{1-r^{n} }{1-r} )[/tex]
Let the expression be r S n = a₁r + a₁ r² + a₁ r³ + . . . . + a₁rⁿ
Sum of first n terms of the Geometric progression is:
Sn = a₁ + a₁r + a₁ r² + . . + a₁ rⁿ⁻¹
On multiplying by r on both sides, we get
rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ
Therefore, rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ
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ax+ 5x = 10b; solve for x
Answer:
[tex](a + 5) \times = 10b \\ \times = \frac{10b}{a + 5} [/tex]
Write –0.67 as a fraction.
Answer:
- [tex]\frac{67}{100}[/tex]
Step-by-step explanation:
there's a negative sign so the our fraction will also have a negative sign
notice each number and its position. 0 is at the ones position. 6 is at the tenths position. 7 is at the hundredths position. 1, 10, 100, 100, etc.
The denominator of a fraction will be 100, because that is the last position of this decimal.
the numerator is just the number value itself.
in total it is
- [tex]\frac{67}{100}[/tex]
Answer:
[tex] - \frac{67}{100} [/tex]
is this what you asked for?
Evaluate 4-0.25g + 0.5h when g=10 and h=5
h(x)
=
x² + 3x
4x + 27
Find h(-8)
Step-by-step explanation:
it is -8 because negative times negative is positive
(-8)I really don't get this can someone help meh please :d
Answer:
this is a vertical problem what is on one side is on the other
Step-by-step explanation:
so r is the same as 95
Use the box method to distribute and simplify (-5x+3)(x+6)
Answer:
-6x * 3
Explanations :
= - 5x + 3 * x + 6
= - 5x - x * 6 - 3
= - 6x * 3
True or False
When naming or labeling a line, it matters which points you use.
Answer:
true
Step-by-step explanation:
when naming or labeling a line it matters which points you use
Find the equation for the line parallel to 3x+5y-4=0, with the same x-intercept as 2x-3y-6=0
Equation of line is 5y = -3x + 9 .
What is equation of line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
3x+5y-4=0
5y = -3x + 4
y = -3/5 x + 4/5
since it is parallel, its slope, m is -3/5
2x-3y-6=0
3y = 2x - 6
y = 2/3x - 2
at x-intercept, y is zero
2 = 2/3x
x = 3
therefore
y = mx + c
0 = (-3/5 * 3 ) + c
c = 9/5
equation is
y = -3/5x + 9/5
5y = -3x + 9
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Alec's car payment is $316 each month.
How much do his car payments
year?
Answer:
$3,792
Step-by-step explanation:
$316 x 12
