The sum of the interior angle is 1080 and each angle measure is 135 degrees.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have an octagon
In an octagon the number of sides = 8
The sum of the angles in the octagon is given by:
= (n - 2)×180
n = 8
= (8 - 2)180
= 6×180
The sum of the interior angle = 1080
Each angle = 1080/8 = 135 degree
Thus, the sum of the interior angle is 1080 and each angle measure is 135 degrees.
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An experiment consists of rolling a standard six-sided die once. Event A is "rolling a 5{}^{\prime\prime} and event B is "rolling an odd number." Are the events dependent or independent? Why? Select the option that correctly answers both questions.
O Events A and B are independent, because P(B) = P(B|A) = 1/2.
O Events A and B are independent, because P(A) = P(B|A) = 1/12.
O Events A and B are dependent, because P(A) =/ P(B|A).
O Events A and B are dependent, because P(B) =/ P(B|A).
Based on the given probability events, we can calculate that Events A and B are independent, because P(B) = P(B|A) = 1/2.
Is event B independent of event A?Events are independent if P(B) = P(B|A)
The probability of event B is:
= 3 odd numbers / 6 numbers
= 1 / 2
The probability of A is:
= 3 prime numers / 6
= 1/2
P(B|A) = ((1 / 2) x (1 / 2)) / (1 / 2)
= 1/2
So P(B) = P(B|A) = 1/2.
The events are independent.
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Will you do the hard questions
Answer:
No
Step-by-step explanation:
I will not do hard questions
Question 2(Multiple Choice Worth 1 points)
(02.02 LC)
If g(x)= x² + 3, find g(4).
11
19
16
8
Answer: 19
Step-by-step explanation:
g(4) = 4² + 3
g(4) = 16 + 3
g(4) = 19
Help ASAP, really stuck
The total length of the wire needed to make this shape is 162cm
Perimeter of a triangleThe perimeter of a triangle is the sum of the external side of the triangle.
Given the following parameters
Length of one side of the outside shape = 24cm
The side length of the smaller triangle = 24/4 = 6cm
The perimeter of the smallest triangle 3(6) = 18cm
The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm
Total length of wire needed. = 3(24) + 3(18) + 36
Total length of wire needed = 72 + 54 + 36
Total length of wire needed = 162cm
Hence the total length of the wire needed to make this shape is 162cm
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The jet stream is traveling nearly due south from Wyoming to Colorado at 110 knots. If the plane’s speed is 400 knots, what will be its ground speed if it travels from Wyoming to Colorado?
Considering the direction of the wind, it is found that the ground speed needs to be of 510 knots.
What is the ground speed?The ground speed, considering that the wind is flowing from Wyoming to Colorado, and the same direction as the trip, is given by:
G = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 400 knots.Wind: 110 knots.Hence the ground speed is given by:
G = 400 + 110 = 510 knots.
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Select the correct answer.
The cost of renting a community center is $100, with an additional cost of $10 per guest.
Which graph has the most appropriate scales and units for this situation?
О А.
B.
Total Rental Cost ($)
tal Cost ($)
500
400
300
200
100
50
40
30
0
10 20 30 40 50
Number of Guests
The cost of renting a community center for x guest is given as y = 10x + 100
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the y intercept.
Let y represent the cost of renting a community center for x guest. Hence:
y = 10x + 100
The cost of renting a community center for x guest is given as y = 10x + 100
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Which function represents exponential growth?
O f(x) = 3x
O f(x) = x³
Of(x) = x + 3
O f(x) = 3x
Answer:
b step by step explanation
The function that represents exponential growth is:
f(x) = x³
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
Exponential growth is a phenomenon that occurs when the rate of change of a quantity is proportional to its current value. In other words, as the value of the quantity increases, the rate at which it increases also increases. This can be represented mathematically using an exponential function of the form f(x) = abˣ, where a is the initial value, b is the growth factor, and x is the time or number of periods.
The function that represents exponential growth is:
f(x) = x³
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After how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds
Answer:
3 seconds
proofi took the test
The object reaches its maximum height after 3 seconds.
The correct option is 3 seconds.
To find the time at which the object reaches its maximum height, we need to determine the vertex of the parabolic function[tex]h(t) = -16t^2 + 96t + 6[/tex] . The vertex form of a parabola is given by [tex]h(t) = a(t - h)^2 + k[/tex], where (h, k) represents the vertex.
In this case, a = -16, so the vertex is given by t = -b/2a. Plugging in the values, we get t = -96/(2 x (-16)) = 96/32 = 3 seconds.
Therefore, the object reaches its maximum height after 3 seconds.
Option B, 3 seconds, is the correct answer.
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The complete Question:
The function [tex]h(t) = -16t^2 + 96t + 6[/tex] represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
After how many seconds does the object reach its maximum height?
A. 2 seconds
B. 3 seconds
C. 6 seconds
D. 9 seconds
the bearing of two points x and y from z are 45° and 135° respectively . if |zx|=8cm and |zy|=6cm, find |xy|.
Answer:
[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].
Step-by-step explanation:
Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.
Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:
[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].
Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:
[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].
Answer the following
The set A satisfying the given inequality is A = (-[tex]\infty[/tex], -10].
What are some properties of an inequality relation?Following are some facts which are true for an inequality relation:
Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.[tex]\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)[/tex]
Since y ∈ B, -2 ≤ y ≤ 7. So,
[tex]\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\; y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.[/tex]
The set {-x | inequality (1) holds ∀ y ∈ B} is [10, [tex]\infty[/tex]) i.e.
10 ≤ -x ≤ [tex]\infty[/tex].
Multiplying -1 throughout gives
-10 ≥ x ≥ -[tex]\infty[/tex].
x, thus, lies in the range A = (-[tex]\mathbf{\infty}[/tex], -10}.
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QuestionFind the set A such that for x ∈ A
[tex]\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y[/tex]
∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.
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if AB= 51, and AC = 120. find BC.
A
B
C
Answer:
Step-by-step explanation:
AB = 51
AC = 120
BC = AC - AB
BC = 120-51
BC = 69 units
Two number cubes are rolled for two separate events:
Event A is the event
that the sum of numbers on
both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Complete the conditional-probability formula for
event B given that event A occurs first by writing A and B in the blanks:
Answer:
Good idea for thanks......
The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms
Answer:
1, 17, 33, 49
Step-by-step explanation:
given the first term is 1 then the next 3 terms are
1 + d, 1 + 2d, 1 + 3d ( d is the common difference )
the sum of the first 4 terms is 100 , then
1 + 1 + d + 1 + 2d + 1 + 3d = 100 , that is
4 + 6d = 100 ( subtract 4 from both sides )
6d = 96 ( divide both sides by 6 )
d = 16
1 + d = 1 + 16 = 17
1 + 2d = 1 + 2(16) = 1 + 32 = 33
1 + 3d = 1 + 3(16) = 1 + 48 = 49
the first 4 terms are
1, 17, 33, 49
Answer:
see the file attached!!!!
A coordinate plane is labeled street on the x-axis and avenue on the y-axis. ping is at point (3, 6) and ari is at point (21, 18). a line is drawn from ping to ari. ping lives at the corner of 3rd street and 6th avenue. ari lives at the corner of 21st street and 18th avenue. there is a gym two-thirds the distance from ping's home to ari's home. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 where is the gym? 9th street and 10th avenue 12th street and 12th avenue 14th street and 12th avenue 15th street and 14th avenue
The gym location is (15th street, 14th Avenue). so the option D is correct.
What is graph ?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given :
Ping's residence = (3rd street, 6th Avenue)
Ari's residence = (21st street, 18th Avenue)
Gym location is 2/3 the distance of Ping's residence to Ari's residence
So, distance between Ping's home to Ari's home will be
Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)
Distance = (21 - 3) street, (18 - 6) avenue
Distance between ping and Ari will be
= (18th , 12th )
We know that
Gym distance = 2/3 × (18), 2/3 ×(12)
Gym distance = (12, 8)
Gym location = Ping's location + gym distance
Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)
Gym location = (15th street, 14th Avenue)
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Find sin (ABC + 60) NEED QUICK 100 PPOINTS
Answer:
B
Step-by-step explanation:
using the addition identity for sine
sin(A + B) = sinAcosB + cosAsinB
using the sine and cosine ratios in the right triangle
sinABC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{5}[/tex]
cosABC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{3}{5}[/tex]
using the exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex]
Then
sin(ABC + 60)
= sinABC cos60 + cosABC sin60
= ( [tex]\frac{4}{5}[/tex] × [tex]\frac{1}{2}[/tex] ) + ([tex]\frac{3}{5}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )
= [tex]\frac{4}{10}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]
= [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]
sin<ABc
Perpendicular/Hypotenuse4/5cos<ABC
Base/Hypotenuse3/5Now
sin(<ABC+60)sin<ABC ×cos60+cos<ABC×sin604/5(1/2)+3/5(√3/2)2/5+3/10√3find the value of cosec^2 30 degree - sin^45 - sec^60
For this question, I will be writing 'csc' instead of 'cosec'
[tex]\sin 30^{\circ}=\frac{1}{2} \implies \csc 30^{\circ}=2\\\\\sin 45^{\circ}=\frac{1}{\sqrt{2}}\\\\\cos 60^{\circ}=\frac{1}{2} \implies \sec 60^{\circ}=2\\\\\\\therefore \csc^{2} 30^{\circ}-\sin^{2} 45^{\circ}-\sec^{2} 60^{\circ}=2^{2}-\left(\frac{1}{\sqrt{2}} \right)^{2}-2^{2}=\boxed{-\frac{1}{2}}[/tex]
If the nth term of a sequence is 11n+2 what is the 12th term
Answer:
134
Step-by-step explanation:
the "nth" term of a sequence means that you can plug in the term number to get the term value
so, if
11n + 2 is the sequence
11(12) + 2 is the 12th term
132 + 2 is the 12th term
134 is the 12th term
By plugging in the term "place" (1st, 2nd, 3rd, 4th, etc.) for the variable "n", we get a term value.
hope this helps!!
The 12th term of the sequence is 133
How to determine the 12th term?The nth term is given as:
Tn = 11n + 1
The 12th term is calculated as:
T(12) = 11(12) + 1
Evaluate
T(12) = 133
Hence, the 12th term of the sequence is 133
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You have $40.00. You wish to buy a T-shirt costing $14.50. You would also like to buy a pair of jeans. There
is a 6% sales tax on clothing. What is the top tag price (excludes sales tax) you could pay for the jeans?
The fuel for a lawn mower is a mixture of 8 parts petrol to one part oil. How much oil is required to make 1 litre of fuel?
The amount of oil required for 1 liter of fuel is 111.11 mL.
Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.
Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.
The total part of the fuel is 8+1=9
the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9
the portion of the oil = parts of oil /total parts of the fuel= 1/9
Now we have to calculate the amount of oil required for 1 liter of fuel.
As discussed before, 1/9 parts of the fuel is oil.
So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL
Similarly, we can calculate the amount of petrol which will be
the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL
Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.
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The following data is a randomly selected sample of 20 state populations. find the measures of central tendency. you may use technology to find the measures.
The mean is 6394530.35 and the median is = 3355572.5
The missing data is attached in the answer.
What is Mean ?Mean is the average value of the data points , it is determined by dividing the total sum of the data points to the number of data points.
Mean and Median is the measure of the central; tendency of the data.
Mean is given by
Sum of the observations/number of observations
= (741894 + 6931071....)/20
= 6394530.35
2) To find median
The data needs to be arranged in ascending order
Then the median is the middle number of the arranged data
Here the median is = 3355572.5
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Write functions for each of the following transformations using function notation. Choose a different letter to
represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in
the counterclockwise direction.
• translation of a units to the right and b units up
reflection across the y-axis
• reflection across the x-axis
• rotation of 90 degrees counterclockwise about the origin, point O
• rotation of 180 degrees counterclockwise about the origin, point O
• rotation of 270 degrees counterclockwise about the origin, point O
Answer:
Step-by-step explanation:
1) = f(x - a) + b
Coordinate change
(x, y) → (x + a, y + b)
2) RFy(x, y) = f(-x)
Coordinate change
(x, y) → (-x, y)
3) RFx(x, y) = -f(x)
Coordinate change
(x, y) → (-y, x)
4) RCCW90(x, y) = f⁻¹(-x)
Coordinate change
(x, y) → (-y, x)
5) RCCW180(x, y) = -(f(-x))
Coordinate change
(x, y) → (-x, -y)
6) A 270 degrees counterclockwise rotation gives;
RCCW270(x, y) = -(f⁻¹(x))
Coordinate change
(x, y) → (y, -x)
Step-by-step explanation:
1) Horizontal translation a units right = f(x - a)
The vertical translation b units up = f(x) + b
Therefore, we get; = f(x - a) + b
The coordinate change
(x, y) → (x + a, y + b)
2) A reflection across the y-axis = RFy(x, y) = f(-x)
The coordinate change
(x, y) → (-x, y)
3) A reflection across the x-axis gives RFx(x, y) → (x, -y)
Therefore, in function notation, we get;
RFx(x, y) = -f(x)
4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)
In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)
5) A 180 degrees counterclockwise rotation about the origin gives;
(x, y) → (-x, -y)
Therefore, we get;
In function notation RotCCW180(x, y) = -(f(-x))
6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)
In function notation RotCCW270(x, y) = -(f⁻¹(x))
Z varies directly as x and y, z=6 when x=2 and y=6 find the value of z when x=3 and y=8
Answer:
12
Step-by-step explanation:
Direct Variation. I think it's gonna be like this.
SInce Z is not inversely to y , its varies directly to both.
Then it's,
Z=kxy, where k is constant.
subst. Z=6,x=2 and y=6.
6=k×2×6
6=k×12=12k
6=12k=½
the formula connecting them is
Z=½xy
Z=½×3×8
Z= 1×3×8÷2
Z=24÷2
Z=12.
That's my solution.
Evaluate:
lim h->0 (√(x+h) - √x) / h
Rationalizing the numerator, it is found the result of the limit is given as follows:
[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{1}{2\sqrt{x}}[/tex]
What is a limit?A limit is given by the value of function f(x) as x tends to a value.
The first step to find the limit is replace the variable by the value, hence:
[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{0}{0}[/tex]
Undefined limit, hence we have to find another way. The numerator includes square roots, hence it should be rationalized using the subtraction of perfect squares, as follows:
[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} \times \frac{(\sqrt{x + h} + \sqrt{x})}{(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{(\sqrt{x + h})^2 - (\sqrt{x})^2}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{x + h - x}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{h}{h(\sqrt{x + h} + \sqrt{x})}[/tex]
Then we simplify the h, so:
[tex]\lim_{h \rightarrow 0} \frac{1}{\sqrt{x + h} + \sqrt{x}} = \frac{1}{2\sqrt{x}}[/tex]
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What is 0.000345 expressed in scientific notation?
3.45 × 102
3.45 × 104
3.45 × 10–2
3.45 × 10–4
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
Expression in scientific notation :
[tex]\qquad \tt \rightarrow \:3.45 × {10}^{-4} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 0.000345[/tex]
[tex]\qquad \tt \rightarrow \: 0.000345 \times \cfrac{10000}{10000} [/tex]
[tex]\qquad \tt \rightarrow \: (0.000345 \times 10000) \times \cfrac{1}{10000} [/tex]
[tex]\qquad \tt \rightarrow \: 3.45 \times \cfrac{1}{10 {}^{4} } [/tex]
[tex]\qquad \tt \rightarrow \: 3.45 \times{10 {}^{ - 4} } [/tex]
[tex] \textsf{Correct option - D} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
3.45 x 10-4
Step-by-step explanation:
Find ZABC
00
A
38⁰
32⁰
Answer:
The answer will be 38° + 32° = 70°
Please mark me as the brainliest
PLEASE HELP ASAP
thank you :)
Answer:
y = x/2 -3
Step-by-step explanation:
x - 2y = 6
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
We need to solve for y
Subtract x from each side
x-2y-x = -x+6
-2y = -x+6
Divide each side by -2
-2y/-2 = -x/-2 +6/-2
y = x/2 -3
The slope intercept form is
y = x/2 -3
Answer: slope intercept form is
y = x/2 -3
Step-by-step explanation:
hope this helps ; )
how many ounces of a 16% alcohol solution must be mixed with 2 ounces of a 20% alcohol solution to make a 17% alcohol solution?
Answer:
x = 6
Step-by-step explanation:
.16x + 2 * .02 = (x + 2) * .17
.16x + .4 = .17x + .34
.06 = .01x
6 = x
Find the value of cos N rounded to the nearest hundredth, if necessary.
cos N = 14/20 = 0.70
bill $42 , tax 9% , tip 18%
Answer:
Tax 3.78 $ and tip 7.56 $
Step-by-step explanation:
42*0.09 = 3.78
42*0.18 = 7.56
What is the range of the function y=-x² +1?
A) y≤ -1
B) y²-1
C) y≤ 1
D) y≥ 1
Answer:
Option (C)
Step-by-step explanation:
The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.
So, this means that adding 1 to this, the range matches with option C.
