The greatest possible value of the perimeter of the triangle is 48
What is the perimeter of a triangle?The perimeter of a triangle is the sum of the lengths of the three sides of the triangle.
An isosceles triangle has 2 equal sides and the length of the 2 sides must be greater than the length of one.
Perimeter A= 12×2+18=42
Perimeter B= 12+18×2=48
Therefore the greatest possible perimeter of the triangle is Perimeter B (48) since the sum of lengths of the two equal sides(18) is greater than the third side (12) and 48 is greater than 42.
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Which set of steps can be used to prove the sine sum identity, sin(x y) = sin(x)cos(y) cos(x)sin(y)?
The trigonometry identity sin(x + y) = sinx cosy + cosx siny.
What is sin(x + y) identity in trigonometry?sin(x + y) is one of the identities in trigonometry for compound angles.
The angle (x + y) represents the compound angles.
sin(x + y) = sinx cosy + cosx siny
To prove sin(x + y) = sinx cosy + cosx siny
Consider OX as a rotating line anti-clockwise. Let angle XOY = a
the making of an acute angle b the rotation in the same direction is
angleYOZ = b , angle XOZ = a + b
From triangle PTR,
∠TPR = 90 - ∠PRT , ∠ROX = a
From the right-angled triangle PQO
sin(a + b) = PQ/OP
= (PT + TQ) / OP
= PT/OP + TQ/OP
= PT/PR × PR/OP + RS/OR × OR/OP
= cos (∠TPR ) sinb + sina cosb
= sina cosb + cosa sinb
if we replace a=x and b=y
Therefore, sin(x + y) = sinx cosy + cosx siny.
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The points represent the vertices of a polygon. Use a matrix to find the coordinates of the image after the given transformation. Graph the preimage and the image.
A(2, 3), B(–1, –4), and C(2, –2); a translation 1 unit left and 4 units down. 30 points
The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, reflection and dilation.
Given the points A(2, 3), B(–1, –4), and C(2, –2), the translation 1 unit left and 4 units down gives:
A'(1, -1), B'(-2, -8) and C'(1, -6)
The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)
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Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?.
As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
Given function is:
[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]
What is a function?A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.
Divide the numerator and denominator of the given function by x.
[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]
[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]
As we know that as x approaches the infinity 1/x approaches 0.
So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]
[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]
Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
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troy organizes a samll party there are 30 glasses of drinks at the party 20 of which contain an orange flavored drink what is the probability that a randomly selected drink will be orange flavored
Answer:
66(2/3) %
Step-by-step explanation:
There are 30 possible outcomes because there are 30 cold drinks.
The Probability of orange flavored 20/30 = 2/3 = 0.6666....
66.6666....%= 66(2/3) %
Write the following expression using an exponent.
1x(4.5)x(4.5)x(4.5)x(4.5)x(4.5)=
Answer:
4.5^5
Step-by-step explanation:
Answer:
(4.5)^5
Step-by-step explanation:
PLEASE HELP!! It's due tomorrow and I don't understand it..
An angle of measure [tex]\frac{4\pi }{3}[/tex] intersects the unit circle at point ([tex]-1/2,- \frac{\sqrt{3} }{2}[/tex]). What is the exact value of tan([tex]\frac{4\pi }{3}[/tex])?
a. -1/2
b. [tex]\sqrt{3[/tex]
c. [tex]\frac{\sqrt{3} }{3}[/tex]
d. [tex]-\frac{\sqrt{3} }{2}[/tex]
Answer:
b. √3
Step-by-step explanation:
Given a point on the unit circle that represents the position of the terminal ray of an angle, the tangent of that angle is the ratio of the y-coordinate to the x-coordinate.
tan(4π/3) = y/x = (-√3/2)/(-1/2) = √3/1
tan(4π/3) = √3
_____
Additional comment
A calculator can confirm this for you.
What is f(4) for the function f(x) = 2x + 5?
f(4) =
Answer:
f(4) = 13
Step-by-step explanation:
f(4) = 2(4)+5
f(4) = 13
Answer:
13
Step-by-step explanation:
f ( x ) = 2x + 5
To find : f ( 4 )
f ( 4 ) = f ( x )
Here,
x = 4
So,
f ( 4 ) = 2 ( 4 ) + 5
= 2*4 + 5
= 8 + 5
f ( 4 ) = 13
A cylinder and a cone have the same volume. The cylinder has a diameter of 4 inches and a height of 3 inches. The cone has a diameter of 6 inches. What is the height of the cone?
We are given a cylinder and a cone of same volume i.e
[tex] \longrightarrow[/tex] Volume of cone = Volume of cylinder
And also the diameter of the cylinder is given 4 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf \dfrac{Diameter}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{4}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 2 inches
The height of cylinder is 3 inches. And the diameter of the cone is 6 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf\dfrac{Diameter}{2} [/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{6}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 3 inches
First, let us recall the Formulas of volume of cylinder and cone:
[tex] \quad\longrightarrow\quad \sf {Cone = \dfrac{1}{3}\pi r^2 h }[/tex]
[tex] \quad\longrightarrow\quad \sf {Cylinder = \pi r^2 h }[/tex]
Now, we know that the volume of cone is equal to the volume of cylinder
[tex] \implies\quad \sf{\dfrac{1}{3}\pi r^2 h = \pi r^2 h }[/tex]
On putting the values:
[tex] :\implies\quad \sf{\dfrac{1}{3}\pi \times 3^2 \times h = \pi \times 2^2 \times 3 }[/tex]
[tex] :\implies\quad \sf{\dfrac{1}{\cancel{3}}\times 3.14 \times\cancel{ 9 }\times h = 3.14 \times 4 \times 3 }[/tex]
[tex] :\implies\quad \sf{3.14 \times 3 \times h = 3.14 \times 12 }[/tex]
[tex]: \implies\quad \sf{ h = \dfrac{ \cancel{3.14} \times 12 }{ \cancel{3.14} \times 3} }[/tex]
[tex] :\implies\quad \sf{ h =\cancel{ \dfrac{12}{3}}}[/tex]
[tex] :\implies\quad \underline{\underline{\pmb{\sf{h = 4 inches }}} }[/tex]
ㅤㅤㅤㅤㅤ~Hence the height of the cone is 4 inches.
I’m thinking trapezoid and rhombus but I don’t know
Help on this pleasee
Answer: 40 degrees
Step-by-step explanation:
Translate the following phrase to an expression: the difference between twenty and twice a number.
Answer:
20 - 2n
n = a number
can someone help me? it’s due in a few hours
Answer:
cars value decreases in value exponentially
Step-by-step explanation:
cant really read it but say that the cars value decreases in value exponentially and compare that to however the other cars decrease in value over time
100 POINTS !! The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 70 meters per second can be modeled by the parabola f(x) = x − 0.002x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground. A.height: 125 m; distance: 500 m B.height: 250 m; distance: 22 m C. height: 500 m; distance: 125 m D. height: 22 m; distance: 250 m
Answer:
height: 125m; distance: 500m
Step-by-step explanation:
x = 250
f(x) = x − 0.002x2
f(x) = 250 − 0.002(250 )2
= 250 − 0.002(62,500)
= 250 − 125
= 125
250 times 2 = 500
[tex]\\ \rm\rightarrowtail y=x-0.002x^2[/tex]
So
Put 250[tex]\\ \rm\rightarrowtail y=250-0.002(250)^2[/tex]
[tex]\\ \rm\rightarrowtail y=250-0.002(62500)[/tex]
[tex]\\ \rm\rightarrowtail y=250-125[/tex]
[tex]\\ \rm\rightarrowtail y=125m[/tex]
This is max heightDistance:-
2×height2×125500mGood afternoon, please help me with this question and if u get it correct ill give u the brainlest
Answer:
5/6
Step-by-step explanation:
it comes out originally like 10/12 but if your simplify it it's 5/6
Answer:5/6
Step-by-step explanation: 12-2 =10 so 10/12 which simplifies to 5/6
Which angles are complementary to each other?
Answer:
<1 and <2
Step-by-step explanation:
Complementary angles are two angles which their measure add up to 90 degrees.
There are only one angle pair that meet this requirement:
angle 2 and angle 1
Make a number line and mark all the points that represent the following values of x. X≤2 or x<5
The inequalities x≤2 or x<5 are unequal expressions
The common points of both inequalities are {.......0,1,2}
What are inequalities?Inequalities are expressions that have unequal values
What are number lines?Number lines are lines that are used to represent numbers and expressions at regular intervals
How to determine the number line?The inequalities are given as;
x≤2 or x<5
This means that:
x is less than or equal to 2
And
x is less than 5
So, we have:
x≤2 = {.......0,1,2}
x<5 = {.......0,1,2,3,4}
The common points of both inequalities are:
x≤2 or x<5 = {.......0,1,2}
See attachment for the number line
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There are 100 cm in a meter. write an expression to find the number of centimeters in 8 meters.
Help me with this question plss
Answer:
800m
Step-by-step explanation:
If 100cm is equivalent to a meter (1 Meter). 8 Meters would be equivalent to 8 Meters multiplied by 100cm and divided by a meter (1 Meter)
No links just the Answer please!!!
Answer:Its -3.5
Step-by-step explanation:
The school has $3,582 to spend on markers. Each package of markers costs $9. How many packages of markers can the school buy?
packages
Answer:
398
Step-by-step explanation:
3582 / 9 = 398
How to find the measure of an interior angle inside a regular polygon
Answer:
Step-by-step explanation:
[tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides
The measure of an interior angle inside a regular polygon is given by;
[tex]\rm S = (n -2) \times 180[/tex].
What is the interior angle?An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or, we can say that the angle measures at the interior part of a polygon are called the interior angle of a polygon.
An Interior Angle is an angle inside a shape.
As per the angle sum theorem, the sum of all the three interior angles of a triangle is 180°.
Multiplying two less than the number of sides times 180° gives us the sum of the interior angles in any polygon.
The measure of an interior angle inside a regular polygon is determined by the following formula;
[tex]\rm S = (n -2) \times 180[/tex]
S = sum of interior angles and n = number of sides of the polygon.
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The length of a rectangular frame is represented by the expression 2x 10, and the width of the rectangular frame is represented by the expression 2x 6. Write an equation to solve for the width of a rectangular frame that has a total area of 140 square inches. 4x2 32x − 80 = 0 4x2 32x 60 = 0 2x2 32x − 80 = 0 x2 16x 60 = 0.
The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
What is the area of the rectangle?The area of the rectangle is the product of its length and its breadth.
As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².
Now we know the area is the product of length and breadth, therefore,
[tex]\rm \text{Area of rectangle} = length \times breadth[/tex]
[tex]140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0[/tex]
Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
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Answer:
A.) 4x2 + 32x − 80 = 0
Step-by-step explanation:
Just took the test
What is the word form for 407,219?
A
Four hundred seventy thousand and two hundred ninety
B
Four hundred seventeen thousand, two hundred nineteen
C
Four hundred seven thousand, two hundred nineteen
D
Four hundred seven thousand, two hundred and nineteen
Answer:
C or D Both basically
Step-by-step explanation:I read them
Simplify this please
(5ab²c)^2
Answer:
25a^2b^4c^2
Step-by-step explanation:
step 1:
Remove the bracket by multiplying all the power inside the bracket with the power outside the bracket.
5^2a^2b^2x2c^2=25a^2b^4c^2
What are the roots of the polynomial equation x superscript 4 baseline x squared = 4 x cubed minus 12 x 12? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth. –12, 20 –2.73, 2, 2.73 –1.73, 1.73, 2 –20, 12
The roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.
What is a factor of polynomial?The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.\
To find the roots of a polynomial, equate these factors of a polynomial to zero.
The given polynomial equation is,
[tex]x^4+x^2=4x^3-12x+12[/tex]
Take all the terms left side of the equation,
[tex]x^4+x^2-4x^3+12x-12=0\\x^4-4x^3+x^2+12x-12=0[/tex]
The factor form of the polynomial on solving the above equation, we get,
[tex](x-2)(x-2)(x-1.73)(x+1.73)=0[/tex]
Equate all the factors to zero, to find the roots. The roots we get are,
[tex]2,2,1.73,-1.73[/tex]
Hence, the roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.
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Answer:
–1.73, 1.73, 2
Step-by-step explanation:
(x+2)(x+7) Write in simplified form
Answer:
x^2+9x+14
Step-by-step explanation:
x×(x+7)+2×(x+7)
x^2+7x+2x +14
x^2+9x+14
15 POINTS
Write an equation in standard form for the given circle
A.) (x+3)^2 + (y+6)^2 = 16
B.) (x-3)^2 + (y+6)^2 = 16
C.) (x+3)^2 + (y-6)^2 = 16
D.) (x-3)^2 + (y-6)^2 = 16
Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2
---Center = (h, k)
---Radius = r (this value will need to be squared in the final answer)
Center = (-3, -6)
---h = -3
---k = -6
Radius = 4
Equation: (x + 3)^2 + (y + 6)^2 = 16
Correct Answer: A
Hope this helps!
Graph the line that represents the equation .
y = -2/3 x + 1
i really need ive tried multiple times and got it wrong every time
Can someone please HELP ME I HAVE A TEST TMRW I STUDIED BUT I FORGOT HOW TO DO THIS STUFF CAN SOMEONE EXPLAIN IT TO ME
Answer:
1. (a. 8 b. 3 d. 6,6,12 e. 3,3,9) 2. (a. 2,3 b. 4,5 c. 6,6,2,3 d. 5,3,5) 3. (a.2/3 b.1/3 c.2/3 f.1/2 g.7/8 h.4/5)
Step-by-step explanation:
OK this is quite simple. Just multiply the top and bottom, otherwise known as the numerators and denominators, by whatever is next to it. In this case, 1a is [tex]\frac{2*4}{5*4}[/tex].
That would result in [tex]\frac{8}{20}[/tex]
Hey there!
In order to multiply fractions, we should multiply the numerator of the 1st fraction by the numerator of the 2nd fraction.
Same with denominators.
Let's multiply these fractions.
2/5=2*4/5*4=8/20
2/3=2*6/3*6=12/18
1/4=1*3/4*3=3/12
3/4=3*3/4*3=9/12
now divide:
10/15=10:5/15:5=2/3
12/18=12:6/18:6=2/3
12/15=12:3/15:3=4/5
15/25=15:5/25:5=3/5
Now, simplify the following fractions:
4/6
divide the top & bottom by 2:
2/3
next:
5/10
divide the top & bottom by 5:
1/2
next
5/15
divide the top & bottom by 5:
1/3
next:
12/18
divide the top & bottom. by 6
2/3
next
5/10
divide the top & bottom by 5
1/2
next
14/16
divide the top & bottom by 2
7/8
and then last but not least
28/35
divide the top & bottom by 7
4/5
And we're done!
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
PLS HELP ME
Use the box-and-whisker plot to complete each of the following statements.
A)The median of Set A is approximately ___ the median of Set B.
Answers I can pick from: Half of, the same, twice
B) The range of Set B is approximately ___ the range of Set A.
Answers I can pick from: Half of, the same, twice
C) The interquartile range of Set A is ____ the interquartile range of Set B.
Answers I can pick from: Less then, greater then, the same
D. There is ____ overlap between the two data sets.
Answers I can pick from: some, much, little, like, no
To find the range, interquartile range, and median of the box plot, see the image attached below to use as a guide.
What is a Box Plot?A box plot consists of a rectangular box, a vertical line that divides the box, and two whiskers extending from the box.
The box plots being referred to in the question are missing, however, the diagram attached shows how to determine the values you will need in solving the question.
The median is represented by the vertical line that divides the rectangular box.
The range = max value - min value.
The interquartile range = the range of the rectangular box = Q3 - Q1.
In summary, to find the range, interquartile range, and median of the box plot, see the image attached below to use as a guide.
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