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Work Shown:
(height)/(shadow length) = (height)/(shadow length)
(5 ft)/(6.5 ft) = (x ft)/(26 ft)
5/(6.5) = x/26
5*26 = 6.5*x
130 = 6.5x
6.5x = 130
x = 130/(6.5)
x = 20
The palm tree is 20 feet tall, which is the same height as a 2 story building (assuming each floor is 10 ft).
Which of the following is the domain of the function based on the input-output table below?
Answer:
C
Step-by-step explanation:
The domain is the left side of the table
One of the angles of a triangle is 110° and the other two angles are equal.What is the measure of each of these equal angles?
Answer:
x = 35
Step-by-step explanation:
Let x be the one of the other angles
X is also the third angle since we know they are equal
The sum of the angles of a triangle is 180
110+x+x = 180
110 +2x= 180
2x = 180-110
2x= 70
Divide by 2
2x/2 = 70/2
x = 35
Answer:
[tex]x = 35 \degree[/tex]
Step-by-step explanation:
Let the unknown angle be x
Unknown Angles are equal to each other so,
[tex]x + x + 110 = 180[/tex]
sum of the interior angles in a triangle is 180°
[tex]2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ \frac{2x}{2} = \frac{70}{2} \\ x = 35 \degree[/tex]
Please answer this!!!!!!
Answer: 39°
Step-by-step explanation:
Angle of depression must be less than 90° but greater than 0°
Which of the following is the graph of f(x) = |x|? An image of a graph. An image of a graph. An image of a graph. An image of a graph.
Is the following number rational or irrational?
-117
Choose 1 answer:
Rational
Irrational
Answer:
-117 is irrational number
Answer:
Irrational
Step-by-step explanation:
Irrational number can't be written as a faction, -11pie can't be written as a fraction. Therefore it is a irrational number.
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Question: "If y > 3, what is the value of n ?"
Answer:
y-3
Problem:
What is the remainder when the dividend is xy-3, the divisor is y, and the quotient is x-1. ?
Step-by-step explanation:
Dividend=quotient×divisor+remainder
So we have
xy-3=(x-1)×(y)+remainder
xy-3=(xy-y)+remainder *distributive property
Now we just need to figure out what polynomial goes in for the remainder so this will be a true identity.
We need to get rid of minus y so we need plus y in the remainder.
We also need minus 3 in the remainder.
So the remainder is y-3.
Let's try it out:
xy-3=(xy-y)+remainder
xy-3=(xy-y)+(y-3)
xy-3=xy-3 is what we wanted so we are done here.
A construction crew is completing about 40 yards of a new highway each day. At this rate, how long will it take them to complete a stretch of 1.6 miles? Round your answer to the nearest tenth if necessary
Answer:
70 days
Step-by-step explanation:
that is the procedure above
If 12(x - a)(x - b) = 12x² - 7x - 12 , then ab =
Answer choices :
1
-1
7
12
-12
Answer: -1
Step-by-step explanation:
12x^2-7x-12 = (4x+3)(3x-4)
4x+3=0. X = -3/4
3x-4=0. X = 4/3
(-3/4) (4/3) = -1
what is the side length of the square in cm
Answer:
8.4 cm^2
Step-by-step explanation:
The area of the rectangle is
A = lw
A = 3x *5x = 15x^2
126 = 15x^2
126/ 15 =15x^2/15
42/5 = x^2
We want to find the area of the square
A = l*w
A = x*x
A = x^2 = 42/5 = 8.4 cm^2
find the slope of the tangent line of the curve r = cos (3theta) at theta = pi / 3
The slope of the tangent line to the curve at a point (x, y) is dy/dx. By the chain rule, this is equivalent to
dy/dθ × dθ/dx = (dy/dθ) / (dx/dθ)
where y = r(θ) sin(θ) and x = r(θ) cos(θ). Then
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
Given r(θ) = cos(3θ), we have
dr/dθ = -3 sin(3θ)
and so
dy/dx = (-3 sin(3θ) sin(θ) + cos(3θ) cos(θ)) / (-3 sin(3θ) cos(θ) - cos(3θ) sin(θ))
When θ = π/3, we end up with a slope of
dy/dx = (-3 sin(π) sin(π/3) + cos(π) cos(π/3)) / (-3 sin(π) cos(π/3) - cos(π) sin(π/3))
dy/dx = -cos(π/3) / sin(π/3)
dy/dx = -cot(π/3) = -1/√3
can she get some help
Answer:
-55
Step-by-step explanation:
the sqeuence seems to be subtracting by 2 everytime.
so it will be -1,-3,-5,-7,-9,-11,-13,-15,-17,-19,-21,-23,-25,-27,-29..
the answer will be 27*-2(-54) -1(because we start at -1 , not 0)
Answer:
Step-by-step explanation:
the formula for an arithmetic sequence that is explicit is
[tex]a_n=a_1+d(n-1)[/tex] where [tex]a_1[/tex] is the first term (so -1), and d is the common difference (-2). n is the number position in the sequence. As soon as we find the formula or model for this sequence we can find any number term we want. Filling in the formula:
[tex]a_n=-1-2(n-1)[/tex] and we'll clean that up just a bit:
[tex]a_n=-1-2n+2[/tex] (I just distributed through the parenthesis) and a bit more to
[tex]a_n=-2n+1[/tex] and if we want the 21st term, fill in a 21 for n:
[tex]a_{21}=-2(21)+1[/tex] and
[tex]a_{21}=-42+1[/tex] so
[tex]a_{21}=-41[/tex]
Given the following coordinates complete the reflection transformation.
Answer:
For a general point (x, y), a reflection across the line x = a transforms the point into:
(a + (a - x), y) = (2a - x, y)
So if we first do a reflection across the line x = 1, the new point will be:
(2*1 - x, y) = (2 - x, y)
And if we now do a reflection across the line x = 3, the new point will be:
(2*3 - (2 - x), y) = (6 - 2 + x, y) = (4 + x, y)
Now that we have the general formula we can solve the question.
For the point (-5, 2)
The generated point after the reflections is:
(4 + (-5), 2) = (-1, 2)
For the point (-1, 5)
The generated point after the reflections is:
(4 + (-1), 5) = (3, 5)
For the point (0, 3)
The generated point after the reflections is:
(4 +0, 3) = (4, 3)
A square has a perimeter of 80 m. What is the length of each side?
Answer:
20 m
[tex]p = 4a \: thus \: a = p \div 4 = 80 \div 4 = 20 \: m[/tex]
Answer:
20
Step-by-step explanation:
P=4L
80=4L
L=80/4
L=20m
Consider the following function.
Place the steps for finding f -1(x) in the correct order.
↓
↓
↓
↓
Answer:
if f(x) = ax + b then f-1(x) = (x - b)/a
Step-by-step explanation:
Now
f(x)=ax + b
then y = ax + b
interchanging x and y , we get
or, x = ay + b
or, x - b = ay
or, (x - b)/a = y
therefore,f-1(x) = (x - b)/a
Find the missing side of triangle
Final Answer:
x = 20
Step-by-step explanation:
we'll be using the pythagorean theorem method, in this triangle the missing letter is a.
formula: [tex]a=\sqrt{c^2-b^2}[/tex]
a = x
b = 21
c = 29
a = [tex]\sqrt{29^2-21^2}[/tex]
a = [tex]\sqrt{841-441}[/tex] (note: 29² = 29 × 29 = 841 and 21² = 21 × 21 = 441)
a = [tex]\sqrt{400}[/tex]
a = 20
x = 20
10 • 4/10y = -28 • 10
Answer:
y=-70
Step-by-step explanation:
10.4/10y=-28.10
4y=-280
y=-70
Need help asap, thanks :)
Answer:
937
425
Step-by-step explanation:
9 is the square of 3
7 is 1 more than 6, the double of 3
4 is the square of 2
5 is 1 more than 4, 2x 2
Is there more?
Answer:
425
Step-by-step explanation:
1st = 2^2
3rd = 2*2 + 1
A group of rowdy teenagers near a wind turbine decide to place a pair of
pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.
a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.
b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.
Answer:
a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex]
b) Hence the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a meter is 5.5 meters
Step-by-step explanation:
a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :
[tex]x^2 + (y-yc)^2 = R^2[/tex] ,
where
R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)
= 14 m / 2
= 7 m (radius of the circle)
Also, center of the circle will be at (0, 2 + R) i.e (0,9)
So, is the trajectory path equation to the circle
Let [tex]x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi)[/tex] be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t
At t= 10s, y = 16 m so we have,
[tex]9 + 7 * sin(10* w + \phi) = 16[/tex] ---------------(1)
Also, at t= 25s, y =2 m so we have,
[tex]9 + 7* sin(25 * w +\phi) = 2[/tex]--------------(2)
Solving we have, [tex]10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2[/tex]
[tex]15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6[/tex]
Therefore [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex] is the instantaneous height of the pink short at time t ( in seconds)
b) At t= 10minutes = 10 * 60 s = 600s, we have,
[tex]y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)[/tex]
= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)
In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C
Answer:
90°
Step-by-step explanation:
Angle C = arccos((84²+13²-85²)/(2×84×13))
= arccos(0/2184)
= arccos(0)
= 90°
Answered by GAUTHMATH
MNOP is a trapezoid with median QR. Find x
[tex]\bf \large \rightarrow \: \:2x \: + \: 8 \: = \: 0[/tex]
[tex]\bf \large \rightarrow \: \:x \: = \: \frac{8}{2} \\ [/tex]
[tex]\bf \large \rightarrow \: \:x \: = \: \cancel\frac{ 8}{ 2} \: \: ^{4} \\ [/tex]
[tex]\bf \large \rightarrow \: \:x \: = \: 4[/tex]
Option ( A ) is the correct answer.
the sum of the following algebraic expression 2x + 15, 7-8x and 3x - 41 is 30 find the value of x..
[tex] \\ \tt \longmapsto2x + 15 + 7 - 8x + 3x - 41 = 30 \\ \\ \tt \longmapsto 2x - 8x + 3x + 15 + 7 - 41 = 30 \\ \\ \tt \longmapsto - 3x - 19 = 30 \\ \\ \tt \longmapsto 3x + 19 = - 30 \\ \\ \tt \longmapsto 3x = - 30 -19 \\ \\ \tt \longmapsto 3x = - 49 \\ \\ \tt \longmapsto x = - \frac{49}{3}[/tex]
Answer:
Step-by-step explanation:
2x + 15 + 7 - 8x + 3x - 41 = 30
2x - 8x + 3x + 15 + 7 - 41 = 30
Combine like terms
-3x - 19 = 30
Add 19 to both sides
-3x = 30 + 19
-3x = 49
Divide both sides by (-3)
x = 49/-3
x = -[tex]16\frac{1}{3}[/tex]
I need help I don't understand this.
9514 1404 393
Answer:
∠4 = 108°
Step-by-step explanation:
Angles 2 and 4 together form a "linear pair". That is, the sum of them is 180°, a "straight angle." They are supplementary.
∠4 = 180° -∠2 = 180° -72°
∠4 = 108°
this graph represents the function f(x)=4sin(x) which statement is true about this function
Answer:
A
Step-by-step explanation:
The function is increasing in the interval in A because as the x-values increase so do the y-values on the graph, which can be shown by the graph sloping upwards at that specific section.
The graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have given a graph of a trigonometric function,
As we know, the trigonometric function is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
From the graph, the function is increasing from 3π/2 to 2π
The graph slopes upward at that particular segment, indicating that the function is increasing in the interval in A as the x-values increase and the y-values on the graph follow suit.
Thus, the graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ5
3+3+3+3+3+3+3+333333
Answer:
333354
Step-by-step explanation:
Simplify the expression.
Answer:
333,354
Step-by-step explanation:
First, we add the 3's. And get 21.
333,333 + 21 = 333,354
find the angle measures given the figure is a rhombus.
[tex] \large \tt{{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]
A rhombus is a parallelogram in which all sides are equal i.e AB = BC = CD = CA Let ∠ A be x. In the ∆ ABC , AB = AC which means they are isosceles triangle and we know the opposite angles of isosceles triangle are equal i.e ∠ A = ∠ C = x. The sum of angles of a triangle is always 180°. Now , Find out the value of x :[tex] \large{ \tt{❁ \:x + x + 98 = 180 \degree \: [ Sum\: of \: angle \: of \: a \: triangle ]}}[/tex]
[tex] \large{ \tt{⟶2x + 98 \degree= 180 \degree}}[/tex]
[tex] \large{ \tt{⟶ \: 2x = 180 \degree - 98 \degree}}[/tex]
[tex] \large{ \tt{⟶ \: 2x = 82 \degree}}[/tex]
[tex] \large{ \tt{ ⟶x = \frac{82 \degree}{2} }}[/tex]
[tex] \large{ \tt{⟶ \: x = 41 \degree}}[/tex]
The value of x is 41°. Now , Find the measure of ∠ 1 :[tex] \large{ \tt{ ↔\angle \: 1 = x \degree = \boxed{41 \degree}}}[/tex] [ Being alternate angles ]
Hence , Our final answer is 41° .- Alternate angles are the non-adjacent interiors pair of angles lying to the opposite side of a transversal when it intersects two straight line segments. Alternate angles form ' Z ' shape.
Hope I helped! Let me know if you have any questions regarding my answer. :)4x^2-12x+9.
4x^2+4x+1.,
1+12x+36^2
Answer:
Step-by-step explanation:
Which statement is true? O A. The number 23 is prime, but 36 is composite. B. The number 33 is prime, but 42 is composite. OC. The number 21 is prime, but 25 is composite. D. The number 27 is prime, but 39 is composite.
Answer: A. The number 23 is prime, but 36 is composite.
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Explanation:
Let's go through the possible answer choices
A) This is true because 23 only has the factors 1 and 23. So that's why 23 is prime. We can say 36 is composite since 2 is a factor, ie 36 = 2*18.B) This is false because 33 is not prime. Note how 33 = 3*11, showing that 3 is a factor of 33.C) Similar to B, the statement "21 is prime" is false. Note how 21 = 3*7.D) Like the other false statements, 27 is not prime because 27 = 3*9.23 is indeed prime, and 36 is indeed composite.
33 is composite, and 42 is indeed composite.
21 is composite, and 25 is composite as well
27 is not prime, and 39 is composite.
Primes have only 2 factors: 1 and themselves.
And 33, 21 and 27 definitely have more than 2 factors. Hope this helps!
~Just a joyful teen
[tex]GraceRosalia[/tex]
for f(x)= -4x + 5, find f(x) when x = -2.
Answer:
13
Step-by-step explanation:
f(x)= -4x + 5
Let x = -2
f(-2) = -4(-2) +5
= 8+5
= 13
Step-by-step explanation:
x = - 2
f ( x ) = - 4x + 5
f ( - 2 )
= - 4 ( - 2 ) + 5
= 8 + 5
= 13
Please help me solve this I’m really struggling
Answer:
y =x^2 +8x +15
factories form
y =( x+5 )( x+3 )
x intercept where the graph meet the x axis
y = x^2 +8x +15
let y =0
0 = x^2 +8x +15
0 = ( x + 5) (x+3)
o = x+5 or 0 = x+3
-5 = x or x = - 3
x intercept
(-5;0)
(-3 ;0)
axis of symmetry : where you will cut the graph into two half
x = - b/2a
x = - 8/2(1)
x = - 8/2
x = - 4
Domain
XER
Range
y > -1
