A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.
The length of the pole is 19.15 feet.
What is the angle of elevation?The angle of elevation is created by the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, the angle formed is an angle of elevation.
Given:
Angle made by straight road = 15°
Angle of elevation of the sun = 57°
Length of the shadow = 75 feet
∠ACB = 90° - 57° = 33°
∠CAB = 57° - 15° = 42°
Using Sine Law to find BC i.e.length of the pole.
[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]
[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]
[tex]BC= \frac{75sin 42}{sin 33}[/tex]
BC ≅ 19.15 feet (to the nearest hundredth.)
Therefore, the approximate length of the pole is 19.15 feet.
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Read image for instructions The shape of the distribution is…
Ok, so
The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.
Which is an equivalent expression using a positive exponent?
(3/5)^-8 ÷ (3/5)^-4
(3/5)^4
(3/5)^12
(5/3)^32
(5/3)^4
The equivalent expression using a positive exponent is (5/3)⁴ .
If an expression was created utilizing integer variables, constants, and algebraic operations, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
However, since they are not produced by using integer constants and algebraic operations, transcendental numbers like such and e are not algebraic. The production of is commonly stated as a geometric expression, although the definition of e requires an infinite number of algebraic operations.An expression is said to be rational if it can be reduced to an acceptable fraction using the characteristics of arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).A positive expression is given as (3/5)⁻⁸ ÷ (3/5)⁻⁴ .
Using the properties of exponents we can calculate the expression as:
(3/5)⁻⁸⁺⁴ = (3/5)⁻⁴ = (5/3)⁴
Hence the required expression is (5/3)⁴
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Ten minutes after jumping into the ocean, a
diver is 25 feet below the surface. After 30
minutes, the diver has descended 75 feet. How
fast was the diver descending?
Guys I need help is this right?
Answer:
The answer is C.
Please help me with this lesson on ixl! I don't understand.
Answer:
8/25
Step-by-step explanation:
change the 5/4 into a 4/5 and change the divide into a mulltiple while you do this
then multiply 2 x 5 = 8
5 x 5 = 25
Solve for X!
Please help
In the given triangle,
sides vx and vw are equal,
and ∠v = 40°
∠w = ∠x (Adjacent angles of the equal sides of a triangle are equal)
Also, ∠v + ∠w + ∠x = 180° (Angle sum property of a triangle)
⇒ 40° + ∠x + ∠x = 180°
⇒ 2∠x = 140°
⇒∠x = 70°
What are Isosceles Triangles?The term "isosceles triangle" refers to a triangle with two equal sides. The isosceles triangle has equal sides and equal measures for two of its three angles. This results in an uneven angle. Assume that if the measure of an unequal angle is given to us, we can quickly determine the other two angles using the angle sum property. The isosceles triangle can be characterized as acute, right, or obtuse depending on the angle formed by the two legs. The isosceles triangle can be sharp if the two angles across from the legs are equal and smaller than 90 degrees (acute angle).A right isosceles triangle has two equivalent sides, one of which serves as the triangle's base and the other as its perpendicular. The third uneven side is known as the hypotenuse. As a result, we may employ the well-known Pythagoras theorem, which states that the hypotenuse's square equals the sum of its base and perpendicular squares.
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Is there a dilation that maps shape I onto shape II? If so, what is the scale factor and is it an enlargement or a reduction?
Give me the actual answer, not explanation, for 10 points
The scale factor for the graph will be 3 and there will be enlargement.
The scale factor may be defined as the ratio of two dimensions such that one figure is large, and another is small. The scale factor is done due to the unpractical measurement of any figure. For example, if a figure is a scale copy of the scale factor of 6/2 it means 2 is converted into 6. We can use the following points to know about enlargement.
A(1, 1) ⇒ A'(3, 3)
B(2, 1) ⇒ B'(6, 3)
C(1, 2) ⇒ C'(3, 6)
D(2, 2) ⇒ D'(6, 6)
Now, to find the scale factor, simply divide the Point' with the original Point. Use any number.
A'(3, 3)/(A(1, 1)) = 3
B'(6, 3)/(B(2, 1)) = 3
C'(3, 6)/(C(1, 2)) = 3
D'(6, 6)/(D(2, 2)) = 3
which shows that the scale factor is 3.
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find an equation for the line that passes through the points (-5,-1) and (-1,1)
Answer:
y = (1/2)x + (3/2)
Step-by-step explanation:
(-5, -1), (-1, 1)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 1 - (-1) 1 + 1 2 1
m = ------------- = ----------- = ------------ = --------- = --------
x₂ - x₁ -1 - (-5) -1 + 5 4 2
y - y₁ = m(x - x₁)
y - (-1) = (1/2)(x - (-5))
y + 1 = (1/2)(x + 5)
y + 1 = (1/2)x + (5/2)
-1 -1
---------------------------------
y = (1/2)x + (3/2)
I hope this helps!
WILL GIVE BRAINLIEST! Please help and explain, thank you! All that is needed is to find the unknown side.
Answer:
X is 9
Step-by-step explanation:
Answer:
On the smaller figure the measures of it are 6 and 3. On the large figure one of the measures is 18. The number 6 and 18 are congruent, and 6 has be tripled in size, so in order to finding the missing measurement, you will simply triple the 3:
3 times 3 = 9
The missing measure is 9.
Step-by-step explanation:
Hope it helps! =D
Solve the inequality 3(x-2) + 12x + 2(x+2).
O A. x≤4
Co B. x2-5
C. no solution
OD. all real numbers
The inequality x > 0 , x all real numbers .
What do you mean by inequality?
The phenomena of unequal and/or unjust allocation of resources and opportunities among members of a certain society is referred to as inequality. Different persons and contexts may interpret the word "inequality" differently.The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity.= 3(x-2) + 12x + 2(x+2)
= 3x - 6 + 12x + 2x + 4
= 12x + 2x + 3x -6 + 4
= 17x - 2
17x - 2 = 0
x = 2/17
x > 0 , x all real numbers ..
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Evaluate a + b for a = 2 and b = 3.
Answer: 5
Step-by-step explanation: Substitute the value of the variable into the expression and simplify
Abby and Lexi each open a savings account on the same day. Both accounts accrue simple interest. The function f(t) = 10t + 500 models the amount of money in Abby’s account over time. The function g(t) = 11.25t + 450 models the amount of money in Lexi’s account over time. Select all the statements that are true of this situation.
The number of months where they will both have same amount in their accounts is 40 months.
How to illustrate the information?From the information given, the function f(t) = 10t + 500 models the amount of money in Abby’s account over time and the function g(t) = 11.25t + 450 models the amount of money in Lexi’s account over time.
It should be noted that the number of years when there value will be the same is:
10t + 500 = 11.25t + 450
Collect like terms
11.25t - 10t = 500 - 450
1.25t = 50
Divide
t = 50/1.25
t = 40
In 40 months, Abby and Lexi will have same amount.
Note that an overview was given as the information is incomplete.
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Determine the values of m in the equation m2 = 16.
answers are
m = ±4
m = 4
m = ±8
m = 8
Answer:
I'll assume m2 is m^2
m = ±4
Step-by-step explanation:
1. m = ±4 m^2 = 16 YES. Both -4 and 4, when squared, are equal to 16
2. m = 4 This also works, but it doiesn't allow for the possibility that m is a -4
3. m = ±8 8^2 = 64 and (-8)^2 = 64 Don't work.
4. m = 8 8^2 = 64 Doesn't work.
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
Write a function to represent the data.
The data in the question will be represented by a geometric sequence given by 3 (2) ⁿ⁻¹.
A geometric sequence is defined as the sequence in which the ratio between the consecutive terms of the sequence remains constant. The ratio is known as common ratio. The nth term of geometric sequence is written as a (r)ⁿ⁻¹ where a is the first term, r is the common ratio and n is the number of terms. We know from the question that the time in minutes Aurora takes to complete the task forms a sequence as 3, 6, 12, 24.....
The common ratio of this sequence is given by 6/3 = 2. The first term being equal to 3. Now, for the nth term the sequence will be represented as
a (r)ⁿ⁻¹
=> 3 (2)ⁿ⁻¹
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Doug dives from a platform that is 5 meters above water. dive takes 1.8 meters below the surface of the water. How far does 's dive take ?
Doug dives a total distance of 6.8 meters from the platform to the bottom of the sea.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
We have been given that a Doug dives from a platform that is 5 meters above the water.
His dive takes him 1.8 meters below the surface of the water.
To determine the total distance Doug dived, add the height of the platform above water and the distance he dived below water.
= (5 + 1.8) meters.
= 6.8 meters.
Thus, Doug dives a total distance of 6.8 meters from the platform to the bottom of the sea.
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A chef bought 3 bags of oranges at the supermarket and it cost her $8.13. Write an equation that can be used to express the relationship between the total cost(t) and the number of bags of oranges(b) purchased.
Answer:
8.13=3b
Step-by-step explanation:
8 13 is the total cost and the bags of oranges are three.
compute, using integration, the area of a circle of radius r centered at the origin by considering this as the area of a region bounded by two curves.
The area of the circle of radius r centered at the origin is π[tex]a^{2}[/tex]
Since the circle is symmetrical in relation to the x and y axes, we can calculate the area of a quarter of a circle and multiply it by 4 to get the entire circle's area.
The equation y y = + mn [a 2 - x 2] must be solved.
Y = [a 2 - x 2] = a [1 - x 2 / a 2] is the equation for the upper semicircle (y positive).
Using integrals, we can calculate the area of the circle's top right quarter as shown below.
(1 / 4) Circle's area is equal to 0a a [1 - x 2 / a 2]. dx
Let's replace x/a with sin t to make sin t equal to x/a, dx equal to a cos t dt, and the area is given by
The formula for area of a circle is (1 / 4) Area of circle = 0/2 a 2 (1 - sin2 t) cos t dt
Now that t can range from 0 to /2, we utilize the trigonometric identity [1 - sin2 t] = cos t, which equals (1 / 4) Circle area equals 0/2 a 2 cos2 t dt.
To linearize the integrand, use the trigonometric equation cos2 t = (cos 2t + 1) / 2;
(1 / 4) Circle's area is equal to 0/2 a (cos 2t + 1) / 2 dt.
the integral (1 / 4) be evaluated. Circle's area is equal to (1/2) a2 [(1/2) sin 2t + t]. 0π/2\s= (1/4) π a 2
The circle's entire area is calculated by multiplying by 4.
Area of a circle is equal to 4 * (1/4) a 2 a 2. additional references on integrals and calculus applications.
Area of circle = 4 * (1/4) π a 2 = π a 2 More references on integrals and their applications in calculus.
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bro please
Which graph represents the inequality 2.5 is less than the product of −0.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
A graph represents the inequality 2.5 is less than the product of −0.5 and a number is: D. number line with open circle on point negative 5 and arrow shaded to the right.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.
In order to solve this word problem, we would assign a variable to the number and then translate the word problem into an algebraic equation as follows: Let x represent the number.
Translating the word problem into an algebraic equation, we have;
2.5 < -0.5x
Next, we would solve the given inequality as follows:
2.5/0.5 < -0.5x/0.5
5 < -x
x > -5
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let g be a translation 2 units up, followed by a reflection in the x-axis and vertical stretch by a factor of 4 of the graph of f(x)=x2
The equation the function after the transformation is g(x) = -4x² - 8
How to determine the transformation of the function?The equation of the function is given as
f(x) = x²
The sequence of transformations is given as follows:
Translate up by 2 unitsReflection across the x-axisVertically stretched by a factor of 4When the above transformations are combined, we have:
Translate up by 2 units: g(x) = f(x) + 2Reflection across the x-axis: g(x) = -(f(x) + 2)Vertically stretched by a factor of 4: g(x) = -4(f(x) + 2)So, we have
g(x) = -4(x² + 2)
Expand
g(x) = -4x² - 8
Hence, the function g(x) is g(x) = -4x² - 8
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1. Here is a graph of the equation 2y - X = 1:
The given the initial equation
[tex]2y-x=1[/tex]we can determine the part of the graph to be shaded if the equation changes to the inequality:
[tex]2y-x>1[/tex]If we make y the subject of the formula, such that
[tex]2y>1+x[/tex]Then we can put in the values of x and y at (0,0)
so that
[tex]\begin{gathered} 0>1+0 \\ 0>1 \end{gathered}[/tex]we can see that the expression is false because 0 is not greater than 1
Hence, we will shade away from the origin this means that we will shade above the line
The graph is shown below
So for question B
We will shade above the line
Question C
The points on the line are not included because the inequality does not include an equal sign
[tex]\begin{gathered} \text{Assuming the inequality were} \\ 2y-x\ge1 \\ \\ The\text{ points would have been inclusive because this inequality also have an equal sign } \end{gathered}[/tex]what is the slope of y=5x+7
Answer: 5
Step-by-step explanation: This equation appears in the Slope-Intercept form, which is Y=Mx+B. In which Y is the coordinate, M is the slope, X is the coordinate and B is the Y-Intercept, or where the line passes the Y-Axis.
Answer: the slope of this equation is 5
Step-by-step explanation: the term "5x" represents the slope of this equation.
slope-intercept form: y = mx + b
m = slope
b = y-intercept
Dion received a paycheck for $800.00 and he wants to invest it in a savings account. A savings account at bank A earns 8% interest compounded monthly and a savings account at bank B earns 9% simple interest. If Dion plans to deposit the $800.00 and leave it in the account for 2 years, at which bank would he earn more interest? A. bank B B. The interest earned cannot be calculated from the given information. C. bank A D. The interest earned at both banks will be the same.
Answer:
A. Bank B
Step-by-step explanation:
First the formulae necessary to calculate compound and simple interest
P = principal = amount deposited
r = interest rate as a decimal (i% interest => r = i/100)
t = number of years
n = number of times compounded
[tex]\text{Compound Interest }= P\left(1 + \dfrac{r}{n}\right)^{nt} - P[/tex]
In this case, we have P = 800
r = 8/100 = 0.08
n = 12 since the interest is compounded monthly
t = 2 years
So compound interest
[tex]CI = 800\left(1 + \dfrac{0.08}{12}\right)^{12 \times 2} - 800\\\\CI = 800(1.00667)^{24} - 800\\\\\\CI = 938.31 - 800\\\\CI = $138.31[/tex]
For Bank B, the interest is calculated at 9% annually and the interest is given by the formula
SI = P x r x t
SI = 800 x 0.09 x 2 (r = 9%/100 = 0.09)
SI = $144.00
So depositing in bank B is preferred
Which postulate or theorem proves A MNQA PNQ?
AAS
ASA
HL
SAS
Answer: AAS
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1/3 divided by 4/5 in the simplest form
Answer:
5/12
Step-by-step explanation:
answers are in the picture above
4(w − 971) = –384
w =
Stuck
Step-by-step explanation:
you can ask questions for clarification
How many gallons of water will be in the
fish tank after 3 minutes? Explain your
reasoning (HURRY I NEED THIS ANSWER STEP BY STEP )
As a result, 4.8 litres of water will be in the fish tank after three minutes if the water release rate is 1.6 gallons per minute.
What is the concept of Linear system?A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties. Linear systems are widely used in automatic control theory, signal processing, and telecommunications as a mathematical abstraction or idealization.
for 0.5 minutes , 0.8 gallons of water is required
To convert to gallons per minute, multiply by 2.
1.6 gallons per minute (0.8 x 2)
Gallons per minute multiplied by three minutes
3.0 minutes = 4.8 liters (1.6 x 3)
Therefore, 4.8 litres of water will be in the fish tank after 3 minutes if per minute water released is 1.6 gallons
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The complete question is:
How many gallons of water will be in the fish tank after 3 minutes? 0.5 mins = 0.8 gallons
what is negative five times negative one third
Answer:
The answer is to this problem is five over three
Please help me asap
y=2x+2 y=-1/2x-3 what is the solution?
•(-2,1)
•(-2,-2)
•(-2,-1)
•(2,-2)
Answer: (-2, -2)
Step-by-step explanation:
Since both equations are set equal to y,
[tex]2x+2=-\frac{1}{2}x-3\\\\\frac{5}{2}x=-5\\\\x=-2\\\\\implies y=2(-2)+2=-2\\\\\therefore (x,y)=(-2, -2)[/tex]
HELP ME PLEASE!!!! will give brainlist , thanks
Answer:
3
Step-by-step explanation:
1. Subtract 2 y-coordinates.
11 - 8 = 3
2. Subtract the corresponding x-coordinates in the same order.
-1 - (-2) = -1 + 2 = 1
3. slope = (difference in y)/(difference in x) = 3/1 = 3