The business owner should be told to angle a spotlight mounted on the roof at the angle of =39°
Calculation of angleThe distance of the flagpole from the building = 55ft
The building has the height of = 45ft
The flagpole has the height of = 25ft
The angle can be calculated using the formula;
Tan θ = opposite/adjacent
Where opposite= 45ft
adjacent = 55ft
Tan θ = 45/55 = 0.82
θ = Tan–¹0.82
θ = 39°
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y=x The point F is the foot of the perpendicular from the point (1, 9) to the line y=x. Find the coordinates of F.
Answer: (5,5)
Step-by-step explanation:
The perpendicular to y=x has slope -1, and thus the equation of the perpendicular from (1,9) is [tex]y=-x+10[/tex].
Finding the point where they intersect, since both equations are set equal to y, we know that -x+10=x, and thus x=5.
If x=5, then y=5 as well.
So, F has coordinates (5,5).
i need help please! I think I know the answer but for some reason my brain's telling me that it's wrong so if someone could explain how to get the answer so I can check that would be great.
Considering the slopes of the segments, the correct option is:
D. No, because the triangle ABC doesn't have a pair of perpendicular sides.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.Here, we have to find if there are perpendicular segments, that is, if two slopes multiplied have a value of -1, then:
mAB = (-7 - 9)/(11 - 1) = -8/5.mAC = (3 - 9)/(-9 - 1) = 3/5.mBC = (3 - (-7))/(-9 - 11) = -1/2.No sides are perpendicular, hence option D is correct.
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A group of 31 friends gets together to play a sport. First, people
must be divided into teams. Each team has to have exactly 3
players, and no one can be on more than one team. How many
teams can they make? (It is possible that not everyone can be on a
team.)
(Do not include units in your answer.)
The number of teams she can make is 10.
How many teams can she make?Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other basic mathematical operations include addition, subtraction, multiplication.
The number of teams that can be made can be determined by dividing the total number of friends by the total number of players in each team. The whole number that is derived from the division process is the number of teams teams that can be made given the total number of friends and the number of people that have to be in each group.
Number of teams she can make = total number of friends / number of people in each group
31 / 3 = 10 remainder 1
So, only 10 teams can be made. one person would not be on any team.
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rewrite each expression without using absolute value notation |7m-56| if m<8
Considering the definition of the absolute value function, the expression is written as -7m + 56.
What is the definition of the absolute value function?The absolute value function is defined as follows:
[tex]|x| = x, x \geq 0[/tex].[tex]|x| = -x, x < 0[/tex]That is, where the expression is negative, it is multiplied by -1, while where it is not negative the expression is kept.
In this problem, the expression is:
|7m - 56|
For m < 8, we have that one example is m = 0:
7(0) - 56 = -56.
The expression is negative, hence the signal is changed, that is:
|7m - 56| = -(7m - 56) = -7m + 56.
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For the graph x = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is undefined and the slope of the perpendicular line is 0
How to determine the slope?The equation is given as:
x = 1
The above do not have any y value.
This means that the slope of the line is undefined
i.e.
m = undefined
The slope of the parallel line is:
Slope = m
This gives
Slope = undefined
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/undefined
Slope = 0
Hence, the slope of the parallel line is undefined and the slope of the perpendicular line is 0
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Which of the following equations describes the graph?
Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.
The base graph has been shifted down 90 units.
The base graph has been shifted right 90 units.
The base graph has been shifted left 90 units.
The base graph has been shifted up 90 units.
Using translation concepts, the change of f(x) = x to g(x) = x - 90 can be described as follows:
The base graph has been shifted down 90 units.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have that g(x) = f(x) - 90, that is, the base graph was shifted down 90 units.
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A rectangular park is 70 meters wide and 120 meters long. Give the length and width of another rectangular park that has the same perimeter but a smaller area.
Answer:
1 m by 189 m
Step-by-step explanation:
The perimeter is 2(70+120)=380.
The area is (70)(120)=8400.
If we let the park have a width of 1 meter and a length of 189 meters, then the area will be 189 square meters, which is smaller than 8400 square meters, as required.
Finding a sunken submarine in the middle of the ocean using Bayes' theorem: the search for the Scorpion.
Finding a sunken submarine in the middle of the ocean using Bayes' theorem to the search for USS Scorpion.
In the event of a missing vessel or aircraft at sea, in this case a submarine, Bayes search theorem can be applied.
The ocean using Bayes' theorem: the search for the Scorpion.
In May 1968, the U.S. Navy's nuclear submarine USS Scorpion (SSN-589) failed to arrive as expected at her home port of Norfolk. The command officers of the U.S. Navy were nearly certain that the vessel had been lost off the Eastern Seaboard, but an extensive search there failed to discover the remains of Scorpion.Then John P. Craven, a Navy deep-water expert, proposed that Scorpion had sunk somewhere else. Based on a contentious approximation of hydrophone triangulation, Craven organized a search southwest of the Azores. He was only given one ship, Mizar, and to make the most of his resources, he sought help from a team of consulting mathematicians. A Bayesian search approach was used. To develop theories regarding what might have led to Scorpion's loss, veteran submarine commanders were questioned.What is Bayes' theorem?
Bayes' theorem is a theorem in probability theory. It is a trivial consequence of the definition of conditional probability.Bayesian search theory is the application of Bayesian statistics to the search for lost objects.Learn more about Bayes' theorem
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Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
The theorem that would be included in the proof is: CPCTC theorem.
What is the CPCTC Theorem?CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.
To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:
1. angle D ≅ angle F [given]
2. angle DBE ≅ angle ECF [given]
3. side DE ≅ side EF [given]
4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]
5. DB ≅ FC [by the CPCTC theorem]
With the given proof, we can state that side DB is congruent to side FC.
Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.
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Lie is solving the quadratic equation by completing the square. 3x2 18x – 8 = 0 3x2 18x = 8
Answer: The answer is factor 3 out the variable terms
Step-by-step explanation:
A recent survey at a local company showed that 300 employees, or 66⅔% of the company’s employees, carpool to work each day. How many employees work at this company?
I'm sorry for all this trouble just really need help I'm in summer school because I was gone most of the school year and its all online so i don't understand anything
Answer:
450 employees work at this company.
Step-by-step explanation:
300 = 2/3 of x
300 × 3 = 2x
900 = 2x
450 = x
Select the correct answer from the drop-down menu.
Consider the equation and the graph.
2/x+4 = 3² + 1
Answer:
x=1/3
Step-by-step explanation:
(2/x)+4=3^3+1
(2/x)+4=10
(2/x)=6
2=6x
1/3=x
x=1/3
There is also a possibility that you meant to write 2/(x+4)=3^2+1
2/(x+4)=3^2+1
2/(x+4)=10
2=10x+40
-38=10x
x=-3.8
Answer: -35/16
Step-by-step explanation:
i just took the test:)
Write the slope-intercept equation of the line that passes through the given points (1,-7),(5,-15)
Answer:
y=-2x+5
Step-by-step explanation:
The slope is
[tex] \frac{ - 15 - ( - 7)}{5 - 1} = \frac{ - 8}{4} = - 2[/tex]
Substituting into point-slope form,
y + 7 = -2(x-1)
y + 7 = -2x + 2
y = -2x + 5
What does 6 * b equal??
Answer:
6b
You can just simply combine the variable, 6, and the coefficient, b.
An angle has turn through 15 one-degree angle. what is a measurement of this angle in degrees
The measurement of the angle is 15° (if initial angle is 0°).
Turning Through One-degree Angles
An angle is said to have an angle measure of n degrees if it rotates across n one-degree angles. Since turning through one degree means making an angle of one degree, every time you take a turn of one degree, you rotate through one degree more. Thus, turning through n one-degree angles give rise to an angle of n degrees.
Measurement of the Angle
It is given that the angle has turned through 15 one-degree angles. Thus, the angle will turn through 15°.
Let us assume the initial angle to be x°.
Then, the new angle after 15 one-degree turns would be (x+15)°
If initial angle, x = 0°, the measurement of the angle formed is 15°.
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The pressure, p, with which water passes through a pipe varies inversely as the square of the pipe's radius, 2. If k is the constant of
variation, which equation represents this situation?
Opr²-k
Op=r²2²+k
Op+r²2²=k
Op=kr²
The variation equation is p = kr^2
How to determine the variation equation?The variables are give as:
Pressure = P
Radius= r
The direct variation from p to the square of r is represented as:
[tex]p\ \alpha\ r^2[/tex]
Express as an equation
p = kr^2
Where k represents the constant of variation
Hence, the variation equation is p = kr^2
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Answer:
The correct answer is the 3rd option
Find the distance between the pair of points: (3,1) and (4,-5).
Answer:
9.2195445 (9.22 rounded)
Step-by-step explanation:
#1: Use the distance formula to determine the distance between the two points:
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
#2: Substitute the actual values of the points into the distance formula:
[tex]\sqrt{((-4)-3)^{2}+(5-(-1))^{2}}[/tex]
#3: Simplify:
- Subtract 3 from -4: [tex]\sqrt{(-7)^{2}+(5-(-1))^{2}}[/tex]
- Raise -7 to the power of 2: [tex]\sqrt{49+(5-(-1))^{2}}[/tex]
- Multiply -1 by -1: [tex]\sqrt{49+(5+1)^{2}}[/tex]
- Add 5 and 1: [tex]\sqrt{49+6^{2}}[/tex]
- Raise 6 to the power of 2: [tex]\sqrt{49+36}[/tex]
- Add 49 and 36: [tex]\sqrt{85}[/tex] (Decimal form: 9.2195445 (9.22 rounded))
The distance between the two points (3,1) and (4,-5) is 9.22.
During the summer, jody earns $10 per hour babysitting and $15 per hour doing yardwork. this week she worked 34 hours and earned $410. if x represents the number hours she babysat and y represents the number of hours she did yardwork, which system of equations models this situation? a. x y = 34 10x 15y = 410 b. x y = 410 10x 15y = 34 c. x y = 34 15x 10y = 410 d. x y = 410 15x 10y = 34
The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.
According to the statement
we have given that the
Jody earns $10 per hour babysitting And jody earns $15 per hour doing yardwork.
And she worked 34 hours and earned $410
and we have to express in the linear equation terms.
So, For this purpose,
Let x represents the number hours she babysat
Let y represents the number of hours she did yardwork
And the equations become
x + y = 34.
10x + 15y = 410
And with the help of these linear equations we find the hours which are x and y.
So, The above written equations perfectly express the given conditions in the statement.
The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.
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A sample of 337 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according to major ("biology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below.
Using it's concept, the relative frequency of business majors in the sample is of 0.16 = 16%.
What is a relative frequency?
A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 337 students, of which 30 + 24 = 54 students are business majors, hence the relative frequency is:
r = 54/337 = 0.16 = 16%.
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. Distribute the among the atoms, giving ( for hydrogen) to as many atoms as possible. First get electrons atoms, then atoms.
Answer:
Bonding theories predict
Step-by-step explanation:
how atoms bond together to form compounds. They predict what combinations of atoms form compounds and what combinations do not. Bonding theories explain the shapes of molecules, which in turn determine many of their physical and chemical properties
When positive integer x is divided by positive integer y, the remainder is 9. If = 96.12, what is the value of y ? 96 75 48 25 12
Y= 75.
Lets try to solve it,
When positive integer x is divided by positive integer y, the remainder is 9
=> x=qy+9;
=> x/y=96.12
=>x=96y+0.12y (so q above equals to 96);
=>0.12y=9
=> y=75.
Hence the value of y would be 75.
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Given the function f(x) = -x - 3x², find the value of f(1/2) in simplest form.
Answer:
-5/4
Step-by-step explanation:
To evaluate the function, put the value of the argument where the variable is and do the arithmetic.
Function evaluationf(x) = -x -3x²
f(1/2) = -(1/2) -3(1/2)² = -1/2 -3(1/4) . . . . . use 1/2 in place of x
f(1/2) = -2/4 -3/4 = -5/4
The value in simplest form is ...
f(1/2) = -5/4
Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?
The table that describes the behavior of the graph of f(x) = 2x3 – 26x – 24 is known to be table B.
What is the function about?To be able to tell the function one need to use a graphing tool and see the attached figure to better tell and know the problem.
The Relation of graph to the x-axis are shown below
Interval (-∞,-3)- below (the function is said to be negative) - x axisInterval (-3,-1) - above (the function is said to be positive) - x axisInterval (-1,4)- below (the function is said to be negative)- x axisInterval (4,∞) - above (the function is said to be positive) - x axisNote also that in the image attached, the vertical line is the y-axis and the horizontal line is the x- axis.
Hence, the table that describes the behavior of the graph of f(x) = 2x3 – 26x– 24 is known to be table B.
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Answer:
B
Step-by-step explanation:
Can you plssss help !!!
The parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.
Parts of the circle shown in the imageThe following are the parts of the circle shown;
Chord: the length DC and DG represent the chord of the circleDiameter: the length HF represent the diameter of the circleRadius: the length HA and FA represents the radius of the circletangent: the line JB represents a tangent to the circleCenter: point A represents the center of the circleThus, the parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.
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Consider the following pair of equations:
y = x + 4
y = −2x − 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Source
StylesFormatFontSize
Answer:
(-2, 2)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x+4\\y=-2x-2 \end{cases}[/tex]
To solve by substitution, substitute the first equation into the second equation:
[tex]\implies x+4=-2x-2[/tex]
Add 2x to both sides:
[tex]\implies x+4+2x=-2x-2+2x[/tex]
[tex]\implies 3x+4=-2[/tex]
Subtract 4 from both sides:
[tex]\implies 3x+4-4=-2-4[/tex]
[tex]\implies 3x=-6[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3}=\dfrac{-6}{3}[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=-2+4[/tex]
[tex]\implies y=2[/tex]
Therefore, the solution to the given system of equations is (-2, 2).
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Substitute y value from first eqn in second equation
y=-2x-2x+4=-2x-23x=-6x=-2Put in first one
y=-2+4=2(-2,2) is the solution
find the only one digit number that is both a square number and a cubic number
Answer:
the only one digit number that is cube and square would be 1
Step-by-step explanation:
because 1 x1 = 1 and 1×1×1= 1
no other one digit number is both a square number and cubic number :)
hope it helps please let me know if you need more help :)
The sum, s, of 4 consecutive odd integers can be represented by the equation s = 4n â 12. what does n represent?
The variable n represents the smallest of the four integers.
How to interpret what n represents?The given parameters are
Number of consecutive odd integers = 4
Sum of consecutive odd integers= s
Where
S = 4n - 12
The variable n represents the smallest of the four integers.
In the sense that, the consecutive odd integers are
n, n + 2, n + 4 and n + 6
Hence, the variable n represents the smallest of the four integers.
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the graph of the derivative of a function f crosses the x-axis 3 times. what does this tell you about the graph of f
Answer:
the graph of f has 3 turning points
Step-by-step explanation:
The graph of a function has a turning point (local extreme) where the derivative is zero and changes sign.
DerivativeThe derivative of a function tells you the slope of that function's graph. When the derivative is positive, the function is increasing. When the derivative is negative, the function is decreasing.
Turning PointWhere the derivative changes sign from positive to negative, the graph of the function changes direction from increasing to decreasing. At the point where the derivative is zero (between positive and negative), the graph is neither increasing nor decreasing. A tangent to the function at that point is a horizontal line, and the function itself is at a local maximum, a turning point.
The reverse is also true. When the derivative changes sign from negative to positive, the function changes from decreasing to increasing. The turning point where that occurs is a local minimum.
3 CrossingsIf the derivative crosses the x-axis (changes sign) 3 times, then there are three local extremes in the graph of f. The graph of f has 3 turning points.
__
Additional comment
In the attached graph, we have constructed a derivative function (red) that crosses the x-axis 3 times. It is the derivative of f(x), which is shown in blue. The purpose is to show the local extremes of f(x) match the zero crossings of the derivative.
A marble has a mass of 5 grams. juan has 17 marbles in his bag.
what is the total mass of the marbles?
o a. 22 grams
o b. 55 grams
o c. 57 grams
o d. 85 grams
Answer:
85 grams
Step-by-step explanation:
Marble: 5 g/marble
17 marbles in a bag: (17 marbles)*(5 g/marble) = 85 grams/bag of 17 marbles
Pls help me on 103 :((
Answer:
J) [tex]18cm^2[/tex]
Step-by-step explanation:
a square inscribed in a circle means that the radius of the circle is the same thing as a line drawn from the center of the square to a corner.
this will give you the side measurements for a triangle (look at the attached picture). now use the Pythagorean theorem to find the hypotenuse aka the side length of the square. then multiply it by itself.
Answer: H
Step-by-step explanation:
Finding the DiameterIf we draw a line through a diagonal of the square, two triangles are formed. The angle opposite the diagonal is 90°, as all angles are 90° in a square. One of the properties of a circle state that the angle in a semicircle is always 90°, which means that the diagonal formed a semi-circle.
A semi-circle only forms when a diameter is drawn in a circle, making the diagonal a diameter. This will be useful information, as we can calculate the side length of a square using the length of its diagonal.
A diameter is just twice the length of a radius, so the diagonal of the square would be 6 cm.
[tex]2*3=6[/tex]
Finding the Length of One SideThe diagonal also splits the square into two 45-45-90 triangles. These triangles have a special property that their hypotenuse is √2 times each leg, and all legs are the same length.
Therefore, we can calculate the length of a leg by dividing the hypotenuse by √2.
[tex]\frac{6}{\sqrt{3}}[/tex]
The length of one side of the square is [tex]\frac{6}{\sqrt{3}}[/tex]
Finding the AreaAs we already know the length of one side, we can just square it to get the area.
[tex](\frac{6}{\sqrt{3}})^2[/tex]
[tex]\frac{6^2}{(\sqrt{3})^2}[/tex] [Properties of Exponents]
[tex]\frac{36}{3}[/tex]
[tex]12[/tex]
Hence, the area of the square is 12 cm².