By using trigonometry, we conclude that the horizontal distance is 785.15ft
How to find the horizontal distance?We can think of this as a right triangle.
Where the height of the observation deck is one cathetus and the horizontal distance is the other cathetus,
We know that the depression angle when looking from above is 42°. If we step on this angle, the adjacent cathetus is the height of the deck, then the horizontal distance is the opposite cathetus.
Then we can use the relation:
tan(a) = (opposite cathteus)/(adjacent cathetus).
Replacing what we know:
tan(42°) = (distance)/(872ft)
tan(42°)*872ft = distance = 785.15ft
The horizontal distance is 785.15ft
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Pretest: Manipulating and Interpreting Expressions
Drag each expression to the correct location on the table.
Place each algebraic expressions next to its corresponding verbal description.
5³-²-1 (5-4)³
the difference of 5 times the cube of x cubed and
the quotient of 4 times x and 3
5 times the cube of x divided by 4 times x
the quotient of the difference of 5 times x cubed and 4 and x
the cube of the difference of 5 times x and 4
Submit
Answer:
9
Step-by-step explanation:
0
Question Progress
Find the following, giving your answers
to 1 decimal place.
10 cm/
Homework Progress
17/21 Marks
6 cm
8 cm
a) The volume of the cone.
b) The curved surface area of the cone.
Vol = ²
Curved
surface area
Answer:
[tex]\pi \times radius \times hieght[/tex]
A rectangular tank measures 1.2m by 0.8m by 0.5m.
(a) Water flows from the full tank into a cylinder at a rate of 0.3m3
/min.
Calculate the time it takes for the full tank to empty.
Give your answer in minutes and seconds.
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
How to determine the draining time of a rectangular tank
In this question we must determine the draining time of a tank whose dimensions are known and whose water outflow is stable. The draining time is equal to the volume of the rectangular tank divided by outflow rate:
V = (1.2 m) · (0.8 m) · (0.5 m)/(0.3 m³/min)
V = 1.6 min
By knowing that water outflow is stable and the known geometry, the draining time of the rectangular tank is equal to a time of a minute and 36 seconds.
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The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?
The complete question is
"The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?
a. The domain of this function represents the total cost for a job
b. H is a function of C
c. The painter charges a $35 service fee in addition to an hourly rate
d. The painters hourly rate is $35.00"
The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. So, the correct option is D. The painters hourly rate is $35.00
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours.
The fixed fee, or service fee, is $60.
$35 is the hourly fee since in the function, it is 35 that is multiplied by the number of hours.
So, the correct option is D. The painters hourly rate is $35.00
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Sunil draws a regular hexagon and a convex quadrilateral on a sheet of paper, so that no side of the quadrilateral lies on the same line as a side of the hexagon. what is the maximum total number of points in which the sides of the quadrilateral can intersect the sides of the hexagon?
Maximum total 8 points in which the sides of the quadrilateral can intersect the sides of the hexagon.
A regular hexagon is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal.
A convex quadrilateral is a four-sided polygon that has interior angles that measure less than 180 degrees each. The diagonals are contained entirely inside of these quadrilaterals
Take a look at just one side of the quadrilateral—a straight line. Since we are told that no side of the quadrilateral lies on the same line as a side of the hexagon, the maximum number of times a side of the quadrilateral could intersect the hexagon is 2. We can use a ruler to test this on the image of the hexagon. There is no way to pass a straight line through the hexagon and have it intersect the shape more than 2 times. Therefore, the maximum number of points at which the quadrilateral could intersect the hexagon would be
at 2 points per side, at 2 × 4 = 8 points.
Hence, Maximum total 8 points in which the sides of the quadrilateral can intersect the sides of the hexagon.
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Please help me smart peeps
Determine if the two triangles below are similar and state how you know.
The first and foremost rule for determining if 2 triangles are similar is checking if their angles are the same. Obviously, in this example, the angles are completely different, so the triangles are not similar.
Have a nice day!
And good luck on the assignment!
Triangle abc is represented. points d and f are marked on side ab and points e and g are marked on side ac. segments de and fg are drawn.
if , then line segment
is parallel to line segment
.
If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.
Given There is a triangle abc.
Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.
Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.
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Answer:D-E is parallel to FG which is parallel to B-C meaning all three are parallel
Step-by-step explanation:
What is necessary to determine the z-score for a raw score in a particular set of scores?.
Answer:
See below
Step-by-step explanation:
The mean score and the standard deviation are needed
change 5/8 to percentage
Answer: 62.5%
Step-by-step explanation:
First, you must simplify 5/8 into a decimal and then multiply that by 100 to get the percentage of the fraction.
[tex]\frac{5}{8}=0.625[/tex] [tex]0.625*100=62.5[/tex]%
I hope this helps!! Pls give brainliest :)
Given that log (p, x) =20 and log (p, y) =5 find log (x, y)
Answer:
1/4
Step-by-step explanation:
The change of base formula for logarithms is ...
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]
__
Using this with the given values, we have ...
[tex]\log_x(y)=\dfrac{\log_p(y)}{\log_p(x)}=\dfrac{5}{20}\\\\\boxed{\log_x(y)=\dfrac{1}{4}}[/tex]
Find the mean of the following group of numbers: 6. 1, 5. 9, 4. 2, 5. 9, and 10. 7. Round your answer to the nearest tenth
Answer:
6.6
Step-by-step explanation:
the "mean" of a data set is what we commonly refer to as the average. We find this estimate of values by adding up all of the values of the data set, and then dividing by the number of values we added together.
{for example: the mean [average] of 1, 5, 6:
1 + 5 + 6 = 12
12 ÷ 3 [we have 3 numbers] = 4}
our values:
6.1 ; 5.9 ; 4.2 ; 5.9 ; 10.7
> 6.1 + 5.9 + 4.2 + 5.9 + 10.7 = 32.8
[we have 5 numbers]
32.8 / 5 = 6.56
when rounding a number, we look to the digit one place to the right. If it is greater than or equal to 5, we "round up" our digit [we move it up to the next digit]
if it is less than 5, we keep our digit the same
(the tenths place = _ . _ _ _ ones. tenths)
so if we round 6.56 to the nearest tenth:
6.56
[6 > 5]
6.6
So, the mean of this data set rounded to the nearest tenth is 6.6
hope this helps!!
what does a equal if 2÷a=(5/2)÷(5/4)
Question:
2÷a=(5/2)÷(5/4)
Answer:
a = 1
I’m confused I need help
Answer:
x-intercept: -4
Step-by-step explanation:
It's where the slope intercepts with the x-axis
Answer:
Step-by-step explanation:
x-intercept: the x-value is that when y = 0: (-4, 0).
y-intercept: the y-value when x = 0: (0, 5)
1
2
3
Click on each graph to enlarge it.
4
Suppose f(x) = x. Find the graph of f(x) + 4.
Click on the correct answer.
graph 1
graph 3
↓
graph 2
graph 4
Answer:
its most likley graph 4
Step-by-step explanation:
hope this helps and if its wrong im very sorry
Joe has an ice cream stand. last week he spent $85 for ice cream and supplies. he earned $125. what was his profit?
Answer:
40 dollars
Step-by-step explanation:
Profit is what he earned minus his costs
Profit = 125 -85
Profit = 40
x= help me please thank u :)
Step-by-step explanation:
the product of segments theorem :
products of segments of intersecting chords are equal.
the 2 chords helping us are
the "4 + 25" chord.
the "x + x" chord (that connects then outwards to the 20 segment).
so, based on that theorem
4 × 25 = x × x
100 = x²
x = sqrt(100) = 10
What is the equation of the line that is parallel to y=x+4 and that passes through (5,–4)?
Answer:
y = [tex]\frac{1}{5}[/tex] x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{5}[/tex] x + 4 ← is in slope- intercept form
with slope m = [tex]\frac{1}{5}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{1}{5}[/tex] x + c ← is the partial equation
to find c substitute (5, - 4 ) into the partial equation
- 4 = 1 + c ⇒ c = - 4 - 1 = - 5
y = [tex]\frac{1}{5}[/tex] x - 5 ← equation of parallel line
What’s not located on a coordinate plane?
Answer:
umm a plane that's all.
dangit and I don't know
Which formula can be used to describe the sequence? f(x) = 1.2(2.5)x – 1 f(x) = 2.5(1.2)x – 1 f(x) = 1.2(2.5)x f(x) = 2.5(1.2)x
The formula which used to describe the sequence is f(x)=1.2(2.5)ˣ⁻¹.
The given sequence is 1.2,3,7.5,18.75.
In geometric series, the ratio of two consecutive terms remains the same and this ratio is known as common ratio. a₁ is the first term of a geometric sequence and r is the common ratio, then the general term of the geometric sequence is of the form:
f(x)=a₁⋅rˣ⁻¹.
In the given sequence, a₁=1.2, a₂=3, a₃=7.5 and a₄=18.75.
Find the common ratio by
r=(aₙ₊₁)÷aₙ
r=a₂÷a₁
r=3÷1.2
r=2.5
Substitute the values in the general formula of geometric sequence.
f(x)=(1.2)(2.5)ˣ⁻¹
Hence, the formula which used to describe the sequence 1.2,3,7.5,18.75 is f(x)=(1.2)(2.5)ˣ⁻¹.
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If a(x) = 3x + 1 and b (x) = square root of x-4, what is the domain of (b o a)(x)
( 1, ∞) is the domain of (b o a)(x)
What is Function?
A function is defined as a relation between a set of inputs having one output each.
According to the question,
[tex]a(x) = 3x + 1 \\\\b (x) =\sqrt{x+4}[/tex]
To find the domain of the composite function,
[tex](b o x) (x) = b(a(x))\\\\(b o x) (x) = b(a(3x-1))\\\\(b o x) (x) = \sqrt{3x+ 1 -4} \\\\(b o x) (x) = \sqrt{3x -3}\\\\[/tex]
Therefore,
[tex]3x - 3 \geq 0\\3x \geq 3\\x \geq 1\\\\[/tex]
Hence , [ 1, ∞ ] is is the domain of (b o a)(x).
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Find the sum of the first 7 terms of the following sequence 3,-5,25/3 Round to the nearest hundredth if necessary.
This is a geometric sequence with first term 3 and a common ratio of -5/3.
Using the sum of a geometric series formula,
[tex]\frac{3(1-(-5/3)^{7}}{1-(-5/3)} \approx \boxed{41.31}[/tex]
Which statements are true about the linear inequality y > three-fourthsx – 2? select three options.
The statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
What is linear inequality?Linear inequality is defined as the comparison of two values using greater than, less than, greater than or equal to, and less than or equal to.
Using the general formula for linear inequality,
y >mx+ b
y > 3/4x - 2
Where m = slope of the graph
b = interception at y axis
Therefore, the statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
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Find the reflection of the point (25, 25) across the y-axis.
Answer:
(-25, 25)
Step-by-step explanation:
let me know if you want an explanation!
Dilate the figure by the scale factor. Then enter the new coordinates.
K= 2
Answer:
A(2, 8)
B(4, 4)
C(-4, 2)
Step-by-step explanation:
Multiply all the coordinates by 2
Match the following reasons with the statements to complete the following proof.
In order to proof that ∠ ABC + m ∠DBE = 180° the correct proof is given as follows:
m ∠CBD - m ∠DBE - Given ∠ABC, ∠CBD are supplementary - Given by the definition of supplementary angels. m ∠ABC + m ∠CBD = 180° - this is is also based on exterior sides in opposite raysm ∠ABC + m ∠DBE = 180° because of the substituted angles.QEDWhat is a supplementary angle?Supplementary angles comprise of angles that are on a straight line and which must add up to 180°
It is right to state therefore, that ∠ABC, ∠CBD are supplementary angels.
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The composite figure is made up of a parallelogram and a rectangle. Find the
area. (choices in picture)
Answer:
88 sq. units
Step-by-step explanation:
1st. BxH
12-4 = 8 is our Base
8x8=64 that is out 1st area
and 2nd area is LxW which is 12x2 = 24
64+24= 88 sq. units
Answer two questions about system a and b
Answer:
Question 1: A. Replace one equation with a multiple of the other equation
Question 2: B. No
Step-by-step explanation:
1) How can we get System B from System A?
Choose 1 answer:
A. Replace one equation with a multiple of the other equation
B. Replace one equation with a multiple of itself
C. Swap the left-hand sides of both equations
D. Swap the order of the equations
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
Choose 1 answer:
A. Yes
B. No
The answer to both questions is in bold and in the "Answer" section.
Hope this helps!
If not, I am sorry.
All of the details to the question are in the picture that is attached in this question, please helpp
Answer:
10
Step-by-step explanation:
The arc length of the semicircle is
a+(a+1)+(a+2)+(a+3)+(a+4)=5a+10As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.
So,
(42/180)(5a+10)=a+442(5a+10)=180(a+4) [multiply both sides by 180]210a+420=180a+720 [distributive property]30a+420=720 [subtract 180a from both sides]30a=300 [subtract 420 from both sides]a=10 [divide both sides by 30]2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?
The value of x is 77 cm which will make the triangles similar by SSS similarity theorem
Given length of the three sides of one triangle are 35 , 20 and 20
and length of the three sides of another triangle are x, 44,44
We need to find the values of x by using SSS Similarity theorem
We know that triangles are are similar by side - side - side similarity creation and hence the sides are in the same ratio
As both the triangles are isosceles triangles
Therefore ,
x/35 = 44/20=44/20 (Using ratio)
Solving the equation we get
x=44*35/20
x= 77
Hence the value of x is 77cm
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Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
The resulting polynomial when 5x -6 is subtracted from 3x² -6x +2 is; 3x² -11x +8.
What is the result of the polynomial subtraction?It follows from the task content that the polynomial 5x -6 is to be subtracted from 3x² -6x +2.
Hence, the subtraction goes thus; 3x² -6x +2 -(5x-6).
Hence, 3x² -6x +2 -5x+6
= 3x² -11x +8.
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