surface area of a square pyramid with side length 6 yd and slant height 7 yd
Answers
Check the picture below.
so the pyramid is really 4 triangular faces with a base of 6 and a height of 7, and a 6x6 square at the bottom.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangular faces}}{4\left[\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{7}) \right]}~~ + ~~\stackrel{square}{(6)(6)}}\implies 84~~ + ~~36\implies 120~yd^2[/tex]
Answer:
127.38
Step-by-step explanation:
The surface area formula for a square pyramid is:
A = a^2 + 2a * sqrt[ (a^2 / 4 ) + h^2 ]
So we input the base height as the a value, and the slant as H)
A = 6^2 + 2(6) * sqrt[ (6^2 / 4 ) + 7^2 ]
When using the exponents we get:
A = 36 + 2(6) * sqrt[ (36) / 4 ) + 49 ]
Then multiply/divide:
A = 36 + 12 * sqrt[ (9) + 49 ]
Then add the value in the sqrt.
A = 36 + 12 * sqrt[ 58 ]
Now, if we find the sqrt of 58, we get: sqrt[ 58 ] ≅ 7.615
A = 36 + 12 * 7.615
When multiplying we get:
A = 36 + 91.38
Finally, after adding, the surface area of the square pyramid is:
A = 127.38
Related Questions
If investments double every 9 years and you start with a $600 investment, how much money would you have after 27 years? First, complete the equation: Future Amount = 600 (1 + [?]) ↑ ↑ initial amount growth rate Hint: Doubling means a 100% growth rate. time periods Enter
Answers
Answer:
600(1+1)^3 with future amount being 4800
Step-by-step explanation:
The amount of the money after 27 years will be $4800.
What is the amount?The quantity of money anyone has is termed as the amount. The solution to the question is given as follows:-
Given that investments double every 9 years and you start with a $600 investment. how much money would you have after 27 years?
We know that the amount is getting double in every 9 years so the number of times the amount will get doubled will be = 27 / 9 = 3
Future amount = 600(1+1)³
Future amount = 600 ( 2 )³
Future amount = 600 ( 8 ) = $4800
Therefore the amount of the money after 27 years will be $4800.
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Odette made this jewelry box by combining two rectangular boxes.
What is the total surface area of this jewelry box?
PLS HURRY WILL GIVE BRAINLIEST
Answers
Adding the sides up we get, 36+36+72+24+24+24+32+48+48+48
What is the measure of angleq to the nearest whole degree? 43° 49° 53° 58°
Answers
Based on the calculations, the measure of angle Q to the nearest whole degree is equal to 53°. The correct answer is option C.
The complete question is attached with the answer below.
How to calculate the measure of angle Q?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Based on the triangle attached in the image above, we can deduce the following parameters:
Side QM = 18 units.
Side MN = 17 units.
Side QN = 20 units.
In this scenario, we would apply the cosine trigonometry function to determine the measure of angle Q:
MN² = QM² + QN² - 2(QM)(QN)cosθ
17² = 18² + 20² - 2(18)(20)cosθ
289 = 324 + 400 - 720cosθ
720cosθ = 724 - 289
720cosθ = 435
θ = cos⁻¹(435/720)
θ = cos⁻¹0.6042
θ = 52.8 ≈ 53°.
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Think about the function f(x) = 3 - 2x.
What does the notation f(0) mean?
Answers
3 - (2*0) => 3-0 = 3
so the answer is 3
Answer:
the answer is 3
In a diving contest five judges score each dive. the highest and lowest scores are discarded and then the arithmetic average of the remaining scores is taken as the diver's score. if the five judges score a dive as 6.0, 6.3, 6.2, 6.8, and 6.1, then the diver's score is?
Answers
Using the given information, the diver's score is 6.2
Calculating average scoreFrom the question, we are to calculate the diver's score
From the given information,
The five judges score a dive as 6.0, 6.3, 6.2, 6.8, and 6.1.
Since the highest and lowest scores are discarded
Then, we will discard 6.8 and 6.0
The remaining scores are 6.1, 6.2, and 6.3
Now, the diver's score will be the average of the remaining scores
∴ The diver's score = (6.1 + 6.2 + 6.3) /3
The diver's score = 18.6 / 3
The diver's score = 6.2
Hence, the diver's score is 6.2
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This line plot shows the estimated amount of glue needed for summer projects at a camp. eric chose to complete a project with the greatest estimated amount of glue needed. the actual amount of glue he used was 3/4 of the estimated amount. how much glue did eric use for his project? enter your answer in the box as a mixed number in simplest form.
Answers
The amount of glue that eric used for his project is [tex]\mathbf{ 1\dfrac{11}{16}}[/tex]
How to interpret the line plot?The interpretation of the line plot involves a careful approach to how a series of data points are connected on coordinate planes.
From the Glue for summer project line plot:
The greatest estimated amount of glue needed can be seen at = 2 (1/4)The actual amount of glue needed = 3/4 of 2 (1/4)The amount of glue Eric used for the project is;
[tex]\mathbf{=\dfrac{3}{4}\times 2\dfrac{1}{4}}[/tex]
[tex]\mathbf{=\dfrac{3}{4}\times \dfrac{9}{4}}[/tex]
[tex]\mathbf{=\dfrac{27}{16}}[/tex]
[tex]\mathbf{= 1\dfrac{11}{16}}[/tex]
Therefore, we can conclude that the amount of glue used by Eric for this project is: [tex]\mathbf{ 1\dfrac{11}{16}}[/tex]
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HELP ME PLEASE I WILL MARK BRAINLIEST
Answers
Answer:
A) -4, -2
Step-by-step explanation:
The translation vector is the distance
point A: (3, 1)
point A': (-7, -3)
3 + (-7) = -4
1 + (-3) = -2
Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 35% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
Answers
Answer:
Based on the data given on Northlake High School, we can infer that B. A greater percentage of second-lunch students (39%) eat outside.
What does the data on the First and Second lunches show?
The percentage of second-lunch students who eat outside is:
= Second lunch students who eat outside / Second lunch students
Solving gives:
= 0.18 / 0.46 x 100%
= 0.3913 x 100%
= 39%
This shows that the percentage of students eating their second lunch outside is 39%.
so the answer is B
Step-by-step explanation:
Helppppppppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
what is 100+24/4*12?????????????? due is 5 minutes plsssssssssssssss
Answers
Answer:
172
Step-by-step explanation:
100 + 24 ÷ 4 × 12
Remember PEMDAS
100 + 6 × 12
100 + 72
172
Hope this helps!
Write the equation of the trigonometric graph.
Answers
Answer:
[tex]f(x)= \sin(6x)+3[/tex]
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
[tex]f(x) = \sf A \sin (B(x + C)) + D[/tex]
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftThe parent function y = sin(x) has the following:
Amplitude (A) = 1Period = 2πPhase shift (C) = 0Vertical shift (D) = 0Mid-line: y = 0From inspection of the given graph:
Amplitude (A) = 1[tex]\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}[/tex]Phase shift (C) = 0Vertical shift (D) = +3 (as mid-line is y = 3)[tex]\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6[/tex]
Substituting the values into the standard form:
[tex]\implies f(x) =1 \sin (6(x + 0)) + 3[/tex]
[tex]\implies f(x) = \sin (6x) + 3[/tex]
Therefore, the equation of the given trigonometric graph is:
[tex]f(x)= \sin(6x)+3[/tex]
Answer(s):
[tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3 \\ y = -sin\:(6x \pm \pi) + 3 \\ y = sin\:6x + 3[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{12}} \hookrightarrow \frac{\frac{\pi}{2}}{6} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cos\:6x + 3,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{12}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{12}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{12}} = \frac{\frac{\pi}{2}}{6}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-\frac{5}{12}\pi, 2],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{12}, 2],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{3}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{3}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 3,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
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The head of the math department compared the scores of students in two classes on the Chapter 2 test. He found that
the mean score of both classes was the same. He also found that there was greater variability in the scores of Ms.
Biren's students than in the scores of Mr. Hayes's students. Which quality of the data sets would lead the department*
head to that conclusion?
The median score i Ms. Biren's class is greater than the median score in Mr. Hayes's class.
The
median score in Ms. Biren's class is less than the median score in Mr. Hayes's class.
The range of scores in Ms. Biren's class is greater than the range of scores in Mr. Hayes's class.
The range of scores in Ms. Biren's class is
less than the range of scores in Mr. Hayes's class. The median score
Answers
Answer: B.
Explanation and reasoning:
Find Measure of angle B (m
18. a = 7 m, b = 5 m, m∠A = 45°
Answers
The value of the variable a is 19.66 and the value of the valriable b is 20.21.
What is the law of sines?For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by the law of sines,
[tex]\rm \dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
The sine angle is the length of the side opposite to that angle.
Then the third angle of the triangle will be
x + 75 + 35 = 180
x = 70
[tex]\rm \dfrac{\sin 75^o}{b} = \dfrac{\sin 35^o}{12} = \dfrac{\sin 70^o}{a}[/tex]
From the first two-term, we have
sin 75 / b = sin 35 / 12
b = 20.21
From the last two-term, we have
sin 70 / a = sin 35 / 12
a = 19.66
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A basket contains six apples, three oranges, ten corn, four pears and six peaches, You randomly select a fruit. What is the conditional probability of selecting a fruit that it is a orange?
Select one:
a.
15.8%
b.
15%
c.
17.5%
d.
10.3%
Answers
Answer:
b. 15%
Step-by-step explanation:
because it is 3 oranges and 3 is equal to 15%
what is 2x-45y=22 when y=21
Answers
answer:
483.5
step by step explanation:
2x-45y=22
2x-45(21)=22
2x-945=22
2x =22+945
2x=967
x=483.5
An exponential function contains the points (1, 0.9) and
(2, 1.62). What is an exponential function that contains
these points?
Answers
Answer:
Hi,
Step-by-step explanation:
Let's say y=a*b^x the equation of the exponential function.
0.9=a*b^1 (1)
1.62=a*b² (2)
(2)/(1) ==> b=1.62/0.9=1.8
and
0.9=a*1.8 ==> a=0.5
y=0.5*1.8^x
Mrs. Rykus does a survey of her 85 students.
20 say math is awesome
35 say math is the best
30 say math is fun
Based on these results, if Mrs. Rykus asks the whole student population 900 students what they think of math, what is the best approximation for how many students will say math is awesome?
A 400
B 212
C 200
D 315
Answers
Answer:
212
Step-by-step explanation:
85 here is 100%
And 900 is also 100%
That's for the different comparisons. So now, what we do is, we should divide 85 by 900, and then, whatever is our answer, multiply that by 20.
That is surely going to equal how many students are going to say that Math is Awesome for 900 student survey.
Step 1
85/900=10.5882352941
Let's round that to make it
10.5
Step 2
10.5x20=210
That means, if we go exactly, like multiplying all of those numbers, then our answer should be 212 or 200.
Just to be sure that our answer is correct, we will do it with 10.58 now.
Step 3
10.58x20=211.6
So now it looks like it's most probably going to be 212
But still, let's do 10.588 now.
Step 4
10.588x20=211.76
Okay, let's do it again, with 10.5882
Step 5
10.5882x20=211.764
Okay, so I just multiplied the whole number this time, and I still got a decimal, so that means that your answer is 212 basically.
The center circle on a playing field has a radius of 7.5m find its circumference
Answers
The circumference of the circular playing field.
Solution:[tex]\huge\boxed{Formula:C= 2\pi{r}}[/tex]
We'll have to multiply 2, π and radius.
Substitute the values according to the formula.
[tex]C= 2× \pi ×7.5[/tex]
[tex]C= 47.12389 [/tex]
[tex]\large\boxed{C= 47.12 \: m}[/tex]
Therefore, the circumference of the circular playing field is 47.12 feets.
Which of the following could be the equation of a line perpendicular to the line 2x−5y=7?
Answers
Answer:
B.
Step-by-step explanation:
First convert the equation to slope-intercept form:
2x - 5y = 7
-5y = -2x + 7
y = 2/5 x - 7/5
So the slope of the given line is 2/5.
So the slope of a perpendicular line will be -1/ 2/5 = -5/2.
Take B:
5x + 2y = 3
2y = -5x + 3
y = -5/2.
So its B.
A father is 30 years older than his son.Three years ago he was 3 times as old as his son.How old are both of them
Answers
Answer:


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Question

A father is 30years older than his son. In 12years, the man will be three times as old as his son. Find their present ages.
Medium
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Solution

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Let the present age of the son be x years
Then father's age will be (x+30) years
Given after 12 years father will be three times as old as his son
Therefore,
(x+12)3=x+30+12
3x+36=x+42
3x−x=42−36
2x=6
x=3
x+30=3+30=33
So, the present age of son is 3 years and present age of the father is 33 years
a tractor driver plowed 1/5 of a field on the first day, and 1/4 on the second day. How much did he plow in the first two days? How much does he still need to plaw?
Answers
Answer:
1) (9/20)x 2) (11/20)x
Step-by-step explanation:
x = total area of the field.
In the first two days he plowed (1/5)x + (1/4)x = (9/20)x
He still needs to plow x - (9/20)x = (11/20)x
A material has a density of 4.5 g/ml and a mass of 2.6 grams, what is the volume?
Answers
Answer:
The volume is 11.7
Step-by-step explanation:
[tex]\frac{m}{v}[/tex] = d
[tex]\frac{2.6}{v}[/tex] = 4.5
4.5 × 2.6 = 11.7
v = 11.7
I don’t know how to do this please help
Answers
Answer:
84 cm²
Step-by-step explanation:
The figure has a uniform horizontal cross section, so its area is the product of that cross section length and its vertical dimension.
__
A = bh
A = (6 cm)(14 cm) = 84 cm²
The area of the shape is 84 square centimeters.
_____
Additional comment
You could decompose the figure into a rectangle with base 6 and height 8, and a parallelogram with base 6 and height 14-8=6. The area formula is the same for each: A = bh, so the area of the composite figure is ...
A = 6×8 +6×(14 -8)
= 6×(8 +(14 -8))
= 6×14 . . . . same as above.
solve for K
7K-6
2K+14
Answers
Answer:
[tex]k=4[/tex]
Step-by-step explanation:
Using the diagram, we can conclude that the given angles are vertical angles. Vertical angles are opposite angles that are formed when two lines intersect. Vertical angles are always congruent.
Using this information we can set up an equation.
[tex]7k-6=2k+14[/tex]
Subtract 2k from both sides.
[tex]7k-2k-6=2k-2k+14\\5k-6=14[/tex]
Add 6 to both sides
[tex]5k-6+6=14+6\\5k=20[/tex]
Divide both sides by 5
[tex]\frac{5k}{5}=\frac{20}{5}\\k=4[/tex]
CHECK:
7(4) - 6 = 28 - 6 = 22
2(4) + 14 = 8 + 14 = 22
22 = 22
Volume of pyramids cones and spheres
Answers
Answer:
48 cm³Step-by-step explanation:
Volume = (1/3) * base_area * height
1/3 * 4 * 4 * 9 =
48 cm³
Based on the data in this two-way table, which statement is true?
Type of Flower/Color Red Pink Yellow Total
Rose 40 20 45 105
Hibiscus 80 40 90 210
Total 120 60 135 315
A.
A flower being pink and a flower being a rose are independent of each other.
B.
A flower being pink is dependent on a flower being a rose.
C.
A flower being a rose is dependent on a flower being pink.
D.
A flower being pink and a flower being a rose are the same.
Answers
given m
m FS =
pls help me this is due tomorrow
Answers
Answer:
arc FS = 84°
Step-by-step explanation:
the inscribed angle QRF is half the measure of its intercepted arc QF , then
arc QF = 2 × 48° = 96°
the sum of the arcs on a semicircle = 180° , that is
QF + FS = 180°
96° + FS = 180° ( subtract 96° from both sides )
FS = 84°
Determine the period, amplitude, and phase shift of[tex]f(x)=3cos2\left \{ x-\frac{\pi }{4}]+1[/tex]
b) List the five critical points for the first cycle. (3 marks)
Use this information to sketch the graph off(x) for two
complete cycles. Determine [tex]\frac{1}{4}[/tex] wave and starting point.
Clearly label the scale on both axes. (3 marks)
Answers
->period = [tex]\frac{2\pi }{2} =\pi[/tex]
->a=3, shift [tex]\frac{\pi }{4}[/tex]
->right 1 unit up
Rest are shown in graph
(Computer science)
The CPU fan rotation rate (R) was directly proportional to the ambient temperature (T). At a temperature of 25 degrees C, the CPU fan was rotating at 1150rpm. What would the rotation rate be for an ambient temperature of 30 degrees C?
Answers
Answer:1380
Step-by-step explanation: proportionality constant equals 1150/25=46. 46x30=1380
A right cone has a slant height of 6 and a radius of 4. What is its surface
area?
Answers
The surface area of the cone is 40π
What is a cone?A cone is a solid shape with a circular base and a tapered side.
Analysis:
surface area of a cone = πrl + π[tex]r^{2}[/tex] = π( 6x4) + π(4 x 4) = 40π
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Find and label the measures of each of the three missing angles, A, B and C, below.
Lines I and M are parallel.
Answers
Hello, the detailed solution is given below.
Lines L and M are parallel. That's why [tex]B[/tex] angle and [tex]50^{o}[/tex] are equal.
What's the Co-Interior Rule? (Known as U Rule)Co-interior angles lie between two lines and on the same side of a transversal. If the two lines are parallel, then co-interior angles add to give [tex]180^{o}[/tex] and so are supplementary.
After that, [tex]C[/tex] angle found as [tex]85^o[/tex].
As [tex]A[/tex] angle and [tex]C[/tex] angle must be equal due to the parallel, the missing angles as;
[tex]A=85\\B=50\\C=85[/tex]
Good luck! If you have any questions, then feel free to ask in comments!