The diagram shows a 7cm x 6cm rectangle-based pyramid all the diagonal sides - TA TB TC and TD are length 10cm M is the midpoint of the rectangular base work out the height MT to one decimal place
Answers
Height MT of the pyramid will be 8.9 cm
Given in the question,
Dimensions of the rectangular base = 7 cm × 6 cmM is the center of the rectangular base.Slant height of the pyramid = 10 cmSince, diagonals of a rectangle bisect each other, point M will be the midpoint of the diagonal AC.
By applying Pythagoras theorem in right triangle ΔABC,
AC² = AB² + BC²
AC = [tex]\sqrt{AB^2+BC^2}[/tex]
AC = [tex]\sqrt{6^2+7^2}[/tex]
AC = [tex]\sqrt{85}[/tex]
Therefore, AM = [tex]\frac{\sqrt{85} }{2}[/tex]
AM = 4.61 cm
Apply Pythagoras theorem in right triangle ΔAMT,
AT² = AM² + TM²
TM = [tex]\sqrt{AT^2-AM^2}[/tex]
TM = [tex]\sqrt{(10)^2-(4.61)^2}[/tex]
= [tex]\sqrt{78.7479}[/tex]
= 8.874
≈ 8.9 cm
Therefore, height MT of the pyramid will be 8.9 cm.
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Related Questions
please help Use elimination to solve each system of equations.
2x + 5y = 3
-x + 3y = -7
Answers
x = 4 and y = -1
If you want the work ask me on the comment if not this is the correct answer
If the área of a right is 6.22sq. In. And its base is 3.11 in. Write an equation that relates the área to the height, h, and the base. Solve the equation to determine the height.
Answers
In the given question one word is missing, the correct question is,
If the área of a right triangle is 6.22sq. In. And its base is 3.11 in. Write an equation that relates the área to the height, h, and the base. Solve the equation to determine the height.
The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.
Step-by-step explanation:
The given is,
Area of right triangle, A = 6.22 square inches
Its base is 3.11 inches
Step:1
Formula for area of right angle triangle is,
[tex]A = \frac{1}{2} bh[/tex]......................................(1)
Where, b - Base
h - Height
Equation (1), that relates the área (A) to the height (h) and the base (b).
Step: 2
From the given values,
Base, b = 3.11 inches
Area, A = 6.22 square inches
Equation (1) becomes,
6.22 = [tex]\frac{1}{2} (3.11)(h)[/tex]
(6.22) (2) = (3.11) (h)
12.44 = (3.11) (h)
[tex]h = \frac{12.44}{3.11}[/tex]
= 4
Height, h = 4 inches
Result:
The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.
An engineer designs a satellite dish with a parabolic cross-section. The dish is 15 ft. wide at the opening and the depth is 4 feet. Find the position of the light source (the focus). How far is it from the deepest part of the dish?
Answers
The position of the light source(the focus) is at; (0, 3.516).
The distance from the position of light source to the deepest part of dish is; 3.516 ft.
We know that standard form of a parabola equation is;
x² = 4ay
Now, we are told the dish is 15 ft wide and the depth is 4ft.
This means that the edge of the parabolic cross section will have an x-coordinate of 15/2 = 7.5 ft
While the y-coordinate is the depth of 4ft.
Thus;
Since;
x² = 4ay
Plugging in 7.5 ft for x and 4 ft for y gives;
7.5² = 4a(4)
a = 7.5²/16
a = 3.516 ft
Thus, position of the light source which is the focus is; (0, 3.516)
And distance from the position of light source to the deepest part of dish = 3.516 ft.
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The position of the light source (the focus) in a satellite dish with a parabolic shape, with a 15 ft diameter opening and depth of 4 ft, is calculated using the formula for the focal length of a parabola. Plugging these values into the formula results in the finding that the focus is 14.0625 ft away from the base of the dish.
Explanation:The parabola can be described by the equation y = x2/4f, where f is the distance of the focus from the vertex. In a practical situation, to determine the position of the light source (the focus) in a satellite dish, which has a parabolic shape, we need to know the dish's width and depth. Here, the dish is 15 ft wide at the opening (which is the diameter of the dish) and the depth is 4 ft.
So, we can use these dimensions to calculate the position of the focus. First, we need to recall that in a parabola, the focus lies at the point (0, p), where p is the focal length. The focal length (p) of a parabolic dish can be calculated using the formula p = D2/16h, where D is the diameter of the dish and h is the depth of the dish. In this case, D = 15 ft and h = 4 ft.
Putting these values in the formula, we get p = (152)/16(4) = 14.0625ft. Therefore, the light source (focus) is placed 14.0625 ft away from the base of the dish.
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24-(-6) what the answer
Answers
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
when you subtract a negative, you are basically adding the number.
*2 negatives equal a positive*
24 (- -) 6 = 30
combine negatives:
24 + 6 = 30
work
18.) The temperature in Chicago is -11.8°F. The temperature in New York is 8.3°F. How much
warmer is it in New York than in Chicago? Show your work
Answers
-11.8+8.3 is basically saying 11.8+8.3
Kim made 4 batches of this fruit punch recipe. Combine: 90 milliliters of strawberry juice 300 milliliters of pineapple juice 3 liters of apple juice How many liters of fruit punch did Kim make?
Answers
Answer:
13.56
Step-by-step explanation:
Each batch makes a total of ...
0.090 +0.300 +3 = 3.39 . . . liters
Then 4 batches makes ...
4 × 3.39 L = 13.56 L
Kim made 13.56 liters of punch.
Final answer:
Kim made a total of 13.56 liters of fruit punch by making 4 batches, with each batch including a combination of strawberry, pineapple, and apple juices.
Explanation:
Kim made 4 batches of fruit punch, each containing 90 milliliters of strawberry juice, 300 milliliters of pineapple juice, and 3 liters of apple juice.
To find the total amount of fruit punch made, we first convert all quantities to liters and then sum them up. Since there are 1,000 milliliters in 1 liter, 90 milliliters is equal to 0.09 liters and 300 milliliters is equal to 0.3 liters.
For one batch, the total liters of juice is:
Strawberry juice: 0.09 litersPineapple juice: 0.3 litersApple juice: 3 litersSo for one batch, the total is 0.09 + 0.3 + 3 = 3.39 liters.
Since Kim made 4 batches, the total amount of fruit punch is:
4 batches × 3.39 liters per batch = 13.56 liters
Therefore, Kim made 13.56 liters of fruit punch in total.
Which of the following is not considered quantitative data?
The height of the Empire State Building.
The weight of a chicken.
The taste of vanilla ice cream.
The speed of a Tesla automobile.
Looking at the scatter plot
Answers
Mr. Smith has a honeybee colony on his farm. On average, 1,000 bees can gather enough nectar for 1 ounce of honey each day. If Mr. Smith wants his bees to produce 3.5 pounds of honey each week, how many bees will he need in his bee colony?
Answers
Answer:
8,000 bees
Step-by-step explanation:
Final answer:
Mr. Smith will need approximately 8,000 bees in his bee colony to produce 3.5 pounds of honey each week, based on the rate of 1,000 bees producing 1 ounce of honey per day.
Explanation:
Mr. Smith needs to calculate the number of bees required to produce 3.5 pounds of honey each week.
First, we need to convert pounds to ounces because the rate given is in ounces:
3.5 pounds = 3.5 * 16 ounces/pound = 56 ounces of honey per week.
Now, we use the given rate of honey production:
1,000 bees produce 1 ounce of honey per day.
Therefore, in one week (7 days), 1,000 bees will produce 7 ounces of honey.
To find out how many bees you need to produce 56 ounces, you divide the target ounces by the ounces produced by
1,000 bees per week:
56 ounces / 7 ounces per 1,000 bees = 8,000 bees.
So, Mr. Smith will need approximately 8,000 bees in his colony to produce 3.5 pounds of honey each week.
Hello, please look at the attachment and do the following :
A) Complete the ven diagram. ( what number goes in the middle and what number goes to the bottom left of the diagram out of the circle?).
B) How many students study only french
C) How many students learn spanish
Answers
Answer:
A) middle: 32
Outside: 9
B) 25
C) 47
Step-by-step explanation:
71 = 14 + 25 + intersection
Intersection = 71 - 39 = 32
Outside: 80 - 71 = 9
Only french: 25
Spanish: 14 + 32 = 46
In how many ways can a quality-
control engineer select a sample
of 3 transistors for testing from a
batch of 100 transistors?
Answers
Answer:161700
Step-by-step explanation:
The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be 161700.
What is combination?Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be
¹⁰⁰C₃ = (100!) / [(100 – 3)! × 3!]
¹⁰⁰C₃ = (100 × 99 × 98 × 97!) / (97! × 3 × 2)
¹⁰⁰C₃ = 50 × 33 × 98
¹⁰⁰C₃ = 161700
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"A bicycle factory runs two assembly lines, A and B. 95% of line A's products pass inspection and 93% of line B's products pass inspection. 60% of the factory's bikes come off assembly line B and the rest come off line A. Find the probability that one of the factory's bikes did not pass inspection and came off assembly line Upper A."
Answers
Answer:
0.02
Step-by-step explanation:
Since 60% of the factory's bikes come off assembly line B, Therefore:
The probability that the factory's bikes come off assembly line B = 60% = 0.6
Percentage line B's products pass inspection = 93% = 0.93
Percentage line B's products that do not pass inspection = 1 - 0.93 = 0.07
The probability that the factory's bikes come off assembly line A = 1 - 0.6 = 0.4
Percentage line A's products pass inspection = 95% = 0.95
Percentage line A's products that do not pass inspection = 1 - 0.95 = 0.05
Let D represent those that passes inspection and D' represent those that do not pass inspection.
P(A ∩ D') = P(A) × P(D'/A) = 0.4 × 0.05 = 0.02
P()bikes did not pass inspection and came off assembly line A) = P(A ∩ D') = 0.02
Final answer:
The probability that a bicycle failed inspection and came from assembly line A is 2%.
Explanation:
We're tasked with finding the probability that a bike did not pass inspection and came from assembly line A. First, we calculate the probability of a bike failing inspection from each line. Since 95% of line A's products pass, there is a 5% (100%-95%) chance a bike from line A fails inspection. For line B with a 93% pass rate, there's a 7% (100%-93%) chance of failure.
Next, we consider the distribution of production between lines A and B. 60% of bikes are from line B, so 40% are from line A. We then calculate the probability of a bike being from line A and failing inspection using the multiplication rule for independent events, which is P(A) times the probability of failure on line A.
P(Fail and from A) = P(A) * P(Fail | A) = 40% * 5% = 0.40 * 0.05 = 0.02 or 2%.
Therefore, the probability that a bike did not pass inspection and came from assembly line A is 2%.
Q)David bed is 9 inches longer than his desk His desk is 66 inches long .
How long is David bed ?
-------inches.
Answers
Answer:75 inches
Step-by-step explanation: 9+66=75
=75 inches
Answer:
75 inches
Step-by-step explanation:
66+9=75
The side of an office building in hamburg Germany is in the shape of a parallelogram the area of the side of the building is about 2150 square meters. What is the length x of the portion of the building that extends over the river
Answers
Answer:
47 meters
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
Given
The building is about 2150 square metersThe height of the building: 25 metersAs we know, the formula to find the area of a parallelogram is:
A = the base* the height
=> the base in this question is:
= The area / the height
= 2150 / 25 = 86 meters
As we can see in the photo, x + 39 meters = the base
=> x = the base - 39 meters
= 86 meters - 39 meters
= 47 meters
"A firefighter stood on the middle rung of a ladder. When the smoke became less thick, the firefighter moved up 4 rungs. Then it got too hot, and the firefighter moved down 6 rungs. Later, the firefighter went up 7 rungs and stayed there till the fire was out. After the fire was out, the firefighter climbed the remaining 4 rungs and entered the building. How many rungs does the ladder have?"
Answers
Answer:
There are 18 rungs on the ladder.
Step-by-step explanation:
Given a firefighter who is standing on the middle of the ladder.
We have to find the number of rungs the ladder have.
Let the number of rungs be "2x" where "x" be the number of rungs from the middle of the ladder to the top of the ladder.
Rungs below the middle of the ladder is equal to rungs above the middle of the ladder.
According to the question:
Let the fire fighter be at "y" rungs this "y" will be the reference point.
⇒ Moved [tex]4[/tex] rungs from 'y' current position [tex]4[/tex] rungs above of 'y'.
⇒ Moved [tex]6[/tex] rungs down meaning that [tex](4-6)= -2[/tex] rung from 'y' below [tex]2[/tex] rung downward from 'y'.
⇒ Moved [tex]7[/tex] rungs upward from here meaning [tex](-2+7) = 5[/tex] rung above 'y'.
Now,
⇒ Further the firefighter climbed [tex]4[/tex] rungs from here [tex](5+4) = 9[/tex] rungs above 'y' .
Finally the firefighter have climbed [tex]9[/tex] rungs from 'y' that is the middle of the ladder so there is equal rungs below of it.
Total rungs of the ladder = '2x' = 2(9) = 18 rungs.
the numbers 525 & 3000 are divisible by 3,5,15,25 and 75.what is the hcf of 525 & 3000?
Answers
Answer:
75.
Step-by-step explanation:
The HCF is the highest common factor of two numbers - if these numbers are both divisible by 75 - this is their HCF.
How can you make the number 25 using 3,6,8 and 9.
Each number has to be used and can only be used once
Answers
6 ÷ 3 × 8 + 9
6÷3=2
2×8=16
16+9=25
What is the area of the following circle?
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answers
To solve the problem we will first calculate the radius of the circle and substitute the value in the formula of the area of a circle.
Area of the circleArea of the circle [tex]=\pi r^2[/tex]
The area of the circle is 49π or 153.86 unit².
Given to usDiameter, d = 14π = 3.14SolutionRadius of the circleRadius,
[tex]\rm{ r = \dfrac{Diameter}{2} = \dfrac{d}{2}=\dfrac{14}{2} =7[/tex]
Thus, the radius of the circle is 7.
Area of the circleArea of the circle [tex]=\pi r^2[/tex]
[tex]=\pi\times (7)^2\\ = 49\pi[/tex]
Substituting the value of π = 3.14,
Area of the circle [tex]=49\pi\\ = 49 \times 3.14\\ = 153.86[/tex]
Hence, the area of the circle is 49π or 153.86 unit².
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The area of the circle is approximately 4.5m².
Explanation:The formula to find the area of a circle is A = πr², where π is approximately 3.14 and r is the radius. In this case, we have a radius of 1.2m. Using a calculator with an eight-digit output, we can calculate A = 3.14 x (1.2m)² = 4.5238934m².
However, since the radius only has two significant figures, we need to limit the calculated quantity to two significant figures. So, the area of the circle is approximately 4.5m² (rounded to two significant figures).
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if 6th term of an ap is -10 and 10 th term is -26 then find thr 15 term plzzzzzzzzzzzzzzzzzzzzzzz answer i will give whatever you want
Answers
Answer:
-46
Step-by-step explanation:
We need to find the common difference of this arithmetic sequence:
[tex]\frac{-26-(-10)}{10-6} =\frac{-16}{4} =-4[/tex]
So, the common difference d = -4. We can now write the equation:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_{15}=a_6+d(15-6)=-10-4(9)=-10-36=-46[/tex]
So, the 15th term is -46.
Hope this helps!
Step-by-step explanation:
the answer and explanation is in the picture
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5 boxes of candles contain a total of 60 candles. Every box holds the same number of candles in each box. How many boxes does the store have if they have 8 boxes?
Answers
Answer: 96 candles in 8 boxes
Step-by-step explanation:
There’s 12 candles in a box
You pick a card at random. Without putting the first card back, you pick a second card at random.
1
2
3
4
What is the probability of picking a 1 and then picking a 4?
Group of answer choices
1/16
1/4
1/12
1/2
Answers
Answer:
1/12
Step-by-step explanation:
On a coordinate plane, 3 parallelograms are shown. Parallelogram A B C D has points (3, 5), (6, 5), (4, 1), (1, 1). Parallelogram A prime B prime C prime D prime has points (3, negative 5), (6, negative 5), (4, negative 1), (1, negative 1). Parallelogram A double-prime B double-prime C double-prime D double-prime has points (negative 3, negative 4), (0, negative 4), (negative 2, 0), (negative 4, 0). Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"? Reflection across the x-axis composition translation of negative 6 units x, 1 unit y. Translation of negative 6 units x, 1 unit y composition reflection across the x-axis. 90 degree rotation about point 0 composition translation of negative 6 units x, 1 unit y. Translation of negative 6 units x, 1 unit y composition 90 degree rotation about point 0.
Answers
The correct answer is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.
Here's the step-by-step breakdown:
Parallelogram A B C D to A' B' C' D':
Reflection across the x-axis: This flips the parallelogram across the x-axis, resulting in A' B' C' D'.
Parallelogram A' B' C' D' to A" B" C" D":
Translation of negative 6 units x, 1 unit y: This shifts the parallelogram 6 units to the left and 1 unit upwards, resulting in A" B" C" D".
Therefore, the overall composition of transformations is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.
The daily supply of oxygen for a particular multicellular organism is provided by 625 square feet of lawn. A total of 6,250 square feet of lawn would provide the daily supplies of oxygen for how many organisms?
Can someone please help me with this problem???
Answers
Answer:
10 organisms.
Step-by-step explanation:
625 Square feet of lawn.
You would simply divide 6250 by 625 and you would get 10.
Feel free to let me know if you need more help! :)
Image: ( A regular hexagon has an apothem of 4 and a side length of
8√3 /3 Its area is:_____)
Answer
A) 16√3 sq units
B) 48√3 sq units
C) 64√sq units
D) 32√3 sq units
Answers
Answer:
D: 32[tex]\sqrt{3}[/tex]
Step-by-step explanation:
8/3[tex]\sqrt{3}[/tex] * 1/2 * 4 = 16[tex]\sqrt{3}[/tex]/3
16[tex]\sqrt{3}[/tex]/3 * 6 = 32[tex]\sqrt{3}[/tex]
A circular pizza that is 16 inches in diameter is cut into 5 equal slices. What is the area of one of the slices?
Answers
Answer:
40.23
Step-by-step explanation:
Area of a circular pizza is calculated by pi radius^2
or 22/7 × (16/2)^2
Radius is diameter/2 = 16/2
= 22/7 × 8^2
= 22 × 8 × 8 ÷ 7
= 201.143 ....
A circular pizza is cut into 5 slices
so the area of 1 slice of a circular pizza is
201.143 / 5 = 40.23 inches^2
what is 11/12 of a full rotation
Answers
Answer:
Turn-0.9166666666666666
Degree-330.00000000081860208
Final answer:
11/12 of a full rotation equates to 330 degrees or approximately 2.91 radians.
Explanation:
11/12 of a full rotation in a mathematical context refers to completing 11 out of 12 equal parts of a circle. Since a circle has 360 degrees, we can calculate this portion of a rotation by finding 11/12 of 360 degrees, which is 330 degrees. In terms of radians, since a full rotation is 2π radians, the same portion in radians would be 11/12 of 2π radians, which is approximately 2.91 radians.
You roll a 6-sided die.
What is P(less than 6)?
Answers
Answer:
21
Step-by-step explanation:
0i s
If a 6-sided die is rolled then P(less than 6) is [tex]\frac{5}{6}[/tex]
What is probability?Probability refers to the chance of occurring of an event.Probability is always ≤ 1How to calculate probability ?Probability can be found by dividing the favourable cases by the total possible cases.
How to find P(less than 6)?P(less than 6) means the probability of getting a number which is less then 6 after the die is rolled.When a die is rolled each outcome has the probability of [tex]\frac{1}{6}[/tex]We know that if a die is rolled, the possible outcomes are {1,2,3,4,5,6}
Here, we should consider the outcomes {1,2,3,4,5}. These are favourable outcomes.To get the probability of getting a number which is less then 6 after the die is rolled, we can add the probabilities of each outcome.
∴ Probability of getting a number which is less then 6 = ( [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex])
= [tex]\frac{5}{6}[/tex]
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A particle starts at point A on the positive x-axis at time t = 0 and travels along the curve from A to B to C to D, as shown above. The coordinates of the particle's position (x(t), y(t)) are differentiable functions of t, where x′(t)=dxdt=−9cos(πt6)sin(πt+1√2) and y′(t)=dydt is not explicitly given. At time t = 9, the particle reaches its final position at point D on the positive x-axis. The slope of the curve is undefined at point B. At what time t is the particle at point B?
Answers
Answer:
the particle is at point B at t = 3 s
Step-by-step explanation:
Solution:-
- The coordinates of the path that a particle follows through points A to B to C.
- The coordinates of the particle position ( x , y ) are differentiable function of t, where, the rate of change of x-coordinate is given by:
[tex]x ' (t) = -9*cos (\frac{\pi *t}{6})*sin (\frac{\pi \sqrt{t + 1} }{2})[/tex]
- The slope of the curve at point B, in mathematical terms that is called the inflection point.
- The independent variable time (t) can be determined for the particle when it is at point B. Where the x'(t) is set to zero, and the critical value defines the point B.
[tex]x ' (t) = -9*cos (\frac{\pi *t}{6})*sin (\frac{\pi \sqrt{t + 1} }{2}) = 0\\\\cos (\frac{\pi *t}{6}) = 0 , sin (\frac{\pi \sqrt{t + 1} }{2}) = 0\\\\\frac{\pi *t}{6} = \frac{\pi }{2} , \frac{\pi \sqrt{t + 1} }{2} = \pi \\\\t = 3 , t = 3[/tex]
- Hence, the particle is at point B at t = 3 s.
What does a daz washing powder look like in 3D net GET IT ASAP
Answers
Answer:
I dont know... Never tried it.
Answer:
47
Step-by-step explanation:
not that difficult
Solve for all values of x by factoring.
x² + 2x - 4 = 2x
Answers
Answer:
x=2 x=-2
Step-by-step explanation:
x² + 2x - 4 = 2x
Subtract 2x from each side
x² + 2x-2x - 4 = 2x-2x
x^2 -4 = 0
Factor
We know this is the difference of squares
(x-2)(x+2) =0
Using the zero product property
x-2 =0 x+2 =0
x=2 x=-2
The price of a bracelet was decreased by 30% to £63.
What was the price before the decrease?
Answers
Answer:
90
Step-by-step explanation:
If the original price of a bracelet was a
70%a = 63
70/100a = 63
a = 63 × 100/70
a = 90
The price before the decrease is 90 euros.
What is decrease?The amount of decrease is the original amount minus the final amount. For example if you are looking for the percent of decrease from 9 to 6, the original amount is 9 and the final amount is 6.
GIVEN
Based on the given conditions, write z= 63/(1-0.3)
Calculate the sum or difference = 63/0.7
Divide a fraction by multiplying its reciprocal:[tex]=63*10/7 =90[/tex]
Hence, The price before the decrease is 90 euros.
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