The longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide and 11cm tall is 19.1cm.
What is a right rectangular prism?A right rectangular prism is a three dimensional solid shape formed by 6 rectangles.
it is also called the cuboid.
Analysis:
The diagonal of the face of the prism with dimensions 14cm long and 13cm wide is the longest line segment that can be drawn.
Since rectangles have 90° on each vertex, we can use Pythagoras theorem to calculate for the length of the diagonal.
[tex](diagonal)^{2}[/tex] = [tex](length)^{2}[/tex] + [tex](width)^{2}[/tex]
[tex](diagonal)^{2}[/tex] = [tex](14)^{2}[/tex] + [tex](13)^{2}[/tex]
= 196 + 169 = 365
[tex](diagonal)^{2}[/tex] = 365
diagonal = [tex]\sqrt{365}[/tex] = 19.1cm
In conclusion, the length of the longest diameter is 19.1cm
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4 1/3
What is the value of this equation?
Answer:
4.33
Step-by-step explanation:
1/3=0.33 recuring
4 just eqauls 4
so you add 0.3 recuring to 4
and depending on significant figures it wants you round it ill assume it wants 3 and go 4.33
NEED HELP PLEASE ANSWER ASAP! (45)
Answer:
45. (4) (2, 2)
Step-by-step explanation:
Question 45
Equate the equationsx = x² - 2x² - x = 2x(x - 1) = 2Solutions
x = 2x - 1 = 2 ⇒ x = 3We'll take x = 2 as no options with x = 3 are listed.
y = xy = 2Ordered pair
(x, y)(4) (2, 2)SOMEONE I NEED HELP PLS HELP ME!!
Answer:
PQ = 6 units
Step-by-step explanation:
note that the y- coordinates of P and Q are both - 7
then PQ is the difference in the x- coordinates, that is
PQ = | 7 - 1 | = | 6 | = 6
or PQ = | 1 - 7 | = | - 6 | = 6
30. The cost of the building materials will depend in part on the surface area of the structure. The larger the surface area to be covered, the more it will cost to build. Which structure has the smallest surface area?
Answer:
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Find arc QT.
Answers are:
A.71
B.23
C.46
D.142
Answer:
d)142º
Step-by-step explanation:
[tex]\widehat{AB}=2\times71\º=142\º[/tex]
i need help on this please
Answer:
C
You have to use radius not the diameter
if you were asked to convert the complex number, -6 + 8i, into polar form, what values of “r” and “0” would be in polar form?
Answer:
10∠126.87°
r = 10; θ = 126.87°
Step-by-step explanation:
The coordinate conversion from (x, y) or (x +yi) to (r; θ) can be done using the relations ...
r = √(x² +y²)
θ = arctan(y/x) . . . . paying attention to quadrant
__
For the given complex number, we have ...
r = √((-6)² +8²) = √(36 +64) = √100 = 10
θ = arctan(8/(-6)) = arctan(-4/3) . . . . in the 2nd quadrant
θ ≈ -53.13° +180° = 126.87°
The equivalence is ...
-6 +8i ⇔ 10∠126.87° . . . . . in the form r∠θ
_____
Additional comment
Many scientific and graphing calculators are equipped to work with complex numbers, including their conversion to or from polar form.
A landscape design company is building a large gazebo for a backyard. It is in the shape of the
regular polygon shown below, where the measurements are in feet. They need to purchase wood
for the floor. It costs $10 per square foot for the special wood the homeowner wants. Find the cost
of the gazebo's flooring. Recall A = ap for the area of a regular polygon:
The area of the heptagon will be 533.61 square feet. Then the cost of the gazebo's flooring will be $ 5336.1.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
A landscape design company is building a large gazebo for a backyard. It is in the shape of the regular polygon shown below, where the measurements are in feet.
A heptagon is given with an apothem of 12.6 ft and a side length of 12.1 ft.
Then the area of the heptagon is given as
Area of heptagon = 7 x area of a triangle
Area of heptagon = 7 x 0.5 x 12.1 x 12.6
Area of heptagon = 533.61 square ft
If the costs $10 per square foot for the special wood the homeowner wants.
Then we have
Total cost = 10 x 533.61
Total cost = $ 5336.1
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What is it called when your point is right on the Y axis?
Y Intercept
Slope- intercept
Answer:
y intercept
Step-by-step explanation:
(√3+√7) (√3-√7) pl and me
[tex]\left( \sqrt 3 + \sqrt 7\right) \left( \sqrt 3 - \sqrt 7\right)\\\\=\left(\sqrt 3 \right)^2 - \left(\sqrt 7 \right)^2\\ \\=3-7\\\\=-4[/tex]
Answer:
- 4
Step-by-step explanation:
([tex]\sqrt{3}[/tex] + [tex]\sqrt{7}[/tex] )([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] )
each term in the second factor is multiplied by each term in the first factor.
[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) + [tex]\sqrt{7}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) ← distribute parenthesis
= 3 - [tex]\sqrt{21}[/tex] + [tex]\sqrt{21}[/tex] - 7 ← collect like terms
= - 4
in 130,426 the digit 2 is in the _____ place?
{20, 25, 19, 18, 21, 24, 15, 25} What is the mean of the data set? Make sure to show ALL of your work
Answer:
20.875
Step-by-step explanation:
Mean is to add up the scores then divide by the number so 20 + 25 + 19 + 18 + 21 + 24 + 15 + 25 which is 167 then divide by 8 which is 20.875
Solve the inequality -4x +1 > 13
Answer:
The inequality is x is less than negative 3.
Answer:
x < -3
Step-by-step explanation:
. subtract 1 from both sides.
. subtract the numbers
. divide both sides by the same factor and flip the relation
because the factor is negative
. cancel the terms that are both in the numerator and the denominator
. divide the numbers
.then you get youre solution
P is a rectangle with length 80 cm and width x cm.
q is a rectangle with width y cm.
p
the length of q is 25% more than the length of p.
the area of q is 20% less than the area of p.
work out the ratio x:y
give your answer in its simplest form.
x cm
80 cm
:
q
y cm
The ratio of x and y will be equal to x:y = 25:16
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
We know that
The length of Q is 25% more than the length of p
length Q=1.25 x 80--------> 100 cm
The area of Q is 20% less than the area of p
Area Q=100 x y
Area P=80 x x
100 x y=0.80 x [80 x x]---------> 100 x y = 64 x x-------> x/y=100/64--> 25/16
Therefore the ratio of x and y will be equal to x:y = 25:16
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Answer:
25:16
Step-by-step explanation:
Write an equivalent expression by distributing the "-−" sign outside the parentheses:
8.9r-(-5s-10)
Answer:
8.9r + (5s + 10)
actually the parenthesis aren't necessary...
8.9r + 5s + 10
Step-by-step explanation:
You can change a subtraction to addition if you change the second term to the opposite sign. This problem is like advanced mode of "Add the Opposite"
8.9r - (-5s - 10)
= 8.9r + (+5s + 10)
= 8.9r + (5s + 10)
= 8.9r + 5s + 10
Tia's tent is in the form of a triangular prism as shown below.
If Tia plans to waterproof the tent, excluding the base, what
is the area in which she will waterproof?
(round to the nearest hundredth)
Answer: 279.43
Step-by-step explanation:
The area of the tent that she will need to waterproof is 279.43 feet².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Given a tent in the form of a triangular prism as given.
We have to find the surface area of the tent excluding the base.
There are 2 triangular faces and 2 rectangular faces.
Area of the prism that needs to waterproof = area of 2 rectangles + area of 2 triangles
Area of rectangles = 2 × 14 × 8 = 2 × 112 feet² = 224 feet²
Height of the triangular face = √(8² - 4²) = √48
Area of 2 triangles = 2 × 1/2 × 8 × (√48) = 8√48 feet²
Area needed to be waterproofed = 224 feet² + 8√48 feet² = 279.43 feet²
Hence the area of the tent is 279.43 feet².
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The first rule is add 2 starting from 0. The second rule is add 6 starting from 2. What is the third ordered pair using the terms in each sequence?
(6, 20)
(2, 8)
(8, 26)
(4, 14)
Answer:
I think it would be 2,8
Step-by-step explanation:
hope it helps u
A bag contains hair ribbons for a spirit rally. The bag contains 8 black ribbons and 12 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability that both Lila and Jessica select a black ribbon? Express your answer as a fraction in simplest form.
Answer:
[tex]\boxed{\sf \dfrac{14}{95}}[/tex]
Explanation:
Black ribbons = 8 ribbons
Green ribbons = 12 ribbons
Total ribbons: 12 + 8 = 20 ribbons
[tex]\sf Probability = \dfrac{Favorable \ Outcomes}{Total \ Possible \ Outcomes}[/tex]
For Lila:
[tex]\sf Lila \ picks \ black \ : \ \dfrac{8}{20}[/tex]
Left black ribbons: 8 - 1 = 7 black ribbons
Left total ribbons: 20 -1 = 19 total ribbons
For Jessica:
[tex]\sf Jessica \ picks \ black \ : \ \dfrac{7}{19}[/tex]
Probability that they both pick black ribbons:
[tex]\sf \rightarrow \dfrac{8}{20} \ x \ \dfrac{7}{19}[/tex]
[tex]\sf \rightarrow \dfrac{14}{95}[/tex]
Three times a number decreased by 2 equals forty
Answer:
14
Step-by-step explanation:
40 plus 2 is 42
42 divided by 3 is 14
Which point on the number line best represents the approximate vault of /23
This is to get easy points but to also be kind
If Carmen drives 17.5 miles to a grocery store and 17.5 miles back then can’t find what she needs so she drive 12.5 miles to a gas station and 12.5 back how many miles did she drive.
I will be giving points out for being on this app so be on the lookout
Answer:
60 miles
Step-by-step explanation:
Distance travelled :
2 x Distance to grocery + 2 x Distance to gas station2(17.5) + 2(12.5)35 + 2560 milesfind the volume of a rectangular prism with a length of 4 inches and a width of 7 inches and a height of 11 inches
Answer:308
Step-by-step explanation:Multiply 4*7*11
A recipe for bread uses 5 cups of white flour and 3 cups
of wheat flour. How many more cups of white flour than
wheat flour are used in the recipe? Write an equation and
complete the bar diagram to solve.
What is the solution of log3x-2 4096=3
A video rental company offers a plan that includes a membership fee of $5 and charges $1 for every DVD borrowed. They also offer a second plan, that costs $47 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?
Answer:
for $5 plan if he rents 47 dvd it will pay 47% as one DVS cost 1 $ .
Step-by-step explanation:
For this problem, a non-integer answer should be entered as a fraction in simplest form using / as the fraction bar. malik randomly picked two numbers from 1 to 9 (including 1 and 9). the same number could be picked more than once. the first of the two numbers he picks is odd and less than 5. what is the probability that the sum of the two numbers malik picks is less than 5, given that the first number is odd and less than 5?
Based on the numbers that Malik can pick and the condition of the sum being less than 5, the probability of this happening is 2/9.
What is the probability that Malik's number are less than 5 when added?The first number that Malik picked is an odd number less than 5 which makes it with 1 or 3.
In order for the two number to be less than 5 when added, the numbers to be picked have to be:
1 and 21 and 33 and 11 and 1These are 4 possibilities out of a total of 18 possibilities so the probability is:
= 4 / 18
= 2 / 9
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Answer:
See image
Step-by-step explanation:
Plato
Leo needs to write an essay for history class. He estimates that he can write 1.5 pages per
hour, and his essay needs to be 6 pages long.
Write an equation that shows the relationship between the number of hours Leo spends
writing, x, and number of pages he has left to write, y.
========================================================
Work Shown:
x = number of hours
1.5x = number of pages written after x hours
y = 6-1.5x = number of pages left after x hours
--------------
In other words, if Leo can write at a pace of 1.5 pages per hour, and works for x hours, then he has written 1.5x pages so far. The difference of this with 6 will tell us what is left over. So the expression 6-1.5x is the amount of pages left, which is the value of y.
--------------
An example:
x = 2 so 1.5x = 1.5*2 = 3
At the 2 hour mark, Leo has written 3 pages. He has 6-1.5x = 6-1.5*2 = 6-3 = 3 pages left.
The diameter of a music CD is 12 centimeters. Find the circumference of a CD to the nearest tenth
Use the Commutative Property of
Multiplication to write a related
number sentence.
4 X 5 = 20
Answer:
5*4= 20
Step-by-step explanation:
The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
4*5 = 20
We can change to order and the result is still the same
5*4= 20
Answer:
so just think of it as you drawing circles with the number of shapes in each one like 4x6=24 draw 6 big circles and 4 squares in each one or in this case do it with 4x5
Step-by-step explanation:
what is the sum of the least and greatest amount of juice1 4/6 is the least 3 is the greatest show your work
Answer:
Min = 1 4/6
Max = 3
Sum = min + max
=> sum = 1 4/6 + 3
=> sum = 4 /4/6
Answer:
4 4/6
Step-by-step explanation:
