Answers
====================================================
Explanation:
Each cube has a side length of 4. Placed together like this, the total horizontal side combines to 4+8 = 8. This is the segment HP as shown in the diagram below. I've also added point Q to form triangle HPQ. This is a right triangle so we can find the hypotenuse QH
Use the pythagorean theorem to find QH
a^2 + b^2 = c^2
(HP)^2 + (PQ)^2 = (QH)^2
8^2 + 4^2 = (QH)^2
(QH)^2 = 64 + 16
(QH)^2 = 80
QH = sqrt(80)
Now we use segment QH to find the length of segment EH. Focus on triangle HQE, which is also a right triangle (right angle at point Q). Use the pythagorean theorem again
a^2 + b^2 = c^2
(QH)^2 + (QE)^2 = (EH)^2
(EH)^2 = (QH)^2 + (QE)^2
(EH)^2 = (sqrt(80))^2 + (4)^2
(EH)^2 = 80 + 16
(EH)^2 = 96
EH = sqrt(96)
EH = sqrt(16*6)
EH = sqrt(16)*sqrt(6)
EH = 4*sqrt(6), showing the answer is choice C
-------------------------
A shortcut is to use the space diagonal formula. As the name suggests, a space diagonal is one that goes through the solid space (rather than stay entirely on a single face; which you could possibly refer to as a planar diagonal or face diagonal).
The space diagonal formula is
d = sqrt(a^2+b^2+c^2)
which is effectively the 3D version of the pythagorean theorem, or a variant of such.
We have a = HP = 8, b = PQ = 4, and c = QE = 4 which leads to...
d = sqrt(a^2+b^2+c^2)
d = sqrt(8^2+4^2+4^2)
d = sqrt(96)
d = sqrt(16*6)
d = sqrt(16)*sqrt(6)
d = 4*sqrt(6), we get the same answer as before
The space diagonal formula being "pythagorean" in nature isn't a coincidence. Repeated uses of the pythagorean theorem is exactly why this is.
Related Questions
What are the solutions of the equation (x+2)^2-2x(x+2)-15=0? Use u substitution to solve.
Answers
Answer:
3
Step-by-step explanation:
Answer: x = -5 and x = 3
Step-by-step explanation:
on edg
Exercise topic: Permutations and Combinations. A company wants to hire 3 new employees, but there are 8 candidates, 6 of them which are men and 2 are women. If the selection is random: a) In how many different ways can choose new employees? b) In how many different ways can choose a single male candidate? c) In how many different ways can choose at least one male candidate? with procedures. Help me please..
Answers
Answer:
(a) 56 ways
(b) 6 ways
(c) 56 ways
Step-by-step explanation:
Given:
candidates: 6 mail, 1 female
number to hire : 3
a) In how many different ways can choose new employees?
use the combination formula to choose r to hire out of n candidates
C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways
b) In how many different ways can choose a single male candidate?
6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways
c) In how many different ways can choose at least one male candidate?
To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.
Since there are only two females, there is no way to choose 3 female candidates.
In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.
PLEASE HELP ME GUYS Consider adjacent angles that measure (2x + 45)° and (3x + 55)°. The sum of the measures of these two angles is 135°. Write and solve and equation to find the value of x and the measure of the two angles.
Answers
Answer:
x=7
2x+45=59
3x+55=76
Step-by-step explanation:
Answer:
7°, 59°, 76°
Step-by-step explanation:
The equation for the sum of the angles:
(2x + 45)° + (3x + 55)° = 135°Solving for x:
(5x + 100)°= 1355x= 35x= 35°/5x= 7°The angles:
(2x + 45)°= 2*7°+45° = 59°(3x+55)°= 3*7° + 55° = 76°Simplify.
B2 x b6=??
Answers
Answer:
b^8
Step-by-step explanation:
When multiplying exponents with the same base, we can add the exponents
b^2 * b^6
b^ (2+6)
b^8
Answer:b8 x
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "b6" was replaced by "b^6". 1 more similar replacement(s).
STEP
1
:
Multiplying exponential expressions
1.1 b2 multiplied by b6 = b(2 + 6) = b8
Final result :
b8x
Determine if the function below is continuous.
Answers
Answer:
No
Step-by-step explanation:
I believe at the point of (1,1) there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous.
Continuous means that there is no abrupt changes (google) and im sure you know this already (im just saying no offence to anyone's intelligence)
The given function is not continuous. The correct option is D.
What is a continuous function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value.
The point of (1,1) there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous. Continuous means that there are no abrupt changes.
It is shown in the graph that the function is reducing continuously at the point ( 1,-1) and after that, there is a sudden change in the function after that it becomes constant or parallel to the x-axis.
Because there is a sudden change in the function it will be termed a discontinuous function.
Hence, the function is not continuous, and the correct option is D.
To know more about continuous function follow
https://brainly.com/question/18102431
#SPJ5
ASAP!!! PLEASE help me with this question!
Answers
Answer:
C. 16π
Step-by-step explanation:
Well we need to find the area of the top circle which has a radius of 4cm.
π(4)^2
16π in terms of pi
Thus,
the answer is C. 16π.
Hope this helps :)
Based on the table, which best predicts the end
behavior of the graph of f(x)?
As x, f(x) —, and as x->-0, f(x) →..
As x 700, f(x) →, and as x -→-00, f(x) →--.
As x, f(x) →-00, and as x———00, f(x)
As x -+-0, f(x) →-00, and as x->-00, f(x) -
->
-→-00
Answers
Answer:
The correct option is;
As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞
Step-by-step explanation:
The values given are;
x, f(x)
-4, 18
-3, 9
-2, 6
-1, 3
0, 0
1, -3
2, -6
3, -9
4, -18
Based on the table, as the magnitude of x increases in the positive direction, the magnitude of f(x) increases in the negative direction
Therefore, the correct option that best predicts the end behavior of the graph of f(x) is As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞.
PLEASE HELPP!!!
Find C to two decimal places and find the measure of angle B.
Answers
Answer:
<B = 32°
c = 9.43
Step-by-step explanation:
To find the measure of <B, add up the measures of the two angles that you know and subtract from 180°.
58° + 90° = 148°
180° - 148° = 32°
The measure of <B is 32°.
To find the length of side c, use the Pythagorean Theorem.
a² + b² = c²
5² + 8² = c²
25 + 64 = c²
89 = c²
c = √89
c = 9.433981132 ⇒ 9.43 (rounded to two decimal places)
The length of side c = 9.43.
Hope that helps.
If y is a positive integer, for how many different values of y is RootIndex 3 StartRoot StartFraction 144 Over y EndFraction EndRoot a whole number? 1 2 6 15
Answers
Answer:
2 possible values
Step-by-step explanation:
The given expression is:
[tex]\sqrt[3]{\frac{144}{y} }[/tex]
In order for this to result in a whole number, 144/y must be a perfect cube, the possible perfect cubes (under 144) are:
1, 8, 27, 64, 125
The values of y that would result in those numbers are:
[tex]y=\frac{144}{1}=144 \\y=\frac{144}{8}=18 \\y=\frac{144}{27}=5.333\\y=\frac{144}{64}=2.25\\y=\frac{144}{125}=1.152[/tex]
Only two values of y are integers, therefore, there are only two possible values of y for which the given expression results in a whole number.
Answer:it’s b
Step-by-step explanation:
Just took quiz on edge 2020
Solve for X and determine the measure of each angle.
X
(x - 35)
X
(2x - 75°)
Answers
it's a quadrilateral
interior angles add up to 360
x + 2x - 75 + x + x - 35 = 360
5x - 110 = 360
5x = 360 + 110
x = 470 ÷ 5
x = 95
and x - 35 = 60
2x - 75
= 190 -75
= 115
Answer:
see explanation
Step-by-step explanation:
The sum of the interior angles of a quadrilateral = 360°
Sum the given angles and equate to 360
x + x + x - 35 + 2x - 75 = 360, that is
5x - 110 = 360 ( add 110 to both sides )
5x = 470 ( divide both sides by 5 )
x = 94 , then
x - 35 = 94 - 35 = 59
2x - 75 = 2(94) - 75 = 188 - 75 = 113
Thus
The 4 angles are 59°, 94°, 94°, 113°
I can’t figure it out
Answers
Answer:
5inch
Step-by-step explanation:
15_10=5
because full length is 15 cm given on another side and length of some part of another side is. given.so we have to subtract it
Answer:
5 inches
Step-by-step explanation:
You can notice that the 15 in side is parallel to the 10 in side and the missing side
let x be the missing side
10+x = 15 substract 10 from both sides 10-10+x = 15-10 x = 5so x is 5 inches
A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters. If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
A. Different sample proportions would result each time, but for sample size 400 they would be centered (have their mean) at the true population proportion, whereas for sample size 1,600 they would not.
B. Different sample proportions would result each time, but for sample size 1,600 they would be centered (have their mean) at the true population proportion, whereas for sample size 400 they would not.
C. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
D. For either sample size, using the same size each time, as long as the samples are drawn with replacement, they would be centered (have a mean) at 0.
Answers
Answer:
C. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
Step-by-step explanation:
From the given information;
A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate.
A random sample is usually an outcome of any experiment that cannot be predicted before the result.
SO;
One plan is to select 400 voters, another plan is to select 1,600 voters
If the study were conducted repeatedly (selecting different samples of people each time);
Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion. This is because a sample proportion deals with random experiments that cannot be predicted in advance and they are quite known to be centered about the population proportion.
I need this done help!!
Answers
Answer:
Because the triangle is isosceles, the base angles are congruent, meaning that the angles that are not right angles are x and x. Since the sum of angles in a triangle is 180°, we can write:
90 + x + x = 180
x + x = 90
2x = 90
x = 45°
Answer:
45 degrees
Step-by-step explanation:
This triangle is "isosceles..." two legs are equal. Thus, the triangle has two 45 degree angles. The indicated angle is 45 degreees.
The hanger image below represents a balanced equation.
3
5
2
Write an equation to represent the image.
Answers
Answer:
The answer is 1/5 + z = 3/5
Step-by-step explanation:
Answer:
1/5+z=3/5
Step-by-step explanation:
A sector with an area of 30 pi cm^2 has a radius of 10cm. What is the central angle measure of the sector of the degree?
Answers
Answer:
108
Step-by-step explanation:
A car manufacturer wants to analyze the safety features of 7 different car models by comparing each model with every other model. If each comparison costs $4,000, how much will the manufacturer spend altogether?
Answers
Answer:
28,000
Step-by-step explanation:
multiply 7 cars with 4,000
Find the interquartile range for a data set having the five-number summary: 5.6, 11.1, 19.2, 24.5, 33.3
Answers
Answer:
interquartile range=20.55
Step-by-step explanation:
5.6, 11.1, 19.2, 24.5, 33.3
median is 19.2
Q1=(5.6+11.1)/2=8.35
Q3=(24.5+33.3)/2=28.9
interquartile range= Q3-Q1=28.9-8.35=20.55
A rectangular prism has a length of 5 meters, a width of 6 3/4 meters, and a height of 3 1/2 meters. What is the volume of the prism?
Answers
Answer:
118.13 m³Step-by-step explanation:
Given,
Length ( l ) = 5 meters
Width ( w ) = [tex]6 \frac{3}{4} [/tex] meters
Height ( h ) = [tex]3 \frac{1}{2} [/tex] meters
Now, Let's find the volume of rectangular prism :
[tex]volume \: = l \: \times \: w \: \times \: h[/tex]
plug the values
[tex] = 5 \times \frac{27}{4} \times \frac{7}{2} [/tex]
Calculate the product
[tex] = \frac{5 \times 27 \times 7}{4 \times 2} [/tex]
[tex] = \frac{945}{8} [/tex]
[tex] = 118.13 \: {m}^{2} [/tex]
Hope this helps..
Best regards!!
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answers
Answer:
x = 50°Step-by-step explanation:
To find x we use cosine
cos ∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 18
So we have
cos 69 = 18/x
x cos 69 = 18
Divide both sides by cos 69
x = 18/cos 69
x = 50.2
x = 50° to the nearest tenth
Hope this helps you
Anyone want to help me out?
Answers
Answer:
SAS Postulate (third option)
Step-by-step explanation:
A trick that I use is that s stands for side and a for angle
the picture shows that two sides are the same which means the SS
and one angle is the same, hence the one A
Hope this helps!
Amelia is looking at the top of a lighthouse. She knows she is 30 feet from the base of
the lighthouse. If she is 5.5 feet tall and the angle of elevation is 34° how tall is the
lighthouse? Write only the number rounded to the nearest tenth of a foot.
Answers
Answer:
25.7 feet
Step-by-step explanation:
We are solving a right angled triangle.
We are the Trigonometric function of Tangent
tan θ = Opposite side/Adjacent
Angle of Elevation = θ = 34°
Opposite side = Height
Adjacent = 30 feet
tan 34° = Opposite side/30 feet.
Opposite side = tan 34° × 30 feet
Opposite side = 20.235255505 feet
The height of the light house =
Opposite side(height) + Amelia's height
20.235255505 feet + 5.5 feet
= 25.735255505 feet
Approximately to the nearest tenth ≈ 25.7 feet
please Evaluate (1/6) to the 3 power A.) 1/216 B.) 1/36 C.) 1/18 D.) 1/9
Answers
Answer:
A-1/216
Step-by-step explanation:
(1/6)^3 is the same as: 1^3/6^3. Since one to any power is always 1, it woudl just be 1/6^3. 6^3 is 216, so the answer would be 1/216.
Hope this is helpfule! :)
Answer:
1/216
Step-by-step explanation:
(1/6)^3
(1/6) * (1/6) * (1/6)
1/216
Represent the expression (1×10,000)
Answers
Answer:
10,000
Step-by-step explanation:
1 * 10,000 = 10,000
Answer:
10000 = 1 *10^4
Step-by-step explanation:
1* 10000
10000
In scientific notation
There are 4 zeros
1 * 10 ^4
Max and Sven bike away from home in the same direction starting at noon. They bike at constant speeds. Max bikes at xmph and he is ymph faster than Sven. By 4pm, how far ahead of Sven would Max be?
Answers
Answer:
Max would be 4y meters ahead by 4pm
Step-by-step explanation:
What we want to calculate here is the difference in the distance they have covered by 4pm given the speed at which they traveled.
Mathematically, distance = speed * time
The time is just the difference between 12 noon and 4pm which is 4 hours
Let’s tackle Max’s
He’s biking at x km/h, so the distance he would have covered by 4pm would be 4 * x = 4x meters
Now let’s tackle Sven
Sven is biking at a speed which is y mph less than Max’s x mph
Thus his speed would be (x-y) mph
His distance covered would be 4(x-y) meters
Now the difference between their bikes distance at 4pm would be;
4x - [4(x-y)]
= 4x -(4x -4y)
4x -4x + 4y
= 4y
Hence, Max would be 4y meters ahead by 4pm
Select the correct answer. What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? A. x2 + y2 − 4x + 2y + 1 = 0 B. x2 + y2 + 4x − 2y + 1 = 0 C. x2 + y2 + 4x − 2y + 9 = 0 D. x2 − y2 + 2x + y + 1 = 0
Answers
Answer:
x^2 +4x + y^2 -2y +1 =0
Step-by-step explanation:
First we need to find the radius
Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2
A circle can be written in the form
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--2)^2 + (y-1)^2 = 2^2
(x+2)^2 + (y-1)^2 = 4
FOIL ing
x^2 +4x+4 + y^2 -2y +1 = 4
Combining like terms
x^2 +4x + y^2 -2y +5 -4 =0
x^2 +4x + y^2 -2y +1 =0
Answer and Step-by-step explanation:
Answer:
x^2 +4x + y^2 -2y +1 =0
Step-by-step explanation:
First we need to find the radius
Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2
A circle can be written in the form
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--2)^2 + (y-1)^2 = 2^2
(x+2)^2 + (y-1)^2 = 4
FOIL ing
x^2 +4x+4 + y^2 -2y +1 = 4
Combining like terms
x^2 +4x + y^2 -2y +5 -4 =0
x^2 +4x + y^2 -2y +1 =0
There are 5 orange bumper cars and 3 green bumper cars that are being tested
for safety for a ride at an amusement park. Two bumper cars are tested at
random, one at a time, without retesting the same car.
Find the probability that both cars are orange.
Enter the correct answer in the box.
Answers
Answer:
5/14
Step-by-step explanation:
I assume after testing the 1st car, it is not placed back into the pool.
So, 1st test orange is 5/8
2nd test orange is 4/7.
Both had to be true, so 5/8 x 4/7 = 5/14
Omar has a new credit card.He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points, how much money did he spend?Easy question for easy points
Answers
Answer:
$600
Step-by-step explanation:
1800/300 = 6
6 x 100 = $600
Answer:
$600
Step-by-step explanation:
1800/300 = 6
6 x 100 = $600
Please answer this in two minutes
Answers
Mr. Berger assigned the following system of equations to be solved for homework. 2 x minus 3 y = negative 12. 4 x + y = negative 10. Which is the x-coordinate of the correct solution? x = negative 3 x = negative one-fifth x = StartFraction 9 Over 7 EndFraction x = 2
Answers
Answer:
x=-3
Step-by-step explanation:
2 x - 3 y = -12.
4 x + y = -10.
The Answer is:
X= -3
For the function whose graph is shown, which is the correct formula for the function?
Answers
Answer:
y=-2x+3 (first choice)
Step-by-step explanation:
-y-intercept is at positive 3, so the "b" value is +3
-the line is going downward from left to right, so the slope is negative
-slope is defined as rise over run, which is 2/1, or 2, so the "m" value is -2
-that gives you the functions equation to be y=-2x+3.