Side BG is the diagonal through the interior of the cube
Step-by-step explanation:
Given Cube with
Top face ABDC
Bottom Face EFHG
In a cube there are 4 interior diagonals
Side AD is the diagonal of the top face ABDC
Side CE is diagonal of the side face ACBE
Side DF is diagonal of the side face BDHF
Side BG is the diagonal through the interior of the cube
Hence , the Side BG is the diagonal through the interior of the cube
John drove from station A to station B a distance of 224 miles. On his way back, he increased his speed by 10 mph. If the journey back took him 24 minutes less, what was his original speed?
Answer: 70 mph
Step-by-step explanation:
224/x =224/x+10 +24/60
Solve equation
John's original speed was 70 mph.
Let's denote John's original speed as v (in mph).
The time taken for the first journey is 224 / v (hours).
His speed on the return trip is v + 10 mph.
The time taken for the return journey is 224 / (v + 10) (hours).
The time difference between the two journeys is 24 minutes, which is 24/60 = 0.4 hours.
Therefore, we set up the following equation:
224 / v - 224 / (v + 10) = 0.4
To solve this, we find a common denominator and solve for v:
224(v + 10) - 224v = 0.4v(v + 10)
2240 = 0.4[tex]v^2[/tex] + 4v
0.4[tex]v^2[/tex]+ 4v - 2240 = 0
Multiply by 10:
4[tex]v^2[/tex]+ 40v - 22400 = 0
Divide by 4:
[tex]v^2[/tex] + 10v - 5600 = 0
We solve this quadratic equation using the quadratic formula v = [-b ± √(b² - 4ac)] / 2a where a = 1, b = 10, and c = -5600:
v = [-10 ± √(10² - 4*1*(-5600))] / 2
v = [-10 ± √(100 + 22400)] / 2
v = [-10 ± √(22500)] / 2
v = [-10 ± 150] / 2
The possible solutions are:
v = (140 / 2) = 70 mph
v = (-160 / 2) = -80 mph (not feasible)
Thus, John's original speed was 70 mph.
Select the expression that is equivalent to the polynomial given below.
(4x + 3) (3x – 8)
O A. 128 - 23x-24
23x + 24
C.
128²-41x-24
D.
12x +41x + 24
Look at the attached picture⤴
Hope it will help u...
d(1)=13 d(n)=d(n−1)+17 Find the 4 th term in the sequence.
Answer:
the 4th term is 64
Step-by-step explanation:
Given
d(1) = 13
d(n) = d( n -1) +17
First
d(2) = d(2-1) + 17
= d(1) + 17
= 13 + 17
= 30
d(3) = d(3-1) +17
= d(2) + 17
= 30 +17
= 47
d(4) = d(4-1) + 17
= d(3) + 17
= 47 +17
=64
To find the 4th term in the sequence defined by d(n)=d(n-1)+17, we can use the formula recursively to compute the subsequent terms. Starting with d(1)=13, we can find d(4) by adding 17 repeatedly.
Explanation:The sequence is defined by the formula d(n)=d(n-1)+17, with d(1)=13. To find the 4th term in the sequence, we can use the formula recursively. Starting with d(1)=13, we can find d(2) by adding 17 to d(1): d(2)= d(1) + 17 = 13 + 17 = 30. Continuing this pattern, we find d(3) = d(2) + 17 = 30 + 17 = 47. Finally, we find d(4) = d(3) + 17 = 47 + 17 = 64.
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Olivia is putting decorations around a picture frame
Answer:
Olivia can decorate 88 inches squared.
Step-by-step explanation:
First, 14*8=112in^2
Next,6*4=24in^2
Lastly,112-24=88in^2
So, the answer is 88 inches squared
express the first quantity as a percentage of the second
a) 35 minute 2 hour
b )650g.3 kg
Answer:
a) 29% b) 22%
Step-by-step explanation:
The quantities must be expressed in the same units.
a) compare 35 minutes to 2 hours. 2 hours is 2 x 60 = 120 minutes.
35/120 = .291667 = 29%
b) compare 650 grams to 3 kilograms. 3 kg = 3 x 1000 = 3000 g.
650/3000 = .21667 = 22%
Answer:
see explanation
Step-by-step explanation:
To express as a percentage, first express as a fraction and multiply by 100%
The quantities must be expressed in the same units.
(a)
2 hours = 2 × 60 = 120 minutes, thus
[tex]\frac{35}{120}[/tex] × 100% ≈ 29.2% ( to 1 dec. place )
(b)
3 Kg = 3 × 1000 = 3000 g, thus
[tex]\frac{650}{3000}[/tex] × 100% ≈ 21.7% ( to 1 dec. place )
If the measure of Angle C A E is 95°, what is the measure of Arc C B A?
90°
95°
190°
195°
Answer: the answer is 190
Step-by-step explanation: I multiplied 95 by two
Answer:
C) 190
Step-by-step explanation:
Quadrilateral DUCK is inscribed in circle O what is the measure of
Answer:
95°
Step-by-step explanation:
Since, quadrilateral DUCK is inscribed in circle O
sum of the opposite angles of the quadrilateral is 180°
m<K +m<U= 180°
m<K= 180°- 85°= 95°
Answer:
95 degrees
Step-by-step explanation:
Quadrilaterals that are inscribed in circles are often called "cylic". Cyclic quadrilaterals have many unique properties. One of these is that opposite angles add up to 180 degrees.
Here, DUCK is a cyclic quadrilateral. "Opposite angles" are < U and < K, as well as < D and < C. So, since < U and < K are opposite angles in this inscribed quadrilateral, they add up to 180 degrees:
< U + < K = 180
We already know that < U = 85, so:
85 + < K = 180
< K = 95
Thus, < K is 95 degrees.
Hope this helps!
Which line is a trend line for the data?
Answer:
i dont know which line is it you tell me man
Step-by-step explanation:
yes so cool
5 Aaron wants to draw rectangles that each have an area of 36 square inches.
The length and width of each rectangle are whole numbers of inches.
Tell whether each statement about Aaron's rectangles is True or False
a. A rectangle can have a width of 3 inches.
True
b. A rectangle can have a length of 8 inches.
True
C. A rectangle can have a length of 18 inches and a width
of 2 inches.
True
False
False
False
d. A rectangle can have a width of 6 inches and a perimeter
that is less than 36 inches.
True
False
e. A rectangle can have a length of 9 inches, a width of
4 inches, and a perimeter equal to its area.
True
False
5 Aaron wants to draw rectangles that each have an area of 36 square inches.
The length and width of each rectangle are whole numbers of inches.
OK, we have Area=L×W where area is 36 and L and W are whole numbers, aka non-negative integers.
36=LW
a. A rectangle can have a width of 3 inches.
Sure, L=36/W = 36/3=12, a whole number. True
b. A rectangle can have a length of 8 inches.
W=36/L=36/8=9/2, not a whole number. False
C. A rectangle can have a length of 18 inches and a width of 2 inches.
Sure 18×2=36, our area. True
d. A rectangle can have a width of 6 inches and a perimeter
that is less than 36 inches.
L=36/6=6
It's a square, perimeter 6+6+6+6=24 which is of course less than 36
True
e. A rectangle can have a length of 9 inches, a width of 4 inches, and a perimeter equal to its area.
Perimeters can never really equal areas; they have different units. Let's just assume they mean they have the same number.
Area is 9×4=36, as desired. Perimeter is 9+4+9+4=26, not equal to its area.
False
This answer explains the possible dimensions for rectangles with an area of 36 square inches. The possible widths include 3 and 6 inches depending on the corresponding length. However, a length of 8 inches or 18 inches with a width of 2 inches, and a rectangle with a length of 9 inches and a width of 4 inches are false scenarios.
Explanation:The subject of these statements is about rectangles with an area of 36 square inches and their possible dimensions. For a rectangular area, you multiply the length by the width.
a. A rectangle can have a width of 3 inches: True. A rectangle with a width of 3 inches could have a length of 12 inches, giving an area of 36 square inches (3x12=36).b. A rectangle can have a length of 8 inches: False. There is no whole number that can be multiplied by 8 to give an area of 36.c. A rectangle can have a length of 18 inches and a width of 2 inches: False. Multiplying 18 by 2 gives an area of 36 square inches which is greater than the area allowable.d. A rectangle can have a width of 6 inches and a perimeter that is less than 36 inches: True. A rectangle with a width of 6 inches and a length of 6 inches has an area of 36 square inches and a perimeter of 24 inches, which is less than 36 inches.e. A rectangle can have a length of 9 inches, a width of 4 inches, and a perimeter equal to its area: False. A rectangle with a length of 9 inches and a width of 4 inches has an area of 36 square inches and a perimeter of 26 inches, and therefore the statement is false.Learn more about Rectangle Dimensions here:https://brainly.com/question/35474401
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If this fish tank is filled only halfway, how much water will it hold?
A. 1920 cubic inches
B. 42 cubic inches
C. 5880 cubic inches
D. 969 cubic inches
Answer:
I believe you typed your final answer choice incorrectly, as it should read 960 which is the correct answer
Step-by-step explanation:
the volume is 1920
1920/2=960
Answer:
960 cubic inches
Step-by-step explanation:
I took the test
I completed 2/3 of my project last month and 1/4 of it this week
Answer:
You've completed 11/12 of your project
Only 1/12 left to go!
Step-by-step explanation:
2/3 + 1/4 = 11/12
Answer:
Step-by-step explanation:
2/3+1/4=11/12
The human population of Earth was approximately 6 billion in 1998. If the rate of
population growth from then on was 2.3% per year, what would be the best
approximation for the human population (in billions) of Earth in 2020?
Answer:
9.89 billion
Step-by-step explanation:
At that rate of growth, the population is multiplied by 1.023 each year. After 22 years, the population would be ...
6·1.023^22 ≈ 9.89 . . . billion
Answer:
Let the equation for the population (P) growth be given by
P = P0ert, where P0 is the initial population in billioins at time t,
t is the number of years since 1987,
r is the rate of growth of population/year
In this case P0 = 5 billion and r = 0.02. Putting these values into the equaation:
P = 5e0.02t
Year 1995 is 8 years after 1987, then the population would be
P = 5e0.02*8 = 5e0.16 ≈ 5.87 billion people
Step-by-step explanation:
Evaluate 6h when h=8
Answer:
The answer is 48
Step-by-step explanation:
Answer:
48
Step-by-step explanation:
First, you plug 8 into the equation in place of h.
You can do this because h is equivalent to 8.
6(8)
Now we just multiply 6 and 8
6(8)=48
which answer choice shows the number four hundred sixty -five ten - thousandths in standard from
Answer:
4.65 x 10^-5
Step-by-step explanation:
.00465
[tex]4.65 x 10^{-5}[/tex]
This so for number 5
Answer:
219.8
Step-by-step explanation:
just multiply 157 times 1.4 and there you go!!
Since Sammy's stride is 1.4 meters, we simplify this to 1 meter for Estimation purposes. The field is 157 strides long, hence the estimated length of the field using compatible numbers is 157 meters.
To estimate the length of the field using compatible numbers, you first need to understand what each stride of Sammy's represents in standard units of length.
Sammy's stride is 1.4 meters.
We can simplify this to 1 meter for the sake of estimation.
Therefore, each stride Sammy takes is estimated to be roughly 1 meter.
Sammy finds that the field is 157 strides long.
To estimate the field's length in meters using compatible numbers, we simply take the number of strides Sammy counted (157) and replace his stride length with our simplified stride length (1 meter).
So, the estimated length of the field is 157 meters.
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The probable question may be:
5. For science class, Sammy is using the length of his stride to measure the length of a field. He finds that the field is 157 strides long. His stride measures 1.4 meters long. Use compatible numbers to estimate the length of the field.
What is the answer to this?
Answer:
9 meters
Step-by-step explanation:
Can you help me with this question please
Answer:
516
Step-by-step explanation:
First
34% small and 40% large means that 100 - (34 + 40) = 26% medium
26% of 600 = 0.26 × 600 = 156
----------------------------------------------------
Second
[tex]\frac{3}{10}[/tex] are small and [tex]\frac{1}{10}[/tex] are large, which means [tex]\frac{6}{10}[/tex] are medium
[tex]\frac{6}{10}[/tex] × 400 = 0.6 × 400 = 240
-----------------------------------------------------
Third
sum the parts of the ratio, 3 + 4 = 7
Divide 210 by 7 to find the value of one part of the ratio
210 ÷ 7 = 30 ← value of 1 part of ratio
Thus medium = 4 × 30 = 120
Total number of medium packets = 156 + 240 + 120 = 516
Transformers the following equation into slope-intercept. I need help ASAP
Answer:
Look at the attached work for a step by step solution and answer.
Step-by-step explanation:
a spere has a diameter of 24 units what is the volume in cubic units
Answer: 7238.23
Step-by-step explanation:
volume of a sphere is (4/3)(pie)(r^3)
so if the diameter is 24 than the radius is 12 so u would substitute that into the formula and you should get 7238.23
The correct answer is option D: 6,912π cubic units.
To find the volume (V) of a sphere, you use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where (r) is the radius of the sphere.
Given that the sphere has a diameter of 24 units, the radius (r) is half of the diameter, which is 24/2 = 12 units.
Now, substitute the value of the radius into the formula:
[tex]\begin{aligned}V & =\frac{4}{3} \pi(12)^3 \\V & =\frac{4}{3} \pi 1728 \\V & =\frac{6912}{3} \pi\end{aligned}[/tex]
Complete Question:
A sphere has a diameter of 24 units. What is its volume in cubic units?
A. 576π cubic units
B. 1,728π cubic units
C. 2,304π cubic units
D. 6,912π cubic units
CLUES
• I'm a 2-digit even number.
• The sum of my digits is 11.
• If you reverse my digits I
would be 27 less than I am.
Who am I?
Answer:
74
Step-by-step explanation:
a + b = 11
ab - ba = 27
10a + b - 10b - a = 27
10a - a + b - 10b = 27
9a - 9b = 27
9(a - b) = 27
a - b = 27 : 9
a - b = 3
a + b = 11
a - b = 3
_______ +
a + b + a - b = 11 + 3
2a = 14
a = 7
a + b = 11 => 7 + b = 11 => b = 11 - 7 => b = 4
ab = 74
What is 0.0068 in scientific notation?
Answer:
6.8 x 10^-3
Step-by-step explanation:
Answer:
6.8 x 10³
Step-by-step explanation:
|7m+4| =1 pls pls.
|7m + 4| = 1
It can equal either 1 or -1, so:
7m + 4 = 1
7m = -3
m = -3/7
7m + 4 = -1
7m = -5
m = -5/7
Three students were asked to find the cube root of 216. Each student’s method is shown below.
Hadley: RootIndex 3 StartRoot 216 EndRoot = 72 because 216 divided by 3 = 72. Florence: RootIndex 3 StartRoot 216 EndRoot = 648 because 216 times 3 = 648. Robi: RootIndex 3 StartRoot 216 EndRoot = 6 because 6 cubed = 6 times 6 times 6 = 216
Which student found the correct cube root of 216?
Answer:
The awnser is Robi
Step-by-step explanation:
I just took this lesson
Answer: Robi
Step-by-step explanation:
What is the expression in scientific notation? (7 x 10^−12)(4 x 10^5)?
Answer:2.8 x 10^-6. hope this helps :)
Final answer:
The expression (7 x 10⁻¹²)(4 x 10⁵) in scientific notation is 2.8 x 10⁻⁷.
Explanation:
The expression in scientific notation for the product (7 x 10⁻¹²)(4 x 10⁵) is found by multiplying the coefficients (7 and 4) and then adding the exponents of 10 (as they have the same base). Multiplying the coefficients gives us 28, and adding the exponents of 10 (-12 + 5) gives us -7 as the new exponent.
The final result in scientific notation is 2.8 x 10⁻⁷. Note that 28 is adjusted to 2.8 to maintain the correct form for scientific notation, which is one non-zero digit to the left of the decimal point.
Solve for a side in right triangles help
Answer:
The length of AB is 7.45 units.
Step-by-step explanation:
You can find the length of AB using Cosine Rule, cosθ = adj./hypo. :
θ = 20°
adj. = 7 units
hypo. = AB
cos 20° = 7/AB
AB = 7/cos 20°
= 7.45 units (3s.f)
Answer:
7.45
Step-by-step explanation:
Coleman graphed the relationship between the number of rotations of his front bike tire and the distance
he traveled past a tree. Negative distance means the tree is in front of Coleman and positive distance
means the tree is behind Coleman
Answer:
I feel like its either c or d but i'm not sure? I'm sorry for the inconvenience. I really did try.
Step-by-step explanation:
Answer:
the anwser is d none of the above
Step-by-step explanation:
What does the yyy-intercept represent?The yyy-intercept tells us the value of the yyy-variable when the xxx-variable equals 000.Hint #22 / 3In this context, xxx represents the number of tire rotations, and yyy represents the distance past the tree. So the y-intercepty-interceptstart color #ca337c, y, start text, negative, i, n, t, e, r, c, e, p, t, end text, end color #ca337c at (0,−15)(0,−15)left parenthesis, 0, comma, minus, 15, right parenthesis says after 000 tire rotations, Coleman was 151515 meters away from the tree and the tree was in front of him.55101015152020252510102020303040405050-10-10Tire rotationsDistance past the tree (m)(0,−15)(0,−15)The first and fourth quadrants of a coordinate plane. The horizontal axis is from zero to thirty with a scale of five and is titled Tire rotations. The vertical axis is from negative twenty to sixty with a scale of five and is titled Distance past the tree in meters. The graph of the line is y equals two point two five x minus fifteen. The point zero, negative fifteen is plotted and labeled.Hint #33 / 3The answerThe yyy-intercept represents the distance Coleman was away the tree when he started traveling.Since that was not an option, the answer is none of the above.
Here are six number cards.
-7 -5 -3 3 1 -1
Arrange the cards into three pairs with the same total.
Answer:
-7 3=-4
-5 1=-4
-3 -1=-4
-7 and 3 make -4. -5 and 1 make -4. -3 and -1 make -4.
The three pairs with the same total are as follow:
-7 + (3) = -4-5 + 1 = -4-3 -1 = -4What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes:
Positive Numbers: A number is positive if it is greater than zero. Example: 1, 2, 3 . . .Negative Numbers: A number is negative if it is less than zero. Example: -1, -2, -3 . . .Zero is defined as neither a negative number nor a positive number. It is a whole number.Given:
Number on cards -7 -5 -3 3 1 -1
Now, we have to make the pair according it gives the same total
-7 + (3) = -4
-5 + 1 = -4
-3 -1 = -4
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Mr. Stoebner has decided to buy MORE halloween costumes. MORE COSTUMES!!! If Mr. Stoebner has 10 costumes already, and his costume collection grows exponentially by 40% each year, what exponential equation would model this scenario.
y=40(10)x
y=10(40x)
y=10(1.4)x
y=10(0.4)x
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------
Answer: y=10(0.4)x.
Explanation: 0.4 is 40% in decimal form.
Which statement could be used to describe the functions?
O Both original functions have a domain of (-0,-).
O Both original functions have a domain of [-0, 2).
The domain of f(x) is [2, o), while the domain of g(x) is
(-0, 2]
O The domain of f(x) is (-00, 2], while the domain of g(x)
is [2, 0).
Answer:
number d im (pretty sure)
Step-by-step explanation:
Explain how to write an equation when given a
description of a mathematical problem or real-world scenario
PLEASE HELP!!!!
Answer:
Find key words
Step-by-step explanation:
The first part is to find your key words like each or more than one of that will normally be you variable. Then your numbers follow the variable. If its comparing 2 things more than likely you will need and equal sign.
Hope this helped!
Answer:
Say you are wanting to build a patio in your back yard but you want to know how much space you'll have let over. You need to find the area of your back yard and then see how big your patio is going to be. So you find the area of you patio and substrate it from the area of the back yard.
Step-by-step explanation:
Lemme know if you need more details