Ava bought a rectangular rug for her hallway. The rug is 2/3 yards wide and 2 3/4 yards long.
What is the area of the rug as a mixed number in simplest form?
Enter your answer in the box.
Answers
Related Questions
Jana finished 1/4 of her homework at school and 2/3 of it before dinner. How much of her homework has she finished so far?
Answers
1/4×3/3+2/3×4/4
3/12+8/12
11/12
Final answer:
Jana has completed 11/12 or 11 out of 12 of her homework so far.
Explanation:
To find out how much of her homework Jana has finished so far, we need to add together the fractions of her homework completed at school and before dinner.
Jana finished 1/4 of her homework at school and 2/3 of it before dinner.
To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we can convert both fractions to have a denominator of 12.
1/4 is equivalent to 3/12, and 2/3 is equivalent to 8/12.
Now, we can add the fractions: 3/12 + 8/12 = 11/12.
Therefore, Jana has completed 11/12 or 11 out of 12 of her homework so far.
HELP!!! What is the slant height x of the square pyramid? Express your answer in radical form.
Answers
make sure your calculator is in Degree mode.
To find the slant height of a square pyramid, we can use the Pythagorean theorem. The theorem should be applied as follows: A² = (y² + h²), to solve for A which is the slant height. Radical form implies that the answer will include the square root symbol.
Explanation:The question asks to find out the slant height x of a square pyramid. In order to do that, we have to invoke the Pythagorean theorem (x² + y² = h²). Here, x represents the slant height, y could be the half of the side of the base of the pyramid and h is the height from the base to the tip of the pyramid. Assuming that the pyramid is a right pyramid, the Pythagorean theorem applies.
So, the equation becomes A² = y² + h², where A is the slant height we are looking for. We solve for A to get, A = √(y² + h²). This is your slant height in radical form.
Please note you would need specific values for y and h to compute the numerical value of A.
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Russ is constructing the inscribed circle for △ABC . He has already used his compass and straightedge to complete the part of the construction shown in the figure.
What could be his next step?
A)Use the straightedge to draw a line through point N that intersects BC¯¯¯¯¯ .
B) Use the straightedge to draw the line through points M and P.
C) Place the point of the compass on point C and draw an arc that intersects AC¯¯¯¯¯ and BC¯¯¯¯¯ .
D)Place the point of the compass on point N and draw an arc that intersects AB¯¯¯¯¯ and BC¯¯¯¯¯ .
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Place the point of the compass on point C and draw an arc that intersects AC¯¯¯¯¯ and BC¯¯¯¯¯ .
Answer: The answer is (C) Place the point of the compass on point C and draw an arc that intersects AC and BC.
Step-by-step explanation: Given that Russ is constructing the inscribed circle for △ABC and he has already used his compass and straightedge to complete the part of the construction shown in the given figure. We are to find his next step.
Since Russ has already constructed the angle bisector of ∠B, so next he shoul construct the angle bisector of either ∠A or ∠C. Since the steps for constructing angle bisector of ∠A are not in the options, so he should go with ∠C. For that, he must place the point of the compass on the point C and draw an arc that intersects AC and BC.
Thus, (C) is the correct option.
Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?
Answers
lets x = measure of angle Y
x + 3x = 180
4x = 180
x = 45
angle Y = 45
angle X = 3 x 45 = 135
answer
Angle X = 135
Answer:
The measure of ∠X is 135°
Step-by-step explanation:
Given that angles X and Y are supplementary and also angle X is 3 times the measure of angle Y.
we have to find the measure of angle X.
Since X and Y are the supplementary therefore these add up to 180° i.e
[tex]\angle X+\angle Y=180\°......(1)[/tex]
Also angle X is 3 times the measure of angle Y i.e
[tex]\angle X=3\angle Y[/tex]
Substitute this value in equation (1), we get
[tex]3\angle Y+\angle Y=180\°......(1)[/tex]
[tex]4\angle Y= 180\°[/tex]
[tex]\angle Y=\frac{180\°}{4}=45\°[/tex]
[tex]\angle X=3\times 45\°=135\° [/tex]
Hence, the measure of ∠X is 135°
What is the value of the missing number in the sequence below? 4, 12, 36,___, 324, 972, 2916
Answers
The missing number will be 108. The sequence is; 4, 12, 36,108, 324, 972, 2916.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The given sequence is;
4, 12, 36,108, 324, 972, 2916
It is observed from the sequence that the following sequence follow a specific rule in which the progressive term is multiplied by a factor of 3.
[tex]\rm 4 \times 3 = 12 \\\\ 12 \times 3 = 36 \\\\ 36 \times 3 =108[/tex]
Hence, the missing number will be 108.
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How do I solve for h
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.. AD = AC -DC = 20 -4
.. AD = 16
Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8
Selection D is appropriate.
_____
You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))
An artist drew a rectangle. the artist then modified the rectangle so thatthe length ofthe rectawngle increased by 30 percent and the width of the rectangle decreased by 40 percent. after the modification, what was the percent decrease in the area of the rectangle?
Answers
length - L
width - W
area = L*W = LW
after the modification, new dimensions are
length increased by 30 %
Length = L * 1.3 = 1.3L
Width = W * 0.6 = 0.6W
new area = 1.3L * 0.6W
= 0.78LW
the percent decrease in area
decrease % = (difference in area)/original area * 100
= (LW - 0.78LW)/LW * 100
= 0.22LW/LW * 100
= 22%
percent decrease is 22%
Out of 1100 discs tested 13 are defective. Estimate the number of defective discs in a batch of 41000
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Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are the coordinates of B' after the translation?
a.(1, 6)
b.(–3, 6)
c.(0, 0)
d.(3, 1)
Answers
Answer:
b. [tex](-3,6)[/tex]
Step-by-step explanation:
We have been given that triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up.
To find the coordinates of B', we will shift x-coordinate of point B to left by 3 units and y-coordinate of point B to 1 unit up.
After the given transformation the coordinates of point B' would be:
[tex]B(0,5)\rightarrow B'((0-3),(5+1))\rightarrow (-3,6)[/tex]
Therefore, the coordinates of point B' are [tex](-3,6)[/tex] and option 'b' is the correct choice.
A $6,300.00 principal earns 6% interest, compounded annually. After 3 years, what is the balance in the account?
Answers
Hope this helped!
To find this answer, you have to start with 6,300 and multiply it by 1.06 three times. We are using 1.06 because we are adding 6% (0.06) onto the total 3 times.
6300 x 1.06 x 1.06 x 1.06 = $7,503.40
OR
6300(1.06)^3 = $7,503.40
The second equation is written as a compound interest equation. You just need to switch the 3 if you want to find the total for a different amount of years.
I hope this helps, Good luck!
If f(x) = 2x - 7, what is the value of f(2)?
A.-3
B.-5
C.5
D.3
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Triangle ABC is translated on the coordinate plane below to create triangle A'B'C':
If parallelogram EFGH is translated according to the same rule that translated triangle ABC, what is the ordered pair of point H'?
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In the triangle, point A is moved 5 units to the right and down 6 units. If you count the same amount of space right and down from point H, you will end up on point (6, -5).
These are the new coordinates after the translation.
The new coordinates of Point H' will be (6, -5) after the translation.
Triangle ABC is translated on the coordinate plane below to create triangle A'B'C':
If parallelogram EFGH is translated according to the same rule that translated triangle ABC.
How to find the point after translation?In the triangle, point A is moved 5 units to the right side and down 6 units.
If we count the same amount of space right side and down from point H, we will end up on a point (6, -5).
Therefore, The new coordinates of Point H' will be (6, -5) after the translation.
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Please help me, i don't understand how to do this.
Solve V = 1 3 πr2h for h.
A) 3V πr2
B) V 3πr2
C) r sqrt 3V π
D) V - 1/3 πr2
Answers
so h = 3v/πr2
Hey can somebody help me? I know it seems easy but I forgot the process on how to do this. Thanks in advance!
---------------------------------
1 1/2 - 1/2 = ???
Show your work please so I understand
Answers
Sorry if this was a bit unclear, I did my best to explain ;)
Hope this helps!
What is the image of the point (4,-2) after a rotation 270 degree clockwise about the origin?
Answers
(4, -2) becomes (2, 4) after rotation.
Answer:
The image of the point (4, -2) is (2, 4).
Step-by-step explanation:
Since, the rule of rotation 270 degree clockwise about the origin is,
[tex](x,y)\rightarrow (-y,x)[/tex]
Where, (-y,x) is the image of the point (x,y),
Thus, by the above rule,
[tex](4,-2)\rightarrow (-(-2), 4)[/tex]
Hence, the image of the point (4, -2) is (2, 4).
At the beginning of an experiment, there are 600 grams of contaminants. Each hour, half of the contaminants are filtered out. How many grams of contaminants remain after 4 hours?
Answers
Second hour - 150
Third hour - 75
Fourth hour - 37.5
A wood frame costs $1.50. Use a property to write an equivalent expression for the cost of a wood frame.
Answers
Let the cost of a linear foot of the frame = y
Let the inside dimension of the length of the frame = a
Let the inside dimension of the width of the frame = b.
The total length of the frame = 2*a + 4x
The total width of the frame = 2b
The total amount of the frame in feet is (2a + 4x + 2b)*y = Cost
If this is incorrect please leave a message on my home page.
Where is the vertex of the parabola?
y = x2 + 6x + 7
above the x-axis
on the x-axis
on the y-axis
below the x-axis
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Answer:
below the x axis
Step-by-step explanation:
i took the test
I need help with this as well
Answers
n 20 ------------> BC/CD=[AC-AB]/[AD-AC]=(6-4)/(9-6)=2/3
n 21-------------> BD/AE=[AD-AB]/[AE]=(9-4)/(12)=5/12
n 22 7 and 28 find the geometric mean of the two number
step 1
Multiply the two numbers together:
28*7=196
step 2
take the square root:
sqrt(196)=14
the answer is 14
n 23 Simplify the ratio 10 ft/30 in---> divided between 2 both members
5 ft/15 in-----> divided between 5 both members ---> 1 ft/3 in
n 24
if AB=4 -------> AB~FG
FG=8
then
AB*factor=FG-------- > 4*factor=8-- > factor=8/4=2
the figure ABCDE is half of the figure FGHJK
then
BC=4
AE=CD=5
and
ED=6
therefore
the perimeter=[4+4+5+5+6]=24 units
Can someone check my answer?
For y = x2 − 4x + 3,
Determine if the parabola opens up or down.
State if the vertex will be a maximum or minimum.
Find the vertex.
Find the x-intercepts.
Describe the graph of the equation.
Show all work and use complete sentences to receive full credit.,
Answers
The function below can be used to calculate the cost of making a long distance call, f(m), which is based on a $2.50 initial charge and a fee of $.12 per minute, m, that the call lasts. If Natalie paid $6.82 for one call, how many minutes long was it?
Answers
if Natalie paid $6.82
6.82 = 2.5 + 0.12m
0.12m = 6.82 - 2.5
0.12m = 4.32
m = 4.32 ÷ 0.12
m = 36
The call was 36 minutes long.
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 7 in?
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Answers
The length of the hypotenuse is 14in
SOH CAH TOA identityGiven a 30-60-90 triangle where:
Length of the shorter leg = 5cm (adjacent)
The hypotenuse is what we need..
[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]
Substitute the given parameters
[tex]cos 60 = \frac{7}{h}\\ h =\frac{7}{cos 60}\\ h = \frac{7}{0.5}\\ h = 14in\\ [/tex]
Hence the length of the hypotenuse is 14in
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Can anyone help me I don’t know how to do this
Answers
y = a(x -h)² +k . . . . . . . . for some stretch factor "a" and vertex (h, k)
1. Vertex = (h, k) = (0, 0). Stretch factor can be found from the given point (x, y).
8 = a(-2 -0)² +0
8 = 4a . . . . . . . . simplify
2 = a . . . . . . . . . divide by the coefficient of "a"
Your equation is y = 2x².
Note the above method for solving these problems. It repeats.
2. As above, substitute what's given and solve for what's not.
3 = a(1 -2)² +0
3 = a
Your equation is y = 3(x -2)²
3. Repeat
-4 = a(-5 +3)² +0
-4 = 4a
-1 = a
Your equation is y = -(x +3)²
4. Are you seeing the pattern yet?
0 = a(-1 -0)² +1
0 = a +1
-1 = a
Your equation is y = -x² +1
5 & 6. You know that if you want a zero (x-intercept) to be located at x=a, then a factor of the quadratic will be (x -a). Multiply the factors together to get your quadratic function.
5. y = (x -0)*(x -2) = x² -2x
6. y = (x +5)*(x -5) = x² -25 . . . . . . . . . . you should recognize this "special form", the factoring of the difference of squares
Easy Algebra 2 Rational Expressions question
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y - 3 = 0
y = 3 - this is where the fraction is undefined (or nonpermissible)
how is jimthompson so smart?
Also can you please help me with that question.
I got everything except for the Euler Diagram.
Answers
Step 1) Draw a large circle and label it circle A
Step 2) Inside this large circle, draw a smaller circle and label it circle B
Circle A will represent the set of all obtuse angles (any angles that are between 90 and 180 degrees). Circle B represents only one item: the angle value of 150 degrees. All of circle B is inside circle A because 150 degrees is between 90 and 180; therefore, 150 is obtuse. This is simply the definition of what "obtuse" means.
So if you threw a dart and it landed in circle B, then you know for sure it landed in circle A as well. This is effectively saying "if you get a 150 degree angle, then you know its obtuse"
This is a visual way to back up the conditional statements you used earlier and help add more evidence that the statement "A 150 degree angle is an obtuse angle" is a valid statement.
angle measure represented by 4.5 rotations counterclockwise
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now, a full rotation, namely a "revolution", is a full go-around the circle, that'd be 360°, now if you 4 times around, that be 4*360 or 1440°, and if you go an extra 0.5 or half a circle, that'd be 180°, that will land us on 1440° + 180°.
is -3 larger than -2?
only answer if you know and not for the points
Answers
Your answer is no.
-3 is not larger than -2. This is because the larger the number is with a negative sign, the smaller the number is!
Hope this helps you.
Have a great day!
No.
-3 is not greater than -2.
When we are speaking about negative numbers, the "lower" the number is, the greater. -2 is greater than -3 because it is closer to the positive side than negative side. -3 is farther away from 0. But as for -2, is alot closer to 0 than -3.
Your answer, No.
I hope this helps you!
What is the length of DD'?
Answers
Answer:
The length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.
Step-by-step explanation:
The distance formula is
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the given figure it is clear that the coordinates of D are (2,0) and coordinates of D' are (7,2).
Using distance formula we get
[tex]DD'=\sqrt{(7-2)^2+(2-0)^2}[/tex]
[tex]DD'=\sqrt{25+4}[/tex]
[tex]DD'=\sqrt{29}[/tex]
[tex]DD'\approx 5.39[/tex]
Therefore the length of DD' is [tex]\sqrt{29}[/tex] or 5.39 units.
A child walks due east on the deck of a ship at 4 miles per hour.
The ship is moving north at a speed of 12 miles per hour.
Find the speed and direction of the child relative to the surface of the water.
Speed = mph
The angle of the direction from the north = (radians)
i have the speed i couldn't find the direction !,
Answers
Therefore, to get the speed relative to the surface you have to sum the two vectors, which means you can apply the Pythagorean theorem to find the hypotenuse, having the two legs.
h = √(4² + 12²) = √160 = 4√10 = 12.65mph
In order to find the direction, you need to use trigonometry:
- the sine of an angle is given by the ratio between the opposite side divided the hypotenuse;
- the cosine of an angle is given by the ratio between the adjacent side divided by the hypotenuse.
You can use either one, I will show you both:
sinα = O / H
inverting the formula: α = arcsin (O / H) = sin⁻¹ (O / H)
these two forms are equivalent.
Similarly:
cosβ = A / H
β = arccos (A / H) = cos⁻¹ (A / H).
Substituting your numbers:
α = sin⁻¹ (12 / 12.65) = sin⁻¹ (0.9486) = 1.25rad
β = cos⁻¹ (4 / 12.65) = cos⁻¹ (0.3162) = 1.25rad
As you can see, α = β so you can use either formula.
Your answer will then be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 1.25rad from East towards North.
ATTENTION!
If you drew first the vector towards North and then the one towards East, you get an equivalent triangle, which is rotated by 180° respect to the previous one. This way, what you earlier called Opposite is now Adjacent and vice-versa, but the formulas are still valid.
You will get:
α = sin⁻¹ (4 / 12.65) = sin⁻¹ (0.3162) = 0.32rad
β = cos⁻¹ (12 / 12.65) = cos⁻¹ (0.9486) = 0.32rad
And your answer will be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 0.32rad from North towards East.
Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6 rolls of quarters containing 40 coins each. How much money does she have?
A. $106.20
B. $17.50
C. $8.00
D. $94.50
Answers
value of penny - $ 0.01
value she has from pennies - $0.01 x 150 = $1.50
total number of nickels she has - 4 x40 = 160
value of nickel - $ 0.05
value she has from nickels - $0.05 x 160 = $8
total number of dimes she has - 5 x 50 = 250
value of dime - $ 0.10
value she has from dimes - $0.10 x 250 = $25
total number of quarters she has - 6 x 40 = 240
value of quarter - $ 0.25
value she has - $ 0.25 x 240 = $ 60
total amount of money she has = 1.50 + 8 + 25 + 60
money she has = $ 94.50
correct answer is D