4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.
[2]
a. Draw a picture of the rectangle
[4]
b. Write an EXACT expression for the base and the height of the rectangle.
[2]
C. Use your expressions to find the EXACT area of the rectangle.
9514 1404 393
Answer:
a) see attachment
b) base: 4, height: 4√3
c) area: 16√3
Step-by-step explanation:
a) The figure is drawn in the attachment
__
b) The side lengths of a 30-60-90 right triangle have the ratio ...
1 : √3 : 2
Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.
__
c) The area is the product of base and height:
A = bh
A = 4(4√3) = 16√3 . . . . square units
3x-2y=1x+4y=33 elimination process
Answer:
x = 5 ; y = 7
Step-by-step explanation:
3x - 2y = 1 --------------------(I)
x + 4y = 33 ------------(II)
Multiply equation (II) by (-3) and then add. So, x will be eliminated and we can find the value of y
(I) 3x - 2y = 1
(II)*(-3) -3x -12y = -99 {Now add}
- 14y = -98
y = -98/14
y = 7
Plugin y = 7 in equation (I)
3x - 2*7 = 1
3x - 14 = 1
3x = 1 + 14
3x = 15
x = 15/3
x = 5
A=
B=
Blank 1:
Blank2:
Answer:
a=3,b=1
Step-by-step explanation:
In a parallelogram opposite sides are equal/congruent.
Using this, we know that 3a-4=a+2 and b+1=2b
1st equation:
3a-4=a+2
-a -a
2a-4=2
+4 +4
2a=6
a=3
2nd equation:
b+1=2b
-b -b
b=1
a=3, b=1
A figure has been dilated from the origin by a scale factor of one seventh. if another dilation from the origin maps the dilated image back
onto the original figure, what is its scale factor?
Answer:
its scale factor is 3
Step-by-step explanation:
plz mark brainliest
To map the dilated image back onto the original figure, the scale factor needed is 7.
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Dilation is the increase or decrease in the size of a figure by a factor.
If a figure is dilated from the origin by a scale factor of one seventh, it is given by:
(x, y) ⇒ [(1/7)x, (1/7)y]
To map the dilated image back onto the original figure, the scale factor needed is 7. Hence:
[(1/7)x, (1/7)y] ⇒ (x, y)
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Please help me asap this is due in 10 min Ill also mark brainliest
As we know that formula of area of circle is πr²
So let's apply formula
π×8.6×8.6
=232.2
=200 is the nearest hundredth.
You have to do rest of all through this method.
50. If angles are complementary, what’s value of x?
Answer:
x = 14
Step-by-step explanation:
For complementary angles, the sum of two angles is equal to 90 degrees.
We have,
[tex]m\angle ABC = 4x-10\\\\m\angle DBC = x+30[/tex]
ATQ,
[tex]4x-10+x+30=90[/tex]
Taking like terms together,
4x+x =90-30+10
5x = 70
x = 14
So, the value of x is 14.
please answer asap correctly dont troll!!!
Answer:
10
Step-by-step explanation:
Bro, again the same question))
a>17-8
a>9
A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale of 1–10, with 1 being the least clean to 10 being the most clean. The mean rating for detergent A is found to be significantly less than the mean rating for detergent B.
Answer:
B is the better detergent
Step-by-step explanation:
If A has a lower number on the 1-10 scale, that means on average it was closer to the lower end, or the least clean end. This means that A cleans worse than B., and B is better.
The two laundry detergents B cleans better.
Although the questions seems to be tricky at the begging because of a lot of numbers, but actually it is not.
Given to us in the question that, 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B.
Thus, we can say that the sample size for both detergent A and detergent B is same. Also, the sample is distributed randomly meaning the sample is unbiased (fair).
Also, as given the mean rating for detergent A is found to be significantly less than the mean rating for detergent B. And we know that the mean is the average of a set of given numbers.
Therefore, we can conclude that if detergent A has a lower mean meaning, it has cleaned the clothes with less effectiveness as compared to detergent B.
Hence, Out of the two laundry detergents, B cleans better.
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30 POINTS WOWWWWWW plz answer :)
Answer:
Step-by-step explanation:
These are so annoying
Answer:
a=4
b=6
perimiter=38
Step-by-step explanation:
you take the side lengths by it and you can subtract and stuff then you add them all up to find the perimeter
Answer:
3-9=6 and 6-10=4
Step-by-step explanation
part of b is cut by 3 as u can see above and 9 is at the bottom on which the part is cut, as for the other one 10 is the main line and is cut by 6. so u just have minus the main line aka the long line by a parallel line next to it
A rectangular mat has an area of 7/12 in2. The length of the mat is 5/6 in. What is the width of the mat
The width of the mat with the given area and length is 7/10 in.
What is the width of the mat?The area of a rectangle is expressed as;
A = l × w
Where l is length and w is width.
Given the data in the question;
Area A = 7/12 in²Length l = 5/6 inWidth w = ?We plug our given values into the above equation and solve for w.
A = l × w
7/12 = 5/6 × w
w = 7/12 ÷ 5/6
w = 7/12 ÷ 6/5
w = 42/60
w = 7/10 in
Therefore, the width of the mat with the given area and length is 7/10 in.
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who want's to do my homework? :D Also this might get deleted cause brainly is out to get me D:
Simplify the following rational expression. Use absolute value symbols when needed.
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
1. [tex]\sqrt[3]{\frac{8}{216} }[/tex]
2. [tex]\sqrt[3]{\frac{1}{27} }[/tex]
3. [tex](\frac{1}{27})^{\frac{1}{3} }[/tex]
3. Since [tex](\frac{1}{3}^{3})[/tex] is [tex]\frac{1}{27}[/tex], the answer should be [tex]\frac{1}{3}[/tex].
Write the slope intercept form of the equation of the line through the given points
Answer:
9) y = -3x - 4
10) y = -1/3x + 14/3
11) y = x - 1
12) y = -7/5x - 18/5
13) y = 3/5x + 9/5
14) y = -2x - 3
Step-by-step explanation:
For this explanation, let's use the last problem as the example. You would use the formula y=mx+b. The first thing you would need to find would be the slope, or m. So, you would find the slope and conclude the answer is -2. After that, you would solve for b and get the answer. Hope this helped!
Ed use 3 2/3 cups of peanut butter and 2 cups of powdered sugar to make 1 batch of peanut butter fudge. How much more peanut butter will Ed use than powdered sugar to make 3 batches of fudge?
Answer:
Ed will use 5 more peanut butter than powdered sugar to make 3 batches of fudge(11-6=5)
Step-by-step explanation:
3 2/3 cups of peanut butter (x)
2 cups of powdered sugar(y)
for every one batch you need 2 cups, and for 3 batches you need 6 cups of powdered sugar(2*3=6)
and for every batch you need 32/3 cups of peanut butter and for three batches you need (3 2/3 *3)= 11/3 *3=33/3=11 cups of peanut butter to make the fudge
Ed will use 5 more peanut butter than powdered sugar to make 3 batches of fudge(11-6=5)
4/x = 2/7 please help ASAP!!
Answer:
use cross multiplication to solve
4*7 = 2*x (multiply)
28 = 2x (divide both sides by 2 to isolate x )
x = 14 (your answer)
Step-by-step explanation:
I hope this helped :)
Answer:
Step-by-step explanation:
Or,2×x=7×4
Or,2x=28
Or,x=14
Geometry question plz help
Answer:
I think A
Step-by-step explanation:
please answer fast!!
I am really confused and I don't know what to do.
Answer:
C
Step-by-step explanation:
find the value of x that makes lines u and line v parallel, help!!
Answer:
We are told they are parallelHence 10x+16+5x+14=18015x+30=180 15x=150x=10Percy bought an encyclopedia pried at $13.85 shipping and handing cost an additional 20 percent of the price
Answer:
Percy spent $2.77 for shipping and handling.
Step-by-step explanation:
2.77 is 20 percent of 13.85
the integers -10 and 10 are=
Answer:
Opposites of each other?
Step-by-step explanation:
I am not sure, the only thing that is not making them equal to each other is that they have opposite signs.
A dragon lived in a cave.
The dragon doubled in size every day.
After 20 days the dragon filled the cave.
After how many days did the dragon half-fill the cave?
Answer: After 19 days, the dragon filled half of the cave.
Step-by-step explanation:
The dragon doubled in size every day and after 20 days he filled the cave.
So, one day before, the dragon occupied half of the cave.
20 - 1 = 19 [days]
After 19 days did the dragon half-fill the cave.
The dragon doubles in size every day, and after 20 days, it completely fills the cave.
To find out when the dragon half-filled the cave, we need to determine how many days it took for the dragon to reach half of the cave's capacity.
we know that,
On the 20th day, the dragon filled the entire cave.
and, The dragon doubled in size every day.
so, we have,
On the 19th day, the dragon's size would have been half of what it was on the 20th day.
On the 18th day, the dragon's size would have been half of what it was on the 19th day.
And so on...
We can see that every day before the 20th day, the dragon's size was halved.
So, on the 19th day, the dragon's size was half of the size it was on the 20th day.
Therefore, on the 19th day, the dragon half-filled the cave, and on the 20th day, it filled the entire cave.
Hence, After 19 days did the dragon half-fill the cave.
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PLS HELP!!! due to inflation nominal prices are usually there were to demand increases. After the second increase the price for a certain item was twice as big as the original. By what percent was the first increase, if the second increase was 25%
Answer:
The first increase was of 60%.
Step-by-step explanation:
The initial value of the product is x.
The first increase was of y.
The second increase is of 25%, that is, 1.25.
The final price was double the original, so 2x.
This situation can be modeled by the following equation:
[tex]xy(1.25) = 2x[/tex]
We want to find y.
Simplifying by x
[tex]1.25y = 2[/tex]
[tex]y = \frac{2}{1.25}[/tex]
[tex]y = 1.6[/tex]
After the first increase, the value was 1.6 of the original value, that is a increase as a percent of (1.6 - 1)*100 = 60%.
The price of an item has been reduced by 15%. The original price was $87.
Answer:
The new cost is $73.95
The discount was $13. 05
Step-by-step explanation:
Turn the % into a decimal so it would be 0.15.
Then multiply it to the total, 87 x 0.15 = 13. 05
so the discount subtracted $13.05 off of the original price.
87 - 13. 05 = 73.95
Help solve inequality
Answer:
n ≥ -95
Step-by-step explanation:
[tex]\frac{n}{-5}[/tex] -4 ≤ 15
[tex]\frac{n}{-5}[/tex] ≤ 19 add 4 to 15
n ≥ -95 multiple -5 to 19; sign flips when multiplying or dividing an inequality
Find the measure of angle b (15
Answer:
Angle b is 15 measure the scale
Find the unit rate of 624 calories in 3 servings. Its 8th grade math.
Answer:
you can look up the exact quizizz your taking and find all the answers
Step-by-step explanation:
for example: look up your question on the quizizz and then type it in the search bar and add quizziz to the end of it and you should find all your answers there<3
s
is inversely proportional to
t
.
When
s
=
0.3
,
t
=
8
Work out
s
when
t
=
0.4
Answer:
s inversely proportional 1/t
s=0.3, t=8
s=k/t
0.3=k/8
k=0.3×8
k=2.4
find s when t=0.4
s=2.4/0.4
s=6.0 or 6
Solve the equation + 6 = 2.
Question 13 options:
A)
No Solution
B)
a = 13
C)
a = 7
D)
a = 61
Question 14 (5 points)
Solve the equation 10 + y√
y
= 14
Question 14 options:
A)
y = 576
B)
y = 4
C)
y = 16
D)
y = 2
If each of the numbers in the following data set were multiplied by 17, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
A. 986
B. 1207
C. 476
D. 612
Answer:
B
Step-by-step explanation:
Thomas ram from the start line to go post and back the distance from the start line to the goalpost is 46 meters how far did Thomas run
Answer:
92m!
Step-by-step explanation:
46 times 46 is 92
please give me brainliest!!!<3