Answer:
5√z/z
Step-by-step explanation:
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The quotient of [tex]20\sqrt{z^{6} }[/tex] ÷ [tex]\sqrt{16z^{7} }[/tex] in simplest radical form is [tex]\frac{5\sqrt{z} }{z}[/tex].
How to express a simplest radical form?Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any radicals in the denominator of a fraction.
Given
[tex]20\sqrt{z^{6} }[/tex] ÷ [tex]\sqrt{16z^{7} }[/tex]
Rewrite as fraction: [tex]\frac{20\sqrt{z^{6} } }{\sqrt{16z^{7} } }[/tex]
Factor and rewrite the radicand in exponential form: [tex]\frac{20\sqrt{z^{6} } }{\sqrt{4^{2}. z^{6} .z} }[/tex]
Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex] :
= [tex]\frac{20\sqrt{z^{6} } }{\sqrt{4^{2} .\sqrt{z^{6}.\sqrt{z} } } }[/tex]
Simply the radical expression, we get:
= [tex]\frac{20z^{3} }{4z^{3}\sqrt{z} }[/tex]
Reduce fraction to the lowest term by canceling the greater common factor, we get
= [tex]\frac{5}{\sqrt{z} }[/tex]
Rationalize the denominator
= [tex]\frac{5\sqrt{z} }{\sqrt{z} .\sqrt{z} }[/tex]
= [tex]\frac{5\sqrt{z} }{z}[/tex]
Hence, the quotient of [tex]20\sqrt{z^{6} }[/tex] ÷ [tex]\sqrt{16z^{7} }[/tex] in simplest radical form is [tex]\frac{5\sqrt{z} }{z}[/tex].
Find out more information about simplest radical form here
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What is the total area of the shaded region? Type just the answer in the blank.
Answer:
240cm
Step-by-step explanation:
6cm*14cm= 84cm
6*6=36
84+36=120*2=240
Answer:
7cm x 8cm
Step-by-step explanation:
The 14cm x 12cm box (top 'box 1') intersects with the 14cm x 12cm box (bottom 'box 2').
Half the values of each side are subtracted from one another, so
horizontal length: 14/2 = 7cm
vertical length: 12/2 = 6cm
Box 2 horizontal length (total) = 14cm devided by half the length of box 1 (7cm)
14 - 7 = 7cm
Box 2 vertical length (total) = 12cm devided by half the length of box 1 (6cm)
12 - 6 = 6cm
The total area is calculated by multiplying the horizontal and vertical lengths
7x6 = 42
the answer is 42
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
Write this multiplication expression using an exponent: 2 . 2 . 2 = ?
Answer:2^3
Step-by-step explanation:
I need this ASAP but it’s ok if you see it late
Answer:
72 square units
Step-by-step explanation:
move above the dotted line to make a rectangel then the numbers are 6 and 12 then times them to get 72
can someone help me with this also? Thanks! i need the explanation to so I can do it by myself after.
Find the value of x.
4x + 5
2x + 21, smby help me wit dis pls
Answer: x = 8
Step-by-step explanation:
4x + 5 = 2x + 21
4x + 5 - 2x = -2x + 2x +21 (Subtract 2x from both sides)
2x + 5 = 21
2x + 5 - 5 = 21 - 5 (Subtract 5 from both sides)
2x = 16
2x/2 = 16/2 (Divide both sides by 2)
x = 8
y = 2x + 1
y = -2x + 1
y = -2x - 0.5
y = 2x - 0.5
have you seen how he answers questions? doesn't deserve to have people answer his
Step-by-step explanation:
Two hoses are used to fill a swimming pool. Together they fill the pool at a rate of 3 gallons every 5 seconds. An equation representing this isg=35t,where t is the time in seconds and g is the number of gallons. About how many hours will it take to fill the pool if it holds 80,000 gallons?
Answer:
about 267 hours
Step-by-step explanation:
can someone help with this question?
What is an equation of the line that passes through the points (7, 4) and (-5, 4)
Answer:
Equation of the line that passes through the points (7, 4) and (-5, 4) is
[tex]y=4[/tex]
Step-by-step explanation:
Equation of line in two point form is given as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex] ----------(1)
Here
[tex](x_1, y_1) = (7, 4) \ \ \ and \ \ \ (x_2, y_2)=(-5, 4)[/tex]
Substituting values in equation (1)
[tex]y-4 =\frac{4-4}{-5-7} (x-7)[/tex]
[tex]y-4 =0[/tex]
[tex]y=4[/tex]
The points (-5, -31) and (3, r) lie on a line with slope 4. Find the missing coordinate r
I’LL MARK BRAINIEST!
To the first correct answer
Answer:
The missing coordinate is 1
Step-by-step explanation:
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order the numbers from least to greatest and then subtract the lowest number from the greatest
ex : 4,6,9,3,7
the lowest number is 3 and the highest is 9 so 9-3 = 6 so for this example the answer is 6.
Which statement explains one reason why unconfirmities occur
Find the total surface area of this triangular prism.
height=24cm
width=14cm
length=10cm
slant height=25cm
If the picture below is the triangular prism
Answer:
976
Step-by-step explanation:
14 x 24 = 336 [It's a triangle you would half it but then as there are 2 you would keep it the same]
10 x 25 = 250 [Times by 2 because there are 2 of them]
10 x 14 = 140
336 + 250 + 250 + 140 = 976
. Laura and Alicia both exercise 5 days a week. Laura exercises for 30 minutes each day. Alicia exercises for 45 minutes each day. How much longer does Alicia exercise than Laura each week?
Answer: 115
Step-by-step explanation: because Laura exercises 150 minuets in all and Alicia exercises 265 in all. so you subtract
265-150 and you get 115
Use the rules of significant figures to answer the following question:
54.313 × 12.09
A. 657
B. 660
C. 656.64
D. 656.6
Solve for x:
a
3
b
9
c
1.5
d
13.5
Hi there! :)
[tex]\large\boxed{\text{ x = 9}}[/tex]
The two angles pictured are vertical angles, therefore:
8x - 6 = 6x + 12
Solve for x by subtracting 6x from both sides:
2x - 6 = 12
Add 6 to both sides:
2x = 18
Divide both sides by 2:
x = 9.
Answer:
9 is ur answer
Step-by-step explanation:
8x-6=6x+12
8x-6x=12+6
2x=18
x=9
Hope this helps u...
What three ratios are equivalent to 10:12
Answer:
5:6, 20:24, 30:36
Step-by-step explanation:
Linear Inequalities Unit Test answers please I cant figure out almost all of it im from pearson online academy and ive been studying for weeks but still dont understand the material
Answer:
without any questions i cant answer
Step-by-step explanation:
(2+6 +8+54 +...);S 12
PLEASE HELP ME WITH THIS ITS NOT EVEN HARD IM JUST REALLY LAZY
Answer:
1) 8
2) 2
3) 1
4) 4
5) skiing, snowboarding,ice skating, sledding
Step-by-step explanation:
Answer:
1.) 8
2.) 2 more people
3.) 1 less for skiing
4.) 4
5.) Skiing, Snowboarding, Ice skating, Sledding,
Write a guess my number clue that is satisfied by an infinite number of solutions
Answer:
1 ?????????.........
jayden had some money in his pocket.Then a friend loaned him $1.35.Now jayden has $3.75 in his pocket.
Answer:
If you were wondering how much he had to begin with, it would be $5.10.
Step-by-step explanation:
Hopefully this helps you :3
6. What is f(-5) for the function f(x) = - 9x - 3?
PLEASE HELP ILL DO ANYTHING
Answer: The answer is 42 :)
Step-by-step explanation: F(x)=-9x-3 plug in the -5 in the -9x
-9(-5)-3
45-3=
42
In parallelogram DEFG if m_DEF=110° find m_FGD.
E
110°
D
G
Answer:
E=x
or 110= x ( opposite angles of parallelogram are congurent)
E+D = 180 ( angles on st line)
110+D =180
D=70
D=F ( opposite angles of parallelogram are congurent)
so F=70
Estimate and solve 4,624 ÷ 72 = ________. (2 points)
66 r 22
66 r 16
64 r 22
64 r 16
Pam walks 7/8 of a mile to school. Paul walks 1/2 of a mile to school. How much
farther does Pam walk than Paul?
Answer:
Pam walks 3/8 of a mile more than Paul
Step-by-step explanation:
1/2 = 4/8
7/8 - 4/8 = 3/8
What is the simplified form of
72x16/50x36 ? assume x ≠ 0
Answer:
Option A
Step-by-step explanation:
[tex]\sqrt{\frac{72x^{16} }{50x^{36} } } = \sqrt{\frac{36x^{16} }{25x^{36} } } = \frac{\sqrt{36x^{16} } }{\sqrt{25x^{36} } } = \frac{\sqrt{36} \times \sqrt{x^{16} } }{\sqrt{25} \times \sqrt{x^{36} } } = \frac{6x^{8} }{5x^{18} } = \frac{6}{5} \times x^{8-18} =\frac{6}{5} \times x^{-10} = \frac{6}{5x^{10} }[/tex]
pleas help me with this
Answer:
B by Pythagorean theorem
Step-by-step explanation:
20² = 12² + 16²
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