5-7
To rationalize the denominator of
9- 114 · you should multiply the expression by which fraction?
o
5+
g-ſ14
9-14
9-14
9+ 14
9+
14
14
14
Answers
Answer:
the third option
Step-by-step explanation:
what does that mean ?
to "rationalize" it is to transform it into a rational number (that is a number that can be described as a/b, and is not an endless sequence of digits after the decimal point without a repeating pattern).
a square root of a not square number is irrational (not rational).
so, what this question is asking us to get rid of the square root part in the denominator (the bottom part).
for this we need to multiply to and bottom with the same expression (to keep the whole value of the quotient the same) that, when multiplied at the bottom, eliminates the square root.
what can I multiply a square root with to eliminate the square root ? the square root again - we are squaring the square root.
so, what works for 9 - sqrt(14) as factor ?
we cannot just square this as
(9- sqrt(14))² = 81 -2sqrt(14) + 14
we still have the square root included.
but remember the little trick :
(a+b)(a-b) = a² - b²
without any mixed elements.
so, we need to multiply (9-sqrt(14)) by (9+sqrt(14)) to get
81-14 = 67 which is a rational number.
therefore, the third answer option is correct.
follow the rule
[tex]\\ \sf\longmapsto \dfrac{a+b}{c-d}[/tex]
To rationalize the above fraction we need to change the sign of denominator patt and multiply with both numerator and denominator
Like
[tex]\\ \sf\longmapsto \dfrac{a+b(c+d)}{(c-d)(c-d)}[/tex]
Here correct option is C
Related Questions
Andre ran 512 laps of a track in 8 minutes at a constant speed. It took Andre x minutes to run each lap. Select all the equations that represent this situation.
Answers
Answer:
(512)x=8 and 512−x=8
Step-by-step explanation:
SCREAMING HELP ALERT !!
Answers
Answer: 1/3
Step-by-step explanation:
On side of the smaller quadrilateral is 8, the same side on the larger one is 24. 8 times 3 is 24. So the scale factor from the smaller to the larger is 1/3.
Answer:
1/3
Step-by-step explanation:
similar means all sides are proportinal, in this case one side is 3x bigger in the 2nd figure, so the same must be true of the other fig.
12
Use upper rectangles with areas equal to
Marks: 1
Area = f(x) · A3
to estimate the area under the curve of f(x) = x, on the interval from (1,3). Partition the interval into four subintervals. Hint:
Area = (F(1.5) + f(2) + f(2.5) + f(3))Ar = (1.53 +23 +2.53 +33)Az, where Ax =
Choose one answer.
ST
3-1
4
a. 35
b. 42
c. 27
d d. 19
Answers
Answer:
42
Step-by-step explanation:
find the missing side lengths
Answers
This says:
The opposite side of 30° is: x
The opposite side of 60° is: x * sqrt(3)
The opposite side of the 90° is: 2x
We have our side length for 90° so we just have to work backwards
To find our 30° side length we must divide by 2
8/2 = 4
Which means your y = 4
Now that we have our 30° side length we can just multiple it by sqrt(3)
That means your x = 4 sqrt(3)
Answer:
x= 4 square root 3 y=4
Step-by-step explanation:
Its 30 60 90 triangle
Hope this helps <3
Find the common ratio of the geometric sequence 17, -51, 153, ...
Answers
Answer:
an = 17 ( − 3 ) n − 1
Step-by-step explanation:
Use the formula an = a 1 r n − 1 to identify the geometric sequence.
Which equation is in slope-y-intercept form?
Question 1 options:
a) 3x + 4y = 7
b) x = 4y - 2
c) y = 3x -1
d) x + 4y -2
Answers
Answer:
C = y - 3x-1
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
C = y - 3x-1 is in slope intercept form
The answer is A.
I took the test.
What is the range of the absolute value function shown in the graph?
A. 3 ≤ y < ∞
B. -∞ < y ≤ 3
C. -6 ≤ y < ∞
D. -∞ < y < ∞
Answers
Answer:
C
Step-by-step explanation:
as we can see on the graph, the lowest y value is the vertex/corner at x=3, y=-6.
all other y values are above (=are larger) that level.
and it goes up without appearant limit, so up to infinity.
find the values of the sine,cosine and tangent of the following angles.
a.153°
b.204°
c.320°
Answers
Answer:
a)sin153°=0.454
cos153°= -0.891
tan153°= -0.510
b)sin 204°= -0.407
cos204°= -0.914
tan204° = 0.445
c)sin320°= -0.643
cos320° = 0.766
tan320°= -0.839
Step-by-step explanation:
What is an equation for this graph?
Answers
Answer:
sinx
Step-by-step explanation:
the shape of the graph shows a sine graph, which is usually denoted by asinbx+c
a is amplitude/2 = 2/2 = 1
b is the period, 360 = 360/b, b=1
since the graph starts at (0,0), c =0
hence, this graph is 1sin1x = sinx
The equation is y = sin(x)
Match the answers……………..
Answers
9 in 8956 = 900
9 in 95675 = 90000
9 = 9 in 124569
9 in 68795 = 90
90000 = 9 in 2549652.........
hope it helps...
How high does rent have to be to be an outlier
Answers
Answer:
congratulate you have Windows 11
A picture is 46 cm by 32 cm. A scale diagram of the picture must fit in a space that is 3 m by 2 m. Which scale would be the most reasonable one to use for the scale diagram?
Answers
Answer:
A picture that is 46cm by 32 cm must fit in a space that is 3m by 2m
First, let's rewrite both of these dimensions in the same units.
Knowing that:
1m = 100cm
Then the dimensions of the space can be rewritten from:
3m by 2m
to:
300cm by 200cm
So, if we enlarge our original picture by a scale factor K, the new dimensions of the picture will be:
K*46cm by K*32cm
Now we just need to find a value of K such that:
K*46cm is something near to 300cm
K*32cm is something near to 200cm
First, we can solve the equation:
K*46cm = 300cm
solving this for K we get:
K = 300cm/46cm = 6.5
While if we solve the equation:
K*32cm = 200cm
we get:
K = 200cm/32cm = 6.25
So we got two possible scale factors.
Which one we should take?
Notice that if we wanted to use the larger one (K = 6.5) for the 32cm side. the new length would be:
32cm*6.5 = 208cm
This is larger than the 200cm of space that we have
Then we can not select the larger option, we can only take the other value:
K = 6.25
Then we can conclude that a reasonable scale factor to use is K = 6.25
by which smallest number should the following number be multiplied to make the perfect square of 384
Answers
The prime factorization of 384 = 2^7 * 3.
So in order to make it a perfect square, you must multiply it by 2*3 = 6 to make is 2^8 * 3^2.
I could really use a hand
Answers
Answer : -5a² + 10a
It was way easy ikr ~w~
Answer:
-5a2+10a
Step-by-step explanation:
distribute
-5a(a-2)
-5a2+ 10
2x(3x - 2) + (3x - 2)
let's writefollowing expression as product of their factor.
Answers
Answer:
6 x ^2 − x − 2
Step-by-step explanation:
Remove parentheses.
2 x ( 3 x − 2 ) + 3 x − 2
Simplify each term.
6 x ^2 − 4 x + 3 x − 2
Add − 4 x and 3 x .
6 x ^2 − x − 2
Answer:
(3x - 2)(2x + 1)
Step-by-step explanation:
Given
2x(3x - 2) + (3x - 2) ← factor out (3x - 2) from each term
= (3x - 2)(2x + 1) ← as a product of factors
Says i need at least 20 characters in order to get this up.. you know i really should know this stuff but oh well
Answers
Answer:
C
-1/5, -1/3,-7
Step-by-step explanation:
Could someone please help me with this
Answers
Answer:
what are the questions
Step-by-step explanation:
Please hurry I will mark you brainliest
Ingrid walks 1 m, and then turns 90° left. She repeats these steps three more times and returns to the exact place she started. Which of the following instructions can she repeat a number of times to arrive at the exact same starting point?
• Walk 1 m, and then turn 40° left.
• Walk 1 m, and then turn 55° left.
• Walk 1 m, and then turn 70° left.
• None of these
Answers
Answer:
• Walk 1 m, and then turn 40° left.
Step-by-step explanation:
Answer:
None of them
Step-by-step explanation:
None of the answers get her back to the same point in only four steps. she would need a different way of walking to get the same result as a square.
ax^2-y^2-x-y factorize
Answers
Answer:
x(ax-1)-y(y+1)
Step-by-step explanation:
you have to group the like terms
ax^2-x-y^2-y
x(ax-1)-y(y+1)
I hope this helps
A scenic train ride has one price for adults and one price for children. One family of two adults and two children pays 1054 Baht for the train ride. Another family of one adult and four children pays 1190 Baht. Find the price x for an adult and the price y for a child?
Answers
Answer:
x = price for adult = 306 Baht
y = price for children = 221 Baht
Step-by-step explanation:
Let
x = price for adult
y = price for children
2x + 2y = 1054 (1)
x + 4y = 1190 (2)
From (1)
x = 1190 - 4y
Substitute x = 1190 - 4y into (1)
2x + 2y = 1054 (1)
2(1190 - 4y) + 2y = 1054
2380 - 8y + 2y = 1054
- 8y + 2y = 1054 - 2380
- 6y = - 1326
y = -1326/-6
y = 221
Substitute y = 221 into (2)
x + 4y = 1190 (2)
x + 4(221) = 1190
x + 884 = 1190
x = 1190 - 884
= 306
x = price for adult = 306 Baht
y = price for children = 221 Baht
Two similar pyramids have similarity ratio 3:5 find the ratio of the areas and the ratio of the volume
Answers
Answer:
Area=9:25 Volume=81:625
Step-by-step explanation:
Should be squared, might be wrong.
The t distribution should be used whenever _____. Group of answer choices the sample size is less than 30 the population is not normally distributed the sample standard deviation is used to estimate the population standard deviation None of the answers is correct.
Answers
Answer:
A: the sample size is less than 30
Step-by-step explanation:
Usually, the t-distribution is used instead of normal distribution in calculation of the mean of a normally distributed population when the sample size is small (n < 30) and if the population standard deviation is not known.
Thus, looking at the options, the correct one is Option A.
Square Root of 9801
With Steps Please
Answers
Answer:
99
Step-by-step explanation:
First give it as a product of prime factors. Divide 9801 with prime numbers. The first picture divides 9801 fron prime numbers. Prime numbers are 2,3,5,7, 11. We can only divide using 3 and 11. So we get 3⁴ and 11². The second picture shows how I got the square root of 9801. Square root is ½. So we multiply each power with ½ so we finally get 99. You can recheck for yourself using a calculator. It is 99.
Find the center and radius of the circle and sketch its graph
X^2+y^2=9
Answers
Answer:
Centre (0,0)
Radius √9 = 3
I've attached a graph if the circle with it
Answered by GAUTHMATH
Find the length of x
Answers
Answer:
20
Step-by-step explanation:
Since the triangles are similar then the sides must be proportional
10/6 = x/12 cross multiply expressions
6x = 120 divide both sides by 6
x = 20
If a semi-circle was rotated about the y-axis, like the one shown below, what would be the resulting three-dimensional shape?
Pyramid
Cylinder
Sphere
Cone
Answers
Answer:
Step-by-step explanation:
This rotation would create a sphere.
If a semi-circle is rotated about the y-axis of the graph, then the resulting three-dimensional shape will be a sphere.
What is a semi-circle?A semicircle is a half-circle formed by a one-dimensional locus of points.
What is a sphere?A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space.
If a semi-circle is rotated about the y-axis of the graph, then the resulting three-dimensional shape will be a sphere. This is because of the fact that when the semi-circle will be rotated about the y-axis then all the points will be at equal distance in all the directions from the centre.
Learn more about Sphere:
https://brainly.com/question/11374994
can someone help me ixl
Answers
Answer:
5.5 cm
Step-by-step explanation:
√(40²-24²) - √(40²-30²)
= 32-10√7
= 5.5 (rounded to the nearest tenth)
Answered by GAUTHMATH
last one help me asap please and thank you
Answers
Answer:
y = -3/4x + 3.
A and B can do the work in 8 days ; B and C can do the work in 12 days ;A ,B and C together can finish it in 6 days .In how many days A and C together will do the same work
Answers
2/4+1=1/6 x-7 what is the value of x in this epuation
Answers
I hope this is correct and is this the answer you’re looking for?
