The simplest form of the square root of 48 is 4√3
Simplifying rational functionsGiven the following rational function √48
The correct prime factorization is given as;
√48 = √3×16
√48 = √16 × √3
Since the square root of 16 is 4, hence;
√48 = 4√3
Hence the simplest form of the square root of 48 is 4√3
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CD is the perpendicular bisector of both XY and ST, and CY = 16. Find TY.
The value of TY is 14
Given that CD is the perpendicular bisector of XY and ST and CY = 16
We need to find the value of TY
Here M is the midpoint of ST and D is the midpoint of XY
As shown in the diagram we can say that
CT = CS =12
We can also say that ST║XY
So , ∠CST = ∠CSY
∠CTS = ∠CYX
ΔSCT = ΔXCY
SX = CS - CX
= CY - CX
We can say that MT = SM = 5
DY = DX = 7
TY = SX = 4
CY = CX = 16
ST = SM + MT
ST= 5+5
∴ ST= 10
XY = XD +DY
XY = 7+7
∴ XY = 14
Hence the value of XY is 14
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A circle has a diameter with endpoints (-7, 1) and (-3, 7).
What is the equation of the circle?
r2 = ( x - 3) 2 + ( y + 4) 2
r2 = ( x + 3) 2 + ( y - 4) 2
r2 = ( x + 5) 2 + ( y - 4) 2
r2 = ( x - 5) 2 + ( y + 4) 2
Answer: (C) r² = (x+5)²+(y-4)²
Solution:-
The given endpoints are (-7,1) and (-3,7)
so the center will be at the mid point of the line connecting these two points.
hence, center ={ (-7+-3)/2, (1+7)/2 }
hence, C= (-5,4)
so, the equation of the circle is:-
⇒ (x-(-5))²+(y-4)²=r²
or, (x+5)²+(y-4)²=r²
3. Find the value of √99225. Hence find the sum of √992.25 and √9.9225.
Step-by-step explanation:
The square root of √9.9225. is 315.
See the decimal places
therefore S,Q,R,T of 9.9225 is 31.5 and 9.9225 is 3.15.
Hence the sum, is (31.5+3.15)= 34.65.
Answer- Value- 315
Sum-34.65
If you can can i get a brain list i don't ever get them
simplify the equation. 3(x+2)-9x+5
Distribute
3(x + 2) - 9x + 53x + 6 - 9x + 5Add the numbers
3x + 6 - 9x + 53x + 11 - 9xCombine like terms
3x + 11 -9x-6x + 11Distribute
3(x + 2) - 9x +5
3x + 6 - 9x + 5
Add the numbers
3x + 6 - 9x + 5
3x + 11 - 9x
Combine like terms
3x + 11 - 9x
6x + 11
the amount a gardener gets paid is directly proportional to the number of hours it takes for him to complete the job.
the gardener got paid £70 for a 12 hour job.
how much would he get paid for a job that took a total of 18 hours?
Answer:
£105
Step-by-step explanation:
The pay is proportional to the time, so working 18/12 = 3/2 times as long will gain the gardener 3/2 times the pay:
3/2 × £70 = £105
He would get paid £105 for an 18-hour job.
__
Here are a couple of other solution methods.
as a proportionpay/hours = ?/(18 hours) = £70/(12 hours)
Multiplying by 18 hours, we get ...
? = £70×(18 hours)/(12 hours) = £70×(18/12)
? = £105 . . . . pay for 18 hours
He would get paid £105 for 18 hours.
__
as direct proportion equationThe equation for a directly proportional relationship is ...
y = kx
If we let y represent pay and x represent hours, then we have ...
70 = k(12) ⇒ k = 70/12 = 35/6
Then for 18 hours, the pay is ...
y = (35/6)x
y = (35/6)(18) = 35(3) = 105
He would get paid £105 for 18 hours.
How would i find the domain of this?
The domain of the graph is {x : x∈ R}
How to determine the domain?The domain of a function or graph is the set of input values the function can take.
This in other words represents the x values
From the graph, we can see that x values extend indefinitely on both axes.
This is indicated by the arrows at the ends of the curve
This means that the domain is the set of all real numbers
Hence, the domain of the graph is {x : x∈ R}
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Figure A
Figure B
Figure A is rotated 180°, then reflected across the line.
Figure B is reflected across the line, then rotated 180°.
Which of the following shows the two figures after they are
transformed?
Answer:
The answer is c
Step-by-step explanation:
look at the picture carefully
Ryan invested $5000 in an account that averaged 5% growth per year. Which equation would be used to best model the situation?
Answer:
f(x)=5000(1+0.05)^x
Step-by-step explanation:
Use the formula: f(x)=P(1+b)^x
P is principal or y-intercept. 5000 is principal.
b is the percentage in decimal form. 0.05 is b.
x is time, in this case years. Since there is not a certain number of years leave x as x.
f(x)=5000(1+0.05)^x
Hope this helps!
If not, I am sorry.
Brian ordered 3 large cheese pizzas and a salad. The salad cost $4.95. if he spent a totai of $47.60 including the $5 tip, how much did each pizza cost? (Assume there is no tax).
Each pizza cost $ 12.65
What is an Equation ?An Equation is used in determination of unknown variables in an expression .
It is given that
Brian ordered 3 large cheese pizzas and a salad.
The salad cost $4.95
Total amount spend = $47.60
Tip = $5
The amount spend in food is $ 47.60-5
= $42.60
Let the price of Pizza is x then the equation that can be formed to determine the price of pizza is
3x + salad = 42.60
3x + 4.95 = 42.60
3x = 37.65
x = $12.65
Therefore each pizza cost $ 12.65
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Answer:
12.55
Step-by-step explanation:
There are two approaches to solving the equation -3x + 10 = 4x - 20
Subtract 4x from both sides. OR Add 3x to both sides.
–7x + 10 = –20 OR 10 = 7x – 20
Solve the equation using both approaches.
Solve the following equations. 2x - y = 8 3x + y = 17
System of equations:
2x - y = 8
3x + y = 17
Solve for x:2x - y = 8
3x + y = 17
________ +
5x = 25
x = 5
Plug in x to one of the equations to solve for Y2(5) - y = 8
10 - y = 8
-y = -2
y = 2
a candy bar is in the shape of a triangular prisim the volume of the box is 2400 cubic centimeters. what is the height of the base
The height of the base will be 15 cm. The candy bar has a 2400 cubic centimeter box with a triangular prism form to it.
What is the definition of a triangular prism?Join the edges of three rectangles. Now, from both ends, seal their triangle mouths. A triangular prism is a name for the form.
The complete question is;
"A candy bar is in the shape of a triangular prism the volume of the box is 2400 cubic centimeters. It is shown with a base of the triangle labeled 16 cm, the sides of triangles labeled 17 cm, and the length of the box equal to 20 cm. what is the height of the base triangular prism"
The volume of the triangular prism;
[tex]\rm V = \frac{1}{2}\times b \times h\times l\\\\ 2400 \ cm^3 = \frac{1}{2}\times 16 \ cm \times h\times 20 \ cm \\\\ h = 15 \ cm[/tex]
Hence, the height of the base will be 15 cm.
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4. Write an equation that describes the verbal description. Then, explain your thinking.
Teddy opens a new bank account by depositing the $245 he has saved from mowing lawns. He chose
this account because it will accrue 2% monthly and he wants to save up $2,000 for a car within a
couple of years.
P
Answer:
245 +4.9m = 2000
Step-by-step explanation:
so 245 is what he has and he puts it where he gets 2 percent monthly so 4.9 is 2 percent of 245. 2000 is there because that's how much he wants to save.
Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method. Note: Interest rate is given as a monthly rate
Previous balance:$179.32
Payments/credits:$85.00
Unpaid balance:$
Monthly rate:1.25%
Finance charge:$
New purchases=$117.42
New balance=$
The Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.
Finance charge
Unpaid balance:
Unpaid balance=Previous balance-Payments/credits
Unpaid balance=$179.32-$85.00
Unpaid balance= $94.32
Finance charge:
Finance charge =Finance charge×Monthly rate
Finance charge=$94.32×1.25%
Finance charge=$1.179
New balance:
New balance =Previous balance-(New purchases-Payments/credits)+Finance charges
New balance=$179.32-($117.42-$85.00)+$1.179
New balance=$179.32-$32.42+$1.179
New balance=$148.079
Therefore the Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.
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Answer:
94.32
1.18
212.92
in order
Step-by-step explanation:
good afternoon can someone please helppp :))))
Triangle XYZ is dilated by a scale factor of 1/4 to form triangle X'Y'Z'. Side YZ measures 18. What is the measure of side Y'Z'?
(Round your answer to the nearest tenth)
y-2-√x-6
what is the domain of this function?
Find a pattern for the sequence. Use the pattern to show the next two terms.
12, 24, 36, 48, . . .
A. Each term is twelve more than the preceding term; 60, 72
B. Each term is twice the preceding term; 72, 96
C. Each term is five times the preceding term; 60, 70
D. Each term is twelve times the preceding term; 60, 72
Answer:
about this question the sequence of the pattern is according to the table of 12.
Step-by-step explanation:
Table of twelve is.
12
24
36
48
then the answer will be 60
Find the missing side lengths. Answers are in simplest radical form with the denominator rationalized.
A 45-45-90 right triangle with one of the legs labeled y, the other leg labeled 4 times the square root of 2, and the hypotenuse labeled x.
,
,
,
,
Answer:
missing side lengths are
leg 1 is 4√2
leg 2 is 4√2
hypotenuse is 8
Step-by-step explanation:
leg 1 is y
leg 2 is 4√2
45-45-90 right triangle means
legs are equal
the longest side is the hypotenuse which is
x
pythagorean theorem =
a² + b² = c²
a and b are the legs
c is hypotenuse
(4√2)² + (4√2)² = c²
4√2 = √16*2 = √32
(√32)² + (√32)² = c²
32 + 32 = c²
64 = c²
take the square root of both sides
√64 = √c²
8 = c
c = 8
The tables represent the functions f(x) and g(x). f(x) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g(x) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions? x = -3 O x = -1 x = 0 Ox=1 The tables represent the functions f ( x ) and g ( x ) . f ( x ) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g ( x ) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions ? x = -3 O x = -1 x = 0 Ox = 1
Answer:
x=1
Step-by-step explanation:
There are two functions (f & g), each of which have a table of inputs and outputs. The same list of inputs is given to both functions, but the outputs are different.
Imagine that you asked your Father 6 questions, (weirdly instead of numbered 1 through 6, numbered -3 through 2), and that he gave you a list of answers.
Imagine that you asked your Grandfather the same 6 questions, and you got a list of answers from him.
On which question did they give the same answer?
It was on question number "1", (really the 5th question, but as we've numbered things from -3 to 2, it's question "1").
Since the "questions" were the input, "x", x=1.
Describe three ways to determine the measure of segment YZ.
Triangle X Y Z is shown. Angle X Y Z is a right angle and angle Z X Y is 30 degrees. The length of hypotenuse X Z is 50 meters.
Step-by-step explanation:
tan 30 degre = perpendicular /base
I wrote the rule than you can easily find hope this help you
Using 3 different methods, we can find that YZ = 25m
The complete image of a triangle is attached with the answer below.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations
sin(θ) = (opposite cathetus)/H
cos(θ) =(adjacent cathetus)/H
tan(θ) =(opposite cathetus)/(adjacent cathetus)
Now, in the given image we can see that:
θ = 30°
H = 50m
XY = adjacent cathetus
YZ = opposite cathetus.
We want to find YZ, so with the known things, we can use the first relation:
Sin 30 = YZ / 50
YZ = 50 x Sin30 = 25 meters
Now let's try another way.
We know that the sum of the internal angles of a triangle is always equal to 180°
In a triangle rectangle, we always have an angle equal to 90°.
Then the missing angle for our triangle can be computed from:
Z + 90° + 30° = 180°
Z = 180° - 90° - 30° = 60°
From this angle, the side YZ is the adjacent cathetus, then we can use the second trigonometric relation:
Cos 60 = YZ / 50
YZ = 50 x Cos 60 = 25 meters
Third way.
Whit the same angle we could find the side XY, the opposite cathetus, with:
Sin 60 = XY / 50
XY = 50Sin 60 = 43.3 meters
Now that we know one of the catheti, we can use the last trigonometric relation
tan 60 = XZ / YZ = 43.3 / YZ
YZ = 43.3 / tan 60 = 25 meters
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What is the nth term rule of the linear
sequence
below?
1, 7, 13, 19, 25, . ..
Answer:
Un= 1+(n-1)6
Step-by-step explanation:
a = 1
d= 7-1= 13-7= 6
and using the formula, Un= a+(n-1)d
The density of copper is 8.94 g/cm^3. What is the mass of a rectangular sheet of copper: 10 cm wide, 45 cm long, and 0.2 cm thick?
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8x and y = 2x + 2 intersect are the solutions of the equation 8x = 2x + 2. (4 points)
Part B: Make tables to find the solution to 8x = 2x + 2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 8x = 2x + 2 graphically? (2 points)
Quickly please! Thank you.
The point of intersection of two given equations is (0.333, 2.667).
Given that, equation with two variables are y = 8x and y = 2x + 2.
The given equations will intersect at some point where y is the same for both equations.
When you replace y in y = 2x + 2 with y = 8x, we get 8x = 2x + 2.
So, the solution of 8x = 2x+2 will satisfy both equations.
Now, we need to find the solutions to take the integer values of x between -3 and 3.
That is,
x = -3 , then 8(-3) = 2(-3) +2⇒-24 = -6+2
⇒-12 = -4 False.
similarly, for x = -2
8(-2) = 2(-2)+2
⇒-16 = -2 False
For, x = -1
8(-1) = 2(-1)+2
⇒-8= 0 False
For, x = 0
8(0) = 2(0)+2
⇒0= 2 False
For, x = 1
8(1) = 2(1)+2
⇒8= 4 False
For, x = 2
8(2) = 2(2)+2
⇒16 = 6 False
For, x = 3
8(3) = 2(3)+2
⇒24 = 8 False
Therefore, there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.
The equations can be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.
The point of intersection is the values of the variables which satisfy both equations at a particular point.
Hence, you can see the graph as shown below, the point of intersection is (0.333, 2.667).
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Expand . ( 3x –2 ) 2 need an answer ASAP.
Answer:
6x - 4
Step-by-step explanation:
For expanding (3x -2) 2 , (3x - 2) is to be multiplied with 2.
(3x - 2) × 2 = 6x - 4
When is the best time to round a number in a multi-step problem?
Answer:
At the end of the multi step problem
The slope of the line below is -4. Which of the following is the point-slope
form of the line?
(2,-8)
Answer:
y+2= -4(x-8)
Step-by-step explanation:
8. Scott drank 3.5 bottles of water yesterday. Each bottle contained 1.2 pints of water. What was the number of pints of water Scott drank yesterday? Ascend Learning 8. Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water . What was the number of pints of water Scott drank yesterday ? Ascend Learning
Answer:
4.2 pints
Step-by-step explanation:
3.5 × 1.2 = 4.2
Answer: 4.2 pints
Three teachers shared 4/5 of a flat paper that was donated to the school. what fraction of the flat paper did each teacher receive
How many significant digits are there in the number 237.16?
Answer:
3
Step-by-step explanation:
Which figure has two circular faces?
Figure A
O figure A
Ofigure B
figure C
figure D
Figure B
Figure C
Figure D
A cylinder is a 3D shape having two circular faces.
The answer is Figure A