[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:A. \:\: 10[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 102[/tex]
[ subtract 2 from both sides ]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - 2 = 102 - 2[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - \bigg( 2 \sdot x \sdot \cfrac{1}{x} \bigg)= 100[/tex]
[ 2 can written like that, as they cancel out each other ]
Apply Identity [ a² + b² -2ab = (a - b)² ]
[tex]\qquad \tt \rightarrow \: \bigg (x - \cfrac{1}{x} \bigg) {}^{2} = 100[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = \sqrt{100}[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = 10[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
r=
help me please thank u
Answer:
[tex]\fbox {r = 34}[/tex]
Step-by-step explanation:
Finding IQ and RJ by tangent rule :
⇒ IQ = QK = 10
⇒ KR = RJ = 8
Finding PJ :
⇒ PJ = 32 - 8
⇒ PJ = 24
∴ But PJ = PI (by tangent rule)
⇒ PI = 24
Finding r :
⇒ PI + IQ
⇒ 24 + 10
⇒ r = 34
erved,
The graph of function fis shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x) = 2f(x-1)
Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
What is the function about?Using the graph, the function is:
f(x-1) =1/2 (x-1) - 3
f(x-1) = 1/2x - 1/2 - 3/1
f(x-1) = 1/2x - 7/2
So:
g(x) = 2f(x-1)
g(x) = 2 (1/2x - 7/2)
g(x) = x - 7
Therefore,:
At x = 0, y = -7
y = 0, x = -7
Thus, Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
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Got it right on Plato/Edmentum UωU <3
What is the period of the function y=tan (4/pi (x-pi/3))
O 3 units
O4 units
O 6 units
O 8 units
Answer:
Period = 4 units
Step-by-step explanation:
Standard form of a tangent function:
[tex]f(x)=\sf A \tan(B(x+C))+D[/tex]
A = vertical stretchπ / |B| = period (distance between any two consecutive vertical asymptotes)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftThe tangent function has a vertical asymptote whenever cos(x) = 0
The tangent function does not have an amplitude because it has no maximum or minimum value.
Given function:
[tex]y=\tan \left(\dfrac{\pi}{4}\left(x-\dfrac{\pi}{3}\right)\right)[/tex]
Therefore:
Vertical stretch (A) = none[tex]\textsf{Period}=\dfrac{\pi}{\left|\dfrac{\pi}{4}\right|}=4[/tex]Phase shift (C) = π/3 to the rightVertical shift = noneAnswer: 4 units
Step-by-step explanation:
Aiden has a smart phone data plan that costs $25 per month that includes 2 GB of data, but will charge an extra $10 per GB over the included amount. How much would Aiden have to pay in a month where he used 2 GB over the limit? How much would Aiden have to pay in a month where he used went over by xx GB?
Total cost when over by 2 GB:
Total cost when over by xx GB:
need answer quick
Answer:
45 dollars for going over 2GB
Step-by-step explanation:
If he pays 25 dollars every month and he goes over 2 GB then he’ll have to pay 20 dollars extra since every GB over cost 10 dollars. The equation is 25+10+10 which equals 45.
An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division.
The amount when 2 GB is used over the limit in a month is $45.
What is an expression?An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division.
Example: 2x + 3x2 is an expression.
We have,
Cost of data plan with 2 GB = $25
Cost of one GB = $10
The equation that can be used to find the amount to pay when using x GB over the limit in a month:
= 25 + 10x
The amount when 2 GB is used over the limit in a month:
= 25 + 10 x 2
= 25 + 20
= $45
Thus,
The amount when 2 GB is used over the limit in a month is $45.
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On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4).
Which explains why the graph is not a function?
If a plane including pints p,q and r cuts through the cube
If a plane including pints p,q, and r cuts through the cube, the shape that will be gotten is a triangle.
What is a triangle?A triangle is a polygon with three edges and three vertices. The sum of the internal angles of a triangle is equal to 180 degrees.
In this case, when a plane including pints p,q, and r cuts through the cube, the shape that will be gotten is a triangle.
The diagram is attached.
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find the linear measure of arc vw on circle p, where pv = 32 inches and angle vpw = 84. use 3.14 for pie and estimate your answer to two decimal places.
The linear measure of arc vw as described in the task content is; 46.89in.
What is the linear measure of the arc vw?It follows from the task content that the radius of the circle with center p is given as pv = 32in. and the angle subtended by the arc is; 84.
On this note, the measure of arc vw is;
= (84/360) × 2 × 3.14 × 32
= 46.89 inches.
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pleasee help with function graphing
Answer: A. The function has two distinct real zeros.
Answer:
C. The function has four distinct real zeros.
Step-by-step explanation:
The function intersects y=0 at x=1/2, 4, and 6 twice. It has two solutions at 6 twice as it is a behavior of polynomial or rational functions
find the number of primes less than 190 using the principle of inclusion-exclusion.
The number of primes less than 190 using the principle of inclusion-exclusion are 42
Principle of inclusion- exclusionThe principle of inclusion-exclusion is known as a counting technique that computes the number of elements satisfying at least one of several properties and guaranteeing that the numbers are not counted twice.
Prime numbers are numbers only divisible by 1 and itself.
Prime numbers less than 190 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181
They are 42 in number
Therefore, the number of primes less than 190 using the principle of inclusion-exclusion are 42
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Combine the radicals 4√7 + 3√28
Answer:
10√7
Step-by-step explanation:
you can simplify the second radical and break it up into
√4 * √7 which then simplifies to 2√7 which you then multiply by 3. 4√7 + 3(2√7) which becomes 4√7 + 6√7 and then you just add the numbers Infront to get 10√7
Make u the subject formula
Please help
X=4uy/M
Answer:
[tex]\frac{XM}{4y}=u[/tex]
Step-by-step explanation:
First, multiply both sides by M.
X M = 4uy
Now, divide both sides by 4y.
[tex]\frac{XM}{4y} =\frac{4uy}{4y}[/tex]
Therefore,
[tex]\frac{XM}{4y}=u[/tex]
Lucy is knitting a blanket and needs to buy some more yarn. at her local craft store, 2 skeins of yarn cost $7 and 8 skeins of yarn cost $28. what is the constant of proportionality in this direct variation?
Answer:
4
Step-by-step explanation:
Proportionality between skein values
8:2=4:1
Proportionality between cost values
28:7=4:1
The variation(both the skein values and cost values) has the constant of 4 ie the 1st skein value × 4= the last skein value & the 1st cost value × 4=the last cost value
True or false: The graph of y=3x2-3 opens up.
Answer: True: The graph of y=3x²-3 opens up
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (0,−3)(0,-3)
Focus: (0,−35/12)
Axis of Symmetry: x=0
Directrix: y=−37/12
X={-2, -1, 0, 1, 2}
Y={9, 0, -3, 0, 9
Step-by-step explanation:
If AB is parallel to CD and the slope of AB is -3, what is the slope of CD?
the sum of a certain number and -3
Answer:
[tex]\huge\boxed{\sf x - 3 }[/tex]
Step-by-step explanation:
Let the certain number be x
So,
Given condition:Sum is to add so we'll use the sign +
= x + (-3)
We know that + and - makes - because - sign will flip the + sign and make it negative, So:
= x - 3
[tex]\rule[225]{225}{2}[/tex]
Solution: c-3
[tex]\searrow[/tex]
Detailed explanation:
[tex]\searrow[/tex]
This problem tells us to convert the verbal phrase (in words) "the sum of a certain number and -3" into an algebraic expression, which is written in numbers.
Let's start by taking a look at our problem.
"the sum of a certain number and -3". We can first write this "certain number" as one letter (any letter you want). Let it be c.
Our expression already looks a little easier: "the sum of c and -3".
Now, the word "sum" tells us to add. So we should add c and -3.
[tex]--\mapsto\boldsymbol{c+-3}[/tex]
Which is the exact same thing as [tex]\boldsymbol{c-3}[/tex].
Voila! There's our answer.
Cheers!! ^-^______________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_______________________
What is the measure of
Calculate the AREA of the shape below. Give your answer in cm²
Answer:
[tex] \boxed{\bf 26\: cm^2} [/tex]Step-by-step explanation:
We got two shapes in the given figure,on the right we got a rectangle and on the left we have a square.
Area of rectangle:-
[tex]\bf 5 \times 2[/tex][tex]\bf 10 \:cm^{2} [/tex]Area of square :-
[tex]\bf 4 \times 4[/tex][tex]\bf 16 \: {cm}^{2} [/tex]Total area :-
[tex]\bf 10 + 16[/tex][tex]\boxed{\bf 26 \: {cm}^{2} }[/tex]_________________________Answer:
26 cm^2Step-by-step explanation:
you have two rectangles, the bigest has the base of 6cm and the height of 4cm, the area is 6 * 4 = 24cm ^ 2, the other rectangle has the base of 6 - 4 = 2 and the height of 5 - 4 = 1, 2*1=2.
we add the dimensions and we have the area of the complete figure 24 + 2 =
26 cm ^ 2
Circle o has a circumference of 28.3 cm. What is the length of the radius r?
How to find the point slope form with the slope of 3 and the point of -2/6
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:y-6 = 3(x + 2) [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Equation of line in point - slope form :
[tex]\qquad \tt \rightarrow \:y-y_1 = m(x - x_1)[/tex]
[tex] \tt \:m = slope=3[/tex][tex]\tt y_1 = y \: \: coordinate \: \: of \: \: point = 6[/tex][tex] \tt \:x_1 = x \: \: coordinate \: \: of \: \: point = - 2[/tex]Here :
[tex]\qquad \tt \rightarrow \:y - 6 = 3(x - ( - 2))[/tex]
[tex]\qquad \tt \rightarrow \:y - 6 = 3(x + 2)[/tex]
A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing
equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the
two pieces of equipment?
Answer:
First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
Step-by-step explanation:
This question deals with Slope of a line.
Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet
Thus, slope = 6/4 = 3/2 ≈ 1.5
For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet
Thus, slope= 10/6 = 5/3 ≈ 1.66
Thus,
Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3
Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
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f(x) = 4x² + 7x-3
g(x) = 6x³ – 7x² - 5
-
Find (f + g)(x).
Answer:
(f + g)(x) = 6x³ - 3x² + 7x - 8
Step-by-step explanation:
Another way of writing (f + g)(x) is f(x) + g(x). So, this question is asking you to combine both of the functions.
f(x) + g(x)
(4x² + 7x - 3) + (6x³ - 7x² - 5) <----- Insert functions
-3x² + 7x - 3 + 6x³ - 5 <----- Combine 4x² and -7x²
-3x² + 7x - 8 + 6x³ <----- Combine -3 and -5
6x³ - 3x² + 7x - 8 <----- Rearrange
Is this correct? If not then whats the answer?????
(image below)
35 points! Which of the following polynomials has an even degree and a positive leading coefficient?
Answer:
1
Even degree: the start and the end of the graph goes either both up or down (1 and 4)
positive leading coefficient: right side of the graph is going up (1 and 2)
Write logb(x/y) as two logs
Answer:
[tex] log_{b}(x) - log_{b}(y) [/tex]
Simplify (3 + √5 )(2 + √5)
need the answer ASAP, WILL GIVE BRAINLIEST
Answer:
11 + 5√5
Step-by-step explanation:
6 + 3√5 +2√5 + 5
11 + 5√5
root n * root n = n , which is why there is a 5 at the end
Answer:
the answer is 11+5√5
Step-by-step explanation:
B/c (a+b).(c+d)=ac+ad+bc+bad(3+√5)(2+√5)=3.2+3.√5+√5.2+√5√5=6+3√5+2√5+√5√5=6+3√5+2√5+5=11+3√52√5=11+5√5PLEASE HELP ANSWER MY QUESTION ASAP!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a_{33} = 1\degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
In a matrix, [tex] \sf a_{ij} [/tex] represents an element in " i " th row and " j " th column.
Henceforth, element [tex] \sf a_{33} [/tex] represents element in 3rd row and 3rd column.
[tex]\qquad \tt \rightarrow \:a_{33} = 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
4. John has his money in a savings
account that earns 3% interest each
year. He never takes money out of the
account. The value of his account is
described by the function
Dollars (years), or D(y).
Is D(2) < D(7) true or false?
Answer:
false
Step-by-step explanation:
so D(2) is equal to how much money he has after 2 years while D(7) is after 7 years. since he earns 3% interest each year he will have more money after 7 years than 2 years
Drag each tile to the correct box. Not all tiles will be used.
Place the steps for finding in the correct order.
Answer+Step-by-step explanation:
[tex]f^{-1}\left( x\right) =\frac{1}{7} x^{2}+3 \ ,\text{where}\ x\geq 0[/tex]
please help thank you !
Answer:
6.6 cm and 14.6 cm
Step-by-step explanation:
(a)
the length of arc AB is calculated as
AB = circumference of circle × fraction of circle
= 2πr × [tex]\frac{95}{360}[/tex]
= 2π × 4 × [tex]\frac{95}{360}[/tex]
= 8π × [tex]\frac{95}{360}[/tex]
= [tex]\frac{8\pi (95)}{360}[/tex]
≈ 6.6 cm ( to the nearest tenth )
(b)
the perimeter (P) of sector AOB is
P = r + r + AB = 4 + 4 + 6.6 = 14.6 cm
Step-by-step explanation:
3.
the circumference of a circle is
2×pi×r
r = 4 cm
so, we know, the full circle circumference is
2×pi×4 = 8×pi = 25.13274123... cm
a.
the arc length of AB is the part of the whole circumference that corresponds to 95° out of the full 360° of a whole circle.
arc AB = 8×pi × 95/360 = pi × 95/45 = pi × 19/9 =
= 6.632251158... cm
b.
the perimeter of OAB (the "pie slice") is then the arc AB plus 2 radius lengths (from the end points on the arc to the center of the circle) :
pi × 19/9 + 2×4 = pi×19/9 + 8 = 14.632251158... cm
Y = 3x + 10
Y = 2x - 8
find the substitution
Show your work please ill give brainlyest
Answer:
x = -18, Y = -44
Step-by-step explanation:
Since Y = 2x - 8, we can substitute that into the first equation:
2x - 8 = 3x + 10
3x - 2x = -8 - 10
x = -18
Now we plug x = -18 back into the second equation:
Y = 2(-18) - 8
Y = -36 - 8
Y = -44
