Answer:
range of f is [0,3]
Step-by-step explanation:
The "square root" symbol, [tex]\sqrt{\text{ \quad }}[/tex], is a function. As a result, it only has a single output because functions must only have a single output for each input.
Thinking about it graphically, if the square root function did give both a positive and a negative result, the function "f" would not pass the vertical line test and it would not be a function.
When solving an equation like [tex]x^2=25[/tex], to solve, we must apply the square root property. The square root property says that to find both solutions, one must look at both the positive and the negative of the square root. So, to solve:
[tex]x^2=25[/tex]
Apply square root property...
[tex]\sqrt{x^2} = \pm \sqrt{25}[/tex]
[tex]x=\sqrt{25}[/tex] or [tex]x=-\sqrt{25}[/tex]
[tex]x=5[/tex] or [tex]x=-5[/tex]
In this case, because the square root function itself only outputs non-negative results (so, including zero, as you already identified), the range will only be [0,3].
solve simulteneusly equation 6p-4r=4 and p-2r=5
Answer:
r = - 3.25, p = -1.5
Step-by-step explanation:
→ Rearrange p - 2r = 5
p = 5 + 2r
→ Substitute into 6p - 4r = 4
6 ( 5 + 2r ) - 4r = 4
→ Expand
30 + 12r - 4r = 4
→ Simplify and solve
r = - 3.25
→ Substitute into p - 2r = 5
p + 6.5 = 5
→ Minus 6.5 from both sides
p = -1.5
Which graph shows the greatest integer function?
The graph of the greatest integer function is graph A.
What is graph?A graph is a diagram or a pictorial representation of data or values that show the relationship between quantities or objects.
Given are graphs we need to find the graph of the greatest integer function,
The graph of the greatest integer function is graph A because since it is a greatest integer function, it includes the highest integer, but excludes the lowest since it is the highest integer when x is less than or equal to an integer but greater than x-1.
Hence the graph of the greatest integer function is graph A.
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If m/BAD = 22°,
what is X?
A
C
22⁰
B
D
Answer:
x = 136
Step-by-step explanation:
x = 180 - 22 - 22
= 136
1-sinA+cosA / sinA+cosA-1 = 1+cosA/sinA
Solution:
[tex]\dfrac{\left[\left(\sin ^{2} A+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]\right.}{\left[\left(1-\cos ^{2} A\right)-(1-\cos A)^{2}\right]}[/tex]
[tex]\dfrac{\left[\left(1-\cos ^{2} A\right)+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]}{\left[(1-\cos A)(1+\cos A)-(1-\cos A)^{2}\right]} [/tex]
[tex]\dfrac{(1-\cos A)[1+\cos A+2 \sin A+1-\cos A]}{[1-\cos A][1+\cos A-1+\cos A]} [/tex]
[tex]\dfrac{[2+2 \sin A]}{[2 \times \cos A]}[/tex]
[tex]\dfrac{2(1+\sin A)}{2 \times \cos A}[/tex]
[tex]\dfrac{1+\cos A}{\sin A} [/tex]
Hence Proved.
Pls answer fast
(√3 + √11)² + (√3 - √11)²
(√3 + √11)² + (√3 - √11)²
(a+b)² = a² + b² + 2ab ( a - b )² = a² + b² - 2abNow ,
(√3 + √11)² + (√3 - √11)²
(3 + 11 + 2√3√11)+ (3 +11 - 2√3√11)
14 + 2√33+ 14 - 2√33
14 + 14 = 28
Hence , The value of (√3 + √11)² + (√3 - √11)² is 28 .
Answer:
28
Step-by-step explanation:
(a + b)² + (a - b)² = 2a² + 2b²
(√3 + √11)² + (√3 - √11)²
= 2√3² + 2√11²
= 28
Given the following formula,A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $300 each, and the desktop computers cost $225 each. How much would it cost to buy 18 notebooks and 12 desktop computers? How much would it cost to buy n notebooks and dd desktop computers?
Total cost, 18 notebooks and 12 desktop computers:
Total cost, n notebooks and dd desktop computers:
The cost to buy 18 notebooks and 12 desktop computers will be $8100.
The cost to buy n notebooks and d desktop computers will be 300n + 225d
What is the cost of a given material?The cost of a given material is the amount attached and to be paid for getting that material.
From the given information:
The cost of notebook computers = $300The cost of desktop computers is $225 eachThe cost to buy 18 notebooks and 12 desktop computers will be:
= 300(18) + 225(12)
= 5400 + 2700
= $8100
The cost to buy n notebooks and d desktop computers will be:
= 300(n) + 225(d)
= 300n + 225d
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18.
(05.06 LC)
A librarian measured the number of young adult books in a library. The number of books in the library as a function of time (in years since 2008) is shown in the scatterplot. Choose the linear function that best describes the scatterplot relating the number of books in the library, y, to time, x. (1 point)
y = 8 − 10x
y = 8 + 10x
y = 10 − 8x
y = 10 + 8x
Answer:
y=8+10x that then answer I guess
What is the area of triangle ABC?
Answer:
3 square units
Step-by-step explanation:
Use BC as the base = 2
Use y -axis to C (or B) as the height = 3
Area of triangle = 1/2 * base * height = 1/2 * 2 * 3 = 3 units^2
What is sin and cos
Sin and cos are trigonometry functions used to find measurements in a right triangle.
[tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]
[tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]
[tex]\frac{4x}{x-1} -\frac{5x}{x-2}=\frac{2}{x^{2} 3x+2}[/tex]
The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
How to solve the equation?The equation is given as:
[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]
Start by taking the LCM
[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]
Expand the denominator
[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]
Cancel out the common factor
4x(x - 2) - 5x(x - 1)= 2
Expand
[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]
Evaluate the like terms
[tex]-x^2 - 3x = 2[/tex]
Rewrite as:
[tex]x^2 + 3x + 2 = 0\\[/tex]
Expand
[tex]x^2 + 2x + x + 2 = 0[/tex]
Factorize
x(x + 2) + 1(x + 2) = 0
Factor out x + 2
(x + 1)(x + 2) = 0
Solve for x
x = -1 or x = -2
Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
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A rectangular field with sides as shown below has to be fenced all around. If fencing posts have to be fixed at 1-metre intervals, how many posts are needed?
1. 167
2. 334
3. 668
4. 6840
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
so, here
2×95 + 2×72 = 190 + 144 = 334 m
so, yes, the answer 2. 334 is correct.
The solution is Option B.
The total number of posts is the total perimeter of the rectangular field and the value of N = 334 posts
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the number of posts be = N
Fencing posts have to be fixed at 1-metre intervals
The perimeter of the rectangular field = number of posts
Now , the equation will be
The length of the rectangular field = 95 m
The width of the rectangular field = 72 m
Perimeter P of the rectangle = 2 ( Length + Width )
Substituting the values in the equation , we get
Perimeter of the rectangle P = 2 ( 95 + 72 )
On simplifying the equation , we get
Perimeter of the rectangle P = 2 ( 167 )
Perimeter of the rectangle P = 334 m
Now , the number of posts = perimeter of the rectangular
So , the number of posts N = 334 posts
Therefore , the value of N is 334
Hence , the number of posts is 334 posts
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HELP ANGJHHGG plssssssssssssssssssfghgg
Answer:
5377
Step-by-step explanation:
this is a vector question where how far is the Resultant. that is, it is determined by the magnitude of the Hypotenuse.
using Pythagoras theorem
Hypotenuse ²= Opposite ²+Adjacent²
Hypotenuse ²= 2865²+4550²
Hypotenuse ²= 8208225+20702500
Hypotenuse ²=28910725
Hypotenuse=√28910725
Hypotenuse=5376.86944234282
Hypotenuse= 5377 approximated
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
D
Step-by-step explanation:
Trust me
How many solutions does the system have?
x + y = 5
x + y = 6
Onone
O one
O two
O infinite
Answer:
none
Step-by-step explanation:
please mark me as brainlest
AandBhave coordinates (-1,1.5) and (3,2).
Tangents to the curve have been drawn at A and B.
Calculate the gradient of the curve at A and at B.
Venn diagram ( attached image )
Assessing the given Venn diagram and the data related to it, we can answer the required question:
Q1. How many people were surveyed = 86.
Q2. What is the probability that a customer chosen at random:
a) takes salt P(S) = 46/85.
b) takes both salt and vinegar P(S ∩ V) = 13/85.
c) takes salt or vinegar or both P(S ∪ V) = 66/85.
The number of people who take salt chips n(S) = 46.
The number of people who take vinegar chips n(V) = 33.
The number of people who takes both n(S ∩ V) = 13.
The number of people who take neither n((S ∪ V)') = 19.
Therefore, the total number of people surveyed n(U) = n(S) + n(V) - n(S ∩ V) + n((S ∪ V)') = 46 + 33 - 13 + 19 = 85.
The number of people who takes salt or vinegar or both n(S ∪ V) = n(U) - n((S ∪ V)') = 85 - 19 = 66.
The probability that a customer chosen at random takes salt P(S) = n(S)/n(U) = 46/85.
The probability that a customer chosen at random takes both salt and vinegar P(S ∩ V) = n(S ∩ V)/n(U) = 13/85.
The probability that a customer chosen at random takes salt or vinegar or both P(S ∪ V) = n(S ∪ V)/n(U) = 66/85.
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Use the formula to solve the equation x^2 + 9x + 8 = 0.
Answer:
[tex]x=-8, -1[/tex]
Step-by-step explanation:
Given the equation [tex]x^{2} +9x+8=0\\[/tex],
By the quadratic formula,
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex],
[tex]x=\frac{-(9)+-\sqrt{(9)^{2}-4(1)(8) } }{2(1)}=\frac{-9+-\sqrt{49 } }{2}=\frac{-9+-7 }{2}[/tex]
We have two different solutions for x where [tex]x=\frac{-9-7 }{2}[/tex] and [tex]x=\frac{-9+7 }{2}[/tex]
So, x = [tex]-16/2=-8[/tex] and [tex]x=-2/2=-1[/tex]
Therefore, the solutions to this quadratic equation is x = -8, -1, by the quadratic formula.
Which expression is not a polynomial?
x³
x² - 2x
x³ +1
12x
Answer:
12x
Step-by-step explanation:
It has no exponent so it is not a polynomial
What is the result of adding the system of equations? Equation 1: 2x + y = 4 Equation 2: 3x - y = 6 A) 5x = 10 B) x = 5 C) x = 10
An equation is formed of two equal expressions. The correct option is A, the sum will be equal to 5x = 10.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the two systems of equations Equation1: 2x+y=4 and Equation 2: 3x-y=6. Now if the two of the given equations are added the result will be,
2x + y + 3x - y = 4 + 6
5x = 10
Hence, the correct option is A, the sum will be equal to 5x = 10.
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What is the quotient of 0.8449 ÷ 0.71?
Answer:
1.19
Step-by-step explanation:
1) Shift the decimals of both 0.8449 and 0.71 to the right by 2 decimal places. (This is needed to convert 0.71 to 71, since long division must divide by a whole number.)
84.49 ÷ 71
2) Use the algorithm method.
1 . 1 9
7 1 | 8 4 . 4 9
7 1 .
1 3 . 4
7 . 1
6 . 3 9
6 . 3 9
3) Therefore, 0.8449 ÷ 0.71 = 1.19.
1.19
Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
1kg of sugar costs ₹25.30 . Find the cost of 13.5kg of sugar
Answer:
₹ 341.55
Step-by-step explanation:
Cost of 1 kg sugar = ₹ 25.30
Cost of 13.5 kg sugar = 25.30 × 13.5 = 341.55
Hence, the cost of 13.5 kg is ₹ 341.55
If you are writing, write statements too as in my school they give extra marks.
Thankyou and have a great day ahead.
Answer:341.55
Step-by-step explanation:
If one KG of sugar does cost ₹25.3 and if you want to know how much 13.5 kg costs you just would have to multiply/times ₹25.3 by 13.5 and what is 25.3 x 13.5. ₹341.55 and that's your answer!
Find (f • g) (x) Assume x>0
Answer:
[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]
[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]
[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]
Rewrite 100 as 10²:
[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]
[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies (f \cdot g)(x)=10x[/tex]
Four students are trying to determine what number must replace the question (x^2)^?=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? In words explain why.
Joe is correct as the unknown number is 6.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
Given :
[tex](x^2)^?=x^4\times x^8[/tex]
Let the question mark exponent outside the bracket be y, which needs to be determined
[tex](x^2)^y=x^4\times x^8[/tex]
Simplify the equation by applying exponent rules to either side of the equation:
Apply the rule [tex](a^b)^c = a^{b \times c}[/tex]
[tex](x^2)^y=x^4\times x^8[/tex]
[tex](x)^{2y}=x^4\times x^8[/tex]
Now apply [tex]a^b \times a^c = a^{b+c}[/tex]
[tex](x)^{2y}=x^{4+8}\\\\(x)^{2y}=x^{12}[/tex]
So, the base is the same the exponent will be the same also,
2y = 12
y = 6
Hence, Joe is correct as the unknown number is 6.
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Plsss helppppp I neeed this
Based on the calculations on the bisector of ST, the value of ST are equal to 38 and 30 respectively.
How to find the bisector of ST?In order to determine the bisector of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
For exercise 1, we have:
ST = SM + MT
ST = 19 + 19
ST = 38.
For exercise 2, we have:
First of all, we would determine the value of x as follows;
3x - 6 = x + 8
3x - x = 8 + 6
2x = 14
x = 14/2
x = 7.
ST = SM + MT
ST = 3x - 6 + x + 8
ST = 3(7) - 6 + 7 + 8
ST = 30.
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Which expression is equivalent to?
The expression obtained is 2g³-5g² +6 , Option C is the correct answer.
What is an Expression ?An expression is a mathematical statement that consists of constant , variable and mathematical operators.
The expression given is
[tex]\rm \dfrac{(5g^4 +5g^3 -17g^2 +6g) -(3g^4 +6g^3-7g^2 -12)}{g+2}[/tex]
On subtracting the numerator
2g⁴-g³-10g²+6g+12
Now dividing the numerator by denominator
The expression obtained is 2g³-5g² +6
Therefore Option C is the correct answer.
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Select the correct answer.
Consider the given functions.
A table with values of x and f of x is given along with a non-linear equation g of x equals 2 power x minus 5 and a graph solving the equation
Select the true statement regarding the end behavior of the functions.
Using limits, it is found that the true statement regarding the end behavior of the function is given by:
B. As the value of x increases, f is the only function to approach 0.
How to find the end behavior of a function?The end behavior of a function is given by the limit of the function as x goes to infinity.
In this problem, we have that:
[tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex], as we can see from the table, when x increases, y decreases. [tex]\lim_{x \rightarrow \infty} g(x) = 2^{\infty} = \infty[/tex].[tex]\lim_{x \rightarrow \infty} h(x) = \infty[/tex], from the graph.Hence statement B is correct.
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I NEED HELP PLEASE OMGOGMOMOG
Answer
c
I'm not sure how to explain my bad
Which describes the graph of y= -(x + 6)² + 6?
O A. Maximum at (-6, 6)
OB. Maximum at (6, 6)
OC. Minimum at (-6, 6)
OD. Minimum at (6, 6)
Answer:
A
Step-by-step explanation:
Since x has a negative coefficient, the graph opens downwards meaning that it has a maximum.
The vertex formula is y = a(x - h)^2 + k so the coordinate must be (-6, 6).
Given the graph of the function, f(x), what is the value of f (–2)?
f (–2) =
Using the graph of the function concept, the numeric value at x = 2 is f(-2) = 0.
How to find the numeric value of a function?To find the numeric value of a function at x = a, we look at the value of y(vertical axis) where x = a has a closed interval.
Researching the problem on the internet, looking at it's graph, it is found that when x = -2, there is a closed interval at y = 0, hence f(-2) = 0.
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Answer:
0A: (-∞, ∞)B: (-2, ∞)Step-by-step explanation:
