The key features are (1) both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
How to determine the key featuresThe functions are given as:
f(x) = 4 - x
[tex]g(x) = -\sqrt{x - 4}[/tex]
Using a graphing calculator:
The domain of g(x) is [4,∞)The range of g(x) is (-∞,0]The domain of f(x) is (-∞,∞) The range of f(x) is (-∞,∞) Both functions have positive values for their domainsBy comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)
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Answer:
B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
b is correct
The linear equation y = 25x describes how far from home Gary is as he drives from Montreal to Miami. Let x represent the number of hours and y represent the number of miles. How far from home is Gary in 12 hours? Graph the equation and tell whether it is linear.The linear equation y = 25x describes how far from home Gary is as he drives from Montreal to Miami. Let × represent the number of hours and y represent the number of miles. How far from home is Gary in 12 hours? Graph the equation and tell whether it is linear.
The distance that Greg is from home after 12 hours is given as follows:
300 miles.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y = 25x.
Hence the distance after 12 hours is given as follows:
y = 25 x 12
y = 300 miles.
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daniel wants to build a sandbox that has a perimeter or 20.5 ft. the length is 5.36 ft. what is the width of the sandbox?
Answer:
20.5 - 5.36
= 15.14/2 (because we are using perimeter, so there are 2 equal lengths and 2 equal widths)
=7.57, therefore the width of the sandbox is 7.57 ft.
Answer:
4.89 ft
Step-by-step explanation:
Perimeter of a rectangle is given by the formula :
P = 2L + 2W
So now we solve for W :
P = 2(L+W)
P/2 = L+W
P/2 - L = W
Now we substitute our P and L into the rearranged formula :
20.5 / 2 - 5.36 = W
10.25 - 5.36 = W
W = 4.89 ft
Hope this helped and brainliest please
Please help Urgently and need working out!
Determinar cuales de las siguientes frases son proposiciones
a) 3+2 = 0 c) ¡Hola!
b) x + 1 = 4 d) Yo estudio
The exercise is designed to test the students knowledge of prepositions. The correct answer thus is (Option D) Yo estudio (which translates) "I study".
What is the explanation for the answer above?To understand the answer, you need to know what a preposition is. A preposition, in simple terms, is a word or group of words that comes before a noun.
The function of a preposition (much like an adjective) is to give clarity to the noun that it precedes.
Let us complete the Preposition phrase to give meaning to it:
"I study Mathematics". Where;
"Mathematics" is the noun;
"I Study" is the prepositional phrase. Hence the correction answer to the question above is Option D.
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HELP NEEDED ASAP
answer this question for me, image below
Answer: Heyaa! ~
Your Answer Is... 13
Step-by-step explanation:
385 divided by 28 = 13. 75Reduce the expression, if possible, by cancelling the common factors.Hopefully this helps you! ~
Click on the pic there will be the question (very easy I’m just lazy lol)
Answer: ......... 14.85
Step-by-step explanation:
4.95 × 3
...
14.85
bros lazy lol
What is the volume of a cylinder with base radius 2 and height 9?
Answer:
V =113.09734
Step-by-step explanation:
[tex]V=\pi r^{2}[/tex]
[tex]= 2^{2}[/tex] x 9= 113.09734
(which you can technically round to 1)
=113.1
Solve 24x ⋅ 321-x = 8x+2
Answer:
[tex]x=2/7695[/tex]
≡ Small number, yes, but the steps explain why x is equal to this.
Step-by-step explanation:
simplify
[tex]24x\cdot 321-x=8x+2\\\left(24\cdot 321\right)x-x=8x+2\\7703x=8x+2[/tex]
group
[tex]7703x=8x+2\\7703x-8x=8~x+2-8x\\7695x=8x+2-8x\\7695x=8x-8x+2\\7695x=2[/tex]
isolate
[tex]7695x=2\\\frac{7695x}{7695}=\frac{2}{7695}\\x=\frac{2}{7695}[/tex]
The fraction is in its simplest form, so that is the final answer.
solve for y :
[tex]\longrightarrow \: \bold{3 + y = 18}[/tex]
ty! ~
Answer:
y = 15
Step-by-step explanation:
Given :
3 + y = 18
This a simple algebraic equation.
Subtract 3 from both sides :
⇒ 3 + y - 3 = 18 - 3
⇒ y = 15
Answer:
y = 15
Step-by-step explanation:
Given equation:
3+y=18To Find:
Value of ySolution:
We can rewrite this equation as:
y+3 = 8[This'll ain't change the answer]
Now we could solve on a easy way.
STEPS:
Transpose +3 to the RHS, make sure to change it's sign from “+” to “-”.
=> y = 18-3
Subtract the integers which's on the RHS:
=> y = 15
Hence,the value of y will be 15.
[tex] \rule{225pt}{2pt}[/tex]
What is the output of this program?
numA = 2
numB = 3
if numA == 2 or numB == 2:
print("yes")
elif numA == 2 and numB == 3:
print("no")
Output:
PLEASE HELP ME PLEASE
[tex]\frac{1}{2} (5x - 9 ) = 2 (\frac{1}{3} + 6 )[/tex]
Answer: 103/15
Step-by-step explanation:
We can simplify the right-hand side to be [tex]2 \left(\frac{1}{3}+6 \right)=2 \left(\frac{19}{3} \right)=\frac{38}{3}[/tex].
This means we need to solve:
[tex]\frac{1}{2}(5x-9)=\frac{38}{3}\\5x-9=\frac{76}{3}\\5x=\frac{103}{3}\\x=\boxed{\frac{103}{15}}[/tex]
Consider the linear system:
[tex]\overrightarrow y'=\begin{bmatrix}-6 & -4 \\12 & 8\end{bmatrix}\overrightarrow y[/tex]
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
b. For each eigenpair in the previous part, form a solution of [tex]\overrightarrow y' = A\overrightarrow y[/tex]. Use [tex]t[/tex] as the independent variable in your answers.
c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions?
a. If A is the coefficient matrix, solve det(A - λI) = 0 for the eigenvalues λ :
[tex]\det\begin{bmatrix}-6-\lambda & -4 \\ 12 & 8-\lambda\end{bmatrix} = (-6-\lambda)(8-\lambda)+48 = 0 \implies \lambda(\lambda-2)=0[/tex]
[tex]\implies \lambda = 0, \lambda = 2[/tex]
Let v = [v₁, v₂]ᵀ be the eigenvector corresponding to λ. Solve Av = λv for v :
[tex]\lambda=0 \implies \begin{bmatrix}-6&-4\\12&8\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 3v_1 + 2v_2 = 0[/tex]
If we pick v₂ = -3, then v₁ = 2, so [2, -3]ᵀ is the eigenvector for λ = 0.
[tex]\lambda = 2 \implies \begin{bmatrix}-8&-4\\12&6\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 2v_1 + v_2 = 0[/tex]
Let v₁ = 1, so v₂ = -2.
b. λ = 0 and v = [2, -3]ᵀ contributes a constant solution,
[tex]\vec y_1 = e^{\lambda t} v = \begin{bmatrix}2\\-3\end{bmatrix}[/tex]
while λ = 2 and v = [1, -2]ᵀ contribute a solution of the form
[tex]\vec y_2 = e^{\lambda t} v = e^{2t} \begin{bmatrix}1\\-2\end{bmatrix}[/tex]
c. Yes; compute the Wronskian of the two fundamental solutions:
[tex]W(1, e^{2t}) = \det\begin{bmatrix}1 & e^{2t} \\ 0 & 2e^{2t}\end{bmatrix} = 2e^{2t} \neq 0[/tex]
The Wronskian is non-zero, so the solutions are independent.
log x + log (2x-1) = log 6
Answer:
x = 2
Step-by-step explanation:
logx + log(2x - 1) = log 6
Apply log rules,
x(2x - 1) = 6
2x^2 - 1x = 6
x = 2 (true) or x = -3/2 (False)
Which equation matches the graph of the greatest integer function given
below?
Answer: is y=[x]-2
I used this app to help me get the answer too lol
How is the product of 3 and –2 shown using integer tiles?
3 positive tiles and 2 negative tiles.
3 negative tiles and 2 positive tiles.
3 sets of 2 negative tiles.
3 sets of 2 positive tiles.
The point −20, 21 is on the terminal arm of an angle = in standard position. Find sin = and cos =.
The point −20, 21 is on the terminal arm of an angle = in standard position. Hence, sinФ = 21/29 and cos Ф = -20/29
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
Given Data
A (-20 , 21)
We have to find sin = ? and cos = ?
The point is in the fourth quadrant
We have the Opposite side and the Adjacent side
Calculate the hypotenuse
c² = (-20)² + (21)²
c² = 400 + 441
c² = 841
c = 29
Hence,
sinФ = 21/29
cos Ф = -20/29
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The table gives information about the height of some trees draw a histogram for the information of some trees
2.3+2.2y uneed to pus the 2 on the 3 and answer is uten
let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²
Answer:
[tex]\dfrac a{b^2} + \dfrac b{a^2} = 10[/tex]
Step-by-step explanation:
[tex]\text{Given that, the roots are a,b and } ~ x^2 -4x+2 = 0\\\\\text{So,}\\\\a+b = -\dfrac{-4}1 = 4\\\\ab = \dfrac 21 = 2\\\\\text{Now,}\\\\~~~~~\dfrac a{b^2} + \dfrac b{a^2}\\\\\\=\dfrac{a^3 +b^3}{a^2b^2}\\\\\\=\dfrac{(a+b)^3 -3ab(a+b)}{(ab)^2}\\\\\\=\dfrac{4^3 -3(2)(4)}{2^2}\\\\\\=\dfrac{64-24}{4}\\\\\\=\dfrac{40}{4}\\\\\\=10[/tex]
Answer:
[tex]\dfrac{a}{b^2}+\dfrac{b}{a^2}=10[/tex]
Step-by-step explanation:
Given equation: [tex]x^2-4x+2=0[/tex]
The roots of the given quadratic equation are the values of x when [tex]y=0[/tex].
To find the roots, use the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=-4, \quad c=2[/tex]
[tex]\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}[/tex]
[tex]\textsf{Let }a=2+\sqrt{2}[/tex]
[tex]\textsf{Let }b=2-\sqrt{2}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}[/tex]
7x-5=30
I need this explained for me please
Step-by-step explanation:
7x-5=30
Firstly -5 will cross the equality sign and become +5. so we'll have
7x=30+5=35
7x=35 we'll divide both sides by 7
giving u
7x/7=35/7
=x=5
therefore x=5.
CONFIRMATION
7*5-5=30
PLS MARK ME AS BRAINLIEST
Answer:
x = 5.Step-by-step explanation:
Solve for X:
7x - 5 = 30= 7 * x= 7(5)= 35 - 5= 30x = 5.Hence, answer is x = 5.If f(x) = 2x + 3, what is f(–2)?
Substitute -2 for x
[tex]f( - 2) = 2( - 2) + 3 \\ y = - 4 + 3 \\ y = - 1[/tex]
Hope it helps
Please give brainliest
Answer:
-1
Step-by-step explanation:
Hi student! Let me help you out on this question.
_____________________
To find the value of f(-2), we need to stick in -2 for x.
[tex]\mathsf{f(-2)=2\cdot(-2)+3}[/tex]. Multiply first.
[tex]\mathrm{f(-2)=-4+3}[/tex]. Now simplify completely.
[tex]\mathsf{f(-2)=-1}[/tex]. Which is our final answer.
Hope that this helped you out! have a good day ahead.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
◆◈-Greetings!-◆◈
__________________
Which choice shows 19 + 32 + 11 rewritten correctly using the commutative property and then simplified correctly?
19+43 = 62
19+11+32= 30+32 = 62
11+9+10+32 20+32 = 52
19+11+32 = 30 +43 = 73
The choice shows 19 + 32 + 11 rewritten correctly using the commutative property and then simplified correctly is option B; 19+11+32= 30+32 = 62.
What is the commutative property of addition?The commutative property of addition says that it doesn't matter how we add two numbers, the result of the addition would be same.
For two numbers x and y, we have:
x + y = y + x
WE have given
19 + 32 + 11
The sum would be 62.
We know that by commutative property of addition,
For two numbers x and y,
x + y = y + x
Thus, if we take 3 numbers as a,b and c, then:
c + a + b = c + b + a
Similarly,
19 + 32 + 11 = 19+11+32
= 30+32
= 62
Therefore, the option B is the correct answer.
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6 children were jumping rope.
5 children joined them.
2 children left because the line was too long.
How many children were jumping rope then
Answer:
9 children were jumping then.
Step-by-step explanation:
6+5 equals to 11 - 2 of the children left would equal 9 children left.
I don’t quite understand this problem could someone help me please
Answer:
[tex]\frac{7\sqrt{65}}{65}[/tex]
Step-by-step explanation:
Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.
[tex]cos[/tex] B = [tex]\frac{7}{\sqrt{65}}[/tex] = [tex]\frac{7\sqrt{65}}{65}[/tex]
√324 + 6 √64
what is the answer to this question.
Answer:
66
Step-by-step explanation:
[tex]\sqrt{324} + 6 \sqrt{64}\\\\=\sqrt{18^2} +6 \sqrt{8^2}\\\\=18+6(8)\\\\=18+48\\\\=66[/tex]
Answer:
hmm
Step-by-step explanation:
not enough words to know u steal my points I steal yours kid
answer the problem please
Answer: Point C is (-2, -2), which is the third option.
Step-by-step explanation:
The midpoint formula is [tex]m=(\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex]
All we have to do is plug in the numbers and solve the fractions from there.
[tex]m=(\frac{-10+6}{2},\frac{-6+2}{2} )[/tex]
[tex](\frac{-4}{2},\frac{-4}{2} )[/tex]
[tex]m=(-2, -2)[/tex]
I hope this helps!!
please help i dont know
In function notation, f(x)is used instead of the letter ___ to represent the __________ variable.
In function notation, f(x) is used instead of the letter y to represent the output variable.
How to complete the blanks?A function is represented as:
f(x)
The above means that:
The function of x
As a general rule, the function can be rewritten using the letter y (i.e. the output variable)
Hence, the words that complete the blanks are y and output
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FGH and HGJ form a linear pair. Find the measurement of the anglesif FGH=11x and HGJ+(6x-7)
The angles are 121 and 59 degrees, respectively
How to determine the angles?The given parameters are:
FGH = 11x
HGJ = 6x - 7
Linear pair angles add up to 180.
So, we have:
11x + 6x - 7 = 180
Evaluate the like terms
17x = 187
Divide both sides by 17
x = 11
Substitute x = 11 in FGH = 11x and HGJ = 6x - 7
FGH = 11 * 11=121
HGJ = 6 * 11 - 7 = 59
Hence, the angles are 121 and 59 degrees, respectively
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with full explanation from the internet like before
1/(x-5)+3/(x+2)=4
Solution :
[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
Step-by-step explanation:[tex] \frac{1}{(x - 5)} + \frac{3}{(x - 2)} - 4[/tex]
1. Multiply by LCM[tex]x = 2 + 3( x - 5) = 4 - (x - 5)(x + 2)[/tex]
2. Solve[tex]x = 2 + 3(x - 5) = 4 (x - 5)(x + 2)[/tex][tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]3.Verify SolutionsFind undefined (singularity) points : x=5,x=–2[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{x-5}+\dfrac{3}{x+2}=4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2+3x-15}{(x-5)(x+2)}=4[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x-5)(x+2)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x(x+2)-5(x+2))[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2+2x-5x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2-3x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4x^2-12x-40[/tex]
[tex]\\ \rm\Rrightarrow 4x^2-16x-53=0[/tex]
On solving we get
[tex]\\ \rm\Rrightarrow x=2\pm\dfrac{69}{2}[/tex]
a man is carrying load attached at the end of a stick load placed over his shoulder . show that the pressure at his shoulder is directly proportional to the distance between the shoulder and the load?
According to the above information, it can be stated that the pressure on the man's shoulders is directly proportional to the distance between the shoulder and the load, since the greater the distance he will feel the more weight due to instability.
What is a directly proportional relationship?A directly proportional relationship is a term that refers to the relationship between two variables in which if one of the variables increases, the other also increases.
How is the directly proportional relationship demonstrated in the situation presented?According to the information, it can be inferred that the man will feel more weight on his shoulders if the load is more distant because this causes greater instability on his shoulders, so he will have to make a greater effort to move the load.
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