Consider the function given below. f(x)=x Plot the x- and y- intercepts of the function.
Find the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8). ( x - 1) 2 + ( y - 4) 2 = 25 ( x - 4) 2 + ( y - 1) 2 = 25 ( x - 1) 2 + ( y - 4) 2 = 5
Answer:
(x-1)^4 + (y-4)^2 = 25
Step-by-step explanation:
Center at 1,4 means the circle is of the form:
(x-1)^4 + (y-4)^2 = r^2
Find r^2 using distance formula from center to the given point
r ^2 = ( 8-4)^2 + (4-1)^2
r^2 = 16 +9 = 25
so you answer is (x-4)^4 + (y-8)^2 = 25
what is the factor expression of x2 + 7x + 10
Answer:
[tex](x+5)(x+2)[/tex]
Step-by-step explanation:
[tex]\textbf{Given that,}\\\\~~~~x^2 +7x +10\\\\=x^2 +5x +2x +10~~~~~~~~~~~~~~~~~~~~;\textbf{Rewrite}~ 7x ~ \textbf{as}~ 5x +2x\\\\=x(x+5) +2(x+5)\\\\=(x+5)(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Take out the common factor}~ x+5[/tex]
Angle AMO is 50 degrees. If ray MB bisects angle AMO, what would be the measure of angle AMB?
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
A. F(x) = 3(x+4)2 +4
B. F(x)=3(x-4)2 - 4
C. F(x)=-3(x+4)² +4
D. F(x) = -3(x-4)² +4
The equation of the function is F(x) = -3(x-4)² +4 , the correct answer is Option D
The missing graph is attached with the answer
What is a function ?A function is a law that relate the independent variable and the dependent variable.
It is given that
The graph of F(x), shown below, resembles the graph of G(x)= x², but it has been changed
From the graph, it is seen that,
G(x) when shifted by -4 on the negative x axis.
and graph shifted by +4 on the positive y axis.
F(x) is scaled by a factor of -⅓ of G(x)
it is reflected across the x-axis.
So the equation of the function is
F(x) = -3(x-4)² +4
Therefore , the correct answer is Option D.
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Question 7 of 25
If f(x)=6x²,-4 and g(x)=2x+2, find (f- g)(x).
OA. 2x-5x2-2
OB. 6x²-2x-6
OC. 4x²-6
O D. 6x²2-2x-2
Answer:
x2
Step-by-step explanation:
x2
R is the midpoint of QS. If QR = 7x and QS = 15x − 7, what is QR?
Answer: 49
Step-by-step explanation:
If R is the midpoint of QS, QS=2(QR)=2(RS).
[tex]15x-7=2(7x)\\15x-7=14x\\-7=-x\\\\x=7\\\\QR=7(7)=\boxed{49}[/tex]
Which expression is equivalent to 3√64ab²c³?
2abc²[√4a²b³c]
4a²b²c³ (3√5)
8a³b³c¹ (3√/bc)
8a²b²c³(3√/b)
Answer:
[tex]4a^2b^2c^3\left(\sqrt[3]{b}\right)[/tex]
Step-by-step explanation:
**Please note that the expression quoted in the question is likely incorrect (see attachment)**
Assuming the expression is:
[tex]\sqrt[3]{64a^6b^7c^9}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}{ \cdot \sqrt{b}[/tex]
[tex]\implies \sqrt[3]{64} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^7}\cdot \sqrt[3]{c^9}[/tex]
Rewrite 64 as 4³:
[tex]\implies \sqrt[3]{4^3} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^7}\cdot \sqrt[3]{c^9}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \sf to\:\:b^7[/tex]
[tex]\implies b^7=b^{6+1}=b^6b^1=b^6b[/tex]
Therefore:
[tex]\implies \sqrt[3]{4^3} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^{6}b}\cdot \sqrt[3]{c^9}[/tex]
[tex]\implies \sqrt[3]{4^3} \cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^{6}}\cdot \sqrt[3]{b}\cdot \sqrt[3]{c^9}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
[tex]\implies 4^{\frac{3}{3}} \cdot a^{\frac{6}{3}} \cdot b^{\frac{6}{3}} \cdot \sqrt[3]{b} \cdot c^{\frac{9}{3}}[/tex]
Simplify:
[tex]\implies 4^1 \cdot a^2 \cdot b^2 \cdot \sqrt[3]{b} \cdot c^3[/tex]
[tex]\implies 4a^2b^2c^3\left(\sqrt[3]{b}\right)[/tex]
The expression is seemed to have none of the above solutions
Find the difference quotient f(x)−(3)−3 when ()=1+4−5^2. Simplify the expression fully as if you were going to compute the limit as →3. In particular, cancel common factors of −3 in the numerator and denominator if possible. (Use symbolic notation and fractions where needed.)
The difference quotient of the expression will be 4.
How to find the quotient?f(x) = 5 + 5x + 4x²
f(3) = 5 + 5(3) + 4(3)³
= 56
Now [f(x) - f(3)]/(x - 3) will be:
= (4x² + 5x + 5 - 56)/(x - 3)
= (4x² + 5x - 51)/(x - 3)
= (4x² + 17x - 12x - 5)/(x - 3)
= (4x + 17)(x - 3)/(x - 3)
= 4x + 17
The difference quotient will be:
g(x + h) = 4(x + h) + 17
= [g(x + h) - g(x)]/h
= (4x + 4h + 17 - 4x - 17)/h
= 4h/h
= 4
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help honestly MARKING BRAINLIESt
Answer:
See below ~
Step-by-step explanation:
a) Forming the equation :
⇒ We start with a number, x
⇒ Now we double it so : 2(x) = 2x
⇒ Then we add 11 to it : 2x + (11) = 2x + 11
⇒ It is equal to 25 : 2x + 11 = 25
b) Solving the equation :
Subtract 11 from both sides :
⇒ 2x + 11 - 11 = 25 - 11
⇒ 2x = 14
Divide 2 on both sides :
⇒ 2x/2 = 14/2
⇒ x = 7
Let unknown number be x
Double it
2xAdd eleven
2x+11You got 25
2x+11=25Lets solve the equation
2x=25-112x=14x=7Josh and Bella picked apples from a tree. Josh had 3 less than 2/3 of Bellas apples. If Josh had 7 apples, how many apples did Bella have?
Answer:
Bella had 15 apples
Step-by-step explanation:
First, you see that Josh has 3 less than 2/3 of Bellas apples. If Josh has 7 apples you would add 3 to 7 which = 10. Assuming that 10 = 2/3 of Bellas apples, then you would subtract half of 10 and get 5. 1/3 = 5 apples. Lastly, you should do 5 * 3 which = 15. Bella had 15 apples.
Determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g.
Answer:
Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit
Step-by-step explanation:
Parent function: [tex]f(x)=x[/tex]
The graph of the parent function is a straight line graph that intersects the axes at the origin (0, 0) and has a positive slope of 1 unit.
To determine the sequence of transformations, find the equation of the transformed function in slope--intercept form.
Slope-intercept form of a linear function: [tex]f(x)=mx+b[/tex]
(where m is the slope and b is the y-intercept)
To calculate the slope of the transformed function, choose two points on the line and use the slope formula:
Let (x₁, y₁) = (0, -1)Let (x₂, y₂) = (1, -4)[tex]\implies \sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-(-1)}{1-0}=-3[/tex]
The y-intercept (where the line crosses the y-axis) of the transformed function is (0, -1).
Therefore the equation of the transformed function is:
[tex]g(x)=-3x-1[/tex]
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Comparing the transformed function's equation with the parent function:
[tex]\begin{cases}f(x)=x\\g(x)=-3x-1\end{cases}[/tex]
Transformations
1. Reflection in the y-axis:
[tex]f(-x)=-x[/tex]
2. Vertically stretched by a factor of 3:
[tex]3f(-x)=-3x[/tex]
3. Shifted 1 unit down:
[tex]3f(-x)-1=-3x-1[/tex]
Summary
Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit
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Which graph represents the function h(x) = |x| + 0.5?
On a coordinate plane, an absolute value graph has a vertex at (0, 1.5).
On a coordinate plane, an absolute value graph has a vertex at (negative 0.5, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, 0.5).
On a coordinate plane, an absolute value graph has a vertex at (negative 1.5, 0).
Answer:
On a coordinate plane, an absolute value graph has a vertex at (0, 0.5).
Step-by-step explanation:
properties of the given function
domain=X€Rrange=[1/2,+♾️)minimum (0,1/2)Answer: it's the second option
Step-by-step explanation:
(9x + 1) − (−7x² + 4x + 10)
Answer:
7x² + 5x - 9
Step-by-step explanation:
(9x + 1) - (- 7x² + 4x + 10) ← distribute parenthesis by - 1
= 9x + 1 + 7x² - 4x - 10 ← collect like terms
= 7x² + 5x - 9
What is the answer?????
Answer:
36.7075 Hz is the answer
A foam cylinder, with a diameter of 3 inches in height of 8 inches, is carved into the shape of a cone. What is the maximum volume of a cone that can be carved? Round your answer to the nearest hundredths place. One point
Answer:
volume of cone = 1/3 volume of cylinder
according to the question, volume of cylinder =
V =
[tex]\pi \times (r) {}^{2} h[/tex]
diameter = 3 inches
radius = 3/2 inches
height = 8 inches
V = 22.7 * (3/2)²* 8
V = 22.7 * 9/4 * 8
V = 22.7 * 18
maximum volume a cone can have = 1/3 of cylinder
Volume of cone = 1/3 * 22.7 * 18
= 22.7 * 6
= 132.6
Need help urgently please
In 20 years charlie will be three times as old as he is now.how old is charlie is he now
Answer:
10 years old
Step-by-step explanation:
let his age be x , then in 20 years
x + 20 = 3x ( subtract x from both sides )
20 = 2x ( divide both sides by 2 )
10 = x
Charlie is 10 years old
what is the value of k such that x-2y=5 and 4x+ky=3 are perpendicular?
Answer:
k= -4/3
Step-by-step explanation:
Question 10(Multiple Choice Worth 1 points)
(04.02 LC)
Solve the system of equations using substitution.
y = -2x + 1
4x + 2y = -3
Answer:
no solutions
Step-by-step explanation:
[tex]4x + 2(-2x+1) = -3\\4x-4x+2 = -3\\2 = -3\\[/tex]
this means there are no solutions.
what are the pair of intergers whose product is -12
Answer:
The answer is -4×3 or -3×4 or -6×2 or -2×6 or -1×12 or -12×1
Step-by-step explanation:
___________is a relation in which each element of the domain is paired with exactly one element of the range.
Answer:
A function
Step-by-step explanation:
A function is a relation in which each element of the domain is paired with exactly one element of the range.
What is the intersection of line CA a and line XA?
Answer:
point A is the intersection point between XA and AC
What can be concluded if ÐABC and ÐCBD are a linear pair? Select all statements that you think are correct.
If ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.
What is Linear pair of angles?Linear pair of angles are angles formed when two lines intersect each other at a single point.
Now, the angles are also said to be linear if they are adjacent to each other after the intersection of the two lines and the sum of the linear pair of angles is always equal to 180°.
Looking at the definition above we can say that if ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.
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anwer this question with full method please
Step-by-step explanation:
Let simplify the identity
[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]
[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]
Combine Like Fractions
[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]
Multiply by reciprocals.
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]
Pythagorean Identity
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]
Double Angle Identity
[tex] \frac{ \cos(2x) }{1} [/tex]
[tex] \cos(2x) [/tex]
Now, we need to find cos 2x. Given that we have tan x.
Note that
[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]
So let find cos x and tan x.
We know that
[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]
We know that
[tex] \tan(x) = \frac{o}{a} [/tex]
[tex] \sin(x) = \frac{o}{h} [/tex]
[tex] \cos(x) = \frac{a}{h} [/tex]
So naturally,
[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]
So we need to find the hypotenuse,
remember Pythagorean theorem.
[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]
Here o is 1
h is root of 5.
So
[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]
[tex] {h}^{2} = 1 + 5[/tex]
[tex] {h}^{2} = 6[/tex]
[tex]h = \sqrt{6} [/tex]
Now, we know h, let plug in to find sin x and cos x.
[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]
[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]
Let's find these values squared
[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]
[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]
Finally, use the trig identity
[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]
So part I.= 2/3
ii. Use the definition of sine and cosine and Pythagorean theorem
Let sin x= o/h
Let cos x= a/h.
So
sin x squared is
[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]
[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]
By definition,
[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]
[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]
Remember that
[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]
So
[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]
[tex]1 = 1[/tex]
If f(x) = 2x² + 3x and g(x)= x - 2, what is (f+ g)(2)?
Answer:
14.
Step-by-step explanation:
If f(x) = 2x2 + 3x and g(x) = x - 2, (f + g)(2) is 14.
Answer:
14
Step-by-step explanation:
f(x) = 2x² + 3x
f(2) = 2 * 2^2 + 3(2) = 2*4 + 6 = 8+6 = 14
g(x)= x - 2
g(2) = 2-2 = 0
(f+ g)(2) = 14+0 = 14
When Manny goes on vacation, he boards his dog at a kennel. The kennel charges a flat fee
of $25, plus $15.50 per night.
Write an equation that shows how the cost of a kennel stay, y, depends on the number of
nights, x.
Step-by-step explanation:
y = 25 + 15.5x
it's $25 plus the number of nights times $15.5 per night
Solve for x (12x-7)/4=(5x+18)/3
Answer:
x = 5.81
Step-by-step explanation:
3(12x-7) = 4(5x+18)
36x-21 = 20x +72
16x = 93
x = 5.81
If side c measures 32.3 units long, how long is side a?
Answer:
16.15
Step-by-step explanation:
sin(30) = a / c
a = c * sin(30)
a = 32.3 * 0.5
a = 16.15
Need help simple explanation if possible
Answer: 21 sqrt(43)/43
Step-by-step explanation: The tangent identity states that tanx = sinx/cosx. Thus, we get 21/22 / sqrt(43)/22. We can simplify this to 21 sqrt(43)/43
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