The graphs of the functions f (x) = 2x+ 7 and g(x) = x2 -1 intersect in t
xy-coordinate plane. What are the points of intersection?

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

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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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:

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.

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]

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:

[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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Answer:

x2

Step-by-step explanation:

x2

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]

The difference quotient of the expression will be 4.

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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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

Answer: it's the second option

Step-by-step explanation:

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.

Answer:

36.7075 Hz is the answer

Answer:

k= -4/3

Step-by-step explanation:

Answer:

x = 5.81

Step-by-step explanation:

3(12x-7) = 4(5x+18)

36x-21 = 20x +72

16x = 93

x = 5.81

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

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

If ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.

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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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

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.

Answer:

point A is the intersection point between XA and AC

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

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

Add eleven

You got 25

Lets solve the equation

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

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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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

Step-by-step explanation:

y = 25 + 15.5x

it's $25 plus the number of nights times $15.5 per night

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]

Answer:

16.15

Step-by-step explanation:

sin(30) = a / c

a = c * sin(30)

a = 32.3 * 0.5

a = 16.15