Which is equivalent to 5√1,215^x

Answer:

20

Step-by-step explanation:

use the Pythagorum  therum (a^2+b^2=c^2

so you get 12^2+16^2=C^2

so that Equtes to 144+256=C^2

400=c^2

so square 400 and you get 20

For this case we have that by definition, the Pythagorean theorem states that:

[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]

Where:

c: It is the hypotenuse of the triangle

a, b: Are the legs

According to the figure, the hypotenuse is represented by BC, then:

[tex]BC = \sqrt {12 ^ 2 + 16 ^ 2}\\BC = \sqrt {144 + 256}\\BC = \sqrt {400}\\BC = 20[/tex]

Thus, the hypotenuse of the triangle is 20

ANswer:

Option D

Answer:

A it's is located halfway between the parabolas focus and directrix

Step-by-step explanation:

hope this helps

Answer:

Option A is correct that is it's is located halfway between the parabolas focus and directrix.

Step-by-step explanation:

We are given a parabola.

To find: Best statement which describes the location of the vertex on the parabola.

Standard Equation of Parabola which open on the Right hand direction.

( y - k )² = 4a( x - h )

Here, ( h , k ) is the vertex of the parabola and ( h + a , k ) is the focus.

Distance of the focus from vertex = a

Equation of the Directrix of the Parabola is , y =  k - a

Distance of the Directrix from vertex = a

Therefore, Option A is correct that is it's is located halfway between the parabolas focus and directrix.

Answer:

So, the simplified version is

[tex]-5\sqrt{7}+7\sqrt{6}[/tex]

In words it can be written as minus 5 square root of 7 end root plus 7 square root of 6 end root

Step-by-step explanation:

[tex]5\sqrt{7}+12\sqrt{6}-10\sqrt{7}-5\sqrt{6}[/tex]

We need to simplify the above expression.

Combining the like terms of the above expression.

Like terms are those that have same variables.

[tex]=(5\sqrt{7}-10\sqrt{7})+(12\sqrt{6}-5\sqrt{6})[/tex]

[tex]=((5-10)(\sqrt{7})+((12-5)(\sqrt{6}))[/tex]

[tex]=((-5)(\sqrt{7})+((7)(\sqrt{6}))[/tex]

So, the simplified version is

[tex]-5\sqrt{7}+7\sqrt{6}[/tex]

In words it can be written as minus 5 square root of 7 end root plus 7 square root of 6

Answer:

False

Step-by-step explanation:

We first write the equation in the form ax² + bx + c=0 which gives us:

3x² - 6x + 9=0

Given the quadratic formula,

x= [-b ±√(b²- 4ac)]/2a ,the discriminant proves whether the equation has real roots or not.

The discriminant, which is the value under the root sign, may either be positive, negative or zero.

Positive discriminant- the equation has two real roots

Negative discriminant- the equation has no real roots

Zero discriminant - The equation has two repeated roots.

In the provided equation, b²-4ac results into:

(-6)²- (4×3×9)

=36-108

= -72

The result is negative therefore the equation has no real solutions.

Answer: FALSE

Step-by-step explanation:

Rewrite the given equation in the form [tex]ax^2+bx+c=0[/tex], then:

[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]

Now, we need to calculate the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

We can identify that:

[tex]a=3\\b=-6\\c=9[/tex]

Then, we only need to substitute these values into the formula:

 [tex]D=(-6)^2-4(3)(9)[/tex]

 [tex]D=-72[/tex]

Since [tex]D<0[/tex] the equation has no real solutions.

E(-3, -4), F(1, -3), G(3, -6), and H(1, -6); a reflection across the x-axis

E(-3, -1), F(1, -2), G(3, 1), and H(1, 1); a translation 5 units down

E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6); a reflection across the y-axis

E(4, 4), F(8, 3), G(10, 6), and H(8, 6);a translation 7 units right

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Hence:

E(-3, -4), F(1, -3), G(3, -6), and H(1, -6); a reflection across the x-axis

E(-3, -1), F(1, -2), G(3, 1), and H(1, 1); a translation 5 units down

E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6); a reflection across the y-axis

E(4, 4), F(8, 3), G(10, 6), and H(8, 6);a translation 7 units right

Find out more on transformation at: https://brainly.com/question/4289712

Answer:

D=15 so N=10

Step-by-step explanation:

N+D=25 where the coins make up the number of nickels, N and the number of dimes, N

Now each nickel is worth .05   (not .5)

Each time is worth .10  or .1

So the two equations are .05N+.1D=2  and N+D=25

I'm going to multiply 100 on both sides so I can clear the decimals from first equation giving me 5N+10D=200.

So I'm going to multiply the second by 5 giving my 5N+5D=125

Line up equations and you should see we can solve this system by elmination by subtracting the equations

5N+10D=200

5N+5D=125

------------------

       5D=75

         D=75/5=15

So N+D=25 and D=15 so N=10.

Final answer:

The line of symmetry of a parabola is a vertical line that passes through its vertex, dividing the parabola into two equal halves. This line of symmetry can be determined mathematically for a parabolic equation by the formula x = -b/(2a). Symmetry plays an important role in the behavior of optical devices such as spherical and parabolic mirrors.

Explanation:

The line of symmetry of a parabola is a vertical line that passes through its vertex, and it divides the parabola into two mirror-image halves. This line is also known as the axis of symmetry. For a parabola described by the equation y = ax² + bx + c, the axis of symmetry can be found using the formula x = -b/(2a), where a, b, and c are coefficients in the quadratic equation, representing the parabola's concavity, slope at the vertex, and the y-intercept, respectively.

In the context of optical devices like mirrors and lenses, the concept of symmetry is crucial. For instance, a spherical mirror reflects rays in a way that demonstrates symmetry with respect to its optical axis. When a parabolic mirror is used, all parallel rays of light are reflected through its focal point, illustrating how symmetry is a fundamental principle in both nature and physics.

Just like in nature, where symmetrical patterns can be seen in butterfly wings and other complex systems, symmetry in mathematical terms is significant and pervasive, revealing fundamental properties of the objects and phenomena in question.

Answer:

yes it can

Step-by-step explanation:

1/2x-5=1/3x+6

Answer: third option.

Step-by-step explanation:

[tex]\frac{1}{2}x-5=\frac{1}{3}x+6[/tex] can be rewritten into two separate equationts:

[tex]\left \{ {{ y=\frac{1}{2}x-5} \atop {y=\frac{1}{3}x+6}} \right.\\\\[/tex]

You can observe that this linear equations are written in Slope-Intercept form:

[tex]y=mx+b[/tex]

  But the equations shown in options provided are written in Standard form:

[tex]Ax+By=C[/tex]

Therefore, you need to move the x term to the left side of the equation (In each equation):

- For the first equation:

[tex]y-\frac{1}{2}x=-5[/tex]

Simplifying:

[tex]\frac{2y-x}{2}=-5\\\\2y-x=-10[/tex]

 - For the second equation:

[tex]y-\frac{1}{3}x=6[/tex]

Simplifying:

[tex]\frac{3y-x}{3}=6\\\\3y-x=18[/tex]

Then the system of equations is:

[tex]\left \{ {{2y-x=-10} \atop {3y-x=18}} \right.[/tex]

Answer:

The answer is the third option- (24n,when n=4.8 the value is 5)

I would recommended reading over the lesson again and maybe watching some videos to help you to grasp the material.

hope this helps!

Answer:

Its 30%

Step-by-step explanation:

I used guess and check.

(25%)

3100*.25 = 775

(30%)

3100*.3 = 930

Answer:

30%.

Step-by-step explanation:

It is the fraction 930/3100 multiplied by 100.

Percentage that is rent = (930 * 100 ) / 3100

=  30%.

Answer:

the answer is 12

Step-by-step explanation:

Answer:

Second option

[tex]x =9[/tex]

Step-by-step explanation:

To solve this problem we use the secant theorem.

If two secant lines intersect with a circumference, the product between the segment external to the circumference and the total segment in one of the secant lines is equal to the product of the corresponding segments in the other secant line.

This means that

[tex](5+4)*4 = (x+3)*3[/tex]

Now we solve the equation for the variable x

[tex](9)*4 = (x+3)*3[/tex]

[tex]36 = 3x + 9[/tex]

[tex]36-9 = 3x[/tex]

[tex]3x =27[/tex]

[tex]x =9[/tex]

Answer:

16302.9432 ft

Step-by-step explanation:

P = 2L + 2W

Where P is the perimeter, L is the length and W is the width

P = 2(1080√30) + 2(500√20) = 16302.9432 ft

Answer:

D

Step-by-step explanation:

took the test :)

Answer:

A. g(x) = 6|x| +10

Step-by-step explanation:

The parent function is given as:

f(x) = 3|x| + 5

Applying transformation:

function f is vertically stretched by a factor of 2 to give function g.

To stretch a function vertically we multiply the function by the factor:

2*f(x) = 2[3|x| + 5]

g(x) = 2*3|x| + 2*5

g(x) = 5|x| + 10

Answer: Option A.

Step-by-step explanation:

There are some transformations for a function f(x).

One of the transformations is:

If [tex]kf(x)[/tex] and [tex]k>1[/tex], then the function is stretched vertically by a factor of "k".

Therefore, if the function provided [tex]f(x) = 3|x| + 5[/tex] is vertically stretched by a factor or 2, then the transformation is the following:

[tex]2f(x)=g(x)=2(3|x| + 5)[/tex]

Applying Disitributive property to simplify, we get that the function g(x) is:

[tex]g(x)=6|x| +10[/tex]

Answer:

[tex]351 \pi[/tex] (about 1102.69902)

Step-by-step explanation:

The volume of a cone is represented by the formula [tex]V=\pi r^2 \frac{h}{3}[/tex], where [tex]V[/tex] is the volume, [tex]r[/tex] is the radius, and [tex]h[/tex] is the height.

This is as simple as the solution can get without estimating, but we can estimate with a calculator.  [tex]351 \pi[/tex] is approximately equal to 1102.69902.

Answer is provided in the image attached.

Answer:

for this question the correct answer is x= 10

Step-by-step explanation:

The true value of the equation In 20+ In 5 = 2 In x is x=10.

It is a function which is denoted through log or ln.

We have been given a log equation

log20+log5=2logx              (log m +log n =log(mn))

log(20*5)=2logx

log(100)=2logx

log[tex](10)^{2}[/tex]=2logx                (log[tex]m^{n}[/tex]=nlogm)

2 log 10=2 log x

x=10

Hence the required answer is x=10

Learn more about logarithmic functions at https://brainly.com/question/13473114

#SPJ2

Answer:

15x+25y=975

x+y=55

Rearrange equation two so x is by itself.

x=-y+55

Plug the rearranged equation two into equation one.

15(-y+55)+25y=975

Evaluate the 'new' equation 1.

-15y+825+25y=975

10y+825=975

10y=150

y=15

Choose an equation to evaluate with y to get x. (i chose equation 2 because it was easier)

x+15=55

Evaluate the equation

x=55-15

x=40

So now we have x=40 and y=15

Evaluate those two terms with both equations to check the correctness.

15(40)+25(15)=975

600+375=975

975=975 (correct)

40+15=55

55=55 (correct)

Both equations are correct so the values of x and y are true.

Please mark as brainliest. :)

Answer:

[tex]\large\boxed{x^2+11x+24=0\Rightarrow(x+5.5)^2=6.25}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\x^2+11x+24=0\qquad\text{subtract 24 from both sides}\\\\x^2+(2)(x)(5.5)=-24\qquad\text{add}\ 5.5^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(5.5)+5.5^2}_{(*)}=-24+5.5^2\\\\(x+5.5)^2=-24+30.25\\\\(x+5.5)^2=6.25\Rightarrow x+5.5=\pm\sqrt{6.25}\\\\x+5.5=-2.5\ \vee\ x+5.5=2.5\qquad\text{subtract 5.5 from both sides}\\\\x=-8\ \vee\ x=-3[/tex]

To rewrite x^2 + 11x + 24 = 0 by completing the square, we first organize terms, then add the square of half the coefficient of x to both sides to create a perfect square. Taking the square root of both sides then provides the solution for x, resulting in x = -5.5 ± √6.25.

To rewrite the equation x^2 + 11x + 24 = 0 by completing the square, we first need to make the quadratic and linear terms to create a square.

1. Rewrite the equation as: x^2 + 11x + __ = -24 + __

2. Take half of the coefficient of x, (11/2) and square it. (11/2)^2 = 30.25

3. Add this value on both sides of the equation:

x^2 + 11x + 30.25 = -24 + 30.25

4. Now, the left side of the equation is a perfect square and it can be written as:

(x + 5.5)^2 = 6.25

5. Finally, to solve for x, take the square root of both sides to get:

x + 5.5 = ± √6.25

x = -5.5 ± √6.25

https://brainly.com/question/36246034

#SPJ2

Answer:

Rotation 90 degree counterclockwise then 2 units up.

Step-by-step explanation:

Given : Quadrilateral ABCD and A'B'C'D'.

To find: What transformation were applied to ABCD to obtain A’B’C’D.

Solution: We have given

A (3,6) →→ A'(-6,5)

B( 3,9)→→ B'(-9 ,5)

C(7,9)→→C'(-9 ,9)

D(7,6)→→D'(-6,9)

By the 90 degree rotational rule :   (x ,y) →→(-y ,x) and unit 2 unit up

A (3,6) →→ A'(-6,3) →→ A'(-6,3+2)

B( 3,9)→→ B'(-9 ,3)→→ B'(-9 ,3+2)

C(7,9)→→C'(-9 ,7) →→C'(-9 ,7+2)

D(7,6)→→D'(-6,7)→→D'(-6,7+2)

Therefore, Rotation 90 degree counterclockwise then 2 units up.

The transformation applied is Rotation 90 degree counterclockwise then 2 units up.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

The transformation which was applied to ABCD to obtain A’B’C’D be found by finding the change in the coordinates of the quadrilateral. Therefore,

As it is observed that the change in the coordinate is 90 degrees counterclockwise then 2 units up. Therefore, the transform of the coordinates can be done as (x ,y)⇒(-y ,x)⇒(-y, x+2).

Since the condition holds true, it can be concluded that the transformation applied is Rotation 90 degree counterclockwise then 2 units up.

Learn more about Coordinates:

https://brainly.com/question/23450276

#SPJ5

well, lateral area means only the area of the sides, namely just the four triangular faces.

[tex]\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}~~ \begin{cases} s=sides\\ \cline{1-1} s=8 \end{cases}\implies A=\cfrac{8^2\sqrt{3}}{4}\implies A=16\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the 4 triangles}}{4(16\sqrt{3})}\implies 64\sqrt{3}[/tex]

Answer:

neither

Step-by-step explanation:

y would 1 but there is no x

Answer:(-1,-5)

Step-by-step explanation:

Because that's how math works. Its also what Khan Academy says soooo...

Answer:

[tex]2y=8[/tex]

Step-by-step explanation:

The given equations are:

[tex]4x+3y=17[/tex]

and

[tex]4x+y=9[/tex]

We subtract the second equation from the first equation to get:

[tex]4x-4x+3y-y=17-9[/tex]

This simplifies to:

[tex]2y=8[/tex]

When we subtract the second equation from the first one, we get:

[tex]2y=8[/tex]

The correct option is Absolute value parent function. The absolute value parent function is a piecewise function because it is defined by different expressions depending on whether the input is positive or negative. In contrast, linear, quadratic, and exponential functions are defined by a single expression over their entire domains and are not piecewise.

The absolute value parent function is an example of a piecewise function. A piecewise function is a function that is defined by multiple sub-functions, each applied to a certain interval of the domain.

On the contrary, linear, quadratic, and exponential parent functions have a single expression defining them throughout their domain.

Linear functions, such as y = ax + b, have a constant rate of change and are not piecewise. Quadratic functions, like y = ax^2 + bx + c, create parabolas and are also defined by a single expression over their entire domain. Exponential functions, such as y = b^x, grow by a consistent percentage rate and are continuous and not piecewise.

[tex]\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=400\pi \end{cases}\implies 400\pi =4\pi r^2 \implies \cfrac{\stackrel{100}{~~\begin{matrix} 400\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} }{~~\begin{matrix} 4\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=r^2 \\\\\\ 100=r^2\implies \sqrt{100}=r\implies 10=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \implies V=\cfrac{4\pi (10)^3}{3}\implies V=\cfrac{4000\pi }{3}\implies V\approx 4188.79[/tex]

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-4}{-6-6}\implies \cfrac{0}{-12}\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=0(x-6)\implies y-4=0\implies y=4[/tex]

Answer: [tex]y-4=0[/tex]

Step-by-step explanation:

The equation of line passing through two points (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

The standard form of equation of a line is given by :-

[tex]Ax+By+C=0[/tex], where A , B , and C are integers.

Then , the equation of line passing through two points  K(6,4) and L(-6,4) is given by :-

[tex](y-4)=\dfrac{4-4}{-6-6}(x-6)\\\\\Rightarrow\ y-4=(0)(x-6)\\\\\Rightarrow\ y-4=0[/tex]

Answer:

The product is -55x³ - 24x² + 22x - 3

Step-by-step explanation:

* Lets revise how to find the product of trinomial and binomial

- If (ax² ± bx ± c) and (dx ± e) are two binomials, where a , b , c , d , e

  are constant, their product is:

# Multiply (ax²) by (dx) ⇒ 1st term in the trinomial and 1st term in the

  binomial

# Multiply (ax²) by (e) ⇒ 1st term in the trinomial and 2nd term in

  the binomial

# Multiply (bx) by (dx) ⇒ 2nd term the trinomial and 1st term in

  the binomial

# Multiply (bx) by (e) ⇒ 2nd term in the trinomial and 2nd term in

  the binomial

# Multiply (c) by (dx) ⇒ 3rd term in the trinomial and 1st term in

  the binomial

# Multiply (c) by (e) ⇒ 3rd term the trinomial and 2nd term in

  the binomial

# (ax² ± bx ± c)(dx ± e) = adx³ ± aex² ± bdx² ± bex ± cdx ± ce

- Add the terms aex² and bdx² because they are like terms

- Add the terms bex and cdx because they are like terms

* Now lets solve the problem

- There are a trinomial and a binomials (11x² + 7x - 3) and (-5x + 1)

- We can find their product by the way above

∵ (11x²)(-5x) = -55x³ ⇒ 1st term in the trinomial and 1st term in the binomial

∵ (11x²)(1) = 11x² ⇒ 1st term in the trinomial and 2nd term in the binomial

∵ (7x)(-5x) = -35x² ⇒ 2nd term the trinomial and 1st term in the binomial

∵ (7x)(1) = 7x ⇒ 2nd term in the trinomial and 2nd term in the binomial

∵ (-3)(-5x) = 15x ⇒ 3rd term in the trinomial and 1st term in the binomial

∵ (-3)(1) = -3 ⇒ 3rd term the trinomial and 2nd term in the binomial

∴ (11x² + 7x - 3)(-5x + 1) = -55x³ + 11x² - 35x² + 7x + 15x - 3

- Add the like terms ⇒ 11x² - 35x² = -24x²

- Add the like terms ⇒ 7x + 15x = 22x

∴ The product is -55x³ - 24x² + 22x - 3

Answer:

[tex]a=\frac{2S -2v_ot-2s_o}{t^2}[/tex]

Step-by-step explanation:

We have the equation of the position of the object

[tex]S = \frac{1}{2}at ^2 + v_ot+s_o[/tex]

We need to solve the equation for the variable a

[tex]S = \frac{1}{2}at ^2 + v_ot+s_o[/tex]

Subtract [tex]s_0[/tex] and [tex]v_0t[/tex] on both sides of the equality

[tex]S -v_ot-s_o = \frac{1}{2}at ^2 + v_ot+s_o - v_ot- s_o[/tex]

[tex]S -v_ot-s_o = \frac{1}{2}at ^2[/tex]

multiply by 2 on both sides of equality

[tex]2S -2v_ot-2s_o = 2*\frac{1}{2}at ^2[/tex]

[tex]2S -2v_ot-2s_o =at ^2[/tex]

Divide between [tex]t ^ 2[/tex] on both sides of the equation

[tex]\frac{2S -2v_ot-2s_o}{t^2} =a\frac{t^2}{t^2}[/tex]

Finally

[tex]a=\frac{2S -2v_ot-2s_o}{t^2}[/tex]

Answer:

47.91 units²

Step-by-step explanation:

This can be solved using Heron's triangle (see attached)

in this case, your lengths are

a = 3+9=12

b=3+5=8

c=5+9=14

Hence,.

S = (1/2) x (a + b + c) = (1/2) (12+8+14) = 17

(s - a) = 17 -12 = 5

(s - b) = 9

(s - c) = 3

Area = √ [  s (s-a) (s-b) (s-c) ]

= √ [  17 x 5 x 9 x 3 ] = √2295 = 47.9061 = 47.91 units² (rounded to nearest hundreth)

The pattern is plus 7

6 + 7 = 13

13 + 7 = 20

20 + 7 = 27

This means to find the next term you must add 7 to 27

27 + 7 = 34

To find the term after 34 add seven to that as well

34 + 7 = 41

so...

6, 13, 20, 27, 34, 41

Hope this helped!

~Just a girl in love with Shawn Mendes