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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]

[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:

y = 2 [tex](3)^{x}[/tex]

Step-by-step explanation:

The exponential function is of the form

y = a [tex](b)^{x}[/tex]

To find a and b substitute the given points into the equation

Using (0, 2), then

2 = a [tex](b)^{0}[/tex] ⇒ a = 2

Using (1, 6), then

6 = 2 [tex](b)^{1}[/tex] ⇒ b = 3

Equation is y = 2 [tex](3)^{x}[/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:

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%.

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:

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:

The answer is the first table: (0, 0), (10, 50), (51, 255), (400, 2000)

Step-by-step explanation:

Let's check all of the tables:

Table 1:

x = 0, y = 0               ⇒        0 = 5 · 0         ⇒          0 = 0  

x = 10, y = 50           ⇒      50 = 5 · 10        ⇒        50 = 50

x = 51, y = 255         ⇒    255 = 5 · 51        ⇒      255 = 255

x = 400, y = 2000    ⇒ 2000 = 5 · 400     ⇒   2000 = 2000

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 :)

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

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]

By completing the square,

[tex]x^2-16x+89=x^2-16x+64+25=(x-8)^2+25=0[/tex]

[tex](x-8)^2=-25[/tex]

[tex]x-8=\pm\sqrt{-25}[/tex]

[tex]x=8\pm5i[/tex]

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:

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)

Ask: Which two numbers add up to -4 and multiply to -5?

-5 and 1

Rewrite the expression using the above

= (x - 5) and (x + 1)

Answer:

what are the questions about it? cant answer if there are no questions

Step-by-step explanation:

Answer:

its domain isn (-10,∞) and its range is (0,∞)

Step-by-step explanation:

if this is the a.pex question regarding what is true about the function below, here you go

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:

[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.

[tex]\bf \begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{antifreeze}&\stackrel{\textit{gallons of }}{antifreeze}\\ \cline{2-4}&\\ \textit{1st brand}&x&0.65&0.65x\\ \textit{2nd brand}&y&0.90&0.9y\\ \cline{2-4}&\\ mixture&40&0.8&32 \end{array}~\hfill \to \begin{cases} x+y&=40\\ \boxed{x}=40-y\\ \cline{1-2} 0.65x+0.9y&=32 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{substituting in the 2nd equation}}{0.65\left( \boxed{40-y} \right)+0.9y=32}\implies 26-0.65y+0.9y=32 \\\\\\ 26+0.25y=32\implies 0.25y=6\implies y=\cfrac{6}{0.25}\implies \blacktriangleright y=24 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{x=40-y\implies }x=40-24\implies \blacktriangleright x=16 \blacktriangleleft[/tex]

Answer:

it should be used 16 gallons of 65% pue antifreeze and 24 gallons of 80% antifreeze.

Step-by-step explanation:

Let 'x' = amount of 65% antifreeze.

Let 'y' = amount of 90% antifreeze.

We need to obtain 40 gallons of mixture, then:

x + y = 40 gallons [1]

Also we know that the mixture should contain 80% pure antifreeze, then:

0.65x + 0.9y = 0.80(x+y) →  0.15x = 0.1y → y = 1.5x  [2]

Now, subtituting the value of 'y' into [1]:

x + y = 40 gallons → x + 1.5x = 40 gallons → 2.5x = 40 gallons

⇒ x = 16 gallons.

Then: y = 40 - 16 = 24 gallons.

Now, it should be used 16 gallons of 65% pue antifreeze and 24 gallons of 80% antifreeze.

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.

[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]

Answer:

-k (k+1) (k+2)

Step-by-step explanation:

-2k - k³ - 3k² (factor-k out)

-k (2 + k² + 3k) (rearrange to standard quadratic form)

-k (k² + 3k + 2) (factor expression inside parentheses using your favorite method)

-k (k+1) (k+2)

Answer:

Option c.

Step-by-step explanation:

The given expression is

[tex]-2k-k^3-3k^2[/tex]

We need to find the factor form of the given expression.

Taking out HCF.

[tex]-k(2+k^2+3k)[/tex]

Arrange the terms according to there degree.

[tex]-k(k^2+3k+2)[/tex]

Splitting the middle terms we get

[tex]-k(k^2+2k+k+2)[/tex]

[tex]-k((k^2+2k)+(k+2))[/tex]

[tex]-k(k(k+2)+(k+2))[/tex]

[tex]-k(k+1)(k+2)[/tex]

The factor form of given expression is -k(k+1)(k+2). Therefore, the correct option is c.

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

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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

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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:

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:

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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.

Answer:

translating it

Step-by-step explanation:

Shifting a function, in mathematics and economics, refers to the process through which the entire graph or model of a function is moved either up, down, left or right. A phase shift, commonly noted by φ, is an example of this, seen when aligning a cosine or sine function with initial conditions of data. In economics, factors like income, household preferences and taxes cause shifts in the consumption function.

When you shift a function in mathematics, you are essentially moving the entire graph of the function either up, down, left, or right. This is done by altering the function equation. For instance, the position of a block on a spring, modeled by a periodic function like a cosine function, can be shifted to the right. This rightward shift is termed a phase shift, typically denoted by the Greek letter phi (φ). The equation for the position as a function of time for the block becomes x(t) = Acos(wt + φ), where φ reflects the phase shift.

A shift in a function can also occur under economic contexts. Factors besides income can trigger the entire consumption function to shift, either parallelly up or down or make the slope of the consumption function steeper or flatter.

Shifting of functions is a crucial concept, whether we're handling a cosine or sine function to align the function with data's initial conditions or in economical situations where changes in income, taxes, or household preferences could cause significant shifts in the consumption function.

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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]