Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and s is the distance (in meters). Find v when u is 6 m/s, a is 3 m/s², and s is 29 meters. A. 210−−−√ m/s B. 15 m/s

Answer:

$587.13

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

where:

Given:

To calculate i, divide the interest rate per annum by 12 and convert to decimal form:

[tex]\implies \sf i=\dfrac{6\%}{12}=\dfrac{0.06}{12}=0.005[/tex]

Substitute the given values into the formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{25000 \cdot 0.005(1+0.005)^{48}}{(1+0.005)^{48}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{125(1.005)^{48}}{(1.005)^{48}-1}[/tex]

[tex]\implies \sf PMT=587.1257262...[/tex]

Therefore, the monthly repayment required to pay this loan off in 48 equal installments is $587.13 (nearest cent).

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The correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

Here, we have to rewrite the expression x² + x - 72 in the form (x + a)(x + b), we need to find two numbers a and b such that when multiplied,

it give us the constant term -72 and when added, it give us the coefficient of the x term, which is 1.

The expression x² + x - 72 can be factored as follows:

x² + x - 72

= x² + 9x - 8x - 72

=x(x+9) -8(x+9)

= (x + 9)(x - 8)

Therefore, the correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

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A picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The complete question is;

"Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .

Use the polygon tool to graph the dilated figure."

The center of dilation and figure are first translated, making the origin the center of dilation.

We map every point because the point (2, 2), which is our center of dilatation, must be translated left 2 and down 2 to become the origin.

(x, y)→(x-2, y-2)

Each point will be multiplied by two when the scale factor is two, giving us the rule.

(x, y)→(2x-4, 2y-4)

In order to return the figure to its original location, we must translate it right 2 and up 2; this gives us the rule.

(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)

At the top of the original figure, the first point is (0, 6). When we use the transformation, we get

(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)

The pre-rightmost image's point is (2, 4). The results of using the transformation rule are;

(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)

The pre-leftmost image's point is at (-3, 3). The transformation rule being applied, w

(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)

Hence,an picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.

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The score of Jane is 27 and the score of Claire is 18.

A linear equation is an equation where highest degree of variables is 1.

Let the score of Jane's mark is x

Given, that score Jane is 9 more than the score of Claire.

So, the score of Claire= x-9

Given, the score of Jane is 60% of the sum of their scores.

the sum of their scores is = x+x-9= 2x-9

from the above it is clear that

the linear equation will be

x=60%(2x-9)

⇒x=0.6(2x-9)

⇒x= 1.2x -5.4

⇒1.2x-x= 5.4

⇒0.2x= 5.4

⇒x= 5.4/0.2

⇒x= 27

So the score of Jane is 27.

As score Jane is 9 more than the score of Claire.

the score of Claire is = x-9= 27-9=18

Therefore the score of Jane is 27 and the score of Claire is 18.

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Answer:

a₁₇ = - 3

Step-by-step explanation:

substitute n = 17 into the nth term rule

a₁₇ = 77 + 16 × - 5 = 77 - 80 = - 3

Answer:

See below

Step-by-step explanation:

The question is garbled.  I don't see a graph nor can I interpret the list of numbers.  

g(x) = 2x-1+3 can be simplified to:

g(x) = 2x+2

This line is shown in the attached graph.  It has a slope of 2 and a y-intercept of 2.

Answer: Choice C  [tex]f(x) = 5(x+4)^2 - 80[/tex]

======================================================

Reason:

The expression [tex]x^2+8x+16[/tex] factors to [tex](x+4)^2[/tex] using the perfect square trinomial formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]. In this case, a = x and b = 4.

The -5(16) simplifies to -80

Therefore, [tex]5(x^2+8x+16) - 5(16)[/tex] turns into [tex]5(x+4)^2 - 80[/tex]

Compare this to [tex]a(x-h)^2 + k[/tex] to see that h = -4 and k = -80. The vertex is located at (h,k) = (-4, -80)

Answer:

c) 5(x+4)² - 80

Step-by-step explanation:

You have already gotten the third (second-last) step for finding the vertex as follows:

f(x) = 5(x² + 8x + 16) -5(16)

= 5(x+4)² - 80

Additional remarks: to find the vertex, you can just use find the value of x when x+4 = 0, meaning x = -4 and y = -80. Hence, the vertex is (-4, -80).

Hope this helps and feel free to mark this as brainliest! :)

Answer:

A

Step-by-step explanation:

y = x² - 6x - 4

(x - 3)² - 3² - 4 = 0

(x - 3)² - 13 = 0

(x - 3)² = 13

x - 3 = ±√13

x = 3 ± √13

The actual height of the building is 67 1/2 feet

The courthouse is the tallest building in the city. If it is 7 1/2 inches tall in the model, how tall is the actual building?

Scale factor: 1 inch = 9 feet

The given parameters are:

This means that:

7 1/2 inches : Actual = 1 inch = 9 feet

So, we have:

Actual =7 1/2 * 9 feet

Evaluate the product

Actual = 67 1/2 feet

Hence, the actual height of the building is 67 1/2 feet

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Answer:

x12×x5x×x-2×9) ____=((140)5

60x × (x-18)x _______=(140)5

60x×x-10x _______=(140)5

60x-18x______=140×5

42x_______=700

42x-42x ____=700-42x

658x

The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the meal cost, hence:

Total cost = x + 0.2x + 0.0725x

15 = 1.2725x

x = 11.79

The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.

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The function is called an exponential function became the exponent is a variable.

The function is called an exponential function became the exponent is a variable.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

So, here given a fill in the blank statement, we need to find the words to be filled in the blanks,

So, the whole statement is =

The function is called an exponential function became the exponent is a variable.

The function y = 3ˣ is an exponential function because it is having a power which is a variable.

The graph of the same is attached to the solution.

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Answer:

A

Step-by-step explanation:

Givens

y2 = 15

y1 = 0

x2 = 3

x1 = 0

Equation

slope = (y2 - y1) / (x2 - x1)

Solution

The question is a bit unfair. It looks like you should be answering one. It's not true. What makes it not so is that the axis (x and  y) have different intervals.

Substitute the givens into the equation

slope = (15 - 0) / (3 - 0)

slope = 15 / 3

slope = 5

Answer Slope = 5 or A

Answer:

it's A

Step-by-step explanation:

that's what i put on that question

The number of biscuits each friend can get would be 2.5.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Margret divides a packet of 20 biscuits among her 8 friends.

In order to find the number of biscuits each friend gets.

20 / 8

= 2.5

Hence, the number of biscuits each friend can get would be 2.5.

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The gym location is (15th street, 14th Avenue). so the option D is correct.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

Given :

Ping's residence = (3rd street, 6th Avenue)

Ari's residence = (21st street, 18th Avenue)

Gym location is 2/3 the distance of Ping's residence to Ari's residence

So, distance between Ping's home to Ari's home will be

Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)

Distance = (21 - 3) street, (18 - 6) avenue

Distance between ping and Ari will be

= (18th , 12th )

We know that

Gym distance = 2/3 × (18),  2/3 ×(12)

Gym distance = (12, 8)

Gym location = Ping's location + gym distance

Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)

Gym location = (15th street, 14th Avenue)

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The reflection of any point across the x-axis:

  ⇒ means that x-coordinate remains the same

     ⇒ but the y-coordinate is multiplied by '-1'

In this case:

 ⇒ (50,25) becomes (50,-25)

Answer: (50,-25)

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Answer:

(50, -25)

Step-by-step explanation:

When we reflect a point across the x-axis, only the sign of the y-value the changes. In this case, the y-value is 25, so after the reflection it becomes -25. The x-value stays the same. So your resulting point is (50, -25)

The zeros and intercepts of the polynomial m^2 + 5m + 4 will be different.

A quadratic function is a function that has a degree of 2.

Given the following equation

f(m) = m^2 + 5m + 4

The x-intercept occurs at the point where f(m) is zero and same is applicable to the zeros of the function.

This shows that the zeros and intercepts of the polynomial m^2 + 5m + 4 will be different.

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The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

[tex]\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}[/tex]

The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.

Then the distance between them will be

[tex]\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units[/tex]

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Finding the proportionality constant :

Finding y when x = 7 :

The value of y is 4/49 when x = 7.

[tex]y = \frac{k}{ {x}^{2} } \\ \\ 64 = \frac{k}{ { (\frac{1}{4}) }^{2} } \\ \\ 64 = \frac{k}{ \frac{1}{16} } \\ \\ 64 = 16k \\ \\ k = \frac{64}{16} \\ \\ k = 4.[/tex]

Finding 'y'

[tex]y = \frac{4}{ {7}^{2} } \\ \\ y = \frac{4}{49} .[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} }{(p - y) {}^{y} } + \cfrac{ - 2p}{(p - y) {}^{y - 1} } + \cfrac{1}{(p - y) {}^{y - 2} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + ( - 2p)(p - y) + 1(p - y) { }^{2} }{(p - y) {}^{y} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2}- 2p {}^{2} + 2py + p {}^{2} + y{ }^{2} - 2py}{(p - y) {}^{y} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + {p}^{2} - 2p {}^{2} + 2py - 2py + y{ }^{2} }{(p - y) {}^{y} }[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

32.59 (nearest hundredth)

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

(where a is the first term and r is the common ratio)

Given:

[tex]\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}[/tex]

Therefore:

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:

[tex]\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]

[tex]\implies S_{20}=32.58609013...[/tex]

[tex]\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)[/tex]                    

General form of geometric progression

On comparing to the summation

Apply Sum formula

[tex]\boxed{\sf S_n=\dfrac{a(1-r^n)}{1-r}}[/tex]

[tex]\\ \implies \sf S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]

[tex]\\ \implies\sf S_{20}=32.586[/tex]

[tex]\\ \sf\mplies S_{20}=32.59[/tex]

Answer:

B. [tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]

Step-by-step explanation:

[tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]

2x - 13 = -13 + 2x

2x - 13 = 2x - 13

As both sides are equal, any value can be substituted for x, and hence it has infinitely many solutions.

Answer:

B. 1/13(26x - 169) = 1/12(-156 + 24x)

Step-by-step explanation:

When looking for an equation with infinetly many solutions, we are looking for an equation that is true when simplified

such as: 3c = 3c

or x - 10 = - 10 + x

this is because any value that we put in for x will simplify to a true equation (will be a solution)

so, let's examine the options:

A. if we combine like-terms on both sides, we will end up with                                23 + 32x = 32x + 26

which is false, for any value that we put in for x

B. this statement is true--regardless of the value for x.

1/13 · 26 is the same as 1/12 · 24 (both equal 2; so both sides would distribute to 2x)

1/13th of -169 is -13; and 1/12th of -156 is -13

so, for all values of x, option B is true

(all values of x are a solution; and "x" could be any value)

C. by distributing the 2 (6 - 4x = -5x + 7), we find an equation that is not true for all values of x [we don't even have to find the solution, we just know that there will only be a/a few solution ]

D) because the variable, x, is only on one side (and when distributed, is not cancelled by any other x), we know that it cannot be true for infinetly many solutions

(the only true solution will be when the equation is simplified to 4/18 = 4/18)

hope this helps!!

Answer: (0,1)

Step-by-step explanation:

If (x,y) lies on the graph of the original function, then (y,x) lies on the graph of the inverse.

Since (1,0) lies on the graph of h(x), (0,1) lies on the graph of its inverse.

(0, 1) point is on the graph of the inverse function h-¹(x).

Two functions f(x) and g(x) are inverses if their composition is equal to the identity.

Equation of line will be

y = -2x + 2 = h(x)

h⁻¹(x) will be calculated as:

x = -2y + 2

x - 2 = -2y

y = (2 - x)/2

So, y = h⁻¹(x) = (2 - x)/2

put x = 0 in the equation y = (2 - x)/2

y = 1

(0, 1) = (0, 1)

This, (0, 1) is the point on h⁻¹(x).

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Answer:  [tex]\textsf{x}^2\textsf{ - 14x + 24}[/tex]

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

Given:  [tex]\textsf{x = 12 and x = 2}[/tex]

Find: [tex]\textsf{Determine the quadratic equation}[/tex]

Solution:  In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.

Move the integers

Create and expression and distribute

Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.

Passengers under the age of 8 and whose height is less than 57 inches must be in the back seat of a vehicle.

When you journey in the backseat of a automobile, you take a seat within the row of seats behind the motive force. Kids once in a while combat over the front seat, not wanting to take a seat within the backseat. you may tour within the backseat of a car except you're the driver or are using a two-seat sports activities vehicle.

The cushion in which the driving force or passenger sits is either known as a horizontal cushion or seat cushion. The back of the automobile seat is called the seat again however it could additionally be called a backrest.

An infant protection seat every so often referred to as an toddler protection seat, infant restraint device, baby seat, child seat, car seat, or booster seat is a seat designed particularly to shield youngsters from injury or death throughout automobile collisions.

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Answer:

.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Adding 2 fractions results in a fraction.

Answer:

B: The sum is a non-terminating and a non-reapeating decimal

Step-by-step explanation:

-11/4 +5/g

There is 15 steps you have to do after (look in the picture)

but this is what you get:

[tex]-\frac{11g-20}{4g}[/tex]

The hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".

It should be noted that a hypothesis means a proposed explanation based on reasoning and evidence.

In this case, the hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".

The conclusion is that kids who wear braces will have straight teeth.

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