i) Factorise 3x^2-13x-10

Vertex of g(x) is: (-2, -4)

acc to our question:

Vertex form of a quadratic function:

f(x) = (x - h)² + k

We have (h, k) = (3, -4)

The function f(x) is:

f(x) = (x - 3)² - 4

The function g(x) is: g(x) = f(x + 5) =

Vertex of g(x) is:(-2, -4)

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Answer:

Step-by-step explanation:

The cost the tiles are = $182.55

acc to our question-

white tiles =W = 1/4

3/5 = yellow

each tile costs= $3

= 0.25+ 0.6+ 60

= 60.85*3

$182.55

hence,The cost the tiles are = $182.55

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The elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

According to the question,

We have the following information:

A = {6,7,8,11} and B = {7,6,7,9}

Now, we know that the elements of AUB means that all the elements which are there in both sets but the elements are not supposed to be repeated.

(Please that AUB can also be found using Venn diagram and questions are asked where the question has to be solved by making Venn diagram and representing all the elements in it.)

So, we have the following expression:

AUB = {6,7,8,9,11}

(Now, note that numbers however repeated in sets are not repeated here.)

Hence, the elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

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The complete general form of the equation of the given sinusoidal function is y = 8sin[(27/2π)*(x - 4)] + c.

The general form of an equation for a sinusoidal function is presented below.

y = a×sin[b*(x - h)] + c

The variable "a" denotes the amplitude of the equation. The variable "T" represents the time period of the equation, and T = 2π/b. The variable "h" denotes the phase shift of the equation. The variable "c" denotes the vertical shift of the equation. The amplitude, period, and phase shift are 8, 27, and 4 units to the left, respectively. The general form of the equation of a sinusoidal function can be written as given below.

y = a×sin[b*(x - h)] + c

y = 8sin[(27/2π)*(x - 4)] + c

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Answer:

[tex]y_1=\boxed{-3}[/tex]

[tex]y_2=\boxed{-8}[/tex]

[tex]y_3=\boxed{-16}[/tex]

[tex]y_4=\boxed{-28.5}[/tex]

Step-by-step explanation:

Given:

Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:

[tex]y'=y-2x, \;\;y(3)=0[/tex]

at x = 3.5, 4, 4.5, 5.

Therefore:

[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]

Euler's Method

[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]

[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]

[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]

Answer:

0.97m : 1.08m

Step-by-step explanation:

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Answer:

Loan analysis is an evaluation method that determines if loans are made on feasible terms and if potential borrowers can and are willing to pay back the loan. It checks the eligibility of the potential borrower against the criteria set forth for lending. Loan analysis helps in assessing the skills and financial knowledge of the borrower to ...

Answer:

A. REFLECTION

Please guys do some research i know you're not that stu p id-_-

The time taken is obtained as 3 years.

We know that radioactivity has to do with the fact that a substances does disintegrate gradually over a period of time.

Let us recall the formula;

N/No = (1/2)^t/t1/2

N = The mass of radioactive atoms at time t

No = The mass of radioactive atoms initially present

t = time taken

t/12 = half life of the radioactive nucleus

Then;

32/50 = (1/2)^t/28

0.64 =  (1/2)^t/28

log 0.64 = t/28 log0.5

t/28 = log(0.64/0.5)

t = 28 * log(0.64/0.5)

t = 3 years

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The linear function for the situation is :-

Amount at the end of 3 years = Original investment + original investment*Rate*Time/100

It is given in the question that:-

Investment of George's friend in startup company = $ 500.

Interest percent = 8 %

Time period of investment = 3 years

We have to find the linear function for this situation.

As this interest is on original investment, the interest will be simple.

Hence,

The linear function for the situation will be :-

Amount at the end of 3 years= Original investment + original investment*Rate*Time/100

Amount at the end of 3 years = 500 +  500*8*3/100 = 500 + 120 = $ 620

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Answer:

5q + 5q + 5 is equivalent to 10q + 5

Answer:

A.

Step-by-step explanation:

Answer:

7 * 5 =35 because if you say 5 10 15 20 25 30 35 then that's your answer

Answer:

a) 7:13  b) 5:13

Step-by-step explanation:

There are 7 new books (-> 7:--) theres 5 used books, add the 7 new books and 5 used books together. it said "The ratio for new books to all books?" it must be in that order. with leads you to 7:13

do the same thing for b) using the same steps.

Answer:

a lot less because 0.4 is not fully of 100%

Step-by-step explanation:

Answer:

52 is 0.4% of 130. You would expect the number to be a lot greater than 52

Step-by-step explanation:

If the number we are trying to find is x, we have to use the equation x*0.4=52 which can be rewritten as 52/0.4=x

If you solve that, you get 130.

The number is expected to be a lot greater than 52 because 0.4 is almost 0.5 and that would mean doubling 52 so the number would be almost double 52. That means it would be a lot greater.

The number of trips after the cost of the plan A and plan B is 16.

According to the question,

We have the following information:

Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.

So, this will make an arithmetic progression.

The formula to find nth term of an A.P:

an = a+(n-1)d where a is the first term

Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.

145+(n-1)5 = 40+(n-1)12

145+5n-5 = 40+12n-12

5n+140 = 12n+28

140-28 = 12n-5n

7n = 112

n = 112/7

n = 16

Hence, the number of trips after the cost of the plan A and plan B is 16.

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Answer:

20/5 is the slope, or 4.

Step-by-step explanation:

It went up 20 units on the y axis, and over 5 units on the x-axis. So 20/5 is the slope.

-Hope this helped

Answer:

-25x-45y, because if we have got + and -, so we will write minus.

Answer: Read explanation

Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.

Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.  

Make any corrections if you want! Make it more comfortable to your style!

The correct expression of the inequality expression is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

From the question, the expression is given as

18 ÷ 6 + 3 □ 6 + 12 ÷ 3

We start by converting the above expression to the same form

So, we start by solving the quotients

This gives

3 + 3 □ 6 + 4

Next, we evaluate the sum

So, we have

6 □ 10

In the above expression, we have

6 and 10

By convention, the number 6 is less than the number 10

This is so because 6 has a smaller value and 10 has a higher value

When the above numbers are compared, we have

6 is less than 10

This means that we make use of the inequality symbol <

So, we have

18 ÷ 6 + 3 < 6 + 12 ÷ 3

Hence, the complete inequality is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

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Answer:

156.7 m (nearest tenth)

Step-by-step explanation:

Define the variables:

If the distance needed to stop a car varies directly as the square of its speed:

[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]

where k is the constant of proportionality.

Given:

To find the constant of proportionality, k, substitute the given values into the equation:

[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]

Substitute the found value of k back into the formula to create an equation for the given relationship:

[tex]\implies d=\dfrac{6v^2}{245}[/tex]

To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:

[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]

[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]

[tex]\implies d=\dfrac{7680}{49}[/tex]

[tex]\implies d=156.73469...\; \sf m[/tex]

[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]

Therefore, the distance required to stop a car at 80 km/h is:

Answer: Center: (-3, 2). Radius: 4.

Step-by-step explanation:

The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.

The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.

The radius of the circle is the square root of the constant on the other side of the equation. So, r = [tex]\sqrt{16}[/tex] = 4.

The explanation is from the equation of a circle in a graph:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:

[tex](x+3)^2 + (y-2)^2 =16[/tex]

Which can also be written as

[tex](x-(-3))^2 + (y-(2))^2=16[/tex]

See the correlation of numbers -3 and 2 with h and k?

Notice also how the equation contains [tex]r^2[/tex], so to find the radius you do [tex]\sqrt{r^2}[/tex].

Answer:

this is how to do it. Now find the answer

Step-by-step explanation:

find the common factor for the denominators, which is 30.

then × the numerator by however much you ×tl the denominator by to get 30

Answer:

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

6(x-6)+2=8x-12

6x-36+2=8x-12 First take care of the parenthesis

6x-34=8x-12 then combine numbers

-2x-34=-12 Subtract 8 from both sides

-2x=22 Add 34 to both sides

x= -11 Divide by -2 on both sides

Answer:

Step-by-step explanation:

Solution

Steps

6(x−6) +2 = 8x−12

Expand by applying the distributive law:     a(b−c)=ab−ac

6(x−6)=6x-36

6x−36+2 = 8x−12

6x−34 = 8x−12

Add 34 to both sides

6x−34+34=8x−12+34

Simplify

6x=8x+22

Subtract 8x from both sides

6x−8x=8x+22−8x

Simplify

−2x=22

Divide both sides by −2

x=−11

The solution to the equation using graph is x= -0.62 or x = 1.62.

What is equation?

A mathematical equation may be a formula that uses the equals sign to represent the equality of two expressions.

Main Body:

For [tex]-x^{2} +y = 1[/tex]

We make y the subject to obtain

[tex]y = x^{2} +1[/tex]

We can easily graph this function, because we just have to transform the graph [tex]y = x^{2}[/tex] of  by shifting the intercept up to 1.

As for the straight line, -x +y = 2

We find the intercepts as follows,

When y = 0 , x = -2

When x = 0 , y = 2

We plot the points (-2,0)  and (0,2).

We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be

x= -0.62 or  x= 1.62

See graph

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Answer:

h(x)= |x-3|-4

Step-by-step explanation:

If f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4

The function is given

f(x) = |x|

Translation of the shape mean the displacement of the shape from one place  to another place. Some usually used displacements are shifted to right / left and shifted to up / down etc.

First f(x) is shifted down 4

Then the function will become

f(x) = |x| - 4

Then the function shifted right 3

Then the function will be

h(x) = |x - 3| - 4

Hence, if f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4

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The greatest common factor of 160, 320 and 480 will be 160.

The largest positive number that can be evenly divided into the supplied numbers is the most common factor. The largest number that evenly divides all the specified numbers is the greatest common factor.

In maths, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y is represented by the symbol GCD(x,y)

Assumed to be 160, 320 and 480. The numbers are factored to determine the largest common factor.

Factorize number 160

160 = 2×2×2×2×2×5

Factorize number 320

320 = 2×2×2×2×2×2×5

Factorize number 480

480 = 2×2×2×2×2×3×5

The common number between all three numbers is 2⁵×5. Therefore, the greatest common factor of 160, 320 and 480 will be 160.

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Answer:

1.) 10: 1, 2, 5, 10.

15: 1, 3, 5, 15,

Answer would be 5.

2.) 18: 1, 2, 3, 6, 9, 18

21: 1, 3, 7, 21

Answer would be 3.

3.) 12: 1, 2, 3, 4, 6, 12.

24: 1, 2, 3, 4, 6, 8, 12, 24.

Answer would be 12.

4.) 8: 1, 2, 4, 8.

20: 1, 2, 4, 5, 10, 20.

Answer would be 4.

5.) 14: 1, 2, 7, 14.

28: 1, 2, 4, 7, 14, 28.

Answer would be 14.

Step-by-step explanation:

Using the listing method, you would first list the common factors of each number, to which that number could be multiplied by. Then, you would search for the greatest common factor.