I need help with this anyone?????????

Answer:

We are given the function:

[tex]f(x)=2x^2-x-10[/tex]

[tex]Here,\\a=2, b=-1,c=-10[/tex]

1. X-intercepts are the points at which the graph of a function intersects or cuts the x-axis. Since the x-intercept always lies on the x-axis, its ordinate or y-coordinate will always be 0. Since the function is quadratic, it will have at most 2 x-intercepts.

In order to find the x intercept, we basically solve for x at y=0:

[tex]f(x)=2x^2-x-10\\As\ y=0,\\0=2x^2-x-10\\2x^2-x-10=0\\ 2x^2-5x+4x-10=0\\x(2x-5)+2(2x-5)=0\\(x+2)(2x-5)=0\\Hence,\\Individually:\\x=-2,\ x=\frac{5}{2}[/tex]

Hence, the x-intercepts of the parabola of f(x) is (-2,0),(2.5,0)

2. The vertex of parabola is determined as maximum or minimum, solely on how it opens. This depends on the nature of the co-efficient of the x^2 term or 'a'. If a is positive the parabola opens upwards (minimum point) and downwards (maximum point) if negative. Hence, here as a=2, the parabola opens upwards and its vertex is minimum.

[tex]Vertex=(\frac{-b}{2a},\frac{-D}{4a})\\Hence,\\D=b^2-4ac\\Substituting\ a=2,b=-1,c=-10:\\D=(-1)^2-4*2*-10=1+80=81\\Hence,\\Vertex\ of\ f(x)=(\frac{-(-1)}{2*2},\frac{-81}{4*2})=(\frac{1}{4},\frac{-81}{8})[/tex]

3. [Please refer to the attachment]

From the graph, we observe that the parabola cuts the x-axis at (-2,0),(2.5,0). Also, its clear that the axis of symmetry passes through [tex](\frac{1}{4},\frac{-81}{8})[/tex], which is its minimum point.

Answer:

A chord of a circle is 9cm long if it's distance from the centre of the circle is 5cm calculate the radius of the circle

Answer:

[tex]A(x) = 12500(1.054)^x[/tex]

Step-by-step explanation:

Exponential equation for population growth:

Considering a constant growth rate, the population, in x years after 2005, is given by:

[tex]A(x) = A(0)(1 + r)^x[/tex]

In which A(0) is the population in 2005 and r is the growth rate, as a decimal.

The initial population of the town was estimated to be 12,500 in 2005.

This means that [tex]A(0) = 12500[/tex]

The population has increased by about 5.4% per year since 2005.

This means that [tex]r = 0.054[/tex]

So

[tex]A(x) = A(0)(1 + r)^x[/tex]

[tex]A(x) = 12500(1 + 0.054)^x[/tex]

[tex]A(x) = 12500(1.054)^x[/tex]

Answer:

Step-by-step explanation:

Assuming the system is solvable in the first place, create an augmented matrix of coefficients from the equations. Then put the matrix into reduced row echelon form.

Example is attached.

"Demonstrate by solving the following system."

You need to provide the system of equations.

Answer:

C. 2x+11

Step-by-step explanation:

2x+11≈21 -55

2x+11≈21 -55

2x+11≈21 -55

2x+11≈21 -55

2x+11≈21 -55

Answer:

4y

They would have the same value if a number was substituted for y

Step-by-step explanation:

y+y+2y =

Combine like terms

4y

These are all like terms

They would have the same value if a number was substituted for y

Let y = 5

5+5+2(5) = 5+5+10 = 20

4(5) =20

Answer:

Perimeter

[tex]202 = x + x + 26 + 4x + 26 + 4x\\202-26-26=10x\\150=10x\\x=15[/tex]

Therefore, the dimensions are

Answer:

soory i dont know just report me if you angry

Answer:

628 mi^3

Step-by-step explanation:

the volume of a cylinder is given by:

V = base area x height

thus,

V = (3.14)(5)^2(8)

V = (3.14)(25)(8)

V = 628 mi^3

the volume of the cylinder is 628 cubic miles

The volume of the cylinder is 628 cubic miles.

We have a cylinder of radius 5 mi and height 8 mi.

We have to find the volume of the figure and round it to nearest tenth.

The volume of cylinder is given by the formula -

Volume [tex]=\pi r^{2} h[/tex]

We can use the above formula to calculate the volume of cylinder. In our case -

r = 5 mi

h = 8 mi

Substituting the values in the formula -

Volume [tex]=\pi\times5^{2}\times 8\\\\[/tex] = 628 cubic miles.

Hence, the volume of the cylinder is 628 cubic miles.

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Answer:

0.5

Step-by-step explanation:

E to E'

(0, 3) to (0, 1.5)  each term of E' is ½ of the corresponding term of E

N to N'

(-1, 1) to (-0.5, 0.5)  each term of N' is ½ of the corresponding term of N

U to U'

(2, -2) to (1, -1)  each term of U' is ½ of the corresponding term of U

V to V'

(1, -3) to (0.5, -1.5)  each term of V' is ½ of the corresponding term of V

Answer:

582-600

1,234-1,200

640-600

770-800

1,104-1,100

Answer:

3.5 inches

Step-by-step explanation:

Sample mean basically means that we need to find the average of the samples.

So the formula for finding average is

Number of observations/ Number of Occurrences

So when we add the values together we get

42.

So there are 12 numbers

So, 42/12 =

3.5 inches

The sample mean of the heights of the plants in Susan's garden is

3.5 inches.

Here,

Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.

She measured the heights (in inches) of 12 randomly selected plants and recorded the data:

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

We have to find the sample mean of the heights of the plants in Susan's garden.

What is Average?

Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.

Now,

The recorded data is;

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.

Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]

Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]

Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.

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Answer:

[tex]f(x) = \sqrt{x} + 2 \\ \\ g(x) = {x}^{2} + 1 \\ \\ f{g(x)} = \sqrt{ {x}^{2} + 1 } + 2 \\ \\ g{f(x)} = {( \sqrt{x} + 2 )}^{2} + 1[/tex]

Answer:

Step-by-step explanation:

I assume the sequence is 0, 2, 4, 6

nth term = 2(n-1)

Answer:

x=10

Step-by-step explanation:

The whole figure is symmetric hence x=10

Answer:

0.045

Step-by-step explanation:

(0,4x0,5x0,3)-(0,2x0,5x0,15)

Answer:

it simple as look

Step-by-step explanation:

He y I a m r a v I t ha n k S

Wowowowowowowowowk

Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]

Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]

                       = 2.145

Substitute the values

[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]

(26.17, 21.83)

When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]

b). The formula to calculate 95% prediction interval is given by :

    [tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]

   [tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]

   (31.13, 16.87)

Answer:

13

Step-by-step explanation:

f(x) = 4x + 1

Let x= 3

f(3) = 4*3+1

    = 12+1

   = 13

Answer:

(-2,0)

Step-by-step explanation:

The x intercept is the value when it crosses the x axis ( the y value is zero)

x = -2 and y =0

(-2,0)

Answer:

D

Step-by-step explanation:

Assuming that the expression is referring to sin²(2πft) and not sin²(2)πft, we can solve as follows:

One trigonometric identity states that sin²x+cos²x = 1. We want to express this in terms of cos²x, so we need to solve for sin²x. Subtracting cos²x from both sides, we get 1-cos²x = sin²x. Plugging (2πft) for x, we get

1-cos²(2πft) = sin²(2πft)

We can plug that into our equation to get

P = I₀²R(1-cos²(2πft)), or D

Answer:

5%

Step-by-step explanation:

Bank amount=PA*(1+r/100)^t

4410=4000*(1+x/100)^2

1.05=(1+x/100), x=5%

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Parabola: y=2x²

Let say (a,b) the focus and y=k the directrix.

[tex]formula\ to\ use:\ \boxed{y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} }\\\\\left \{\begin {array}{ccc}a&=&0\\2&=&\dfrac{1}{2(b-k)} \\\dfrac{b+k}{2} &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b-k&=&\dfrac{1}{4} \\b+k &=&0\\\end {array} \right.\\\\\\\left \{\begin {array}{ccc}a&=&0\\b&=&\dfrac{1}{8} \\k &=&\dfrac{-1}{8} \\\end {array} \right.\\\\\\focus=(0,\dfrac{1}{8} )\\\\directrix:\ y=\dfrac{-1}{8}[/tex]

The system of inequalities that is graphed is:

y ≤ - (2/3)*x

y < x - 3

So the correct option is B.

First, we can see that for both of the inequalities the shaded part is below the lines.

You also can see that the solid line (correspondent to the symbol ≤) is the one with a negative slope, and the dashed line (correspondent with the line <) is the one with a positive slope.

Only with that, we conclude that the correct option is B.

y ≤ - (2/3)*x

y < x - 3

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9514 1404 393

Answer:

  10.7 years

Step-by-step explanation:

The formula for the balance in an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. We want to solve for t.

  5800 = 3500(1 +0.0475/4)^(4t)

  58/35 = 1.011875^(4t) . . .  divide by 3500 and simplify a bit

  log(58/35) = 4t·log(1.011875) . . . . take logs

  t = log(58/35)/(4·log(1.011875)) . . . . divide by the coefficient of t

  t ≈ 10.6966 ≈ 10.7

The person must leave the money n the bank for about 10.7 years for it to reach $5800.

Answer:

4 units

Step-by-step explanation:

A'B' = 2 × AB

8 = 2×AB

AB = 8/2 = 4

Answer:

16 units

Step-by-step explanation:

The triangle will get bigger because it has a scale factor that is greater than 1.

k=scale factor

k<1=reduction

k>1=enlargement

Using the binomial distribution, it is found that:

a) The expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]

b) You need to select at least 587 people.

For each person, there are only two possible outcomes, either they share your birthday, or they do not. The probability of a person sharing your birthday is independent of any other person, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

There are 365 days in a non-leap year, hence, the probability of each person sharing your birthday is [tex]p = \frac{1}{365}[/tex]

Item a:

This probability is P(X = 0), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{n,0}.\left(\frac{1}{365}\right)^{0}.\left(\frac{364}{365}\right)^{n} = \left(\frac{364}{365}\right)^{n}[/tex]

Hence, the expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]

Item b:

The probability that at least one person shares your birthday is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

We want that:

[tex]P(X \geq 1) \geq 0.8[/tex]

Hence:

[tex]1 - P(X = 0) \geq 0.8[/tex]

[tex]P(X = 0) \leq 0.2[/tex]

Hence:

[tex]\left(\frac{364}{365}\right)^{n} \leq 0.2[/tex]

[tex]n\log{\left(\frac{364}{365}\right)} \leq \log{0.2}[/tex]

[tex]n \geq \frac{\log{0.2}}{\log{\left(\frac{364}{365}\right)}}[/tex]

[tex]n \geq 586.6[/tex]

Rounding up: You need to select at least 587 people.

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Answer:

rationalising factor wud be

2 - root3

as on multiying both and applying identity we end up

2^2 - (root3)^2

4 - 3 = 1

we got a rational number so rationalisng factor is

2 - root3