2√5x-4-3= -11
Is there roots or no roots?

Step-by-step explanation:

g(x) is f(x) shifted up by 2 units.

that is simply expressed as

g(x) = f(x) + 2

h(x) if f(x) shifted left by 1 unit.

that is trickier.

h(x) = f(x + 1)

why ?

every result that f(x) had at x+1, is now happening for h(x) at x ("earlier", shifted to the left). so, the function result for f(x+1) is the function result for h(x).

and therefore,

h(x) = f(x + 1)

FYI

a shift to the right by 1 unit would be

i(x) = f(x - 1)

for the same reasons as for the shift to the left, just in the other direction.

Answer:

V = 8446.9 in³

Step-by-step explanation:

Just use the cylinder formula.

V = πr²h

V = (3.14)(21)²(6.1)

V = 8446.9 in³

The line in coordinate form passing through the point (−4,−6,6) in the direction is x - y - z + 4 = 0

The term called coordinates in math is called a system that uses one or more numbers, or coordinates and it is uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Here we have the line in coordinate form passing through the point (−4,−6,6) in the direction.

As we all know that the equation of line through the point (-4, -6, 6) is written as,

=> ( x - (-4)) = (y - (-6))  = (z - 6)

When we simplify this one then we get,

=> x + 4 = y + 6 = x - 6

=> x - y - z + 4 - 6 + 6

=> x - y - z + 4 = 0

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The correct answer that is least capable of responding quickly to shifting consumer needs and of keeping a customer-focused attitude matrix.

Given that,

From given below which of the three organizational types—projectized, matrix, or functional—is least suited to providing quick responses to changing customer needs and upholding a customer-focused attitude

Matrix of the three organizational forms – projectized, matrix, or functional – is least suited for fast response to changing customer requirements and for maintaining a customer focus.

The correct answer is functional.

Functional  of the three organizational forms – projectized, matrix, or functional – is most suited for aligned project accountability and authority, and for rapid reaction to customer needs.

The correct answer is projectized.

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Answer: e is the correct option.

Step-by-step explanation:

Option e  If z = xy, then z = 2.

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Answer:

Ben's savings (S) can be related to the number of hours he babysits (h) by the equation:

S = r * h

where r is the rate of pay per hour that Ben receives for babysitting. This equation shows that Ben's savings increase linearly with the number of hours he babysits, as long as the rate of pay remains constant.

Rectangle EFGH is assumed, the value of x and m<EIH is 102 degree

Rectangle EFGH is assumed. Each side of a rectangle has an equal length. Each side of a rectangle has an equal length.

FH- =7x-2,

EI-20, and

mZIFG=39°,

Length width equals the area of a rectangle. Therefore, breadth is equal to the product of the area and the length, which is either 20 units or 39 square units.

You need to know a box's height, breadth, and depth in order to determine its volume. These three dimensions may be multiplied to determine the volume.

if < f = 39 degree

so

<G = 39 degree

then

<FIG = 39 + 39 + x = 180 degree

180 - 78 = 102 degree

so <FIG = <EIH

The value of x and m<EIH is 102 degree

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Answer: y=-2x

Step-by-step explanation:

take formula (y-y1)=m(x-x1), m is slope

plug in x and y values and slope, (y-7)=-2(x-10)

distribute, y-7=-2x+20

y=-2x+27

Answer:

x= 1, y=3

Step-by-step explanation:

x + (2x+1)= 4

3x+1=4

3x=4-1

x=1

Take x as 1

1 + y =4

y=4-1

y=3

Answer:

-18x + -144

Step-by-step explanation:

The equation of the parabola in any form is; (x + 5)² = 4(y - 4)

The general equation of a parabola is given by the expression;

y = a(x – h)² + k or x = a(y – k)² + h.

Where (h, k) denotes the coordinates of the vertex

2p = 5 - 3

2p = 2

p = 1.

Thus, the coordinates of the vertex will be;

Vertex (-5, 5 - 1) = (-5, 4)

Therefore the equation of parabola is expressed as;

(x + 5)² = 4(y - 4)

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Answer:

20-15-60 is the answer to the question

The meaning of the y-intercept of the linear function is given as follows:

The tablet starts with 80 percent of battery remaining.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph of the function touches the y-axis at y = 80, hence the intercept b is given as follows:

b = 80.

As the output variable is the battery percentage, it represents the initial battery percentage.

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The meaning of the y-intercept of the linear function is given as follows:

The tablet starts with 80 percent of battery remaining.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope m represents the rate of change of the output variable relative to the input variable.

The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.

The graph of the function touches the y-axis at y = 80, hence the intercept b is given as follows:

b = 80.

As the output variable is the battery percentage, it represents the initial battery percentage.

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The time at which the velocity falls to zero can be expressed as the cube root of 5/9.

What is velocity ?

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.

The velocity of an object can be found by taking the derivative of the position with respect to time.

So, the velocity can be expressed as:

v(t) = d(x(t))/dt = (-0.20)3t^2 (3.0)2t (10.0) + 6.0

The velocity of an object is zero when v(t) = 0, so we can set v(t) = 0 and solve for t:

(-0.20)3t^2 (3.0)2t (10.0) + 6.0 = 0

(-0.20)3t^2 (3.0)2t = -6.0 / (10.0)

(-0.20)3t^2 (3.0)2t = -0.6

t^2 (3.0)2t = -0.6 / (-0.20)3 = 5.0

t^3 = 5.0 / (3.0)2 = 5.0 / 9.0

t = (5.0 / 9.0)^(1/3)

So, the time at which the velocity falls to zero can be expressed as the cube root of 5/9.

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Alicia was paid $ 51.25.

According to the question,

Let the amount that Alicia was paid by Y.

If she already spent $10.25 of her paycheck and this is 20% of her paycheck, then

    20 % of  Y =  10.25

   ⇒ [tex]\frac{20}{100} * Y[/tex] = 10.25

    ⇒0.2 * Y = 10.25

     ⇒  Y = [tex]\frac{10.25}{0.2}[/tex]  ( by using division)

       ∴ Y =  51.25

So, Alicia was paid $ 51.25.

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Answer:

110 miles

Step-by-step explanation:

See the attached worksheet.  A spreadsheet was used to add each of the mileage options to the start of 18981 and observe which one was a palindrome.  110 miles added to 18981 is 19091, a palindrome.

Total percent markup in the price of the scooter is 66.67 % ≈ 67%

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

use the unitary approach.

by adjusting the fraction's denominator to 100.

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

Cost of Scooter at retailer is $ 75

Cost of Scooter at local Store is $125

Total price markup = 125- 75 = $50

Total percent markup is = 50/75 * 100 = 66.67 % ≈ 67%(approx.)

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The average height of a tree whose age is 25 years old is 364 inches.

A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.

Given that, a table giving a relation between the height and age of trees.

The linear model representing the same is given by,

y = 13.7x + 21.7, where y is the height and x is the age of a tree,

We need to find the average height of a tree whose age is 25 years old,

To find this, put x = 25 in the linear model given,

y = 13.7 × 25 + 21.7

y = 342.5 + 21.7

y = 364.2

y ≈ 364

Hence, the average height of a tree whose age is 25 years old is 364 inches.

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The approximate number of time does an average human heart beat in a lifetime is 3 x 10⁹

The term called average in math is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Here we need to find the number of time does an average human heart beat in a lifetime.

As we all know that a normal heart rate when you're not being active is generally between 60 – 100 beats per minute.

And this is called your resting heart rate.

Based on this we have calculated as average of 80 beats per minute, your heart beats about 4,800 times per hour. That's a whopping 115,200 times per day.

Then during an average lifetime, then the human heart will beat more than 2.5 billion times.

When we round off the value then we get approximately 3 billon.

In a scientific notation it can be written as,

=> 3 x 10⁹

Therefore option (c) is correct.

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If there were 132 crayons in John's backpack, the number of blue crayons is equal to blue crayons.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

3 crayons = 8 blue crayons

132 crayons = X blue crayons

By cross-multiplying, we have the following:

3x = 132 × 8

3x = 1,056

x = 1,056/3

x = 352 blue crayons.

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By the compare to y =mx + b, the value of slope (m) is 1/10 and value of y - intercept is 0.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The expression is,

⇒ v = 1/10u

Now, We can write as;

⇒ v = 1/10u

⇒ v = 1/10u + 0

By compare with y = mx + b, we get;

⇒ slope (m) = 1/10

⇒ y - intercept (b) = 0

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Answer:

An isosceles triangle because it will have two side lengths that are equal.

Step-by-step explanation:

B) The Rational Root Theorem may be used to identify the potential rational roots of the equation in Part A.

The divisors of 9 with the opposite sign are possibly rational roots.

Then, for each rational root, we can see if it is a factor of the polynomial.

A) The remaining of f(x) divided by (x - a) is R, while the remainder of f(x) divided by (x - a) is 2R.

As a result, we may write the following polynomials:

f(x) = (x - a) (x - a)

Q(x) + R f(x) = (x - a)

Q(x) + 2R

Where Q(x) represents the quotient and R represents the remainder.

By combining the two polynomials, we obtain:

(x - a)

Q(x) + R = (x - a) (x - a)

Q(x) + 2R

When we subtract (x - a)Q(x) from both sides, we get:

R = 2R

R = 0 when we solve for R

As a result, the remaining when f(x) is divided by (x - a) is zero.

That is, (x - a) is a factor of f(x), and f(x) is represented as:

f(x) = (x - a)(x^2 + bx + c)

Comparing the coefficients, we get:

a = -a

b = 2a

c = -9

So we have the following equation:

x^3 - 2x^2 - 18x - 9 = 0

B) If it is a factor, we may use synthetic division to divide the polynomial by the factor, resulting in a new polynomial, which we can continue until we have a polynomial with no rational roots. We can utilize numerical methods such as the bisection method or the Newton-Raphson method to thoroughly solve the problem.

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The reliability corresponds to the design factor of 1. 2 is R=0.9616 and d=1.02, for 1.5 R=0.9999 and d=1.14.

To find the reliabilities we first have to find z. There is a formula to find z.

[tex]z=\frac{n_d-1}{\sqrt{n_d^2C_s^2+C_s_d^2} }[/tex]

Factor c is defined as:

C=sd/u

For the strength, this is simply because we are given μs and sd's so we have

[tex]C_s=\frac{6.59kpsi}{95.5kpsi}[/tex]

Cs=0.069

For the stress, it's a bit different since we are given the μp and sd p:

sd=4P/πd².

The standard deviation is:

σ=4/πd²*σP

From this we have:

Cσ=σP/⁻P

=5kip/65kip

Cσ=1/13

For nd=1.2 we have:

[tex]z=-\frac{1.2-1}{\sqrt{1.2^2(0.069)^2+(1/13)^2} }[/tex]

z=-1.77

from table A-10 we see that the probability of failure is 0.0384, meaning the reliability is

R=1-F

R=1-0.0384

R=0.9616

We can express the diameter from 2 equations for stress:

[tex]\frac{4P}{\pi d^2} =\frac{S}{n_d} - > d=\sqrt{\frac{4Pn_d}{\pi S} } \\\\d=\sqrt{\frac{4.65kips.1.2}{\pi .95.5kpsi} }[/tex]

d=1.02

from nd=1.5 we have:

[tex]z=-\frac{1.5-1}{\sqrt{1.5^2(0.069)^2+(1/13)^2} }[/tex]

z=-3.88

from table A-10 we see that the probability of failure is 0.0001, meaning the reliability is:

R=1-F

R=1-0.0001

R=0.9999

The diameter is:

[tex]d=\sqrt{\frac{4.65kips.1.5}{\pi .95.5kpsi} }[/tex]

d=1.14

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The solution of the given initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 4 where f(t) = [tex]\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.[/tex] is 1 + 6cost + 4sint + u(t - π/2)(cos(t - π/2) - 1).

The initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 6 where

f(t) = [tex]\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.[/tex]

Now f(t) = 1[u(t-0) - u(t-π/2)]

f(t) = u(t) - u(t-π/2)

Laplace transformation of f(t) is

L{f(t)} = L{u(t)} - L{u(t-π/2)}

L{f(t)} = 1/S - [tex]e^{\pi S/2}[/tex]/S

Now taking the Laplace transformation on both side to the equation y'' + y = f(t).

L{y''} + L{y} = L{f(t)}

S^2Y(S) - SY(0) - Y'(0) + Y(S) = 1/S - [tex]e^{\pi S/2}[/tex]/S

S^2Y(S) - 7S - 4 +Y(S) = 1/S - [tex]e^{\pi S/2}[/tex]/S

(S^2 + 1)Y(S) - 7S - 4 = 1/S - [tex]e^{\pi S/2}[/tex]/S

(S^2 + 1)Y(S) = 1/S - [tex]e^{\pi S/2}[/tex]/S + 7S + 4

Divide by (S^2 + 1) on both side, we get

[tex]Y(S) = \frac{1}{S(S^2 + 1)} -\frac{e^{\pi S/2}}{S(S^2 + 1)} + \frac{7S}{(S^2 + 1)}+\frac{4}{S^2 + 1}[/tex]

Simplify

[tex]Y(S) = \frac{1}{S}-\frac{S}{S^2 + 1} -\left[\frac{1}{S}-\frac{S}{S^2 + 1}\right]e^{\pi S/2} + \frac{7S}{(S^2 + 1)}+\frac{4}{S^2 + 1}[/tex]

Now Y(t) = [tex]L^{-1}(Y(S))[/tex]

Y(t) = [tex]L^{-1}\left[\frac{1}{S}\right]-L^{-1}\left[\frac{S}{S^2 + 1}\right] -L^{-1}\left[\frac{e^{\pi S/2}}{S}\right]-L^{-1}\left[\frac{Se^{\pi S/2}}{S^2 + 1}\right] + L^{-1}\left[\frac{7S}{(S^2 + 1)}\right]+L^{-1}\left[\frac{4}{S^2 + 1}\right][/tex]

Y(t) = 1 - cost - u(t - π/2) + cos(t - π/2) u(t - π/2) + 7cost + 4sint

Y(t) = 1 + 6cost + 4sint + u(t - π/2)(cos(t - π/2) - 1)

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The complete question is:

Find the solution of the given initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 4 where f(t) = [tex]\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.[/tex]

The required average temperature of the last summer is given as 22.10 °C.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Let the temperature of last summer's average be x insert,

According to the question,
21 = x - 5%x
x = 21 / 0.95
x = 22.10 °C

Thus, the required average temperature of the last summer is given as 22.10 °C.

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That m is odd, then the integers between 1 and m − 1 equals 2−1 mod m it must be k=1 and n = 1+m2.

Given an integer m, two integers a and b are congruent modulo m if

m| (a − b).

We write a ≡ b (mod m).

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

I will also sometimes say equivalent modulo m. Notation note: we are using that "mod" symbol in two different ways.

Let n be the inverse of 2( mod m)

Where 1<n<m−1

2n≡1 ( mod m)

⇒ 2n=1+mk

Since m is odd then m=2l+1

⇒ 2n=1+(2l+1)k

Then solve for n(mod m) as that would put it within 1<n<m−1.

As an aside, we only care for 1≤n≤m−1, we don't care about strict inequalities. Indeed, if m=3 then you'd have a problem as there aren't even any integers strictly between 1 and 3−1

Supposing that m = [tex]2l+1[/tex] then [tex]2*(l+1)[/tex] = [tex]2l + 2[/tex] = m+1

We want integer n=1+mk2 between 1 and m−1.

Since m is odd, we need k to be odd, in order for 1+mk to be divisible by 2 so n is an integer.

If k≥3 then 1+mk2>m−1.

If k≤−1 then 1+mk2<1.

So it must be k=1 and n = 1+m2.

Therefore,

That m is odd, then the integers between 1 and m − 1 equals 2−1 mod m it must be k=1 and n = 1+m2.

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Answer:

7

Step-by-step explanation:

If the bell tolls every 30mins on the hour and at half past the hour, then the bell will toll at 12 noon, 12:30pm, 1pm, 1:30pm, 2pm, 2:30pm and 3pm which is 7 times.

i hope is help

The sign of the derivative of a function at a certain point indicates the nature of the function's change at that point.

If the derivative is positive at a point, the function is increasing at that point. If the derivative is negative at a point, the function is decreasing at that point. If the derivative is undefined at a point, there may be a sharp turn or a discontinuity at that point.

Here's a more specific method to determine the sign of the derivative at a point:

It's also possible to determine the sign of the derivative by analyzing the graph of the function, or by using calculus theorems such as the First Derivative Test or the Second Derivative Test.

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