6.Find by suitable rearrangement
a)4x2984x250
b) 495+114+205
factor of 13965

Step-by-step explanation:

5x-16 = 3 (10+x)

=> x= 23

Answer:

Step-by-step explanation:

4.8 x 10^3   heartbeats/day

Answer: A humans heart average per minute is 80 then you got one hour 60 x 80 equals 4800

which would be 4.8x 10 over 3 which is your answer

Step-by-step explanation:

1KM = 1000metres

3KM =3000metres

Surface area of A = 50 square inches, S.A of B = 120 square inches, S.A of C = 60 square inches, S.A of D = 50 square inches, S.A of E = 60 square inches, S.A of F = 120 inches.

S.A of the box = 460 square inches.

A cuboid is a three dimensional solid shape made of 6 rectangles.

Analysis:

surface area of A = surface area of D which is the smallest from the diagram = 5 x 10 = 50 square inches

surface area of C = surface area of E = the second largest = 5 x 12 = 60 square inches

surface area of B = surface area of F = 10 x 12 = 120 square inches

surface area of shape = 2( 50 + 60 = 120) = 2(230) = 460 square inches.

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The function is decreasing on the interval (–3, ∞). Therefore, the correct option is B.

A linear function can be represented by a line. The standard form for this equation is: ax+b where,

a= the slope

b= the constant term that represents the y-intercept.

The domain of a function is the set of input values for which the function is real and defined.

Here, the function is decreasing on the interval (–3, ∞).

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Hello,

2/9 - 1/9 = (2 - 1)/9 = 1/9

Answer:

x = 25

Step-by-step explanation:

The mistake here is the squaring. When you square one side, you have to do the same on the other side:

[tex]\sqrt{3x+6}[/tex] = 9

[tex](\sqrt{3x+6}) ^{2}[/tex] = [tex]9^{2}[/tex]

3x + 6 = 81

3x = 75

x = 25

[tex]\huge\boxed{x=25}[/tex]

The mistake is in Step 1. The solver should have also squared [tex]9[/tex] when squaring the other side of the equation.

[tex]\begin{aligned}\sqrt{3x+6}&=9\\(\sqrt{3x+6})^2&=9^2\\3x+6&=81\\3x+6-6&=81-6\\3x&=75\\\frac{3x}{3}&=\frac{75}{3}\\x&=25\end{aligned}[/tex]

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is

[tex](\sqrt{2},\sqrt{-2}  )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]

We have given that,

f(x) = 2x^2 + x + 4

x                          g(x)      

-2                               1      

  -1                              3        

  0                              5      

  1                              7

  2                              9

A polynomial function is a relation where a dependent variable is equal to a  polynomial expression.

A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.

The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

The quadratic function is given to us:f(x) = 2x^2 + x + 4.

We need to determine the linear equation g(x).

Since it's a linear equation we use the two-point method to determine the equation.

y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(-2) =1, g(-1) = 3

g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,

g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,

g(x) = x - 1 + 1 = x

∴ g(x) = x , is the linear function g(x)

We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2  - 4 = 02(x^2-2)=0x^2-2=0[tex]x^2-\sqrt{2}=0[/tex][tex](x-\sqrt{2}) (x+\sqrt{2})=0[/tex][tex](x-\sqrt{2})=0 \\x=\sqrt{2}  or x=-\sqrt{2}[/tex]g(-1) = 3(from the table)[tex]g(\sqrt{2})=\sqrt{2}  \ and \ g(\sqrt{-2}) =-\sqrt{2}[/tex][tex]f(\sqrt{2}) = 2(\sqrt{2} )^2 + (\sqrt{2} ) + 3\\=2(2)+\sqrt{2} +3\\=7+\sqrt{2}[/tex][tex]g(-\sqrt{2} )= 2(\sqrt{-2} )^2 + (\sqrt{-2} ) + 3\\=2(2)+\sqrt{-2} +3\\=7+\sqrt{-2}[/tex]

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is [tex](\sqrt{2},\sqrt{-2}  )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]

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Answer: x=1

Step-by-step explanation:

1/2+3/2=2^x

4/2=2^x

2=2^x

x=1

The expression |x - y| without using absolute value notation is x - y

The expression is given as:

|x - y|

Also, we have:

x > y

This means that:

|x - y| > 0

Remove the absolute notation

x - y

Hence, the expression |x - y| without using absolute value notation is x - y

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Answer:

[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]

Step-by-step explanation:

The given equation:

[tex]\cos(x)=2\cos^2(x)-1[/tex]

Let [tex]\cos(x)[/tex] be [tex]y[/tex]:

[tex]y=2y^2-1[/tex]

Rewrite as:

[tex]2y^2-y-1=0[/tex]

After solving quadratic equation, the solutions are:

[tex]y=1~~~~y=-\frac{1}{2}[/tex]

Substitute back [tex]\cos(x)[/tex], it follows:

[tex]\cos(x)=1~~~~\cos(x)=-\frac12[/tex]

For the first equation, the solution is [tex]x=0[/tex] and [tex]x=2\pi[/tex].

For the second equation, general solution is:

[tex]x=\frac{2\pi }{3}+2\pi n,\:x=\frac{4\pi }{3}+2\pi n[/tex]

But for the given interval, we must substitute n=0 into the equations so that the values of x must be within interval. Therefore:

[tex]x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}[/tex]

So, the answers are:

[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]

Answer:

[tex]y\ne-5[/tex]

Step-by-step explanation:

So you have the equation:

  [tex]x=\frac{10}{5+y}[/tex]. As you may know, you cannot divide by 0, so y has to be restricted in a way that the denominator is never equal to 0. So to find when y makes the denominator 0, simply set the denominator equal to 0, and solve for y. This gives you the equation: 5+y = 0, y=-5. So the y value CANNOT be equal to -5. Because it makes the denominator 0. so [tex]y\ne-5[/tex] would be the restriction.

By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.

The figure presents a circle, the arc of a circle (s), in inches, is equal to the product of the central angle (θ), in radians, and the radius (r), in inches. Please notice that a complete circle has a central angle of 360°.

If we know that θ = 52π/180 and r = 6 inches, then the length of the arc CD is:

s = [(360π/180) - (52π/180)] · (6 in)

s ≈ 32.254 in

By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.

The statement has typing mistakes, correct form is shown below:

Find the length of the arc EF shown in red below. Show all the work.

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The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x). The correct option is C.

A straight line equation is represented by y = mx+c, where m is the slope and c is the y-intercept.

m is given by (y₂-y₁)/(x₂-x₁)

From the graph , the y-intercept is 4 and the two points on the line are    ( 0,4) and ( 1,1).

m = -3

c =4

The equation of the function g(x) is g(x) = -3x+4

The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x).

Therefore, the correct option is C.

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Step-by-step explanation:

the equation is

2x² + 3x - 8 = 0

the generic solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 2

b = 3

c = -8

x = (-3 ± sqrt(9 - 4×2×-8))/(2×2) =

= (-3 ± sqrt(9 + 64))/4 = (-3 ± sqrt(73))/4

x1 = (-3 + sqrt(73))/4 = (-3 + 8.544003745)/4 =

= 1.386000936... ≈ 1.39

x2 = (-3 - sqrt(73))/4

but that would negative, and therefore not a wanted solution.

x ≈ 1.39

is the targeted solution.

Answer:

y < 3x + 2

Step-by-step explanation:

We will be solving this in slope-intercept form, which is a form that gives us the slope and the y-intercept of the graph explicitly:

[tex]y=mx+b[/tex], m is the slope and b is the y-intercept

We are given that everything to the left of the resulting line is shaded, so we know that the inequality sign will be < (less than). That already eliminates the second and fourth options. We also know the y-intercept, or the point where the graph crosses the y-axis and x is 0. because it is given to us (2, which comes from the point (0,2)). To figure out the slope, we can use the formula since we are given two points [(-3, -7) and (0, 2)] the line passes through. The formula, which is mapped out below, tells us that the slope is just the difference in rise (vertical movement) divided by the difference in run (horizontal movement).

[tex]m=\frac{-7-2}{-3-0} =\frac{-9}{-3} =3[/tex]

Now we have all the information we need to find the inequality. The slope is 3, the y-intercept is 2, and the sign is <. The first inequality fits these criteria, meaning the correct linear inequality is y < 3x + 2

Answer:

cylinder to cone = 3:1

sphere to cylinder = 4r:3h

cone to sphere = h:4r

hemisphere to cylinder = 2r:3h

Step-by-step explanation:

Some habits that you can engage in that would increase your risk of being victim of fraud or identity theft are:

You can be less at risk of fraud or identity theft if you:

When you use the same password for various accounts, all those accounts are at risk if the password is stolen. So using multiple passwords is best.

You should also regularly monitor your credit card statements and bank reports to check for unfamiliar expenses which can be flagged immediately.

Also update your apps regularly as they come with security patches to protect your data. Avoid sharing too much information on social media as these can be used to predict your passwords.

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Answer:

a = 8.1

Step-by-step explanation:

Use the cosine rule:

[tex]a = \sqrt{b^2 + c^2 -2 bc \space\ cosA }[/tex]

Substituting the values:

[tex]a = \sqrt{10^2 + 12^2 -2(10)(12) \space\ cos 42 \textdegree\ }[/tex]

⇒ [tex]a = \sqrt{4 \space\ cos 42\textdegree\ }[/tex]

⇒ [tex]a = 8.1[/tex]

The expected value of the discrete distribution, if you have to pay $.50 to pick one package at random, is of -$0.08.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For this problem, considering the cost of $0.5, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 0.2 x 0.24 - 0.3 x 0.1 - 0.2 x 0.46 = -$0.08.

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Step-by-step explanation:

To reflect a function about the vertical axis, just negate the variable.

For example, if we want to reflect this function

[tex] y = log(x) [/tex]

about the y axis or vertical axis, we just make the x negative

[tex]y = log( - x) [/tex]

Another example,

[tex]y = |x| [/tex]

To reflect about y axis or vertical axis,

[tex]y = | - x| [/tex]

So here l,the answer with negative variables are function that are reflected about the y axis.

The options are the first and the fifth option.

The graphed rational function is:

[tex]f(x)= \frac{6}{x + 2}[/tex]

Here we can see that we have a rational function of the form:

[tex]f(x) = \frac{q(x)}{p(x)}[/tex]

Now we notice two things, as x increases, we have a horizontal asymptote that tends to zero.

Then q(x) is a constant, let's say:

q(x) = k

We also can see that we have a vertical asymptote at x = -2, then:

p(x) = (x + 2)

So the rational function is:

[tex]f(x) = \frac{K}{x + 2}[/tex]

Now, notice that when x = 0, the curve intercepts the y-axis at y = 3, then if we evaluate the function in x = 0 we must get:

[tex]f(0) = 3 = \frac{K}{0 + 2} = \frac{K}{ 2} \\\\3*2 = K = 6[/tex]

Then the rational function is:

[tex]f(x)= \frac{6}{x + 2}[/tex]

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Answer:

Step-by-step explanation:

14+(−7)+7

Now −7 is the idea or the construct that is the complete opposite of 7, when it comes to additive regions. So, they would cancel out.

And we are left with

14.

In this case using the elimination method is actually easier, but the question asks you to use substitution method so....

2x+y= -10

3x-y=0

1st equation: It is better to isolate 2x on both sides because the y is going to be positive no matter what, 2x+y=-10 => y=-2x-10

If you isolated 3x for the 2nd equation, the y will be negative, and you have to divide the whole equation by -1 to make it positive

Now we got y=-2x-10, lets substitute it in the 2nd equation and solve for x:

3x-(-2x-10) = 0

5x+10=0

5x=-10

x=-2

Now lets solve for y:

3(-2)-y=0

-6-y=0

y=-6

Lets see if the same is applicable for 1st equation

2(-2)+(-6)=-10

-10=-10

Yess!!

(-2,-6) is the solution

The answer to the question is explained at the beginning

Hope it helps!

Answer:

[tex]y = - \frac{3}{4}x + 3[/tex]

Step-by-step explanation:

the standard form of any straight line is:

y = m × x + c

where: y is the y value of the point

x is the x value of the point

m is the gradient/slope

SOLUTION

[tex]y = mx + c \\ 6 = - \frac{3}{4} ( - 4) + c \\ c = 3[/tex]

Answer:

c or b

Step-by-step explanation:

Answer:

Answer:B

Step-by-step explanation:

I did the test and got it right the person above help thx

Step-by-step explanation:

Since we have a vertical major axis, our ellipse is vertical.

The equation of a vertical ellipse is

[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]

where

(h,k) is the center

a is the semi major axis,

b is the semi minor axis

First, let plug in our center

[tex] \frac{(y + 3) {}^{2} }{ {a}^{2} } + \frac{(x + 2) {}^{2} }{ {b}^{2} } = 1[/tex]

Semi means half, so

a is half of 14 which is 7

B is half of 8, which is 4.

[tex] \frac{(y + 3) {}^{2} }{49} + \frac{(x + 2) {}^{2} }{16} = 1[/tex]

tan is 15/8

Since cos = adjacent/ hypotenuse

Adjacent = 8

Hypotenuse = 17

Let's find opposite

Using the Pythagoras theorem

Opposite ^2 = Hypotenuse^2 - adjacent^2

Opposite = [tex]\sqrt{17^2 - 8^2}[/tex]

Opposite = [tex]\sqrt{289 - 64}[/tex]

Opposite = [tex]\sqrt{225}[/tex]

Opposite = 15

Tan = opposite/ adjacent

Tan = 15/ 8

Thus, tan is 15/8

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