24. Find the slope and y-intercept of the line.
Y=7/5x-3

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]

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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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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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]

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

1KM = 1000metres

3KM =3000metres

By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].

Trigonometric functions are trascendent functions, these are, that cannot be described algebraically. Herein we must utilize trigonometric formulae to calculate the exact value of a trigonometric function:

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{2+\sqrt{3}}{4} }[/tex]

[tex]\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].

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The expression square root of 25/49 can be given as 5/7

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

Inequality is the non equal comparison of two or more numbers and variables.

The solution to the system of inequalities x – 4y < 4 and y < x + 1 is shown in the graph.

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Answer:

its c

Step-by-step explanation:

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:

Answer: C. Y = 5x + 5

Step-by-step explanation:

    We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. See attached for a visual.

    First, we will find our slope. We will use [tex]\frac{rise}{run}[/tex] for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.

     -> Slope = 5

   Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.

     -> Y-intercept = 5

   Lastly, we will write our equation and decide on an answer.

y = mx + b

y = (5)x + (5)

Y = 5x + 5

             C. Y = 5x + 5

Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

We know that the sum of angles of a triangle is always. In ΔXYZ,

[tex]\angle A + \angle B + \angle C=180^0[/tex]

[tex]35^0+\angle Y+47^0=180^0[/tex]

[tex]\angle y=98^0[/tex]

In both triangles, it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A=\angle X=35^0[/tex]and.[tex]\angle B = \angle Y =98^0[/tex]

By the AAS rule of congruence, ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having the same angle and rotate the triangle to align the sides and angles.

Since vertex X and vertex A have the same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.

Hence the correct option is d.

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Answer:

D: Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

Step-by-step explanation:

edge 2022

Answer:

(f + g)(x) = x² + 4x - 4  

Step-by-step explanation:

The statement (f + g)(x) is the same as f(x) + g(x). In other words, the question simply wants you to add the two functions together.

f(x) = 4x + 1

g(x) = x² - 5

(f + g)(x)                                  <----- Original statement

f(x) + g(x)                                <----- Rewrite

(4x + 1) + (x² - 5)                     <----- Substitute the equations in f(x) and g(x)

4x + x² - 4                              <----- Add 1 and -5

x² + 4x - 4                              <----- Rearrange the terms

Answer:

x=−9 and y=8

Step-by-step explanation:

Let's solve your system by elimination.

2x+3y=6;4x−y=−44

Multiply the first equation by -2,and multiply the second equation by 1.

−2(2x+3y=6)

1(4x−y=−44)

Becomes:

−4x−6y=−12

4x−y=−44

Add these equations to eliminate x:

−7y=−56

Then solve−7y=−56for y:

−7y=−56

-7y/-7 = = -56/-7

(Divide both sides by -7)

y=8

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

2x+3y=6

Substitute8 for y in 2x+3y=6:

2x+(3)(8)=6

2x+24=6(Simplify both sides of the equation)

2x+24+−24=6+−24(Add -24 to both sides)

2x=−18

2x/2 = -18/2 (Divide both sides by 2)

x=−9

Answer:

x=−9 and y=8

Answer:

x = -9

y = 8

Step-by-step explanation:

(using substitution)

4x-y = -44

4x + 44 = y

substitute (4x+44) as y in the other equation

2x + 3(4x+44) = 6

2x+12x+132 = 6

14x = -126

x = -9

then plug -9 as x into one of the equations to find y

4(-9) - y = -44

-36-y=-44

-y=-8

y=8

then check the answer by plugging in the values of x and y (-9 and 8) for x and y in one of the equations

4(-9) - (8) = -44

you get: -44 = -44, which is true, so the x and y values are correct

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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The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

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

Step 1:

ax² + bx + c = 0

Step 2:

ax² + bx = -c

Step 3:

x² + (b/a)x = -c/a

Step 4:

x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

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Step-by-step explanation:

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:

cylinder to cone = 3:1

sphere to cylinder = 4r:3h

cone to sphere = h:4r

hemisphere to cylinder = 2r:3h

Step-by-step explanation:

Hello,

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

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.

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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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.

Answer: x=1

Step-by-step explanation:

1/2+3/2=2^x

4/2=2^x

2=2^x

x=1

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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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]

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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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]