What is a correct equation for the line passing through the point (-2,1) and having slope m=1/2

Answer:

[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex]

Step-by-step explanation:

First step is to arrange so it is in the form [tex]ax^2+bx+c=0[/tex].

We have [tex]5x=6x^2-3[/tex].

Add we really need to do is subtract 5x on both sides:

[tex]0=6x^2-5x-3[/tex].

Now let's compare [tex]6x^2-5x-3[/tex] to [tex]ax^2+bx+c[/tex].

We have [tex]a=6,b=-5,c=-3[/tex].

The quadratic formula is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

I like to break this into parts:

Part 1:  Find [tex]-b[/tex].

Part 2: Find [tex]b^2-4ac[/tex].

Part 3: Find [tex]2a[/tex].

Answering the parts:

Part 1: [tex]-b=5[/tex] since [tex]b=-5[/tex].

Part 2: [tex]b^2-4ac=(-5)^2-4(6)(-3)=25-24(-3)=25+72=97[/tex].

Part 3: [tex]2a=2(6)=12[/tex].

Now our formula in terms of my parts looks like this:

[tex]x=\frac{\text{Part 1} \pm \sqrt{Part 2}}{Part 3}[/tex]

Our formula with my parts evaluated looks like this:

[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex].

Answer:

19 t-shirts

Step-by-step explanation:

x= number of t-shirts

6x+54=168; now subtract 54 from both sides of the equation

6x=114; now divide both sides by 6 to isolate the "x"

x=19

Answer:

x > -3

Step-by-step explanation:

We are given the following inequality that we are to solve:

[tex]3(x+2)>x[/tex]

Applying the distributive property of multiplication on the left side of the inequality to get:

[tex] 3 x + 6 > x [/tex]

Rearranging the inequality:

[tex] 3 x - x > - 6 [/tex]

[tex] 2 x > - 6 [/tex]

[tex] x > \frac { - 6 } { 2 } [/tex]

x > -3

Answer:

[tex]\large\boxed{x>-3\to\{x\ |\ x>-3\}\to x\in(-3,\ \infty)}[/tex]

Step-by-step explanation:

[tex]3(x+2)>x\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(2)>x\\\\3x+6>x\qquad\text{subtract 6 from both sides}\\\\3x+6-6>x-6\\\\3x>x-6\qquad\text{subtract x from both sides}\\\\3x-x>x-x-6\\\\2x>-6\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}>\dfrac{-6}{2}\\\\x>-3[/tex]

Answer:

y = 3

Step-by-step explanation:

The y-coordinate of all points on the graph is 3.

The equation is y = 3

Answer:

y = 3

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

Where c is the value of the y- coordinates the line passes through.

In this case the line passes through points with a y- coordinate of 3, hence

Equation of horizontal line is y = 3

Answer:

So the other x-intercept we are looking for is (2.29 , 0).

Step-by-step explanation:

The equation for a parabola in vertex form is

[tex]y=a(x-h)^2+k[/tex] where (h,k) is the vertex.

So we are given (h,k)=(1,5) so let's plug that in.  This gives us the following equation for our parabola:

[tex]y=a(x-1)^2+5[/tex].

Now we need to find [tex]a[/tex]. Let's find [tex]a[/tex] by using another point (x,y) given.  We are given that (0,2) is on our parabola. So when x is 0, y is 2.

This gives us the equation:

[tex]2=a(0-1)^2+5[/tex]

[tex]2=a(-1)^2+5[/tex]

[tex]2=a(1)+5[/tex]

[tex]2=a+5[/tex]

[tex]2-5=a[/tex]

[tex]-3=a[/tex]

So our parabola in vertex form looks like this:

[tex]y=-3(x-1)^2+5[/tex]

Now we are asked to find the x-intercepts.

You can find the x-intercepts by setting y equal to 0 and solving for x.

So let's do that:

[tex]0=-3(x-1)^2+5[/tex]

Subtract 5 on both sides:

[tex]-5=-3(x-1)^2[/tex]

Divide both sides by -3:

[tex]\frac{5}{3}=(x-1)^2[/tex]

Take the square root of both sides:

[tex]\pm \sqrt{\frac{5}{3}}=x-1[/tex]

Add 1 on both sides:

[tex]\pm \sqrt{\frac{5}{3}}+1=x[/tex]

So the two solutions in exact form are

[tex]x=\sqrt{\frac{5}{3}}+1 \text{ or } -\sqrt{\frac{5}{3}}+1[/tex]

Putting both into calculator (separately) gives:

[tex]x \approx 2.29 \text{ or } -0.29[/tex]

So the other x-intercept we are looking for is (2.29 , 0).

Answer:

x=8

Step-by-step explanation:

(x+4) = (x+8)

------     -------

3            4

Multiply each side by 12 to get rid of the fraction

      (x+4) = (x+8)

12 *------     ------- *12

       3            4

4*(x+4) = (x+8)*3

Distribute

​4x+16 = 3x+24

Subtract 3x from each side

4x-3x+16 = 3x-3x+24

x+16 = 24

Subtract 16 from each side

x+16-16 = 24-16

x = 8

Answer:

Step-by-step explanation:

Convert the given equation to the form y = mx + b:

[tex]-x+2y=11[/tex]          add x to both sides

[tex]2y=x+11[/tex]          divide both sides by 2

[tex]y=\dfrac{1}{2}x+\dfrac{11}{2}[/tex]

It's a linear function.

We need only two points to plot the graph. Select any two x values, insert into the equation and calculate y values.

for x = 1

[tex]y=\dfrac{1}{2}(1)+\dfrac{11}{2}=\dfrac{1}{2}+\dfrac{11}{2}=\dfrac{12}{2}=6\to(1,\ 6)[/tex]

for x = -5

[tex]y=\dfrac{1}{2}(-5)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to(-5,\ 3)[/tex]

Answer:

22,338 is the smallest number that is divisible by both 306 and 657. In other words, 22,338 is the least common multiple of 306 and 657.

Step-by-step explanation:

The question is asking for the smallest number that is divisible by 306 and 657. That number in question is also known as the least common multiple of 306 and 657.

Neither 306 nor 657 is prime; the two numbers themselves are made of prime factors. For the number in question to be divisible by both 306 and 657, it needs to include the factors of both 306 and 657. However, for this number to be as small as possible, it needs to contain only the necessary factors and nothing else.

To find the factors required for this number, start by finding all the prime factors of the two divisors.

[tex]\begin{aligned}306&=2 \times 153\\ &= 2\times 3 \times 51\\ &= 2 \times 3 \times 3 \times 17 \\ &= 2 \times 3^{2} \times 17\end{aligned}[/tex].

In other words, the prime factors of 306 are:

Similarly,

[tex]\begin{aligned}657&= 3 \times 219\\ & = 3 \times 3 \times 73\\&=3^{2}\times 73 \end{aligned}[/tex].

The prime factors of 657 are:

[tex]\begin{array}{l||l|l||l}\text{Factor}& 306 & 657 & \text{New Number}\\\cline{1-4} \\[-1.0em]2 &\text{1 Occurrence}& \text{0 Occurrence} & \text{1 Occurrence}\\3 &\text{2 Occurrence} & \text{2 Occurrence}& \text{2 Occurrence}\\ 17 &\text{1 Occurrence}& \text{0 Occurrence} & \text{1 Occurrence}\\73 &\text{0 Occurrence}& \text{1 Occurrence} & \text{1 Occurrence}\end{array}[/tex].

The number in question shall contain at least

As a result, that number shall be equal to [tex]2 \times 3^{2}\times 17 \times 73 = 22338[/tex].

Answer:

[tex]x \geq 0.5[/tex]

Step-by-step explanation:

Im assuming you want to know the value of x.

Let's use algebraic rules and solve for the intervals (values) of x. Shown below:

[tex]3.8-1.4x \geq 5.6-5x\\-1.4x+5x \geq 5.6 - 3.8\\3.6x \geq 1.8\\x \geq \frac{1.8}{3.6}\\x \geq 0.5[/tex]

Hence, x is greater than or equal to 0.5

Answer: By phaythagores I think you mean pythagorean.

The Pythagorean theorem states that a^2+b^2=c^2. In a right angled triangle the square of the long side is equal to the sum of the squares of the other two sides.

Step-by-step explanation: Pythagoras was a greek philosopher and mathematician. He was often described as one of the purest mathematicians of his time. He had many followers and his teachings are still renowned today.The mystical Pythagoras was so excited by this discovery that he became convinced that the whole universe was based on numbers, and that the planets and stars moved according to mathematical equations!

Answer:

the madnes

Step-by-step explanation:

Answer:

140°

Step-by-step explanation:

<3 = 40 because they are vertical angles

<3 +<4 = 180 because they are same side interior angles

40 + <4 = 180

Subtract 40 from each side

40-40 + <4 = 180-40

<4 = 140

Answer:

x = 3 and x = 7

Step-by-step explanation:

Equate the product of the factors to zero, that is

(x - 3)(x - 7) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 7 = 0 ⇒ x = 7

Final answer:

To find the values of x that make a polynomial equal to zero, set each factor equal to zero and solve for x. The values of x that would make the polynomial equal to zero are x = 3, and x = 7.

Explanation:

To find the values of x that make a polynomial equal to zero, you need to set each factor equal to zero and solve for x.

Set x-3=0 and solve for x to get x=3.

Set x-7=0 and solve for x to get x=7.

Therefore, the values of x that would make the polynomial equal to zero are x = 3 and x = 7.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\bold{{32 = [4(2 + 5) - 2\times6]}}[/tex]

[tex]\text{[4(2 + 5) - 2} \ \times \ 6][/tex]

[tex]\text{Do PEMDAS}\downarrow[/tex]

[tex]\huge\text{Parentheses}\\\huge\text{Exponents}\\\huge\text{Multiplication}[/tex] [tex]\huge\text{Division}\\\huge\text{Addition}\\\huge\text{Substraction}[/tex]

[tex]\huge\text{First, we do PARENTHESES}[/tex]

[tex]\huge\text{2 + 5 which equals 7}[/tex]

[tex]\huge\text{4(7) - 2(6)}[/tex]

[tex]\huge\text{Next step is multiplication since we don't have}[/tex] [tex]\huge\text{exponents}[/tex]

[tex]\huge\text{4(7) = 28}\\\\\huge{\text{2(6) = 12 }[/tex]

[tex]\huge\text{Thirdly, we have to do subtraction since}[/tex] [tex]\huge\text{we don't have have any division or addition}[/tex]

[tex]\huge\text{28 - 12 = 16}[/tex]

[tex]\boxed{\boxed{\huge\bf{Answer: 32\neq16\ so,\ it \ is \ FALSE}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

13/20

Step-by-step explanation:

This is actually pretty simple. I had trouble with this for the longest time but it makes sense to me now. A number that is a percent is equal to that number over 100.

65%=65/100

Then all you have to do is simplify! (yaaay)

65/100=13/20

If you need anymore help with this or anything else just let me know!

Write 65% as a fraction in simplest form.

13/20

65%=65/100

65/100=13/20

Answer:

See below.

Step-by-step explanation:

It decreases in the interval where x  > -2.

In interval notation this is (-2, ∞).

The quadratic function decreasing at x>-2.

A quadratic polynomial is a polynomial of degree two in one or more variables.

Given is a graph,

It decreases in the interval where x  > -2.

In interval notation, this is (-2, ∞).

Hence, the quadratic function decreasing at x>-2.

For more references on a quadratic function, click;

https://brainly.com/question/18958913

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Answer:

D.

Step-by-step explanation:

The last option, 1.2, cannot represent the probability of an event happening since it is more than 100% (120%). And event cannot have a higher probability of happening than "happening".

A. 0.33 is a valid response, since it represents 33%.

B. 56% is also a valid response.

C. 7/8 is also a valid response since it represents 0,875 or 87,5%.

Hope it helped,

BiologiaMagister

D. 1.2

Hope i Helped ❤

Answer:

8*6 + 12*h ≥144

Step-by-step explanation:

8 dollars at the movie theater

12 dollars at the restaurant

scheduled 6 hours at the movie theater

need to make at least 144 dollars

The money he makes is the hours times the rate

rate * hours at movie theater + rate *hours at restaurant

This must be greater than or equal to 144

Let h be the hours at the movie theater

8*6 + 12*h ≥144

Answer:

mass

Step-by-step explanation:

From the universal law of gravity

[tex]F=G\frac{Mm}{r^2}[/tex]

Where

G = Gravitational constant = 6.674×10⁻¹¹ m³/kg⋅s²

M = Mass of Earth = 5.972×10²⁴ kg

r = Radius of Earth = 6.371×10⁶ m

[tex]\\\Rightarrow ma=G\frac{Mm}{r^2}\\\Rightarrow a=G\frac{M}{r^2}\\\Rightarrow a=6.674\times 10^{-11}\frac{5.972\times 10^{24}}{(6.371\times 10^6)^2}\\\Rightarrow a=9.81\ m/s^2[/tex]

So the force of gravity acting on the mass of an object is

W = m×9.81

∴ Weight of an object is the product of mass and acceleration due to gravity

Answer:

D:456.2 units²

Step-by-step explanation:

Step 1: Area of all 4 sides of cuboid

Area of rectangle = 4 x length x breadth

Area of rectangle = 4 x 10 x 5

Area of rectangle = 200

Step 2: Calculate bottom of cuboid

Area = length x breadth

Area = 10 x 10

Area = 100

Step 3: Calculate slant height of pyramid

c² = a² + b²

c² is hypotenuse

a² is the base which is half of w (10/2 = 5)

b² is y which is 6

c² = a² + b²

c² = 5² + 6²

c = √61

Step 4: Calculate area of one face of the pyramid

Area of triangle = 1/2 x base x height

Area of triangle = 1/2 x 10 x √61

Area of triangle = 5√61

Step 5: Calculate areas of all 4 faces of the pyramid

4 x 5√61 = 20√61

Step 6: Calculate the total surface area

Total surface area = 200 + 100 + 20√61

Total surface area = 456.2

The surface area of the figure is 456.2 units²

Option D is correct.

!!

Answer:

22/9

Step-by-step explanation:

The slope of a line can be found by using the slope formula

[tex]\frac{y_2-y_1}{x_2-x_1} \text{ where we have points } (x_1,y_1) \text{ and } (x_2,y_2) \text{ on the line }[/tex].

Or what I like to do is line up the points and subtract vertically, then put 2nd difference over 1st difference. Like so:

 ( 10  , 25)

- (  1  ,    3)

----------------

9         22

So the slope is 22/9.

You could have done it the other way too. That is:

 (1  ,  3)

-(10 , 25)

------------

-9    -22

So the slope is -22/-9 or just 22/9.

Answer:

The slope of a trend line is:

[tex]m=\frac{22}{9}[/tex]

Step-by-step explanation:

The slope m of a line is calculated using the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For any pair of points [tex](x_1, y_1),\ (x_2, y_2)[/tex] that belong to the line

In this case the points are (1,3) and (10,25)

Therefore the slope is:

[tex]m=\frac{25-3}{10-1}[/tex]

[tex]m=\frac{22}{9}[/tex]

Answer:

Angle of elevation of the highest point of the mountain is 77°

Step-by-step explanation:

Lynne is hiking. When she stands at the base of the mountain, the horizontal distance between Lynne and the highest point of the mountain is 588 feet.

Elevation of the mountain is 2610 feet.

We have to calculate the angle of elevation ∠C.

tanC = [tex]\frac{2610}{588}[/tex]

tanC = 4.439

C = [tex]tan^{-1}(4.439)[/tex]

C = 77.30 ≈ 77°

Therefore, angle of elevation of the mountain is 77°

Answer:

The median is 11.

Step-by-step explanation:

First arrange the data in ascending order:

4, 5, 5, 8, 9 , 10, 10, 10, 12, 14, 15, 16, 16, 18, 19, 21

There are 16 numbers so the median is the mean of the middle 2 numbers in the list. That is the  mean of the 8th and ninth number.

Median = 10 + 12 / 2

= 11.

Answer:

answer is 12 ape x

Step-by-step explanation:

i am not sure why tho to be honest if a verified answer is 11

The full length of one line times the length of the line outside the circle is equal the the other line.

(7+x)*7 = (13 +8) * 8

Simplify:

7x +49 = 21 * 8

7x +49 = 168

Subtract 49 from each side:

7x = 119

Divide both sides by 7:

x = 17

The answer is B. 17

The value of x for the given circle will be 17 so option (B) will be correct.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.

By theorem in circle

( 13 + 8) × 8 = ( x + 7) × 7

21 × 8 =  ( x + 7) × 7

x + 7 = 3 × 8

x = 24 - 7

x = 17

Hence, The value of x for the given circle will be 17.

To learn more about the circle,

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Answer:

[tex]A=76.44\ units^{2}[/tex]

Step-by-step explanation:

To find the approximate area of the circle, calculate the area of one sector and then multiply by 16

Remember that

The area of a triangle (one sector) is equal to

[tex]A=\frac{1}{2}(b)(h)[/tex]

therefore

The approximate area of the circle is equal to

[tex]A=(16)\frac{1}{2}(1.95)(4.9)[/tex]

[tex]A=76.44\ units^{2}[/tex]

Answer:

D.76.44 square units

Step-by-step explanation:

We are given that

Base of one sector=b=1.95 units

Height of sector=h=4.9 units

Total number of sectors=16

Area of one sector is equal to area of triangle (approximately)

Area of sector=[tex]\frac{1}{2}bh[/tex]

Using the formula

Area of one sector=[tex]\frac{1}{2}(1.95)(4.9)=4.7775[/tex] square units

Area of circle A=[tex]16\times [/tex]area of sector

Area of circle A=[tex]16\times 4.7775=76.44[/tex] square units

Hence,option D is true.

[tex]x^3-3x^2+81x-243=\\x^2(x-3)+81(x-3)=\\(x^2+81)(x-3)=\\(x-3)(x-9i)(x+9i)[/tex]

Answer:

y = - x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x + 2 ← is in slope- intercept form

with slope m = 1

Given a line with slope m then the slope of a perpendicular line is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1, hence

y = - x + c ← is the partial equation of the perpendicular line

To find c substitute (4, - 1) into the partial equation

- 1 = - 4 + c ⇒ c = - 1 + 4 = 3

y = - x + 3 ← equation of perpendicular line

Solutions are denoted by index. Most of the equations you listed has 2 solutions.

Number one cannot be factored using whole numbers.

Number two.

[tex]

4x^2+25=0\Longrightarrow(2x+5)(2x-5)=0 \\

x_1\Longleftrightarrow\boxed{2x+5=0\Longrightarrow x=-\dfrac{5}{2}} \\

x_2\Longleftrightarrow\boxed{2x-5=0\Longrightarrow x=\dfrac{5}{2}}

[/tex]

Number three.

[tex]

x^2+121=0\Longrightarrow(x+11)(x-11)=0 \\

x_1\Longleftrightarrow\boxed{x+11=0\Longrightarrow x=-11} \\

x_2\Longleftrightarrow\boxed{x-11=0\Longrightarrow x=11}

[/tex]

Hope this helps.

Check the picture for the correct answer:                                          

Answer:

The correct answer is C. 2.

Step-by-step explanation:

To solve this problem, we should begin with the second step and work backwards in order to find the unknown value.  If given the equation -15x + 30 = 25, we should factor out a -15 to simplify.  This method is shown below.

-15x + 30 = 25

-15(x-2) = 25

We know this is correct because if we redistribute the -15 through the parentheses using the distributive property, we would get our original equation again.  In other words, this answer is confirmed by the fact that -15 * -2 equals positive 30.

However, we need to look closely at the question that is asked.  The box that we must fill in is already preceded by a negative sign, thus the correct answer is C. 2.

We can check our work by replacing the box with the number 2, getting -15(x-2) + 30 = 25, which was the equation we got earlier.

Hope this helps!

Answer:



Thank Me later lol

Answer:

D. 5

Step-by-step explanation:

AC = AB + BC

Substituting what we know

3x+20 = 12 + 5x-2

Combining like terms

3x+20 = 10 +5x

Subtract 3x from each side

3x+20-3x = 10 +5x-3x

20 = 10+2x

Subtract 10 from each side

20-10 = 10-10 +2x

10 = 2x

Divide by 2

10/2 =2x/2

5 =x

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 5 =  - 3(x + 2) ← is in point- slope form

with slope m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

and (a, b) = (6, - 1), hence

y - (- 1) = [tex]\frac{1}{3}[/tex](x - 6), that is

y + 1 = [tex]\frac{1}{3}[/tex](x - 6) → C