Write the equation of the line that is perpendicular to x + 4y = 12 and passes through the point (-8, 5) in slope-intercept form.
y = mx + b

m=
b=​

Answer: id k if this was what you were looking for but i tried

Step-by-step explanation:

h=acute

rhp=acute

vhp=acute

v=straight angle

phv=acute

The screen size of the HDTV is approximately 36.65 inches.

Here,

The screen aspect ratio of a high-definition television is 16:9, which means the width is 16 units and the height is 9 units.

We are given that the width of the HDTV is 41 inches.

To find the screen size, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal distance across the screen) is equal to the sum of the squares of the other two sides (width and height).

Let's assume the height is h inches.

Using the Pythagorean theorem, we have:

[tex](41^2) = (16^2) + (9^2) + (h^2)[/tex]

Simplifying this equation, we get:

[tex]1681 = 256 + 81 + h^2\\1681 = 337 + h^2\\h^2 = 1681 - 337\\h^2 = 1344\\[/tex]

Taking the square root of both sides, we find:

h ≈ 36.65 inches

Therefore, the screen size of the HDTV is approximately 36.65 inches.

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The graph of the normal distribution is given at the end of the answer.

It states that, for a normally distributed random variable, approximately:

The normal distribution is symmetric, hence, from the Empirical Rule, we get that most observations will be clustered around the mean, which is the center of the distribution.

The mean is of 9.12 and the standard deviation is of 0.05, hence:

The graph of the distribution is given at the end of the answer.

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The value of the given expression 9 + [tex]6^{2}[/tex] -2.8 is 29.

PEMDAS stands for parentheses, exponents, multiplication, division, addition, then subtraction. It is basically the rule of the order in which a mathematical expression must be solved.

Here, we are given an expression 9 + [tex]6^{2}[/tex] -2.8

We solve this expression as per the rules of PEMDAS as follows-

9 + [tex]6^{2}[/tex] -2.8

Since, there are no parentheses and also no exponentials to be solved, we first perform the multiplication of terms-

= 9 + [tex]6^{2}[/tex] -16

= 9 + 36 -16

Now, we move on to addition-

= 45 -16

Finally, we perform subtraction to get the answer-

= 29

Thus, the value of the expression is 29.

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The ratio of the volume of the large sphere to the volume of the small sphere is 125/8.

Given two spheres having surface areas of 100π square centimeters and 16π square centimeters, solve for the radius of each spheres using the formula for the surface area of sphere.

A = 4πr^2

Sphere 1 : 100π cm^2 = 4πr^2

r^2 = 25

r = 5 cm

Sphere 2 : 16π cm^2 = 4πr^2

r^2 = 4

r = 2 cm

Then, solve for the volume of each spheres using the formula:

V = 4/3πr^3

Sphere 1 : V = 4/3π(5cm)^3

V = 500/3 π cm^3

Sphere 2 : V = 4/3π(2cm)^3

V = 32/3 π cm^3

Getting the ratio of the volume of the large sphere to the volume of the small sphere,

ratio = 500/3 π cm^3 / 32/3 π cm^3

ratio = 125/8

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Using the Division Property of Inequality, Paige was able to get x > 12 and solve the inequality -1/2x > -6. Paige solve the inequality correctly.

Given that,

Using the Division Property of Inequality, Paige was able to get x > 12 and solve the inequality -1/2x > -6.

According to the division property of inequality, if we divide an equation's two sides by the same number, the equation doesn't change.

Let's say you have two identically sized pizzas. You divide each one into halves and serve your buddies one half of each pizza. You will have equal pieces of both pizzas left over if you measure the remaining portions.

-1/2x>-6

-1x>-6[tex]\times[/tex]2

-1x>-12

multiplying -1 on both sides we get

x>12

Therefore, Paige solve the inequality correctly.

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The value of 184 is 21th term value.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the terms of arithmetic sequence,

a2 = 4 and d = 9.

now find the which term is 184.

a(n) = a1 + (n - 1)d

now, substitute a(n) = 184, d = 9.

184 = 4 + (n - 1)9

184 = 4 + 9n -9

184 = -5 +9n

184 + 5 = 9n

n = 189/9

n = 21

Hence,the value of 184 is 21th term value.

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The number of tacos that you can get if a drink cost $1.50 and each taco cost $.75 is 4.67.

5 = 1.50 + 0.75t

5 - 1.50 = 0.75t

3.50 = 0.75t

t = 3.50 / 0.75

t = 4.666666666666666

Approximately,

t = 4.67

Therefore, the number of tacos that you can get if a drink cost $1.50 and each taco cost $.75 is 4.67

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A triangle PRS is an equilateral triangle.

An equilateral triangle is a triangle whose all the three sides are equal and each angle measures 60º.

To construct an equilateral triangle:

1) First draw a ray PQ.

2) Then, with P as center and radius equal to 5 cm, draw an arc to cut ray PQ at R.

⇒ PR = 5 cm

3) Then, with R as the center and radius equal to 5 cm, draw an arc to intersect the initial arc at S.

4) Join PS and RS.

Now, the triangle PRS is an equilateral triangle with each side length of 5 cm.

Now mathematically we prove that the triangle we've constructed is an equilateral triangle.

PR = PS                   .......................(the radius of the arc is same)

PR = RS                  .......................(the radius of the arc is same)

Hence by transitivity property,

PR = RS = PS  which is 5 cm

Therefore, triangle PRS is an equilateral triangle.

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The reference angle of the angle of -240º is of 60º.

The sine of the angle is given by:

[tex]\sin{-240^\circ} = \frac{\sqrt{3}}{2}[/tex]

The first step towards finding the equivalent angle of a negative angle is finding it's positive equivalent, adding 360º to it, hence:

-240º + 360º = 120º.

Then we have to find the equivalent on the first quadrant. 120º is on the second quadrant, hence:

180º - 120º = 60º.

The reference angle of the angle of -240º is of 60º.

On the second quadrant, the sine is positive, hence:

[tex]\sin{-240^\circ} = \sin{60^\circ} = \frac{\sqrt{3}}{2}[/tex]

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Answer:

40

Step-by-step explanation:

15 + 15 = 30  do this twice you get 60 which can be converted to 1 Hour.

for every 15 minutes, she sends 40 messages.

The original coordinates of flea were  (  5 , - 3) .

What does coordinate mean in this case?

F' = ( 4 , - 1 )

To undo translation of 9 units’ right and 4 units down, translate 9 units left and 4 units up

( 4, - 1 ) →  ( 4 - 9 , -1 + 4 )

           →   ( -5,3)

Reflect back across Y-axis to undo reflection means change x -coordinate by -1

(- 5,3)    →    ( 5, 3)

Reflect back across x-axis to undo reflection means change y-coordinate by -1

( 5 , 3) → (  5 , - 3)

Therefore the original coordinates of flea were (  5 , - 3)

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The names of the three angles are:

∠ABC = acute angle

∠FGH = right angle

∠QRS = obtuse angle

We have,

From the figure given,

The angles must be either right angles, acute angles, or obtuse angle.

Acute Angle: An acute angle is an angle that measures less than 90 degrees. It is smaller than a right angle.

Obtuse Angle: An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees. It is larger than a right angle.

Right Angle: A right angle is an angle that measures exactly 90 degrees. It forms a perfect "L" shape and is typically denoted by a square corner symbol (∟).

Now,

The angle is less than 90 degrees.

∠ABC = acute angle

The angle is 90 degrees.

∠FGH = right angle

The angle is greater than 90 degrees.

∠QRS = obtuse angle

Thus,

The names of the three angles are:

∠ABC = acute angle

∠FGH = right angle

∠QRS = obtuse angle

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According to the given statement the perpendicular distance form the point  (4,3)  is 3.

Coordinate Geometry can be used to define points in space. The primary axis labeled a x- and y-axes is defined first, and then the points were measured and labelled in relation to these points. Furthermore, numerous geometric forms such as a line, curve, circle, ellipse, and hyperbola can be plotted inside the coordinate axes and their attributes studied.

the equation for line ℓ.

Begin by finding the slope of the line through the given points, (-3,0) and (3,0):

m = (Y₂ - Y₁)/(x₂ - x₁)

   = (0 - 0)/(-3 - (-3))

   = 0/0

The equation of the line using point (3,0) on the line:

Y - Y₁ = m(x - x₁)

putting value we get: (m = 0)

Y =0(x + x₁)

Y = 0

The equation of the line w perpendicular to line ℓ through P(4,3).

The slop of line l is 0.

hence this will be x- axis

and perpendicular distance from a point (x1,y1) to x- axis will be y1.

So the perpendicular distance form the point  (4,3)  is 3.

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The required value of x is 6 / 7.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx     —-- 1

Now, find constant of proportion for given x = 2 and y = 7, we need to put these values in equation 1, i.e.

7 = k(2)

k = 7 / 2

Further calculate x for given y = 3 i.e.

3 = (7 / 2)x

x = 6 / 7

Hence, the required value of x is 6 / 7.

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Based on the speed of the object at 1 yard every 7.5 months, the speed in centimeters per hour is 0.01693 cm/ hour

First, convert 1 yard to centimeters:

1 yard = 91.44 cm

Convert 7.5 months to hours:
= 7.5 months  x 30 days per month x 24 hours per day

= 5,400 hours

The speed in centimeters per hour can therefore be found to be:

= 91.44 / 5,400

= 0.01693

= 0.01693 cm/ hour

In conclusion, the object is moving at a speed of 0.01693 cm/ hour

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The f(-3), f(0) , and f(1) is (-16/5), -2 and (-8/5).

The given function is f(x) = (2/5)x-2

1) f(-3) = x = -3

Substituting the value of x in the equation f(x) = (2/5)x - 2, we get -

f(-3) = (2/5)x - 2

f(-3) = (2/5)(-3) - 2

f(-3) = (-6/5) - 2

f(-3) = (-6 -10)/5

f(-3) = -16/5

2) f(0) = x = 0

Substituting the value of x in the equation f(x) = (2/5)x - 2, we get -

f(0) = (2/5)(0) - 2

f(0) = -2

3) f(1) = x = 1

Substituting the value fo x in the equation f(x) = (2/5)x - 2, we get -

f(1) = (2/5)(1) - 2

f(1) = (2/5) - 2

f(1) = (2 - 10)/5

f(1) = -8/5

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The values of x to make the triangle acute is [tex]2 < x < 2\sqrt{13}[/tex].

Triangle inequality theorem states that that the sum of any two sides of the triangle is greater than the third side of of the triangle

Pythagorean Inequality theorem states that if the square of the longest side  is less than the sum of squares of other two sides then the triangle is acute.

In the given question

Longest side = 2x

other two shorter side =  8 and 12.

By Triangle Inequality theorem

(i) 8+12>2x    ⇒20>2x  ⇒x<10

(ii) 2x+8>12  ⇒2x>4  ⇒x>2

(iii) 2x+12>8  ⇒2x>-4  ⇒x>-2

From (I), (ii) & (iii) we conclude that value of x should be in between 2<x<10.

To make the triangle acute

Using Pythagorean Inequality theorem

[tex](2x)^{2} < 8^{2} +12^{2} \\ \\ 4x^{2} < 64+144\\ \\ 4x^{2} < 208\\ \\ x^{2} < \frac{208}{4}[/tex]

[tex]x^{2} < 52\\ \\ taking. Square. Root . both . the . sides \\ \\ x < \sqrt{52} \\ \\ x < 2\sqrt{13}[/tex]

Therefore , the value of x to make the triangle acute is [tex]2 < x < 2\sqrt{13}[/tex].

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The values of the x in number line are  -7 -6 -5 -4.

According to the statement

We have to find that the numbers in the number line.

So, For this purpose, we know that the

A number line is a horizontal line that has equally spread number increments

From the given information:

The given equation is a x < -3 And a numbers givens On a Number Line are:

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

It means we have to find the numbers in a number line less than the -3.

we know that the large numbers with the negative sign are a smaller number and

the Small numbers with the negative sign are a larger number.

According to this,

The numbers -7 -6 -5 -4 are the values of the x less than the -3.

So, The values of the x in number line are  -7 -6 -5 -4.

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Answer:

Integers

Step-by-step explanation:

They are not all positive integers because -72 is negative.

They are not all negative because 45 is positive. The + sign is implied.

They are all whole numbers and not irrational.

Thus, they are integers, which by looking at the data, we see is true.

The slope of the line passing through the pair of points, (-2 , -4) and (1 , 2), is 2.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:

m = (y2 - y1)/(x2 - x1)

where m is the slope

x1 and y1 are the coordinates of one point

x2 and y2 are the coordinates of the 2nd point

Given two points in the line, (-2 , -4) and (1 , 2), plug in the values to the formula for the slope.

m = (y2 - y1)/(x2 - x1)

m = (2 - -4)/(1 - -2)

m = 6/3

m = 2

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The simplified form of given expression 3√{27x^6y^4} is x³y²9√3

In this question, we have been given an expression 3\sqrt{27x^6y^4}

We need to simplify given expression.

3√{27x^6y^4}

= 3√{(3 × 9) x^6 y^4}

= 3√(3 × 9) × √x^6 × √y^4

= 3 (3√3) × x^(6/2) × y^(4/2)

= 9√3 × x³ × y²

= x³y²9√3

Therefore, the simplified form of given expression 3√{27x^6y^4} is x³y²9√3

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Answer:

Pi is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction.

Answer:

No

Step-by-step explanation:

It can not be a fraction because it is a never-ending/infinite decimal.

Step-by-step explanation:

-4x-6=-4x-4-2

-4x+4x=6-4-2

x=1

A factor exists a number that completely divides another number.

The factor of x²y³ - 11x²y + 6y² - 66 is (x²y + 6)(y² - 11).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we exists adding are factors of the product because the product exists divisible by them.

By eliminating the common variables, one may get the components of the equation x²y³ - 11x²y + 6y² - 66.

x²y³ - 11x²y + 6y² - 66

Take out the common from the first two terms.

⇒ x²y(y² - 11) ..........(1)

Take out common in the last two terms.

⇒ 6 (y² - 11) ..........(2)

Adding both the equations, (1) and (2) then

[x²y(y² - 11)] + [6 (y² - 11)] = x²y(y² - 11) + 6(y² - 11)

simplifying the above equation, we get

⇒ (x²y + 6)(y² - 11)

Therefore, the factor of x²y³ - 11x²y + 6y² - 66 is (x²y + 6)(y² - 11).

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Answer:

See explanation

Step-by-step explanation:

f(x)=|x|

f(x) ==> f(x+3): translation of function 3 units to the left, f(x-3) would be translation 3 units right

f(x+3) ==> 3f(x+3): vertical stretch by a factor of 3

f(x+3) ==> -3f(x+3): Reflection over the x-axis, since y value changes over the x-axis while x value changes over the y-axis

-3f(x+3) ==> h(x)=-3f(x+3)+1: Translation one unit up.

f(x) = −3x + 60 is the linear equation in function form to show the amount of trash removed each week.

Let x be the number of weeks and y be the trash removed

Then , the linear equation can be given as

y=mx+c

To find out the slope and intercept, let's have a look at the given conditions.

For week 5, we can write the equation as

45 = 5m +c ... (1)

For week 10, we can write the equation as

30 =10m +c ......(2)

Solving both the equation by elimination method

(45 = 5m +c) * 2

30 = 10m+c

c = 60

Now, finding the value of x by substituting value of c in eq (1)

45 = 5m + 60

-15 = 5m

m = -3

Now, the required linear equation becomes

y = -3x + 60

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Using the given quadratic function, it is found that:

1. The ball has a height of 33.4 meters after 3 seconds.

2. The maximum height of the ball is of 34.18 meters, taking 2.6 seconds to reach it's height.

3. The ball will be in the air for 5.24 seconds.

The quadratic equation for the ball's height after t seconds is given by:

h(t) = -4.9t²+ 25.5t + 1.

Hence, after 3 seconds, the height is:

h(3) = -4.9(3)² + 25.5(3) + 1 = 33.4 meters.

The ball has a height of 33.4 meters after 3 seconds.

To find the maximum height of the ball, we have to find the vertex of the function.

A quadratic equation is modeled by:

y = ax^2 + bx + c

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

For this problem, the coefficients are given as follows:

a = -4.9, b = 25.5, c = 1.

Hence:

The maximum height of the ball is of 34.18 meters, taking 2.6 seconds to reach it's height.

To find how long the ball was in the air, we have to solve the quadratic equation, hence:

Time has to assume positive values, hence:

The ball will be in the air for 5.24 seconds.

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The coordinates of the midpoint M of the segment AB are; (-4, 6).

It follows from the task content that points A and B have coordinates; (-8,5) and (0,7) respectively.

Since Midpoint is given as; {(x1 +x2)/2, (y1 +y2)/2}.

It follows that the midpoint in this scenario is;

= {(-8 +0)/2, (5 +7)/2}

= (-4, 6).

Ultimately, the midpoint is; (-4, 6).

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