What is the slope of the line through (6,0) and (7,1)

Answer:

Step-by-step explanation:

1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit

2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.

We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square, so the probability that you can form a triangle is 25%

Answer:

12

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 60 = 6/hyp

hyp = 6 / cos 60

hyp = 6 / (1/2)

htp = 12

Answer:

x=14

Step-by-step explanation:

g(x) = 2(x − 4)

Let g(x) = 20

20 = 2(x − 4)

Divide each side by 2

20/2 = 2(x-4)/2

10 = x-4

Add 4 to each side

10+4 = x-4+4

14 =x

Step-by-step explanation:

you're just going to switch x and y and then solve for y

Answer:

Hello,

Step-by-step explanation:

The problem is that the inverse function is not a function but

an union of 2 functions.

[tex]y=(x+6)^2+1\ is\ the\ orignal\ function\ f(x).\\\\Inverting\ x\ and\ y\ gives: \ x=(y+6)^2+1\\\\(y+6)^2=x-1 \ nota\ bene\ x-1\geq 0 \\(y+6)^2-(x-1)=0\\\\((y+6)-\sqrt{x-1} ) * ((y+6)+\sqrt{x-1}) =0\\\\y=-6+\sqrt{x-1}-6\ or\ y=-6-\sqrt{x-1}\\[/tex]

For the fun

,[tex]f_1(x)= (x+6)^2+1=0\ if\ x<6\\f_1^{-1}(x)=-6-\sqrt{x-1} =0\ if\ x<6\\\\f_2(x)=(x+6)^2+1=0\ if\ x \geq 6\\\\f_2^{-1}(x)=-6+\sqrt{x-1} =0\ if\ x\geq 6\\[/tex]

QUESTION:- DETERMINE THE X-INTERCEPT AND THE Y-INTERCEPT FOR THE GRAPH OF THE EQUATION.

EQUATION:- 2x - 3y + 36 = 0

STANDARD EQUATION:- y=mx+c

where

SO GIVEN EQUATION:- 2x - 3y + 36 = 0

WE CAN SOLVE THIS TO CHANGE IN FORMAT OF STANDARD EQUATION

[tex]2x - 3y + 36 = 0 \\ 2x + 36 =3y \\ y = \frac{2}{3} x + \frac{36}{3} \\ y = \frac{2}{3} x + \frac{ \cancel{36}^{ \: \: 12} }{ \cancel3} \\ y = \frac{2}{3} x + 12 \\ [/tex]

SO :-

[tex]m = \frac{2}{3} \\ y - intercept = 12 \: ans[/tex]

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ \frac{2}{3} = \frac{0 - 12}{x - 0} \\ 2x = ( - 12) \times 3 \\ x = \frac{ - \cancel{12}^{ \: \: 6} \times 3 }{ \cancel{2}} \\ x = - 18 \: \: ans[/tex]

Answer:

Therefore, the value of x is 5.

Step-by-step explanation:

We can match each equation to find the solutions.

[tex]8x-40=x^{2}-2x-15[/tex]

[tex]0=x^{2}-2x-8x-15+40[/tex]

[tex]x^{2}-10x+25=0[/tex]

Now, we need solve this quadratic equation.

[tex](x-5)^{2}=0[/tex]

Therefore, the value of x is 5.

I hope it helps you!

Answer:

[tex]a * b = 210^4[/tex]

Step-by-step explanation:

Given

[tex]a,b>0[/tex]

[tex]gcd(a,b) = 210[/tex]

[tex]lcm(a,b) = 210^3[/tex]

Required

The product of a and b --- missing from the question

To do this, we make use of the following formula:

[tex]a * b = gcd(a, b) * lcm(a, b)[/tex]

So, we have:

[tex]a * b = 210 * 210^3[/tex]

Using the product law of indices, we have:

[tex]a * b = 210^4[/tex]

This means that the product of a and b gives [tex]210^4[/tex]

Answer:

20 batches

Step-by-step explanation:

Cups of sugar in a bag = 15

Cups of sugar per batch of cookie = 3/4 cup

Cups of sugar per batch of cookie : batch of cookies = 3/4 : 1

what's the greatest number of batches of cookies that can be made with the bag of sugar

Let

x = batches of cookies made with a bag of sugar

Cups of sugar per batch of cookie : batch of cookies = 15 : x

Equate the ratios

3/4 : 1 = 15 : x

3/4 ÷ 1 = 15/x

3/4 × 1/1 = 15/x

3/4 = 15/x

Cross product

3 * x = 4 * 15

3x = 60

x = 60/3

x = 20

x = batches of cookies made with a bag of sugar = 20 batches

Answer:

120

Step-by-step explanation:

white : blue : green

5        :4          :1

48 are blue

48/4 = 12

Multiply each by 12

white : blue : green

5*12   4*12     1*12

60        48        12

Add the numbers together to get the total

60+48+12

120

Answer:

5

Step-by-step explanation:

Given: i = 5¹

5¹ = 5

Therefore, the correct option is 5

Answer:

Area = 14.8

Step-by-step explanation:

Area = 5/2 + a^2*sqrt(5 + 2 sqrt(5) )

This formula given the side length, calculates the area.

a = 2

Area = 2.5 + 2^2 * sqrt(5 + 2*sqrt(5) )

Area = 2.5 + 4 * sqrt(5 + 2*2.236)

Area = 2.5 + 4* sqrt(5+ 4.4721)

Area = 2.5 + 4*sqrt(9.4721)

Area = 2.5 + 4*3.0776

Area = 2.5 + 12.3107

Area = 14.8107

Answer:

A ≈ 30.8 m2

Step-by-step explanation:

Answer:/11-5/9×14/11

Step-by-step explanation:

-4/5+1/4÷3

Answer:

[tex]900\sqrt{3}\:\mathrm{cm^2}\text{ or }\approx 1,558.85\:\mathrm{cm^2}[/tex]

Step-by-step explanation:

Heron's formula can be used to find the area of any triangle and is given by:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are three sides of the triangle and [tex]s[/tex] is the semi-perimeter ([tex]s=\frac{a+b+c}{2}[/tex]).

By definition, all three sides and angles of an equilateral triangle are equal. Therefore, if the total perimeter is 180 cm, each side must have a length of [tex]180\div 3=60\text{ cm}[/tex].

The semi-perimeter is therefore:

[tex]s=\frac{60+60+60}{2}=90\text{ cm}[/tex]

Substitute values into Heron's formula to get:

[tex]A=\sqrt{90(90-60)(90-60)(90-60)},\\A=\sqrt{90\cdot 30\cdot30\cdot 30},\\A=\sqrt{2,430,000},\\A=\boxed{900\sqrt{3} \:\mathrm{cm^2}}\approx \boxed{1,558.85\:\mathrm{cm^2}}[/tex]

Answer:

Step-by-step explanation:

To make x the subject, isolate x

7x + 8f = E

Subtract 8f from both sides

7x = E - 8f

Divide both sides by 7

[tex]x =\frac{E-8f}{7}[/tex]

Answer:

x = [tex]\frac{E-8f}{7}[/tex]

Step-by-step explanation:

Given

E = 7x + 8f ( subtract 8f from both sides )

E - 8f = 7x ( isolate x by dividing both sides by 7 )

[tex]\frac{E-8f}{7}[/tex] = x

Answer:

(x, y) → (y, -x)

Step-by-step explanation:

The coordinates of the vertices of parallelogram ABCD are; A(2, 5), B(5, 4), C(5, 2), and D(2, 3)

The coordinates of the vertices of parallelogram A'B'C'D' are; A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)

The rule that escribes the transformation of the rotation of parallelogram ABCD to create the image A'B'C'D' is presented, by observation, is therefore;

(x, y) → (y, -x)

The resulting transformation used will be (x, y) -> (y, -x)

Transformation are rules applied to an object to change its orientation

For the given parallelogram, in order to know the rule used, we need the coordinate of the image and preimage

The coordinate of A is (2, 5) while that of A' is (5, -2).

From both coordinates, you can see that the coordinate was switched and the resulting y coordinate negated.

Hence the resulting transformation used will be (x, y) -> (y, -x)

Learn more on transformation here:  https://brainly.com/question/17311824

Answer:

70.875

Step-by-step explanation:

Area of park=Area of rectangle+Area of triangle

Area of park=13.5*4.8+(0.5)*(13.5)*0.9=70.875

Answer:

[tex]\frac{12}{16} =\frac{16-x}{12}[/tex] → [tex]144=256-16x[/tex]

[tex]16x=256-144[/tex]

[tex]16x=112[/tex] → [tex]x=7[/tex]

OAmalOHopeO

Given:

The equation is:

[tex]y=\sqrt[3]{x}[/tex]

To find:

The graph of the given equation.

Solution:

We have,

[tex]y=\sqrt[3]{x}[/tex]

The table of values is:

x                 y

-8              -2

-1                -1

0               0

1                 1

8                8

Plot these points on a coordinate plane and connect them by a free hand curve as shown in the below graph.

Answer:

D

Step-by-step explanation:

edge 2020

Answer:

6,7 x+9

Step-by-step explanation:

[tex]3( \frac{7}{5} x + 4) - 2( \frac{3}{2} - \frac{5}{4} x) \\ 4.2x + 12 - 3 + 2.5x \\ 6.7x + 9[/tex]

Answer:

x=1

Step-by-step explanation:

3х - 6 = 6x - 9

Subtract 3x from each side

3х-3x - 6 = 6x-3x - 9

-6 = 3x-9

Add 9 to each side

-6+9 = 3x-9+9

3 =3x

Divide by 3

3/3 = 3x/3

1 =x

Answer:

3x-6=6x-9

3x-6x=-9+6

-3x=-3

-3x÷-3=-3÷-3

x=1

Answer:

1) slope intercept y= (-7/4)*x-19/2 2) point slope y-1= -7/4*(x+6)

Step-by-step explanation:

4x-7y=2

7y= 4x-2

y=(4/7)*x-2/7

To find the m2 (the number near x, it is called slope) for searched the slope intercept

use the formula for perpendicular lines

m1*m2=-1

m1= 4/7

m2= -1/ (4/7)= -7/4.

The slope intercept must look like y=m2*x+b

Use the coordinates of given point of the searched line (-6,1)  and m2= -7/4.

1= (-7/4) *(-6) +b

b= -19/2

So slope intercept is y= (-7/4)*x-19/2

Point slope formula is y-y1= m2(x-x1)  m2=-7/4. x1=-6 y1=1

y-1= -7/4(x+6)

Answer:

continuous, continuous

Step-by-step explanation:

Answer:

parallelogram has 4 right angle.

Answer:

It has 4 angles

Step-by-step explanation:

Answer:

11.3 feet

Step-by-step explanation:

let x= answer

x²+4²=12²

x²=128

x=11.3137085

which rounds to

11.3

Answer:

≈ 11.3 ft.

Step-by-step explanation:

In order to solve this, we must use some trigonometry, in this case, SOH-CAH-TOA. If you don't know what it is, here's a quick explanation:

- SOH: Sin(θ) = Opposite / Hypotenuse

- CAH: Cos(θ) = Adjacent / Hypotenuse

- TOA: Tan(θ) = Opposite / Adjacent

(Remember, SOH-CAH-TOA can ONLY be used for right triangles. If the problem does not clearly show a right triangle, meaning that there's no box in the corner, you cannot use it)

When using SOH-CAH-TOA, we first must choose an angle, either the top one or the bottom one. We can't use the right angle as, well, you just can't :). First, we have to find the bottom angle, so circle it. Literally, just circle the angle, you'll thank me later. I'll explain why we don't solve the top angle later on.

After that, we just do some labeling on the sides of the triangle. First, label the shortest side that forms the circled angle, which is the floor (4 ft), as the Adjacent side. Then label the longest side of the triangle, which is the ladder (12 ft), as the Hypotenuse. Finally, label the side that doesn't form the circled angle as the Opposite side. This is why the circling comes in handy :)

Then, out of SOH, CAH, and TOA, we choose the one that has the sides that forms the circled angle. In this case, it's CAH, or cosine, as the adjacent and hypotenuse form the circled angle.

Next, we write out the formula and solve:

Cos(m∠Circled Angle) = Adjacent/Hypotenuse

Cos(m∠Circled Angle) = 4/12

Cos(m∠Circled Angle) x Cos^-1 = 1/3 x Cos^-1

m∠Circled Angle ≈ 70.5288 (Rounding to the nearest ten-thousandth)

Note: Pay attention to the 3rd line. 'Cos^-1' is basically the equivalent of '÷ Cos'.

The reason why we did the bottom angle first is because you cannot have two unknown variables when solving for one of them. That would've been the case if we did choose the top angle as we wouldn't know the measure of the wall nor the angle. Now that we have solved the bottom angle, we can move onto solving the length of the wall.

Looking at SOH-CAH-TOA, we can either use sine or tangent as we have the measures for both the adjacent and hypotenuse. I'll use sine cause why not? Anyways, let's move on!

Just like last time, we write out the formula and solve:

Sin(m∠Circled Angle) = Opposite/Hypotenuse

Sin(70.5288) = Opposite/12

0.9428 = Opposite/12

0.9428 x 12 = Opposite/12 x 12

11.3137 ≈ Opposite (Wall)

Wall ≈ 11.3 ft. (Rounding to the nearest tenth, as asked to do so by the problem)

Note: Be careful with SOH-CAH-TOA because I've messed up multiple times with my calculator while typing out my explanation, so just make sure you go over it several times before submitting your answer when solving trig problems :). But I'm confident with my answer, so just submit it without hesitation as I've already double-checked my work.

Answer:

Optiom B

Step-by-step explanation:

If you use sine rule here, you'll find the other two sides

for the angle, do 180-24-115 = 41

Answered by GAUTHMATH

Answer:

The correct answer would be A. 4

By using the given functions, you can simplify g(3) and you'd get your answer.

Answer: B

No, because y does not change by 5 every time x changes by 1

Step-by-step explanation:

rate of change is basically slope

if the rate of change of the function of 5, then the slope will be 5/1

The x changes by 1 every time y changes by 4

so the slope of the function is 4

Respuesta:

A = 1/16 × x²

Explicación paso a paso:

Un alambre de longitud x se dobla en forma de cuadrado. Como un cuadrado tiene 4 lados iguales la longitud de cada lado (l) será:

l = 1/4 × x

Para calcular el área de un cuadrado (A) usaremos la siguiente fórmula.

A = l²

A = (1/4 × x)²

A = 1/16 × x²