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Answer:

From the sum of angles on a straight line, given that the rotation of each triangle attached to the sides of the octagon is 45° as they move round the perimeter of the octagon, the angle a which is supplementary to the angle turned by the triangles must be 135 degrees

Step-by-step explanation:

Given that the triangles are eight in number we have;

1)  (To simplify), we consider the five triangles on the left portion of the figure, starting from the bottom-most triangle which is inverted upside down

2) We note that to get to the topmost triangle which is upright , we count four triangles, which is four turns

3) Since the bottom-most triangle is upside down and the topmost triangle, we have made a turn of 180° to go from bottom to top

4) Therefore, the angle of each of the four turns we turned = 180°/4 = 45°

5) When we extend the side of the octagon that bounds the bottom-most triangle to the left to form a straight line, we see the 45° which is the angle formed between the base of the next triangle on the left and the straight line we drew

6) Knowing that the angles on a straight line sum to 180° we get interior angle in between the base of the next triangle on the left referred to above and the base of the bottom-most triangle as 180° - 45° = 135°.

Answer:

y = -1/2x + 2

Step-by-step explanation:

If two lines are perpendicular then the product of their slopes are -1

m1*m2 = -1

where m1 amd m2 is slope of two lines.

_______________________________________

Given line

y = 2x-3\

it is in form of y = mx+c (slope intercept form)

where m is slope and c is y intercept

Thus, slope of line  y = 2x-3 is 2

Now we know that product of two lines are -1

let m be slope of other line

then m*2 = -1

m = -1/2

thus, slope of required line is -1/2

let the line be y = mx+c but m = -1/2

thus

y = -1/2 x + c

given that point(-6,5) lies on it

we use -6 in plca of x and 5 in place of y

5 = -1/2 *-6 + c

=>5 = 3 +c

=> c = 5-3 = 2

Thus, equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5) is y = -1/2x + 2

Answer:

If a is negative or zero  there are no real solutions

Step-by-step explanation:

y=ax^2-8

Set equal to zero to find the solution

0 =ax^2-8

Add 8 to each side

8 = ax^2

Divide by a  a cannot be zero or we cannot divide by it

8/a = x^2

Take the square root of each side

sqrt(8/a) = sqrt(x^2)

We need 8/a to be positive for it to have real solutions

That means a has to be positive

If a is negative or zero  there are no real solutions

Answer:

C. 5

Step-by-step explanation:

XY= -1-(-5)= 4

ZA= A-1= 4 ⇒ A=1+4= 5

A=5

Answer:

x=-9

Step-by-step explanation:

3 x=-27

x = -9

Answer:

-9

Step-by-step explanation:

x3 = -27 OR 3x = -27

3x/3 = -27/3

x = - 9

Answer:

1/4 & 1/2

Step-by-step explanation:

4 sides to the dice

2 sides to coin

Answer:1/12

Step-by-step explanation:

The probability of getting a three on a fair die is 1/6

The probability of getting tails on an unbiased coin is 1/2

Then the probability of getting a three on a fair die and tails on an unbiased coin is 1/6 x1/2=1/12

Answer:

Step-by-step explanation:

We'll call height h.

The equations of a cone and sphere are:

Cones: 1/3 * base area * h

Spheres: 4/3 π * r³

The base area of a cone would be the area of a circle equation:

π * r² = π * 2² = 4π.

Because you're converting from sphere to cone, you would set their equations equal to each other.

1/3 * 4π * h = 4/3 π * 5³

Next, isolate h.

h = (4/3 π * 5³)/(1/3 * 4π)

h = 125

Hope this helps!

Answer:125

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The original amount will be the coefficient of (1 + 0.04)^r which is $728.00.

Answer:

true it's A....

Answer:

A

Step-by-step explanation:

64x³ + 125

∛(64x³ + 125)

= 4x + 5

The expression is a sum of cubes.

Answer:

the answer is -6, 2

Step-by-step explanation:

Answer:

the answer is -6, 2

Step-by-step explanation:

Answer:

ANSWER

x =  { - 20}{7}

y={ 4}{7}

Step-by-step explanation:

Answer:

Angle 1

Step-by-step explanation:

Angle 3 and angle 1 are vertical angles. That means that whatever the measure of angle 3 is, angle 1 is also the same.

Answer: -3 and 7

Step-by-step explanation:

x - 7

Add 7 to get 0

x - 7 ( + 7) = 0

x + 3

Subtract 3 to get 0

x + 3 ( - 3) = 0

Step-by-step explanation:

X= raspberry

X = 600 ÷ 11 = 54 batches

[ 60 minutes = 1 hour]

[600 minutes = 10 hours]

Y = peach

Y = 600 ÷ 8 = 75 batches

Answer:

its b

Step-by-step explanation:

it just is

Answer:

Selling price of 5 gives the maximum profit

Step-by-step explanation:

What we do here is to find the first derivative, since at maximum points, the profit will be set to zero.

Mathematically, we have;

dp/dx = -120x + 600

We now equate this to zero

0 = -120x + 600

120x = 600

x = 600/120

x = 5

Answer:

Step-by-step explanation:

0.35

0.453

4/5

Answer:

One invariant point;

Point A = (2, 0)

Step-by-step explanation:

The coordinates of the square vertices are;

O = (0, 0)

A = (2, 0)

B = (2, 2)

C = (0, 2)

Therefore, we have by 90° clockwise rotation;

O' = (2, 2)

A' = (2, 0)

B' = (4, 0)

C' = (2, 4)

Therefore, since only A' (2, 0) = A (2, 0), we have only one invariant point on the perimeter of the square when it is rotated 90° about the center (2, 0) which is the point A = (2, 0).

Answer:

2(x+y)

Step-by-step explanation:

Simple 5-3 with some added variables that don't change.

Answer:

Option (1)

Step-by-step explanation:

''A perpendicular bisector makes 90° with the other line segment and divides the segment into two equal parts."

From the given picture,

If [tex]\overleftrightarrow{DE}[/tex] is a perpendicular bisector of [tex]\overline{AC}[/tex] following properties must be followed.

1). m(∠DBC) = m(∠DBA) = 90°

2). AB ≅ BC

Therefore, additional information we will require is AB ≅ BC

Option (1) will be the answer.

Answer: -7, -1, 5, -5

Step-by-step explanation:

In order to find the inverse, swap the x's and y's and solve for y.

[tex]y=\dfrac{5x+1}{-x+7}\\\\\\\underline{Swap\ the\ x's\ and\ y's}:\\x=\dfrac{5y+1}{-y+7}\\\\\\\underline{\text{Multiply both sides by -y+1 to clear the denominator}}:\\x(-y+7)=5y+1\\-xy+7x=5y+1\\\\\\\underline{\text{Add xy and subtract 1 from both sides}}:\\7x-1=xy+5y\\\\\\\underline{\text{Factor out the y from the right side}}:\\7x-1=y(x+5)\\\\\\\underline{\text{Divide x+5 from both sides}}:\\\dfrac{7x-1}{x+5}=y[/tex]

Since the boxes you need to fill in show -x in the denominator, multiply the equation by -1/-1:

[tex]y=\dfrac{-1}{-1}\bigg(\dfrac{7x+1}{x+5}\bigg)\\\\\\\large\boxed{f^{-1}(x)=\dfrac{-7x-1}{-x-5}\qquad for\ x \neq -5}[/tex]

Answer:

A=1.5 units²

Step-by-step explanation:

a²+b²=c²

2.5²+1.5²=c²

a²+2.25=6.25

a²=4.00

a=2

A=1/2 x b x h

A=1/2 x 1.5 x 2

A=1.5 units²

Answer:

1.5

Step-by-step explanation:

Use the pythagorean theorem.  a^2+b^2=c^2.  a and b are the legs, or the shorter sides of the triangle.  If you don't know which ones are shorter, just know that c is opposite of the right angle which is 2.5 in this case.  So c is 2.5 and a is 1.5.  Now you plug the values into the equation

1.5^2+b^2=2.5^2

2.25+b^2= 6.25 .Simplify the equation

b^2= 4 .Subtract 2.25 from both sides.

b= 2.  Square root both sides.  

Based on the picture, a is the base and b is the height.  The area of a triangle is 1/2(bh) .You already know the base and height you you plug it in again

1/2(1.5*2)= 1/2(3)= 1.5  

Step-by-step explanation:

(-2)-(+15)=(-17)

the difference between those two temperature s is (-17)

Answer:

The distance between (-3, -4) and (6, -4) is 9 units.

Step-by-step explanation:

First, we must know the distance formula between two points.

[tex]Distance(d)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We will use (-3, -4) for (x₁, y₁) and we will use (6, -4) for (x₂, y₂).

[tex]Distance=\sqrt{(6-(-3)^2+(-4-(-4))^2)}[/tex]

[tex]Distance=\sqrt{(9)^2+(0)^2}[/tex]

[tex]Distance=\sqrt{81+0}[/tex]

[tex]Distance=9[/tex]

So, the distance between the two points is 9 units.

Answer:

3/10

Step-by-step explanation:

Josh and Lucy share some money in the ratio 3:7.

3+7=10

The fraction Lucy gets is 7/10

The fraction Josh must get is 3/10.

Answer:

x = -9

Step-by-step explanation:

-7x = 63

Divide -7 into both sides.

-7x/-7 = 63/-7

x = 63/-7

x = -9

Put x as -9 in the function to check.

h(x) = -7x

h(-9) = -7(-9)

h(-9) = 63

Answer:

x = -9

Step-by-step explanation:

h(x)=−7x ; h(x)=63

Set the two equal

-7x = 63

Divide by -7

-7x/-7 = 63/-7

x = -9

Answer:

f(x) = 9(x + 5)2 - 6 (-5,-6)

f(x) = 6(x + 9)2 - 5 (-9,-5)

f(x) = 9(x - 5)2 + 6 (5,6)

f(x) = 6(x - 5)2 - 9. (5,-9)

f(x) = 5(x - 6) +9. (6,9)

Step-by-step explanation:

To find the vertex: for the x-coordinate, take the "h" in the parentheses (x + h) and reverse its sign. For the y-coordinate, use the "k" term as-is.

The coordinates of the vertex of the equations are:

The vertex form of the quadratic function is given as:

y = a(x -h)^2 + k

Where:

Vertex = (h,k)

Using the above highlight, the coordinates of the vertex of the equations would be:

f(x) = 9(x + 5)^2 - 6

Vertex = (-5,-6)

f(x) = 6(x + 9)^2 - 5

Vertex = (-9,-5)

f(x) = 9(x - 5)2 + 6

Vertex =(5,6)

f(x) = 6(x - 5)^2 - 9

Vertex = (5,-9)

f(x) = 5(x - 6) +9

Vertex = (6,9)

Read more about vertex quadratic functions at:

https://brainly.com/question/1480401

Answer: -38,686

Step-by-step explanation:

3 x 4= 12

-19 x 2037= -38,703

12 + 15= 17

17 -38,703= -38,686

Answer:

17

Step-by-step explanation:

Plot in the points for each variable to find the y-intercept.

1=-4(4)+c

1=-16+c

1+16=c

17=c

9=-4(2)+c

9=-8+c

9+8=c

17=c

Answer:

Step-by-step explanation:

Given:

2 Points

(4,1) and

(2,9)

Slope

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

y2 = 9

y1 = 1

x2 = 2

x1 = 4

m = (9 - 1) / (2 - 4)

m = 8 / - 2

m = - 4

y intercept

y = mx + b

y = -4x + b

Use (9, 1) to find the y intercept

1 = - 4*9 + b

1 = - 36 + b

b = 37

Answer

The equation is y = - 4x + 37

Answer:

0.50

Step-by-step explanation:

Simply plug -2 in for x into the equation.

2(2^-2) = 0.50

Answer:

0.50

Step-by-step explanation:

Answer:

a. cone. Since it's the only shape with one base and a vertex not on the same plane