.The endpoints of AB are A(1,4) and B(6,-1).

Answer:

x = 60 cm

Step-by-step explanation:

using Pythagoras theorem which states that:-

Hypotenuse (h)² = perpendicular (p)² + base (b)²

100² = 80² + x²

100² - 80² = x²

10000 - 6400 = x²

3600 = x²

x = 60 cm

Answer: 9 full journeys

Step-by-step explanation:

4.5 litres * 1.3 gallons = 5.8 litres of petrol

52 litres ÷ 5.8 litres of petrol = 8.9 journeys ≈ 9 full journeys

Answer:

(a) 52°

(b) 322°

Step-by-step explanation:

(a) The details of the circle are;

The diameter of the circle = AOC

The center of the circle = Point O

The point the line AT cuts the circle = Point B

The point the tangent PT touches the circle = Point C

Angle ∠COB = 76°

We have that angle AOB and angle COB are supplementary angles, therefore;

∠AOB + ∠COB = 180°

∠AOB = 180° - ∠COB

∴ ∠AOB = 180° - 76° = 104°

∠AOB = 104°

OA = OB = The radius of the circle

Therefore, ΔAOB  =  An isosceles triangle

∠OAB = ∠OBA by base angles of an isosceles triangle are equal

∠AOB + ∠OAB + ∠OBA = 180° by angle summation property

∴ ∠AOB + ∠OAB + ∠OBA = ∠AOB + ∠OAB + ∠OAB = ∠AOB + 2×∠OAB = 180°

∠OAB = (180° - ∠AOB)/2

∴ ∠OAB = (180° - 104°)/2 = 38°

∠TAC = ∠OAB = 38° by reflexive property

AOC is perpendicular to tangent PT at point C, by tangent to a circle property, therefore;

∠TCA = 90° and ΔTCA = A right triangle

∠TAC + ∠ATC + ∠TCA = 180° by angle sum property

∠ATC = 180° - (∠TAC + ∠TCA)

∴ ∠ATC = 180° - (38° + 90°) = 52°

Angle ATC = 52°

(b) In ΔABC, ∠ABC = Angle subtended by the diameter = 90°

∴ ΔABC = A right triangle

∠ABC and ∠TBC are supplementary angles, therefore;

∠ABC + ∠TBC = 180°

∠TBC = 180° - ∠ABC

∴ ∠TBC = 180° - 90° = 90°

∠TCB = 180° - (∠TBC + ∠ATC)

∴ ∠TCB = 180° - (90° + 52°) = 38°

The bearing of B from C = (360° - 38°) = 322°.

Answer:

2, 3, 7 or 8

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

Answer:

13.95 units

Step-by-step explanation:

[tex] \sin \: 35 \degree = \frac{8}{x} \\ \\ \therefore \: x \: = \frac{8}{\sin \: 35 \degree} \\ \\ \therefore \: x \: = 13.9475744 \\ \\ \therefore \: x \: = 13.95 \: units[/tex]

hope it helps

Answer:

4a + b)( 1 + 4a - b )

Step-by-step explanation:

4a + b + 16a² - b²

Step 1 :- Use a² - b² = ( a - b ) ( a + b ) to factor the expression.

4a + b + ( 4a - b ) ( 4a + b ).

Step 2 :- Factor out 4a + b from the expression.

(4a + b)( 1 + 4a - b )

Given:

The vertices of a triangle are D(1,5), O(7,-1) and G(3,-1).

To find:

The perpendicular bisector of line segment DO.

Solution:

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

The midpoint of DO is:

[tex]Midpoint=\left(\dfrac{1+7}{2},\dfrac{5+(-1)}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{8}{2},\dfrac{4}{2}\right)[/tex]

[tex]Midpoint=\left(4,2\right)[/tex]

Therefore, the midpoint of DO is (4,2).

Slope formula:

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

Slope of DO is:

[tex]m=\dfrac{-1-5}{7-1}[/tex]

[tex]m=\dfrac{-6}{6}[/tex]

[tex]m=-1[/tex]

Therefore, the slope of DO is -1.

We know that the product of slopes of two perpendicular line is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]m_1\times (-1)=-1[/tex]

[tex]m_1=1[/tex]

The slope of perpendicular bisector is 1 and it passes through the point (4,2). So, the equation of the perpendicular bisector of DO is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-2=1(x-4)[/tex]

[tex]y-2+2=x-4+2[/tex]

[tex]y=x-2[/tex]

Therefore, the equation of the perpendicular bisector of DO is [tex]y=x-2[/tex].

Answer:

1,968

Step-by-step explanation:

Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;

Set X represent the set where the siblings x₁ and x₂ sit together

Set Y represent the set where the siblings y₁ and y₂ sit together

Set Z represent the set where the siblings z₁ and z₂ sit together

We have;

Where the three siblings don't sit together given as [tex]X^c[/tex]∩[tex]Y^c[/tex]∩[tex]Z^c[/tex]

By set theory, we have;

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = [tex]\left | X^c \cup Y^c \cup Z^c \right |[/tex] =  [tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex]

[tex]\left | U \right | - \left | X \cup Y \cup Z \right |[/tex] = [tex]\left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]

Therefore;

[tex]\left | X^c \cap Y^c \cap Z^c \right | = \left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)[/tex]

Where;

[tex]\left | U\right |[/tex] = The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!

[tex]\left | X\right |[/tex] = The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | Y\right |[/tex] = The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | Z\right |[/tex] = The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!

[tex]\left | X \cap Y\right |[/tex] = The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | X \cap Z\right |[/tex] = The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | Y \cap Z\right |[/tex] = The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

[tex]\left | X \cap Y \cap Z\right |[/tex] = The number of ways x₁ and x₂,  y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!

Therefore, we get;

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)

[tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex] = 5,040 - 3072 = 1,968

The number of ways where the three siblings don't sit together given as [tex]\left | X^c \cap Y^c \cap Z^c \right |[/tex]  = 1,968

Answer:

38

Step-by-step explanation:

To find the value of f(6), we substitute the value 6 where x is into the function. You would get:

7(6) - 4

42 - 4

f(6) = 38

Answer:

See my writting here have answer

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Answer:

80 square units

536.6 [tex]cm^{2}[/tex]

Step-by-step explanation:

First one.

2 Trapezoids

A = [tex]\frac{(base_{1} +base_{2}) }{2}[/tex] x h

A = [tex]\frac{10 + 6}{2}[/tex] x 2

A = 16

One rectangle

A = b x h

A = 6 x 8

A = 48

Total Area = 16 + 16 + 48 = 80

Second one:

Two triangles:

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

A = [tex]\frac{10(8.66)}{2}[/tex]

A = [tex]\frac{86.6}{2}[/tex]

A = 43.3

One large rectangle

A = b x h

A = 30 x 15

A = 450

Total Area = 450 + 43.3 + 43.3 = 536.6

Answer:

A=80

Step-by-step explanation:

A=1/2(6+10)2

A=16(2)

A=32

A=8x6

A=48+32

A=80

Answer:

[tex]\displaystyle A = 12[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

y = x

Interval: x = 1 to x = 5

Step 2: Sort

Graph the function. See Attachment.

Bounds of Integration: [1, 5]

Step 3: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

C

Step-by-step explanation:

The other answers have inputs (x) that have multiple outputs (y) which goes against the definition of a function.  For example in answer D zero has both the outputs of 7 and 52 which can not happen in order to be a function.  However outputs can have multiple inputs just not the other way around.

Answer:

g-21=129

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Let

S = sum of the measures of the interior angles of a polygon

n = number of sides of a polygon

The equation is

S = (n - 2) * 180°

Where,

S = 2,880°

S = (n - 2) * 180°

2,880° = (n - 2) * 180°

2,880° = 180°n - 360°

2,880° + 360° = 180°n

3,240° = 180°n

Divide both sides by 180°

n = 3,240° / 180°

n = 18

Good evening everyone, the correct answer is 18 sides.

A polygon with 18 sides' interior angles will add up to 2880 degrees.

Have a blessed night.

Answer:

1.75 × 10⁶

Step-by-step explanation:

7,000,000 ÷ 4 = 1750000

Which is 1.75 × 10⁶ in standard form

Answer:

[tex]p = \{x \ | \ x \in Q^+ \ and \ x \leq \$5,000 \}[/tex]

Step-by-step explanation:

The expression for the cost of John's bike (p) using set notation can written as follows;

We note that the cost of the bike is a member of the positive rational number  and the cost price of the bike cannot exceed $5,000, therefore, it is less than or equal to $5,000, therefore, we get the following set notation;

[tex]p = \{x \ | \ x \in Q^+ \ and \ x \leq \$5,000 \}[/tex]

Answer:

150 + (.05x) = 355

.05x = 205

x = $4100

Step-by-step explanation:

Subtract to find amount of commission made:

355 - 150 = 205

She made $205 in commissions

Divide the amount she made in commission by the percentage she gets:

205 / 0.05 = 4,100

Her sales was $4,100

Answer:

C) Chloroplast; thylakoid membrane

Step-by-step explanation:

The question is a biological science question

The light-dependent reactions also known as the light reactions take place at the location site of the chlorophyll of the plant cell, within the chloroplast thylakoid membrane, and involves the energizing of the electrons within the pigment molecules, the electrons are then transferred through a transport chain within the thylakoid membrane

The dark reactions take place inside the stroma

Therefore, the correct option is chloroplast; thylakoid membrane

Answer:

b

Step-by-step explanation:

Answer:

x+y-5=0

Step-by-step explanation:

let eqn Perpendicular to eqn 5y-5x=-20 be -5x-5y+k=0------(1)

eqn (1) passes through (-3,8)

-5×-3-5×8+k=0

15-40+k=0

K=25

since required eqn perpendicular to 5y-5x=-20 is -5x-5y+25=0

x+y-5=0ans.

Answer:

x = 5

arcEF = 58degrees

arcGH = 55degrees

Step-by-step explanation:

Find the diagram attached

The sum of angle on the straight line EH is 180degrees

Hence arcEF+ arcFG + arcGH = 180

10x+8 + 67 + 11x = 180

21x + 75 = 180

21x = 180 - 75

21x = 105

x = 105/21

x = 5

Since EF = 10x+8

arcEF = 10(5) + 8

arcEF = 50+8

arcEF = 58degrees

Also, arcGH = 11x

arcGH = 11(5)

arcGH = 55degrees

Hi there!

[tex]\large\boxed{A. \text{ } 7}[/tex]

The following trapezoidal theorem states that:

Middle segment = average of top and bottom side

Thus:

M = 1/2(b1 + b2)

21 - x = 1/2(17 + 11)

Solve:

21 - x = 1/2(28)

21 - x = 14

Subtract 21 from both sides:

-x = 14 - 21

-x = -7

Multiply both sides by -1:

x = 7

Answer:

Area of a Sector of Circle = (θ/360º) × πr²

[tex]area \: = \: \frac{70}{360} \times \frac{22}{7} \times 10 {}^{2} \\ = 61.11[/tex]

on rounding off to two decimal places:-

Answer:

40°

Step-by-step explanation:

As sum of angles of the triangle is 180°

therefore the third angle will be 180 -( 75 + 65)=40°

x=40°= vertically opposite angle

Answer:

x = 40°

Step-by-step explanation:

a + 65 + 75 = 180  {Angle sum property}

a + 140 = 180

     a = 180 - 140

    a = 40

x = a  {Vertically opposite angles}

x = 40°

Answer:

Lines  C and D

Step-by-step explanation:

For a pair of lines to be perpendicular ,

    the product of their slope must be - 1 .

Slope of A:

[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{-2x}{-3} + \frac{6}{-3}\\\\[/tex]

[tex]y = \frac{2}{3}x - 2\\\\slope_A = \frac{2}{3}[/tex]

Slope of B:

[tex]3x - 2y = - 9\\\\-2y = - 3x - 9\\\\y = \frac{-3x}{-2} - \frac{9}{-2}\\\\y =\frac{3x}{2} + \frac{9}{2}\\\\slope_B = \frac{3}{2}[/tex]

Slope of C:

[tex]y = - \frac{3}{2}x - 5 \\\\slope_C = -\frac{3}{2}[/tex]

Slope of D:

[tex]y = \frac{2}{3}x + 2\\\\slope_D = \frac{2}{3}[/tex]

Product of the slopes = - 1

[tex]slope_A \times slope_B = \frac{2}{3} \times \frac{3}{2} = 1 \neq - 1 \\\\Therefore, not\ perpendicular.\\\\Slope_B \times slope_C = \frac{3}{2} \times \frac{-3}{2} = \frac{-9}{4} \neq -1\\\\Therefore , not \ perpendiucalr.\\\\Slope_C \times slope_D = -\frac{3}{2} \times \frac{2}{3} = - 1\\\\Therefore , perpendicular\\\\\\Slope_A \times slope_D = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \neq 1\\\\therefore , not \ perpendicular.[/tex]

Answer:

a) t²- 4x + 4

b) 9y² - 4z

c) 10290v

Step-by-step explanation:

a+b) use identity (ax+b)(ax+c) = ax² + (b+c)x + bc

c) a × bx = abx