álgebra 1 solve
0.1 + 0.008 = 0.06 − 0.172

i dont know

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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:

80 units

Step-by-step explanation:

KN = MN

9x - 5 = 7x + 7

2x = 12

x = 6

KM = 2KL

KM = 2(6x + 4)

KM = 12x + 8

KM = 12(6) + 8

KM = 80

Answer:

80

Step-by-step explanation:

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:

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

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

Hello,

[tex]f^{-1}(6)=5[/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:

[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:

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:

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:

28

Step-by-step explanation:

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:

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:

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:

I think it's 155 cm

Step-by-step explanation:

=(5×5×3)+(5×2×4)

= 75+40

= 155 cm2

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:

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]

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

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:

The coordinate of point C is (m,m) and the coordinate of point D is (m,0).

Step-by-step explanation:

Square:

In a square, all sides have the same length.

A (0, 0) and B (0, m).

This means that the length of the sides is m.

So:

From A, adding m vertically, we get point (0,m), which is B.

From A, adding m horizontally, we get point (m,0), which I will call D.

From B, adding m horizontally, we get point (m,m), which I will call C.

The coordinate of point C is (m,m) and the coordinate of point D is (m,0).

Answer:

( -4, -3 )

Step-by-step explanation:

Let's solve by elimination. Reason being there are no variables without coefficients.

−5y+3x=3     Multiply equation by 3. Each term.  

−8y+9x=−12

-15y + 9x = 9       Subtract the to equations

-8y  + 9x = -12

___________

-7y = 21

y = -3

Substitute y into original equation

-5(-3) + 3x = 3

15 + 3x = 3            Subtract 15 both sides

3x = -12                 Divide by 3, both sides

x = -4

Answer:

y=-3

x=-4

Check:

-5(-3)+3(-4) =3

15-12=3

3=3 ✅

-8(-3)+9(-4)=-12

24-36=-12

-12=-12✅

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

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 )

Answer:

Step-by-step explanation:

No Graph

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