Alistar is going to build fence around the outside of his garden

a) draw an accurate scale drawing of the garden using a ruler and compasses.use scale 1 cm to 2m

b) how long the fence be?

The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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Answer:

The original number is -22

Step-by-step explanation:

We'll label our mystery number x.

2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22

Plug in to confirm

-44 + 36 = -88/11S
8 = 8

Answer:

x= -1/95

Step-by-step explanation:

Step 1: Subtract 110x from both sides.

15x+8−110x=110x+9−110x

−95x+8=9

Step 2: Subtract 8 from both sides.

−95x+8−8=9−8

−95x=1

Step 3: Divide both sides by -95.

−95x

−95

=

-1/95

x=

−1/95

Using distributive property the solution of the equation is x= −1/95

The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

This property is known by distributive law and applies to subtraction also.

Given that the equation; 15x + 8 = 110x + 9.

Step 1: Subtract 110x from both sides.

15x + 8 − 110x = 110x + 9 − 110x

−95x + 8 = 9

Step 2: Subtract 8 from both sides;

−95x + 8 − 8 = 9 − 8

−95x = 1

Step 3: Divide both sides by -95;

x= −1/95

Hence, Using distributive property the solution of the equation is x= −1/95

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Answer:

number is 5

Step-by-step explanation:

let the number be n, then

30 subtracted from 14 times the number is

14n - 30

the result is 20 more than 4 times the number, that is

4n + 20

the equation is then

14n - 30 = 4n + 20 ( subtract 4n from both sides )

10n - 30 = 20 ( add 30 to both sides )

10n = 50 ( divide both sides by 10 )

n = 5

the number is then 5

Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

Answer:

\(9.7 \times 10 {}^{ - 4} \)

The standard form of given number \(9.7\)×\(10^{-4}\)

Standard form is a way of writing down in easy form of very large or very small numbers.

Let E is the standard form of given number

E=0.00097

E= \(\frac{97}{100000}\)

E=97×\(10^{-5}\)

E=\(9.7\)×\(10^{-4}\)

The standard form of given number \(9.7\)×\(10^{-4}\)

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The equation for the growth of the number of bacteria is x(t) = 10000t - 550t² + 110000

The growth rate of the number of bacteria is given as:

V = 10000 - 100mt,

Such that

t = time in hours,

m = 11.

To find the equation for the growth of the number of bacteria x(t), we can integrate this formula with respect to t.

Using the initial condition x(0) = 10000*m, we have

x(t) = ∫V dt + C

Substitute the known values in the above equation, so, we have the following representation

x(t) = ∫(10000 - 100mt) dt + C

Integrate

x(t) = 10000t - 50mt² + C

Recall that x(0) = 10000*m.

So, we have

10000m = 10000 * 0 - 50 * m * 0² + c

Evaluate

c = 10000m

c = 10000 * 11

c = 110000

So, the equation is

x(t) = 10000t - 50mt² + 110000

Since m = 11, we have

x(t) = 10000t - 550t² + 110000

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The value of length BD in the given parallelogram is 10 units.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In other words, opposing sides and angles are congruent and parallel. There are numerous crucial characteristics of parallelograms, including:

A parallelogram's opposing sides are congruent.

A parallelogram's opposing angles are congruent.

The parallelogram's subsequent angles are additional (add up to 180 degrees).

A parallelogram's diagonals cut each other in half (i.e. they intersect at their midpoints).

According to the properties of parallelogram the diagonals of a parallelogram bisect each other.

Thus, BE = ED

Given BE = 5

Thus, ED = 5.

Now, the value of BD = BE + ED = 5 + 5 = 10

Hence, the value of BD in the given parallelogram is 10 units.

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The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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Step-by-step explanation:

Given the formula

a(n+1)=an−3

The first term a(1) = 31

For the second term

a(2)

We have

a( 1 + 1) = a(1) - 3

a(2) = 31 - 3

a(2) = 28

For the third term

a(3)

We have

a(2+1) = a(2) - 3

a(3) = 28 - 3

a(3) = 25

For the fourth term

a(4)

That's

a(3+1) = a(3) - 3

a(4) = 25 - 3

a(4) = 22

Hope this helps you

Thus, the values of missing length of the triangle using 45°-45°-90° triangle theorem is found as: x = 49√2 and y = 7.

Special right triangles containing angles of 45 and 90 degrees are known as 45-45-90 triangles. Special isosceles triangles are all 45-45-90 triangles. The 45-45-90 triangle has three distinct qualities that make it exceedingly special though unlike all the other triangles.

For the given triangle, using 45°-45°-90° triangle theorem

y = 7 ( as two angles are equal of 45°-45°, the two adjacent side of the right angle will also be equal.

now using Pythagorean theorem.

x² = y² + 7²

x² = 7²+ 7²

x² = 49 + 49

x² = 98

x = 49√2

Thus, the values of missing length of the triangle using 45°-45°-90° triangle theorem is found as: x = 49√2 and y = 7.

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A rectangle has a perimeter of 60 feet. The rectangle's length is four times its width. The area of rectangle is 144 square feet.

Given that,

A rectangle has a perimeter of 60 feet.

The rectangle's length is four times its width.

We have to find the area of rectangle.

Let us take length as x

The width will be 4x

The perimeter =2(4x+x)

2(4x+x)=60

4x+x=60/2

5x=30

x=30/5

x=6

The length will be 6.

The width will be 4×6=24.

The area of rectangle is length×width

=6×24

=144 square feet.

Therefore, the area of rectangle is 144 square feet.

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Answer:

(D). 17 in.

Step-by-step explanation:

c² = a² + b² - 2abcosC

cosC = \(\frac{a^2 + b^2 -c^2}{2ab}\)

m∠C = \(cos^{-1}\) ( \(\frac{a^2 + b^2 -c^2}{2ab}\) )

m∠C = \(cos^{-1}\) ( \(\frac{28^2 +18^2 -12^2 }{2(28)(18)}\) )

m∠C = \(cos^{-1}\) ( \(\frac{964}{1008}\) ) ≈ 17 in.

\( = > \frac{10}{14} \\ \)

\( = > \frac{5}{7} \\ \)

\( = > 0.71428\)

Answer:

9d+3

Step-by-step explanation:

(6D+5)-(2-3D);next step I disributed the negative sign into parenthesis wil resulted in no paranthesis.

6d+5-2+3d

9d+3

the problaty of getting Gray tile is 6 time

Answer:

15:24, 20:32 and 40:64.

Step-by-step explanation:

hope this helps

Answer:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Step-by-step explanation:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Answer:

You can just type it in the calculator. 1/2=0.5 so 1 - .05= 0.5 . Lmk if there is more to the question!

Step-by-step explanation:

Answer:

\(\sqrt[12]{8} ^x\)

Step-by-step explanation:

\(3 / \frac{1}{4} = 12\)

The probability that the metal bars can be cut and sold as a 12cm bar would be = 4/5

Probability is defined as the likelihood or possibility that an event will or will not occur.

The actual length of the metal bars produced by the manufacturer = 15cm.

The malfunctioning of the equipments can lead to the metal being sold at a different length such as = 12 cm

The probability of selling the equipment at 12cm;

= 12/15

= 4/5

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Answer:

(b) 2 / (1/6) = 2 * (6/1) = 12

(a)There are six sixths in a whole. In terms of numbers, 6/6 = 1.

Answer:

6 sixths in one whole and 12 sixths in 2.

Therefore, the solutions to the quadratic equation x² + 7x - 8 = 0 are -8 and 1. The answers are D and E.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.

Here,

To check which values are solutions to the quadratic equation, we can substitute each value into the equation and see if it equals zero.

Substituting -1 into the equation:

(-1)² + 7(-1) - 8 = 1 - 7 - 8 = -14, which is not equal to zero.

Substituting 2 into the equation:

2² + 7(2) - 8 = 4 + 14 - 8 = 10, which is not equal to zero.

Substituting -4 into the equation:

(-4)² + 7(-4) - 8 = 16 - 28 - 8 = -20, which is not equal to zero.

Substituting -8 into the equation:

(-8)² + 7(-8) - 8 = 64 - 56 - 8 = 0, which is equal to zero. Therefore, -8 is a solution to the equation.

Substituting 1 into the equation:

1² + 7(1) - 8 = 1 + 7 - 8 = 0, which is equal to zero. Therefore, 1 is a solution to the equation.

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Range is the difference between the highest score and lowest score.

To find the range the teacher needs to know the highest and lowest grades in the test.

Answer: 20

Step-by-step explanation:

Multiply 2.4*10-4

Calculate 24-4

the answer is (12x^10000)/5

Answer:

1764

Step-by-step explanation:

Y=6b+12ab^2

Let a = 4

b = 6

Y = 6(6) +12 (4)(6)^2

   = 36 + 12 (4) (36)

   = 36+1728

   =1764

Answer:

\(\huge\boxed{\sf Y = 1764}\)

Step-by-step explanation:

\(Y = 6b+12ab^2\\\\Given \ that \ a = 4 , \ b = 6\\\\Putting \ values\ in \ given \ equation\\\\Y = 6(6) +12(4)(6)^2\\\\Y = 36 + 48(36)\\\\Y = 36 + 1728\\\\Y = 1764\\\\\rule[225]{225}{2}\)

Hope this helped!

The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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Answer:

3

Step-by-step explanation:

-(4)+7=3

plug in 4 for d and since it is -d it would be -4

7-4=3

Answer:

Step-by-step explanation:

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