02.
39
za
Diagram NOT
accurately drawn
63
D
E
G
ABC is parallel to DEFG
BCBF
Angle ABE = 39"
Angle CFG = 63
Work out the size of angle x
Give a reason for each stage in your working.
HELP

➲ ( 1 + sec x )( cosec x - cot x ) = tan x

[tex] \implies\quad \sf{(1+sec\:x)(cosec\:x-cot\:x) }[/tex]

[tex] \implies\quad \sf{ \left(1+\dfrac{1}{cos\:x}\right)\left(\dfrac{1}{sin\:x}-\dfrac{cos\:x}{sin\:x}\right)}[/tex]

[tex] \implies\quad \sf{ \left(\dfrac{1+cos\:x}{cos\:x}\right)\left(\dfrac{1-cos\:x}{sin\:x}\right)}[/tex]

[tex] \implies\quad \sf{ \left(\dfrac{1-cos^2 x}{cos\:x.sin\:x}\right)}[/tex]

[tex] \implies\quad \sf{ \left( \dfrac{sin^2 x}{cos\:x.sin\:x}\right)}[/tex]

[tex] \implies\quad \sf{ \left( \dfrac{sin\:x.\cancel{sin\:x}}{cos\:x.\cancel{sin\:x}}\right)}[/tex]

[tex] \implies\quad \sf{\left( \dfrac{sin\:x}{cos\:x}\right) }[/tex]

[tex] \implies\quad\underline{\underline{\pmb{ \sf{tan\:x}}} }[/tex]

➲ ( 1+ sec x )( 1- cos x ) = sin x. tan x

[tex] \implies\quad \sf{ ( 1+ sec\:x)(1-cos\:x)}[/tex]

[tex] \implies\quad \sf{\left(1+\dfrac{1}{cos\:x} \right) \left( 1-cos\:x\right)}[/tex]

[tex] \implies\quad \sf{ \left(\dfrac{cos\:x+1}{cos\:x} \right)(1-cos \:x)}[/tex]

[tex] \implies\quad \sf{\dfrac{1-cos^2 x}{cos\:x} }[/tex]

[tex] \implies\quad \sf{\dfrac{sin^2x}{cos\:x} }[/tex]

[tex] \implies\quad \sf{sin\:x.\left( \dfrac{sin\:}{cos\:x}\right) }[/tex]

[tex] \implies\quad\underline{\underline{\pmb{ \sf{sin\:x.tan\:x}}} }[/tex]

Call KE as a, KI as b

To calculate the perimeter of a kite, we use the formula : 2(a+b)

The perimeter is 42cm, hence a + b = 42/2 = 21 cm

Now, we can write the ratio between a and b as 2:1 (because KE is twice as long)

So, we can calculate KI by taking the sum and divide by the total ratio parts

21 : (2 + 1 ) = 7

Recheck : KI = 7 -> KE = 14

Perimeter = (7+14) x 2 = 42, and 14 is indeed 2 x 7.

The most helpful form to find the coordinates of the minimum is the vertex form.

Remember that for a quadratic equation with a positive leading coefficient, the minimum is at the vertex.

So the better form to determinate the coordinates of the minimum value will be the vertex form, where if the vertex is (h, k), we get:

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

In this case, the first option is in that form:

y = (x + 1)^2 - 25

so:

h = -1

k = -25

This means that the coordinates of the minimum are (-1, -25)

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333

The product of the factors (5x − 8) and (5x + 8) is 25x² −  64. Then the correct option is C.

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

One factor of the polynomial is given which is 5x − 8.

Then the polynomial will be

Let the other factor be 5x + 8

Then their product will be

(5x − 8)(5x + 8)

(5x)² − 8²

25x² −  64

More about the polynomial link is given below.

https://brainly.com/question/17822016

Answer:

D

Step-by-step explanation:

I hope this helps :) Have a lovely day!!!

Answer:

157.741

Step-by-step explanation:

3000=800 ( 1 + 0.05)^t

-800

2200=1.05^t

log(1.05)2200=t

log2200/log1.05

t=157.7...

Answer:

1/3

Step-by-step explanation:

3/9 = 1/3 in simplest form

7/9 - 4/9 = 3/9

If you need further help, let me know!

- profparis

Answer:

Heather is 1.6 m tall and casts a shadow of 3.5 m. At the same time, a barn casts a shadow of 17.5 m. Find the height of the barn in meters. (6y +11307 IH=71° 20.

Step-by-step explanation:

Answer:

  296.1 yards

Step-by-step explanation:

The surveyor is interested in solving a triangle with two sides and the enclosed angle known. The Law of Cosines is used for that purpose.

The angle interior to the triangle where the surveyor turned is the supplement of the turning angle:

  180° -110° = 70°

The law of cosines tells us the relation of the given sides (a, b) and angle (C) to the unknown side (c) is ...

  c² = a² +b² -2ab·cos(C)

  c² = 245² +270² -2·245·270·cos(70°) ≈ 87675.7350

  c ≈ √87675.7350 ≈ 296.10

The length of the lake is about 296.1 yards.

Answer:

C. One hundred twenty-five inches cubed

Step-by-step explanation:

To find the answer,

The volume of a cube is side * side * side

In a cube all the sides are the same.

5 * 5 * 5 = 125

Answer:

c

Step-by-step explanation:

bc i say so, And also With volume it is always cubed

Answer:The correct answer is:

90 feet.

Explanation:

Each wire forms a right triangle with the tree and the ground. The height from the ground to the point on the tree the wire is attached to, 3 feet, is one leg. The length from the tree to where the wire is staked in the ground, 4 feet, is the other leg.

We use the Pythagorean theorem to find the hypotenuse: 3²+4²=c²; 9+16=c²; 25=c²; √25=√(c²); 5=c

This means each wire will be 5 feet long. There are 3 wires per tree, which gives us 5*3 = 15 feet. There are 6 tree, so this is 15*6 = 90 feet of wire.

Step-by-step explanation:

Answer:

An hour and 24 minutes have passed.

Step-by-step explanation:

4:37 minus 3:13 is an hour and 24 minutes.

Answer:

B) B=10(2)^(t/3)

Step-by-step explanation:

The Formula used to find Exponential Growth is

[tex]y=a*b^{\frac{t}{t_{1} } }[/tex]

where y is the Final Amount

a is the Initial Amount

b is the Growth Factor

t is Time

t1 is Time to Complete one Growth

so for our Problem

a=10 and b=2 and t1=3 and y=B

so B=10(2)^(t/3)

So

The expression is

[tex]\\ \rm\rightarrowtail B=10(2)^{\frac{t}{3}}[/tex]

Option B is correct

Answer: D

Step-by-step explanation:

When we are finding f(x) given a value of x, we must identify the value of y that results from the value of x.

We are asked to find f(2).

On the graph, first find the location of x=2.

Then, identify where the function is at x=2.

Finally, identify the corresponding y-value: 12.

The value of f(2) is 12.

Trinomial is an expression. The factors of the given trinomial x²-3x-4 are (x+1)(x-4).

An algebraic expression with three non-zero terms and more than one variable is known as a trinomial.

To know the factors of the trinomial, we need to find the factors of the given trinomial. therefore, we need to divide the middle term of the trinomial into two parts, such that the sum of that two terms is the middle term(-3x), while their product is equal to the product of the first and the last term(ac=-4x²).

Later on, we need to take the common terms out of the first two and the last two terms.

[tex]x^2-3x-4\\\\= x^2-4x+x-4\\\\=x(x-4)+(x-4)\\\\=(x+1)(x-4)[/tex]

Hence, the factors of the given trinomial x²-3x-4 are (x+1)(x-4).

Learn more about Trinomial:

https://brainly.com/question/11067801

Answer:

The circumference of the circles should be 40.84 (rounded is 40.8)

Step-by-step explanation:

You find the circumference by doing 2 x pi * 6.5 which = 40.84

Answer: 16 cm

Step-by-step explanation:

By the triangle midsegment theorem, 2(ST)=2(8)=16=GF

The length of GF in the triangle illustrated will be 16cm.

From the information given, the lengths of HT and T F are 6 centimeters, the lengths of HS and SG are 4 centimeters, and the length of ST is 8 centimeters.

Therefore, the length of GF will be:

= 2 × ST

= 2 × 8

= 16 cm

Learn more about triangles on:

brainly.com/question/1058720

#SPJ9

Answer:

2000 × 9% × 6/12 = 90

2000+90 =2090

Answer:

here (edit I made a mistake)

Step-by-step explanation:

9) [tex]y=\frac{3}{5} x +5[/tex]

10) y = x - 3

11)  [tex]y=-\frac{3}{5} x - 3[/tex]

12) [tex]y=\frac{5}{4} x + 2[/tex]

these are the slop int forms, my bad...

sorry

Answer:

9) -3/5x + y = 5

10) -x + y = -3

11) 3/5x + y = -3

12) -5/4x + y = 2

Step-by-step explanation:

Answer:

where is circle pls send picture of circle

Step-by-step explanation:

Answer:

x = 31°

Step-by-step explanation:

z is the length of the midsegment of the triangle. (Given)

[tex]\implies[/tex] midsegment will be parallel to the third side of the triangle.

[tex]\implies x=31\degree[/tex] (Corresponding angles)

Answer:

Share of A = 150 grams

Share if B = 135 grams

Step-by-step explanation:

Weight of A = 50 kg

Weight of B = 45 kg

ratio of weights = 50 : 45 = 10 : 9

Let the common multiplier of the ratio be x.

-> 10x + 9x = 285

-> 19x = 285

-> x = 285/19

-> x = 15

-> 10x = 150

-> 9x = 135

Share of A = 150 grams

Share if B = 135 grams

Answer:

  175°

Step-by-step explanation:

Bearing angles are usually measured clockwise from North. Reverse bearing angles differ from forward bearing angles by 180°. These relations and the usual angle sum relation for a triangle can be used to solve this problem.

Angle PQR will be the difference in the bearings from Q to P and Q to R:

  ∠PQR = 124° -46° = 78°

Triangle PQR is isosceles, so the base angle at P will be ...

  ∠QPR = (180° -78°)/2 = 51°

__

The bearing from P to R will be 51° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.

  PR bearing = PQ bearing - ∠QPR

  = PQ bearing - 51°

  = (46° +180°) -51° = 175°

The bearing of R from P is 175°.

Answer:

2 and 4

Step-by-step explanation: