Use cosine law to find the value of x. Show working. use ^ for power and sqrt for square root

Answer:

[tex](-9.5,2.63)[/tex]

Step-by-step explanation:

In essence, this problem asks one to find the vertex of the given equation. An easy way to find the vertex of a quadratic equation in standard form is to complete the square.

Completeting the square involves grouping the quadratic and linear term, then factoring out the coefficient of the quadratic term. After doing so, one will add a term to make the grouped terms a perfect square trinomial and then balance the equation. Finally, one will simplify the equation and get the quadratic equation in vertex form. From there, finding vertex is quite easy, the x-coordinate is the additive inverse of the quadratic term, and the y-coordinate is the constant.

Once a quadratic equation in standard form has been converted to vertex form by the process of completing the square, its equation is amongst the lines of the following,

[tex]a(x-k)^2+h[/tex]

(k, h) is the vertex of the parabola.

The quadratic equation in standard form,

[tex]2x^2+19x+42.5[/tex]

Group the quadratic and linear terms,

[tex](2x^2+19x)+42.5[/tex]

Factor out the coefficient of the quadratic term,

[tex]2(x^2+9.5x)+42.5[/tex]

Add a term to make the grouped part a perfect square trinomial, then balance the equation,

[tex]2(x^2+9.5x+22.5625)+42.5-2(22.5625)[/tex]

Simplify,

[tex]2(x^2+9.5x+22.5626)+42.5-45.125[/tex]

[tex]2(x+9.5)^2+2.625[/tex]

The vertex of the equation is the following,

[tex](-9.5,2.625)[/tex]

Rounded,

[tex](-9.5,2.63)[/tex]

Answer:

y=x+12

Step-by-step explanation:

m (slope)=1

y-intercept=12

hope this helped have a great day :)

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{gold}{Answer \red{:)}}}}}}}}[/tex]

In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked.

In 200 eggs cracked =6

in 1 egg cracked =[tex]\dfrac{6}{200}[/tex]

According to the question,

If the store has 3,000 eggs for sale, how many can expect to be cracked.

In 3000 eggs cracked=[tex]\dfrac{6}{200}×3000[/tex]

If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked

If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked.

A proportion is an equation in which two ratios are set equal to each other.

For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

Given that :

In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked.

In 200 eggs cracked = 6 / 200 in 1 egg cracked

According to the question,

If the store has 3,000 eggs for sale, how many can expect to be cracked.

In 3000 eggs cracked = 6 / 200 x 3000

= 90 eggs

Hence, If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked.

Learned more about Proportion, click;

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Answer:

15.48 yd squared

Step-by-step explanation:

This is because 6 yards can be used as the radius of your circle. square your radius, so 6x6 which is 36 then multiply by 3.14. You then get 113.04. Since it is a semicircle, divide it by 2. You now get 56.52. If you know your radius, you know your diameter which is 12. 12 is also the length of the rectangle so 6x12 is 72 which is the area of the rectangle. Now subtract 56.52 from 72 to get 15.48 which is the shaded region of the rectangle. So I believe that you are doing yards, so 15.48 yd squared. I hope this helps :)

Answer:

How do I ask a question on here?

Step-by-step explanation:

Answer:

B.6 points

Step-by-step explanation:

First you can see that one is bigger and taller and if you count on the number line it will be 18, and 18 has 6 dots so it is B which says 6 dots.

Answer:

128

Step-by-step explanation:

If the area of a figure is 32 square centimeters then the length/breadth could be 8cm and 4cm or 16cm and 2cm.

Let’s assume that the the sides of the figure are doubled, if that’s the case then we would arrive at 8*2 * 4*2 or 16*2 * 2*2 in which 16*8 or 32*4 which will both result to 128 as the answer.

Answer: 240.6cm *squared*

Step-by-step explanation:

Surface Area= (2 x Area of 1st face) + (2 x Area of 2nd face) + (2 x Area of 3rd face)

= (2 x 10.5cm x 5.4 cm) + (2 x 10.5 cm x 4.0cm) + (2 x 5.4cm x 4.0cm)

= 113.4cm*squared* + 84.0cm *squared* + 43.2cm *squared*

= 240.6cm *squared*

OR

= 2 x (sum of the 3 faces)

= 2 x (56.7cm * squared* + 42.0cm *squared* + 21.6cm *squared*)

= 2 x 120.3cm *squared*

= 240.6cm *squared*

Answer:

30.8936

Step-by-step explanation:

Pressure guage reading is 8% lower than tbe actual pressure.

Therefore, for a tyre with guage pressure, 33.58 ;

The actual pressure of tyre would be :

Guage pressure - 8% of guage pressure

33.58 - (0.08 * 33.58)

33.58 - 2.6864

= 30.8936

Actual pressure = 30.8936

Given:

The vertices of the rectangle ABCD are A(0,1), B(2,4), C(6,0), D(4,-3).

To find:

The area of the rectangle.

Solution:

Distance formula:

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

Using the distance formula, we get

[tex]AB=\sqrt{(2-0)^2+(4-1)^2}[/tex]

[tex]AB=\sqrt{(2)^2+(3)^2}[/tex]

[tex]AB=\sqrt{4+9}[/tex]

[tex]AB=\sqrt{13}[/tex]

Similarly,

[tex]BC=\sqrt{(6-2)^2+(0-4)^2}[/tex]

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

[tex]BC=\sqrt{16+16}[/tex]

[tex]BC=\sqrt{32}[/tex]

[tex]BC=4\sqrt{2}[/tex]

Now, the length of the rectangle is [tex]AB=\sqrt{13}[/tex] and the width of the rectangle is [tex]BC=4\sqrt{2}[/tex]. So, the area of the rectangle is:

[tex]A=length \times width[/tex]

[tex]A=\sqrt{13}\times 4\sqrt{2}[/tex]

[tex]A=4\sqrt{26}[/tex]

[tex]A\approx 20[/tex]

Therefore, the area of the rectangle is 20 square units.

Answer:

9

Step-by-step explanation:

No.of words in

- 8 minutes = 72

- 1 minute = 72/8

                = 9

Answer:

9 words per every minute

Step-by-step explanation:

Theres 72 words in 8 minutes, so to get her words to minute, ratio you do 72 divided by 8 to get 9, words per minute.

Answer:

14.04 ft^3

Step-by-step explanation:

2.4 ft x 4.5 ft x 1.3 = 14.04 ft^3

Answer:

Attached below

Step-by-step explanation:

Given that A is a matrix with independent rows

A) Prove [tex]AA^{T}[/tex] is invertible

rank of A = number of rows of Matrix A

This shows that | A | ≠ 0  ( i.e. A has a full rank )

also  [tex]|A^{T} |[/tex] ≠ 0

and [tex]|AA^{T}|[/tex] = | A | [tex]|A^{T} |[/tex]   ≠ 0

Hence we can conclude that [tex]AA^{T}[/tex] is invertible

B) Prove that b is any vector in Col( A )

Attached below is the detailed solution

C) Mapping of Col ( A ) to Row ( A )

b is a non-zero vector hence AXr = 0 ( i.e. there is no solution )

also the kernel of the mapping will be Null

show that mapping preserves the operation

attached below is the detailed solution

Answer:

B) If you use 9 cups of almonds, you need 5 cups of flour

Step-by-step explanation:

If 9 is your x-coordinate, that represents 9 cups of almond.

If 5 is your y-coordinate, that represents 5 cups of flour.

Therefore, B is correct

Answer: x=4y+24

b=b

How to:  Solve in terms of the arbitrary variable  y  .

Have a great day and stay safe ! So sorry if im wrong .

Answer:

3.6 cm

Step-by-step explanation:

Note that:

Area = 1/2 x perimeter x apothem.

To find the Apothem, the formula =

Area ÷ (1/2 × Perimeter)

Area = 100.8cm²

Perimeter = 56 cm

Hence,

Apothem =

100.8 cm² ÷ (1/2 × 56 cm)

= 100.8cm² ÷ 28cm

= 3.6 cm

Therefore, the Length of the apothem is 3.6 cm

Answer: your picture is blocked btw

Step-by-step explanation:

Answer:

the arc length of minor arc AC is

[tex] \frac{165}{360} .2\pi.3 = \frac{11\pi}{4} [/tex]

Step-by-step explanation:

you can use that same formula to answer that same question

The volume of the rectangular prism is [tex]6.75ft^{3}[/tex]

Diagram of a rectangular prism is shown in the attachment below.

Given that:

the height (h) = 1.5 ft

base area (B) = 4.5 sq ft

Volume of rectangular prism (V) [tex]= Bh[/tex]

Plug in the known values into the formula:

[tex]V = 4.5 \times 1.5\\V = 6.75 ft^{3}[/tex]

Volume of the rectangular prism is [tex]6.75ft^{3}[/tex]

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Answer:

Answer:

discovery of jupiter's mons which did not orbit earth

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

x² + 2x + 1 = 2x² - 2 ( subtract x² + 2x + 1 from both sides

0 = x² - 2x - 3 ← in standard form

0 = (x - 3)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

-----------------------------------

(b)

[tex]\frac{x+2}{3}[/tex] - [tex]\frac{2}{15}[/tex] = [tex]\frac{x-2}{5}[/tex] ( multiply through by 15 to clear the fractions )

5(x + 2) - 2 = 3(x - 2) ← distribute parenthesis on both sides

5x + 10 - 2 = 3x - 6

5x + 8 = 3x - 6 ( subtract 3x from both sides )

2x + 8 = - 6 ( subtract 8 from both sides )

2x = - 14 ( divide both sides by 2 )

x = - 7

--------------------------------------------

(c) Assuming lg means log then using the rules of logarithms

log [tex]x^{n}[/tex] ⇔ nlogx

log x = log y ⇒ x = y

Given

log(2x + 3) = 2logx

log(2x + 3) = log x² , so

x² = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 , x = - 1

x > 0 then x = 3

Answer:

45

Step-by-step explanation:

Ratio is 2 baseballs to 3 golf balls you have 30 baseballs.

2×15= 30

3x15= 45

Answer:

El comerciante NO PUEDE guardar todas las cajas de zapatos en el cajón

Step-by-step explanation:

Tenemos que encontrar el volumen de la caja.

Se nos dice en la pregunta que:

Coloca 20 a lo largo, 7 a lo ancho y 8 a la altura.

Volumen = Largo × Ancho × Alto

Largo = 20, Ancho = 7, Alto = 8

Volumen = 20 × 7 × 8

= 1120

También se nos dice que: el comerciante tiene 1108 cajas de zapatos y quiere guardarlas en el cajón de su camión.

Comparando esto con nuestro cálculo anterior, el comerciante NO PUEDE guardar todas las cajas de zapatos en el cajón

Answer:

c.) 7 units to the right

Step-by-step explanation:

A is 7 units away from A', B is 7 units away from B', and so on...

:)

Answer:

There are 10,000 possible combinations that the digits 0-9 can be arranged into to form a four-digit code. Suprisingly, people have an intense lack of imagination when it comes to choosing codes.

Answer:

I’m not sure but I need this too!!

Step-by-step explanation: