Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates. slope: −2, ordered pair: (−5,1)

To solve this question we will have to make use of one of the properties of the inscribed quadrilateral. That property is: "Opposite angles in any quadrilateral inscribed in a circle are supplements of each other".

Thus, as we can see from the diagram given, [tex] \angle B+\angle D=180^{\circ} [/tex]

[tex] (2x+3)+(4x+3)=180^{\circ} [/tex]

[tex] \therefore 6x+6=180^{\circ} [/tex]

[tex] 6x=174^{\circ} [/tex]

[tex] \therefore x=\frac{174^{\circ}}{6} =28^{\circ} [/tex]

Thus, now that we know the value of x, we can easily find the value of the [tex] \angle C [/tex] because we know that:

[tex] \angle C=2x+1 [/tex]

[tex] \therefore \angle C=2(29^{\circ})+1=59^{\circ} [/tex]

Thus, [tex] \boldsymbol{59^{\circ}} [/tex] is the correct answer.

The largest pair of consecutive integers are 198 and 200.

If the sum of two equal even numbers is 400, the numbers will be 200+200.
Therefore the largest possible consecutive even numbers which have a sum of 400 or less are 198 and 200 which have a sum of 398.

Any pair of consecutive numbers less than these will have a sum of less than 400.

To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits. The number of different seven-digit phone numbers that satisfy the given property is 7.

To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits.

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a)[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.

b) you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.

Let's break down this problem step by step:

a. To find a formula for the distance ( h ) (in meters) from you to the ground after ( t ) seconds of riding, we can use trigonometry and the properties of circular motion.

1. The Ferris wheel has a radius of 6 meters and is centered 7 meters above the ground. This means that at the lowest point, you are ( 7 + 6 = 13 ) meters above the ground, and at the highest point, you are ( 7 - 6 = 1 ) meter above the ground.

2. The angular speed of the Ferris wheel is given as 24 degrees per second. Since the Ferris wheel completes one full rotation (360 degrees) in[tex]\( \frac{360^\circ}{24^\circ/\text{sec}} = 15 \)[/tex] seconds, its angular velocity is[tex]\( \omega = \frac{2\pi}{15} \)[/tex]radians per second.

3. Let [tex]\( \theta \)[/tex] be the angle in radians that the Ferris wheel has rotated through at time ( t ) seconds. The height ( h ) above the ground can be expressed as:

[tex]\[ h = 13 - 6\cos(\theta) \][/tex]

To relate[tex]\( \theta \) to time \( t \)[/tex], we use the formula for angular displacement in circular motion:

[tex]\[ \theta = \omega t \][/tex]

Substitute [tex]\( \omega = \frac{2\pi}{15} \)[/tex] into the equation above to get:

[tex]\[ \theta = \frac{2\pi}{15} t \][/tex]

Now, substitute [tex]\( \theta \)[/tex]back into the equation for height \( h \):

[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.

b. To find the times when you are 10 meters above the ground, we set \( h(t) = 10 \) and solve for \( t \):

[tex]\[ 10 = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

First, subtract 10 from both sides:

[tex]\[ -3 = -6\cos\left(\frac{2\pi}{15} t\right) \][/tex]

Divide both sides by -6:

[tex]\[ \frac{1}{2} = \cos\left(\frac{2\pi}{15} t\right) \][/tex]

Now, take the inverse cosine (arccos) of both sides:

[tex]\[ \frac{2\pi}{15} t = \cos^{-1}\left(\frac{1}{2}\right) \][/tex]

Solve for \( t \) by dividing both sides by [tex]\( \frac{2\pi}{15} \)[/tex]:

[tex]\[ t = \frac{15}{2\pi} \cos^{-1}\left(\frac{1}{2}\right) \][/tex]

Using the fact that [tex]\( \cos^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} \)[/tex], substitute this value into the equation:

[tex]\[ t = \frac{15}{2\pi} \times \frac{\pi}{3} \]\[ t = \frac{5}{2} \][/tex]

So, you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.

Final Answer:

In the isosceles triangle, the base angles are congruent, and the given angle at the top is [tex]\(70^\circ\)[/tex]. Using the sum of angles in a triangle, we find that the value of (x) is [tex]\(40^\circ\)[/tex]. Therefore, the final answer is [tex]\(x = 40^\circ\)[/tex].

Step-by-step explanation:

The base angles of the isosceles triangle as (A) and (B), and the vertex angle as (x). Since we know that the angles opposite the congruent sides are congruent, we have:

[ A = B ]

Now, let's consider the sum of angles in a triangle. The sum of all angles in a triangle is always [tex]\(180^\circ\)[/tex]. Therefore:

[tex]\[ A + B + x = 180^\circ \][/tex]

But since (A = B), we can rewrite this as:

[tex]\[ 2A + x = 180^\circ \][/tex]

Now, substitute (A) with [tex]\(70^\circ\)[/tex] (as given in the problem):

[tex]\[ 2(70^\circ) + x = 180^\circ \][/tex]

Simplify the equation:

[tex]\[ 140^\circ + x = 180^\circ \][/tex]

Now, isolate (x) by subtracting [tex]\(140^\circ\)[/tex] from both sides of the equation:

[tex]\[ x = 180^\circ - 140^\circ \][/tex]

[tex]\[ x = 40^\circ \][/tex]

So, the value of (x) in the given isosceles triangle is [tex]\(40^\circ\)[/tex].

Final answer:

The value of x in the isosceles triangle is 40 degrees, which is found by using the property that the angles opposite the congruent sides are congruent and the sum of the angles in any triangle is always 180 degrees.

Explanation:

To find the value of x in an isosceles triangle where one of the angles at the base is 70 degrees, we employ the property that the angles opposite the congruent sides of an isosceles triangle are also congruent. This means that the other angle at the base is also 70 degrees. Since the sum of the angles in any triangle is always 180 degrees, we can set up an equation to solve for x:

70° (angle at the left base) + 70° (angle at the right base) + x (angle at the top) = 180°

Adding the base angles together gives us:

70° + 70° = 140°

To find x, we simply subtract the sum of the base angles from 180 degrees:

180° - 140° = 40°

Therefore, the value of x, the angle at the top of the isosceles triangle, is 40 degrees.

Answer:

The value of [tex]\sum_{n=3}^{8}5n[/tex] is 165.

Step-by-step explanation:

We have to evaluate sigma 5n from n=3 to 8 taht is:

[tex]\sum_{n=3}^{8}5n[/tex]

Thus, substituting the value of n from 3 to 8 in the above equation, we get

=[tex]5(3)+5(4)+5(5)+5(6)+5(7)+5(8)[/tex]

=[tex]15+20+25+30+35+40[/tex]

=[tex]165[/tex]

Thus, the value of [tex]\sum_{n=3}^{8}5n[/tex] is 165.

Answer:

D) 5.45 hours

Step-by-step explanation:

I got it correct on USATP.

Hope this helps!

From: Aug1e

Answer:

Convection

Step-by-step explanation:

A is the correct answer.

Answer:

9x3 (B)

Step-by-step explanation:

i just took the unit test, it was correct

The sum of the polynomial function is 9x^3 - 8x^2

Polynomial functions area function with a leading degree of 3 and above. Given the sum;

(7x^3-4x^2)+(2x^3-4x^2)

Expand

(7x^3-4x^2)+(2x^3-4x^2)

= 7x^3-4x^2 + 2x^3-4x^2

Collect like terms

7x^3 + 2x^3 - 4x^2 -4x^2

9x^3 - 8x^2

Hence the sum of the polynomial function is 9x^3 - 8x^2

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You didn't add the system of inequalities. But when you are posting a question and you don't know how to type the question or the answer or if you don't feel like it. Hold down shift, ctrl (control), and the button that divides/spaces  each tab out, amd you're screen if go dime so you can highlight a part of the screen so it will take a picture and you can post it.

___________________________

I posted the question and answer below.

!!Hope this helped!!

Please rate "excellent"

Step-by-step explanation:

Answer: In the picture below the correct answer is

D. The system represents the minimum amount that Ms. Jones can spend on cheese pizzas, x, and pepperoni pizzas, y, and the relationship between the number of cheese pizzas and pepperoni pizzas.

no lo sé, pero como necesito puntos, ¿sí?

Answer:

C

Step-by-step explanation:

Answer:  The correct options are :

(4). (A) [tex](5b+3y)(a+1).[/tex]

(5). (C) [tex] (x+7)(4x^2+7).[/tex]

(6). (D) [tex] (3x+5)(7x^2+3).[/tex]

(7). (C) [tex] (10x+3)(y+2a).[/tex]

Step-by-step explanation:  We are given to completely factor the following expressions :

Expression 4 :

The given expression is

[tex]E_1=5ab+3ay+5b+3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

The factorization of expression (i) is as follows :

[tex]E_1\\\\=5ab+3ay+5b+3y\\\\=a(5b+3y)+1(5b+3y)\\\\=(5b+3y)(a+1).[/tex]

So, option (A) is CORRECT.

Expression 5 :

The given expression is

[tex]E_2=4x^3+28x^2+7x+49~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

The factorization of expression (ii) is as follows :

[tex]E_2\\\\=4x^3+28x^2+7x+49\\\\=4x^2(x+7)+7(x+7)\\\\=(x+7)(4x^2+7).[/tex]

So, option (C) is CORRECT.

Expression 6 :

The given expression is

[tex]E_3=21x^3+35x^2+9x+15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

The factorization of expression (iii) is as follows :

[tex]E_3\\\\=21x^3+35x^2+9x+15\\\\=7x^2(3x+5)+3(3x+5)\\\\=(3x+5)(7x^2+3).[/tex]

So, option (D) is CORRECT.

Expression 7 :

The given expression is

[tex]E_4=10xy+3y+20ax+6a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]

The factorization of expression (iv) is as follows :

[tex]E_4\\\\=10xy+3y+20ax+6a\\\\=y(10x+3)+2a(10x+3)\\\\=(10x+3)(y+2a).[/tex]

So, option (C) is CORRECT.