Please help me!
Write and solve the compound inequality
A student scored a 73 and 81 on their first
two tests. Write and solve a compound
inequality to find the possible values for a
3rd quiz score that would give them an
average between 80 and 85
my answer is 86<=x<=101, but I don't know if it is right 

Let's suppose the breadth of the rectangle be x cm 

The length of the rectangle = x + 3 cm

It is assumed that the length and breadth of the rectangle is amplified by 2.

Now, the breadth of the rectangle = x + 2

The length of the rectangle = x + 3 + 2 = x + 5

It is also assumed that the area of the rectangle is 70 sq. cm

Hence, the area of the rectangle = length x breadth = (x + 2)(x + 5) = 70

= x2 + 5x + 2x + 10 = 70

= x2 + 7x = 70 - 10

=  x2 + 7x = 60

= x2 + 7x - 60 = 0

= x2 + 12x - 5x - 60 = 0

=  x( x + 12) -5(x + 12) = 0

= ( x + 12) (x - 5) = 0

=x + 12 = 10               or              =x - 5 = 0

= x = 10 - 12 = -2               = x = 5

The breadth of a rectangle is never negative, so the value of x is 5 cm

Therefore, the breadth of the rectangle = 5 cm

The length of the rectangle = 5 + 3 = 8 cm

Answer:

a) [tex]4\left(3x+2\right)-2=12x+6[/tex]

b) [tex]20b-16= 4\left(5b-4\right)[/tex]

Step-by-step explanation:

a) To simplify the expression you must:

Expand [tex]4(3x + 2)[/tex]:

Apply the distributive law: [tex]\:a\left(b+c\right)=ab+ac[/tex]

[tex]a=4,\:b=3x,\:c=2\\\\4\left(3x+2\right)=4\cdot \:3x+4\cdot \:2[/tex]

Simplify [tex]4\cdot \:3x+4\cdot \:2= 12x+8[/tex]

[tex]12x+8-2[/tex]

Subtract the numbers: [tex]4\left(3x+2\right)-2=12x+6[/tex]

b) To factor the expression [tex]20b - 16[/tex] you must:

Rewrite 16 as [tex]4\cdot 4[/tex] and 20 as [tex]4\cdot 5[/tex]

[tex]20b-16=4\cdot \:5b-4\cdot \:4[/tex]

Factor out common term 4

[tex]20b-16= 4\left(5b-4\right)[/tex]

Answer:  The required sequence of transformations is

Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒  (-y, x).

Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).

Step-by-step explanation:  We are given to describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.

From the figure, we note that

the co-ordinates of the vertices of triangle ABC are A(0, 4), B(0, 0) and C(2, 3).

And, the co-ordinates of the vertices of triangle A'B'C' are A'(-2, -3), B'(2, -3) and C'(-1, -1).

We see that if triangle ABC is rotated 90 degrees in anticlockwise direction about the origin, then its co-ordinates changes according to the following rule :

(x, y)  ⇒  (-y, x).

That is

A(0, 4)  ⇒  (-4, 0),

B(0, 0)   ⇒ (0, 0),

C(2, 3)    ⇒ (-3, 2).

Now, if the vertices of the rotated triangle are translated  2 units right and 3 units down, then

(x, y)  ⇒  (x+2, y-3).

That is, the final co-ordinates after rotation and translation will be

(-4, 0)  ⇒  (-4+2, 0-3) = (-2, -3),

(0, 0)   ⇒ (0+2, 0-3) = (2, -3),

(-3, 2)   ⇒ (-3+2, 2-3) = (-1, -1).

We see that the final co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.

Thus, the required sequence of transformations is

Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒  (-y, x).

Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).

Answer:

I hope this helps

Step-by-step explanation:

Answer:

- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).

- m∠BAC = 130°.

- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).

Explanation:

We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.

1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.

Therefore, m∠DCB = 30°.

2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.

3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.

4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.

5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,

we find m∠BAC = 180° - 25° - 25° = 130°.

To solve for "p" in the equation "t = d + pm," isolate "p" by subtracting "d" from both sides: "t - d = pm." Then, divide both sides by "m" to find "p": "p = (t - d) / m." This formula allows you to calculate "p" based on given values of "t," "d," and "m."

To solve for "p" in the equation "t = d + pm," you need to isolate "p" on one side of the equation. Here's how you do it step by step:

Start with the Equation:

The equation is t = d + pm, where "t" represents a value, "d" represents another value, "p" is the variable we want to solve for, and "m" is yet another value.

Isolate the "pm" Term:

To get "pm" by itself, we need to eliminate the "d" term on the right side. We can do this by subtracting "d" from both sides of the equation:

t - d = pm

Solve for "p":

Now that "pm" is isolated on the right side, we can solve for "p" by dividing both sides by "m":

p = (t - d) / m

So, the solution for "p" in terms of "t," "d," and "m" is given by the formula p = (t - d) / m. This formula tells you how to calculate the value of "p" based on the values of "t," "d," and "m."

In practical terms, this equation might be used in various scenarios. For example, if "t" represents total distance, "d" represents a fixed distance, and "m" represents a constant speed, then "p" would represent the time it takes to cover the remaining distance to reach "t." This formula can be quite useful in solving real-world problems involving time, distance, and speed.

For more such question on equation

https://brainly.com/question/29174899

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The area of the triangle is 6 square units.

To find the area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4), we can use the formula for the area of a triangle: Area = 1/2 × base × height.

First, we need to find the base and height of the triangle. The base is the distance between the points (-2, 1) and (2, 1), which is 4 units. The height is the distance between the point (3, 4) and the line formed by the base, which is the vertical distance from (3, 4) to the line y=1, which is 3 units.

Plugging these values into the formula, we get Area = 1/2 × 4 ×3 = 6 square units.

from x15 to x 25 is 4 - -16 = -20 degree change

25 -15 = 10000 feet

-20/10 = -2 degrees every 1000 feet

Answer:  The required probability of getting two green marbles is 49.45%.

Step-by-step explanation:  Given that a bag contains 10 green marbles and 4 yellow marbles. Two marbles are chosen at random, one at a time and without replacement.

We are to find the probability of getting two green marbles.

Let S denote the sample space for the experiment of choosing a marble from the bag and A denote the event of getting a green marble.

The, n(S) = 10 + 4 = 14   and   n(A) = 10.

So, the probability of event A will be

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{10}{14}=\dfrac{5}{7}.[/tex]

After getting one green marble and not replacing, let S' denote the sample space for the experiment of choosing a marble from the bag

and

let B denote the event of getting another green marble.

Then, n(S') = 14 - 1 = 13    and    n(B) = 10 - 1 = 9.

Then, the probability of getting two green marbles is given by

[tex]P\\\\=P(A)\times P(B)\\\\=\dfrac{5}{7}\times\dfrac{n(B)}{n(S')}\\\\\\=\dfrac{5}{7}\times\dfrac{9}{13}\\\\\\=\dfrac{45}{91}\times100\%\\\\=49.45\%.[/tex]

Thus, the required probability of getting two marbles is 49.45%.