If the area of the outer square is 4x2, then the area of the inner square is

Answer:

Last graph is the answer.

Step-by-step explanation:

The inequalities are y < [tex]\frac{2}{3}x[/tex] and y ≥ -x + 2

Now first inequality y < [tex]\frac{2}{3}x[/tex] will represent a dotted line passing through origin and a point (3, 2)

This inequality will be in the form a dotted line and shaded area will be below the line.

Second inequality is y ≥ -x + 2

Line representing the inequality will be solid in shape and shaded area will be above this line.

Common shaded area of both the inequalities matches with the last option.

Therefore, Last option (second row last figure) will be the answer.

The base of the triangle is calculated to be 12 inches using the area and height. Then, through the Pythagorean theorem, the hypotenuse is found to be approximately 36.06 inches.

The subject of the question is related to the calculation of a triangle's hypotenuse using the area and height of a right triangle. Given that the area of a triangle is calculated by halving the product of the base and the height (Area = 1/2 * base * height), we can use the given area to find the base of the right triangle.

First, we call the base of the triangle 'x'. The area is 210 square inches and the height is 35 inches.

We rearrange the formula for the area of a triangle to find 'x' as follows:  base = (2*Area) / height.

Our calculation then becomes x = (2*210) / 35. This simplifies to x = 12 inches.  

Next, we use the Pythagorean Theorem, that states: a² + b² = c², where 'c' represents the hypotenuse. Here, 'a' is the base found (12 inches), 'b' is the height (35 inches), and 'c' is the hypotenuse we're seeking.

Plugging the values into the theorem, we get c = √(12² + 35²). Hence, the hypotenuse of the right triangle is approximately 36.06 inches.

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(5,-1) because it would turn the points to their opposite "charge" and turn the positive to a negative and a negative to a positive

For the function f (x) = 15x - 7, the value of f ⁻¹ (x) is,

⇒ f ⁻¹ (x) = (x + 7) / 15

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 15x - 7

Now, We can find the inverse of f (x) as;

⇒ f (x) = 15x - 7

Substitute y = f (x),

⇒ y = 15x - 7

Solve for x;

⇒ y + 7 = 15x

⇒ x = (y + 7) / 15

Hence, We get;

⇒ f ⁻¹ (x) = (x + 7) / 15

Thus, The inverse function is,

⇒ f ⁻¹ (x) = (x + 7) / 15

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1/2 x 80 x 60 = 2400 square feet was the area

Answer:

Option C. [tex]BC=31.2\ units[/tex]

Step-by-step explanation:

step 1

In the right triangle ABD find the length side AB

Applying the Pythagoras Theorem

[tex]AB^{2}=5^{2}+12^{2}[/tex]

[tex]AB^{2}=169[/tex]

[tex]AB=13\ units[/tex]

step 2

In the right triangle ABD

we know that

[tex]m<ABD=m<BCD[/tex]

[tex]sin(<ABD)=\frac{5}{13}[/tex] -------> equation A

step 3

In the right triangle ABC

[tex]sin(<BCD)=\frac{13}{5+DC}[/tex] ------> equation B

Remember that

[tex]m<ABD=m<BCD[/tex]

so equate equation A and equation B solve for DC

[tex]\frac{5}{13}=\frac{13}{5+DC}[/tex]

[tex]5(5+DC)=13*13[/tex]

[tex]25+5DC=169[/tex]

[tex]5DC=169-25[/tex]

[tex]5DC=144[/tex]

[tex]DC=144/5=28.8\ units[/tex]

step 4

In the right triangle BDC find the length side BC

Applying the Pythagoras Theorem

[tex]BC^{2}=28.8^{2}+12^{2}[/tex]

[tex]BC^{2}=973.44[/tex]

[tex]BC=31.2\ units[/tex]

log(35) = 1.544

 rounded to nearest tenth = 1.5

Answer: The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5

Step-by-step explanation:

Given : The magnitude M of an earthquake is defined to be  [tex]M=\log \frac{I}{S}[/tex]---(1)

, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and

S is the intensity of a “standard” earthquake, which is barely detectable.

If  the magnitude of an earthquake that is 35 times more intense than a standard earthquake

⇒Intensity of earthquake I=35 S

Substitute the value of I in (1), we get [tex]M=\log(\frac{35S}{S})=\log(35)=\log(5\times7)=1.544068[/tex] [tex]\approx1.5[/tex]

∴ The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5

The required number is 27.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Let x be the number,

Then

Twenty-four is subtracted from a number = x - 24

and number divided by nine = x/9

Now according to the question,

x - 24 = x/9

Multiplying whole equation by 9 we get,

9x - 216 = x

Adding 216 both the sides we get

9x  = x + 216

Substracting x both the side we get

8x = 216

Dividing whole equation by 8 we get

x = 27

which is the required number.

Hence,the required Number is 27.

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Answer:

The tip of the minute hand moves approximately 37.7 inches in 15 minutes.

Explanation:

To find how far the tip of the minute hand moves in 15 minutes, we can use the formula for the circumference of a circle:

[tex]\[ \text{Circumference} = 2 \pi r \][/tex]

Where:

- [tex]\( r \)[/tex] is the length of the minute hand (radius of the circle).

Given:

- The length of the minute hand, [tex]\( r = 6 \)[/tex] inches.

Substitute the given value into the formula:

[tex]\[ \text{Circumference} = 2 \pi \times 6 \][/tex]

[tex]\[ \text{Circumference} = 12 \pi \][/tex]

So, the tip of the minute hand moves a distance of [tex]\( 12 \pi \)[/tex] inches in 15 minutes.

To approximate this value:

[tex]\[ 12 \pi \approx 37.7 \][/tex] inches (rounded to one decimal place).

Final answer:

The student made an error in describing the expression 5/n as "the quotient of n and 5." The correct phrase to describe this expression would be "the quotient of 5 and n."

Explanation:

The student made an error in describing the expression 5/n as "the quotient of n and 5." The correct phrase to describe this expression would be "the quotient of 5 and n."

When describing division, it is important to remember that the dividend (the number being divided) comes before the divisor (the number dividing the dividend).

Answer:

A) Variables

A) Independent

A) X

Step-by-step explanation:

Answer:  The required measure of angle ABD is 148°.  

Step-by-step explanation:  Given that ray BD bisects angle CBE, ray BC is transparent to ray BA.

Also,

[tex]m\angle CBD=(3x+25)^\circ,~~m\angle DBE=(7x-19)^\circ,~~m\angle ABC=90^\circ.[/tex]

We are to find the measure of angle ABD.

Since ray BD bisects angle CBE, so we have

[tex]m\angle CBD=m\angle DBE\\\\\Rightarrow (3x+25)^\circ=(7x-19)^\circ\\\\\Rightarrow 3x+25=7x-19\\\\\Rightarrow 7x-3x=25+19\\\\\Rightarrow 4x=44\\\\\Rightarrow x=\dfrac{44}{4}\\\\\Rightarrow x=11.[/tex]

So, we get

[tex]m\angle CBD=(3\times11+25)^\circ=58^\circ.[/tex]

Therefore,

[tex]m\angle ABD=m\angle ABC+m\angle CBD=90^\circ+58^\circ=148^\circ.[/tex]

Thus, the required measure of angle ABD is 148°.  

Answer:50 percent

Step-by-step explanation:You need to subtract 2.25 and 1.50 and get 0.75 then divide it to 1.5 and 0.5 then convert it into decimal form and its 50%.

Answer:

the answer is c} 375