A) –2n + 9m – 17p

B) –2n – 9mn + 17np

C) –2n + 9mn – 17np

D) –18n + 81mn – 153np

Answer:  the correct option is (D) [tex]x=\dfrac{k-11}{3}.[/tex]

Step-by-step explanation:  We are given to solve the following equation for the value of x :

[tex]3x+11=k~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for x, we need to take x on one side and all other terms on the other side of the equality.

The solution of equation (i) is as follows :

[tex]3x+11=k\\\\\Rightarrow 3x=k-11\\\\\Rightarrow x=\dfrac{k-11}{3}.[/tex]

Thus, the required value of x is [tex]x=\dfrac{k-11}{3}.[/tex]

Option (D) is CORRECT.

Answer:

Robin is 9 years old and Batman is 36 years old

Step-by-step explanation:

Batman: 4x

Robin: x

4x + x = 45

5x = 45

x= 9

Answer:

(A) [tex]x=7.2 ft[/tex]

Step-by-step explanation:

Given: A triangle whose base angle is 44° and hypotenuse is 10ft.

To find: The value of x.

solution: Using the trigonometry, we have

[tex]\frac{x}{10}=cos44^{{\circ}}[/tex]

⇒[tex]x=10{\times}cos44^{{\circ}}[/tex]

⇒[tex]x=10{\times}0.72[/tex]

⇒[tex]x=7.2 ft[/tex]

Thus,the value of [tex]x=7.2 ft[/tex]

Answer: A. 7.2 ft

Step-by-step explanation:

Given: A right triangle with hypotenuse 10 ft and base angle [tex]44^{\circ}[/tex]

By using Trigonometry, we have

[tex]\cos (44^{\circ})=\frac{\text{side adjacent to }44^{\circ}}{\text{hypotenuse}}\\\\\Rightarrow \cos (44^{\circ})=\frac{x}{10}\\\\\Rightarrow0.71933980033=\frac{x}{10}\\\\\Rightarrow\ x=10\times0.71933980033=7.1933980033\approx7.2\ ft.[/tex]

Hence, the value of x = 7.2 ft.

About 15 tons of trout were caught in the lake in the years 1999 and 2011.

To determine the years when about 15 tons of trout were caught in the lake, we need to solve the equation [tex]\( y = -0.08x^2 + 1.6x + 10 \) for \( y = 15 \).[/tex]

The equation becomes:

[tex]\[ 15 = -0.08x^2 + 1.6x + 10 \][/tex]

Subtract 15 from both sides to set the equation to zero:

[tex]\[ 0 = -0.08x^2 + 1.6x - 5 \][/tex]

This is a quadratic equation in the form of [tex]\( ax^2 + bx + c = 0 \)[/tex], where:

- ( a = -0.08 )

- ( b = 1.6 )

- ( c = -5 )

We solve this quadratic equation using the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):[/tex]

First, calculate the discriminant [tex]\( \Delta = b^2 - 4ac \):[/tex]

[tex]\[ \Delta = (1.6)^2 - 4(-0.08)(-5) \][/tex]

[tex]\[ \Delta = 2.56 - 1.6 \][/tex]

[tex]\[ \Delta = 0.96 \][/tex]

Now, calculate the two possible values of ( x ):

[tex]\[ x = \frac{-1.6 \pm \sqrt{0.96}}{2(-0.08)} \][/tex]

Calculate [tex]\( \sqrt{0.96} \):[/tex]

[tex]\[ \sqrt{0.96} \approx 0.9798 \][/tex]

Now solve for ( x ):

[tex]\[ x_1 = \frac{-1.6 + 0.9798}{-0.16} \][/tex]

[tex]\[ x_1 = \frac{-0.6202}{-0.16} \][/tex]

[tex]\[ x_1 \approx 3.88 \][/tex]

[tex]\[ x_2 = \frac{-1.6 - 0.9798}{-0.16} \][/tex]

[tex]\[ x_2 = \frac{-2.5798}{-0.16} \][/tex]

[tex]\[ x_2 \approx 16.12 \][/tex]

Since ( x ) is the number of years since 1995:

For [tex]\( x_1 \approx 3.88 \):[/tex]

[tex]\[ \text{Year} = 1995 + 4 = 1999 \][/tex]

For [tex]\( x_2 \approx 16.12 \):[/tex]

[tex]\[ \text{Year} = 1995 + 16 = 2011 \][/tex]

Therefore, about 15 tons of trout were caught in the lake in the years 1999 and 2011.

Answer:

Sum = (n -2) * 180

Step-by-step explanation:

Step 1 : The formula for calculating the sum of the interior angles = (n - 2) × 180, where "n" is the number of sides of a regular polygon.

Step 2: Here we are given the sum of the interior angles is 180 degrees. Therefore, the given figure must be triangle.

In a convex polygon, all interior angles are less than or equal to 180. So pentagons are polygons of five sides. We need to draw two different pentagons with the previous characteristics and measures of the internal angles. Therefore, we will choose to type of pentagons.

Every pentagon can be divided up into three triangles, either a regular or irregular one and each triangle adds up to 180 degrees. Therefore, the angles in every pentagon must add up to 540 degrees.

1. Drawing of the first convex pentagon (Regular Pentagon).

A polygon is regular when all angles are equal and all sides are equal. The regular pentagon is a 5-sided polygon. This is shown in Figure 1. Note that all angles are equal to 108°.

1.1. Sum of the interior angles of the first convex pentagon.

According to Figure 1, the sum of its interior angles is as follows:

[tex]\alpha=5 \times 108^{\circ}=540^{\circ}[/tex]

As we said, the angles in every pentagon must add up to 540 degrees. If the pentagon is regular each internal angle measures 108°. In fact, in a Regular Polygon with N sides, each angle is:

[tex]\frac{(N-2)180{^\circ}}{N} \\ \\ Since \ N=5 \\ \\ \\ \frac{(5-2)180{^\circ}}{5}= 108^{\circ}[/tex]

2. Drawing of the second convex pentagon (Irregular Pentagon)

This is a type of polygon that does not have all sides equal and all angles equal. In Figure 2 is shown this pentagon. Note that there are five sides and all angles are not equal.

2.1 Sum of the interior angles of the second convex pentagon.

According to Figure 2, the sum of its interior angles is given by:

 [tex]\beta=81^{\circ}+139^{\circ}+139^{\circ}+94^{\circ}+87^{\circ}=540^{\circ}[/tex]

As we said, no matter if the pentagon is irregular, the angles in every pentagon must add up to 540 degrees.

Answer with explanation:

A Polygon is said to be convex, if all the diagonals of the polygon lies in the interior of the polygon.

→Sum of interior angle of polygon =(n-2)×180°, where n is the number of sides of the polygon.-----(1)

→A pentagon is said to be convex, if it has 5 sides and all the Diagonals of pentagon lies in the interior.

Sum of interior Angles of Triangle =(3-2)×180°=180°

Sum of interior angles of Quadrilateral = (4-2)×180°=2×180°=360°

Sum of Interior angles of Polygon =(5-2)×180°=3×180°=540°

Used the formula (1) in all the three cases.

Final answer:

When Isaac uses 24cm of string to make rectangles, no matter the individual dimensions, the sum of the length and width of these rectangles must always be 12 cm. This is a direct result of the fixed perimeter, which requires that the combined measurements of length and width halves the total perimeter to maintain the consistent total string usage.

Explanation:

Isaac made all these rectangles with 24cm lengths of string, which implies that the perimeter of all these rectangles is equal. The observation about the sum of the length and the width of these rectangles is that regardless of the individual measurements of the length and width, their sum must always be half the total perimeter of the rectangle. Given a fixed perimeter of 24cm, the formula for the perimeter of a rectangle (P) is

P = 2(l + w),

where l is the length and w is the width. Since the perimeter is given as 24cm, this simplifies to

24 = 2(l + w), or 12 = l + w.

This equation means that the sum of the length and width of the rectangles must always equal 12 cm. This is because the total loop made by the string when forming the rectangle has to be divided into four edges, two lengths, and two widths, which totals the provided 24cm of string. Therefore, if we adjust either the length or the width, the other measurement must adjust in such a way that their sum remains constant at 12 cm to maintain the total perimeter as 24cm.

Answer:

B is correct.

Step-by-step explanation:

The congruence theorem that can be used to prove △MLQ ≅ △NPQ is the SAS (Side-Angle-Side) congruence theorem.

To prove that triangles MLQ and NPQ are congruent, we can use the SAS (Side-Angle-Side) congruence theorem. The given information MQ = NQ indicates that the sides MQ and NQ are congruent. Since Q is the midpoint of LP, we can conclude that the side LQ is congruent to side PQ. Lastly, the fact that LM ≅ PN means that the side LM is congruent to side PN. Therefore, we have congruent corresponding sides and an included congruent angle, allowing us to use the SAS congruence theorem. So, △MLQ ≅ △NPQ.

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Answer:

The correct option is 2.

Step-by-step explanation:

Given information: WZ is tangent to circle O at point B.

According to the tangent of circle theorem: The tangent line is perpendicular to the radius at the point of tangency. It means the angle formed on the point of tangency by tangent and radius is a right angle.

Since WZ is tangent to circle O at point B and OB is radius, therefore

[tex]\angle OBZ=90^{\circ}[/tex]

Therefore correct option is 2.

The measure of angle ∠OBZ is 90°, as the tangent line to a circle at a point is perpendicular to the radius at that point.

The question regards the measure of angle ∠OBZ where WZ↔ is tangent to circle O at point B. By a well-known theorem in geometry, a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. Therefore, the measure of angle ∠OBZ, which is formed by the radius OB and the tangent line at B, must be 90°.

The possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.

Let's denote the length of one part of the wire as x and the length of the other part as 32−x. Each part is bent to form a square.

The perimeter (P) of a square is given by 4 × side length.

The side length of the first square ([tex]S_1[/tex] ) is x/4, and the side length of the second square ([tex]S_2[/tex] ) is (32−x)/4.

The total area of the two squares is given as [tex]34cm^2[/tex] , so we can write the equation:

[tex]S^2_1 + S^2_2 = 34[/tex]

Substitute the expressions for [tex]S_1 and S_2[/tex] :

[tex](\frac{x}{4})^2 + (\frac{(32-x)}{4})^2 =34[/tex]

Now, solve for x:

[tex]\frac{x^2}{16} + \frac{(32-x)^2}{4} =34[/tex]

Multiply both sides by 16 to get rid of the denominators:

[tex]x^2 +(32-x)^2=544[/tex]

Expand and simplify:

[tex]x^2+1024-64x+x^2 =544[/tex]

Combine like terms:

−64x+480=0

Divide the entire equation by 2 to simplify:

−32x+240=0

Now, factor the quadratic equation:

(x−20)(x−12)=0

So, x=20 or x=12.

If x=20, the lengths of the two parts are 20 cm and

32−20=12 cm.

If x=12, the lengths of the two parts are 12 cm and

32−12=20 cm.

Now, we can find the perimeter of each square by multiplying the side length by 4:

For x=20, the perimeter is [tex]4 \times \frac{20}{4} = 20 cm[/tex]

For x=12, the perimeter is [tex]4 \times \frac{12}{4} = 12 cm[/tex]

So, the possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.

Final answer:

The slope of the skateboard ramp, calculated using the rise over run formula, is 0.3. This is found by dividing the rise of 1.2 meters by the run of 4 meters.

Explanation:

The slope of a ramp is calculated as the rise divided by the run. To find the slope of the skateboard ramp, which rises 1.2 meters above the ground and runs 4 meters horizontally at the base, you would use the formula:

Slope (m) = Rise / Run

Here, the rise is the height the ramp rises above the ground, which is 1.2 meters, and the run is the distance along the ground, which is 4 meters horizontally. By substituting the given rise and run into the formula, you obtain:

Slope (m) = 1.2 m / 4 m = 0.3

So, the slope of the skateboard ramp is 0.3.

The sperm whale's underwater duration is seven times that of the sea cow, showcasing remarkable breath-holding abilities, likely adapted for deep-sea foraging and hunting.

The relationship between the underwater durations of a sperm whale and a sea cow suggests that the sperm whale's capability is sevenfold that of the sea cow. Let's denote the sea cow's duration as "x." Accordingly, the sperm whale's underwater duration would be 7 times x.

In practical terms, if we assume the sea cow can stay submerged for 10 minutes (x = 10), then the sperm whale, being seven times more proficient, can stay underwater for 7 times 10, which is 70 minutes (7x = 7 * 10 = 70). This sevenfold difference implies a significant contrast in their breath-holding abilities.

The numerical representation extends universally; if the sea cow can endure underwater for "x" units of time, the sperm whale can endure for 7 times "x" units of time. This relationship showcases the remarkable adaptation of the sperm whale to extended submersion, likely linked to its deep-sea foraging behavior and hunting strategies.

In essence, the sperm whale can stay underwater for a duration that is seven times longer than that of the sea cow, highlighting its remarkable breath-holding capacity.

A sperm whale can stay underwater for 7 times longer than a sea cow, so it can stay underwater for 7 times the duration of a sea cow.

If a sperm whale can stay underwater 7 times longer than a sea cow, we can express this relationship as:

Time a sperm whale can stay underwater = 7 * Time a sea cow can stay underwater

So, if we let the time a sea cow can stay underwater be represented by 'x', then the time a sperm whale can stay underwater is:

7 * x

Therefore, a sperm whale can stay underwater for 7 times longer than a sea cow, which means it can stay underwater for 7x.

Answer:

The correct answer is pilot. I took the test

Step-by-step explanation:

true transformation is a dilation

Yes it is true!! Dilation is a transformation because each point of the object is moved- like tracing- a perfectly strait line! The strait line is drawn from a point called the center of dilation!

Have a great day! :)

Answer:

The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]

Step-by-step explanation:

We are required to find the intervals in which the function is increasing.

From the figure, we see that,

The graph is going up towards the origin to reach the point (0,0).

Then, it is going down in the interval (0,1).

Then, it is again going up to reach the point (2,0).

Finally, it is going downwards towards infinity.

Thus, we see that,

The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]

Answer:(−∞, 0) and(1,2)

Step-by-step explanation: