A. 21.50
B. 32.25
C. 30.15
D. 20.75

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

baseline and height must be at a right angle with each other.

so, in our case

6 × 11 / 2 = 3 × 11 = 33 cm²

Answer:

Area = 33 cm²

Step-by-step explanation:

[tex]\textsf{Area of a triangle}=\sf \dfrac{1}{2}bh[/tex]

where:

If we turn the triangle counterclockwise, so that the side that measures 6 cm is the base, we will see that the length that measures 11 cm is the height of the triangle (see attached).

Therefore:

Substitute the found values into the formula and solve for A:

[tex]\implies \sf A=\dfrac{1}{2}(6)(11)[/tex]

[tex]\implies \sf A=\dfrac{1}{2}(66)[/tex]

[tex]\implies \sf A=33[/tex]

Therefore, the area of the triangle is 33 cm²

The angle of depression from the top of the lighthouse to the sinking boat is 6.9°.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

From ΔABC it is obtained that;

Height of lighthouse, AC = 25 meters

Distance of boat from the lighthouse, BC = 204 meters

The angle of depression from the top of the lighthouse to the sinking boat is;

[tex]\rm tan \theta = \frac{P}{B} \\\\ \rm tan \theta = \frac{AC}{BC} \\\\ tan \theta = \frac{25}{204} \\\\ \theta = tan^{-1}(0.12)\\\\ \theta = 6.9 ^0[/tex]

Hence, the angle of depression from the top of the lighthouse to the sinking boat is 6.9°

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Answer:

Step-by-step explanation:

(√6 - √2)/4

Answer:

x=10, y=14

Step-by-step explanation:

added in the picture

The z-score of an appliance that stopped working at 64 months is 2.

The mean of observations is equal to the ratio of sum of all the observations and the number of observations.

Given, the set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 months

The z-score is then calculated as

z = x - μ /σ

For an appliance that stopped working at 64 months, we have

x = 64

On substituting the values, we get

z = 64-48/8

z = 2

Hence, the z-score of an appliance that stopped working at 64 months is 2

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Answer:

D on edge

Step-by-step explanation:

2

A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Here we have.

-3(2x - 5) < 5*(2 - x)

First, we need to isolate x in one side, let's expand both sides:

-6x + 15 < 10 - 5x

15 - 10 < 6x - 5x

5 < x

This will be represented with a number line where we have an open circle at 5, and an arrow that goes to the right. So the correct option is:

"A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right."

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The figure second represents the foundation drawing of a provided front, right, and top view option second is correct.

Three-dimensional objects can be represented in two dimensions via an orthographic projection.

As we have given orthographic drawings.

The front, right, and the top view is shown in the picture of the cuboid if merge all the view we will find the three-dimensional figure is a cuboid.

We can represent the cuboid by 2×3 grids as shown in the picture second.

Thus, the figure second represents the foundation drawing of a provided front, right, and top view option second is correct.

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If BCD was reflected over the x axis then the coordinates will be B(-1,0) C(-1,2) and D(-4,1).

Given BCD is a triangle having coordinates (-1,0),(-1,-2),(-4,-1).

When the triangle is reflected over the x axis then all the values of y will change from negative to positive and the values of x remains same because in the second and third quadrant the values of x remains same and in the second quadrant the values of y used to  be positive  and in the third quadrant the values of y used to be negative.

So coordinates of B will change from (-1,0) to (-1,0)

coordinates of C will change from (-1,-2) to (-1,2)

coordinates of D will change from (-4,-1) to (-4,1)

New coordinates will be (-1,0) (-1,2) (-4,1).

Hence if BCD was reflected over x axis the new coordinates will be (-1,0) (-1,2) (-4,1).

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x = 2/3 , 0 .

Question :

[tex] {3x}^{2} - 2x = 0[/tex]

use quadratic formula :

[tex]x = \frac{( - b)± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

Solution :

[tex]a {x}^{2} + bx + c = 0 \\ a = 3 \\ b = - 2 \\ c = 0[/tex]

[tex]x = \frac{ - ( - 2)± \sqrt{ { (- 2)}^{2} - 4 \times 3 \times 0} }{2 \times 3} \\ \\ x = \frac{2± \sqrt{4 - 0} }{6} \\ \\ x = \frac{2± \sqrt{4} }{6} \\ \\ x = \frac{2± 2}{6} [/tex]

separate into two equations :

[tex]x = \frac{2 + 2}{6} = \frac{4}{6} = \frac{2}{3} .[/tex]

[tex]x = \frac{2 - 2}{6} = \frac{0}{6} = 0.[/tex]

the values of x are 2/3 and 0 .

The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

[tex]\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}[/tex]

The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.

Then the distance between them will be

[tex]\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units[/tex]

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Answer:

h = A / ( 1/2 a - 1/2 b)

Step-by-step explanation:

A = ½ ah - ½ bh

Factor out an h

A = h( 1/2 a - 1/2 b)

Divide each side by ( 1/2 a - 1/2 b)

A / ( 1/2 a - 1/2 b) = h ( 1/2 a - 1/2 b)/ ( 1/2 a - 1/2 b)

A / ( 1/2 a - 1/2 b) = h

h = A / ( 1/2 a - 1/2 b)

The two cars in relation to each other when they began travelling will be car B was 20 miles east of car A. Then the correct option is A.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Car A is travelling east at a steady speed of 50 miles per hour.

Then the equation of car A is given as

y = 50x + C

where x be the number of miles and x be the number of hours.

Then we have

After 2 hours, it is 140 miles east of Johns town.

Then we have

y = 50x ..1

Car B is travelling east on the same road. its distance east of Johns town is represented by the graph.

Then the equation of car B will be

y = [(120 - 20) / (2 - 0)]x + 20

y = 50x + 20 ...2

Then the two cars in relation to each other when they began travelling will be car B was 20 miles east of car A.

Then the correct option is A.

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Answer:
Car A was 20 miles east of car B.

Step-by-step explanation:

x = the quantity of 3 plus or minus the square root of 29 all over 2. Then the correct option is B.

The quadratic equation is given as ax² + bx + c = 0.

Then the solution is given as

[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The quadratic equation is given below.

x² – 3x – 5 = 0

Then the solution of the equation will be

[tex]\rm x = \dfrac{-(-3)\pm \sqrt{(-3)^2 - 4 *1*(-5)}}{2*1}\\x = \dfrac{3 \pm \sqrt{29}}{2}[/tex]

Then the correct option is B.

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Answer:

okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

will you be my friend

Step-by-step explanation:

.......... okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

Answer:

[tex]\fbox {See below} \downarrow[/tex]

Step-by-step explanation:

Question 1 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(4x^{3})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 4(3)x^{3-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 12x^{2}}[/tex]

Question 2 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{2}{x^{4}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(2x^{-4})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 2(-4)x^{-4-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -8x^{-5}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -\frac{8}{x^{5}}}[/tex]

Question 3 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3\sqrt{x})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3(x)^{\frac{1}{2}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 3(\frac{1}{2})x^{\frac{1}{2}-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2}x^{-\frac{1}{2}}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2\sqrt{x}}}[/tex]

Question 4 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{3}{\sqrt{x}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{-\frac{1}{2}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 3(-\frac{1}{2})x^{-\frac{1}{2}-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2}x^{-\frac{3}{2}}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2x\sqrt{x}}}[/tex]

Question 5 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{x^{3}}{4})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{1}{4}(3)x^{3-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{3}{4}x^{2}}[/tex]

Question 6 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{5})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 3(5)x^{5-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 15x^{4}}[/tex]

Answer: C

Step-by-step explanation:

The inverse of a function maps the domain onto the range.

Answer:

Step-by-step explanation:

ore energy entered the Earth system than exited due to the greenhouse effect, solar energy trapping systems like solar panel, etc.

How CO₂ changed the energy in the Earth system due to many reasons:-

Carbon dioxide forces the Earth's energy budget out of balance by absorbing thermal infrared energy radiated by the surface. It absorbs thermal infrared energy with wavelengths in a part of the energy spectrum that other gases, such as water vapor, co₂, etc.

The greenhouse effect also increases energy in the earth's system.

An increase in the amount of carbon dioxide creates an overabundance of greenhouse gases that trap additional heat.

These greenhouse gas emissions have increased the greenhouse effect and caused the earth's surface temperature to rise.

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Answer:

14

Step-by-step explanation:

First divide 24 and 6 to find how much 6's there are in 24.

24/6=4

Now, we take that number and multiply it by 3.5 to find how long it will take the group to walk 24km.

3.5*4=14.

It will take the group 14 hours to walk 24 km.

Hope this helps!

If not, I am sorry.

Answer:

see below

Step-by-step explanation:

2: letter at the vertex,  placing a letter or number inside .... , or by using 3 letters

3:

WXY

WXZ

YXZ

4: X

Answer:

The values x = 7 and y = 3 make the equation true.

Step-by-step explanation:

hope this helps

Answer:

Decreases

Step-by-step explanation:

A negative correlation means the y is big when the x is small. As x gets bigger, y gets smaller.

Answer:  2/6+5/6 + 1.167

Answer:

1.16

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:.

Step-by-step explanation:

The expected enrolment in 7 years is  1845.

The formula for calculating future value of the number of students is an exponential equation with this form:

FV = P (1 + r) ^n

1500 x (1.03)^7 = 1845

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Answer:

Θ = 39°

Step-by-step explanation:

OA = OB ( radii of the circle ) , then

Δ AOB is isosceles with base angles congruent , that is

∠ ABO = ∠ BAO = 52°

the exterior angle of a triangle is equal to the 2 opposite interior angles.

∠ DOB is an exterior angle of the triangle , so

∠ DOB = ∠ ABO + ∠ BAO = 52° + 52° = 114°

the angle between a tangent and the radius at the point of contact is 90°, then

∠ OBC = ∠ ODE = 90°

the sum of the 4 interior angles of quadrilateral OBCD = 360°

∠ OBC + ∠ DOB + ∠ ODC + ∠ BCD = 360°

90° + 114° + (90 + 27)° + Θ = 360°

90° + 114° + 117° + Θ = 360°

321° + Θ = 360° ( subtract 321° from both sides )

Θ = 39°