A circle with radius of \greenD{1\,\text{cm}}1cmstart color #1fab54, 1, start text, c, m, end text, end color #1fab54 sits inside a \blueD{3\,\text{cm} \times 4\,\text{cm}}3cm×4cmstart color #11accd, 3, start text, c, m, end text, times, 4, start text, c, m, end text, end color #11accd rectangle

Answer:

[tex]x = - 2 \\ y = - 4[/tex]

Step-by-step explanation:

[tex] - 2x + 2y = - 4 \: \: \: \: \: \\ i.e. \: \: \: - x + y = - 2 \: \: \: \: \: \: \: ...(1)\\ \\ 3x + 3y = - 18 \\ i.e. \: \: \: \: \: \: x + y = - 6\: \: \: \: \: \: \: ...(2)[/tex]

From (1) we get

[tex] x = 2 + y[/tex]

Now put x = 2 + y in equation (2)

[tex]2 + y + y = - 6 \\ 2 + 2y = - 6 \\ 2y = - 6 - 2 \\ 2y = - 8 \\ \\ y = - \frac{8}{2} \\ \\ y = - 4[/tex]

now put y = -4 in equation (1) we get

[tex] - x + ( - 4) = - 2 \\ - x - 4 = - 2 \\ x + 4 = 2 \\ x = 2 - 4 \\ x = - 2[/tex]

Answer:

Arrange this data in numerical order:

120, 125, 130, 134, 136, 140, 145, 145, 150, 170, 190

We have 11 observations.

Minimum = 120

First quartile = 130

Median = 140

Third quartile = 150

Maximum = 190

Check for outliers:

130 - 1.5(150 - 130) = 100

150 + 1.5(150 - 130) = 180, so 190 is an outlier.

See the attachment.

Step-by-step explanation:

|x+3| = -2 doesn't have a solution because the exact values can't be negative

wait I try it !! ,!!!!!!

Answer:

the best model function of the set is 3,11

Answer:

3i + 2j

Step-by-step explanation:

Acceleration = change in velocity/time

Change in velocity

(14i + j) - (2i - 7j)

= 12i + 8j

Divide by time (t = 4)

3i + 2j

The acceleration of the drone in terms of i and j is 3i+2j.

Acceleration is the amount by which the velocity of something changes over a set period of time.

The formula to find the acceleration is a=(v-v₀)/t, where a=average acceleration, v=final velocity, v₀=initial velocity and t=time.

Given that, a drone is flown, with constant acceleration, in a horizontal plane. When initially observed, at a point P, it has a velocity of (2i-7j) ms⁻¹.

Four seconds later the drone is at a point Q and has a velocity of (14i+j) ms⁻¹.

Acceleration = change in velocity/time

Change in velocity

(14i + j) - (2i - 7j)

= 12i + 8j

Divide by time (t = 4)

= 4(3i+2j)/4

= 3i+2j

Therefore, the acceleration of the drone in terms of i and j is 3i+2j.

Learn more about the average acceleration here:

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Answer:

w=5

Step-by-step explanation:

the triangle has the same size of area as the side of the rectangle so therefore 5

Answer:

The area of a triangle is [tex]A\Delta=\frac{1}{2}(base)(height)[/tex]

So, the area of the given triangle is:

[tex]A\Delta=\frac{1}{2}(5)(6)\\A\Delta=\frac{1}{2}(30)\\A\Delta=15cm^2[/tex]

The area of a rectangle is

[tex]A=(length)(width)\\A=(6)w\\A=6wcm^2[/tex]

Once the area of both are the same:

[tex]6w=15\\w=\frac{15}{6} \\w=2.5cm[/tex]

Answer:

Option C is correct.

The expression is undefined when theta is equal to 0° or 90°.

Step-by-step explanation:

If you ignore the friction, the amount of time required for a box to slide down an inclined plane is √(2a/g•sin(theta)•cos(theta)), where a is the horizontal distance defined by the inclined plane, g is the acceleration due to gravity and theta is the angle of the inclined plane. For what values of theta is the expression undefined?

A. 0°

B. 90°

C. Both A and B

D. None

An expression is said to be undefined when its value doesnt take on a real number value, e.g., its value goes to infinity.

And the value of a fractional expression goes to infinity when the denominator is equal to 0.

In the given expression for time,

√(2a/g•sin(theta)•cos(theta)),

The denominator of the expression is

g•sin(theta)•cos(theta)

Since g (acceleration due to gravity) cannot be zero, this expression will go to zero if either

Sin (theta) = 0

or

Cos (theta) = 0

Sin (theta) = 0 when (theta) = 0°

Cos (theta) = 0 when (theta) = 90°

Hence, it is easy to see that the expression given for the amount of time required for a box to slide down an inclined plane becomes undefined when (theta) = 0° or 90°.

Hope this Helps!!!

Answer:

y=3

x=1.5

Step-by-step explanation:

if :

y=3

x=1.5

then:

y-x=1.5

Answer:

4.55

Step-by-step explanation:

You add up all the numbers which is 18.2 and then you divide by the # of data.

Answer:

It's 4.55 because you add all the numbers together and then divide it by the numbers there are.

Answer:

32.60/100*15 = $4.89 = 15%

Step-by-step explanation:

Answer:

$4.89

Step-by-step explanation:

To find the tip, multiply the tip rate by the price of the bill

tip rate * bill

15% * 32.60

Convert 15% to a decimal by dividing by 100, or moving the decimal 2 spaces to the left

15%/100=0.15

15.0 -->0.15

Substitute the decimal in for the percent and multiply

0.15* 32.60=4.89

So, a 15% tip on $32.60 is $4.89

Answer:

C

Step-by-step explanation:

Start at the origin

Go to the right 4 units

Go up 8 units

We will end up at point C

Answer:

The coordinate of C is (4,8)

Answer:

A. y=90+8x

B. After 8 weeks he would be 154 pounds.

Step-by-step explanation:

You use the equation and plug in your x variable as 8 and you get 154 as the y.

Answer:

can u please add more detail

Step-by-step explanation:

Answer:

(B) 7.1 is the estimated square  root of 50

Step-by-step explanation:

A. √50 =  √2 √25

= 5√2.

Jaclyn did not take the square root of 2.

B. We estimate the square root of 2.

Trial and improvement:

It must lie between 1 and 2 so we try 1.5:

1.5 * 1.5 = 2.25

Its  < 1.5 so try 1.4

1.4 * 1.4 = 1.96.

So it is a little above 1.4.

Try 1.45:

1.45 * 1.45                        

     1.45

  *  1.45

       -------

            725

          5800

         14500

       2.1025

= 2.1025.

- this is above 2 so the answer is between 1.40 and 1.45 but closer to 1.4.

A good estimate is 1.42

So the square root of 50 is about 5*1.42 = 7.1

Answer:

B is 7.1!

Step-by-step explanation:

To find out how many square tiles Mr. Grant needs, you need to know the total area he wants to cover. The area of each tile is 9 square feet. Divide the total area by 9 to find the number of tiles he needs.

In order to figure out how many square tiles Mr. Grant needs to buy, more information is needed, such as the size of the area he needs to cover. The area of a single tile can be calculated using the formula Area = length × width. Since the tiles are squares, the length and width are the same, so if each side is 3 feet, then the area of a single tile is 9 square feet. If, for example, Mr. Grant needed to cover an area of 27 square feet, he would divide the total area by the area of a single tile: 27 ÷ 9 = 3, so he would need 3 tiles.

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Answer:

Step-by-step explanation:

hello :

cot x + 2cot x  sin x = 0        0≤ x≤ 180

cotx(1+2sinx) =0    means : cotx=0   or  1+2sinx=0

1)  cotx=0   so :  cosx=0  and  sinx ≠ 0   because cotx = cosx/sinx

when :  0≤ x≤ 180  : x=90°

2) 1+2sinx=0  means : sinx = -1/2

when :  0≤ x≤ 180  : no solutions because  :  sinx ≥ 0

conclusion : one solution : x=90°

Answer: D

Step-by-step explanation:

simplify

Answer:

When dealing with area (2 dimensions) when we deal with  a one dimensional quantity (distance) it changes a 2 dimensional quantity by the square of the difference.

Comparing a 3, 4, 5 triangle to a 6, 8, 10 triangle, the larger triangle has 4 times the area of the smaller triangle.

20)  6 / 4 = 1.5  1.5 ^2 = 2.25

Therefore, ABC's area is 2.25 larger than A'B'C's area.

21) 21 / 7 = 3 and 3^3 = 9

Therefore, ABC's area is 9 times larger than A'B'C's area.

Step-by-step explanation:

Answer:

[tex]6\sqrt{19} \approx 26.153[/tex] inches.

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment [tex]\mathsf{AG}[/tex].

In this diagram (not to scale,) [tex]\mathsf{AB} = 26[/tex] (length of prism,) [tex]\mathsf{AC} = 2[/tex] (width of prism,) [tex]\mathsf{AE} = 2[/tex] (height of prism.)

Pythagorean Theorem can help find the length of [tex]\mathsf{AG}[/tex], one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.

Start by finding the length of line segment [tex]\mathsf{AD}[/tex]. That's the black dotted line in the diagram. In right triangle [tex]\triangle\mathsf{ABD}[/tex] (second diagram,)

Apply the Pythagorean Theorem to right triangle [tex]\triangle\mathsf{ABD}[/tex] to find the length of [tex]\mathsf{AB}[/tex], the hypotenuse of this triangle:

[tex]\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}[/tex].

Consider right triangle [tex]\triangle \mathsf{ADG}[/tex] (third diagram.) In this triangle,

[tex]\mathsf{AD} = \sqrt{26^2 + 2^2}[/tex]. The length of segment [tex]\mathsf{DG}[/tex] is the same as the height of the rectangular prism, [tex]2[/tex] (inches.) Apply the Pythagorean Theorem to right triangle [tex]\triangle \mathsf{ADG}[/tex] to find the length of the hypotenuse [tex]\mathsf{AG}[/tex]:

[tex]\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}[/tex].

Hence, the length of the longest line segment in this prism is [tex]6\sqrt{19} \approx 26.153[/tex] inches.

The longest line segment in a right rectangular prism with dimensions 26 inches by 2 inches by 2 inches is found using the Pythagorean theorem: d = sqrt(l^2 + w^2 + h^2), which gives approximately 26.2 inches.

To find the measurement of the longest line segment in a right rectangular prism, we need to calculate the space diagonal, which is the diagonal that cuts through the body of the prism. In this case, the dimensions of the right rectangular prism are 26 inches long, 2 inches wide, and 2 inches tall. We use the Pythagorean theorem in three dimensions to calculate this, which is the square root of the sum of the squares of the length, width, and height. The formula can be written as:

Where d is the diagonal, l is the length, w is the width, and h is the height. Plugging in the given dimensions:

Calculating the square of each term and adding them gives:

So:

Finally, taking the square root gives us the length of the longest line segment:

Therefore, the longest line segment of the rectangular prism measures approximately 26.2 inches.

Answer:

A and C

Step-by-step explanation:

I did the test and got a 100%

Answer:

= 480 u2

Step-by-step explanation:

=

1

2 bh + bh +

1

2 (b1 + b2)h + bh

=

1

2 (16)(6) + (16)(6) +

1

2 (16 + 32)(6) + (32)(6)

= 48 + 96 + 144 + 192

Answer:

Once the height of the figures are the same and the total height is 24, each one height is 6.

Note: I wil consider square metre as the unit of area.

First, I will calculate the half-length of the triangle base using the pythagorean theorem:

[tex]10^{2}=6^2+x^2\\ 100=36+x^2\\64=x^2\\x=8m[/tex]

∴The base is equal to 16m

Let's calculate the area of the triangle:

[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2} (16)(6)\\\\A=\frac{1}{2} (16)(6)= 48m^2[/tex]

Now, let's calculate the first rectangle Area:

[tex]A=wh\\A=(16)(6)\\A=96m^2[/tex]

Now, the trapezoid area:

The width length of the longer side is equal to 16 plus the length of 2 little triangles. Those triangles base length equal to half-length of the first triangle. Therefore, the longer side/base is equal to 32.

[tex]A=\frac{1}{2} (longerSide+shorterSide)height\\A=\frac{1}{2} (32+16)6\\A=144m^2[/tex]

Now, the last rectangle:

[tex]A=wh\\A=(32)(6)\\A=192m^2[/tex]

Therefore, the figure Total Area is the sum of the triangle, trapezoid and rectangles:

[tex]48+96+144+192=480m^2[/tex]

A = 480 unit of area

Answer: 12 hours

Step-by-step explanation: For this problem we will write a percent equation to solve for 100% and how many total hours it will take angel to finish the entire project.

Lets write a equation to solve for w, total amount of hours.

9/w = 75/100

9/w x w = 75/100 x w

9 = 75w/100

9 x 100/75 = 75w/100 x 100/75

w = 12

So, it will take Angel 12 hours to finish his entire project.

Final answer:

Angel will need 3 more hours to complete the art project, for a total of 12 hours when he continues to work at the same rate.

Explanation:

Angel has completed 75% of his art project in 9 hours. To find out how much time it will take to complete the entire project, we need to determine the time taken to complete 100% of the project. First, we calculate the time taken for 1% of the work, which is 9 hours divided by 75 (the percentage completed so far). This gives us 0.12 hours per percent.

Now, we can find out the total time for 100% completion by multiplying 0.12 hours by 100, which totals 12 hours. Since Angel has already completed 9 hours of work, the remaining time to finish the project is 12 hours minus 9 hours, which equals 3 more hours of work.

Answer:

A) 65.87

B) 326.59

C) 13.56

D) 7.96

Step-by-step explanation:

Answer:

C) 12

Step-by-step explanation:

Absolute value always means it is the positive version of the number

This switches -7 to 7 and 5 stays the same.

5 + 7 = 12

The absolute value returns the "positive version" of a number. This means that if the number is already positive, it does nothing. Otherwise, it gets rid of the negative sign.

So, you have

[tex]|5|=5,\quad |-7|=7[/tex]

and thus

[tex]|5|+|-7|=5+7=12[/tex]

Answer:

(2/3) + or - .943i

Step-by-step explanation:

Use quadratic formula.

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

A = 3

B = -4

C = 4

[tex]\sqrt{16 - 2(3)(4)} = \sqrt{-8}[/tex] or 2.828i

4/6= 2/3

Answer: 2, -2/3 ********************************************************************************************************

Look at the attached picture ⤴

Hope it will help u...

Answer:

i believe the answer on the photo is C. 200

The options are different on the question and the photo

Answer:B

Step-by-step explanation:

Edge

10

Step-by-step explanation:

3y-8=22

3y=22+8

3y=30

y=30/3

y =10

Answer:

15adults

Step-by-step explanation:

Ratio of Children : Adult = 8 : 3

Number of children = 8x

Number of Adult = 3x

8x + 3x =55

11x = 55

x = 55/11

x = 5

Number of Adults = 3x = 3*5 = 15

Answer:

40 adults

Step-by-step explanation:

Let x:y represent the ratio of children to adults. As of now, x:y is 3:8.

To solve this problem, all we need to do is find a solution where x + y = 55. Let's begin by using the guess-and-check method.  

First, I will multiply the ratio by 2.

When x = 6, y = 16

6 + 16 = 22

Not applicable; I need higher numbers

Next, I'll multiply the ratio by 4.

When x = 12, y = 32.

12 + 32 = 44

Not applicable, I need slightly higher numbers

I'll multiply the ratio by 5.

When x = 15, y = 40

15 + 40 = 55

Since 55 is the total number of people, 15 children and 40 adults is the correct answer. Therefore, the total number of adults is 40.