Lyla made a scale drawing of a city park. She used the scale 1 millimeter = 1 meter. What is the scale factor of the drawing?

Answer:

x = 9, GH = 21, CD = 17

Step-by-step explanation:

Quadrilateral CDEF is a trapezoid in which G and H are mid points of the sides CF and DE respectively.

In a trapezoid, segment joining the mid points is equal to the half of the sum of the parallel sides.

[tex] \therefore \: GH = \frac{1}{2} (CD + FE) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x + 24) \\ \\ \therefore \:3x - 6 =\frac{1}{2} \times 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = \frac{18}{2} \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 \times 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 \times 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\ [/tex]

Answer:

6 m

Step-by-step explanation:

a squared + b squared = c squared

8 squared plus ? squared = 10 squared

64 + ? = 100

100 - 64 = 36

the square root of 36 is 6

Final answer:

Using the Pythagorean theorem, the length of the other leg of the right triangle is found to be 6 meters.

Explanation:

The student is asking to find the length of the other leg of a right triangle, given the lengths of the hypotenuse (10m) and one leg (8m). To solve this problem, we use the Pythagorean theorem, which relates the lengths of the sides of a right triangle: a² + b² = c², where c is the hypotenuse and a and b are the legs of the triangle. Since the hypotenuse length (c) is 10m and one leg (a) is 8m, we can solve for the length of the other leg (b) using the equation 8² + b² = 10².

First, square the known length of one leg: 8² = 64.

Next, square the hypotenuse: 10² = 100.

Now, subtract the squared length of the known leg from the squared hypotenuse to find b²: 100 - 64 = 36.

Finally, take the square root of 36 to find b: √36 = 6m. So, the length of the other leg is 6 meters.

Answer:

[tex] \frac{7}{30} [/tex]

Step-by-step explanation:

In a class of 150 students, 95 are taking Math, 75 are taking Science and 55 are taking both.

We want to determine the probability that a student is taking neither Math or science.

The number taking only Math is

[tex] = 95 - 55 = 40[/tex]

The number taking only Science

[tex] = 75 - 55 = 20[/tex]

The number of students taking Math, Science, or both

[tex] = 40 + 55 + 20 = 115[/tex]

The number taking neither Mathematics or Science

[tex] = 150 - 115 = 35[/tex]

The probability that a student is taking neither Math or science

[tex] = \frac{35}{150} [/tex]

[tex] = \frac{7}{30} [/tex]

Answer:

d. 84.5

Step-by-step explanation:

You will have to put the numbers in order than cross out one from each side;

70x

80x

83      

86      

88x

88x

In doing this you have taken out B,E, and F.  The answer would have to be somewhere in between 83 and 86, which would be around 84 and 85, so therefore the answer would be 84.5

Answer:

78.

Step-by-step explanation:

13/2=6.5

6.5X12=78.

78/2=39

39X2=39. You times it by 2 because there are two equivalent sides.

Answer:

3 < s

Step-by-step explanation:

−4>−4/3s

Multiply each side by -3/4 to isolate s.  Remember to flip the inequality since we are multiplying by a negative

-4 * -3/4 < -4/3s * -3/4

3 < s

Answer:

The value of h is 7.

Step-by-step explanation:

3h - 4 = 15 + 2

15 + 2 = 17

3h - 4 = 17

Add 4 to each side

3h = 21

Divide each side by 3

h = 7

Answer:

No he does not

Step-by-step explanation:

158 / 60 = 2.63

which is about a 3 hour long movie.

Answer:

The value of the given expresion is zero.

Step-by-step explanation:

I am assuming that, your exprssion is

[tex] {( - 1)}^{r} + 1[/tex]

where r is an integer greater than 1.

Let us see what a negative base 1 to an off exponent give us:

[tex] {( - 1)}^{1} =-1[/tex]

[tex] {( - 1)}^{3} =-1[/tex]

[tex] {( - 1)}^{5} =-1[/tex]

[tex] {( - 1)}^{7} =-1[/tex]

If r is odd, then

[tex] {( - 1)}^{r} = - 1[/tex]

This implies that:

[tex] {( - 1)}^{r} + 1 = - 1 + 1 = 0[/tex]

The value of the given expresion is 0.

Answer:

24

Step-by-step explanation:

cos(x) is just a trigonometric function. To find it on a right triangle, you take the "adjacent" side, which should be the side next to the angle x, and divide it by the hypotenuse.

In this case, the adjacent side is 12. We don't know the hypotenuse, but we can figure it out using the Pythagorean Theorem: [tex]\sqrt{9^{2}+12^{2}}[/tex] = [tex]\sqrt{225}[/tex] = 15. So, the hypotenuse is 15.

Thus, cos(x) = 12/15 = 4/5. We want 30 * cos(x), so we get: 30 * (4/5) = 24, and that is our answer.

Answer:

24

Step-by-step explanation:

From the mnemonic SOHCAHTOA you would know that cos x = adjacent/hypotenuse.

Adjacent side is given as 12, but we must calculate the hypotenuse.

For that we use Pythagoras.

hypotenuse = √(9²+12²) = 15

Now you can calculate

30×cos(x) = 30×12/15 = 24

Answer:

0.14285714285

Hope this helps :)

Step-by-step explanation:

Answer:

.1428

Step-by-step explanation:

1/3 times 3/7= .1428

Answer:

d = 12,021.1 ft

The Gateway Arch is 12,021.1 ft away

Step-by-step explanation:

Given;

Angle of elevation = 3°

Height of arch = 630 ft

Tanθ = opposite/adjacent

Opposite = 630 ft

Adjacent = d

Substituting the values;

Tan3 = 630/d

d = 630/tan3

d = 12,021.1 ft

The Gateway Arch is 12,021.1 ft away

Answer:

[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]

Step-by-step explanation:

The distance is given by the following trigonometric equation:

[tex]x = \frac{y}{\tan \alpha}[/tex]

[tex]x = \frac{630\,ft}{\tan 3^{\textdegree}}[/tex]

[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]

Answer:

D. 2(6x + 5+ 2y)

Step-by-step explanation:

12x + 10 + 4y

Factor out a 2

2(6x+5+2y)

Answer:

362880 ways

Step-by-step explanation:

In this case, the order does matter therefore to know how many ways it can be aligned, we must resort to permutations.

The formula for permutations is:

P = n!

we know that there are 9 trumpet players, therefore:

P = 9!

P = 362880

So there are 362,880 ways to line up

Answer:

1/8

Step-by-step explanation:

I'm going to try to explain this as easy as possible. What I did was take the original shape and divide it by the new shape. For this question, I solved it by dividing 32(the original base) by 4(the new base) and got 8. So the scale factor of the reduction was 1/8.

Answer:

1/8

Step-by-step explanation:

The only one that makes sense

To solve the equation 2e^3x = 400, we isolate e^3x and then use the natural logarithm to solve for x, which gives x ≈ 2.995 when rounded to three decimals.

The question asks us to solve the equation 2e^3x = 400 for the variable x. First, we isolate e^3x by dividing both sides of the equation by 2. We get: e^3x = 400/2 which is e^3x = 200. Finding x means solving for 'x' in an exponential equation, which involves using the natural logarithm.

So, our equation becomes: x = ln(200)/3. Using a calculator, x ≈ 2.995 when rounded to three decimals.

-4k + 6k -13 +23

2k +10

you can even write it like this:

2 ( k+ 5)

Answer:

12, 5, 1 1/2, -12, -19

Step-by-step explanation:

hope this helped!

Answer:

C

Step-by-step explanation:

A doesn't include the term "2"

B doesn't include "5" or "10"

D doesn't include "10"

SO... it's C

Answer:

1 :2

Step-by-step explanation:

18 oranges

12 bad

-------

6 good

good: bad

6      :12

Divide each by 6

6/6    : 12/6

1 :2

The ratio of good oranges to bad oranges is 1:2.

To find the ratio of good oranges to bad oranges in a bag containing 18 oranges, where 12 oranges have gone bad, follow these steps:

Determine the number of good oranges:

Find the ratio of good oranges to bad oranges:

Simplify the ratio:

Answer:

help with what

Step-by-step explanation:

Answer:

What do you want help with?

Step-by-step explanation:

Answer:

[tex]w^{20}[/tex]; [tex]y^7[/tex]

Step-by-step explanation:

[tex](w^4)^5=\\w^{4*5}=\\w^{20}\\\\\frac{y^9}{y^2}=\\ y^{9-2}=\\y^7[/tex]

Answer:

1) =W20

2=Y7

Both 20 and 7 are exponents but i cannot type them in that format since I am  on a computer. Hope this helps!

Step-by-step explanation:

The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.

Given that, in the triangle ABC, AC=4.1 cm, AB=4.5 cm and BC=2.7 cm.

We need to find the measure of angle B.

The trigonometric function to find the angle in the triangle is b²=a²+c²-2ac cosB.

Now, (4.1)²=(4.5)²+(2.7)²-2×4.5×2.7 cosB.

⇒16.81=20.25+7.29-24.3 cosB

⇒16.81-27.54=-24.3 cos B

⇒cos B=0.44

⇒B=63.9°

The measure of angle B in triangle ABC is 63.9°. Hence, Bethany has done a mistake in step 2.

To learn more about the angles of a triangle visit:

https://brainly.com/question/27682397.

#SPJ2

Answer:

B. Bethany took the square root of each squared term before isolating cosB and solving for B.

Step-by-step explanation:

took the quiz

Answer:

volume = 179.59

please give this the brainliest!!

Step-by-step explanation:

formula = V=4/3πr3

4/3·π·3.5^3

≈179.59438

Answer:

8.9

Step-by-step explanation:

Answer:

8 pie

Step-by-step explanation:

area of a circle is pie(radius squared)

radius is 4

4 squared is 16

divide by two because its a semi circle

Answer:

8pi

Step-by-step explanation:

A=pi*r^2

A=pi(4^2)

A=16pi

16pi would be the area if the circle was complete, but since this is a semicircle you just have to divide by two which would give us:

A=8pi

The area of the square will be 640 sq cm.

Step-by-step explanation:

Given,

Number of strip = 4

Length (l) of each strip = 40 cm

Width (b) of each strip = 4 cm

To find the area of the inner square.

Formula

The area of rectangle = l×b

If the area of a square is A, each side will be √A

Now,

Area of each strip = 40×4 sq cm = 160 sq cm

Area of 4 strips = 160×4 sq cm = 640 sq cm

Hence,

The area of the square will be 640 sq cm.

Answer:

c

Step-by-step explanation:

The points that show the triangle when it is translated two units down are (2, 3) (0, 1), and (2, 1).

A function, f, that maps to itself are known as a transformation, or f: X- X. The pre-image X becomes the picture X following the transformation. This transformation can use any operation, or a combination of operations, including translation, rotation, reflection, and dilation. Translation, rotation, reflection, and dilation can all be used to move a function in one direction or another.

Given that the initial coordinate of triangles ABC are at points

(2, 1), (0, -1), (2, -1).

The coordinate base of the triangle must be (2, 1) and (2, -1)

When the triangle is translated two units down.

2 will be added to all its y coordinates. While the x coordinate remains the same

The new coordinate will be

(2, 2+1), (0, 2-1), (2, 2-1)

(2, 3) (0, 1) and (2, 1)

Hence the new coordinates are (2, 3) (0, 1), and (2, 1).

Learn more about transformations;

https://brainly.com/question/15200241

#SPJ5

The complete question is,

The triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down