A boy stands 12 metres from the foot of the building and observes the angle of elevation of the top of the building. The height is of the building is approximately

The given ratios expresses the number of time a value is larger or smaller

than another value.

The correct responses are;

Reasons:

3. Given that the perimeter of the rectangle = 72

The ratio of the lengths of the sides = 1:2

Let a and b represent the sides, we have;

2·a + 2·b = 72

[tex]\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}[/tex]

Which gives;

2·a = b

2·a + 2·(2·a) = 72

6·a = 72

a = 72 ÷ 6 = 12

b = 2·a = 2 × 12 = 24

The lengths of the sides are; (B) 12 and 24

4. Extended ratio = 2:3:7

The perimeter = 36

The lengths of the sides are;

[tex]\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}[/tex]

[tex]\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}[/tex]

[tex]\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}[/tex]

The lengths are; (D) 6, 9, 21

5. The given equation is presented as follows;

[tex]\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}[/tex]

5 × (x + 2) = 3 × (x + 7)

5·x + 10 = 3·x + 21

5·x - 3·x  = 21 - 10

2·x = 11

[tex]\displaystyle x = \mathbf{ \frac{11}{2}}[/tex]

The correct option is; [tex]\displaystyle \underline{(E) \ \frac{11}{2}}[/tex]

6. The width to length ratio is [tex]\displaystyle \mathbf{\frac{2.5}{7.0}}[/tex]

The simplified ratio is therefore;

[tex]\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}[/tex]

The correct option is (E) [tex]\displaystyle \underline{(E) \ \frac{5}{14}}[/tex]

7. The given ratio of the lengths is 3:1

Therefore;

[tex]\overline{BC}[/tex]:[tex]\overline{EF}[/tex] = 3:1

Which gives;

[tex]\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}[/tex]

[tex]\overline{BC}[/tex] = 18

Therefore;

[tex]\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}[/tex]

18 × 1 = 3 × [tex]\overline{EF}[/tex]

[tex]\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6[/tex]

[tex]\overline{EF}[/tex] = 6

By Pythagorean theorem, we have;

[tex]\overline{DF}[/tex]² = [tex]\mathbf{\overline{DE}}[/tex]² + [tex]\mathbf{\overline{EF}}[/tex]²

Which gives;

[tex]\overline{DF}[/tex]² = 3² + 6² = 45

[tex]\overline{DF}[/tex] = √(45) = 3·√5

Using the given ratio, we have;

[tex]\overline{AC}[/tex] = 3 × [tex]\mathbf{\overline{DF}}[/tex]

Which gives;

[tex]\overline{AC}[/tex] = 3 × 3·√5 = 9·√5

[tex]\overline{AC}[/tex] = 9·√5

The correct option is; (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√5

8. EF = 1, AB = 2

CD = 2, CE = 4

Therefore;

[tex]\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}[/tex]

[tex]\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}[/tex]

Which gives;

[tex]\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}[/tex]

(C) The values are equal

9. AC = 6, BE = 8

DF = 3, BD = 6

Column A

[tex]\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}[/tex]

Column B

[tex]\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}[/tex]

[tex]\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}[/tex]

Therefore;

Column A is greater than column B

(A) The value in column A is greater

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Answer:

Step-by-step explanation:

The prime factor representation of 150 is 2 x 3 x 5^2

Step-by-step explanation:

this is a rectangle. so, all things are symmetric.

EI = IG = FI = IH

IGF = IFG = IEH = IHE

therefore, since EI = FI

2x + 8 = 6x - 20

28 = 4x

x = 7

now,

EG = EI + IG = 2×EI = 2×(2×7 + 8) = 2×22 = 44

IFE is a complementary angle to IFG (together they have 90°).

and because IFG = IGF = 30°

IFE = 90 - 30 = 60°

Work Shown:

1 pound = 16 ounces

3 pounds = 48 ounces (multiply both sides by 3)

Based on that, we can then say,

(750 calories)/(10 ounces) = (x calories)/(48 ounces)

750/10 = x/48

75 = x/48

x/48 = 75

x = 48*75

x = 3600

Answer:

A

Step-by-step explanation:

Answer: Yes the win level is greater than 1/2

Step-by-step explanation: 32/52 is greater than 1/2

Answer: 21

Step-by-step explanation:

The number of basket balls donated is; 28 basket balls

We are told that;

Ratio of basket balls to soccer balls = 7:6

Now, the number of soccer balls donated was 24.

This, means fraction of the total number of balls x for soccer balls was; [6/(7 + 6)]x

Thus;

[6/(7 + 6)]x = 24

6x/13 = 24

6x = 24 × 13

6x = 312

x = 312/6

x = 52 balls

Now, since total balls are 52 and soccer balls are 24, then;

Number of basketballs = 52 - 24

Number of basketballs = 28 basketballs

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Answer:

4/8 = 1/2 = 0.5 is your answer

Kind of, Market day as in make stuff and then sell it or Market day as in Sell food, I remember this in elementary school 2 Different Kind of Market day :)

Answer:

48

Step-by-step explanation:

75/100 = 36/x

x = 48

[tex](9+7i)(6+3i)\\\\=54+27i + 42i + 21i^2\\\\=54+69i -21~~~;[i^2 =-1]\\\\=33+69i[/tex]

We have: 5m 75cm = 5.75 m

So the length of each piece is : [tex]l = \frac{5.75}{5} =1.15<m>[/tex]

ok done. Thank to me :>

Answer:

The distance formula is 22.360679775

if you round it to the nearest tenth, then the answer is 22.4

Step-by-step explanation:

(-6, -12) and (4,8)

(x2 - x1)² + (y2 - y1)²

Place the x and y values

(4 - - 6)² + (8 - - 12)²

= 10² + 20²

= 100 + 400 = 500

√500 = 22.360679775

Round it to the nearest tenth and you will get 22.4

Hope this helps!

please mark me as the brainliest

The formula in finding the distance between two points is given below:

where:

Substitute the given values into the distance formula and solve for d:

Therefore, the distance between the two points is 22.4 units (nearest tenth).

Cheers!

Answer:

UP THE DOWN THAT WHAT I GOT

Step-by-step explanation:

Answer:

first one is second

Step-by-step explanation:

second one is A

Answer:

Step-by-step explanation:

Angles 1 and 2 have common side, so they are adjacent. They are not making a right or straight angle.

Correct choice is D

Answer:

Coordinate  form is [tex](x,y)=(2,3)[/tex]

Step-by-step explanation:

Usually the form is

[tex]f(x)=y[/tex]

Here

We have [tex]f(2)=3[/tex]

Hence [tex](x,y)=(2,3)[/tex]

didn't know how to workout iam only 3rd standard

The domain of the function to know the number of cars remaining on any day during the month is [0, 40]. The maximum and minimum values are 120 and 0 respectively.

The domain is the all inputted value for which the function is defined. All the x values are domain of a function.

Now, finding the domain of the function,

We know that, the number of cars cannot be negative, so

[tex]f(x)\geq0\\120-3x\geq0\\3x\leq120\\x\leq40[/tex]

The number of cars should be greater than 0, so x > 0.

So, the domain will be [0, 40].

The maximum value is given by putting x = 0,

[tex]f(0)=120-3(0)\\=120[/tex]

The minimum value is given by putting x = 40,

[tex]f(40)=120-3\times40\\=120-120\\=0[/tex]

Therefore, the domain of the function f(x)=120-3x to know the number of cars remaining on any day during the month is [0, 40]. The maximum and minimum values are 120 and 0 respectively.

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Answer:

x = -9/2

Step-by-step explanation:

64 = 2^6

if you have the same base, you can set the exponents equal and solve for x.

-2x-3 = 6

-2x = 9

x = -9/2

good luck on your final! you got this!

Step-by-step explanation:

[tex] {2}^{ - 2x - 3} = 64[/tex]

first, get 64 to a base of 2

[tex] {2}^{ - 2x - 3} = {2}^{6} [/tex]

now we can drop the bases

[tex] - 2x - 3 = 6[/tex]

And now we can solve it like any other equation

[tex] - 2x = 6 + 3[/tex]

[tex] - 2x = 9[/tex]

[tex]x = - \frac{9}{2} [/tex]

Answer:

77

Step-by-step explanation:

6x2 = 12

13x5 = 65

65+12 = 77

The answer is 77.

Using the Central Limit Theorem, it is found that the mean of the sampling distribution of sample proportions is 0.37.

The Central Limit Theorem establishes that, for a proportion p in a sample of size n, the sampling distribution of sample proportions has:

For this problem, about 37% of high school seniors have vaped in the past year, hence [tex]p = 0.37[/tex].

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A. - 7x² + 7x + 1 + 8 = 0

- 7x² + 7x + 9 = 0

x = - b ± √b² - 4ac / 2a

= - 7 ± √7² - 4 (-7) (9) / 2 (-7)

= - 7 ± √49 + 252 / - 14

= - 7 ± √ 301 / - 14

x = - 7 + 17.349 / - 14 x = - 7 - 17.349 / - 14

= 10.349 / - 14 = - 24.349 / - 14

= - 0.739 = - 1.739

B. 8x² - 5x² + 6x + 1 = 0

3x² + 6x + 1 = 0

x = - b ± √b² - 4ac / 2a

= - (-5) ± √-5² - 4 (3) (1) / 2 (3)

= 5 ± √25 - 12 / 6

= 5 ± √ 13 / 6

x = 5 + 3.606 /6 x = - 5 - 3.606 / 6

= 8.606/6 = - 8.606/6

= 1.434. = - 1.434

please re-check the answers hope this helps

Answer:

1,390 I think that's the answer

Step-by-step explanation:

hope that helps

The expression equivalent to 40x + 30y are 5(8x + 6y), 10(4x + 3y) and 2(20x + 15y).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are some expressions in the options.

Distributive rule says that,

a ( b + c ) = (a b) + (a c), where a, b and c are any numbers.

5x(8 + 6) = 5x(14) = 70x

5(8x + 6y) = 40x + 30y

10(40x + 30y) = 400x + 300y

10(4x + 3y) = 40x + 30y

2y(20x + 15) = 40xy + 30y

2(20x + 15y) = 40x + 30y

Hence the expressions which are equivalent to 40x + 30y are 5(8x + 6y), 10(4x + 3y) and 2(20x + 15y).

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The complete question is :

Which of the following expressions are equivalent to 40x+30y. Choose all that apply.

5x(8 + 6)

5(8x + 6y)

10(40x + 30y)

10(4x + 3y)

2y(20x + 15)

2(20x + 15y)

Answer:

52

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

The top has 6 faces, so 6 x 2 = 12

The bottom has the same, 12

The left side has 3, 3 x 2 = 6

The front and inside has 6, x 2 = 12

The right side has 2 x 2 = 4

The back has 3 x 2 = 6

12 + 12 + 6 + 12 + 4 + 6 = 52

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