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Answer:

(i) ∠ABH = 14.46⁰

(ii) The length of AH = 4.6 m

Step-by-step explanation:

From the image uploaded;

Consider △ABC;

the length of b is calculated by applying Pythagoras theorem as follows;

b² = c² - a²

b² = (13.2)² - (6.9)²

b² = 126.63

b = √126.63

b = 11.25 m

Also, ∠ABC is calculated as;

[tex]Cos \ B = \frac{a^2+c^2-b^2}{2ac} \\\\Cos \ B = \frac{(6.9)^2+(13.2)^2-(11.25)^2}{2(6.9 \times13.2)}\\\\ Cos \ B = \frac{95.288}{182.16} \\\\ Cos \ B = 0.5219 \\\\B = Cos ^{-1} (0.5231)\\\\B = 58.46 ^o[/tex]

Consider △CBH, ∠CBH is calculated as;

∠CBH = 90⁰ - 46⁰ = 44⁰

(i) ∠ABH will be calculated as;

∠ABH = θ

θ + 44⁰ = ∠ABC

θ + 44⁰ = 58.46⁰

θ = 58.46⁰  - 44⁰

θ = 14.46⁰

Thus, ∠ABH = 14.46⁰

(ii) The length of AH

length HC is calculated as;

[tex]tan \ 46^o =\frac{6.9}{HC} \\\\HC = \frac{6.9}{tan \ 46^o } \\\\HC = 6.66 \ m[/tex]

length of AH = CA - HC

x = b - HC

x = 11.25 - 6.66

x = 4.6 m

length of AH = 4.6 m

Answer:

a. i. 1.11 h ii. 1 h. b. Liam

Step-by-step explanation:

a.

i. Sam's time

We know distance d = vt where v = speed and t = time.

Since our distance here is the length of the path, d = 1 mile.

For Sam, his speed up the hill is v = 1 mph, so, the time it takes him to go uphill is t = d/v = 1 mi/1 mph = 1 h.

He goes down hill at a speed of v = 9 mph, so the time it takes him to go down hill is t = d/v = 1 mi/9 mph = 1/9 h = 0.11 h

So, the total time it takes him to complete the trip is t = 1 h + 0.11 h = 1.11 h

ii. Liam's time

For Liam, his speed both uphill and downhill is v = 2 mph, so, the time it takes to cover each trip is t = d/v = 1 mi/2 mph = 0.5 h.

So for both uphill and downhill trip, the total time is t' = 2 × 0.5 h = 1 h

b. Since Liam's time t' = 1 h < Sam's time t = 1.11 h, that is t' = 1h < t = 1.11 h, Liam is the winner.

Answer:

3/2

Step-by-step explanation:

If you wanted whole number, it would be 1 1/2, but you said as a fraction, so that would be 3/2

Answer:

3b(2a+1)(2a-1)

Step-by-step explanation:

12a²b-3b

3b(4a²-1)

3b{(2a)²-1²)}

3b(2a+1)(2a-1)

Answer:

cos 38, sin 38, sin 1580, cos 1589

Answer:

Step-by-step explanation:

- (3/4)

Answer:

13.44

Step-by-step explanation:

she is right...........

Answer:

The correct unit price is $1.12 per pair. The error comes from dividing $67.20 by only 5 pairs (instead of 60 pairs).

Step-by-step explanation:

The contractor should have calculated the unit price as $67.20 divided by 60 pairs. Five dozen pairs is 5x12=60. This results in $67.20/60=$1.12 per pair. The error comes from dividing $67.20 by only 5 pairs (instead of 60 pairs).

Answer: y=7x^2−42x+69

Step-by-step explanation:

Answer:

36/25

Step-by-step explanation:

7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9

((7 * 3 * 2)/(7 * 5))^2 * (7^0/5^-3)^3 * 5^-9 =

= (42/35)^2 * (1 * 5^3)^3 * 5^-9

= (6/5)^2 * 5^9* 5^-9

= 36/25 * 5^0

= 36/25

Answer:

12.4 feet

 Proportion of giraffe's height vs the height of its shadow = 16/24 = 2/3

If Dustin's height is x feet tall, then the proportion of his height and the height of his shadow (93/5 feet)should be the same as that of the giraffe, which is 2/3

so,

x/93/5 = 2/3

Multiplying both sides with 93/5

x = 2/3 * 93/5

x = 62/5 =12.4

Answer:

5.61 billion dollars.

Step-by-step explanation:

4.61+1.03=5.61

Answer:

0.223

Step-by-step explanation:

Change the divisor 4.61 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.

We then have the equations:

103 ÷ 461 = 0.223

and therefore:

1.03 ÷ 4.61 = 0.223

Both calculated to 3 decimal places.

Answer:

(10, -2)

Step-by-step explanation:

x = 10 (its given in the problem)

then plug in 10 for x in the second equation and solve for y

3(10) + 5y = 20

30 + 5y = 20

5y = -10

y = -2

so the solution is (10, -2)

Answer:

um B

Step-by-step explanation:

???????

Answer:

[tex]m=\frac{-5}{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (1, 1)

Point (3, -4)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

25:10

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The number of triangles in the figure is given as 15 triangles.

Given that,
To determine the number of triangles inside the triangles.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

here,
here in the figure inside the parent figure, there are 6 segments that contribute two triangles in the figure,
Number of triangle  = 6C2
Number of triangle = 15

Thus, the number of triangles in the figure is given as 15 triangles.

Learn more about permutations and combinations here: https://brainly.com/question/2295036

#SPJ2

Answer:

I think this is my best solution for your question

0.78= 78%

13/20=0.65

7/25=28%

17/50=34%

Answer:

64 ounces = 4 pounds

Step-by-step explanation:

The side of the square is [tex]x^5[/tex].

area of a square = (side)² = a²,

area of a square = [tex]x^{10}[/tex]

Equating it with the general formula of square

[tex]\rm {Area\ of\ square}={Area\ of\ square}[/tex]

[tex]x^{10} = a^2[/tex]

Taking square root on both sides,

[tex]\sqrt{x^{10}} = \sqrt{a^2}\\\\a=\sqrt{x^{10}}[/tex]

[tex]a = x^5[/tex]

Hence, the side of the square is [tex]x^5[/tex].

Learn more about the Area of square:

https://brainly.com/question/1658516

The monomial which represents a side of the square is; x⁵

Area of a square

The area of a square is a 2-dimensional quantity and can be evaluated by the formula;

Hence, the length of the sides of the square is;

According to the question, the given area is x¹⁰.

Therefore, the length of each side is;

Read more on area of a square;

https://brainly.com/question/16758129

Answer:

Step-by-step explanation:

2 2/3 = 8/3

24 ÷ 8/3

= 9

Answer:

y = 3x -3

Step-by-step explanation:

Find the slope first

Givens

y2 = 3

y1 = - 3

x2 = 3

x1 = 1

Equation

m= (y2 - y1)/(x2 - x1)

Solution

m = (3 - - 3) / (3 - 1)

m = (3 + 3) / 2

m = 3

Find the y intercept next

Use either point to find the y intercept

y = 3x + b

x = 3

y = 3

y = 3*3 + b

3 = 6 + b

-3 = b

Answer

y = 3x - 3

Answer:

72

Step-by-step explanation:

To calculate how much 20% of 360 makes we multiply 360 with 20 then divide it with 100

360 × 20 ÷ 100 = 72

Answer:23

Step-by-step explanation:

:)

Additive inverse of 23 will be -23

Its the opposite which is negative on the number line

Answer:

The answer is 11

Step-by-step explanation:

so substitute 3 for x, then your equation would be 3^2 + 2

3^2 is 9

9 + 2 = 11

Answer:

(6, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

3x - 5y = 13

x + 4y = 10

Step 2: Rewrite Systems

x + 4y = 10

Step 3: Redefine Systems

3x - 5y = 13

x = 10 - 4y

Step 4: Solve for y

Substitution

Step 5: Solve for x

Answer:

(6,1)    x=6 and y=1        

Step-by-step explanation:

EASY we can use Elimination or Substitution process

We are going to solve by

Elimination process

Subtract each other

(3x-5y=13)

(x+4y=10)

3x-5y=13;x+4y=10

To solve this multiply (x-4y=10) by 3 to get rid of the x

3x-12y=30

now u can subtract both

3x-12y=30 minus

3x-5y=13

17y=17

Divide both sides by 17

y=1

Now we have y lets plug it in to find x

x+4(1)=10

x+4=10

subtract 4 from both sides

x=6

x=6 and y=1

Step-by-step explanation:

Given

3d² - 16dc - 12c²

Using middle term break

= 3d² - (18 - 2 )dc - 12c²

= 3d² - 18dc - 2dc - 12c²

= 3d( d - 6c) - 2c( d - 6c)

= ( d - 6c) ( 3d - 2c)

Hope it helps and have a great day onwards ❤

Answer:

= 3d² - (18 - 2 )dc - 12c²

= 3d² - 18dc - 2dc - 12c²

= 3d( d - 6c) - 2c( d - 6c)

= ( d - 6c) ( 3d - 2c)

Step-by-step explanation:

Answer:

Whole numbers are also integers. There are other integers which are the opposites of the whole numbers (−1, −2, −3, ...). These negative numbers lie to the left of 0 on the number line. Integers are the whole numbers and their opposites.

Answer:

x = 16

Step-by-step explanation:

90 = x+8+66

x = 90-74

x = 16

Answer:

16

Step-by-step explanation:

:D