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lianna [129]
3 years ago
12

A 13 Ft ladder is leaning up against a building, with the base of the ladder 2 feet from the building. How high up on the buildi

ng will the top of the ladder reach?
Mathematics
1 answer:
Lelechka [254]3 years ago
6 0

Visualize the image in your mind and you can see that it forms a right angled triangle with a base,altitude and hypotenuse

base=2 feet

hypotenuse(ladder)=13 ft

We need to find the altitude,

By applying pythagoras theorem,

base square+altitude square=hypotenuse square

Take altitude as x

2 square+x square=13 square

4+x square=169

x square=169-4

x square=165

x= root of 165

x=12.8 feet(approx.)

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What do you multiply by itself to get 49?
kirza4 [7]
We try the all of the numbers until we find it
1*1=1
2*2=4
3*3=9
4*4=16
5*5=25
6*6=36
7*7=49
So the answer is 7
3 0
3 years ago
Anil completes the 72km journey between Bristol and Cardiff in 48 minutes.
eimsori [14]

total distance travelled=72+69=141

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Find the dot product of U and V <br><br> u=7i, v = -2i + 5j
alexandr1967 [171]

Answer:

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Multiply the is together. Multiply the j's together. Add the answer. The answer is a scalar.

(7 × -2) + (5 × 0)

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6 0
3 years ago
1.) Determine the type of solutions for the function (Picture 1)
NNADVOKAT [17]

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

7 0
2 years ago
Put this number from LEAST to GREATEST
Pepsi [2]

Answer:

70 thousand

12 million

25 million

208 million

293 million

535 million

8 0
3 years ago
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