5 A) SSS C) SAS B) ASA D) AAS

Mariana [72]

The two whole numbers between which is √12 are 3 and 4.

What is an example of a whole number?

Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.

The closest perfect squares near 12 are 16 and 9 which are the perfect squares of 4 and 3 respectively Therefore the root of 12 lies between 3 and 4.

i.e 3 < √12 < 4

To learn more about whole numbers click on the link below:

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6 0

1 year ago

Mr. Pete just got a great deal at Lowe’s on tiles for his new patio. He wants to

sdas [7]

Answer:

The fewest square tiles he can use without cutting any of them = 12 square tiles

Step-by-step explanation:

The given dimensions of Mr. Pete's rectangular patio = 108 inches by 144 inches

The area of the patio = 108 in. × 144 in. = 15,552 in.²

We note that when square tiles are used the must fit both the length and the with of the rectangular patio

Therefore, we have;

The dimensions of the square tiles that the fewest number of tiles is the highest common factor, HCF, of 108 inches and 144

The HCF of 108 and 144 are found from by the prime factors as follows;

108 = 2² × 3³ = 2² × 3² × 3

144 = 2⁴ × 3² = 2² × 3² × 4

From which we have;

The HCF of 108 and 144 = 2² × 3² = 36

Therefore, the size of the sides of the square tiles that will give the fewest number of tiles is 36 inches

The number of the 36 inches square tiles that fit into the length of the rectangular patio = 144 inches/(36 inches/tile) = 4 tiles

The number of the 36 inches square tiles that fit into the breadth of the rectangular patio = 108 inches/(36 inches/tile) = 3 tiles

The total number of tiles he will use = (4 × 3) tiles = 12 tiles = The fewest square tiles he can use without cutting any of them.

8 0

2 years ago

Hey surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 150 feet from a Pi

AleksAgata [21]

Answer: 87 feet

Step-by-step explanation:

The angle between the pilling is 60°

The adjacent side of the right angle is 150

So let the distance between the pilling be y, that is opposite side.

Opposite / adjacent = tan (60°)

y / 150 = tan (60)

y × tan (60°) = 150

Divide both side by tan (60°)

y = 150 / tan (60°)

y = 150 / 1.7321

y = 87 feet

4 0

3 years ago

What basic trigonometric identity would you use to verify that sin^2x +cos^2x/cos x = sec x

gogolik [260]

Answer:

The basic identity used is $\bold{\sin ^{2} x+\cos ^{2} x=1}$ .

Solution:

In this problem some of the basic trigonometric identities are used to prove the given expression.

Let’s first take the LHS:

$\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}$

Step one:

The sum of squares of Sine and Cosine is 1 which is:

$\sin ^{2} x+\cos ^{2} x=1$

On substituting the above identity in the given expression, we get,

$\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}=\frac{1}{\cos x} \rightarrow(1)$

Step two:

The reciprocal of cosine is secant which is:

$\cos x=\frac{1}{\sec x}$

On substituting the above identity in equation (1), we get,

$\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}=\sec x$

Thus, RHS is obtained.

Using the identity $\sin ^{2} x+\cos ^{2} x=1$ , the given expression is verified.

6 0

3 years ago

8x - 2y = - 8 5x - 4y = 17

11111nata11111 [884]

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

( − 3 , − 8 )

Equation Form:

x =- 3 , y = − 8

Step-by-step explanation:

4 0

2 years ago