Find the distance between the points L(7, -1) and M(-2, 4).

What is the length of line segment EF if DE is 6ft and DF is 11ft and angle FDE is 40 degrees

Anna [14]

Answer:

The length of EF = 7.48 feet

Step-by-step explanation:

* Lets consider these tree segment formed triangle DEF

- We have the length of two sides and the measure of the

including angle between these two sides

* So we can use the cos Rule to find the length of the third side

- The cos rule ⇒ a² = b² + c² - 2bc cosA

# a is the side opposite to angle A

# b is the side opposite to angle B

# c is the side opposite to angle C

# Angle A is the including angle between b and c

* In the problem

∵ DE = 6 feet

∵ DF = 11 feet

∵ m∠FDE = 40° ⇒ including angle between DE and DF

and opposite to EF

- By using cos Rule

∴ (EF)² = (DE)² + (DF)² - 2(DE)(DF) cos∠FDE

∴ (EF)² = (6)² + (11)² - 2(6)(11) cos(40)

∴ (EF)² = 55.882133 ⇒ take square root for both sides

∴ EF = 7.47543 ≅ 7.48 feet

* The length of EF = 7.48 feet

6 0

2 years ago

Figure ABCD is transformed to obtain figure A'B'C'D': A coordinate grid is shown from negative 6 to 6 on both axes at increments

nika2105 [10]

Given:

Vertices of ABCD are A(-4,4), (-2,2), C(-2,-1) and D(-4,1).

Vertices of A'B'C'D' are A'(3,-4), B'(5,-2), C'(5,1) and D'(3,-1).

To find:

The sequence of transformations that changes figure ABCD to figure A'B'C'D'.

Solution:

Part A:

The figure ABCD reflected across the x-axis, then

$(x,y)\to (x,-y)$

Using this rule, we get

$A(-4,4)\to A_1(-4,-4)$

Similarly, the other points are $B_1(-2,-2),C_1(-2,1),D_1(-4,-1)$ .

Then figure translated 7 units right to get A'B'C'D'.

$(x,y)\to (x+7,y)$

$A_1(-4,-4)\to A'(-4+7,-4)=A'(3,-4)$

Similarly, the other points are $B'(5,-2), C'(5,1),D'(3,-1)$ .

Therefore, the figure ABCD reflected across the x-axis and then translated 7 units right to get A'B'C'D'.

Part B:

Reflection and translation are rigid transformation, it means shape and size of figures remains same after reflection and translation.

Therefore, the two figures congruent.

8 0

2 years ago

Which statements can be represented by this equation? Select three options.

mars1129 [50]

Answer:

Options A,C and E.

Step-by-step explanation:

The given equation is

$2n-9.2=n+\dfrac{4}{5}$

Let n be the unknown number, then

Twice a number minus nine and two-tenths is the same as the number plus four-fifths.

$2n-9.2=n+\dfrac{4}{5}$

So, option A is correct.

Nine point two decreased by double a number is the same as the number added to four-fifths.

$9.2-2n=n+\dfrac{4}{5}$

Nine point two less than twice a number is equal to the number added to four-fifths.

$2n-9.2=n+\dfrac{4}{5}$

So, option C is correct.

Two times the difference of a number and nine and two-tenths is equal to the number plus four-fifths.

$2(n-9.2)=n+\dfrac{4}{5}$

Double a number decreased by nine and two-tenths is the same as the sum of four-fifths and the number.

$2n-9.2=n+\dfrac{4}{5}$

So, option E is correct.

Therefore, the correct options are A,C and E.

5 0

2 years ago

Read 2 more answers

Riya is applying mulch to her garden. She applies it at a rate of 250{,}000\text{ cm}^3250,000 cm 3 250, comma, 000, start text,

koban [17]

Complete Question

Riya is applying to her garden. She applies it at a rate of 25, 000 cm³ of mulch for every m² of garden space. At what rate is Riya applying mulch in m³/m²

Answer:

0.25m³/m²

Step-by-step explanation:

We are told the Riya sprays mulch at 250,000cm³ per m²

To find the rate at which Riya is spaying the mulch in m³/m² we would have to convert 250,00cm³/m² to m³/m²

1 cm³ = 1 × 10^-6m³

250,000 cm³ = x m³

Cross Multiply

1 cm³ × xm³ = 250,000cm³ × 1 × 10^-6 m³

X

x m³ = 250,000cm³ × 1 × 10^-6 m³/1 cm³

= 0.25m³

Therefore, the rate at which Riya is spraying the mulch = 0.25m³/m²

3 0

2 years ago

A dog's weight increased by 50% in 3 years. by the end of 3 years, the dog weighed 45 pounds. how much did the dog weigh 3 years

weeeeeb [17]

I hope this helps you

45+45.50%

45+45.50/100

45+22,5

67,5

6 0

2 years ago

Read 2 more answers