Dennis and Eduardo are studying transformations using triangles. A ABC and A DEF are both plotted on a coordinate plane

Find AC What Is The Equation To AC?

In-s [12.5K]

Given:

Given that ABC is a right triangle.

The length of AB is 7 units.

The measure of ∠A is 65°

We need to determine the length of AC

Length of AC:

The length of AC can be determined using the trigonometric ratio.

Thus, we have;

$cos \ \theta=\frac{adj}{hyp}$

Where the value of $\theta$ is 65° and the side adjacent to the angle is AC and the side hypotenuse to the angle is AB.

Substituting the values, we have;

$cos \ 65^{\circ}=\frac{AC}{AB}$

Substituting AB = 7, we have;

$cos \ 65^{\circ}=\frac{AC}{7}$

Multiplying both sides by 7, we get;

$cos \ 65^{\circ} \times 7=AC$

$0.423 \times 7=AC$

$2.961=AC$

Rounding off to the nearest hundredth, we get;

$2.96=AC$

Thus, the length of AC is 2.96 units.

6 0

3 years ago

3 folders cost $2.91 which equation would help determine the cost of 2 folders

eimsori [14]

Answer:

The equation that will determine the cost of two folders is; 3x = 2× $2.91

and the cost of the 2 folders is $1.94

Step-by-step explanation:

To solve this problem, we will follow the steps below;

Using proportion;

Let x be the cost of 2 folders

3 folders = $2.91

2 folders = x

Cross-multiply

3x = 2× $2.91

The equation that will determine the cost of two folders is

3x = 2× $2.91

We can go ahead and solve

3x = $5.82

Divide both-side of the equation by 3

$\frac{3x}{3}$ = $\frac{5.82}{3}$

x = $ 1.94

The cost of 2 folders is $1.94

5 0

3 years ago

Read 2 more answers

Factor out the GCF 56x^2? + 16x + 64

ycow [4]

I’m not 100% sure but I think it’s 4 for the gcf

4 0

2 years ago

According to The Wedding Report, Inc., the mean cost for a wedding in the United States is $28732 (as of November 2008). Suppose

Stella [2.4K]

Answer:

Following are the solution to the given points:

Step-by-step explanation:

$X = \text{cost of wedding}\sim \text{Normal}\ (\mu = 28732, \sigma= 1500)\\\\$

For point a:

$Probability\ = 0.00000359\\\\ \text{(Using Excel function:} =NORMDIST(22000,28732,1500,1)).$

For point b:

$Probability \ = 0.014678\\\\\text{(Using Excel function:} =1-NORMDIST(32000,28732,1500,1))\\\\$

For point c:

$Probability\ = 0.794614436 \\\\$

$\text{(Using Excel function:} \\=NORMDIST (30000,28732,1500,1)-NORMDIST(25000,28732,1500,1))\\\\$

For point d:

$Q_1 = 27720.26537 \\\\\text{(Using Excel function:} =NORMINV(0.25,28732,1500)) \\\\Q_3 = 29743.73463 \\\\\text{(Using Excel function:} =NORMINV(0.75,28732,1500)).$

For point e:

$IQR = Q_3 - Q_1 = 29743.73463 - 27720.26537 = 2023.469251.$

For point f:

$Top\ 10\% = 30654.32735 \\\\\text{(Using Excel function:} =NORMINV(0.9,28732,1500)).$

5 0

2 years ago

Name the line of reflection used to map each preimage to its image

rewona [7]

Answer:

From the picture attached,

9). When pre-image KLMN is a reflected across x = -2, we get image K'L'M'N'.

Therefore, line of reflection will be x = -2

10). In this picture line of reflection which passes through origin (0, 0) and slope = 1 will be,

y = x.

11). Since, all the points of image and preimage points are equidistant from x-axis, line of reflection will be x-axis or y = 0.

12). Line passing through midpoint of the line joining BB' will be the line of reflection.

Coordinates of B → (5, 3)

Coordinates of B' → (5, 7)

Coordinates of BB' → → (5, 5)

Therefore, line of reflection will be y = 5.

13). Coordinates of G → (2, 5)

Coordinates of G' → (-2, 5)

Midpoint joining the segment GG' → → (0, 5)

Therefore, line of reflection → x = 0

14). Line of reflection passing through (0, 0) and slope = -1

y = -x

Step-by-step explanation:

3 0

2 years ago