Find tan A for the triangle below. a 1.5 b. 0.667 C. 0.832 d. 1.202

Is this positive correlation , negative correlation or no correlation?

max2010maxim [7]

Positive correlation

3 0

3 years ago

What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

Solnce55 [7]

The coordinates of the points A and B are not given. We'll assume: A(3,1) B(12,-5)

Answer:

The coordinates of E are (6,-1)

Step-by-step explanation:

Partition of a Segment

The length of segment directed from A(xa,ya) to B(xb,yb) can be decomposed in its x,y coordinates:

$x_{AB}=x_b-x_a$

$y_{AB}=y_b-y_a$

If a point E is to be in the segment and partition it into a ratio 1:2, then

\displaystyle \frac{x_{AE}}{{x_{EB}}=\frac{y_{AE}}{{y_{EB}}=\frac{1}{2}

But

$x_{AE}=x_e-x_a$

$y_{AE}=y_e-y_a$

$x_{EB}=x_b-x_e$

$y_{EB}=y_b-y_e$

Then we set the equation:

$\frac{x_{AE}}{{x_{EB}}=\frac{1}{2}$

$2(x_e-x_a)=x_b-x_e$

Operating and rearranging

$3x_e=x_b+2x_a$

Solving

$\displaystyle x_e=\frac{x_b+2x_a}{3}=\frac{12+6}{3}$

$x_e=6$

Similarily

$\displaystyle y_e=\frac{y_b+2y_a}{3}=\frac{-5+2}{3}$

$y_e=-1$

The coordinates of E are (6,-1)

8 0

4 years ago

Read 2 more answers

Describe how you would create a model to represent the expression .

Elanso [62]

To write an expression, we often have to interpret a written phrase. For example, the phrase “6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.

5 0

3 years ago

Read 2 more answers

Celeste is making fruit baskets for a local hospital. The directions say to use 5 apples for every 6 oranges. Celeste is filling

MariettaO [177]

Answer:

A. Equivalent ratios of 5:6

We multiply both the numerator and the denominator by the same number, this way:

10:12 , 15:18, 20:24, 25:30

B. Equivalent ratios of 2:3

We multiply both the numerator and the denominator by the same number, this way:

4:6 , 6:9, 8:12, 10:15, 12:18

C. We have the same number of oranges at:

10:12 and 8:12

15:18 and 12:18

Like Celeste decided not to follow the directions, she's actually using less apples than expected to fill the baskets.

Step-by-step explanation:

1. Let's check all the information provided to answer the question correctly:

Ratio that the local hospital say to Celeste to use : 5 apples for every 6 oranges

Ratio that Celeste is actually using: 2 apples for every 3 oranges

2. Complete the tables to find equivalent ratios.

A. Equivalent ratios of 5:6

We multiply both the numerator and the denominator by the same number, this way:

10:12 , 15:18, 20:24, 25:30

B. Equivalent ratios of 2:3

We multiply both the numerator and the denominator by the same number, this way:

4:6 , 6:9, 8:12, 10:15, 12:18

3. Circle two columns, one in each table, in which the number of oranges is the same.

We have the same number of oranges at:

10:12 and 8:12

15:18 and 12:18

Like Celeste decided not to follow the directions, she's actually using less apples than expected to fill the baskets.

8 0

3 years ago

Ben bought 4 pints of apple juice. he drinks 1/3 pint each day. how many days will the apple juice last ben?

liberstina [14]

Answer:

12 days

Step-by-step explanation:

6 0

2 years ago