Juan drove 126 miles in 3 hours. If he continued at the same rate, how long would it

The distance from point Y to the flag post measures 38.13 m. Step-by-step explanation: Assuming point Y is located at the intersection of both lines shown. Point X is positioned 34 meters east of point Y. The flagpole at point X is observed at a bearing of N18°W, meaning it creates an angle of 18° to the west from the north at point X. Conversely, at point Y, the flagpole has a bearing of N40°E, which makes a 40° angle towards the east from the north. Considering ∆ AXY as a right triangle, the angle FXY is established. Then, concerning ∆ BYX as another right triangle, the angle FYX is also determined. To find the third angle ∠YFX in triangle FYX, the angle sum property of triangles can be applied: ∠YFX + ∠FYX + ∠FXY = 180° Thus, we have: ∠YFX + 50° + 72° = 180° leading to ∠YFX = 58°. Now we can calculate the distance FY using the sine rule.

Answer:

The correct option is:

On the coordinate plane, there is a parabola that opens upwards, passing through the points (2, 10), having its vertex at (5, 1), and intersecting (8, 10).

Step-by-step explanation:

Initially, we must understand the translation rules

1) {f(x) + a} signifies f(x) moved up by (a) units

2) {f(x) – a} means f(x) moved down by (a) units

3) {f(x + a)} represents f(x) moved left by (a) units.

4) {f(x – a)} indicates f(x) moved right by (a) units.

Given information:

f(x) = x²

g(x) = (x-5)² + 1

By comparing the transformation from f(x) to g(x) with the translation rules

It can be concluded that g(x) represents f(x) through a translation of 5 units to the right and 1 unit upwards (rules 1 and 4)

Refer to the attached image, which illustrates the graphs of both f(x) and g(x)

As depicted, g(x) intersects (2, 10), has a vertex at (5, 1), and crosses through (8, 10)

Answer:

4

Step-by-step explanation:

Each sandwich costs 6 dollars, while chips sell for 3 dollars. She purchased 5 sandwiches at 6 dollars each, amounting to 30 dollars (5*6=30). This leaves her with 12 dollars to use since her total expenditure was 42 dollars. Given that chips are 3 dollars each, with 12 dollars left, 4 bags could be bought (4 * 3 = 12).

a. The point estimate for the population mean is b. The confidence interval at 80% is c. This means there is an 80% probability that the true mean of the population lies within the given confidence interval.

Response:

∠PQL=∠TRN [Angles corresponding]

Thus, PQ║RS and PQ=RS

Detailed explanation:

The side PQ has been drawn.

A second side QR is traced, forming an acute angle with side PQ.

Now side QR is extended to the left.

Create an arc from point Q such that it intersects QP at M and extends RQ at L. Without altering the compass width (i.e., the distance between the nib and pencil), draw an arc from R to intersect RQ at N. Now measure the distance LM with a compass. Position the compass at N and mark an arc cut from point R. Designate this intersection as T. Draw a line from point R through T. Then measure the length of PQ with the compass. Position your compass at R and create an arc on the produced line RT at S. Thus, we ascertain that PQ║RS and PQ=RS.

This occurs because

∠MQL=∠NRT [corresponding angles, with QR acting as the transversal]

∵PQ║RS  and PQ=RS [This identifies PQRS as a parallelogram]

Out of the four students who illustrated their explanations

Student 2 presented a partially correct but valid explanation.