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3 years ago

A group of friends wants to go to the amusement park. They have no more than $165

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

3 0

Answer:

17.75x + 5.25 $\leq$ 165

x $\leq$ 9

Step-by-step explanation:

The total cost can be represented by 17.75x + 5.25, where x is the number of people.

They can only spend a maximum of $165, so a less than or equal sign has to be used.

The inequality will be 17.75x + 5.25 $\leq$ 165

Now, solve for x:

17.75x + 5.25 $\leq$ 165

17.75x $\leq$ 159.75

x $\leq$ 9

So, x $\leq$ 9 is the answer, meaning 9 people or less can go to the amusement park.

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Use an algebraic equation to find the measure of each angle that is represented in terms of x.

GuDViN [60]

The measure of each angle is 117°

Explanation:

Given that the two angles are (11x-26)° and (7x+26)°

We need to determine the measure of each angle.

<u>Measure of angles:</u>

From the figure, it is obvious that the two angles are vertically opposite angles.

By definition, we know that, the vertically opposite angles are always equal.

To determine the measure of each angle, we shall first find the value of x.

Thus, we have,

$11x-26=7x+26$

$4x-26=26$

$4x=52$

$x=13$

Thus, the value of x is 13

Now, substituting $x=13$ in the angle (11x-26)°, we get,

$(11(13)-26)^{\circ}=(143-26)^{\circ}$

$=117^{\circ}$

The measure of the angle is 117°

Similarly, substituting $x=13$ in the angle (7x+26)°, we get,

$(7x+26)^{\circ}=(7(13)+26)^{\circ}$

$=117^{\circ}$

The measure of the angle is 117°

Hence, the measure of each angle is 117°

6 0

4 years ago

Solve for X and solve for Y?

Llana [10]

Answer:

$x=3\sqrt 5\\$

$y = \sqrt {126}$

Step-by-step explanation:

By geometric mean property:

$x = \sqrt{9 \times 5} = \sqrt{45} = 3 \sqrt{5} \\ \\ by \: pythagoras \: theorem \\ \\ {y}^{2} = {9}^{2} + {x}^{2} \\ \\ {y}^{2} = {9}^{2} + {(3 \sqrt{5}) }^{2} \\ \\ {y}^{2} = 81 + 45 \\ \\ {y}^{2} = 126 \\ \\ y = \sqrt{126}$

7 0

3 years ago

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vladimir2022 [97]

Answer:

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Step-by-step explanation:

Formula for volume of rectangular prism is length x width x height. So in this case, we're just multiplying:

20 x 8 x 16

160 x 16

= 2560

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3 years ago

Which diagram shows that the two triangles must be congruent

Arte-miy333 [17]

Answer:

D. 2 and 3 only

Step-by-step explanation:

I took the test. I am in Honors Geometry.

5 0

3 years ago

SOMEONE HELP ME ASAP PLZZ!!!

Black_prince [1.1K]

Answer:

The distance of the plane from the base of the tower is 25.5 foot.

Step-by-step explanation:

As given

Max is in a control tower at a small airport.

He is located 50 feet above the ground when he spots a small plane on the runway at an angle of depression of 27°.

Now by using the trigonometric identity.

$tan\theta = \frac{Perpendicular}{Base}$

As shown in the figure given below

Perpendicular = CB

Base = AC = 50 feet

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Put in the identity.

$tan\ 27^{\circ} = \frac{CB}{AC}$

$tan\ 27^{\circ} = \frac{CB}{50}$

$tan\ 27^{\circ} = 0.51\ (Approx)$

Put in the above

$0.51 = \frac{CB}{50}$

CB = 0.51 × 50

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Therefore the distance of the plane from the base of the tower is 25.5 foot.

4 0

3 years ago