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3 years ago

The functions fand g are defined as follows:

Mathematics

1 answer:

LuckyWell [14K]3 years ago

6 0

Step-by-step explanation:

Given

f(x) = -5x - 1

and

g(x) = 2x + 2

Now

f(3) = - 5 * 3 - 1

= -15 -1

= -16

Also

g(-4) = 2 * (-4) + 2

= - 8 + 2

= - 6

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6 children and 2 adults are going to the circus, children tickets are on sale, half the price of adult tickets totaling $54. How

inna [77]

Answer:

Price of 1 child ticket is $5.4

Price of 1 adult ticket is $10.8

Step-by-step explanation:

Given:-

6 children and 2 adults are going for circus.

Children ticket is half the price of adult ticket.

Total ticketing cost =$54

To find:-

Cost of 1 child ticket=?

Cost of 1 Adult ticket=?

Solution:-

Let price of 1 child ticket be x and price of 1 adult ticket be y,

therefore from the given data we get 2 equations,

$6x+2y=54$ -----------------------------------(1)

$x=\frac{1}{2} y$ --------------------------------(2)

Now, substituting the value of x from equation 2 in equation 1,

$6x+2y=54$

$6(\frac{1}{2} y)+2y=54$

$\frac{6}{2}y+2y=54$

$3y+2y=54$

$5y=54$

$\therefore y=\frac{54}{5}$

$\therefore y =10.8$ ------------------------(3)

Now, substituting the value of y from equation 3 in equation 2,

$x=\frac{1}{2} y$

$\therefore x=\frac{1}{2} \times 10.8$ ------------(from equation 3)

$\therefore x=\frac{10.8}{2}$

$\therefore x=5.4$ ----------------------(4)

As, x is price of 1 child ticket and y is price of 1 adult ticket,

Therefore price of 1 child ticket is $5.4 and price of 1 adult ticket is $10.8

7 0

3 years ago

Please assist me with these problems

blondinia [14]

Answer:

The function of f(x) is 20 for the middle problem idk the others

Step-by-step explanation:

3 0

2 years ago

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity. In the given triangle ABC, angle A

lana66690 [7]

The relationship between the lengths of the sides of a right triangle are

given by Pythagoras theorem.

Part A: ΔABC is similar to ΔADC

Part B: ΔABC and ΔADC are similar according AA similarity postulate

Part C: DA = 6

Reasons:

Part A:

∠A = 90°

Segment AD ⊥ Segment BC

Location of point D = Side BC

Part A: In triangle ΔABC, we have;

∠A = 90°, ∠B = 90° - ∠C

In triangle ΔADC, we have;

∠ADC = 90°, ∠DAC = 90° - ∠C

∴ ΔABC is similar to ΔADC by Angle-Angle, AA, Similarity Postulate

Part B: The triangles are similar according to AA similarity postulate,

because two angles in one triangle are equal to two angles in the other

triangle and therefore, by subtraction property of equality, the third angle

in both triangles are also equal.

Part C: The length of DB = 9

The length of DC = 4

Required: Length of segment DA

In triangle ΔABD, we have;

∠BDA = 90°= ∠ADC

∠DAC ≅ ∠B by Congruent Parts of Congruent Triangles are Congruent

Therefore;

ΔABD ~ ΔADC by AA similarity, which gives;

$\displaystyle \frac{\overline{DA}}{\overline{DC}} = \frac{\overline{BD}}{\overline{DA}}$

$\overline{DA}^2$ = $\overline{DC} \times \overline{BD}$

Which gives;

$\overline{DA}^2$ = 4 × 9 = 36

$\overline{DA}$ = √(36) = 6

$\overline{DA}$ = 6

Learn more here:

brainly.com/question/2269451

3 0

2 years ago

A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 89 feet from a building an

Anna007 [38]

The distance to the top of the building above the range finder can be found from the Pythagorean theorem.
.. d = √(115² -89²) ≈ 72.8 . . . . feet

Adding the height of the range finder, we find the height of the building to be
.. h = d+3 = 75.8 ft

8 0

3 years ago

6-a/a+5 =

Anni [7]

d) (6-a) divide (a+5)

7 0

2 years ago