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2 years ago

Y=x² – 8x + 16So right now I'm trying to figure out the inverse relation

Mathematics

1 answer:

anzhelika [568]2 years ago

7 0

Answer:

The inverse relation is:

$y=4 \pm \sqrt{x}$

Step-by-step explanation:

We need to solve for x.

Useful formula: (x-y)^2=x^2-2xy+y^2.

$y=x^2-8x+16$

$y=(x-4)^2$

Now, take the square root of both sides:

$\pm \sqrt{y}=x-4$

Add 4 on both sides:

$4 \pm \sqrt{y}=x$

Interchange x and y:

$4 \pm \sqrt{x}=y$

The inverse relation is:

$y=4 \pm \sqrt{x}$

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Find all the missing elements : C=120degrees b= 5 c=11

mezya [45]

Answer:

A = 36.8°

B = 23.2°

a = 7.6

Step-by-step explanation:

Given:

C = 120°

b = 5

c = 11

Required:

Find A, B, and a.

Solution:

✔️To find B, apply the Law of Sines

$\frac{sin(B)}{b} = \frac{sin(C)}{c}$

Plug in the values

$\frac{sin(B)}{5} = \frac{sin(120)}{11}$

Cross multiply

Sin(B)*11 = sin(120)*5

Divide both sides by 11

$sin(B) = \frac{sin(120)*5}{11}$

Sin(B) = 0.3936

B = $sin^{-1}(0.3936)$

B = 23.1786882° ≈ 23.2° (nearest tenth)

✔️Find A:

A = 180° - (B + C) (sum of triangle)

A = 180° - (23.2° + 120°)

A = 36.8°

✔️To find a, apply the Law of sines:

$\frac{sin(A)}{a} = \frac{sin(B)}{b}$

Plug in the values

$\frac{sin(36.8)}{a} = \frac{sin(23.2)}{5}$

Cross multiply

a*sin(23.2) = 5*sin(36.8)

Divide both sides by sin(23.2)

$a = \frac{5*sin(36.8)}{sin(23.2)$

a = 7.60294329 ≈ 7.6 (nearest tenth)

5 0

2 years ago

Triangle ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the s

Allisa [31]

For line B to AC: y - 6 = (1/3)(x - 4); y - 6 = (x/3) - (4/3); 3y - 18 = x - 4, so 3y - x = 14

For line A to BC: y - 6 = (-1)(x - 0); y - 6 = -x, so y + x = 6

Since these lines intersect at one point (the orthocenter), we can use simultaneous equations to solve for x and/or y:

(3y - x = 14) + (y + x = 6) => 4y = 20, y = +5; Substitute this into y + x = 6: 5 + x = 6, x = +1

So the orthocenter is at coordinates (1,5), and the slopes of all three orthocenter lines are above.

5 0

2 years ago

Wnite and graph an inequality for the given solution set . {x | x < 7}

Svetradugi [14.3K]

Answer:

im not in high school sorry

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

The American Civil War was a civil war in the United States from 1861 to 1865, fought between northern states loyal to the Union

Sloan [31]

Answer:

The American Civil War was a civil war in the United States from 1861 to 1865, fought between northern states loyal to the Union and southern states that had seceded to form the Confederate States of America.

Why do phase changes occur?

1. Compare: Set the Water temperature to 0 °C and click Play. Observe the water molecules.

Click Reset, set the Water temperature to 100 °C, and click Play again.

What do you notice? The water molecules are moving slightly faster at 100 °C than at 0 °C.

[Note: This difference may be too small to observe easily.]

2. Observe: Click Reset. The mean molecular speed of the water molecules is displayed

below the container. Set the Water temperature to 0 °C and Add/remove heat energy to

400 J/s. Click Play.

A. How does the mean speed of the water molecules change as they are heated?

The average speed of water molecules increases as they are heated.

B. Does the mean molecular speed change as much as the temperature as the

water heats up? Explain.

Sample answer: For each degree of temperature change, the mean molecular

speed increases by about 1 m/s. At 100 °C, the mean molecular speed is about

17% faster than at 0 °C.

3. Explain: How is temperature related to the motions of molecules?

The higher the temperature, the faster the molecules move.

4. Observe: Click Reset. Set the Water temperature to 20 °C and the Ice volume to 50 cc.

Set Add/remove heat energy to 0 J/s. Click Play. How do the molecules in the liquid

interact with the molecules in the solid?

The molecules of the liquid collide with the molecules of solid, gradually breaking the bonds

between the molecules in the solid and causing the ice to melt.

Step-by-step explanation:

7 0

2 years ago

A box holding pennies, nickels and dimes contains thirteen coins with a total value of 83 cents. How many coins of each type are

Art [367]

Answer:

The number of pennies,nickels and dimes are (p,n,d)=(3,4,6).

Further explanation:

Given:

A box holding pennies, nickels and dimes contains thirteen coins in a box.

Total value is 83 cents.

Calculation:

Consider p,n and d be the number of pennies, nickel and dimes.

Now, total is 13 coins so $p+n+d=13$

As we know that these following are US coin.

Penny=1 cent

Nickel=5 cents

Dime=10 cents

Step 1:

The value is already given as 83 cents that is 80+3 cents.

80 cents can be possible in many combinations as follows:

(N,D)=(0,8),(2,7),(4,6),(6,5),(8,4),(10,3),(12,2),(14,1),(16,0)

It is given that the total number of cents is 13 so we choose (4,6) as (n,d) .

So the value of nickel n=4

Dimes d=6

Step 2:

The value of p is calculated as follows:

Substitute 4 for n, 6 for d in equation $p+n+d=13$ as follows:

$p+4+6=13$

$p+10=13$

$p=13-10$

p=3

Thus, the number of pennies,nickels and dimes are (p,n,d)=(3,4,6).

3 0

3 years ago

Y=x² – 8x + 16So right now I'm trying to figure out the inverse relation ​

Y=x² – 8x + 16So right now I'm trying to figure out the inverse relation