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3 years ago

Graph the line of the equation x4+y=−2 using its slope and y-intercept

Mathematics

1 answer:

k0ka [10]3 years ago

4 0

Answer:

y-intercept = c = -2

slope = y = - 4

Step-by-step explanation:

The correct equation is:

4x + y = -2

We need to graph the line using its slope and y-intercept. The slope intercept form of the equation is:

y = mx + c

Here, m is the slope and c is the y-intercept. Transforming the given equation to this form gives us:

y = - 4x - 2

This means, the slope is:

m = - 4

and y-intercept is:

c = - 2

y-intercept in ordered pair is written as (0, c). So for the given case the y intercept will be (0, -2). This gives us first point on the graph.

The slope tells us that by how many units will the y variable will change for one unit change in x-axis.

So slope, m = - 4, tells us that the y-variable will change by negative 4 units for 1 unit change in x variable.

Based on this change, we can get another point from (0, -2) which will be (0+1, -2 - 4) = (1, - 6)

This gives us the second point on the graph. Plot these two points and join them using a straight line. This straight line will be the graph of equation y = 4x - 2 or 4x + y = -2

The graph is attached below.

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A person recently read that 84% of cat owners are women. How large a sample should the researcher take if she wishes to be 90% c

Lana71 [14]

Answer:

405

Step-by-step explanation:

To find sample size, use the following equation, where n = sample size, za/2 = the critical value, p = probability of success, q = probability of failure, and E = margin of error.

$n=\frac{(z_{\frac{\alpha }{2} })^{2} *p*q }{E^2}$

The values that are given are p = 0.84 and E = 0.03.

You can solve for the critical value which is equal to the z-score of (1 - confidence level)/2. Use the calculator function of invNorm to find the z-score. The value will given with a negative sign, but you can ignore that.

(1 - 0.9) = 0.1/2 = 0.05

invNorm(0.05, 0, 1) = 1.645

You can also solve for q which is 1 - p. For this problem q = 1 - 0.84 = 0.16

Plug the values into the equation and solve for n.

$n =\frac{(1.645)^2*0.84*0.16}{(0.03)^2}\\n= 404.0997333$

Round up to the next number, giving you 405.

6 0

3 years ago

In ΔOPQ, q = 110 inches, o = 970 inches and ∠P=167°. Find the area of ΔOPQ, to the nearest square inch.

ki77a [65]

Answer:

$Area = 12004$ square inches

Step-by-step explanation:

Given

$q = 110$

$o = 970$

$\angle P =167$

Required

The area of the triangle

To do this, we use:

$Area = \frac{1}{2} * o * q * sin(P)$

So, we have:

$Area = \frac{1}{2} * 970 * 110 * sin(167^\circ)$

$Area = \frac{1}{2} * 970 * 110 * 0.2250$

$Area = 12003.75$

Approximate

$Area = 12004$

3 0

3 years ago

Read 2 more answers

Find the values of the variables.

Lunna [17]

Answer:

A. 118°

B. 62°

C. 59°

Step-by-step explanation:

Hooe this helps!:) If you want me to explain just ask in the comments

5 0

2 years ago

Read 2 more answers

Plz answer!! ASAP!!

Wittaler [7]

(1) ∠ABC = 65°, ∠DBE = 65°, ∠CBE = 115°, ∠ABD = 115°

(2) ∠ABC = 62°, ∠DBE = 62°, ∠CBE = 118°, ∠ABD = 118°

Solution:

(1) In the given image ABC and DBE are vertical angles.

Vertical angle theorem:

If two angles are vertical then they are congruent.

⇒ ∠ABC = ∠DBE

⇒ 3x° + 38° = 5x° + 20°

Arrange like terms one side.

⇒ 38° – 20° = 5x° – 3x°

⇒ 18° = 2x°

⇒ x° = 9°

∠ABC = 3(9°) + 38° = 65°

∠DBE = 5(9°) + 20° = 65°

Adjacent angles in a straight line = 180°

⇒ ∠ABC + ∠CBE = 180°

⇒ 65° + ∠CBE = 180°

⇒ ∠CBE = 115°

∠ABD and ∠CBE are vertical angles.

∠ABD = 115°

(2) In the given image ABC and DBE are vertical angles.

⇒ ∠ABC = ∠DBE

⇒ 4x° + 2° = 5x° – 13°

Arrange like terms one side.

⇒ 13° + 2° = 5x° – 4x°

⇒ 15° = x°

∠ABC = (4(15°) + 2°) = 62°

∠DBE = 5(15°) – 13° = 62°

Adjacent angles in a straight line = 180°

⇒ ∠ABC + ∠CBE = 180°

⇒ 62° + ∠CBE = 180°

⇒ ∠CBE = 118°

∠ABD and ∠CBE are vertical angles.

∠ABD = 118°

3 0

3 years ago

Could someone help me understand how to solve this?

monitta

Answer:

Amount in 4% account: $550

Step-by-step explanation:

Use simple interest formula $I=P\cdot r\cdot t,$ where

I = interest

P = principal

r = rate (as decimal)

t = time.

4% account:

$P_1=x\\ \\r_1=0.04\\ \\t_1=1,$

then

$I_1=x\cdot 0.04\cdot 1=0.04x$

5% account:

$P_2=1,500-x\\ \\r_2=0.05\\ \\t_2=1,$

then

$I_2=(1,500-x)\cdot 0.05\cdot 1=0.05(1,500-x)$

You have earned $69.50 in total, so

$I_1+I_2=69.50\\ \\0.04x+0.05(1,500-x)=69.50\\ \\4x+5(1,500-x)=6,950\\ \\4x+7,500-5x=6,950\\ \\4x-5x=6,950-7,500\\ \\-x=-550\\ \\x=550\\ \\1,500-x=1,500-550=950$

Amount in 4% account: $550

Amount in 5% account: $950

8 0

3 years ago