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2 years ago

Find the x- and y-intercepts of −x+y=−3. (Enter each intercept in the form (a,b).)

Mathematics

2 answers:

I am Lyosha [343]2 years ago

7 0

Step-by-step explanation:

first of all, let's convert this into a regular line equation :

-x + y = -3

y = x - 3

the x-intercept (the point of the line, where y = 0) is

0 = x - 3

x = 3

so, the point is (3, 0).

the y-intercept (the point of the line, where x = 0) is logically the constant term in the equation : y = -3.

so, the point is (0, -3)

Ostrovityanka [42]2 years ago

3 0

Answer:

(1,-2)

(0,-3)

(-3,0)

Step-by-step explanation:

each point on the line -x+y=-3

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Identify the graph of 9X^2+4xy+5y^2-40=0 and find theta to the nearest degree.

lubasha [3.4K]

Answer:

The answer is ellipse; 23° to the nearest degree ⇒ answer (d)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy² + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

- 9x² + 4xy + 5y² - 40 = 0

∵ A = 9 , B = 4 , 5 = 5

∴ B² - 4 AC = (4)² - 4(9)(5) = -164 < 0

∴ B² - 4AC < 0

∴ If a conic exists, it will be either a circle or an ellipse.

* To find the type of the graph lets check;

- If A and C are nonzero, have the same sign, and are not

equal to each other, then the graph is an ellipse.

- If A and C are equal and nonzero and have the same

sign, then the graph is a circle.

∵ A and C have same signs and are not equal

∴ The graph is an ellipse

* If we have term xy ⇒ B ≠ 0

∴ The graph is rotate by angle Ф

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 9 , B = 4 , C = 5

∴ cot(2Ф) = (9 - 5)/4 = 4/4 = 1

∴ tan(2Ф) = 1

∴ 2Ф = 45°

∴ Ф = 22.5° ≅ 23° to the nearest degree

* The answer is ellipse; with angle of rotation = 23°

4 0

4 years ago

If AACD ~ AABE, find the value of x.

Anastaziya [24]

9514 1404 393

Answer:

x = 16

Step-by-step explanation:

Corresponding sides are proportional.

BE/CD = AE/AD

20/(3x+8) = (x-1)/(x-1+27)

20(x+26) = (3x+8)(x -1)

In standard form, this is ...

3x^2 -15x -528 = 0

x^2 -5x -176 = 0 . . . . . . divide by 3

(x -16)(x +11) = 0 . . . . . . . factor

x = 16

This is the positive value that makes the product zero. x=-11 will also make the product 0, but gives negative segment lengths in the geometry. It is an extraneous solution.

4 0

3 years ago

How many whole cans can the company make out of each sheet of metal?

klio [65]

Answer:

Step-by-step explanation:

Total Surface Area of the Metal Sheet = $1000\:in^2$

Given a cylinder with diameter 3 Inch and height $4\frac{1}{4} in$

To determine how many whole cans can be made, the first step is to find the total surface area of each of the cylindrical can.

Total Surface Area of a cylinder = $2\pi r^2+2\pi rh$

Radius =3÷2=1.5 Inch

Height of the can = $4\frac{1}{4} in$

<u>Total Surface Area of each can </u>

$2\pi r^2+2\pi rh=2\pi r(r+h)\\=2*1.5*\pi(1.5+4.25)\\=3\pi *5.75\\=17.25\pi \:in^2$

<u>Number of Cans that can be Made </u>

To determine this, we divide the total surface area of the metal sheet by the total surface area of each can.

Number of Cans=Total surface area of the metal sheet÷Total surface area of each can.

$=1000 \div 17.25\pi\\=18.45$

Therefore, the company can make 18 whole cans from each sheet of metal.

6 0

3 years ago

The number 0.4 is written as a ____________ ( decimal , decimal point, hundred, hundredth)?

Anuta_ua [19.1K]

The number 0.4 is written as a decimal.

5 0

3 years ago

Read 2 more answers

It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minute

NemiM [27]

Answer:

a) 10.93% probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes.

b) 99.22% probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mildly obese

Normally distributed with mean 373 minutes and standard deviation 67 minutes. So $\mu = 373, \sigma = 67$

A) What is the probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes?

So $n = 5, s = \frac{67}{\sqrt{5}} = 29.96$

This probability is 1 subtracted by the pvalue of Z when X = 410.

$Z = \frac{X - \mu}{s}$

$Z = \frac{410 - 373}{29.96}$

$Z = 1.23$

$Z = 1.23$ has a pvalue of 0.8907.

So there is a 1-0.8907 = 0.1093 = 10.93% probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes.

Lean

Normally distributed with mean 526 minutes and standard deviation 107 minutes. So $\mu = 526, \sigma = 107$