Solve using the quadratic formula. Choose all the correct responses.<br> X^2+ 10x + 22 = 0

Ind the equation of the tangent line to 9x^2+16y^2=52 through (2, -1)

EastWind [94]

Here are the steps.

In order to get the answer, first we need to get the x and y value of the center of the circle by using the equation of a circle (x^2 + y^2 = r^2)

<span>The center is (-9, -4)</span>

Once you get the center point, find the equation of the line (in a form of a radius) from the center point to point (2, -1). Get the slope.

The slope from center to point (2, -1) is 11/3

Finally, get the negative reciprocal of the slope from the previous step and form the equation using slope-intercept form ( y=mx + b). Then, that's the equation of the tangent line.

The slope of the tangent line is -3/11
The equation is y = -3/11x - 5/11

6 0

2 years ago

250 students out of 3,000 have found that math is their favorite subject among 10 subjects they are studying. If the choice of f

Oksi-84 [34.3K]

Answer:

The randomization distribution is created under the assumption that H₀: p = 0.1

The randomization distribution will also be centred at 0.1

Step-by-step explanation:

If the distribution was truly random, 1 out of 10 students will choose math as his/her favorite subject.

This means that the randomization will have the null hypothesis saying that the proportion of students who will choose maths as their favourite subject = 0.1

Mathematically, it'll be written as

The null hypothesis is given as

H₀: p = 0.1

And the randomization distribution will be centred at 0.1 too.

The alternative hypothesis will now prove the theory they're looking to see in the question that

Hₐ: p < 0.1

Hope this Helps!!!

5 0

2 years ago

How many integers are there that consist of four digits (from 1000 to 9999) where the first digit is a 5 or an 8 and the third d

Ostrovityanka [42]

Answer:

1600 integers

Step-by-step explanation:

Since we have a four digit number, there are four digit placements.

For the first digit, since there can either be a 5 or an 8, we have the arrangement as ²P₁ = 2 ways.

For the second digit, we have ten numbers to choose from, so we have ¹⁰P₁ = 10.

For the third digit, since it neither be a 5 or an 8, we have two less digit from the total of ten digits which is 10 - 2 = 8. So, the number of ways of arranging that is ⁸P₁ = 8.

For the last digit, we have ten numbers to choose from, so we have ¹⁰P₁ = 10.

So, the number of integers that can be formed are 2 × 10 × 8 × 10 = 20 × 80 = 1600 integers

5 0

2 years ago

Marcus needs 3 1/10 m of blue fabric and 1 1/5 m of yellow fabric to make his costume. How much more blue fabric than yellow fab

Kamila [148]

Answer:

$1\frac{9}{10}\ m$