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SCORPION-xisa [38]
3 years ago
5

A line passes through point (-10, 1) and has a slope of -

Mathematics
1 answer:
cupoosta [38]3 years ago
4 0

Step-by-step explanation:

(X1, Y1) = (-10 , 1)

slope/m = -2

y - y1 = m(x - x1)

y - 1 = -2(x + 10)

y = -2x - 20 + 1

y = -2x - 19

2x + y = -19 → equation

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Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -
rosijanka [135]

Answer:

Step-by-step explanation:

Our equations are

y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by  D and its formula is

D=b^2-4ac\\

Where

a= the coefficient of the x^{2}

b= the coefficient of x

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant  and evaluate our answer accordingly .

Let us start with

y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\

Hence we have two real roots for this equation.

y = 2x^2 - 6x + 5\\

y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D

Hence we do not have any real root for this quadratic

y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\

Hence D>0 and thus we have two real roots for this equation.

y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\

Hence we have one real root to this quadratic equation.

7 0
3 years ago
Question 9 (0.5 points)
exis [7]
The correct answer is C. 2,400

Explanation- I’m a freshman trust me I know!
6 0
3 years ago
You are spreading fertilizer on a golf course at the rate of 40 pounds per 10,000 square feet. If the course is 320 acres, how m
AnnyKZ [126]
If you are spreading fertilizer on a golf course at the rate of 40 pounds per 10,000 square feet and the course is 320 acres, you can calculate the amount of fertilizer that will be needed by converting acres to square feet. So, 320 acres are 13,939,200 square feet which means you will need 55,756.8 pounds of fertilizer. 
4 0
4 years ago
What is the difference between the population and sample regression functions? Is this a distinction without difference?
GrogVix [38]

Answer:

See explanation below.

Step-by-step explanation:

When we want to fit a linear model given by:

y = \beta_0 + \beta_1 x

Where y is a vector with the observations of the dependent variable, \beta_0 , \beta_1 the parameters of the model and x the vector with the observations of the independent variable.

For this case this population regression function represent the conditional mean of the variable Y with values of X constant. And since is a population regression the parameters are not known, for this reason we use the sample data to obtain the sample regression in order to estimate the parameters of interest \beta_0, \beta_1

We can use any method in order to estimate the parameters for example least squares minimizing the difference between the fitted and the real observations for the dependenet variable.  After we find the estimators for the regression model then we have a model with the estimated parameters like this one:

\hat y = \hat b_0 +\hat b_1 x

With \hat \beta_0 = b_o , \hat \beta_1 = b_1

And this model represent the sample regression function, and this equation shows to use the estimated relation between the dependent and the independent variable.

8 0
3 years ago
Please help me out with this please
dedylja [7]

Intersecting Chord Theorem:

X = 1/2(78 + 76)

X = 1/2(154)

x = 77

3 0
4 years ago
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