All categories

2 years ago

What is the point-slope form of line with slope -3 that contains the point (10,-1)?

Mathematics

1 answer:

Shalnov [3]2 years ago

4 0

Answer:

D. y+1=-3(x-10)

Step-by-step explanation:

the equation for point-slope form of the line is given as y-y1=m(x-x1) where (x1,y1) is a given point, and m is the slope

we are given the point (10,-1) that passes through the line and a slope of -3

so we can substitute what we know into our equation

y--1=-3(x-10)

simplify

y+1=-3(x-10)

therefore the answer is D

Hope this helps! Good luck on your assignment!

You might be interested in

Show in fact that 1=9m + 20n for some integers m and n

marta [7]

Answer:

$1=9\cdot 9+20\cdpt (-4)=81-80$

Step-by-step explanation:

The greatest common divisor between 9 and 20 is 1, so we know the equation $1=9m+20n$ has a solution. A solution can be found either by inspection, or by applying Euclidean algorithm.

By inspection we just list some multiples of 9:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

and also list some mutiples of 20:

20, 40, 60, 80, 100, 120

And so we see that we can find a multiple of 9 (81) which is 1 away from a multiple of 20 (80). Which is the solution given at the start.

For the Euclidean algorithm, we should divide the greatest of the two numbers, by the smallest one, and keep track of the remainder:

20 = 9 * 2 + 2

Then we divide 9 by the remainder we got, which is 2:

9 = 2 * 4 + 1

we would continue doing this until getting a remainder of 1 (which we just did). Finally we "solve" for 1, from the last equation:

9 - 2*4 = 1

And then we solve for 2 from the first equation, and plug that in into the previous equation:

20 - 9*2 =2

9 - ( 20 - 9*2)*4 = 1

which does give us the same solution: $9\cdot 9 +20\cdot (-4)=1$

5 0

3 years ago

Sarah had 1/2 gallon of ice cream and wants to divide it into one cup servings to share with her class. A cup is one-sixteenth o

sergey [27]

She needs 8 serving dishes because you can only make 8 one cup servings out of a half gallon of ice-cream.

6 0

3 years ago

Please help me solve this short problem I’m really struggling

bearhunter [10]

Answer:

Step-by-step explanation:

In the standard form of a quadratic,

$h(x)=-x^2+v_0x+h_0$ ,

that last term, the h0, is the initial height off the ground that the object is. That means that for the first question, the irrigation system is initially 9.5 feet off the ground.

In order to answer the next question, we need to find the vertex of the parabola, because this is where the max height will occur and at how many feet away from the system. The max height is the k of the vertex and the horizontal distance away is the h of the vertex: (h, k). Thankfully, we have simple formulas to find those:

$h=-\frac{b}{2a}$ and $k=c-\frac{b^2}{4a}$ where a, b, and c come from the coefficients in the equation. For us, a = -1, b = 10, and c = 9.5. Finding h first:

$h=-\frac{10}{2(-1)}=\frac{-10}{-2}=5$

and now k:

$k=9.5-(\frac{10^2}{4(-1)})=9.5-(\frac{100}{-4} )=9.5-(-25)=9.5+25=34.5$

Summing it up, the vertex is at (5, 34.5), The interpretation of that is that "The spray reaches a max height of 34.5 feet at a horizontal distance of 5 feet away from the sprinkler head."

Next we are asked how far away from the sprinkler head the water hits the ground. To do this we factor the expression to find the zeros. The zeros tell us where the water will hit the ground after it reaches its max height and then falls back down to earth.

I used my calculator to factor this for me to get that the water will hit the ground 10.87 feet away from the sprinkler head.

7 0

3 years ago

I’m stuck on this please help?

Aleks04 [339]

Hello from MrBillDoesMath!

Answer:

2291/990

Discussion:

Let

x = 2.3141414...... then

10x = 23.141414... (*)

and

1000x = 2314.141414..... (**)

Subtract (*) from (**):

1000x - 10x = (2314 + .141414....) - (23 + .141414....)

990x = 2314 - 23 as the decimal parts cancel

990x = 2291

x = 2291/990

Thank you,

MrB

5 0

3 years ago

Heeeeelp ayuda amigos 4. En un famoso juicio por asesinato, cuatro amigos: Arturo (A), Bety (B), Carlos (C) y Dora (D) testifica

abruzzese [7]

Answer:

Bety es culpable y los demas son inocentes

Step-by-step explanation:

Siguiendo dos lineas de argumento diferente, Bety es la culpable. Si seguimos las otras dos opciones, el resultado no sera congruente:

Si Arturo es inocente y dice la verdad, el asesino es Bety o Carlos

Si Bety es culpable y miente, Dora sera inocente

Si Carlos es inocente y dice la verdad, Bety es la asesina

Si Dora es inocente y dice la verdad, Arturo es inocente y Bety culpable

Si Dora es inocente y dice la verdad, entonces Arturo o Bety es inocente.

Si Bety es culpable y miente, entonces Dora es inocente.

Si Carlos es inocente y dice la verdad, Bety es la asesina

Si Arturo es inocente y dice la verdad, Bety es la asesina.

Si Arturo es culpable y miente, Bety y Carlos son inocentes

Si Bety es inocente y dice la verdad, Dora sera culpable (ESTO REPRESENTA UNA FALLA EN EL ARGUMENTO)

Si Carlos es culpable y miente, Bety es inocente y el culpable.

Si Arturo es inocente y dice la verdad, el asesino es Carlos y Bety es inocente.

Si Bety es inocente y dice la verdad, Dora sera culpable (ESTO REPRESENTA UNA FALLA EN EL ARGUMENTO)

3 0

2 years ago