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2 years ago

Write the point-slope equation of the line that goes through (1, 4) with a slope of -10

Mathematics

2 answers:

amid [387]2 years ago

4 0

Answer:

y - 4= -10(x - 1)

Step-by-step explanation:

(y - y 1) = m(x - x 1 )

sammy [17]2 years ago

3 0

Answer:

y-4=-10(x-1)

Step-by-step explanation:

Point-slope form is:

$y-y_1=m(x-x_1)\\m-slope\\(x_1,y_1)-point$

We are given the slope of -10 and the point (1,4). So:

m = -10

x1 = 1

y1= 4

Replace the appropriate values:

$y-4=-10(x-1)$

So, y-4=-10(x-1) should be the point-slope equation.

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7. What is the length of side a?<br> Help please

padilas [110]

Answer:

a= 63

Step-by-step explanation:

16+11=27

90-27= 63

8 0

2 years ago

Read 2 more answers

In a park,a sidewalk is built around the edge of a circular pond.The sidewalk is 7 feet wide,and the pond measure 15 feet across

densk [106]

Answer:

91.14 feet

Step-by-step explanation:

Given:

In a park,a sidewalk is built around the edge of a circular pond.

The sidewalk is 7 feet wide, and the pond measure 15 feet across.

Question asked:

What amount of railing would be needed to go completely around the outer edge of the sidewalk?

Solution:

From distance from one edge of the pond to the another = 15 feet

That means diameter of the pond = 15 feet

And width of the sidewalk = 7 feet all around

combined diameter = 15 + 7 + 7 = 29 feet

Radius,r = $\frac{Diameter}{2} =\frac{29}{2} ==14.5\ feet$

That means distance between outer edge of the sidewalk to the center of the circular pond = 14.5 feet

Now, we will have to find circumference of outer circular edge of sidewalk:

$Circumference\ of\ circle=2\pi r$

$=2\times\frac{22}{7} \times14.5\\ \\ =\frac{638}{7} \\ \\ =91.14\ feet$

Therefore, 91.14 feet would be needed to go around the outer edge of the sidewalk.

7 0

2 years ago

A(-2,3)

Anika [276]

Answer:

The perimeter of triangle is 19.8 units

Step-by-step explanation:

we know that

The perimeter of triangle ABC is

$P=AB+BC+AC$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

we have

$A(-2,3),B(3,0)$

substitute in the formula

$d=\sqrt{(0-3)^{2}+(3+2)^{2}}$

$d=\sqrt{(-3)^{2}+(5)^{2}}$

$d_A_B=\sqrt{34}\ units$

step 2

Find the distance BC

we have

$B(3,0),C (-4,-3)$

substitute in the formula

$d=\sqrt{(-3-0)^{2}+(-4-3)^{2}}$

$d=\sqrt{(-3)^{2}+(-7)^{2}}$

$d_B_C=\sqrt{58}\ units$

step 3

Find the distance AC

we have

$A(-2,3),C (-4,-3)$

substitute in the formula

$d=\sqrt{(-3-3)^{2}+(-4+2)^{2}}$

$d=\sqrt{(-6)^{2}+(-2)^{2}}$

$d_A_C=\sqrt{40}\ units$

step 4

Find the perimeter

$P=AB+BC+AC$

substitute the values

$P=\sqrt{34}+\sqrt{58}+\sqrt{40}$

$P=19.8\ units$

4 0

2 years ago

Planes A and B intersect.

myrzilka [38]

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

Two planes have been given as plane A and plane B.

Two lines 'm' and 'n' are on the plane A.

These lines intersect each other at a point W.

Therefore, point W describes the point of intersection of the lines 'm' and 'n'.

Option (1) will be the correct option.

8 0

3 years ago

3. The following sets are not equal - An (BUC) and AU(BnC) Construct a universe U and non-empty sets A, B, and C so that the abo

yarga [219]

Answer:

1.U={1,2,3,4,5}

A={2}

B={2,3}

C={4,5}

2.U={1,2,3,4}

A={1,2}

B={2,3}

C={4}

Step-by-step explanation:

We are given that $A\cap (B\cup C)$ and $A\cup (B\cap C)$

are different sets

1.We have to construct a universe set U and non empty sets A,B and C so that above set in fact the same

Suppose U={1,2,3,4,5}

A={2}

B={2,3}

C={4,5}

$B\cap C=\phi$

$B\cup C=$ {2,3,4,5}

$A\cap (B\cup C)$ ={2} $\cap$ {2,3,4,5}={2}

$A\cup (B\cap C)$ ={2} $\cup\phi$ ={2}

Hence, $A\cap (B\cup C)=A\cup (B\cap C)$

2.We have to construct a universe set U and non empty sets A,B and C so that above sets are in fact different

Suppose U={1,2,3,4}

A={1,2}

B={2,3}

C={4}

$B\cap C=\phi$

$B\cup C$ ={2,3,4}

$A\cup (B\cap C)$ ={1,2} $\cup \phi$ ={1,2}

$A\cap (B\cup C)$ ={1,2} $\cap$ {2,3,4}={2}

Hence, $A\cap (B\cup C)\neq A\cup (B\cap C)$

3 0

2 years ago