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3 years ago

Plz help i need to find slope here

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

3 0

The answer is d which is 6/5

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Write an equation of a line in slope intercept form that is parallel to y = 3x+6 and passes through the point (-10, 2.5)

TiliK225 [7]

1) Line should be parallel to y = 3x+6, so slope of this line should be =3.

y=mx +b

y=3x +b

Now we have to find b (y-intercept), using the point (-10, 2.5).

2.5 = 3*(-10)+b

b=2.5+30=32.5

y=3x + 32.5

2) The line should be perpendicular to y = -4x -2, so its slope is going to be negative reciprocal m= 1/4.

Now we have to find b (y-intercept), using the point (-16, -11).

y=(1/4)x +b

-11=(1/4)*(-16) + b

-11 = -4 +b

b = -7

y=(1/4)x - 7

3 0

3 years ago

Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and pro

Neporo4naja [7]

${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ Sanya has a piece of land which is in the shape of a rhombus.

★ She wants her one daughter and one son to work on the land and produce different crops, for which she divides the land in two equal parts.

★ Perimeter of land = 400 m.

★ One of the diagonal = 160 m.

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ Area each of them [son and daughter] will get.

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

Let, ABCD be the rhombus shaped field and each side of the field be $x$

[ All sides of the rhombus are equal, therefore we will let the each side of the field be $x$ ]

Now,

• Perimeter = 400m

$\longrightarrow \tt AB+BC+CD+AD=400m$

$\longrightarrow \tt x + x + x + x=400$

$\longrightarrow \tt 4x=400$

$\longrightarrow \tt \: x = \dfrac{400}{4}$

$\longrightarrow \tt x= \red{100m}$

$\therefore$ Each side of the field = 100m.

Now, we have to find the area each [son and daughter] will get.

So, For $\triangle$ ABD,

Here,

• a = 100 [AB]

• b = 100 [AD]

• c = 160 [BD]

$\therefore \tt Simi \: perimeter \: [S] = \boxed{ \sf \dfrac{a + b + c}{2} }$

$\longrightarrow \tt S = \dfrac{100 + 100 + 160}{2}$

$\longrightarrow \tt S = \cancel{ \dfrac{360}{2}}$

$\longrightarrow \tt S = 180m$

Using herons formula,

$\star \tt Area \: of \: \triangle = \boxed{\bf{{ \sqrt{s(s - a)(s - b)(s - c) } }}} \star$

where

• s is the simi perimeter = 180m

• a, b and c are sides of the triangle which are 100m, 100m and 160m respectively.

Putting the values,

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(180 - 100)(180 - 100)(180 - 160) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(80)(80)(20) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180 \times 80 \times 80 \times 20 }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{9 \times 20 \times 20 \times 80 \times 80}$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{ {3}^{2} \times {20}^{2} \times {80}^{2} }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = 3 \times 20 \times 80$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \red{ 4800 \: {m}^{2} }$

Thus, area of $\triangle$ ABD = 4800 m²

As both the triangles have same sides

So,

Area of $\triangle$ BCD = 4800 m²

Therefore, area each of them [son and daughter] will get = 4800 m²

${\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}$

★ Figure in attachment.

${\underline{\rule{290pt}{2pt}}}$

7 0

1 year ago

Read 2 more answers

Solve for x. 5x^2 – 45 = 0

mamaluj [8]

5x^2-45=0

*Add 45 to both sides*

5x^2=45

*Divide both sides by 5*

x^2=9

*Take the square root of both sides*

x=+/-9

Hope this helps!!

3 0

3 years ago

Read 2 more answers

A factory worker productivity is normally distributed. one worker produces an average of 75 units per day with a standard deviat

Angelina_Jolie [31]

Let Xi be the random variable representing the number of units the ﬁrst worker produces in day i.
Deﬁne X = X1 + X2 + X3 + X4 + X5 as the random variable representing the number of units the
ﬁrst worker produces during the entire week. It is easy to prove that X is normally distributed with mean µx = 5·75 = 375 and standard deviation σx = 20√5.
Similarly, deﬁne random variables Y1, Y2,...,Y5 representing the number of units produces by
the second worker during each of the ﬁve days and deﬁne Y = Y1 + Y2 + Y3 + Y4 + Y5. Again, Y is normally distributed with mean µy = 5·65 = 325 and standard deviation σy = 25√5. Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X −Y > 0). It is a quite surprising fact that the random variable U = X−Y , the diﬀerence between X and Y , is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σU, where σ2 U = σ2 x+σ2 y = 400·5+625·5 = 1025·5 = 5125. It follows that σU = √5125. A reference to the above fact can be found online at http://mathworld.wolfram.com/NormalDiﬀerenceDistribution.html.
Now everything reduces to ﬁnding P(U > 0) P(U > 0) = P(U −50 √5125 > − 50 √5125)≈ P(Z > −0.69843) ≈ 0.757546 .

5 0

3 years ago

A(x + 1) - b(x + 1) - x - 1

Andrei [34K]

Answer:

Step-by-step explanation:

Solution

I'm assuming you want this simplified. If not leave a note.

a(x + 1) - b(x + 1) - x - 1 remove the brackets

ax + a - bx - b - x - 1 gather like terms

ax - bx - x + a - b - 1

x(a - b - 1) + (a - b - 1) Use the distributive property to simplify

Answer

(x + 1)(a - b - 1)

The common factor is (a - b - 1). That can be pulled out on either side of the isolated + sign

8 0

1 year ago