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3 years ago

U and v are position vectors with terminal points at (-1, 5) and (2, 7), respectively. Find the terminal point of -2u + v.

Mathematics

1 answer:

Papessa [141]3 years ago

4 0

Answer:

(4, -3)

Step-by-step explanation:

-2u +v = -2(-1, 5) +(2, 7) = (-2(-1)+2, -2(5)+7)

= (4, -3)

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Which ratio is equivalent to 12 : 32?<br> A. 48/128<br> B. 28/63<br> C. 7/15<br> D. 48/64

Sladkaya [172]

A because 12*4=48 and 32*4=128

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3 years ago

A rectangle has an area of 171 square meters. Its width is ten meters less than the length. Find the measures of the length and

9966 [12]

Step-by-step explanation:

The area of a rectangle is 171 m²

Let l is the length and b is the width of the rectangle

It width is 10 m less than the length. So,

b = l-10 ...(1)

Area of a rectangle is given by :

$A=l\times b\\\\171=l(l-10)\\\\l^2-10l=171\\\\l^2-10l-171=0\\\\l^2-19l+9l-171=0\\\\\text{taking common together}\\\\l(l-19)+9(l-19)=0\\\\(l-9)(l-19)=0$

l = 9 m or l = 19 m

If l = 9 m,

b = 9-10 = -1 m (can't be possible)

If l = 19 m

b = 19-10 = 9 m

So, the length an the breadth of the rectangle is 19 m and 9 m respectively.

8 0

3 years ago

Please help! An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain

Eduardwww [97]

draw a perpendicular line from the directrix passing through the focus, this will be the line of symmetry. The vertex(h, k) will be located on the line half way between the focus and directrix. The distance from the focus to the vertex is called the focal length, call it a. The then equation is (x - h)^2 = 4a(y - k) the equation can be manipulated to y = 1/4a(x - h)^2 + k hope it helps

8 0

3 years ago

Read 2 more answers

The equation y+6=1/3(x-9) is written in point-slope form. What is the equation written in slope-intercept form?

Margaret [11]

y+6=1/3(x-9)

Moved all terms from left to right that doesn't contain y

Y=-6 +1/3x-3

Simplify

Y=1/3x-9

Your answer is c.

3 0

3 years ago

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Find the sum of a finite geometric sequence from n = 1 to n = 7, using the expression −4(6)n − 1.

Verizon [17]

Answer:

Step-by-step explanation:

The formula of a sum of terms of a gometric sequence:

$S_n=a_1\cdot\dfrac{1-r^n}{1-r}$

a₁ - first term

r - common ratio

We have

$a_n=-4(6)^{n-1}$

Calculate a₁. Put n = 1:

$a_1=-4(6)^{1-1}=-4(6)^0=-4(1)=-4$

Calculate the common ratio:

$r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=-4(6)^{n+1-1}=-4(6)^n\\\\r=\dfrac{-4(6)^n}{-4(6)^{n-1}}=6^n:6^{n-1}\\\\\text{use}\ a^n:a^m=a^{n-m}\\\\r=6^{n-(n-1)}=6^{n-n+1}=6^1=6$

$\text{Substitute}\ a_1=-4,\ n=7,\ r=6:\\\\S_7=-4\cdot\dfrac{1-6^7}{1-6}=-4\cdot\dfrac{1-279936}{-5}=-4\cdot\dfrac{-279935}{-5}=(-4)(55987)\\\\S_7=-223948$

7 0

3 years ago