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3 years ago

Rectangle EFGH is shown with a line IJ passing vertically through the center of the rectangle.

Mathematics

2 answers:

Dovator [93]3 years ago

6 0

C) shift six units up

castortr0y [4]3 years ago

3 0

Answer: B

Step-by-step explanation:

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For what values of q are the two vectors A = i + j + kq each other and B-iq-23 + 2kg perpendicular to

Sloan [31]

Answer:

The value of q are 0.781,-1.281.

Step-by-step explanation:

Given : Two vectors $A=i+j+kq$ and $B=iq-2j+2kq$ are perpendicular to each other.

To find : The value of q ?

Solution :

When two vectors are perpendicular to each other then their dot product is zero.

i.e. $\vec{A}\cdot \vec{B}=0$

Two vectors $A=i+j+kq$ and $B=iq-2j+2kq$

$(i+j+kq)\cdot (iq-2j+2kq)=0$

$(1)(q)+(1)(-2)+(q)(2q)=0$

$q-2+2q^2=0$

$2q^2+q-2=0$

Using quadratic formula,

$q=\frac{-1\pm\sqrt{1^2-4(2)(-2)}}{2(2)}$

$q=\frac{-1\pm\sqrt{17}}{4}$

$q=\frac{-1+\sqrt{17}}{4},\frac{-1-\sqrt{17}}{4}$

$q=0.781,-1.281$

Therefore, The value of q are 0.781,-1.281.

6 0

3 years ago

The length of a deck is 4 times its width. if the perimeter is 30 feet what is the area

Fantom [35]

I hope this helps you

4 0

3 years ago

Sofian's current age is (2x + 3) times Mastura's age. Given that Mastura's current age is (x + 5) years and 6 years ago, the sum

Sliva [168]

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

★ Sofian's current age is (2x + 3) times Mastura's age.

★ Mastura's current age is (x + 5) years

★ 6 years ago, the sum of their ages is 44 years.

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

★ The value of x.

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

According to the question,

Present age of Mastura = (x + 5) years

Present age of Sofian = (2x + 3) (x + 5) years, i.e :

$\longrightarrow \tt (2x + 3) (x + 5)$

$\longrightarrow \tt 2 {x}^{2} + 10x + 3x + 15$

$\longrightarrow \tt 2 {x}^{2} + 13x + 15 \: years$

Now,

Mastura's age 6 years ago = (x + 5) - 6

=> x + 5 - 6

=> x - 1

Sofian's age 6 years ago = 2x² + 13x + 15 - 6

= 2x² + 13x + 9

Using the condition provided by the question, 

Mastura's age 6 years ago + Sofian's age 6 years ago = 44

$\longrightarrow \tt (x - 1) + (2 {x}^{2} + 13x + 9) = 44$

$\longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44$

$\longrightarrow \tt 2 {x}^{2} + 14x + 8 = 44$

$\longrightarrow \tt 2 {x}^{2} + 14x + 8 - 44 = 0$

$\longrightarrow \tt 2 {x}^{2} + 14x - 36= 0$

• Taking "2" common.

$\longrightarrow \tt 2 ({x}^{2} + 7x - 18) = 0$

$\longrightarrow \tt {x}^{2} + 7x - 18 = \dfrac{0}{2}$

$\longrightarrow \tt {x}^{2} + 7x - 18= 0$

• Using splitting the middle term

$\longrightarrow \tt {x}^{2} + 9x - 2x - 18 = 0$

$\longrightarrow \tt x(x + 9) - 2(x + 9) = 0$

$\longrightarrow \tt (x + 9) (x - 2) = 0$

either $\tt (x + 9) = 0 \: \: or \: \: (x - 2) = 0$

$\longrightarrow \tt x = - 9 \: \: or \: \: x = 2$

[As the age cannot be negative. So x = - 9 is rejected]

$\therefore \tt \: x = \red{ 2}$

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

According to the condition provided by the question, 

• Mastura's age 6 years ago + Sofian's age 6 years ago = 44

$\longrightarrow \tt x - 1 + 2 {x}^{2} + 13x + 9 = 44$

Putting x = 2 we get,

$\longrightarrow \tt 2 - 1 + 2( {2})^{2} + 13(2) + 9 = 44$

$\longrightarrow \tt 1 + 2 \times 4 + 26+ 9 = 44$

$\longrightarrow \tt 1 + 8 + 26+ 9 = 44$

$\longrightarrow \tt 9 + 26+ 9 = 44$

$\longrightarrow \tt 18 + 26 = 44$

$\longrightarrow \tt 44 = 44$

Hence verified.

$\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}$

Hope it helps you! :))

6 0

3 years ago

If the angle is in standard position and P(x, y) is a point on the terminal side of , and r is the distance from the origin to P

Ghella [55]

Answer:

x^2 + y^2 = r^2

Step-by-step explanation:

See image. "An angle in standard position" means the vertex (point part) of the angle is at the origin (0,0). And one side of the angle is glued onto the x-axis. The other side of the angle is free to rotate around the axis. That's the terminal side. Then there's a point P (x,y) on that side. See image. And r is labelled there. This set up makes a right triangle. So I put Pythagorean theorem as the answer here, but honestly if you are learning any right triangle theorems or trigonometry, you could use this set up. The leg that lays along the x-axis is x units long and the other leg is y units long. The hypotenuse is r units long.

8 0

2 years ago

A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker

siniylev [52]

Answer: t<40

8p+<184

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers