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1 year ago

6

Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right

angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?

3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units

1 answer:

Agata [3.3K]1 year ago

7 0

Answer:

6 StartRoot 3 EndRoot units

Step-by-step explanation:

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Devon made a box with length x+1, width x+3, and height x-3. What is the volume of Devon's box as a function of x?

erica [24]

Answer:

(a)

$V=x^3+x^2-9x-9$

(b)

$x=10$

(c)

$x=\frac{7}{2}$

Step-by-step explanation:

we are given

length is x+1

$L=x+1$

width is x+3

$W=x+3$

height is x-3

$H=x-3$

(a)

we can use volume formula

$V=L\times W\times H$

now, we can plug it

$V=(x+1)\times (x+3)\times (x-3)$

now, we can simplify it

$V=x^3+x^2-9x-9$

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

$V=x^3+x^2-9x-9=1001$

now, we can factor it

$\left(x-10\right)\left(x^2+11x+101\right)=0$

$x-10=0$

$x=10$

(b)

we are given volume

so, we can set

$V=14\frac{5}{8}=\frac{14\times 8+5}{8}$

$V=\frac{117}{8}$

and then we can solve for x

$V=x^3+x^2-9x-9=\frac{117}{8}$

now, we can factor it

$8x^3+8x^2-72x-189=0$

$\left(2x-7\right)\left(4x^2+18x+27\right)=0$

$2x-7=0$

$x=\frac{7}{2}$

8 0

3 years ago

The midpoint of AB is M(3, -1). If the coordinates of A are (5,1), what are the

Vera_Pavlovna [14]

Given parameters:

Midpoint of AB = M(3, -1)

Coordinates of A = (5,1)

Unknown:

Coordinates of B = ?

Solution:

To find the mid point of any line, we use the expression below;

$x_{m} = \frac{x_{1} + x_{2} }{2}$ and $y_{m} = \frac{y_{1} + y_{2} }{2}$

where $x_{m}$ and $y_{m}$ = coordinates of the mid points = 3 and -1

x₁ = 5 and y₁ = 1

x₂ = ? and y₂ = ?

Now let us input the variables and solve,

3 = $\frac{5 + x_{2} }{2}$ and -1 = $\frac{1 + y_{2} }{2}$

5 + x₂ = 6 -2 = 1 + y₂

x₂ = 1 y₂ = -2 -1 = -3

The coordinates of B = 1, -3

6 0

3 years ago

3 and 1 half to the power of 2 simplify

Elenna [48]

3 and 1 half is also known as 3.5,
3.5 x 3.5 = 12.25
in fractions that is 12 and 1 quarter

8 0

3 years ago

Read 2 more answers

Write the slope intercept form of the equation of the line through the given points. (5,-1) and (-5,2)

Lelu [443]

Answer:

$y=-\frac{3}{10} x+\frac{1}{2}$ or $-\frac{3}{10}$

Step-by-step explanation:

first use the y2-y1/x2-x1 formula then use y=mx+b after

plug in 2 for y2 and -1 for y1

plug in -5 for x2 and 5 for x1

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

2+1=3

-5-5=-10

$-\frac{3}{10}$ is ur slope

_____________________

this is the y=mx+b formula *extra info ig*

i usually use the first point for this but u can use watever point u want

plug in 5 for x

plug in -1 for y

and plug -3/10 for m

-1=-3/10(5)+b

-3/10*5=-3/2

-1=-3/2+b

add -3/2 on both sides

-1+3/2=1/2

1/2=b and b is ur y-intercept

y=-3/10x+1/2

hope this helps

7 0

2 years ago

If f(x) = 3x2 - 2x + 1, then find f(0)

MissTica

f (0) = 3.(0)(0) - 3.(0)

= 0

3 0

2 years ago