All categories

3 years ago

If U is between T and B, find TU. TU = 6x + 16, UB = 2x – 1, TB = 55.

Mathematics

1 answer:

enot [183]3 years ago

3 0

Answer:

TU = 46

Step-by-step explanation:

Here, we are concerned with finding TU

Mathematically;

Since U is between T and B, by convention;

TB = TU + UB

Substituting the values so we can find x;

55 = 6x + 16 + 2x -1

55 = 6x + 2x + 16-1

55 = 8x + 15

8x = 55-15

8x = 40

x = 40/8

x = 5

But TU = 6x + 16; substitute the value of 5 for x

TU = 6(5) + 16

TU = 30 + 16

TU = 46

You might be interested in

Find the inverse of the function. y=x2 + 4x + 4

adoni [48]

Answer: To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i.e. make x as y and y as x)

y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation

y = (x+2)(x+2)

y = (x+2)² ⇒⇒⇒ take the square root to both sides

√y = x+2

x = √y - 2 ⇒⇒⇒ x becomes a function of y

final step:

∴ y = √x - 2 ⇒⇒⇒ the inverse of the given function

So, as a conclusion:

f(x) = y = x² + 4x + 4 ⇒⇒⇒ the given function

f⁻¹(x) = y = √x - 2 ⇒⇒⇒ the inverse of the given function

7 0

3 years ago

A cabinet is the shape of a triangular prism. The triangular base has a base length of 14 inches and a base height of 22 inches.

Gekata [30.6K]

Answer:

gat

Step-by-step explanation:

3 0

2 years ago

Please help with this I’m garbage at math:/

Ronch [10]

Answer:

Thale's theorem stated that if a line parallel to the base of the triangle intersects it, the ratio of sides of the respective sides is equal

In this diagram, since the 2 horizontal lines are parallel

the ratio of the 2 sides on the left and the 2 sides on the right will be equal

Hence,

x/15 = 2/10

x = 30/10

x = 3

8 0

3 years ago

Compare the line passing through the points (−3, −11) and (6, 4) to the line given by the equation y=35x−6.

Aleks04 [339]

Let
A------> (−3, −11)
B------> (6, 4)

step 1
find the slope m point A and point B
m=(y2-y1)/(x2-x1)-----> m=(4+11)/(6+3)----> m=15/9---> 5/3

step 2
with m=5/3 and point B (6, 4) find the equation of a line
y-y1=m*(x-x1)-----> y-4=(5/3)*(x-6)---> y=(5/3)x-6

case a. they have the same slope------> is not correct
because
y=35x−6------> the slope m=35
y=(5/3)x-6---> the slope m =5/3

case b. they have the same x-intercept.----> is not correct
because
the x-intercept is for y=0

y=35x−6-----> 0=35x-6----> 35x=6-----> x=6/35
the x-intercept is the point (6/35,0)

y=(5/3)x-6----> 0=(5/3)x-6----> (5/3)x=6---> x=18/5
the x-intercept is the point (18/5,0)

case c. the two lines are perpendicular. do. they have the same y-intercept-----> is nor correct
because

if two lines are perpendicular
m1*m2=-1-------> this condition is not satisfied

the y intercept is for x=0

y=35x−6-------> y=-6
the y intercept is the point (0,-6)

y=(5/3)x-6-----> y=-6
the y intercept is the point (0,-6)

they have the same y-intercept but the two lines are not perpendicular

see the attached figure

7 0

3 years ago

Find the distance between the pair of coordinates: (-4, -3) and (-8, 7). A 10.77 B 3.74 C 04 D 12.65 Question

kenny6666 [7]

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8 - (-4)]^2 + [7 - (-3)]^2}\implies d=\sqrt{(-8+4)^2 + (7+3)^2} \\\\\\ d=\sqrt{(-4)^2 + 10^2}\implies d=\sqrt{116}\implies d\approx 10.77$

6 0

2 years ago