In triangle XYZ,XY=15,YZ=21, and XZ=27. What is the measure of angle Z to the nearest degree?

Velocity of a Car The velocity of a car (in feet per second) t sec after starting from rest is given by the function f(t) = 11 t

pochemuha

Answer:

Step-by-step explanation:

Velocity is defined as the rate of change in displacement of a body. It is expressed mathematically as v = change in displacement/time

v(t) = ds(t)/dt

ds(t) = v(t)dt

integrating both sides;

s(t) = $\int\limits v(t)dt$

Given the velocity function f(t) = 11t, the car's position (displacement) is expressed as s(t) = $\int\limits 11t\ dt$

s(t) = 11t²/2 + C

at the initial point, s(0) = 0 i.e when t = 0, s(t) = 0. The resulting equation becomes;

0 = 11(0)²/2+ C

0 = 0+C

C = 0

To find the car's position, s(t), we will substitute C = 0 into the equayion above;

s(t) = 11t²/2 + 0

s(t) = 11t²/2

Hence s(t) = 11t²/2 is the required position of the car in terms of t.

6 0

3 years ago

A cat can run 30 miles per hour. At this rate, how many minutes would it take a cat to run 1.5 miles?

vlabodo [156]

Answer:

3 minutes

Step-by-step explanation:

30/60 which is how many minutes are in an hour, gives you .5 miles per minute and .5 x 3 = 1.5miles

6 0

3 years ago

Tell if each equation represents exponential growth, exponential decay or neither.

scoray [572]

Answer:

Exponential growth A, B;

exponential decay C, E;

neither D.

Step-by-step explanation:

The function $y=a\cdot b^x$

represents exponential growth when $b>1;$
represents exponential decay when $0$

A. The equation $f(t)=\dfrac{2}{3}\cdot \left(\dfrac{7}{3}\right)^t$ represents exponential growth, because $\dfrac{7}{3}>1.$

B. The equation $P=22\cdot \left(1.76\right)^x$ represents exponential growth, because $1.76>1.$

C. The equation $V=\dfrac{1}{3}\cdot \left(0.45\right)^x$ represents exponential decay, because $0$

D. The equation $W=3.2\cdot (x)$ represents neither exponential growth nor exponential decay, because this function is linear.

E. The equation $g(x)=4.2\cdot \left(\dfrac{1}{3}\right)^x$ represents exponential decay, because $0$

3 0

3 years ago

Is this triangle a SSS, SAS, ASA, AAS, or HL?

Harman [31]

Answer:

sss

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A rectangle has a length of 20 inches. if its perimeter is 64 inches, what is the area?

zzz [600]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf 240 \: {inches}^{2} }}}}$

Step-by-step explanation:

Given,

Length of a rectangle = 20 inches

Perimeter of a rectangle = 64 inches

Area of a rectangle = ?

Let width of a rectangle be ' w ' .

First, finding the width of a rectangle

$\boxed{ \sf{perimeter = 2(l + w)}}$

plug the values

⇒ $\sf{64 = 2(20 + w)}$

Distribute 2 through the parentheses

⇒ $\sf{64 = 40 + 2w}$

Swap the sides of the equation

⇒ $\sf{40 + 2w = 64}$

Move 2w to right hand side and change it's sign

⇒ $\sf{2w = 64 - 40}$

Subtract 40 from 64

⇒ $\sf{2w = 24}$

Divide both sides of the equation by 2

⇒ $\sf{ \frac{2w}{2} = \frac{24}{2} }$

Calculate

⇒ $\sf{w = 12 \: inches}$

Width of a rectangle ( w ) = 12 inches

Now, finding the area of a rectangle having length of 20 inches and width of 12 inches

$\boxed{ \sf{area \: of \: rectangle = length \: \times \: \: width}}$

plug the values

⇒ $\sf{area \: of \: rectangle =20 \times 12 }$

Multiply the numbers : 20 and 12

⇒ $\sf{area \: of \: rectangle = 240 \: {inches}^{2} }$

Hence, Area of a rectangle = 240 inches²

Hope I helped !

Best regards!

7 0

3 years ago