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2 years ago

rectangle abcd is similar to rectangle pqrs. given ab=14 cm, BC=8cm and pq=21cm, calculate the length of QR

Mathematics

1 answer:

weqwewe [10]2 years ago

6 0

QR =12 because you set up a proportion 21/14=x/8 then cross multiply and get 14x=168 then you divide and get 12

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Congratulations! You just won the lottery and plan to buy a bunch of cars and motorcycles for all your friends. You purchase 50

Sedaia [141]

Step 1

Let n represent car and m represent motorcycles.

n + m = 50 ...................1

car has four wheels and motorcycle has two wheels

4n + 2m = 164 .............................. 2

Step 2

Solve equation 1 and 2 simultaneously.

from (1), make n subject of relation and substitute in equation 2.

n = 50 - m

Step 3

Substitute n in equation 2

4(50 - m) + 2m = 164

200 - 4m + 2m = 164

collect like terms

200 - 164 = 4m - 2m

36 = 2m

m = 36/2

m = 18

next find n

n = 50 - m

n = 50 - 18

n = 32

There are 32 cars and 18 motorcycles.

8 0

3 months ago

F(x) = x + 4 and g(x) = 2x + 3, evaluate each expression.

Rom4ik [11]

Answer:

$15.~f(g(2))=\Large\boxed{11}\\$

$16.~g(f(2.5))=\Large\boxed{16}$

$17.~g(f(-5))=\Large\boxed{1}$

$18.~f(g(-5))=\Large\boxed{-3}$

Step-by-step explanation:

<h3>Given information</h3>

$f(x)=x+4$

$g(x)=2x+3$

<h3>Question 15. f(g(2))</h3>

<u>Substitute values into the first function</u>

$g(2)=2(2)+3$

$g(2)=4+3$

$g(2)=7$

<u>Substitute the values of the first function into the second</u>

$f(g(2))=f(7)$

$f(7)=(7)+4$

$f(7)=\Large\boxed{11}$

<h3>Question 16. g(f(2.5))</h3>

<u>Substitute values into the first function</u>

$f(2.5)=(2.5)+4$

$f(2.5)=6.5$

<u />

<u>Substitute the values of the first function into the second</u>

$g(f(2.5))=g(6.5)$

$g(6.5)=2(6.5)+3$

$g(6.5)=13+3$

$g(6.5)=\Large\boxed{16}$

<h3>Question 17. g(f(-5))</h3>

<u>Substitute values into the first function</u>

$f(-5)=(-5)+4$

$f(-5)=-1$

<u>Substitute the values of the first function into the second</u>

$g(f(-5))=g(-1)$

$g(-1)=2(-1)+3$

$g(-1)=-2+3$

$g(-1)=\Large\boxed{1}$

<h3>Question 18. f(g(-5))</h3>

<u>Substitute values into the first function</u>

$g(-5)=2(-5)+3$

$g(-5)=-10+3$

$g(-5)=-7$

<u>Substitute the values of the first function into the second</u>

$f(g(-5))=f(-7)$

$f(-7)=(-7)+4$

$f(-7)=\Large\boxed{-3}$

Hope this helps!! :)

Please let me know if you have any questions

7 0

1 year ago

PLZ HELP, DUE TONIGHT!! Find the values of a and b such that f(x) is continuous at x=1

Sedaia [141]

Answer:

a = 2, b = -4

Step-by-step explanation:

<u>To make the given piecewise function continuous we need:</u>

ax² - b = 6 and 5ax + b = 6 at x = 1

<u>It gives us the system:</u>

a(1²) - b = 6 ⇒ a - b = 6
5a(1) + b = 6 ⇒ 5a + b = 6

a - b + 5a + b = 6 + 6
6a = 12
a = 2

2 - b = 6
b = -4

6 0

2 years ago

In 2000, the population of a state was approximately 659 thousand. If the population decreased by 0.8% between 200 and 2009, fin

Aleks04 [339]

Answer:

613297

Step-by-step explanation:

The equation for exponential decay is y=A(1-r)^t

A=654,000

r (rate)=0.008 (0.8% as a decimal)

t=8 (2009-2000=8)

y=659,000(1-0.008)^8

y=613297.4028

Since you can't have part of a person, round: y=613297

3 0

2 years ago

Select all irrational numbers. 1/8 1/2 1/4 1/10 1/16

NNADVOKAT [17]

There are no irrational numbers because all these fractions come to a stop

6 0

3 years ago

Read 2 more answers