Use compatible numbers to estimate 5 × 1,021

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes.

mote1985 [20]

Answer:

5 large boxes

3 small boxes

Step-by-step explanation:

Create two equations to represent the problem.

let "a" be the number of small boxes

let "b" be the number of large boxes

20a + 40b = 260 This equation shows the numbers of books

a + b = 8 This equations shows the number of boxes

Solve the system of equations (solve for a and b). We can solve using the substitution method.

Rearrange a + b = 8 to isolate one of the variables.

a = 8 - b New equation that represents "a"

Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.

Substitute "a" for 8 - b

20a + 40b = 260

20(8 - b) + 40b = 260 Distribute 20 over the brackets by multiplying

160 - 20b + 40b = 260 Collect like terms (numbers with same variables)

160 + 20b = 260 Start isolating "b". Subtract 160 from both sides

20b = 260 - 160

20b = 100 Divide both sides by 20

b = 5 Number of large boxes

Substitute "b" for 5 in the simplest equation

a + b = 8

a + 5 = 8 Subtract 5 from both sides to isolate "a"

a = 8 - 5

a = 3 Number of small boxes

Therefore there were 5 large boxes and 3 small boxes sent.

3 0

3 years ago

Which triangles are right triangles? Select all that apply.

Setler79 [48]

Answer:

triangle 1, triangle 3,

Step-by-step explanation:

Triangle 1= $14^{2} + 24^{2} = 772\\196+ 576 = 772$

Triangle 2= is wrong

Triangle 3= $11^{2} + 22^{2} = 605\\121+ 484= 605$

Triangle 4= is wrong.

7 0

2 years ago

Please provide answer and work to show how you got the answer!!

yan [13]

X=8
Here my
Work message me if u have questions

7 0

2 years ago

Read 2 more answers

Are the triangles similar? If so, write a similarity statement for the triangles and explain how you know the triangles are simi

andrew-mc [135]

right-handThe triangles are similar if, the ratios of their sides are equal

$\frac{AE}{AC}=\frac{AW}{AL}$

$\frac{8+8}{6+6}=\frac{8}{6}$

On the left-hand side

$\frac{16}{12}=\frac{4}{3}$

and in the right-hand side, we have

$\frac{8}{6}=\frac{4}{3}$

The left-hand side equals the right-hand side; therefore, the triangles are similar.

4 0

1 year ago

Which statement is true about whether A and B are independent events? A and B are independent events because P(A∣B) = P(A) = 0.1

love history [14]

The events A and B are independent if the probability that event A occurs does not affect the probability that event B occurs.
A and B are independent if the equation P(A∩B) = P(A) P(B) holds true.
P(A∩B) is the probability that both event A and B occur.
Conditional probability is the probability of an event given that some other event first occurs.
P(B|A)=P(A∩B)/P(A)
In the case where events A and B are independent the conditional probability of event B given event A is simply the probability of event B, that is P(B).
Statement 1:A and B are independent events because P(A∣B) = P(A) = 0.12. This is true.
Statement 2:A and B are independent events because P(A∣B) = P(A) = 0.25.
This is true.
Statement 3:A and B are not independent events because P(A∣B) = 0.12 and P(A) = 0.25.
This is true.
Statement 4:A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25
This is true.

5 0

3 years ago

Read 2 more answers