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2 years ago

Ben is reading a book. Rounded to the nearest ten, he reads 150 pages. What is the least number of pages he could read?

Mathematics

1 answer:

Semenov [28]2 years ago

7 0

145 pages because 145 would round up to 150 but anything below 145 would round to 140

You might be interested in

What value of b will cause the system to have an infinite number of solutions?

irga5000 [103]

b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

$\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}$

Let us bring the equations in same form for sake of simplicity in comparison

$\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}$

Now we have two equations

$\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}$

Let us first see what is requirement for system of equations have an infinite number of solutions

If $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are two equation

$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the given system of equation has no infinitely many solutions.

In our case,

$\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}$

As for infinitely many solutions $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}$

Hence b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

8 0

2 years ago

Simplify the expression and identify which property is used in each step.

777dan777 [17]

Answer:

1.2

Step-by-step explanation:

(0.85 + 0.50 + 0.15) - 0.30 Given

Simplify by adding in the parentheses first

(0.85 + 0.50 + 0.15) - 0.30

(1.35 + 0.15) - 0.30

(1.5) - 0.30

Subtraction Property

1.5 - 0.30

1.2

7 0

2 years ago

I need to show work and Idk how for 2 or 3. The -5,-2 and 8,3 is the answers just need work shown thanks

prisoha [69]

#2
2x - 4y = -2
2x + 3y = -16
------------------subtract
-7y = 14
y = 14/-7
y = -2

2x - 4y = -2
2x - 4(-2) = -2
2x + 8 = -2
2x = -2 -8
2x = -10
x = -10/2
x = -5
answer x = -2 and y = -5

check:

2(-5)- 4(-2) = -2
-10 +8 = -2
-2 = -2.....true

2x + 3y = -16
2(-5)+3(-2) = -16
-10 + (-6) = -16
-16 = -16...true

3 0

2 years ago

The distance from the school to the library is 12 miles. The distance from the school to the park is 75% of this distance.

strojnjashka [21]

75% of 12 can be represented with the equation 75/100=x/12

Then to solve
75(12)= 100x
900 = 100x
9=x

So the distance from the school to the park is 9 miles.

8 0

3 years ago

Read 2 more answers

Plz help me thanks very nuch whoever helped me

photoshop1234 [79]

Answer:

(1) 56 miles/hour

Step-by-step explanation:

We need to find the average rate of change from t = 2 to t = 9.

At t = 2 hours, d = 106 miles.

At t = 9 hours, d = 498 miles.

The average rate of change in function f(x) from x = a to x = b is

[f(b) - f(a)]/(b - a)

average rate of change from t = 2 to t = 9 =

(498 - 106)/(9 - 2) = 392/7 = 56

Answer: (1) 56 miles/hour

7 0

2 years ago