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2 years ago

Manuel thinks the tens digit goes up by 1 in these numbers. Do you agree? Explain. 460,470,480, 490,500,510

Mathematics

1 answer:

laila [671]2 years ago

7 0

Answer:

Manuel is correct, since adding 10 is the same as the tens digit going up by 1.

Step-by-step explanation:

It is important to know the concepts of units, tenths and cents.

For example

1 = 1 unit

10 = 1*10 + 0 = The tens digit is one the unit digit is 0

21 = 2*10 + 1 = The tens digit is two and the unit digit is 1.

120 = 1*100 + 2*10 + 0 = The cents digit is 1, the tens digit is two and the unit digit is 0.

Adding 1 is the same as the unit digit going up by 1.

Adding 10 is the same as the tens digit going up by 1.

Adding 100 is the same as the cents digit going up by 1.

In this problem, we have that:

460,470,480, 490,500,510

Each number is 10 added to the previous, that is, the tens digit going up by 1.

Manuel thinks the tens digit goes up by 1 in these numbers. Do you agree?

Manuel is correct, since adding 10 is the same as the tens digit going up by 1.

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Diane owes $11901.00 to the bank after completing her college degree. With the funds from her new job she is paying back $153.00

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2 years ago

Read 2 more answers

PLEASE GIVE AN EXPLANATION!! In your grade of 380 students, 70% play a musical instrument. 60% of the boys play a musical instru

Liula [17]

Answer:

270 girls

Step-by-step explanation:

Total number of students = 380

Play musical instrument = 70%

Boys who play musical instrument = 60%

Number of girls who play musical instrument = 200

How many girls are in the class?

Number of play musical instrument = 70% of 380

(0.7 * 380) = 266

Since number of girls who play musical instrument = 200

Then number of boys who play = (266 - 200) = 66

Hence, 66 boys is equivalent 60% of the boy's population

Let population of boys = b

0.6b = 66

b = 110

Number of girls in class :

Number of boys + number of girls

110 + number of girls = 380

Number of girls = 380 - 110

Number of girls = 270

6 0

2 years ago

Anna and Hannah have \$80$80dollar sign, 80 each. Their friend offered to invest their money, promising to return a sum rrr time

sergey [27]

9514 1404 393

Answer:

2r(20r +60) = 80r^2

Step-by-step explanation:

Anna's first investment:

Anna's first return:

20r

Anna's second investment:

20r +60

Anna's second return:

r(20r +60)

Hannah's first investment:

Hannah's first return, and her second investment:

80r

Hannah's second return:

80r^2

Twice Anna's return was equal to Hannah's return:

2r(20r +60) = 80r^2

7 0

2 years ago

Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters t

SashulF [63]

Answer:

Cliff is 45 m tall.

Step-by-step explanation:

Given:

Height of Sarah = 1.8 m

Angle of elevation = 60°

Angle of elevation 50 m back = 30°

As shown in the figure we have two right angled triangles SPQ and SPR.

Let the height of the cliff be $h$ meters and $h= h_1+h_s$ .

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ. In ΔSPR.

⇒ $tan(60) = \frac{h_1}{x}$ ...equation (i) ⇒ $tan (30)=\frac{h_1}{x+50}$ ...equation (ii)

Dividing equation (i) and (ii)

⇒ $\frac{tan(60)}{tan(30)} = \frac{h_1}{x} \times \frac{x+50}{h_1}$

⇒ $3 = \frac{x+50}{x}$

⇒ $3x=x+50$

⇒ $3x-x=50$

⇒ $2x=50$

⇒ $x=\frac{50}{2}$

⇒ $x=25$ meters

To find $h_1$ plugging $x=25$ in equation (i)

⇒ $h_1=x\times tan(60)$

⇒ $h_1=25\times 1.73$

⇒ $h_1=43.25$ meters

The height of the cliff from ground :

⇒ $h= h_1+h_s$

⇒ $h= 43.25+1.8$

⇒ $h=45.05$ meters

The cliff is 45 m tall to the nearest meter.

8 0

2 years ago

The first three terms of an arithmetic series are 6p+2, 4p²-10 and 4p+3 respectively. Find the possible values of p. Calculate t

Doss [256]

Answer:

First Case:

$\displaystyle p=\frac{5}{2}\text{ and } d=-2$

Second Case:

$\displaystyle p=-\frac{5}{4}\text{ and } d=\frac{7}{4}$

Step-by-step explanation:

We know that the first three terms of an arithmetic series are:

$6p+2, 4p^2-10, \text{ and } 4p+3$

Since this is an arithmetic sequence, each subsequent term is d more than the previous term, where d is our common difference.

Therefore, we can write the second term as;

$4p^2-10=(6p+2)+d$

And, likewise, for the third term:

$4p+3=(6p+2)+2d$

Let's solve for d for each of the equations.

Subtracting in the first equation yields:

$d=4p^2-6p-12$

And for the second equation:

$2d=-2p+1$

To avoid fractions, let's multiply the first equation by 2. Hence:

$2d=8p^2-12p-24$

Therefore:

$8p^2-12p-24=-2p+1$

Simplifying yields:

$8p^2-10p-25=0$

Solve for p. We can factor:

$8p^2+10p-20p-25=0$

Factor:

$2p(4p+5)-5(4p+5)=0$

Grouping:

$(2p-5)(4p+5)=0$

Zero Product Property:

$\displaystyle p_1=\frac{5}{2} \text{ or } p_2=-\frac{5}{4}$

Then, we can use the second equation to solve for d. So:

$2d_1=-2p_1+1$

Substituting:

$\begin{aligned} 2d_1&=-2(\frac{5}{2})+1 \\ 2d_1&=-5+1 \\ 2d_1&=-4 \\ d_1&=-2\end{aligned}$

So, for the first case, p is 5/2 and d is -2.

Likewise, for the second case:

$\begin{aligned} 2d_2&=-2(-\frac{5}{4})+1 \\ 2d_2&=\frac{5}{2}+1 \\ 2d_2&=\frac{7}{2} \\ d_2&=\frac{7}{4}\end{aligned}$

So, for the second case, p is -5/4, and d is 7/4.

By using the values, we can determine our series.

For Case 1, we will have:

17, 15, 13.

For Case 2, we will have:

-11/2, -15/4, -2.

8 0

1 year ago