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3 years ago

Nari says, "The sum of 10 and one-third of a number is 25." She uses the bar model to write an equation to represent her

Mathematics

2 answers:

arsen [322]3 years ago

8 0

Answer:

Nari says, “The sum of 10 and one-third of a number is 25.” She uses the bar model to write an equation to represent her statement.

A bar diagram. The top box contains 25. The bottom boxes contain 10 and one-third n.

Which equation can Nari write using the bar model?

25 = 10 + one-third n

10 = one-third n + 25

25 = 10 minus one-third

10 = one-third n minus 25

Step-by-step explanation:

Mariana [72]3 years ago

4 0

Answer:

$25=10+\frac{1}{3}n$ .

Step-by-step explanation:

It is given that the sum of 10 and one-third of a number is 25.

Let as consider n be the unknown number.

One-third of a number $=\frac{1}{3}n$

Sum of 10 and one-third of a number $=10+\frac{1}{3}n$

The sum of 10 and one-third of a number is 25. It can be written as

$25=10+\frac{1}{3}n$

Therefore, the required equation is $25=10+\frac{1}{3}n$ .

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Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added toge

WARRIOR [948]

You can use the fact that when coefficient of x variable are of equal magnitude but opposite sign, then adding them will make the coefficient 0, thus, making the x variable eliminated.

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

<h3>How does elimination works?</h3>

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

$a_1x + b_1y = c_1\\a_2x + b_2y = c_2$

then, if we want to eliminate variable x, then we have to multiply equation 1 with

$- \dfrac{a_2}{a_1}$

which will make coefficient of x in first equation as

$a_1 \times - \dfrac{a_2}{a_1} = -a_1$

Then adding both equation will eliminate the variable x.

We could've skipped that -ve sign and at then end, instead of adding, we could've subtracted the equations.

<h3>What is magnitude and sign?</h3>

5 has 5 as magnitude, and sign isn't present which means its of positive (+) sign.

-5 has 5 as magnitude and sign is negative(-).

For this case, we're multiplying both the equations but the core concept or aim is same, ie, making the coefficients of equal magnitude but with opposite sign.

<h3>Using the above facts to get the numbers to multiply the equations of the given system</h3>

The given system of equations is

$\dfrac{1}{5}x + \dfrac{3}{4}y = 9\\\\\dfrac{2}{3}x - \dfrac{5}{6}y = 8$

Let two numbers be p,and q who multiply equation first and second respectively to make coefficient of x of equal magnitude but opposite sign.

We have

$\text{Coefficient of x in first equation}= a_1 = \dfrac{1}{5}\\\\\text{Coefficient of x in second equation} = a_2 = \dfrac{2}{3}$

Multiplying with p and q will give us

$p\times a_1 = \dfrac{p}{5}\\\\q \times a_2 = \dfrac{2q}{3}$

We need both resultant coefficient to add up to 0, or

$p/5 + 2q/3 = 0\\p = -10q/3\\q = -3p/10$

Now in options, we see first equation is either getting multiplied with -10, 10, or -3,3

If we put q = 3, we get p = -10q/3= -10

If we put q = -3, we get p = 10

If we put q = 5, we get p = -50/3

Thus only first choice is matching the correct pairs.

Thus,

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

Learn more about method of elimination here:

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7 0

2 years ago

Read 2 more answers

How many times does 13 go into 80

Tcecarenko [31]

13 x 6 = 78 you cant multiply anymore so that's how many times it can go in 80.

6 0

3 years ago

The sum of two consecutive integers is greater than 50. Could 25 be one of the numbers?

AlekseyPX

Answer:

Yes. 25 and 26 equal 51, so one of the consecutive numbers could be 25.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Which ordered pairs are solutions to the inequality 3x-4y>5

Sloan [31]

Note: you did not provide the answer options, so I am, in general, solving this query to solve your concept, which anyways would clear your concept.

Answer:

Please check the explanation.

Step-by-step explanation:

Given the inequality

$3x-4y>5$

All we need is to find any random value of 'x' and then solve the inequality.

For example, putting x=3

$3\left(3\right)-4y>5$

$9-4y>5$

$-4y>-4$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$

$\left(-4y\right)\left(-1\right)$

$4y$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4y}{4}$

$y$

So, at x = 3, the calculation shows that the value of y must be less

than 1 i.e. y<1 in order to be the solution.

Let us take the random y value that is less than 1.

As y=0.9 < 1

so putting y=0.9 in the inequality

$3\left(3\right)-4\left(0.9\right)$

$=9-3.6$

$=5.4$

As 5.4 > 5

Means at x=3, and y=0.9, the inequality is satisfied.

Thus, (3, 0.9) is one of the many ordered pairs solutions to the inequality 3x-4y>5.

6 0

3 years ago

A rancher wishes to build a fence to enclose a rectangular pen having area 24 square yards. Along one side the fence is to be ma

Gnoma [55]

Answer:

The value is $C \approx \$76$

Step-by-step explanation:

From the question we are told that

The area of the rectangular pen is $A = 24 \ yard^2$

The cost of material used to make one side is $z = \$ 6$

The cost of material used to make the other sides is $r = \$ 3$

Now , the fence to be build around the rectangular pen has four sides, the first opposite sides are equal, let assume each of the to be x yard and the other opposite sides are also equal as well let assume of the to be y yard

So the cost is mathematically represented as

$C = zx + r (x + 2y )$