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mafiozo [28]
4 years ago
8

David bought three DVDs in for books for $40 at a yard sale and I bought one DVD and six books for $18 how much did each DVD and

book cost
Mathematics
1 answer:
grandymaker [24]4 years ago
4 0

Answer: One DVD is $12 and one book is $1

Step-by-step explanation:

Let the DVD be d and the book be b.

Case 1:

3d + 4b = $40.......(1)

Case 2:

1d + 6b = $18........... (2)

In this equations above, I intend to eliminate variable d, so I'm going to multiply the coefficient of d in (1) to multiply (2)

3 × (1d + 6b = 18)

3d + 18b = 54........ .(3)

Then, subtract (1) from (3)

3d + 18b = 54

- ( 3d + 4b = 40)

3d - 3d + 18b - 4b = 54 - 40

0 + 14b = 14

b = 14/14

b = 1.

Then substitute 1 for b in (2)

1d + 6(1) = 18

d + 6 = 18

d = 18 - 6

d = 12.

(d,b) = (12,1)

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Y+5=2(x+1)<br><br><br> what is the slope for this Math
Stells [14]

Answer:

2

Step-by-step explanation:

The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept.y=mx+bRewrite in slope-intercept form.Simplify 2(x+1).Apply the distributive property.

y+5=2x+2⋅1

multiply 2 by 1.

y+5=2x+2

y+5=2x+2

Move all terms not containing y to the right side of the equation.Subtract 5 from both sides of the equation.

y=2x+2−5

y=2x−3

the slope is the "m" so the slope is 2

7 0
3 years ago
Solve this equation algebraically!!
NeTakaya

Answer:

See Explanation

Step-by-step explanation:

1 -  \sqrt{x}  \neq \: 0 \\  \\  \therefore \: 1 \neq \sqrt{x}  \\  \\  {1}^{2}  \neq ({ \sqrt{x}) }^{2}  \\  \\ 1 \neq \: x \\

Hence, x will take values other than 1.

5 0
3 years ago
Mary pays income tax according to the graduated schedule shown below. A 3-column table with 6 rows. Column 1 is labeled If taxab
Katarina [22]

Answer:

$13564

Step-by-step explanation:

\left|\begin{array}{c|c|c}$If taxable&& \\$income&&\\$ is over&$but not over&$the tax is\\---&---&---\\$0 &7,825 &$10\%  of the amount over 0\\7,825 &31,850 &$782.50 plus $15\% $ of the amount over 7,825$ \end{array}\right|\left|\begin{array}{c|c|c}31,850 &77,100 &$4,386.25 plus 25\%  of the amount over 31,850 \\77,100 &160,850 &$15,698.75 plus 28\%  of the amount over 77,100\end{array}\right|

\left|\begin{array}{c|c|c}160,850 &349,700 &$39,148.75 plus 33\%  of the amount over 160,850 \\349,700 &$no limit&$101,469.25 plus 35\%  of the amount over 349,700\end{array}\right|

Mary’s taxable income= $68,562

From the table, If taxable income is over $31,850 but not over $77,100

The tax = $4386.25 + 25% of the amount over 31,850

Amount over $31,850=$68,562-$31,850

=$36,712

Therefore:

Mary's tax = $4386.25 + (25% of $36,712)

=$4386.25 +9,178

=$13564.25

=$13564 (to the nearest dollar)

5 0
3 years ago
Read 2 more answers
Solve the following inequality.<br> -4(1 - 5a) &gt; -124
NemiM [27]

Answer:

a>−6

Step-by-step explanation:

−4(1−5a)>−124

Step 1: Simplify both sides of the inequality.

20a−4>−124

Step 2: Add 4 to both sides.

20a−4+4>−124+4

20a>−120

Step 3: Divide both sides by 20.

20a/20> −120/20

a>−6

8 0
2 years ago
For the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled b
dmitriy555 [2]

Answer:

2019.

Step-by-step explanation:

We have been given that for the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled by H = 1,500e^{0.053t} where t is the number of years past 2000.

To find the year in which national health care expenditures expected to reach $4.0 trillion (that is, $4,000 billion), we will substitute H=4,000 in our given formula and solve for t as:

4,000= 1,500e^{0.053t}

\frac{4,000}{1,500}=\frac{ 1,500e^{0.053t}}{1,500}

\frac{8}{3}=e^{0.053t}

e^{0.053t}=\frac{8}{3}

Take natural log of both sides:

\text{ln}(e^{0.053t})=\text{ln}(\frac{8}{3})

0.053t\cdot \text{ln}(e)=\text{ln}(\frac{8}{3})

0.053t\cdot (1)=0.9808292530117262

\frac{0.053t}{0.053}=\frac{0.9808292530117262}{0.053}

t=18.506212320

So in the 18.5 years after 2000 the expenditure will reach 4 trillion.

2000+18.5=2018.5

Therefore, in year 2019 national health care expenditures are expected to reach $4.0 trillion.

7 0
3 years ago
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