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3 years ago

7

Sam began with $45 in his bank account. He then saved $15 a week until he had $210 in his account. How many weeks did Sam save $

15?

2 answers:

Natalka [10]3 years ago

8 0

Answer: Sam had to save $15 for 11 weeks

Step-by-step explanation:

$45+$15w=$210

Subtract $45 on both sides:

$45-$45+$15w=$210-$45

$15w=$165

Divide 15 on both sides:

15/15w=165/15

w=11

AlladinOne [14]3 years ago

4 0

Answer:

11 weeks

Step-by-step explanation:

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The Johnson twins were born five years after their older sister. This year, the product of the three siblings' ages is exactly

Mamont248 [21]

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1 2 3 4 5

13 | 1 5 -3 -3003 (Row 1)

______|______<u> _13__234___3003</u> (Row 2)

| 1 18 231 0 (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

8 0

3 years ago

If you dont know what 3x4= its 12

Marysya12 [62]

Answer:

thanks im not smart

Step-by-step explanation:

sn i knew that...

6 0

3 years ago

Read 2 more answers

I only need 12 and 17, first good response i will give brainliest please i’m desperate

Mumz [18]

Answer:

$\textsf{12.} \quad y = 6x - 5$

$\textsf{17.} \quad y=-\dfrac{1}{4}x-2$

Step-by-step explanation:

<h3><u>Question 12</u></h3>

Find the slope of the line by substituting two points from the given table into the slope formula.

<u>Define the points</u>:

Let (x₁, y₁) = (2, 7)
Let (x₂, y₂) = (3, 13)

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6$

Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:

$\implies y-y_1=m(x-x_1)$

$\implies y-7=6(x-2)$

$\implies y-7=6x-12$

$\implies y=6x-5$

<h3><u>Question 17</u></h3>

Given:

f(4) = 3
f(0) = -2

Therefore, two points on the line are:

(4, -3)
(0, -2)

The y-intercept is the y-value when x = 0.

Therefore, the y-intercept of the line is -2.

$\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}$

Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for <em>m</em> to find the slope:

$\implies y=mx+b$

$\implies -3=m(4)-2$

$\implies -1=4m$

$\implies m=-\dfrac{1}{4}$

Therefore, the equation of the line is:

$y=-\dfrac{1}{4}x-2$

7 0

1 year ago

Find the range of the function for given domain <br> f(x)=2x-7; (-2,-1,0,1,2)

Gelneren [198K]

Answer:

{-11, -9, -7, -5, -3}

Step-by-step explanation:

Put each domain value into the function to find the corresponding range value. The range is the list of all of those values.

__

range = f(domain)

= 2{-2, -1, 0, 1, 2} -7 = {-4, -2, 0, 2, 4} -7

= {-11, -9, -7, -5, -3} . . . . . the range for the given domain

_____

If you have a lot of function values to find, a spreadsheet or calculator can be helpful.

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3 years ago

What is the japanese poetry of a pattern of 5 7-5 syllables?

xenn [34]

Haiku is the name of the Japanese poem

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3 years ago