A woman has a total of $8,000 to invest. She invests part of the money in an account that pays 11 % per year
and the rest in an account that pays 12% per year. If the interest earned in the first year is $920, how much did
she invest in each account?

⇒Logically we know that to find the  [tex]3^{rd}[/tex] term we use [tex]T_{3} =a+2d[/tex]

⇒From

[tex]T_{3} =a+(3-1)d\\T_{3}=a+2d[/tex]

⇒And the [tex]4^{th}[/tex] is equal [tex]T_{4} =a+3d[/tex] from the same method I used above from the general equation of finding the [tex]n^{th}[/tex] term.

⇒It is said the sum of [tex]T_{3}[/tex] and [tex]T_{4}[/tex] is -2  meaning

[tex]T_{3} +T_{4} =(a+2d)+(a+3d)\\-2=a+2d+a+3d\\-2=a+a+2d+3d\\-2=2a+5d[/tex]

⇒It is also said that [tex]T_{2}[/tex] is 2 and we know at this point that

[tex]T_{2} =a+d\\2=a+d[/tex]

⇒Then we can use the simultaneous equations technique to find the value of d.

I will use the substitution method by deriving the third equation from the second equation 2=a+d

a=2-d  is the [tex]3^{rd}[/tex] equation that I will substitute in the  equation

In the place of a it means I will plug in  2-d in the place of a.

[tex]-2=2a+5d\\-2=2(2-d)+5d\\-2=2(2)+2(-d)+5d\\-2=4-2d+5d\\-2-4=3d\\\\3d=-6\\\\[/tex]

[tex]\frac{3d}{3} =\frac{-6}{3} \\d=-2[/tex]

NOTE if you were also asked to find the value of a you can use the equations above to find the value of a which is the first term. the difference represented by letter d is -2.

GOODLUCK!!

The linear equation that best models the situation is: y = 15x + 125.

To write a linear equation, you need to determine the value of the unit rate or slope (m), and the value of the y-intercept or starting value (b). The linear equation in slope-intercept form that models the relationship between two variables x and y is expressed as, y = mx + b.

From the information given, we have:

Let y represent total cost

let x represents number of months.

To write the linear equation that models this situation, substitute m = 15 and b = 125 into y = mx + b:

y = 15x + 125.

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Answer:

2.7 feet

Step-by-step explanation:

S = a²

S = 7.29

a = sqrt(7.29) = 2.7

Answer:

2.7

Step-by-step explanation:

Area is [tex]side^{2}[/tex]

a= [tex]s^{2}[/tex]

[tex]\sqrt{7.29}[/tex] = 2.7

2.7 x 2.7 = 7.29

Answer:

  D.  f(x - k) = f(x) + k​

Step-by-step explanation:

You want to know the effect on f(x) = -x +8 when x is replaced by x±k.

A function is evaluated by replacing the independent variable in its definition by the function argument.

  f(x) = -x +8

  f(x +k) = -(x +k) +8 = (-x +8) -k = f(x) -k

When the sign of k changes, we have ...

  f(x -k) = f(x) +k

The correct statement for the function is: f(x -k) = f(x) +k​. And option(D) is write answer.

How to perform function evaluation?

In mathematics, function expression is mainly consist of dependent variable and the independent variable. And the function is evaluated by replacing the independent variable in its definition by the function argument.

According to the question, the given function expression is: f(x) = -x +8

Now, to know the effect on f(x) = -x +8 when x is replaced by x ± k. This transformation is known as scaling translation.

Therefore, the function expression can be written as:

f(x) = -x +8

⇒ f(x +k) = -(x +k) +8 = (-x +8) -k = f(x) -k

When the sign of k changes, we get:  f(x -k) = f(x) +k

Hence, the correct statement for the function is: f(x -k) = f(x) +k

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The expression 5xy - x²t + 2xy + 3x²t has a value of 7xy + 2x²t

From the question, the expression is given as

5xy - x squared t + 2xy + 3x squared t

Rewrite the above expression properly

This is represented as

5xy - x²t + 2xy + 3x²t

Next, we collect the like terms in the above expression

So, we have the following equation

5xy - x²t + 2xy + 3x²t = 5xy + 2xy - x²t  + 3x²t

Evaluate the like terms in the above expression

So, we have the following equation

5xy - x²t + 2xy + 3x²t = 7xy + 2x²t

The equation cannot be further simplified

Hence, the value of 5xy - x²t + 2xy + 3x²t is 7xy + 2x²t

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The point slope equation of the line that passes through the points (-9,6) and (-7,-8) is  7x + y = -57 .

The point slope equation of the line passing through the points (x₁,y₁) having slope as m is given by the formula .

y-y₁ = m(x-x₁)

In the question ,

it is given that

the required line passes through the points (-9,6) and (-7,-8) ,

So , the slope(m) is = (-8-6)/(-7 -(-9))

= -14/(-7+9)

= -14/2

= -7

the equation of the line passing through (-7,-8) and slope as 7 in the point slope form is

(y -(-8)) = -7(x -(-7))

y + 8 = -7x -49

7x + y = -8-49

7x + y = -57

Therefore , The point slope equation of the line that passes through the points (-9,6) and (-7,-8) is 7x + y = -57  .

The given question is incomplete , the complete question is

Write the point slope equation of the line that passes through the points (-9,6) and (-7,-8) .

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By solving a linear equation we will see that the value of x is x = $4.00

We know that a store owner mixes 2 Ib of candy that costs x dollars per pound with 3 Ib of candy that costs $1.50 per pound. She sells the mix for $2.50

The total amount of the mix is:

2lb + 3lb = 5lb, now, the total cost at the beginning must be the same as the final cost, so we can write the equation:

2*x + 3*$1.50 = 5*$2.50

Now we can solve this linear equation for x:

2*x = 5*$2.50 - 3*$1.50 = $8.00

x = $8.00/2 = $4.00

The cost of the candy is 4 dollars.

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Answer:

W

Step-by-step explanation:

9 + 7 = 16 and P is the 16th letter of the English Alphabet

4 + 1 = 5 and E is the 5th letter of the English Alphabet

15 + 8 = 23 and W is the 20th letter of the English Alphabet

The correct answer is The complete price (minus returns) is due within 30 days, or a 2 percent discount for payments made within 10 days.

2. Net Sales are Going Up.

Explanation:

1. The breakdown of a company's sales discounts with terms 2/10, n/30 is as follows:

The % discount is represented by 2,

You must pay the business within 10 days to be eligible for the discount.

If you were unable to pay the corporation within the first 10 days, you would have had n/30 days to do so. You are not eligible for the discount if you pay during this time frame after the first 10 days.

Consequently, the parameters of the sales discount mentioned above are a 2 percent discount for payment within 10 days, or the full amount (less returns) due within 30 days.

2. As goods are returned and risk must be managed, sales returns and sales allowances have the impact of lowering the net sales total. Therefore, if they decrease, net sales increase.

A decrease in the credit card company's discount also causes a rise in sales because it increases the amount made per sale or transaction and decreases the amount the company must provide in discounts.

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The value of q in the given equation is 0.

This is a problem from an algebraic equation, we can solve this problem by following a few steps.

The given equation is,

8(q-2) = 44+5(2q-12)

Let's simplify the equation.

8(q-2) = 44+5(2q-12)

Or, 8q- 16= 44+ 10q- 60

Now, we have to organize the equation.

8q- 10q= 44- 60+ 16

Or, -2q = 0

Or, q = 0/2        ( dividing both side by 2 )

Or, q = 0

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The complete question is:

Find the value in the given equation,

8(q-2) = 44+5(2q-12)

Answer:

B

Step-by-step explanation:

x(2y - 3) ← multiply each term in the parenthesis by x

= 2xy - 3x

Answer:

The answer is 476, so the third option is correct.

Step-by-step explanation:

Step 1: Recall the Order Of Operations

The order of operations tells us in which order we have to solve expressions, if there are different operations.

The order is (from first solved to lastly solved) Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

Step 2: Calculate the expression

As we can see, there are parentheses present, so we will solve the expression in them first:

[tex](6+4)\\=(10)[/tex]

The expression becomes:

[tex]10\cdot 49 -7\cdot 2[/tex]

Multiplication should occur first before the subtraction, so let's multiply the numbers:

[tex]10\cdot49-7\cdot2\\\\\text{Multiply the first expression:}\\=490-7\cdot 2\\\\\text{Multiply the second expression:}\\=490-14[/tex]

Now, you can subtract the numbers:

[tex]490-14\\=476[/tex]

The probability that a sample of 10 items will contain at most 1 defective item is 0.7361

Consider X to denote the number of defective items which follows binomial distribution with sample size, n equals to 10.

The probability p of an item produced by a certain machine will be defective is 0.1.

Therefore, the probability q of an item produced by a certain machine will not be defective is:

(1−0.1)

=0.9

The probability of at most one defective item can be calculated as follows:

[tex]P(X\leq 1)=P(X=0)+P(X=1)\\[/tex]

[tex]=^{10} C_{0} p^{0} (1-p)^{10} +^{10} C_{1} p^{1}(1-p)^{9}[/tex]

[tex]=(0.9)^{10} +10(0.1)(0.9)^{9}[/tex]

[tex]=0.7361[/tex]

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The solved matrix system is (x y z) =(4,-1, 3)

The problem we are dealing with is related to gauss -Jordan elimination is a calculation that can be utilized to illuminate systems of linear conditions and to discover the inverse of any invertible matrix. It depends upon three elementary row operations one can utilize on a matrix: Swap the positions of two of the rows and Multiply one of the rows by a nonzero scalar. Add or subtract the scalar numerous of one row to another row.

For the given equations

x+2y+z=5

2x-y+2z=15

3x+y-z=8

In the matrix form

1   2    1       | 5

2   -1    2      | 15

3     1   -1      | 8

R2 -> R2-2R1

1     2      1       | 5

0   -5     0       | 5

3     1     -1       | 8

R3->R3-3R1

1      2       1         | 5

0   -5      0          | 5

0    -5   -4          | -7

R2->R2/(-5)

1      2       1         | 5

0     1       0         | -1

0    -5    -4          | -7

R3->R3-(-5).R2

1      2       1         | 5

0     1       0         | -1

0    0     -4          | -12

R3= R3/(-4)

1      2       1     | 5

0     1     0       | -1

0    0      1        | 3

R1= R1-1R3

1      2       0        | 2

0     1     0           | -1

0    0      1            | 3

R1= R1-2R2

1      0      0         | 4

0     1       0         | -1

0    0       1          | 3

x    | 4

y    | -1

z    | 3

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Answer: y=-1/8x

Step-by-step explanation:

Choose a point that the perpendicular line will pass through.

(0,0)

Use the slope-intercept form to find the slope.

m=8

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

perpendicular

m= −1/8

Find the equation of the perpendicular line using the point-slope formula.

y+0=−1/8⋅(x+0)

Write in

y=mx+b

form.

y=−1/8x

Hope this helps

The largest possible number of red socks in the drawer that is consistent with this data is 990.

To solve the given question, we will form equations according to the given data including a known and an unknown variable.

Let r be the number of socks that are red, and t be the total number of socks.

We get,

2(r(r-1)+(t-r)(t-r-1))=t(t-1)

Expanding the left hand side and the right hand side

we get,

4r^2-4rt+2t^2-2t = t^2-t

moving the terms, we will get that

4r^2-4rt+t^2 = t

We notice that the left side is a perfect square.

(2r-t)^2 = t

Thus t is a perfect square.

And, the higher t is, the higher r will be. So, we should set

t = 44^2

= 1936

we see, 2r-1936 = 44

We will use the positive root, to get that

2r-1936 = 44,

2r = 1980

r = 990

Therefore, we can conclude that the largest possible number of red socks in the drawer that is consistent with this data is 990.

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15x + 25 y = 230 and x - y = 2 is a system of equations that could be used to calculate the number of hours Mamadou worked and Brianna worked.

Given:

Mamadou can iron 15 shirts in one hour, whereas Brianna can do 25. Mamadou put in two more hours of work than Brianna, and the two of them combined to iron 230 shirts.

Let y be the number of hours Brianna, works, and x be the number of hours Mamadou  works.

In y hours, Brianna would iron 25y shirts.

In x hours, Mamadou would iron 15x shirts.

Combining total number of shirts,

15x + 25 y = 230

Since, Mamadou put in two more hours of work than Brianna.

x = y +2

x - y = 2

Therefore, for the number of hours Mamadou and Brianna worked, a system of equations 15x + 25 y = 230 and x - y = 2 could be utilised.

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Answer:

15x + 25 y = 230 and x - y = 2

Step-by-step explanation:

Answer:

x=110

Step-by-step explanation:

You can set the equation up like this:

100=x-10

Make x by itself

x=110

Answer: cosφ=-3/5

Step-by-step explanation:

[tex]\displaystyle\\sin\phi=\frac{4}{5} \ \ \ \ \ 90^0 < \phi < 180^0\\\\sin^2\phi+cos^2\phi=1\\\\\cos^2\phi=1-sin^2\phi\\\\cos^2\phi=1-(\frac{4}{5})^2\\\\ cos^2\phi=1-\frac{16}{25} \\\\cos^2\phi=\frac{1(25)-16}{25}\\\\ cos^2\phi=\frac{25-16}{25} \\\\cos^2\phi=\frac{9}{25} \\\\cos\phi=б\sqrt{\frac{9}{25} } \\\\cos\phi=б\sqrt{\frac{3^2}{5^2} }\\\\cos\phi=б\sqrt{(\frac{3}{5})^2} \\\\cos\phi=б\frac{3}{5} \\\\90^0 < \phi < 180^0\\\\Hence,\ \\\\cos\phi=-\frac{3}{5}[/tex]

You can see the three points where the result is equal to an integer in the photo below. Good luck!

Converting each of the question mentioned decimal into fractions in their simplest form, we get,

(i) 0.6 with 6 recurring = (2/3)

(ii) 3.405 with (405) recurring = (378/37)

(iii) 0.75 with (75) recurring = (25/33)

(iv) 0.3 with 3 recurring = (1/3)

As per the question statement and the attached reference along with the question, we are provided with four recurring decimal values.

We are required to convert each of the decimal values into fractions in their simplest form.

Starting with (i), 0.6 with 6 recurring = 0.66666...

Now, let [x = 0.6666...]

Or, [10x = 6.6666...]

Or, [(10x - x) = (6.6666...) - (0.6666...)]

Or, (9x = 6)

Or, [x = (6/9)]

Or, [x = (2/3)]

Or, [0.6666... = (2/3)]

Similarly for (ii), 3.405 with (405) recurring = 3.405405405405...

Now, let [x = 3.405405405...]

Or, [1000x = 3405.405405405...]

Or, [(1000x - x) = (3405.405405405...) - (3.405405405...)]

Or, (999x = 3402)

Or, [x = (3402/999)]

Or, [x = (378/37)]

Or, [3.40540405... = (378/37)]

Coming to (iii), 0.75 with (75) recurring = 0.757575...

Now, let [x = 0.757575...]

Or, [100x = 75.757575...]

Or, [(100x - x) = (75.757575...) - (0.757575...)]

Or, (99x = 75)

Or, [x = (75/99)]

Or, [x = (25/33)]

Or, [0.757575... = (25/33)]

Finally coming to (iv), 0.3 with (3) recurring = 0.333...

Now, let [x = 0.333...]

Or, [10x = 3.333...]

Or, [(10x - x) = (3.333...) - (0.333...)]

Or, (9x = 3)

Or, [x = (3/9)]

Or, [x = (1/3)]

Or, [0.333... = (1/3)]

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Given:

The fraction of treaters dressed up us halloween, x=2/15.

Let the total trickers be taken as 1.

Now, the proportion of treakers that were not dressed up as spiderman is,

Given:

If you borrow $100, you will have an interest of $10.

Asked: How much do you owe at the end of four weeks?

Solution:

To solve this problem, we need to find the rate, r.

According to the given, we can get the rate by:

$100 x rate = $10

rate = $10/$100

rate = 0.10

Now, if you borrow $1100, you will pay at the end of four weeks the amount of:

$1100 x 0.10 = $110

Total amount = $1100 + $110 = $1210

ANSWER: You will owe $1210 at the end of four weeks.

Answer:

You will owe $1210 at the end of four weeks.

The equivalent ratios of 2:6 can be 4:12, 6:18, 8:24, etc.

According to the question,

We have the following ratio:

2:6

Now, we have to find its equivalent ratios.

We know that equivalent ratios mean that when we compare any obtained ratio with the given ratio it should be same. So, to find equivalent ratios, we need to multiply both the numbers in the ratio by the same number.

In this case, we will find the three equivalent ratios. We will multiply both the numbers by 2, 3 and 4.

The given ratio = 2:6

Multiplying by 2:

4:12

Multiplying by 3:

6:18

Multiplying by 4:

8:24

Hence, the equivalent ratios of 2:6 are 4:12, 6:18 and 8:24.

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The graph of the quadratic function y = x² - 2x + 3 is shown in attached figure.

What is Quadratic equation?

An equation is called a quadratic equation if the highest power of variable of the equation is 2.

Given that;

The quadratic equation is,

y = x² - 2x + 3

Now,

The graph of the quadratic function y = x² - 2x + 3 has vertex (1, 2).

Thus,

The graph of the quadratic function y = x² - 2x + 3 is shown in attached figure with vertex (1, 2).

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The phrase "six more than nine times n is twenty" as an equation will be;  (6+9)n=20

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The phrase "six more than nine times n is twenty" as an equation will be;

Since we are multiplying n by the addition of 6 and 9, we put 6 and 9 in parenthesis with the n on the outside which is equal to 20.

Then 6 + 9 goes inside the parenthesis.

Therefore, it will be;

(6+9)n=20

Hence, The phrase "six more than nine times n is twenty" as an equation will be;  (6+9)n=20

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Answer:

  y +7 = 3(x +4)

Step-by-step explanation:

You want the point-slope equation of the line with slope 3 through point (-4, -7).

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For m=3 and (h, k) = (-4, -7), this is ...

  y -(-7) = 3(x -(-4)) . . . . . substitute for m, h, k

  y +7 = 3(x +4)

In order for the ratio of AP to PB to be 3/2, the coordinates of point P along the directed line segment AB are (14/5, -1).

The section formula returns the coordinates of a point that divides the line connecting two points in a ratio, either internally or externally.

Section formula is given as follows:

[tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]

It is given that the coordinates of the points A and B are A(-2, -4), B(6, 1) and   AP/PB = 3/2

Let the coordinates of the point P be (a, b).

By using section formula,

(a, b) = [tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]

(a, b) =  [tex](\frac{3(6)+2(-2)}{3+2} , \frac{3(1) +2(-4)}{3+2} )[/tex]

(a, b) = [tex](\frac{18 - 4}{5} , \frac{3-8}{5})[/tex]

(a, b) = [tex](14/5, -5/5)[/tex]

(a, b) = [tex](14/5, -1)[/tex]

Therefore, the coordinates of the point P along the directed line segment AB so that the ratio of AP to PB is 3/2 are (14/5, -1).

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B = 47°

a = 10.9

b = 11.7

How are the angles and sides of the right triangle calculated?

a) Finding B

We know that ,the sum of every angles of a triangle = 180°

So, B + 90° +43° = 180°

     B+ 133° = 180°

     B = 180° - 133°

        =47°

b) Finding a

We know,

[tex]sin\theta =\frac{opposite}{hypotenuse} \\\\sin 43^{\circ} =\frac{a}{16} \\\\a= 16(sin 43^{\circ})\\\\a = 16 (0.681)\\\\a=10.9[/tex]

c) Finding b

We know,

[tex]cos\theta = \frac{adjacent}{hypotenuse} \\\\cos 43^{\circ} =\frac{b}{16} \\\\b = (cos 43^{\circ})16\\\\b= (0.731) 16\\\\b= 11.7[/tex]

What is a right triangle?

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