In a discount clothing​ store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and four shirts cost ​$47​, while four sweaters and three shirts cost ​$84​, find the price of one sweater and the price of one shirt.

The value of f(5) is 4375.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(1)= 7,

f(n) = 5f(n-1)

f(2) = 5f(1)

     =5*7

f(2)= 35

f(3) =  5f(3-1)

f(3) =  5f(2)

f(3) =  5*35

f(3) = 175

f(4) =  5f(4-1)

f(4) =  5f(3)

f(4) =  5*175

f(4) = 875

f(5) =  5f(5-1)

f(5) =  5f(4)

f(5) =  5*875

f(5) = 4375

Hence, the value of f(5) is 4375.

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The dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.

Leth the width of the revtangle be x.

According to the given question.

The perimeter of the rectangle is 126 inches.

The length of the rectangle is three more than double the width.

⇒ Length of the rectangle  = 3 + 2x

Now, according to the given conditions we can say that

Perimeter of the rectangle = 2( length + width)

⇒ 126 = 2(3 + 2x + x)

⇒ 126  = 2(3 + 3x)

⇒ 63  = 3 + 3x

⇒ 63 - 3 = 3x

⇒ 60 = 3x

⇒ x = 20 inches

Therefore, the length of the rectangle = 3 + 2(20) = 3 + 40 = 43

Hence, the dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.

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b+3=12

because a+5=b+3 and a+5=12 which means b+3 must be 12 as well

Answer:

5

Step-by-step explanation:

4(|−2|)−|−3|

=(4)(2)−|−3|

=8−|−3|

=8−3

=5

8,615-4,229=4386 Answer took the quiz!

Answer:

4386

Step-by-step explanation:

8615-4229

= (8000 + 600 + 10 + 5) - (4000 + 200 + 20 + 9)

= (8000-4000) + (600-200) + (10-20) + (5-9)

= 4000 + 400 + (-10) + (-4)

= 4000 + 300 + (100-10) + (-4)

= 4300 + 80 + (10-4) = 4386

The absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.

Here, we are given that the population of a town increased from 3,250 in 2008 to 4,300 in 2010.

The absolute change can be calculate as-

Final population count - initial population count

= 4,300 - 3,250

= 1,050

Thus, absolute increase = 1,050

Now, the percentage increase can be calculated as follows-

percentage change = absolute change in population/ initial population count × 100

= 1,050/ 3,250 × 100

= 10500/ 325

= 32.3%

Thus, the absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.

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Answer:

see explanation

Step-by-step explanation:

the relationship between angles a and b

they are alternate interior angles

these angle pairs are on opposite ( alternate) sides of the transversal and are in between ( in the interior of )the parallel lines.

Greetings from Brasil...

It is possible to answer this question through Determinant

| X     Y     1 |

| X₁    Y₁    1 |  = 0

| X₂    Y₂   1 |

We have:

(X₁; Y₁) = (-9; 8)

(X₂; Y₂) = (-3; -1)

then

| X   Y   1 |

| -9  8   1 |  = 0

| -3  -1   1 |

Answer:

  x2 = 7/6

Step-by-step explanation:

You want the second approximation using Newton's method, given that the first approximation is x1=1 and the function tangent at x=1 is y=7-6x.

Newton's method approximates the function by its tangent line at the point (x, f(x)). That is, the second approximation is the x-intercept of the tangent line y = 7 -6x. That value of x is ...

  0 = 7 -6x

  6x = 7 . . . . . add 6x

  x = 7/6 . . . . divide by 6

The second approximation is x2 = 7/6.

The shorter side of the rectangle is 18 feet.

Perimeter of a rectangle = 2(l + w), where w is the width of the rectangle and l is its length.

Given the following:

Another side of the rectangle = width = w

One side of the rectangle = length = 3w - 9

Perimeter of the rectangle = 126 feet

Therefore:

2(3w - 9 + w) = 126

2(4w - 9) = 126

8w - 18 = 126

8w = 126 + 18

8w = 144

8w/8 = 144/8

w = 18

One side of the rectangle = 3w - 9 = 3(18) - 9 = 45

Therefore, the shorter side of the rectangle is 18 feet.

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Step-by-step explanation:

this is similar to the complete approach to find the midpoint. just instead of 1/2 we are looking for 3/10 of the distance.

the general approach is

A + (B - A)×factor

factor can be 1/2 or 3/10 or 7/10 or 24/29 or ...

so, we have

(-3, -6) + ((9 - -3)×3/10, (5 - -6)×3/10) =

= (-3, -6) + (12×3/10, 11×3/10) =

= (-3, -6) + (3.6, 3.3) = (0.6, -2.7)

the point 3/10 of the way from A to B is

(0.6, -2.7)

The limit dimensions of the part are 3.135 inches and 3.155 inches

The given parameters are

Thickness = 3.145 inches

Tolerance = 0.010 inches

The limit dimensions of the part are calculated as

Limit = Thickness +/- Tolerance

So, we have

Limit = 3.145 inches +/- 0.010 inches

Expand the above expression

So, we have

Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)

Evaluate the sum

Limit = (3.135 inches, 3.155 inches)

Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches

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The equivalent expression for a*(b*c) is (a*b)*c.

when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.

The given expression is a*(b*c).

The associative property is holds for multiplication.

According to the definition of associative property when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.

The equivalent expression for a*(b*c) is (a*b)*c.

For example a=2,b=3 and c=1 then

a*(b*c) =2*(3*1)=6

(a*b)*c=(2*3)*1=6

a*(b*c)=(a*b)*c

Therefore (a*b)*c is equivalent expression for a*(b*c).

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Answer: D.

hope this helps

Answer:

1. 11.7

2. 15

3. 20.5

4. 15.3

Step-by-step explanation:

Use the Pythagorean theorem for each of the problems.

Answer:

Step-by-step explanation:

The expression that is equivalent to the given expression (10^−2 • 4^5)^−2 is 10^(4) • 4^(−10)

The expression is given as

(10−2 • 45)−2

Rewrite the above expression properly as follows:

(10^−2 • 4^5)^−2

Apply the power rule of indices

So, we have

(10^−2 • 4^5)^−2 = 10^(−2 * −2) • 4^(−2 * 5)

Evaluate the product of powers

So, we have

(10^−2 • 4^5)^−2 = 10^(4) • 4^(−10)

Hence, the expression that is equivalent to the given expression (10^−2 • 4^5)^−2 is 10^(4) • 4^(−10)

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Answer: The prime number are 23,29,31

Step-by-step explanation:

The volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it.

The formula for the volume of a cylinder is given as:

V=π r² h

Now from the figure,

We have, for the first cylinder the height is 16 units and the radius is 7 units.

Hence,

V = 22/7 × 7² × 16

V = 22/7 × 7 × 7 × 16

V = 2424

Therefore the volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.

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Answer:

2745

jow to get this is you do this then dis

Answer:

v = 4.4

Step-by-step explanation:

Let's solve your equation step-by-step.

8/11 = v/6

Step 1: Cross-multiply.

8/11 = v/6

(8)*(6)=v*(11)

48=11v

Step 2: Flip the equation.

11v=48

Step 3: Divide both sides by 11.

11v/11 = 48/11

v= 48/11

v = 4.4

Step-by-step explanation:

[tex] \frac{1}{ {x}^{ \frac{ - 1}{3} } } \times \frac{1}{3x} \\ \frac{1}{ {3x}^{ \frac{2}{3} } } \\ \frac{1}{ 3\sqrt[3]{x {}^{2} } } [/tex]

f(t) = 80,00[tex](1+ 0.056)^{t}[/tex] is the exponential function that represents the model. The number of visits increase by 0.015% daily.

Here, we are given that a blogger found that the number of visits to her Web site increases 5.6% annually.

The exponential function is given as-

Final value = initial value [tex](1 + r)^{t}[/tex]

where r = rate of change

and t = time

here, r = 5.6%

r = 0.056

Further, the Web site had 80,000 visits this year ⇒ initial value = 80,000

Thus, we can get the following function-

f(t) = 80,00[tex](1+ 0.056)^{t}[/tex]

where f(t) represents the views after t years.

Now, since we are given that the views increase by 5.6% in 1 year

and 1 year = 365 days

⇒ daily rate = 5.6/365

= 0.015

Thus, the number of visits increase by 0.015% daily.

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5x-2y = -2 is the equation of line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6.

Given that, (x₁, y₁) = (-2, -4) and parallel to 5x - 2y = 6

Let's calculate the slope of 5x - 2y = 6

Rewrite the equation in y = mx + c form

5x - 2y = 6

⇒ -2y = 6 - 5x

⇒ -y = 3 - 5/2x

⇒ y = -3 + 5/2x

⇒ y = 5/2x - 3

Thus, the slope (m) = 5/2

As the line is parallel to 5x - 2y = 6 it will have a slope of 5/2.

The point-slope formula states (y - y₁) = m(x - x₁)

Now, substituting the value of m = 5/2 and (x₁, y₁) = (-2, -4), we get

(y - y₁) = m(x - x₁)

⇒ (y - (-4)) = 5/2(x - (-2))

⇒ (y+4) = 5/2(x+2)

⇒ 2(y+4) = 5(x+2)

⇒ 2y+8 = 5x+10

⇒ 5x-2y+10-8 = 0

⇒ 5x-2y+2 = 0

⇒ 5x-2y = -2

Hence, the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6 is 5x-2y = -2.

Therefore, 5x-2y = -2 is the required answer.

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Answer:1

Step-by-step explanation:

The number of mums created every hour by each friend are:

Given data

Friend A, Friend B, and Friend C working = 6 mums per hour

Friend B and Friend C working = 5 mums per hour

Friend A and Friend B are working = 4 mums per hour

A + B + C = 6         equation 1

B + C = 5               equation 2

A + B = 4                equation 3

from equation 2, make C the subject of the formula

B + C = 5

C = 5 - B

from equation 3, make A the subject of the formula

A + B = 4

A = 4 - B

substitute A and C into equation 1 to get

A + B + C = 6

4 - B + B + 5 - B = 6

4 + 5 - B = 6

9 - B = 6

-B = 6 - 9

-B = -3

B = 3

substituting B for A we have

A = 4 - 3

A = 1

substituting B for C we have

C = 5 - 3

C = 2

Therefore , Friend A working every hour creates 1 mum, Friend B working every hour creates 3 mums, and Friend C working every hour creates 2 mums,

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Expanding out the equation, we get

[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]

Considering the discriminant,

[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]

This is always non-negative, meaning the roots are real.

The roots are equal if and only if the discriminant is 0, which is when a=b=c.