The width of a rectangle is 4 units less than the length. The area of the rectangle is 12 units. What is the width, in units, of the rectangle?

The unit price of the pair of gloves is $5.19.

Here, a package of 5 pairs of insulated gloves costs $25.95.

We have to find the unit price of the pairs of gloves.

5 pairs of insulted gloves = $25.95

So we have to find the value of 1 pair of gloves, so by dividing the value by 5 we will get the value of 1 pair of gloves.

Unitary method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit.

So by using the unitary method we have:

1 pair of insulated gloves = 25.95/ 5

                                          = 5.19

Therefore the unit price of the pair of gloves = is $5.19.

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Answer:

[tex]x = 16[/tex]

Step-by-step explanation:

Because of the fact, the angle is ∠BCA = 10x - 10 and ∠ABC = 30 lies on a straight line and ∠BCA is obtuse while ∠ABC is acute, we can just set them equal to 180 to find the value of x.

So we will set up the equation:
   10x - 10 + 30 = 180

1. Combine Like Terms (eg. -10 and 30)
[tex]10x - 10 + 30 = 180[/tex]
= [tex]10 x + 20 = 180[/tex]

2. Subtract 20 on both sides
[tex]10x + 20 = 180[/tex]
       [tex]-20 -20[/tex]

= [tex]10x = 160[/tex]
3. Divide 10 into both sides
[tex]\frac{10x}{10} = \frac{160}{10}[/tex]

And we will get:
[tex]x = 16[/tex]

Check Your Work!
Now if we replace x in the equation for 16 like below we do in fact get 180:
[tex]10(16) - 10 + 30 = 180[/tex]
[tex]160 - 10 + 30 = 180[/tex]

[tex]150 + 30 = 180[/tex]

The points (2, - 5) and (- 1, 1) lie on the equation of the line - 2 · x - y = 1.

According to Euclidean geometry, a line can be constructed from two distinct points on a plane. Then, we can find the equation of the line based on the coordinates of two points set on Cartesian plane, whose standard form is shown below:

a · x + b · y = 1

In this question we have the coordinates of two points: (2, -5), (- 1, 1). If we substitute in the equation of the line, then we find the following system of linear equations:

2 · a - 5 · b = 1

- a + b = 1

Then, we find the solution to the system by using numerical methods:

(a, b) = (- 2, - 1)

The equation of the line - 2 · x - y = 1 contains the points (2, - 5) and (- 1, 1).

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Answer:

800/920

400/460

40/46

20/23

The distance between the two points (-2, 4) and (3, 7) is found as 5.83.

For the given question;

The two coordinates are-

(x1, y1) = (-2, 4)

(x2, y2) = (3, 7)

The distance between two points are calculated as-

d = √(x1 - x2)² + (y1 - y2)²

Put the values;

d = √(-2 - 3)² + (7 - 4)²

d = √25 + 9

d = √34

d = 5.83

Thus, the distance between the two points (-2, 4) and (3, 7) is found as 5.83.

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Using the conversion factor, we know that 30 miles are approximately 48 km.

So, 30 miles is how many kilometers:

Then, 5 miles:

Similarly 30 miles:

Rounding off: 48 km approximately

Therefore, using the conversion factor, we know that 30 miles are approximately 48 km.

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The answer as a decimal to the nearest hundredth is -3.45.

For the given question;

The expression is given as;

= -3.7 + 1/4

Now, the fraction 1/4 can be written in decimal as 0.25.

Put the value of 1/4.

=  -3.7 + 0.25

The subtraction of larger negative to smaller positive gives negative number.

= -3.45

Thus, the answer as a decimal to the nearest hundredth is -3.45.

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The triangle has an area of 3.37 square units

The equations are given as

y= -1/2x + 8

y = 9x

On the y-axis, the value of x is 0

i.e. x = 0

Substitute 0 for x in the equations y= -1/2x + 8 and y = 9x

So, we have

y= -1/2(0) + 8 = 8

y = 9(0)  = 0

The base of the triangle is the difference between these values

So, we have

Base = 8 - 0

Base = 0

Substitute y = 9x in y= -1/2x + 8

So, we have

9x = -1/2x + 8

This gives

9.5x = 8

Divide both sides

x = 16/19

The area of the triangle is then calculated as

Area = 0.5 * Base * x

This gives

Area = 0.5 * 8 * 16/19

Evaluate

Area = 3.37

Hence, the area of the triangle is 3.37 square units

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The inequality of the equation x(2x+3) > 20 is x<-4 or x>5/2.

Given, the expression is x(2x+3) > 20

open the brackets.

⇒ 2x²+3x>20

⇒ 2x²+3x-20>0

Factorize the equation.

⇒ 2x²+8x-5x-20>0

⇒ 2x(x+4)-5(x+4)>0

⇒ (x+4)(2x-5)>0

hence, (x+4)>0 or (2x-5)>0

(x+4)>0

⇒ x<-4

(2x-5)>0

⇒ 2x > 5

⇒ x >5/2

Hence we get the required inequality for the given equation.

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Problem

Solution

For this case the surface area is given by:

And solving we got:

The number of miles that the truck drove is 550 miles.

From the information, Xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile. This can be illustrated as:

20x + 2.25y = 1457.50 ....... i

x = number of hours

y = number of miles driven

The driver drove an average of 50 miles per hour. This will be illustrated as:

y/x = 50

y = 50x

Substitute into equation i

20x + 2.25y = 1457.50

20x + 2.25(50x) = 1457.50

20x + 112.50x = 1457.50

Collect like terms

132.50x = 1457.50

Divide

x = 1457.50 / 132.50

x = 11

y = 50x = 50 × 11 = 550 miles

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Since 1 dozen = 12, 12 cupcakes = 1 1/4 cups of flour

36/12 = 3

36 = 1 1/4(3)
36 cupcakes = 3 3/4 cups of flour

Answer:

8 1/4 cups

Step-by-step explanation:

You multiple 11/4 by 3 and change the answer to a mixed fraction

The vertex f(x) = x² - 8x +7 is (4,-9)

A quadratic equation is a second-order polynomial equation with a single variable, such as x = ax2 + bx + c = 0, where a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated. Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

Given Data

Establishing the axis of symmetry is the first step that you should take (the x co-ordinate of the vertex). You must factor the equation in order to do this. You need to find two values that sum up to -8 and multiply to +7 in order to factor this easy trinomial. This pair of numbers, -1 and -7, means:

-7 x -1 = +7 \s-7 + -1 = -8

Now, you take these two components and mark each one with an x in brackets as follows:

f(x) = (x -1)(x-7)

Set each bracket to zero now, and then solve. Get x = 7 and x = 1, respectively. Add the zeros together and divide by 2 to find the axis of symmetry:

[tex]\frac{7+1}{2}[/tex]

= 4

Consequently, x=4 is the equation for the axis of symmetry.

You may now insert the axis of symmetry into the equation (either the factored version or the original; in this case, factored would be the simplest) to obtain the best value (y co-ordinate of the vertex):

f(4) = (4-1)(4-7)

f(4) = (3)(-3)

f(4) = -9

Therefore, -9 is the ideal value.

Together, it makes the vertex (4, -9)!

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Answer:

First number = 4

Second number = 9

Step-by-step explanation:

If the first number = x, the second number = x + 5.

The calculation can be expressed as follows:

x + 2(x + 5) = 22

First, expand the bracket 2(x + 5):

x + 2x + 10 = 22

Combine like terms:

3x + 10 = 22

Subtract 10 from both sides:

3x = 12

Divide both sides by 3:

x = 4

First number = 4

Second number = 4 + 5 = 9

The compound interest formula is given by the formula

Where A = Amount after t years

r = rate = 6

t = time = 5

p = $ 25000

For the first year

For the second year

P=26500+25000=51500

For the third year

P=54590 + 25000=79590

For the fourth year

P=84365.4 + 25000=109365.4

For the fifth year

P= 115927.324 + 25000 =140927.324

At the start of the 6th year

P= 149382.962+25000= 174382.96

Answer = $174382.96

Option B is correct

Answer: Janessa would have 27 and Emily would have 19.

The most appropriate choice for percentage and fraction will be given by-

The process of conversion of fraction to percentage has been explained.

What is fraction and percentage?

Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

If a number is taken as fraction of 100 then the fraction is known as percentage.

To convert a fraction into percentage, we have to simply multiply the fraction with 100.

For example.

Suppose we have a fraction [tex]\frac{1}{4}[/tex], we need to convert  [tex]\frac{1}{4}[/tex] to percentage.

So on multiplying [tex]\frac{1}{4}[/tex] by 100, we obtain = [tex]\frac{1}{4} \times 100[/tex] = 25%

So, [tex]\frac{1}{4}[/tex] is equivalent to 25%

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Answer:

x - 13

Step-by-step explanation:

To get this equation, we must look at the description.

13 less than x makes an equation of x - 13.

The answer is x - 13.

Hope this helps!

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The 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.

What is a quartile of a data set and how is it conceived?
A quartile is a set of values with three points that divides a data set into four equally sized portions. The values that divide a list of numerical data into three quarters are known as quartiles. The center of the three quadrants measures the point of distribution's center and displays data that are close to the center. Only half of the data set is represented by the lower part of the quarters, which is below the median, while the upper section represents the other half, which is above the median. The distribution or dispersion of the data set is shown overall by the quartiles.
When the data points are organized in ascending order, 25% of them are found in the lower quartile, often known as the first quartile (Q1). When presented in increasing order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).
Mathematically, First quartile (Q1) = [(n+1)/4] term
Third quartile (Q3) = [3(n+1)/4] term
The interquartile range is calculated as: Upper Quartile – Lower Quartile = Q3 - Q1

Arranging the given values in ascending order, we have the data set:
40, 42, 46, 47, 51, 55, 58, 67, 67, 68, 69
The total number of terms in the data set = n = 11
Using the formulae established in the literature, we have:
Now, first quartile = Q1 = [(11+1)/4] term = 3rd term = 46
Again, third quartile = Q3 = [3(11+1)/4] term = 9th term = 67
Therefore, interquartile range = Q3 - Q1 = 67 - 46 = 21
Thus, the 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.

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The value of f(2k+4) for k=1 and f(x)= 4-x is -2

What is the value of a function?

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value.

We are given a function f(x)= 4-x

We have to find f(2k+4).

[tex]f(2k+4)=4-2k-4[/tex]

Now substitute k=1

We get,

[tex]f(2+4)=4-2-4\\f(6)=-2[/tex]

Hence, The value of function f(2k+4) at k=1 for the function f(x)=4-x is -2

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If Mr. Jamison bought 8 dozen sketch pencils, 6dozen colored pencils and 3 dozen art gum, with a sales tax of 8 percent, considering each dozen of sketch pencils costed $x, colored pencils costed $y and art gums costed $z, the total bill approximately would be

$[(8x + 6y + 3z) + 0.08(8x + 6y + 3z)].

As per the question statement, Mr. Jamison bought 8 dozen sketch pencils, 6dozen colored pencils and 3 dozen art gum, with a sales tax of 8 Percent, and since no information is provided about the price of the sketch pencils, colored pencils or art gums, let us consider that each dozen of sketch pencils costed $x, colored pencils costed $y and art gums costed $z.

We are required to calculate the total approximate bill, Mr. Jamison would have to pay for the items he picked up.

To solve this question, first we will have to calculate the total price of the items he picked, without any taxes, i.e.,

$[(8 * x) + (6 * y) + (3 * z)] = $(8x + 6y + 3z).

Now an 8% sales tax on the price of the items bought will be

8% of $[(8x + 6y + 3z), i.e.,

[(8/100) * (8x + 6y + 3z)]

= $[0.08(8x + 6y + 3z)]

Therefore, total bill = (Total item costs + tax)

                                = $(8x + 6y + 3z) + $[0.08(8x + 6y + 3z)]

                                = $[(8x + 6y + 3z) + 0.08(8x + 6y + 3z)]

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Step-by-step explanation:

the axis of symmetry for a regular parabola (opens up or down) is a line parallel to the y-axis (vertical) going through the vertex of the parabola.

the standard form of a parabola is

y = a(x - h)² + k

with (h, k) being the vertex.

so, we see for f(x) the vertex is (-4, 1).

the axis of symmetry uses the x coordinate of the vertex and is

x = -4

for h(x) we see in the graphic that the vertex is (1, -3).

so, the axis of symmetry is

x = 1

FYI - based on what we see : vertex is (1, -3), h(0) = -1 the function here would be

h(x) = 2(x - 1)² - 3

The equation for a rectangle's perimeter is P = length + breadth + length + breadth. Alternatively, P=2(length + breadth). The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter.  

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As per direct variation,

Part A) Decorators fee is $198.132

Part B) Tax for the purchase is $71.10

Part C) The total amount spend by the family is $1849.232.

Direct variation:

Direct variation depicts a simple relationship between two variables . We say y varies directly with x if:

y=kx

for some constant kk , called the constant of variation or constant of proportionality. Which means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

Given,

A family used a professional decorator to furnish their new home.

The decorator selected $1,580 worth of furnishings for their home.

The payment will be made by the family for the furnishings, plus 4.5% tax on the purchases.

The decorator’s fee was 12% of the furnishings , excluding the tax.

Here we need to find the following:

Part A) Decorator's fee

Part B) Tax amount

Part C) Total cost.

We know that, the decorator’s fee was 12% of the purchases.

So, the equation is then be calculated as:

y = kx

where,

y = decorators fee

k = percentage of decorators fee for the purchases

x = amount paid

y = 12% × $1651.10

= 0.12 × $1651.10

Therefore, the decorators fee is $198.132

Decorator selected furnishings cost = $1,580.

Tax = 4.5%

Decorator’s fee = 12% of the purchases.

So, it can be calculated as,

Tax = 4.5% × 1580

Tax = 0.045 × 1580

Therefore, the tax for the purchase is $71.10

Amount paid = 1580 + 71.10 = 1651.10

Now, the total amount paid by the family is,

=> purchase amount + decorator fee

=> 1651.10 + 198.132

=> 1849.232

Therefore, the total amount spend by the family is $1849.232.

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Answer:

x=6

Step-by-step explanation:

1. Combine like terms

2. Add 9 to both sides

3. Divide by 4 on both sides

4. Arrive at solution

5. Plug solution in to equation.

Answer:

-3

Step-by-step explanation:

first you start with by adding 9 to both sides to balance

-2x+6x-9=15

          +9 +9

Giving you -2x+6x=24 now you start by dividing

I started by dividing -2

-2x+6x=24

÷(-2)      ÷(-2)

Giving you x+6x=(-12) again divide

x+6x=(-12)

 ÷6   ÷6

Giving you x+x=(-6) we know that x+x is = to 2x next we divide agian

2x=(-6)

÷2  ÷2

Giving you the answr x=(-3)

The total amount of Zach's paycheck was $174.

The fraction of the paycheck spent by Zach on the new video game is 2/6. The cost of the video game is $58. We need to find the total amount that Zach had in the paycheck.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.

Let the total amount of the paycheck be "x". Using the information above, we can form an equation as given below :

(2/6)*x = 58

x = (6/2)*58

x = 174

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The point slope from the line with slope -3/7 that passes through the point (5,8) is y-8 = -3/7 ( x-5).

Two crucial constants are present in a linear function: the slope, which is represented by the letter m, and the y-intercept, which is represented by the letter b. Y = m x + b is the slope-intercept equation's formula. The point-slope equation is a different manner that we can occasionally express the equation of a line. It reads as follows y-y₀ = m(x-x₀).

Given that :

Slope m = -3/7

passes through the point p ( 5, 8 )

Equation is  y-y₀ = m(x-x₀)

y-8=-3/7 ( x-5)

here the point slope is y-8=-3/7 ( x-5)

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The inequality (302+5)-1+4 (202)- 3) ≤ 125 is false for the given question.

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on either side are not equal.

It indicates that the expressions on the left and right should be greater or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is defined by the inequality symbols '≠'.

We have given the inequality  

(302+5)-1+4 (202)- 3) ≤ 125

Lets simplify

(302+5)-1+4 (202)- 3) ≤ 125

1111 ≤ 125

Thus, The inequality is false.

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