A quilt is made of 8 rows of squares, and there are 6 squares in each row. Each square measures 1 foot on a side. Explain how to find the area of the quilt in a square feet. Then write the area.

Answer:

Step-by-step explanation:

10) The opposite sides of a parallelogram are equal. It means that

a + 15 = 3a + 11

3a - a = 15 - 11

2a = 4

a = 4/2 = 2

Also,

3b + 5 = b + 11

3b - b = 11 - 5

2b = 4

b = 4/2 = 2

11) The opposite angles of a parallelogram are congruent and the adjacent angles are supplementary. This means that

2x + 11 + x - 5 = 180

3x + 6 = 180

3x = 180 - 6 = 174

x = 174/3 = 58

Therefore,

2x + 11 = 2×58 + 11 = 127 degrees

The opposite angles of a parallelogram are congruent, therefore,

2y = 127

y = 127/2 = 63.5

12) The diagonals of a parallelogram bisect each other. This means that each diagonal is divided equally at the midpoint. Therefore

3y - 5 = y + 5

3y - y = 5 + 5

2y = 10

y = 10/2 = 5

Also,

z + 9 = 2z + 7

2z - z = 9 - 7

z = 2

Answer: the price of 1 yard of chicken wire is $2

Step-by-step explanation:

Let x represent the cost of one yard of landscaping fabric.

Let y represent the cost of one yard of chicken wire.

Charlotte pays $24 for 3 yards of landscaping fabric and 6 yards of chicken wire. This means that

3x + 6y = 24 - - - - - - - - - - 1

Kami pays $30 for 6 yards of landscaping fabric and 3 yards of chicken wire. This means that

6x + 3y = 30 - - - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 3, it becomes

18x + 36y = 144

18x + 9y = 90

Subtracting

27y = 54

y = 54/27 = 2

Substituting y = 2 into equation 1, it becomes

3x + 6×2 = 24

3x = 24 - 12 = 12

x = 12/3 = 4

Answer:

$2 per yard.

Step-by-step explanation:

Let the price per yard of landscaping fabric be f and the price of chicken wire per yard be c.

3f + 6c = 24     Multiply this equation by  - 2:

-6f - 12c = -48 Also:

6f + 3c = 30

Adding the last 2 equations:

-9c = -18

c = 2.

Answer:the perimeter of the regular pentagon is 5x + 20

Step-by-step explanation:

The perimeter of a plane figure is the distance around the plane figure. The pentagon is a plane figure. It has 5 sides. Since it is a regular Pentagon, it means that all the sides are equal.

From the information given, the length of each side of the regular Pentagon is x + 4

The perimeter of the regular Pentagon would be 5 times the length of each side. It becomes

5(x + 4) = 5x + 20

The question is not complete without a picture depicting the pot stickers production. I found a similar question with a table for the production of pot stickers which is attached to this answer. If the actual table is different from the table in this answer, you can still answer your question accordingly using my working and reasoning.

Answer:

Day 6

Step-by-step explanation:

It was given that the usual production of the kitchen is between 20 to 22 pot stickers per hour. Day 1 to 3, the production is within the range given.

However on day 4 and 5, the production is dropped to 10 and 15 - probably due to the workers unfamiliar with the machine.

On day 6 and 7, the production increases to 50 and 55. Therefore the day the machine makes positive impact is on day 6 where the production starts to make a significant increase.

We cannot determine the exact day when the new machine makes a positive impact on production at Sayuri's Asian Café.

The question asks on which day the new machine makes a positive impact on production at Sayuri's Asian Café. To determine this, we need to compare the production before and after the machine was introduced. Unfortunately, the statement provided does not mention the production levels before the machine. Therefore, we cannot determine the exact day when the machine makes a positive impact.

Answer:

(about) 61.1

Step-by-step explanation:

To find the height, or H, we can use

sin (45 degree angle) =H/85

rearrange as H=85* sin (45 degrees) =(about) 61.1

Answer:

Step-by-step explanation:

Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = points scored by students

u = mean time

s = standard deviation

From the information given,

u = 102 minutes

s = 18 minutes

1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as

P(x > 120 minutes) = 1 - P(x ≤ 120)

For x = 120

z = (120 - 102)/18 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x > 120) = 1 - 0.8413 = 0.1587

2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as

P(x < 66 minutes)

For x = 66

z = (66 - 102)/18 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

P(x < 66 minutes) = 0.02275

Answer:

[tex]A_{new}=9A_{original}[/tex]

Step-by-step explanation:

The are of a trapezoid is:

[tex]A_{original}=\frac{(a+b)}{2}h[/tex]

where:

When a geometric figure dilates, every coordinate of the original figure must be multiplied by the scale factor of this dilatation. In our case this factor is 3, therefore we will have:

[tex]A_{new}=\frac{(3a+3b)}{2}3h[/tex]

[tex]A_{new}=9\frac{(a+b)}{2}h[/tex]

[tex]A_{new}=9A_{original}[/tex]

The new area is 9 times the original one.

I hope it helps you!

Answer:  The correct option is

(E) 70.

Step-by-step explanation:  We are given to find the number of  triangles and quadrilaterals altogether that can be formed using the vertices of a 7-sided regular polygon.

To form a triangle, we need any 3 vertices of the 7-sided regular polygon. So, the number of triangles that can be formed is

[tex]n_t=^7C_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}=35.[/tex]

Also, to form a quadrilateral, we need any 4 vertices of the 7-sided regular polygon. So, the number of quadrilateral that can be formed is

[tex]n_q=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.[/tex]

Therefore, the total number of triangles and quadrilaterals is

[tex]n=n_t+n_q=35+35=70.[/tex]

Thus, option (E) is CORRECT.

When considering mortgage payments, homeowners insurance, property tax and maintenance costs over 30 years, the true cost of the $96,000 home is $287,068.80.

The true cost of a home not only includes the original purchase price but also takes into account annual homeowners insurance, property taxes, and maintenance costs. In this case, the purchase price is $96,000, homeowners insurance costs $1012 per year, property taxes are 1.1% of the home price each year, and annual home maintenance is 1% of the home price.

First, calculate the total mortgage payments made over 30 years. The monthly payment is $545.08, so the total mortgage payments are:

30 years * 12 months/year * $545.08/month = $196,228.80

Next, calculate the total cost of homeowners insurance over 30 years:

30 years * $1012/year = $30,360

Then, calculate the total property taxes over 30 years:

30 years * 1.1% of $96,000/year = $31,680

Lastly, calculate the total home maintenance over 30 years:

30 years * 1% of $96,000/year = $28,800

Adding all of these costs together gives the total cost of the home:

$196,228.80 + $30,360 + $31,680 + $28,800 = $287,068.80

So, the correct answer is option C: $287,068.80.

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Answer: The value of 528 would change by 40 if 6 replaced 2

Step-by-step explanation:

The given number is 528. If we replace 2 by 6, the new number becomes 568. This is greater than the previous number. The difference between the new number and the previous number would be

568 - 528 = 40

Answer:

The radii of the circles are 12 cm and 7cm.

Step-by-step explanation:

Let the radii of the circles be [tex]r_{1}\ and\ r_{2}[/tex]

Given:

Sum of circumference of two circles= 38π cm

Formula for circumference of a circle with radius r = 2πr

[tex]2\pi r_{1}+2\pi r_{2}=38\pi \\r_{1}+r_{2}=19[/tex]------------1

Sum of areas of two circles= 193π cm²

Area of circle with radius r = πr²

[tex]\pi r_{1}^{2}+\pi r_{2}^{2}=193\pi \\r_{1}^{2}+r_{2}^{2}=193[/tex]-------2

Substituting r2 = 19 - r1 in equation 2 we get:

[tex]r_{1}^{2}+(19-r_{1})^{2}=193\\2r_{1}^{2}-38r_{1}+168=0\\r_{1}^{2}-19r_{1}+84=0\\(r_{1}-12)(r_{1}-7)=0\\r_{1}=12\ or\ 7[/tex]

Then r2 = 19 - r1

[tex]r_{2}=12\ or\ 7[/tex]

Answer:

y + b > 15

Step-by-step explanation:

given data

positive integers = x, y, a, b

x divided by y then remainder = 6

a divided by b then remainder = 9

to find out

possible value for y + b

solution

we know that here when  x divided by y then remainder is 6

its mean y is greater than 6 and when a divided by b then remainder is 9

so its mean b is greater than 9

and we know remainder is less than divisor

so here y + b must be greater than = 6 + 9

y + b > 15

We can use the points (-30, 42) and (-27, -30) to solve.

Slope formula: y2-y1/x2-x1

= -30-42/-27-(-30)

= -72/3

= -24 (Answer)

Best of Luck!

Answer:

The shorter piece   x  =  8.4 in

The longer one    y  =  15.6 in

Step-by-step explanation:

If we cut  a string length  L  in to unequal  pieces we get two pieces

first one with length  x  and the other one with length  y

Let call  x  the smaller piece,  then   y = L  -  x will be the longer one

If   x  =  35 %    then

x  =  0,35* L     and

y = L -  x  =  L - 0,35*L      ⇒  y  =  0,65 L     ⇒ y  =  0.65*24

Now if L  =  24  in

x  =  0,35*24          ⇒               x = 8.4 in

and

L  -  x  =  0.65*L      ⇒       L - x  =  0.65*24     y  =  L  -  x  =  15.6 in

as way of verification you can add the length of the two pieces and find:

8.4  +  15.6  = 24 in

Final answer:

The ratio of the length of the small piece to the big piece is found to be 7/13 after calculating the lengths of each piece, with the small piece being 28 inches and the big piece being 52 inches.

Explanation:

Given that the length of the small piece is 35% of the total length L, we can denote the length of the small piece as 0.35L. The big piece is 24 inches longer than the small piece, so the length of the big piece is 0.35L + 24 inches. Since the string is cut into only two pieces, the total length L is the sum of the lengths of the two pieces, which means L = 0.35L + (0.35L + 24).

Simplifying, we have L = 0.7L + 24. Subtracting 0.7L from both sides gives 0.3L = 24 inches. Therefore, the total length of the string is L = 24 / 0.3 = 80 inches. So the small piece is 0.35L = 0.35 * 80 = 28 inches, and the big piece is 28 + 24 = 52 inches.

To find the ratio of the lengths of the small piece to the big piece, we divide the length of the small piece by the length of the big piece: 28/52. Simplifying this ratio by dividing both the numerator and denominator by 4 gives us 7/13. Therefore, the ratio of the length of the small piece to the big piece in its lowest terms is 7/13.

Answer:

78/2,652, or 0.0294, or 2.94%.

Answer:

[tex]\frac{x-3}{3x}[/tex]

Step-by-step explanation:

Lindsay can paint 1/x of a certain room in 20 minutes.

1 hour = 3 times 20 minutes

rate of work by Lindsay in 20 minutes is [tex]\frac{3}{x}[/tex]

Let 't' be the work done by Joseph

rate of work by Joseph in 20 minutes is [tex]\frac{3}{t}[/tex]

Both completed the work in 1 hour

[tex]\frac{3}{x} +\frac{3}{t} =1[/tex]

solve the equation for 't'

Subtract 3/x on both sides

[tex]\frac{3}{t} =1-\frac{3}{x}[/tex]

[tex]\frac{3}{t} =\frac{x-3}{x}[/tex]

cross multiply it

[tex]3x=t(x-3)[/tex]

Divide both sides by x-3

[tex]\frac{3x}{x-3} =t[/tex]

Work done together is

[tex]\frac{x-3}{3x}[/tex]

Answer:her total sales is 25

Step-by-step explanation:

Let x represent her total sales.

Nicole's job pays her salary plus commission. She earns a daily salary of $60 plus 15% commission of her total sales. This means that the amount that she receives for x total sales would be

60 + 15/100× x

= 60 + 0.15x

On Monday, she earned a total of $63.75. This means that

63.75 = 60 + 0.15x

63.75 - 60 = 0.15x

0.15x = 3.75

x = 3.75/0.15 = 25

Answer:sdxfrcgtvyhujikokjhgfdsasdfghjknbv 6yujhgtrfgb         srry .\.

Amount saved by Nicole is $ 105

Solution:

Given that Patrician saves $ 1.20 everyday and Nicole saves $ 2.80 daily

The two girls saved $ 150.00 together

To find: Amount saved by Nicole

Let "x" be the number of days for which Patrician and Nicole saved money

Given that they both saved $ 150.00 together

So we can frame a equation as:

[tex]\text{(amount saved by patrician + amount saved by nicole) } \times x = 150.00[/tex]

[tex](1.20 + 2.80) \times x = 150\\\\4x = 150\\\\x = 37.5[/tex]

Therefore amount saved by nicole:

Nicole has saved $ 2.80 daily for "x" days

[tex]\text{ Amount saved by Nicole } = x \times 2.80\\\\\text{ Amount saved by Nicole } = 37.5 \times 2.80 = 105[/tex]

Thus amount saved by Nicole is $ 105

Answer:

D

Step-by-step explanation:

Remember how absolute values turn everything inside of it into a positive number? Like |-4|=4 and |4|=4 as well.

Well, it works the same for equations.

When you have an absolute value equation like this, you have to split it into two parts.

The positive version

| d-3.5 | ≤ 1.5

and the negative version

|-(d-3.5)| ≤ 1.5

solve for the value of d in both equation.

Remember that you have to flip the inequality sign when dividing or multiplying by a negative number

I assume you know how to graph the inequality once you get the value for d.

d≤5 and d≥2

so

2 ≤ d ≤ 5

meaning d is between 2 and 5.

Answer:one piece is 42 centimeters and the other piece is 14 centimeters

Step-by-step explanation:

Let x represent the length, in centimeters, of one piece of the ribbon.

Let y represent the length, in centimeters, of the other piece of the ribbon.

The ribbon, 56 cm long is cut into two pieces. This means that

x + y = 56 - - - - -- - - - -1

One of the pieces is three times longer than the other. This means that

x = 3y

Substituting x = 3y into equation 1, it becomes

3y + y = 56

4y = 56

y = 56/4 = 14 centimeters

x = 3y = 2×14 = 42 centimeters

Answer:

Therefore the THREE roots are

[tex]x=0\ or\ x=-3\ or x=-4[/tex]

Step-by-step explanation:

Given:

[tex]x^{3}+7x^{2} +12x= 0[/tex]

To Find:

All  the Roots = ?

Solution:

As the degree of the polynomial is THREE then the number of root are also THREE.

[tex]x^{3}+7x^{2} +12x= 0\\\\x(x^{2}+7x +12)= 0\\\\x=0\\or\\x^{2}+7x +12= 0\\[/tex]

Now one root is Zero For other we need to Factorize

So by Splitting the middle term

i.e Factor of 12 such that sum should be 7

i.e 3 × 4 = 12  and 3 + 4 = 7

∴ [tex]x^{2}+7x +12= 0\\x^{2}+3x+4x +12= 0\\x(x+3)+4(x+3)=0\\(x+3)(x+4)=0\\\\x+3=0\ or\ x+4 = 0\\\\\therefore x=-3\ or x=-4\ \textrm{Which are the roots}[/tex]

Therefore the THREE roots are

[tex]x=0\ or\ x=-3\ or x=-4[/tex]

Answer: Infrequent decisions and long lasting decisions

Step-by-step explanation:

Infrequent: decisions made infrequently, they are not urgent, and deeper consideration is appropriate (ex., product strategy, international expansion).

Long-lasting: Once made, these decisions are unlikely to change not immediately but at least in the short term (e.g., commitment to a standard technology platform, commitment to organizational realignment around Value Streams)

Answer:

30 gallons

Step-by-step explanation:

let x represent the full container, then

[tex]\frac{1}{10}[/tex] x + 21 = [tex]\frac{4}{5}[/tex] x

Multiply through by 10 to clear the fractions

x + 210 = 8x ( subtract x from both sides )

210 = 7x ( divide both sides by 7 )

30 = x

The volume of the container is 30 gallons

Answer: the volume of the container is 30 gallons

Step-by-step explanation:

Let V represent the volume of the container, in gallons.

The initial volume of grains in the container is 1/0 × V = V/10

If 21 additional gallons of grain are added, the container is 4/5 full. This means that 21 gallons of grain + V/10 will occupy 4/5 of the volume of the container. Therefore

4/5 × V = 21 + V/10

4V/5 = 21 + V/10

4V/5 - V/10 = 21

7V/10 = 21

Multiplying the left hand side and right hand side of the equation by 10, it becomes

7V/10 × 5 = 21 × 10 = 210

7V = 210

V = 210/7 = 30

Answer:

  (-10, -6), (4, -6), (-3, -13), (-3, 1)

Step-by-step explanation:

The easiest points to find that have rational coordinates are the ones 7 units up or down, left or right from the given point. Those are listed above.

We used the distance formula to find four points that could serve as the other end of a line segment with one end at (-3, -6) and length of 7 units. The four points are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).

Finding the Other End Point of a Line Segment

To find four points that can serve as the other end point of a line segment with one end point at (-3, -6) and a length of 7 units, we use the distance formula. The distance formula is:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Given, (x₁, y₁) is (-3, -6) and the distance is 7, we need to find (x₂, y₂) such that:

√((x₂ + 3)² + (y₂ + 6)²) = 7

Squaring both sides: (x₂ + 3)² + (y₂ + 6)² = 49

(0 + 3)² + (y₂ + 6)² = 49

9 + (y₂ + 6)² = 49

(y₂ + 6)² = 40

y₂ + 6 = ±√40

y₂ = -6 ± √40

(x₂ + 3)² + (0 + 6)² = 49

(x₂ + 3)² + 36 = 49

(x₂ + 3)² = 13

x₂ + 3 = ±√13

x₂ = -3 ± √13

Thus, the four possible points for the other end point of the line segment are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).

Answer:

Step-by-step explanation:

Perpendicular slopes are the opposite reciprocals of the slopes given.  Our slope in 8 is -2.  That means that the perpendicular slope is 1/2.  If the line goes through (2, -1), then

[tex]y-(-1)=\frac{1}{2}(x-2)[/tex] and

[tex]y+1=\frac{1}{2}x-1[/tex] and

[tex]y=\frac{1}{2}x-2[/tex]

9 is a tiny bit trickier because we don't have the slope, the x term, on the opposite side of the equals sign from the y.  Let's do that and then we can determine the slope of that given line.  Moving over the 3x and isolating the y:

y = -3x + 5

So the slope is -3.  That means that the perpendicular slope is 1/3.  If the line goes through (-9, 3), then

[tex]y-3=\frac{1}{3}(x-(-9))[/tex] and

[tex]y-3=\frac{1}{3}(x+9)[/tex] and

[tex]y-3=\frac{1}{3}x+3[/tex] so

[tex]y=\frac{1}{3}x+6[/tex]

Answer:

Step-by-step explanation:

8) y = -2x + 1 and the line passes through (2, - 1)

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y= -2x + 1

Comparing with the slope intercept form, slope = - 2

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (2,-1) is 1/2

To determine the intercept, we would substitute m = 1/2, x = 2 and y = -1 into y = mx + c. It becomes

- 1 = 1/2 × 2 + c = 1 + c

c = - 1 - 1 = - 2

The equation becomes

y = x/2 - 2

9) 3x + y = 5 and the line passes through (-9, 3)

The equation of the given line is

3x + y = 5

y = -3x + 5

Comparing with the slope intercept form, slope = - 3

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (- 9, 3) is 1/3

To determine the intercept, we would substitute m = 1/3, x = -9 and y = 3 into y = mx + c. It becomes

3 = 1/3 × -9 + c = - 3 + c

c = 3 + 3 = 6

The equation becomes

y = x/3 + 6

Answer:

4/33

Step-by-step explanation:

x=0.121212...

100x=12.1212...

100 x-x=12

99 x=12

x=12/99=4/33

Given a decimal number 0.12, we have that its expression as a fraction in its simplest form is mathematically given as x=4/33

A fraction is simply a numerical quantity or use of integers in a form that is not in a whole number form.

Question Parameter(s):

X=0.121212...

Generally, the equation for the statement  is mathematically given as

x=0.121212

Therefore

100x=12.1212...

100 x-x=12

99 x=12

x=12/99

x=4/33

In conclusion, X=0.121212 as a fraction is x=4/33.

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Answer:

Step-by-step explanation:

Chrissie likes to tip a server in a restaurant a minimum of 25% of her lunch bill. She and her friend have a lunch bill that is $13.78. This means that the amount of tip that she would give to the server would be

25/100 × 13.78 = 0.25 × 13.78 = $3.445

If Chrissie says the tip will be $3.00, he is incorrect because the tip is $3.445 which is higher than $3

If her friend says that the amount is not a minimum of 25% he is correct because a minimum if 25% is $3.445 which is higher than $3

Lacy would earn a commission of $104.

Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.

Step-by-step explanation:

Given,

Commission earned on phones sales = 6% = [tex]\frac{6}{100}=0.06[/tex]

Commission earned on computer sales = 2% = [tex]\frac{2}{100}=0.02[/tex]

Worth of phones sold = $1100

Commission amount = 0.06*1100 = $66

Worth of computers sold = $1900

Commission amount = 0.02*1900 = $38

Total commission amount = 66+38 = $104

Lacy would earn a commission of $104.

For $x of phones, we will multiply the given amount with commission rate;

Commission amount of $x phones = 0.06*x = 0.06x

For $y computers;

Commission amount of $y computers = 0.02*y = 0.02y

Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.

Keywords: percentage, addition

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XY = 17

Step-by-step explanation:

It is given that x is the mid-point of WY, so it divides WY in two equal parts

WX and XY so the sum of both lengths will constitute the length of WY

[tex]WY = WX+XY\\XY = WY - WX[/tex]

putting values

[tex]XY = 10x-26 -(3x-1)\\= 10x-26-3x+1\\= 7x-25[/tex]

As X is the mid-point,

[tex]WX = XY\\3x-1 = 7x-25\\3x-1-3x = 7x-25-3x\\-1 = 4x-25\\-1+25 = 4x-25+25\\24 = 4x[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4} = \frac{24}{4}\\x = 6[/tex]

XY = 7x-25

[tex]=7(6) -25\\= 42-25\\=17[/tex]

So,

XY = 17

Verification:

WX = XY

[tex]3x-1 = 7x-25\\3(6)-1 = 7(6)-25\\18-1 = 42-25\\17 = 17[/tex]

Keywords: Linear equations, polynomials

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