Please help me set this question up so I can solve by quadratic equation and by completing the square.

When the length of each side of a
square is increased by 10 cm, the area
is increased by 200 cm². What was
the length of each side of the original
square?

The initial amount is worth $ 1538.46

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that may be added over time.

Simple interest is calculated as a percentage of the principal amount and is usually expressed as an annual rate.

The formula to calculate simple interest is:

Simple Interest = Principal x Rate x Time/ 100

Here we have

You are going to receive $2,000 in 6 years from now

The annual simple interest rate is 5%

Let 'P' be the initial or principal amount

Using the formula, I = PTR/100

Simple interest will gain on 'P' at 5% for 6 years

=> I = P(6)(5)/100  

=> I = 0.3P

And total amount = P + 0.3P = 1.3P

It is given that after 6 years we get $ 2000

=> 1.3P = 2000

=> P = 1538.46

Therefore,

The initial amount is worth $ 1538.46

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The expression has basic mathematical operators. is The measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given to us

∠J = (7x + 13)°,

∠K = (83 - 2x)°,

the sum of the two angles is 141°.

As it is given that the sum of the two angles is 141°, therefore, the expression for the sum of the two angles can be written as,

∠J + ∠K = 141°

(7x + 13)° + (83 - 2x)° = 141°

7x + 13 +83 - 2x = 141

5x = 141 - 83 - 13

5x = 45

x = 9

Now, we got the value of x, substitute the value of x in given measurements, therefore,

∠J = (7x + 13)°

∠J = 7(9) + 13

∠J = 63 + 13

∠J = 76°

∠K = (83 - 2x)°

∠K = (83 - 2(9))°

∠K = (83 - 18)°

∠K = 65°

Hence, the measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

Answer:

x=15

Step-by-step explanation:

(2x+60)=6x

2x+60=6x

subtract 2x from both sides

60=4x

divide by 4

15=x

The area of the stained glass is given as 20ft².

Let's start by finding the length of one side of the square stained glass. Since the area of a square is given by the formula A = s^2, where s is the length of one side of the square, we have:

s^2 = A

s^2 = 20ft²

s = sqrt(20)ft

s = 2sqrt(5)ft

Now, we can use the given equation p^2 = 5A to find the perimeter p of the square, by substituting the value of A:

p^2 = 5A

p^2 = 5(20ft²)

p^2 = 100ft²

p = sqrt(100ft²)

p = 10ft

Therefore, the perimeter of the square stained glass is 10 feet.

Answer: -125

Step-by-step explanation:

-5*-5=25

But, because its squared you have to multiply 25 * -5

A negative times a positive is a negative so,

25 * -5 = -125

Hope this helped!

Answer:

15 yards and 2 feet

Step-by-step explanation:

There are 3 feet in a yard

47/3= 15 and R 2

15 yard and 2 feet

Step-by-step explanation:

c = y axis intercept  =  6   ( from the graph)

slope = rise/run = 6/3 = 2  ( using points  (-3,0) and  (0,6)  )

then

y =  2x + 6

Applying the appropriate circle theorem, the values are:

1. x = 9; 2. Measure of arc DL = 66°; 3.x = 11; 4. x = 0; 5. x = 15

The central angle theorem is a circle theorem that states that the measure of the central angle is the same as the measure of the arc it intercepts.

1. 63 + 44 + 7x + 10 = 180

117 + 7x = 180

7x = 180 - 117

7x = 63

x = 9

2. Measure of arc DL = 2(33) [based on the inscribed angle theorem]

Measure of arc DL = 66°

3. 9x + 3 = 1/2(154 + 50) [based on the angle of intersecting chords theorem]

Solve for x:

9x + 3 = 102

9x = 102 - 3

9x = 99

x = 11

4. 35 = 1/2(171 + 2x - 101) [based on the secant-tangent theore]

Solve for x:

70 = 2x + 70

70 - 70 = 2x

2x = 0

x = 0

5. 8 * x = 12 * 10 [based on the intersecting chords theorem]

8x = 120

x = 15

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Ans :-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ∼

Answer:

3a⁴bc-3a²4b²c²-3a²bc³

Step-by-step explanation:

remove brackets by multiplying by the numbers out the brackets.As they are no like terms that is where we end our answers

Answer: Falso. Las razones trigonométricas dependen tanto del tamaño del triángulo como de la medida del ángulo. Esto se debe a que las razones trigonométricas de un triángulo se calculan relacionando los lados del triángulo con el ángulo. Por lo tanto, si cambia el tamaño del triángulo, los lados cambiarán y, por consiguiente, las razones trigonométricas también cambiarán.

Step-by-step explanation:

Answer:

( 4x + 3 ) ( x + 3 )

Step-by-step explanation:

9 × 4 = 36

Factors of 36 = { 1, 2, 3, 4, 6, 9, 12, 18, 36 }

3 and 12 add up to 15

4x² + 15x + 9

4x² + 3x + 12x + 9

( 4x² + 3x ) + ( 12x + 9 )

x (4x + 3) + 3 ( 4x + 3 )

( 4x + 3 ) ( x + 3 )

The distance DE is 338.25m

Similar triangles are triangles that have the same shape, but their sizes may vary. . The ratio of corresponding sides of Similar triangles are equal.

Therefore AB /DE = CB/CE

CE = 80+250

= 330

represent DE by x

82/x = 80/330

330× 82 = 80x

80x = 27060

x = 338.25

Therefore the distance DE is 338.25m

Using cosine rule to find the angle of D

c² = a²+b² +2abcos C

330² = 300²+ 338.25²+2× 300× 338.25cos D

108900 = 90000 + 114413.1 + 202950cosD

202950cos D = 108900-204413.1

202950cos D = -955131

cos D = -955131/202950

cosD = -0.471

D = cos^-1( 0.471)

D = 62° ( nearest degree)

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Answer: $10,00; $15,00 and $20,00

First, let’s mark the streaming platforms as letters x, y, z:

x - Disney +

y - Netflix

z - Hulu

Each platform costs $540,00 per year, so that would be $540,00/12=$45,00 per month

Since we know that Disney + and Hulu per year cost $300,00 and all three platforms cost $540,00 per year, we can find how much does Netflix cost per year:

$540,00-$300,00 = $240,00

Per month: $240,00/12 = $20,00

Now we can write equations according to the given information:

y = 2x

x+y+z = 540,00

x+z = 300,00

We can find how much does Disney + cost per year from the first equation, since we already know the price of Netflix per year:

2x = 240,00 / : 2

x = 120,00 (per year)

Per month: $120,00/12 = $10,00

And finally, since we know that all three platforms cost $45,00 per month, we can find the price of Hulu per month:

$45,00 - $20,00 - $10,00 = $15,00

So, Netflix costs $20,00 per month, Disney + - $10,00 per month and Hulu - $15,00 per month

Answer:

To determine the cost of the shirt, we can set up an equation using algebra. Let x be the cost of the shirt in dollars. We know that Marissa spent a total of 45 on the hat and the shirt, and the hat cost 10. Therefore, we can write the equation:

x + 10 = 45

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 10 from both sides:

x = 35

Thus, the cost of the shirt is $35.

Answer:

The combined taxable income of the couple is $61,900 + $59,400 = $121,300. This falls in the tax bracket for Married Filing Jointly between $67,900 and $137,050. Therefore, their tax rate will be 25%.

Step-by-step explanation:

The rate of tax couple has to pay is 25 percent.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

The combined taxable income of the couple is $61,900 + $59,400 = $121,300.

This falls in the tax bracket for Married Filing Jointly between $67,900 and $137,050.

Therefore, their tax rate will be 25%.

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The nurse will advise the patient to take 1 ml of medication with each dose.

The physician orders medication at 400 mg po twice daily. The pharmacy supplies medication with a dosage strength of 2 grams per 5 ml.

How many milliliters does the nurse advise the patient to take with each dose?

The nurse should advise the patient to take 1 ml of medication with each dose.

To find the number of milliliters, the following formula will be used.

Dose × Volume/Strength

Given, Dose = 400 mg

Strength = 2 grams per 5 ml

Volume = ?

To convert 400 mg to grams, divide by 1000.

400 mg = 400/1000 = 0.4 g

Now, put the values in the formula,

0.4 g × Volume / 2 g/ 5 ml= 5/2 × 0.4/1= 5/2 × 0.4= 1 ml

Hence, the nurse will advise the patient to take 1 ml of medication with each dose.

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there are 200 green balloons,  there are 120 red balloons ,  there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits.  To solve this problem, we need to use the given ratio and the total number of balloons to find the number of green balloons.

Let's assume the number of green balloons is x. Then, the number of red balloons is 3/5 of x, or (3/5)x.

The total number of balloons is 320, so we can write an equation based on the given information:

x + (3/5)x = 320

To solve for x, we can simplify the equation:

(8/5)x = 320

x = 200

Therefore, there are 200 green balloons.

To check our answer, we can use the ratio given in the problem:

(3/5)x = (3/5) * 200 = 120

So there are 120 red balloons.

Let's assume the number of bananas is x. According to the given ratio, the number of apples is twice that of bananas, or 2x.

The total number of fruits in the bowl is 15, so we can write an equation based on the given information:

x + 2x = 15

To solve for x, we can simplify the equation:

3x = 15

x = 5

Therefore, there are 5 bananas in the bowl.

To find the number of apples, we can use the ratio given in the problem:

2x = 2 * 5 = 10

So there are 10 apples in the bowl.

To check our answer, we can verify that the ratio of apples to bananas is 2:1:

10/5 = 2

Therefore, there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits.

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Answer:

X = 34, Y=56

Step-by-step explanation:

BOA is an isosceles triangle.

Angle CBO = 90°

Angle DBO = 90 - 56 = 34

Angle ODB = 34° and ODB is x

Angle EBD is also 90°

Y = 180 - (90+34) = 56

The value of x is 34 degree and y is 56 degree.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.

We have, BOA is an isosceles triangle.

< CBO = 90°

So, < DBO = 90 - 56

<DBO = 34

and, <ODB = 34°

Now, let the angle ODB be x

As, from the figure < EBD is also 90°

So, <y = 180 - (90+34)  (Angle sum property)

<y = 56

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To have a margin of error within 4% at a 99% confidence level, a sample size of at least 469 graduates is needed for the administrator's analysis of the proportion of graduates who have not found employment in their major field one year after graduation.

To determine the sample size needed for the administrator's analysis, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

where:

n = sample size needed

Z = the Z-score corresponding to the desired confidence level (99% corresponds to a Z-score of approximately 2.576)

p = the expected proportion of graduates who have not found employment in their major field (13%, or 0.13)

E = the desired margin of error (4%, or 0.04)

Substituting the given values into the formula, we get:

n = (2.576^2 * 0.13 * (1 - 0.13)) / 0.04^2

Simplifying and solving for n, we get:

n ≈ 468.42

Rounding up to the nearest whole number, we get:

n = 469

Therefore, a sample size of at least 469 graduates is needed for the administrator's analysis to have a margin of error within 4% at a 99% confidence level.

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The flag pole is 6.8 meters tall.

Trigonometric functions are mathematical formulas that connect the angles and side lengths of a right triangle. The six trigonometric functions are sin, cos, tangent, cosec, sec, and cotangent.

Height,p of the flagpole should be calculated.

Given;

base,b=2.9m

Angle subtended=67

Using trigonomteric identity

tan67=Height/base

Tan67=h/b

Tan67=h/2.9

h=2.9tan67

h=6.8m

Height pf the flag pole is 6.8m.

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The complete question is attached below:

According to the question, Tyler's playlist has 36 songs. Noah's playlist has one-quarter as many songs as Tyler's playlist. then Noah's playlist has 9 songs.

     Let the number of songs on Noah's playlist be represented by x.

     To solve the question, we'll set up an equation, which is given as:

                      36 / 4 = x

      Simplifying the above equation we get:

                         9 = x

     Therefore, Noah's playlist has 9 songs.

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The points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16) and The slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(a) To find where the tangent line is horizontal, we need to find values of t where the derivative of y with respect to x (dy/dx) is equal to 0.

We have:

dy/dx = (dy/dt)/(dx/dt) = (5t^4 - 5)/(12t^2 - 3)

Setting dy/dx = 0, we get:

5t^4 - 5 = 0

t^4 = 1

t = ±1 or t = ±i

Substituting t = 1 into the parametric equations gives us the point (1,-4). Substituting t = -1 gives us the point (-1,4). Substituting t = i or t = -i gives us points on the imaginary axis, which are not part of the real plane.

Therefore, the points where the tangent line is horizontal are (1,-4) and (-1,4).

To find where the tangent line is vertical, we need to find values of t where dx/dt is equal to 0.

We have:

dx/dt = 12t^2 - 3

Setting dx/dt = 0, we get:

t^2 = 1/4

t = ±1/2

Substituting t = 1/2 into the parametric equations gives us the point (13/16, -5/16). Substituting t = -1/2 gives us the point (-13/16, 5/16).

Therefore, the points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16).

(b) To determine the intervals where the slope of the tangent line is positive or negative, we need to examine the sign of the derivative dy/dx.

From part (a), we know that dy/dx is equal to:

dy/dx = (5t^4 - 5)/(12t^2 - 3)

The denominator is always positive, so the sign of dy/dx is determined by the numerator.

For t < -1, we have 5t^4 - 5 > 0, so dy/dx > 0.

For -1 < t < 1, we have 5t^4 - 5 < 0, so dy/dx < 0.

For t > 1, we have 5t^4 - 5 > 0, so dy/dx > 0.

Therefore, the slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(c) To determine the intervals where the curve is concave upward or downward, we need to examine the sign of the second derivative d^2y/dx^2.

We have:

d^2y/dx^2 = ((d^2y/dt^2)(dx/dt) - (dy/dt)(d^2x/dt^2)) / (dx/dt)^3

Calculating the second derivatives, we get:

d^2y/dt^2 = 20t^3

d^2x/dt^2 = 24t

Substituting these into the expression for d^2y/dx^2, we get:

d^2y/dx^2 = (20t^3)(12t^2 - 3) - (5t^4 - 5)(24t) / (12t^2 - 3)^3

Simplifying this expression, we get:

d^2

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The surface area of right triangular prism of height 3 in, base 8 in, slop 5 in and  width 4 in is 76  in².

Surface area is a measure of the total area occupied by the surfaces of a three-dimensional object. 

It is the sum of the areas of all the faces, including the base(s), of the object.

The units for measuring surface area are squared units, such as square meters or square inches.

To find the surface area of a right triangular prism, we need to add the areas of all of its faces.The prism has two congruent triangular faces and three rectangular faces.

The area of ​​every single triangle face is (1/2)bh, where b is the base of the triangle and h is its height.

In this case, the base is 8 in and the height is 5 in, so the area of each triangular face is (1/2)(8)(5) = 20  inches². Since there are two triangular faces, their combined area is 2(20) = 40 inches².

The area of ​​each rectangular face is lw.

In this case, the width is 4 in and the height is 3 in, so the area of each rectangular face is (4)(3) = 12 inches². Since there are three rectangular faces, their combined area is 3(12) = 36 inches²

Therefore, the total surface area of the right triangular prism is the sum of the areas of all its faces:

Surface area = 2(triangular face area) + 3(rectangular face area)

Surface area = 2(20) + 3(12)

Surface area = 40 + 36

Surface area = 76 inches²

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The total amount allocated to the Department of Health is R145,026,540,000, calculated by multiplying the total expenditure by the percentage allocated to the department expressed as a decimal.

To calculate the total amount allocated to the Department of Health, we need to multiply the total expenditure by the percentage allocated to the department, which is 12.6%.

Then, we must divide the percentage by 100 to get the decimal equivalent:

12.6/100 = 0.126

Next, we can calculate the total amount allocated to the Department of Health by multiplying the total expenditure by the decimal equivalent of the percentage:

Total amount allocated to the Department of Health = 0.126 x R1 149 390bn

Simplifying this expression, we get:

Total amount allocated to the Department of Health = R145,026,540,000

Therefore, the total amount allocated to the Department of Health is R145,026,540,000.

The calculation involves multiplying the total expenditure by the decimal equivalent of the percentage allocated to the department, which gives the amount allocated to the Department of Health.

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The fraction of vehicles on the road are trucks is 3/7

Let's assume there are a total of x vehicles on the road.

According to the first statement, 3/7 of those vehicles are trucks followed by a car. This means that (3/7)x trucks are on the road and are followed by a car.

According to the second statement, 3/9 of the vehicles are cars followed by a truck. This means that (3/9)x cars are on the road and are followed by a truck.

We know that the total number of vehicles on the road is x. So we can write

(3/7)x + (3/9)x = x

Simplifying this equation

(27/63)x + (21/63)x = x

(48/63)x = x

We can then solve for x

x = 63

So there are 63 vehicles on the road.

To find out what fraction of vehicles on the road are trucks, we need to determine what fraction of those 63 vehicles are trucks.

According to the first statement, 3/7 of the vehicles are trucks followed by a car.

So the fraction of vehicles that are trucks is 3/7

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Yes, all rational and irrational numbers have decimal expansions. Rational numbers can be expressed as terminating or repeating decimals, while irrational numbers have non-repeating, non-terminating decimal expansions.

In decimal form, rational numbers have a finite or repeating pattern of digits after the decimal point, while irrational numbers have an infinite, non-repeating pattern of digits after the decimal point. For example, the rational number 1/4 is expressed as 0.25, while the irrational number pi is expressed as 3.14159265358979323846... where the decimal goes on infinitely without repeating. In conclusion, every real number can be represented in decimal form, either as a terminating or repeating decimal, or as a non-repeating, non-terminating decimal.

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By using the complement probability that none of the 6 people prefer brand A paint, the probability that at least 1 person in a sample of 6 prefers brand A paint is 0.9939 or approximately 99.39%.

To find the probability that at least 1 person in the sample of 6 prefers brand A paint, we need to find the probability of the complement event that none of the 6 people prefer brand A paint, and subtract it from 1.

The probability that one person prefers brand A paint is 0.53, and the probability that one person does not prefer brand A paint is 0.47. Since we are dealing with a binomial distribution, we can use the formula for the probability of k successes in n trials:

P(k successes) = n! / (k! * (n - k)!) * p^k * (1 - p)^(n - k)

Using this formula, we can calculate the probability of 0 people preferring brand A paint:

P(0 people prefer brand A) = 6! / (0! * 6!) * 0.53^0 * 0.47^6 = 0.0061

Therefore, the probability of at least 1 person preferring brand A paint is:

P(at least 1 person prefers brand A) = 1 - P(0 people prefer brand A) = 1 - 0.0061 = 0.9939

So, the probability that at least 1 person prefers brand A paint is 0.9939 or approximately 99.39%.

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