Determine the value of real parameters p in such a way that the equation 3x2−24x+p=0 has one root equal to triple of the second root

has one root equal to triple of the second root.

The square root of y is not simplified and can be represented as:

y = √([tex]2^4 \times[/tex] 5) or y = 4√5.

To solve the proportion y/8 = 10/y for y, we can cross-multiply:

y [tex]\times[/tex] y = 8 [tex]\times[/tex]10

This simplifies to:

[tex]y^2[/tex] = 80

To solve for y, we can take the square root of both sides of the equation:

[tex]\sqrt{y^2[/tex] = √80

Since the square root of [tex]y^2[/tex] is simply y, we have:

y = √80

The square root of 80 can be further simplified by breaking it down into its prime factors. Since 80 can be expressed as 2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]5, we can simplify the square root:

y = [tex]\sqrt(2 \times 2 \times 2 \times 2 \times 5)[/tex]

Therefore, the square root of y is not simplified and can be represented as:

y = [tex]\sqrt{(2^4 \times 5)[/tex] or y = 4√5.

For more such answers on Square root

https://brainly.com/question/428672

#SPJ8

Answer:

[tex]y = \sqrt{80\\} =4\sqrt{5}[/tex]

Step-by-step explanation:

Answer:

24 cakes.

Step-by-step explanation:

6 cups of oil divided by 1/4 cup oil per cake = 24 cakes

6/(1/4) = 24

or 6/(0.25) = 24

She can make 24 cakes with 6 cups of oil.

The coordinates in the solution to the systems of inequalities is (12, 1)

From the question, we have the following parameters that can be used in our computation:

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

Read more about inequalities at

brainly.com/question/30977554

#SPJ1

Answer:

8

Step-by-step explanation:

3x - 10 = x + 2

2x = 12

x = 6

3x - 10 = 3(6) - 10 = 8

The length of each leg of the triangle is 8.

Answer:

Eat that cookie and you will not regret about it

The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

Learn more about parallelograms click;

https://brainly.com/question/29147156

#SPJ1

Answer:

I apologize, I am not able to provide visual drawings or diagrams. However, I can still provide a step-by-step guide to solve the problem.

To find the area of each shape, we need to use rectangles to determine the areas of right triangles that are inside the rectangles. Here are the steps:

1. Draw the given shape on geoboard paper.

2. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle.

3. Identify the right triangles that are inside the rectangles.

4. Use the formula for the area of a triangle, which is A = (base x height) / 2, to find the area of each right triangle.

5. Use the formula for the area of a rectangle, which is A = length x width, to find the area of each rectangle.

6. Add up the areas of the triangles and rectangles to find the total area of the shape.

Remember to label your answers with the correct units (square units).

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Given values:

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies B=180^{\circ}-A-C[/tex]

[tex]\implies B=180^{\circ}-29^{\circ}-63^{\circ}[/tex]

[tex]\implies B=88^{\circ}[/tex]

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

Solve for a:

[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

[tex]\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}[/tex]

[tex]\implies a=13.0876493...[/tex]

[tex]\implies a=13.1[/tex]

Solve for b:

[tex]\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]

[tex]\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}[/tex]

[tex]\implies b=26.9194211...[/tex]

[tex]\implies b=26.9[/tex]

[tex]\hrulefill[/tex]

Given values:

As the interior angles of a triangle sum to 180°:

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies C=180^{\circ}-A-B[/tex]

[tex]\implies C=180^{\circ}-72^{\circ}-35^{\circ}[/tex]

[tex]\implies C=73^{\circ}[/tex]

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

Solve for a:

[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

[tex]\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}[/tex]

[tex]\implies a=20.8847511...[/tex]

[tex]\implies a=20.9[/tex]

Solve for b:

[tex]\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]

[tex]\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}[/tex]

[tex]\implies b=12.5954671...[/tex]

[tex]\implies b=12.6[/tex]

Using the first two points we can get an exponential model:

[tex]y = (225/23)*(23/15)^x[/tex]

The general exponential equation can be written as:

[tex]y = A*(b)^x[/tex]

We can replace any two values of the table to get the system of eqautions:

[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]

Taking the quotient between the second and the first equation we get:

[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]

Replacing that on the first equation we will get:

[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]

Then an exponential model is:

[tex]y = (225/23)*(23/15)^x[/tex]

LEarn more about exponential equations at:

https://brainly.com/question/11464095

#SPJ1

The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

For more question on profit

https://brainly.com/question/1446002

#SPJ8

Answer:91.26ft squared

The statements that complete the function transformations are left, up, stretch and stretch

From the question, we have the following parameters that can be used in our computation:

f(x) = (x + 94)²

Also, we have

f(x) = x²

This implies that f(x) = (x + 94)² is obtained by shifting f(x) = x² left by 94 units

Next, we have

f(x) = x² + 94

This implies that f(x) = x² + 94² is obtained by shifting f(x) = x² up by 94 units

Next, we have

f(x) = 94√x from f(x) = √x

This implies that f(x) = 94√x can be obtained from vertically stretching f(x) = √x by a factor of 94

Also, the graph of f(x) = √94x can be obtained from horizontally stretching f(x) = √x by a factor of 1/94

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}. Thus, the correct option is D.

Given that:

A coin is tossed.

A spinner has 3 equal sections: Red, White, and Blue.

The samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The total number of samples is calculated as,

Total samples = 2 x 3

Total samples = 6

The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}.

Thus, the correct option is D.

More about the sample link is given below.

https://brainly.com/question/8053622

#SPJ1

The system of inequalities for the graph is

a) y < 3x - 4

b) y = x + 3

Given data ,

Let the inequality equations be represented as A and B

where

Let the first point be P ( 0 , 3 )

Let the second point be Q ( -3 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 + 3 )

m = 1

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 0 = 1 ( x + 3 )

y = x + 3

And , the second equation is

Let the first point be R ( 0 , -4 )

Let the second point be S ( 2 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -4 - 2 ) / ( 0 - 2 )

m = -6/-2

m = 3

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 2 = 3 ( x - 2 )

Adding 2 on both sides , we get

y = 3x - 4

Since , it is a dotted line ,

y < 3x - 4

And , the solution to the inequality is point of intersection

where A ( 3.5 , 6.5 ) is the solution

Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

To know more about Area here

https://brainly.com/question/14994710

#SPJ1

The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?

Step-by-step explanation:

3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:

P(t) = 400 * 1.25^t

Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.

To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:

P(t) = 400 * 1.25^t

P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))

P(t) ≈ 2,343

Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.

4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:

P(t) = 10,800 * 0.975^t

Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.

To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:

5,400 = 10,800 * 0.975^t

0.5 = 0.975^t

log(0.5) = t * log(0.975)

t ≈ 28.2

Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.

Answer:

3) 9.03 days

4)  27.38 years

Step-by-step explanation:

To model the spread of the virus over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the virus has infected 400 people in the town and is spreading to 25% more people each day:

Substitute these values into the formula to create a function for P in terms of t:

[tex]P(t) = 400(1 + 0.25)^t[/tex]

[tex]P(t) = 400(1.25)^t[/tex]

To find how many days it will take for 3000 people to be infected, set P(t) equal to 3000 and solve for t:

[tex]\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}[/tex]

Therefore, it will take approximately 9.03 days for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.

Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.

[tex]\hrulefill[/tex]

To model the population of the town over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 - r)^t}[/tex]

where:

Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:

Substitute these values into the formula to create a function for P in terms of t:

[tex]P(t) = 10800(1 -0.025)^t[/tex]

[tex]P(t) = 10800(0.975)^t[/tex]

To find how many days it will take for the population to halve, set P(t) equal to 5400 and solve for t:

[tex]\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}[/tex]

Therefore, it will take approximately 27.38 years for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.

The requried area of the shaded shape is 5 square millimeters.

From the figure,
The area of the green shaded area is given by:
The area of a single square is given as = 1 * 1 = 1 square millimeters.
Now there is 5 square in the shaded region, So the area is given as:

= 5 * 1 = 5 square millimeters.

Thus, the requried area of the shaded shape is 5 square millimeters.

Learn more about the area here:

https://brainly.com/question/14326675

#SPJ1

The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.

The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.

This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.

Find out more on temperature at https://brainly.com/question/30554883

#SPJ1

The constant term of the polynomial 2x³-5x²+8x+3 is 3.

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, which are combined using addition, subtraction, and multiplication, but not division by a variable.

The variables in a polynomial are typically denoted by x, y, or z, and the coefficients can be constants or other polynomials.

The constant term of a polynomial is the term that doesn't have any variable attached to it. In this case, the constant term is the one that only has a number, which is 3.

Therefore, the constant term of the polynomial 2x³-5x²+8x+3 is 3.

To know more about polynomials follow

https://brainly.com/question/29804635

#SPJ1

The length of gateleg of the table whose leg swings from one corner of the table to the middle of the far side of the table top is 53 inches long.

The shape forms a trapezoid

The length of the parallel side = is 56 in

The length of the base = is 45 in

To the length of the triangle formed  when the base of the gateleg is connected with the middle of the table

The length of the side when connected with the midpoint = 56/2 = 28

The length of gateleg = hypotenuse

Using Pythagorean theorem :

(hypotenuse)² = (base)² + (perpendicular)²

(hypotenuse)² = (45)² + (28)²

(hypotenuse)² = 2025 + 784

(hypotenuse)² = 2809

hypotenuse = 53

Know more about length click here :

https://brainly.com/question/9461061

#SPJ1

The question is incomplete the complete question is :

Philippa has a gateleg table in her kitchen. The leg swings from one corner of the table to the middle of the far side of the tabletop, as shown in the sketch below.

Note: The figure is not drawn to scale.

How long is the gateleg of the table?

A.) 53 inches

B.) 49 inches

C.) 73 inches

D.) 72 inches

Answer:

61 principals

Step-by-step explanation:

189 total - 128 teachers = 61 principals

The area of the composite shape is 125units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A composite shape can be defines as a shape created with two or more basic shapes.

The composite shape can be divided into 2 equal squares and a rectangles.

Area of the square = l²

= 5× 5 = 25

For two squares it will be;

25 × 2

= 50 units²

area of the rectangle = l× w

where w is the width

A = 15 × 5

= 75 units²

Therefore the area of the composite shape = 50 + 75 = 125 units²

learn more about area of composite shapes from

https://brainly.com/question/25965491

#SPJ1

The length of a side of the square garden is 5.75 feet.

(x+10)(x+5) - x² + (x+13)(x+8) - x² = 700

Simplifying and solving for x, we get:

2x^2 + 46x - 177 = 0

Using the quadratic formula, we can solve for x:

x = (-46 ± ✓46² - 4(2)(-177))) / (2(2))

x = (-46 ± 26) / 4

x = 5.75

The length of a side of the square garden is 5.75 feet.

Learn more about length on

https://brainly.com/question/28108430

#SPJ1

For the "regression-line",  Ŷ = -6 + 0.41(X), the predicted value,

(a) when X=25 is 4.25,

(b) when X=50 is 14.50,

(c) when X=75 is 24.75.

The "Regression-Line", is Ŷ = -6 + 0.41(X), we can make predictions for the value of Y (the dependent variable) for different values of X (the independent variable).

(a) To predict the value of "Y" when X = 25, we substitute 25 into the regression line equation:

Ŷ = -6 + 0.41(25)

Ŷ = -6 + 10.25

Ŷ = 4.25

So, the predicted value of Y when X = 25 is 4.25.

(b) To predict the value of Y when X = 50, we substitute 50 into the regression line equation:

Ŷ = -6 + 0.41(50)

Ŷ = -6 + 20.50

Ŷ = 14.50

So, the predicted value of Y when X = 50 is 14.50.

(c) To predict the value of Y when X = 75, we substitute 75 into the regression line equation:

Ŷ = -6 + 0.41(75)

Ŷ = -6 + 30.75

Ŷ = 24.75

So, the "predicted-value" of Y when X = 75 is 24.75.

Learn more about Regression Line here

https://brainly.com/question/29753986

#SPJ1

Step-by-step explanation:

There are   pi radians in 180 degrees

  you want   1/4 of 180 degrees   (45/180 = 1/4)  

    so this would be   1/4 pi radians  or   pi / 4   radians

45 *   pi / 180 = pi/4  

Answer:

147

Step-by-step explanation:

V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188

Answer:

7, 14

Step-by-step explanation:

Look at the first column of numbers: 2.8 m in 2 min.

We can get a unit rate from those numbers:

2.8 m / 2 min = 1.4 m/min

He walks at a rate of 1.4 m/min

Now multiply the unit rate by each number of minutes to find the number of meter.

Let's do the second column as a check: time = 3 min

1.4 m/min × 3 min = 4.2 m

4.2 m is the number on the table, so our unti rate is correct.

5 min:

1/4 m/min × 5 min = 7 m

10 min:

1.4 m/min × 10 min = 14 m

Okay, here are the steps to solve this problem:

Fixed costs per month: $1121

Variable cost per gallon: $7.50

Selling price per gallon: $9.00

Monthly sales (gallons): 1494

Cost of goods sold = Variable cost per gallon * Monthly sales

= $7.50 * 1494 gallons

= $11,105

Gross margin = Revenue - Cost of goods sold

= $9 * 1494 gallons

= $13,446

- $11,105 (Cost of goods sold)

= $2,341

Margin of profit = Gross margin - Fixed costs

= $2,341 - $1121

= $1,220

So the margin of profit if 1494 gallons are produced and sold each month is $1,220.

The answer is:

B $1,220

If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.

In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;

where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;

Substituting the values,

We get;

⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;

Simplifying this expression,

We get;

⇒ P = (111.3 million) × (1.0078)³⁷;

⇒ P ≈ 148.37 million;

Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.

Learn more about Growth Rate here

https://brainly.com/question/29203229

#SPJ1