is this statement true sometimes always or never ??

The formula for the function f(x): (x-  k)q(x) + r for the specified value of k. F(x) = x3 − x2 − 10x + 5, k = 3 is f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5).

To write the function in form f(x) = (x − k)q(x) + r, we need to divide the given polynomial by (x-k) using long division. Here's the long division process:

           [tex]x^2[/tex] + 2x - 1

   ----------------------

x - 3 | [tex]x^3[/tex] - [tex]x^2[/tex] - 10x + 5

       - [tex]x^3[/tex] + [tex]3x^2[/tex]

       ---------------

            - [tex]2x^2[/tex] - 10x

            + [tex]2x^2[/tex] - 6x

            ------------

                    - 4x + 5

Therefore, we have:

f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5)

Thus, the function with the formula f(x)= (x-k)q(x) + r for k= 3 is:

f(x) = (x - 3)([tex]x^2[/tex] + 2x - 1) - (4x - 5)

To learn more about function, refer:-

https://brainly.com/question/30721594

#SPJ4

Answer:

429

Step-by-step explanation:

60 tablets of the multivitamin, with 17g (17,000mg) of vitamin C per tablet, contains 1,020,000mg of vitamin C in total.

If one tablet of the multivitamin contains 17g of vitamin C, then 60 tablets would contain 60 times that amount:

60 tablets x 17g of vitamin C per tablet = 1020g of vitamin C

However, it is more common to express vitamin C (and other nutrients) in milligrams (mg) rather than grams (g). To convert from grams to milligrams, we can multiply by 1000:

1020g of vitamin C x 1000 mg/g = 1,020,000 mg of vitamin C

Therefore, 60 tablets of the multivitamin contain 1,020,000 mg of vitamin C.

Just to clarify, in the answer above, I made a mistake in the units. 17g is actually 17,000mg, not 17mg. So the correct calculation is:

If one tablet of the multivitamin contains 17,000mg of vitamin C, then 60 tablets would contain 60 times that amount:

60 tablets x 17,000mg of vitamin C per tablet = 1,020,000mg of vitamin C

Therefore, 60 tablets of the multivitamin contain 1,020,000mg of vitamin C.

Learn more about milligrams here:

https://brainly.com/question/29827935

#SPJ4

Answer: 1/6 x  3,  1/6 of 3

Step-by-step explanation: i did this in iready one time and got it write :))))))

have a great day/night or whatever ididdkk

Each girl will receive the ratio of Girl 1: R2000, Girl 2: R3000 Girl 3: R7000

To find out how much each girl will get, we need to first add up the ratios:

2 + 3 + 7 = 12

Then, we can divide the total amount of money by the total ratio:

12000 ÷ 12 = 1000

This means that each "part" of the ratio is worth R1000.

To calculate how much each girl will get, we need to multiply their respective ratios by R1000:

Girl 1: 2 parts x R1000/part = R2000

Girl 2: 3 parts x R1000/part = R3000

Girl 3: 7 parts x R1000/part = R7000

To learn more about Ratio :

https://brainly.com/question/12024093

#SPJ4

The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

The formula for the volume of a cylinder is [tex]V = \pi r^2h,[/tex] where V is the volume, r is the radius, and h is the height.

Let's assume that the cone and cylinder have a radius of 'r' and a height of 'h'.

The volume of the cylinder is given by [tex]= \pi r^2h.[/tex]

The volume of the cone is given by V_cone = [tex](1/3)\pi r^2h.[/tex]

Since the cone and cylinder have the same base and height, their radius and height are the same.

Therefore, we can simplify the volumes as V_cylinder = [tex]\pi r^2h[/tex] and V_cone = [tex](1/3)\pi r^2h.[/tex]

The ratio of the volume of the cone to the volume of the cylinder is then:

V_cone/V_cylinder = [tex]((1/3)\pi r^2h) / (\pi r^2h) = (1/3) / 1 = 1/3[/tex]

So, the volume of the cone is one-third of the volume of the cylinder.

Alternatively, we can write this as the ratio of the volume of the cone to the volume of the cylinder being 1:2, since the volume of the cylinder is twice the volume of the cone.

Therefore,The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

To learn more about the volume of the cylinder visit:

brainly.com/question/6204273

#SPJ1o

The reciprocal of the complex number [tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}[/tex] is determined as  [tex]\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}.[/tex]

To find the reciprocal of a complex number, we need to divide 1 by the complex number. We can simplify the division by multiplying the numerator and denominator by the complex conjugate of the denominator.

The complex conjugate of

[tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}= \frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}[/tex]

So, the reciprocal of the complex number is:

[tex]\begin{aligned} \frac{1}{\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}} &= \frac{1}{\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}} \cdot \frac{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}}{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}} \ &= \frac{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}}{\frac{2}{2}} \ &= \frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2} \end{aligned}[/tex]

Therefore, the reciprocal of the complex number;

[tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}[/tex] is [tex]\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}.[/tex]

Learn more about reciprocal of complex numbers here: https://brainly.com/question/29441809

#SPJ1

As the density of Mercury is higher than that of both Copper and Zinc, so both the new & old penny will float on mercury.

By dividing the object's mass by its volume, we may determine the density of metal.

Mass/volume equals density.

For ex, the object would have a density of 0.284 per cubic inch if its mass were 7.952 pounds and its volume were 28 cubic inches.

Now here in the given question,

Density of copper = 8.8g/cm³

Density of zinc = 7.2g/cm³

Here, both the densities are lesser than that of mercury.

Hence, both the metal pennies will float when dropped into a beaker of mercury.

To know more about density, visit:

https://brainly.com/question/29775886

#SPJ1

Linda traveled faster than Imani because when t =1 , linda traveled 65 miles and Imani traveled 60 miles and linda travelled at a faster rate because when t=0,

She travelled 10 miles and Imani travelled 0 miles these are cοrrect answer. The prοvided graph's cοοrdinates are (2, 120) and (4, 240).

A graph is a structure that amοunts tο a set οf items where sοme pairs οf the οbjects are in sοme manner "cοnnected" in discrete mathematics, mοre specifically in graph theοry. The items are represented by mathematical abstractiοns knοwn as vertices (sοmetimes knοwn as nοdes οr pοints), and each pair οf cοnnected vertices is knοwn as an edge. Generally, a graph is represented diagrammatically as a cοllectiοn οf dοts οr circles fοr the vertices cοnnected by lines οr curves fοr the edges. Graphs are οne οf the tοpics studied in discrete mathematics.

Slοpe with (2, 120) and (4, 240) is

Slοpe (y2-y1)/(x2-x1)

= (240-120)/(4-2)

= 120/2

= 60

Put m=60 and (x, y)=(2, 120) in y=mx+c, we get

120=60(2)+c

c=0

Sο, equatiοn is y=60x

Put x=0, 1, 2, 3 and 4, we get

y= 0, 60, 120, 180, 240

(0, 0), (1, 60), (2, 120), (3, 180) and (4, 240)

To learn more about graph from the given link

https://brainly.com/question/19040584

#SPJ1

The true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.

Calculation of a 95% two-sided confidence interval for standard deviation of resistance, σ95% two-sided confidence interval for standard deviation of resistance is given by:\[\left(\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.025,n-1}^2}},\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.975,n-1}^2}}\right)\]where s = 0.194 Ω, n = 15, and Χ² distribution with df = 14 at α = 0.05/2 = 0.025/0.975The range of the 95% two-sided confidence interval for the standard deviation of resistance is given as follows:95% two-sided confidence interval for standard deviation of resistance = (0.12, 0.3757)Hence, the 95% two-sided confidence interval for the standard deviation of resistance is given as (0.12, 0.3757).b) Explanation:The standard deviation of the resistance is believed to be 0.12 Ω. From the 95% confidence interval obtained in part (a), 0.12 Ω is not within the 95% confidence interval. This means it is not reasonable to believe that the standard deviation of all resistors produced is 0.12 Ω. Since the true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.

Learn more about Standard deviation

brainly.com/question/23907081

#SPJ11

The answer is 3.18.

The given equation is sin(4x)cos(6x) − cos(4x)sin(6x) = -0.9. To find the smallest positive solution, we can use the following identities: sin(A + B) = sinAcosB + cosAsinBcos(A + B) = cosAcosB - sinAsinBWe can rewrite the given equation using these identities as follows:sin(4x + 6x) = -0.9sin(10x) = -0.9sinx = -0.09We need to solve for the smallest positive value of x. To do this, we can find the value of x in the interval [0, 2π] such that sinx = -0.09.Using a calculator, we get:x ≈ 3.176 rad ≈ 181.97°The smallest positive solution in degrees is 181.97°. To get the answer to 2 decimal places, we can round off the value of x to 2 decimal places, giving:smallest positive solution ≈ 3.18 rad (to 2 decimal places) or ≈ 181.97° (to 2 decimal places)Thus, the answer is 3.18.

Learn more about Equation

brainly.com/question/29657992

#SPJ4

The multiplication problem that matches the model is: 5 * 1/2

A representation is a way of showing multiplication.  A model for multiplication is slightly more sophisticated and it is comprised of several related representations that all have the same structure. There are two models for multiplication  namely repeated addition and arrays.

From the attached file, we see that there are 5 images. Now, each image depicts a triangle that is shaded in half.

Thus, it means that each triangle represents the fraction 1/2.

Thus, the model will be expressed as a multiplication model as;

5 * 1/2

Read more about Multiplication Model at; https://brainly.com/question/10873737

#SPJ1

Answer:

(x-6)(x-2)

Step-by-step explanation:

To factor, we use the quadratic formula, which gives us the roots of the equation. In an equation as ax²+ bx + c, we can use (-b±√(b^2-4ac))/2a. Since we have x² - 8x +12, a will be 1, b will be -8, and c will be 12.

(-(-8)±√((-8)²-4(1)(12))/2(1)

(8±√(64-48)/2

(8±√16)/2

(8±4)/2

We now have two cases: (8+4)/2 and (8-4)/2. We can solve these:

(8+4)/2 = 12/2 = 6

(8-4)/2 = 4/2 = 2

Since we have to factor this, we have to write it in the form of

(x-z)(x-y)

for z, we have 6, and for y, we have 2

(x-6)(x-2) is our final answer.

If you liked this answer, please mark brainiest!

composite shape

becuse thats what its called

Answer:5/2=2.5

Step-by-step explanation:

[tex]\sqrt{27}=\sqrt{3^{3}}=3^\frac{3}{2}\\\\we \ can \ show \ \sqrt{3^{3}} \ as \ 3^\frac{3}{2}\\3^{1}*3{\frac{3}{2}}=3^{1+\frac{3}{2}}=3^{\frac{5}{2}}\\n=\frac{5}{2}[/tex]

Answer:

[tex]n=\dfrac{5}{2}[/tex]

Step-by-step explanation:

Rewrite 27 as the product of prime numbers:

[tex]\implies 27 = 3 \cdot 3 \cdot 3 = 3^3[/tex]

Therefore, replace 27 with 3³ in the given equation:

[tex]\implies 3 \times \sqrt{3^3}=3^n[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]

[tex]\implies 3 \times 3^{\frac{3}{2}}=3^n[/tex]

[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 3^1 \times 3^{\frac{3}{2}}=3^n[/tex]

[tex]\implies 3^{1 +\frac{3}{2}}=3^n[/tex]

[tex]\implies 3^{\frac{2}{2} +\frac{3}{2}}=3^n[/tex]

[tex]\implies 3^{\frac{5}{2}}=3^n[/tex]

[tex]\textsf{Apply the exponent rule:} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies \dfrac{5}{2}=n[/tex]

Therefore, the value of n is 5/2.

Answer:

4.5 m^3

Step-by-step explanation:

Volume = length × breadth × height

= 5m × 1.2m ×(75÷100)m

= 4.5 m^3

Therefore , the solution of the given problem of percentage comes out to be down payment is 32% of the overall cost of the vehicle.

In statistics, a% is a number or value that is expressed as a fraction of 100. The terms "pct.," "pct.," but also "pc" are also infrequently used. Nevertheless, the symbol "%" is frequently used to indicate it. The percentage sum is flat; there are no dimensions. Since the numerator of a percentage is always 100, percentages truly constitute integers. Either the percent symbol (%) or the word "percent" must come before a number to denote that it is a percentage.

Here,

Levi Hempke wishes to borrow a maximum of $14,280 to finance a $21,000 vehicle. Consequently, he intends to put down:

=> $21,000 - $14,280 = $6,720

We must divide his down payment by the total cost of the car, multiply by 100 to convert to a percentage, and

then determine the percentage of the total cost of the car that he should put down:

=>  ($6,720 ÷ $21,000) × 100 = 32%

Levi's down payment should therefore equal 32% of the overall cost of the vehicle.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

Therefore, the area of the composite figure is 65 square centimeters. Therefore, the area of the composite figure is approximately 150.8 square centimeters.

In mathematics, the area is the measure of the size of a two-dimensional surface or shape. It is the amount of space inside the boundary of a flat object, such as a triangle, rectangle, circle, or any other polygon. The standard unit of measurement for area is square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). To calculate the area of a shape, we usually use a formula that depends on the shape's geometry and dimensions, such as its length, width, radius, or height. Area has many applications in everyday life, such as calculating the size of a room, the amount of paint needed to cover a wall, or the area of land required to build a house or grow crops. In mathematics and science, area is also used to solve problems in geometry, physics, engineering, and other fields.

Here,

1. Combination of Square and Rectangle

To find the area of this composite figure, we need to break it down into simpler shapes and add up their areas. The figure consists of a square with sides of 5 cm, a rectangle with sides of 4 cm and 9 cm, and a square with sides of 2 cm.

The area of the square with sides of 5 cm is:

A1 = (side)²

= (5 cm)²

= 25 cm²

The area of the rectangle with sides of 4 cm and 9 cm is:

A2 = length x width

= (9 cm) x (4 cm)

= 36 cm²

The area of the square with sides of 2 cm is:

A3 = (side)²

= (2 cm)²

= 4 cm²

To find the total area of the composite figure, we add up the areas of these three shapes:

A = A1 + A2 + A3

A = 25 cm² + 36 cm² + 4 cm²

A = 65 cm²

To know more about area,

https://brainly.com/question/30106292

#SPJ1

Answer: 3/8

Step-by-step explanation: You have a 1 in 5 chance of pulling an orange.

5/25, or if you need to simplify then 1/5

Answer:

There are 16 ounces in 1 pound, so Brianna bought 2 x 16 = <<2*16=32>>32 ounces of strawberries.

The total cost was 4.80 dollars for 32 ounces.

To find the price per ounce, we divide the total cost by the number of ounces:

4.80 / 32 = 0.15

Therefore, the price of dollars per ounce for strawberries is $0.15.

Step-by-step explanation:

The number of males in the village in 1999 was 1200, given that the male to female ratio was 3:5 and the total population was 2000.

Let's assume that in the year 1999, there were M males and W females living in the village, so the total population would be P = M + W = 2000.

Then, in the year 2004, the male population increased by 10%, so the number of males became 1.1M, and the female population decreased by 6%, so the number of females became 0.94W.

The total population remained unchanged, so we have:

1.1M + 0.94W = P = 2000

We also know that P = M + W, so we can substitute this into the above equation:

1.1M + 0.94W = M + W

0.1M = 0.06W

M/W = 3/5

So the ratio of males to females in the village in 1999 was 3:5. Therefore, we can write:

M + W = 2000

3/5 (M + W) = 3/5 (2000)

M = 1200

Therefore, there were 1200 males living in the village in the year 1999.

We can check that this answer is consistent with the information given in the problem. In 1999, there were 2000 people in the village, and the ratio of males to females was 3:5. This means that the number of males is 3/8 of the total population, and the number of females is 5/8 of the total population:

Number of males = 3/8 x 2000 = 750

Number of females = 5/8 x 2000 = 1250

Now let's apply the changes that occurred between 1999 and 2004. The male population increased by 10%, so the new number of males is:

1.1 x 750 = 825

The female population decreased by 6%, so the new number of females is:

0.94 x 1250 = 1175

The total population is:

825 + 1175 = 2000

So the total population remained unchanged, as required by the problem statement. Therefore, our answer of 1200 males in 1999 is consistent with the information given in the problem.

Learn more about ratio here:

https://brainly.com/question/1504221

#SPJ4

The formulas will calculate the average profitability for customers with income < 40,000 and those with income >= 40,000 respectively.

The first step towards completing the given analysis is to create two groups of customers based on their income levels. The groups should consist of customers with income < 40,000 and those with income > = 40,000. The detailed explanation is provided below:Step-by-step explanation:Here, we need to compare the average profitability of two groups of customers based on their income levels, one with income less than 40,000 and the other with income greater than or equal to 40,000.The first step towards completing this analysis is to create two groups of customers based on their income levels. The groups should consist of customers with income < 40,000 and those with income > = 40,000. This can be achieved using the following steps:1. Open a new Excel workbook and import the dataset that needs to be analyzed.2. Once the data is imported, create a new column named 'Income Group' that will classify customers into the two groups based on their income level. To do this, we can use the following formula: =IF(B2<40000,"<40,000",">=40,000")Here, B2 is the cell that contains the income value of the first customer.3. Drag the formula down to the last cell in the column to apply it to all customers. This will create two groups of customers based on their income levels.4. Now, we need to calculate the average profitability of each group. To do this, we can use the following formula: =AVERAGEIF(C2:C11,"<40,000",D2:D11) and =AVERAGEIF(C2:C11,">=40,000",D2:D11)Here, C2:C11 contains the income group values, D2:D11 contains the profitability values, and "<40,000" and ">=40,000" are the criteria for each group. These formulas will calculate the average profitability for customers with income < 40,000 and those with income >= 40,000 respectively.

Learn more about Average

brainly.com/question/24057012

#SPJ4

Answer: V(t) = 5000 * (1.07)^t

Step-by-step explanation:

Los dos números que multiplicados den 30 son 5 y 6. Para encontrar dos números que sumados o restados den -11, debemos verificar todas las posibles combinaciones. Al hacerlo, descubrimos que -5 y -6 sumados dan -11. Por lo tanto, los dos números son 5 y -6.

Answer:

If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate. Expert Answer.

1 answer

·

Top answer:

Given that P=1,250A=1,406.08n=9 month

Step-by-step explanation:

Answer:

Area = π*r^2

Area = 113.1 units^2

Step-by-step explanation:

The figure drawn is a circle.  The ancient Greeks devised an approximation of the area of circles by dividing the circle into a series of small triangles with their peaks at the center of the circle and their bases  are formed by the curve of the circle.  Although this means there is an error because the circumference is not a straight line, they made the triangles small enough so that the error would be minimized.  They found that the area of the circle was related to it's radius by the expression: Area = π*r^2.  

Without retracing their steps, let's simply use the formula that is now the accepted measure of the area of a circle.  Pi (π) is 3.14 to 3 decimal places.  Far more accurate values are known, but 3.14 offers reasonable accuracy, assuming this is not intended for space flight.

Area = π*r^2

Area = 3.34*(6)^2

Area = 113.1 units^2