The sum of a daughter and mother's age is 55. The age of the daughter is the
mother's age reversed. Find the age of the daughter if the age of the mother is
greater than 40 years.

Answer:

  (x -1)(x -5)

Step-by-step explanation:

We recognize that 6 is the sum of the factors of 1·5, so we can write the factorization as ...

  x^2 -6x +5 = (x -1)(x -5)

_____

The product of factors will be ...

  (x +a)(x +b) = x^2 +(a+b)x +ab

So, the binomial constants "a" and "b" are factors of the trinomial constant that have a sum equal to the coefficient of the linear term. Here, those are factors of +5 that have a sum of -6. The factors of interest are -1 and -5: 5 = (-1)(-5); -6 = (-1) +(-5).

Answer:

To solve this quadratic equation, take the square root of both sides.

Since the left side is a perfect square, it will just be reduced to:

4y - 3

For the constant on the right side, the positive and negative roots must be considered.

√72 = ±6√2

Equating the two:

4y - 3 = ±6√2

4y = 3 ± 6√2

y = (3 ± 6√2)/4

y = (3 + 6√2) / 4 = 2.87

and

y = (3 - 6√2) / 4 = -1.37

Answer:

whats the question i will edit it with the right answer

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

substitute x=-2 and y=6, we know

8×6 +4×(-2) -(2×(-2) +3) = 48-8-(-1) =41

Answer:

41

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

8y + 4x - (2x + 3)

x = -2

y = 6

Step 2: Evaluate

Answer:

A circle has a circumference of 113.04What is the diameter of the circle?so do 113.04 and divide it by 3.14 and youget 36 units.

Answer:

a. shown below

b. 9x+14

Step-by-step explanation:

a. (on the bottom)

b. (3x+7)(3x+2)

multiply the terms:

9x+14

thats the area

Answer:

Pythagorean Theorem says B would be 36

The amount that would be in the account when Alana is 21  is $2890

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

Learn more about simple interest at: https://brainly.com/question/20690803

#SPJ1

Square Area = side x side = 3x3 = 9

Rectangle Area = side x side= 7x3= 21

9 + 21 = 30 square inches

Answer:

30 square inches

Step-by-step explanation:

   \(\boxed{\text{\bf Area of rectangle = length *width}}\)

Rectangle1:

     Area = 6 * 3

              = 18 square inches

Rectangle2:

Area = 4 * 3

          = 12 square inches

Area of the figure = area of rectangle1 + area of rectangle2

                             = 18 + 12

                             = 30 square inches

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.

The area of each triangle is 200 square inches.

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.

We have,

The area of a right triangle is given by:

= 1/2 x base x height

We have from the figure,

Base = 20 inches

Height = 20 inches

Area = 1/2 x 20 x 20

Area = 10 x 20

Area = 200 square inches

Thus the area of each triangle is 200 square inches.

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ1

The complete question is:

You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches?

A. 200 square inches

B. 400 square inches

C. 570 square inches

D. 2,800 square inches

E. 5,600 square inches

The length of the arc on a circle of mentioned radius intercepted by the central angle is 3π feet.

The formula to calculate the arc angle from radius and central angle is simply by finding their product. The formula for arc length is -

S = r×theta, where r is radius and theta is the central angle

Now we are given angle in degree and we need to convert it in radian. So the formula is -

Central angle = 60 × π/180

Central angle = π/3 radians

Keep the values in formula

S = 9 × π/3

Performing division

S = 3π

Thus, the arc length is 3π.

Learn more about arc -

https://brainly.com/question/2005046

#SPJ4

Gender is categorical nominal, end-of-the-year stock classification is categorical and ordinal, and distance is quantitative and ratio.

Quantitative variables are measured with numbers. Some examples include:

Weight measured in kilos

The distance measured in meters or kilometers

Time measured in seconds or hours

On the other hand, a categorical variable is defined by features, categories, or concepts rather than numbers. Here is an example:

Breeds of dogs: Poodles, Boston Terriers, German shepherds, etc.

Moreover, variables can be classified as:

Learn more about ordinal and nominal in: https://brainly.com/question/13168982

#SPJ1

Answer:

B. y = –2.9x + 13.5

Step-by-step explanation:

You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is

y = a + bx, where a is the y intercept and b is the slope.

To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.

x    y    xy    x²  

1  .  11 = 11 → x² = 1² = 1

2 .  8 = 16 → x² = 2² = 4

3 .  4 = 12 → x² = 3² = 9

4 .  1 = 4 → x² = 4² = 16

5 .  0 = 0 → x² = 5² = 25

Total x = 1 + 2 + 3 + 4 + 5 = 15

Total y = 11 + 8 + 4+ 1 + 0 = 24

Sum of xy = 11 + 16 + 12 + 4 + 0 = 43

Sum of x² =  1 + 4 + 9 + 16 + 25 = 55

n = 5

So b =  5 (43) - (15) . (24) / 5 (55) - 15² = -2.9

a =  y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5

Answer:

n = -24/7

Step-by-step explanation:

3 -7n = 27

-7n = 24         Subtract 3 from both sides

n = -24/7        Divided by -7 both sides

So, the answer is n = -24/7

Answer:

Below

Step-by-step explanation:

Subtract 3 from both sides of the equation THEN divide both sides of the equation by  - 7

Answer:

$2.16

Step-by-step explanation:

The rate is \(\frac{6.48}{3} \\\).

Divide it to get one box:

6.48 ÷ 3 = 2.16

Therefore, one box of hot chocolate mix costs $2.16.

The birth rate in units of births per minute is approximately 5.327.

The approximate number of births in a country per year is 2.8 million. We need to find the birth rate in units of births per minute. We need to convert the units. We will first convert years to into days. There are 1*365 = 365 days in a year. Now we will convert days into hours. There are 365*24 = 8,760 hours in a year. Now we will convert hours into minutes. There are 8,760*60 = 525,600 minutes in a year. Now, to find the rate of births per minute, we will calculate the ratio of the total number of births in a year to the number of minutes in a year.

R = 2,800,000/525,600 = 5.327

To learn more about rate, visit :

brainly.com/question/12786410

#SPJ9

Answer:

-7.69%

Step-by-step explanation:

Answer:

Step-by-step explanation:

a = 5

b = 15

c = ?

c^2 = a^2 + b^2

c^2 = 5^2 + 15^2

c^2 = 25 + 125

c^2 = 250

sqrt(c^2) = sqrt(250)

c = sqrt(250)

Scale factor back to original size = 1/7

        7x and 7 years.

This means the original size will be;

Length = 7x × 1/7

Width = 7y × 1/7

Hence, the scale factor will be 1/7 back to the original size.

Learn more about transformation of objects here

https://brainly.com/question/17292295

#SPJ9

The length of the hypotenuse is 10.61 yd.

We have,

The sum of the angles in a triangle = 180

Now,

Two angles are 45.

This means,

The side opposite to angle 45 are equal.

So,

a = c

And,

a = 7.5 yd

Now,

Applying the Pythagorean theorem.

b² = a² + c²

b² = 7.5² + 7.5²

b² = 112.5

b = √112.5

b = 10.61

Thus,

The length of the hypotenuse is 10.61 yd.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

Answer:

y - 8 = 3(x - 6)

Step-by-step explanation:

Point slope-equation formula:

y - y1 = m(x - x1)

y - 8 = 3(x - 6)

The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

Know more about circle here: https://brainly.com/question/20489969

#SPJ1

Answer:

$6.45/hour

110.26%

Step-by-step explanation:

The absolute change is the difference between salaries now ands then.

12.30 - 5.85 = 6.45

The relative change in the percent increase.

percent increase = (new number - old number)/(old number) × 100%

percent increase = (12.3 - 5.85)/(5.85) × 100%

percent increase = 110.26%

Check the picture below.

Answer:

6

Step-by-step explanation:

The two triangles are similar which means the the two length is parallel

.°., the Length of the smaller triangle=6

To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

For more such question on polar equation

https://brainly.com/question/9363127

#SPJ8

The solution of given system of equations is (1/5, 6).

What is system of equation?

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one with two equations and two variables. Linear equations are simpler than non-linear equations because they graph as straight lines.

Given equations : 5x+y=7

                             20x+2=y

We can solve it by using substitution method:

Now, we have 5x+y=7

it can be written as,

         y = 7 - 5x .... equation 1

Similarly, we have 20x+2=y

can be written as,

           y = 20x+2 ..... equation 2

Subtracting equation 1 from equation 2

we get,  20x+2 - ( 7 - 5x ) = 0

             20x + 5x + 2 - 7 = 0

             25x = 5

               x = 1/5

Putting x=1/5 in equation 1,

we get, y = 20 × 1/5 + 2

               = 4 +2

               = 6

To learn more about System of equation, visit the ink:

https://brainly.com/question/13729904

#SPJ1

Answer:

one is 2 and another is 7

Step-by-step explanation:

let n be the positive integer and n' be the greater integer.

Given condition

n+5=n' ......eqn i

n×n'=14

n(n+5)=14. [from equation i]

n²+5n-14=0

n²+7n-2n-14=0

(n-2)(n+7)=0

either. or

n=2. n=-7(impossible)

therefore n=2 and hence n'=n+5=7.

Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

Answer:

-134

Step-by-step explanation: