The product of two consecutive numbers exceeds the square
of the smaller number by 20. Find the two numbers.

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Answer:

Sometimes.

Step-by-step explanation:

For example 1/2 / 1/4 = 2

but 1/4 / 1/2 = 1/2.

Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

\(x=\frac{18}{7}\)

Step-by-step explanation:

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20..

To estimate the value of the vehicle after 4 years, we can use the given equation A = 39500(0.86)^t, where A represents the value of the vehicle and t represents the number of years.

Substituting t = 4 into the equation:

A = 39500(0.86)^4

A ≈ 39500(0.5996)

A ≈ 23726.20

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20.

This estimation is based on the assumption that the vehicle's value decreases by 14% each year. The equation A = 39500(0.86)^t models the exponential decay of the vehicle's value over time. By raising the decay factor of 0.86 to the power of 4, we account for the 4-year period. The final result suggests that the value of the vehicle would be around $23,726.20 after 4 years of ownership.

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

he went $9.56 over

Step-by-step explanation:

Answer: 36, because 18 is not a miltiple of four, and 27 is only a multiply of nine. Although 72 is a multiple of 2, 4, and 9, it’s not the least common multiple. The LCM of 2, 4, and 9 is 36.

The completed calculation with regards to the area of the congruent triangles can be presented as follows;

The distance formula indicates;

AM = √((x₂ - x₁)² + (y₂ - y₁)²)

Therefore, we get;

AM = √((4 - 0)² + (0 - 0)²) = √(4²)

AM = √(4²) = 4

BM = √((x₂ - x₁)² + (y₂ - y₁)²)

BM = √((4 - 4)² + (6 - 0)²) = √(6²)

BM = √(6²) = 6

AM ≅ CM Definition of the midpoint of AC

AM = CM Definition of congruent segments

CM = 4 Substitution property

Area ΔABM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Area ΔCBM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Therefore Area ΔABM = area ΔCBM by congruence

Triangles are congruent if they have the same size and shape.

The details of the reasons for the calculation steps and values are presented as follows;

Definition of midpoint of a segment

The midpoint of a line segment is the point that divides the segment into two parts of the same length

Definition of congruence?

Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement

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there isn't really any specification for any of the questions but you can find volume of a pyramid on g00gle

Answer:

x= 3±sqrt(15)

Step-by-step explanation:

x^2 -6x = 6

Take the coefficient of x

-6

Divide by 2

-6/2 = -3

Square it

(-3)^2 = 9

Add this to each side

x^2 -6x+9 = 6+9

(x-3)^2 = 15

Take the square root of each side

sqrt((x-3)^2) = ±sqrt(15)

x-3 = ±sqrt(15)

Add 3 to each side

x-3+3 = 3±sqrt(15)

x= 3±sqrt(15)

Simplify the inequality and then check which of those values is included in the solution set:

From the options -1, 2,7 and 3, the only number which is less tan 2 is -1.

Therefore, the only value below included in the solution set is:

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

simplifying this expression (√8^4 × √6^4)^3/2 = 110592

so 2^12 ×3^3= 110592

similar 2^9 ×6^3 =110592

The question represents a binomial distribution.

The binomial probability formula is calculated using the formula:

where

P = binomial probability

X = number of times for a specific outcome within n trials

n C x = number of combinations

p = probability of success on a single trial

n = number of trials

From the question, we have the following parameters:

We are to evaluate the probability that more than 5 and less than 9, hence:

At X = 7:

At X = 8:

Therefore, the probability will be:

Answer:

The answer is G = (4,3)

Step-by-step explanation:

G = (4,3)

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

c = -2.5

Step-by-step explanation:

13/4 + c =3/4

2.5 + c = 0

c=-2.5

The first question have the unknown sides a = 12.29 and b = 275. 84 approximately to 2 decimal place using the trigonometric ratio of cosine the the angles 35° and 25° for the respective right triangles.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios are: sine cosine and tangent.

cos 35° = a/15 {adjacent/hypotenuse}

a = 15 × cos 35° {cross multiplication}

a = 12.2873

cos 25° = 250/b {adjacent/hypotenuse}

b = 250/cos 25° {cross multiplication}

b= 274.8445

Therefore, the unknown lengths a is equal to 12.29 and b is equal to 275.84 approximately to 2 decimal place for the respective right triangles using the trigonometric ratio of cosine for angles 35° and 25°.

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Answer:

- 1 1/3 degree

Step-by-step explanation:

- 16 / 12

Answer:

\(Area = 65.94\)

Step-by-step explanation:

I will assume that the shaded region is the fire pit

Given

\(R = 5\)

\(r = 2\)

Required

Determine the area of the fire pit

First, calculate the area of the big circle.

\(A_2 = \pi R^2\)

Area of the small is:

\(A_1 = \pi r^2\)

The area of the pit is:

\(Area = A_2 - A_1\)

\(Area = \pi R^2 - \pi r^2\)

\(Area = \pi (R^2 - r^2)\)

\(Area = 3.14 (5^2 - 2^2)\)

\(Area = 3.14 (25 - 4)\)

\(Area = 3.14 * 21\)

\(Area = 65.94\)

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

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Answer:

2/3

Step-by-step explanation:

y = xk

6 = 72K  Solve for k  Divide both sides by 72

\(\frac{1}{12}\) = k

y = xk

y = \(\frac{8}{1}\) x \(\frac{1}{12}\)

y = \(\frac{8}{12}\)  I can simplify by dividing the numerator and denominator by 4

y = 2/3

Answer:

x=37 and scalene or right triangle

Step-by-step explanation:

Answer:

37°

Step-by-step explanation:

Any Triangle his total angles = 180

then: 53 + 90 + X = 180

then: X= 180 - (90+53)

= 37

Answer:

32

Step-by-step explanation:

Step 1:

24 : 45 = x : 60

Step 2:

45x = 1440

Answer:

x = 32

Hope This Helps :)

The number of the cabinet doors machine will paint is 32.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that machine can paint 24 cabinet doors in 45 minutes. The number of cabinets painted in 1 hour will be calculated as below:-

24 : 45 = x : 60

45x = 1440

x = 32

Therefore, the number of the cabinet doors machine will paint is 32.

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The solution to the expression is 33/16

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

Convert 11/8 into 2/3​

The above statement means that we divide 11/8 by 2/3

Using the above as a guide, we have the following:

So, we have

11/8 divides 2/3

Express as product

11/8 * 3/2

Evaluate the product

33/16

Hence. the solution is 33/16

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Answer:

  D.  2x -y = 2

Step-by-step explanation:

You want to know the standard-form equation of the line through points (-1, 4) and (2, 2) as shown on the graph.

The graph shows the x-intercept of the line is a=1, and the y-intercept of the line is b=-2. This means the intercept form of the equation is ...

  x/a +y/b = 1

  x/1 +y/(-2) = 1

Multiplying this equation by 2 gives ...

  2x -y = 2 . . . . the standard form equation for the line

__

Additional comment

The standard form equation can also be developed from the coordinates of points on the line:

  (y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1

  (2 -(-4))x -(2 -(-1))y = (2 -(-4))(-1) -(2 -(-1))(-4)

  6x -3y = -6 +12

Dividing by 3 gives the standard form equation ...

  2x -y = 2