Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

Answer:

40

Step-by-step explanation:

Let x=how old Myra is.

3x + 10 = x

x + 3x + 10 = 40

4x + 10 = 40

4x = 40 - 10

4x = 30

x = 30/4

x = 7.5

3x + 10= 32.5

x + 3x + 10= 40

7.5 + 32.5 = 40

40 = 40

Answer: 40

Step-by-step explanation:

Answer:

the nearest thousandth is 241.006.

The correct graph that represents the given compound inequality -2x + 5 < 7 and 5x - 4 ≤ 6 is: graph D.

In Mathematics, it is very important for students to note that they do not flip the inequality symbol (sign) when you are solving an inequality by multiplication or division with a positive numerical value (number).

Next, we would simplify each of the compound inequality as follows;

-2x + 5 < 7

Subtracting 5 from both sides of the inequality, we have the following:

-2x + 5 - 5 < 7 - 5

-2x < 2

Dividing both sides of the inequality by -2, we have the following:

-2x/-2 < -2/2

x < -1

Next, we would flip the inequality symbol (sign) because it was divided by a negative numerical value (number);

x > -1

Simplifying 5x - 4 ≤ 6, we have;

5x - 4 + 4 ≤ 6 + 4

5x ≤ 10

x ≤ 10/5

x ≤ 2

Therefore, the compound inequality {x > -1 and x < 2} can be re-written as follows;

-1 < x ≤ 2

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There are 23% more 41+ year olds have a preference for Enterprise Content Management in comparison to 18-25 year olds

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We are given that the table shows the Technology career types for different ages groups.

The 41+ year olds have a preference for Enterprise Content Management = 3215

The percent become

3215 / (3215 + 4673 + 5822) x 100

3215 / (3215 + 4673 + 5822) x 100

3215 / 13710 x 100

23.45

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The description does NOT guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other

A quadrilateral is a four-sided polygon. It is a closed geometric figure with four straight sides and four angles and A rectangle is a four-sided shape with two pairs of parallel, perpendicular sides. Its opposite sides are equal in length and also opposite angles are equal in measurement.

Therefore, the correct answer is as identified. It can be concluded that the one that does not guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other

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Answer:

Below

Step-by-step explanation:

(25380 - 18000) / 18000     * 100% =

7380/18000 * 100 = 41 % increase

The new lengths triangle that is formed after the given dilation is; Height = 4 and base = 2

Dilation is defined as a transformation that is used to resize an object. This means that dilation is used to make the objects larger or smaller. When the objects get larger, it is called an enlargement but when the object becomes smaller, it is called a reduction.

Now, we want to dilate the given triangle by the scale factor 2/3. Since the factor of dilation is less than 1, then we can call it a reduction of shape.

Thus, we multiply each side of the given triangle by 2/3 to get;

Height = 6 * 2/3 = 4

Base = 2/3 * 3 = 2

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Answer:

To compare the length of the plankton to the length of the jellyfish, we can express the length of the plankton as a percentage of the length of the jellyfish.

First, we need to convert the length of the jellyfish from inches to centimeters so that we can compare the two measurements in the same unit.

12 inches = 12*2.54 = 30.48 cm

Next, we divide the length of the plankton by the length of the jellyfish and multiply by 100 to get the percentage.

0.08 inches / 30.48 cm * 100 = 0.00262 * 100 = 0.262%

So, the length of the plankton is 0.262% of the length of the jellyfish.

Answer:

2,506

Step-by-step explanation:

1/5/2023

7:37PM

Answer:

x=7

Step-by-step explanation:

hope this helps :)

The measure of ∠A is 123 degrees.

The angle made between the radius and the tangent at the point of contact on a circle is 90°.  

Therefore,

∠D = 90 degrees

∠E = 90 degrees

The diagram ACDE forms a quadrilateral. The sum of angles in a quadrilateral is 360 degrees.  Therefore, we have to equate the sum of the quadrilateral angles to 360 degrees.

Hence,

90 + 90 + 2x + 7 + 5x - 2 = 360

180 + 7x + 5 = 360

7x = 360 - 180 - 5

7x = 180 - 5

7x = 175

x = 175 / 7

x = 25

Therefore,

∠A = 5(25) - 2 = 125 - 2 = 123 degrees.

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The value of the equation g ( x ) = -x + 4 , when g ( x ) = 0 , is x = 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

g ( x ) = -x + 4   be equation (1)

On simplifying the equation , we get

when g ( x ) = 0

Substitute the values in the equation , we get

0 = -x + 4

Adding x on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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Answer:

y = -8/3x + 8/3

Step-by-step explanation:

(-2, 8) and (1, 0)

m = 0-8/1+2

m = -8/3

y = -8/3x + b

0 = -8/3(1) + b

0 = -8/3 + b

b = 8/3

y = -8/3x + 8/3

The area of a rectangle ABCD is 60 square inches and the area of triangle ACD is 30 square inches.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

In the given rectangle ABCD, AD= 5 in. and DC=12 in.

a) Now, area of rectangle ABCD =DC×AD

= 12×5

= 60 square inches

b) By joining vertices A and C, we get triangle ACD.

c) Now, the area of triangle ADC is

Area =1/2 ×Base×Height

= 1/2 ×12×5

= 30 square inches

Therefore, the area of a rectangle ABCD is 60 square inches.

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Answer:

8 [tex]\frac{2}{3}[/tex] cups of dough

Step-by-step explanation:

2/3 cup for every dumpling

13 dumplings

x = dough

x = 2/3 * 13

x = 26/3

x = 8 [tex]\frac{2}{3}[/tex] = 8.667

Answer:

  x ≈ 8.9

Step-by-step explanation:

You want the value of x in the diagram showing two right triangles.

The Pythagorean theorem tells you the relationship between legs 'a' and 'b' and hypotenuse 'c' in a right triangle is ...

  a² +b² = c²

For the smaller triangle, this tells you the square of the length of its hypotenuse is ...

  c² = 2² +4² = 4 +16 = 20

That square can be used directly in the equation for the larger triangle:

  20 +x² = 10²

 x² = 100 -20 = 80

 x = √80 ≈ 8.9

The value of x is about 8.9 units.

volume of cone is  =1/3 x³.

The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.

here, given that,

The base diameter and the height of a cone are both equal to x units.

Volume =  ⅓ r²h

              =1/3 x²x

              =1/3 x³

Hence, volume of cone is  =1/3 x³.

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Answer: 5

Step-by-step explanation:

A triangle's area is half of a squares, so we can treat this as a square for now. It says the area is 20 units squared, and if we convert this to the area of the square, it is 40 units. 40/8 is 5, and so 5 is the length of x

Answer: (0,0) (4, -3) (8, -6)

Step-by-step explanation:

It is correct.

The volume of the pyramid, in cubic meters, given the length of each side and the height, is 2, 592, 100 meters ³

The Volume of a pyramid can be found by the formula :

= ( Base length x Base width x Height ) / 3

Base length = 230 meters

Base width = 230 meters as this is a square base

Height = 147 meters

The volume is therefore:

= ( 230 x 230 x 147 ) / 3

= 2, 592, 100 meters ³

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The required least number is n - p and the highest number is p - n.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

here,
The given numbers that are to be plotted on the number line are,
n - p, n + p, p -n

Since on the number line n comes former and p comes later it tends that p > n.

So the least number would be n - p because it will be negative,
And the height number would be p - n because
n is negative and in the operation, it becomes more than n + p.

Thus, the required least number is n - p and the highest number is p - n.

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The compound interest rate is 3.9%.

We know that when we talk about the compound interest, we mean the kind of interest that is going to accrue both on the principal and on the interest.

In this case we know that;

A = P(1 + r)^n

A = amount

P = principal

r = rate

n = number of years

710.89  = 658.20(1 + r)^2

710.89/658.20 = (1 + r)^2

1.08 = (1 + r)^2

ln(1.08) =ln (1 + r)^2

0.077 = 2ln(1 + r)

0.077/2 = ln(1 + r)

ln(1 + r) = 0.0385

1 + r = 1.039

r = 1.039 - 1

r = 0.039

r = 3.9%

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The value of the inequalities will be:

a. x > 6

b. x ≤ 24

c. x ≥ 6

d. x < 6

e. x ≥ 24

It should be noted that inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x + 28 > 34

Collect the like terms

x > 34 - 28

x > 6

x/2 ≤ 12

Cross multiply

x ≤ 12 × 2

x ≤ 24.

7x ≥ 42

Divide

x ≥ 42/7

x ≥ 6

x - 2 < 4

x < 4 + 2

x < 6.

3x ≥ 72

Divide

x ≥ 72/3

x ≥ 24

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Answer:

3186.25

Step-by-step explanation:

318,625*10 = 3186.25

1. The length of the sides of the two smaller squares are 3 and 4

2. Area of 4 triangles and middles square = 25

3. Area of the big square = 5

The dimensions of the the triangle and the square are

length of square = 1

base = 3

height = 4

Area of the triangle

= 1/2 base * height

= 0.5 * 3 * 4

= 6

For four triangles

= 4 * 6

= 24

Area of small square

= 1 * 1

= 1

summation of the areas

= 24 + 1

= 25

Solving for side of the big square from the area

= √25

= 5

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The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The person who pays more after each additional day d after day 0 is Patricia.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Emily:

P = 2d - 1

After 3 days, the price for renting the book.

P = 2 x 3 - 1 = 6 - 1 = $5

Patricia:

After 3 days, the price for renting the book.

= $20

Thus,

Patricia pays more for each additional day.

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The compound inequality on the number line is shown below.

We have been given a compound inequality. We are asked to graph the given inequality on number line.    

x>8 and x≤3

The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.

We will have solid dots at  x>-8 and x≤-3 .

One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.

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The solutions for the given Cubic equation y = x³ - x² - 41 x + 105 are x = -7 and x = 5.

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three.

Given, a polynomial y = x³ - x² - 41x + 105

The difference between the remainder theorem and the factor theorem:

The remaining factor theorem really consists of two theorems that link a polynomial's roots to its linear factors. The theorem is frequently applied to avoid using long division while factoring polynomials. This gives us a strong tool to factor polynomials, especially when coupled with the rational root theorem.

Use the factor theorem to find the roots of a cubic equation.

possible roots are factors of the constant theorem.

Once you get one root then you can use synthetic division to get the other roots.

For instance,

x³ - x² - 41x + 105 = 0,

use synthetic division

3    1     -1     -41    105    

           1     2     -35

    1         2      -35       0   (1, 2, -35 are co-efficient of the quadratic equation)

So now we have

x³ - x² - 41x + 105 = (x-3 )( x² + 2x - 35)

(x-3 )( x² + 2x - 35)

(x-3)(x(x+7)-5(x+7))

(x- 3)(x +7) (x - 5)

Solution means that at values 3, -7, and 5 of x, y will be zero.

Therefore, all X intercepts of the given Polynomial function are 3, -7, and 5.

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