Rectangle A is 5 in by 7 in. If the scale factor is 4, what is the area of the new rectangle B? How does it compare with the first rectangle?

Answer:

A

Step-by-step explanation:

x² - 2x + y² + 6y - 4 = 0 ( add 4 to both sides )

x² - 2x + y² + 6y = 4

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

= x² + 2(- 1)x + 1 + y² + 2(3)y + 9 = 4 + 1 + 9

(x - 1)² + (y + 3)² = 14 ← in standard form

In linear equation, You are the only person in the garden at the time the 34 people.

What in mathematics is a linear equation?

You are the only person in the garden at the time the 34 people are on their homicidal spree.

Alternatively, if the backyard and garden are in the same place, then there are no longer any individuals in the garden because you would officially count as one of the 34 people who are all killed.

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Given the volume of the box is 100 cm^3

And to made the box we need to cut a square measuring 4 centimeters on a side from a square piece of cardboard.

so, the height of the box = 4 cm

so, the volume = height * area of the base

100 = 4 * area of the base

Area of the base = 100/4 = 25 cm^2

so, the side length of the base of the box =

so, the lenght of the a side of the original square = 5 + 2*4 = 5 + 8 = 13 cm

The probability that the diameter of a selected bearing is greater than 152 millimeters is 64.05%.

For the given question;

The data for the ball bearing is given as-

Z-score = (x - μ)/σ

Put the values;

z = (152 - 139)/36

z = 0.36

P(x > 125) = P(z > 0.36), see p values from z table for 0.36.

P(x > 125) = 0.6405

P(x > 125) = 64.05%

Thus, the probability that the diameter of a selected bearing is greater than 152 millimeters is 64.05%.

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Answer:

12 weeks

Step-by-step explanation:

if 280=420

then 8=×

cross multiply

280×=420×8

280×=3360

divide both sides with the co efficient of x

280×/280=3360/280

leaving the answer to be 12

He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit and the maximum profit is [tex]\$18,200[/tex].

A Virginia Beach farmer has [tex]480[/tex] acres of land on which to grow either corn or soybeans.

He has labor available during the crucial summer [tex]=800[/tex] hours

The farmer can expect a profit of [tex]\$40[/tex] per acre on corn.

The farmer can expect a profit of [tex]\$30[/tex] per acre on soybeans.

The corn requires hours to raise [tex]=2[/tex] hours per acre.

The soybeans requires hours to raise [tex]=1[/tex] hours per acre.

We have to find how many acres of each should he plant to maximize profit and his maximum profit.

To solve the question we let he plant [tex]x[/tex] acres of corn and [tex]y[/tex] acres of soybeans.

Total land is available for grow either corn or soybeans is [tex]480[/tex] acre.

So the equation should be

[tex]x+y\leq 480\dots\dots Equation (1)[/tex]

He requires [tex]2[/tex] hours to raise corn per acre and [tex]1[/tex] hours to raise soybeans per acre and he has 800 hours of labor available during the crucial summer season.

So the equation should be

[tex]2x+y\leq 800\dots\dots Equation (2)[/tex]

He expect a profit of [tex]\$40[/tex] per acre on corn and [tex]\$30[/tex] per acre on soybeans.

So profit equation should be

[tex]P=40x+30y[/tex]

Now the subject of constraints

[tex]x+y\leq 480[/tex]

[tex]2x+y\leq 800[/tex]

[tex]x,y\geq 0[/tex]

Now solving the equation [tex]1[/tex] and [tex]2[/tex] to find the value of [tex]x[/tex] and [tex]y[/tex].

Multiplying the equation [tex]1[/tex] by [tex]2[/tex].

After multiplying with [tex]2[/tex] the equation [tex]1[/tex]

[tex]2x+2y\leq 960\dots\dotsEquation (3)[/tex]

Now subtracting Equation [tex](3)[/tex] and Equation [tex](2)[/tex].

[tex]2x+2y-(2x+y)\leq 960-800[/tex]

[tex]2x+2y-2x-y\leq 960-800[/tex]

[tex]y\leq 160[/tex]

Now putting the value of [tex]y[/tex] in Equation [tex](1)[/tex]

[tex]x+160\leq 480[/tex]

Subtract [tex]160[/tex] on both side

[tex]x+160-160\leq 480-160[/tex]

[tex]x\leq 320[/tex]

He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit.

The maximum profit

[tex]P=40x+30y\\P=40\times320+30\times180\\P=12,800+5400\\P=18,200[/tex]

The maximum profit is [tex]\$18,200[/tex].

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Answer:

42 dollars

Step-by-step explanation:

Jaynee's money is 11 out of (11+3) = 14   or 11/14ths of the total

11/14  x = 33

x = total amount = 33 * 14/11= 42 dollars

35 encyclopedias can be fit on the bookrack.

What is an encyclopedia?

An encyclopedia (American English) or encyclopaedia (British English) is a reference source or compendium that provides summaries of general or specific information to a certain topic or discipline. Encyclopedias are organized into articles or entries that are either alphabetically sorted by article name or by subject categories, or are hyperlinked and searchable by random access. The entries in encyclopedias are longer and more thorough than those in most dictionaries. In general, encyclopedia articles focus on factual information about the subject specified in the title, as opposed to dictionary entries, which focus on linguistic information about words, such as their derivation, meaning, pronunciation, use, and grammatical forms.

Width of bookrack = 61 1/4 inches

Width of an encyclopedia = 1 3/4 inches

no. of encyclopedias to be fit = (61 1/4)/(1 3/4)

                                                  = (245/4)/(7/4)

                                                  = 245/7

                                                  = 35

Hence, 35 encyclopedias can be fit on the bookrack.

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Answer: 2.5 inches

Step-by-step explanation: 3*5/6= 2.5

Answer:

y=3 / y=6

x=0 / x=3

Step-by-step explanation:

Follow the steps given in the picture attached above.

The sets of number to which - 2/5 belongs is a rational number.

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth. A rational number is any number that can be expressed as a ratio (or fraction) of two integers.

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.

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Answer:[tex]\sqrt{36} > 5 \\[/tex]

Step-by-step explanation:

because [tex]\sqrt{36} =6[/tex]

Therefore  6 > 5

Answer:

a

Step-by-step explanation:

Let's look at Enrique:

He starts with $50 and every time he buys lunch his account goes down by 5.  The y would represent how much money he has left in his account.

So, say he buys 3 lunches how much is in his account if he started with 50?

50 - 5-5-5 = 35

Use the equation

50 - 5(3) = y

50 - 15 = y

35 = y

Answer:

3

Step-by-step explanation:

We need to isolate x in order to solve it:

First, subtract 4 from both sides

15 - 3x = 2x

Add 3x to both sides

15 = 5x

Divide each side by 5 to get x

x = 3

Answer:

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

the perpendicular bisector of AB passes through the midpoint of AB at right angles.

find the midpoint using the midpoint formula

with A (- 2, 0 ) and B (0, 6 )

midpoint = ( [tex]\frac{-2+0}{2}[/tex] , [tex]\frac{0+6}{2}[/tex] ) = ( [tex]\frac{-2}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = (- 1, 3 )

find the gradient m of AB using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (- 2, 0 ) and (x₂, y₂ ) = B (0, 6 )

m = [tex]\frac{6-0}{0-(-2)}[/tex] = [tex]\frac{6}{0+2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

given a line with gradient m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex]

the equation of a line in gradient- slope form is

y = mx + c ( m is the gradient and c the y- intercept )

here m = - [tex]\frac{1}{3}[/tex] , then

y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 1, 3 ) into the partial equation

3 = [tex]\frac{1}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{1}{3}[/tex] = [tex]\frac{8}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex] ← equation of perpendicular bisector

40% of 8 is 3.2

hope this helped

Answer:

61 degrees

Step-by-step explanation:

Bro its that easy

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges. 

The diagonal of a cube is √3 side.

If the volume of a cube is 4096 cm³ the diagonal of a cube is 16√3 cm.

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges. 

The volume of a cube is given as:

Volume = side³

The diagonal of a cube = √3 side.

We have,

The volume of a cube = 4069 cm³

The volume of a cube = side³

4096 = side³

side = ∛4096

side = 16 cm

Now,

The diagonal of a cube:

= √3 side

= √3 x 16

= 16√3 cm

Thus,

The diagonal of a cube is 16√3 cm.

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The following must be true:

SU + UT = RT

By dividing the base's length by its height, one may calculate any quadrilateral's surface area. We can conclude that all of the sides are the same length because the shape is square. Using the square root of the area to determine the length of one side, we can then work backwards from this information. A square has four sides, thus to determine the length of one side, divide the perimeter by 4. Assumed Area: Since s2 is the formula for a square's area and that number corresponds to one of its sides, you must get the square root of the area. A side is the line segment that connects two vertices of a shape or two-dimensional figure according to the definition of geometry.

Length of SU

= RS - RT - TU

= 24 - 12 - 6

= 24 - 1

= 6

Thus, the length of the US is 6 units.

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Using angle sum property we found that ∠ x = 113°, ∠y = 67°  and ∠z = 49°

The angle sum property of triangle states that the sum of all the interior angles of a triangle is 180°.

If ΔABC is a triangle then,

m ∠A + m ∠B + m ∠C = 180°

Given from the figure in the question that 28°, 39° and x° are interior angles of a triangle, then using angle sum property:

28° + 39° + x° = 180°

⇒ 67° + x° = 180°

⇒ x° = 180° - 67° = 113°

∠x and ∠y are on the same line same point therefore their sum will be 180°

⇒ x° + y° = 180°

⇒ 113° + y° = 180°

⇒ y° = 180° - 113° = 67°

Also an exterior angle of a triangle is equal to sum of interior opposite angles.

∴ y ° = 28° + 39° = 67°

Now, 64° , y° and z° are interior angles of same triangle from the figure in the question.

∴ Using angle sum property,

64° + y° + z° = 180°

⇒ y ° + z° = 180° - 64° = 116°

⇒ y° + z° = 116°

⇒ z° = 116° - y° = 116° - 67°  = 49°

Therefore ∠x, ∠y , ∠z are 113° , 67° and 49° respectively

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95.61 percent of pig pregnancies are longer than 109 days with 0.8413 probability.

A standard normal distribution or z-table can be used to approximate the probability of multiple ranges of values for a random normal variable X with a particular mean and standard deviation. This method entails changing X to a typical normal variable Z.

The normal, random variable X equals the length of pregnancy.

The mean and standard deviation are then calculated.

u, Mean = 114 days

σ, Standard deviation = 5 days

Then, as follows, transform X to its standard normal variable:

Z = (X - u) ÷ σ

Z = (X - 114) ÷ 5

To determine the likelihood of a pregnancy lasting more than 109 days,

P(X ≤ 109) = P(Z ≤ 114 - 109 ÷ 5)

P(X ≤ 109) = P(Z ≤ 1)

P(Z ≤ 1) = 0.8413 when using a typical normal distribution or z-table.

The percentage of pig pregnancies that last more than 109 days,

P = (109 ÷ 114) × 100

P = 95.61%

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Answer:  You are correct

The decreasing interval is (-3, infinity)

This is the same as writing [tex](-3, \infty)[/tex]

===============================================

Explanation:

If a < b and f(a) > f(b), then the function is decreasing.

Visually this means that if the graph is going downhill when moving to the right, the function is decreasing.

The graph shown goes downhill throughout its entire domain of (-3, infinity)

The segment AB = AC is proved for the given line AC.

For the given question;

AC = AB + AB

This can be written as;

AC = 2AB

or AB = (1/2)AC

It means, B is the mid point of AC

So, B will also divide the complete line segment AC into two equal halves.

AB = AC

Thus, the segment AB = AC is proved for the given line AC.

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Answer:

6x^2-x-2

Step-by-step explanation:

A lift ratio of 1.52 implies that identifying a person who purchases coffee and a breakfast sandwich is 52% better than guessing that a random person will purchase a breakfast sandwich.

Stronger relationships are indicated by higher lift values.We divide the confidence ratio by the support of the consequent to arrive at the lift ratio.

Lift ratios greater than one are typically thought to imply a significant link between the components. Lift ratios below 1 indicate that a purchase of the items is unlikely. Lift is simply the ratio of target response divided by the average response.

Carmen analyzed data from the month of March to see if there was a link between coffee and breakfast sandwich purchases. She calculated the lift ratio to be 1.52 after running confidence and expected confidence calculations.

In this case, she wants to know the association between coffee and breakfast sandwich purchases. There's 52% better off than a random individual.

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Answer:

Explanation: The product has two square-roots being multipled together, the inside of each of the root must be greater than or equal to zero, this in Mathematics can be written as follows:

Therefore, applying the condition leads us to the following conclusion:

Therefore it follows that x must be:

Answer:

6y + 3x + 9

Step-by-step explanation:

→ Combine all equivalent terms

4y + 2y + 3x + 6 + 3

→ Simplify

6y + 3x + 9

Answer:

3x + 6y + 9

Step-by-step explanation:

Combine like terms.

4y + 2y = 6y

6 + 3 = 9

3x does not have a like term.

6y + 3x + 9

Order the variables in alphabetical order. (In this case, x goes before y.)

Simplify.

3x + 6y + 9

Por medio de expresiones trigonométricas y el diagrama geométrico se concluye los dos barcos tienen una distancia aproximada de 129.441 metros.

En este problema se debe determinar la distancia entre dos barcos. La situación es representanda por dos triángulos rectángulos con un cateto vertical común, correspondiente a la altura del faro. La distancia entre los barcos se determina mediante la siguiente expresión trigonomética:

d = 30 / tan 5° - 30 / tan 8°

d ≈ 129.441 m

La distancia entre los dos barcos es aproximadamente 129.441 metros.

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