Draw at least six different sized rectangles that have an area of 64 square units then find the perimeter of each rectangle.

Answer: x = 9 and x  = 6

Step-by-step explanation:

[tex]x^2-15x+54=0\\(x-9)(x-6)\\x-9=0\\x=9\\x-6=0\\x=6[/tex]

Therefore, x = 9 and x  = 6

Answer:

x - intercept: (3, 0)

y - intercept: (0, 9)

Step-by-step explanation:

This equation is written in standard form,

To find the intercepts it would be easier to put the equation in

slope-intercept form y = mx + b

9x + 3y = 27

subtract 9x from both sides

(9x - 9x) + 3y = 27 - 9x

3y = 27 - 9x

Divided both sides by 3

3y / 3 = 27 - 9x / 3

y = 27 / 3 - 9x / 3

y = - 3x + 9

Now we can plug in x = 0, to find y - intercept:

y = - 3(0) + 9

y = 0 + 9

y = 9

Now we can plug in y = 0, to find x - intercept:

0 = - 3x + 9

0 - 9 = - 3x + 9 - 9

-9/3 = -3x/3

-3 = -x

3 = x

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Answer:

  ∠1 = 36°

Step-by-step explanation:

All angles of a regular polygon are congruent, as are the sides. A regular decagon will have 10 congruent angles.

The sum of the measures of the exterior angles of a convex polygon is always 360°. This decagon has 10 congruent exterior angles, so the measure of each is given by ...

  10(∠1) = 360°

  ∠1 = 36° . . . . . . . . divide by 10

Answer:   36°

Step-by-step explanation:   Trust Me!

Answer is correct on Edge.  Good Luck! :)

In the regular decagon shown, what is the measure of angle 1?

360° is always the sum of all measures of all exterior angles of a convex polygon. A decagon have 10 sides.

Since ∠1 = 36°, then each other angle should measure the same, 36°.

In order to know whether the sum of all the angles equal 360°,
we need to multiply:  36° x 10.

36° x 10= 360°.

And sure enough the answer is correct.

The value of P such that P*3=1 is 4

The set of Real numbers, R is given as

m*n=(√m +√n) (√m-√n).

The values of P, if P*3=1 is represented as:

P * 3=(√P +√3) (√P-√3).

The result of this operation is 1.

So, we have:

(√P +√3) (√P-√3) = 1

Apply the difference of two squares

P - 3 = 1

Add 3 to both sides

P = 4

Hence, the value of P such that P*3=1 is 4

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The number of two year old boys that wear a size 6 is greater than the number of three year  old boys that wear a size 6  by 35.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines called the whiskers and a box. The whiskers represent the minimum and maximum scores.

On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile

50% of the two year olds wear a size 6 = 50% x 100 = 50

25% of the three year olds wear a size 6 = 25% x 60 = 15

Difference in the number : 50 - 15 = 35

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Answer:

a) height =14in

b) height =27cm

Step-by-step explanation:

a)

[tex]v = \frac{l \times w \times h}{3} [/tex]

where,

Substitute these values and solve for h.

[tex]h = 3 \frac{v}{lw} \\ h = 3. \frac{448}{8.12} = 14[/tex]

b)

[tex]v = \frac{1}{3} ah[/tex]

where, a=area of the base

plug in the given values and solve for h

[tex]v = \frac{1}{3} ah \\ 3v = ah \\ h = \frac{3v}{a} \\ h = \frac{3(270)}{30} \\ h = 27cm[/tex]

Answer:

x = 6

Step-by-step explanation:

• the diagonals of a parallelogram bisect each other , then

5x + 11 = 4x + 17 ( subtract 4x from both sides )

x + 11 = 17 ( subtract 11 from both sides )

x = 6

Since it's divided equally diagonally, 4x+17 and 5x+11 are equal.

Let's set them equal to each other and solve.]

[tex]4x+17=5x+11[/tex]

Subtract 4x from both sides to combine like terms.

[tex]17=x+11[/tex]

Now subtract 11 from both sides to isolate the variable and solve for x.

[tex]6=x[/tex]

Flip the equation to put in standard form and now you have x :)

[tex]x=6[/tex]

hope this helped!

Answer:

x ≤ -2

Step-by-step explanation:

3(x + 2) ≤ 5(-2 - x)

Distribute on both sides.

3x + 6 ≤ -10 - 5x

Add 5x to both sides.

8x + 6 ≤ -10

Subtract 6 from both sides.

8x ≤ -16

Divide both sides by 8.

x ≤ -2

Answer:

[tex]\textsf{D. }x\leq-2[/tex]

Step-by-step explanation:

Given inequality: [tex]3(x+2)\leq5(-2-x)[/tex]

Step 1: Distribute [tex]3[/tex] and [tex]5[/tex] through the parentheses.

[tex]\implies 3(x)+3(2)\leq5(-2)+5(-x)[/tex]

[tex]\implies 3x+6\leq-10-5x[/tex]

Step 2: Subtract [tex]6[/tex] from both sides.

[tex]\implies 3x+6-6\leq-10-6-5x[/tex]

[tex]\implies 3x\leq-16-5x[/tex]

Step 3: Add [tex]5x[/tex] to both sides.

[tex]\implies 3x+5x\leq-16-5x+5x[/tex]

[tex]\implies 8x\leq-16[/tex]

Step 4: Divide both sides by [tex]8[/tex].

[tex]\implies \dfrac{8x}{8}\leq\dfrac{-16}{8}[/tex]

[tex]\implies x\leq-2[/tex]

If the ratio of a model train to a real train exists 1:3 and the real train exists 12 feet then the model train exists 3 feet long.

Given that the model train contains a scale of 1: 3 and the real train exists 12 feet tall.

The ratio indicates how many times one number has another number.

A ratio exists as the relationship in quantity between two things.

It conveys the quantity of one thing in words of another.

The ratio of a model train to a real train exists at 1 inch :3 inches.

Height of model train = 12 [tex]*[/tex] 1/4

Height of model train = 3 inches

Therefore, the ratio of a model train to a real train exists 1: 3 and if the real train exists 12 feet then the model train exists 3 feet long.

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Answer:

shown below

Step-by-step explanation:

1) tanY = 0.2334

Y = arctan(0.2334)

Y = 13.14 degrees

2) X = 12 / tan(40)

X = 14.3km

3) x = arctan(5/8)

x = 32°

Answer:

  -3√11

Step-by-step explanation:

If the coefficients of a polynomial are rational, any irrational root will have a conjugate that is also a root.

The root 3√11 is irrational, so its conjugate, -3√11, will also be a root.

__

Additional comments

The conjugate of a root of the form a+√b or a+bi will be the same form with the sign changed: a-√b or a-bi.

The conjugate of 3√11 = 0 +√99 will be 0 -√99 = -3√11.

__

A quadratic with rational coefficients can only have irrational roots of the form a±√b, where 'a' and 'b' may be any rational number.

3 - √11  also be a root of f(x).

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Get the conjugate of any irrational zero if you want rational coefficients.

The conjugate of 3 + √11  is  3 - √11

x = 3 +√ 11

Subtract 3 on both sides

x minus 3 = 3 + √11 - 3

x - 3 = √11

By squaring on both sides

(x - 3)² =√ 11

Now subtract 11 on both sides

(x - 3)² - 11 = 0

To factor use the difference of squares

u² minus v² = (u minus v) (u plus v)

[(x - 3) - 11][(x - 3) + 11] = 0

We get,

(x - 3) - 1 = 0 or (x - 3) + 11 = 0

Solve for x - 3 and x

Add √11 on both sides of first equation and subtract √11 on both sides of second equation

x minus 3 = √11 or x minus 3 = - √11

By adding 3 on both sides

x = 3 + √11 or x = 3 - √11

As a result,

the root of 3 - √11 must likewise be f(x).

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The price of the board game before the markup is $21.50.

Percentage can be described as a fraction an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.

When the price of an item is marked up, it means that the price of the item has been increased by a predetermined percentage. In this question, the price of the board game is increased by 25%.

Price of the item before the mark up = price the retailer sells / ( 1 + percentage)

$26.88 / 1.25 = $21.50

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The equation to represent the given scenario is a=b-5 and the age of Ana is 18 years when her sister Beatriz is 23 year old.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Ana is 5 years younger than her sister, Beatriz

1) Let the age of Ana be a and the age of Beatriz be b

Now, a=b-5

2) Beatriz is 23 years old

Substitute b=23 in the equation a=b-5, we get

a=18 years

Therefore, the age of Ana is 18 years when her sister Beatriz is 23 year old.

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"Your question is incomplete, probably the complete question/missing part is:"

Ana is 5 years younger than her sister, Beatriz.

1. Write an equation that represents how old Ana is (a) when Beatriz is b years old.

2. How old is Ana when Beatriz is 23 years old?

The absolute value exists its distance from zero on the number line.

⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0

⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8

⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8

The function containing an algebraic expression inside absolute value symbols exists comprehended as an absolute functional form, and the calculation exists as pursues:

An absolute functional form has an algebraic expression inside absolute value symbols.

Remember that a number's absolute value exists its distance from zero on the number line.

⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0

⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8

⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8

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The minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls is 4

The total number of balls is

Total = 50

Let k represent the minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls

Using the pigeonhole principle, we have

n + 1 = k

Where n = 3

So, we have

3 + 1 = k

Evaluate the sum

4 = k

Rewrite the equation as

k = 3

Hence, the minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls is 4

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The factors of the trinomial are:

Options C and E

This is further explained below.

Generally, A trinomial is a kind of polynomial that is used in basic mathematics. It is composed of three components, also known as monomials.

In conclusion, The following expressions are the components of the trinomial: x - 7, x + 2

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Answer:

Round the decimal values however needed.

Step-by-step explanation:

The uppercase letters represent the angles, while the lowercase counterparts are the side lengths opposite said angle. For example, side b is opposite angle B.

Angle B is 41 and angle C is 90 because of the square marker. The remaining angle A is...

A+B+C = 180

A+41+90 = 180

A+131 = 180

A = 180-131

A = 49

Or note that

A = 90 - B = 90 - 41 = 49

This shortcut works since we have a right triangle.

---------

That takes care of the angles. Now onto the sides.

We'll need to use trig ratios to determine the missing sides. There are a few approaches, but this is one you could take

tan(angle) = opposite/adjacent

tan(A) = a/b

tan(49) = a/15

a = 15*tan(49)

a = 17.255526 approximately

Furthermore,

sin(angle) = opposite/hypotenuse

sin(B) = b/c

sin(41) = 15/c

c*sin(41) = 15

c = 15/sin(41)

c = 22.863796 approximately

There is another trig function (cosine) that you could use. Also, you could use the pythagorean theorem once you know two sides of the right triangle.

The pythagorean theorem is a^2+b^2 = c^2

The answers have been confirmed with GeoGebra which is a useful geometry app.

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:

x + y = 52   (1)

Also:

x + 2.25y = 72    (2)

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

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Answer:

182,156.8

Step-by-step explanation:

214 x 912 x 14 = 2,732,352

1/15 of that Volume is 182,156.8

P.S. I'm assuming you meant 1/15, when you said the volume was 15 of

Follow my gram it's Greyhasnoshame

Total parrot=40

Caught=8

Fraction

#2

Out of 40 parrots 8 are ringed

Parrots per one ringed=40/8=5

Total ringed before=32

Total no of parrots

There are 160 parrots

Answer:

[tex]\sf 1) \quad \dfrac{1}{5}[/tex]

[tex]\sf 2) \quad 160\:parrots[/tex]

Step-by-step explanation:

Given information:

Therefore, the fraction of ringed parrots from the second catch is:

[tex]\implies \sf \dfrac{ringed\:parrots}{total\:caught\:parrots}= \dfrac{8}{40}=\dfrac{1 \times 8}{5 \times 8}=\dfrac{1}{5}[/tex]

If she caught and ringed 32 parrots in her first catch, but only 1/5 of the parrots caught in the second catch were ringed, then 32 parrots represents 1/5 of the total number of parrots.  To find the total number of parrots, simply multiply the total number of ringed parrots by 5:

[tex]\implies \sf \textsf{Total number of parrots}=32 \times 5 = 160[/tex]

Answer: 87,654,321

Step-by-step explanation: All the digits of the number A are different so the max length of the number A is 10 digits. But, then you realise that 9 can't be used because 9+1 = 10. So, A is only 9 digits long. If we arrange them from largest to least it would be 87,654,321.

Answer:

66/65.

Step-by-step explanation:

22/5 / 13/3

Invert the divisor and multiply.

---> 22/5 * 3/13

= 66/ 65

The angle m∠A can be represented as follows:

The above circle, a secant and a tangent intersect outside the circle.

A secant is a straight line that intersects a circle in two points.

A tangent  is a line that never enters the circle's interior.

Therefore, when a secant and a tangent intersect, the following rules applies:

m∠A = 1 / 2 (BD - BC)

m∠A = 1 / 2 (164 - 70)

m∠A = 1 / 2 (94)

m∠A = 47 degrees.

Therefore, the angle m∠A can be represented as follows:

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Using a linear function, it is found that Sarah can use 3.7 gigabytes while staying within her budget.

A linear function is modeled by:

y = mx + b

In which:

Considering the flat cost as the y-intercept and the cost per gigabyte as the slope, the cost of using g gigabytes is:

C(g) = 4g + 69.

She wants to keep her bill at $83.80 per month, hence:

C(g) = 83.80

4g + 69 = 83.80

4g = 14.80

g = 14.80/4

g = 3.7.

Sarah can use 3.7 gigabytes while staying within her budget.

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Answer:

The other person is correct!

Step-by-step explanation:

Yes

During the Civil War, the North's heavy industrialization provided an advantage.

According to the information:

The distinct economic division between the northern and southern economies played a key role in the Union's Civil War victory. First, the vast capitalist industry was expanding, with a significant concentration of salaried labor, in full force, and on the verge of the Second Industrial Revolution (to which the development of new military technologies, such as battleships and the mass production of weapons, helped to the war. These northern bourgeois sectors were represented by the liberal nationalist new Republican Party, which worked to enact protectionist laws.

On the other hand, the south remained rooted in an economic structure that was adverse to the growth of capitalism (mechanization and hiring of workers were cheaper than the maintenance of slaves). To protect slavery would be the Democratic Party. This party, which had spearheaded the nation's significant southern expansion (pro-Mexican territorial annexation movement), now served as a proxy for the region's elites, who essentially favored the growth of the slave trade and unrestricted trade in manufactured products and raw resources.

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I understand that the question you are looking for is:

A resource comparison of the Union and Confederacy during the Civil War. The title is Comparing Resources. The data are as follows. For each category, the Union percentage is listed first, the Confederate percentage, second. Horses, 72, 28, Food Crops, 72, 28, Cotton, 1, 99, Prewar Exports, 30, 70, Soldiers, 67, 33, Firearm Production, 97, 3, Railroad Tracks, 71, 29, Factories, 86, 14, Bank Deposits, 81, 19, Total Population, 71, 29. Public domain Use the graph and your knowledge of U.S. history to answer the question. Which of these explains the differences in Union vs. Confederate firearm production during the Civil War? The North had a highly skilled labor force to make them. The North's heavy industrialization provided an advantage. The South had fewer men who were trained as metalworkers. The South's means of production were destroyed by General William Tecumseh Sherman.

The expression √180 * 2√30 is equivalent to the expression 60√6

An equation is an expression that shows the relationship between two numbers and variables.

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given the expression √180 * 2√30

Collecting like terms give:

= 2√(180 * 30)

Simplifying:

= 60√6

The expression √180 * 2√30 is equivalent to the expression 60√6

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The inverse of a function is given as √x - 1

To get the inverse of any function f(x) we need to ensure that it passes the horizontal line test.

Given the following function

f(x) = (x+1)^2

Let y= f(x) to have:

y = (x+1)^2

Replace y with x to have:

x = (y+1)^2

Make y the subject of the formula

√x =y + 1

Subtract 1 from both sides

√x - 1 = y

Swap

y = √x - 1

Hence the inverse of a function is given as √x - 1

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It's tempting to say that increasing the speed limit has led to higher accident rates, but you have to be careful because other variables (e.g. cheaper gas or time of year the change was introduced) can also affect accident rates. The option C is correct.

Given the impact of the speed limit increase from 55 to 65 mph, there are more crashes in the 6 months after the speed limit change than in the 6 months before the speed limit change. speed.

The dependent variable is the variable that is attempted and expected in a survey and is "dependent" on the free aspect. In a survey, the scientist tries to find the conceivable influence on the reliable variable, which can be approximated by changing the free thing. The free aspect is the variable that the experimenter adjusts or controls, and should directly affect the dependent variable. Therefore, increasing the speed limit from 55 to 65 mph resulted in higher accident rates, you have to be careful with other variables.

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