What is the lateral area of the prism? What is the surface area of the prism?

Answer:

[tex]\huge\boxed{\bf\:1}[/tex]

Step-by-step explanation:

[tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }[/tex]

Take [tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 }[/tex] & factorise it at first.

[tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}[/tex]

Now factorise the next set : [tex]\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }[/tex].

[tex]\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\= \frac{x-4}{x-1}[/tex]

Now, multiply the two simplified results.

[tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

Step-by-step explanation:

The given relation between length and width can be used to write an expression for area. The equation setting that equal to the given area can be solved to find the shed dimensions.

__

Let x represent the width of the shed. Then the length is (2x+3), and the area is ...

  A = LW

  20 = (2x+3)(x) . . . . . area of the shed

__

Completing the square gives ...

  2x² +3x +1.125 = 21.125 . . . . . . add 2(9/16) to both sides

  2(x +0.75)² = 21.125 . . . . . . . write as a square

  x +0.75 = √10.5625 . . . . . divide by 2, take the square root

  x = -0.75 +3.25 = 2.50 . . . . . subtract 0.75, keep the positive solution

The width of the shed is 2.5 feet; the length is 2(2.5)+3 = 8 feet.

Answer:

80 yds^2

Step-by-step explanation:

A=2(wl+hl+hw)=2·(2·2+9·2+9·2)=80

Answer:

Step-by-step explanation:

20x+21=0

20x=-21

x=-1.05

Answer:

See below ↓↓

Step-by-step explanation:

Equation of line k

a. parallel line

b. perpendicular line

Answer:

they are 13 points away from eachother

Step-by-step explanation:

count up or down then left or right

Answer:

13 units.

Step-by-step explanation:

Distance = √[(x2-x1)^2 + (y2-y1)^2]     where (x1,y1) and (x2,y2) are the 2 points

So here the distance =  √(-4 - -4)^2 + (8 - -5)^2)

√(0 + 13^2)

= 13

started= 2:30 PM

ended= 4:00 PM

the duration of the concert.

( just find the difference of finishing time and starting time)

= 1 hour 30 mins

so, the duration of the concert is 1 hour 30 mins.

0400-0230

= 1 hour 30 minutes

hope this helps :)

Answer:

  a)  y = 3.80x +5.00

  b)  see attached

Step-by-step explanation:

A graph shows the given table values lie on a straight line.

__

Finding the slope of the line is made easier by an appropriate choice of a pair of table values:

  m = (y2 -y1)/(x2 -x1)

  m = (24 -20.20)/(5 -4) = 3.80/1 = 3.80 . . . . using (4, 20.20) and (5, 24)

The y-intercept can likewise be found with an appropriate choice of table values. Solving the slope-intercept equation for b, we get ...

  y = mx +b

  b = y -mx

  b = 8.80 -3.80 × 1 = 5.00 . . . . using the first table value

An equation that represents the cost of parking could be ...

  y = 3.80x +5.00

__

A graph of the table values and the equation is shown in the attachment.

Answer:

3/5

Step-by-step explanation:

6x  - 10y = -100

Write this equation in slope-intercept form: y = mx +b

-10y = -6x - 100

Divide the entire equation by (-10)

[tex]\dfrac{-10}{-10}y=\dfrac{-6}{-10}x-\dfrac{100}{-10}\\\\y =\dfrac{3}{5}x+10[/tex]

Slope = 3/5

Parallel lines have same slope.

Slope of the parallle line = 3/5

The temperature difference between the pan and room temperature would be 77.9⁰C in the next 15 minutes,

Let y represent the temperature difference after x minutes.

The difference between the pan and room temperature is currently 197°C and is decreasing by 6% every minute, hence:

y = 197(100% - 6%)ˣ

y = 197(0.94)ˣ

The temperature in the next 15 minute is:

y = 197(0.94)¹⁵ = 77.9⁰C

The temperature difference between the pan and room temperature would be 77.9⁰C in the next 15 minutes.

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An example of 7th grade geometry Math in the Midwest 2019 is Puzzle: Simplify -5 + 8 - 7.

Geometry is known to be an aspect of mathematics that  deals with the study of sizes, positions of angles, and others.

To simply the above, -5 + 8 - 7, follow the rule of BODMAS. and thus: we solve for addition before subtraction.

= -5 + 8 = 3

3 - 7 = -4

Therefore the simplified form of  -5 + 8 - 7 is -4

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[tex][text]\orange{ \rule{100pt}99999pt}[/tex]

The area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

Suppose that the two adjacent sides of a rectangle be of 'a' units and 'b' unit lengths.

Then, we get the area of that rectangle as:

[tex]S = a \times b \: \rm unit^2[/tex]

For this case, we're specfied that:

Let the other side (adjacent) be of 'b' units length

Then, as perimeter of a rectangle = 2(sum of lengths of one pair of adjacent sides of the rectangle)

Therefore, we get:

[tex]24 = 2(a+b)\\\text{Dividing both the sides by 2}\\12 = a + b\\b = 12 - a[/tex]

We expressed 'b' in terms of 'a' so that we can represent the area of the considered rectangle in terms of 'a' alone.

The area of the rectangle is:

[tex]S =a \times b = a \times (12 - a) \: \rm unit^2[/tex]

Thus, the area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

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Answer:

[tex]\frac{-17}{6}[/tex]

Step-by-step explanation:

Let x be the number we want to find.

First we analyze the given informations

Info 1 : Two times the sum of four times a number plus six

We translate this statement (info 1) mathematically as :  2×(4x + 6)

Info 2 : five less than twice the same number

We translate this statement (info 2) mathematically as : 2x - 5

Info 1 is the same as Info 2 ⇔ 2×(4x + 6) = 2x - 5

2×(4x + 6) = 2x - 5

⇔ 8x + 12 = 2x - 5

⇔ 8x - 2x = -5 - 12

⇔ 6x = - 17

⇔ x = -17/6

Answer:

It's (5,4)

Step-by-step explanation:

hope this helps :)

The expression that represents the value of the stock after two years have passed is 1.5498x

Percentage is the fraction of an amount expressed as a number out of hundred. The sign used to represent percentages is %.

The value of the stock after year 1 = worth of the stock when it was bought x (1 + percentage increase in year one)

1.23x

The value of the stock after year 2 = worth of the stock in year 1 x (1 + percentage increase in year two)

1.26 x 1.23x = 1.5498x

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Let's solve your system by substitution.

2x−2y=−4;2x+y=11

Rewrite equations:

2x+y=11;2x−2y=−4

Step: Solve2x+y=11for y:

2x+y=11

2x+y+−2x=11+−2x(Add -2x to both sides)

y=−2x+11

Step: Substitute−2x+11foryin2x−2y=−4:

2x−2y=−4

2x−2(−2x+11)=−4

6x−22=−4(Simplify both sides of the equation)

6x−22+22=−4+22(Add 22 to both sides)

6x=18

6x/6 = 18/6

(Divide both sides by 6)

x=3

Step: Substitute3forxiny=−2x+11:

y=−2x+11

y=(−2)(3)+11

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

Answer:

3/4

hope this helps. have a nice day :>

The statement that is true about the trinomial is the greatest common factor of the terms is 1.

A trinomial is a polynomial with three terms or monomials.

To know which statements about the polynomial are true, let's check each of the statements individual.

A.) The polynomial can be rewritten after factoring as [tex]10(3x^2+4xy+5y^2)[/tex]

Since the product of 5 and 10 is equal to 50, the third term is 51. Therefore, the statement about the polynomial is false.

B.) The polynomial can be rewritten as the product of a trinomial and xy.

All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.

C.) The greatest common factor of the polynomial is 51x2y2.

All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.

D.) The greatest common factor of the terms is 1.

As all the greatest common factors of the terms are completely different, therefore, the only common factor between the three terms will be 1.

Hence, the statement that is true about the trinomial is the greatest common factor of the terms is 1.

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Answer:

Step-by-step explanation:The statement that is true about the trinomial is the greatest common factor of the terms is 1.

What is a trinomial?

A trinomial is a polynomial with three terms or monomials.

To know which statements about the polynomial are true, let's check each of the statements individual.

A.) The polynomial can be rewritten after factoring as

Since the product of 5 and 10 is equal to 50, the third term is 51. Therefore, the statement about the polynomial is false.

B.) The polynomial can be rewritten as the product of a trinomial and xy.

All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.

C.) The greatest common factor of the polynomial is 51x2y2.

All the terms in the polynomial are completely different therefore, can not be written as the product of a trinomial and xy.

D.) The greatest common factor of the terms is 1.

As all the greatest common factors of the terms are completely different, therefore, the only common factor between the three terms will be 1.

Hence, the statement that is true about the trinomial is the greatest common factor of the terms is 1.

The approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have  [tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z-tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

For this case, we have to find:

[tex]P(-0.78\leq Z \leq 1.16)[/tex]

It can be rewritten as:

[tex]P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z < -0.78) \\P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z \leq -0.78)[/tex]

The p-values for Z = 1.16 and Z = -0.78 from the z-table is found as 0.8770 and 0.2177 respectively, and therefore, we get:

[tex]P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z \leq -0.78)\\P(-0.78\leq Z \leq 1.16) = 0.8770 - 0.2177 = 0.6593[/tex]

Thus, the approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593

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Answer:

B.) The answer is 66% if you convert it from decimals

Answer:

I think for A It is 3.

Step-by-step explanation:

Answer:

The cross section of a cube is square...

and we know that ,Area of square = side²

so, Area of cross section= l²

Hope it helps you

Answer: $950

1250-299=951

round off to nearest hundred, $950

The estimated sale price of the couch after rounding each number to the nearest hundred is $901.

To estimate the sale price of the couch, we first need to round each number to the nearest hundred.

Original price: $1250

Rounded to the nearest hundred: $1200

Discount amount: $299

Now, let's calculate the estimated sale price by subtracting the discount from the rounded original price:

Estimated Sale Price = Rounded Original Price - Discount Amount

Estimated Sale Price = $1200 - $299

Estimated Sale Price = $901

The estimated sale price of the couch after rounding each number to the nearest hundred is $901.

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Answer:1/8, 2/5 3/4

Step-by-step explanation: you can turn each into decimal

0.125, 0.4 and 0.75

Answer:

[tex]\dfrac{1}{8} < \dfrac{2}{5} < \dfrac{3}{4}[/tex]

Step-by-step explanation:

[tex]\text{You can rewrite the fractions as}\\\\\dfrac 18=\dfrac{5}{40}\\\\\\\dfrac 25 = \dfrac{16}{40}\\\\\\\dfrac 34 = \dfrac{30}{40}\\\\\\\text{So,} ~\dfrac{5}{40} < \dfrac{16}{40} < \dfrac{30}{40}[/tex]

Step-by-step explanation:

I hope this helps, you take the substitution and put it in where the variable once was in parenthesis, then you let them interact as the vaiable onece was but now you can solve because you know the value.

Step-by-step explanation:

[tex]area \: of \: rectangle = length \times \: width[/tex]

Given

[tex]l = 2w - 3[/tex]

using this

[tex]area = l \times w = (2w - 3)(w) = 27[/tex]

[tex]2 {w}^{2} - 3w = 27[/tex]

[tex]2 {w}^{2} - 3w - 27 = 0[/tex]

[tex]2 {w}^{2} - 9w + 6w - 27 = 0[/tex]

[tex]2w(w - 4.5) + 6(w - 4.5) = 0[/tex]

[tex](2w + 6)(w - 4.5) = 0[/tex]

[tex]w = - 3 \: \: or \: \: w= 4.5[/tex]

Since size cannot be negative therefore

[tex]w = 4.5cm[/tex]

[tex]l = 2w - 3 = 9 - 3 = 6[/tex]

Hence length of the rectangle=6m

width of the rectangle=4.5m

Answer:

Let length and breadth of rectangle be x metres and y metres respectively.

xy = 27 ---- eqn 1

x = 2y-3 ---- eqn 2

Sub eqn 2 into eqn 1:

(2y-3) × y = 27

2y² - 3y = 27

2y² - 3y - 27 = 0

(y+3)(2y-9) = 0

y+3=0 or 2y-9=0

y=-3 (rejected) 2y=9

y=4.5

Sub y=4.4 into eqn 2:

x = 2(4.5) - 3

= 6

Hence,

length of rectangle = x metres

= 6m

breadth of rectangle = y metres

= 4.5m