the perimeter of a rectangle is 68 cm. the length is 4 cm less than three times ots width. write a system of equation to find the dimensions of the rectangle.​

Answer:

[tex]\left(a+3\right)\left(a-2\right)=a^2+a-6=[/tex]

Step-by-step explanation:

Given expression is [tex]\left(a+3\right)\left(a-2\right)[/tex].

Now we need to multiply this using FOIL.

F = First [tex]=\left(a\right)\left(a\right)= a^2[/tex]

O = Outside [tex]=\left(a\right)\left(-2\right)= -2a[/tex]

I = Inside [tex]=\left(3\right)\left(a\right)= 3a[/tex]

L = Last [tex]=\left(3\right)\left(-2\right)= -6[/tex]

Hence we get :

[tex]\left(a+3\right)\left(a-2\right)=a^2-2a+3a-6=a^2+a-6=[/tex]

Answer:

[tex](a+3)(a-2)=a^2+a-6[/tex]

Step-by-step explanation:

The given expression is:

[tex](a+3)(a-2)[/tex]

Using FOIL, we multiply the;

First terms:[tex]a\times a=a^2[/tex]

Outside terms: [tex]a\times -2=-2a[/tex]

Inner terms:[tex]3\times a=3a[/tex]

Last terms:[tex]3\times -2=-6[/tex]

Putting all together we have:

[tex](a+3)(a-2)=a^2-2a+3a-6[/tex]

This simplifies to [tex](a+3)(a-2)=a^2+a-6[/tex]

Answer might be d I think

Answer: D -2

Step-by-step explanation:

Answer:

∆AMN ≅ ∆NOA

Step-by-step explanation:

Given:

Quadrilateral AMNO

MN║AO

AM║ON

To prove:∆AMN ≅ ∆NOA

Lets first draw two diagonals represented by lines MO and AN inside the given quadrilateral AMNO

Now we know if lines are parallel then the alternate interior angles are congruent , hence

∠NMO≅∠AOM

∠MNA≅∠NAO

∠AMO≅∠NOM

∠MAN≅∠ANO

Also by Reflexive Property we have

NA≅NA

MO≅MO

From ASA congruence property of triangles that states that if two angles and a side of two triangles are congruent then the two triangle are said to be congruent, hence we have

ΔAMN≅ΔNOA

ΔMAO≅ΔONM  !

Answer:

∆AMN=∆NOA by rule SSS

Answer: [tex]x=-5[/tex]

Step-by-step explanation:

You need to find the value of the variable "x".

Solve for "x":

Subtract [tex]\frac{5}{6}x[/tex] from both sides of the equation:

[tex]\frac{2}{3}x-\frac{1}{2}-\frac{5}{6}x}=\frac{1}{3}+\frac{5}{6}x\\\\-\frac{1}{6}x-\frac{1}{2} =\frac{1}{3}[/tex]

Add  [tex]\frac{1}{2}[/tex]  to both sides of the equation:

[tex]-\frac{1}{6}x-\frac{1}{2}+\frac{1}{2} =\frac{1}{3}+\frac{1}{2}\\\\-\frac{1}{6}x=\frac{5}{6}[/tex]

Multiply both sides of the equation by -6:

[tex](-\frac{1}{6}x)(-6)=(\frac{5}{6})(-6)\\\\x=-5[/tex]

[tex]\bf \cfrac{4^2-20\div 5}{1-5+7}\implies \cfrac{\stackrel{\downarrow }{16}-20\div 5}{1-5+7}\implies \cfrac{16-\stackrel{\downarrow }{4}}{1-5+7}\implies \cfrac{\stackrel{\downarrow }{12}}{1-5+7} \\\\\\ \cfrac{12}{\stackrel{\downarrow }{-4}+7}\implies \cfrac{12}{\stackrel{\downarrow }{3}}\implies 4[/tex]

Answer:

60

Step-by-step explanation:

124−4(3−5(17−14)+2(9+5))

=124−4(3−(5)(3)+2(9+5))

=124−4(3−15+2(9+5))

=124−4(−12+2(9+5))

=124−4(−12+(2)(14))

=124−4(−12+28)

=124−(4)(16)

=124−64

=60

Answer:

0.2

Step-by-step explanation:

2 divided by 10 gives you the decimal.

Separate the kite into two triangles.

The base of the triangles would be 6 ( half the width is given as 3, so the full width would be 3 x 2 = 6).

The height of the bottom triangle is given as 10.

The area of a triangle is 1/2 x base x height.

Bottom triangle = 1/2 x 10 x 6 = 30 square units.

For the top triangle you need to find the height using the Pythagorean theorem.

Height = √(5^2 - 3^2) = √(25-9) = √16 = 4

Now the area of the top triangle is 1/2 x 4 x 6 = 12 square units.

Total area = Bottom + top = 30 + 12 = 42 square units.

Answer:

1 out of 5

Step-by-step explanation:

There are 5 answer choices total and you're supposed to choose 1 answer so 1 outta 5.

The probability that Peter will choose the correct answer by chance is 1/5 or 0.2 (or 20%).

If Peter has no knowledge about the correct answer to question number 4 on a multiple-choice test with 5 answer choices, the probability of him randomly selecting the correct answer is 1 out of 5.

This probability can be calculated by dividing the number of favorable outcomes (1, since there is only one correct answer) by the total number of possible outcomes (5, since there are 5 answer choices).

Mathematically, it can be represented as 1/5. Thus, the probability that Peter will choose the correct answer by chance is 1/5 or 0.2 (or 20%). This means that, on average, he would be expected to choose the correct answer 20% of the time if he were to guess without any knowledge or information.

To know more about probability:

https://brainly.com/question/32117953

#SPJ2

Answer:

(9,-6)

Step-by-step explanation:

4x+3y=18

3x+4y=3

Multiply the first equation by 3

3(4x+3y)=18*3

12x+9y = 54

Multiply the second equation by -4

-4(3x+4y)=3*-4

-12x -16y = -12

Add these two new equations together to eliminate x

12x+9y = 54

-12x -16y = -12

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

    -7y = 42

Divide each side by -7

-7y/-7 = 42/-7

y = -6

Now we can find x

3x+4y =3

3x +4(-6) = 3

3x -24 =3

Add 24 to each side

3x-24+24 = 3+24

3x = 27

3x/3 = 27/3

x = 9

(9,-6)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x+3y=18&(1)\\3x+4y=3&(2)\end{array}\right\\\\(1)\\4x+3y=18\qquad\text{subtract}\ 4x\ \text{from both sides}\\3y=-4x+18\qquad\text{divide both sides by 3}\\y=-\dfrac{4}{3}x+6\qquad\text{substitute it in (2):}\\\\3x+4\left(-\dfrac{4}{3}x+6\right)=3\qquad\text{use the distributive property}\\\\3x+(4)\left(-\dfrac{4}{3}x\right)+(4)(6)=3\\\\3x-\dfrac{16}{3}x+24=3\qquad\text{multiply both sides by 3}\\\\9x-16x+72=9\qquad\text{subtract 72 from both sides}\\\\-7x=-63\qquad\text{divide both sides by (-7)}\\\\\boxed{x=9}[/tex]

[tex]\text{Put the value of x to (1):}\\\\y=-\dfrac{4}{3}(9)+6\\\\y=(-4)(3)+6\\\\y=-12+6\\\\\boxed{y=-6}[/tex]

Answer:

The area of the biggest possible square that fit into the circle is 18 cm²

Step-by-step explanation:

* Lets talk about the square inscribed in a circle

- The square is fit into the circle if its four vertices lie on the

  circumference of the circle

- The diagonal of the square is the diameter of the circle

- The vertices of the square divide the circle into 4 equal arcs

* Look to the attached figure

- The square ABCD fit into the circle M

- A , B , C , D lie on the circumference of the circle M

- The four arcs AB , BC , CD , AD are equal in measure and length

- The diagonal of the square is DB

- The diameter of the circle M is DB

∵ The radius of the circle is 3 cm

∵ The diameter = twice the radius

∴ The diameter of the circle = 2 × 3 = 6 cm

∴ DB = 6 cm

- The rule of the area of the square = (diagonal)²/2

∵ The length of the diagonal is 6 cm

∴ The Area of the square = (6)²/2 = 36/2 = 18 cm²

* The area of the biggest possible square that fit into the circle is 18 cm²

Answer:

The area of the biggest possible square = 36 cm²

Step-by-step explanation:

From the figure attached with this answer shows that, the biggest possible square that would fit into a circle having a radius of 3 cm.

To find the area of square

Side of square  = 2 * radius of circle = 2 * 3 = 6 cm

Area of square = side * side = 6 * 6 = 36 cm²

Answer:

Step-by-step explanation:

1. Due to the stretchiness of shirt fabric and the waste involved in cutting pattern pieces, it is unrealistic to require that the length of the fabric be specified to a hundredth of a centimeter. Measurement to the nearest half-centimeter is sufficiently accurate for the purpose. The appropriate choice is the measurement with a precision of 1 cm:

  232 cm

__

2. The most appropriate choice is the one that shows cubing 6^(1/3) will result in 6, just as cubing ∛6 will result in 6.

Answer:

∠EFA

Step-by-step explanation:

Linear pair : A linear pair is a pair of adjacent angles formed when two lines intersect and the sum of these angles is 180°

Vertical angles: The opposite angles formed by the two intersecting lines are called vertical angles.

Option 1) ∠BFC

Line BE and CF intersect at point F

So, the two adjacent angles formed when two lines intersect are ∠BFC and ∠EFC.

These are linear pair.

So,  ∠BFC is a part of linear pair.

Now by the definition of vertical angles , ∠BFC has no vertical pair.

So, ∠BFC is not a part of vertical pair.

Option 2) ∠CFG

According to the definition of linear pair ∠CFG is not a part of linear pair.

According to the definition of vertical pair ∠CFG is not a part of vertical pair.

Option 3) ∠GFD

According to the definition of linear pair ∠GFD has a linear pair ∠AFG

Thus ∠GFD is a part of linear pair

According to the definition of vertical pair ∠GFD is not a part of vertical pair.

Option 4) ∠EFA

According to the definition of linear pair ∠EFA has a linear pair ∠EFD

Thus ∠EFA is a part of linear pair

According to the definition of vertical pair ∠EFA has a ∠BFD vertical pair.

Thus ∠EFA is a part of vertical pair.

Hence ∠EFA is part of a linear pair and part of a vertical pair.

Answer:

D) EFA

Step-by-step explanation:

Let's see the definition of linear pair and vertical angles.

A linear pair of angles are the adjacent angles, when the angles add upto 180°.

Vertical angles are the  opposite angles when the two lines are intersecting. The vertical angles are equal in measure.

In the given figure there are only two lines, they are AD and BE. Othere are just rays.

By look at the figure, ∠EFA is a linear pair to∠EFD and as well as vertical angle to ∠DFB.

Therefore, the answer is D) EFA

Answer:

The numbers between 30 and 40 whose only factors are one and themselves, also called prime numbers, are 31 and 37.  :)

Answer:

It is 31 and 37

Numbers that have only one and itself as a factor are called prime numbers.

The distribution is very simple. Using FOIL.

It states that [tex](a+b)(c+d)=ac+ad+bc+bd[/tex].

Also note that when multiplying expressions we multiply variables and values differently. If we have variables like [tex]x[/tex] their exponents will add. If we have values like 3 we multiply them normally.

For example your practise 3.

[tex](x+3)(2x^2+4)=2x^2\cdot x+4x+3\cdot2x^2+3\cdot4 \\

\underline{2x^3+4x+6x^2+12}

[/tex]

Now just order the expressions from bigger exponent to smaller and than values. (Usual notation although no need).

And solution is:

[tex]\boxed{2x^3+6x^2+4x+12}[/tex]

Hope this helps.

r3t40

Answer:

See below

Step-by-step explanation:

[tex]a\cdot(b + c) = a\cdot b + a\cdot c[/tex]

3) Practice: Organizing information

[tex]\begin{array}{lll}\qquad \textbf{Steps} & \textbf{Problem: }(x + 3)(2x^{2} + 4) & \\\textbf{1. List variables} & a = x + 3 & \\ & b = 2x^{2} & \\ & c = 4 &\\\\\textbf{2. Distribute} & (x + 3)(2x^{2} + 4)& = (x + 3)(2x^{2}) + (x + 3)(4)\\\\\textbf{3. Redistribute} & (x + 3)(2x^{2})& (x + 3)(4)\\& a = 2x^{2} & a = 4\\& b = x & b = x\\& c = 3 & c = 3\\& 2x^{3} + 6x^{2} & 4x + 12\\\textbf{4. Combine}& & \\\qquad\textbf{terms} & 2x^{3} + 6x^{2}+ 4x + 12 & \\\end{array}[/tex]

4. Practice: Summarizing

[tex]\text{You can use the FOIL method to multiply two }\underline{\text{binomials}}.\\\text{The letters in FOIL stand for }\underline{\text{First, Outer, Inner, Last}}.\\\text{The FOIL method helps you to remember how to multiply each term in one }\\\underline{\text{binomial}} \text{ by each term in the other }\underline{\text{binomial}}.[/tex]

Answer:

500000x4000000000000 = 2 x 10^18

Answer: [tex]2*10^{18}[/tex]  or  [tex]2,000,000,000,000,000,000[/tex]

Step-by-step explanation:

You can just make the multiplication indicated:

[tex]500,000*4,000,000,000,000=2,000,000,000,000,000,000[/tex]

You can rewrite the product in scientific notation form. This form is:

[tex]a*10^n[/tex]

Where "a" is a number between 1 and 10 but lesss than 10, and "n" is an integer.

In scientific notation, the decimal point must be after the first digit.

So, for the product [tex]2,000,000,000,000,000,000[/tex] the decimal point must be moved 18 places to the left.

Then, you get:

[tex]=2*10^{18}[/tex]

Answer:

410.5 yards cubed

Step-by-step explanation:

Volume of a cone is 1/3Bh

h is the height of the cone

B is the area of the base, which is a circle, so use πr^2 to find area of the circle

The radius is 7, so:

π7^2

π49(8)(1/3) = 410.5

Answer:

Step-by-step explanation:

Equation

Volume = (1/3) * pi * r^2 * h

Givens

pi = 3.14

r = 7 yd

h = 8 yd

Solution

V = (1/3) * 3.14 * 7^2 * 8

V = (1/3) * 3.14 * 49 * 8

V = (1/3) *  1231.5

V = 410.5 cubic yds.

Answer:

36 watts.

Step-by-step explanation:

Power is calculated from

W = E^2/R

E = 24 volts.

R = 16 ohms

W = 24^2 / 16

W = 576 / 16

W = 36 watts.

Answer:

Step-by-step explanation:

(x+3)^2=35+1

(x+3)^2=36

(x+3)^2=6^2

taking squareroot

x+3=+-6

x+3=6,-6

x=6-3=3

or x=-6-3=-9

Answer:

Step-by-step explanation:

x(7x^2+4x) can be expanded by multiplying each of the two terms inside the parentheses by x:

x(7x^2+4x) = 7x^3 + 4x^2

Step-by-step explanation:

*****************here is the answer

area=28.61+12=40.61**************

I have no idea about the part A, but part b, all you have to do is get all the numbers of the fans, and put them in least to greatest. Then you count how fans are from 0-9, then you count how much fans are from 10 - 19, and so on. Im sorry that i couldn't answer it completely but i hope this helps.

Answer:

Step-by-step explanation:

First we will arrange the ages of fans of the basketball game in the increasing order.

9, 11, 14, 14, 16, 25, 25, 27, 28 30, 33, 35, 35, 37, 38, 39, 42, 46, 47, 60

Part A. Now we will make stem-and-leaf plot

0  |  9

1   |  1, 4, 4, 6

2  |  5, 5, 7, 8

3  |  0, 3, 5, 5, 7, 8, 9

4  |  2, 6, 7

5  |

6  |  0

Part B.

Frequency table

Age           Number of Fans

0 - 9                  1

10 - 19               4

20 - 29             4

30 - 39             7

40 - 49             3

50 - 59             0

60 - 69             1

For this case we must find the solutions of the following quadratic equation:

[tex]x ^ 2-5x-1 = 0[/tex]

We solve by means of[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Where:

[tex]a = 1\\b = -5\\c = -1[/tex]

Substituting:

[tex]x = \frac {- (- 5) \pm \sqrt {(- 5) ^ 2-4 (1) (- 1)}} {2 (1)}\\x = \frac {5 \pm \sqrt {25 + 4}} {2}\\x = \frac {5\pm\sqrt {29}} {2}[/tex]

Finally, the roots are:

[tex]x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}[/tex]

Answer:

[tex]x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}[/tex]

Answer:

Surface Area = Sum of area of all sides = 203.2 Units Squared

Step-by-step explanation:

Top and Bottom: A = ((.5*4*6) + (.5*3.6*2)) * 2 => (12+3.6) *2 => 15.6*2 = 31.2

Sides: A = ((5*10)+(3.6*10)) *2 => (50 + 36) *2 => 86*2 = 172

Total Surface Area = Top + Bottom + Sides = 203.2 units squared

First you must distribute the 3 to the numbers in the parentheses

(3*m) + (3 * -5) + m

3m + (-15) + m

3m - 15 + m

Combine like terms (3m and m)

4m - 15

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3m - 15 + m

Step-by-step explanation:

Multiply (m - 5) by 3.

m * 3 = 3m

-5 * 3 = -15

This doesn't apply with +m.

So this leaves it as 3m - 15 + m.

Hope this helps! :)

When r varies inversely with x and r = -2 when x = 6, the value of r when x = -3 is 4.

r varies inversely with x, meaning that as one increases, the other decreases. Given r = -2 when x = 6, we can find the constant of variation by using the formula for inverse variation: r₁ * x₁ = r₂ * x₂. Plugging in the values, we have (-2) * 6 = r₂ * -3, which simplifies to r₂ = 4. Therefore, when x = -3, the value of r is 4. This demonstrates the relationship between variables in an inversely proportional scenario, elucidating the concept of variation in algebraic contexts.

Answer:

15

Step-by-step explanation:

if you have 2/5 lengths each time, if you divide that by 6 it gives 15.

Or if you go 2/5 to 4/5 to 6/5 until you have 30/5 because that is how long 6 feet is.

The answer is 8x^4y^5.It has the highest degree and that is 4 in x and 5 in y.

Answer:

Step-by-step explanation:

Answer:

[tex]r^2=4\sec 2\theta}[/tex]

Step-by-step explanation:

The given equation is:

[tex]x^2-y^2=4[/tex]

We substitute [tex]x=r\cos (\theta)[/tex] and [tex]y=r\sin (\theta)[/tex] to obtain:

[tex]r^2\cos^2\theta-r^2\sin^2\theta=4[/tex]

This implies that:

[tex]r^2(\cos^2\theta-\sin^2\theta)=4[/tex]

Apply double angle identity to obtain:

[tex]r^2\cos 2\theta=4[/tex]

This implies that:

[tex]r^2=\frac{4}{\cos 2\theta}[/tex]

This simplifies to:

[tex]r^2=4\sec 2\theta}[/tex]

Answer:

-13

Step-by-step explanation:

-4-8+3+6-10

Answer:-13

Step-by-step explanation: