what is the value of the constant in the equation that relates the height and width of the rectangle

Answer:  [tex](-9,-3)[/tex]

Step-by-step explanation:

Given the following system of equations:

[tex]\left \{ {{2x=-78-20y} \atop {-x=-51-20y}} \right.[/tex]

In order to solve the System of equations, you can use the Substitution method. The steps are:

1. You can solve for "x" from the second equation:

[tex]-x=-51-20y\\\\x=51+20y[/tex]

2. Substitute the equation obtained into the first original equation:

[tex]2x=-78-20y\\\\2(51+20y)=-78-20y[/tex]

3. Now you must solve for "y":

[tex]102+40y=-78-20y\\\\40y+20y=-78-102\\\\60y=-180\\\\y=\frac{-180}{60}\\\\y=-3[/tex]

4. Substitute the value of "y" into the equation [tex]x=51+20y[/tex] and evaluate:

[tex]x=51+20(-3)\\\\x=51-60\\\\x=-9[/tex]

Then, the solution is:

[tex](-9,-3)[/tex]

Answer:

Model B is wider car I think for the question which ones wider

Answer:

y = 1/5x

Graph Below:  

Answer:

The length and the width of the rectangle are 11 units and 5 units

Step-by-step explanation:

Let us use the factorization to find the length and the width of the rectangle

∵ The trinomial is r² - 6r - 55

∵ r² = (r)(r)

∵ -55 = (-11)(5)

- Multiply r by -11 and r by 5, then add the products, the sum

   must be equal the middle term of the trinomial

∵ (r)(-11) = -11r

∵ (r)(5) = 5r

∵ -11r + 5r = -6r ⇒ the middle term of the trinomial

∴ r² - 6r - 55 = (r - 11)(r + 5)

- Equate each factor by 0 to find the value of r

∵ r - 11 = 0

- Add 11 to both sides

∴ r = 11

OR

∵ r + 5 = 0

- Subtract 5 from both sides

∴ r = -5 ⇒ rejected because no negative dimensions

∴ The length of the rectangle is 11 units

∵ The area of the rectangle is 55 units²

∵ Area of a rectangle = length × width

∴ 55 = 11 × width

- Divide both sides by 11

∴ 5 = width

∴ The width of the rectangle is 5 units

Answer:

4

Step-by-step explanation:

Answer:

2+2 = 4

Step-by-step explanation:

2 + 2 = 4...

Step-by-step explanation:

[tex]0.031 \times 1000000 \\ = 31000 \\ moves \: 4 \: places \: to \: the \: right[/tex]

Answer: [tex]tan(x)^{2}[/tex]

Step-by-step explanation:

We will use the trigonometric identities to solve this problem:

[tex]\frac{sec(x)^{2}}{cot(x)^{2}+1}[/tex] (1)

Let's begin by the following trigonometric identity:

[tex]sec(x)^{2}=tan(x)^{2}+1[/tex] (2)

An substitute it in (1):

[tex]\frac{tan(x)^{2}+1}{cot(x)^{2}+1}[/tex] (3)

Then, taking into account [tex]tan(x)^{2}=\frac{sin(x)^{2}}{cos(x)^{2}}[/tex] and [tex]cot(x)^{2}=\frac{cos(x)^{2}}{sin(x)^{2}}[/tex], we rewrite (3):

[tex]\frac{\frac{sin(x)^{2}}{cos(x)^{2}}+1}{\frac{cos(x)^{2}}{sin(x)^{2}}+1}[/tex] (4)

[tex]\frac{\frac{sin(x)^{2}+cos(x)^{2}}{cos(x)^{2}}}{\frac{cos(x)^{2}+sin(x)^{2}}{sin(x)^{2}}}[/tex] (5)

Then, applying the trigonometric identity [tex]sin(x)^{2}+cos(x)^{2}=1[/tex]

[tex]\frac{1}{cos(x)^{2}}}{\frac{1}{sin(x)^{2}}}[/tex] (6)

Finally

[tex]\frac{sin(x)^{2}}{cos(x)^{2}}}=tan(x)^{2}[/tex] (7)

Answer:

1440 degrees

Step-by-step explanation:

The sum of the interior angles of a polygon can be found by

(n-2)*180

where n is the number of sides

a decagon has 10 sides, so n=10

(10-2) *180

8*180

1440

The sum of all the interior angles of a decagon is calculated as (n-2) × 180°. For a decagon, where n is 10, the sum is 1440°.

The correct option is (C).

The sum of all the interior angles of a decagon can be found using the formula for calculating the sum of interior angles of any polygon, which is (n-2) × 180°, where n is the number of sides of the polygon. In the case of a decagon, n is 10. Therefore, the sum of all the interior angles of a decagon is (10-2) × 180° = 8 × 180° = 1440°. Thus, the correct answer is C.1440°.

complete question given below:

The sum of all the interior angles of a decagon is

A.1000∘

B.960∘

C.1440∘

D.1200∘

Answer:

[tex] \frac{1}{ {4}^{3} } [/tex]

Step-by-step explanation:

[tex] \frac{ {4}^{2} }{ {4}^{5} } = \frac{1}{ {4}^{ - 2} \times {4}^{5} } = \frac{1}{ {4}^{(5 - 2)} } = \frac{1}{ {4}^{3} } [/tex]

Answer:

-0.259 or (√2 - √6) / 4

Step-by-step explanation:

Sin (195) using sum and difference formula.

Let's break the figure for convenience.

It becomes sin ( 135 + 60)

Invoking the sin formula we have

sin (A + B) = sin (A) cos (B) + cos (A) sin(B)

Where A = 135, B = 60

Therefore it becomes

sin(135) cos(60) + cos(135) sin (60)

From reference angle relationship we have:

(sin (45))cos (60) + cos (135) sin (60)

From trigonometric ratios, sin (45) = √2/2

Therefore, the equation becomes,

(√2/2) cos(60) + cos (135)sin (60)

(√2/2) (0.5) + cos (135) sin (60)

= (√2/2) (1/2) + ( - √2/2) ( √3/2)

Simplifying the equation

√2/4 + ( -√2/2) ( √3/2)

= √2/4 - √6/4

= (√2 - √6) / 4

OR

=( 1.414 - 2.449 ) / 4

= -1.035/4

= -0.25875

Answer:

(x - 10)(x + 10)

Step-by-step explanation:

x² - 100 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

Thus

x² - 100

= x² - 10²

= (x - 10)(x + 10)

The expression x² - 100 can be factored using the difference of squares rule in algebra. The factors are (x - 10) and (x + 10).

The question asks for the factors of the polynomial expression x² – 100. This is a special kind of polynomial that can be factored using the difference of squares rule, a powerful tool in algebra which states that any expression in the form a² - b² can be rewritten as (a - b)(a + b).

In our case, a would be x (since x² is the first term) and b will be 10 (since 10² equals 100, the second term).

Applying the difference of squares rule to your expression, we get:

x² – 100 = (x - 10)(x + 10)

The factors of the expression are therefore x - 10 and x + 10.

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Answer:

Option 1

Step-by-step explanation:

1/6 × 5/3

Step-by-step explanation:

[tex] \frac{1}{6} \div \frac{3}{5} [/tex]

[tex] \frac{1}{6} \times \frac{5}{3} [/tex]

a= 6,b=5,c=3 option A

Answer: 11/30

Step-by-step explanation: looking at this question that was given to us and to find the probability, then we will go by saying that;

Probability of an event (E) = number of outcome of Event E/total number of all event

Prob(Basebase player)=11/30

Going by this, then we are going to have our answer as 11/30

The probability that a randomly selected person from the group is a Toronto Blue Jays fan is 11/30.

The question asks for the probability that a randomly selected person from the group of 30 people at a baseball game is a Toronto Blue Jays fan, given that 11 out of the 30 people are fans of that team. To calculate the probability, you divide the number of Blue Jays fans by the total number of people in the group.

Probability = Number of Toronto Blue Jays fans ÷ Total number of people

Probability = 11 ÷ 30

The probability can be simplified into the simple fraction form of:

Probability = 11/30

Answer:

reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

Answer: A 1 million

Step-by-step explanation:

The amount of the lump sum that the insurance company must put

into a bank account is $1 million.

Option A is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We can use the present value formula for an annuity to find the lump sum that the insurance company must put into a bank account:

PV = PMT / r

where PV is the present value, PMT is the annual payment, and r is the interest rate.

Substituting the given values, we get:

PV = 40,000 / 0.04

= $1,000,000

Therefore,

The amount of the lump sum that the insurance company must put

into a bank account is $1 million.

Learn more about expressions here:

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Two mixed numbers as [tex]\frac{5}{6}[/tex] and [tex]\frac{5}{12}[/tex] the least common denominator (LCD) is 12.

Step-by-step explanation:

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Steps to find the LCD of fractions, integers and mixed numbers:

Let's us have two mixed numbers as [tex]\frac{5}{6}[/tex] and [tex]\frac{5}{12}[/tex].

Equivalent Fractions with the LCD

[tex]\frac{5}{6}[/tex] = [tex]\frac{10}{12}[/tex]

[tex]\frac{5}{12}[/tex] = [tex]\frac{5}{12}[/tex]

For the denominators (6, 12) the least common multiple (LCM) is 12. Therefore, the least common denominator (LCD) is 12.

Final answer:

The mixed numbers 1 1/4 and 2 1/3 can be converted to have the lowest common denominator of 12, resulting in 1 3/12 and 2 4/12 respectively.

Explanation:

To write two different mixed numbers where the lowest common denominator (LCD) is 12, we can choose denominators that are factors of 12 and numerators that result in proper fractions (where the numerators are less than the denominators). An example would be 1 1/4 and 2 1/3. Here's how these mixed numbers have 12 as their common denominator:

Now we have two mixed numbers with the LCD of 12.

Answer:

angle AOC is what i think it is but please dont go on my word wait to see what other people say first sorry

Answer:

Step-by-step explanation:

5+8(3+x)=5+24+8x=29+8x

x+3+5x=3+6x

5(z+4)+5(2-z)=5z+20+10-5z=30

Answer:

Step-by-step explanation:

4(x+2) = 16

4x + 8 = 16

4x =16-8

4x = 8

x = 8/4

x = 2

The solution to the equation 4(x + 2) = 16 is x = 2.

The Distributive Property states that a(b + c) = ab + ac. Apply this to the equation:

4(x + 2) = 4 * x + 4 * 2.

Thus, the equation becomes:

4x + 8 = 16.

To solve for x, first subtract 8 from both sides of the equation:

4x + 8 - 8 = 16 - 8

4x = 8.

Divide both sides of the equation by 4:

4x / 4 = 8 / 4

x = 2.

Answer:

V≈44602.24

Step-by-step explanation:

The volume of a sphere is  V=4/3πr^3. All you have to do is replace 22 for r and calculate it

Answer:

5575.28

Step by step explanation:

Answer:

23

Step-by-step explanation:

log27(9) can be interpreted as " 27 to what power is equal to 9 . Since 2723=32=9,log27(9)=23

Answer:

2/3

Step-by-step explanation:

Hi

72 Hours before 2:12 am, Monday is 2:12 am, Friday, because 72 hours before is 3 days in the past.

Answer:

She needs to work 8 hours

Answer:

5 peices of pizza for $4 each

and 4 drinks for $2

Step-by-step explanation:

The area of the largest circular fire pit is 452 square inches.

Explanation:

Given that at a campground, a rectangular fire pit is 3 feet by 2 feet

The radius is given by 1 feet.

Area:

The area of the largest circular fire is given by

[tex]A=\pi r^2[/tex]

Substituting the values in the formula, we get,

[tex]A=(3.14)1^2[/tex]

[tex]A=3.14 \ ft^2[/tex]

Thus, the area of the largest circular fire is 3.14 square feet.

To convert feet to inches:

The feet can be converted into inches by multiplying by 12.

Thus, we have,

[tex]1 \ft= 12 \ inches[/tex]

Hence, we have,

[tex]Area= 3.14\times 12^2[/tex]

Simplifying,we get,

[tex]Area= 3.14\times144[/tex]

[tex]Area=452.16 \ in^2[/tex]

Rounding off to the nearest square inch.

Thus, we have,

[tex]Area= 452 \ in^2[/tex]

Thus, the area of the largest circular fire pit is 452 square inches.

Answer:

X=7 and y=45

Step-by-step explanation:

5(7)+10=45

35+10=45

I have attached a graph

Answer:

angle 1

Step-by-step explanation:

[tex] \angle \: 1 \: is \: complementary \: to \: \angle \: 2 \\ [/tex]

Answer:

x = -8

Y = -11

Step-by-step explanation:

Given

Y = 3x + 13

Y = x - 3

Substitute x - 3 for Y in the first equation

We have

Y = 3x + 13

x - 3 = 3x + 13

Add 3 to both sides

x - 3 + 3 = 3x + 13 + 3

x = 3x + 16

Subtract 3x from both sides

x - 3x = 3x - 3x + 16

-2x = 16

Divide both sides by -2

x = 16/-2

x = -8

Now substitute -8 for x in any of the above equations to get Y.

Using the second equation, we have

Y = x - 3

Y = -8 - 3

Y = -11

Answer:

-2

Step-by-step explanation:

f(x) = –2x^2 + 5x – 4.

            A        B     C

Leading coefficient is always a which is -2x^2

Answer:

B

Step-by-step explanation:

STN is the alt exterior angle of angle 73 which means that it is congruent. STN is the vertical angle is MTQ which means that it is also equal to 73. Then you can use linear pair to find MTS. 180 - 73 which is 107.

Answer:

A

Step-by-step explanation: