Solve using substitution.

x + 7y = 18
2x + 9y = 16

The domain of f(x) = 2x² + 2x + 4  is (-∞, ∞).  

A quadratic equation, or quadratics, is a polynomial equation with a maximum degree of two. It will be in the form of ax² + bx + c = 0.

When a quadratic function is represented in a graph on the x and y grid, It will represent a parabola. Either it will open upwards or downwards.

The domain of a parabola is the entire set of real numbers [ Without any restrictions ]

Here we have

Ethan uses the function, f(x) = 2x² + 2x + 4

As we know all quadratic functions are parabolas

And its domain is the set of real numbers

Therefore,

The domain of f(x) = 2x² + 2x + 4  is (-∞, ∞).

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Therefore, the numerator of the given equation comes out to be 4x+6

A fraction denotes a component of a whole or, more generally, any number of equal parts. In conversational English, a fraction, such as one-half, eight-fifths, or three-quarters, denotes the quantity of a specific size of portions.

Given

[tex]\frac{x}{x^{2} +3x+2} + \frac{3}{x+1}[/tex]

A common denominator must exist for the fractions before we can add them.

Factor the denominator of the first fraction

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

Subtract (x + 2) from the second fraction's numerator and denominator.

[tex]\frac{x}{(x+1) (x+2)} + \frac{3(x+2)}{(x+2)(x+1)}[/tex]  ← Currently, fractions share a common denominator.

Add the numerators leaving the denominators

= [tex]\frac{(x+2)(x+3)}{(x+2)(x+1)}[/tex]  

= [tex]\frac{x^{2} +3x+6}{(x+2)(x+1)}[/tex]

=  [tex]\frac{4x+6}{(x+2)(x+1)}[/tex]

simplified sum with numerator 4x + 6

Therefore the numerator of the given equation comes out to be 4x+6.

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Answer:

1/8

Step-by-step explanation:

9/72 = 1/8

The range of the function f(x) = 3x - 4, having domain x ≥ 1 is x ≥ -1 and the graph is attached below so, option D is correct.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

The function, f(x) = 3x - 4,

Domain = x ≥ 1

When domain = 1,

Range = 3 × 1 - 4 = -1

When domain = 2

Range = 3 × 2 - 4 = 2

Thus, you can conclude the range of the function as x [-1, ∞) or x ≥ -1

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The value of f(-7) is -29.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x)=-x² + 2x + 6

So, to find f(-7) put x= -7

f(-7) =  -(7)² + 2(7) + 6

f(-7) =  -49 + 14 + 6

f(-7) =  -29

Hence, the value of f(-7) is -29.

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Answer: I believe it is reflected over the y-axis.

Step-by-step explanation:

Always look for the dum (I know it is spelled wrong but Brainly won't let me type it) and dummer answer choices. The other two choices aren't even a type of transformation. Think about it. If you are reflecting over the y-axis, the y-values stay the same and the x-values change.

Answer:

A

Step-by-step explanation:

s must be a number greater than 7

Answer: Z=35(4)^7

Step-by-step explanation:b = multiplier = 4b = multiplier = 4a = starting amount = 35a = starting amount = 35t = time = 7 hourst = time = 7 hours. a⋅b^t

35(4)735(4)7Equivalent forms:Equivalent forms:35(4)(4)(4)(4)(4)(4)(4)35(4)(4)(4)(4)(4)(4)(4)

Using the concept of probability, the probability of not landing on yellow or red at all is 1/4.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Creating a square model of the two spins :

Red(R) ; Blue(B) ; Green(G) ; Yellow(Y)

___ R ___ B ___ G ___ Y

R_ RR __ RB __ RG __ RY

B_ BR __ BB __ BG __ BY

G_ GR __GB __ GG __GY

Y_ YR __ YB __ YG __ YY

Sample space = 4² = 16

Combinations without red and yellow :

{BB, BG, GB, GG}

Number of selections without red or yellow = 4

Recall :

Probability = required outcome / Total possible outcomes

P(without Red or Yellow) = 4/16 = 1/4

Hence, the probability of not landing on yellow or red at all is 1/4.

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There were 1080 seats in the theater.

In this question, we have been given that the 6th grade students went on a field trip to see a ballet.

The students filled 702 seats leaving 35% vacant.

We need to find the total seats in the theater.

Let there were n seats in the theater.

Given that 35 percent of total seats were vacant.

So, we get an equation,

702 + (35% of n) = n

702 + 0.35n = n

(1 - 0.35)n = 702

0.65n = 702

n = 1080

Therefore, the total seats in the theater = 1080

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The solution to the system of equations is ( -2, 0)

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

y = -2x - 4 ------------1

y = x + 2--------------2

Equating equation 1 and 2 we have

-2x - 4 = x + 2

collect like terms

-2x - x = 2 + 4

-3x = 6

x = 6/-3

x = -2

but y = x + 2

substitute x = -2

y = -2 + 2, y = 0

In conclusion the solution of the system of linear equations is (-2, 0 )

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The statement that is proportion is 3/4 = 6/8

What is statement ?

Depending on the context, the term "statement" in logic can refer to either a proposition or a coherent declarative utterance that can be true or untrue. Which is the claim a true or untrue declarative phrase makes.

A sentence that asserts something to be true is called a statement.

In the fields of law, banking, and government, there are more types of statements. Every statement makes a claim or a point. If you see an accident, you have to tell the police what you observed in a statement.

A statement is a directive issued to the computer that tells it to carry out a specific task, like display something on the screen or gather input. A succession of assertions make up a computer program.

3/4 = 5/8

3:4 ≠ 5:8

3/4 = 4/8

3/4 = 1/2

3:4 ≠ 1:2

3/4 = 6/8

3/4 = 3/4

3:4 = 3:4

3/4 = 7/8

3:4  ≠ 7/8

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Answer:

the slope is -1/9

Step-by-step explanation:

The first thing to do is use the slope formula y^1 - y^2 over x^1 - x^2. You substitute each value into these variables and solve, which will then give you a negative slope of -1/9.

hope this helps!! :3

Answer: 36.72 G

Step-by-step explanation:

I sell

The actual quotient and the estimated quotient of 78,070÷37 is 2110 , so the difference between them is 0.

On dividing 78,070 by 37 ,

we get

78,070 /37

=2110

Since , the number gets divided completely

therefore the estimated quotient and the actual quotient will be 2110.

We first round the dividend and the divisor to the closest tens, hundreds, or thousands, and then divide the rounded figures to approximate the quotient. When the divisor in a division sum has two or more digits, it is helpful to first estimate the quotient before attempting to discover the exact number.

The outcome of dividing two numbers is known as the quotient. Divided divisor = quotient + remainder is the formula for expressing the terms of division.

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The value of f(3) is 10.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here, we have

Given function :

f(x) = 4x - 2

We have to find the value of f(3).

Now we put x = 3 and we get

f(3) = 4 × 3 - 2

f(3) = 12 - 2

f(3) = 10

Hence, the value of f(3) is 10.

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Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

What is a Pythagoras theorem?

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:

a² + b² = c²

To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:

KL² = KM² + KN²

Substituting the given values, we get:

24² = 10² + KN²

Solving for KN, we get:

KN² = 24² - 10²

= 576 - 100

= 476

KN = √476

= 21.84

Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

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Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

What is a Pythagoras theorem?

The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:

a² + b² = c²

To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:

KL² = KM² + KN²

Substituting the given values, we get:

24² = 10² + KN²

Solving for KN, we get:

KN² = 24² - 10²

= 576 - 100

= 476

KN = √476

= 21.84

Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.

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you will be on floor no. -8 and your friend will be in floor no. 5 if you and your friend started at floor no. 0

YOU CAN ALSO VISUALISE THIS WAY

Answer:

s = 3

Step-by-step explanation:

We model the proportion with the equation:

[tex]s =\frac{k}{t}[/tex]

We have s and t, but we need to find the k (i.e., the constant of proportionality) by plugging in the s and t we already have:

[tex]0.9=\frac{k}{2}\\ 1.8=k\\s=\frac{1.8}{t}[/tex]

To find s when t = 0.6, we simply plug in 0.6 for t in last equation we found with k:

[tex]s=\frac{1.8}{0.6}\\ s=3[/tex]

Answer:

23.5 degrees north

Step-by-step explanation:

In linear equation, Sofia will order 7 more rolls of sushi (84 pieces) and pay $56.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

They need at least 100 pieces of sushi

Sofia had ordered and paid for 24 pieces of sushi already

Sushi comes in rolls

Each roll=12 pieces at $8

R=additional rolls that Sofia orders

Additional sushi= Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

Each roll has 12 pieces

76/12=6.33

Sofia has to order in rolls

So, she will order 7 more rolls of sushi of 12 pieces each

12*7=84 pieces

Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100

If Sofia orders 84 pieces + the already ordered 24 pieces

Total pieces=108 pieces

She has paid for 24 pieces (3 rolls) at $8 per roll

7 rolls=$8*7

=$56

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The calculated value of the rocket's greatest height is 196 feet

From the question, we have the following parameters that can be used in our computation:

height function,  h(t) =-16t² + 80t + 96

So, we have

h(t) =-16t² + 80t + 96

The maximum value of t is calculated as

t = -b/2a

So, we have

t = -80/(2 * -16)

Evaluate

t = 2.5

The rocket's greatest height is at t = 2.5

So, we have

h(2.5) =-16(2.5)² + 80(2.5) + 96

Evaluate

h(2.5) = 196

Hence, the rocket's greatest height is 196 feet

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Answer:

$1,018.39

Step-by-step explanation:

Interest formula is I = Prt/100

where P = principal

r = interest rate (in percent)

t = number of time periods

Here we have P = 740

interest = 0.66% per day

t = 57 days

I = 740 x 0.66 x 57 /100 = 278.39 (rounded)

Total amount to pay back = 740 + 278.39 = $1,018.39

Answer:

56

Step-by-step explanation:

divide 7 into 28 which is 4.

Then substitute 4 for M so 4 times 14 which is 56.

Figure D was reflected over the y axis and translated 4 units upwards to form figure E

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

According to the given question:

On translating the figure D over y-axis, the figure E will be 4 units above.

Therefore,  Figure D was reflected over the y axis and translated 4 units upwards to form figure E.

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The required factors of the given polynomial is (r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10).

A factor  is a number that partitions another number, leaving no remainder portion.  if multiplying two whole number gives us an item, the numbers we are increasing are variables of the item since they are separable by the item.

We have given,

t^12 - r^3(s)^15

By using formula

(a³ - b³) = ( a+ b)( a² -ab + b²)

Then,

(r^4)^3 - (rs^5)^3

(r^4 + rs^5)((t^4)^2 - rs^5t^4 + (r^5)^2)

(r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10)

Thus, required answer is (r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10), So option (D) is correct.

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Answer:

the answer to this should be no solution

Step-by-step explanation:

the first step would be adding seven to both sides, but all that does is leave a zero on the other side, so the equation ends up being 9x=0.

The value of x in the expression is 0.

We have,

Expression: 9x - 7 = -7

To solve for x.

Add 7 on both sides.

9x - 7 + 7 = -7 + 7

9x = 0

x = 0

Thus,

The value of x in the expression is 0.

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Answer:

4

Step-by-step explanation:

[tex] \frac{2}{3} \times 6 = 4[/tex]

I think she can make 4 throw pillows if she should use 6 yards of fabric

i hope this helped

Answer:

x^3y^2√xy

Step-by-step explanation:

First, you calculate what's in the square root. x^2 becomes x and y^4 becomes y^2.

Then you distribute the 1/2 to the x^5 and the y so they become x^5/2 and y^1/2.

Next, you combine the like terms. x and x^5/2 becomes x^7/2. y^2 and y^1/2 become y^5/2.

So you have x^7/2 y^5/2

To get rid of the 2 on the bottom of the exponents you square root both variables.

So you get √x^7 y^5 (square rooted x^7 and y^5)

Simplify the square rooted problem to x^3 y^2 √xy

You get x to the third power y to the second power and square rooted xy.