Graph the function. Identify whether or not the graph is a function

Answer:

x = 6

Step-by-step explanation:

∠ 1 and ∠ 2 are alternate exterior angles and are congruent , then

5x - 4 = 3x + 8 ( subtract 3x from both sides )

2x - 4 = 8 ( add 4 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

The equation of the line perpendicular to the line y = 2x and is passes through (10,2) is given by  y = (-1/2)x + 7.

As given in the question,

Equation of the line is given by :

y = 2x

Point (x₁ , y₁ ) = (10, 2) through which line passes .

Slope intercept form is given by :

y = mx + c

'm' is the slope of the line.

slope of the line y = 2x is equal to  'm₁' = 2

let 'm₂' be the slope of the line perpendicular to the given line y = 2x.

Relation between the slopes of two perpendicular lines is given by :

m₁ × m₂ = -1

⇒2 × m₂ = -1

Divide both the side by 2 we get,

⇒m₂ = -1/2

Equation of the required line is:

(x₁ , y₁ ) = (10, 2)

y - y₁ = m₂ ( x - x₁ )

⇒ y - 2 = (-1/2) ( x - 10 )

⇒ y =(-1/2)x + 7

Therefore, the equation of the line perpendicular to the given line y =2x  is given by  y = (-1/ 2)x + 7 .

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Answer:

[tex]90^{\circ}[/tex]

Step-by-step explanation:

A right angle measures [tex]90^{\circ}[/tex].

-12 will be the term for y

Let us suppose that x= 0

then we will get

3y + 4 = x

and then it will be

3y+ 4 = 0

Now, we will move 4 to the right hand side and it being positive this side will become negative on right hand side

3y= -4

now,

3y = 1/4

y = 1/[4*3]

y=1/12

y= - 12

Hence the answer will be y= -12

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Therefore , the required inequality expression is 4.50x+1.75y ≤50

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

One cupcake costs $4.50,

So, “x” cupcakes cost = 4.50x.

One brownie cost $1.75,

so “y” brownies cost = 1.75y.

thus, the total 4.50x+1.75y  must be less or equal to $50.

Therefore , the required inequality expression is 4.50x+1.75y ≤50

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Answer:

Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Here are 4 options available to choose from:

1) 45 = 3² x 5 (multiply the sum of 3 times 3 by 5)

2) (3 x 8 )+ (24 x 2) - 3 (multiply 8 times 3 and then 24 times 2 add expressions together then subtract 3 from sum of expressions)

3)  (9 x 9)- 36 = 45 (multiply 9 times 9 and subtract 36 from 81)

4) [tex]6^{2}[/tex] -9 (multiply 6 times 6 and subtract 9 from 36)

(Hope this helped you )

Answer:

Step-by-step explanation:

The 25° angle the light ray makes with the normal, B which is the angle of incidence, according to the laws of reflection, indicates that the angle of reflection, which is the angle the reflected ray makes with the normal, C, is 25°

The laws of reflection states that (1) The angle of incidence and the angle of reflection have the same value (2) The incident ray, the reflected ray and the normal are coplanar (3) The refracted ray is on the opposite side of the normal with regards to the incident ray.

The law of reflection states that the angle the in of reflection and the angle of incidence are equal; [tex]\theta_i = \theta_r[/tex]

The angle the incident ray makes with the normal of the plain mirror and the angle the reflected ray makes with the normal are the same.

The angle the incident ray in the diagram of the question makes with the normal line segment, B = 25°

The angle the reflected ray makes with the normal line segment = C

Therefore, according the to the laws of reflection, we get;

Angle B = Angle C

Angle B = 25°

Therefore;

Angle C = Angle B = 25° (symmetric property)

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The number of terms in the algebraic expression is 3 terms.

An algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

Coefficient refees to a constant by which an algebraic term is multiplied.

Constant is a quantity that remains at a fixed value throughout a given discussion.

x + 3 + 7x

Thr terms are;

x;

3;

7x

Therefore, the algebraic expression has Coefficient, constant, and like terms.

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Perpendicular lines intersect at 90° - definition of perpendicular.

Here is the two column proof:

     Statement                                        Reason                                              

The linear approximation found to estimate ln(0.97) is 9.1%.

The definition of a linear approximation of a function is simply utilising a line to approximate the value of the function at a point. We recall the idea of the tangent line as soon as we see a curve (of a function) and a point on it. The value of the function at any point that is very close to the provided point can be roughly determined using the equation of the tangent line if the equation of the tangent line is found at the supplied point.

The given function is f(x) = ln(x).

We start by finding the equation of the tangent line at x=1 to the graph of y=lnx.

f(1)=ln(1)=0

We know the derivative of f(x) will be f'(x)=1/x

f'(1)=1/1=1

Therefore, the equation of the tangent is:y−y1=m(x−x1)

y−0=1(x−1)

y=x−1

An approximation for ln(1.19) would be y=1.19−1=0.19

The actual value, obtained using a calculator, would be 0.174. This means the percent error is (0.19−0.174)/0.174 ×100

= 9.1%

Therefore, the linear approximation found to estimate ln(0.97) is 9.1%.

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Answer:

  Ms finch has the higher ratio

Step-by-step explanation:

Given ratios 2 : 6 and 3 : 5, you want to know which is greater.

There are several ways to compare ratios. You can express them over a common denominator, compare them to a common value, convert them to decimal, subtract one from the other.

  2 : 6 vs 3 : 5 = 10 : 30 vs 18 : 30

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.

  2 : 6 vs 3 : 5

We can compare each of these to 1/2.

  2 : 6 < 3 : 6 = 1/2

  3 : 5 > 2.5 : 5 = 1/2

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.

  2 : 6 ≈ 0.333

  3 : 5 = 0.600

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.

  2/6 -3/5 = (10 -18)/(30) = -8/30 so the second ratio is higher

3 : 5 is greater than 2 : 6, so Ms finch has the higher ratio.

Answer:

18x24=432 so basically 432 should go to the carpenters

Barry will post all of his parcels separately at £17.84

The information in the table have the amount to post certain weights of the parcel. This will be used to ascertain how much to send Barry's parcel

Barry's parcel will contains (starting from the least)

weight of parcel                    cost of posting as from the table

less than 1 kg (1kg to 5kg)      £2.04

0.245 kg (1kg to 5kg)             £2.04

2.7 kg (1kg to 5kg)                  £2.04

4.16 kg (1kg to 5kg)                £2.04

27.3 kg (More than 20kg)      £9.68

addition of the costs

= £2.04 * 4 + £9.68

= £17.84

hence the cost of sending the five parcels is £17.84

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The required value of c is 16 which is the correct answer that would be an option (C).

In triangle LMN, m∠L = (4c + 47). If the exterior angle to L measures 69°,

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

In the case of triangle LMN, we can use the given information to write the following equation:

⇒ 180 - 69 =  (4c + 47)

⇒ 111 = 4c + 47

⇒ 4c = 111- 47

⇒ 4c = 64

⇒ c = 64/4

Apply the division operation, and we get

⇒ c = 16

Thus, the value of c is 16.

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As BD intersects AC and EC in the same ratio length of AB is 1.5 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

As BD is parallel to AD BD intersects AC and EC in the same ratio.

Now, CD is 8 units and DE is 2 units so, CD is (8/2) = 4 times larger than

DE.

Therefore BC is also 4 times larger than AB,

So, 4AB = BC.

4AB = 6.

AB = 1.5

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The height of the given pentagonal such that its base area is 42 units² will be 7.9 units.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of the cuboid = length × height × width.

Suppose that height of the pentagonal is h.

Volume = base area x height h

331.8 = 42 x h

h = 7.9 units.

Hence "The height of the specified pentagonal will be 7.9 units such that its base area is 42 units²".

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Answer:

the answer for slope is -1

Answer:

x=2.5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

substitute x = 9 into f(x) and evaluate for output

f(x) = [tex]\frac{1}{2}[/tex] (3x + 7)

f(9) = [tex]\frac{1}{2}[/tex] (3(9) + 7)

     = [tex]\frac{1}{2}[/tex] (27 + 7)

     = [tex]\frac{1}{2}[/tex] × 34

     = 17

The value of 45 less than the product of 18 and a number written as an algebraic expression will be B. 45 - 18n

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

45 less than the product of 18 and a number written as an algebraic expression will be:

= 45 - (18 × n)

= 45 - 18n.

The correct option is B.

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Answer:

D) [tex]\frac{\sqrt{14}}{7}[/tex]

Step-by-step explanation:

[tex]\sqrt{\frac{2}{7}}=\frac{\sqrt{2}}{\sqrt{7}}=\frac{\sqrt{14}}{7}[/tex]

Answer:

90

Step-by-step explanation:

Let's call the initial distance from the jet to the airport $x$. We are told that $x = 5$ miles.

Let's call the initial ground distance from the projection of the jet onto the ground to the airport $y$. We are told that $y = 4$ miles.

Let's call the rate at which the distance from the jet to the airport is increasing $v_x$. We are told that $v_x = 180$ miles/hour.

Let's call the rate at which the ground distance from the projection of the jet to the ground to the airport is increasing $v_y$. We are told that $v_y = 150$ miles/hour.

We want to find the vertical speed of the jet at this moment in time. Let's call this quantity $v_z$.

Since the jet is flying in the eastward direction, we can use the Pythagorean theorem to relate the three sides of the right triangle formed by the jet, the projection of the jet onto the ground, and the airport. Specifically, we have

$$x^2 = y^2 + z^2$$

where $z$ is the vertical distance from the jet to the ground (i.e., the height of the jet above the ground).

Since the distance from the jet to the airport and the ground distance from the projection of the jet to the airport are both increasing, we can take the derivative of both sides of the equation above to find the rate of change of $z$ with respect to time. This gives us

$$2x \frac{dx}{dt} = 2y \frac{dy}{dt} + 2z \frac{dz}{dt}$$

where $t$ is time.

We are given the values of $x$, $y$, $v_x$, and $v_y$, so we can plug these values into the equation above to solve for $v_z$. This gives us

$$2 \cdot 5 \cdot 180 = 2 \cdot 4 \cdot 150 + 2z \frac{dz}{dt}$$

Solving for $\frac{dz}{dt}$, we get

$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2z}$$

We are told that $z = x - y$, so we can plug this into the equation above to find $\frac{dz}{dt}$. This gives us

$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2(x-y)}$$

Substituting the values of the known quantities, we get

$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2(5-4)} = \frac{180}{2} = 90$$

Therefore, the vertical speed of the jet at this moment in time is $v_z = 90$ miles/hour.

The vertical speed of the jet is approximately 300 miles/hour.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is traveling along a route.

Let's call the distance from the jet to the airport "d" and the height of the jet "h". Then we have two related rates:

d is increasing at a rate of 180 miles/hour.

The horizontal distance is increasing at a rate of 150 miles/hour.

Using the Pythagorean theorem, we can relate these two distances:

d² = h² + 4²

Taking the derivative of both sides with respect to time, we get:

2d(dd/dt) = 2h(dh/dt)

Simplifying, we get:

dd/dt = (h/d)(dh/dt)

We're looking for the vertical speed of the jet, which is dh/dt. We can solve for this by plugging in the given values:

d = 5 miles

dd/dt = 180 miles/hour

h² + 4² = 5² (from the Pythagorean theorem)

dh/dt = ?

Solving for h, we get:

h² = 5² - 4² = 9

h = 3 miles

Now we can plug in all the values and solve for dh/dt:

dh/dt = (dd/dt)(d/h) = (180 miles/hour)(5 miles/3 miles) ≈ 300 miles/hour

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Answer: c

Step-by-step explanation:

A function cannot have repeated X value in a set

Answer: y=7/4x-2

Step-by-step explanation:

I find the slope first, using 5--2/4-0. This is 7/4. I then plug it into point-slope form, which is y--2=7/4(x-0). Simplifying get y=7/4x-2.

The discount amount would Chester receive from using his coupon is $17.34

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.

2/5 ---> .40---> 40%

$28.90(.40)= $11.56

$28.90-$11.56

=$17.34

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The remainder of the given polynomials is x-3 is 12x³+x.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

Given that, the polynomial [tex]x^5+x^3+x[/tex] is divided by x-3.

Here, [tex]x^5+x^3+x[/tex]/(x-3)

ow,

x-3 |[tex]x^5+x^3+x[/tex]| [tex]x^4[/tex][tex]+4x^3[/tex]

    -([tex]x^5-3x^4[/tex])

   __________

             [tex]4x^4[/tex][tex]+x[/tex]

           -([tex]4x^4[/tex][tex]-12x^3[/tex])

         __________

             12x³+x

Therefore, the remainder of the given polynomials is x-3 is 12x³+x.

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