The diagram shows the graph of y = x² - 4x + 6, with a tangent drawn to the
curve at x = 3.
Use the tangent to estimate the gradient of the curve at
=
3.

So, on solving the provided question, we can say that the equation, we have been provided with is x = 48

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.

A mathematical formula explains the connection between the two sentences on either side of a letter. There is typically just one variable, which also acts as the symbol. As an illustration, 2x - 4 = 2.

the equation, we have been provided with is

x + 2 = 50

x = 50-2

x = 48

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Answer:

y=-2x+1

Explanation:

you can see that the x goes up by 1 every time. Y goes down by 2 every time, because 1-2=-1, -1-2=-3, etc. So the -2 goes in your m part of y=mx+b. Then you need to figure out what y is when x is 0, for your y-intercept, or your b part of y=mx+b. The picture makes it simpler, showing that when x is 0, y is 1. Therefore, 1 is your b part of y=mx+b. If you put it all together, it looks like this:

Y=-2x+1

Step-by-step explanation:

It looks Iike the equation is in slope intercept form

[tex]y = mx + b[/tex]

m is the slope

b is the y intercept

Finding B is easy, it's just where X = 0. On this table, Y is 1 when X is 0.

Finding the slope. We'll take two different (X,Y) coordinates. Let's do the first two rows (0,1) and (1,-1)

Next we apply the slope formula. That being

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

So plugging that in

[tex] = \frac{ - 1 - 1}{1 - 0} [/tex]

That gives you -2/1, also known as -2

Now that we have everything, we can put the forumla together

[tex]y = - 2x + 1[/tex]

Where -2 is the answer that belongs in the [?]

The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".

The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:

a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100

Simplifying the expression, we get:

5a + 10d = 100

Dividing both sides by 5, we get:

a + 2d = 20

Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:

1 + 2 * 1 = 3

Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.

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The error made by the student in the exponential function, y = 48,000(1.03)^x is that the function represented an exponential growth rather than an exponential decay.

An exponential function is written in the form y = abˣ.

In the exponential function, the exponent, x is a variable.

Annual decreasing rate of the fish population = 3% or 0.03

Original population = 48,000

Let the number of years = x

Exponential function: 48,000 (1 - 0.03)^x

= 48,000(0.97)^x

Thus, to represent an exponential decay, the exponential function should have been written as y = 48,000(0.97)^x.

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Answer:

B

Step-by-step explanation:

cause the premeter is way around the area

Answer:

B. V = pi*r^2*H/6

Step-by-step explanation:

The formula for the volume of a cone is V=pi*r^2*h/3, where h is the height of the cone, and r is the radius of the base. In this case, the hieght of the cone is equal to half the height of the cylinder, so it's h=H/2

If we substitute, we get

V = pi * r^2 * h / 3 = pi * r^2 * (H / 2) / 3 = pi * r^2 * H / 6

The value of the expression xy - x² - 5x - 4 when x = -1 and y = 6 is -6.

Given the expression in the question;

xy - x² - 5x - 4

To find the value of the expression; substitute in x = -1 and y = 6 for all occurrence of x and y in the expression and simplify.

xy - x² - 5x - 4

Plug in  x = -1

(-1)y - (-1)² - 5(-1) - 4

Plug in y = 6

(-1)(6) - (-1)² - 5(-1) - 4

Simplify

-6 - 1 + 5 - 4

Add -6 and -1

-7 + 5 - 4

Add -7 and 5

-2 - 4

Add -2 and -4

-6

Therefore, the value of the expression is -6.

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Answer:i don't realy now so 5 point 3

Answer:

It should be 8...

Step-by-step explanation:

16 / 8 = 2 and there is no higher number 16 that can be divided by. 56 is dividable by 8 so it makes sense.

Also 56 isn't dividable by 16

Given a parallelogram ABCD with points B and D, we draw two lines such that line BM intersects CD at point M and line DN intersects BC at point N, and BM = DN. The intersection of these lines is point I. Our goal is to prove that IA is a bisector of angle BID.

To prove this, we first note that since ABCD is a parallelogram, AB is parallel to CD and AD is parallel to BC. This means that ∠BAD and ∠CDA are congruent, and ∠BAC and ∠DCB are congruent.

Next, we consider triangle ABM. Since BM is perpendicular to AB, we have ∠BAM = 90°. By the same reasoning, we have ∠BID = 90°. This means that IA is perpendicular to both AB and BD.

Since IA is perpendicular to AB and BD, it follows that IA bisects ∠BAD and ∠BDC. Additionally, we know that AB = BD and ∠BAD = ∠BDC, so it follows that IA bisects ∠BID.

This completes the proof that IA is a bisector of ∠BID. The key idea here is that a line perpendicular to two parallel lines bisects the angles formed by the intersection of the two parallel lines with a third line.

In conclusion, given a parallelogram ABCD with points B and D, the intersection of lines BM and DN, point I, is the bisector of angle BID. This result can be used to prove various geometric theorems and helps to understand the properties of parallelograms and their related figures.

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Answer: $140 each weekend

Step-by-step explanation:

$1250 - $130 = $1,120

$1,120 divided by 8 weekends = $140

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

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The solution to the expression ⁴√(-15/16) is (-15/16)^1/4

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

⁴√(-15/16)

The above expression means that we calculate the 4th root of -15/16

-15 and 16 do not have perfect fourth roots

This means that the expression can only be rewritten as

(-15/16)^1/4

It cannot be evaluated

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Answer:

-3

Step-by-step explanation:

you can use elimination to remove y from this equation

your first equation will be

4x+10y=-2; and you can multiply the other one by -10

30x-10y=-100

if you add the two equations, 10y and -10y will cancel out and you'll get

34x = -102

divide both sides by 34

x=-3

A possible formula for the trigonometric function whose values are in the given table is u(x) = 3cos(πx/2)

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The surface area of the right triangular prism with legs of 5 centimeters and 12 centimeters, a hypotenuse of 13 centimeters, and a height of 2 centimeters is 108 square centimeters.

Surface area refers to the total area of the surface of a three-dimensional object. When it comes to a right triangular prism, the surface area includes the area of all six faces.

Let's call the height of the triangular prism "h" and label the legs of the triangle "a" and "b". Using these values, we can find the area of the base of the triangular prism. The area of a right triangle is equal to 1/2 times the product of the legs, so the area of the base is

=> (1/2) * a * b = (1/2) * 5 * 12 = 30 square centimeters.

Next, we need to find the surface area of each of the three lateral faces. Each of these faces is a rectangle, so we can find the area by multiplying the height of the prism by the length of one of the sides of the triangle base.

The length of one side of the triangle base is equal to the hypotenuse, which is 13 centimeters. So, the surface area of each of the three lateral faces is

=> h * 13 = 2 * 13 = 26 square centimeters.

Finally, we can find the total surface area by adding the surface area of the base and the surface area of the three lateral faces.

The surface area of the base is 30 square centimeters, and the surface area of each lateral face is 26 square centimeters, so the total surface area is

=> 30 + 3 * 26 = 30 + 78 = 108 square centimeters.

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By applying the algebra concept, it can be concluded that p = 3x or p = 2 - 3x.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

We want to express p in terms of x of this equation:

9x² – 6x + 5 = p² – 2p + 5

First, we have to eliminate 5, so we have:

9x² – 6x = p² – 2p

Then we add 1 on each side, so we have:

9x² – 6x + 1 = p² – 2p + 1

       (3x - 1)² = (p - 1)²

            p - 1 = √(3x - 1)²

Thus the solutions are:

p - 1 = 3x - 1      ⇔     p = 3x

or

p - 1 = -(3x - 1)   ⇔     p = 2 - 3x

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If all 4 posts are painted, 44 square feet must be painted.

We know that the formula for the surface area of the cylinder is:

A = 2πrh + 2πr²

Here, the dimensions of the each cylindrical post:

the diameter d = 1 foot and the height is 3 feet high.

So, the radius r = 0.5 ft and height h = 3 ft

Let us assume that the surface area of one post be A₁

Using above formula of surface area of cylinder,

A₁ =  2πr(h + r)

A₁ =  2 × π × 0.5 × (3 + 0.5)

A₁ =  2 × 3.14 × 0.5 × (3.5)

A₁ =  10.99

A₁ ≈ 11 sq.ft.

So, the total surface area of  4 cylindrical posts would be,

A = 4 × A₁

A = 4 × 11

A = 44 sq.ft.

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The number of terms in the expression -11 - 7c + 5 - 2x - 13b - 7 is 6

Algebraic expressions are defined as expressions that are composed with coefficients, terms, factors, constants and variables.

They are also known to consist of mathematical operations, such as;

From the information given, we have the algebraic expression as;

-11 - 7c + 5 - 2x - 13b - 7

The terms are either single number or variables in the expression. They are six

Hence, the number is 6

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Answer: 16

Step-by-step explanation:

      The geometric number between 7 and 28 is 16. Geometric numbers are the numbers you get by multiplying by a factor. If we multiply by 2 for this common geometric sequence, we get 16:

1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16,16 * 2 = 32, etc.

         7 < 16 < 28

Answer:

Step-by-step explanation:

To find the missing side lengths in the given right triangles, use trigonometric ratios.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:

[tex]\implies \tan 18^{\circ}=\dfrac{15}{x}[/tex]

[tex]\implies x\tan 18^{\circ}=15[/tex]

[tex]\implies x=\dfrac{15}{\tan 18^{\circ}}[/tex]

[tex]\implies x=46.165253...[/tex]

[tex]\implies x=46.2\;\;\sf(nearest\;tenth)[/tex]

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

Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.

Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.

As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.

As KL is parallel to NM, then m∠K = 90°.  Therefore, m∠KLN = 40°.

(Refer to the attached diagram).

For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:

[tex]\implies \tan 50^{\circ}=\dfrac{LN}{45}[/tex]

[tex]\implies LN=45\tan 50^{\circ}[/tex]

LN is the hypotenuse of right triangle KLN.

If we use ∠KNL as θ, then side KN is adjacent to the angle.

Therefore, to find the KN use the cosine ratio:

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{LN}[/tex]

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}[/tex]

[tex]\implies KN=45\tan 50^{\circ}\cos 50^{\circ}[/tex]

[tex]\implies KN=34.471999...[/tex]

[tex]\implies KN=34.5\;\; \sf (nearest\;tenth)[/tex]

As KL is the side opposite ∠KNL, to find KL use the sine ratio:

[tex]\implies \sin 50^{\circ}=\dfrac{KL}{LN}[/tex]

[tex]\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}[/tex]

[tex]\implies KL=45\tan 50^{\circ}\sin50^{\circ}[/tex]

[tex]\implies KL=41.0821297...[/tex]

[tex]\implies KL=41.1\;\;\sf (nearest\;tenth)[/tex]

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

From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:

[tex]\implies \cos 70^{\circ}=\dfrac{x}{46}[/tex]

[tex]\implies x=46\cos 70^{\circ}[/tex]

[tex]\implies x=15.732926...[/tex]

[tex]\implies x=15.7\;\;\sf(nearest\;tenth)[/tex]

The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

In the given box it is given sides are 2, 3 and 4 ft.

So the volume of the rectangular prism is V = 2*3*4 = 24 ft².

So the greater surface area in the given description is 6ft, 2ft and 2ft.

Where the surface area will be 12ft ²

Hence The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.

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The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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Answer:

Step-by-step explanation:

The transformations that have been applied to the parent function y = 1/x^2 are:

shift 3 units to the right

shift 5 units down

reflection over the x-axis

So the correct options are:

shift 3 to the right

shift 5 down

reflection over the x-axis

Answer:

9.6a + (-2)

Step-by-step explanation:

(6 + 12.5a) - (8 + 2.9a)  Distribute the negative sign

6 + 12.5a - 8 - 2.9a  Combine like terms

12.5a - 2.9a +6 - 8

9.6a + (-2)

Answer:

To find the sum of two complex numbers on the complex plane, we can simply add their real and imaginary parts separately. The real part of a complex number is the x-coordinate on the complex plane, while the imaginary part is the y-coordinate.

In this case, the two complex numbers are (-4-4i) and (4+2i). To find their sum, we add their real and imaginary parts separately:

Real part: -4 + 4 = 0

Imaginary part: -4 + 2 = -2

So, the sum of (-4-4i) and (4+2i) is 0 - 2i, which can be represented as a point on the complex plane with x-coordinate 0 and y-coordinate -2.

Step-by-step explanation:

The recursive rule for the sequence is T(n) = T(n - 2) - T(n - 1)

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

100, 3 , 97 ,-94 , 191

The above definitions imply that we simply subtract the current from the previous term to get the next term

Using the above as a guide,

So, we have the following representation

T(n) = T(n - 2) - T(n - 1)

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