Work out the values of a, b, c and d. ​

Answer:

[tex]\fbox {x = 6 and y = 12}[/tex]

Step-by-step explanation:

Taking the tan and cos values to find x and y :

Answer:

x = 6 and y = 12

Step-by-step explanation:

30-60-90 Triangle Theorem

A special right-angled triangle where:

Therefore, the formula for the sides is  b : b√3 : 2b where:

The given triangle is a 30-60-90 triangle, therefore the ratio of its sides is  b : b√3 : 2b

We have been given the measure of the side opposite the 60° angle.

⇒ b√3 = 6√3

So b = 6

Therefore, substituting the found value of b into the formula, the sides are in the ratio:  6 : 6√3 : 12

⇒ x = 6  (shortest side)

⇒ y = 12  (longest sides)

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The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E

An equation is an expression that shows the relationship between two or more numbers and variables.

Sine rule shows the relationship between the sides and angles of a triangle.

The triangle formed has angles A = 10°, B = 50°, C = 120°, c = 4 km, a = distance from point y.

Hence:

a / sinA = c / sinC

a / sin(10) = 4 / sin(120)

a = 0.8 km

The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E

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The equation of the line will be 3y + 8x = 165.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

The given equation of the line is:-

3 x + 8 y = 4.

The slope of this line will be:-

3 x + 8 y = 4.

8y = -3x + 4

y = -3 /8x + ( 1 / 2)

y = mx + c

m = -3 / 8

Since the line is perpendicular to the other line 3x +8y = 4 so the slope will be inverse and negative for the line.

So the slope of the line will be -8 / 3

The equation of the line passing through the point will be given as:-

y - y 1 = m ( x- x1)

y - (-9) = ( -8 / 3) ( x - 8)

Y + 9 = ( -8 / 3 ) ( x -8 )

3 y = -8x + 165

3y + 8x = 165

Therefore the equation of the line will be 3y + 8x = 165.

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Answer:

b6,4

Step-by-step explanation:

becust tehf sdj

The average rate of change for a function over an interval is the slope

Take for instance, we have the function to be

Function f(x)

And the interval is (a,b)

The average rate of change for the function over the interval is

Rate = (f(b) - f(a))/(b - a)

The above represents the slope

Take for instance, we have:

f(x) = x^2 [2, 4]

We have:

f(2) = 2^2 = 4

f(4) = 4^2 = 16

So, we have:

Rate = (16 - 4)/(4 - 2)

Rate = 6

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Answer:

-3

Step-by-step explanation:

5x³ + 2 , when x = -1

5(-1)³ + 2

= -5 + 2

= -3

Answer:

-3

(first option listed)

Step-by-step explanation:

we know that 5x³ + 2 is our expression

we want to "evaluate" (find/solve for) when x = -1

we can do this by plugging in -1 to the expression:

5x³ + 2          {note, x = -1}

5(-1)³ + 2    {-1³ = -1}

5(-1) + 2

(-5) + 2

-5 + 2 = - 3

so, when x = -1, the statement is equivalent to -3

hope this helps! :)

Answer:

The answer is B=10 and the top is called hypothenus

Answer:

x = 10

Step-by-step explanation:

The given is a right triangle, in right triangles the sum of square value of two legs (base and height) is equal to square value of hypotenuse.

Now, know the value of base and hypotenuse are 24  and 26

let x represent the missing side:

26^2 = x^2 + 24^2

676 = x^2 + 576 subtract 576 from both sides

100 = x^2 find the root of both sides

10 = x this is the length of the missing side

Step-by-step explanation:

0 = sqrt(x - 4) + 3 Set equation equal to 0

-3 = sqrt(x - 4). Subtract 3 from both sides

the principle square root will only output positive values, since if it every outputted a negative value it would not be a function since a function cannot have 2 outputs for the same input.

no x-intercept

Answer:

there are 2 cups in a pint is correct.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

A constant in an expression is the number that is not attached to any variable, and this includes the sign that comes with the number.

0.05m +12

In the expression above, m is the variable thus 0.05 is known as the coefficient of m instead of a constant. Coefficients are numbers that are multiplied to variables.

+12, which can simply be written as 12, is not multiplied to any variable and is thus the constant.

The value of the number 12 will not change no matter the value of m. The fact that the value stays the same makes it a constant.

Additional:

To learn more about constant, check out the following!

Answer: 12 ✅

Step-by-step explanation:

Hii, I'd love to help you! (:

This problem is about finding the constant in the expression. This is fun! Let's start our search...

____________________________________________

Wait, how can we find a constant if we don't even know what it is?

No reason to panic!

A constant is a number that is not added (or subtracted) from any variables (and a variable is a letter).

_____________________________________________

Ohh now it's easy as winking!

Because the only number in this particular expression that is not added to any letters at all is 12.

______________________________________________

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Answer:

Step-by-step explanation:

We solve an equation for a specific variable by using inverse operations to undo what is done to the variable. The resulting function is evaluated by substituting the given value for the variable.

__

We are given the equation ...

  6x -3y = 2

Solving for y, we get ...

  6x -2 = 3y . . . . . add 3y-2 to both sides

  2x -2/3 = y . . . . . divide by 3

  f(x) = 2x -2/3 . . . . write using functional notation

__

To find f(3), we use x=3 in the function.

  f(3) = 2(3) -2/3 = 6 -2/3

  f(3) = 5 1/3

The two-dimensional net of this pyramid that is surface area will be 34,416 square feet.

Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.

The surface area of the pyramid will be

SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)

The largest pyramid at Giza is a square pyramid. It has a base of 756 feet and a slant height of 612 feet.

We have

L = W = 27.5 feet

Then the two-dimensional net of this pyramid that is surface area will be

SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)

SA = 4(1/2 × 27.5 × 612) + 756

SA = 33,660 + 756

SA = 34,416 square feet

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Answer:

13

Step-by-step explanation:

square root of 12^2 + 5^2

Answer:

4 × 4000 = 16000cm or 160 meters

Answer:

y= 2x - 3

Step-by-step explanation:

To calculate the slope (or gradient) of a line, take two points on the line whose x and y values are easy to read. Then divide the difference of they y-coordinate values by the difference of their x-coordinate values.

Here I have taken the points p (3, 3) and q (1, -1) to calculate the slope.

• slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]

         = [tex]\frac{3 - (-1)}{3 - 1}[/tex]

         = [tex]\frac{4}{2}[/tex]

         = 2  

The intercept is the y-coordinate value of the point at which the line crosses ("intercepts") the y-axis. I've marked the intercept point with a green line.

• intercept = -3

The slope-intercept equation of a line takes the form:

y = mx + c

where 'm' is the slope and 'c' is the y-intercept.

Substituting the values we found into the equation gives us:

y = 2x + (-3)

∴ y = 2x - 3

Answer:

x^4 - 3x^2 - 4.

Step-by-step explanation:

Imaginary roots  occur as conjugate pairs  so a 4th roots is -i.

So in factor form we have:

f(x) = (x - 2)(x + 2)(x - i)x + i)

     = (x^2 + 1)(x - 2)(x + 2)

     = (x^2 + 1)(x^2 - 4)

      = x^4 - 3x^2 - 4.

Answer:b.f(x) = x^4 – 3x^2 – 4

Step-by-step explanation:

Answer: circumference 1.5714

Answer:

Circumference formula: 2πr

2π(0.25) = 0.5π or 1.57

Answer:

-1/2

Step-by-step explanation:

Answer:x is -1

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

n÷12=36

n=36*12

hence n=432

hope it helps you and give me a brainliest

Answer:

(redacted answer - it was wrong - moderator please delete)

false

Answer:

it already is rounded up to the nearest hundredth

Step-by-step explanation:

Answer:

-125 is the correct answer

Answer:

x = -125

Explanation:

[tex]\Longrightarrow \dfrac{1}{x} = (-5)^{-3}[/tex]

Apply the negative exponent rule: a⁻ᵇ = 1/aᵇ

[tex]\Longrightarrow \dfrac{1}{x} = \dfrac{1}{\left(-5\right)^3}[/tex]

Expand the power:

[tex]\Longrightarrow \dfrac{1}{x} = \dfrac{1}{\left(-5\right)\left(-5\right)\left(-5\right)}[/tex]

Simplify the following:

[tex]\Longrightarrow \dfrac{1}{x} =- \dfrac{1}{\left125}[/tex]

Flip the following:

[tex]\Longrightarrow x = -125[/tex]

Points Z, L, and S are collinear points

When 2 or more points are on a line, the points are said to be collinear.

From the figure, we have:

Points Z, L and S on the same line

This means that they are collinear points

Hence, points Z, L, and S are collinear points

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Answer:

The function [tex]2(3^x)[/tex] has an initial value of [tex]2[/tex].

Step-by-step explanation:

An exponential function is a mathematical function of the following form: [tex]f(x)=a^x[/tex]where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828. The exponential value can be found by solving the expression to proceed with a solution.

At the initial value,  the exponential function is in the [tex]y[/tex] direction and [tex]x[/tex] is [tex]0[/tex] .

[tex]f(x)=2(3^x)\\f(x)=2(3^0)\\f(x)=2[/tex]

Therefore, the function that has an initial value of [tex]2[/tex] is [tex]2(3^x)[/tex].

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The things that are to be done before creating a research question for a presentation are: option C, D, and E.

A research question can be defined as an issue, event or subject of inquiry that a researcher is keenly and deeply interested to provide a response or an answer to, when conducting a research.

Basically, the things that are to be done before creating a research question for a presentation are:

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Answer:

C, D, E

Step-by-step explanation:

The solution to the quadratic equation 3x² + 8x - 10 by using the quadratic formula is x = 0.927 or -3.594

Quadratic equations are algebraic expressions that are represented in the power of the second degree. They usually take the form ax² + bx + c

From the given information, we are to solve the quadratic equation:

Using the quadratic formula:

[tex]\mathbf{=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

where:

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{(8)^2 - 4(3 \times (-10))}}{2(3)}}[/tex]

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64 -4 (-30)}}{6}}[/tex]

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64+120}}{6}}[/tex]

x = 0.927 or -3.594

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Answer:

$2,753.79

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2000\left(1+\frac{0.0325}{1}\right)^{(1 \times 10)}[/tex]

[tex]\implies \sf A=2000(1.0325)^{10}[/tex]

[tex]\implies \sf A=2753.788608...[/tex]

Therefore, the value of the investment after 10 years will be $2,753.79 to the nearest cent.

Answer:

450 in^2

Step-by-step explanation:

Width = 15       Length is twice as much = 30 in

Area = L * W   = 15 * 30 = 450 in^2

The inverse function is [tex]f^{-1} = (x + 8)^2[/tex], and the domain is the set of all real numbers equal to or larger than -8. So the correct option is C.

Remember that two functions are inverses if and only if:

[tex]f( f^{-1}(x)) = x\\f^{-1}(f(x)) = x[/tex]

Here we have:

[tex]f(x) = \sqrt{x} - 8[/tex]

Then we want to have:

[tex]f(f^{-1}(x)) = \sqrt{f^{-1}(x)} - 8 = x[/tex]

Solving that for the inverse function, we get:

[tex]f^{-1} = (x + 8)^2[/tex]

Now, how to get the domain. The domain of the inverse function is equal to the range of the original function.

[tex]f(x) = \sqrt{x} - 8[/tex]

The range of f(x) is the set of all real numbers larger or equal than -8 (because the smallest value that x can take is 0).

Then the domain of the inverse function is the set of all real numbers equal to or larger than -8.

The correct option is C.

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Answer:

  31

Step-by-step explanation:

We can solve the given equation for 'b', then find the integer values of 'a' that make 'b' a positive integer. There are 3 such values. One of these minimizes the objective function.

__

  ab +5b = 373 +6a . . . . . . isolate b terms by adding 6a

  b = (6a +373)/(a +5) . . . . . divide by the coefficient of b

  b = 6 +343/(a +5) . . . . . . . find quotient and remainder

The value of 'b' will only be an integer when (a+5) is a factor of 343. The divisors of 343 = 7³ are {1, 7, 49, 343}. so these are the possible values of a+5. Since a > 0, we must eliminate a+5=1. That leaves ...

  a = {7, 49, 343} -5 = {2, 44, 338}.

Possible values of b are ...

  b = 6 +343/{7, 49, 343} = 6 +{49, 7, 1} = {55, 13, 7}

Then possible (a, b) pairs are ...

  (a, b) = {(2, 55), (44, 13), (338, 7)}

The values of the objective function for these pairs are ...

  |a -b| = |2 -55| = 53

 |a -b| = |44 -13| = 31 . . . . . the minimum value of the objective function

  |a -b| = |338 -7| = 331