Find the values of a and b if 5+3√3/7+4√3 = a + √3b

Let's take this problem step by step:

To find the ordered pair of the system:

 ⇒ must set both equations equal to each other

     ⇒ solve for 'x'

Let's solve:

 [tex]x^2-2x+3=-2x+12\\x^2-2x+2x+3-12\\x^2-9=0\\(x+3)(x-3)=0[/tex]

Let's find the x-values:

 [tex](x+3)=0\\x=-3\\\\(x-3)=0\\x+3[/tex]

Let's find f(x)'s value for each 'x':

 [tex]x=-3\\f(-3)=-2(-3)+12=6+12=18\\\\x=3\\f(3)=-2(3)+12=-6+12=6[/tex]

Answer: (3, 6), (-3,18)

Hope that helps!

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Answer:

-3/2 ≤ x < 5

Decimal form:

-1.5 ≤ x < 5

(hope this helps)

Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]

Step-by-step explanation:

The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.

Linear function that is represented by the graph is f(x)= -1/2 x+1.

Here, we have,

From the graph,

y - intercept of the linear function is 1 , i.e. c = 1

and there are two points on the line (-4, 3), (4, -1)

We can get the equation of line by applying slope-intercept formula,

Slope of the line,

m = y₂ -y₁ / x₂-x₁

so, we get,

m = -1 -3 / 4 + 4

   = -4/8

   = -1/2

Now applying slope-intercept formula,

y = mx+c

Putting the values,

=> y = -1/2 x + 1

=>f(x) = -1/2 x + 1.

Therefore, linear function that is represented by the graph is

f(x) = -1/2 x + 1.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{4 + \sqrt{45} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{4}{6} + \cfrac{ \sqrt{45} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{3 \times 3 \times 5} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ 3\sqrt{5} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Add \:\: -6 \hat i - 6\hat j \:\:with \:\; Vector \:\; c[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Vector d can be represented as :

[tex]\qquad \tt \rightarrow \: - 2 \hat i - 2 \hat j[/tex]

Vector c can be represented as :

[tex]\qquad \tt \rightarrow \: 4 \hat i + 4\hat j[/tex]

we have to create vector d from vector c

So, let's assume a vector x, such that sum of vector x and vector c equals to vector d

[tex]\qquad \tt \rightarrow \: x + ( 4 \hat i + 4 \hat j) = - 2 \hat i - 2 \hat j[/tex]

[tex]\qquad \tt \rightarrow \: x = - ( 4 \hat i + 4 \hat j) - 2 \hat i - 2 \hat j[/tex]

[tex]\qquad \tt \rightarrow \: x = (- 4 \hat i - 2 \hat i) + ( - 4 \hat j - 2 \hat j)[/tex]

[tex]\qquad \tt \rightarrow \: x = - 6 \hat i -6 \hat j[/tex]

Henceforth, in order to get vector d, we need to add (-6i - 6j) in vector c

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The lateral surface area of the Pyramid will be 850547 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called as the area of the circle.

The lateral surface area will be calculated as:-

A = [tex]= l\sqrt{(\dfrac{w}{2})^2+h^2} + w\sqrt{(\dfrac{l}{2})^2+h^2}[/tex]

A = [tex]= 750\sqrt{(\dfrac{750}{2})^2+450^2} + 750\sqrt{(\dfrac{750}{2})^2+450^2}[/tex]

A = 750 √321525 + 750 √321525

A = 150 √√321525

A = 1500 x 567.031

A  = 850547 square feet

Therefore the lateral surface area of the Pyramid will be 850547 square feet.

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A figure can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

The cartesian coordinate plane is an infinite 2 dimensional plane and each point of a cartesian plane is tracked by a location.

Now, the perpendicular distance of point from the horizontal axis and vertical axis are respectively usually named x-axis and y-axis. The location is then written as (a,b) where;

a is that point's shortest distance from the y-axis and called x-coordinate of that point.

b is that point's shortest distance from the x-axis, and called y-coordinate of that point.

Thus, those given geometric figures can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

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Answer:

cost price = £ 600

discount = 5%

selling price =

5/100 * 600.

5 * 6

30 £

price = 600 - 30

= 570

First find the Slope-intercept form of the graph:

b=1

Given the points: (0,1)&(3,0)

slope= [tex]\frac{y1-y2}{x1-x2} =\frac{1-0}{0-3} =\frac{-1}{3}[/tex]

The line is not a dashed line, so that means the values on the slope (blue) are also counted

All the y values below the slope are counted, the inequality is:

y[tex]\leq \frac{-1}{3}x +1[/tex]

Hope it helps!

la componente "cubica" será aquella que tenga un exponente igual a 3.

Un polinomio tiene la forma general:

[tex]p(x) = a_n*x^n + ... + a_1*x^1 + a_0[/tex]

Donde todos los exponentes de x son numeros naturales.

Particularmente, la componente "cubica" será aquella que tenga un exponente igual a 3.

Entonces, por ejemplo, en:

[tex]p(x) = 4*x^5 + 2*x^4 + 5*x^3[/tex]

La parte cubica será:

[tex]5*x^3[/tex]

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The angle of depression from the top of the lighthouse to the sinking boat is 6.9°.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

From ΔABC it is obtained that;

Height of lighthouse, AC = 25 meters

Distance of boat from the lighthouse, BC = 204 meters

The angle of depression from the top of the lighthouse to the sinking boat is;

[tex]\rm tan \theta = \frac{P}{B} \\\\ \rm tan \theta = \frac{AC}{BC} \\\\ tan \theta = \frac{25}{204} \\\\ \theta = tan^{-1}(0.12)\\\\ \theta = 6.9 ^0[/tex]

Hence, the angle of depression from the top of the lighthouse to the sinking boat is 6.9°

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The least to greatest slope, the segments are B, C and A.

Given that,

Segments A, B, and C on the graph below represent the water level of the tank every minute since it started filling.

A graph shows the water level needed to fill the tank on the y axis per unit of time on the x axis.

The segment's slope indicates how quickly the water level is rising. The slope, which is determined by the segment's angle with the positive x axis, is the ratio of rise to run.

slope of segment A = 60₋10/2 = 25

slope of segment B = 80₋60/4 = 5

slope of segment C = 110₋80/3 = 10

We can see that section B has the least slope, followed by segment C, and then segment A, which has the greatest slope.

B, C, and A are the segments in descending order of least to greatest slope.

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Answer:

m=(-5y-3y)

Step-by-step explanation:

5m+5y=4m-3y

5m-4m=-5y-3y

m(5-4)=-5y-3y

m=(-5y-3y)/1

Answer:

only AAS,ASA and SSA Are classified

It's false

Step-by-step explanation:

please mark me as brainlest

False

The key reason is the formula 's limitations

As SSS means only three sides and no angles are given Law of sines can't be used

The limit [tex]\lim_{X \to \ 3^{-} } f(x)[/tex] is equal to -1 to infinity for the function whose graph is being shown in the question.

Given Graph of a function.

If we see the graph carefully then we can find that it is not a straight linear means it is not the graph of a linear function. From x=-3 to infinity  the range is from -1 to -infinity and from 3 onwards it is a straight line at y=-4. means when we put the value of x in the function equal to or less than 3 then we gets different answers than the values equal to or greater than 3 gives.

Hence the limit  is equal to (-infinity,-1]

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Answer:

it already is rounded up to the nearest hundredth

Step-by-step explanation:

Answer:

a and b

Step-by-step explanation: you can move the exponent to the front and lne is also equal to one times 2 = 2

Hello! I hope you are having a nice day. My name is Galaxy and I will be helping you with this problem. We can solve this problem in 2 steps, respectively Theory and Solving.

I'll go ahead and start with the Theory.

Before we attempt to solve the problem mathematically, we must first figure out how we're going to solve this problem.  

We know that we have a line and a point, we can start by graphing the equation and point that we've received.

Now that we have our points plotted and our equations graphed, we can start to see that something odd is happening, the given point is on the line itself.

We can check this by inputting the points into our equation:

[tex](-4)+2(-3)=-10?\\(-4)+(-6)=-10?\\-10=-10[/tex]

This proves that our point is on the line that we were given.

According to the basic rules of Euclidean Geometry, we know that parallel lines can never intersect each other and due to this there cannot be any solution to this problem.

Any other line using this point would intersect the given line, and due to this, this problem has no real solutions.

* The only line that can use these points and graph is the line provided, and that cannot work due to the lines intersecting at an infinite number of points.

Cheers,
Galaxy.

Answer:

The diameter is 10 cm. the radius is 5 cm. the area is πr² = π x 5² = 78.5 cm².

1 m² = 10,000 cm².

78.5/10,000 = 3,300/n n is the cost per square meter.

78.5n = 10,000 x 3300

n = 420,382.1656

The cost per square meter is $420,382.17.

The equation that represents Camille's profit p as a function of the number of doughnuts sold, n is P = 1.35n - 60

She bought 120 doughnuts for $60.

Therefore,

cost  = $60

Her profit was $48 once she sold 80 doughnuts.

p = profit

n = number of doughnuts sold.

Therefore,

let

x = amount she is selling each doughnuts

p = nx - 60

Using the information given we have:

48 = (80x) - 60

Therefore,

x = $1.35

Hence, for any number of doughnuts then, we have the profit equation as follows:

P = 1.35n - 60

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The statements that describe a triangular prism are:

A triangular prism is a three-dimensional object that is made up of one base that has the shape of a triangle and three lateral sides that have the shape of a rectangle. A triangular prism has 5 faces, 9 edges and 6 vertices.

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Answer: f(x) = -2 (x+3) (x-1)

Step-by-step explanation: See Attachment

The diameter of the sphere is 14 cm.

Sphere is a three dimensional object , it has no edges or vertices and is round in shape.

The surface area of the sphere is given by 4πr²

As radius = diameter /2

Surface area =  4π r²

196 π = 4π *(d/2)²

196/4 = d²/4

49 *4 = d²

d = 14 cm

Therefore the diameter of the sphere is 14 cm.

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Answer: -4

Step-by-step explanation: Notice that the increments in the graph do not go in 1's, but in 2's. Meaning the first line is 2, and second line is 4, and in the middle is 3. Be careful.

The range is where the line on the graph hits the y-axis (horizontal line, or line going up). The only possible place the line hits the y-axis is at -4. No other y-value. Thus, the range of the function is -4.

Answer:

Add all of the sides up:

x^2 + y + 6x + 2y + y^2 + 6x + 2y + y^2 + 4x^2

= 5x^2 + 12x + 2y^2 + 5y

Answer:

(-2,-9)

(-1,8)

(0,-5)

(1,0)

(2,7)

Step-by-step explanation:

The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.

It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Triangle ABC ~ EDC

Angle ACD = Angle BCE = 90 degree  (vertically opposite angle)

Angle ACB = Angle DCE = 90 degree  (vertically opposite angle)

BE ║ AD

Angle EBC = Angle CDA = 40 degree  (alternative angles)

Triangle ABC ~ Triangle EDC

Angle ABC = Angle CDE

Angle BAC = Angle DEC

∴ AB ║ DE

Triangle ACD ~ Triangle ECB

Angle EBC = Angle CDA and

Angle BEC = Angle CAD

∴ Triangle ACD ~ Triangle ECB

Angle A + Angle E = 180 degree

∠x + 50 + 50 + ∠x = 180

∠x = 40

Angle CAD = 40 degree

We know,

Angle A = Angle E = Angle B = Angle D = 90 degree

So ABCD is a square

AB = ED = 12

AD = AB  = BE = ED = 12

Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.

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