SAT/ACT If 4 a+6 b=6 and -2 a+b=-7 , what is the value of a ?
A -2
B -1
C 2
D 3
E 4

Answer:

5 - 17 = -12

-12/4 = -3

Answer:

number is - 3

Step-by-step explanation:

let the number be n then the product ( multiplication ) of n and 4 is 4n , so

4n + 17 = 5 ( subtract 17 from both sides )

4n = - 12 ( divide both sides by 4 )

n = - 3

the number n is - 3

The measure of ∠C in ΔABC is 35°.

Angle Sum Property of a triangle states that sum of all the interior angle of a triangle is 180°.

In the given Question

∠B=90° , ∠A=∠C+20°...(1)

By angle sum property of triangle for ΔABC

we get

∠A+∠B+∠C=180°

Substituting the values of ∠B and ∠C from equation (1) we get

∠C+20°+90°+∠C=180°

2∠C+110°=180°

2∠C=180°-110°

2∠C=70°

∠C=35°

Therefore  , the value of ∠C in ΔABC is 35°.

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Answer:

650 Rupees

Step-by-step explanation:

Add all together

Answer:

well done .... keep practicing....

Answer:

Step-by-step explanation:

42=24+9h

Given an arithmetic sequence -2,-13,-24, . . . , the recursive formula is: a(n) = a(n-1) -11 and the explicit formula is a(n) = 9 - 11n

Suppose we are given an arithmetic sequence:

  a(1), a(2), a(3), a(4), ....

Then, in an arithmetic sequence, the next term is obtained by adding a constant to the previous term. This constant is called a common difference.

Let d = common difference, then
a(2) = a(1) + d

a(3) = a(2) + d

and so on, until

a(n) = a(n-1) + d

This is a recursive formula. Here a(n) = nth term, and a(n-1) = (n-1)th term.

The sequence in the problem:

       -2,-13,-24, . .

Notice that:

-13 = -2 + (-11)

-24 = -13 + ( -11)

Hence, d = -11, and therefore, the recursive formula for the nth term is:

a(n) = a(n-1) -11

To find the nth term, we can also use the explicit formula:

a(n) = a(1) + (n-1).d

In the given sequence, a(1) = -2, and d = -11. Substitute these parameters:

a(n) = -2 + (n-1) . (-11)

      = -2 - 11n + 11

      = 9 - 11n

Thus, the explicit formula is a(n) = 9 - 11n.

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The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².

In this problem we find a quadratic equation, of which we must infer the series of rigid transformations to be used to obtain a resulting expression. Rigid transformations are transformations applied on functions such that Euclidean distance is not changed. The most used rigid transformations are listed below:

After comparing the two expressions, we find that this procedure was applied in the following order:

Finally, we show the procedure to prove this manner:

y = x²

Step 1

y' = (x + 8)²

Step 2

y'' = 3 · (x + 8)²

Step 3

f(x) = 3 · (x + 8)² + 4

The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².

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There are two different sequences of transformation.

What is sequence of transformation?

A sequence of transformation is an operator acting on a given space of sequences. Sequence transformations include linear mappings such as convolution with another sequence, and resummation.

What is origin?

A graph in the two-dimensional coordinate plane has the point (0,0) as its origin. The origin is located at the intersection of the vertical and horizontal axes, and the distance to all points can be measured from this point.

Given figure is in which the blue figure is the image of the red figure

The above figure can be transformed in two sequences

a) We could first rotate clockwise 90 degrees from the origin, and then reflect on the x axis. And translate two units right side.

b) We could rotate counter clockwise 90 degrees and then reflect on the y axis. And translate two  units upwards.

By these sequence of transformation, blue figure is the image of red figure.

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An isosceles triangle is a triangle with (at least) two equal sides. In the picture above, we have two equal side lengths and the remaining side length. .This property corresponds to two equal angles in a triangle.

verify the following equation:

Find the equation is possible or not?

Yes, it is possible to draw an isosceles obtuse triangle.

An isosceles obtuse triangle is a triangle in which one of its three angles is obtuse (between [tex]90[/tex] and [tex]180[/tex]degrees) and the other two are acute angles.

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Answer:

x=9

Step-by-step explanation:

[tex]\sqrt{x+5}=\sqrt{2x-4} \\ \\ x+5=2x-4 \\ \\ x=9 [/tex]

On substituting this back into the equation, we see x=9 satisfies it.

Formula for arithmetic sequence 5,2,-1,-4, . . . . is an = 3n + 8.

An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

This is an A.P. series.

a = 5

d = -3

an = a + (n-1)d

an = a + (n-1)-3

an = a + 3n + 3

an = 5 + 3n + 3

an = 3n + 8

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  The given function  y = 2x - y - 13² , is a linear function

 where:

A function is the definition of a mathematical expression or equation that helps us to give a visual representation, through graphs to analyze the behavior of the same, a function is not real when it cuts the vertical axis at a same point of x.

 The function we have is particular because it has two variables, and these two are "x" and "y", but the y is the image so we do not consider it a variable.

y + y = 2x - 13

2y = 2x - 13

y = (2x - 13)/2

y = x - 13/2

y = x - 6.5

  Here we notice that we have a linear function

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The slope of the line that passes through the given points is equal to 3/5.

Given the following data:

Points on x-axis = (2, 5).

Points on y-axis = (1, 6).

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (5 - 2)/6 - 1)

Slope = 3/5

In conclusion, the slope of the line that passes through the given points is equal to 3/5.

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There are a couple ways we can get the equation of a line, depending on what we're given.

Most linear equations are organized in slope-intercept form:

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

The slope of a line can be calculated algebraically when we know two points that fall on the line:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The y-intercept is the value of y when the line crosses the y-axis, or when x = 0. When given a graph, you can sometimes read the y-intercept directly from the graph.

For instance, if the line passes through the point (0,5), then the y-intercept is 5.

You can also find the y-intercept algebraically if you know the slope and one point that falls on the line. You plug in that point as (x,y) and isolate b.

For most cases, you can use the following method to find the equation of a line:

Answer: Less than. (9/7<3/1)

Step-by-step explanation: We know the answer is 9/7<3/1 because 3/1 as a whole number will be 3. If we convert 9/7 into a proper fraction with a whole number, it will be 1 2/7. 3 is greater than 1 and 2/7ths.

   The value of the volume of the other rectangular prism is V = 101.25 yd³.

  A numerical ratio is a constant value that relates a system of two or more variables, it allows us to know how their variations will be as the values change.

   First we must find the ratio between the heights of the rectangular prisms, for this we determine the height in the same unit:

 We express the following:

For volume

1/2³ = 1/8 = V/810

V = 101.25 yd³

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The sequence 1,1,2,3,5,8, ........... doesn't form an AP as they have the varying common difference.

In Arithmetic Progression, the difference between these two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come across a few specific keywords in AP that had been labeled as:

As shown below, the AP can also be explained in expressed in the form of common differences.

Now, the sequence given is; 1,1,2,3,5,8, ...........

The series contains of given 6 terms.

Let the initial term be 'a₁' = 1.

The second term be 'a₂' = 1.

The third term be 'a₃' = 2.

And, the fourth term is 'a₄' = 3.

For the sequence to form the AP, they must have the equal common difference. So,

d = a₃ - a₂

Substitute the values.

d₁ = 2 - 1

d₁ = 1

Thus, the calculated common difference is 1.

or d = a₅ - a₄  (Put the values)

d₂ = 5 - 3

d₂ = 2

Since, d₁ ≠ d₂

Thus, we can say that the given sequence is not forming an AP.

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The slope of the line through each pair of points (1,2) and (2,3) is 1.

Find the coordinates of two points along the selected line.

Find the difference in these two locations' y-coordinates (rise).

Find the difference in these two locations' x coordinates (run). Add the difference in x-coordinates (rise/run or slope) to the difference in y-coordinates.

The formula to calculate slope is -

m = y2 - y1 / x2 - x1

m = 3 - 2 / 2 - 1

m = 1  

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Applying the midpoint formula, the coordinates of point M are: (-3, -4).

The midpoint formula is given as, (x, y) = [(x2 + x1)/2, (y2 + y1)/2].

Given the following:

N(x, y) = (1.5, 2.5)

P(x1, y1) = (6, 9)

M(x2, y2) = (?, ?)

Plug in the values into the midpoint formula

N(1.5, 2.5) = [(x2 + 6)/2, (y2 + 9)/2]

Isolate each coordinate

1.5 = (x2 + 6)/2

2(1.5) = x2 + 6

3 = x2 + 6

3 - 6 = x2

x2 = -3

2.5 = (y2 + 9)/2

5 = y2 + 9

5 - 9 = y2

y2 = -4

Therefore, applying the midpoint formula, the coordinates of point M are: (-3, -4).

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Answer:

3 option

Step-by-step explanation:

To find the missing side (c) you need to do a^2 and b^2

Formula a^2 + a^2 = c^2

The number of glasses of iced tea is x = 44 − y.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

She has only 44 glasses in which to serve the drinks.

x represents the number of glasses of iced tea

y represents the number of glasses of lemonade

According to given question we have

x is the number of glasses of iced tea, and y is the number of glasses of lemonade.  The sum is 44,

x + y = 44

Solving for x:

x = 44 − y

Therefore, the number of glasses of iced tea is x = 44 − y.

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The height of the tree, which Dave is standing 66 feet away from, is 34 feet and 2.4 inches.

If Dave's and the tree's shadows end at the same point, then the length of the shadow of the tree must be the sum of Dave's shadow and his distance from the tree.

tree's shadow = Dave's shadow + distance from the tree

tree's shadow = 15 feet + 66 feet

tree's shadow = 81 feet

Using ratio and proportion, we can solve for the height of the tree.

Dave's height : height of tree = Dave's shadow : tree's shadow

let x = height of the tree

6 feet 4 inches : x = 15 feet : 81 feet

converting feet to inches (1 feet = 12 inches)

76 : x = 180 : 972

Solving for x by evaluating the proportion:

180 x = 76 (972)

x = 410.4 inches

x = 34 feet and 2.4 inches

Hence, the height of the tree is 34 feet and 2.4 inches.

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The angles that has C as a vertex are:

13. ∠HVJ, ∠HVI, ∠JVI

14. ∠DVF, ∠DVE, ∠FVE

Angles that have letter V at their vertex can be named as an angle contain V as a point.

13. The angles that have V as vertex are:

∠HVJ

∠HVI

∠JVI

They all contain vertex V.

14. The angles that have V as vertex are:

∠DVF

∠DVE

∠FVE

They all contain vertex V.

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Answer:

Step-by-step explanation:

The value of the equation cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0

Now , the value of cos A + cos B = 2 cos ( A + B / 2 ) cos ( A - B / 2 )

Substituting the values in the equation , we get

cos x + cos ( x + 2π/3 + x + 4π/3 / 2 ) cos ( x + 2π/3 - x - 4π/3 / 2 )

On simplifying the equation , we get

cos  x + 2cos ( 2x + 2π / 2 ) cos ( -π/3 )

cos x + 2cos ( x + π ) ( -1/2 )

cos x + ( -cos x ) = 0

So , 0 = 0

Hence , the equation is solved

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A rectangle as the only parallelogram that can be inscribed in a circle.

Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.

The only parallelogram that can be inscribed in a circle is a rectangle. Because every rectangle can be inscribed in a (unique circle), the important point is that the radius of the circle is R. (I think). One of the properties of a rectangle is that the diagonals bisect in the 'center,' which is also the center of the circumscribing circle.

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The missing term in the sequence is A5 = 5 .

Let's assume for the sake of simplicity that the third term they provided you was >3, and the twenty-fifth is >25. As a result, you put 3 as A sub-one rather than specifying that A sub-3 is 3 and A sub-25 is 25. Here's where things become tough. Set A sub-23 to 25. (why? because 1 to 23 and 3 to 25 are equally distant.

A3=3, A25=25 } A1=3, A23=25

Apply the equation An = A1 + (n-1)D.

(Read: A-sub n = A sub 1 - the nth term - D)

A23(A sub-23)= 3 Plus (23-1)

D 25 = 3 + 22D \s-3 -3

22 = 22D

D = 1

Once more, An = A1 + (n-1)D.

A3 = A1 + (3-1) X 1

3 = A1 + 2

-2 -2

A1 = 1

An = 1 + (n-1) X 1

An = 1 + 1n - 1

An = 1n + 0

So you are left with the general formula An = 1n. You can use this formula to find any term in the sequence, all you got to do is plug in (An) the number you want. In this case, plug in A sub-5 if you want to find the fifth term. You get

An = 1n

A5 = 1X5

A5 = 5

The fifth term in the sequence is 5. (it goes 1,2,3,4,,5,..)

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