Suppose y varies directly with x and inversely with z. When y=3, x=5, and z=9. Find y when x=12 and z=21.

Answer: the answer would be 2

Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.

2x3=6-4=2

Answer: [tex]x=13, y=132[/tex]

Step-by-step explanation:

Using the same-side interior angles theorem, [tex]y=132[/tex].

Using the alternate interior angles theorem, [tex]5x-17=48 \implies x=13[/tex]

Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

Step-by-step explanation:

so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.

cost1(x) = 19x + 50

cost2(x) = 23x + 42

to get the value for x we know that the cost is the same either way.

that means

cost1(x) = cost2(x) = 19x + 50 = 23x + 42

19x + 50 = 23x + 42

50 = 4x + 42

8 = 4x

x = 2

so, she orders 2 small arrangements.

the total cost is

19×2 + 50 = 38 + 50 = $88

cross check with the other function :

23×2 + 42 = 46 + 42 = $88

correct

Answer:

  y = x² +8x -9

Step-by-step explanation:

You want the least-degree polynomial with roots 1 and -9, written in standard form.

Each root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...

  y = (x -1)(x +9)

Expanding this to standard form, we get ...

  y = x² +8x -9

__

Additional comment

A quadratic that has two roots, p and q, will have the standard form ...

  y = (x -p)(x -q) = x² -(p+q)x +pq

That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:

  y = x² -(1-9)x +(1)(-9) = x² +8x -9

The value of x is 10.6 which is equivalent to 11.

In the given triangle

the triangle is divided into two triangles which are both right angled

However in the bigger triangle

we would use the Pythagoras Theorem

( y + 6 )² = x² + 100 ---------- equation 1

In the smaller triangle;

x² = y² + 64 --------------equation 2

Thus substituting the value of x in equation 1

Thus the equation becomes

( y + 6 )² = y² + 64 + 100

y² + 36 + 12x = y² + 164

Cancelling y² on both sides we will get

36 + 12x = 164

12x = 164 - 36

this implies 12 x = 128

x = [tex]\frac{128}{12}[/tex]

x = 10.6 ≈ 11

Thus the required value of x is 10.6 or 11

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The function rule for each are:

f(x) = -2x - 6

g(x) = 5x - 4

f(x) is less than g(x), in terms of slope, while in terms of y-intercept, f(x) is greater than g(x).

The rule of a function can be written in slope intercept form as, f(x) = mx + b, where the slope is m and the y-intercept is the value of b.

To write the function rule for f(x), substitute m = -2 and b = -6 into f(x) = mx + b:

f(x) = -2x - 6

Find the slope of the function g(x) whose graph is given:

Slope of g(x) = rise/run = 5/1 = 5

m = 5

The y-intercept is at y = -4, therefore b = -4.

To write the function rule for g(x), substitute m = 5 and b = -4 into g(x) = mx + b:

g(x) = 5x - 4

In terms of slope, f(x) is less than g(x)

In terms of y-intercept, f(x) is greater than g(x).

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Answer:

see image

Step-by-step explanation:

Use new exponent rules like:

A power raised to a power is the product of the powers. (power to a power, times the exponents)

and,

Square root is a half power. (Converting radicals to fractional exponents)

Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)

see image.

Here's the plan:

Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.

see image.

The proof of the equation  (√5)³ = √(5³) is given below.

Exponentiation is one of the mathematics operation.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a times to itself.

So, a is the exponent of m.

Given:

A radical equation,

(√5)³ = √(5³).

LHS =  (√5)³

Simplifying,

(√5)³ = {(5[tex])^{1/2}[/tex]}³

        = [tex]5^{3/2}[/tex]

        = √(5³)

        = RHS.

Therefore,  (√5)³ = √(5³).

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The complete question:

Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.

Answer:

X = 2, Y = 0

Step-by-step explanation:

Add the two equations together to cancel out -4y and +4y

leaving you with:

8x = 16

8x = 16

divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)

leaving you with:

x = 2

substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):

8(2) - 4 y = 16

8 x 2 = 16

leaving you with:

16 - 4y = 16

subtract 16 from both sides to get 4y on its own

leaving you with:

-4y = 0

so y = 0, and x = 2

The probability of selecting two students (a and b) randomly is found as 1/380.

The formula for evaluating the Probability is-

Probability = Favourable outcomes / Total outcomes.

As, per the given question.

Total number of students = 20.

The probability for selection of 'a' is 1/20.

Now, the total students left is 19.

Thus, the probability for selection of 'b' is 1/19.

The total probability for selection of both is -

Probability(a and b) = 1/20×1/19

Probability(a and b) = 1/380

Thus, the probability of selecting two students ( a and b) randomly is found as 1/380.

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The probability that there is a continuous stripe encircling the cube is 3/16.

A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.

For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.

A continuous stripe surrounds the cube as a consequence of a total of

3 * 2 * 2 = 12 stripe variations.

The necessary probability is 12/64, which equals 3/16.

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The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.

What is the Least Common Denominator?

The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.

The given fractions are 8/9 and 5/8.

The denominators of these fractions are 8 and 9.

so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9

                                                                                   = 72.

so the equivalent fraction can be calculated as

for 8/9 = [tex]\frac{8*8}{9*8}[/tex]

           = 64/72

and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]

                   = 45/72

Hence, the equivalent fractions are 64/72 and 45/72.

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The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.

Given that,

In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.

Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)

16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)

(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8

8 * Raina's velocity = 24

Raina's velocity = 3 kilometers per hour

As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.

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The table of solutions for this quadratic equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

A graph of the solution of the given quadratic equation has been plotted in the image attached below.

In Mathematics, the graph of any quadratic equation or function always forms a parabola, which simply means a u-shaped curve. In order to determine the correct solutions to the given quadratic equation, we would have to substitute the x-values contained in the table into the quadratic equation.

At point x = -2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At point x = -1, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At point x = 0, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At point x = 1, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At point x = 2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.

Answer: MP = 13

The sides of ΔTUV in order from longest to shortest is as follows -

TV > TU > VU

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is ΔTUV, m∠T = 58° and m∠U = 97°.

Refer to the image attached.

TV > VU

TU + VU > TV

TV > TU + VU

So we can arrange the sides as follows -

TV > TU > VU

Therefore, the sides of ΔTUV in order from longest to shortest is as follows -

TV > TU > VU

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The domain of the function d(t)=1/2t+6 is (-∞, ∞) and the range of the function is (-∞, ∞).

Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A  → B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.

The domain of the function d(t)=1/2t+6 is given by

Domain: (-∞, ∞), {x|x ∈ R}

The range of the function is given by

Domain: (-∞, ∞) , {y|y ∈ R}

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When the sum M+N is divided by 6 , the remainder is 8

The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). We always have remainder when the denominator is a factor of numerator.

For example 5/2, diving 5 with 2, 2 is not a factor of 5,

There are 2 2s in 5 with remainder 1.

M/6= x y/6

where is the factor and y is the remainder

therefore m/6= (6x+y)/6

y= 3,. m/6= (6x+3)/6

N/6= (6x+5)/6

therefore dividing both sides by 6

m= 6x+3

n= 6x+5

adding m and n

m+n= 12x+8

dividing m+n by 6

(m+n)/6 = (12x+8)/6

relating (12x+8)/6 with (6x+y)/6

y = 8

Therefore the remainder is 8

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Call the number of hours of labor x.

A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)

Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.

We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000

The length and width of the rectangle are 50 feet and 25 feet respectively, the product of which gives the area of the rectangle which is 1250 feet.

Given, 100 feet of fence to make a rectangular play area that is side by side with the wall of your house.

The perimeter of the rectangle is = 2x+2y, since the wall bounds from one side as given in the question perimeter changes to = x+2y.

Perimeter = x+2y

100 = x+2y

100 = 50+2y

2y = 50

y = 25

Using this we found the length and width of the rectangle which is equal to 50 feet and 25 feet respectively. The area which is the final answer comes out to be 1250 feet.

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Answer:

a) 6 km

b) 66 km

Step-by-step explanation:

a) According to the graph:

To find how much further, subtract the distance cycled those two days:

22 - 16 = 6 km

b) The three days he cycled the most are the three days with the highest lines on the graph, so that would be:

Add them all up to find the total distance cycled:

24 + 22 + 20 = 66 km

The model which properly represent the information in given axioms is Cross geometry (+).

In the given question we have following information,

by using the above axioms we draw a geometry of Cross sign Geometry as seen above .

We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .

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Number of square tiles that are needed to fit the rectangular region are

(a)  30000 tiles and (b)  20000 tiles  .

In the question ,

it is given that

the side of the square tile is = 6 cm

so ,the area  of the square tile = 6*6= 36 cm²

Part(a)

the length of the rectangular region = 9m = 900 cm

the breadth of the rectangular region = 12m = 1200 cm

So, the area of the rectangular region = 900 * 1200 = 1080000 cm²

the number of tiles required = (area of rectangular region)/(area of tile )

= 1080000/36

= 30000

hence , 30000 tiles are needed.

Part(b)

the length of the rectangular region = 8m = 800 cm

the breadth of the rectangular region = 9m = 900 cm

So, the area of the rectangular region = 800 * 900 = 720000 cm²

the number of tiles required = 720000/36

= 20000

hence , 20000 tiles are needed .

Therefore ,Number of square tiles that are needed to fit the rectangular region are

(a)  30000 tiles and (b)  20000 tiles  .

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Norman will measure the light pole to be 12 feet tall

Information from the question

Norman uses his sextant to measure the angle of elevation to be 36

5 feet from the ground. if he is 10 feet away from the light pole

how tall is the light pole = ?

The height of the light pole is calculated using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = height of the light pole

adjacent = 10 feet away from the light pole

The height is is calculated using tan, TOA let the angle be x = 36

tan x = Opposite / Adjacent

tan 36 = opposite  / 10

opposite = tans 35 * 10

opposite = 7 feet

this is height 5 feet from the ground, so total height is calculated to be

5 + 7 = 12 feet

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Graph will shift in both horizontal and vertical direction by 4 units.

What is straight line?

An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.

What is general equation of a Straight Line?

The general equation of a straight line can be given as ax + by + c = 0, where

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.

We have function,

fn(x) = x + 5

when the graph is translated by 4 units, we can write it as;

g(x) = fn(x) + 4

the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.

Therefore, graph will shift in both horizontal and vertical direction by 4 units.

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The statement about the given expression is described below.

A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.

Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2

Thus, given expression has two factors which consist 3 terms.

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Answer

you do 420x0.7= 29.40

Answer:

The sales tax is 29.4

Step-by-step explanation:

Just divide in half until you reach 5 and then calculate the other 2 percent of it and add the 2 percent back onto it.

Answer: -22/5 or -4.4

Step-by-step explanation:

Simplify so 2(22/7*10)(10+h)=352

Distribute so (2*22/7*10)(10) + (2*22/7*10)(h) = 352

Which would equal 4400/7 +440/7h=352

Subtract 4400/7 to both sides

That equals 440/7h=-1396/7

Multiply both sides by 7/440

h=-22/5

Answer:

hello\\

Step-by-step explanation: