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What is the area of the trapezoid?

33 in2
52.5 in2
82.5 in2
91 in2

Y=4x+5 and y=4x-5 has no solution

What are Linear Equations in two Variables?

The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. A linear equation with two variables, for instance, is 7x + 9y + 4 = 0. These two linear equations are referred to be simultaneous linear equations if we take them into consideration.

Steps

[tex]Y=4x+5\\ Y=4x-5[/tex]

Substitute y=4x+5

[tex][4x+5=4x-5][/tex]

Refine [tex][4x+5=4x-5][/tex]

-10=0

-10=0 is a false ,therefore the system of a equation have no solution

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Answer:

we spend maths class in a. day =85m

.:we spend in a maths class in a 9 week period=85x9x7:- 24=223.125

Answer: 13.6

Step-by-step explanation: Use a theorem which exists s. then you use pythagoreom

The length of the segment indicated is 13.6

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

The circle

Assuming that lines which appear to be tangent are tangent, we have

?² = (2 * 6)² + 6.4²

Evaluate

?² = 184.96

So, we have

? = 13.6

Hence, the length of the segment indicated is 13.6

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The green mathematics tells about the impulse response of an in homogeneous linear differential operator.

According to the statement

we have to explain the green mathematics.

In mathematics, Actually there is a Green Function which was founded by a mathematician George Green.

In this function, a Green's function is the impulse response of an in homogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.

The example of green function is the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function; the solution of the initial-value problem Ly = f is the convolution (G ⁎ f), where G is the Green's function.

Actually in this function, it gives the relationship between the line integral of two dimensional vector over a closed path by a integral.

In this there is a green theorem, which  relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C.

So, The green mathematics tells about the impulse response of an in homogeneous linear differential operator.

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All the relevant transformations are as shown in the explanations below.

We are given the original function as y = x and told the transformation is as follows;

1) y = x + 5; This means that the function was shifted 5 units to the left.

2) y = ³/₈x; This means that the function was vertically stretched by a scale factor of  ³/₈.

3) y = -x - 2 or y = -(x + 2); This means that the function was first shifted by 2 units to the left before being reflected over the x-axis.

4) y = 6x + 1; This means that the function was stretched by a factor of 6 and then shifted 1  unit to the left.

5) y = x - 11; This means that the function was shifted 11 units to the right.

6) y = 8x; This means that the function was vertically stretched by a scale factor of  8.

7) y = -1/3x; This means that the function was horizontally stretched by a scale factor of  1/3.

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Answer:

{x  = -1 + √13  ,  x  = -1 - √13}

Step-by-step explanation:

Completing the square:

f(x) = x² + 2x - 12

     = x² + 2x + 1 - 1 - 12

     = (x² + 2x + 1) - 1 - 12

     = (x + 1)² - 13

Solving:

f(x) = 0

⇔ (x + 1)² - 13 = 0

⇔ (x + 1)² = 13

⇔ x + 1 = √13  or  x + 1 = -√13

⇔ x  = -1 + √13  or  x  = -1 - √13

Answer:

Step-by-step explanation:

a) it is a reflection

b) it is vertex B"

Answer:

Step-by-step explanation:

The factored form of the equation are as follows;

Converting a quadratic function to factored form is called factoring.

Therefore,

let's factor the equation,

a.

d² - 7d + 6 = 0

d² - d - 6d + 6 = 0

d(d - 1) - 6(d - 1) = 0

(d - 6)(d - 1) = 0

b.

x² + 18x + 81 = 0

x² + 9x + 9x + 81 = 0

x(x + 9) + 9(x + 9) = 0

(x + 9)(x + 9) = 0

c.

u² + 7u - 60 = 0

u² - 5u + 12u - 60 = 0

u(u - 5) 12(u - 5) = 0

(u + 12)(u - 5) = 0

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The equation which can be used to find the number of quarters and nickels is; n + q = 84, 0.05n + 0.25q = 17.80.

let

n + q = 84

0.05n + 0.25q = 17.80

From equation (1)

n = 84 - q

Substitute into (2)

0.05n + 0.25q = 17.80

0.05(84 - q) + 0.25q = 17.80

4.2 - 0.05q + 0.25q = 17.80

- 0.05q + 0.25q = 17.80 - 4.2

0.20q = 13.60

q = 13.60 / 0.20

q = 68

Substitute q = 68 into

n + q = 84

n + 68 = 84

n = 84 - 68

n = 16

Therefore, the number of quarters and nickels are 68 and 16 respectively.

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Answer:

Step-by-step explanation:

We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping.  The third colum does not equal the sum of the first two, so we'll assume it is the total paid for both options.  Let set the price of Plain Wrapping to x and the Decorative Wrapping to y.  The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.

Take the first row and set it as an equation:

10x+9y = 47   [10 Plain Wraps and 9 Decorative Wraps bring a total of $47]

Do the same for the second and third rows:

25x + 12y = 86, and

16x +12y =  68

===========

We can take any equation and rearrange it to isolate one of the 2 variables, x or y.  I'll pick 10x = 47-9y and isolate x:

10x = 47-9y

x = (47-9y)/10

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

Now use this definition of x in another equation.  I'll use 25x + 12y = 86.

25x + 12y = 86

25(47-9y)/10 + 12y = 86     [since x = (47-9y)/10 from above]

117.5 - 22.5y + 12y = 86

-10.5y = -31.5

y = 3                                     [the price for decorative wrapping is $3]

If y = 3, then we can use this in any of the equations to find x:

x = (47-9y)/10

x = (47-9(3))/10     [Use y = 3]

x = (47-27)/10

x = 2                              [The price for plain wrapping is $3]

======================

Check to see if these values will expalin the total value of the three rows of numbers:

CHECK:

______UNITS____         $2 each          $3 each

PlainW DecG Total      PlainW ($)      DecG ($)      Total ($)

   x           y                          x                       y

   10         9        $47          $20                    $27              $ 47         OK

   25        12       $86          $50                    $36              $ 86         OK

   16        12       $68          $32                    $36              $ 68         OK

The values work.  Merry Christmas.

Answer:

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

Step-by-step explanation:

just did it in edg

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

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

Let a represent the time flown by the goose and b represent the time flown by the heron. Hence:

a + b = 14    (1)

Also:

20a + 10b = 180   (2)

From equation 1 and 2:

a = 4, b = 10

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

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The probability of having, at most, 9 girls, is 0.9515

The probability that a random baby is a girl is:

p = 0.5

And the probability that a random baby is a boy is:

q = 0.5

Then the probability that, at most, 9 out of 11 babys are girls, is given by:

1 - p(10) - p(11)

Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.

p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11

Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:

C(11, 10)=  11!/(11 - 10)!*10! = 11

Replacing that, we get:

P = 11*(0.5)^11 = 0.0054

p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005

Then the probability is:

P = 1 - 0.0054 - 0.0005 = 0.9515

The probability of having, at most, 9 girls, is 0.9515

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Answer:

1:216

Step-by-step explanation:

The probability of getting a 4 would be 1/6.  The probability of getting a 5 would be 1/6 and the probability of getting a 6 would be 1/6.  The bottom number is the total number of outcomes (1,2,3,4,5,6) and the top number is out of that set, how many do I want.  In the case of wanting a 4, I want 1 out of those 6 numbers and so on.

Now we multiple these together 1/6 x 1/6 x 1/6 and get  1/216 or another way to write this is 1:216

[tex] \sqrt{5612} = \frac{5612 + 5625}{2 \sqrt{5625} } = \frac{11237}{2 \times 75} = 74.913333[/tex]

=========================================================

Explanation:

You could use the AC method to factor this, but the quadratic formula is the most efficient route in my opinion. This will avoid any guess-and-check.

Compare the original equation to the form [tex]a\text{x}^2 + b\text{x} + c = 0[/tex]

We have a = 9, b = 6, and c = -8

Those values lead to...

[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(9)(-8)}}{2(9)}\\\\\text{x} = \frac{-6\pm\sqrt{324}}{18}\\\\\text{x} = \frac{-6\pm18}{18}\\\\\text{x} = \frac{-6+18}{18} \ \text{ or } \ \text{x} = \frac{-6-18}{18}\\\\\text{x} = \frac{12}{18} \ \text{ or } \ \text{x} = \frac{-24}{18}\\\\\boldsymbol{\text{x} = \frac{2}{3} \ \text{ or } \ \text{x} = -\frac{4}{3}}\\\\[/tex]

Side notes:

Answer:

Step-by-step explanation:

rounded to the nearest cent his answer would be $212.24

Answer: (x + 11) cm²

Step-by-step explanation:

The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where

For this figure, [tex]a = 5[/tex] and [tex]b= x+6[/tex] (the top and bottom sides), while [tex]h=2[/tex] (the height).

If we suppose [tex]A[/tex] is the area, plugging these values in, we get

[tex]A = \frac{1}{2}(5 + x + 6)*2[/tex]

[tex]A = \frac{1}{2} * 2 * (x + 11)[/tex]

[tex]A = x + 11[/tex]

All the lengths are in cm, so the area will be (x + 11) cm².

Step-by-step explanation:

12 inches

djaikfnshaidifb

Answer: 7 Switches will be made.

Step-by-step explanation:

[tex]\frac{90}{12.5}=[/tex] number of switches

[tex]7.2=[/tex] number of switches

Considering the critical points of the function, we have that:

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = 3x^3 - 16x + 2[/tex]

The derivative is:

[tex]f^{\prime}{x} = 6x^2 - 16[/tex]

The critical points are given as follows:

[tex]6x^2 - 16 = 0[/tex]

[tex]x^2 = \frac{16}{6}[/tex]

[tex]x = \pm \sqrt{\frac{16}{6}}[/tex]

[tex]x = \pm 1.63[/tex]

For x < -1.63, one example of the derivative is:

[tex]f^{\prime}{-2} = 6(-2)^2 - 16 = 8[/tex]

Positive, hence increasing.

For -1.63 < x < 1.63, one example of the derivative is:

[tex]f^{\prime}{0} = 6(0)^2 - 16 = -16[/tex]

Negative, hence decreasing.

For x > 1.63, one example of the derivative is:

[tex]f^{\prime}{2} = 6(2)^2 - 16 = 8[/tex]

Positive, hence increasing.

Hence:

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The value of the function is h(w - 5) = w^2 - 11w +25

The function is given as:

h(y) = y^2 - y - 5

Substitute w - 5 for y

h(w - 5) = (w - 5)^2 - (w - 5) - 5

Expand the equation

h(w - 5) = w^2 - 10w + 25 - w + 5 - 5

Evaluate the like terms

h(w - 5) = w^2 - 11w +25

Hence, the value of the function is h(w - 5) = w^2 - 11w +25

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Parallel cousins are found in the iroquois system of kinship and are defined as bifurcate merging.

Parallel cousins, or the offspring of one's mother's or father's brothers or sisters, were frequently referred to and regarded in the same way as one's siblings. Contrarily, cross-cousins, or the offspring of one's mother's brothers or father's sisters, were frequently regarded as the best source of children.

Bifurcate merging is the underlying idea of the Iroquois system. The ego divides his family into those on his mother's side and those on his father's side (bifurcation) and combines his father with his brother (A) and his mother with her sister (B) .

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El precio resultante con descuento de 12 % es igual a 342.32 pesos.

En este problema tenemos que determinar el precio resultante, el cual es igual al precio inicial menos el descuento. A continuación, se presenta la siguiente expresión:

x = 389 · (1 - 12/100)

x = 389 - 46.68

x = 342.32

El precio resultante con descuento de 12 % es igual a 342.32 pesos.

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Answer: D

Step-by-step explanation:

Answer:

153

Step-by-step explanation:

i = square root of -1

i = √-1

(3+12√-1) (3-12√-1)

√a times √b = √ab

a√b times c√d = (a times c) √ (b times d)

9 - (36√-1) + (36√-1) - (144(√-1)^2) =

9 - 0 - (144 * -1) =

9 - 0 - (-144) =

9 - (-144) =

9 + 144 =

153

*** funny thing is if you put

(3+12i) (3-12i)  

in a calculator

it works!

it gives you the answer 153

another way:

Expand the expression using

(a-b) (a+b) =

a²-b² :

3²-(12i)²

Simplify using exponent rule with same exponent

(a*b)^n =

a^n*b^n:

3²-12²* i²

Calculate the power:

9-144* i²

Rewrite by definition

i²=-1:

9–144×(−1)

Calculate the product or quotient: 9+144

Calculate the sum or difference: 153

Answer: 153

gathmath

The equation of the unique function exists g(x) = -4(x-3)².

The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.

Given: F(x) = x²

The vertical stretch by a factor of 4 exists can be satisfied by (b)

if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.

Multiply 4 by f(x) which provides 4x².

As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².

Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.

Hence, the unique graph would be g(x) = -4(x-3)²

Therefore, the correct answer is option B. g(x) = -4(x-3)².

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Answer:

24.4

Step-by-step explanation:

Answer:

51 liters.

Step-by-step explanation:

By proportion  number of litres for 1428 miles

=  17 * 1428/476

= 17 * 3

= 51 liters.