Find a second equation for the system so it has infinitely many solutions. Simplify fractions and write in the form a/b

Answer:

58.27 mm (2 d.p.)

Step-by-step explanation:

Assuming the given prism is a rectangular prism, triangles ADC and ACG are right triangles.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

AC is the hypotenuse of right triangle ADC.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AC:

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{AD}{AC}[/tex]

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{42}{AC}[/tex]

[tex]\implies AC=\dfrac{42}{\cos\left(36^{\circ}\right)}[/tex]

AC is the hypotenuse of right triangle ACG.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AG:

[tex]\implies \cos\left(27^{\circ}\right)=\dfrac{AC}{AG}[/tex]

[tex]\implies AG=\dfrac{AC}{\cos\left(27^{\circ}\right)}[/tex]

To find the length of AG, substitute the found expression for AC into the expression for AG:

[tex]\implies AG=\dfrac{\frac{42}{\cos\left(36^{\circ}\right)}}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)} \times \dfrac{1}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=58.2654039...[/tex]

[tex]\implies AG=58.27\;\sf mm \;(2\;d.p.)[/tex]

Answer:

65.9

Step-by-step explanation:

The equation x² – 12x = 30 (x>0) promises that we can determine possible values of x if we solve the equation.  So let's start there:

We can factor the equation or solve it with the quadratic equation.

Factor

  x² – 12x = 30

  x² – 12x - 30 = 0

I don't see an easy factor solution.  One possibility is to first rewrite the equation as

  (x-12)x-30 = 0

  (x-6)^2 - 66 = 0

 -(-x+[tex]\sqrt66}[/tex]+6)(x+[tex]\sqrt{66}[/tex]-6)

The roots are:

x = 6-[tex]\sqrt{66}[/tex] and

x = 6+[tex]\sqrt{66}[/tex]

Since x>0, only the second root is valid:  x = 6+[tex]\sqrt{66}[/tex]

x = 6 + (8.12)

x = 14.12

[That was painful]

Quadratic Equation

Solving with the quadratic equation gives values of:

14.12, and -2.12  Again, only the positive value is valid:  14.12

[The quadratic approach was far easier than factoring, in this case]

==

Since we established x = 14.12, (x − 6)² bcomes:

  (14.12 − 6)²

 (8.12)² = 65.9

You can order 6 different one-topping pizzas. You can order 15 different one-topping pizzas.

What is the combination?

A combination is a method of selecting items from a collection where the order of selection is irrelevant.

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

The formula of combination is nCr = n!/[r!(n-r)!]

Where n is the total number of objects and r is the number of objects those are selected.

Case 1: one-topping pizzas

The number of different toppings is 6.

Selecting one topping is ₆C₁  = 6!/[1!5!] = 6

Case 2: two-topping pizzas

The number of different toppings is 6.

Selecting two topping is ₆C₂  = 6!/[2!4!] = 15

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Answer: 33 - g = 56

less than means -

is means =

Answer:

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

Given equation:

Recall the identity for a square of a sum:

Complete the square by adding the missing part:

Answer:

x = -2, x = -4

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+6x+8=0[/tex]

Solve by the method of Completing the Square.

Step 1

When completing the square for a quadratic equation in the form ax²+bx+c=0, the first step is to move the constant to the right side of the equation:

[tex]\implies x^2+6x=-8[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+6x+\left(\dfrac{6}{2}\right)^2=-8+\left(\dfrac{6}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+6x+3^2=-8+3^2[/tex]

[tex]\implies x^2+6x+9=-8+9[/tex]

[tex]\implies x^2+6x+9=1[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+3)^2=1[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+3)^2}=\sqrt{1}[/tex]

[tex]\implies x+3=\pm1[/tex]

Step 5

Subtract 3 from both sides:

[tex]\implies x+3-3=\pm1-3[/tex]

[tex]\implies x=-4, -2[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=-4, \;\; x=-2[/tex]

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Answer:

Step-by-step explanation:

We can find height of triangle by using pythagoras theorem

By theorem  (hypotenuse)^2 = (perpendicular or height)^2 + (base)^2

            =>    Height of triangle = sqrt{(hypotenuse)^{2} - (base)^{2}

Answer: 1200 mm/s

Step-by-step explanation:

Step 1: As for point B, each small case represent 2mm/s. So, when A is 3 mm/s, B is 12 mm/s

Step 2: Assuming point A: x, Point B: y and y= k, x through (0,0) and (3,12)

So, 12=3k=k=4

so, y=4x

then, x=300 and y = 4×300

which is 1200 mm/s

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Answer:

19

Step-by-step explanation:

If g(x) = [tex]x^{2} + 3[/tex], then we will substitute 4 in for x, giving us:

[tex]4^{2} + 3[/tex]

Simplifying:

[tex]16 + 3 = 19[/tex]

So g(4) = 19.

Hope this helped!

A triangle with the given side lengths 6cm , 8cm , and 10cm represents a scalene right angled triangle.

As given in the question,

For the given triangle,

Side lengths of the given triangle is equal to :

6cm , 8cm , and 10cm

Longest side length of the given triangle is equal to 10cm.

Apply Pythagoras theorem to check whether the given triangle is right angled triangle or not.

( longest side ) ² = ( side 1)² + ( Side 2)²

Hypotenuse = longest side

Side 1 = base

Side 2 = Altitude

In the given triangle,

10²

= 100

= 36 + 64

= 6² + 8²

which satisfies the condition of Pythagoras triplets.

All the sides are of different measure so it is a scalene triangle.

Therefore, a triangle with given side lengths is a scalene right angles triangle.

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The maximum number of pens he can buy now is 71.

We are given that;

A regular octagon has equal sides = 9 feet and an apothem of 10.9 feet

The cost of the railing if it sells = $7.90 per foot

Now,

Let’s assume that the person has bought x pens.

The total cost of the pens would be 9x dollars.

The shopkeeper has given a discount of 70 dollars. So the total cost of the pens after discount would be 9x - 70 dollars.

We need to find the maximum number of pens he can buy now.

we need to find the maximum value of x such that 9x - 70 ≤ 0.

Solving this inequality gives us x ≤ 70/9 ≈ 7.78.

Therefore, by algebra the answer will be 71.

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Answer:

j+k=468

j=52 + j

are the correct equations

The requried value of 'a' in the given expression is a = -12.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
8⁻⁵⁵ / 8ᵃ = 8⁻⁴³
8ᵃ = 8⁻⁵⁵ / 8⁻⁴³
8ᵃ = 8 ⁻⁵⁵ ⁺ ⁴³
8ᵃ = 8⁻¹²

Taking logs on both sides
a ln 8 = -12 ln 8   [lnbˣ = x lnb]
a = -12

Thus, the requried value of 'a' in the given expression is a = -12.

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To determine the value in a ratio when the difference between two amounts is given, divide the difference by the ratio. For example, if the ratio is 3:2 and the difference between the two amounts is 12, then the value of the first amount is 18 (12/3 = 4 x 3 = 18). The value of the second amount is 12 (18 - 12 = 6 x 2 = 12).

1. Identify the ratio given in the problem.

2. Identify the difference between the two amounts.

3. Divide the difference by the ratio to determine the value of the first amount.

4. Subtract the difference from the first amount to determine the value of the second amount.

To determine the value in a ratio when the difference between two amounts is given, divide the difference by the ratio. For example, if the ratio is 3:2 and the difference between the two amounts is 12, then the value of the first amount is 18 (12/3 = 4 x 3 = 18). The value of the second amount is 12 (18 - 12 = 6 x 2 = 12).

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If Annual Salary: $24,872; personal exemptions: $1,500.  the income tax withheld per pay is: $29.57 per pay period.

Total taxable income = $24,872 - $1,500

Total taxable income = $23,372

The first $10,000 is taxed at a rate of 2.75%.  The tax owed on the first $10,000 is:

$10,000 * 0.0275

= $275.

The remaining $13,372 ($23,372 - $10,000) is taxed at a rate of 3.25%, so the tax owed on this amount is:

$13,372 * 0.0325

= $434.57

The total tax owed is:

$275 + $434.57

= $709.57

Since the person is paid semimonthly, we divide the annual tax owed by 24 to find the tax withheld per pay period:

$709.57 / 24

= $29.57 per pay period

Therefore the income tax withheld per pay is: $29.57 per pay period.

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Answer: We know that T is the midpoint of VW, which means that ZW = ZV. So we can say that ZV = ZW = 41°.

Also, we know that Y is the midpoint of UW, so the angle ZYU is half of ZUW. So we can say that ZYU = ZUW/2.

We know that X is the midpoint of UV, so the angle ZXU is half of ZUV. So we can say that ZXU = ZUV/2.

Since Y is the midpoint of UW, ZYU + ZXU = ZUW/2 + ZUV/2 = ZUW/2 + (ZUW - ZXU)/2 = ZUW/2 + (ZUW - ZUV/2)/2 = ZUW/2 + (ZUW - ZUW/2)/2 = ZUW/2 + ZUW/4 = (3/4)ZUW

We know that X is the midpoint of UV, so ZXU + ZVU = ZUV/2 + ZUV = ZUV

The angle ZTYW is supplementary to the angle ZXU + ZVU + ZYU so mZTYW = 180 - ( ZXU + ZVU + ZYU)

Therefore, mZTYW = 180 - ( ZUV + (3/4)ZUW + 41)

mZTYW = 180 - (56 + (3/4)56 + 41) = 180 - (56 + 42 + 41) = 180 - 139 = 41 degrees

Step-by-step explanation:

The solution to the system in given tables of line 1 and line 2, using linear equation is (b) (0,5)

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

from the table of line 1, the equation of line is

y = 2x +5.

from the table of line 2, the equation of line is

y = 5 - x

to find the solution of the system, we compare both of the equation, we get

2x + 5 = 5 - x

add x from both side, we get

3x + 5 = 5

subtract 5 from both side, we get

3x = 0

So that, x = 0

putting the value of x in the equation of line 2

y = 5 - x

y = 5 - 0

y = 5

The solution to the system in given tables of line 1 and line 2 is (0,5)

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Answer:

Step-by-step explanation:

-10.9p + 3.9

-10.9p turns positive.

The (p) is isolated.

10.9 - 3.9= 9.18 = -9.18

Answer

-9.18

A vector theory and descriptive coefficients for the line are provided by the statement: r(t) = 0,15,-9> +t4,-2,9>.

There are different quantities, which include direction and magnitude. If the quantity has both magnitude and direction, it is said to be a vector. These are referred to as vector quantities. Examples include displacement, speed, acceleration, energy, weight, impetus, and electric intensity. Consequently, the vector quantity is and the SI unit for it is m/s².

The given line is-

x = -1+4t, y = 6-2t, z = 3+9t

That is,

r(t) = <-1+4t, 6-2t, 3+9t> = < -1,6,3> +t<4, -2,9>

The line concurrent to the given line's direction vector is

u = <4,-2,9>

Equation for line going through point (x0,y0,z0) and has direction vector u is line passing through point (0,15,-9)

r(t) = < x0, y0,z0> +tu

That is

r(t) = <0,15, -9> +t<4,-2,9>

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Answer:

(a) 8800000

(b) Barcelona had the least population in 2018

(c) The difference in population is 2.9 x [tex]10^{7}[/tex]

Step-by-step explanation:

(a) Since '10' is raised to a positive power, the decimal will be moving in the forward direction, In other words, it will move towards the right. Therefore, the decimal will be moving 6 places forward. After which, the empty slot(s) will be occupied by zeros

8.8 x [tex]10^{6}[/tex] = 8800000

(b) First notice that three out of the five cities have population expressed in [tex]10^{6}[/tex] (where 6 is the least power). Then notice that out of those three cities, the smallest number corresponds to Barcelona (i.e. 5.5).

Therefore, Barcelona had the least population in 2018

(c) Population of:

Tokyo: 3.7 x [tex]10^{7}[/tex]

Ahmedabad: 7.7 x [tex]10^{6}[/tex]

First, make sure the two numbers are expressed in the same standard form (meaning 10 is raised to the same power in both cases):

Tokyo: 3.7 x [tex]10^{7}[/tex] = 3.7 x 10 x [tex]10^{6}[/tex]  =37 x [tex]10^{6}[/tex]

Ahmedabad: 7.7 x [tex]10^{6}[/tex]

Next step:

37 x [tex]10^{6}[/tex] - 7.7 x [tex]10^{6}[/tex]

= (37 - 7.7) x [tex]10^{6}[/tex]

= 29.3 x [tex]10^{6}[/tex]  

= 29 x [tex]10^{6}[/tex] (Corrected to 3 significant figures)

= 2.9 x 10 x [tex]10^{6}[/tex]

= 2.9 x [tex]10^{7}[/tex]

The standard error of the mean 0.79

The margin of error  1.55

The standard error of the mean is one of the components of the margin of error.

The margin of error is the multiplication of standard error of the mean and critical value. Margin of error is denoted by E

sample size, n= 40,

Sample mean,   = 25 and

population standard deviation, [tex]\alpha[/tex]= 5

[tex]SE_{x}[/tex]

The standard error of the mean, [tex]SE_{x}[/tex]

[tex]SE_{x}[/tex] = [tex]\alpha[/tex]/√n

[tex]SE_{x}[/tex] = 5/√40

[tex]SE_{x}[/tex] = 5/6.3246

[tex]SE_{x}[/tex] = 0.79

We have to find the critical value  

[tex]\alpha[/tex]/2 = 0.05/2 = 0.025 is ± 1.96

The margin of error, E

E =  [tex]Z_{\alpha /2 }[/tex] * [tex]SE_{x}[/tex]

E= 1.96×0.79

E= 1.55

The standard error of the mean 0.79

The margin of error  1.55

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Answer:

y = -0.5x + 5.5

Step-by-step explanation:

A linear function can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is the ratio of the change in y to the change in x (rise over run) and the y-intercept is the point where the line crosses the y-axis.

To find the rule for this linear function, we can use the two points (x1, y1) and (x2, y2) to find the slope m:

m = (y2 - y1) / (x2 - x1)

If we use the points (7, 2) and (5, 3) to find the slope, we have:

m = (3 - 2) / (5 - 7) = 1 / (-2) = -0.5

We can also use the point (x1, y1) to find the y-intercept b:

b = y1 - m * x1

If we use the point (7, 2) to find the y-intercept, we have:

b = 2 - (-0.5) * 7 = 2 + 3.5 = 5.5

So the rule for the linear function is:

y = -0.5x + 5.5

We can confirm this rule by checking the point (x=-1,y=6)

y = -0.5(-1) + 5.5 = 6

The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.The best method and reasoning to calculate the gas mileage is: D. 243.8 miles ÷ 7.71 gallon s

​The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.

The best method and reasoning to calculate the gas mileage is:

D. 243.8 miles ÷ 7.71 gallon s

because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.

The mileage of the car is calculated by dividing the number of miles traveled by the amount of gas used.

mileage

= 243.8 /7.71

From the given parameters;

The unit of miles traveled is miles

The unit of gallons used is gallons

Because the miles traveled is divided by the gallons used, then the unit of the mileage would be miles per gallon

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A day is a unit of time and cannot be divided into a fraction,  Therefore Wesley would need to run for at least 5 days to meet his goal of 19 miles.

To find out how many days Wesley needs to run to meet his goal, we need to divide the total distance he wants to run (19 miles) by the distance he runs each day (4.2 miles):

19 miles ÷ 4.2 miles/day = 4.52 days

Since a day is a unit of time and cannot be divided into a fraction, Wesley would need to run for at least 5 days to meet his goal of 19 miles.

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Answer:

0=3x-y=-13

Step-by-step explanation:

Answer:

In the equation y+4=3(x-3), we can see that x and y are the variables and 4 and -3 are the constants.

To convert the equation to the form Ax + By = C, we'll first distribute the 3 on the right side:

y + 4 = 3x - 9

Next, we'll move all the terms with x to one side of the equation and all the terms with y to the other side:

-3x + y =  - 13

Now we have the equation in the form Ax + By = C, where A = -3, B = 1, and C = -13.

Answer:

A = -5

B = -2

C = 3

This simplifies to x<3/2. So the graph of f(x) = –x^2 + 3x + 8 is increasing over the interval (-infinity,3/2)

Generally, The vertex form of a parabola that opens downward is

f(x) = a(x-h)^2 + k,

where (h,k) is the vertex of the parabola.

We know that the vertex of the parabola is at (1.5, 10) so we can use that to find the value of a and h. So,

f(x) = a(x-1.5)^2 + 10

Given that the parabola goes through (- 2, - 2) and (5, - 2), we can substitute these points into the equation to find a and k.

Substituting (-2, -2) into the equation:

-2 = a((-2) - 1.5)^2 + 10

Substituting (5, - 2) into the equation:

-2 = a(5 - 1.5)^2 + 10

Solving these two equations will give you a = -1/2 and k = -8

So the equation is f(x) = -1/2(x-1.5)^2 - 8

The graph of a parabola is increasing on the interval where the derivative is greater than 0.

To find the derivative, we use the power rule and the chain rule:

f'(x) = -1/2(2x-3)

= -x+3/2

So, the graph of f(x) is increasing when -x+3/2 > 0

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The probability of Amar drawing a spade in the first five attempts is approximately 24.5%, as there are 13 spades in a deck of 52 cards.

The probability of drawing a spade in the first attempt is 13/52 or 25%.

The probability of drawing a spade in the second attempt is 12/51 or 23.5%.

The probability of drawing a spade in the third attempt is 11/50 or 22%.

The probability of drawing a spade in the fourth attempt is 10/49 or 20.4%.

The probability of drawing a spade in the fifth attempt is 9/48 or 18.8%.

The total probability of drawing a spade in the first five attempts is the sum of the above probabilities, which is 24.5%.

The probability of drawing a spade in the first five attempts is 24.5%, calculated by summing the separate probabilities.

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Answer:

5 cm per hour

if this helps

Step-by-step explanation:

Answer:

There are many varying characteristics and exceptions to each type of protist.

They have been previously categorized based on what they are not.

Recent studies show that protists have not descended from one common ancestor.

Step-by-step explanation: