1. Calculate the sum of the infinite series S. = 16+4+1+....

The quadratic formula used to solve the equation [tex]5x^{2} +3x-4=0[/tex] is [tex]x=\frac{-3 \pm \sqrt{(3)^{2}-4(5)(-4)}}{2(5)}[/tex]

Explanation:

The equation is [tex]5x^{2} +3x-4=0[/tex]

The equation is of the form [tex]ax^{2} +bx+c=0[/tex]

Thus, [tex]a=5, b=3,c=-4[/tex]

To find the quadratic formula, the general formula to find the quadratic roots is [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Hence, substituting the values of a,b,c in the formula, we get,

[tex]x=\frac{-3 \pm \sqrt{(3)^{2}-4(5)(-4)}}{2(5)}[/tex]

Thus, Option A is the correct answer.

The quadratic formula used to solve the equation [tex]5x^{2} +3x-4=0[/tex] is [tex]x=\frac{-3 \pm \sqrt{(3)^{2}-4(5)(-4)}}{2(5)}[/tex]

Answer:

Explanation:

You can set a system of equation using the following steps:

1. Name the variables:

2. Set the equations that relate the variables:

        equation (1): x = 2y - 46

         equation (2): x + y = 122

3. Solve the system:

Substitute equation (1) into equation (2)

Solve for y:

Subsitute the value on y in equation 1, to find the value of x:

Thus, the average yearly salary of a person with a masters degree is $ 66 thousand.

Final answer:

Using a system of equations with the variables B (the average salary for a bachelor's degree) and M (the average salary for a master's degree), we solved to find that the average yearly salary for an individual with a bachelor's degree is $56,000 and with a master's degree is $66,000.

Explanation:

The problem at hand involves creating two algebraic equations to solve for the average yearly salaries of individuals with a bachelor's degree and a master's degree based on the provided information. Let the average yearly salary for an individual with a bachelor's degree be represented by B, and the salary for an individual with a master's degree be represented by M.

According to the problem, the average yearly salary of an individual with a master's degree is $46 thousand less than twice the salary of an individual with a bachelor's degree, so we can write the first equation as: M = 2B - 46.

The second equation comes from the fact that combined, their earnings amount to $122 thousand, so: B + M = 122.

Now, we can substitute the first equation into the second to solve for B: B + (2B - 46) = 122. Simplifying, we get 3B - 46 = 122. Adding 46 to both sides gives 3B = 168, and dividing by 3 yields B = 56. So, the average salary for someone with a bachelor's degree is $56,000.

To find the salary for a master's degree holder, we substitute B = 56 into the first equation: M = 2(56) - 46. That simplifies to M = 112 - 46, giving us M = 66. Hence, the average salary for someone with a master's degree is $66,000.

Domain: [tex](-\infty, \infty)[/tex]

Range: [tex](-\infty, \infty)[/tex]

Explanation:

The function is [tex]y=-\frac{1}{4} x[/tex]

The domain of a function is the set of all input values for which the function is well defined. Generally, domain consists of all x-values of the function. Hence, the function [tex]y=-\frac{1}{4} x[/tex] is defined in the interval [tex](-\infty, \infty)[/tex].

The range of a function is the set of output values obtained by substituting the value of x in the function. Hence, the function [tex]y=-\frac{1}{4} x[/tex] is defined in the interval [tex](-\infty, \infty)[/tex].

Answer:

160 good luck tho on whatever

Step-by-step explanation:

450-290

The question is about determining the initial elevation of a hiker's journey given the increase in elevation and the current elevation. The hiker started at an elevation of 160 feet before the hike.

The student is asking a question related to change in elevation during a hike. If a hiker increased their elevation by 290 feet and is currently at 450 feet, they must have started at an elevation of 160 feet that morning. This is calculated by subtracting the increase from the current elevation: 450 feet - 290 feet = 160 feet.

Answer:

I'm Going With A.) Hope It Helps

Answer:

y = -2x -7

Step-by-step explanation:

y + 5 = -2 (x +1)

y + 5 = -2x -2 . move 5 to the other side by subtracting from both sides.

y = -2x -7

Answer:

46 hours

Step-by-step explanation:

We are given the information;

Required to determine the number of hours;

We need to know that;

Number of hours = Amount earned ÷ rate per hour

Therefore;

First week;

Number of hours = $192 ÷ $8 per hour

                             = 24 hours

Next week

Number of hours = $176 ÷ $8 per hour

                             = 22 hours

Thus, number of hours she worked = 22 + 24

                                                           = 46 hours

Therefore, in the two weeks Molly baby-sited for 46 hours

Answer:

71.5

Step-by-step explanation:

650 / 100 = 6.5

6.5 x 11 = 71.5

Answer:

What is it you would like help with, because the file does not work for me.

Step-by-step explanation:

The product of f(x) = 2x + 6 and g(x) = -5x - 9 is found by multiplying out the terms, resulting in -10x^2 - 48x - 54, which corresponds to option B.

The student is asking to find the product of two functions f(x) = 2x + 6 and g(x) = -5x - 9. To find the product, we multiply the two functions together:

f(x) * g(x) = (2x + 6) * (-5x - 9)

Distribute each term in the first function by each term in the second function:

2x*(-5x) + 2x*(-9) + 6*(-5x) + 6*(-9)

= -10x^2 - 18x - 30x - 54

Combine like terms:

= -10x^2 - 48x - 54

Therefore, the correct answer is B. -10x^2 - 48x - 54.

Answer:

slope = 0

Step-by-step explanation:

recall that the equation of a line can be expressed as:

y = mx + b, where m is the slope and b is the y-intercept.

in our case we are given y = 3

which can be re-written:

y = (0)x + 3

if we compare this with the general equation above, we can see that

slope = m = 0

Answer: the slope is zero

Step-by-step explanation:

The equation of line in slope - intercept form is given as : y = mx + c , where m is the slope and c is the y - intercept. This means that the line y = 3 is a horizontal line that passes through the point y = 3 , therefore , the slope is zero

Answer:

The order of operations is PEMDAS

First step is to do everything is parenthesis or brackets

5+{2*[(5-1)+6]}/4

{2*[(5-1)+6]}

First you would go 5-1=4, because that is the first equation that is in parenthesis by itself.

{2*[4+6]}

Next you would go 4+6=10, because that is your next smallest bracket

{2*10}

Last you would go 2*10=20

Your equation now looks like this

5+{20}/4

In PEMDAS your next step is exponents, but we don't have any so we go on to the next one which is multiply/division

5+5

You would go 20/4=5

Last step is to add/subtract

5+5=10

Your final answer would be 10

Hope this helps ;)

Step-by-step explanation:

Answer: .679

Step-by-step explanation:

move the decimal to the left two places.

Answer:

-2

Step-by-step explanation:

-6x=5x+22

-6x-5x=22

-11x=22

x=22/-11

x=-2

The terms that are called means are 2 and 36

Solution:

A proportion is simply a statement that two ratios are equal

Proportion is written as:

[tex]\frac{a}{b} = \frac{c}{d}[/tex]

In ratios, we can write as,

a : b = c : d

To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

[tex]\frac{a}{b} = \frac{c}{d}\\\\a \times d = b \times c[/tex]

Here, a and d are extremes

b and c are means

In the given proportion,

[tex]\frac{12}{36} = \frac{2}{6}[/tex]

[tex]12 \times 6 = 2 \times 36[/tex]

Here, 12 and 6 are extremes

2 and 36 are means

In the given proportion 12/36=2/6, the mean terms are 12 and 6. To verify the proportion, one can use the cross-products method, which confirms its correctness since the multiplication of means and extremes produces equal results.

In the proportion 12/36=2/6, the terms that are known as the means are the two numbers that are on the inside of the proportion, which are 12 and 6 in this case. Proportions are made up of four terms, with the first and last terms called the extremes, and the two terms in the middle called the means. To solve a proportion and check if it is true, you can use the cross-products method, which involves multiplying the means and the extremes. If the cross-products are equal, then the proportion is true. In this example, 12 (the mean) multiplied by 2 (an extreme) is equal to 24, and 36 (the other extreme) multiplied by 6 (the mean) also gives 24, confirming that this proportion is correct.

Answer:

$1.29

Step-by-step explanation:

5.16 divided by 4

Answer:

Ur answer

Step-by-step explanation:

If A4 paper has width 21cm and length of 30cm

Then,

A5 paper has a length of 21cm

So find the width,

A4 has width 30cm

so,

A5 must have half the answer

15cm

The width of A5 paper is 21cm, which is derived from the length of A4 paper, based on the standard ratio of the A series paper sizes.

The width of A5 paper can be determined using the properties of the standardized A series paper sizes. As A4 paper has dimensions of 21cm by 30cm and the A series has a height to width ratio of the square root of 2, when an A4 sheet is cut in half, it results in two A5 sheets.

Thus the length of A4 becomes the width of A5. To find the width of A5, we simply take the length of A4, which is 21cm in this case.

Therefore, the width of an A5 sheet is also 21cm, making the dimensions of A5 paper 21cm by 14.85cm (since half of 30cm is 14.85cm).

Answer:

90

Step-by-step explanation:

450/5

Answer:

90

Step-by-step explanation:

450 / 5 = 90

Answer:

Hi

Step-by-step explanation:

Sunndmdmd

Answer:

The Answer is 4 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Since both fractions have like denominators  , you can just add them:

12/3 + 2/3 = 14/3

Since 14/3 is improper fraction, it should be turning to a mixed number:

14 can go into 3, 4 times since 4 times 3 is 12. 14 - 12 is 2, so it will be your numerator.

4 2/3

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

The formula of a slope:

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

We have two points (-5, -1) and (6, -5). Substitute:

[tex]m=\dfrac{-5-(-1)}{6-(-5)}=\dfrac{-5+1}{6+5}=-\dfrac{4}{11}[/tex]

Put the value of a slope and coordinates of a point to the equation of a line:

[tex](-5,\ -1),\ m=-\dfrac{4}{11}\\\\y-(-1)=-\dfrac{4}{11}(x-(-5))\\\\y+1=-\dfrac{4}{11}(x+5)[/tex]

[tex](6,\ -5),\ m=-\dfrac{4}{11}\\\\y-(-5)=-\dfrac{4}{11}(x-6)\\\\y+5=-\dfrac{4}{11}(x-6)[/tex]

Step-by-step explanation:

We have,

[tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]

To find, the value of h = ?

∴ [tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]

⇒ [tex]6h^5[/tex] + (0)[tex]h^4[/tex] - 12[tex]h^3[/tex] + (0)[tex]h^3[/tex] + (0)h = 0

⇒ [tex]6h^5[/tex] + 0 - 12[tex]h^3[/tex] + 0 + 0 = 0

⇒ [tex]6h^5[/tex]  - 12[tex]h^3[/tex] = 0

Taking 6 [tex]h^3[/tex] as common, we get

[tex]6h^3(h^2-2)[/tex] = 0

⇒6[tex]h^3[/tex] = 0 or,   [tex]h^2[/tex] - 2 = 0

⇒ 6[tex]h^3[/tex] = 0 ⇒ h = 0

⇒ [tex]h^2[/tex] = 2  

⇒ h = ± [tex]\sqrt{2}[/tex]

Hence, the value of h = 0,  ± [tex]\sqrt{2}[/tex]

Answer:

The correct answer is B. 144°

Step-by-step explanation:

Let's recall that in a trapezium the bases are parallel and one of its properties is that  the two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°.

Upon saying that, we can find out the value of a and b, this way:

∠a = 180 - 36

∠a = 144

∠b = 180 - 113

∠b = 67

But the question is regarding ∠a. Then the correct answer is B. 144°

Answer:

a) A=π(r×r)

Where π=constant pie of 3.143

           r= half of diameter

b) 31420 square units

Step-by-step explanation:

The Atlanta Traffic Commission needs to know how much space the Ferris Wheel takes up.  

A)What is the AREA formula for a circle?

A=π(r×r)

Where π=constant pie of 3.143

           r= half of diameter

B)Show your work to find the AREA of the Ferris Wheel. Don't forget to add your square units

A=π(r×r)

   =3.142×100×100

   =31420 square units

The formula for the area of a circle is A=πr². To find the area of a circular object, like a Ferris Wheel, you need to know the radius. If the radius is 10 units, then A=π(10)² = 314 square units.

The subject of this question is Mathematics and it's a Middle School level question. It's about calculating the area of a circle, which in this case is the Ferris Wheel.

A) The formula for the area of a circle is Pi times the radius squared (A=πr²). Pi (π) is approximately 3.14 and the radius (r) is the distance from the center of the circle to the outside of the circle.

B) To find the area of the Ferris Wheel, you'll need to know the radius. Let's assume the radius of our Ferris Wheel is 10 units. Plugging these values into the formula we have: A=π(10)² = π * 100 = 314 square units. The unit of measurement for the area depends on the unit used for the radius. If the radius was in meters, then the area is in square meters, if the radius was in feet, then the area is in square feet, and so on. If no units is given, we just call it 'square units'.

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Answer:

Step-by-step explanation:

you put the equation in slope and intercept form by making y the subject of the formula

i.e

y = -2x + 2

-2 is the slope and 2 is the intercept

Answer:

Step-by-step explanation:

2x + y = 2

Making y as subject

y = - 2x + 2

And the equation is y = mx + c

Where m is slope = -2

Y intercept = 2

Answer:hfgjvggunycdvjk8nyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyunyum

Step-by-step explanation:

Answer: probility that it lands on

Head up is 1/8 or 12.5%

Step-by-step explanation:

Answer:

You cant solve for how far you can go, but you can make an equation.

Step-by-step explanation:

A= The initial fee

$1.80=per mile

$12=The max amount of money

A+1.80x=$12

And you would subtract A from the $12 first!

Good Luck!

The height of wall of play structure is 8.48 feet

Solution:

A climbing wall leaning against the top of a play structure forms a right triangle with the ground

The figure is attached below

ABC is a right angled triangle

AB is the height of wall of play structure

Let "x" be the height of wall of play structure

AB = x

BC is distance from the bottom of the climbing wall to the base of the play structure

BC = 7 feet

AC is the length of climbing wall

AC = 11 feet

We can apply pythogoras theorem for right angled triangle

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Therefore, by above definition for right angled triangle ABC,

[tex]AC^2 = AB^2+BC^2[/tex]

Substituting the values we get,

[tex]11^2 = x^2 + 7^2\\\\121 = x^2 + 49\\\\x^2 = 121-49\\\\x^2 = 72\\\\\text{Take square root on both sides }\\\\x = \sqrt{72}\\\\x = 8.48[/tex]

Thus the height of wall of play structure is 8.48 feet

Answer:

8ft

Step-by-step explanation:

i did the test on T4L

Answer:

Substitute x = 6 into the equation 3x-18

Answer:

A.) Subsitute 6 for x in the equation.

Step-by-step explanation:

I’m smart :).

Answer:

27:72

Step-by-step explanation:

First I would convert three days to hours. 24×3=72

Answer: 27:72

The ratio of the two times will be 3 / 8.

A ratio in mathematics shows how many times one number is contained in another. For instance, if a dish of fruit contains eight oranges and six lemons.

The ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given that compare in hours: 27 hours to 3 days. The ratio will be calculated as:-

In 3 days there are 72 hours.

Ratio = 27 / 72 = 3 / 8

Therefore, the ratio of the two times will be 3 / 8.

To know more about a ratio follow

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