4/6 times what equals 1/6

Answer:

Step-by-step explanation:

Final answer:

The shortest distance from the park to the library, forming a right-angled triangle with sides of 6 miles and 11 miles, can be found using the Pythagorean theorem, and it is approximately 12.5 miles when rounded to the nearest half mile.

Explanation:

The question involves finding the shortest distance from the park to the library. This is a basic problem of geometry that can be solved using the Pythagorean theorem. Since the park is 6 miles due west of your house and the library is 11 miles north, we can form a right-angled triangle with one side as 6 miles and the other side as 11 miles.

We find the shortest distance by calculating the hypotenuse of the right-angled triangle:

Represent the distances as sides of a triangle: one leg is 6 miles (west) and the other is 11 miles (north).

Apply the Pythagorean theorem: hypotenuse2 = 62 + 112

Calculate the hypotenuse: hypotenuse = √(62 + 112) = √(36 + 121) = √157

Find the nearest half mile: √157 is approximately 12.53. So rounded to the nearest half mile, the distance is 12.5 miles.

Therefore, the shortest distance from the park to the library is about 12.5 miles.

Answer:

k=-5

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]6x^{2} +7x+k=0[/tex]  

so

[tex]a=6\\b=7\\c=k[/tex]

substitute in the formula

[tex]x=\frac{-7\pm\sqrt{7^{2}-4(6)(k)}} {2(6)}[/tex]

[tex]x=\frac{-7\pm\sqrt{49-24k}} {12}[/tex]

so

[tex]x_1=\frac{-7+\sqrt{49-24k}} {12}[/tex]

[tex]x_2=\frac{-7-\sqrt{49-24k}} {12}[/tex]

Remember that

[tex]2x_1+3x_2=-4[/tex]

substitute

[tex]2(\frac{-7+\sqrt{49-24k}} {12})+3(\frac{-7-\sqrt{49-24k}} {12})=-4[/tex]

[tex](\frac{-14+2\sqrt{49-24k}} {12})+(\frac{-21-3\sqrt{49-24k}} {12})=-4[/tex]

Multiply by 12 both sides

[tex](-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48[/tex]

[tex]-35-\sqrt{49-24k}=-48[/tex]

[tex]\sqrt{49-24k}=48-35[/tex]

[tex]\sqrt{49-24k}=13[/tex]

squared both sides

[tex]49-24k=169\\24k=49-169\\24k=-120\\k=-5[/tex]

therefore

The equation is

[tex]6x^{2} +7x-5=0[/tex]  

The roots are

[tex]x=\frac{-7\pm\sqrt{49-24(-5)}} {12}[/tex]

[tex]x=\frac{-7\pm\sqrt{169}} {12}[/tex]

[tex]x=\frac{-7\pm13} {12}[/tex]

[tex]x_1=\frac{-7+13} {12}=\frac{1} {2}[/tex]

[tex]x_2=\frac{-7-13} {12}=-\frac{5} {3}[/tex]

Final answer:

To find the constant k, use Vieta's formulas to express x_1 and x_2 in terms of the equation coefficients, then solve the given equation 2x_1+3x_2=−4 to find individual values for x_1 and x_2, and use these values to determine k through the product of the roots.

Explanation:

The student needs to find the constant k in the equation 6x^2+7x+k=0, given that x_1 and x_2 are roots of this equation, and that 2x_1+3x_2=−4. According to Vieta's formulas, which relate the roots of a polynomial to its coefficients, the sum of the roots is −(b/a) and the product of the roots is (c/a). Since the coefficient of x^2 (a) is 6 and the coefficient of x (b) is 7, we can state that x_1 + x_2= −7/6 and x_1x_2 = k/6.

Using the second given condition, 2x_1+3x_2=−4, we can substitute x_2 from the first Vieta's formula: x_2= −(7/6)−x_1, and plug this into the second condition to get 2x_1+3(−(7/6)−x_1)=−4. Simplifying, we find a value for x_1. We then substitute this x1 back into the expression for x_2 to find its value. With both x_1 and x_2 found, we use the product of the roots to find k: k = 6(x_1x_2).

Answer:

The square root of 49 is 7. 7*7=49

Hope this helps,

:)

Answer:

The square root of 49 is 7

Step-by-step explanation:

7 multiplied by 7 equals 49, that is how you are sure.

- MoonQue

Answer:

7

Step-by-step explanation:

Answer:

[tex]New\ level\ of\ cholesterol = 192[/tex]

Step-by-step explanation:

Given:

Reduced level of cholesterol = 20%

Original level of cholesterol = 240

We need to find cholesterol level now

Solution:

First we find reduced level of cholesterol using percentage formula.

[tex]Percentage = \frac{Value}{Toatl\ value}\times 100[/tex]

Substitute all known value in above formula.

[tex]20 = \frac{Value}{240}\times 100[/tex]

[tex]Value = \frac{20\times 240}{100}[/tex]

[tex]Value = \frac{4800}{100}[/tex]

[tex]value = 48[/tex]

So reduced level of cholesterol = 48

But we need to find cholesterol level now, so we subtract reduced level from original level of cholesterol.

[tex]New\ level = original\ level - reduced\ level[/tex]

[tex]New\ level = 240 -48[/tex]

[tex]New\ level = 192[/tex]

Therefore, Cholesterol level at present = 192

Answer:

2

Step-by-step explanation:

slope = difference of y/ difference of x

m = (9-5) / (4-2) = 4/2 = 2

Answer:

It D

Step-by-step explanation:

Answer:

It's D

Step-by-step explanation:

I did it on UsaTestPrep

Answer:

Step-by-step explanation:

5(x - 1) + 3 = 13....distribute thru the parenthesis

5x - 5 + 3 = 13

5x - 2 = 13....add 2 to both sides

5x = 13 + 2

5x = 15 ....divide both sides by 5

x = 15/5

x = 3 <====

Answer:

1/1 9

Step-by-step explanation:

ok

Answer:

see attached picture please

Answer:

slope = dY/dX

Step-by-step explanation:

dY/dX = (-2 - 6 ) / (4 - 0)

dY/dX = -2

Answer:

If im correct it actually equals 18x because you add the like terms.

Step-by-step explanation:

it equals 18x because you add the like terms.

Step-by-step explanation:

. .                 . .               . .                . .

Answer:

d

Step-by-step explanation:

took test

The correct statement about the Internet connection cost would be; Any amount of time over an hour and a half would cost $10.

The function is a type of relation, or rule, that maps one input to a specific single output.

The function f(t) represents the cost to connect to the Internet at an online gaming store.

It is a function of t, the time in minutes spent on the Internet.

The function is as follows;

(500 f(t) = $5 30 | $ 10 1 > 90

f (t), when t is a value lie between 0 and 30

The cost is US$ 0 for the first 30 minutes.

f (t), when t is a value lying between 30 and 90

The cost is US$ 5 if the connection takes between 30 and 90 minutes.

f (t), when t is a value greater than 90

The cost is US$ 10 if the connection takes more than 90 minutes

Therefore, The correct statement about the Internet connection cost would be; Any amount of time over an hour and a half would cost $10.

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Answer:

-51

Step-by-step explanation:

Let's do order of operations.

10+8-70-(-1)     <- We did negative 7 times 10.

18-70-(-1)    <- We did 10 plus 18.

-52-(-1)     <- We did 18 minus 70

When you open the () we get:

-52--1

Negative minus a negative equals a positive.

-52+1=

-51

Answer:

7.2cm

Step-by-step explanation:

Answer: 7.2 cm

Explanation: It's important to understand that the radius is equal to half of the diameter so to find the diameter of a circle with a radius of 3.6 cm, we simply multiply 3.6 cm by 2 and we will get the diameter or the distance across a circle.

To multiply a decimal times a whole number such as 3.6 x 2, first line up the numbers and begin multiplying as if we were multiplying 2 whole numbers.

6 x 2 is 12 so we bring down the 2 and carry the 1.

2 x 3 is 6 and if we add 1 we get 7.

So we have 7.2 cm which is our diameter

Answer:

I think it would be 100

Step-by-step explanation:

because 10^2 is 10 x 10 which equals 100 and so if you have 1/10^2 it's basically saying 1 divided by 10^2 and 10^2 is 100 so it would be 1 divided by 100 which equals 100.

I hope this helped any.

1/10^2 equals 1 divided by 100 or 10 to the power of -2 in exponent notation. The negative sign indicates division by the base (10) raised to the positive power (2).

The expression

1/10^2

represents a fraction where the denominator is 10 raised to the power of 2. By definition, any number (except 0) raised to the power of 2 is that number multiplied by itself. So, 10^2 equals 10*10 which is 100. Therefore,

1/10^2 = 1/100

. This can be written using exponents as

10^-2

, because 1 divided by any number is equivalent to that number raised to the power of -1, and if the number itself is an exponent, then the negative applies to the power. So, 1/10^2 (1 divided by 10 squared) is equivalent to 10 to the power of -2.

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Answer:

n = 0

Step-by-step explanation:

Answer:

the required ans is 48

Step-by-step explanation:

given,

15-n/6 =n/6-1

or,15-n/6-n/6=-1

or,15-2n/6=-1

or,-2n/6=-1-15

or,-2n/6=-16

or,-2n=-96

or,n= -96/-2

therefore,n=48.

henece the required value of n is 48.

explanation in word.

firstly we write the question.

n/6 of right side bring ti the left side and being negative.

we solve -n/6-n/6 by sing LCM method.

again, we bring 15 to the right side of tge queation and being negative

in 6 step there is in multiply so when we bring that multiply in left side it become in divide. we can find the answer this way

Answer:

1/12 of the pie is left

Step-by-step explanation:

3/4-2/3=9/12-8/12=1/12

Answer:

Step-by-step explanation:

first question:

angles opposite to equal sides are equal

angle a + angle b + angle c =180

angle a = angle b

2 * angle B + angle c = 180

2* angle B = 128

angle B = 44

The percentage of the students that like country and also in grades 9-10 is 61%

Step-by-step explanation:

                          Rap    Rock   Country   Total

Grades 9-10       40        30          55          125

Grades 11-12     60        25          35          120

Total                  100       55          90          245

Percentage= (Number of students in both country and grades/ Total students in country)*100

Total students in country= 90

Number of students in both country and grades 9-10= 55

Percentage= (55/90)*100

                   = 61.11%= 61%(rounded to the nearest whole %)

Answer:

D 61%

Step-by-step explanation:

Answer: that will be 900

Step-by-step explanation: add 60 + 300 =

Answer:

$95.38

Step-by-step explanation:

step 1

Find the area of one button

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=9/2=4.5\ cm[/tex] ---> the radius is half the diameter

Convert to meters

[tex]r=4.5\ cm=4.5/100=0.045\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(0.045)^{2}\\A=0.0063585\ m^2[/tex]

step 2

Find the area of 1,00 buttons

Multiply by 1,000

[tex]A=0.0063585(1,000)=6.3585\ m^2[/tex]

step 3

Find the cost

Multiply $15 per square meter by the total area of 1,000 buttons

[tex](15)6.3585=\$95.38[/tex]

The amount of money in account after 8 years is $ 111569.36

Solution:

Given that, Suppose that 70,000 is invested at 6% interest

We have to find the amount of money in the account after 8 years if the interest is compounded annually

Formula for Amount compounded annually is as follows:

[tex]\mathrm{A}=P\left(1+\frac{r}{100}\right)^{n}[/tex]

Where,

"A" is the total amount after "n" years

"P" is the principal

"r" is the rate of interest

"n" is the number of years

Here in this sum,

P = 70000

r = 6 %

n = 8 years

Substituting the values in formula,

[tex]A = 70000(1+\frac{6}{100})^8\\\\A = 70000(1+0.06)^8\\\\A =70000 \times 1.06^8\\\\A = 70000 \times 1.59384\\\\A = 111569.36[/tex]

Therefore, the amount of money in account after 8 years is $ 111569.36

When $70,000 is invested at an annual interest rate of 6%, compounded annually for 8 years, the amount in the account will grow to approximately $104,613.78.

This question asks you to calculate future investment value when $70,000 is invested at 6% interest, compounded annually for 8 years. The formula we use for compound interest is A = P(1 + r/n)^(nt), where 'A' is the amount of money accumulated after n years, 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal), 'n' is the number of times that interest is compounded per year, and 't' is the time the money is invested for in years.

Since it's compounded annually, n equals to 1. So the formula now becomes A = P(1 + r)^(t). Plug in the given amounts into the formula: A = 70000(1 + 0.06)^(8). Solving this equation, we find that the amount of money in the account after 8 years will be approximately $104,613.78.

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The equation that represents the plant's height H after M months is H = 45 + M. Substituting 33 for M gives us a plant height of 78 centimeters after 33 months.

To find the equation that relates H to M, we start with the initial height of the plant, which is 45 centimeters. We are given that the plant grows by one centimeter each month, this information provides us with a constant rate of growth.

The equation can therefore be expressed as:

H = 45 + M

Using this equation, we can calculate the height of the plant after 33 months. To do this, we simply substitute 33 for M in our equation:

H = 45 + 33

H = 78

Therefore, the plant's height after 33 months will be 78 centimeters.

Answer:

[tex]Distance\ cover\ by\ Rosa = 141.3\ m[/tex]

Step-by-step explanation:

Given:

Rosa has to skate around a face off circle five times.

[tex]Distance = 5\times circumfrance\ of\ circle[/tex]

Diameter of a circle = 9.0 m

Radius of a circle = [tex]\frac{d}{2} =\frac{9}{2}=4.5\ m[/tex]

Solution:

We know that the circumference of a circle.

[tex]C = 2\pi r[/tex]

Where;

r = Radius of a circle

Substitute [tex]\pi =3.14\ and\ r = 4.5[/tex] in above equation.

[tex]C = 2\times 3.14\times 4.5[/tex]

[tex]C = 28.26\ m[/tex]

So, the circumference of the circle is 28.26 m.

Rosa has to skate around a face off circle five times, so Rosa cover 28.26 m 5 times.

[tex]Distance\ cover\ by\ Rosa = 5\times 28.26[/tex]

[tex]Distance\ cover\ by\ Rosa = 141.3\ m[/tex]

Therefore, the distance cover by Rosa to skate 141.3 m.

Rosa has to skate approximately 141.35 meters to go around the face off circle with a diameter of 9.0m five times.

To calculate how far Rosa has to skate, we need to determine the circumference of the face off circle, which can be calculated using the formula C = pi × d, where C is the circumference and d is the diameter of the circle. Since Rosa skates around the circle five times, we will multiply the circumference by five.

Given that the diameter (d) of the face off circle is 9.0 meters, the circumference is:

Now, we calculate the total distance Rosa skates by going around the circle five times.

Total distance = Circumference × Number of laps

Total distance = 28.27m × 5 = 141.35m

Therefore, Rosa has to skate approximately 141.35 meters around the face off circle.

Answer:

-3x - 1

Step-by-step explanation:

(6x + 2)-(9x + 3)

We Begin by opening the brackets.

6x + 2 -9x - 3

Please note the change in the signs.

6x - 9x + 2 - 3

-3x - 1

Answer:

1) The slope of the function [tex]g(x)[/tex] is [tex]0[/tex] and the slope of the function [tex]f(x)[/tex] is [tex]-1[/tex].

2) The negative slope of the function [tex]f(x)[/tex] shows that it is the line is increasing and the slope [tex]0[/tex]  of the function  [tex]g(x)[/tex]  shows that the line will always have the same y-coordinate.

3) The slope of the function is [tex]f(x)[/tex] is greater than the slope of the function  [tex]g(x)[/tex].

Step-by-step explanation:

 For this exercise you need to know that the slope of any horizontal line is zero ([tex]m=0[/tex])

The slope of a line can be found with the following formula:

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

You can observe in the graph of the function  [tex]g(x)[/tex]  given in the exercise, that this is an horizontal line.  Then,  you can conclude that its slope is:

[tex]m=0[/tex]

The steps to find the slope of the function [tex]f(x)[/tex] shown in the table attached, are the following:

- Choose two points, from the table:

[tex](0,3)[/tex] and [tex](4,-1)[/tex]

- You can say that:

[tex]y_2=-1\\y_1=3\\\\x_2=4\\x_1=0[/tex]

- Substitute values into the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]:

[tex]m=\frac{-1-3}{4-0}[/tex]

- Finally, evaluating, you get:

[tex]m=\frac{-4}{4}\\\\m=-1[/tex]

Therefore:

1) The slope of the function [tex]g(x)[/tex] is [tex]0[/tex] and the slope of the function [tex]f(x)[/tex] is [tex]-1[/tex].

2) The negative slope of the function [tex]f(x)[/tex] shows that it is the line is increasing and the slope [tex]0[/tex]  of the function  [tex]g(x)[/tex]  shows that the line will always have the same y-coordinate.

3) The slope of the function is [tex]f(x)[/tex] is greater than the slope of the function  [tex]g(x)[/tex].

Answer:

-1 11/24

Step-by-step explanation:

Answer:

Good job

Step-by-step explanation:

Answer:

-5x^2

Step-by-step explanation:

-x times 5x = -5x^2, because there is a X being multiplied with an X.

Answer:

-5x^2

Step-by-step explanation:

Multiplying a negative variable by the same variable would equal that variable as a negative and also squared

Answer:

Thus, the equivalent expression in standard form is:

⇒ [tex]-23.9m+121.1n[/tex]

Step-by-step explanation:

Given expression:

[tex](-87.9m+35.1n)+(64m+86n)[/tex]

To give the equivalent expression in standard form.

Solution:

In order to find the equivalent expression in standard form we will simplify the expression.

We have:

[tex](-87.9m+35.1n)+(64m+86n)[/tex]

Simplifying by removing parenthesis.

⇒ [tex]-87.9m + 35.1n+ 64m + 86n[/tex]

Combining like terms.

⇒ [tex]-87.9m+64m + 35.1n + 86n[/tex]

⇒ [tex]-23.9m+121.1n[/tex]

Thus, the equivalent expression in standard form is:

⇒ [tex]-23.9m+121.1n[/tex]

Answer : $8

Step-by-step explanation:

24 divided by 3 equals 8