A runner jogged 4 miles in ten laps around a circular
track. What is the greatest distance straight across
the track?

Answer:

(-2, 4, 2)

Where x = -2, y = 4, and z = 2.

Step-by-step explanation:

We are given the system of three equations:

[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]

And we want to find the value of each variable.

Note that both the second and third equations have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.

Solve the second equation for z:

[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]

Likewise, solve the third equation for y:

[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]

Substitute the above equations into the first:

[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]

Hence, x = -2.

Find z and y using their respective equations:

Second equation:

[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]

Third equation:

[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]

In conclusion, the solution is (-2, 4, -2)

Answer:

x = -2

y =4

z=-2

Step-by-step explanation:

4x−y−2z=−8

−2x+4z=−4

x+2y=6

Solve the second equation for x

x = 6 -2y

Substitute into the first two equations

4x−y−2z=−8

4(6-2y) -y -2 = 8  

24 -8y-y -2z = 8

-9y -2z = -32

−2(6-2y)+4z=−4

-12 +4y +4z = -4

4y+4z = 8

Divide by 4

y+z = 2

z =2-y

Substitute this into -9y -2z = -32

-9y -2(2-y) = -32

-9y -4 +2y = -32

-7y -4 = -32

-7y =-28

y =4

Now find z

z = 2-y

z = 2-4

z = -2

Now find x

x = 6 -2y

x = 6 -2(4)

x =6-8

x = -2

7.5-3.25=4.25 tons.

The truck weights 4.25 tons.

Check with other answers, although I'm pretty sure its correct.

Heart if helpful :D

Answer:

To be a function, each input must only have one output. In this case, input 4 has two outputs, so (4 , -2) can be removed for it to be a function.

Let me know if you have any other questions!

The ordered pair (4,2) could be removed to make the given relation a function.

A relation is a function if for every input (x-value) there is exactly one output (y-value).

If there are two or more ordered pairs with the same x-value but different y-values, then the relation is not a function. In this case, one of those ordered pairs would need to be removed in order to make it a function.

As per the question, the relation was given as {(-5,0), (2, -3), (-1, -3), (4, -2), (4, -2), (6,-1)}, the ordered pair (4,-2) would need to be removed because there are two outputs (-2 and 2) for the input of 4.

Thus, removing (4,2) would result in the function.

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Answer:

B is the answer

Step-by-step explanation:

Answer:

B. y = x^2+7x+10

Step-by-step explanation:

The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137.

A statement expressing the equality of two mathematical expressions is known as an equation.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given,

Initial fixed money = $95

Per week saving $7/week

Total money = fixed money + money in w weeks.

⇒ 95 + 7w

For 6 weeks, w = 6

⇒ 95 + 7× 6 = $137.

Hence "The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137".

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Answer:

Step-by-step explanation:

h=√[34²-24²]=√[(34-24)(34+24)]=√[10×58]=√(5×29)=√145 ≈12 m

The height of the building is 10 meters.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's call the height of the building "h".

We can use the Pythagorean theorem to relate the height, shadow, and hypotenuse of the right triangle:

h² + 24² = 34²

Simplifying and solving for h.

h² = 34² - 24²

h² = 676 - 576

h² = 100

h = 10

Therefore,

The height of the building is 10 meters.

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Answer:

First, you have to add 9, 18, and 12. When we add this we get 39. She has 30 dollars, do we can see that she needs $9 more to get all three books.

Step-by-step explanation:

Answer:2/6, 7/21, 15/45

Step-by-step explanation:

So we know that 6,21,45 are all multiples of 3

To find the numerator we have to divide each multiple by 3

so for the first one it would be 6/3 which is 2. So 2 is the numerator and the answer for the first one is 2/6

now we have to do the same method for the next fraction so we do 21/3=7

so the numerator is 7 and the fraction is 7/21

now for the last one we have to do the same method again

45/3=15 so the numerator is 15 and the answer is 15/45

You can use this method for any question like this

so the final answers are 1/3=2/6=7/21=15/45

Hope this helps

[tex] \large{ \tt{❁ \: S \: O \: L \: U \: T \: I \: O \: N \: ❁}}[/tex]

[tex] \large{ \tt{❇ \: FIND \: SP \: WITHOUT \: VAT \: / \: SP\: ❇}}[/tex]

[tex] \large{ \tt{❃ \: SP \: with \: VAT= SP + VAT\% \: of \: SP}}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = SP + 13\% \: of \: SP}}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = SP + \frac{13}{100} \: sp}}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = \frac{100 \: \: SP + 13 \: SP}{100} }}[/tex]

[tex] \large{ \tt{⇢ \: 4068 = \frac{113 \: SP}{100} }}[/tex]

[tex] \large{ \tt{⇢ \: 113 \: SP = 406800}}[/tex]

[tex] \large{ \tt{⇢ \: SP = \frac{406800}{113} }}[/tex]

[tex] \large{ \tt{⇢ \: SP = 3600}}[/tex]

[tex] \large{ \tt{✽ \: NOW , \: FIND \: THE \: MP \:✽ }}[/tex]

[tex] \large {\tt{❃ \: SP = MP - dis\% \: of \: MP}}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = x - 10\% \: of \: x}}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = x - \frac{10}{100} } \: x}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = \frac{100x - 10x}{100} }}[/tex]

[tex] \large{ \tt{⇾ \: 3600 = \frac{90x}{100} }}[/tex]

[tex] \large{ \tt{⇾ \: 90x = 360000}}[/tex]

[tex] \large{ \tt{⇾ \: x = \frac{360000}{90} }}[/tex]

[tex] \large{ \tt{⇾ \: x = Rs \: 4000}}[/tex]

[tex] \large{ \boxed{ \boxed{ \tt{☂ \: OUR \: FINAL \: ANSWER : \boxed {\tt {\: Rs \: 4000}}}}}}[/tex]

Answer: 9ft

One side is given 16ft

The other is 7ft

The 7ft is in the same length of the 16ft line

So 16-7 = 9ft

Must click thanks and mark brainliest

Answer:

(x - 5)(x - 5)

Step-by-step explanation:

[tex] {x}^{2} - 10x + 25 \: is \: the \: expansion \\ of \: {(x - 5)}^{2} \\ {(x - 5)}^{2} = (x - 5)(x - 5)[/tex]

The complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.

A quadratic expression of the form ax² + bx + c is factored by using the mid-term factorization method, which suggests that b should be broken in such two components that their product = ac. After this, we can factorize using the grouping method.

In the question, we are asked to factor the quadratic expression x² - 10x + 25 completely.

Comparing x² - 10x + 25 to ax² + bx + c, we get a = 1, b = -10, and c = 25.

To factor the expression we will use the mid-term factorization method, and try to break b in such two numbers whose product = ac.

Now, ac = 1 * 25 = 25. b = -10, which can be broken as -5, and -5.

Therefore, we can write the given expression as:

x² - 10x + 25

= x² - 5x - 5x + 25, mid-term factorization

= x(x - 5) -5(x - 5), grouping

= (x - 5)(x - 5), grouping.

Therefore, the complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.

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Answer:

[tex]\huge \boxed{729}[/tex]

Step-by-step explanation:

9 raised to 3 is the base 9 with an exponent of 3.

[tex]9^3[/tex]

9 is being multiplied by itself 3 times.

[tex]9^3 =9 \times 9 \times 9 = 729[/tex]

Answer:

all of them

Step-by-step explanation:

Answer:

40600

Step-by-step explanation:

(4 * 10^4) + (6 * 10^2) =

= 4 * 10000 + 6 * 100

= 40000 + 600

= 40600

Answer:

4.06 x 10^4

Step-by-step explanation:

Answer:

180 units

Step-by-step explanation:

In order to solve this, we need to find the length of the missing side of the triangle using the Pythagorean theorem.

a²+b²=c²

a= 7

b=x

c= 25

7²+x²=25²

49+x²=625

Subtract 49 from both sides

x²=576

x=24

The length of the missing side of the triangle is 24, which is also the base of the triangle. We need to find the area of the triangle so we use the formula for the area of a triangle, A=1/2bh.

A= 1/2 (24 x 7)

A=84

Now, we need to find the area of the rectangle.

Formula for area of rectangle: A= bh

A= bh

A= 4 x 24

A= 96

Next, we add the areas of both shapes to get the area of the entire figure.

96+84=180

Area of figure= 180

Answer:

area = 180

Step-by-step explanation:

will make it simple and short

area of a trapezoid = (a + b) h/2

h = sqrt(25² - 7²) = 24

Area = (4 + 11) * 24/2

area = 180

Answer:

The age of Noi is 13.333 Years and the age of Noy is 12.67 years

Step-by-step explanation:

The given  information are;

The sum of the ages of Noi and Noy = 26 years

Four times Noi's age - Two times Noy's age = 28

Let the age of Noi = X and let the age of Noy = Y

We have;

X + Y = 26 years.................(1)

4X - 2Y = 28 years.............(2)

Divide equation (2) by 2 to get;

(4X - 2Y)/2 = (28 years)/2 which gives;

2X - Y = 14 years.................(3)

Add equation (3) to equation (1), to get;

X + Y +  2X - Y = 26 years + 14  years

3X = 40 years

X = 40/3 = 13.333 Years

From equation (1), X + Y = 26 years, therefore;

Y = 26 - X = 26 - 13.33 = 12.67 years

Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.

Answer:

The way to consider this problem is to realize that the

% symbol actually is equal to a number just like [tex]\pi[/tex] is

whereas [tex]\pi[/tex] is equal to 3.1415... , % is equal to .1 (as a decimal ) or 1/100 as

a fraction... thus

10% is actually 10 * 1/100 or 10/100 which is not 10...

as for the size the 1/100 essentially a DIVISION thus it ends up being SMALLER

Step-by-step explanation:

We can not compare a number and a percentage. 10% of something means 1/10th of something and it can be anything for instance.

The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin phrase made its way into English. Later, it was shortened to percent and ended with a period. Later, the period was eliminated, and the two portions were combined to create the current one-word form of a percent.

The best way to approach this issue is to understand the percentage. The % sign actually corresponds to a number. While equals 3.1415, % is equivalent to.1 (as a decimal) or 1/100 as a portion, hence, 10% is actually 10 * 1/100, which is not the same as 10. Regarding size, since 1/100 is essentially a division, it becomes smaller.

Therefore, A number and a percentage cannot be compared. 10% of something is equal to one-tenth of it, and it can be anything, for example.

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Answer:

1.) Neither

2.) Area

3.) Perimeter

4.) Neither

Step-by-step explanation:

Given that the lengths of the rectangle are r and s

The perimeter of the rectangle will be:

Perimeter = 2r + 2s

Perimeter = 2(r+s)

While the area will be:

Area = r × s

Area = rs

For each expression, say whether it gives the perimeter of the rectangle, the area of the

rectangle, or neither.

1. rts = neither

2. r.s = Area of rectangle

3. 2r + 2s = Perimeter of rectangle

4.72 +82 = neither.

Answer:

B. The second choice.

Step-by-step explanation:

A function cannot have two points with the same x-coordinate.

If you graph two different points that have the same x-coordinate, they will both lie on the same vertical line. Therefore, if in a relation, more than one point lie on the same vertical line, then the relation is not a function.

Treat the matrices on the right side of each equation like you would a constant.

Let 2X + Y = A and 3X - 4Y = B.

Then you can eliminate Y by taking the sum

4A + B = 4 (2X + Y) + (3X - 4Y) = 11X

==>   X = (4A + B)/11

Similarly, you can eliminate X by using

-3A + 2B = -3 (2X + Y) + 2 (3X - 4Y) = -11Y

==>   Y = (3A - 2B)/11

It follows that

[tex]X=\dfrac4{11}\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\dfrac1{11}\begin{bmatrix}7&-10\\-7&11\end{bmatrix} \\\\ X=\dfrac1{11}\left(4\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\left(\begin{bmatrix}48&-12\\40&88\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\begin{bmatrix}55&-22\\33&99\end{bmatrix} \\\\ X=\begin{bmatrix}5&-2\\3&9\end{bmatrix}[/tex]

Similarly, you would find

[tex]Y=\begin{bmatrix}2&1\\4&4\end{bmatrix}[/tex]

You can solve the second system in the same fashion. You would end up with

[tex]P=\begin{bmatrix}2&-3\\0&1\end{bmatrix} \text{ and } Q=\begin{bmatrix}1&2\\3&-1\end{bmatrix}[/tex]

Step-by-step explanation:

hence it has been done . check the file .

hope this helped you

any problem then comment it .

Answer:

c

Step-by-step explanation:

i think this is the greatest because if you solve all of the expressions you will find out that this is the greatest.

a.4×-5=-20

b.-5+4=-1

c.-4-(-5)=1

therefore 1 is the greatest so the expression c is the greatest.

I hope this helps

Answer:

The forms are:

Given:

Use point slope form:

Convert it to slope-intercept form:

Convert it to standard form:

Answer:

-8

Step-by-step explanation:

i checked it out on ... and it was negative eight

Answer:

B: -8

Step-by-step explanation:

edg2021

Just plug 8 into the equation.

Answer: 1.18 dollars

Step-by-step explanation:

Given that:

E = Euros

D = US dollars

If the equation showing the relationship between Euros and Dollar

is E = 17/20D

To find the equivalent amount of dollars for 1 euros, substitute E for 1 in the formula and make D the subject of formula

1 = 17/20 D

Cross multiply

17D = 20

D = 20/17

D = 1.18 dollars approximately

Therefore, 1.18 dollars have the same value as 1 euro.

Answer: The ice sheet's thickness decrease every 6 weeks= 1.5 meters

Step-by-step explanation:

GIven: At the beginning of spring, the ice starts to melt. The variable sss models the ice sheet's thickness (in meters) t weeks after the beginning of spring. [tex]s=-0.25t+4[/tex]

At t=0, [tex]s=4[/tex]

So, Thickness of ice sheet at the beginning = 4 meters

Now at t= 6, we get

[tex]s=-0.25(6)+4=-1.5+4=2.5[/tex]

Thickness of ice sheet after 6 weeks = 2.5 meters

Decrease in thickness = 4 meters - 2.5 meters = 1.5 meters

Hence, the ice sheet's thickness decrease every 6 weeks= 1.5 meters

Answer:

1.5

Step-by-step explanation:

Answer:

dicontinuity at (-4.-2)zero at (-2.0)

Step-by-step explanation:

answer c

this shoud be correct

Answer:

14 hours 20 minutes

Step-by-step explanation:

→ Convert 2 hours and 40 minutes into minutes

2 hours + 40 minutes ⇒ 2 hours = 120 minutes + 40 minutes ⇒ 120 + 40 ⇒ 160 minutes

→ Convert 11 hours and 40 minutes into minutes

11 hours + 40 minutes ⇒ 11 hours = 660 minutes + 40 minutes ⇒ 660 + 40 ⇒ 700 minutes

→ Add the total minutes together

700 minutes + 160 minutes = 860 minutes

→ Convert 860 minutes into hours

860 minutes = 14 hours + 20 minutes

Refer the attached image for the answer

HOPE SO IT HELPS YOU

Answer:

523.6 to 1 decimal place

Step-by-step explanation:

→ Utilise the formula for a volume of a sphere

[tex]\frac{4}{3}[/tex]  × π × r³

→ Substitute in the radius

[tex]\frac{4}{3}[/tex]  × π × 5³

→ Simplify

523.6 to 1 decimal place