Select all of the situations that represent a linear relationship between x and y.
the total area, in square meters, y, of a square garden if the side length is x meters
the height, y, of a 6-foot tree that grows 0.2 feet per month for x months
the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days
the total miles, y, traveled by a car going 62 miles per hour in x hours

ANSWER

6

EXPLANATION

The given equation is:

[tex] \frac{1}{3} (12x - 24) = 16[/tex]

Multiply through by 3.

12x-24=16×3

12x-24=48

Group similar terms:

12x=48+24

12x=72

Divide both sides by 12

x=6

The answer is 6.hope this helps. please add brainlist

Answer:

E, F and G have determinants.

Step-by-step explanation:

Only square matrices have determinants so D which is not square does not have a determinant.

Determinant of F (2*3) - (1 * -1)

= 6 +1

= 7.

The determinant of G is obtained in the same way.,

THe determinant of E is worked out as follows

I 0  -1   1 |        0 *  | -1  -3 | - ( -1) *  | 3 -3| + 1 * | 3 -1|

I 3  -1  -3 |  =           |  0  5 !            |2  5|         |2 0|

I 2   0 5  |

= 0 *  -5 + 1 * 21 + 1 * 2

= 23.

Answer:

Yes.

Step-by-step explanation:

Yes they are because that is the definition of congruency.

Answer:

113.1

Step-by-step explanation:

Volume of sphere = [tex]\frac{4}{3}[/tex] × π × r²

Volume of sphere =  [tex]\frac{4}{3}[/tex] × π × 3²

Volume of sphere =  [tex]\frac{4}{3}[/tex] × π × 9

Volume of sphere =  [tex]\frac{4}{3}[/tex] × 9 π

Volume of sphere = 113.1

Answer:

[tex]V=113.1cm^3[/tex]

Step-by-step explanation:

The formula to calculate the volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where r is the radius of the sphere.

In this case we do not know the radius of the sphere, but we know the diameter.

By definition the diameter of a sphere is equal to twice the radius. This is:

[tex]d = 2r[/tex]

[tex]r = \frac{d}{2}[/tex]

In this case d=6 cm

So

[tex]r = \frac{6}{2}[/tex]

[tex]r = 3\ cm[/tex]

Finally

[tex]V=\frac{4}{3}\pi 3^3[/tex]

[tex]V=36\pi\ cm^3[/tex]

[tex]V=113.1cm^3[/tex]

Answer: 12 pies.

Step-by-step explanation: Divide 72(pieces) by 6 = 12

72÷6=12.

Hope it's the answer you are looking for.✌

Answer:

x = -2 or x=6

Step-by-step explanation:

Given

f(x) = 3Ix-2I + 6

As we know that

f(x) = 18

Putting both equal

3Ix-2I+6 = 18

Two cases are possible

Case 1: Negative Modulus

3* -(x-2) + 6 = 18

3(-x+2)+6 = 18

-3x+6+6 = 18

-3x +12 = 18

-3x = 18 - 12

-3x = 6

x = 6/-3

x = -2

Case 2: Positive Modulus

3(x-2)+6 = 18

3x-6+6 = 18

3x = 18

x = 18/3

x = 6

So for x= -2 or x=6 the value of function will be 18..

3.542 is the answer; you just need to move the decimal 2 places to the left.

Answer:

c(h) = 40*h + 50

Step-by-step explanation:

Let h be the variable that represents the number of hours

As the cable operator charges $40.00 for an hour so for h hours, the expression will be 40*h

And  

Lastly, he has to charge $50.00 must as service charge,

As the number of hours is variable here so the function will be in terms of hours.

So the resulting function will be:

c(h) = 40*h + 50

Answer:

40 meters

Step-by-step explanation:

add 28 and 12

Answer: its 300

aka D

Step-by-step explanation:

I did the quiz

let's notice something, angles α and β are both in the I Quadrant, and on the first quadrant the x-coordinate/cosine and y-coordinate/sine are both positive.

[tex]\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\alpha)=\cfrac{\stackrel{opposite}{15}}{\stackrel{hypotenuse}{17}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{17^2-15^2}=a\implies \pm\sqrt{64}=a\implies \pm 8 = a\implies \stackrel{I~Quadrant}{\boxed{+8=a}} \\\\[-0.35em] ~\dotfill\\\\ cos(\beta)=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{5^2-3^2}=b\implies \pm\sqrt{16}=b\implies \pm 4=b\implies \stackrel{\textit{I~Quadrant}}{\boxed{+4=b}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf cos(\alpha - \beta)=\stackrel{cos(\alpha)}{\left( \cfrac{8}{17} \right)}\stackrel{cos(\beta)}{\left( \cfrac{3}{5} \right)}+\stackrel{sin(\alpha)}{\left( \cfrac{15}{17} \right)}\stackrel{sin(\beta)}{\left( \cfrac{4}{5} \right)}\implies cos(\alpha - \beta)=\cfrac{24}{85}+\cfrac{60}{85} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\alpha - \beta)=\cfrac{84}{85}~\hfill[/tex]

Answer:

(x - 6)(x+4)

Step-by-step explanation:

Final answer:

The quadratic expression x^2 - 2x - 24 can be factored into two binomials as (x - 6)(x + 4).

Explanation:

To factor the quadratic expression x^2 - 2x - 24 completely, we start by looking for two numbers that multiply to give -24 (the constant term) and add to give -2 (the coefficient of x). These two numbers are -6 and +4 because (-6) * (+4) = -24 and (-6) + (+4) = -2.

We can now rewrite the quadratic expression as:

(x - 6)(x + 4) = 0

Therefore, the factored form of the expression x^2 - 2x - 24 is (x - 6)(x + 4).

Answer:

what ratio man??

Step-by-step explanation:

Answer: A

Step-by-step explanation:

'A' can't be reduced anymore because 17 is a prime number.

Prime number: a number with only two factors- 1 & itself

Answer:

$7.50

Step-by-step explanation:

Since the price of the picnic cooler 7.95 with 6% sales tax, we can write:

X*1.06 = 7.95

Dividing both sides by 1.06,

X= 7.50

So Anton paid $7.50 alone without tax

Answer: Cost of cooler alone = $7.47

Step-by-step explanation:

Anton's bill including tax = $7.95

6% of his bill accounts for sales tax.

Sales tax = 6/100 × 7.95 ≈ $0.48

So cost of cooler alone =  Total bill - tax

= 7.95 − 0.48

= $7.47

There is another way of doing this problem as well, but which ever one is easier for you could it.

Anton's bill including tax = $7.95, out of this 6% is sales tax. This implies 94% (100 − 6) of total bill accounts for cooler alone.

Cost of cooler alone:

=94/100 ×7.95

= 0.94 ×7.95

= $7.47

* Hopefully this helps:) Mark me the brainliest:)!!!

~234483279c20~

Answer:

x = 21

Step-by-step explanation:

the only like-terms are on the right-hand-side, since the left-hand-side has only 1 term anyway.

[tex]\bf \cfrac{5}{2}s=\cfrac{3}{2}s+s\implies \cfrac{5}{2}s=\cfrac{3}{2}s+\cfrac{s}{1}\implies \cfrac{5}{2}s=\stackrel{\textit{using the LCD of 2}}{\cfrac{(1)3s+(2)s}{2}} \\\\\\ \cfrac{5}{2}s=\cfrac{3s+2s}{2}\implies \cfrac{5}{2}s = \cfrac{5}{2}s[/tex]

Hello there! The value of y is -5/4.

So, basically look at it like an ordered pair, (x, y). When we have (5, y), we have a value of x and are looking for a value of y. To do this, plug the value for x (5) into the equation and solve for y.

5x+4y-20=0

5(5)+4y-20=0

Now that you have the value for x, solve for y.

5(5)+4y-20=0 - Start by multiplying out the parenthesis.

25 + 4y - 20 = 0 - Next, combine like terms.

25 - 20 + 4y = 0

5 + 4y = 0 - Now, subtract 5 from both sides.

4y = -5 - Lastly, divide both sides by 4.

y = -5/4.

This is your final answer. I hope this helps and have a great day! :)

To find the value of y, substitute the given coordinates (5, y) into the equation 5x + 4y - 20 = 0. Simplify the equation and solve for y to get y = -1.25.

To find the value of y, we can substitute the given coordinates (5, y) into the equation.

According to the equation 5x + 4y - 20 = 0, when x is 5, we have:

5(5) + 4y - 20 = 0.

Simplifying this equation gives us:

25 + 4y - 20 = 0.

Combining like terms, we get:

4y + 5 = 0.

Next, we can isolate the y-term by subtracting 5 from both sides of the equation:

4y = -5.

Finally, we can solve for y by dividing both sides of the equation by 4:

y = -5/4, or y = -1.25.

Answer:

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=3x+1;\ g(x)=x^2-6\\\\(f+g)(x)=(3x+1)+(x^2-6)=x^2+3x+1-6=x^2+3x-5[/tex]

the answer is 8 hoped this helped !!!

Answer:

8

Step-by-step explanation:

This is because the slope of a line in an equation is m. In the equation given m=8, so that makes the slope 8.

a=80 because it is equal to the 80 by the corner R

ANSWER

The correct answer is B

EXPLANATION

The given expression is:

[tex] \sqrt[3]{ {x}^{5}y } [/tex]

We split the radical sign to obtain;

[tex] \sqrt[3]{ {x}^{5} } \times \sqrt[3]{ y } [/tex]

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

We rewrite each radical expression in exponential form to obtain:

[tex] {x}^{ \frac{5}{3} } {y}^{ \frac{1}{3} } [/tex]

The correct answer is B.

Answer:

See below

Step-by-step explanation:

Step 1.

P = $400

r = 0.04

t = 10 years

n = 12  ( as there are 12 months in a year).

Step 2.

A(10) = 400(1 + 0.04/12)^12^10

= 400 * 1.00333333^120

= $596.33 to the nearest hundredth (answer).

Answer and Explanation:

Given : The value of $400 invested at 4% interest compounded monthly for 10 years.    

To find : The value of each of the following for this problem ?

Solution :

The interest formula is [tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]

Step 1 -

P is the amount invested, P=$400

r is the interest rate, r=4%=0.04

t is the time , t=10 years

n is the number of compounding periods per year, n=12

Step 2 - To find A(10),

Substitute all the values in the formula,

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A(10)=400(1+\frac{0.04}{12})^{12\times 10}[/tex]

[tex]A(10)=400(1+0.0033)^{120}[/tex]

[tex]A(10)=400(1.0033)^{120}[/tex]

[tex]A(10)=400(1.490)[/tex]

[tex]A(10)=596.33[/tex]

Therefore, The amount after 10 year is $596.33.

Answer: [tex]\angle G=23\°[/tex]

Step-by-step explanation:

Remember that an inscribed angle is defined as an angle formed by two chords and whose vertex lies on the circle.

By definition, the measure of an inscribed angle is:

[tex]Inscribed\ Angle=\frac{Intercepted\ Arc}{2}[/tex]

You know that:

[tex]Intercepted\ Arc=AD = (6x -80)\\\\Inscribed\ Angle=\angle G=(x + 2)[/tex]

Then, you need to substitute values and solve for "x":

[tex](x+2)=\frac{(6x -80)}{2}\\\\2(x+2)=6x-80\\\\2x+4=6x-80\\\\4+80=6x-2x\\\\84=4x\\\\x=\frac{84}{4}\\\\x=21[/tex]

Substituting the value of "x" into [tex]\angle G=(x + 2)\°[/tex] you get:

 [tex]\angle G=(21 + 2)\°=23\°[/tex]

Answer:

The measure of <G =  23°

Step-by-step explanation:

From the figure we can write,

The measure of <G is half the  the measure of arc AD

To find the value of x

We have  AD = (6x - 80)° and <G = (x + 2)°

6x - 80 = 2(x + 2)

6x - 80 = 2x + 4

6x - 2x = 4 + 80

4x = 84

x = 84/4 = 21

To find the measure of <g

m<G = x + 2

 = 21 + 2 = 23°

Therefore the measure of <G =  23°

Simplify the expression.

Exact Form:

−37/4

Decimal Form:

−9.25

Mixed Number Form:

−9 1/4

[tex]\text{Hey there!}[/tex]

[tex]-5\frac{3}{4}-3\frac{1}{2}=?[/tex]

[tex]\text{-5}\frac{3}{4}=\text{-5}\times\text{4+3}\rightarrow\text{-5}\times4=-20\rightarrow\text{-20 + 3 = -23}[/tex]

[tex]\text{The denominator stays the same:}-5\frac{3}{4}=-\frac{23}{4}[/tex]

[tex]\text{3}\frac{1}{2}=3\times2+1\rightarrow3\times2=6+1\rightarrow6+1=7[/tex]

[tex]\text{3}\frac{1}{2}=\frac{7}{2}[/tex]

[tex]\frac{-23}{7}-\frac{7}{2}=?[/tex]

[tex]\text{Solve the NEWER question above}\uparrow\text{and you will see your answer}[/tex]

[tex]\boxed{\boxed{\bf{Answer:Improper\ fraction:\frac{-37}{4}\ or\ Mixed\ number:-9\frac{1}{4}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

1,206

Step-by-step explanation:

Since we'll have to deal with cubic inches (with the ball volume), we should also calculate the volume of the car in cubic inches.

We are told the car is a rectangular prism measuring 10ft x 5 ft x 3 ft.

So, in inches (12 inches/foot), we have: 120 in x 60 in x 36 in = 259,200 cu inches.

The ball is a sphere with a radius of 3 inches.

Real volume of the ball: V = (4/3) π r³

V = (4/3) π 3³ = 36 π = 113.1 cu inches

But of course, balls don't fit perfectly one next to another, like cubes, so we have to take into account the loss... the question tells us to use a factor of 190%.

So, the packing volume of a ball is 190% its real volume:

PV = 190% * 113.1 = 214.9 cu inches

Now, how many times does that fit inside the car?

259,200 / 214.9 = 1,206.14

Let's round it to 1,206, which is a possible answer.

Below is an image of the table cloth with its measurements

The formula for Area is:

A = length x height

The length of this shape is 8 feet

The height of this shape is 4 feet

so...

A = 8 x 4

A = 32

Hope this helped!

Answer:

The original number is 4 1 5 3 OR 4 5 8 3

Step-by-step explanation:

* Lets find a way to solve this problem

- The end of the 4-digit number is 3

∴ The number is # # # 3

- The number decrease by 738 if the 3 becomes the first number

∴ The new number is 3 # # #

- Make it as a subtraction problem

∵ # # # 3 - 3 # # # = 0 7 3 8

- Lets subtract

∵ 3 - # = 8

∵ 8 > 3 we must borrow 1 from the number before 3

∴ 13 - 8 = 5

∴ # # # 3 - 3 # # 5 = 0 7 3 8

- Put the 5 in the first number, we can not pot it as a first number

 bwcause when we subtract it from 3 the answer will be 2 but we

 need answer zero

∴ Lets put it before the 3

∴ # # 5 3 - 3 # # 5 = 0 7 3 8

∵ we borrowed 1 from the 5 before

∴ 4 - # = 3

∴ # = 4 - 3 = 1

∴ # # 5 3 - 3 # 1 5 = 0 7 3 8

- Now we must use the 1 in the first number we can not put it as a

 number because it is smaller than 3, we must put it in the 2nd

 missing place

∴ # 1 5 3 - 3 # 1 5 = 0 7 3 8

∵ 1 - # = 7

∵ 1 < 7 so we must borrow 1 from the number before it

∴ 11 - # = 7

∴ # = 11 - 7 = 4

∴ # 1 5 3 - 3 4 1 5 = 0 7 3 8

- We must use the 4 in the first number and we have only one

 missing place (the first place)

∴ 4 1 5 3 - 3 4 1 5 = 0 7 3 8

∴ The original number is 4 1 5 3

* You can find another answer if you put the 5 in the 2nd place in the

 first number the answer will be 4 5 8 3 try to do it

If [tex]m\widehat{BY}=40^\circ[/tex], then the central angle [tex]\angle BOY[/tex] has the same measure, and by the inscribed angle theorem we have

[tex]m\angle BAY=\dfrac12m\angle BOY=20^\circ[/tex]

It's impossible to know what the measure of angle YAC is from this information alone, but assuming AC is tangent to the circle, then angles BAY and YAC are complementary, so that [tex]m\angle YAC=70^\circ[/tex].

The line AC is the tangent of the line, and the measure of the angle YAC is 70 degrees

The measure of the arc is given as:

Arc BY = 40 degrees

The measure of angle BAY is calculated using:

BAY = 0.5 * BY

This gives

BAY = 0.5 * 40

BAY = 20

The angle at a tangent is 90 degrees.

This means that:

BAY + YAC = 90

Substitute 20 for BAY

20 + YAC = 90

Subtract 20 from both sides

YAC = 70

Hence, the measure of the angle YAC is 70 degrees

Read more about tangent lines at:

https://brainly.com/question/6617153

#SPJ2

Answer:

The centre is at (-12, 9) and the radius = 5 units.

Step-by-step explanation:

x^2 + y^2 + 24x - 18y + 200 = 0

x^2 + 24x + y^2 - 18y = -200

Completing the square on the x and y terms:

(x + 12)^2 - 144 + (y - 9)^2 - 81 = -200

(x + 12)^2 + (y - 9)^2 = -200 + 144 + 81

(x + 12)^2 + (y - 9)^2 = 25

So the centre is at (-12, 9) and the radius = the square root of 25 = 5.

Answer:

centre = (- 12, 9), radius = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² + 24x - 18y + 200 = 0

Collect the terms in x/ y together and subtract 200 from both sides

x² + 24x + y² - 18y = - 200

Using the method of completing the square

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(12)x + 144 + y² + 2(- 9)y + 81 = - 200 + 144 + 81

(x + 12)² + (y - 9)² = 25 ← in standard form

with centre (- 12, 9) and r = [tex]\sqrt{25}[/tex] = 5

Answer:

[tex]-16t^2 + 1,000>300[/tex]

[tex]t<6.61\ s[/tex]

Step-by-step explanation:

We know that the distance of the object while falling is given by the equation:

[tex]d = -16t^2 + 1,000[/tex]

To find the time interval in which the object is at a height greater than 300 ft, we must do

[tex]d> 300[/tex]

So

[tex]-16t^2 + 1,000>300[/tex]

[tex]-16t^2>-700[/tex]

[tex]16t^2<700[/tex]

[tex]t^2<\frac{700}{16}[/tex]

[tex]t<\sqrt{\frac{700}{16}}[/tex]

[tex]t<6.61\ s[/tex]

The interval is

t ∈ (0, 6.61)

And the inequality used  is: [tex]-16t^2 + 1,000>300[/tex]