Paul is looking at two vacation packages while planning a trip to Cancun, Mexico. In the first vacation package, round-trip airfare costs $799, and it costs $139 per night to stay at the resort. In the second vacation package, it costs $587 per night to stay in the resort and $285 for round-trip airfare. Let x represent the number of nights spent at the resort, and let y represent the total cost of the trip. Which system of equations could be used to find how many nights Paul needs to stay at either resort so that both vacation packages have the same cost? A. B. C. D.

Step-by-step explanation:

[tex]\begin{array}{c|cc}12&2\\6&2\\3&3\\1\end{array}\qquad\qquad\begin{array}{c|cc}56&2\\28&2\\14&2\\7&7\\1\end{array}\\\\12=\boxed{2}\cdot\boxed{2}\cdot3\\\\56=\boxed{2}\cdot\boxed{2}\cdot2\cdot7\\\\GCF(12,\ 56)=\boxed{2}\cdot\boxed{2}=4\\\\LCM(12,\ 56)=\boxed{2}\cdot\boxed{2}\cdot3\cdot2\cdot7=168[/tex]

Answer:

-41/36

Step-by-step explanation:

-5/9 + -7/12

x4        x3

-20/36 + -21/36

Negative + Negative = Negative

-41/36

Simplfy - > Can't, it's in the simpliest form.

Step-by-step explanation:

you can convert both inequalities to slope intercept form and then graph it.

So 4x+y>-1 would convert to y>-4x-1

And x+y ≥ 2 would be y≥-x+2

Then graph it

Working with the first one

4x+y > -1

Treat as an equation and find the x and y intercept

4x+y= -1

when x=0

4(0)+y = -1

y= -1

(0,-1)

when y=0

4x+0=-1

4x= -1

divide both sides by 4

x= -1/4 or -0.25

(-0.25, 0)

working with the second one

x+y≥2

same process

when x=0

0+y=2

y=2

(0,2)

when y=0

x+0=2

x=2

(2,0)

Now on your graph you have to plot the points (0, -1) ,( -0.25,0), (0,2) ,(2,0) using an appropriate scale

Answer:

-8 i think

Step-by-step explanation:

The y-intercept of the graph for the function y = (x - 2)(x + 4) is found by setting x to zero, which results in a y-intercept of -8.

The y-intercept on a graph represents the point where the curve or line crosses the y-axis.

To find the y-intercept of the graph of y = (x - 2)(x + 4), you need to determine the value of y when x is zero. By substituting x with 0 in the equation,

we calculate the y-intercept:

Therefore, the y-intercept of the graph is -8.

Answer: z = 3

Step-by-step explanation: To solve this equation for z, we can first combine our like terms on the left side of the equation. Since 12 and 7 both have z after their coefficient, we can subtract 12z - 7z to get 5z.

Now we have 5z - 2 = 13.

To solve from here, we add 2 to the left side of the equation in order to isolate 5z. If we add 2 to the left side, we must also add 2 to the right side. On the left side, the -2 and +2 cancel out. On the right, 13 + 2 simplifies to 15.

Now we have 5z = 15.

Solving from here, we divide both sides of the equation by 5 to get z alone. On the left side, the 5's cancel out and we are simply left with z. On the right side, 15 divided by 5 simplifies to 3 so we have z = 3.

Answer:

$7.56

Step-by-step explanation:

37%=0.37

0.37*12=4.44

12-4.44=7.56

Answer:

$7.56

37% of 12= 4.44

12-4.44

Answer:

About 14.29 minutes

Step-by-step explanation:

Each page has 125 words

There are 4 pages

SO, total number of words:

125 * 4 = 500 words

The rate of typing is 35 wpm (words per minute)

So, to find time it will take to type 500 words is found by dividing the number of words (500) by the rate (35), so we have:

500/35 = 14.2857 minutes

So, it will take about 14.29 minutes to type up the whole documentary

Answer:

- 1 2/3 < 1/4

Step-by-step explanation:

hope this helps!!

The relationship between the numbers -1 2/3 and -1/4 in an inequality is -1 2/3 > -1/4. This is because -1 2/3 is closer to zero than -1/4, meaning in the negative number line, -1 2/3 is greater than -1/4.

To create an inequality that describes the relationship between the given numbers, -1 2/3 and -1/4, first convert them into the same form. Both of these numbers are negative, but -1 2/3 is greater because it is closer to zero.

So the inequality which represents this relationship is -1 2/3 > -1/4.

Let's convert them into improper fractions to make it easier to understand.

So, -1 2/3 becomes -5/3 and -1/4 remains the same as -1/4. Hence our inequality becomes -5/3 > -1/4, which confirms that -1 2/3 is greater than -1/4.

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Answer: number 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

[tex]3-\frac{1}{2}n[/tex]

Step-by-step explanation:

We will use the distributive property shown below to break it down first.

Distributive Property:  [tex]a(b-c)=ab-ac[/tex]

The expression is:

[tex]\frac{1}{2}(n-8)+7-n[/tex]

Let's distribute:

[tex]\frac{1}{2}(n-8)+7-n\\=\frac{1}{2}(n)-\frac{1}{2}(8)+7-n[/tex]

Now, we multiply:

[tex]\frac{1}{2}(n)-\frac{1}{2}(8)+7-n\\=\frac{1}{2}n-4+7-n[/tex]

Now we combine like terms (variables and numbers separately):

[tex]\frac{1}{2}n-4+7-n\\=-4+7-n+\frac{1}{2}n\\=3-\frac{1}{2}n[/tex]

This is the simplified expression.

Answer:

OPTION B: {5, 7, 9}

Step-by-step explanation:

D [tex]$ \cap $[/tex] E is the collection of elements that are present in both D and E.

Given the set D = {5, 6, 7, 8, 9, 10}

and                 E = {1, 3, 5, 7, 9, 11}

So, the elements present in both D and E are: {5, 7, 9}.

Hence, D [tex]$ \cap $[/tex] E = {5, 7, 9}.

OPTION B is the answer.

Answer:

The area of the larger square is 20 [tex]cm^2[/tex]

Step-by-step explanation:

Given:

The area of the smaller square   =  [tex]10 cm^2[/tex]

To Find:

The are of the larger square = ?

Solution:

The diagonal of the smaller square = diameter of the circle = sides of the larger square

The diagonal of the smaller square is

=>[tex]\sqrt{2(10)}[/tex]

=>[tex]\sqrt{20}[/tex]

=>[tex]\sqrt{2\times 2 \times 5}[/tex]

=>[tex]2\sqrt{5}[/tex]

Now this diagonal is equal to the side of the larger square

so the are of the larger square is

=>[tex](2\sqrt{5})^2[/tex]

=>[tex](2\sqrt{5}) \times (2\sqrt{5}) [/tex]

=> 20 [tex]cm^2[/tex]

Answer:

[tex]y=\frac{1}{4}(x+1)^2-9[/tex]

Step-by-step explanation:

Method 1

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^2+k[/tex]

where

a is the leading coefficient

(h,k) is the vertex

we have

(h,k)=(-1,-9)

substitute

[tex]y=a(x+1)^2-9[/tex]

Remember that

one root is (-7,0)

substitute and solve for a

[tex]0=a(-7+1)^2-9[/tex]

[tex]0=a(-6)^2-9[/tex]

[tex]0=36a-9[/tex]

[tex]a=\frac{1}{4}[/tex]

therefore

[tex]y=\frac{1}{4}(x+1)^2-9[/tex]

Method 2

I use the fact that the roots are the same distance from the vertex

the distance from the given root to the vertex is equal to

6 units

so

If one root is x=-7

then the other root is

x=-1+6=5

The general equation of the quadratic equation is equal to

[tex]y=a(x+7)(x-5)[/tex]

we have the vertex (-1,-9)

substitute the value of x and the value of y and solve for a

[tex]-9=a(-1+7)(-1-5)[/tex]

[tex]-9=a(6)(-6)[/tex]

[tex]-9=-36a[/tex]

[tex]a=\frac{1}{4}[/tex]

[tex]y=\frac{1}{4}(x+7)(x-5)[/tex]

so

Expanded the equation, complete the square and rewrite as vertex form

The other parallel side is 44 m

Step-by-step explanation:

Let us revise the formula of the area of a trapezium

[tex]A=\frac{1}{2}(b_{1}+b_{2})h[/tex] , where

∵ The area of a trapezium is shaped field is 480 m²

∴ A = 480 m²

∵ The distance between two parallel sides is 15 m

∴ h = 15 m

∵ One of the parallel side is 20 m

∴ [tex]b_{1}[/tex] = 20 m

We need to find [tex]b_{2}[/tex]

Substitute all these value in the rule of the area below

∵ [tex]A=\frac{1}{2}(b_{1}+b_{2})h[/tex]

∴ [tex]480=\frac{1}{2}(20+b_{2})(15)[/tex]

- Multiply the two sides by 2

∴ [tex]960=(20+b_{2})(15)[/tex]

- Divide both sides by 15

∴ [tex]64=20+b_{2}[/tex]

- Subtract 20 from both sides

∴ [tex]44=b_{2}[/tex]

The other parallel side is 44 m

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Answer:

(-4,2)

Step-by-step explanation:

Answer:

(-4,2)

Step-by-step explanation:

Answer:

91.6

Step-by-step explanation:

7786/85

Answer:

Step-by-step explanation:

a>−64/3

Hope this helps mark me as brainiest pls

The solution of the a is greater than negative 21 and one-third. Then the correct option is A.

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

The inequality equation is given below.

[tex]\dfrac{3}{4} \times a > -16\\[/tex]

On solving the inequality, the value of the a will be

[tex]\rm a > -16 \times \dfrac{4}{3}\\\\a > - \dfrac{64}{3}\\\\a > - 21 \dfrac{1}{3}[/tex]

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Answer: [tex]x=105\°[/tex]

Step-by-step explanation:

You can identify from the given figure that the angle  that measures 70 degrees is formed by two intersecting Chords.

It is important to remembe that, by definition:

[tex]Angle\ Formed\ by\ Two\ Chords =\frac{1}{2}(Sum\ of\ Intercepted\ Arcs)[/tex]

Based on this, you know that:

[tex]70\°=\frac{35\°+x}{2}[/tex]

Having this equation, the final step is to solve for "x" in order to find its value. You get that this is:

[tex](70\°)(2)=35\°+x\\\\140\°=35\°+x\\\\140\°-35\°=x\\\\x=105\°[/tex]

Answer:

15.7 years

Step-by-step explanation:

Use the formula for compound interest. A = P(1 + i)ⁿ

A is the total amount of money. A = 7200

P is the principal, starting money. P = 3000

i is the interest per compounding period in decimal form. Since interest is compounded annually, i = 0.0575

n is the number of compounding periods. n = ?

Substitute the information into the formula and isolate n.

A = P(1 + i)ⁿ

7200 = 3000(1 + 0.0575)ⁿ    Solve inside the brackets

7200 = 3000(1.0575)ⁿ

7200/3000 = 1.0575ⁿ       Divide both sides by 3000

2.4 = 1.0575ⁿ

n = (㏒ ans) / (㏒ base)

n = (㏒ (2.4)) / (㏒ (1.0575))

n = 15.659.....     Exact answer

n ≈ 15.7       Rounded to the nearest tenth of a year

Therefore the person must leave the money in the bank for 15.7 years until it reaches 7200 dollars.

Answer:

After evaluating the expression, the result is 2/3

Step-by-step explanation:

Let's evaluate the expression given to us:

-2 + 12 - 2³/ 2⁰ * 3

-2 + 12 - 8/ 1 * 3 ⇒ 2⁰ = 1 and 2³ = 8

-10 + 12/ 3

2/3

After evaluating the expression, the result is 2/3

The correct answer is:

Jessica can wax approximately 34,533,185 square meters per hour at her constant rate of waxing the floor.

To find out how many square meters Jessica can wax per hour, we first need to convert the square miles to square meters, then divide by the time taken.

1. Convert square miles to square meters:

  Since 1 mile = 1609.34 meters, to convert square miles to square meters, we square this conversion factor:

[tex]\[ 1 \text{ mile}^2 = (1609.34)^2 \text{ meters}^2 \] \[ 1 \text{ mile}^2 = 2,589,988.36 \text{ meters}^2 \][/tex]

  So, 20 square miles would be:

[tex]\[ 20 \text{ miles}^2 \times 2,589,988.36 \text{ meters}^2/\text{mile}^2 = 51,799,767.2 \text{ meters}^2 \][/tex]

2. Calculate the rate per hour:

  Jessica waxes 20 square miles in [tex]\( \frac{3}{5} \)[/tex] of an hour.

  So, her rate per hour is:

 [tex]\[ \frac{20 \times 2,589,988.36}{\frac{3}{5}} \text{ meters}^2/\text{hour} \][/tex]

  To simplify the calculation, we'll first find the reciprocal of [tex]\( \frac{3}{5} \): \[ \frac{1}{\frac{3}{5}} = \frac{5}{3} \][/tex]

  Now, we multiply the reciprocal by 20 square miles:

 [tex]\[ 20 \times 2,589,988.36 \times \frac{5}{3} \text{ meters}^2/\text{hour} \] \[ \text{meters}^2/\text{hour} = 34,533,184.8 \][/tex]

So, Jessica can wax approximately [tex]\( 34,533,184.8 \)[/tex] square meters per hour at her constant rate.

Answer:

slope is undefined

Step-by-step explanation:

Using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

If x₂ - x₁ = 0

Since division by zero is undefined then the slope of the line is undefined

This applies to a vertical line parallel to the y- axis

Answer: The total price of a bench is 1.008x.

Step-by-step explanation:

Since we have given that

Let the cost price be 'x'.

Mark up % = 120%

So, Mark up value would be

[tex]\dfrac{120}{100}x\\\\=1.20x[/tex]

Discount % = 20%

Amount of discount is given by

[tex]\dfrac{20}{100}\times 1.2x\\\\=0.2\times 1.2x\\\\=0.24x[/tex]

So, it becomes,

Amount after discount is given by

[tex]1.2x-0.24x\\\\=0.96x[/tex]

Sales tax = 5%

Amount of sales tax would be

[tex]\dfrac{100+5}{100}\times 0.96x\\\\=\dfrac{105}{100}\times 0.96x\\\\=1.05\times 0.96x\\\\=1.008x[/tex]

Hence, the total price of a bench is 1.008x.

Answer:

30 or 52

I'm not sure. Sorry. I tried my best. Don't let the "Helping Hand" fool you. You see you said 6 forks and twice as many spoons which equals 12+6. Then "as" knives. I got confused there. I think there it's either 12 or twice as many knives as spoons. In other words, 12×2.

6 + (6 × 2) + (6 × 2) = 30

6 + (6 ×2) + (12 × 2) = 52

Answer:

Step-by-step explanation:

Let us suppose r be the total number of meals eaten in a restaurant

Let us suppose c be the total number of meals eaten in a car

Let us suppose h be the total number of meals eaten in a home

Substituting Equation [B] into [A],

[tex]r + c + h = 171.....[A][/tex]

[tex]r + r + 11 = 171[/tex]

[tex]2r + 11 = 171[/tex]

[tex]2r = 160[/tex]

[tex]r = 80[/tex]

Putting [tex]r = 80[/tex] in [tex]r = h + 20.....[C][/tex]

[tex]80 = h + 20[/tex]

[tex]h = 60[/tex]

Putting [tex]r = 80[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171.....[A][/tex]

[tex]80 + c + 60 = 171[/tex]

[tex]c = 171 - 60 - 80[/tex]

[tex]c = 31[/tex]

Therefore,

Verification:

[tex]r + c + h = 171[/tex]

Putting [tex]r = 80[/tex], [tex]c = 31[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171[/tex]

[tex]80 + 31 + 60 = 171[/tex]

[tex]171 = 171[/tex]

Keywords: number, equation

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m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Solution:

Given that Harita must memorize 90 measures of music for her cello solo at a concert

To find: equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Let "m" be the number of measures Harita still needs to  memorize

Let "d" be the number of days of practice since she began learning the piece

Given that She plans on memorizing 18 new measures for  every 3 days of practice

Rate per day is given as:

[tex]\frac{18}{3} = 6[/tex]

Therefore she memorises 6 per day

Therefore, the equation that relates 'm' to 'd' is:

m = total measures of music she must memorise - (number of measures she memorises per day x d)

m = 90 - 6(d)

m = 90 - 6d

Thus the required equation is found

Answer:

m = 90 - 6d is the equation to determine m, the number of measures Harita still needs to  memorize, as a function of d, the number of days of practice since she began learning the piece

Step-by-step explanation:

Answer:

[tex]h=\frac{SA}{2\pi r}-r[/tex]

Step-by-step explanation:

The surface area of a cylinder is equal to

[tex]SA=2\pi r^{2} +2\pi rh[/tex]

Solve for h

That means ----> isolate the variable h

subtract  2πr² both sides

[tex](SA-2\pi r^{2})=2\pi rh[/tex]

Divide by 2πr both sides

[tex]\frac{SA-2\pi r^{2}}{2\pi r}=h[/tex]

Rewrite

[tex]h=\frac{SA-2\pi r^{2}}{2\pi r}[/tex]

Simplify

[tex]h=\frac{SA}{2\pi r}-r[/tex]

Answer:

The length of the rectangular field is (3 a - 3) meters

Step-by-step explanation:

Given as :

The Perimeter of rectangular field = p = ( 10 a - 6 ) meters

The width of the rectangular field = w = 2 a meters

Let The length of the rectangular field = L meters

Now From The perimeter formula

Perimeter of rectangular field = 2 × Length + 2 × width

Or, p =  2 × L +  2 × w

Or,  ( 10 a - 6 ) meters =  2 × L meters + 2 × 2 a meters

Or, 10 a - 6 =  2 × L + 4 a

Or, 10 a - 4 a - 6 = 2 L

Or, 6 a - 6 = 2 L

∴  L = [tex]\dfrac{6 a - 6}{2}[/tex]

i,e L = 3 a - 3

So, The length of the rectangular field = L = (3 a - 3) meters

Hence,The length of the rectangular field is (3 a - 3) meters  Answer

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ [tex]x_{1}[/tex] = -12 , [tex]x_{2}[/tex] = 0

∴ [tex]y_{1}[/tex] = -2 , [tex]y_{2}[/tex] = -4

- Use the formula of the slope above to find the slope of the given line

∵ [tex]m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}[/tex]

∴ The slope of the given line is [tex]\frac{-1}{6}[/tex]

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = [tex]\frac{-1}{6}[/tex]

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

  and b is the y-intercept (y when x = 0)

∵ m = [tex]\frac{-1}{6}[/tex] and b = 6

∴ The equation of the parallel line is y = [tex]\frac{-1}{6}[/tex] x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = [tex]\frac{-1}{6}[/tex] (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

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The point on the line that passes through (0, 6) and is parallel to the given line is (2, 8).

To find a point on a line parallel to the given line, we can use the slope of the given line, which is equal to the slope of the parallel line.

The slope of the given line can be calculated using the coordinates (-12, -2) and (0, -4):

Slope (m) = (change in y) / (change in x) = (-4 - (-2)) / (0 - (-12)) = (-2) / (12) = -1/6.

Now that we know the slope of the parallel line is -1/6, we can use the point-slope form of a linear equation to find the equation of the parallel line:

y - y1 = m(x - x1),

where (x1, y1) is the point (0, 6) and m is the slope (-1/6). Plugging in these values:

y - 6 = (-1/6)(x - 0),

y - 6 = (-1/6)x,

y = (-1/6)x + 6.

Now, we can choose any x-value to find the corresponding y-value. If we plug in x = 2 into the equation, we get:

y = (-1/6)(2) + 6 = -1/3 + 6 = 8.

So, the point (2, 8) is on the line that passes through (0, 6) and is parallel to the given line.

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