Gem and her three friends are going on a holiday.
There is a buy 2 get one free offer on plane tickets.
Tickets cost £200 each.
If Gem and her friends are each expected to pay an equal amount towards their tickets, how much does each person pay?

Answer:

  a. $461.67

  b. $12771.73

Step-by-step explanation:

You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.

The formula for the monthly payment is ...

  A = P(r/12)/(1 -(1 +r/12)^-n)

where P is the amount borrowed at interest rate r compounded monthly for n months.

Here, the down payment of $4000 reduces the loan amount to ...

  $12500 -4000 = 8500

So, the monthly payment is ...

  A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67

Matteo needs to pay $461.67 each month.

The total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:

  total = $4000 +19×461.67 = $12771.73

Matteo will end up paying $12771.73 for his car.

Answer: 9x - 4

Step-by-step explanation:

We know that a number must be decreased by four. Let's break it up a little.

Nine times some number. We don't know what nine will be multiplied by, so we will just write a placeholder number: x. This number will be multiplied by nine. So it will turn into 9x.

We must decrease (subtract) from this by four. Subtracting 9x by four can be written as 9x - 4.

Answer:

It will take 9 years

Step-by-step explanation:

use formula A=P(1+ r/n)^nt

37,500= 25,475(1+.046/1)^1*x

37,500/25,475=1.046^x

1.47203= 1.046^x

try out different numbers for x and use whole number since it asks for the nearest year

1.046^8 = 1.43302 and 1.046^9 = 1.4989

so we know its inbetween

8 and 9 to figure out one is the closest whole number try raising it to the power of 8.5 and if it passes 1.47203 then its 9, if it doesnt then its 8

1.046^8.5 = 1.46561

1.46561< 1.47203

since 1.046561 is lower than 1.47203 its safe to assume that the year is between 8.5-8.99 thus we can round up to 9

Answer:Add answer+5 pts. is there a picture to go with it. Log in to add comment.

Step-by-step explanation:

A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.

In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.

Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).

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Answer:

it’s D dotted line with shading below

Step-by-step explanation:

i got it on my quiz

Answer:

y= -2x + (-6)

or

y= -2x - 6

both work !

Step-by-step explanation:

The statement that is a good definition is D. Parallel lines are lines that do not intersect.

A type of quadrilateral with all sides being equal and all angles being 90 degrees is a square.

Lines that do not cross each other but have a constant perpendicular distance are known as parallel lines. Right angles and skew lines are perpendicular to one another but not parallel. Therefore, a square is a type of rectangle in which all four sides are parallel to one another.

Therefore, based on the information, the correct option is D

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Answer: 64 1/2

Step-by-step explanation:

Answer:

2³

Step-by-step explanation:

Square root of 64 = 8

exponential notation = 2×2×2 = 2³

The 58 m/s initial velocity of the arrow with height, y = 58•t - 0.83•t², gives;

(1) 55.925 m/s

(2) 56.257 m/s

(3) 56.3317 m/s

(4) 56.33917 m/s

(b) 56.34 m/s

Initial velocity of the arrow = 58 m/s

Height of the arrow is; y = 58•t - 0.83•t²

The above kinematic equation can be analyzed as follows;

(1) The height at t = 1 is found as follows;

y = 58 × 1 - 0.83 × 1² = 57.17

Height at t = 1.5 s. is y = 58×1.5 - 0.83×1.5² = 85.1325

Which gives;

Average velocity = (85.1325-57.17)/(1.5-1) = 55.925

The average velocity in the interval [1, 1.5] is therefore;

(2) [1, 1.1]

Height at t = 1.1 s. is y = 58×1.1 - 0.83×1.1² = 62.7957

Which gives;

Average velocity = (62.7957-57.17)/(1.1-1) = 56.257

(3) [1, 1.01]

Height at t = 1.01 s. is y = 58×1.01 - 0.83×1.01² = 57.733317

Which gives;

Average velocity = (57.733317-57.17)/(1.01-1) = 56.3317

The average velocity is 56.33 m/s

(4) [1, 1.001]

Height at t = 1.01 s. is y = 58×1.001 - 0.83×1.001² = 57.22633917

Which gives;

Average velocity = (57.22633917-57.17)/(1.001-1) = 56.33917

(b) The equation for the instantaneous velocity is found as follows;

v = dy/dt = 58 - 2×0.83•t

After 1 second, we have;

t = 1

v = 58 - 2×0.83 × 1 = 56.34

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Answer:

\(in \: this \: shape \: you \: have \: two \: pieces \: one \: square \: ad \: half \: of \: circle \\ area \: of \: circle = 12 \times 12 = 144 \\ area \: of \: hafl \: of \: circle = 12 \times 12 \times 0.25 \times 3.14 = 113.04 \\ whole \: area = 144 + 113.04 = 257.04\)

Answer: E. 200.5 ft

so first you’d find the area of the square which is 12 x 12 = 144 (area = length x width)

next, find the radius of the semi circle which is 12 divided by 2 (because we used the measurements from the square and the diameter is 12 and radius is half of diameter)

pretend your solving for a full circle and then divide it by 2 to get the answer for the semi circle since a semi circle is half of a circle (formula for circle A = pi r^2)

area of circle = 113.04 divided by 2 to get semi circle = 56.5

then add both areas together

56.52 + 144 = 200.5

Answer:

7mins

Step-by-step explanation:

Answer:

It will take her 7.5 minutes.

Step-by-step explanation:

600 divided by 80 = 7.5

+add unit

Answer:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Answer:

24000

Step-by-step explanation:

instead of 20000 you've got to round the no before it then you'll know your answer as 24000

Answer:

\(x+y = 80\\325x+50y = 6, 750\)

Step-by-step explanation:

Le x represents the set of new tires

Let y be the set of used tires

If a tire shop counted 80 invoices at the end of the month, then the equal that represents the total amount of invoices counted at the end of the month is:

\(x+y = 80 ............ 1\)

If they charge $325 for a set of new tires, the total amount charged for new tires will be:

\(325 \times x \\325x\)

If they charge $50 for a set of used tires, the total amount charged for used tires will be:

\(50 \times y\\50y\)

If the total dollar amount of the invoices was $6,750, then the expression that models the amount generated on tickets will be:

\(325x+50y = 6,750 .............. 2\)

Hence the system of equations represents the situation is:

\(x+y = 80\\325x+50y = 6, 750\)

Answer:

x + y = 80

325x = -50y + 6,750

Step-by-step explanation:

Answer:

$47.48

Step-by-step explanation:

Let x = the amount owed Sept.

x + x - 2.23 = 292.43  Combine like terms

2x -2.23 = 292.43  Add 2.23 to both sides

2x - 2.23 + 2.23 = 292.43 + 2.23

2x = 294.66  Divide both sides by 2

\(\frac{2x}{2}\) = \(\frac{294.66}{2}\)

x = 147.33 this is the bill for September

Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.

Total:

147.33 + 145.10 = 292.43

292.43 ÷ 3 = 97.48  This is what each will owe rounded to the nearest penny.

One way to describe the associative property of the equation is as follows: LHS = RHS

This is further explained below.

Generally, We would consider each side of the equation respectively

Considering the LHS

= 70+2+0.3(-30)+(-9)+(0.1)

=72+0.3(-30)+(-9)+(0.1)

=72.3(-30)+(-9)+(0.1)

=33.2

RHS

70+(-30)+2+(-9)+0.3+(-0.1)

=40+2+(-9)+0.3+(-0.1)

=42(-9)+0.3+(-0.1)

=33.2

In conclusion, We can say the equation is associative property as

LHS =RHS

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A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

We need to find the ratio between the two capacities.

Given that there are \(10^9\) bytes in a gigabyte and\(10^6\) bytes in a megabyte, we can calculate the ratio as follows:

Ratio = (1 GB) / (1 MB)

= \((10^9 bytes) / (10^6 bytes)\)

= \(10^(9 - 6)\)

=\(10^3\)

= 1000

Therefore, A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

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For the first equation, the line integral is equal to 8π since the line integral is being calculated over the top half of a circle. For the second equation, the line integral is equal to -8π since the line integral is being calculated over the part of the paraboloid that is inside the cylinder and has a downwards orientation.

For the first equation, the line integral can be calculated by parametrizing the given equation. Letting x = 2 and y = 2rcosθ and z = 2rsinθ, the line integral can be written as:

∫sc2rcosθdθ + 4r2cos2θr2sinθdθ + 4r2cosθr2sinθdθ

By integrating, the result is 8π.

For the second equation, the line integral can be calculated by parametrizing the given equation. Letting x = 2cosθ, y = 2sinθ, and z = 9-2cosθ-2sinθ, the line integral can be written as:

∫S(2sinθî+2cosθſ+(-2sinθ-2cosθ)ł)nas

By integrating, the result is -8π.

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Answer: 48 feet squared is the answer

Step-by-step explanation: All you do is take the length which is 8 and multiply it by the width which is 6, and the answer is 48.

I hope it helped comment if you have questions. :)

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Let A be a matrix, v and λ be vectors. Therefore, Av = λv, where v is an eigenvector of A with eigenvalue λ, and if there is another non-zero vector w such that Aw = μw, then w is an eigenvector of A with eigenvalue μ. Therefore, v is an eigenvector of A with eigenvalue λ, and w is an eigenvector of A with eigenvalue μ.

Allow a to be a matrix, and v and λ to be vectors. Consequently, av = λv, wherein v is a non-zero vector and λ is a scalar. This means that v is an eigenvector of a with eigenvalue λ.

Further, if there may be every other non-0 vector w such that aw = μw, then w is an eigenvector of a with eigenvalue μ. The eigenvectors and eigenvalues of a matrix are vital in lots of packages, including fixing systems of linear equations, studying dynamical systems, and studying facts using strategies along with main thing evaluation.

By computing the eigenvectors and eigenvalues of a matrix, we will benefit perception of its shape and conduct, and use these records to solve problems and make predictions.

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An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer:

Slope = 1/5

Step-by-step explanation:

Given equation,

→ -x + 5y = 10

The slope-intercept form,

→ y = mx + b

→ slope = m

Now the slope-intercept form is,

→ -x + 5y = 10

→ 5y = x + 10

→ y = (x + 10)/5

→ [ y = (1/5)x + 2 ]

Then the required slope will be,

→ y = (1/5)x + 2

→ Slope = m = 1/5

Hence, the required slope is 1/5.

Answer:

\(\textsf{Slope}=\dfrac{1}{5}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Given equation:

\(-x+5y=10\)

To find the slope of the given equation, use algebraic operations to isolate y.

Add x to both sides of the equation:

\(\implies -x+5y+x=10+x\)

\(\implies 5y=x+10\)

Divide both sides of the equation by 5:

\(\implies \dfrac{5y}{5}=\dfrac{x+10}{5}\)

\(\implies y=\dfrac{1}{5}x+\dfrac{10}{5}\)

\(\implies y=\dfrac{1}{5}x+2\)

The coefficient of x is the slope of the equation.

Therefore, the slope of the given equation is ¹/₅.

\(\frac{7}{8} (-32-48x) + 36 = \frac{2}{3} (-33x-18) -10x\)

\(\frac{7}{8} (-32)+\frac{7}{8} (-48)+36=\frac{2}{3} (-33x)+\frac{2}{3} (-18)-10x\)

\(-28-42+36=-22x-12-10x\)

\(22x+10x=28+42-36-12\)

\(32x=22\)

\(x=\frac{22}{32} =\frac{11}{16} =0,6875\)

Answer: x = 0.6875

Ok done. Thank to me :>

Answer:

x = 2

Step-by-step explanation:

7/8 (-32-48x) + 36 = 2/3 (-33x-18) - 10x

Multiply,

7(-32-48x)/8 + 36 = 2(-33x-18)/3 -10x

Simpliy,

-336(3x+2) + 864 = -48(11x+6) - 240x

Expand,

-1008x + 192 = -768x - 288

Simplify,

-1008x = -768x -480

Simplify,

-240x = -480

Simplify,

x = -480/-240

Answer,

x = 2

Answer: D

Step-by-step explanation: 3 goes in to 57, 19 times and 19 goes into 57, 3 times. No other components other than 1 and 59

Answer:

D

Step-by-step explanation:

T4L 2021

Answer: Bill weighs 230 pounds and he needs to carry boxes that weigh 75 pounds each. Use the equation 75b+230&lt; =1805 to find the greatest number of boxes Bill can carry in the elevator in one trip.

Step-by-step explanation:

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

12

Step-by-step explanation:

if this helped, please mark me as brainliest thank you!

12,

The multiples of 12 are 12,24,36,48,60,72

6,

The multiples of 6 are 6,12,18,24,30,36

After checking the numbers, the least multiple shared by the denominators is 12.

LCD = 12.

Answer:

A.  (x - 80)² = -320(y = 20)

B.  Focus:  (80, -60)

     Directrix:  y = 100

     Axis of symmetry:  x = 80

Step-by-step explanation:

If the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:

Standard form of a parabola with a vertical axis of symmetry:

\(\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute one of the x-intercepts and the vertex into the formula and solve for p:

\(\implies (0-80)^2=4p(0-20)\)

\(\implies (-80)^2=4p(-20)\)

\(\implies 6400=-80p\)

\(\implies p=-80\)

Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:

\(\implies (x-80)^2=4(-80)(y-20)\)

\(\implies (x-80)^2=-320(y-20)\)

Given:

\(\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}\)

\(\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}\)

\(\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}\)