Write an equation with slope of 2/3 and y intercept of -3

Answer:

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

The maximum area is 450 feet²

Step-by-step explanation:

The garden is fencing for three sides only, That means the length of the fencing is equal to the sum of the length of the three sides

Assume that garden is y feet long and x feet wide and the fencing will cover on side of y feet and two sides of x feet

∵ The sum of the length of the 3 sides = y + x + x

∴ The sum of the length of the 3 sides = y + 2x

- The length of the fencing is equal to the sum of the sides

∵ The fencing is 60 feet

- Equate y + 2x by 60

∴ y + 2x = 60

- Find y in terms of x by subtracting 2x from both sides

∴ y = 60 - 2x

To find the dimensions which make the maximum area, find the area of the garden, then substitute y by x, and differentiate it with respect to x, then equate the differentiation by 0 to find the value of x, and substitute this value in the equation of y to find y and in the equation of the area to find the maximum area

∵ The formula of the area of a rectangle is A = l × w

∵ l = y and w = x

∴ A = x y

- Substitute the value of y above in A

∵ A = x(60 - 2x)

- Multiply bracket by x

∴ A = 60x - 2x²

Now differentiate x with respect to x

∵ A' = 60(1) - 2(2)x

∴ A' = 60 - 4x

- Equate A' by 0 to find x

∴ 0 = 60 - 4x

- Add 4x to both sides

∴ 4x = 60

- Divide both sides by 4

∴ x = 15

- Substitute the value of x in the equation of y to find it

∵ y = 60 - 2(15)

∴ y = 30

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

To find the maximum area substitute x by 15 in the equation of the area

∵ A = 60(15) - 2(15)²

∴ A = 900 - 450

∴ A = 450

The maximum area is 450 feet²

A maximum area for the rectangular garden is achieved when the rectangle is a square, having side lengths of 15 and 30 feet. This yields an area of 450 square feet.

The question is a classic problem of optimization in Mathematics, where we want to maximize the area of the garden given a constraint, which in this case, is the total length of fence available. We consider the garden to have sides of lengths x and y, where y is the side against the building, and we don't need fencing there. Because we're working with a total of 60 feet of fencing, the length of the other three sides of the rectangle (two sides of length x, one side of length y) give us the equation 2x + y = 60.

We want to maximize the area of the rectangle, which is given by A = x*y. We can substitute y from the above equation into this to give A = x*(60-2x) = 60x - 2x^2. This is a quadratic function and it attains its maximum when x = -b/2a. Here, a = -2, b = -60, so x is 15 feet. The maximum area occurs when x and y are equal, which is when the rectangle is a square.

So, the corresponding value of y = 60 - 2*15 = 30 feet. Therefore, we have a maximum area  of 15*30 = 450 square feet.

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Answer:

Both are corrects but bear different meaning

Step-by-step explanation:

While naming arcs is to name arcs based on their angle.

While finding arc measures is a measure of the angle of the arcs.

system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is  [tex]x+8y=68[/tex] and [tex]3x+4y=64[/tex]   .

Step-by-step explanation:

Here we have , A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. We need to find Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y . Let's find out:

Let the price in dollars of each large candle, x, and each small candle, y .So

A customer at a store paid $64 for 3 large candles and 4 small candles

Equation is  :

⇒ [tex]3x+4y=64[/tex]  .....(1)

At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles.

Equation is  :

⇒ [tex]x+8y=68[/tex]  .......(2)

3(2)-(1) i.e.

⇒ [tex]3(x+8y)-(3x+4y)=68(3)-64[/tex]

⇒ [tex]20y=140[/tex]

⇒ [tex]y=7[/tex]

So , [tex]x+8y=68[/tex]  

⇒  [tex]x+8(7)=68[/tex]

⇒  [tex]x=12[/tex]

Therefore , system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is  [tex]x+8y=68[/tex] and [tex]3x+4y=64[/tex]   .

The system of equations that can be used to find the price in dollars of each large candle, x, and each small candle, y are;

3x + 4y = 64

x + 8y = 68

$64 was paid for 3 large candles and 4 small candles. If large candle cost x and small candle cost y, then;

3x + 4y = 64

Now, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles.

Thus;

x + 8y = 64 + 4

x + 8y = 68

Thus, the system of equations that can be used to find the price in dollars of each large candle, x, and each small candle, y is;

3x + 4y = 64

x + 8y = 68

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Answer:

that is the solution to the question

Final Answer:

31 degree.

Explanation:

The sum of the interior angles of any triangle in a Euclidean plane is always 180°.
Given one angle of the isosceles triangle measures 118°, we can find the possible measures of the other two angles using the following steps:
Step 1: Calculate the sum of the two remaining angles.
Since the total sum of the angles in a triangle is 180° and we already have one angle measuring 118°, we can subtract the known angle from 180° to find the sum of the remaining two angles:
180° - 118° = 62°
Step 2: Divide the sum between the two equal angles.
Because the triangle is isosceles, the remaining two angles are equal in measure. We found their sum (62°), so to determine each individual angle's measurement, we divide that sum by 2:
62° ÷ 2 = 31°
Thus, both of the remaining angles in the isosceles triangle must measure 31° each.
In conclusion, an isosceles triangle with one angle measuring 118° will have the other two angles both measuring 31°.

Answer:

Area of the square base: 144 in²

Area of each triangular face: 66 in²

Amount of paint needed: 408 in²

Step-by-step explanation:

We basically want to find the surface area of this square pyramid.

First, find the areas of the 4 triangular sides. The area of a triangle is denoted by: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.

Here, the base coincides with the side length of the square, so b = 12. The height is 11, so h = 11. Plug these in:

[tex]A=\frac{1}{2} bh[/tex]

[tex]A=\frac{1}{2}[/tex] * 12 * 11 = 66 inches squared

Each triangular face is thus 66 inches squared.

Since there are 4 triangles, multiply 66 by 4: 66 * 4 = 264 inches squared

Now, find the area of the square base. The area of a square is: A = s * s, where s is the side length. Here, the side length is 12, so s = 12. Plug this into the equation:

A = s * s

A = 12 * 12 = 144

So, the square base is 144 inches squared.

Finally, add 144 to 264 to get the total area Gabriel needs to paint:

144 + 264 = 408 inches squared

Answer:

The area of the square base is 144 in²

The area of each triangular face is 66 in²

Gabriel will need 408 in² of paint.

Step-by-step explanation:

The area of the square base is:

12² = 144 in²

The area of each triangular face:

½(12×11) = 66 in²

Gabriel will need:

4(66) + 144 = 408 in²

Answer:

V= 9202.77 in³

Step-by-step explanation:

Answer:

C: <6 and <8

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

1250/ 54 = 23.14814814

Answer: 28 (exponent 2) = 56

Step-by-step explanation:

28 and exponent two (sry my keyboard doesnt have the special characters) = 56, since 28 x 2 = 56.

Answer:

Step-by-step explanation:

If you had a solid cylinder, in order to find the amount of material that makes up that solid cylinder, you would find the volume using the radius of 4 (half of the diameter 8).  BUT we want to know the volume of the solid with the radius of 4 minus the solid that has a radius of 2.5 (half of the diameter 5).

[tex]V_o-V_i[/tex]  That's volume outer - volume inner.  To find the outer volume:

[tex]V=\pi r^2h[/tex] so

[tex]V_o=\pi (4^2)(300)[/tex] and

[tex]V_o=4800\pi[/tex]  and do the same for the inner volume:

[tex]V_i=\pi (2.5^2)(300)[/tex] and

[tex]V_i=1875\pi[/tex]

Subtract the inner from the outer:

[tex]4800\pi-1875\pi=2925\pi cm^3[/tex]

If you need your answer in decimal form, then the volume is

9189.16 cm³

Answer:

equal to: =

Step-by-step explanation:

1 gallon has 4 quarts and half a gallon has two quarts, all together there is 6 quarts in 1 1/2 gallons

1 1/2 gallons is equal to 6 quarts.

1 1/2 gallons is equivalent to 6 quarts. Since the two quantities are equal, 1 1/2 gallons is not greater than 6 quarts. This can be shown by converting the gallons to quarts.

1 gallon is equal to 4 quarts, so 1 1/2 gallons is equal to 6 quarts (1.5 x 4 = 6). Therefore, 1 1/2 gallons is not greater than 6 quarts.

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Answer:

C) Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.

Step-by-step explanation:

When naming congruent shapes, the orders of the congruent vertex letters need to be the same.

Since these are isosceles triangles, the base angles are the same:

m∠R = m∠T = m∠A = m∠C

Therefore the congruency statement can be written two different ways.

ΔABC ≅ ΔRST

ΔABC ≅ ΔTSR

Both statements could be correct.

Choosing between B) and C):

To move ΔABC to where ΔRST or ΔTSR is, you could either:

i) Translate 6 units to the left, and translate 3 units down

ii) Reflect across the y-axis, and translate 3 units down

It can be the result of two translations or a reflection and a translation.

In the result, the base side RT is on the bottom of the shape, like side AC. If you rotated the shape, the base side would not be on the bottom. Therefore B) is incorrect.

Answer:

c

Step-by-step explanation:

Answer:

(-2,-3)

Step-by-step explanation:

The first step is to find the equations of the two lines. For the first line, the slope is 3/2, while the y intercept is 0. This gives it an equation of y=3/2x. For the second line, it has a slope of -3/2, and a y intercept of -6. This gives it an equation of y=-3/2x-6. Setting these two equations equal to each other, you get

3/2x=-3/2x-6

3x=-6

x=-2

y=-3

(-2,-3) Hope this helps!

Answer:

25(x)

Step-by-step explanation:

if you cave 4 quarters, this will be 25(40) which is 100 cents.

Answer:

A) base = 6 units

B) height = 4 units

C) Area = 24 square units

Step-by-step explanation:

Base on the gragh given,

The base = |-5| + |1| = 6 unit

The height = |2| + |-2| = 4 unit

The area = base × height

The area = 6 × 4 = 24 square units.

Answer:

The parallelogram has vertices at (–2, 2), (4, 2), (1, –2), and (–5, –2).

Complete each sentence.

The base of the parallelogram is

✔ 6

units.

The height of the parallelogram is

✔ 4

units.

The area of the parallelogram is

✔ 24

square units.

Step-by-step explanation:

Answer: 1 ounce = 0.0295735 liters rounded it is 0.03  liters

Formula: Divide the volume value by 33.814

1÷33.814 =0.0295735

0.02957354941 rounded to the nearest hundredths is 0.03  

Answer:

[tex]1 litre =33.814 \: \: us \: \: fluid \: \: \: ounces[/tex]

Step-by-step explanation:

So to find the amount of liters you have to multiply amount by 33.814 ounces

And to find the amount of ounces you have to divide the amount by 33.814.

hope this helps.

thanks..

Answer: the efficiency of the first car is 25 miles per gallon.

the efficiency of the second car is 30 miles per gallon.

Step-by-step explanation:

Let x represent the efficiency of the first car.

Let y represent the efficiency of the second car.

Distance = car efficiency × number of gallons.

The first car consume 25 gallons of gas and the second consumed 15 gallons of gas. The two cars Drove a combined total of 1075 miles. It means that

25x + 15y = 1075- - - - - - - - - - -1

The sum of the fuel efficiencies was 55 miles per gallon. It means that

x + y = 55

Substituting x = 55 - y into equation 1, it becomes

25(55 - y) + 15y = 1075

1375 - 25y + 15y = 1075

- 25y + 15y = 1075 - 1375

- 10y = - 300

y = - 300/-10

y = 30

x = 55 - y = 55 - 30

x = 25

Answer: 23400 workers

Step-by-step explanation:

In a factory, 10,750 workers come in the first shift while 12,650 workers in the second shift . To get the total number of workers that come in the factory, we add the number of those workers that come in the first shift and those that come in the second shift together. This will be:

Total number of workers in the factory= 10750 + 12650 = 23400

The total number of workers that come to the factory is 23400.

The divisors of 240 which are multiples of tens are 10, 20, 30, and 60.

To identify divisors of 240 that are multiples of tens, we must first understand what a divisor is. A divisor is a number that divides another number evenly. For example, in the case of 240, some notable divisors are 1, 2, 3, 4, 5, and so on. However, we are specifically looking for divisors that are themselves multiples of 10. These are numbers that end in zero and could be multiplied by some integer to get 240. In this instance, four such divisors are 10, 20, 30, and 60. For each of these examples, one can multiply these by a whole number to produce 240. For instance, 10*24 is 240, so is 20*12, 30*8, and 60*4.

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Answer:

Reflection: your object or shape is either side by side (y axis) or above each other (x axis)

Rotation: Spinning your object or shape around a point

Translation: Shifting all the points of your object or figure

Dilation: The shape or object is either shrinking or expanding

Step-by-step explanation:

Answer:

V=2x4x5

Step-by-step explanation:

Volume of a solid can be obtained by multiplying lengths of all the three dimensions i.e. Length, width and height.

[tex]V = l \times b \times h \\ \therefore V = 2 \times 4 \times 5[/tex]

The Volume of Solid is, V=2x4x5.

'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

We know few formulas for Volume as

Volume of cuboid = l × w × h

Volume of cube = a³

Volume of Cylinder = πr²h

Volume of Prism= B × h

Volume of sphere = (4⁄3)πr³

Volume of Cone = (1⁄3)πr²h

From all the options given we have to find the relation with multiplication.

So, the volume of this solid is V=2x4x5 which is same as Volume of cuboid = l × w × h

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FOLLOW ME FOR CLEARING YOUR NEXT DOUBT

The length of the hypotenuse QS of the triangle ΔRPQ will be 16 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The length of the right-angle triangle will be 8√3 units and 8 units.

Then the length of the hypotenuse QS will be given as,

H² = (8√3)² + (8)²

H² = 192 + 64

H² = 256

H² = 16²

H = 16 units

The length of the hypotenuse QS of the triangle ΔRPQ will be 16 units.

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Answer:

Hence the Distance from each other chord to center  is 84 inches.

Step-by-step explanation:

Given:

Diameter =170 inches

2 chords with each length =26 inches.

To Find:

Distance of each chord from the circle.

Solution:

Consider a circle with center as O ,

And OA as Radius

(Refer the attachment)

So as chord be BC and DE respectively with each of 26 length

They have both same length so they should located at same distance from center but as mirror images of each other opposite side of the diameter as shown in fig.

Hence we can calculate for one chord as follows:

Radius =diameter/2=170/2=85

r=85 inches.

Let distance from center t o chord be 'x'

Now draw perpendicular to chord BC with F as midpoint for chord and join endpoints  of chord to the center which forms triangle OFC as right angled triangle,

By using pythagorus Theorem

[tex]OC^2=FC^2+OF^2[/tex]

Here OC=85 inches , FC=26/2=13 inches.

So

[tex]85^2=13^2+OF^2[/tex]

[tex]OF^2=85^2 -13^2[/tex]

[tex]OF^2=7225-169[/tex]

[tex]OF^2=[/tex]7056

[tex]OF=84[/tex] inches

Hence the Distance from each other chord to center  is 84 inches.

The dimensions of the rectangle would be (6-2) x (7-0) = 4 x 7

That makes the area (4)(7) = 28.

That makes the perimeter (7+4)(2) = 22

That makes the diagonal sqrt((7^2)+(4^2)) = sqrt(49+16) = sqrt(65)

Answer:

[tex]n\geq 23[/tex]

Step-by-step explanation:

-For a known standard deviation, the sample size for a desired margin of error is calculated using the formula:

[tex]n\geq (\frac{z\sigma}{ME})^2[/tex]

Where:

We substitute our given values to calculate the sample size:

[tex]n\geq (\frac{z\sigma}{ME})^2\\\\\geq (\frac{1.96\times 12}{5})^2\\\\\geq 22.13\approx23[/tex]

Hence, the smallest desired sample size is 23

Hernando needs to take a sample size of at least 23 members.

To determine the smallest sample size required for Hernando to achieve a 95% confidence interval with a margin of error no more than 5 years, we can use the formula:

n = (Z * σ / E)²

where:

Plugging in the values, we get:

n = (1.96 * 12 / 5)²
n = (23.52 / 5)²
n = (4.704)²
n ≈ 22.14

Since the sample size must be a whole number, we round up to the nearest integer, making the smallest required sample size n = 23.

Answer:

Blue Terrace: 0.92 and Paradiso Grill 1.1 and Which restaurant has the most variation in customer ratings = Paradiso grill

Step-by-step explanation:

Answer:

.92 and 1.1

Step-by-step explanation:

Answer:

[tex]X \sim Binom(n=10, p=0.96)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

For this case the expected value is given by:

[tex] E(X) = np = 10 *0.96 = 9.6[/tex]

Part b

For this case the standard deviation is given by:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{10 *0.96*(1-0.96)}= 0.620[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of workers in the sample who are union members", on this case we now that:

[tex]X \sim Binom(n=10, p=0.96)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

For this case the expected value is given by:

[tex] E(X) = np = 10 *0.96 = 9.6[/tex]

Part b

For this case the standard deviation is given by:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{10 *0.96*(1-0.96)}= 0.620[/tex]

A. The mean number of union members in a sample of 10 workers is 9.6. B. The standard deviation is approximately 0.620.

A) Mean (Expectation) Calculation

The number of union members in the sample can be modeled using a binomial distribution since each worker either is or isn't a union member.

For a binomial distribution, the expectation (mean) is given by:

Mean (μ) = n * p

where n is the number of trials (in this case, the number of workers in the sample), and p is the probability of success in a single trial (the probability that a worker is a union member).

Here, n = 10 and p = 0.96, so:

Mean (μ) = 10 * 0.96 = 9.6

B) Standard Deviation Calculation

For the same binomial distribution, the standard deviation (σ) is given by:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(10 * 0.96 * (1 - 0.96))

= √(10 * 0.96 * 0.04)

= √0.384

= 0.620

Thus, the standard deviation of the distribution is approximately 0.620

Answer:

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

Step-by-step explanation:

Assume x be the width of the rectangle.

The length of the rectangle is to be 6 cm more than twice the width.

The length of the rectangle is= (2x+6) cm

Then the diagonal of the rectangle is [tex]\sqrt{length^2+width^2}[/tex]

                                                             [tex]=\sqrt{(2x+6)^2+x^2}[/tex]

                                                            [tex]=\sqrt{4x^2+24x+36+x^2}[/tex]

                                                             [tex]=\sqrt{5x^2+24x+36}[/tex] cm

According to the problem,

[tex]\sqrt{5x^2+24x+36}=15[/tex]

Squaring both sides

[tex]\Rightarrow{5x^2+24x+36}=15^2[/tex]

[tex]\Rightarrow{5x^2+24x+36}=225[/tex]

[tex]\Rightarrow{5x^2+24x+36-225=0[/tex]

[tex]\Rightarrow{5x^2+24x-189=0[/tex]

⇒5x²+45x-21x-189=0

⇒5x(x+9)-21(x+9)=0

⇒(x+9)(5x-21)=0

⇒x+9=0  or,   5x-21=0

[tex]\Rightarrow x=-9, \frac{21}5[/tex]

⇒x= -9, 4.2

Since the width of a rectangle can not negative.

So, x=4.2 cm

The width of rectangle is = 4.2 cm

The length of the rectangle is =(2×4.2+6)

                                                  =14.4 cm

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

To find the dimensions of a rectangle with a given diagonal length and a relationship between its length and width, we can set up a system of equations and use the Pythagorean theorem.

To solve this problem, we can set up a system of equations using the given information. Let's assume the width of the rectangle is x. The length of the rectangle is then 2x + 6. We can use the Pythagorean theorem to set up an equation using the diagonal and the sides of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

x^2 + (2x + 6)^2 = 15^2

Simplifying and solving this equation will give us the value of x, which is the width of the rectangle. We can then calculate the length of the rectangle by substituting the value of x into the expression 2x + 6.

Let's solve the equation:

x^2 + (2x + 6)^2 = 15^2

Expanding the equation and simplifying:

x^2 + 4x^2 + 24x + 36 = 225

Combining like terms:

5x^2 + 24x + 36 = 225

Moving 225 to the other side of the equation:

5x^2 + 24x + 36 - 225 = 0

Simplifying further:

5x^2 + 24x - 189 = 0

Now we can solve this quadratic equation for x. We can factor it or use the quadratic formula.

By factoring, we find that x = -9 or x = 7.8. Since we are dealing with dimensions, we can ignore the negative value and take x = 7.8 centimeters as the width of the rectangle.

The length would then be 2(7.8) + 6 = 22.6 centimeters. So, the dimensions of the rectangle should be a width of 7.8 centimeters and a length of 22.6 centimeters.

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