When the length of a rectangle with a width of 1/6 foot was increased by 2/3 foot, the area of the rectangle became 11/72 square feet. Find the original length of the rectangle. Explain your reasoning.

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Step-by-step explanation:

8+4=12

12×5=60

60÷-10=-6

-6-2=-8

the correct answer is A. -8

The weight of 20 buckets is 141 Kg.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

weight of 1 bucket of gravel = 7.05

weight of 20 buckets = 7.05 x 20

                                  = 141 Kg

Hence, the weight of 20 buckets is 141 Kg.

Question

One bucket of gravel has a mass of 7.05 kg. what is the mass of 20 buckets of gravel in kilograms?

Answer:

1: This is a 8-sided polygon, so it is a octagon.

2: No, this is not a regular polygon.

Step-by-step explanation:

1: Since the polygon has 8 sides, it is an octagon.

2:

This is not a regular polygon.

Regular polygons MUST be equilateral and equiangular.

This polygon is neither, so it is not a regular polygon.

Answer:

Step-by-step explanation:

y = 2*3^x

x = 1

y = ?

y = 2*3^1

y =2 * 3

y = 6

The answer is the first graph.

Answer:

Graph A is the correct graph for the transformations shown in the function g(x)

Step-by-step explanation:

Within the function [tex]g(x)=\sqrt[3]{x+2} -4[/tex]

We can see two transformations occur from the parent function. The first is a slide along the x-axis and the second is a slide along the y-axis

Under the radicand we see that it is x+2. This means that the function has been shifted 2 units left from the parent function

As there is a -4 outside of the radicand, it would mean that the function has been shifted 4 units down as well.

This means that we are looking for a function centered around the point (-2,-4)

The graph of ∛(x) is shifted backwards by 2 units along the x - axis and then is shifted 4 units in the downward direction along the y - axis.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -

y = 4x⁴ + 3x³ + 2x² + 6x + 7

We have the function -

{∛(x)}  and {∛(x + 2) - 4}

We can write the functions as -

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

and

[tex](x + 2)^{\frac{1}{3} } - 4[/tex]

The graph of ∛(x) is shifted backwards by 2 units along the x - axis. Then it is shifted 4 units in the downward direction.

Therefore, the graph of ∛(x) is shifted backwards by 2 units along the x - axis and then is shifted 4 units in the downward direction along the y - axis.

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Answer:

C

118 - 4 (-12)= 166

118 + 48 = 166

166 = 166

The answer is:

The center of the circle is the point (-9,-2) and the circle has a radius of 6 units.

To solve the problem, we need to use the given equation which is in the general form, and then, use it transform it to the standard form in order to find the center of the circle and its radius.

So,

We are given the circle:

[tex]x^{2}+y^{2}+18x+4y+49=0[/tex]

We know that a circle can be written in the following form:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

Where,

h is the x-coordinate of the center of the circle

k is the y-coordinate of the center of the circle

r is the radius of the circle.

So, to find the center and the radius, we need to perform the following steps:

- Moving the constant to the other side of the equation:

[tex]x^{2}+y^{2}+18x+4y=-49[/tex]

- Grouping the terms (x and y):

[tex]x^{2}+18x+y^{2}+4y=-49[/tex]

- Completing squares for both variables, we have:

We need to sum to each side of the equation the following term:

[tex](\frac{b}{2})^{2}[/tex]

Where, b, for this case, will the coefficients for both terms that have linear variables (x and y)

So, the variable "x", we have:

[tex]x^{2} +18x[/tex]

Where,

[tex]b=18[/tex]

Then,

[tex](\frac{18}{2})^{2}=(9)^{2}=81[/tex]

So, we need to add the number 81 to each side of the circle equation.

Now, for the variable "y", we have:

[tex]y^{2} +4y[/tex]

Where,

[tex]b=4[/tex]

[tex](\frac{4}{2})^{2}=(2)^{2}=4[/tex]

So, we need to add the number 4 to each side of the circle equation.

Therefore, we have:

[tex](x^{2}+18x+81)+(y^{2}+4y+4)=-49+81+4[/tex]

Then, factoring, we have that the expression will be:

[tex](x+9)^{2}+(y+2)^{2}=36[/tex]

- Writing the standard form of the circle:

Now,  from the simplified expression (after factoring), we can write the circle in the standard form:

[tex](x+9)^{2}+(y+2)^{2}=36[/tex]

Is also equal to:

[tex](x-(-9))^{2}+(y-(-2))^{2}=36[/tex]

Where,

[tex]h=-9\\k=-2\\r=\sqrt{36}=6[/tex]

Hence, the center of the circle is the point (-9,-2) and the circle has a radius of 6 units.

Have a nice day!

Answer:

see explanation

Step-by-step explanation:

P - G

= 8[tex]w^{4}[/tex] - 3w²z² + [tex]z^{4}[/tex] - ( - 3[tex]w^{4}[/tex] + 2w²z² + 5[tex]z^{4}[/tex] )

= 8[tex]w^{4}[/tex] + 2w²z² + [tex]z^{4}[/tex] + 3[tex]w^{4}[/tex] - 2w²z² - 5[tex]z^{4}[/tex]

Collect like terms

= (8[tex]w^{4}[/tex] + 3[tex]w^{4}[/tex] ) + (- 3w²z² - 2w²z² ) + ([tex]z^{4}[/tex] - 5[tex]z^{4}[/tex] )

= 11[tex]w^{4}[/tex] - 5w²z² - 4[tex]z^{4}[/tex]

Answer:

these are the answers -

i took the test theses were the answers -

A1 = more than two 1s

A2 = 0.4286

hope this helped !

Answer:

0.148

Step-by-step explanation:

Given that

probability that a candy will include a coupon for second candy bar = 0.20

Each candy having a coupon is independent of the other also there ae ony two outcomes.

Hence X no of candies which attract a coupon for second candy is binomial

with n = 7 and p = 0.20

Probability that  if she buys 7 candy bars, more than 2 will include a coupon.​

=P(X>2)

=P(x=2)+P(X=3)+P(x=4)+P(x=4)+P(X=5)+P(x=6)+P(x=7)

=0.148

Answer:

400° F = 204.4° C

Step-by-step explanation:

We are given a temperature 400 degree in Fahrenheit and we are to convert in into another unit that is Centigrade (also known as Celsius).

We know that 0 degree Centigrade is equal to 32 Fahrenheit so we will use the following formula for conversion of units:

(32°F − 32) × 5/9 = 0°C

(400°F − 32) × 5/9 = 204.4° C

ANSWER

[tex]y = - \frac{8}{x} [/tex]

EXPLANATION

An inverse variation equation is of the form:

[tex]y = \frac{k}{x} [/tex]

We plug in the point (-1,8).

[tex] 8= \frac{k}{ - 1} [/tex]

This implies that k=-8

Therefore the inverse variation equation is :

[tex]y = - \frac{8}{x} [/tex]

Final answer:

The set of points {(-1,8),(4,-2),(-2,4)} represents an inverse variation with the equation xy = -8, as the product of x and y is consistently -8 for all given points.

Explanation:

An inverse variation can be defined by an equation of the form xy = k, where k is a nonzero constant. Given the set of points {(-1,8),(4,-2),(-2,4)}, we can find the constant k by multiplying the x-coordinate with the y-coordinate for each point, as follows:

(-1)(8) = -8

(4)(-2) = -8

(-2)(4) = -8

Since the product of x and y is consistent and equal to -8 across all points, we can confirm that k = -8 and thus the equation representing this relation is xy = -8.

Answer:

Tip Total: $ 6

Tip Each Person: $ 6

Total (Bill + Tip): $ 46

Answer:

$6

total cost: $45.51

Step-by-step explanation:

to find 15% of the dinner bill. we multiply 39.51 by the decimal form of 15%, which is 0.15

39.51 x 0.15 ≈ 5.926

you can estimate this by rounding up to a $6 tip, or to include cents, you can round to $5.93

to find the total cost with the estimated amount we can add:

39.51 + 6= $45.51 is the total cost

The answer is choice B.

The denominator always goes outside the radical and the numerator is always inside the radical.

B. 7 radical a^5

Answer:

10d - 3x

Step-by-step explanation:

Distribute the 4: 12d - 8x

Distribute the -1: -2d + 5x

Add like terms: 10d - 3x

Answer:

36 meters, A

Step-by-step explanation:

I assume that P is the perimeter

So, all you have to do is count the sides and add them up

10+16+10=36 meters

Answer:

Density of the board = M/V [tex]= 650 kg m^{-3} [/tex]

Step-by-step explanation:

A rectangular prism has six faces which are all rectangular. It has a cross-sectional area with an additional length which makes it a six-sided solid object.

Mass of the board = 146.25 kg

height = 0.75 m

width = 0.2 m

length = 1.5 m

Volume of the rectangular prism = height * width * length

= 0.75*0.2*1.5

=0.225 meters

Density of the board = mass/volume

= 146.25/0.225

[tex]= 650 kg m^{-3} \\[/tex]

Answer:

Step-by-step explanation:

I think you are just asking for the decimal answers.

3/20 = 0.15

9/50 = 0.18

38/200 = 0.19

Answer:

y=-1, x=-3

Step-by-step explanation:

First isolate x:

x+5y-5y=-8-5y

x=-8-5y

Then substitute (-8-5y) for x:

-6(-8-5y)+8y=10

Distribute and solve for y:

48+30y+8y=10

38y-48=10-48

38y=-38

y=-1

Use y to solve for x:

x+5(-1)=-8

x-5=-8

x-5+5=-8+5

x=-3

Answer:

Step-by-step explanation:

Look at the picture.

ΔABC and ΔDBE are similar.Therefore the corresponding sides are in proportion:

[tex]\dfrac{DE}{AC}=\dfrac{DB}{AB}[/tex]

We have

[tex]DE=x,\ AC=36,\ DB=y,\ AB=y+y=2y[/tex]

Substitute:

[tex]\dfrac{x}{36}=\dfrac{y}{2y}[/tex]             cancel y

[tex]\dfrac{x}{36}=\dfrac{1}{2}[/tex]           cross multiply

[tex]2x=36[/tex]             divide both sides by 2

[tex]x=18[/tex]

The measure of G is 28 because it is an isosceles triangle

The measure of G depends on the given information or the type of angle it represents.

The measure of G refers to the numerical value or the angle of G. To determine the measure of angle G, we need more information, such as the type of angle or any given angles in the problem. However, if we assume that G is a generic angle, we can measure it using a protractor or rely on the properties of different types of angles.

For example, if G is a right angle, it measures 90 degrees. If G is a straight angle, it measures 180 degrees. But without specific details, it is challenging to determine the exact measure of G.

Remember to always provide more information in order to find the measure of an angle accurately.

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Answer:

see explanation

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

8x + x² - 2y = 64 - y²

Collect the x/y terms, leaving 64 on the right side, that is

x² + 8x + y² - 2y = 64

To obtain standard form use the method of completing the square.

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

x² + 2(4)x + 16 + y² + 2(- 1)y + 1 = 64 + 16 + 1

(x + 4)² + (y - 1)² = 81 ← in standard form

with centre (- 4, 1) and radius = 9

Answer:

Step-by-step explanation:

[tex]-x^2+2x=-3\qquad\text{add 3 to both sides}\\\\-x^2+2x+3=0\\\\a=-1,\ b=2,\ c=3\\\\\text{Substitute to}\ D=b^2-4ac:\\\\D=2^2-4(-1)(3)=4+12=16[/tex]

Answer:

Discriminant = 16

Step-by-step explanation:

We have the following expression: -3 = -x^2 + 2x

Organizing the expression, we have: x^2 - 2x -3 = 0

We know that for an equation of the type: ax^2 + bx + c = 0, the discriminant is: b^2-4ac

From our equation we know that a=1, b=-2, and c=-3.

Then Discriminant = (-2)^2 - 4(1)(-3)

Discriminant = 4 +12 = 16

The mean weight of the three reserve players is found by rearranging the formula for calculating the mean, substituting known values, and solving the equation.

Given that the mean weight of all 12 players (nine players + three reserve players) is 188 pounds. Let's denote the missing weight of the three reserve players as 'x', 'y', and 'z'.

The formula to calculate mean is the sum of all the weights divided by the number of players. Here, mean weight equals (9*188 + x + y + z) / 12.

As we know that the mean weight is 188 pounds. We can substitute it back into the formula:
9*188 + x + y + z = 188 * 12.
This simplifies to x + y + z = 188 * 12 - 9 * 188.

We divide by 3 (since we are looking for the mean weight of three players): (x + y + z) / 3 = (188*12 - 9*188) / 3. Thus, the mean weight of the three reserve players can be found by solving this equation.

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Answer:

whole number, integer, real numberrational

Step-by-step explanation:

Answer:

Option D. LN=64 units

Step-by-step explanation:

step 1

Find the value of x

we know that

LN=LM+MN -----> equation A

we have

LN=12x+16

LM=10x+8

MN=5x-4

substitute the values in the equation A

12x+16=(10x+8)+(5x-4)

Solve for x

12x+16=15x+4

15x-12x=16-4

3x=12

x=4

step 2

Find the value of LN

LN=12x+16

LN=12(4)+16=64 units

The length of LN in units is 64 units

From the question, we are to determine the length of LN

In the given diagram

/LM/ = 10x + 8

/MN/ = 5x - 4

We can observe that

/LM/ + /MN/ = /LN/

From the given information,

/LN/ = 12x + 16

Therefore,

10x + 8 + 5x -4 = 12x + 16

Solving for x

15x +4 = 12x + 16

Then,

15x - 12x = 16 - 4

3x = 12

Thus,

x = 4

Then, substitute the value of x into LN = 12x + 16

LN = 12(4) + 16

LN = 48 + 16

LN = 64 units

Hence, the length of LN in units is 64 units

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It could be anything from 450 - 549 so pick a number within those two (for example, 460, 499, 523, 538, all of those work)

When rounding to the nearest hundred, any whole number from 450 to 549 will round to 500. We consider the tens place in a number to decide whether to round up or down.

In the field of Mathematics, when we are rounding a whole number to the nearest hundred, we look at the tens place. If the tens digit is 5 or above, we round up. If it's 4 or below, we round down. So, any whole number ranging from 450 to 549 will round up or down to 500 when rounding to the nearest hundred. For example, numbers like 475, 500, 525, or 543.

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Answer:

D  110

Step-by-step explanation:

Vertical angles are equal

50 = x+2y

Adjacent angles equal 180 degrees when they make a straight line

50+x-2y = 180

subtract 50 from each side

50-50+x-2y = 180-50

x-2y = 130

Flipping sides on the first equation

x+2y = 50

Adding the two equations together

x-2y = 130

x+2y = 50

-------------------

2x = 180

Divide by 2

2x/2 = 180/2

x = 90

Now we need to find y

x+2y = 50

90 +2y = 50

Subtract 90 from each side

90-90+2y = 50-90

2y = -40

Divide by 2

2y/2 = -40/2

y = -20

We want the difference between x and y

x-y

90-(-20)

90+20

110

What is the term used to describe the distribution of a data set with one mode? b. Unimodal

A.

Step-by-step explanation:

Multimodal

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the answer is d bc the common ratio is 6 and the previous term is 3 for a geometric recursive. the formula is a_n=a_n-1(3) btw

Answer:

To find the value of the y units, u have to multiply any x unit with the first y unit given but not 0

Step-by-step explanation: