What is the ratio for 3 rectangles and 4 ovals in its simplest form?

The graph will look like a circle centered at (2, 1) with radius 3.

To graph the equation [tex]x^2 - 4x + y^2 - 2y - 4 = 0[/tex]  by completing the square, we need to rearrange the terms as follows:

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

This can be simplified to:

[tex](x - 2)^2 + (y - 1)^2 = 3^2[/tex]

So the equation represents a circle with a center at (2, 1) and a radius 3. To graph the circle, we can plot the center point (2, 1) and then draw a circle with radius 3 around that point.

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Donna can expect her total monthly housing expenses to be approximately $842.71 for the first month after purchasing the house, assuming no tax benefits or amortization on the loan.

To calculate Donna's monthly housing expenses, we first need to determine the total amount of the mortgage. Since she puts down $25,000 on a $125,000 house, she will need to take out a mortgage for $100,000.

Next, we can calculate the annual cost of owning the house beyond the 5% cost of mortgage interest, which is given as 4.09% of the value of the house. So, 4.09% of $125,000 is:

0.0409 x $125,000 = $5,112.50

This means that Donna can expect to pay approximately $5,112.50 per year in additional expenses associated with owning the house.

To calculate the monthly cost, we simply divide this by 12:

$5,112.50 / 12 = $426.04

So, Donna can expect to pay approximately $426.04 per month in additional expenses associated with owning the house.

Adding the cost of the mortgage interest, we can calculate her total monthly housing expenses as follows:

Total monthly housing expenses = Mortgage interest + Additional annual costs / 12

Mortgage interest = 5% of $100,000 = $5,000 per year or $416.67 per month

Total monthly housing expenses = $416.67 + ($5,112.50 / 12) = $416.67 + $426.04 = $842.71

Hence, Donna can expect her total monthly housing expenses to be approximately $842.71

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Answer:

AA sim post

Step-by-step explanation:

They DO have equal (similar) angles.....but they do not have equal sides

Mrs. Garcia invested $2240 in the 8.5% account and $4091 in the 8% account.

Let x be the amount invested in the 8.5% account, and y be the amount invested in the 8% account. Since the total investment is $6331, we have x + y = 6331.

The total interest received is $517.68, which can be expressed as 0.085x + 0.08y = 517.68, where 0.085 and 0.08 are the decimal equivalents of the interest rates.

We can now solve this system of equations to find x and y. One possible method is to use substitution, where we solve for one variable in terms of the other from one of the equations, and substitute it into the other equation. From x + y = 6331, we have y = 6331 - x. Substituting this into the second equation, we get:

0.085x + 0.08(6331 - x) = 517.68

Simplifying and solving for x, we get:

0.005x + 506.48 = 517.68

0.005x = 11.2

x = 2240

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Answer:

The slope is 5.

Hope this helps!

Step-by-step explanation:

( x, y )

( 6, 50 ) and ( 12, 80 )

[tex]\frac{80-50}{12 - 6} < = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

[tex]\frac{30}{6} = \frac{5}{1} = 5[/tex]

The slope is 5.

A total of 8 workers are required for a building time of 15 days.

In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:

n ∝ 1 / t

n = k / t

Where k is the proportionality ratio, which can be eliminated by building the following formula:

n₁ · t₁ = n₂ · t₂

If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:

n₂ = n₁ · (t₁ / t₂)

n₂ = 10 · (12 / 15)

n₂ = 10 · (4 / 5)

n₂ = 8

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Answer:0

Step-by-step explanation:

so if x = -3 that means u take -3 * 2 and u get -6 because a negative * A positive is negative so -6 + 6 is 0

Answer:

0

Step-by-step explanation:

Just substitute x=-3

2x+6 =

2(-3) + 6 =

-6 + 6 = 0

The expression that equals D + 3C in standard form is 2w² + 8w - 25.

To find an expression that equals D + 3C in standard form, we first need to simplify D and C.

Starting with D = 2w² - w - 7, we can rearrange the terms to put it in standard form:

D = 2w² - w - 7

D = 2w² - 2w + w - 7

D = 2w(w - 1) + (w - 7)

Next, simplifying C = 3w - 6:

C = 3w - 6

Now, we can substitute these expressions into D + 3C:

D + 3C = (2w² - w - 7) + 3(3w - 6)

Expanding and simplifying:

D + 3C = 2w² - w - 7 + 9w - 18

D + 3C = 2w² + 8w - 25

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The solution set of given inequalities are represented by Part A.

The given inequalities are

⇒ y ≥ x + 1 and y + x > -1

Hence, The related equations of both inequalities are

y = x + 1

Put x=0, to find the y-intercept and put y=0, to find x intercept.

y = 0 + 1

y = 1

And, 0 = x + 1

x = - 1

Therefore, x-intercept of the equation is (-1,0) and y-intercept is (0,1).

Similarly, for the second related equation

y + x = - 1

y + 0 = - 1

y = - 1

0 + x = - 1

x = - 1

Therefore x-intercept of the equation is (-1,0) and y-intercept is (0,-1).

Now, join the x and y-intercepts of both lines to draw the line.

Now check the given inequalities by (0,0).

0 ≥ 0 + 1

0 ≥ 1

It is a false statement, therefore the shaded region is in the opposite side of origin.

0 + 0 ≥ - 1

0 ≥ - 1

It is a true statement, therefore the shaded region is about the origin.

Hence, From the below figure we can say that the solution set of given inequalities are represented by Part A.

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144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.

145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.

For question 144.)

Two triangles are congruent means that the angles are equal to each other. That is;

2.3x +25 = 5.8x + 11

Bring like terms together;

5.8x-2.3x = 25-11

3.5x = 14

X = 14/3.5

= 4.

For question 145.)

When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.

The two given angles are congruent;

That is;

13x -15 = 22x + 9

Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9

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Safiya can use either ∛12 or ∛(1/6) to find a rational product when multiplied by ∛18. So, correct options are e and f.

The cube root of 18 is an irrational number because it cannot be expressed as a fraction of two integers. Safiya needs to find a rational number that, when multiplied by ∛18, results in a rational product. To do this, she needs to look for cube roots of numbers that are perfect cubes of integers.

Option a) ∛4 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.

Option b) ∛18 is the given number and is not a perfect cube of any integer. Therefore, it is not a valid choice.

Option c) ∛3 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.

Option d) ∛(1/18) is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.

Option e) ∛12 is a rational number and it can be expressed as ∛(2³ × 3). Therefore, it is a valid choice.

Option f) ∛(1/6) is a rational number and can be expressed as ∛(1/216). Therefore, it is a valid choice.

So, correct options are e and f.

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The length of side A, in centimeters is 12. Option A

To determine the value, we need to know that;

When two sides of a figure are equal in length, that is in (measure).

For example in a square all sides are equal in length so they're all corresponding measurements.

From the information given, we have that;

Side A corresponds to 24 cm

Length 6 cm corresponds to Length 12 cm

The given parameters can be represented mathematically as;

A/24 = 6/12

cross multiply the values, we have;

12A = 6(24)

Multiply the values

12A = 144

Divide by the coefficient, we have;

A = 12 centimeters

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The correct answer is, A (aka 12)

The evaluation of the geometric series is found as:

[tex]5(1- \frac{2}{3}^{8} / 1- \frac{2}{3} )[/tex]

The given series is

[tex]8∑k=1 5(2/3)^k-1[/tex]

A  geometric series is described as the sum of an infinite number of terms that have a constant ratio between successive terms.

Since this is a geometric series, we apply  formula for the sum of the first k terms.

[tex]S= a( 1- r^{k} / 1-r )[/tex]

From the series, first term  a = 5, common ratio  r = 2/3 , k = 8

We substitute the values to obtain:

he evaluation of the series is found as:

[tex]5(1- \frac{2}{3}^{8} / 1- \frac{2}{3} )[/tex]

Geometric series finds its applications in Physics, engineering, biology, economics, computer science, queueing theory, and finance.

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complete question is attached in image

The percentage of the total budgeted category is given by

a) Clothing : 12 %

b) Insurance : 3 %

c) Taxes : 22 %

Given data ,

Let the percentage value be represented as A

Now , the value of A is

Let the total budgeted amount be = $ 6,200

Now , the amount for clothing = $ 744

So , the percentage for clothing = 744 / 6200 = 12 %

And , the amount for insurance = $ 186

Now , the percentage for insurance = 186 / 6200 = 3 %

And , the amount for taxes = $ 1,364

So , the percentage for taxes = 1364 / 6200 = 22 %

Hence , the percentages are solved

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Answer:

Question 6 :  True

Question 7:  False

Step-by-step explanation:

To find g(f(x)) given f(x) and g(x), substitute the expression for f(x) for every x in g(x)

f(x) = 2x

g(x) = x²

g(f(x) = (2x)² = 4x²

So True

f(x) = x² + x

g(x) = 2x + 1

g(f(x)) = 2(x² + x) + 1 = 2x² + 2x + 1

So False

The value of a scalar does not depend on the orientation.

The magnitude of a vector does not depend on the orientation of the axes.

(a) The value of a scalar does not depend on the orientation of the axes. Scalar is a quantity that has only magnitude and no direction, so it is independent of the coordinate system. Examples of scalars include temperature, mass, and time.

(b) Component of a vector depends on the orientation of the axes. If the coordinate axes are rotated or shifted, the components of a vector will change accordingly.

(c) A vector depends on the orientation of the axes. A vector has both magnitude and direction and changes when the orientation of the axes is changed.

(d) The magnitude of a vector does not depend on the orientation of the axes. The magnitude of a vector is defined as the length of the vector, which is independent of the coordinate system. For example, the magnitude of a velocity vector is the speed, which is the same regardless of the orientation of the axes.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

the surface area is the sum of all areas of the individual outside faces/sides.

so, what do we see here, what outside sides do we have here ?

of course, we have to assume that this is a regular object (left and right sides are the same).

2 right-angled triangles (left and right).

1 rectangle in the back.

1 rectangle at the bottom.

1 times rectangle in the front.

the area of a right-angled triangle is

leg1 × leg2 / 2

in our case that is

6 × 2.5 /2 = 3 × 2.5 = 7.5 mm²

we have 2 of these triangles :

2×7.5 = 15 mm²

the area of the rectangle in the back is

8 × 6 = 48 mm²

the area of the rectangle at the bottom is

8 × 2.5 = 20 mm²

the area of the rectangle in the front is

8 × 6.5 = 52 mm²

the surface of the object is the sum of all that :

15 + 48 + 20 + 52 = 135 mm²

The area of the triangle is 6 sq units.

The area of the triangle is calculated by applying the following formula;

A = ¹/₂ x b x h

where;

The base of the triangle = 3 - 0 = 3

The vertical height of the triangle = 5 - 1 = 4

Area = ¹/₂ x 4 x 3

Area = 6 sq units.

Thus, the area of the triangle is a function of base and height.

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The surface area of the prism is 248.88 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.

Base area = 61.94 cm²

height = 5cm

perimeter = 5 × 5 = 25cm

SA = 2 × 61.94 + 25 × 5

SA = 123.88+ 125

SA = 248.88 cm²

Therefore the surface area of the prism is 258.88 cm²

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Solving a system of equations we can see that Gavin worked 7 hours tutoring.

Let's define the variables:

x = number of hours tutoring.

y = number of hours land scaping.

We know that he worked for 10 hours and earned $137, then we can write a system of equations:

x + y = 10

14x + 13y = 137

Isolating y on the first equation we get:

y = 10 - x

Replace that in the second one to get:

14x + 13*(10 - x) = 137

14x + 130 - 13x = 137

x = 137 - 130 = 7

He worked 7 hours tutoring.

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The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

We have,

To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:

x² + 12 = x² + (2√3)²

Now we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

In this case, we have a = x and b = 2√3. So we can write:

= x² + 12

= x² + (2√3)²

= (x + 2√3)(x - 2√3)

Therefore,

The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

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The total surface area of the cylinder is 414.7 cm².

The curved surface area of the cylinder is calculated as follows;

C.S.A = 2πrh

where;

The curved surface area of the cylinder is calculated as;

C.S.A = 2π(6 cm) x (5 cm)

C.S.A = 188.5 cm²

The total surface area of the cylinder is calculated as follows;

T.S.A = 2πrh + 2πr²

circular area = 2πr² = 2π x (6cm)² = 226.2 cm²

The total surface area = 188.5 cm² + 226.2 cm² = 414.7 cm²

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The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

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Answer:

1 1/6 metre

Step-by-step explanation:

1/3 pink + 5/6 purple

To add, we need to get a common denominator

1/3 *2/2 = 2/6

2/6 + 5/6

7/6

Change from an improper fraction to a mixed number

1 1/6 metre

The equation of the line that passes through point (-3,-7) and point (-3,10) is x = -3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the points through which the line passes: (-3,-7) and (-3,10).

The two given points (-3, -7) and (-3, 10) have the same x-coordinate -3

Hence, the two lines  lie on a vertical line.

since the slope of the vertical line is undefined.

The equation of the line passing through these two points is simply the equation of the vertical line:

x = -3

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Option C (15 17 19) has a similar mean absolute deviation to the data set in the given dot plot.

The informational collection in the given speck plot has a mean of roughly 55 and a moderately little scope of values, with most of the information bunched around the mean. An informational index with a comparable mean outright deviation would have a comparative degree of variety in the information values.

Out of the given choices, the informational index that has a variety like the given informational collection is choice C: 15 17 19. This informational collection has a mean of roughly 17 and a little scope of values, with most of the information bunched around the mean.

The mean outright deviation of this informational collection is around 1.63, which is like the mean outright deviation of the given informational collection. Choice A (50 51 52 53 54 55 56 57 58 59 60 61) has a bigger scope of values and a bigger mean outright deviation contrasted with the given informational collection.

Choice B (4612) and Choice D (8 9 1011 and 55 57 59 61 63 65) have altogether unique mean qualities and scopes of values, and consequently their mean outright deviations are not quite the same as the given informational collection.

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