Aurora thinks of a number. What is her number?
My number is odd and
greater than 4.
54 and 36 are multiples of
my number.

Answer: (-3,5)

Step-by-Step Solution:

1. Set 1 equation equal to y

3y-2x=21

3y=2x+21

y=2/3x+7

2. Set the other equation equal to y

4y+5x=5

4y=-5x+5

y=-5/4x+5/4

3. Set the equations equal to each other, and solve for x

2/3x+7=-5/4x+5/4

2/3x+23/4=-5/4x

(Multiply by 12 on both sides to get rid of fractions)

8x+69=-15x

8x=-15x-69

23x=-69

x=-3

4. Solve for y

(Choose any of the equations)

y=2/3x+7

y=2/3(-3)+7

y=-2+7

y=5

ANSWER: (-3,5)

The number of books that her sister has before giving any to Sarah is 30 books

Sarah received three fifths of her sister's book collection

Number of books that Sarah received = 18 books

The fraction of the books that Sarah received = 3/5

Consider the total number of books as x

Then we have to find the total number of books

So the equation will be

x × (3/5) = 18

Divide the terms in the equation

x × 0.6 = 18

Move 0.6 to the right hand side of the equation

x = 18 / 0.6

Divide the terms

x = 30 books

Hence, number of books that her sister has before giving any to Sarah is 30 books

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The area of the square that has 3 cm of side is 9 cm^2

The formula and procedure to solve this geometry exercise is:

A = s²

Where:

Problem information:

Using the formula of the square area we get:

A = s²

A = (3 cm)²

A = 9 cm²

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2

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Answer:

Scale Factor

[tex]k=5[/tex]

Side Congruency

AL ≅ TD

TK ≅ AH

DK ≅ LH

Angle Congruency

∠A ≅ ∠T

∠D ≅ ∠L

∠H ≅ ∠K  or  ∠K ≅ ∠H

Step-by-step explanation:

Scale Factor

First, to determine the scale factor, I will choose two corresponding segments: AL and TD.

By counting on the graph, I can see that they are the following lengths:

[tex]TD=15\\AL=3[/tex]

Therefore the ratio of the large triangle to the small triangle is 15:3. Written as a fraction and simplified, this is:

[tex]\frac{15}{3}=5[/tex]

5 is the scale factor, or k.

Congruency

Each segment on the small triangle corresponds to the same side on the large triangle. Therefore:

AL ≅ TD

TK ≅ AH

DK ≅ LH

The same goes for the angles, except the angles are actually equal as well:

∠A ≅ ∠T

∠D ≅ ∠L

The bottom of your image is cut off, but I assume the question is one of these:

∠H ≅ ∠K

∠K ≅ ∠H

The number of problem that can she grade in hour is 60 problems

The number of problems that math teacher graded in 3/4 of an hour = 45 problem

Here we have to use the unitary method

The unitary method is defined as the method of finding the value of the single unit.

The number of problem that can math teacher grade in 1 hour = The number of problems that math teacher graded in 3/4 of an hour ÷ 3/4

Substitute the value in the equation

The number of problem that can math teacher grade in 1 hour = 45 ÷ (3/4)

= 45 × (4/3)

= 60 problem

Hence, the number of problem that can she grade in hour is 60 problems

The complete question is:

A math teacher graded 45 problems in 3/4 of an hour. At that rate, how many problems can she grade in 1 hour?

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Answer:

x(x - 6)(x + 4)

Step-by-step explanation:

x³ - 2x² - 24x ← factor out x from each term

= x(x² - 2x - 24) ← factor the quadratic

consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)

the factors are - 6 and + 4 , then

x² - 2x - 24 = (x - 6)(x + 4)

then

x³ - 2x² - 24x = x(x - 6)(x + 4)

The inequality of the interval notation [-10, ∞) is x ≥ -10

The given interval notation is

[-10, ∞)

We have to convert the interval notation to inequality

The inequality is the mathematical statement that shows the relationship between two expression with inequality sign. The inequality signs are less than, less than or equal, greater than, greater than or equal. The inequality consist of different variables, numbers and mathematical operators.

Interval notation is defined as the method of writing subsets of the real number line

The given interval notation is

[-10, ∞)

Convert the interval notation to inequality

x ≥ -10

Hence, the inequality of the interval notation [-10, ∞) is x ≥ -10

The complete question is

Convert the interval notation  [-10, ∞) to inequality

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According to the given standard deviation, the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence is 10.6

Standard deviation:

Basically, the standard deviation refers a quantity expressing by how much the members of a group differ from the mean value for the group.

Given,

It is desired to estimate the mean number of chocolate chips in a chocolate chip cookie.

Here we need to find how many cookies need to be sampled to estimate the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence and assume that the population standard deviation is 3.7 chocolate chips.

From the given question we have identified the following details,

Confidence interval = 99%

Standard deviation = 3.7

So, the critical value is calculated as,

=> 1 - 0.99

=> 0.01

So, the z scores is 2.576.

Now, the formula to confidence interval is given by : -

=> 10.6 ± 2.576 (0.01)/ √3.7

=> 10.6

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B) direction ratio of any two diagonals in vector form is 60°.

C) cos²α+cos²β+cos²γ+cos²δ= [tex]\frac{4}{3}[/tex]

​In Euclidean geometry, a perspective is a parent created by rays, often referred to as the angle's perimeters, sharing a single endpoint known as the perspective's vertex. Angles created by rays are located in the plane that contains the rays. Angles can also be created by intersecting two planes. They are referred to as dihedral angles. Curves that cross may also define an angle, which is the angle formed by rays that are perpendicular to the individual curves at the point of junction.

The degree of an angle or rotation is also expressed in terms of perspective. This metric represents the relationship between a circular arc's length and radius.

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The approximate value of the vehicle 10 years after purchase is $11,945.68.

Depreciation is when the value of an asset falls with the passage of time as a result of wear and tear of the asset. Deprecation would reduce the price of the vehicle each year.

The equation that can be used to determine the value of the vehicle after 10 years is:

FV = P (1 - r)^t

Where:

FV = 27,500 (1 - 0.08)^10

FV = 27,500 x (0.92^10)

FV = $11,945.68

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Using trigonometric ratio, the horizontal distance from A to B is 314 feet

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

To calculate the distance from point A to point B, we can use trigonometric ratio here.

Note: We are going to add the two angles and then use the vertical distance as the adjacent side of the triangle.

Data;

Using tangent of the angle;

Tanθ = opposite / adjacent

tan 66 = AB / 140

AB = 140 tan66

AB = 314ft

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Answer:

Step-by-step explanation:

Let M(x,y) be the median of ΔABC through A to BC.M will be the midpoint of BC.x1​=5,y1​=3x2​=3,y2​=−1By midpoint formula, x=(x1​+x2​)/2∴x=(5+3)/2=8/2=4By midpoint formula, y=(y1​+y2​)/2∴y=(3+(−2))/2=2/2=1Hence the co-ordinates of M are (4,1).By diatnce formula, d(AM)=[(x2​−x1​)2+(y2​−y1​)2]​x1​=7,y1​=−3x2​=4,y2​=1

Answer:

  12.1 hours

Step-by-step explanation:

You want to know the mowing time for 5 acres if Hannah can mow 1000 square yards in 1/2 hour.

We can convert the acreage to square yards to facilitate the calculation:

  5 ac × (4840 yd²)/(1 ac) = 24,200 yd²

Hannah mows her lawn at the rate of ...

  (1000 yd²)/(0.5 h) = 2000 yd²/h

At this rate, the time it takes for 24200 yd² will be ...

  (24,200 yd²)/(2000 yd²/h) = 12.1 h

It would take Hannah 12.1 hours to mow 5 acres.

Answer: 18.75%

Step-by-step explanation:

To find the percentage decrease, the formula is shown below.

Plug in the values and calculate:

[tex]\frac{8-6.5}{8} *100=18.75%[/tex]

So, the chunk of meat lost 18.75% of its initial weight.

The missing values for the exponential function are y = 16.875 and y = 25.3125

The general form of the exponential function is y = abˣ

From the table, when x = 0, y = 11.25. Substitute the values into the function:

y = abˣ

11.25 = ab⁰             (Note: b⁰ = 1)

11.25 = a(1)

11.25 = a

a = 11.25

Also, from the table, when x = -1, y = 7.5. Substitute the values into the function:

7.5 = 11.25b⁻¹

7.5 = 11.25/b                (Note: b⁻¹ = 1/b)

7.5b = 11.25

b = 11.25/7.5 = 1.5

We can now write the exponential function for this case:

y = abˣ

y = 11.25(1.5)ˣ

We can find the missing values now:

when x = 1:

y = 11.25(1.5)ˣ

y = 11.25(1.5)¹

y = 16.875

when x = 2:

y = 11.25(1.5)ˣ

y = 11.25(1.5)²

y = 25.3125

Therefore, the missing values are 16.875 and 25.3125. Option c is the correct answer

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After the multiplication of (3+√16) (6-√64), the resultant answer is -14.

Multiplying in math is the same as adding equal groups.

The number of items in the group grows as we multiply.

Parts of a multiplication issue include the product, the two factors, and the product.

The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

So, the multiplication of:

(3+√16) (6-√64)

Now, multiply as follows:

(3+√16) (6-√64)

We know that: 3+√16 = 7

7(6-√64)

We know that: 6-√64 = -2

7(-2)

-14

Therefore, after the multiplication of (3+√16) (6-√64), the resultant answer is -14.

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Linear Equations

2y+x=6 ... (i)

2y-3x=-2 (ii)

x=2

y=2

To solve this problem, we will use a substitution method.

We would first transform equation (i) to get the formula for x-value.

2y+x=6

x=6-2y... (iii)

Next, we will substitute the equation (iii) into (ii) to find the value of y.

2y-3x=-2

2y-3(6-2y)=-2

2y-18+6y=-2

8y-18=-2

8y=16

y=2... (iv)

Then we would substitute the equation (iii) with the value y on the equation (iv)

x=6-2y

x=6-2(2)

x=6-4

×=2

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Answer:

(2, 2 )

Step-by-step explanation:

2y + x = 6 → (1)

2y - 3x = - 2 → (2)

subtract (2) from (1) term by term to eliminate y

(2y - 2y) + x - (- 3x) = 6 - (- 2) , that is

x + 3x = 6 + 2

4x = 8 ( divide both sides by 4 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (1)

2y + 2 = 6 ( subtract 2 from both sides )

2y = 4 ( divide both sides by 2 )

y = 2

solution is (2, 2 )

If x represents the cost of each bag of oranges then the equation will be 7x+5.65 = 34.07 and the value of x is $4.06.

According to the question,

We have the following information:

Alexander buys ice cream and oranges at the store.

• He pays a total of $34.07.

• He pays $5.65 for the ice cream.

• He buys 7 bags of oranges that each cost the same amount.

Let's take the cost of each bag of oranges to be $x.

We have the following equation:

7x+5.65 = 34.07

Subtracting 5.65 from both sides:

7x = 34.07-5.65

7x = 28.42

x = 28.42/7

x = 4.06

Hence, if x represents the cost of each bag of oranges then the equation will be 7x+5.65 = 34.07 and the value of x is $4.06.

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Answer:

circumference of the circle is= 2πr

if radius is 15 then we should put that into the formula

30π

if pie is given as 3.14 then it would be

94.2

good luck

Answer:

30 pi inches

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi * r

C = 2 * pi * 15

C = 30 pi inches

The animal that is farthest from 0 on the number line is the Fanfin anglerfish.

A number line is a marked straight line that is used to visually represent real numbers.

The values given in the table are negative number. A negative number is a number that has a value less than zero. A negative number is represented with a minus sign. The table has decimals, mixed numbers and fractions.

The larger a number is, the farther the distance of the number from 0 on the number line. In the given table, the largest number is -2 1/4. Thus, -2 1/4 is the farthest from the number line.

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Answer:

y=1/10x+2

Step-by-step explanation:

y-3=-10(x-2) This equation is in point-slope form so the slope is -10

The perpendicular slope is the negative reciprocal so 1/10.

Slope intercept form is y=mx+b

Plug in the points of the x-intercept and slope into y=mx+b

0=-20(1/10)+b

0=-2+b

b=2

y=1/10x+2

Answer:

7

Step-by-step explanation:

4 divided by 4/7 = 7

(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .

(b) The distance between points (2,-5) and (-7,-5) is 9 units .

(c) The midpoint of the line segment that joins the given points is given by: (-5/2,-5) .

In the question ,

it is given that ,

the points given is (3/5 , 4/5)

(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)^2 + (4/5)^2 = 1

that is

9/25 + 16/25 = 1

25/25 = 1

1 = 1

hence proved that the point (3/5, 4/5) is on the unit circle .

(b)  The distance between (2, -5) and (-7, -5) is calculated using the formula

[tex]=[/tex]√(x₂ - x₁)² [tex]+[/tex] (y₂ - y₁)²

= √(-7 - 2)² + (-5 -(-5))²

= √(-9)² + (-5 + 5)²

= √(-9)² = √81

= 9 units

(c) the mid point joining the points (2, -5) and (-7, -5) is (a,b) that is calculated by

a = (2-7)/2     ,   b = (-5-5)/2

a = -5/2        ,     b = -10/2

a = -5/2 and b = -5

the mid point is (-5/2,-5)  .

Therefore , (a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .

(b) The distance between points (2, -5) and (-7, -5) is 9 units  .

(c) The midpoint of the line segment that joins the given points is given by (-5/2,-5)  .

The given question is incomplete , the complete question is

(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² =        .

(b) The distance between (2, -5) and (-7, -5) is         .

(c) The midpoint of the line segment that joins the given points is given by  (     ,     )    .

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Answer:

False

Step-by-step explanation:

[tex]10^{-2}[/tex] id not a negative number it means

[tex]\frac{1}{10^{2} }[/tex] or [tex]\frac{1}{100}[/tex]  Which is a number with a lesser value than 1, but it is not a negative number.

There are 19 triangels can be formed whose vertices are among the 9 points.

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides. In other words, a triangle is defined as a three-sided two-dimensional figure whose interior angles are equal to 180°.

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.

From the question, we know that we have 9 point from 2 line parallel. There are 19 triangels (the same shape is not counted twice) can be formed whose vertices are among the 9 points that shown in the following picture.

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Answer:5,149 pounds of sawdust for $1,132.78

Step-by-step explanation:

Step 1 is to convert 4 tons into pounds is:

4 tons * 2000 pounds per ton = 8000 pounds

Step 2 is to find the cost of saw dust per pound in each scenario:

Scenario 1: $1132.78 / 5149 = .22 dollars per pound

Scenario 2: $2800 / 8000 = .35 dollars per pound

Step 3 is just comparing which one is the cheapest per pound based on step 2:

.22 per pound is less than .35 per pound. So the answer is scenario 1 (5149 pounds for 1132.78) is the better buy