Prove that the median to the hypotenuse of a right triangle is half the hypotenuse. Plan: since midpoints will be involved, use multiples of __ to name the coordinates for m and n.

Answer:

Below

Step-by-step explanation:

30%   is   .3 in decimal

So the family used 100 %  of last month PLUS .3 of last month MORE

 12 000 = 100 %      now add  .3 (12 000) more =

    12 000  + .3 ( 12 000) = 15600 gallons this month

There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.

In the given question, we have to find the solution of the system Y>2x+2/3 and y<2x+1/3 change.

We firstly draw the two lines y=2x+2/3, and y=2x+1/3.

They are parallel and the line y=2x+2/3 is located over the line y=2x+1/3.

There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.

The solution of y2x+2/3 is the region below the line y=2x+2/3, and the solution of y>2x +1/3 is the region above the line y=2x+1/3 when the inequality sign of both inequalities is reversed. This implies that the area between the two lines is where the system's solution lies.

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The right question is:

How will the solution of the system Y>2x+2/3 and y<2x+1/3 change? If the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?

By using the properties of triangle, it can be calculated that-

Smallest angle = 30°

Next larger angle = 60°

Largest angle = 90°

What is a triangle?

Triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.

The angles of a triangle are x, 2x and 90

Sum = x + 2x + 90 = 3x + 90

By the problem,

3x + 90 = 180

3x = 180 - 90

3x = 90

x = [tex]\frac{90}{3}[/tex]

x = 30

Smallest angle = 30°

Next largest angle = 2 [tex]\times[/tex] 30 = 60°

Third angle = 90°

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Answer:

MP = 12 cm

Step-by-step explanation:

4cm : 6cm

8cm : x

8 * [tex]\frac{6}{4}[/tex] = 12 cm

MP = 12 cm

Answer:

not a solution

Step-by-step explanation:

2x-3=2x+5

-2x.  -2x

-3=5

not a solution because -3 does not equal 5

Answer: The ratio of the breadth to the height of the hall is 7:8

Step-by-step explanation:

The ratio of the length to the height of the hall is 7:6, which means that if the length of the hall is represented by 7, the height is represented by 6. We can write this as a proportion as follows:

7/6 = L/H

We know that the length of the hall is 28 meters, so we can substitute this value for L in the proportion to find the height:

7/6 = 28/H

Solving for H, we get:

7/6 = 28/H

7H = 168

H = 168/7 = 24

The height of the hall is 24 meters.

The ratio of the breadth of the hall to its height is the same as the ratio of 21 to 24, which simplifies to 7:8. Therefore, the ratio of the breadth to the height of the hall is 7:8.

Amy's measurement of the salt's mass is not accurate because it is not close to the actual value. Amy's measurement of the salt's mass is precise because the individual measurements are similar.

In Mathematics, measurement can be defined as an act or process through which the size, weight, magnitude, quantity, volume (capacity), dimensions, or distance traveled by a physical object or body is taken, especially for the purpose of an experiment.

In Science, precision is a quality which is independent of accuracy because it only describes how close together are numerical values that are obtained in a series of measurements.

In conclusion, accuracy is a quality which measures how close a measurement is to the actual value.

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Complete Question:

Amy forgot to subtract the mass of the empty weighing dish from her measurements, and she reported the mass of the salt as 5.608 grams. Amy's measurement of the salt's mass (1) ______ accurate because (2) ______ . Amy's measurement of the salt's mass (3)_____ precise because (4) _______ .

1. is

is not

2. it is not close to the actual value

she used five different balances

the individual measurements are similar

3. is

is not

4. it is not close to the actual value

she used five different balances

the individual measurements are similar

Answer: No

Step-by-step explanation:

Graph: You can use the vertical line test to determine if it is a function. Draw a vertical line (going up and down) on the graph. If it only intersects one

point, then it is a function. If it crosses two points, it is not a function.

Chart: If the x repeats and the y does not repeat, it is not a function. y can repeat as much as it wants, as long as the x does not.

Lines: If one x connects to multiple y, it is not a function. If one y connects to multiple x, it is a function.

Coordinates: Same as the chart

Answer:

29 years old

Step-by-step explanation:

Answer: 29

Step-by-step explanation: 29 but we want to round that up to 30 because 29 is odd but due to science and polls nobody likes the number 30 so we go back to 29 but it’s uneven so we go to 28 to make it even but we also don’t like that number so we go back to 29 and that how we get it.

Answer:

The answer is $87.5

Step-by-step explanation:

350 × 25 ÷ 100

8750/100 = 87.5

Thus, Mr. Wright deposit $87.5

The value of x is obtained as 9.4 units.

Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².

The value of x for the given figure can be calculated as,

Use pythagoras theorem for lower triangle as below,

p² + b² = h²

=> p² = h² - b²

=> p² = 12² - 6²

         = 108

Now, substitute the value of p² in the expression for upper triangle as,

x² + p² = 14²

=> x² + 108 = 196

=> x² = 88

=> x = 9.4

Hence, the value of x for the given figure is 9.4 units.

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The square of given expression √1 ( square root of 1 ) is equal to 1.

As given in the question,

Given expression is equal to √1 ( square root of 1 )

To calculate the square of √1 we have,

Let us consider variable x is equal to √1

x = √1

Now take square on both the sides of the given expression we get,

x² =  (√1 )²

⇒ x² = √1  × √1

Multiplying square root of 1 to square root of 1 is equal to 1 we get,

or use law of exponent :

√1 × √1 = [tex]1^{\frac{1}{2} + \frac{1}{2} }[/tex]

            = 1

⇒ x² = 1

Therefore, the square of the given expression √1 ( square root of 1 )is equal to 1.

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Answer:

588

Step-by-step explanation:

Answer:

3X−9=

4

6⋅6

​

Multiply both sides of the equation by 4.

12X−36=6×6

Multiply 6 and 6 to get 36.

12X−36=36

Add 36 to both sides.

12X=36+36

Add 36 and 36 to get 72.

12X=72

Divide both sides by 12.

X=

12

72

​

Divide 72 by 12 to get 6.

X=6

Integers have a greater and more suitable range to be closed for subtraction than whole numbers.

According to the closure property of subtraction, the difference between two integers will always be an integer.

An integer is a number that ranges from minus infinity and infinity and is not a fraction.

Whereas all positive valued integers including 0 are whole numbers.

Now if we subtract a larger whole number from a smaller whole number, then the difference will obviously be negative. Hence, the result will be an integer and not a whole number.

example= 25 - 30

= -5

Here both 25 and 30 are whole numbers but -5 is not. But all three are considered integers.

Hence, subtraction is closed under integers and not whole numbers.

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The required probability is approximately 0.3066 or 0.31. Option B is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
There are a total of 77 + 60 = 137 students in the group.

Out of these students, 42 sophomores attended the volleyball game.

So the probability of a randomly chosen person from this group being a sophomore and attending the volleyball game is:

P(sophomore and volleyball) = 42/137

Therefore, the probability is approximately 0.3066 or 0.31. Option B is correct.

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Answer:

  f(x) = x³ -10x² +28x +104

Step-by-step explanation:

You want a cubic polynomial f(x) with real coefficients, and its graph, such that one root is -2, another is 6+4i, and f(2) = 128.

A polynomial with real coefficients will have complex (or radical) roots that are conjugate pairs. That means the root 6+4i will be paired with a root 6-4i. The factored form of the required polynomial will be ...

  f(x) = a(x -(-2))(x -(6 +4i))(x -(6 -4i))

  f(x) = a(x +2)(x² -12x +52)

We can use the given value of f(2) to find the scale factor, a.

  f(2) = 128 = a(2 +2)(2² -12·2 +52) = a(4)(32) = 128a

  a = 1 . . . . . divide by 128

The required polynomial is ...

  f(x) = (x +2)(x² -12x +52)

  f(x) = x³ -10x² +28x +104

Parallel slope intercept form is a form of linear equation that describes a line parallel to a given line with slope m.

It is written as y = mx + b, where m is the slope of the line and b is the y-intercept of the line. This form is useful for finding equations of lines that are parallel to a given line.

y = mx + b

y = mx + b is an equation in the form of a straight line, where m is the slope of the line and b is the y-intercept of the line. This form can be used to determine the equation of a line that is parallel to a given line. The equation can be re-arranged to solve for x, if needed. To solve for x, the equation can be rewritten as x = (y - b) / m.

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There are 16 ounces in a pound.

The proper serving size of french fries is reportedly only 12 to 15 fries.

The equation of a line that passes through [tex](-1,4)[/tex] and is parallel to the y-axis is [tex]x=-1[/tex]

The equation of the line passes through the point is [tex](-1,4)[/tex]

The line is parallel to the y-axis which means it cuts the x-axis at the point [tex](-1,0)[/tex]

The equation of the line parallel to the y-axis is [tex]x=-1[/tex]

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Answer:

420 calories

Step-by-step explanation:

Multiply 140 by 3 because there are three servings in a can, and each serving is 140 calories, so the number of calories in the can is the product of the numbers.

Justification for the last two steps of the proof is

3. Reflexive Property of (Congruence) ≅

4. SSS (Side to Side to Side Congruence rule)

What is SSS congruence postulate ?

A type of triangle congruence rule called Side-Side-Side (SSS) asserts that two triangles are congruent if their three sides are equal to their respective three sides of another triangle. When the dimensions of the matching sides and angles of two or more triangles match, the triangles are said to be congruent.

3. Any geometric figure compared to itself is congruent to itself so this is why:

AC ≅ CA

∠B ≅  ∠B

4. Since we have a parallelogram, therefore we can say:

BC ≅ DA

BA ≅ DC

CA ≅ AC

Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent.

So, It's D.

P.S.

Notice that the angle measure information is not included in the data above that's why we cannot say it is SAS congruence.

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The coordinate is (2√2 , 0).

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

If you rotate the point (2,-2) positive 45 around the origin.

To find the coordinates:

the formula;

X = xcosФ - ysinФ

And Y = xsinФ + ycosФ

and here Ф = 45° and x = 2 and y = -2

Now, X = 2/√2 + 2/√2 = 2√2

Y = 2/√2 - 2/√2 = 0

Therefore, the coordinate is  (2√2 , 0).

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At least Eight yards need to raked to earn minimum $52. The equation of model is $6.50 Y≥ $52. So, the correct answer is option(C).

The total earned income by rake leaves in your neighborhood after school is $6.50 per yard. The Minimum amount that you want to earn = at least $52

We have determined a equation of model for the given situation.

Let Y be the number of yards raked to earn at least $52. We have one yard raked which implies to earn $6.50

So,for Y yards raked it implies to earn $6.50× Y. But Y has to rake in atleast $52 , here the minimum is to earn either $52 or more than $52. So,Y($6.50 ) ≥ $52

dividing both sides by $6.50 we get,

Y ≥ 52/6.50

=> Y ≥ 52/6.50 = 8

Hence , at least 8 yards must be raked to earn minimum $52.

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Complete question:

You rake leaves in your neighborhood after school and earn $6.50 per yard you rake. How many yards do you need to rake to earn at least $52? What equation models this situation?

A. at least 45 yards; y + 6.5 ≥ 52.00,

y = number of yards raked

B. at most 8 yards; 6.50y 52.00,

y = number of dollars earned

C. at least 8 yards; 6.50y ≥ 52.00,

y = number of yards raked

D. at most 52 yards; y − 6.5 > 52.00,

y = number of dollars earned

Answer: The blimp is 82% full

Step-by-step explanation:

To find the percentage of the blimp that is filled with gas, we need to divide the volume of the gas that is in the blimp by the total volume of the blimp and then multiply the result by 100%.

The blimp is filled with 28,700 cubic feet of gas, and it has a total volume of 35,000 cubic feet when fully expanded, so the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.

To express this as a percentage, we need to multiply the result by 100%, so the blimp is 82% full.

Here's the complete solution:

The blimp is filled with 28,700 cubic feet of gas.

The blimp has a total volume of 35,000 cubic feet when fully expanded.

Therefore, the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.

To express this as a percentage, we multiply the result by 100%, so the blimp is 82% full.

(a) The balance after first transaction is, $162.66.

(b) The balance after second transaction is, $109.63.

(c) The balance after third transaction is,  $2.33.

What is transaction?

An agreement that has been fulfilled between a buyer and a seller to exchange goods, services, or financial assets in exchange for cash is referred to as a transaction.

The following are a few examples of transactions: paying a supplier after receiving goods or services from them. acquiring ownership of a property the seller previously owned by paying the seller with cash and a note. remuneration for hours worked.

Given:

Mac Valent opened a new checking account and deposited his paycheck for $209.81.

We have to find the balance after each transactions.

The first transaction is of electric cooperative for $47.15.

So, the balance after first transaction is, $209.81 - $47.15 = $162.66.

The second transaction is of Sharp's Groceries for $53.03.

So, the balance after second transaction is, $162.66 - $53.03 = $109.63.

The third transaction is of Gimbles Auto Repair for $107.30.

So, the balance after third transaction is, $109.63 - $107.30 = $2.33.

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Complete question:

Complete question is attached below.

Answer:

No

Step-by-step explanation:

The equation of the circle if diameter has endpoints (-3,-1) and (1,2) is x² + 2x + y² - y = 5.

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).

Given:

The endpoints of the circle diameter are (-3,-1) and (1,2),

Calculate the coordinates of the center of the circle as shown below,

Center = (-3 + 1 / 2, -1 + 2 / 2)

Center = (-2/2, 1/2)

Center = (-1, 1/2)

Calculate the length of diameter as shown below,

Diameter = [tex]\sqrt{[1- (-3)]^2+[2-(-1)]^2}[/tex]

Diameter = √(4² + 3²)

Diameter = 5

Thus, radius = 5 / 2 =

Calculate the equation of the circle as shown below,

[x - (-1)]² + [y - 1/2]² = (5/2)²

Simplify the above equation as shown below,

x² + 2x + y² - y = 5

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Answer:

33

Step-by-step explanation:

All triangle angles together add up to 180

So we can set up this equation to find angle z:

98 + 49 + z = 180

Now solve:

98 + 49 + z = 180

147 + z = 180

-147        -147

z = 33

The coordinates of the vertices after a reflection over the line x = 2.

D = (8, 5)

E = (6, 5)

F = (4, 8)

G = (7, 8)

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The coordinates:

D = (-4, 5)

E = (-2, 5)

F = (0, 8)

G = (3, 8)

The line x = 2.

We count the units from the line x = 2.

After the reflection, the number of units of each coordinate from the line

x = 2 must be equal to the number of units from the line x = 2 before the reflection.

Thus,

The reflected coordinates of the vertices are:

D = (8, 5)

E = (6, 5)

F = (4, 8)

G = (7, 8)

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