A scale on a map shows that 2. 5 2. 52, point, 5 centimeters represents 15 1515 kilometers. What number of actual kilometers are represented by 17. 5 17. 517, point, 5 centimeters on the map?.

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:

The answer is $87.5

Step-by-step explanation:

350 × 25 ÷ 100

8750/100 = 87.5

Thus, Mr. Wright deposit $87.5

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?

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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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.

The relation that is able to model the decay is given as N = 690e^-0.04r. The quarterly rate of change is 0.21%.

We know that the term radioactivity has to do with the fact that the object is able to undergo the process of a spontaneous disintegration. The implication of this is that the element is going to be gradually be transformed into a different element and this is going to occur at a given rate which we have called the decay constant for the reaction.

We know that element X is a radioactive isotope such that its mass decreases by 4% every year then an experiment starts out with 690 grams of Element X.

It follows that;

Initial amount of X No = 690 g

Decay rate of X (r) = 0.04

Time taken for decay = t

Amount of X at time t = N

The model now becomes;

N = 690e^-0.04r

The  quarterly rate of change is obtained from;

A(t) = (1- 0.04)Ao

= 0.96 Ao

0.96Ao = Ao(1 - r)^30

0.94 = (1 - r)^30

30√0.94  = (1 - r)

r = -0.0021 or -0.21%

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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 maximum height of the projectile will be 226 feet that is, as per question, the option c.

A quadratic equation , y = ax²+bx+c  (equation 1)

given, axis of symmetry is

x = [tex]\frac{b}{2a}[/tex]

As per the question:

The path of the projectile is modeled using the equation :

h(t) = -16t²+48t+190  (equation 2)

h(t) = height after t time.

comparing equation 1 and equation 2, we get

a = -16 and b = 48

further, t = [tex]\frac{48}{2(-16)}[/tex]

= [tex]\frac{48}{32}[/tex]

= 1.5sec

Substituting the found value in equation 2, we get

h(1.5) = -16(1.5)²+48(1.5)+190

h(1.5) = -36+72+190

h(1.5) = 226ft.

Thus, the maximum height of the projectile at 1.5 sec is, 226 feet.

Note that the full question is:

A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = –16t2 + 48t + 190.

What is the maximum height of the projectile?

A. 82 feet

B. 190 feet

C. 226 feet

D. 250 feet

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Answer:

$10.79

Step-by-step explanation:

1) Make an equation

40x + 48.67 = 480.17

where x is hourly pay

2) Solve

40x + 48.67 = 480.17

40x + 48.67 - 48.67 = 480.17 - 48.67

40x = 431.50

40x / 40 = 431.50 / 40

x = 10.79

Answer:

MP = 12 cm

Step-by-step explanation:

4cm : 6cm

8cm : x

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

MP = 12 cm

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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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:

1)  x=16

2) x=15

3) x=10

Step-by-step explanation:

1)  Since the triangles are similar and the ratio of the sides is 1 : 2, 1/2=(3x-4)/(10x-72). Cross multiplying, we get 6x-8=10x-72.

10x-72=6x-8 |+72

10x=6x+64 |-6x

4x=64  |/4

x=16

2) Angles HGJ and KLJ are corresponding (they are equal angles).

So, 5x-2=9x-62.

5x-2=9x-62  |+62

5x+60=9x  |-5x

60=4x |/4

x=15

3) If KM is a perpendicular bisector, KJ=KL.

So, 4x+9=11x-61.

4x+9=11x-61 |-4x

9=7x-61   |+61

70=7x  |/7

x=10

Answer:

Erin will pay a total of $21.196 in shipping and handling fees.

Step-by-step explanation:

To calculate the shipping and handling fees, we first need to find 20% of the price of the trampoline. Since 20% is the same as 0.20, we can multiply the price of the trampoline by 0.20 to find the shipping and handling fees. If the trampoline costs $105.98, then the shipping and handling fees would be $105.98 * 0.20 = $<<105.98*0.20=21.196>>21.196.

There are 16 ounces in a pound.

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

The equation y' = x + y + 1  is not seperable. Therefore the statement is false.

In mathematics, an ordinary differential equation (also known as an ODE) is an equation made up of one or more functions of a single independent variable and its derivatives. A function having one or more derivatives is a component of a differential equation.

Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

If you can express a differential equation as y′=f(x)g(y), where f(x) is only a function of x and g(y) is only a function of y, then the problem is separable. Here, it is not the situation.

But we are not limited to solving separable differential equations. We frequently use integrating factors to solve linear first-order differential equations, such as this one. Using the product rule, multiply your differential equation by an integrating factor—in this example, e—and you get (eyy)′=eyy+eyy′=eyx,

which you may integrate to get your differential equation's solution. Finding integrating factors for generic linear first-order differential equations of the type y′+p(x)y=q may be done in a general way (x).

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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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The value of x that makes the expressions equivalent is 8

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

4(x-5)= 32-20

Distribute the 4

4x-20=12

4x= 12+20 = 32

x= 32/4 = 8

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Answer:

(-2^6) is 64, which is positive.

Step-by-step explanation:

To write -2^6 as repeated multiplication, we can write it as (-2)(-2)(-2)(-2)(-2)*(-2). To evaluate this expression, we can compute it as follows:

(-2)(-2)(-2)(-2)(-2)(-2)

= ((-2)(-2)(-2)(-2)(-2))(-2)

= ((((-2)(-2)(-2)(-2))(-2))(-2)

= (((((-2)(-2)(-2))(-2))(-2))(-2)

= (((((-2)(-2))(-2))(-2))(-2))(-2)

= (((((-2)(-2))(-2))(-2))(-2))(-2)

= (((-2)(-2)(-2))(-2))(-2)(-2)

= (((-2)(-2)(-2))(-2))(-2)(-2)

= ((-2)(-2))(-2)(-2)(-2)(-2)

= (-2)(-2)(-2)(-2)(-2)(-2)

= 64

Therefore, the result of (-2^6) is 64, which is positive.

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

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

A raw score is the actual number of correct answers a person gets on a test, without any adjustment for factors such as difficulty or time. For example, if a student takes a test with 10 questions and answers 8 correctly, their raw score would be 8 out of 10.

A raw score is the actual number of correct answers a person gets on a test, without any adjustment for factors such as difficulty or time. This means that the raw score is not adjusted or changed in any way.

For example, if a student takes a test with 10 questions and answers 8 correctly, their raw score would be 8 out of 10. This means that the student answered 8 out of the 10 questions correctly, without any adjustment for difficulty or time.

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(a) There are 10 vertical rise per step.

(b) There are 58 steps needed to climb from road level to the 2nd floor.

What is angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

(a) First to find the vertical rise per step.

x = 13 x tan(37)

x = 9.80

x ≈ 10

Hence, there are 10 vertical rise per step.

(b) Now to find number of steps needed to climb from road level to the 2nd floor.

The total elevation = 24 + 24 = 48 feet

Vertical rise of each step = 10

To convert 48 feet into inches

⇒  48 x 12 = 576 inches

So, the number of steps = 576 / 10 = 57.6 ≈ 58

Hence, there are 58 steps needed to climb from road level to the 2nd floor.

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On a test with a range of 110–410, these students received a mean score of 370 and a standard deviation of 50. What range would roughly 95% of the students' scores fall into, presuming a mound-shaped and symmetric distribution.

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling. Categorical and numeric variables are the two basic types of variables that can be categorized.

Answer:

This equation does not have the same solution as the original equation.

In conclusion, equations 1 and 2 have the same solution as the original equation (2.3p – 10.1 = 6.5p – 4 – 0.01p). Equations 3, 4, and 5 do not have the same solution.

Step-by-step explanation:

2.3p – 10.1 = 6.4p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.4p + 2.3p = -4 + 10.1

Combining like terms, we have:

-4.1p = 6.1

Dividing both sides by -4.1, we get:

p = -1.49

This equation has the same solution as the original equation.

2.3p – 10.1 = 6.49p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.49p + 2.3p = -4 + 10.1

Combining like terms, we have:

-4.19p = 6.1

Dividing both sides by -4.19, we get:

p = -1.46

This equation has the same solution as the original equation.

230p – 1010 = 650p – 400 – p

This equation does not have the same solution as the original equation.

23p – 101 = 65p – 40 – p

This equation does not have the same solution as the original equation.

2.3p – 14.1 = 6.4p – 4

Using the commutative property of addition, we can rearrange the terms on the left-hand side of the equation to get:

-6.4p + 2.3p = -4 + 14.1

Combining like terms, we have:

-4.1p = 10.1

Dividing both sides by -4.1, we get:

p = -2.47

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

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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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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