Similar shapes and scale drawings worksheet

(a) The function in standard form is f(x) = -2x² + 4x + 5.

(b) The height of the ball when it is thrown is 5 feet.

(c) The horizontal distance from the point where the ball is thrown to the highest point that the ball reaches is 1 foot.

To write the function in standard form, we need to expand the square and simplify the expression:

f(x) = -2(x - 1)² + 7

f(x) = -2(x² - 2x + 1) + 7

f(x) = -2x² + 4x - 2 + 7

f(x) = -2x² + 4x + 5

B. The height of the ball when it is thrown is the y-intercept of the function, which occurs when x = 0. So we can find the height by plugging x = 0 into the function:

f(0) = -2(0)² + 4(0) + 5

f(0) = 5

C. The highest point that the ball reaches is the vertex of the parabola, which occurs at x = 1 (from the given vertex form). To find the height of this point, we can plug x = 1 into the vertex form of the function:

f(1) = -2(1 - 1)² + 7

f(1) = -2(0) + 7

f(1) = 7

Therefore, the highest point that the ball reaches is 7 feet above the ground. The horizontal distance from the point where the ball is thrown to this point is the distance between the point (0,5) and the vertex (1,7), which is 1 unit.

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Answer:

29.68

Step-by-step explanation:

If you are rounding to the hundredth place, you take the number in the hundredth place and round it. If it is less than five, for example, if you were rounding 29.674 then it would be 29.67 because 4 is not 5 or more. With 29.675 you will round to 29.68. A saying to remember is, five or above, give it a shove.

The solution is x^-5y^3 = y^3/x^5.

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given that,

x^-5×y^3      

[ as, the power of x is negative 5, so, we make it positive 5 by dividing}

=1/x^5 * y^3

=y^3/x^5

Hence, The solution is x^-5y^3 = y^3/x^5.

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The value of x is 9.4 in the equation 8x−14+2x+10=90.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 8x−14+2x+10=90

Eight times of x minus forteen plus two times of x plus ten equal to ninety.

In the given equation x is the variable

Plus and minus are the operators.

Add the like terms

Ten times of x minus four equal to ninety

10x-4=90

Add 4 on both sides to cancel four on the left hand side.

10x-4+4=90+4

10x=94

Divide both sides by 10

x=94/10

Divide numerator and denominator by 10.

x=9.4

Hence, the value of x is 9.4 in the equation 8x−14+2x+10=90.

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The complete question

Solve the equation 8x−14+2x+10=90

A research question is an inquiry that a study or research project aims to resolve. Quantitative and Qualitative research questions are the components of questions.

Descriptive research questions are used to determine how the population of the study will react to one or more variables or to describe the factors that the study will evaluate. These questions typically begin with "what."

Comparative research questions aim to identify differences between two or more groups for an outcome variable. These inquiries could possibly be the cause. A comparison between two groups, one in which a certain variable is present and the other in which it is not, may be made, for instance.

Relationship research themes aim to find patterns and interactions between two or more variables. The phrases "association" and "trends," as well as dependent and independent variables, are commonly used in these enquiries.

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Answer: Let's call the speed of the airplane in still air "x".

Since the airplane takes 7 hours to fly 2800 kilometers against the wind, its speed against the wind is 2800/7 = 400 km/hr.

Since the return trip with the wind takes only 4 hours, the speed of the wind must be 400 - x.

The total speed of the airplane on the return trip is x + (400 - x) = 400 km/hr.

So, we have:

400 = x + (400 - x)

Expanding the right side:

400 = 400

Therefore, x = 400 km/hr, which is the speed of the airplane in still air.

Step-by-step explanation:

60 s²t² is the lowest common multiple of 3st, 4s^2, 5t^2

LCM is known as the lowest common multiple. This is the smallest number that is a multiple of both of two numbers is called the least common multiple.

Given the terms 3st, 4s^2, 5t^2

Find the factors

3st = 3 * s * t

4s² = 4 * s * s

5t² = 5 * t * t

The LCM is calculated as thus:

LCM = (3*4*5) * s²t²

LCM = 60 s²t²

Hence the LCM of the terms 3st, 4s^2, 5t^2 is 60 s²t²

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Answer:

8 books

Step-by-step explanation:

On a box plot, there is a line in the middle that says where the median is. In this situation, the median is 8.

Answer:

483

Step-by-step explanation:

Answer:483

Step-by-step explanation:

69*7=483

Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.

Non occurrence patterns identifies the absence of events when detecting a pattern.

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Answer:

5=0.40x+3.50

He can get 3 extra ounces

Step-by-step explanation:

5.00-3.50=1.50 so an extra $1.50 to spend on extra ounces

1.50/0.40=3

0.40(3)+3.50= $4.70

So the most ounces he can get is 3

He will have $0.30 left

The equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).

The given expression is c² - 64.

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

1) The factorization of c² - 64 is as follows:

Now, factors of c² - 64 is c² - 8²=(c-8)(c+8)

2) 12y² -75 = 3 (4y²-25)

= 3((2y)²-5²)

= 3 (2y+5)(2y-5)   (∵ a²-b²=(a-b)(a + b))

3) 9y²-36 = 9(y²-4)

= 9(y²-2²)

= 9(y-2)(y+2)   (∵ a²-b²=(a-b)(a + b))

4) -x²+5x-4

= x²-5x+4

= x²-4x-x+4

= x(x-4)-1(x-4)   (∵ a²-b²=(a-b)(a + b))

= (x-4)(x-1)

5) ab²-b

=b(ab-1)

Therefore, the equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).

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To have a unique outfit for each day of the week, you would need at 3 pairs of pants and 3 shirts.

To have a unique outfit for a month you would need at 6 pairs of pants and 5 shirts.

To have a unique outfit for each day of the year, you would need 26 pairs of pants and 15 pairs of shirts.

To find the unique outfits, you need to have enough clothes to have a unique outfit made from those clothes.

There are 7 days in a week. If you had 3 pairs of pants and 3 shirts, the unique outfits would be :

= 3 x 3

= 9 unique outfits

For a month :

= 6 x 5

= 30 unique outfits

For a year :

= 26 x 15

= 390 unique outfits for 365 days

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Answer: 27

Step-by-step explanation: in order to find out the LCM, you have to list out the multiples of 9 ( 9: 9, 18, 27, 36, etc.) and 27 ( 27: 27, 54, etc). Then you find the least common multiple which in this case is 27.

The measure of the angle is 60 degrees. Option B

It is important to value of the angle, we have to take note of the following;

From the information given, we have that;

The angles 80,690 and x are on a straight line, that is, the sum of the angles is 180

This is represented as;

60 + 80 + x = 180

collect like terms

x = 180 - 140

substract the like terms

x = 60 degrees

Hence, the value is 60 degrees

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Answer: 737 miles

Step-by-step explanation:  335/5=x/11.

Cross Multiply and divide to get x=737

There were 65 more adults than students who bought tickets to the concert.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let the number of discounted student tickets sold be x.

Then the number of adult tickets sold is 10 more than twice x, which is 2x+10.

The total number of tickets sold is the sum of the student and adult tickets, which is x + (2x+10) = 3x+10.

We know that the total number of tickets sold is 175, so:

3x+10 = 175

Subtracting 10 from both sides gives:

3x = 165

Dividing by 3 gives:

x = 55

Thus, the number of discounted student tickets sold is 55, and the number of adult tickets sold is:

2x+10 = 2(55) + 10 = 120.

The number of adults who bought tickets is 120, and the number of students who bought tickets is 55.

difference = 120 - 55 = 65

Therefore, there were 65 more adults than students who bought tickets to the concert.

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The temperature 350°F is equivalent to 176.667°C. This is because the temperature in Fahrenheit can be converted to Celsius using the formula, °C = (°F - 32) / 1.8. Using this formula, 350°F - 32 = 318 and 318/1.8 = 176.667°C.

The relationship between Fahrenheit and Celsius scales is a linear one, meaning that for every degree increase in Fahrenheit, there is a corresponding increase of 1.8 degrees in Celsius. This means that if the temperature increases from 350°F to 351°F, then the corresponding temperature in Celsius would increase from 176.667°C to 178.472°C. The same formula can be used to convert Celsius to Fahrenheit, with the formula °F = (°C x 1.8) + 32. In this case, 176.667°C x 1.8 = 319.2 and 319.2 + 32 = 351.2°F, which is a close approximation of the original temperature of 350°F..

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Answer:

Step-by-step explanation:

1200

Answer:

$960

Step-by-step explanation:

September = 1000

20% * 1000 = 200

1000+200 = 1200

October = 1200

20% * 1200 = 240

1200-240 = 960

November = 960

$189.13

That's the correct answer On Ax

Answer:

  $189.13

Step-by-step explanation:

You want to know the interest saved if interest at 30.8% compounded monthly on a balance of $1400 is waived for 5 months.

The balance with interest compounded would be ...

  A = P(1 +r/12)^n

where P is the principal earning interest at annual rate r for n months.

The amount of interest earned in that time is ...

  I = P((1 +r/12)^n -1) = $1400(1 +0.308/12)^5 -1) ≈ $189.13

Hugo will save $189.13 in interest charges for the first 5 months.

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Answer:

b = - 12

Step-by-step explanation:

calculate the slope of the line passing through the 2 points and equate to [tex]\frac{1}{2}[/tex]

calculate the slope ( gradient ) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (b, 2 )

m = [tex]\frac{2-6}{b-(-4)}[/tex] = [tex]\frac{-4}{b+4}[/tex]

equating gives

[tex]\frac{-4}{b+4}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

b + 4 = - 8 ( subtract 4 from both sides )

b = - 12

Answer:

Step-by-step explanation:

f

Answer:

The Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function  f(x)=2x-5

What is a function?

A relation is a function if it has only One y-value for each x-value.

We have to find the domain and range of f(x)=2x-5

The domain of the expression is all real numbers except where the expression is undefined.

In this case, there is no real number that makes the expression undefined.

Interval Notation:(−∞,∞)

The range is the set of all valid y values.

Domain : {(−∞,∞), {x/x∈R}

Range : {(−∞,∞), {y/y∈R}

Hence, the Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function  f(x)=2x-5

Have a wonderful day! :-)

The distance between the points in simplest radical form is equal to 2√10 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (5 - 3)²]

Distance = √[6² + 2²]

Distance = √[36 + 4]

Distance = √40

Distance = 2√10 units.

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Answer: The equation y + 6 = 3/4 (x + 4) can be solved for y to find the corresponding graph:

First, isolate x by subtracting 4 from both sides:

y + 6 - 6 = 3/4 (x + 4) - 6

y = -6 + 3/4 (x + 4)

Next, isolate y by dividing both sides by 3/4:

y = -6 + 3/4 (x + 4) ÷ (3/4)

y = -6 + (x + 4)

y = x - 2 + 10

This equation represents a line with a slope of 1 and a y-intercept of 10 - 2 = 8. The graph of this line is a line that passes through the points (0, 8) and (1, 9).

Step-by-step explanation:

A unit of measurement equal to one thousand meters is called a kilometer.

The prefix "kilo" means one thousand, so a kilometer is a unit of length in the metric system that is equal to 1000 meters. Kilometers are commonly used to measure longer distances, such as the distance between cities or countries, or the length of a marathon race. In contrast, smaller distances may be measured in meters, centimeters, or millimeters, which are all smaller units of length in the metric system.

a metric measurement of length that is equal to 1,760 yards or 5,280 feet. A thousandth of a liter is the same as a metric unit of capacity. a length measurement in meters that is one-thousandth of a meter. a time interval that is frequently used and equates to 60 seconds and 1/60 of an hour.

The complete question is:-

What word goes with a unit of measurement equal to one thousand meters?

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The magnitude of acceleration of the car just before it reaches point C is -0.79 m/s^2.

The magnitude of acceleration of the car just before it reaches point C can be calculated using the given formula for acceleration, at= (-1/4t^1/2)m/s^2.

First, we need to determine the time it takes for the car to travel from point A to point C.

Since the speed of the car at point A is 25 m/s, and the speed at point C is 0 m/s, we can use the formula for speed, v=at, to find the time it takes for the car to travel from point A to point C.

Rearranging the formula, we get t=v/a.

Substituting the values for speed and acceleration, we get t=25/(-1/4t^1/2).

Solving for t, we get t^3/2 = -100.

Taking the square root of both sides, we get t=10 seconds.

Now, we can substitute the value of t back into the formula for acceleration to find the magnitude of acceleration just before the car reaches point C.

at= (-1/4t^1/2)m/s^2

= (-1/4)(10^1/2)m/s^2

= (-1/4)(3.16)m/s^2

= -0.79 m/s^2

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Answer:

the value of b is 3.

Step-by-step explanation:

The vertex of the graph of a parabola in the form y = a(x - h)^2 + k is given by (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.

So in this case, the vertex of the graph of y = -1(x - 2)^2 + 3 is (2, 3), and the value of b is 3.

Answer:

b=3

Step-by-step explanation:

[tex]y=a(x-h)^2+k\\y=-1(x-2)^2+3[/tex]

If we compare the vertex-form equation of a parabola to our given function, we can see the vertex is [tex](2,3)[/tex], which means that b=3.

Only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.

Neron Co. should report the gains from the fair value hedge related to instrument A in its income statement. This is because fair value hedges are used to offset changes in the fair value of a financial instrument, and any gains or losses from these hedges are recognized in income.

On the other hand, gains from the cash flow hedge related to instrument B should be reported in other comprehensive income, not in the income statement.

This is because cash flow hedges are used to offset changes in the cash flows of a financial instrument, and any gains or losses from these hedges are recognized in other comprehensive income until the hedged item affects income.

Therefore, only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.

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