1) Work out the area and the perimeter of the shape below.
10 cm
12 cm
4 cm
Diagram NOT
accurately dr

The y-intercept of f(x) is equal to the y-intercept of g(x).

the y-coordinate of a point on a surface, curve, or line where they cross the y-axis.

Finding the value of y at x=0 will help you locate the y-intercept on a graph. The graph's intersection with the y-axis occurs here.

When the slope of the line being studied is known, and the provided point is also the y - intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B is used in the equation to indicate the y value of the y intercept point.

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The actual area of the apartment's living room is 10 [tex]m^{2}[/tex]

Given

Room is in the shape of a rectangle

Length of the room  (L)= 10 cm

Width of the room    (W) = 4 cm

Also the scale of floor plan is 2 cm for every 1 meter

Initially the are of the living room = area of rectangle

Area of the rectangle = length × width

                                   = 10 × 40

                                   = 40  [tex]cm^{2}[/tex]

To find actual floor area we need to scale the dimensions

Since 2cm = 1 m

10cm = 5m and 4 cm = 2m

Now calculating the actual area

Area = length × width

        = 5×2

        =10 [tex]m^{2}[/tex]

Hence the actual area of the living room is 10 [tex]m^{2}[/tex]

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Answer:

y= 3/2 x + -4

Step-by-step explanation:

-4 Is the y intercept (the vertical axis)
the 3/2 is the rise over run of the line (how many up over how many across). It's positive because of the slope up to the right.

Answer:

x=-4.5 x=-0.5

y=-1

vertex=-2

Answer:

Positive

Step-by-step explanation:

Below sea level would be negative and at sea level would be zero.

The proportional relationship that models this situation is given by:

y = 16.99x, 0 ≤ x ≤ 12.

In a direct proportional relationship, the output variable y is found as the multiplication as the multiplication of the constant k by the input variable x, according to the following rule:

y = kx

In the context of this problem, the input variable and the output variable are given as follows:

The monthly cost for the first 12 months is of $16.99, hence the constant is given as follows:

k = 16.99.

Considering the given domain, the relationship is modeled by the following equation:

y = 16.99x, 0 ≤ x ≤ 12.

The missing information is that for the first 12 months, the monthly cost of the plan is of $16.99.

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The percentage of students that use other means to travel school is  24%

Percentage is the ratio of  the number for which you want to find  percentage to the total number with which you want to compare or out of and multiply this ratio with 100.

percentage = (part / whole) ×100

Given that a school has 825 total students.

Percentage of students travelling by car = 20%

Percentage of students travelling by bus = 48%

Percentage of students travelling by bicycle = 8%

Number of students travelling by car = 20% of 825 = (20/100)×825 = 165

Number of students travelling by bus = 48% of 825

= (48/100)×825 = 396

Number of students travelling by bus  = 8% of 825 = (8/100)×825 = 66

Number of students travelling by other means = 825-165-396-66 = 198

Therefore, the Percentage of students travelling by other means  = (198/825) ×100 = 24%

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Assume √2 is rational, so

√2 = p/q

for some relatively prime integers p,q - meaning we can't reduce p/q any further - and q ≠ 0.

Then

p = √2 q

and squaring both sides gives

p² = 2q²

This tells us that p² is even, so 2 divides p². But if 2 divides p², it must also divide p, since p is a square number. So p = 2r for some integer r, and we have

(2r)² = 2q²

4r² = 2q²

2r² = q²

We're in the same situation as before - 2 divides q², so 2 divides q. Both p and q are thus divisible by 2, but this contradicts our assumption that p and q are relatively prime, which means √2 cannot be expressed as a rational number p/q. Therefore √2 is irrational.

What you've written in your proof is technically correct, but it doesn't help in the irrationality proof.

Answer:

See below

Step-by-step explanation:

y  =  -(x-1)^2 +4       Expand  R side

y = - ( x^2 -2x+1) + 4

y = -x^2 +2x -1  + 4

y = -x^2 + 2x + 3          a = -1     b = 2    c   = 3  

He used 647.75 square meters of wrapping paper to wrap the gift.

According to the question,

We have the following information:

We have a figure made of 2 same triangles and 3 rectangles with different measurements.

Area of triangle = 1/2 * base*height

Area of triangle = (1*7*14)/2

Area of triangle = 49 [tex]m^{2}[/tex]

Now, the area of another same triangle will also be 49 [tex]m^{2}[/tex].

Now, we have:

Area of upper rectangle = length*breadth

Area of upper rectangle = 15*14

Area of upper rectangle = 210 [tex]m^{2}[/tex]

Area of middle rectangle = length*breadth

Area of middle rectangle = 15*7

Area of middle rectangle = 105 [tex]m^{2}[/tex]

Area of lower rectangle = length*breadth

Area of lower rectangle = 15.65*15

Area of lower rectangle = 234.75 [tex]m^{2}[/tex]

Now, the area of the wrapping paper will be the sum of all of these areas.

Area of paper = Area of 2 triangles + area of upper rectangle + area of middle rectangle + area of lower rectangle

Area of paper = 49+49+210+105+234.75

Area of paper = 647.75 [tex]m^{2}[/tex]

Hence, the area of wrapping paper is 647.75 [tex]m^{2}[/tex].

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The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).

The value for which the line is a tangent is k = 4.

The coordinates of the point where the line touches the curves is point of tangency = ( 1/2 , 2).

What is tangent?

Tangents in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.

Given equations in the question:

y = kx² + 1  

y = kx

Equating y

kx² + 1   = kx

kx² -kx  + 1 =  0

This is Quadratic equation is of the form ax²+bx+c=0  where a  , b and c are real also  a≠0.

D =  b²-4ac is called discriminant.

and we know that,

D >0 roots are real and distinct

D =0 roots are real and equal

D < 0 roots are imaginary ( not real ) and different

For no common solution  D < 0

For tangent  D = 0

so,

kx² -kx  + 1 =  0

D = (-k)² - 4k  = k² - 4k = k(k - 4)

k(k - 4) < 0

if  0 < k < 4

Hence values of k for which the curve and the line have no common points is k ∈ (0 , 4).

for tangent

k(k - 4)  = 0

k is non zero

Hence k = 4

After putting the value of k, given equations are:

y = 4x² + 1  

y = 4x

solving these equations to get value of x and y:

4x² + 1   = 4x

4x² - 4x + 1 = 0

(2x - 1)² = 0

x = 1/2

y = 2

Point of tangency = ( 1/2 , 2)

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They are similar because they have the same slope the equation is

y = -2/3x + 531

What is in slope-intercept form?

changing 2x+3y=1470 to slope intercept form is solving for y

minus 2x both sides and divide by 3

y = -2/3x + 490

the slope is -2/3

the y intercept is y=490 or the point (0,490)

to graph it, I would start at the origin and go up 490 units on the y axis and put a point there

then go -2 units up (2 down) and 3 to the right and put a point there

then connect the 2 points with a line

in function notation, replace y with f(x) to get

y = -2/3x + 490

graph below

intercepts labeled

2x+3y=1593

they are similar because they have the same slope

the equation is  y = -2/3x + 531

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Answer:

Must be less than 12.15 dm

Step-by-step explanation:

the answer in scientific notation rounding to 2 decimal places is given by 68490.98

What is 6.849 times ten to the fourth power minus 2.329 times ten to the negative second power express the answer in scientific notation rounding to 2 decimal places.

6.849 *(10)^4=6.849* 10000=68490

2.329*(10)^-2= 0.02329

according to the question

6.849 times ten to the fourth power minus 2.329 times ten to the negative second power

therefore 68490-0.02329

           =68489.9767

round to 2 decimal

the answer in scientific notation rounding to 2 decimal places is given by 68490.98

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The number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.

What is an integer ?

Integer is the collection of whole numbers and negative numbers. It does not include the fractional part.

It is given that square root of a decimal number is 9.2371 and we have to find out that the number lies between which 2 integers.

We know that the integer 9 is less than 9.2371 , so the square of 9 will be :

9² = 81

And

The square of next integer 10 is equal to 100.

The square of 9.2371 will be equal to :

= (9.2371)²

= 85.32

So , the number is 85.32 and it lies between 2 integers which are 81 and 100.

Therefore , the number square root of which is 9.2371 is equal to 85.32 and it lies between two integers which are 81 and 100.

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Answer:

f(x) = -3x + 4

Step-by-step explanation:

Plug domain into each function and see if it matches any values in the range.

Answer:

the answer is 101 !!!

There's isn't nothing strange your just over thinking it!

Given Data:

The initial investment is: P=$100

The total period of investment is: t=3

The annual interest is: 6%.

For the simple interest, the expression to calculate the interest in t years is,

Here r is in percentage.

Substitute known values in the above expression.

Thus, the total intrest for 3 years will be $18.

The value of x is approximately 5.4 when x^3 -10x = 100

How to solve the equation?

The equation is given as:

x^3 -10x = 100

Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100

After several attempts, we have:

x = 5.4 (approximately)

Substitute 5.4 for x in x^3 -10x = 100

5.4^3 -10 * 5.4 = 100

Evaluate

103.5 = 100

Approximate

100 = 100This means that x is approximately 5.4 when x^3 -10x = 100

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Answer:

1, -1 and 2

Step-by-step explanation:

The zeros of the given polynomial function are 1, -1 and 2

Given the polynomial function

First, we need to assume a value of x to check if it will give us zero after substituting:

Assuming x = 1

Since f(1) =0, hence x - 1 is a factor

Dividing x - 1 by the given polynomial function, we will have:

Equating the result to zero

x + 1 = 0 and x - 2 = 0

x = -1 and 2

Hence the zeros of the given polynomial function are 1, -1 and 2

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Answer:4

Step-by-step explanation:

image dimension = 24 by 6 feet

preimage dimension = 32 by 8 feet

so 24/6 = 32/8 = 4

scale factor = 4

The population in the year 2015 is 31296.

In 1995 the population was 7824. It was found that the population gets double every 10 years.

We have to find the population in the year 2015.

Rate = 200% = 2

Time =( 2015 - 1995) / 10

        = 20/10

        = 2

The population in 2015 = population in 1995 ×[tex]rate^{time}[/tex]

                                       = 7824 × [tex]2^{2}[/tex]

                                       = 7824 × 4

                                       = 31296

Therefore the population in the year 2015 is 31296.

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The goalpost is 15.13 meters tall which is labeled as X in the figure which has been attached below.

She walks 13.45 meters away from the goalpost, then places a mirror flat on the ground with an X in the center. She next walks 1.2 meters to the opposite side of the mirror, where she can easily see the top of the goalpost depicted in the X. Her partner determines that the distance between her eyes and the ground is 1.35 meters.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

As per the given information, the figure has been attached below.

Set up the proportional and solve for x

1.2 : 13.45 = 1.35 : x

⇒ 1.2 / 13.45 = 1.35 / x

Cross multiplication, and we get

⇒ 1.2x  = 1.35 × 13.45

Divided by 1.2 into both sides of the above equation,

⇒ x = (1.35 × 13.45) / 1.2

⇒ x = 15.13

Therefore, the goalpost is 15.13 meters tall.

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Answer:

This is your graph to the following equation f(x) = 1/4(x) - 7

By ASA or SAS the triangles can be proves congruent.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.

As, from the given figure we can find some equal parts.

First we have two triangles named KOE and LOB

Now, in both triangles

EO = OB  ( given)

<KOE =< LOB (Vertically opposite angle)

Now, we have one side and one angle congruent.

There are two possibilities now either we have another pair of side to make SAS Congruence or we have another angle congruent to make ASA congruence.

So, either KO = OL or

<LBO = <OKE.

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Answer:

1.264×10^-5

Step-by-step explanation:

If you are allowed to use a calculator, it will totally do this question for you. Check mode for Sci Not or use the ^ or EE button.

If no calculator allowed, factor out the 10^-6 and add the numbers. Change back to Scientific Notation and fix the first number. It has to have one digit to the left of the decimal. Adjust the exponent to account for changing 12.64 to 1.264 See image.

Answer:

7

Step-by-step explanation:

slope = rise/run = (difference in y)/(difference in x)

First, we find a difference in y.

Subtract any two values of y.

For example: 35 - 14 = 21

Now we find the corresponding difference in x.

Now subtract the x values corresponding to those y values in the same order.

-1 in x corresponds to 35 in y.

-4 in x corresponds to 14 in y.

That means your difference in x is the subtraction -1 - (-4) = -1 + 4 = 3

The difference in y is 21.

The difference in x is 3.

slope = (difference in y)/(difference in x) = 21/3 = 7

Answer: 7