Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-angled triangle. Give your answer in centimetres (cm) to 1 d.p. 4.8 cm 2 cm Not drawn accurately​

The scale factor of the dilation is the ratio of the lengths of the corresponding sides of the two triangles. Since triangle ABC and triangle A'B'C' both have side lengths of AB, BC, and CA, the scale factor is 1.

1. Calculate the length of the sides of triangle ABC:

AB = length of side AB of triangle ABC

BC = length of side BC of triangle ABC

CA = length of side CA of triangle ABC

2. Calculate the length of the sides of triangle A'B'C':

A'B' = length of side A'B' of triangle A'B'C'

B'C' = length of side B'C' of triangle A'B'C'

C'A' = length of side C'A' of triangle A'B'C'

3. Calculate the scale factor of the dilation:

Scale factor = (AB/A'B') x (BC/B'C') x (CA/C'A')

= (length of side AB of triangle ABC / length of side A'B' of triangle A'B'C')

x (length of side BC of triangle ABC / length of side B'C' of triangle A'B'C')

x (length of side CA of triangle ABC / length of side C'A' of triangle A'B'C')

= 1 x 1 x 1

= 1

Therefore, the scale factor of the dilation is 1.

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The area enclosed by the figure is 6425 square meters.

The area enclosed by the figure is made up of a square of 50m x 50m = 2500 m^2 There are four semicircles attached to each side of the square.

Each semicircle has a radius of 25m, so the area of each semicircle is,

(1/2) * pi * 25^2

= (1/2) * 3.14 * 625 m^2.

The total area of the four semicircles is,

4 * (1/2) * 3.14 * 625 m^2

= 2 * 3.14 * 625 m^2

= 3925 m^2

To find the total area enclosed by the figure, add the area of the square to the area of the semicircles:

2500 m^2 + 2 * 3.14 * 625 m^2

= 2500 m^2 + 3950 m^2

= 6425 m^2.

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The number of dimes are 2 and number of nickels are 8 according to the sum and number of coins.

Let the number of dimes be x. The number of nickels will be 4x. Also, as per the known fact, the value of dimes is 0.1 and value of nickels is 0.05. Keeping the values in formula -

0.05x + 0.1×4x = 0.90

0.05x + 0.4x = 0.90

Performing addition on Left Hand Side of the equation

0.45x = 0.9

Rewriting the equation

x = 0.9/0.45

Performing division on Right Hand Side of the equation

x = 2

Number of dimes = 2

Number of nickels = 4×2

Performing multiplication

Number of nickels = 8

Thus, there 2 dimes and 8 nickles.

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The rule of transformation will be (x,y) → (8x, 8y). Then the correct option is D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

Square UVWX is dilated by a scale factor of 8.

Then the rule of transformation is given as,

(x,y) → 8(x, y)

(x,y) → (8x, 8y)

The rule of transformation will be (x,y) → (8x, 8y). Then the correct option is D.

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The equation must satisfies the Kent calculation is k² - 8k + 12 = 0

The term equation in math is called as a mathematical expression that contains an equals symbol.

Here we have given that Kent multiplies both sides of the equation below by an expression.

And then he moves all the terms to one side of the equal sign in the resulting equation.

Here we have the given equation is

=> k+12/k= 8

When we multiply both sides by k.

=> k² + 12 = 8k

Now we have to subtract 8k from both sides to move all the terms to one side of the equal sign then we get

=> k² + 12 - 8k = 0

Hence the required equation is k2 - 8k + 12 = 0.

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The width of the tabletop is t feet when its length is 12 feet.

In contrast to width, which is used to describe how wide an object is, length simply states how long something is.

The term "width" is also used to refer to "breadth." It is the distance measured across a specific shape or object, such as a rectangle, whose lengths form right angles with the sides.

In contrast to the measurement of the area of the rectangle, which is a product of two units, the length and width. Length and width are two fundamental one-dimensional units. Today, a variety of length units are in use. The metre in SI units of measurement is the most fundamental of all.

Given that:

The length of a larger tabletop is 2 more than 2 times its width

l = 2(w) + 2

The length is 12

12 = 2(w) + 2

12 - 2 = 2w

10 = 2w

w = 10/2

w = 5

Thus, the width of the tabletop is t feet when its length is 12 feet.

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Full question:

The width of a larger tabletop is 2 more than 2 times its length. The length of the larger tabletop is 12 feet. What is its width, x?

The expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as:

[tex]P(E) = \frac{Number of Favourable Cases}{Number of Total Cases} = \frac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as:

[tex]P(X = x) = ^nC_{x} p^{x} (1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\Var(X) = np(1-p)[/tex]

Each of the 800 spins are independent in terms of their result from each other.

Each spin ends up either in shaded region (call it success), or non-shaded region(failure).

P(success) = P(A spin landing in shaded region) = 4/5 (as there are total 5 partition of spinner possible (assuming no other outcome possible), and that there are 4 shaded regions (favorable elementary events).

If we take X = number of successes in those 800 spins, then:

[tex]X[/tex] ~ [tex]B (n=800, p = 4/5=0.8)[/tex]

The expected value of X is:

[tex]E(X) = np = 800 * 0.8 = 640[/tex]

Thus, the expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640.

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To write an absolute value equation with two solutions, we need to separate the equation into two cases: one for the positive value and one for the negative value.

The general form of an absolute value equation is |x - h| = k, where h is the value that the variable is being compared to and k is the value that the absolute value is equal to.

For example, to write an absolute value equation with two solutions that equal 3, we can separate the equation into two cases:

Case 1: x - h = k

x - 3 = 3

x = 6

Case 2: x - h = -k

x - 3 = -3

x = 0

So the equation is |x - 3| = 3 with solutions x = 6 and x = 0.

Another example is |x+2| = 4. The solutions to this equation can be found by setting x+2 = 4 and x+2 = -4.

x+2 = 4 => x = 2

x+2 = -4 => x = -6

So the equation |x+2| = 4 has solutions x = 2 and x = -6

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For given circle value of arc KT will be 147m.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now,

as for a given circle when the vertex of angle falls outside of circle

then (larger arc-smaller arc/2)=angle

Therefore,  55=(KT-37)/2

KT=110+37

KT=147m

Hence,

              Value of arc KT will be 147m.

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The cost of 250 kg of coal is 500 dollars.

One tonne of coal cost $2000. The cost of 250kg of the same coal can be found as follows:

Let's convert the mass of the coal in kilograms to tonnes.

Hence,

1 kilogram = 0.001 tonnes

250 kilogram = ?

cross multiply

mass of the coal in tonnes = 0.001 × 250

mass of the coal in tonnes = 0.25 tonnes

Hence,

1 tonne = 2000 dollars

0.25 tones = ?

cross multiply

mass of 250 kg of coal = 0.25 × 2000

Therefore,

mass of 250 kg of coal = 500 dollars

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Answer:

Option B

Step-by-step explanation:

Hi!

y = m x + c is the slope intercept form of a line whose slope is m and

y intercept is c. Hence

y=x/2+5

LCM

y=x+10/2

2y=x+10

x-2y+10=o

Required equation of the line is x - 2 y +10 = 0

keep the highest averaging do no harm imagine that your instructor chose to use the do no harm scoring method in grade it now mode. so My final score is 5/10

What is Mode?

In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.

For a limited number of observations, the mode is simple to find. There could be one mode, several modes, or none at all for a given collection of values.

When we use highest scoring method in Mode, we keep the Highest will give the highest score if the scores are different.

So that the final score is 5/10

because average of 2/10+3/10+10/10  /3= 5/10

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The value of the given function f(x) and g(x) is [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere and are crucial for constructing physical relationships.

The given functions are:

[tex]f(x) = 5x^2 - 3 \\\\g(x) = x^2 -4x-8[/tex]

(f - g)(x) is equivalent to the following:

(f - g)(x) = f(x) - g(x)

[tex]f(x) - g(x) = 5x^2 - 3 - x^2 +4x+8\\\\f(x) - g(x) = 4x^2 +4x+5[/tex]

Hence, the value of [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

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Answer: If you mean simplify then here: 20d+5f+5h

Step-by-step explanation:

Use distributive property to remove the parentheses.

20d+5f+5h

Please give brainliest

Answer:

To solve this problem, we will use the following steps:

Step 1: Nick and Chloe paddled downstream at an average speed of 12 km/h and back upstream at an average rate of 8 km/h. So, we can find the total distance they travelled by finding the distance they travelled downstream plus the distance they travelled upstream.

Step 2: We know that the total trip took 7 hours and they took a 45-minute lunch break. To convert 45 minutes to hours, we can divide 45 by 60, so 45/60 = 0.75 hours.

Step 3: We can then subtract the time they took for lunch break from the total trip time, so 7 - 0.75 = 6.25 hours

Step 4: To find the distance travelled downstream, we can multiply the time spent traveling downstream by the speed of the canoe, so 6.25 x 12 = 75 km

Step 5: To find the distance travelled upstream, we can multiply the time spent traveling upstream by the speed of the canoe, so 6.25 x 8 = 50 km

Step 6: We can then add the distance travelled downstream and the distance travelled upstream to find the total distance travelled, so 75 + 50 = 125 km

Final Answer: Nick and Chloe travelled a total distance of 125 km.

Answer:

1. To find the gradient of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.

a) To find the gradient of (x+7)/(y-2) = 0, we can first rewrite the equation as y = (2x+14)/(x+7). To find the slope, we can take the derivative of y with respect to x. We get the slope or the gradient of the line as m = 2/(x+7).

b) To find the gradient of the line through (p,5) and (6,2p), we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and solve for m.

y - 5 = m(x - p)

2p - 5 = m(6 - p)

2p - 5 = 6m - mp

mp + 6m = 2p + 5

m(p+6) = 2p + 5

m = (2p+5)/(p+6)

2. To find the equation of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.

a) To find the equation of the line with a gradient of 3, passing through (0,5), we can substitute the values into the slope-intercept form.

y = 3x + b

5 = 3(0) + b

b = 5

The equation of the line is y = 3x + 5

3. To find the value of p, if the gradient of the line joining (-1,p) and (p, 4) is 2/3, we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and the gradient, and solve for p.

y - p = (2/3)(x - (-1))

4 - p = (2/3)(p - (-1))

4 - p = (2/3)p + (2/3)

(2/3)p - 4 + p = (2/3)

p = 6

Final Answer: The value of p is 6.

If set of ordered pairs (1,8.50) , (3,25.50) , (5,42.50) , (6,51) , (7,59.50) represents cost of tickets for school play , it means that the function that represents the relationship between the number of tickets and the cost for ticket is  [tex]y = 8.5\times x[/tex] .

The Ordered Pairs are given as : (1,8.50) , (3,25.50) , (5,42.50) , (6,51) , (7,59.50) ;

the input represents the number of ticket and

the output represents the total cost of number of tickets ,

So , the domain is = { 1 , 3 , 5 , 6 , 7 } ;

and the range for this function is = {8.50 , 25.50 , 42.50 , 51 , 59.50 } ;

Considering the first pair ,

when the number of ticket is 1 , then the cost is 8.50 ,

for second pair when the number of ticket is 3 , then the cost is 25.50 ;

So , we can say that the cost of 1 ticket is = 8.50 ;

if x represents number of tickets , and y represents the cost for that tickets , then  function that can represent given situation is [tex]y = 8.5\times x[/tex] .

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Answer:

Step-by-step explanation:

52.2 : 1 = x : 1.5

x = 52.2 × 1.5 : 1

78.3 miles

Answer:

Step-by-step explanation:

A polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 1, 3 is (x- -2)(x-1)(x-3) = x^3 - 6x^2 + 11x - 6

If the two circle centered at P and Q with radius 10 and 8 respectively , and if the common external tangent intersects line PQ at R , then the length of QR is 72  .

The radius of the circle that is centered at P is = 10 ;

the radius of circle that is centered at Q is = 8 ;

the common external tangent intersects the line PQ at R ,

Let XYR be external tangent with X on the Circle with center P , and at point Y on circle with center Q .

we extend , the line PQ to point R ,

we get , that triangle XPR is similar to triangle YQR ,

it means that , [tex]\frac{RQ}{RP} =\frac{QY}{PX}[/tex] ;

let the length of RQ be = x , then

length of RP will be = [tex]x+18[/tex]  ;

we get ; [tex]\frac{x}{x+18} =\frac{8}{10}[/tex] ;

⇒ [tex]10x=8x+144[/tex] ;

⇒ [tex]2x=144[/tex] ;

⇒ [tex]x=72[/tex] .

Therefore , the length of QR is 72 .

The given question is incomplete , the complete question is

A circle centered at P with radius 10 and a circle centered at Q with radius 8 are externally tangent. A common external tangent intersects line PQ at R. Find QR .

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Answer:

(6, 2 )

Step-by-step explanation:

3x - 2y = 14 → (1)

5x + 6y = 42 → (2)

multiply (1) through by - 1

- 3x + 2y = - 14 ( add 3x to both sides )

2y = 3x - 14

substitute 2y = 3x - 14 into (2)

5x + 3(2y) = 42

5x + 3(3x - 14) = 42

5x + 9x - 42 = 42

14x - 42 = 42 ( add 42 to both sides )

14x = 84 ( divide both sides by 14 )

x = 6

substitute x = 6 into either of the 2 equations and solve for y

substituting into (2)

5(6) + 6y = 42

30 + 6y = 42 ( subtract 30 from both sides )

6y = 12 ( divide both sides by 6 )

y = 2

solution is (6, 2 )

The total amount deposited is $300.

percentage, a relative value indicating hundredth parts of any quantity.

Given that rate of interest for 5 years is 2.5 and the interest is 2400

We have to find the  total amount deposited.

Simple interest=PNR/100

Principal P=2400Rs

Rate =2.5 per annum

N=time in year=5

Now plu in the value in the formula.

simple Interest=2400×2.5×5/100

=300

Hence, 300 is the amount which is deposited.

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There are a few ways to tell if a dataset contains outliers, one of which is by using summary statistics.

Outliers are data points that fall far outside of the main body of a dataset. They can have a significant impact on the overall summary statistics of a dataset, such as the mean and standard deviation.

Given the summary statistics below for the size of a sample of automobile engines:

Mean: 2.5

Median: 2.5

Mode: 2.5

Standard deviation: 0.5

We can tell that there are no outliers in the data set because the mean, median, and mode are all equal. This indicates that the values in the dataset are tightly clustered around a central value, which is a good indication that there are no outliers. Additionally, the standard deviation is relatively small, which also suggests that the values in the dataset are not spread out very much, again indicating that there are no outliers.

Another approach is using the interquartile range (IQR). This can be calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3) of a dataset. Values that fall outside of the range of 1.5*IQR below the first quartile (Q1) or above the 3rd quartile (Q3) are considered outliers.

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Significant figures are in this measurement 1.090

In a number, to determine the number of significant figures following three rules are used:  

The digits which are non-zero are always significant.

Any zeros between two digits which are non-zero are significant.

In the decimal portion, trailing zeros are significant.  

Significant figures = Numbers that carry meaning in the measurements of a number.

The number is 1.090, it has two non-zero digits, 1 zero in between two non-zero digit and one trailing zero thus, all of them are significant figures.

Therefore, it has 4 significant figures : 1.090

Significant figures are in this measurement 1.090

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The polyhedron with 10 vertices and 7 faces has 15 edges.

What is polyhedron?

A polyhedron is a three-dimensional object or solid that has flat faces, straight edges, and sharp corners or vertices. It is a geometric shape that is bounded by a finite number of polygons, which are shapes with straight sides.

Based on the Euler's formula for polyhedra, which states that the number of vertices plus the number of faces minus the number of edges is always equal to 2, we can solve for the number of edges:

10 (vertices) + 7 (faces) - E (edges) = 2

Simplifying the equation:

10 + 7 - E = 2

17 - E = 2

E = 17 - 2

E = 15

Therefore, the polyhedron with 10 vertices and 7 faces has 13 edges.

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Answer: 10.5 miles

Step-by-step explanation:

Answer: 8 shirts for 128 shekels

Step-by-step explanation:

First, we can set up fractions and simplify to find the cost of one shirt.

5shirts/100shekels = 1shirt/20 shekels

8 shirts/128 shekels = 1shirt/16 shekels

Ultimately, whichever cost per shirt is lower is going to be the better buy. Since 16shekels/shirt is less than 20shekels/shirt, you are ultimately buying more shirts for a lower cost. Hope this helps

To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.

1. Identify the two numbers you want to compare as the numerator and denominator

2. Divide the numerator by the denominator

3. The resulting answer is the ratio of the two numbers

To find a ratio in 8th grade math, divide the numerator by the denominator to get the ratio.

To find a ratio in 8th grade math, you need to divide one number by another number to get the ratio. For example, if you want to find the ratio of 10 to 8, you would divide 10 by 8 to get a ratio of 1.25.

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