The diagram shows a right-angled triangle.
14 cm
hcm
47°
What is the value of h?
Give your answer correct to 1 decimal place.

Step-by-step explanation:

Notice that KM = 0.5BC, KL = 0.5AC

and ML = 0.5AB. Therefore the perimeter of triangle KLM is half of the perimeter of triangle ABC. => 0.5 * 24cm = 12cm.

Each of the 3 purple triangles have perimeters which are 1/4 of the perimeter of triangle ABC. (Their vertices are midpoints of midpoints => 1/2 * 1/2)

Perimeter of 3 small purple triangles

= 3 * [24cm * (1/4)]

= 3 * 6cm = 18cm.

Hence Total perimeter of shaded parts

= 12cm + 18cm = 30cm.

Answer: [tex]\frac{7x-6}{6x}[/tex]

Step-by-step explanation:

The value of the equation is ( 7/6 ) - ( 1/x )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be = A

Now , the equation is

A = ( 5/3 ) - ( x + 2 ) / 2x

On simplifying the equation , we get

A = [ ( 5/3 ) ( 2x ) - ( 3 )( x + 2 ) ] / 2x ( 3 )

A = [ ( 10x) - 3x - 6 ] / 6x

A = ( 7x - 6 ) / 6x

On simplifying the equation , we get

A = ( 7/6 ) - ( 1/x )

Therefore , the value of A is ( 7/6 ) - ( 1/x )

Hence , The value of the equation is ( 7/6 ) - ( 1/x )

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Given:

The equation of a circle is

[tex]10y+x^2=-18+5x-y^2[/tex]

To find:

The center and radius of the given equation by completing the square.

Solution:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]            ...(i)

where, (h,k) is center and r is radius of the circle.

We have,

[tex]10y+x^2=-18+5x-y^2[/tex]

It can be written as

[tex](x^2-5x)+(y^2+10y)=-18[/tex]

[tex]\left(x^2-5x+\left(\dfrac{5}{2}\right)^2\right)+\left(y^2+10y+\left(\dfrac{10}{2}\right)^2\right)=-18+\left(\dfrac{5}{2}\right)^2+\left(\dfrac{10}{2}\right)^2[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+\left(y^2+10y+5^2\right)=-18+\dfrac{25}{4}+5^2[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=-18+\dfrac{25}{4}+25[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{-72+25+100}{4}[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{53}{4}[/tex]

[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\left(\dfrac{\sqrt{53}}{2}\right)^2[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]h=\dfrac{5}{2},k=-5,r=\dfrac{\sqrt{53}}{2}[/tex]

Therefore, the center is [tex]\left(\dfrac{5}{2},-5\right)[/tex] and the radius is [tex]\dfrac{\sqrt{53}}{2}[/tex] units.

Answer:

D

Step-by-step explanation:

It is D because the scuba diver was 35 m below the surface of the water at the start of the ascent. Meaning that the Y value is showing how deep the diver was in the water

Answer:

40 ounces ;

2.5 pounds

Step-by-step explanation:

Given that:

Number of ounces of food per day = 4 ounces

Number of days for which cats were fed = 10

The smallest bag that has enough food to feed the cats should be :

(ounces of food per day * Number of days)

(4 ounces * 10)

= 40 ounces

1 pound = 16 ounces

40 ounces = 40/16 = 2.5 pounds

Answer:

40 divided by 16 = 2.5 pounds .

Answer:

Parallel

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a)Total number of candies = 120

The number of candies in the rows form AP sequence:

The first term is a=3 and common difference is d=2

Sum of n terms:

Substitute values and solve for n:

Correct choice is (ii) 10

(b) Formula for nth term:

Correct choice is (ii) 21

(c) Use same formula:

Correct choice is (i) 8

(d) Sum of candies in 15 rows

Correct choice is (iii) 255

(e) Number of candies in 12th row:

Correct choice is (iii) 25

Answer:

[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]

Step-by-step explanation:

Given

[tex](81x^4y^{16})^{\frac{1}{2}}[/tex]

Required

Determine an equivalent expression

Express 81 as [tex]9^2[/tex]

[tex](9^2x^4y^{16})^{\frac{1}{2}}[/tex]

Apply law of indices

[tex]9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}[/tex]

[tex]9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}[/tex]

[tex]9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}[/tex]

[tex]9^1 * x^2 * y^8[/tex]

[tex]9 * x^2 * y^8[/tex]

[tex]9 x^2 y^8[/tex]

Hence:

[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]

Answer:

The explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]

Option A is correct option.

Step-by-step explanation:

Third term of sequence is 18

Sixth term of sequence is 33

We need to find the explicit equation for the sequence.

The explicit sequence is [tex]a_n=a_1+(n-1)d[/tex]

We need to find a_1 the first term and common difference d

We have a₃=18

We can write it as: [tex]a_3=a_1+(3-1)d\\[/tex]

[tex]18=a_1+2d[/tex]

a₆=33

We can write it as: [tex]a_6=a_1+(6-1)d\\33=a_1+5d[/tex]

Now, solving these equation s we can find value of d

[tex]18=a_1+2d[/tex]

[tex]33=a_1+5d[/tex]

Subtract both equations

[tex]18=a_1+2d[/tex]

[tex]33=a_1+5d[/tex]

[tex]--------\\-15=-3d\\d=\frac{-15}{-3}\\d=5[/tex]

So, we get common difference d = 5

Now finding a_1

Put value of d in equation [tex]18=a_1+2d[/tex]

[tex]18=a_1+2(5)\\18=a_1+10\\a_1=18-10\\a_1=8[/tex]

So, we get a₁ = 12

Now, the explicit equation is:

[tex]a_n=a_1+(n-1)d\\a_n=8+(n-1)5\\a_n=8+5n-5\\a_n=5n+3[/tex]

So, the explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]

Option A is correct option.

Answer:

Face Value = 8

Place Value = 80

Step-by-step explanation:

What is the difference between face value and place value of 8 in the number 281 ?

First we define Place value and Face Value

Place value

Place value is defined as the digit multiplied wherever it is placed, either by tens, hundreds or thousands.

Face Value

Face value is defined as the digit itself within a number.

Now: we will find face value and place value of 8 in the number 281.

Face Value = 8

Place Value = 8 x 10 (because 8 is at tens place) = 80

So, the answer is:

Face Value = 8

Place Value = 80

Answer:

Area of the triangle :---

1/2×base×height

1/2×5×6

15 square unit

15 square unit is the right answer.

Answer: Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

Step-by-step explanation:

When dividing fractions, the second term becomes the reciprocal.

Fractions are numbers which are of the form a/b where a and b are real numbers which implies that 'a' parts of a number 'b'.

Here, a is called the numerator and b is called the denominator.

Let a/b and c/d be the two fractions.

Division of these fractions will result as a/b ÷ c/d.

Now the second term c/d will change into d/c and the operation changed into multiplication.

a/b ÷ c/d = a/b × d/c

For example, let 1/2 and 3/4 are two fractions.

We have to divide 3/4 into 1/2 parts.

The actual operation is 3/4 ÷ 1/2.

But using the reciprocal and change in the operation, we will get it as,

3/4 ÷ 1/2 = 3/4 × 2/1 = 3/4 × 2

Dividing 3/4 into 1/2 parts is same as doubling 3/4.

Hence the second term will become reciprocal in the division of fractions.

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Answer:

(1)  4

Step-by-step explanation:

Isolate x.

[tex]\frac{x-2}{3}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{5}{6}[/tex]

[tex]\frac{x-2}{3}[/tex] = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex]

[tex]\frac{x-2}{3}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\frac{x-2}{3}[/tex] × 3 = [tex]\frac{2}{3}[/tex] × 3

x - 2 = 2

x = 2 + 2

x = 4

0.75x+3=15

16 chocolate bars

Answer:

a= 15 = 3+ .75c

b= 16 chocolate bars

Step-by-step explanation:

15 = 3 + .75c

c= chocolate bars

to solve for the number of chocolate bars:

subtract three for the snowcone he bought= 12=.75c

then just divide by .75 = 16 = c=16

Answer:

$5.60

Step-by-step explanation:

So each pound equals to $1.75 which means that we need to multiply by 3.2 because we're trying to find the number of money we'll spend on a certain amount of coffee. So if we multiply, we get 5.6. Though in context with the problem, it should be $5.60.

Answer:

-25

Step-by-step explanation:

When subtracting a negative from a negative, ignore the negative sign, ADD the 2 numbers, then add a negative sign to the sum.

Answer:

The probability is 63/1000 or 0.063

Step-by-step explanation:

Here, given that she takes 3 coins , we want to calculate the probability that the sum is £2.50

What we simply have to do here is to get the different ways to arrange £2.50 within 3 selections ONLY

we can only have this as;

taking 2 £1 coins and 1 50 pence coins

The probability of taking a £1 coin is 3/10

The probability of taking a 50 pence coin is 7/10

So the probability of 2 £1 coins and 1 50 pence coins will be;

3/10 * 3/10 * 7/10 = 63/1000

From analysis, it is seen that the probability of winning when playing regular defense is higher than the probability of winning with *prevent* defence.

We will assume that a total of 100 games were reviewed.

50 games used regular defense method.

The remaining 50 games used the prevent defense method.

Out of the 50 regular defense games, 38 were win while 12 games were lose.

Out of 50 prevent defense game, 29 were win, while 21 games were lose.

Thus, the Probability of winning by regular defense is:

P(win | regular) = 38/50

P(win | regular) = 0.76

Probability of winning by playing prevent defense is:

P(win | prevent) = 29/50 = 0.58

From the above analysis we observe that the probability of winning by using the regular defense method is greater than the probability of winning by prevent defense method.

That is 0.76 > 0.58.

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Answer:

13.75

Step-by-step explanation:

6.25+7.50=13.75

Answer:

$11.05

Step-by-step explanation:

The hot dog is $3.55, and the cheeseburger is $7.50. Thus, adding them together, the whole total is $11.05.

Hope this helps

Answer:

t=8/3+4/3u  

Step-by-step explanation:

4u=3t+8

-3t+8-4u

t=8/3+4/3u

hope it helps

Answer:

y=13.15x+14

Step-by-step explanation:

That is the equation, if you need the graph lmk

Answer:

?=14+13.15x

14+13.15x=?

?=13.15x+14

13.15x+14=?

Answer:

B) [3, 5]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, the line's y-values span from 3 to 5. Since both are closed dot, they are inclusive in the range:

[3, 5] or 3 ≤ y ≤ 5

Answer:

The number of

Dimes = d = 20 dimes

Quarters = q = 10 quarters

Step-by-step explanation:

Let us represent

The number of :

Dimes = d

Quarters = q

Note that:

A dime is worth 10 cents = 0.10d

A quarter is worth 25 cents = 0.25q

A Wonsan has 30 coins in her pocket, all of which are dimes and quarters .

d + q = 30...... Equation 1

d = 30 - q

If the total value of the coins is $4.50

0.10d + 0.25 q = 4.50.....Equation 2

We substitute 30 - q for d in Equation 2

0.10(30 - q) + 0.25q = 4.50

3 - 0.10q + 0.25q = 4.50

- 0.10q + 0.25q = 4.50 - 3

0.15q = 1.5

q = 1.5/0.15

q = 10 quarters

Solving for d

d = 30 - q

d = 30 - 10

d = 20 dimes

Therefore:

The number of

Dimes = d = 20 dimes

Quarters = q = 10 quarters

Answer:

3 of the DVDs were documentaries.

Step-by-step explanation:

We know that at first, there were 15 DVDs in total.

Now, we need to find how much 1/5 of 15 DVDs were equal to.

1/5 of 15 is equal to the number 3.

So, that means our answer is 3 of the DVDs are documentaries.

Hope this helps.

Answer:

I think the answer should be 3.

Answer:

MP is approximately equal to ON because one side of a rectangle is always the same as another side of a rectangle.  

Step-by-step explanation: