a rectangle is inscribed in a right isosceles triangle with a hypotenuse of length . what is the largest area the rectangle can have?

The value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

From the figure:

MZ is a perpendicular bisector of ∆GHJ.

GM = MJ

GM = 14.5

KZ is a perpendicular bisector of ∆GHJ.

GK = KH

GK = 18.6

Z is the circumcenter of ∆GHJ.

JZ = GZ

JZ = 19.9

Therefore the value of GK = 18.6, GM = 14.5 AND JZ = 19.9.

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Explanation:

Let x = depth of the gutter

then

14-2x = width of the gutter

:

Cross section area:

A = depth * width

A = x(14-2x)

A = 14x - 2x^2

:

Axis of symmetry will give x value for max area: x = -b/(2a)

x = -14/2 * -2

x = -14/-4

x = +3.5 inches is the depth for max area

:

:

Max area: 3.5 * 9 = 31.5 sq/in

The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4

Given that,

y forms a circle of radius r

y=2[tex]\pi[/tex]r

r=y/2[tex]\pi[/tex]

(2-y)- forms Square Side x

(2-y) = 4x

x=(2-y)/4

Now Sum of Area's=Area of Square +Area of Circle

Sum = [tex]\pi[/tex]r² + x²

Substitute the r and x values in above equation,

A(y)= y²/4[tex]\pi[/tex]+(y-2)²/ 16

To maximize Area A(y)

A'(y)= 0

2y/4[tex]\pi[/tex] + 2(y-2)/16 =0

y/2[tex]\pi[/tex] + (y-2)/8 =0

y = 2[tex]\pi[/tex]/[tex]\pi[/tex]+4

Y max will be max, x to be maximum.

for maximum sum of areas,

x=2/[tex]\pi[/tex]+4

Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4

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Answer:The mean of combined group is 71.12 kg

Step-by-step explanation:

Mean of 35 students test score=75.3

Total score of 35 students=mean×test score

=35×75.3

=2635.5

Mean of 26 students test score=65=65.6

Total score of 26 students= 26×65.6

=1705.6

Mean of combined group=(Total score of 35 students+Total score of 26 student ÷Number of total students

=(12635.5+1705.6)÷61

=71.16

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The combined group's average is 71.16.

Given;

If the average test score for one class of 35 students is 75.3 while the average test score for another class of 26 students is 65.6

Mean of 35 student's test scores = 75.3

The total score of 35 students is the mean * test score

=35 * 75.3   =2635.5

Mean of 26 student's test scores = 65.6

The total score of 26 students = 26 * 65.6  =1705.6

Mean of combined group = (Total score of 35 students + Total score of 26 students) / Number of total students

                                          = (12635.5 + 1705.6)  / 61

                                           = 71.16

Hence, the mean of the combined group is 71.16

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The equation of line with slope is -1/3 and y intercept 5/3 is : x + 3y = 5.

In the form of a slope intercept, the line's equation looks like this:

y = mx + b

where

slope = m

y-intercept = b

Here given slope = -1/3

y-intercept at 5/3

As a result, the line's equation has a slope of -1 / 3.

Let's use the locations to determine the y-intercept 5/3.

y = mx + b

Here b = 5/3

By substituting ,

y = -1/3x + 5/3

Multiplying both sides by 3,

3y = -x + 5

3y + x = 5

= x + 3y = 5.

Therefore the equation of line is x + 3y = 5.

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The time taken for the increase in temperature by 4 degrees Celsius is 1/2 minute.

Suraj took a slice of pizza from the freezer and put it in the oven. The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is given in the form of a graph. The coordinates of the points through which the line passes are (2, 10) and (4.5, 30). We can find the slope of the straight line. If the coordinates of two points are (x1, y1) and (x2, y2), then the slope of the passing line is given as below.

m = (y2 - y1)/(x2 - x2)

m = (30 - 10)/(4.5 - 2)

m = 20/2.5

m = 8

This means there is an increase of 8 degrees in temperature in one minute. We need to calculate the time taken for a 4-degree increase in temperature.

m = Δy/Δx

8 = 4/Δx

Δx = 4/8 = 1/2

Hence, the increase in temperature by 4 degrees Celsius took half a minute.

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The amount of slushy that was originally in the cup is 225 milliliters and the time it took Mariana to drink all the slushy is 50 seconds.

Total quantity she took

Total quantity = 4.5 × 17

Total quantity = 76.5 milliliters

Original quantity = 148.5 + 76.5

Original quantity = 225 milliliters

b. Time taken to drink all

Time =225 milliliters /2.5

Time = 50 seconds

Therefore original quantity  225 milliliters  and the time is 50 seconds.

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Answer:

a= im not sure sorry

h= horizontal shift

k= vertical shift

Step-by-step explanation:

a = the vertical stretch or compression factor

h = is the x-translation, that is it moves the graph right or left

k = The 'k' is the "vertical shift".

If positive, moves graph up k units.

If negative, moves graph down k units.

Answer:

1898

Step-by-step explanation:

Multiply both numbers together to find the area.

The rate of interest half yearly is 8.25 and monthly is 1.375%.

In the given question we have to find the effective rate of intereset, if a amount of money is borrowed an interest rate of 16.5% p.a. and is compounded.

The interest rate annually = 16.5%

(a) We have to calculate rate of interest half yearly.

In a half year have 6 months and in total have 12 months. So their is rate of interest for 2 times.

So the rate of interest half yearly = 16.5%/2

The rate of interest half yearly = 8.25%

(b) We have to calculate rate of interest monthly.

As we know that in a year have 12 months.

So the rate of interest monthly = 16.5%/12

The rate of interest monthly = 1.375%

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If Joe spent a total of $23.65 , then the cost of the paints is $5.75  .

In the question ,

it is given that ,

From the hobby shop , Joe bought 2 model sportscars for $8.95 each

the cost for 2 sports car = 8.95*2 = 17.9

the total amount spent by Joe at the shop = $23.65

let the cost of the paint be "$x" .

the above situation can be represented by the equation .

total cost = cost for 2 model cars + cost of paint

substituting the values from above ,

we get ,

23.65 = 17.9 + x

x = 23.65 - 17.9

x = 5.75

Therefore , If Joe spent a total of $23.65 , then the cost of the paints is $5.75  .

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Using the fraction concept, we can say that The number of beads each friend will get is 4.

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

Number of bead = 32 bead;

Total number of friends = 8;

So,

we need to find how many beads will one friend get:

So,

The number of beads each friend will get : [tex]\frac{32}{8}[/tex]

The number of beads each friend will get is 4.

Hence,

using the fraction concept, we can say that The number of beads each friend will get is 4.

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The transformations to function f(x) that results in function g(x) are described as follows:

5. Reflection over the x-axis, vertical stretch by a factor of 2.

6. Shift right of 6 units, shift up of 4 units.

7. The rule for g(x) after the transformation is given as follows:

[tex]g(x) = \sqrt[3]{-x + 7}[/tex]

For item 5, the functions are given as follows:

The transformation is a multiplication by -2, which means that the function was:

For item 6, the functions are given as follows:

Then the transformations are explained as follows:

For item 7, the parent function is:

[tex]f(x) = \sqrt[3]{x}[/tex]

Then the transformations and their effects are given as follows:

Hence the function is:

[tex]g(x) = \sqrt[3]{-x + 7}[/tex]

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Answer: -28w + 7x -35

Step-by-step explanation:

[tex]-7(-4w -x +5)\\\\= -7*-4w + (-7)*(-x) + (-7)*5= -28w + 7x -35[/tex]

Answer:

28w+7x-35

Step-by-step explanation:

For the given pair of intersecting lines, we find out that the value of x is 1 and the measure of the angle 1 is 169°.

From the figure we see that there are two lines intersecting each other.

We know,

Sum of all the angles formed = 360

We also know that

If there are a pair of two intersecting lines, then the vertically opposite angles are equal.

=> 20x+11 = 25x-14

=> 5x = 5

=> x = 1

Substituting the value of x in 20x+11 , we have

20*1 + 11 = 21°

Substituting the value of x in 25x-14 , we have

25*1 - 14 = 11°

It is also known to us that the sum of the adjacent angles of a pair of intersecting lines is equal to 180°. This implies that

11° + 1 = 180°

=> 1 = 180° - 11°

=> 1 = 169°

Thus, for the given pair of intersecting lines, we find out that the value of x is 1 and the measure of the angle 1 is 169°.

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The probability of the next customer paying with a debit or credit card other than cash is =94.82%

We have given,

Genesis owns a small business selling clothing.

She knows that in the last week 6 customers paid cash, 66 customers used a debit card, and 44 customers used a credit card.

we are asked to determine  the probability that the next customer will pay with something other than cash as a percent to the nearest whole number

P(A)= number of favorable outcome in event A divided by the total outcome in a sample space

customers will pay through debit or credit card other than cash.

last week of customers paid cash: 6

last week of customers paid w/ a debit card: 66

last week of customers paid w/ a credit card: 44

Therefore, 6+66+44= 116

=110/116

=0.9482

= 94.82% is the probability that the next customer will pay with

something other than cash as a percent to the nearest whole number.

Hence we get the required answer.
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Answer:

Step-by-step explanation:

Halie,  find angle EAD.... see it?   next think about the definition of vertical angles: each of the pairs of opposite angles made by two intersecting lines.

which angle is EAD  an opposite pair of?   ∠IAH  looks like a good one.  

Answer: -11.3875

Step-by-step explanation:

The general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]

The given arithmetic sequence is -2, -8, -14, -20

The first term = a = -2,

The common difference = d = -8 -(-2) = -8 +2 = -6

The general term of the arithmetic sequence is given by

[tex]T_{n} = a + (n-1)d[/tex]

Now, putting the values of the first term and common difference in the general term.

[tex]T_{n} = -2 +(n-1) (-6)\\\\T_{n} = -2 -6n +6\\ \\T_{n} = -6n +4[/tex]

Hence, the general term of the Arithmetic sequence is [tex]T_{n} = -6n +4[/tex]

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Check the picture below.

[tex]18m^2~~ + ~~10m^2\implies 28m^2\hspace{5em}(\stackrel{m^2}{28})(\stackrel{\pounds}{10})\implies \text{\LARGE \pounds280}[/tex]

Answer:

B . 72 you have to skip count by 12

C . 18 because 54 divide by 3 is 18 because they frame 3 houses in one week

Sorry I tried to do the rest but got confused I hope this helps u

Step-by-step explanation:

The rearranged form of equation 4(x-3)/a=y will be x=ay+3.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the expression is, 4(x-3)/a=y

First, we open the bracket to make x the variable in the equation.

4x - 12/a = y

4x - 12 = ay

4x = ay + 12

x = ay + 12/4

x = ay + 3

Thus, the rearranged form of equation 4(x-3)/a=y will be x=ay+3.

The question is incomplete,

The complete question is"Rearrange to make x the subject of 4(x-3)/a=y:

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Answer:

12

Step-by-step explanation:

12*12=144

Answer: 12 is the correct answer

Step-by-step explanation:

144 = a × a = 122

Then a = √144 = √(12 × 12)

12 × 12 = 144 or -12 × -12 = 144

The square root of 144 is +12 or -12

This shows that 144 is a perfect square.

The number for this equation is 5.

What is equation?

In arithmetic, Associate in Nursing equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

let the number be x.

So , according to question =

3(x+2) = x+16

Now solving this equation , we will get the answer

⇒ 3x +6 = x+16

now moving x to left side and taking the constant to right,

⇒ 3x-x = 16 -6

⇒ 2x = 10

⇒ x=5

Hence the number is 5.

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Answer:

23/20

Step-by-step explanation:

110% of 20 is 22/20, so 23/20 is more.

Step-by-step explanation:

23/20 = 1,15

110% = 1,1

1,15 > 1,1

⇒ 23/20 > 110%

The diagonal EG is a line of symmetry for rhombus EFGH

A rhombus is a quadrilateral with equal sides. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.

Given rhombus EFGH

We have to prove that diagonal EG is a line of symmetry for rhombus EFGH

According to the property of the rhombus

Four sides of EFGH are equal

So EF = EH

FG =HG

Meanwhile EG =EG(common side)

So triangle EFG = triangle EHG

The diagonal EG is a line of symmetry for rhombus EFGH

Therefore the diagonal EG is a line of symmetry for rhombus EFGH

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Answer:

10mm = 1cm

Step-by-step explanation:

Milli means 1000th of

Centi means 100th of

1000 / 100 = 10

So,

10mm = 1cm

The measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Given data ,

The angles of the triangle ABC are

∠A = ( 2x + 10 )°

∠B = ( 4x + 2 )°

Let angle ∠C be y

The sum of ∠A + ∠B + ∠C = 180°  

So ,

( 2x + 10 )° + ( 4x + 2 )° + y = 180°   be equation (1)

Now , we can see that AD is a straight line and C is a point on the line AD

The total angle of C on the line AD is 180°

So , ( 5x + 27 )° + y = 180°

y = 180° - ( 5x + 27 )°   be equation (2)

Substituting the value of equation (2) in equation (1) , we get

( 2x + 10 )° + ( 4x + 2 )° + 180° - ( 5x + 27 )° = 180°

On Simplifying , we get

( 2x + 10 )° + ( 4x + 2 )° - ( 5x + 27 )° = 0

( 2x + 4x - 5x ) + ( 10 + 2 - 27 ) = 0

x - 15 = 0

Adding 15 on both sides , we get

x = 15°

Substituting the value of x in the ∠A , ∠B and ∠C equation , we get

∠A = ( 2x + 10 )°

     = 40°

∠B = ( 4x + 2 )°

     = 62°

∠C = 180° - ( ∠A + ∠B )

     = 180° - 102°

     = 78°

Therefore , the angles of the triangle ABC are 40° , 62° and 78°

The measure of ( 5x + 27 )° is

= ( 5 x 15 + 27 )°

= 102°

Hence , the measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

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