a) Work out the size of angle x. b) Give reasons for your answer. + A E C xº B F 105° G D H​

Answer:

  6 square units

Step-by-step explanation:

The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.

__

Any right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.

Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.

The fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.

The tangent ratio is ...

  Tan = Opposite/Adjacent

Applying that to angle β, we have

  tan(β) = OD/AD   [eqn 1]

  tan(β) = BC/AC   [eqn 2]

These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.

Equation [eqn 1] tells us ...

  AD = OD/tan(β)

Equation [eqn 2] tells us ...

  BC = AC·tan(β)

The area of ΔADB is ...

  Area = 1/2bh

  Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))

  Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel

The length of AC is given as 6, and we know OD = 2, so the area is ...

  Area = 1/2(2)(6) = 6

The area of triangle ADB is 6 square units.

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

Given that;

First, we determine the mark price.

Since the Furniture Store marks up all furniture by 45%.

Mark up price = mark up × purchase price

Mark up price = 45% × $113.00

Mark up price = 0.45 × $113.00

Mark up price = $50.85

Now, the selling price will be;

Selling price = Purchase price + mark up price

Selling price = $113.00 + $50.85

Selling price = $163.85

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

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Answer:

6xy(2x²-3y)

Step-by-step explanation:

factorized completely

3/4 + -5/8

---Find a common denominator

6/8 + -5/8

---Simplify

1/8

Hope this helps!

Answer:

3/4 + -5/8 = 1/8

Step-by-step explanation:

When adding fractions, you always need to find a common denominator. 4 and 8 share a common denominator of 8.

You multiply 3/4 by 2/2 and get 6/8.

When adding negative numbers, it is the same as subtracting.

6/8  + (-5/8)  =

6/8 - 5/8 = 1/8

So 1/8 is the answer.

I hope this helps!

The phenotypic ratio of the offspring as shown in the given Punnett square is: 1:3:3:9.

Phenotypic ratio is quantitative relation of the number of offspring of a cross that manifest a certain combination of traits or characteristic.

From the Punnett square given, there are:

Therefore, the phenotypic ratio would be: 1:3:3:9.

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Answer:

B it the answer 1:3:3:9

Step-by-step explanation:

Answer:

107.86 to 2 d.p.

Step-by-step explanation:

makes a triangle. 120 feet is the hypotenuse.

we want to find the opposite so we will use sine.

sin(x) = opp/hyp which means opp = sin(x)hyp.

opp = sin(64)120

opp = 107.86 to 2d.p.

The translation rule that maps point D' to D" is (x + 3, y) and  the coordinate of point A" is (9,3)

The coordinates are given as:

A(-6,3) B(-4,5) C(-1,6) and D(-3,2)

When reflected across the y-axis, the transformation rule is:

(x,y) -> (-x,y)

So, we have:

A' = (6,3)

D' = (3,2)

Point D" on the grid is (6,2).

This means that the translation rule that maps both point is (x + 3, y)

In (a), we have:

A' = (6,3)

Using the translation rule (x + 3, y), we have:

A" = (6 + 3,3)

A" = (9,3)

Hence, the coordinate of point A" is (9,3)

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Answer:

[tex]\text{Perimeter of sector = 43.6 (Rounded to the nearest tenth.)}[/tex]

Step-by-step explanation:

[tex]\text{Perimeter of the sector = Radius + arc length + radius}[/tex]

[tex]\text{Radius = 10 cm}[/tex]

[tex]\text{Perimeter of the sector = 10 + arc length + 10 }[/tex]

 [tex]\text{Perimeter of the sector = 20 + arc length }[/tex]

[tex]\text{arc length = (sector angle/ 360 ) * perimeter of the circle}[/tex]

[tex]\text{Perimeter of a circle }=2\pi r[/tex]

[tex]\text{sector angle} = 135[/tex]

[tex]\text{arc length} = (135/ 360 ) * 2\pi (10)[/tex]

[tex]= (3/8) 20\pi[/tex]

[tex]= 15\pi /2[/tex]

[tex]\text{Using }\pi =3.14[/tex]

[tex]= 15 * 3.14 /2[/tex]

[tex]= 23.55[/tex]

[tex]\text{Perimeter of the sector = 20 + 23.55}[/tex]

[tex]= 43.55[/tex]

[tex]= 43.6 cm[/tex]

[tex]\text{perimeter of the sector = 43.6 cm }[/tex]

Answer:

Slope is undefined.

Step-by-step explanation:

Answer:

To find the value of x, use the formula

(n-2) x 180,  where n is the number of sides.

In this case, we have a TRIangle, which has THREE sides.

So, n=3

(3-2) x 180

1 x 180

180

If the total sum of the angles  is 180, then  the  measure of one angle would be 180 divided by 3, which is 60.

Let me know if this helps, or if you got any more questions

Step-by-step explanation:

the perimeter is simply the distance you would have to walk when going around the whole object once.

so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.

so, the perimeter of a rectangle is

2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m

Quadrilaterals are angles that has 4 sides and angles.  The measure of the angle m<SPQ is 110 degrees

Quadrilaterals are angles that has 4 sides and angles. The given quadrilateral is a rhombus with equal opposite sides.

Given the following angles

m<SPR = 2x + 15

m<QPR = 3x - 5

From the figure

m<SPR = m<QPR

Substitute

2x+ 15 = 3x - 5

2x - 3x = -5 - 15

x = 20

Determine the measure of <SPQ
m<SPQ = 3x - 5 +2x +15

m<SPQ = 5x + 10
m<SPQ =5(20) + 10
m<SPQ = 110 degrees

Hence the measure of the angle m<SPQ is 110 degrees

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Answer:

Step-by-step explanation:

Answer:

y = -7/8x + 4

Step-by-step explanation:

Slope-intercept form :

y = mx + b

Hence, the equation formed is :

The area of sector AOB  whose radius OA 5 units is 19.6 sq. units.

A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.

Here, Radius of Circle = 5 units

         length of arc AB / circumference = 1/4

        So, Area of Sector AOB = one fourth of area of circle

                                                  = 1/4 X π X r²

                                                 = 0.25 X 3.14 X 5²

                                                 = 0.25 X 3.14 X 25

                                                 = 19.625 sq. units

Thus, the area of sector AOB  whose radius OA 5 units is 19.6 sq. units.

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Answer:

19.6

Step-by-step explanation:

Answer:

The answer is c, hope this helps

Step-by-step explanation:

Answer:

The final price for the coffee table is $98.9.

Step-by-step explanation:

1. First, is to convert the percentage to decimal form

We can do this by changing 7.5% to decimal number by dividing 7.5 by 100, we get:

\frac{7.5}{100}

100

7.5

= 0.0750.075

2. Then multiply 0.075 to the original price of $115

0.075(115) = 8.625

Then, add 8.625 to the original price of $115, we get:

115 + 8.625 = $123.625

3. After this, we subtract the 20% discount to $123.625

We can do this by converting 20% to decimal form, we get:

\frac{20}{100}

100

20

= 0.20.2

Then, multiply $123.625 by 0.2, we get:

123.625(0.2) = $24.725

4. Then subtract 24.725 from $123.625, we get:

123.625 -123.625−24.725 = $98.9

Final price of the table coffee which is on sale by 20% with a sales tax of 7.5% is $98.9.

Answer:

Correct (192)

Step-by-step explanation:

The formula for a parallelogram's area is just base times height. 16x12 is equal to 192, so you are correct.

A parallelogram can be:

Therefore we calculate the rectangle of a square, which is a parallelogram.

To start solving, we obtain the following data:

The formula to calculate the area is:

[tex]\bf{a=b*h }[/tex]

To calculate the area, multiply the base by the height (which is represented in "h")

We clear formula, calculate the area:

[tex]\bf{A=(16 \ cm)(12 \ cm) \ \ \ ==== > \ Multiply }[/tex]

[tex]\bf{A=192 \ cm^{2} }[/tex]

Answer: The area of the parallelogram is 192 cm2. So if you're right, it was a rectangle.

Answer:

Step-by-step explanation:

If you use the formula [tex]m = \frac{y2 - y1} {x2 - x1}[/tex] with x1 being 7, y1 being 0, -5 being x2 and 5 being y2, then you can subtract. 5(y2) minus 0(y1) is 5, and -5(x2) minus 7(x1) is -12. The formula would look like this: [tex]m = \frac{5 - 0}{-5 - 7} \frac{5}{-12}[/tex].

(tip: you need to do rise over run, aka y over x, shown as [tex]\frac{y}{x}[/tex] or [tex]\frac{rise}{run}[/tex])

I hope I helped you answer your question, and helped better understand it as well

Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.

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Answer:

a) 12/18

b) 6

Step-by-step explanation:

If adding 6 white balls doubles the probability then the original amount of balls is 6 and with the new amount of 18, the likelihood of picking a white ball becomes 12/18.

Answer:

45

Step-by-step explanation:

how many number you rolled 3 times how many times its rolled 15 x 3 +45

Therefore,the answer would be 45

Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the player hits 10 home runs in 45 games, hence the proportion is:

p = 10/45.

Then, in 162 games, the amount is:

HR = 10/45 x 162 = 36.

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Answer:

1/3 liters. or 33.33333 ml

Step-by-step explanation:

1 2/5 + 1 3/5 = 3

3 liters of juice is there.

3 liters of juice/9 glasses.

1/3 liters of juice is in every glass

The coordinate of the point between point A and point B on the line segment AB is [tex](\frac 92, -\frac{19}4)[/tex]

The points are given as:

A = (4,-5)

B = (6,-4)

m : n = 1 : 3

The coordinate of the point is then calculated using:

[tex]P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)[/tex]

So, we have:

[tex]P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)[/tex]

Evaluate the sum of product

[tex]P = \frac{1}{4}(18, -19)[/tex]

Evaluate the product

[tex]P = (\frac 92, -\frac{19}4)[/tex]

Hence, the coordinate of the point is [tex](\frac 92, -\frac{19}4)[/tex]

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