2. In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs
intercepted have the following ratio of measurements:
P
mRS : mST :MTU : mUR=1:4:4:3
R
(a) If mRS = x, then write an equation that could be used to solve for x
and find the value of x.
I
4
(b) State the measure of each of the four arcs.
mRS =
mST =
MTU
MUR =

Answer:

The answer is actually a proper fraction = 7/20

Step-by-step explanation:

A mixed fraction is expressed as : a b/c

Let the mixed fraction be represented by Y

a) The fraction is halved

= Y ÷ 1/2 = Y/ (1/2)

In mathematics, when we divide a number by a fraction, the number is multiplied by the reciprocal of the fraction.

Y × 2 = 2Y

b) Then 3/4 is added

= 2Y + 3/4

c)The result is 1 9/20

2Y + 3/4 = 1 9/20

Converting the mixed fraction to improper fraction, we have

1 9/20 = (20 × 1) + 9/ 20 = 29/20

Therefore,

2Y + 3/4 = 29/20

2Y = 29/20 - 3/4

The Lowest common multiple of the right hand side = 20

2Y = (29 - 3×5)/ 20

2Y = 29 - 15/20

2Y = 14/20

2Y = 7/10

To find Y , we cross multiply

2Y × 10 = 7

20Y = 7

Y = 7/20

Therefore, the mixed fraction represented by Y is actually a proper fraction = is 7/20

Answer:

a = 1

b = 2

c = 5

Step-by-step explanation:

Given

Mixed fraction: a b/c

Result after arithmetic operations = 1 ⁹/20

Required.

Find a, b, c

From the question, the fraction is halved. This is represented as follows

a b/c ÷ 2

= a b/c * ½

Then, ¾ is added. This is represented by

a b/c * ½ + ¾

The result is 1 ⁹/20. This is represented by

a b/c * ½ + ¾ = 1⁹/20

Convert mixed fraction to improper fraction

a b/c * ½ + ¾ = 29/20

Subtract ¾ from both sides

a b/c * ½ + ¾ - ¾ = 29/20 - ¾

a b/c * ½ = (29 - 15)/20

a b/c * ½ = 14/20

a b/c * ½= 7/10

Multiply both sides by 2

2 * a b/c * ½= 7/10 * 2

a b/c = 14/10

a b/c = 7/5

Convert mixed fraction to improper fraction

a b/c = 1⅖

By comparison,

a = 1

b = 2

c = 5

When the chords intersect inside the circle the sum of the vertical angles and the sum of the referenced arcs are the same.  Since the vertical angles are congruent, each is half the sum of the referenced arcs.

Similarly when the chords intersect outside the circle, the angle is half the difference of the arc measures.

It's the same with a tangent; in that case there's just not a part of the arc that's not counted on the side with the tangent.

OK, that's how.  Let's try some.

1.  x = (88 + 86)/2 = 87

2. x = (150 - 60)/2 = 45

3. The angle is exactly half the subtended arc,

x = 110/2 = 55

4. The referenced arc is 360 - 220 = 140 degrees and x is half, 70.

5.  Outside, half the difference, x = (90-20)/2 = 35

6.  Angle outside, inner arc 6 degrees, vertical angle is 90 degrees.

90 = (x - 6)/2

180 = x - 6

x = 186

7.  There's a special rule for this case but we can treat it as outside, little arc x, big arc 360-x,

60 = (360 - x  - x)/2

120 = 360 - 2x

2x = 240

x = 120

8. Inner arc x, outer arc is 360-140-x = 220-x.  Half the difference is 38,

38 = (220 - x - x)/2

76 = 220 - 2x

2x = 220 - 76

x = (220 - 76)/2 = 72

9.  x is formed by a tangent and a radius, so a right angle, x=90

y is subtended by a 35 degree angle so y=70

10.  Remaining triangle angle is 180 - 62 - 28 = 90.  Arc that subtends it is double, 180.  That means the long side is a diameter.

11.  Remaining triangle angle is 180 - 50 - 70 = 60. x=120, y=100, z=140

12.  Remaining arc 360 - 170 - 90 = 100.  Angles are half.

x=45, y=50, z=85

Answer:I don't know if your answer is there:/ -6.858

Step-by-step explanation:

64.2

100

−7.5

=0.642−7.5

=−6.858

Answer:

the answer is B.

Step-by-step explanation:i passed on the quiz if you would like to do the math you can ^^

Answer:

5. DBE and CBA both=48 degrees

6. a. scalene, right

b.isosceles, obtuse

c. scalene, acute

7. 50 degrees

8. im not completely sure how to do this one but ill check into it

Step-by-step explanation:

its a lot to explain, in 5 find p and plug it in.

in 6, just look at the sides and angles.

scalene- no sides equal

isosceles- 2 sides equal

equilateral- all sides equal

right- one 90 degree angle

acute- all acute angles (less than 90)

obtuse- one obtuse angle (more than 90)

7. add 90 and 40 to get 130. 180-130=50

8. im gonna look up how to do this one right now

Answer:

DE = 11.25 units

Step-by-step explanation:

The image of the quadilateral BCED and the extensions of BD and CE to move past B and C to meet at A is presented in the attached file to this answer.

Let the angle at A be θ

Let the length of DE be x

ABC forms a triangle which van allow θ to be obtained using cosine rule.

BC² = AB² + AC² - (2×AB×AC×cos θ)

BC = 9

AB = 24

AC = 28

9² = 24² + 28² - (2×24×28×cos θ)

-1279 = -1344 cos θ

Cos θ = (1279/1344) = 0.9516

θ = 17.89°

Note that ADE also forms a triangle and we can also use cosine rule to obtain the required side DE

DE² = AD² + AE² - (2×AD×AE×cos θ)

DE = ?

AD = AB + BD = 24 + 11 = 35

AE = AC + CE = 28 + 2 = 30

θ = 17.89°

DE² = 35² + 30² - (2×35×30×cos 17.89°)

DE² = 126.54

DE = √126.54 = 11.25

Hope this Helps!!!

The value of DE in the quadrilateral is 11.25 units.

From the information given, the cosine rule can be used. This will be:

BC² = AB² + AC² - (2 × AB ×AC × cos)

Therefore,

9² = 24² + 28² - (2 × 24 × 28 × cos)

cos = 17.89°

Therefore, the value of DE will be calculated thus:

DE² = 35² + 30² - (2 × 35 × 30 × cos 17.89)

DE = ✓126.54

DE = 11.25

In conclusion, the value of DE is 11.25 units.

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Answer:

10π

Step-by-step explanation:

The circumference of a circle can be found with the formula πd, where d is the diameter. When we plug in 10 for d, we get 10π inches. Hope this helps!

Answer:

DE=3 cm

Step-by-step explanation:

From the information we know, we can tell that triangle ABC is a scale factor of 2 from triangle DEF, because 10/5=2.

Side DE would be proportional to side AB.

Side AB is 6, so we would have to divide that by 2, because of our scale factor.

6/2=3.

Hope this helped! Have a good rest of your day!

Answer:

Nathan buys six socks

Step-by-step explanation:

You times 0.99 by six and get your answer when you add the number you add to the cost of the sweater

The first four iterates of the function f(x) are 23, 163, 1143 and 8003

The function is given as:

[tex]f(x) = 7x + 2[/tex]

Where:

[tex]x_o=3[/tex]

Substitute 3 for x in f(x)

[tex]f(3) = 7 \times 3 + 2[/tex]

[tex]f(3) = 23[/tex]

Substitute 23 for x in f(x), for the next iteration

[tex]f(23) = 7 \times 23 + 2[/tex]

[tex]f(23) = 163[/tex]

Substitute 163 for x in f(x), for the next iteration

[tex]f(163) = 7 \times 163 + 2[/tex]

[tex]f(163) = 1143[/tex]

Substitute 1143 for x in f(x), for the next iteration

[tex]f(1143) = 7 \times 1143 +2[/tex]

[tex]f(1143) = 8003[/tex]

Hence, the first four iterates of the function f(x) are 23, 163, 1143 and 8003

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That's a vertical line, no slope, so no y=something.  

Answer: x = -9

Answer: O = m + 40

Step-by-step explanation: O is 40 feet taller than the maple, so we can use m (maple). However tall the maple is, we just add 40.

Hope this helps :)

Answer:

3 <_ w and w <_ 9

Step-by-step explanation:

The <_ are underlined btw

Hope this helped!

Answer:

Q: How much of the cylinder does the sphere fill

A: The sphere fills the whole cylinder

Step-by-step explanation:

The sphere's height, as written in the picture (The red words) says 2r and the same goes for the cylinder, therefore if they both say, "h = 2r" then it is evident that they both are equivalent. Therefore, the Sphere fills up the whole cylinder.

Answer:

6√2

Step-by-step explanation:

This is a right triangle. The legs of a right triangle are the sides that make up the right angle, and the hypotenuse is the side opposite to the right angle. To find x, we will use the Pythagorean Theorem. This states that a² + b² = c², where a and b are the legs and c is the hypotenuse. Since we know that the legs are both x and the hypotenuse is 12, we can plug these values into our equation to get  x² + x² = 12².

2x²=144 → x² = 72 → x = √72, which simplifies to x = 6√2. Hope this made sense and helps!

Answer:

I will answer when you explain what you mean by sample space.

Step-by-step explanation:

please do not delete.

Answer:

The Last Equation

Step-by-step explanation:

[tex]2(x+3)=32[/tex] is the same thing as [tex]2x+6=32[/tex].

Why? Because if you apply the distributive property...

[tex]2(x+3)=32\\2 * x =2x\\2*3 = 6\\\boxed {2x+6=32}[/tex]

You get what was mentioned in the question!

So, 2(x+3)=32 should have the same solution as 2x + 6 =32.

Brainilest Appreciated.

Answer:

The bottom choice, 2(x + 3) = 32

Step-by-step explanation:

2x + 6 = 32

Subtract 6 from both sides of the equation

2x = 26

x = 13

Substitute the new value for x into all of the possible equations

1) 2x = 38,       2)  x - 3 = 16        3)  x + 6 = 16       4)   2(x - 3) = 16        

13 * 2 = 38           13 - 3 = 16           13 + 6 = 16              2x - 6 = 16

26 = 38                 10 = 16                  19 = 16                 13(2) - 6 = 16

False                     False                    False                   26 - 6 = 16

                                                                                           20 = 16

                                                                                             False

5)  2(x + 3) = 32

     2x + 6 = 32

    2(13) + 6 = 32        

      26 + 6 = 32

          32 = 32

             True

              The last answer choice, (the 5th one down) is correct

                                              Hope this helps :)

Answer:

Divide the outcome with the frequency

An experiment consists of rolling a standard number cube. The experimental probability of each event is as follows 1/6, 1/8, 5/36, and 2/13.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Form the result in the table of outcomes and the frequency

a. The probability of rolling a 1 = 1/6

b. The probability of rolling a 5 = 1/8

c. The probability of not rolling a 3 = 5/36

d. The probability of not rolling a number less than 5 = 2/13

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Answer:

$4

Step-by-step explanation:

Simple math

Answer:

1.5

---------------------

Answer:

6x2 3 + 4(2x - 1)

Step-by-step explanation:

6x23+4(2x−1)

Distribute:

=6x23+(4)(2x)+(4)(−1)

=6x23+8x+−4

Answer:

=6x23+8x−4

Answer:

(2/3) bagel per student

Step-by-step explanation:

Find the unit rate (fraction of a bagel per person):

 4 bagels

----------------- = (2/3) bagel per student

6 students

Answer:

y = - 3x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, - 7) and (x₂, y₂ ) = (2, - 10) ← 2 ordered pairs from the table

m = [tex]\frac{-10+7}{2-1}[/tex] = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute any ordered pair into the partial equation

Using (2, - 10) , then

- 10 = - 6 + c ⇒ c = - 10 + 6 = - 4

y = - 3x - 4 ← equation of linear function

Answer:

x = 9

Step-by-step explanation:

8x - 10 = 62

Add 10 to each side

8x-10+10 = 62+10

8x = 72

Divide each side by 8

8x/8=72/8

x = 9

Answer:

The second answer is correct

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

56 Swedish Fish

Step-by-step explanation:

1 = T

2 = H

3 = U

4 = N

5 = D

6 = E

7 = R

8 = C

9 = L

10 = A

11 = P

Thunderclap means a crash of thunder

T h u n d e r = 7 letter word

Hence the number of fishes Viking gives Norman is 8 × 7 = 56 Swedish Fish

Answer: >,<

Step-by-step explanation:

18 qt = 4.5 gallons which is not greater than 5 gallons

4.5km = 4,500 m is not greater than 5,000 m

Answer:

1st: 5 gal > 18 qt

2nd: 4.5 km < 5,000 m

Step-by-step explanation:

1 gallon is equal to 4 quarts

Going by this logic, 5 gallons should be 20 quarts. Since it says 18, 5 gallons is more than it. So the answer is '>'.

1 kilometer is the same as 1000 meters

4.5 kilometers * 1000 = 4,500 meters

5000 meters / 1000 = 5km

So the answer should be '<' since 5,000m is greater than 4.5km.

Answer:

c

Step-by-step explanation:

the answer is c

The simplified value of the exponential expression 16^(1/4) is 2.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The simplified value of the exponential expression 16^(1/4) is,

[tex]16^{\frac14}\\\\= \sqrt[4]{16}\\\\= \sqrt[4]{2^4}\\\\= 2[/tex]

Hence, the simplified value of the exponential expression 16^(1/4) is 2.

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Answer:

Shape B (The 2 by 12 one)

Step-by-step explanation:

Because the volume of shape B is 24 and the volume of shape A is 18.

The prism that could represent the prism that jake built is prism B.

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

The volume of the prism = 24 cubic centimetres.

The volume of a cube = 1 cube centimetre

This means a total of 24 cubes would have been used to make a prism of 24 cubic centimetres volume.

So, the prism that jake built is prism B i.e. 2*18 type prism.

Hence, the prism that could represent the prism that jake built is prism B.

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I'm pretty sure you would be evaluating P(6,2)

Answer:

P(6,4)

Step-by-step explanation:

If you divide 6! by 4! you are evaluating P(6,4).

Answer:

this is a tought one but ima just say 19 in because i feel like this is in a pattern

Answer:

36, Triangle, +, +, 36

Step-by-step explanation: