Which ordered pair is in the solution set of the following system of inequalities
y≤ 3x+1
x-y>1

SOLUTION :

c² = 5² + 5²

c² = 25 + 25

c² = 50

c = √50 ft

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In the given figure of circle, if RT = 90, SU = 25, and SO is perpendicular to RT, the length of the radius RO is 53.

In the given figure,

RT = 90

SU = 25

SO is perpendicular to RT.

Here, SO and RO are the radii of the circle and RT is a chord.

The length of the chord, RT is given as,

RT = 2 √(r² - d²)

Here, r is the radius and d is the distance of the chord RT from the center O.

Radius, r = RO and distance, d = OU

∴ RT = 2 √(RO² - OU²)

Substituting RT = 90 in the above equation, we get,

90 = 2 √[(RO)² - (OU)²]

√[RO)² - (OU)²]  = 45

(RO)² - (OU)² = 45²

(RO)² - (OU)² = 2025 ........... (1)

Now, OU = SO - SU   [From the figure]

⇒ OU = SO - 25

Substituting OU = SO - 25 in equation (1), we obtain,

(RO)² - (SO - 25)² = 2025

(RO)²- [(SO)² + (25)² - 2(SO)(25)] = 2025    [ ∵ (a-b)² = a²+b²-2ab ]

(RO)²- (SO)² - (25)² + 50(SO) = 2025 ........... (2)

Since, RO and SO both are the radii of the same circle, we have,

SO = RO

Thus, we can write equation (2), as follows,

⇒ (RO)² - (RO)² - (25)² + 50(RO) = 2025

⇒ -625 + 50RO = 2025

⇒ 50RO = 2025 + 625

⇒ RO = 2650/50

⇒ RO = 53

Hence, the length of the radius RO of the given circle is 53.

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Answer:

Gavin has 19 nickels & 114 quarters

Step-by-step explanation:

N : D : Q

1 : 3 : 6 = 57

x : 57 : y

57 / 3 = 19

1 x 19 : 3 x 19 : 6 x 19

19 : 57 : 114

The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

Heptagons are polygons with seven sides, seven vertices, seven interior angles and seven central angles. Herein we know the value of the sum of six interior angles and we need to know the measure of the seventh interior angle. We can determine the measure of the seven interior angles by using the following expression:

θ = (n - 2) · 180°, where n is the number of sides of the polygon.     (1)

If we know that n = 7, then sum of the internal angles in the heptagon is:

θ = (7 - 2) · 180°

θ = 900°

And the measure of the final interior angle is found by subtraction:

θ₇ = 900° - 776°

θ₇ = 124°

The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

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Answer:

B) 7/9

Step-by-step explanation:

          LCM of 3 and 9 is 9.

          [tex]\sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\[/tex]

              [tex]\sf =\dfrac{3}{9}[/tex]

      [tex]\sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\[/tex]

                 [tex]\sf =\dfrac{7}{9}[/tex]

The probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.

For any two events A and B, the probability of event A and B, that is, P(A ∩ B) is given as:-

In the question, we asked the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333.

We know that when the events are independent, P(A ∩ B) = P(A).P(B).

Thus, P(A ∩ B) = (0.25)*(0.333),

or, P(A ∩ B) = 0.08325.

Thus, the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.

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The value of n from the given expression is 35/36

Given the equation below expressed as:

1/5n+3/5n=7/9

Find the LCM

(n+3n)/5 = 7/9

4n/5 = 7/9

Cross multiply

4n * 9 = 5* 7

36n = 35

n = 35/36

Hence the value of n from the given expression is 35/36

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The function that gives the value of tn for the geometric series is presented as follows;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

The given geometric series is presented as follows;

2 + 6 + 18 + 54 +...

From the above series, we have;

The nth term of the geometric series is therefore;

[tex]t_n = a \cdot r^{(n - 1)} [/tex]

Which gives;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

Where, tn is the nth term

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Answer: [tex]x^{16}y^{22}[/tex]

Step-by-step explanation:

[tex]\frac{(x^6 y^8)^3}{x^2 y^2}=\frac{x^{18}y^{24}}{x^2 y^2}=x^{16}y^{22}[/tex]

Angles T and V of the parallelogram are equal to 91°.

Calculating the Value of x

In the parallelogram TUVS, adjacent angles U and V are given as,

U = 4x+9

V = 6x-29

Since U and V are adjacent angles, and as per the properties of a parallelogram, sum of adjacent angles is equal to 180°.

4x+9 + 6x-29 = 180

10x - 20 =180

10x = 200

x = 20

Calculating the Angles of the Parallelogram

∠U = 4x + 9

∠U = 4(20) + 9

∠U = 80 + 9

∠U = 89°

∠V = 6x - 29

∠V = 6(20) - 29

∠V = 120 - 29

∠V = 91°

According to the properties of a parallelogram, opposite angles are of equal measure.

∴ ∠T = ∠V and ∠S = ∠U

⇒ ∠T = 91° and ∠S = 89°

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Answer:

angles t and v

Step-by-step explanation:

edge

The quantity spent on amusement = 720

quantity spent on food = 510

they have got 3000 for vacation.

amount spent on food = 17% of 3000

⇒ 17/one hundred*3000

17*30= 510

amount spent on amusement = 24% of 3000

⇒ 24/100*3000

24*30= 720

A person would possibly account for a terrible temper or general rude conduct by explaining that bad site visitors affected the morning travel, for example. someone who is exceeded over for a promotion would possibly rationalize the frustration by means of claiming to not have desired so much responsibility in the end.

To carry into accord with cause or reason something to appear reasonable especially: to characteristic (one's actions) to rational and creditable motives without evaluation of proper and especially unconscious motives he attempted to rationalize his merciless behavior. intransitive verb.

Ego protection wherein apparently logical motives are given to justify unacceptable behavior that is influenced by subconscious instinctual impulses. In the psychoanalytic concept, such conduct is considered to be a defense mechanism.

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Answer:

circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

[tex] \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}[/tex]

[tex] \large {\boxed{ \tt{p = 2 \times \pi \times r}}}[/tex]

If the radius is 2 inches and

Use 3,14 for π So:

[tex] \tt{ {A = \pi \times {r}^{2} }}[/tex]

[tex] \tt{A = (3.14 \times 2 \times 2)} [/tex]

[tex] \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}[/tex]

Answer:

48π

Step-by-step explanation:

To find the area of the shaded region, find the area of the large circle and the small circle then subtract.

Large circle:

8²π=64π

Small circle:

4²π=16π

Now subtract 16 from 64.

64-16=48

The area of the shaded region is 48π.

Hope this helps!

65 sequences.

Lets solve the problem,

The last term is 0.

To form the first 18 terms, we must combine the following two sequences:

0-1 and 0-1-1

Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent

So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:

2x + 3y = 18

Case 1: x=9 and y=0

Number of ways to arrange 9 identical 2-term sequences = 1

Case 2: x=6 and y=2

Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28

Case 3: x=3 and y=4

Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35

Case 4: x=0 and y=6

Number of ways to arrange 6 identical 3-term sequences = 1

Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65

Hence the number of sequences are 65.

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The volume of the region in first octant is 9.

Given that the region in the first octant bounded by the cylinder r=3 and the plane z=y.

The graph is shown below.

we are given that first octant is bound by r=3  and z=y

We will use the conversion formula, i.e.

x²+y²=r² where x=rcos∅ and y=rsin∅

Firstly, we will find bound octant

0≤∅≤π/2

0≤r≤3

0≤z≤r sin∅

Now, we can set up integral

[tex]V=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}\int_{0}^{rsin(\theta)}rdzdrd\theta[/tex]

Further, we can solve it.

Firstly, we solve integral for z then we solve for r and after that we will solve for ∅, we get

[tex]\begin{aligned}V&=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}r^2 \sin (\theta)dr d\theta\\&=\int_{0}^{\frac{\pi}{2}}\frac{1}{3}r^3\sin \theta d\theta\left|_{0}^{3}\\ &=\int_{0}^{\frac{\pi}{2}}\left(\frac{1}{3}\sin\theta d\theta(27-0)\right)\\ &=\int_{0}^{\frac{\pi}{2}}9\sin \theta d\theta\\ &=0-(-9)\\ &=9\end[/tex]

Hence, the volume of the region in the first octant is bounded by the cylinder r=3 and the plane z=y is 9.

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The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:

r = √ (A / π)     (1)

r = √ (354 / π)

r ≈ 10.615 cm

Then, the measure of the central angle in radians is found by the equation of circular arc:

θ = s/r

θ = 2.9 cm / 10.615 cm

θ = 0.273 radians

Finally, we convert the angle into DMS system:

θ = 0.273 rad × 180°/π

θ = 15.641°

Degrees: 15°

Minutes and seconds: 0.641° (38.46')

Minutes: 38'

Seconds: (0.46' = 27.6'')

The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

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Answer:

Below in bold.

Step-by-step explanation:

f(x) = 2x^2 - 12x + 24

Convert to vertex form:

f(x) = 2(x^2 - 6x) + 24

     = 2[(x - 3)^2 - 9] + 24

     = 2(x - 3)^2 - 18 + 24

     = 2(x - 3)^2 + 6

So the vertex is at (3, 6) and the axis of symmetry is x = 3.

Answer:

(3, - 6 )

Step-by-step explanation:

x - 2y = 15 ( add 2y to both sides )

x = 2y + 15 → (1)

2x + 4y = - 18 → (2)

substitute x = 2y + 15 into (2)

2(2y + 15) + 4y = - 18 ← distribute parenthesis and simplify left side

4y + 30 + 4y = - 18

8y + 30 = - 18 ( subtract 30 from both sides )

8y = - 48 ( divide both sides by 8 )

y = - 6

substitute y = - 6 into (1)

x = 2(- 6) + 15 = - 12 + 15 = 3

solution is (3, - 6 )

Answer:

x is 3 y is -6 I really hope this helps

Answer:

3. 6 5. 3

Step-by-step explanation:

PEMDAS

3. 0.5 x (24) / 3 + 2

12/3 +2

4 + 2

6

5. (4 + 6/3) x 0.5

(4 + 2) x 0.5

6 x 0.5

3

Answer: number 3. is 6 and number 5. is 3

hope it helped

Answer:

Rotation, Reflection, Dilation.

Step-by-step explanation:

Answer: Y-intercept: (0,5) X-intercept: (3,0)

Step-by-step explanation: Set x and y equal to 0.

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

A = -8

You're welcome! :)

Answer: a = -8

Step-by-step explanation:

Combine multiplied terms into a single fraction

then find a Find common denominator for the fraction

then Combine fractions with common denominator,

Multiply the numbers, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator,

Multiply the numbers making your equation like this -5a+10=50

subtract 10 by both sides and then you will need to simplify making it

-5a + 40 then you divide them both by the same factor which is -5 then you simplify again making the answer to your question -8  

Answer: Graph provided below.

Step-by-step explanation:

Draw the graph of y = -2x and then shade the region below it because y is less than and equal to -2x. To draw the graph of y = -2x, plug in x values into the equation and plot the corresponding coordinates. See this video on how to graph linear equations:

https://www.khanacademy.org/math/in-in-grade-9-ncert/xfd53e0255cd302f8:linear-equations-in-two-variables/xfd53e0255cd302f8:graph-of-a-linear-equation-in-two-variables/v/graphs-of-linear-equations

The average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

a. Average force

Using  this formula

Force (F) = Mass ×Acceleration

Where:

Mass (m) = 57 g = 57 / 1000= 0.057 Kg

Acceleration (a) = u / t = 50 / 0.05 = 1000 m/s²

Let plug in the formula

Force (F) = 0.057 × 1000

Force (F) = 57 N

b. Resistive force

F = m(v – u) / t

Where:

Force (F) = ?

Mass (m) = 3000 Kg

Initial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/s

Final velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/s

Time (t) = 40s

Let plug in the formula

Force = 3000(5 – 20) / 40

Force = 3000(-15) / 40

Force=-45,000/40

Force = -1125 N

Therefore the average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

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Question 11

1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)

4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)

Question 12

1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)

2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)

4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)

5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)

6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)

7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)

Note: I changed the names of the segments in Question 11 because of the word filter.

This is a budgeting exercise. Based on the estimated cost of college which was set at $58,000, the following steps indicate how I intend to pay for college:

                                        $58,000

Budgeting is simply the process of outlining the total expense requirements of an individual person or a corporate entity and how those expenses will be satisfied and efficiently allocated.

From the above, the total sum of $58,000 will be satisfied from three sources:

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The value of n in 1/5n+3/5n=7/9 is 35/36

The equation is given as:

1/5n+3/5n=7/9

Multiply through by 5

n + 3n = 35/9

Evaluate the sum

4n = 35/9

Divide both sides by 4

n = 35/36

Hence, the value of n in 1/5n+3/5n=7/9 is 35/36

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