the diagram on the right shows a circle.given that the length of arcs RS=2QR , angle QPR=35° and anglePSQ=45°,determine the value of
(a) angle SPR
(b) angle SRP

Answer:

#1 Haley is correct and Lacey is incorrect

#2 Kenji is incorrect.

Step-by-step explanation:

#1. x^3 (x^2) = x^5 but this same law doesn't apply to addition of numbers with exponents.

#2 The law of exponents doesn't apply to numbers with different bases that are not multiples of each other such as 3 and 4, so Kenji's simplification is not correct.

Answer:

Part 1;

(0, 0)

Part 2;

(0, 2.5)

Step-by-step explanation:

Part 1

The given system of inequalities is presented as follows;

f(x) < x + 4; f(x) > -x - 3; and f(x) < 5

We check each of the points as follows;

The point (0, 0) in the inequality f(x) < x + 4, gives;

f(0) < 0 + 4

f(0) = 0 < (is less than) 0 + 4 = 4

Therefore, (0, 0) is a solution of the inequality f(x) < x + 4

The point (0, 0) in the inequality f(x) > -x - 3, gives;

f(0) < -0 - 3

f(0) = 0 > (is larger than) -0 - 3 = -3

Therefore, (0, 0) is a solution of the inequality f(x) > -x - 3

The point (0, 0) in the inequality f(x) < 5, gives;

f(0) < 5

f(0) = 0 < (is less than) 5

Therefore, (0, 0) is a solution of the inequality f(x) < 5

The point (-6, 0) in the inequality f(x) > -x - 3, gives;

f(-6) = -6 - 3 = 3

The point (-6, 0) with y = 0 < (is less than) f(-6) = 3, therefore (-6, 0) is not a solution to (not included in the graph of) the inequality f(x) > -x - 3 and therefore to the system of inequalities because at x = -6, the values of f(x) > -x - 3 are larger than 3

The point (-3, 4) in the inequality f(x) < x + 4, gives;

f(-3) = -3 + 4 = 1

The point (-3, 4) with y = 4 < (is larger than) f(-2) = 1, therefore (-3, 4) is not a solution to (not included in the graph of) the inequality f(x) < x + 4  and therefore to the system of inequalities because at x = -3, the values of f(x) < x + 4 are less than 1

The point (4, 6) is not a solution to (not included in the graph of) the inequality f(x) < 5  and therefore to the system of inequalities because f(x) is larger than 5 for all x

Therefore, the point which is part of the solution set of the system of inequalities is (0, 0)

Part 2

The given system of inequalities are, f(x) ≥ 2·x + 2; f(x) ≤ -4·x + 3; and f(x) ≤ 6·x + 5

Plotting the given system of inequalities on MS Excel the point which is part of the solution is given by points which are within the triangular intersection area of the three inequalities, with coordinates, (1/6, 7/3), (-3/4, 1/2), and (-1/5, 19/5)

Therefore, the points, (0, 0), (-2.5, 0) are not solutions because, the y-value of the solution area are all higher than the line y = 0

The point (0. 6.5) is not a solution because the points in the triangular solution area all have x-values lesser than x = 6.5

The point which is part of the solution by examination is the point (0, 2.5) which is a point between the lines y = 19/5 = 3.8, y = 1/2, x = -3/4, and x = 1/6.

Answer:

8.0%

Step-by-step explanation:

1. [tex]1895-1755=140[/tex]

2.[tex]\frac{140}{1755} =0.07977208[/tex]

3. 8.0%

Answer:

75

Step-by-step explanation:

Answer:

Neither (Answer)

Step-by-step explanation:

Comparing both the equations with slope-intercept form (y = mx + c), where 'm' is the (slope/gradient) and and 'c' is the (y-intercept).

Note: If the slopes are equal as well as the y-intercepts then they are same lines (overlapping) i.e lines are scaler multiple of each other.

Slope of line 1 = m1 = 7

slope of line 2 = m2 = 1/7

neither the slopes are equal nor the their product is equal to '-1'

Answer:

[tex]{ \bf{c(g) = 5g + 3}} \\ { \bf{c(6) = 5(6) + 3}} \\ { \boxed{ \tt{c(6) = 33}}}[/tex]

Answer:

12x-1

Step-by-step explanation:

First, you would have to distribute. Would mean to multiply the 4 with every number in the parenthesis.

4(3x+2)-9

12x+8-9

Now combine like terms

8-9 = -1

The answer is 12x-1

Step-by-step explanation:

4 times 3x+2 subtracted by9

hope it helps

Step-by-step explanation:

It is so simple Hope u understand

Answer:

Step-by-step explanation:

Sum = -5

Product = 2*(-3) = -6

Factors = -6 , 1   {-6 + 1 = -5  & -6 *1 = -6}

2m² - 5m -3 = 0

2m² - 6m + m -3 = 0

2m(m - 3) + (m -3) = 0

(m -3)(2m + 1) = 0

m - 3 =  0    or 2m + 1 = 0

    m = 3      or 2m = -1

                          m = -1/2

Ans: m = 3 , (-1/2)

Answer:

The answer is C.) m∠RCD = m∠ACD ÷ 2

RCD = ACD divided by two.

RCD = 90 degrees

ACD ÷2 = 180÷2 = 90 degrees.

So, your answer is C.

Hope this helped. Have a grey day!

Answer:

C. m∠RCD = m∠ACD ÷ 2

Hope this helps!

Step-by-step explanation:

I got it right.

Answer:

Step-by-step explanation:

by considering  2 + 3 = 95

3² = 9

2 + 3 = 5      

by considering  4 + 5 = 259

5² = 25

4 + 5 = 9  

by considering  6 + 7 = 4913

7² = 49

6 + 7 = 13  

by considering  8 + 9 = ????

9² = 81

8 + 9 = 17  

∴ 8 + 9 = 8117

[tex]\red{\frak{Given}}\Bigg\{ \sf \dfrac{x - 1}{ {x}^{2} - 3x + 2} + \dfrac{x - 2}{ {x}^{2} - 5x + 6 } + \dfrac{x - 5}{ {x}^{2} - 8x + 15 } [/tex]

[tex]\rule{200}4[/tex]

[tex]\sf\longrightarrow \small \dfrac{x - 1}{ {x}^{2} - 3x + 2} + \dfrac{x - 2}{ {x}^{2} - 5x + 6 } + \dfrac{x - 5}{ {x}^{2} - 8x + 15 } \\\\\\\sf\longrightarrow \small \dfrac{ x-1}{x^2-x -2x +2} +\dfrac{ x-2}{x^2-3x-2x+6} +\dfrac{ x -5}{x^2-5x -3x + 15 } \\\\\\\sf\longrightarrow\small \dfrac{ x -1}{ x ( x - 1) -2(x-1) } +\dfrac{ x-2}{x ( x -3) -2( x -3)} +\dfrac{ x -5}{ x(x-5) -3( x -5) } \\\\\\\sf\longrightarrow \small \dfrac{ x -1}{ ( x-2) (x-1) } +\dfrac{ x-2}{( x -2)(x-3) } +\dfrac{ x -5}{ (x-3)(x-5) } \\\\\\\sf\longrightarrow\small \dfrac{ 1}{ x-2} +\dfrac{ 1}{ x -3} +\dfrac{1}{ x -3} \\\\\\\sf\longrightarrow \small \dfrac{1}{x-2} +\dfrac{2}{x-3} \\\\\\\sf\longrightarrow \small \dfrac{ x-3 +2(x-2)}{ ( x -3)(x-2) } \\\\\\\sf\longrightarrow \small \dfrac{ x - 3 +2x -4 }{ (x-3)(x-2) } \\\\\\\sf\longrightarrow \underset{\blue{\sf Required \ Answer }}{\underbrace{\boxed{\pink{\frak{ \dfrac{ 3x -7}{ ( x -2)(x-3) } }}}}}[/tex]

[tex]\rule{200}4[/tex]

Answer:

Your solution ..................

Answer:

Probability of getting a number which is not 2 = 7/8

Step-by-step explanation:

Given;

Total number of faces = 8

Number of face with 2 = 1

Number of face with 3 = 2

Number of face with 4 = 1

Number of face with 7 = 3

Number of face with 9 = 1

Find:

Probability of getting a number which is not 2

Computation:

Probability of not an event = 1 - [Number of favourable outcomes / Total number of outcomes]

Probability of getting a number which is not 2 = 1 - [1/8]

Probability of getting a number which is not 2 = [8-1] / 8

Probability of getting a number which is not 2 = 7/8

Answer:

20

Step-by-step explanation:

f = 2f - 20

f - 2f = - 20

- f = - 20

f = 20

Answer:

The answer will be 0.45%

Step-by-step explanation:

im right

Answer:

Bob Saves 168$.  

Step-by-step explanation:

According to the Question,

Thus, A + B + H = 1012 ⇒ Amy saved $85.

So, B + H = 927 ----- Equation 1

So, H - 3B = 255  ----- Equation 2

4B = 672 ⇒ B = 168

Bob Saves 168$.

Answer:

40 units

Step-by-step explanation:

9x-5=7x+7

9x-7x=7+5

2x=12

x=6

6x+4

6(6)+4

36+4

40

Answer:

50

Step-by-step explanation:

simplify the radical by breaking the redicand up into a product of known factors, assuming positive real numbers.

Answer:

10.

Step-by-step explanation:

Answer:

The number is 10.

Step-by-step explanation:

x/5 = 2

Multiply both sides by 5.

5 * x/5 = 5 * 2

x = 10

Answer: The number is 10.

Answer:

[tex](\sqrt{x+3} )^{2} + 4^{2} = 5^{2}[/tex]

x + 3 + 16 = 25

x + 19 = 25

x = 6

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Step-by-step explanation:

16 arrangement can be done

The 24 arrangements could be made if the position of the last boy remains unchanged.

Arrangement is a plans or preparations for a future event.

The steps are as follow:

x! , where,! is factorial

x! is equal to x*(x-1)*(x-2)*(x-3)*…(x-(x-1))

∴ 4*3*2*1 = 24 arrangments

Therefore total 24 arrangements could be made if the position of the last boy remains unchanged.

Learn more about arrangment here:

https://brainly.com/question/251701

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Answer:

[tex]\begin{array}{ccl}x \ value&&Pythagorean \ triple\\3&&(6, 8, 10)\\4&&(8, 15, 17)\\5&&(10, 24, 26)\\6&&(12, 35, 37)\end{array}[/tex]

Step-by-step explanation:

The given side lengths of the right triangle are;

x² - 1, 2·x and x² + 1

A Pythagorean triple are three numbers, a, b, and c, such that, we have;

a² + b² = c²

From the given side lengths, we have;

We note that (x² + 1) > (x² - 1)

(x² + 1) > 2·x for x > 1

Therefore, with (x² + 1) as the hypotenuse side, we have;

(x² - 1)² + (2·x)² = (x² + 1)²

Therefore, when the x-value is 3, we have;

(3² - 1)² + (2 × 3)² = (3² + 1)²

8² + 6² = 10²

The least is 6² = (2 × 3)², from (2·x)²

Therefore;

The Pythagorean triple is 6, 8, 10

The order of the triple is (2·x), (x² - 1), (x² + 1)

2) The x-value for the triple, (8, 15, 17), is obtained as follows;

The least, 8 = 2·x

∴ x = 8/2 = 4

The x-value = 4

3) The Pythagorean triple where the x-value = 5 is therefore;

(2·x), (x² - 1), (x² + 1), where x = 5 gives;  (2×5 = 10), (5² - 1 = 24), (5² + 1 = 26)

Therefore, the Pythagorean triple where x = 5 is 10, 24, and 26

4) The x-value for the Pythagorean triple (12, 35, 37) is given by 12 = 2·x

Therefore, x = 12/2 = 6

Therefore, we get;

[tex]\begin{array}{ccl}x \ value&&Pythagorean \ triple\\3&&(6, 8, 10)\\4&&(8, 15, 17)\\5&&(10, 24, 26)\\6&&(12, 35, 37)\end{array}[/tex]

Answer:

about 27.6

Step-by-step explanation:

The sum of interior angles for this rectangle is 1080

119+140+124+6x+132+132+102 = 1080 add like terms

749 + 12x = 1080 subtract 749 from both sides

12x = 331 divide both sides by 12

x = 27.6 approximately

Answer: C. x > 0

Step-by-step explanation:

The answer would be x > 0.

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

use Pythagorean theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

c is the longest side

if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] > [tex]c^{2}[/tex] then it's acute (greater than)

if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] < [tex]c^{2}[/tex] then it's obtuse   (less than)

if they are equal, then its a right triangle

[tex]6^{2}[/tex] + [tex]10^{2}[/tex] = [tex]12^{2}[/tex]

36 + 100 = 144

136 = 144

136 < 144   obtuse

The correct classification for this triangle is:

obtuse, because 6² + 10² < 12²

Option C is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To determine the classification of a triangle based on its side lengths, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have a triangle with side lengths of 6 cm, 10 cm, and 12 cm. Checking the sum of the lengths of each pair of sides, we have:

6 + 10 = 16 > 12

6 + 12 = 18 > 10

10 + 12 = 22 > 6

Since all three pairs satisfy the triangle inequality theorem, the given side lengths do form a valid triangle.

Next, we can use the law of cosines to determine the measure of the largest angle in the triangle, which will allow us to classify it.

The law of cosines states that, for a triangle with side lengths a, b, and c, and the angle opposite c denoted as C, we have:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

In this case, the side lengths are a = 6 cm, b = 10 cm, and c = 12 cm. Substituting these values into the formula and solving for cos(C), we get:

cos(C) = (6² + 10² - 12²) / (2 x 6 x 10)

cos(C) = -1/5

Since the cosine function is negative for angles between 90 and 180 degrees, we know that angle C is obtuse.

Therefore,

The correct classification for this triangle is:

obtuse, because 6² + 10² < 12²

Learn more about triangles here:

https://brainly.com/question/25950519

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Answer:

Step-by-step explanation:

Well the percent of growth is 6%

The reason is because when we look at a exponential function, if the number in the percent is more than 1 subtract the number from 1 and multiply it by 100 thats your percent

Now to find the company's value in 2009 or 9 years after 2000

we just replace the variable representing time "t" for 9

221(1.06^9)= 373.37484994

the value of the company in 9 years is 373.37484994  (in million dollars)

the percentage of annual growth is 6%

pls give brainliest

Answer:

no solution

Step-by-step explanation:

7x-12<7x-7

-13<-7

no solution