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Which student's expression results in a quotient of 12.5?
KWAN
VERA
16.25 : 1.3
- 11.25 = (-9)
Mark only one oval.
0000
a. Kwan's only
b. Vera's only
c. Both Kwan and Vera's
d. Neither Kwan nor Vera's

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

#SPJ7

Answer:

The answer is D.

Step-by-step explanation:

When a graph of a line goes down and to the right, it shows that as the value of x increases, the value of y decreases. This represents a negative coefficient for x.

The graph is a drawn out version of the question.

Te graph of a line goes down and to the right when the coefficient of x is negative, option (D) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

y = mx + c

We have:

The graph of a line goes down and to the right when.

The orientation of the line depends on the slope.

If the slope of the line is positive, the line will go up.

If the slop of the line is negative, the line will go down.

Thus, the graph of a line goes down and to the right when the coefficient of x is negative, option (D) is correct.

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ2

[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:

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

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.

If semi-monthly means every half a month, then my take home pay is 22864.58333

Answer:

548750/12

approximately 45729

Step-by-step explanation:

given the geometric sequence 2, -4, 8, -16, ...

a1 = 2

r = -4/2 = -2

find : a9 and a15

solutions:

an = a1. r^(n-1)

=> a9 = 2. (-2)^(9-1)

= 2. (-2)^8

= 2. 2^8

= 2^9

= 512.

=> a15 = 2. (-2)^(15-1)

= 2. (-2)^14

= 2. 2^14

= 2^15

= 32,768

Step-by-step explanation:

Hey there!

The given geometric sequence is: 2, -4, 8, -16.

The;

a1 = 2

Common ratio (r) = T2/T1

= -4/2

= -2

Now;

Use general formula of geometric sequence;

[tex]tn = {a1.r}^{n - 1} [/tex]

Where, "a1" is first term, "n" is no.of terms and "r" is common ratio.

Then;

[tex]t9 = 2 \times { (- 2)}^{9 - 1} [/tex]

or, t9 = 2*256

Therefore, t9 = 512.

Again;

[tex]t15 = 2. { (- 2)}^{15 - 1} [/tex]

or, t15= 2*16384

Therefore, t15 = 32768.

Hope it helps!

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:

20

Step-by-step explanation:

f = 2f - 20

f - 2f = - 20

- f = - 20

f = 20

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.

Answer:

75

Step-by-step explanation:

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:

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:

[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:

The answer will be 0.45%

Step-by-step explanation:

im right

Answer:

Step-by-step explanation:

Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:

and

Now for the slope of AB:

and

 So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):

and filling in:

y - 3 = -3(x - 0) and

y - 3 = -3x + 0 and

y - 3 = -3x so

y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):

0 = -3x + 3 and

-3 = -3x so

x = 1

The coordinate on the x-axis such that AC = BC is (1, 0)

Answer:

0.037

Step-by-step explanation:

Given that,

Let a and b be the solutions to [tex]x^2 + x -3 = 0[/tex]

It can be solved using quadratic formula where a = 1, b = 1 and c = -3

So,

[tex]x=\dfrac{-1+\sqrt{1^2-4\times 1\times (-3)}}{2(1)},\dfrac{-1-\sqrt{1^2-4\times 1\times (-3)}}{2(1)}\\\\x=1.30,-2.3[/tex]

Let a = 1.3, b = -2.3

The value of [tex]a^3 -4b^2 + 19[/tex] can be given by :

[tex]a^3 -4b^2 + 19=(1.3)^3-4\times (-2.3)^2+19\\\\=0.037[/tex]

So, the value of the given expression is 0.037.

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:

The correct answer is y = | x + 6 |

Answer:

Check explanation

Step-by-step explanation:

Let

x = original price

Percentage increase in price = 17%

New price = original price + Percentage increase in price

= x + 17% of x

= x + 0.17 * x

= x + 0.17x

= 1.17x

Shipping cost = $3

Total cost = $43

Total cost = New price + Shipping cost

43 = 1.17x + 3

43 - 3 = 1.17x

40 = 1.17x

x = 40 / 1.17

x = $34.188034188034

Approximately,

x = $34.2

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:

PLZZ MARK ME BRAINLIEST..!

Step-by-step explanation:

Bridgets fish: f , 2f, 3f+2 , 1/2f, 3/5f

Add for total weight: 7 1/10 f +2

Dads fish: 3f+2, 4/5f, 2f+4, 1/2f

Add for total weight:  6 3/10f +6

set the 2 total weights equal:

6 3/10f +6 = 7 1/10f +2

Subtract 6 3/10f from each side:

6 = 8/10f  + 2

Subtract 2 from each side:

4 = 8/10f

Divide both sides by 8/10:

f =  5

Bridget's first fish weighed 5 ounces.

Dads first fish weighed:  2 more than 3 times :3(5) + 2 = 15 +2 = 17 ounces.

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:

x = 5

Step-by-step explanation:

5x + 10 = 35

Subtract 10 from both sides

5x + (10-10) = 35 - 10

Simplify

5x = 25

Divide both sides by 5

5x/5 = x

25/5 = 5

We're left with x = 5

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\boxed{x = 5}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'....}}\\\\5x + 10 = 35\\-------------\\\rightarrow 5x + 10 - 10 = 35 - 10\\\\\rightarrow 5x = 25\\\\\rightarrow \frac{5x=25}{5}\\\\\rightarrow \boxed{x = 5}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

The more spread out your graph is, the greater the standard deviation.

So the option with the most spread out graph, which I think is A, can't see very clear.

Answer:

[tex]Bike = 7[/tex]

[tex]Car = 8[/tex]

[tex]Walk = 9[/tex]

[tex]Bus = 12[/tex]

Step-by-step explanation:

Given

[tex]Bus = 120^o[/tex]

[tex]Walk = 90^o[/tex]

[tex]Car = 80^o[/tex]

[tex]n = 36[/tex] --- pupils

Required

Determine the number of students in each category

This is calculated by dividing the measure of each category by 360; then multiply the result by the number of pupils:

So, we have:

[tex]Bus = \frac{120}{360} * 36 = \frac{1}{3} * 36 = 12[/tex]

[tex]Walk = \frac{90}{360} * 36= \frac{1}{4} * 36 = 9[/tex]

[tex]Car = \frac{80}{360} * 36 = \frac{80}{10} = 8[/tex]

To calculate the number of students that travel by bike, we have:

[tex]Car + Bike + Walk + Bus= n[/tex]

Substitute values

[tex]8 + Bike + 9+ 12= 36[/tex]

Collect like terms

[tex]Bike = 36 - 8 - 9 - 12[/tex]

[tex]Bike = 7[/tex]

Answer:

Look at picture

Step-by-step explanation: