Perform the Operation k^2+3k-10/36 × 3/k^2-4

ANSWER

58°

EXPLANATION

The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is

[tex]51 \degree = \frac{1}{2} (160 - x)[/tex]

Multiply through by 2

This implies that

[tex]2 \times 51 \degree =2 \times \frac{1}{2} (160 - x)[/tex]

We simplify to get:

[tex]102 \degree =160 - x[/tex]

Solve for x.

[tex]102 \degree - 160 \degree =- x[/tex]

[tex] - 58 \degree =- x[/tex]

[tex]58 \degree =x[/tex]

Answer:

(5,-1)

Step-by-step explanation:

4x+3y=17

3x+2y=13

So elimination sounds fun but we will have to do manipulation:

Multiply top equation by 2 and bottom equation by 3. This will cause the second term in both by 6y which means we would be setup for elimination.

8x+6y=34

9x+6y=39

--------------------now subtract the equations

-x+0=-5

So x=5

Now plug it into either question (no matter which-pick and choose)

I will go with the second original 3x+2y=13

So if x=5 we have 15+2y=13

Subtract 15 on both sides:        2y=-2

Now divide both sides by 2:      y=-1

Answer (5,-1)

Final answer:

To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, the elimination method shows that the solution is x = 5 and y = -1.

Explanation:

To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, one could use either the substitution method, the elimination method, or matrix methods. However, as per the guidance, we will follow the elimination method which is efficient and easily understandable.'

Let's multiply the first equation by 2 and the second equation by 3, which will give us:

8x + 6y = 34 (equation 1 multiplied by 2)

9x + 6y = 39 (equation 2 multiplied by 3)

Now, subtract the first new equation from the second new equation to eliminate y:

9x - 8x + 6y - 6y = 39 - 34

x = 5

Substitute x = 5 into one of the original equations to find y. For example, put x = 5 in 4x + 3y = 17:

4(5) + 3y = 17

20 + 3y = 17

3y = -3

y = -1

Therefore, the solution to the system of equations is x = 5 and y = -1.

Answer:

D) e

Step-by-step explanation:

ln e^e

We know that ln x^a is the same as a ln x

e ln (e)

we know that ln e =1

e (1)

e

Answer:

The correct answer is:  [D]:  " e " .

Step-by-step explanation:

__________________________________________________

  ln e^e = e * (ln e)  = e * (1) = e .

__________________________________________________

[tex]\bf \begin{array}{rrlll} term&\stackrel{f(n+1)=-0.5f(n)}{~\hfill value~ }\\ \cline{1-2} f(1)&120\\ f(2)&-0.5(120)\\ &-60\\ f(3)&-0.5(-60)\\ &30\\ f(4)&-0.5(30)\\ &-15\\ f(5)&-0.5(-15)\\ &7.5 \end{array}[/tex]

Answer:

f(5) = 7.5

Step-by-step explanation:

The recursive formula allows a term in the sequence to be found from the previous term, thus

f(2) = - 0.5 f(1) = - 0.5 × 120 = - 60

f(3) = - 0.5f(2) = - 0.5 × - 60 = 30

f(4) = - 0.5f(3) = - 0.5 × 30 = - 15

f(5) = - 0.5f(4) = - 0.5 × - 15 = 7.5

Answer:

D) 50+31.5x

Step-by-step explanation:

10% of 35 is 3.5

35-3.5=31.5

[tex]f(x)=9\Longrightarrow f(-2)=9[/tex]

The function is a constant. No matter the input the output will always be equal to 9.

Hope this helps.

r3t40

3x +11 = K

To solve for X, we need to isolate x on one side.

Subtract 11 from both sides:

3x = K -11

Divide both sides by 3:

x = (k-11)/3

Answer:

3x +11 = K

x = (k-11)/3

Step-by-step explanation:

Answer:

[tex]\large\boxed{d)\ 12}[/tex]

Step-by-step explanation:

[tex]x-\dfrac{1}{2}y=-6\\\\\text{y-intercept is for x = 0. Substitute:}\\\\0-\dfrac{1}{2}y=-6\\\\-\dfrac{1}{2}y=-6\qquad\text{multiply both sides by (-2)}\\\\\left(-2\!\!\!\!\diagup^1\right)\left(-\dfrac{1}{2\!\!\!\!\diagup_1}y\right)=(-2)(-6)\\\\y=12[/tex]

Answer:

[tex]x-12[/tex]

Step-by-step explanation:

First open the brackets

[tex]=(4x-6)-(3x+6)\\\\\\=4x-6-3x-6[/tex]

Then collect the like terms

[tex]4x-3x-6-6[/tex]

Solve the like terms

[tex]4x-3x=x\\\\\\-6-6=-12\\\\\\=x-12[/tex]

The simplified form is

[tex]x-12[/tex]

Answer:

the box is cheaper

Step-by-step explanation:

2L bottle=$2,8(1L=$1,4)

[tex]6 \times 12 \: l \: bottle = 3.9(1l = \frac{0.65}{12} )[/tex]

the box is cheaper

Answer:

3

Step-by-step explanation:

Answer:

The correct answer is (3,2)

Answer:

(

k

+

9

)

(

k

−

9

)

(k+9)(k-9)

Step-by-step explanation:

Answer:

It's C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The measures of angle B and angle D of the given parallelogram will be 55°, i.e. option A.

Parallelogram is a 2D shape, having opposite sides parallel and equal. Also the opposite angles of parallelogram are congruent means equal.

We have,

A Parallelogram with,

Angle B = (2n + 15)° and,

Angle D = (3n - 5)°

So,

As mentioned above in the definition that the opposite angles of parallelogram are congruent means equal.

i.e.

Angle B = Angle D

i.e.

2n + 15 = 3n - 5

On solving we get,

20 = n

⇒ n = 20,

So,

Angle B = (2n + 15)° = (2 * 20 + 15)° = 55°

And,

Angle D = (3n - 5)° = (3 * 20 - 5)° = 55°

Hence, we can say that the measures of angle B and angle D of the given parallelogram will be 55°, i.e. option A.

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Answer: -12

Step-by-step explanation:

Answer:

Hi there!

The answer to this question is negative 12.

Answer:

A! Straight up!

Answer:

The correct answer is B

Step-by-step explanation:

You want an even number per grade level to get comparable results.

Answer: um well it’s b... sorry for being 2 years late yk I was getting a drink of water

Step-by-step explanation:

Answer:

53 miles

Step-by-step explanation:

I'm going to assume "$0.25 for each time" is "$0.25 per mile."

$1.75 is the flat fee. It costs 25 cents for each mile. We can represent this as:

1.75 + 0.25m

The sum of this equation has to be less than or equal to $15. We can display this as:

1.75 + 0.25m ≤ 15.

To solve, we must first isolate 0.25m. To do this, we subtract 1.75 from each side.

0.25m ≤ 15 - 1.75

0.25m ≤ 13.25.

Now, we must isolate the variable 'm' to determine how many miles Eddie can travel. To do this, we divide 0.25 from each side.

m ≤ 13.25 / 0.25

m ≤ 53.

Therefore, Eddie can travel 53 miles if he has $15 to spend.

Answer:

The next number is 1321232112

Step-by-step explanation:

32 is read off as "one 3, one 2" = 1312

1312 is read off as "one 1, one 3, one 1, one 2" = 11131112

11131112 is read off as "three 1s, one 3, three 1s, one 2" = 31133112

31133112 is read off as "one 3, two 1s, two 3s, two 1s, one 2" = 1321232112

Answer:

[tex]=\frac{12w+15g-100}{20}[/tex]

Step-by-step explanation:

Three-fifth of w is 3/5 of w

[tex]=\frac{3}{5} *w=\frac{3}{5} w[/tex]

Three-fourths of g is three-quarters of g

[tex]=\frac{3}{4} *g=\frac{3}{4} g[/tex]

find the sum of the fractions then subtract 5

[tex]=\frac{3}{5}w-\frac{3}{4} g-5\\\\\\=\frac{3}{5}w-\frac{3}{4}g-\frac{5}{1}[/tex]

The LCM here is 20 i.e 5*4

=[tex]\frac{3}{5} w+\frac{3}{4}g-\frac{5}{1}=\frac{12w+15g-100}{20} \\[/tex]

Answer:

32 students

Step-by-step explanation:

We are given that at the beginning of a class period, half of the students in a class go to the library and half of the remaining to the computer lab.

Given that there are 8 students remaining, we are to find the total number of students in the class initially.

At beginning = [tex]x[/tex] students

After half of them leave = [tex]\frac{x}{2}[/tex] students

After half of the remaining leave = [tex]\frac{x}{4}[/tex] students

So, [tex]\frac{x}{4} = 8[/tex]

[tex]x=8\times 4[/tex]

x = 32

Therefore, there were 32 students in the class originally.

there were 32 students in the class originally.

because in the computer lab before there were 16.  16 times 2 equals 32.

Answer:

3 TERMS

Step-by-step explanation:

There are total 3 terms in the polynomial  [tex]x^{2} + xy - y^{2}[/tex] .

The given polynomial expression is  [tex]x^{2} + xy - y^{2}[/tex] .  

The number of terms of any expression is the total number of independent variables present in the given polynomial expression.

We can see that there are total 3 independent variables present in the polynomial expression and therefore the number of terms present is also three.    

Thus, there are total 3 terms in the polynomial  [tex]x^{2} + xy - y^{2}[/tex] .

To learn more about terms in the polynomial, refer -

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Answer:

60y = 30x - 12

y = 1/2x - 1/5

The slope is 1/2

Answer:

1/2

Step-by-step explanation:

30 over 60 is half

Answer:

The simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8

Step-by-step explanation:

We have to simplify the following

-6.3x+14 and 1.5x-6

it can be written as:

=(-6.3x+14) + (1.5x-6)

Adding the like terms

=(-6.3x+1.5x)+(14-6)

= (-4.8x)+(8)

= -4.8x+8

So, the simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8

Answer:

8 Gauss

Step-by-step explanation:

Since your moving the magnet from 10 to 20cm you're essentially multpliying the distance by 2.

K = 2

Therefore k ^ 3 = 2^3

64/2^3

=8

Answer:

8 Guass

Step-by-step explanation:

We multiply the distance by a factor of $2$, and thus divide the magnetic field strength by a factor of $2^3 = 2 \cdot 2 \cdot 2 = 8$. We get a magnetic field strength of 64/8 = 8

The answer is:

The first option shows the graph of the given function.

Since the given function is an exponential function, we are looking for an exponential function graph, with a function that intercepts the y-axis at y equal to 2, or the point (0,2).

So, since we are given just one exponential graph, let's find the y-axis intercept in order to assure that the correct option is the first graph.

The function is:

[tex]y=2e^{x}[/tex]

Finding the y-axis intercept, we need to make "x" equal to 0, so:

[tex]y=2e^{0}[/tex]

We need to remember that any number elevated or powered to 0 is equal to 1, so:

[tex]y=2*1=2[/tex]

We have that the function intercepts the y-axis at y equal to 2, or the point (0,2).

Finding the x-axis intercept, we need to make "y" equal to 0, so:

[tex]y=2e^{x}[/tex]

[tex]0=2e^{x}[/tex]

[tex]Ln(0)=Ln(2e^{x})[/tex]

Now, since the natural logarithm of "0" does not exist in the real numbers, we can see that there is not x-axis intercept for this function.

Hence, the first option shows the graph of the given function.

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

Graph A

Step-by-step explanation:

Correct on edge!

Answer:

The set {10 , 24 , 26} formed a right triangle

Step-by-step explanation:

* Lets explain how to check the sides lengths which formed a  

 right triangle

- In triangle ABC

# If AC is the longest side in length

# If (AC)² = (AB)² + (BC)²

∴ AB , BC , AC formed a right angle triangle  

∴ m∠B = 90°  (The angle opposite to the longest side)

∴ AC is the hypotenuse

* Now lets solve the problem

- In set 8 , 12 , 15

∵ The longest side is 15 cm

∴ (15)² = 225

∵ (8)² + (12)² = 64 + 144 = 208

∵ (15)² ≠ (8)² + (12)²

∴ The set not formed a right triangle

- In set 10 , 24 , 26

∵ The longest side is 26 cm

∴ (26)² = 676

∵ (10)² + (24)² = 100 + 576 = 676

∵ (26)² = (10)² + (24)²

∴ The set formed a right triangle

- In set 12 , 20 , 25

∵ The longest side is 25 cm

∴ (25)² = 625

∵ (12)² + (20)² = 144 + 400 = 544

∵ (25)² ≠ (12)² + (20)²

∴ The set not formed a right triangle

- In set 15 , 18 , 20

∵ The longest side is 20 cm

∴ (20)² = 400

∵ (15)² + (18)² = 225 + 324 = 549

∵ (20)² ≠ (15)² + (18)²

∴ The set not formed a right triangle

* The set {10 , 24 , 26} formed a right triangle

Answer:

3x + 8

Step-by-step explanation:

Please use the symbol " ^ " to indicate exponentiation:  12x^2 + 29x – 8.

To answer this question, try dividing this 12x^2 + 29x – 8 by each of the given possible factors, one by one.  If the end result is a zero remainder, that indicates that the particular factor is in fact a factor of 12x^2 + 29x – 8.

Alternatively, use synthetic division; if the end result is zero, then you have identified a root of 12x^2 + 29x – 8, as well as a factor.

Let's focus on x - 8:  Is this a factor?  Is 8 a root?  Set up synthetic division as follows:

8   )   12    29    -8

                96   1000

         -----------------

         12   125   992    

The non-zero remainder (992) indicates that 8 is not a root of 12x^2 + 29x – 8, and that x - 8 is not a factor.

Continuing onto the next given possible factor, 2x - 1, we set this = to 0 and solve for x, obtaining x = 1/2.  Use synthetic division again:

1/2      )    12    29    -8

                        6     35/2

         ------------------------

              12      35    19/2                    No, 1/2 is not a root and

                                                             2x - 1 is not a factor of 12x^2 + 29x – 8.

Try possible root x = -8/3:

-8/3   )   12      29      -8

                     -32       8

        ----------------------------

            12       -3         0

This zero remainder tells us that 3x + 8 is a factor of 12x^2 + 29x – 8.

Answer:

C. on edge

Step-by-step explanation:

Answer:

See attachment.

If altitude = 45 then

side = 2 * height (or altitude) / square root of 3

side = 2 * 45 / 1.7320508076

side = 90 / 1.7320508076

side = 51.9615242271

Step-by-step explanation:

Follow below steps;

When dealing with an equilateral triangle, dividing it by an altitude creates two 30-60-90 right triangles. Since we know the length of the altitude (45), which corresponds to the shorter leg in the 30-60-90 triangle, we can find the length of the side of the equilateral triangle (which is the hypotenuse of the 30-60-90 triangle) using the properties of this special right triangle.

To begin, we recognize that the ratios of the sides of a 30-60-90 triangle are 1:\\(extbackslashsqrt{3}\\):2. Thus, if the shorter leg is 45, the hypotenuse will be twice that length, because the ratio of the shorter leg to the hypotenuse is 1:2. Therefore, the length of a side of the equilateral triangle is 45 * 2, which equals 90.

ANSWER

66 cubic units

EXPLANATION

The volume of a triangular prism is the area of the triangular base times the height of the prism.

We calculate the volume using the formula:

[tex]volume = \frac{1}{2} bh \times H[/tex]

where b=4 is the base of the triangle and h=3 is the height of the triangle.

H=11 is the height of the prism.

We substitute these values to get;

[tex]volume = \frac{1}{2} \times 4 \times 3 \times 11[/tex]

[tex]volume = 66 \: cubic \: \: units[/tex]