What’s the simplification

Answer:

the number of students that enrolled after 15 year is 317

Step-by-step explanation:

The computation of the number of students that enrolled after 15 year is shown below;

We know that

Future value = Present value × (1 +rate of interest)^number of years

 = 100 × (1+8%)^15

= 100 × 1.08^15

= 317

Hence, the  number of students that enrolled after 15 year is 317

The same should be considered and relevant

Answer:

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

f(x) = x² - X + 2.

Quadratic equation with [tex]a = 1, b = -1, c = 2[/tex]

So

[tex]\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]

[tex]x_{v} = -\frac{(-1)}{2} = \frac{1}{2}[/tex]

[tex]y_{v} = -\frac{-7}{4} = \frac{7}{4}[/tex]

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

It looks like the number 6 goes there. It seems to be the only one missing :|

Answer: 37.28 mph

Step-by-step explanation:

Answer:

1) Yes, it is a right angle triangle

2)Yes, it is a right angle triangle

3) No, they are not similar.

Step-by-step explanation:

Dimension of triangle A = 48, 55 & 73

Dimension of triangle B = 36, 77 & 85

For any of the triangles to be a right angled one, then;

c = √(a² + b²)

Where a,b & c are side dimensions of a triangle.

Thus;

Triangle A: c = √(48² + 55²)

c = √5329

c = 73

This tallies with what we are given and so it is a right angled triangle.

Triangle B: c = √(36² + 77²)

c = √(7225)

c = 85

Similar to the third side dimension of 85, thus it is true.

For Triangle A & B to be similar, the ratio of the 3 corresponding sides must be in a whole number ratio.

Thus, we have;

48/36 = 1.5

55/77 = 5/7

73/85 = 73/85

Since the ratios are not similar, then we can say that the triangles are not similar.

Answer:K=-2

Step-by-step explanation:

becuase you do the opposite of +9 which is -9 and you do 7-9 which is -2 so K=-2

Answer:

5/8 the answer answer answer

Answer:

[tex]x = 0.1349[/tex]

Step-by-step explanation:

Given

[tex]96x (730) = (85/x)(15[/tex]

Multiply both sides by x

[tex]96x^2 (730) = 85 * 15[/tex]

[tex]96x^2 (730) = 1275[/tex]

Rewrite as:

[tex]96*730x^2 = 1275[/tex]

[tex]70080x^2 = 1275[/tex]

Divide by 70080

[tex]x^2 = 0.01819349315[/tex]

Take square roots of both sides

[tex]x = 0.1349[/tex]

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

Answer:

Let's define:

s1 = (3, 4)

s2 = (-1, 1)

s3 = (2, 0)

The system will be linearly dependent if we can write one of the vectors as a linear combination of the other two, so for example:

s1 = a*s2 + b*s3

where a and b are real numbers.

So let's try to solve this:

(3, 4) = a*(-1, 1) + b*(2, 0)

Note that the second term in the left only modifies the x-component. And the y-component in the left is 4, so we can conclude that a = 4 (because the first term is the only that has an y-component different than zero)

(3, 4) = 4*(-1, 1) + b*(2, 0)

(3, 4) = (-4, 4) + b*(2, 0)

Now we need to solve:

3 = -4 + b*2

3 + 4 = b*2

7 = b*2

7/2 = b

Then the linear combination is:

s1 = 4*s2 + (7/2)*s3

(3, 4) = 4*(-1, 1) + (7/2)*(2, 0)

Then the set is linearly dependent.

Answer:

<ABC = 15

< BAC = 150

Step-by-step explanation:

<C = <B since this is an isosceles triangle.  We know this because AC = AB

<C = 15 so <ABC = 15

The sum of the angles of a triangle is 180

A + B+ C = 180

A + 15+15 = 180

A +30 =180

A = 180-30

A = 150

< BAC = 150

Answer:

hat mather chosen to be mather

Answer:

a) true.

if 3 can divide a without remainder, then a = 3×x.

doubling that number makes it 2×3×x. because of that still included factor 3, it is still divisible by 3 without remainder.

b) false.

example :

a=6, b=4, c=3

bc = 12

6 can divide 12 without remainder, but 6 cannot do that with 4 and not with 3.

or

a=7, b=35, c=10

bc=350

7 can divide 350 without remainder, and can do that also with 35, but not with 10.

Answer:

y = -4x+14

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

m = (2-10)/(3-1)

   =-8/2

   = -4

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -4x+b

Substitute a point into the equation

10 = -4(1)+b

Add 4 to each side

14 = b

y = -4x+14

Answer:

Step-by-step explanation:

64

128°

Step-by-step explanation:

The measure of the intercepted arc is twice the measure of the inscribed angle in a circle. Since the inscribed angle is given as 64°, that means that the intercepted arc x is 2×64° = 128°

Answer:

1=110 2=70 3=70 4=110 5=110 6=70 7=70 8 =110

Step-by-step explanation:

its the answer

Answer:

-5/2 because there is -5y/2 but we have to take coefficient only so -5/2

Answer:

The "Standard Form" for writing down a Linear Equation is

Ax + By = C

A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

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

y = 4/5x + 2

Multiply both sides by 5 to clear the fraction

5y = 4x + 10

Subtract 4x from both sides

-4x + 5y = 10     This is answer D, BUT A shouldn't be negative

Multiply both sies by -1

4x - 5y = -10    This is correct Standard Form, BUT it is not one of the choices

Answer D is closest to being correct

Answer:

[tex]{ \boxed{ \bf {general \: equation : y = mx + c}}} \\ m \: is \: the \: slope \\ { \green{slope = \frac{ \triangle \: y}{ \triangle \: x} }} \\ m = \frac{(4 - 5)}{(3 - ( - 2))} \\ m = - \frac{1}{5} \\ \therefore \: { \red{y = - \frac{1}{5} x + c}} \\ consinder \: the \: first \: point : \\ 5 = ( - \frac{1}{5} \times - 2) + c \\ c = \frac{23}{5} \\ \therefore \: { \boxed{ \bf{answer : 5y = - x + 23}}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

Answer:

95% confidence interval for adults in age group 18-29 is (-0.007, 0.107)

Step-by-step explanation:

Given  

N1 = n2 = 500

% of males = 0.30

% of females = 0.35

95% confidence interval  

(p2-p1) + z(0.025) sqrt (p1q1/n1 + p2q2/n2)  and (p2-p1) - z(0.025) sqrt (p1q1/n1 + p2q2/n2)  

Substituting the given values, we get –  

(0.35-0.30) + 1.96 sqrt (0.3*0.7/500 + 0.35*0.65/500) and (0.35-0.30) - 1.96 sqrt (0.3*0.7/500 + 0.35*0.65/500)

0.05 + (1.96 *0.029) and 0.05 - (1.96 *0.029)

0.05 + 0.057 and 0.05 – 0.057  

(-0.007, 0.107)

Answer:

-1 over 2

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

The line joins (-2, 2) and (0, 1).

Remember that slope equals change in y all divided by the change in x.

Here,

change in y = 1 - 2 =- 1

change in x = 0 -(-2) = 2

Thus, slope =- 1/2

Answer:

if you still need the answer its B here the explenation in a picture:

Step-by-step explanation:

Answer:

315

Step-by-step explanation:

the formula is V = B * h

B is the area of the base

V = (1/2)(10)(7) * 9

Answer:

5

Step-by-step explanation:

5 l 25,55

   l 5,11

Answer:

Step-by-step explanation:

question no . 5

ratio of angle L

take angle as reference angle

using cos rule

cos L = base / hypotenuse

= 4/5

ratio of angle N

take angle N as reference angle

using sin rule

sin N = opposite / hypotenuse

= 4/5

for measure of angle L

cos L = 4/5

cos L = 0.8

L = [tex]cos^{-1}(0.8)[/tex]

L = 36.9

for meanure of angle N

sin N = 4/5

sin N = 0.8

N = [tex]sin^{-1}(0.8)[/tex]

N = 53.1

Answer:

domain=0

range=2

Step-by-step explanation:

this might be helpful..

Answer:

step 1 : 8/b = sin 45 degree so b = 11.31

step 2 : a/b = sin 60 degree, so a = 9.8

step 3: c/b = cos 60 degree, so c = 5.66

Answer:

The sequence converges to 1

Step-by-step explanation:

Given

[tex]\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},...[/tex]

Require

Description of the sequence

The given sequence follows:

[tex]\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},... \frac{n+1}{n+3}[/tex]

i.e.

[tex]T_n = \frac{n+1}{n+3}[/tex]

For every term,

[tex]\frac{n+1}{n+3} < 1[/tex]

In other words,

as the value of n increases, [tex]\frac{n+1}{n+3}[/tex] approaches 1

Hence, (c) is true

Answer:

(3,10)

Step-by-step explanation:

When x is 3

[tex]{ \bf{y = 3x + 2}} \\ { \bf{y = (3 \times 3) + 2}} \\ { \bf{y = 11}}[/tex]

y is 11, and this is invalid because it is not at accord.

The correct coordinates which is NOT a solution to the linear equation

y = 3x+2 is,

⇒ (3, 10)

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Linear equation is,

⇒ y = 3x + 2

We know that;

The solution of linear equation is satisfy the eqaution.

Hence, We can check as;

⇒ y = 3x + 2

Put x = 1. y = 5

⇒ 5 = 3 × 1 + 2

⇒ 5 = 5

Thus, It is solution of linear equation.

⇒ y = 3x + 2

Put x = 2. y = 8

⇒ 8 = 3 × 2 + 2

⇒ 8 = 8

Thus, It is solution of linear equation.

⇒ y = 3x + 2

Put x = 3, y = 10

⇒ 10 = 3 × 3 + 2

⇒ 10 ≠ 11

Thus, It is not solution of linear equation.

Thus, The correct coordinates which is NOT a solution to the linear equation y = 3x+2 is,

⇒ (3, 10)

Learn more about the equation of line visit:

https://brainly.com/question/18831322

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Answer:

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