write the equation of the line that passes through the point (-2,4) and (5,8). Put your answer in fully reduced point slope form, unless it is a vertical or horizontal line.

Answer:

(2,5)

Step-by-step explanation:

4x - 2y = -2

6x + 3y = 27

Divide the first equation by 2 and the second equation by 3

2x - y = -1

2x + y = 9

Add the equations together

2x - y = -1

2x + y = 9

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

4x = 8

Divide by 4

4x/4 = 8/2

x =2

2x+y = 9

2(2) +y = 9

4+u = 9

y = 9-4

y=5

(2,5)

Answer:

√13

Step-by-step explanation:

To get the side a, we will use the cosine rule as shown;

a² = b²+c²-2bcCosθ

Substitute the given values

a² = 5²+(3√2)²-2(5)(3√2)Cos45

a² = 25+18-30√2*1/√2

a² = 25+18-30

a² = 13

a = √13

Hence the value of a is √13

Answer:

The amount Tobie invests in a bank, P = $25

The annual compound interest rate, i = 4%

a. The principal is amount invested in the bank, P = $25

The annual interest rate, i = 4%

b. The function that represents Tobie's account balance, A, after t years is given as follows;

[tex]A(t) = P \cdot (1 + i)^t[/tex]

Where;

A(t) = The amount in the account after t years

P = The principal amount

i = The annual compound interest rate

t = The number of years

c. The values to place in the table are found as follows;

At t = 0, [tex]A(0) = 25 \times(1 + 0.04)^0[/tex]  = 25

At t = 10, [tex]A(10) = 25 \times(1 + 0.04)^{10}[/tex] = 37

The given table is presented as follows;

[tex]\begin{array}{ccc}t&&A(t)\\0&&25\\10&&37\end{array}[/tex]

Step-by-step explanation:

Answer:

the area sector is 123.2

Answer:

f (x)=11

Step-by-step explanation:

f (x)= x + 8

f (3)= (3 +8)

=f(x) =11

**replace the x with a variable which is 3

Answer:

3(2×2+1)+3×(2×2)/3=1×3=4×3

36+3+4=3=12

36+3+4-3-12

43-15

28

Answer:

B. y=1/2+2

Step-by-step explanation:

since parallel lines always have the same slope, the only two possible answers could be B and C. in order to find if one of those goes through point (-2,1), we have to set up an equation to find the base:

1=1/2(-2)+b

1=-1+b

2=b

We can plug in the base with the slope for the equation and the new equation would be y=1/2x+2

Answer:

x = ±1/2

Step-by-step explanation:

x^2-1/4=0

Add 1/4 to each side

x^2 -1/4+1/4 = 0+1/4

x^2 = 1/4

Take the square root of each side

sqrt(x^2) = sqrt(1/4)

x = ±1/2

Answer:

a)11cm

b)49.5cm²

Step-by-step explanation:

to find the perimeter you use the formula

o/360×2piR

since 2pi R=18pi cm,to find the radius you cancel pi from both sides 2r/2=18/2...so the radius is 9cm

therefore the perimeter will be:

70/360×2×22/7×9

27720/2520

=11cm

then to find the area you say

o/360×pi R²

70/360×22/7×9²

124740/2520

=49.5cm²

I hope this helps

Answer: -1

Step-by-step explanation:

12x^2-7x-12 = (4x+3)(3x-4)

4x+3=0. X = -3/4

3x-4=0. X = 4/3

(-3/4) (4/3) = -1

Set up a ratio of height/ shadow

2.7/1.56 = x/38.25

Cross multiply:

1.56x = 103.275

Divide both sides by 1.56

X = 66.2

Round to nearest meter = 66

Answer: 66 meters

Answer:

D. exponential; y = 98 • 0.79x

Step-by-step explanation:

Answer:

Option D is correct.

Exponential model are the data best represented.

Equation:  

Step-by-step explanation:

An exponential function is in the form of   .....[1] where a is the initial value and b≠0 , b > 1.

Consider any two points from the table;

(0, 98) and ( 1, 77)

Then substitute these in [1];

For (0, 98)

x = 0 and y = 98 substitute in [1] we get;

98 = a

Similarly, For (1, 77)

we have;

77 = ab

Substitute the value of a =98 we get;

Divide both sides by 98 we get;

⇒ b = 0.79

We get an equation;  

Therefore, the data represent here is, Exponential function.

also, an equation to model the data is;  

...............................................................................................................................................

All the functions grow with x except B that decreases when x grows. That i your function. Also check that when you divide the population of two consecutive years, the ratio remains 0.79 approx

The solution is D

...............................................................................................................................................

Exponential would be the correct answer I believe...

...............................................................................................................................................

For a better understanding of the explanation provided here please find the attachment.

The solution will employ the use of the trial and error method and basic math.

As can be see from the given data, the deer population keeps on falling from the year zero. Thus, we can safely conclude that the quadratic and the linear models will not represent the situation at all.

We are left with the exponential model and since we have  in it we can see that the deer population will fall as the years pass.

We have checked it in the table that has been provided and we have concluded that the data is best represented by the exponential model because when the exponential formula is applied it is almost equal to the actual number of deers.

Please check the attached table for a better understanding.

Answer:

See explanation

Step-by-step explanation:

Given

[tex]\triangle LMN \to \triangle PQR[/tex]

[tex]k = 1.25[/tex]

Required

The length of PQ

[tex]\triangle LMN \to \triangle PQR[/tex] means that the side lengths of LMN are multiplied by 1.25 to get the side lengths of PQR

And it implies that the following sides are corresponding

[tex]LM \to PQ[/tex]

[tex]MN \to QR[/tex]

[tex]LN \to PR[/tex]

So, we have:

[tex]PQ = k * LM[/tex]

[tex]PQ = 1.25* LM[/tex]

The question is incomplete.

Assume LM = 16, then:

[tex]PQ = 1.25* 16[/tex]

[tex]PQ = 20[/tex]

Answer:

Domain: [tex](-\infty,\infty)[/tex]

Range: [tex]f(x) \ge 0[/tex]

Step-by-step explanation:

Given

[tex]f(x) = |x + 6|[/tex]

Required

The domain and the range

First, we calculate the domain

[tex]f(x) = |x + 6|[/tex]

The above function does not have roots or fraction, where x is the denominator. This means that the domain is all real numbers, i.e. [tex](-\infty,\infty)[/tex]

The range

The function is an absolute function; So, the minimum value is 0.

Hence, the range is:

[tex]f(x) \ge 0[/tex]

Answer:

A

Step-by-step explanation:

on edge

Answer:

since each side of a square is the same it can simply be the length of one side squared. if a square has one side of 4 inches ,the area would be 4 inches times 4 inches,or 16 square inches

Answer:

x + y + z.

Step-by-step explanation:

x² + y² + 2xy - z²

= (x + y)^2 - z^2

This is the difference between 2 squares so the factors are:

(x + y + z) and (a + y - z).

Answer: The factors are (x+y+z) and (x+y-z)

In other words, it factors to (x+y+z)*(x+y-z)

=====================================================

Work Shown:

[tex]x^2 + y^2 + 2xy - z^2\\\\(x^2 + 2xy + y^2) - z^2\\\\(x+y)^2 - z^2\\\\(x+y+z)(x+y-z)\\\\[/tex]

Notes:

Answer: Hello your question lacks vital information attached below is the vital information

Along with the image below, Use your knowledge of the unit circle and radian measure of angles to answer the following questions. [Note: When the questions ask you to consider circles and their angle in relation to the main circle, the question is referring to the location of the center of each circle.]

answer:

Circle 7 = π / 4

Circle 8 = 7π / 12

Circle 9 = 11 π / 12

Circle 10 = 5π / 4

Circle 11 = 19π / 12

Circle 12 = 23π / 12

Step-by-step explanation:

Given that 45° = π/4.

∴  All the six(6) circles ( 7 through 12 ) are separated by : 60° = π/3

The Radian measure of the remaining circles through 12 :

Circle 8 = π/3 + π /4 = 7π / 12

Circle 9 = π/4 + 2 π/3 = 11 π / 12

Circle 10 = 5π / 4

Circle 11 = 19π / 12

Circle 12 = 23π / 12

Reason : All the six(6) circles ( 7 through 12 ) are separated by : 60° = π/3

Answer:

A=2

B=4

C=6

D=5

E=7

F=8

G=3

H=1

Step-by-step explanation:

explanation is in the picture!

Answer: The range is  [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

Explanation:

The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.

The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.

Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

This translates to "y is a real number such that y is -6 or smaller".

So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.

See below for a visual example of what's going on.

Answer:

26

Step-by-step explanation:

Let x = the third angle in the triangle

x = 102 because they are vertical angles

The sum of the angles in the triangle are 180

b+2b+102 =180

3b+102 =180

3b = 180-102

3b = 78

Divide by 3

3b/3 = 78/3

b = 26

Answer:

Its is 26 aka E

Step-by-step explanation:

So we know that a triangle has 180 degrees in total. So we know one side is 102 degrees. 180-102=78. we can do 78 divide by 3 since there is 3b's in total. 78/3=26. Therefore, it is 26 which is E. I hope this helped ^^.

Answer:

10.52

Step-by-step explanation

Answer:

Let x= the ones digit

Then x+5=the tens digit

Hence the equation is: 10(x+5)+x=x+5+x+63

10(x+5)+x=x+5+x+63

10x+50+x=2x+68

11x+50=2x+68

-2x-50  -2x-50

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

       9x=18  Divide both sides of the equation by 9

         x=2

Hence the number is 10(2+5)+2=10(7)+2=70+2=72.

An example of an exponential function is given as follows:

A. Investing $1,000 at an annual interest rate of 3%, compounded monthly.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

As we saw above, the rate of change is a percent, and in this problem, only option A has a rate of change as a percent, hence it is an exponential function.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Answer:

A

Step-by-step explanation:

Observe the coordinates of C, it's (5,2). Now observe C' which is (2, - 5). Hence the rule is (x, y) -> (y, - x)

Answer: A) 4

Explanation:

For any 30-60-90 triangle, the short leg is half as long as the hypotenuse.

The short leg is opposite the smallest angle (30 degrees), so we see that

x = 8/2 = 4.

Answer:

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangle

Step-by-step explanation:

Part A: Linear Equation.

We can find the slope

[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]

So our equation is

[tex]y = - 10x + 15[/tex]

Part B: Exponential Equation

We know that

[tex]15 = a \times b {}^{0} [/tex]

B to the zero power is 1 so

[tex]15 = a[/tex]

This means a =15. Now let find b.

[tex]5 = 15 \times b {}^{1} [/tex]

[tex] \frac{1}{3} = b[/tex]

So the equation is

[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]

Answer:

Bajaj Pulsar of a great time in the 7th century there where you will have the gall the subcontinent the

=====================================================

Explanation:

We can rewrite 5 as 5s^0, since s^0 = 1 where s is nonzero.

Think of 2s as 2s^1

With those ideas in mind, the original polynomial turns into 5s^0 + 2s^1

Sorting the terms so that the largest exponent is first gets us the standard form 2s^1 + 5s^0

The largest exponent is the degree, so the degree is 1.

Side note: This trick only works for single variable polynomials.

Answer:

m∠1 = 90º

m∠2 = 25º

Step-by-step explanation:

m∠1

diagonals of a kite are perpendicular by definition

m∠2

the 65º angle, the angle to the right of ∠1, and ∠2 form a triangle

we know that triangles are 180º

65º + 90º + m∠2 = 180º

m∠2 = 25º