7. [Decimal +,-]
16
9.74
+2 6.80

The equation of the line from give points is y = 2/3x - 5/3.

According to the statement

We have given that the two points which are (-2,-3) and (4,1)

And we have to find the equation of a line that passes through the given points.

So,For this purpose,

First, we need to determine the slope of the line. The slope can be found by using the formula:

[tex]m = \frac{(y_2) -(y_1)}{(x_2) -(x_1)}[/tex]

Where

m is the slope and

Substituting the values from the points in the problem gives:

m = 1 + 3 /4 + 2

m = 4/6

m = 2/3.

And then

Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:

[tex]y - (y_1) = m(x -x_1)[/tex]

Put the values in it then

y - (-3) = 2/3 (x-(-2))

y +3 = 2/3 (x +2)

3y + 9 = 2x + 4

3y - 2x = 4 -9

3y -2x = -5

3y = 2x - 5

y = 2/3x - 5/3.

So, The equation of the line from give points is y = 2/3x - 5/3.

Learn more about equation of the line here

https://brainly.com/question/13763238

#SPJ1

Answer:Many

Step-by-step explanation:

As the unknown cancels itself out, it could be absolutely any number. So there are many solutions.

a.  The expressions for c and d in terms of a and b are

b.  The inverse of (2,1) is (13/15, -4/15)

The question has to do with binary operation.

A binary operation is a rule of mathematical operation on two sets of elements defined on a given set.

Since The operation * is defined over the set of ordered pairs by (a,b)*(c,d)=(ac-bd,ad+bc) for all (a,b),(c,d)€R given that the inverse of (a,b) is (c,d).

Let (e, e') be the identity element.

We know that for any binary operation * on a given set, a*e = a where e is the identity element.

So,  (a,b)*(e,e') =  (a,b)

So, (a,b)*(c,d) = (ac - bd, ad + bc)

(a,b)*(e,e') = (ae - be, ae' + be')

Since  (a,b)*(e,e') =  (a,b)

(ae - be, ae' + be') = (a, b)

So,

e = a/(a - b) and e' = b/(a + b)

So, (e, e') = (a/(a - b), b/(a + b))

Also, for any binary operation * under a given set a*a⁻¹ = e where a⁻¹ = inverse of a.

Since (c,d) is the inverse of (a,b), we have that

(a,b)*(c,d) = (e, e')

So, (a,b)*(c,d) = (ac - bd, ad + bc)

=  (a/(a - b), b/(a + b))

So,

From (3), c = bd/a + 1/(a - b)

Substituting c into (4), we have

ad + bc = b/(a + b)  

ad + b[bd/a + 1/(a - b)] = b/(a + b)  

ad + b²d/a + b/(a - b) = b/(a + b)  

ad + b²d/a = b/(a + b) -  b/(a - b)]

(a + b²/a)d = b[1/(a + b) -  1/(a - b)]

[(a² + b²)/a]d = b[a - b - (a + b)]/(a - b)(a + b)

[(a² + b²)/a]d = b[a - b - a - b)]/(a - b)(a + b)

[(a² + b²)/a]d = b(-2b)/(a² - b²)

d = -2ab²/[(a² - b²)(a² + b²)]

d = -2ab²/(a⁴ - b⁴)

Substitutind d into c, we have

c = bd/a + 1/(a - b)

c = -2ab³/(a⁴ - b⁴)a + 1/(a - b)

c = -2b³/(a⁴ - b⁴) + 1/(a - b)

So, the expressions for c and d in terms of a and b are

Since (c,d) is the inverse of (a,b) is

So, with a = 2 and b = 1, c = -2b³/(a⁴ - b⁴) + 1/(a - b)

= -2(1)³/(2⁴ - 1⁴) + 1/(2 - 1)

= -2/(16 - 1) + 1/1

= -2/15 + 1

= (-2 + 15)/15

= 13/15

So, with a = 2 and b = 1, d = -2ab²/(a⁴ - b⁴)

= -2(2)(1)²/(2⁴ - 1⁴)

= -4(1)/(16 - 1)

= -4/15

So, the inverse of (2,1) is (13/15, -4/15)

Learn more about binary operation here:

https://brainly.com/question/16827196

#SPJ1

Answer:   100 square cm

Step-by-step explanation:   the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.

Answer: 104

Step-by-step explanation:

area of trangle =33 because 6*11/2=33

area of rectangle 9*7=63

area of rectangle  2*2=4

33+63+4=100^2

Answer:

here's your answer step by step explanation

Step-by-step explanation:

page 6 is missing comment me i will send you page 6

Answer: A

Step-by-step explanation:

Let f(y)=x.

[tex]x=\frac{y+2}{7}\\\\7x=y+2\\\\y=7x-2\\\\f^{-1}(x)=7x-2[/tex]

Answer:

a₁ = 5

a₂ = 8

a₃ = 13

a₄ = 20

Step-by-step explanation:

Given sequence formula

aₙ = n² + 4

Requirement of the question

Find the 4 terms in the sequence

Substitute 4 values into the sequence formula

a₁ = (1)² + 4 = 1 + 4 = [tex]\Large\boxed{5}[/tex]

a₂ = (2)² + 4 = 4 + 4 = [tex]\Large\boxed{8}[/tex]

a₃ = (3)² + 4 = 9 + 4 = [tex]\Large\boxed{13}[/tex]

a₄ = (4)² + 4 = 16 + 4 = [tex]\Large\boxed{20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

$525

Step-by-step explanation:

We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:

[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]

To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:

525 * 0.36 = 189

525 - 189 = 336

Modeling the first formula gives us:

525 - (0.36 * 525) = 336

525 - 189 = 336

Answer:

d

Step-by-step explanation:

the opposite angles of a cyclic quadrilateral sum to 180° , that is

∠ ABD + ∠ ACD = 180°

∠ ABD + 48° = 180° ( subtract 48° from both sides )

∠ ABD = 132°

Answer:

The answer is: (x,y) = (-2,5)

Answer: 9 diagonals

Step-by-step explanation:

Answer:

X=36

Step-by-step explanation:

2x + 3x=5x

if given figure is 180 then

5x=180

X=180/5

X=36

Answer:

the answer is 1,2,4,5 and 7.

Answer: The answer is A,B,D,E,G

Step-by-step explanation: just trust me and enjoy your write answers. Have a nice day.

[tex](-7+9, 1-3)=\boxed{(2, -2)}[/tex]

The answer is (2,-2).

Find the image of the given point under the given translation:

The rule of translation is (x+9, y - 3), P (-7, 1).

Here we need to add 9 from

x value is -7+9=2

y We need to subtract -3 from

y value is (1-3)=-2

So, P’=( 2,-2)

To learn more about translation, refer to:

https://brainly.com/question/24086234

#SPJ9

Answer:

135 is correct answer of this question

The algebraic expression of the statement is 4x + 6

The statement is given as:

The sum of four times a number and six

Rewrite as:

The sum of 4 times a number and 6

Let the number be x

So, we have

The sum of 4 times x and 6

Evaluate the product

The sum of 4x and 6

Evaluate the sum

4x + 6

Hence, the algebraic expression of the statement is 4x + 6

Read more about algebraic expression at

https://brainly.com/question/4541471

#SPJ1

u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1). This can be obtained by simplifying the equation and taking w to one side of the equation with other constants.

Simplifying an equation can be done by using the following steps:

Here it is given that the equation is,

⇒ u - 5= - 4(w - 1)

We have to find an equation in which w is taken to one side of the equation with other constants.

First by adding both side of the equation with 5 we get,

⇒ u - 5 + 5 = - 4(w - 1) + 5

By opening the bracket we get,

⇒ u = - 4w + 4 + 5

Finally by adding the constants we get,

⇒ u = - 4w + 9

Hence u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1).

Learn more about algebraic equation here:

brainly.com/question/25678139

#SPJ1  

The probability that the machine produces fewer than 3 defective widgets in a production run of 75 items is 0.041.

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 3 widgets.

It has a 0.12 defective rate.

Defective rate fewer than 3

Total Probability = P of 2 defective + P for 1 defective

Total Probability = 2/74 + 1/73

Total Probability ≈ 0.04072565716

Total Probability ≈ 0.041

Therefore, the required probability for fewer than 3 defective rate is 0.041

Read more about probability

brainly.com/question/14290572

#SPJ1

Answer:

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

Step-by-step explanation:

m∠RSU = m∠RST + m∠TSU

10x - 9 = 2x + (2x + 75)

10x - 9 = 2x + 2x + 75

10x - 9 = 4x + 75

-4x +9     -4x  +9

      6x = 84

         x = 14

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

The system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:

To find the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse:

The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k

Where (h, k) is the vertex of the parabola, a is constant.

For the sailboat we have vertex: (h, k) = (2, -6) and one point: (-7, 8) that is f(-7) = 8.

We will find a using f(-7) = 8:

The quadratic function for the sailboat is given by:

The equation for a circle with a radius of 5 and center (1, 2) is:

Therefore, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:

Know more about equations here:
https://brainly.com/question/22688504

#SPJ4

The correct form of the question is given below:
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?

The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

The given coordinates on the graph are;

(-3, 0), (0, 3), (2, 4), and (5, 5)

The coordinates of the starting point of the graph = (-3, 0)

Shape of the graph = Extends from point (-3, 0), upwards and to the right

Therefore;

As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.

However, given that the graph is for a square root function, the correct option is option C;

C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.

Learn more about functions and variables here:

https://brainly.com/question/8590101

https://brainly.com/question/14288182

https://brainly.com/question/13097291

#SPJ1

From my analysis, the answer is likely to be D. I don't have a formula to prove it though.

Answer: 78 degrees.

Step-by-step explanation:

The other guy is wrong don't listen to him.

Answer:

j = 7.8.

Step-by-step explanation:

The slope of the line = difference in y-values / corresponding difference in x-values.

Slope = (7-3) / (j-5) = 10/7

so 10(j - 5) = 7*4

10j - 50 = 28

10j = 78

j = 7.8.

Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]

Step-by-step explanation:

Given information

Number of coins = 24 coins

Total amount = $1.95

Dime = 10 cents = $0.1

Nickel = 5 cents = $0.05

Set variables

Let d be the number of dimes

Let n be the number of nickels

Set a system of equation

1) d + n = 24

2) 0.1d + 0.05n = 1.95

Multiply 10 on both sides of 2) equation

0.1d · 10 + 0.05n · 10 = 1.95 · 10

d + 0.5n = 19.5

Current system

1) d + n = 24

2) d + 0.5n = 19.5

Subtract 2) equation from the 1) equation

(d + n) - (d + 0.5n) = (24) - (19.5)

Expand the parenthesis

d + n - d - 0.5n = 24 - 19.5

Combine like terms

d - d + n - 0.5n = 4.5

0.5n = 4.5

Divide 0.5 on both sides

0.5n / 0.5 = 4.5 / 0.5

[tex]\Large\boxed{n=9}[/tex]

Substitute the n value into one of the equations to find the d value

d + n = 24

d + (9) = 24

d = 24 - 9

[tex]\Large\boxed{d=15}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The probability that the service time will be more than three minutes is 0.3012.

Given that the average wait time at the Rivertown bank's neighborhood branch is 2.5 minutes and has an exponential distribution,

The time it takes to succeed in a continuous sequence of independent trials is described by the exponential distribution, which is a continuous probability distribution.

At the River Town Bank's neighborhood branch, the random variable X service time has an exponential distribution with a mean value of 2.5 minutes. Therefore,

[tex]f(x)=\left\{\begin{array}{ll}\theta e^{-\theta x},& \theta \geq 0,0\leq x\leq \infty\\0&\text{otherwise}\end{array}[/tex]

E(x)=1/θ

θ=1/2.5

θ=0.4

The probability that the service time will be longer than three minutes:

[tex]\begin{aligned}P(X > 3)&=1-P(X\leq 3)\\ &=1-(1-e^{-0.4\times 3}\\ &=e^{-1.2}\\ &=0.3012\end[/tex]

Since the service duration has an exponential distribution and a mean of 2.5 minutes, the needed chance that it will exceed 3 minutes is 0.3012.

Learn more about exponential function from here brainly.com/question/18596455

#SPJ1

If the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.

Given a function of x f(x)=1/(6x+6).

We are told to find out the value of the variable x for which the function does not lie.

Function is like a relationship between two or more variables expressed in equal to form. The values entered in a function is known as domain and the values which we get after entering of values are known as range.

f(x)=1/(6x+6)

It is in form of fraction. Fraction is a combination of numbers in which the above number is numerator and below number is denominator.

In this (6x+6) cannot be equal to 0 because if (6x+6) equal to 0 then the value of function becomes infinity.

So,

6x+6=0

6x=-6

x=-1

Hence if the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.

Learn more about function at https://brainly.com/question/10439235

#SPJ1

Answer:

22, 23

Step-by-step explanation:

4x + 3(x + 1) = 157

4x + 3x + 3 = 157

7x + 3 = 157

7x = 154

x = 22

A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

In this question we must determine both the surface area and the number of shingles to cover two roof configurations as well. In the first case, we calculate the surface area, which is the sum of the area of rectangles:

A = 2 · (8 ft) · (12 ft) + 2 · (6 ft) · (12 ft)

A = 336 ft²

And the number of shingles required to cover the root is:

n = (336 ft²) / (4 ft²)

n = 84

A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

In the second, we only need to cover the very top surface. The area and the number of shingles are, respectively:

A = 2 · (5 ft) · (22 ft)

A = 220 ft²

n = (220 ft²) / (2 ft²)

n = 110

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

To learn more on surface areas: https://brainly.com/question/2835293

#SPJ1

Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:

(8.34%, 17.66%).

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the estimate and the sample size are given, respectively, by:

[tex]\pi = 0.13, n = 200[/tex]

Hence the bounds of the interval are:

As a percentage, the interval is:

(8.34%, 17.66%).

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

x = 35.

Step-by-step explanation:

since they are odd, the second number isn't x + 1, it is x + 2.

x + x + 2 = 72

2x + 2 = 72

2x = 70

x = 35