Open Ended
a. Find the slope of the line that passes through the points (2,-5) and (-2,3).
b. What are the slope and y-intercept of the equation 2x - 5y = -10?
c. Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4.
d. Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b.
(PLEASE SHOW WORK, IT CAN BE SIMPLE I JUST NEED TO PUT IT IN FOR CREDIT)

The value of the expression 2n - 1 when n = 7 is 13.

2n - 1

when n = 7

2n - 1

= 2(7) - 1

= 14 - 1

= 13

Mathematical expression is an expression which involves the combination of numbers and variables in a valid way, in a function of addition, subtraction, multiplication, division and exponentiation

Therefore, the value of the expression 2n - 1 when n = 7 is 13.

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The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.

Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.

The discriminant is described below:

Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d²      (1)

Where:

If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:

Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²

Δ = - 1024

The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

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Step-by-step explanation:

5)f(g(8))

from the table g(8)=4

f(4) =4 from the table

7)g(f(5))

from the table f(5)=0

g(0)=9 from the table

9)f(f(4))

from the table f(4)=4

f(4)=4 from the table

Answer:

Step-by-step explanation:

You want to begin by making each fraction have  the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.

1. 5/7*11/11=55/77

2. 9/11 * 7/7 =63/77

Now we can add

55/77 + 63/77 + 21/77 = 139/77 or 1.805194805

Answer:

389 is the answer

Hope you like it!

The solution to the equation is 0.07, 0.17, 0.27, 0.38........

The trigonometry equation is given as:

tan(30x - 90°) = -x³

We start by splitting the trigonometry equation as follows, by creating two different equations

y = tan(30x - 90°)

y = -x³

Next, we plot the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³

From the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³, we have the x coordinate of the point of intersection to be:

x = 0.07, 0.17, 0.27, 0.38........

Hence, the solution to the trigonometry equation is 0.07, 0.17, 0.27, 0.38........ .

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The value |x−9|≤9 is equivalent to [18,0] in interval notation.

According to the statement

We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.

So, For find all x value we use absolute value inequalities.

distance of 9 from number 9.

So, when we draw the number line

we see that the number will become

The distance from x to 9 can be represented using an absolute value symbol, |x−9|.

Write the values of x that satisfy the condition as an absolute value inequality.

So, it become

|x−9|≤9

Now write two inequalities then it become

x−9≤9 and x−9≥−9

x≤18  and x≥0

So, The solution set is x≤18 and x≥0,

then the solution set is an interval including all real numbers between and including 18 and 0.

So |x−9|≤9 is equivalent to [18,0] in interval notation.

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Answer: square of 459 is 210681

Answer:

B) 9:35

Step-by-step explanation:

the travel time we get by dividing the distance by the speed

distance / distance/time = time

so,

60 / 80 = 6/8 = 3/4 = 0.75 hours or 45 minutes.

since she arrived 20 minutes late, that means at 10:20 am, she left home 45 - 20 = 25 minutes before 10:00am.

and that is 9:35 am.

Answer:

GC and GD

Step-by-step explanation:

The only points on plane L are: J, C, G, D

GC and GD

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:2x + 6 + 5x + 90 = 180[/tex]

[ by linear pair ]

[tex]\qquad❖ \: \sf \:7x + 6 = 180 - 90[/tex]

[tex]\qquad❖ \: \sf \:7x + 6 = 90[/tex]

[tex]\qquad❖ \: \sf \:7x = 90 - 6[/tex]

[tex]\qquad❖ \: \sf \:7x = 84[/tex]

[tex]\qquad❖ \: \sf \:x = 84 \div 7[/tex]

[tex]\qquad❖ \: \sf \:x = 12[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:x = 12 \degree[/tex]

Answer:

5,526

Step-by-step explanation:

Mean of scores = Total Value of Scores / Number of Values

= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]

= 5,526

Answer:5526

Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers

Answer:

mLx = 144

mLy=154

Step-by-step explanation:

180-36=144

x=144

180-62=118

36+118=154

180-154=26

180-26=154

y=154

Answer:

154 degrees

Step-by-step explanation:

you can find measure of angle y, since it is the supplement of angle a, so

measure of angle y = 180 - measure of angle a, which is 144 degrees

you can find the measure of angle x, by finding its complement.

Looking at the center triangle, we see that it is formed from angle a, the supplement of angle b, and the supplement of angle x, so the equation is 180 = 36 + 180 - 62 + supplement of angle x

so, the supplement of angle x is 26 degrees, so x is 154 degrees

Based on the number of periods for the simple discount note to reach maturity and the discount rate, the proceeds are $7,598.74.

You can solve for the discounted price as:

= Maturity value x discount rate x number of periods

Solving gives:

= 7,700 x (6% / 365) x 80

= $101.26

The proceeds can then be found by subtracting the discounted price from the maturity price.

Solving for the proceeds gives:

= 7,700 - 101.26

= $7,598.74

Based on the simple discount note period, the maturity value, and the discount rate, the proceeds can be found to be $7,598.74.

In conclusion, the proceeds are $7,598.74.

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Answer:

index of m is -2

Step-by-step explanation:

any number or letter to the negatIve power(index) is the same as 1 divided by that number or letter to the positive index.

for example, 10^-2 = 1/10^2 and X^-4 is the same as 1/X^4.

First of all, we would calculate the predetermined overhead rate by using this formula:

Predetermined overhead rate = Manufacturing overhead/Direct material costs

Predetermined overhead rate = $2,342,400/$1,464,000

Predetermined overhead rate = 1.6 per DM $.

Next, we would calculate the overhead applied by using this formula:

Overhead applied = Job × DM cost

For job 0701, we have:

Overhead applied = 76,000 × 1.6

Overhead applied = $121,600.

For job 0702, we have:

Overhead applied = 104,000 × 1.6

Overhead applied = $166,400.

For job 0703, we have:

Overhead applied = 135,000 × 1.6

Overhead applied = $216,000.

For job 0704, we have:

Overhead applied = 67,000 × 1.6

Overhead applied = $107,200.

For the overapplied manufacturing overhead for year 1:

Less applied overhead = $1,630,000 × 1.6

Less applied overhead = $2,608,000.

Overapplied manufacturing overhead = Actual overhead cost - Less applied overhead

Overapplied manufacturing overhead = $2,480,000 - $2,608,000

Overapplied manufacturing overhead = $128,000.

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Answer:

8v-28/v^2-2v-24

Step-by-step explanation:

1. Find common denominator

2. Combine fractions with common denominator

3. Re-order terms so constants are on the left

Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

Exponential Function can be used for increase rate and also for decay rate.  The difference between the two are the plus and minus signs. To put it in another perspective, If Y = P(M)³

If M is less than one, that means it is decaying or decreasing. And if M is greater than one, that means it is increasing.

Given that Some banks charge a fee on savings accounts that are left inactive for an extended period of time. And the equation

y = 5000(0.98)^x  represents the value, y, of one account that was left inactive for a period of x years.

According to the equation, to know if the balance in this account is increasing or decreasing, we will analyze the value 0.98.

Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

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Answer:

(0, 8/3) = y-intercept

Step-by-step explanation:

I chose to find the y-intercept since it is easy to find with the given information.

The equation for a line is y = mx + b

To find the y-intercept, we must plug in the info we have and solve for b:

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

4 = -4/3 + b

8/3 = b

To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:

(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)

Answer:

Step-by-step explanation:

9.05737

The length of the radius of the cone to the nearest foot is 5 feet.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The surface area of a cone is 216π sq units and the height of the cone is  (5/3) times of the radius.

∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.

∴ πrl = 216π.

√{(34/9)r³ = 216.

1.9r³ = 216.

r³ = 113.7.

r = 4.8 feet Or 5 feet.

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Answer:

x - 2, x - 3

Step-by-step explanation:

3x² - 5x + 2

x² - 5x + 6

(x - 3)(x - 2)

length = x - 2

width = x - 3

The value of x from the given circle is 4

The intersecting chords theorem is a statement in geometry that describes a relation of the four line segments created by two intersecting chords within a circle.

It states that the products of the lengths of the line segments on each chord are equal.

According to the theorem;

x * 3 = 2 * (4 + 2)

3x = 2(6)

3x = 12

Divide both sides by 3

3x/3 = 12/3

x =4

Hence the value of x from the given circle is 4

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An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

The term triangle refers to a figure that has three sides. There are several types of triangles such as the;

Despite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.

Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

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From all the steps below, we have been able to prove that; 1 - cot23° = 2/(1 - cot22°).

We want to prove that  1 - cot23° = 2/(1 - cot22°).

We will prove it using the trigonometric expression

cot(22° + 23°) = cot45°

Using trigonometric identities, we can rewrite as;

(cot22° cot23° - 1)/(cot22° + cot23°) = 1

Cross multiply to get;

cot22° cot23° - 1 = cot22° + cot23°

Rearrange to get;

cot22° cot23° - 1 - cot22° - cot23° =0

⇒ cot22° cot23° - 1 - cot22° - cot23° + 2 =2

⇒ cot22° cot23° + 1 - cot22° - cot23° =2

⇒ cot22° cot23° - cot22° - cot23° + 1 = 2

⇒ cot22° (cot23° - 1) - 1 (cot23° - 1) = 2

⇒ (cot22° - 1) (cot23° - 1) = 2

Divide both sides by  (cot23° - 1) to get;

cot23° - 1 = 2/(cot22° - 1)

⇒ 1 - cot23° = 2/(1 - cot22°).

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Answer:

Now, the father is 60, and the son is 24.

Step-by-step explanation:

Now:

Father's age = f

Son's age = s

4 years ago:

Father's age = f - 4

Son's age = s - 4

In 12 years:

Father's age = f + 12

Son's age = s + 12

Now:

f = 3(s - 4)

In 12 years:

f + 12 = 2(s + 12)

We have 2 equations that we can solve in a system of equations.

f = 3(s - 4)

f + 12 = 2(s + 12)

f = 3s - 12

f + 12 = 2s + 24

f = 3s - 12

f = 2s + 12

Since above both equations are in terms of f, set the right sides equal and solve for s.

3s - 12 = 2s + 12

s = 24

f = 3(s - 4)

f = 3(24 - 4)

f = 3(20)

f = 60

Now, the father is 60, and the son is 24.

The material-handling cost per wall mirror under activity-based costing is $280

What is activity-based costing?

Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.

There 25 materials move in both divisions (i.e. 7+18=25)

Material-handling cost per material move=Budgeted material-handling costs /total material moves

Budgeted material-handling costs =$30,000

Material-handling cost per material move=$30,000/25

Material-handling cost per material move=$1,200

Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move

Total material-handing costs for wall mirror=7*$120

Total material-handing costs for wall mirror=$8,400

material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors

material-handling cost per wall mirror=$8,400/30

material-handling cost per wall mirror=$280

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Answer: 55.2 in

Step-by-step explanation:

1ft = 12 in

41.4/9 = 4.6 ft

4.6 x 12 = 55.2 in

Using relations in a right triangle, it is found that the length of AC is of 14 cm.

The relations in a right triangle are given as follows:

Researching this problem on the internet, we have that:

Hence the hypotenuse is found as follows:

sin(A) = 48/h

0.96 = 48/h

h = 48/0.96

h = 50 cm.

The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:

[tex]x^2 + 48^2 = 50^2[/tex]

[tex]x^2 = \sqrt{50^2 - 48^2}[/tex]

x = 14 cm.

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The length of the vine wounded to the tree is 21 feet.

Circumference is the perimeter of a circular object. Therefore,

circumference = 2πr

where

The circumference of the tree is 3 feet. A vine was wound around 7 times .

The length of the vine can be calculated as follows:

Therefore,

circumference = 3 ft

length of the vine = 7 × 3

length of the vine = 21 feet

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