Using Euler's formula, how many
edges does a polyhedron with 9
faces and 14 vertices have?
[?] edges
Euler's Formula: F+ V=E+2

Using Euler's Formula, How Manyedges Does A Polyhedron With 9faces And 14 Vertices Have?[?] EdgesEuler's

Answers

Answer 1

Answer:

Euler's Formula = F+V=E+2

F=9

V=14

So, 9+14=E+2

23=E+2

23-2=E

21=E

Hence, E (edges) = 21

Step-by-step explanation:


Related Questions

Can someone help me? And possibley tell me how to solve this as well? I'm totally clueless haha

Answers

Answer:

3

Step-by-step explanation:

-2 * 3= -6

-1 * 3= -3

0 *3= 0

1 *3 = 3

2* 3 = 6

3 * 3 =9

Answer:

? = 3

Step-by-step explanation:

To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.

Given formula:

[tex]\sf y=\boxed{?} \:x[/tex]

Substitute x = 1 and y = 3 into the formula:

[tex]\sf 3=\boxed{?} \:1[/tex]

To isolate ? divide both sides by 1:

[tex]\implies \sf \dfrac{3}{1}=\dfrac{\boxed{?} \:1}{1}[/tex]

[tex]\implies \sf 3=\boxed{?}[/tex]

Therefore, ? = 3:

[tex]\implies \sf y=3x[/tex]

Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:

[tex]\sf x=-2 \implies y=3(-2)=-6 \quad \boxed{\sf correct}[/tex]

[tex]\sf x=3 \implies y=3(3)=9 \quad \boxed{\sf correct}[/tex]

The cosine law is writen as question, and 2 more Questions down below. Please solve.

Answers

When to use the law of cosine is explained below.

Using the labelled triangle, we have: sin D/d = sin E/e = sin F/f.

Using the sine law, the measure of angle M is: 74.9°.

What is the Cosine Law?

The cosine law is given as, c = a² + b² - 2ab(cos C). It is used to solve a triangle with missing angle or side.

What are the Two Instances When the Cosine Law is Applied?

When we are given two sides and an angle between the two sides, and we need to find the third side.

When we are given the all three sides of a triangle and we need to find the angles of the triangle.

What is the Law of Sines?

Using the labelled triangle DEF in the diagram below, the law of sines is:

sin D/d = sin E/e = sin F/f.

How to Find Angle M using the Law of Sines?

m∠N = 56°

n = 8.5 cm

m = 9.9 cm

Plug in the values into sin N/n = sin M/m:

sin 56/8.5 = sin M/9.9

sin M = (sin 56 × 9.9)/8.5

sin M = 0.9656

M = sin^(-1)(0.9656)

M = 74.9°

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Use a composite figure to estimate the area of the figure. The grid has squares with side lengths of 1.5 cm.

Answers

The area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex]

Given that the grid has squares with side lengths of 1.5 cm.

We are required to find the area of the composite figure.

The area of the composite figure is approximate to the area of the rectangle plus the are of the semicircle at the top of the rectngle plus the semicircle at the right side of the rectangle.

Finding the area of the rectangle.

A=(3*1.5)(4*1.5)=27 [tex]cm^{2}[/tex]

Finding the area of the semicircle at the top of the rectangle.

A=1/2 π[tex](2*1.5)^{2}[/tex]=4.5 π [tex]cm^{2}[/tex]

Finding the area of the semicircle at the right of the rectangle.

A=1/2 π[tex](1.5*1.5)^{2}[/tex]

=2.53π [tex]cm^{2}[/tex]

Total area =27+4.5π+2.53π

=27+7.03π

Use π=3.14

=27+7.03*3.14

=49.1 [tex]cm^{2}[/tex]

Hence the area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex].

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Hurry A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annual interest is $510?

Answers

Answer:

Step-by-step explanation:

We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:

[tex]5x+10x=510[/tex]

Solve for x

[tex]15x=510\\x=34[/tex]

Now multiply x by the corresponding percentages to find how much was invested into each percentage.

[tex]34*5=170[/tex]

[tex]34*10=340[/tex]

Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.

We can of course check our answer by adding 170+340 which equals our original investment of 510.

$1800 is invested at 5% and the remainder, $4200, is invested at 10%.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Let us consider the amount invested at 5% x.

The amount invested at 10% is then the remainder, which is:

$6000 - x

Now we can set up an equation for the total interest earned:

0.05x + 0.10($6000 - x) = $510

Simplifying and solving for x:

0.05x + $600 - 0.10x = $510

-0.05x + $600 = $510

-0.05x = -$90

Divide both sides by 0.05

x = $1800

Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.

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Select the correct answer from each drop-down menu.

Answers

(x^2 - 3x - 10) * (x - 2) over
(x^2 - 6x + 5) * (x - 5)

(x - 5)(x + 2)(x - 2) over
(x - 5)(x - 1)(x - 5)

(x + 2)(x - 2) is the numerator
(x - 1)(x - 5) is the denominator
excluded values are 1 and 5

Mr. Nero drives to work each day 35 miles one way. If he were in a hurry, could he legally make it to work in less than a half hour with the legal speed limit set to 65 MPH? Reference the formula, d = rt, when explaining the answer.

Answers

Answer:

Nope.  It would take 32 and 4/13 minutes, which is longer than 30 min.

Step-by-step explanation:

The distance is 35 miles and the speed 65 miles/hour

Dividie the distance by the speed to obtian the time required,

(35 miles)/(65 miles/hour) = 0.538 hours

No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour.  2 and 4/13 minutes more than 30 minutes.

Geometry: complete this proof, ASAP!

Answers

For the given diagram, it has been proved that angle A is congruent to angle B.

Given Information:

Angle A and Angle B are such that,

Ray AC ║ Ray BE

Ray AD ║ Ray BF

Proof:

Since a straight line is the shortest line connecting two points in a plane,

Extend ray AD and ray BE, such that both intersect at point G.

Now, since, angle A and angle 1 both make corresponding angles,

∠A = ∠1 .......... (1)

Ray ADG is parallel to the ray BF.

Thus, again, angle B and angle 1 make corresponding angles,

∠B = ∠1 ............ (2)

From (1) and (2), as per transitive relationship of angles,

∠A ≅ ∠B

Hence proved.

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Please really need help with question d really don't understand

The answer to the question is the second image, I don't get how they got this answer and why it isn't finding x for t=0, t=1 and t=2.

Answers

Answer:

[tex]\textsf{a)} \quad v=12t^2-6t-18[/tex]

[tex]\textsf{b)} \quad a=24t-6[/tex]

c)   1.5 s

d)  -19.25 m

e)   24.5 m

Step-by-step explanation:

Displacement

[tex]x=4t^3-3t^2-18t+1[/tex]

(where t ≥ 0 and x is in meters)

Part (a)

To find the equation for velocity, differentiate the equation for displacement:

[tex]\implies v=\dfrac{\text{d}x}{\text{d}t}=12t^2-6t-18[/tex]

(where t ≥ 0 and v is in meters per second)

Part (b)

To find the equation for acceleration, differentiate the equation for velocity:

[tex]\implies a=\dfrac{\text{d}v}{\text{d}t}=24t-6[/tex]

(where t ≥ 0 and a is in meters per second squared)

Part (c)

The particle comes to rest when its velocity is zero:

[tex]\begin{aligned}v & = 0\\\implies 12t^2-6t-18 & = 0\\6(2t^2-t-3) & = 0\\2t^2-t-3 & = 0\\2t^2-3t+2t-3 & = 0\\t(2t-3)+1(2t-3) & = 0\\(t+1)(2t-3) & = 0\\\implies t & =-1, \dfrac{3}{2}\end{aligned}[/tex]

As t ≥ 0, the particle comes to rest at 1.5 s.

Part (d)

Substitute the found value of t from part (c) into the equation for displacement to find where the particle comes to rest:

[tex]\implies 4(1.5)^3-3(1.5)^2-18(1.5)+1=-19.25\: \sf m[/tex]

Part (e)

We have determined that the particle is at rest at 1.5 s.

Therefore, to find how far the particle traveled in the first 2 seconds, we need to divide the journey into two parts: before and after it was at rest.  

The first leg of the journey is the first 1.5 s and the second leg of the journey is the next 0.5 s.

At the beginning of the journey, t = 0 s.

[tex]\textsf{when }t=0: \quad x=4(0)^3-3(0)^2-18(0)+1=1[/tex]

Therefore, when t = 0, x = 1

When t = 1.5 s, x = -19.25 m (from part (d)).

⇒ Total distance traveled in first 1.5 s = 1 + 19.25 = 20.25 m

When t = 2, x = -15 m.

Therefore, the particle has traveled 19.25 - 15 = 4.25 m in the last 0.5 s of its journey.

Total distance traveled:

1 + 19.25 + 4.25 = 24.5 m

Refer to the attached diagram

When the particle is at rest, it changes direction.  If we model its journey using the x-axis, for the first leg of its journey (0 - 1.5 s) it travels in the negative direction (to the left). At 1.5 s it stops, then changes direction and travels in the positive direction (to the right), arriving at -15 at 2 seconds.

1/?
Which number produces a rational number when Multiplied 1/5

Answers

Answer:

-2/3

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number

Solve for the value of x in the diagram below. Show your work and explain the steps you used to solve.

Answers

Answer: x = 2

Step-by-Step Solution:

Given:

OH = WO = LW

OH = 2x + 1

WO = 3x - 1

LW = 5

To Find:

The value of 'x'

Solution:

We know, OH = WO = LW

So, equate any two of the values given :-

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, x = 2.

Test the claim that the proportion of people who own cats is larger than 60 t the 0. 10 significance level?

Answers

The null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Given that the significance level is 0.10.

We are required to form the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% the significance level.

Hypothesis is a statement which is tested for its validity. Null hypothesis is the statement which is accepted or not by z test,t test,f test ,chi-square test or any other test.

We have to take opposite of the statement to form a null hypothesis. Since we have to check whether the proportion of people who owns cats is larger than 60% of the significance level, we have to assume that it is smaller than 60% of the significance level.

60% of the significance level=0.60*0.10=0.06.

Null hypothesis is [tex]H_{0}[/tex]:μ<0.06

Hence the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.

Question is incomplete.The question should include the following:

Find the null hypothesis for the testing.

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James covers a distance of 8 meters in the first second of a 100 meter race. then, he sprints at a speed of 9 meters per second. how far is james from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80 please select the best answer from the choices provided a b c d

Answers

James is (B) 20 meters far from the finish line 9 seconds after the race has started.

What is the distance?Distance is a numerical measurement of the distance between two objects or places. The distance can refer to a physical length or an estimate based on other criteria in physics or common usage. The distance between two points A and B is commonly expressed as |AB|.

To find the distance:

James covers 8 meters in the opening second of the 100-meter race.Then he sprints at a 9-meter-per-second pace.We need to figure out how far James is from the finish line 9 seconds after the race begins.James travels 8 meters in the first second.After running 8 meters, the time remaining in 9 seconds is 9 - 1 = 8 seconds.James completes the distance = speed time = 9 8 = 72 meters in another 8 seconds.The total distance traveled in 9 seconds is equal to 8 + 72 = 80 meters.After 9 seconds, the distance remaining in a 100-meter race is 100 - 80 = 20 meters.9 seconds into the race, James is 20 meters from the finish line.

Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.

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The complete question is given below:

James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?

a. 11

b. 20

c. 28

d. 80

If the graph of a budget function has an x-intercept at 2 and the y-intercept at 5, name two ordered pairs that would fall on this line.

(2, 0) (0, 5)

(0, 2) (5, 0)

(2, 0) (2, 5)

(0, 2) (2, 5)

Answers

Based on the graph of the budget function with the x-intercept and the y-intercept, the two ordered pairs that would fall on this line are (2, 0) (0, 5).

What points fall on this line?

The x-intercept is the point on the graph where the budget function would cross the x-intercept.

At this point, the value of y would be 0 because the x-axis intersects the y-axis at y = 0.

An x-intercept of 2 would therefore have the point, (2,0).

The y-intercept would be the point where the y axis is crossed. At this point, x will be zero because the y-axis intercepts the x-axis at the value, x = 0.

A y-intercept of 5 would therefore yield a point of (0, 5).

In conclusion, option A is correct.

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If ABC = 2x and BAC = 3x + 10 what is the value of x ?

Answers

The value of x from the given diagram is -10

Similar triangle

Two triangles are known to be similar if the ratio of their similar sides is equal. The diagram shown is similar to the required diagram.

Given the following parameters

<ABC = 2x

<BAC = 3x + 10

Equate the expression since both angles are equal. Substitute;

2x = 3x + 10

Subtract 3x from both sides

2x-3x = 3x-3x+10

-x = 10

x = -10

Hence the value of x from the given diagram is -10

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103h=7(
7
2


7
3

h)−103

Answers

Answer:

I think its -10 or -8

Step-by-step explanation:

The volume of the fish tank needs to be tripled. What scale factor should be applied to the dimensions to produce a fish tank with three times the volume

Answers

Answer:

assuming it's a perfect world and that the fish lives in a 1 cubic meter fish tank 1*1.4422 will increase the volume my a factor of 3

Determine the domain and range of the function f (x) = 2 rootindex 3 startroot 108 endroot superscript 2 x.

Answers

Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

What is the domain and range of a function?

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. A function's range is its potential output, whereas its domain is the set of all possible input data.

The function can be written as :

[tex]f(x)=\sqrt[\frac{2}{3} ]{108^{2x} } \\f(x)=108^{\frac{3}{2}^{2x} }[/tex]

Now that x is an exponent, all real values are possible for it. Therefore, all real numbers make up its domain for f(x). But value of f(x) cannot be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1

So, Range of f(x) is all real numbers greater than 0

Hence, Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

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Determine whether the series is convergent or divergent. 1 1 2 2 1 3 3 1 4 4 1 5 5 ⋯

Answers

Step-by-step explanation:

clearly divergent.

the elements of the series are getting bigger and bigger intercepted by some constant "1" (but they don't help here - after every intercepting "1" are 2 numbers that are larger by 1 than the 2 numbers before the intercepting "1", and that continues into infinity, so, the numbers will go to infinity, and that shows that the series is divergent).

If a = 1,b=2 and c=-3 find
a^b-c b^c-a c^a-b

Answers

Answer:

The value of

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b \: [/tex]

is

[tex] \frac { 19}{8} [/tex]

Step-by-step explanation:

Greetings !

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b[/tex]

where,

a=1b=2c=-3

Thus, substitute these values to the given equation to find the values.

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b ... \: substitute \: \\ given \: values \\ (1) {}^{2} - ( - 3)(2) {}^{ - 3} - 1( - 3) {}^{1} - 2 \\ 1 + 3 \: ( \frac{1}{8} ) - 1( - 3) - 2 \\ 1 + \frac{3}{8} + 3 - 2 \\ \frac{11}{8} + 3 - 2 \\ \frac{35}{8} - 2 \\ \frac{19}{8} = 2 \frac{3}{8} [/tex]

Hope it helps

Last week a painter painted 6 houses in 2 days. this week she painted 5 houses in 4 days. in which week was the painter more productive?

Answers

Answer:

The painter was more productive in week a.

Step-by-step explanation:

Find the unit rate.  How many houses could be painted in 1 day?

6/2 means that she could paint 3 houses per day

5/4 means that she could paint 1.25 houses per day.

Answer:

The painter was more productive in the last week.

Explanation:

In this problem, we need to find in which week did the painter paint the most.

To find the solution to this problem, first, we need to divide 6 by 2 (last week)

which equals 3.

Next, divide 5 by 4 (this week)

which equals 1.25

Now, compare the two quotients and identify the larger number (3 and 1.25).

Basically, we can see that the number 3 is larger.

This means that the painter could paint 3 houses per day in the last week, and 1.25 houses per day in this week.

Therefore, we can say that the painter was more productive in the last week.

I hope this helps :)

Which expression is equivalent to RootIndex 4 StartRoot StartFraction 24 x Superscript 6 Baseline y Over 128 x Superscript 4 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x not-equals 0 and y

Answers

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

What is an equation?

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the expression:

[tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }\\ \\Simplifying:\\\\=\frac{\sqrt[4]{3x^2}}{2y}[/tex]

The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]

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Answer:

The answer is D

Step-by-step explanation:

An airplane travels 1350 miles in 5 hours, going against the wind. The return trip is with the wind, and takes only 3.75 hours. Find the rate of the airplane with no wind. Find the rate of the wind.

Answers

Solving a system of equations we can see that:

The airplane rate is 315 mi/hThe wind rate is 45 mi/h.How to find the rate of the airplane?

Let's define:

A = rate of the airplane.W = rate of the wind.

When the airplane travels against the wind, the total speed is:

(A - W)

In this way, we know that the airplane travels 1350 miles in 5 hours, then:

(A - W) = 1350mi/5h

When the airplane travels with the wind, it takes 3.75 hours to travel the same distance, then:

(A + W) = 1350mi/3.75h

We have now a system of equations:

(A - W) = 1350mi/5h

(A + W) = 1350mi/3.75h

If we isolate A on the first equation, we get:

A = 270mi/h + W

Replacing that in the other equation we get:

270mi/h + W + W = 360 mi/h

Solving for W we get:

2*W = 360mi/h - 270mi/h = 90mi/h

W = 90mi/h = 45mi/h

And the airplane rate is:

A =  270mi/h + W = 270mi/h + 45mi/h = 315 mi/h

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What angle of descent ( depression) should the pilot use to safely bring the plane to the airport runway? The plane is 10,000 feet above the ground and is a little more than 30 miles ( approximately 160,000 feet) from the airport. Write an equation and show work . Round the angle measure to the nearest whole degree. ( Picture is not drawn to scale )

Answers

Answer:

4 degrees ( to nearest degree).

Step-by-step explanation:

The trig ratio you want is the tangent.

tan x = 10,000 / 160,000    where x is the angle of depression.

tan x = 0.0625

x = 3.576 degrees.

How many numbers from 100 to 999 have exactly one zero digit

Answers

Answer:

180.

Step-by-step explanation:

100 contains 2  zero digits.

101 - 109 have 9 numbers,  110 to 200 have 11 numbers

so for 101 to 200 its 20 numbers

Its also 20 for 201 to 300  and for all sets of 100 up to 900.

- that is 7 * 20 = 140 numbers

Finally from 901 to 999 we have 18.

Total = 20 + 140 + 18

= 2 + 20 + 140 + 18

= 180.

Justine wants to go to the school dance next week, but only if her friend kelly goes. she asks her mom to go, saying she will complete all her homework on time. her mom says she can go to the dance as long as she completes all her chores for the week. using this situation, describe the concepts of conditional probability and independent and dependent events and how they relate to justine’s situation.

Answers

Justine only goes when her friend goes [Conditional probability].

Mom going to PROM and Justine going to PROM are separate events. [Independent events].

Mom can't go until she finishes the housework is dependent on events

independent events. [Dependent events]

What is probability?

The probability exists in the analysis of the possibilities of happening of a result, which exists acquired by the ratio between favorable cases and possible cases.

Conditional probability directs to the possibility that some outcome happens given that another possibility contains also occurred.

Justine only goes when her friend goes [Conditional probability]

Independent events exist as those possibilities whose occurrence exists not dependent on any other event.

Mom going to PROM and Justine going to PROM are separate events. [Independent events]

Dependent events exist that depend upon what occurred before.

Mom can't go until she finishes the housework is dependent on events

independent events. [Dependent events]

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Plsss helppp I’m dying!! —> Complete the square to determine if the equation is a circle, quadratic equation, or other

Answers

a) The equation represents an ellipse.

b) The equation represents a circle.

c) The equation represents a parabola.

How to infer the graphical form of a general equation

In this problem we have general equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into standard form to infer its graphical form. This procedure can be done by algebra properties:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84

[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64

(4 · x + 12)² + (2 · y + 2)² = 64

4² · (x + 3)² + 2² · (y + 2)² = 64

(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse

x² + y² + 8 · x - 6 · y - 15 = 0

(x² + 8 · x) + (y² - 6 · y) = 15

(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40

(x + 4)² + (y - 3)² = 40 : Circle

x² + 6 · x + 4 · y + 5 = 0

x² + 6 · x + 5 = - 4 · y

y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola

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What type of construction is illustrated in the figure?

A
The bisection of ∠D

B
A line segment congruent to segment AB

C
An angle congruent to ∠D

D
The bisection of segment BD

Answers

Option A is correct. The type of construction that we have here is the bisection of the <D.

What is the bisection of an angle?

The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.

In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.

The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.

If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option

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Geometry: Write a formal proof, ASAP!!!

Answers

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

As we can see in the figure, lines m and n are parallel to each other. so we can apply Angle pair properties ~

So,

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle2[/tex]

[ they form corresponding angle pair ]

and it's given that :

[tex]\qquad \sf  \dashrightarrow \: \angle2 \cong\angle 3[/tex]

therefore, by using above information. we can conclude that :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle3[/tex]

Find the explicit form of the arithmetic function of p if the first term is 12 and the common difference is 2. Then find the seventh term.

Answers

The explicit form of the arithmetic function as described is; f(p) = 2(p-1) + 12. and the seventh term is; 24.

What is the seventh term of the arithmetic function?

Since it follows from the task content, that the first term is 12 and the common difference is 2.

It therefore follows from convention that the explicit function is; f(p) = 2(p-1) + 12 and by substituting n= 7 into, the equation, we have; f(7) = 24.

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How do you determine the
solution to a system of equations
when graphing? Is it possible to
have more than 1 solution when
graphing? Is it possible to have no
solutions? How?

Answers

When graphing, the intersections of the graphs represent the solutions of the system.

How to determine the solutions of a system by graphing?

When graphing a system of equations, you just need to graph both equations in the same coordinate axis.

The solutions of the system are all the points where the graphs of the two equations intersect.

This means that if there is only one intersection, there is one solution.

But we can have more than one intersection, like in the case where at least one of the equations is a polynomial of degree 2 or more.

And there is also the case that the graphs never intersect, like in parallel lines, in these cases we have no solutions.

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