The polygon angle sum theorem states that the sum of the measures of the interior angles of an n-gon is

n-2/180

(n-1) 180

180/n-1

(n-2) 180

Answer: 3 field goals, 4 touchdowns

Step-by-step explanation:

The number of field goals and touchdowns of the team score will be 3 and 4, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A football team scored a total of 37 points in a game. The team scored some field goals worth 3 points each and some touchdowns with extra points, each together worth 7 points. The team made 19 more points in touchdowns with extra points than in field goals.

Let 'x' be the number of field goals and 'y' be the number of touchdowns. Then the equations are given as,

3x + 7y = 37        ...1

7y = 3x + 19        ...2

From equations 1 and 2, then we have

14y = 56

y = 4

Then the value of 'x' is calculated as,

7(4) = 3x + 19

28 = 3x + 19

3x = 9

x = 3

The number of field goals and touchdowns of the team score will be 3 and 4, respectively.

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Answer:

60%

Step-by-step explanation:

Sales Price = 100 - 40 = 60%

The sales price is $30.00

Therefore 60% is equal to $30.00

60% = $30

1% = 30 ÷ 60 = $0.50

100% = 5 x 100 = $50

The original price is $50

Percentage of the original price = 30/50 x 100 = 60%

Answer:

Z = 5 + 3i and Z = -8 - 2i

Step-by-step explanation:

* Lets study the drawing of the complex numbers

- The x-axis is the real axis

- The y-axis is the imaginary axis

* Look to the attached figure

- Any point in the first quadrant is above the real axis and right

 to the imaginary axis (Z4)

# Z = x + yi

- Any point in the second quadrant is above the real axis and left

 to the imaginary axis (Z2)

# Z = -x + yi

- Any point in the third quadrant is below the real axis and left

 to the imaginary axis (Z3)

# Z = -x - yi

- Any point in the fourth quadrant is below the real axis and right

 to the imaginary axis (Z1)

# Z = x - yi

* Now lets solve the problem

- The point above the real axis and right to the imaginary axis lies

 in the first quadrant

∴ The real part is positive and the imaginary part is positive

∴ Z = 5 + 3i

- The point below the real axis and left to the imaginary axis lies

 in the third quadrant

∴ The real part is negative and the imaginary part is negative

∴ Z = -8 - 2i

A complex number that lies above the real axis and to the right of the imaginary axis could be '2 + 3i', while a complex number that lies below the real axis and to the left of the imaginary axis could be '-2 - 3i'. The direction in the coordinate system (upward or rightward is positive, downward or leftward is negative) determines the signs of real and imaginary components.

In the complex plane, a complex number is considered to lie above the real axis if its imaginary part is positive, and to the right of the imaginary axis if its real part is positive. Hence, an example of a complex number that lies above the real axis and to the right of the imaginary axis is 2 + 3i, where 2 is the real part and 3i is the imaginary part.

Conversely, a complex number lies below the real axis if its imaginary part is negative, and to the left of the imaginary axis if its real part is negative. So, an example of such a number could be -2 - 3i, where -2 is the real part and -3i is the imaginary part.

Remember, in the coordinate system used to plot complex numbers, motion upward or to the right is usually considered positive, while motion downward or to the left is considered negative.

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Answer:

No, it is not.

Step-by-step explanation:

This is not proportional, however, it is linear

Answer:

it should be 9,8

Step-by-step explanation:

After 3 days Chelsea and Zack earn the same amount for dog sitting.

Equation for Chelsea: y = 3x + 2

Equation for Zack: y = 3x

After how many days they earn the same amount: After 3 days; both Chelsea and Zack earn $9.

the possible solutions of this equation. Is that they are not real.

Answer:

Step-by-step explanation:

6x-2y<10 :  3x -y <5

then :  3x -y -5< 0

given the line : 3x-y-5 = 0

the points is a solution to the system of equalities? 6x-2y<10 Located on the line : 3x-y-5 = 0 and under the x - axis.

Answer:

it's the 2nd one

Step-by-step explanation:

d = 3 + at^2

-3 | -3

d - 3 = at^2

d - 3/a = t^2

√d - 3/a = √t^2

t = √d - 3/a

The blue triangle is the dilated shape from the red triangle.

The dimensions of the blue triangle are half the red one.

The answer is B)1/2.

Answer:1/2

Step-by-step explanation:

Took the test on edge

Answer:

1556.25

Step-by-step explanation:

5 3/16.25×300=1556.25

Step-by-step explanation:

So if segment QS and segment PR are equal then all parts are equal which means segment QT= segment PT, segment TR= segment TS. segment QS id equal to 12 which means segment PR is equal to 12. You get segment TR by subtracting 4.9 from 12. Now you know that segment TR is 7.1 which means that segment TS is 7.1.

You also know that segment PS is equal to segment QR so you know that segment QR is 9cm because segment PS is 9cm.

m∠QPR is 33° because you know that ΔQPR's sum is 180 and you know that ∠PQR is 114° b/c 44+70 is 144, 180-144=66 now you take 66 and divide it by 2 (for the two angles left) that equals 33.

m∠STR is 92°. You know this by taking the base angle in ΔPTQ and multiplying it by two (which now equals 88, the base angle is 44°) and you take this number and subtract it from 180. 180-88=92. 92 is you measure of angle STR.

Answer:

2.5 & 1.1

Step-by-step explanation:

that answer is correct ^

Step-by-step explanation:

[tex]\text{Put}\ x=-2,\ x=0\ \text{and}\ x=3\ \text{to the equation}\ y=4^x:\\\\y=4^{-2}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\y=\dfrac{1}{4^2}=\dfrac{1}{16}\\-----------------\\\\y=4^0=1\\-----------------\\\\y=4^3=64[/tex]

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given y = 5(x + 1) = 5x + 5 ← in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex], thus

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (10, 2) into the partial equation

2 = - 2 + c ⇒ c = - 2 + 2 = 4

y = - [tex]\frac{1}{5}[/tex] x + 4 ← in slope intercept form

Multiply all terms by 5

5y = - x + 20 ( add x to both sides )

x + 5y = 20 ← in standard form → D

Answer:

2x^2+7x-61

Step-by-step explanation:

the answer is negative 5

It’s negative 5, because you have to substitute the x in 3x for negative one, so the equation looks like f(x)= 3(-1) - 2. Then, you solve

Based on the phrase they gave, the inequality would look like this:

[tex]\frac{4-g}{8} >-15[/tex]

[tex]\frac{4-g}{8}\leq-15[/tex]

the quotient(÷) of [the difference(- subtraction) of 4 and a number(g) and 8] is at MOST -15.

since the sign is ≤, this means that the inequality is less than or equal to -15, so -15 is the maximum number for the inequality.

Your answer is the last option

Answer:

(D)

Step-by-step explanation:

I got it right on edge/quiz.

y = 3(-x - 2)

Any horizontal transformations or reflections you make to y = x must be within the parentheses.

The transformed function is g(x) = -7 [tex]log_6[/tex] (-x) +2

The given base function is

f(x) = [tex]log_6[/tex] (x)

Then we have to find the transformed function.

First of all, the graph of the base function f(x) = [tex]log_6[/tex] (x) is vertically stretched by a factor of 7, then the newly transformed function becomes y = 7[tex]log_6[/tex](x)

Then the graph of y = 7[tex]log_6[/tex](x) is reflected over the x-axis, then the newly transformed function becomes y = -7log6(x)

Then the graph of y = -7[tex]log_6[/tex](x) is reflected over the y-axis, then the newly transformed function becomes y = -7[tex]log_6[/tex](-x)

And finally, the graph of y=7log6(-x) is vertically shifted up by 2 units, then the newly transformed function becomes

y = -7 [tex]log_6[/tex] (-x) +2

which is the required equation for the transformed function.

Answer:

Length of garden will be 30 metres.

Step-by-step explanation:

Let the Width of garden be x metres.

then,

Length of garden will be (x+6) metres.

Area = Length × Breadth

720 = x X (c+6)

720 = x²+6x

0 = x²+6x-720

As we can see above equation is a quadratic equation in the form of ax²+bx+C.

so,

[tex] = \frac{ - b ± \sqrt{{b}^{2} - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^{2} - 4 \times 1 \times - 720} }{2} \\ = \frac{ - 6 ± \sqrt{36 + 2880} }{2} \\ = \frac{ - 6 ± \sqrt{2916} }{2} \\ = \frac{ - 6 ± 54}{2}\\= \frac{-6+54}{2} ... \frac{ - 6 - 54}{2} \\ = \frac{48}{2} ... \frac{ - 60}{2} \\ = 24... - 30[/tex]

One of the Roots of the Quadratic equation is 24 and other is -30.

And as we know width of any garden cannot be negative so the width of garden will be 24 metres.

As we got the width,

adding 6 to it will give us the Length,

So,

24 metres + 6 = 30 metres.

Length of the garden is 30 metres.

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The answer is C. because the train will arrive any minute. This is because an adverb clause is a clause that functions as an adverb, and it modifies or describes a verb, adverb or adjective.

Answer:

Step-by-step explanation:

The answer is a I am not sure

The relationship described by y = 4x + 4 is not proportional because Option D. the graph does not pass through the origin. The y-intercept is 4, indicating it does not meet the criteria for direct proportionality.

The equation y = 4x + 4 describes a linear relationship between x and y. However, for two quantities to be directly proportional, their relationship must be of the form y = kx, meaning that the graph of their relationship must pass through the origin (0, 0).

In the equation y = 4x + 4, the y-intercept is 4, not 0. Therefore, the graph of this equation does not pass through the origin.

Option D) No, because the graph of the equation does not pass through the origin.

To determine the percentage of students who passed both exams, we first calculate the percentage of students who failed in either subject, then subtract that from 100%. Given that 15% failed in Science, 20% in Mathematics, and that 10% failed in both, we find that 75% of students passed both courses.

In this question, we have to find out the percentage of the candidates that passed in both subjects, Science and Mathematics. The percentages given show the failure rates in Science, Mathematics, and in both. Here, we need to use the concept of sets where we sum the individual percentages and subtract the intersection. It is defined as P(A U B) = P(A) + P(B) - P(A ∩ B).

According to the problem, 15% failed in Science and 20% in Mathematics. So, the candidates failing in any one of the subjects would be 15% + 20% = 35%. However, those who failed in both subjects (i.e., intersection part) is 10%, and double-counted when we added up the individual percentages. Therefore, we subtract this from our earlier total, giving us 35% - 10% = 25%. This implies that 25% of candidates fail in at least one subject.

As for those who pass in both, since we know that the total should be 100%, and we've figured out that 25% failed in at least one subject, thus, those who passed should be the remaining 75%.

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The percentage of those who passed in both the subjects is equal to 85%.

In order to determine the percentage of those who passed in both the subjects, we can use the principle of inclusion and exclusion;

Based on the principle of inclusion and exclusion, we have:

Total percentage of candidates who failed in either Science or Mathematics = A + B - C

Percentage of candidates who passed in both subjects = 100% - (A + B - C)

Percentage of candidates who passed in both subjects = 100% - (15% + 20% - 10%)

Percentage of candidates who passed in both subjects = 100% - 15%

Percentage of candidates who passed in both subjects = 85%.

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Answer:

f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

Given that three roots of a fifth degree polynomial function f(x) are -2,2 and (4+i).

Now we need to find about which of the given statements describes the number and nature of all roots for this function.

We know that imaginary roots always occur in conjugate pairs.

So if (4+i) is root then (4-i) must also be the root.

So now we have total 4 roots

-2, 2, (4+i) and (4-i).

Degree of the polynomial is 5 so that means 1 root is still remaining. It can't be imaginary as that must be in pairs

So that means 5th root is real.

Hence correct choice is :

f(x) has three real roots and two imaginary roots.

Quadrilateral. If you add the angles up on any quadrilateral, it equals 360 (it should always add to 360 for a quadrilateral)

The polygon you're describing is a kite.

To verify this, let's calculate the sum of the interior angles of the polygon:

Sum of interior angles = [tex](n - 2) * 180 degrees[/tex]

For a polygon with 4 sides: [tex](4 - 2) * 180 = 360 degrees[/tex]

Now, let's add up the given angle measures: 80 + 100 + 80 + 100 = 360 degrees

Since the sum of the interior angles matches the calculated sum for a four-sided polygon, and the sides are congruent, the polygon is indeed a kite.

1. Calculate the sum of interior angles: The sum of interior angles of any polygon can be found using the formula (n - 2) * 180 degrees, where 'n' represents the number of sides. For a four-sided polygon, the sum is (4 - 2) * 180 = 360 degrees.

2. Add up the given angle measures: The given angle measures are 80, 100, 80, and 100 degrees. Adding them together gives a total of 360 degrees, which matches the sum calculated for a four-sided polygon.

3. Confirming the polygon type: Since the sum of the interior angles matches the calculated sum for a four-sided polygon, and the sides are congruent (meaning all sides have the same length), the polygon fits the definition of a kite.

Therefore, the polygon with four congruent sides and angle measures of 80, 100, 80, and 100 degrees is indeed a kite.

Complete question:

What is the name of a polygon that has four congruent sides and these angle measures 80,100,80,100

Answer:

There are 286 possible combinations

Step-by-step explanation:

To solve this problem we must use the formula of combinations.

[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]

Where n is the number of players that there are and elect r of them

In this case there are 7 + 6 = 13 players and you choose 10 of them

Then we look for  13C10

[tex]13C10 =\frac{13!}{10!(13-10)!}[/tex]

[tex]13C10 =\frac{13!}{10!*3!}[/tex]

[tex]13C10 =286[/tex]

There are 286 possible combinations

[tex]d[/tex] stands for distance.

[tex]

d(J, K)=\sqrt{(7-2)^2+(8-4)^2}=\sqrt{25+16}\approx6.4

[/tex]

[tex]

d(J, L)=\sqrt{(1-2)^2+(-1-4)^2}=\sqrt{1+16}\approx4.12

[/tex]

[tex]d(J, K)>d(J, L)[/tex] therefore the answer is D.

Answer:

1.1818...

Step-by-step explanation:

Divide 13 by 11

13 ÷ 11 = 1.1818...

Answer: 1.1818...

The decimal 1.182 is equivalent to 13/11.

A fraction can be converted to a decimal by dividing the numerator by the denominator.

The fraction is given as 13/11.

The numerator is 13 and the denominator is 11.

We are asked to find the decimal form of the given fraction.

This can be done by simplifying the fraction and dividing the numerator by the denominator.

This can be done as shown below:

The fraction = 13/11

= 1.1818

≈ 1.182

The decimal form of the fraction is found. The decimal form of the fraction is 1.182.

Therefore, we have found that the decimal 1.182 is equivalent to 13/11.

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Answer:

I think the answer is  w = 16

Step-by-step explanation:

start by dividing -5 from both sides.

-5w=-80

/

-5

w=-16

The answer is 2^(9/10). I did it assuming with the ^5 you mean the 5th root of 4

ANSWER

[tex] {2}^{ \frac{9}{10} } [/tex]

EXPLANATION

The given expression is

[tex] \sqrt[5]{4} \times \sqrt{2} [/tex]

Recall that:

[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex]

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} } [/tex]

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} } = {2}^{ \frac{2}{5} } \times {2}^{ \frac{1}{2} } [/tex]

Recall that:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We now apply this property of a exponents to obtain:

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{2} = {2}^{ \frac{2}{5} + \frac{1}{2} } = {2}^{ \frac{9}{10} } [/tex]

22.27

You need to divide the amount of servings by the amount of ounces in total

Answer:

10^5 = 100.000

Step-by-step explanation:

We know that 10^5 = 10 * 10* 10 * 10 * 10 = 100.000.

So, we have that 10^5 = 100.000

For this case we have the following expression:

[tex]10 ^ 5[/tex]

Then, as the exponent is positive, we must move the decimal as many times as indicated by the exponent. In this case, we must move it 5 spaces to the right, that is:

[tex]10 ^ 5 = 100000[/tex]

Answer:

[tex]10 ^ 5 = 100000[/tex]