COORDINATE GEOMETRY
Graph each figure with the given vertices and identify the figure. Then find the perimeter and area of the figure.
7) O(3, 2), P(1, 2), Q(1, –4), R(3, –4)

8) S(0, 0), T(3, –2), U(8, 0)

Answer:e=8/7=1.143

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*e-5+2*e-(e+3-2*e)=0

Add  8  to both sides of the equation :

                     7e = 8

Divide both sides of the equation by 7:

                    e = 8/7 = 1.143

And then you get

Divide both sides of the equation by 7:

                    e = 8/7 = 1.143

Answer:

                   4*e-5+2*e-(e+3-2*e)=0

Add  8  to both sides of the equation :

                    7e = 8

Divide both sides of the equation by 7:

                   e = 8/7 = 1.143

And then you get

Divide both sides of the equation by 7:

                   e = 8/7 = 1.143

Step-by-step explanation:

By 2228 ways i can select the team to have more girls than boys

We have, total number of boys = 6, while the total number of girls = 8

Total size of team = 6

Condition given: In every case the total number of girls should be more than the total number of boys.

As for that we can choose the team like

(6G, 0B) + (5G, 1B) + (4G, 2B)

Making the combination as per above arrangements:

We will get it as:

=8C6*6C0+8C5*6C1+8C4*6C2

As we know,

The formula of combination is:

\($${ }_n C_r=\frac{n !}{r !(n-r) !}$$\)

\(${ }_n C_r=$\) number of combinations

n= total number of objects in the set

r= number of choosing objects from the set

So, applying the concept of combination in the above,

So, from above we can write it as:

8C6*6C0+8C5*6C1+8C4*6C2

=\([\frac{8!}{6! \times 2!}\times \frac{6!}{6!\times 0!}]+[\frac{8!}{5!\times 3!}\times \frac{6!}{5!\times 1}]+[\frac{8!}{4!\times 4!}\times \frac{6!}{2!\times 4!}]\\\\\)

\([\frac{8 \times7\times6! }{6!\times2} \times \frac{1}{1}]+[\frac{8\times7\times6\times5!}{5!} \times \frac{6\times5!}{5!}]+[\frac{8\times7\times6\times5\times4!}{4!\times24} \times \frac{6\times5\times4!}{4!\times2}]\)

[28*1]+[336*6]+[70*2]

=28+2016+140

=2228

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Answer:

x = 36.27

Step-by-step explanation:

By using the steps to find sin θ backwards, we can find x, the hypotenuse.

sin θ = \(\frac{opposite}{hypotenuse}\) or side \(\frac{a}{c}\) (as seen in my example picture).

We already know the value for sin (α), which is 32° because its given. The opposite side (a) is 20 and the hypotenuse side (c) is x which are both also given.

So the equation now looks like:

sin 32° = \(\frac{20}{x}\)

Don't solve for the sin 32 yet! First, we have to isolate the variable.

To get rid of the x in the denominator you have to multiply both sides by x:

( sin 32 ) · x = ( \(\frac{20}{x}\) ) · x

( sin 32 ) x = 20

Then, you have to divide both sides by sin 32 to get x by itself:

(( sin 32 ) x ) ÷ ( sin 32 ) = 20 ÷ ( sin 32 )

x = 20 ÷ ( sin 32 )

Lastly, you have to use a calculator to find 20 ÷ ( sin 32 ), and it should give you 36.2695543766.

The question asks you to round to 2 decimal places so:

x = 36.27

Answer:

X-axis

Step-by-step explanation:

Maybe

Answer:

16.33 cm

Explanation :

The formula to find the circumference is 2πr where r is the radius. The problem above gives the diameter so we must divide it with 2 first before we proceed.

Correct me if I'm wrong. I hope it helps.

Answer:

16.328m is answer

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Answer :

To find the product of (x + 8)(x – 10)

We know that

(x + a)(x + b) = x2 + (a + b)x + ab

In the expression (x + 8)(x – 10)

a = 8

b = -10

a + b = 8- 10 = -2

ab = 8 × (-10) = – 80

Substitute the values in the above equation

(x + 8)(x – 10) = x2 + (8 – 10)x + 8 × (-10)

(x + 8)(x – 10) = x2 – 2x – 80.

Thank you !

Answer:

The slope is 4/5 and the y intercept is -3

Step-by-step explanation:

The equation is in slope intercept form

y= mx+b where m is the slope and b is the y intercept

y = 4/5x -3

The slope is 4/5 and the y intercept is -3

After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

Answer:

12 gallons

Step-by-step explanation:

If it takes 20 h for 5 gallons to be filled, it takes 4 h for 1 gallon to be filled. This is the ratio. You multiply 4 h by 12 to get 48 h, so you multiply 1 gallon by 12 as well. This is 12 gallons.

In the attached diagram the perimeter of the hall way is

The perimeter of the hall way is calculated by adding all the sides of the hallway

The perimeter of the hall way  = 2x - 7 + x + 1 + 4x - 9 + x - 2 + x + 2 + 3x - 11 + x - 2 + 3x - 11 + x + 4

adding like terms results to

The perimeter of the hall way  =  17x + (-34)

Finally, the simplified expression is:

17x - 34

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The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

If A(2,3) is on the line kx - 2y + k = 0 the value of k is 3.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

We have,

A line with an equation is given by:

kx - 2y + k = 0

A point is given as:

A(2, 3)

Point A is on the line so it should satisfy the equation of the line.

(2, 3) = (x, y) ______(1)

kx - 2y + k = 0 ______(2)

Put (1) on (2)

k(2) - 2(3) + k = 0

2k - 6 + k = 0

3k = 6

k = 3

Thus the value of k is 3.

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The value of s, which is the measure of the exterior angle, is 99°.

What is the exterior angle of a triangle?

An exterior angle of a triangle is an angle that is formed by extending one of the sides of the triangle. Specifically, it is the angle that is formed between that extended side and the adjacent side of the triangle that it doesn't share a vertex with.

In other words, if you choose one of the sides of a triangle and extend it, the angle that is formed between the extension and the adjacent side of the triangle is called an exterior angle.

Each of the three sides of a triangle has a corresponding exterior angle, and the sum of the measures of the three exterior angles of a triangle is always 360 degrees.

The sum of the measures of the exterior angles of any triangle is always 360 degrees.

In this case, we have two interior angles of the triangle given as s-50° and s-49°, and we are told that s is the measure of the exterior angle.

By definition, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

So, we have:

s = (s-50°) + (s-49°)

Simplifying the equation:

s = s - 50° + s - 49°

s = 2s - 99°

99° = s

s = 99°

Therefore, the value of s, which is the measure of the exterior angle, is 99 degrees.

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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The output of the function can be calculated by plugging in 2 for x and evaluating the equation:\(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

The Common Core standards for Pre-Calculus focus on the study of functions and their applications, as well as the development of a deeper understanding of the algebraic and geometric principles in the mathematical field. One of the core concepts covered in Pre-Calculus is the concept of polynomial functions. A polynomial function is an expression made up of terms that involve only constants, variables, and exponents. It is represented by the equation \(f(x) = ax^n + bx^n-1 + cx^n-2 + … + z\), where a, b, c, …, z are constants and n is a non-negative integer. To find the value of a polynomial function at a given value of x, the equation can be evaluated by plugging in the x value and calculating the output. For example, if a polynomial function is represented by the equation f(x) = 2x^3 + 5x^2 - 7x + 4, and the x value is 2, then the output of the function can be calculated by plugging in 2 for x and evaluating the equation: \(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

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Complete question:

What is the output of the polynomial function f(x) = 2x^3 + 5x^2 - 7x + 4 when x = 2?

The scale factor that takes quadrilateral T to quadrilateral U would be = 1.6

A scale factor is defined as the factor that is used to creat a similar shape of an object with a different dimension.

The formula that is used for the new object = original object × scale factor

The original object = quadrilateral T

The new object = quadrilateral U.

The scale factor the was used to form U using the length of the quadrilateral as 16;

16 = 10 * Scale factor

This gives

Scale factor = 16/10

Scale factor = 1.6

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Answer:

Since they're both equated to y...

7x² + 6x – 13 = 3x – 3

Bringing all the left

7x² + 3x – 10 = 0

Solving for x

you have

x = 1 or x = –10/3

Now substitute to get y

y = 0 or –13

Answer:

Domain: \(x > -5\) or \((-5,\infty)\)

Range: \(y\geq -3\) or \([-3,\infty)\)

Step-by-step explanation:

The domain is essentially the set of x-values in a given graph. In this graph. we see that the lowest x-value is an unfilled dot when x=-5. The unfilled dot means that the function \(f(x)\) doesn't include -5. We then see that the x-value goes to positive infinity. This means that \(x\) must be greater than -5. It is not greater or equal to -5 because the dot is not filled.

Therefore, we have that \(x > -5\). To convert to interval notation we can take the lower value (-5) and put it on the left side and put the higher value (\(\infty\)) and put it on the right side. Since the graph doesn't include -5, we can put parentheses around both values to get \((-5,\infty)\).

Note: We always put parentheses around both \(\infty\) and \(-\infty\).

The range is basically the same as the domain but with the y-value. We can see that the lowest y-value is y=-3. This includes -3 since the line fills the point in. Then we see that the highest y-value is once again positive infinity. This means that \(y\geq-3\).

Now when we convert to interval notation, we have -3 and \(\infty\). This time since y=-3 is included in the function, we put a hard bracket around -3. Thus, we get \([-3,\infty)\).

Hope this helps!

Answer:

rectangle

Step-by-step explanation:

The geometric shape that is modeled by a strip on a flag would be a rectangle. That is because just like a rectangle the shape has a total of four sides in which both parallel sides are equal in length to its matching counterpart but at the same time different from its adjacent sides. All of which are characteristics of a rectangle and at the same time found on all strips of flags.

Step-by-step explanation:

-7-13>-15x

-20>-15x

x>-20/-15

x>4/3

please give the domain.

or write on your own.!

Answer:

\(1 \frac{1}{3} < x \: \: \: or \: \: \: x > 1 \frac{1}{3} \\ \)

Step-by-step explanation:

\( - 7 > 13 - 15x \\ - 7 - 13 > - 15x \\ - 20 > - 15x \\ \frac{ - 20}{ - 15} < x \\ \frac{4}{3} < x \\ 1 \frac{1}{3} < x \\ \)

The expression is expanded and simplified to 7y - 4

Note that algebraic expressions are described as mathematical expressions that are composed of coefficients, factors, constants, variables and terms.

They are also made up of some mathematical operations. These operations are;

From the information given, we have that;

5(y - 2) + 2(y - 3)

expand the bracket, we have;

5y - 10 + 2y - 6

collect the like terms

5y + 2y - 10 + 6

add the values

7y - 4

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Let:

x = Her new salary

using proportions:

solving for x:

She needs to earn approximately $3856

Answer:

0.285714 is the answer to your question

Adding all of the remaining pizzas, and dividing the total pizza into 5 equal fractions, the fraction of pizza that each person gets would be 11/24

A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number. It is different from an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4 is an improper fraction.

To convert a mixed number to an improper fraction, you must first multiply the whole number by the denominator of the fraction. Then add the result to the numerator. Finally, place the sum over the denominator. For example, to convert 3 1/2 to an improper fraction, you would first multiply 3 by 2 (the denominator of the fraction 1/2) to get 6, then add 1 (the numerator of the fraction 1/2) to get 7. So 3 1/2 is equivalent to 7/2 as an improper fraction.

So to find out the fraction of a whole pizza  that each person gets out of the different remaining pizzas, first we need to all the remaining pizzas as shown below,

3/4 of pepperoni + 5/8 of cheese + 11/12 of sausage = 55/24

Now to equally divide this into 5 person, we need to divide this fraction by 5,

i.e 55/(24*5) = 11/24

Therefore, each person gets 11/24 of the whole pizza.

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Answer:

52°

Step-by-step explanation:

it should always add up to 180°

Answer:

The answer is below

Step-by-step explanation:

Chicken costs $1.85 per pound, and the beef costs $3.70 per pound. Let x represent the pounds of chicken and y represent the pound of beef. If he spent a total of $12.95, therefore:

1.85x + 3.7y = 12.95           (1)

He bought twice as much beef as chicken, therefore:

y = 2x

y - 2x = 0                             (2)

Solving eqn 1 and eqn 2 simultaneously. Multiply equation (2) by 3.7 and subtract from equation (1)

9.25x = 12.95

x = 1.4 pounds

Also substitute x = 1.4 in equation 2:

y - 2(1.4) = 0

y = 2(1.4)

y = 2.8 pounds

The graph was plotted using geogra, the y coordinate of the point of intersection of the two lines, is the approximate pounds of beef.

Answer: Part A. First line= (0,0), (1,2). Second line= (0,3.5), (1,3)

Part B. 2.75 pounds

Step-by-step explanation: It's correct.

Given the following exponential function, y = 180(1.093)ˣ, the change represents growth and the percentage rate of increase is 9.3%.

An exponential function is a mathematical equation that depicts exponential growth or decay.

It is written in the form of y = a(1±r)ˣ, depending on whether the percentage rate increases or decreases.

y = 180(1.093)ˣ

where y = the current value or value after x periods

180 = the initial value

1.093 = the growth factor

0.093 (1.093 - 1) = the rate of increase

= 9.3% (0.093 x 100)

x = (the exponent) time interval between the beginning and the end.

Thus, the function is an exponential growth function because the initial value increases by 9.3% per period.

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Answer:

you can buy 5 cans

Step-by-step explanation:

$2 per can

have $10

10 divided by 2

5

Answer:

Step-by-step explanation:

1. Notice that these angles are vertical angles which are angles opposite each other when two lines cross, they share the same vertex. Vertical angles are congruent angles.

Therefore,

2. In this case, the angles shown are complementary, which mean they must add up 90 degrees: