Graph the system of equations. f(x)=−x^2+2x+4g(x)=−x+4 Which statements are true about the solutions to the system of equations? Select each correct answer.

An ordered pair that is the solution to the system of equations lies in Quadrant I .

An ordered pair that is the solution to the system of equations lies in Quadrant III .
An ordered pair that is the solution to the system of equations lies on the y-axis.

The x-coordinate of a solution to the system of equation is 3.

The y-coordinate of a solution to the system of equations is 4.

The y-coordinate of a solution to the system of equations is 0.

Step-by-step explanation:

1. 4x - 7 = -2x + 12, Given

2. 4x - 7 + 2x = -2x + 12 + 2x, Addition property of equality

3. 6x - 7 = 12, Simplification

4. 6x - 7 + 7 = 12 + 7, Addition property of equality

5. 6x = 19, Simplification

6. 6x/6 = 19/6, Division property of equality

7. x = 19/6, Simplification

Answer:

The steps are :

1. [tex]4x-7=-2x+12[/tex] - This is Given

2. [tex]4x-7+2x=-2x+12+2x[/tex] - Here, addition property of equality is used.

3. [tex]6x-7=12[/tex] - This step is simplification as both the LHS and RHS are being calculated and simplified.

4. [tex]6x-7+ 7=12+7[/tex] - Here, again addition property of equality is applied.

5. [tex]6x =19[/tex] - This is simplification again.

6. [tex]\frac{6x}{6}=\frac{19}{6}[/tex] - Here the division property of equality is applied.

7. [tex]x=\frac{19}{6}[/tex] - This step is simplification.

The answer is:

[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]

To find the resultant expression, we need to apply the distributive property.

It  can be defined by the following way:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

Also, we need to remember how to add like terms: The like terms are the terms that share the same variable and exponent, for example:

[tex]x+x+x^{2}=2x+x^{2}[/tex]

We were able to add only the two first terms since they were like terms (they share the same variable and the same exponent)

So , we are given the expression:

[tex](x+y)(x^{2}-xy+y^{2})[/tex]

Then, applying the distributive property, we have:

[tex](x+y)(x^{2}-xy+y^{2})=x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}\\\\x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}=x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}\\\\x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}=x^{3}+y^{3}[/tex]

Hence, the answer is:

[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]

Have a nice day!

Answer:

D)  [tex]S_{14} = 875[/tex].

Step-by-step explanation:

Given  : If the first term of the series is 30 and the 14th term is 95,

To find : what is the sum of all the terms of the series.

Solution : We have given

First term = 30 .

14 th term = 95.

Sum of all term = [tex]S_{n} =\frac{n(first\ term +\ last\ term)}{2}[/tex].

Here, n = 14.

 [tex]S_{14} =\frac{14(30 +95)}{2}[/tex].

 [tex]S_{14} =\frac{14(125)}{2}[/tex].

 [tex]S_{14} =\frac{1750}{2}[/tex].

 [tex]S_{14} = 875[/tex].

Therefore, D)  [tex]S_{14} = 875[/tex].

Answer:

The sum of all the terms in series is 875.

Step-by-step explanation:

Given : If the first term of the series is 30 and the 14th term is 95,

To find : What is the sum of all the terms of the series?            

Solution :

The first term of the  series is 30 i.e. a=30

The 14th term of series is 95 i.e. [tex]a_{14}=95[/tex]

We know that in arithmetic series the 14th term is defined as

[tex]a_{14}=a+13d[/tex]

Substitute the value of a,

[tex]95=30+13d[/tex]

[tex]95-30=13d[/tex]

[tex]65=13d[/tex]

[tex]d=\frac{65}{13}[/tex]

[tex]d=5[/tex]

The common difference is 5.

The sum of the series is given by,

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

[tex]S_{14}=\frac{14}{2}[2(30)+(14-1)5][/tex]

[tex]S_{14}=7[60+(13)5][/tex]

[tex]S_{14}=7[60+65][/tex]

[tex]S_{14}=7[125][/tex]

[tex]S_{14}=875[/tex]

Therefore, The sum of all the terms in series is 875.

Answer:

9^2 = 81

12^2 = 144

63^= 3969

A^2 + B^2 = C^2

81 + 144 = 225

so these numbers do not make a right triangle

Final answer:

The numbers square root of 63, 9, and 12 do make a right triangle as their squares satisfy the Pythagorean theorem. The sum of the squares of 9 and square root of 63 equals the square of 12, which validates that we have a right triangle.

Explanation:

To determine if the numbers square root of 63, 9, and 12 make a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side (the hypotenuse). Let's calculate the squares of each provided number:

Since the longest side here must be 12 (as it is the largest number), the Pythagorean theorem for these numbers would be as follows:
81 + 63 = 144?

That simplifies to:
144 = 144?

This is a true statement, which means that these numbers do indeed represent the sides of a right triangle.

Answer:

Option D is correct.

Step-by-step explanation:

2x^2 -4x +9

We need to find root of the equation.

We will use quadratic equation to solve.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

here a =2, b=-4 and c=9

Putting values and finding the value of x

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-4)\pm\sqrt{(-4)^2-4(2)(9)}}{2(2)}\\x=\frac{4\pm\sqrt{16-72}}{4}\\x=\frac{4\pm\sqrt{-56}}{4}\\x=\frac{4\pm\sqrt{-(2*2*2*7)}}{4}\\x=\frac{4\pm\sqrt{-(2^2*2*7)}}{4}\\x=\frac{4\pm\sqrt{2^2}\sqrt{-14}}{4}\\We\,\,know\,\,\sqrt{-1}=i\,\,\\x=\frac{4\pm2\sqrt{14}i}{4}\\Dividing\,\,by\,\,4\,\,\\x= 1\pm\frac{\sqrt{14}i}{2} \\So,\\x=1+\frac{\sqrt{14}i}{2} \,\,and\,\, x=1-\frac{\sqrt{14}i}{2}[/tex]

So, one of the root is [tex]x=1+\frac{\sqrt{14}i}{2}[/tex]

So, Option D is correct.

Answer:

[tex]y=\frac{-3}{2}x +\frac{5}{2} \\or \\y=\frac{5}{2} -\frac{3}{2} x[/tex]

Step-by-step explanation:

slope-intercept form is: [tex]y= mx+b[/tex]

3x + 2y = 5.

rearrange

[tex]2y=5-3x\\y=\frac{5}{2} -\frac{3x}{2}[/tex]

Answer:

b on ed2020

IG: user_6232003

Step-by-step explanation:

Answer:

-6 -4 -2 4

Step-by-step explanation:

A B C F

Answer:

A. B. C. F.

Step-by-step explanation:

Step-by-step explanation:

it is solved directly by using the formula

To calculate the length of CE, use the properties of similar triangles. Use the same proportion to calculate the length of DE. To find the area of the quadrilateral BDEC, calculate the area of the triangle CDE and subtract it from the area of ABCD.

To calculate the length of CE, we need to use the properties of similar triangles. Since ABC and AED are similar, we can set up the proportion AB/AC = AD/AE. We know that AB = 5cm and AC = 10cm, and we need to solve for AE. Rearranging the proportion, we get AE = AD * AC / AB. Plugging in the values, AE = 6cm.

To calculate the length of DE, we can use the same proportion from above, but this time solving for DE. Rearranging the proportion, we get DE = AD * AC / AB. Plugging in the values, DE = 3cm.

The area of triangle ABD is given as 36cm. To calculate the area of the quadrilateral BDEC, we need to find the area of the triangle CDE and subtract it from the area of the quadrilateral ABCD. Since triangles CDE and ABC share the same height, we can use the ratios of their bases to calculate the area of CDE. The ratio of CE to CB is 6/10, so the ratio of the areas of CDE to ABC is (6/10)^2 = 0.36. Therefore, the area of CDE is 0.36 times the area of ABC, or 0.36 * 36cm = 12.96cm.

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To determine the numerator of a fraction that simplifies to 36 with a denominator of 6x^5, you solve the equation Numerator/6x^5 = 36 by multiplying both sides by 6x^5, resulting in a numerator of 216x^5.

To find the numerator of a fraction that reduces to 36 with a denominator of 6x^5, we set up an equation to represent the fraction in its simplest form.

We know that when we divide the numerator by the denominator, the result is 36. Therefore, the equation to solve is Numerator/6x^5 = 36.

Multiplying both sides of the equation by 6x^5 will isolate the numerator on one side.

The calculation becomes:

Numerator = 36 × 6x^5

Next, we carry out the multiplication to find:

Numerator = 216x^5

This means that the numerator of the original fraction is 216x^5.

Jay spent 19 hours painting both parts of his house, which is obtained by adding the time he spent painting each side: 7 hours and 12 hours.

The question is asking about the total time Jay spent painting two sides of his house. We know that he spent 7 hours painting one side and 12 hours painting another side. To find the total time spent, we simply need to add the two times together. So, 7 hours + 12 hours equals 19 hours. Therefore, Jay spent 19 hours in total painting both parts of his house.

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Answer:

D

Step-by-step explanation:

It's easiest to divide everything by 3.

The best variable to solve for is x in the first equation.

Let 3x+6y=9 be equation (1)

and 2x-10y=13 be equation (2)

2x-10y=13

10y = 2x - 13

y =[tex]\frac{2x - 13}{10}[/tex]  

substitute the value of y in equation (1)

3x+6y=9

3x + [tex]6(\frac{2x - 13}{10})[/tex] = 9

3x + [tex]3(\frac{2x - 13}{5})[/tex] = 9

[tex]\frac{15x + 6x - 39}{5}[/tex] = 9

21x - 39 = 45

21x = 84

x = [tex]\frac{84}{21}[/tex]

x = 4

Therefore, option D) x in the first equation is the correct answer

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ANSWER

[tex]\theta = 0 ,\frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]

EXPLANATION

We want to solve

[tex] \sin( \theta) + 1 = \cos(2 \theta) [/tex]

on the interval

[tex]0 \leqslant \theta \: < \: 2\pi[/tex]

Use the double angle identity to obtain:

[tex] \sin( \theta) + 1 = 1 - 2\sin ^{2} \theta[/tex]

Simplify to get;

[tex] 2\sin ^{2} \theta + \sin( \theta) + 1 - 1 = 0[/tex]

[tex]2\sin ^{2} \theta + \sin( \theta) = 0[/tex]

Factorize to obtain:

[tex]\sin \theta (2\sin \theta + 1) = 0[/tex]

Either

[tex]\sin \theta = 0[/tex]

This gives us

[tex] \theta = 0[/tex]

on the given interval.

Or

[tex]2\sin \theta + 1= 0[/tex]

[tex]\sin \theta = - \frac{1}{2} [/tex]

This gives us

[tex]\theta = \frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]

Therefore the solutions within the interval are:

[tex]\theta = 0 ,\frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]

Answer:

# x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

# 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

# 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

# x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

* Lets study the problem to solve it

- Use the terms of x and y in the general form to find the standard form

∵ x² + y² - 4x + 12y - 20 = 0

- Use the term x term

∵ -4x ÷ 2 = -2x ⇒ x × -2

∴ (x - 2)²

- Use the term y term

∵ 12y ÷ 2 = 6y ⇒ y × 6

∴ (y + 6)²

∵ (-2)² + (6)² + 20 = 4 + 36 + 20 = 60

∴ x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

∵ x² + y² + 6x - 8y + 10 = 0

- Use the term x term

∵ 6x ÷ 2 = 3x ⇒ x × 3

∴ (x + 3)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (3)² + (-4)² - 10 = 9 + 16 - 10 = 5

∴ x² + y² + 6x - 8y + 10 = 0 ⇒ (x + 3)² + (y - 4)² = 5 ⇒ not in answer

∵ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ divide all terms by 3

∴ x² + y² + 4x + 6y - 5 = 0

- Use the term x term

∵ 4x ÷ 2 = 2x ⇒ x × 2

∴ (x + 2)²

- Use the term y term

∵ 6y ÷ 2 = 3y ⇒ y × 3

∴ (y + 3)²

∵ (2)² + (3)² + 5 = 4 + 9 + 5 = 18

∴ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

∵ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ divide both sides by 5

∴ x² + y² - 2x + 4y - 6 = 0

- Use the term x term

∵ -2x ÷ 2 = -x ⇒ x × -1

∴ (x - 1)²

- Use the term y term

∵ 4y ÷ 2 = 2y ⇒ y × 2

∴ (y + 2)²

∵ (-1)² + (2)² + 6 = 1 + 4 + 6 = 11

∴ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ (x - 1)² + (y + 2)² = 11 ⇒ not in answer

∵ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ divide both sides by 2

∴ x² + y² - 12x - 8y - 4 = 0

- Use the term x term

∵ -12x ÷ 2 = -6x ⇒ x × -6

∴ (x - 6)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (-6)² + (-4)² + 4 = 36 + 16 + 4 = 56

∴ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

∵ x² + y² + 2x - 12y - 9 = 0

- Use the term x term

∵ 2x ÷ 2 = x ⇒ x × 1

∴ (x + 1)²

- Use the term y term

∵ -12y ÷ 2 = -6y ⇒ y × -6

∴ (y - 6)²

∵ (1)² + (-6)² + 9 = 1 + 36 + 9 = 46

∴ x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Answer:

∠7 = 34°

Step-by-step explanation:

Since a and b are parallel lines then

∠3 and ∠7 are corresponding angles and congruent, so

∠7 = ∠3 = 34°

Answer:

34 degrees

Step-by-step explanation:

Answer:

113.0 inches per square

Step-by-step explanation:

Given

r=6 inches

The formula for finding the area of a circle is:

A= πr^2

Here, A denotes the area and r denotes the radius whereas the value of π is 22/7 or 3.14.

As in the question it is directed to use 3.14 for the value of π  

So,

A=3.14*(6)^2

=3.14*36

=113.04 inches^2

Rounding off to the nearest 10

A=113.0 inches^2

So the area of given circle is 113.0 inches per square ..  

Answer:

32

Step-by-step explanation:

Answer:

Tn = -4^n/2

Step-by-step explanation:

The formula for nth tern of a geometric sequence is given as:

Tn = ar^n-1 where;

a is the first term

r is the common ratio

n is the number of terms

Since we are looking for the nth term if the geometric sequence, we will write our answer as a function if 'n'.

Given the second and fifth terms to be -8 and 512, respectively, this can be interpreted as;

T2 = ar^2-1 = -8

T5 = ar^5-1 = 512

From the equations above, we have;

ar = -8... (1)

ar⁴ = 512

Dividing both equation, we have;

ar⁴/ar = -512/8

r³ = -64

r = -4

Substituting r = -4 into equation 1, we have;

a(-4) = -8

-4a = -8

a = 2

Since nth term Tn = ar^n-1

Substituting the value of a and r into the equation will give;

Tn = 2(-4)^n-1

2(-4^n × -4^-1)

2(-4^n × -1/4)

= -4^n/2

Answer:

A. (0,0)

Step-by-step explanation:

both lines run through (4,-4)

they meet at 0 on the Y axis

so the answer is (0,0)

To perform a horizontal translation on a function, replace x with x - h in the function

To perform a horizontal translation on a function, we need to replace x with x - h in the function where h is the amount of translation. In the given case, the correct equation for a horizontal translation would be g(x) = f(x - h) = (x - h)² - 12, where h represents the amount of horizontal translation.

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My answers are in the picture above.

Bill is the one who wrote this statistical question so there will be there will be variability in the responses collected.

Bill, because there will be variability in the responses collected

For this case we must simplify the following expression:

[tex](\frac {n ^ {\frac {3} {2}}} {n ^ {- \frac {1} {6}}}) ^ {- 3}[/tex]

By definition of power properties we have:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex](n ^ {\frac {3} {2}} * n ^ {\frac {1} {6}}) ^ {- 3} =[/tex]

To multiply powers of the same base, we put the same base and add the exponents:

[tex](n ^ {\frac {3} {2} + \frac {1} {6}}) ^ {- 3} =\\(n ^ {\frac {18 + 2} {12}}) ^ {- 3} =\\(n ^ {\frac {20} {12}}) ^ {- 3} =\\(n ^ {\frac {5} {3}}) ^ {- 3} =[/tex]

We multiply the exponents:

[tex]n ^ {\frac {-15} {3}} =\\n^{-5}[/tex]

ANswer:

Option D

Answer:

a. 38.3

b. 41.0

Step-by-step explanation:

We have been given the linear model;

a = 0.25t + 29

where a represents the median age of females in the United States and t the number of years since 1970

a.

We are required to predict the median age of females in 2007. The first step is to determine the number of years from 1970 to 2007 by finding the difference;

2007 - 1970 = 37

2007 is  thus 37 years after 1970.

The next step is to substitute t = 37 in the given linear model;

a = 0.25( 37) + 29 = 38.25

b.

We are required to predict the median age of females in 2018. The first step is to determine the number of years from 1970 to 2018 by finding the difference;

2018 - 1970 = 48

2018 is thus 48 years after 1970

The next step is to substitute t = 48 in the given linear model;

a = 0.25( 48) + 29 = 41

Answer:

The answer is C, the graph has the y intercept of 2

Step-by-step explanation:

You can see from the graph that the line intercepts the y axis at 2

It wouldn't be the slope of 1/2 because that choice isn't negative and this is a decreasing/negative graph

You could use a ruler, think about how you want the polygon inside of the circle or how you want the circle to surround the polygon. When you use a ruler, make sure your co-ordinates inside of the circle are correct though before drawing the line.

I hope this info helps! :3

To construct a regular polygon inside a circle, divide the circle into "n" equal sectors using "n" radii, where "n" represents the number of sides in the polygon. Connect the center of the circle to each of the marked points on the circumference to create the regular polygon.

Determine the Circle: Start by drawing the given circle with a compass, and label its center as "O."

Select the Number of Sides: Decide on the number of sides for the regular polygon. Let's assume "n" as the number of sides.

Construct Diameter: Draw a diameter of the circle passing through the center "O," using a straightedge.

Construct Central Angle: To create a regular polygon with "n" sides, divide the circle into "n" equal sectors by constructing "n" radii (lines from the center to the circumference) evenly spaced around the circle. Each of these radii forms a central angle of 360°/n.

Find Vertices: On the circumference of the circle, mark "n" points (labeled A₁, A₂, A₃, ..., Aₙ) evenly spaced. These points will serve as the vertices of the regular polygon.

Connect Vertices: Use a straightedge to draw lines connecting the center "O" of the circle to each of the marked points (A₁, A₂, ..., Aₙ).

Construct Regular Polygon: The polygon with vertices A₁, A₂, ..., Aₙ, and center "O" is the regular polygon inscribed inside the circle.

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Answer:

as you all saw the rating of the above answer, it is incorrect. here is the correct answer with proof down in the photo below

The point-slope equation of the line passing through the points (-5,4) and (1,6) is y - 6 = 1/3(x - 1). This is derived from the standard point-slope formula y - y1 = m(x - x1) where m is the slope of the line.

In mathematics, specifically in linear algebra, the point-slope formula is used to determine the equation of a line given a point on the line and its slope. The point-slope equation of the line through the points (-5,4) and (1,6) is found by first calculating the slope between these two points, defined as the change in y divided by the change in x. So, y2 - y1 divided by x2 - x1. In this case, (6-4) / (1 - (-5)) = 2/6 = 1/3. So, the slope of the line is 1/3. We can then use one of these coordinates (for instance, 1, 6) and the slope in the point-slope formula: y - y1 = m(x - x1). Therefore, the point-slope equation of the line through (-5,4) and (1,6) is y - 6 = 1/3(x - 1).

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Answer:

y=50x+100

Step-by-step explanation:

y=mx+b

100 is b because its a flat fee

The slope is 50 because it is dependent on x, the amount of people.

The correct answer is y=150x.For example, if I were to equal 300. Then that would mean two people would have bought the membership. So, X equals two.

Answer:

[tex]f(g)=25g[/tex]

Step-by-step explanation:

Let [tex]g[/tex] be the number of gallons so [tex]f(g)[/tex] is the number of miles traveled per [tex]g[/tex] gallons.

We know for our problem that Brian's car gets 25 miles per gallon. Since the gallons is represented by [tex]g[/tex], his car will travel a total distance of 25g (where g is the number of gallons.

We also know that the total distance is given by [tex]f(g)[/tex], so we can put the two expressions together to get our function:

[tex]f(g)=25g[/tex]

Let's check:

- If he uses 1 gallon (g=1), so

[tex]f(1)=25(1)[/tex]

[tex]f(1)=25[/tex] miles

He will travel 25 miles with one gallon.

- If he uses 2 gallons (g=2), so

[tex]f(2)=25(2)[/tex]

[tex]f(2)=50[/tex]

He will travel 50 miles with two gallon.

Answer:

b=10

Step-by-step explanation:

A=1/2bh

The A and h are already given

100=1/2b(20)

So what times 20 equals 2 times as much as 100? Its 10

100=1/2(10)(20)

100=1/2(200)

100=100

So the answer is b=10

Answer:

[tex]\large\boxed{A=(223.3+49\pi)m^2}[/tex]

Step-by-step explanation:

(look at the picture)

We have:

two halves of circle (whole circle) with radius r = 7m;

the suqare wih length side a = 14m;

the triangle with base b = 14m and hight h = 3.9m.

The formula of an area of a circle:

[tex]A_1=\pi r^2[/tex]

Substitute:

[tex]A_1=\pi(7^2)=49\pi\ m^2[/tex]

The formula of an area of a square:

[tex]A_2=a^2[/tex]

Substitute:

[tex]A_2=14^2=196\ m^2[/tex]

The formula of an area of a triangle:

[tex]A_3=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_3=\dfrac{(14)(3.9)}{2}=(7)(3.9)=27.3\ m^2[/tex]

The area of a figure:

[tex]A=A_1+A_2+A_3\\\\A=49\pi+196+27.3=223.3+49\pi[/tex]