The sum of a rational number and an irrational number equals:

Answer:

First exercise: [tex]x=7[/tex]

Second exercise: [tex]x=2[/tex]

Step-by-step explanation:

According to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.

Knowing this, in order to solve the first exercise and the second exercise, we can write  the following expressions and solve for "x":

For the first exercise, we get:

[tex](5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=\frac{35}{5}\\\\x=7[/tex]

For the second exercise, we get:

[tex](4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=\frac{8}{4}\\\\x=2[/tex]

E is exponents, D is division, A is addition

Answer:

E- exponent D- division A- addition

Step-by-step explanation:

PEMDAS is an acronym which means

P- parenthesis

E- exponents

M- multiplication

D- division

A- addition

S- subtraction

used for two or more operation in a single expression, the order of letters in the PEMDAS tells us what to calculate first, second, third and so on, until the calculation is complete.

Answer:

$1050

Step-by-step explanation:

To solve, multiply your two expenses against your $6000 and find the difference.

The man spends 1/5 of his salary on children's education.

To find how much he spends on his children's education in dollars, multiply 1/5 against $6000.

[tex]\frac{1}{5} *6000\\1200[/tex]

The man spends $1200 on children's education.

The man spends 5/8 of his salary on his aged mother and unemployed sister.

Repeat the same process as the first step, this time multiplying 5/8 against $6000.

[tex]\frac{5}{8} *6000\\3750[/tex]

The man spends $3750 on his aged mother and unemployed sister.

Add these two expenses together.

[tex]1200+3750\\4950[/tex]

The man has combined expenses of $4950.

To find how much money he has left, subtract his expenses from his $6000 income.

[tex]6000-4950\\1050[/tex]

The man has $1050 remaining.

Answer : The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Answer:

The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Step-by-step explanation:

An equation is shown below:

4(x − 3) − 5(x + 1) = 3

This equation shows, the equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

The distributive property is when you multiply the sum in the equation and multiply each number or addend in the equation.

Answer:

A. S

Step-by-step explanation:

The edge of the circle would be M and there is a line to the center showing the radius. The second letter shows the center.

point S is the centre of the given circle.

You need to know some details about a circle, such as its equation or certain locations on the circle, in order to locate its center.

Drawing the perpendicular bisectors of each chord will allow you to determine the circle's center if you are aware of the location where two perpendicular chords connect. The center of the circle is where the perpendicular bisectors intersect.

Therefore, based on the given figure, the centre is the point S.

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Answer:

The third table is an arithmetic sequence . Its difference is -1.4.

Step-by-step explanation:

In an arithmetic sequence the difference between one term and the next is a constant

8.7 - 1.4 = 7.3

7.3 - 1.4 = 5.9

5.9 - 1.4 = 4.5

4.5 - 1.4 = 3.1

Answer:3rd table

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

1/2x-3/4=3/8-5/8

Combine like terms on the right hand side

1/2x-3/4=-2/8

Simplify the fraction

1/2x-3/4=-1/4

Add 3/4 to each side

1/2x-3/4+3/4 = -1/4+3/4

1/2x = 2/4

Multiply each side by 2

1/2x *2 = 2/4*2

x = 4/4

x=1

Answer:

the answer its 1

Step-by-step explanation:

Answer:

y-1=0

Step-by-step explanation:

I'm going to write into y=mx+b form first.

m is the slope and b is the y-intercept.

First step is to find the slope.

To find the slope given two points you can use m=(y2-y1)/(x2-x1).

Instead, I like to line up the points and subtract vertically.  Then put 2nd difference on top of 1st difference.

Let's do that:

 (-2,1)

- (2,1)

--------

 -4, 0

The slope is 0/-4=0.  That means the line is horizontal and is of the form y=a number.

If you look at the points, you see the y-coordinate doesn't change.  The y-coordinate is always 1.  So the equation for the line is y=1.

If we subtract 1 on both sides we get y-1=0.

So general form is Ax+By+C=0 which is why I decide to move the one on the other side of the equation.  

If I had noticed earlier that the y-coordinates were the same I would have stopped and say y=whatever y-coordinate I seen. However, I really didn't take notice of that until after I found the slope.

The equation of the line is y = 0.6*x - 1, the graph is in the image at the end.

How to find the linear equation?

A linear equation in the slope-intercept form can be written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the points (−5,−4) and (5,2), so the slope is:

a = (2 + 4)/(5 + 5) = 6/10 = 0.6

y = 0.6*x + b

And it passes through (5, 2), then:

2 = 0.6*5 + b

2 - 0.6*5 = b

-1 = b

The equation is:

y = 0.6*x - 1

The graph is in the image below.

Answer:

The length in the draw is 10 cm

Step-by-step explanation:

step 1

Find the scale plan

Divide the width in the draw by the width in the real

so

[tex]\frac{4}{8}=\frac{1}{2}\frac{cm}{m}[/tex]

That means----> 1 cm in the draw is equal to 2 m in the real

step 2

Find the length in the draw

using proportion

[tex]\frac{1}{2}\frac{cm}{m}=\frac{x}{20}\frac{cm}{m}\\ \\x=20/2\\ \\x=10\ cm[/tex]

Answer:

False; this is the law of syllogism.

Step-by-step explanation:

Law of Detachment is:

1) p->q

2) p

------------------------

Conclusion: q

Law of syllogism is:

1) p->q

2) q->r

---------------------

Conclusion: p->r

Answer:

3 and 9

if f(x)=x^2+13 and g(x)=12x-14

Step-by-step explanation:

So when we are looking for the intersection of two functions, we are trying to figure out when they are the same.  When you think same, you should think equal (=).

So we want to find when f(x)=g(x) for x.

f(x)=g(x)

[tex]x^2+13=12x-14[/tex]

Let's get everything to one side.

Subtracting 12x and adding 14 to both sides.

[tex]x^2+13+14-12x=0[/tex]

I'm going to reorder the left hand side and also simplify the 13+14 part:

[tex]x^2-12x+27=0[/tex]

Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.

Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.

So the factored form of our equation is

[tex](x-3)(x-9)=0[/tex]

Since the product is 0, then at least one of the factors must be 0.

So we want to solve both x-3=0 and x-9=0.

x-3=0 can be solved by adding 3 on both sides. This gives us x=3.

x-9=9 can be solved by adding 9 on both sides. This gives us x=9.

The intersection of f and g happens at x=3 or x=9.

Answer:

x = 9 and x = 3

Step-by-step explanation:

Given

f(x) = x² + 13 and g(x) = 12x - 14

To find the points of intersection equate the 2 functions, that is

f(x) = g(x)

x² + 13 = 12x - 14 ← subtract 12x - 14 from both sides

x² - 12x + 27 = 0 ← in standard form

Consider the factors of the constant term ( + 27) which sum to give the coefficient of the x- term ( - 12)

The factors are - 3 and - 9, since

- 3 × - 9 = + 27 and - 3 - 9 = - 12, hence

(x - 3)(x - 9) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 9 = 0 ⇒ x = 9

The functions intersect at x = 3 and x = 9

Answer:

Should be 1st number, 3rd number, 2nd number

Step-by-step explanation:

Mixed fraction has a 3 in it, which means its over 100%. 6/20 is 30%, and the other one is negative.

Answer:

3 32/40, 6/20, - 2/10

Step-by-step explanation:

3 32/40,  -2/10  , 6/20

We want greatest to least

Positive numbers are greater than negative numbers, so the negative number is the smallest

Since there is only one number with a whole number attached and none of the numbers are improper fractions (numerator larger than denominator) it would be the largest

3 32/40, 6/20, - 2/10

Answer:

Part 1) [tex]324\pi\ units^{2}[/tex] ------> [tex]7,776\pi\ units^{3}[/tex]

Part 2) [tex]36\pi\ units^{2}[/tex] ------> [tex]288\pi\ units^{3}[/tex]

Part 3) [tex]81\pi\ units^{2}[/tex] ------> [tex]972\pi\ units^{3}[/tex]

Part 4) [tex]144\pi\ units^{2}[/tex] ------> [tex]2,304\pi\ units^{3}[/tex]

Step-by-step explanation:

we know that

The largest cross sectional area of that sphere is equal to the area of a circle with the same radius of the sphere

Part 1) we have

[tex]A=324\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]324\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=324[/tex]

[tex]r=18\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=18\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (18)^{3}[/tex]

[tex]V=7,776\pi\ units^{3}[/tex]

Part 2) we have

[tex]A=36\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]36\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=36[/tex]

[tex]r=6\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=6\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ units^{3}[/tex]

Part 3) we have

[tex]A=81\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]81\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=81[/tex]

[tex]r=9\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=9\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (9)^{3}[/tex]

[tex]V=972\pi\ units^{3}[/tex]

Part 4) we have

[tex]A=144\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]144\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=144[/tex]

[tex]r=12\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=12\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (12)^{3}[/tex]

[tex]V=2,304\pi\ units^{3}[/tex]

Answer:

90

Step-by-step explanation:

90-20%=72

72-20-52

plus everything else doesnt match up and with taxes involved so the oroginal price was 90

Answer:

Angle D is 70, I believe

Angle D would be supplementary to A

Answer:

36cm

Step-by-step explanation:

If the current banner is a reduction of 1/6, then you have to expand it by the reciprocal. 6/1 *6 =36.

Answer:

36 cm.

Step-by-step explanation:

It is given that A button with a diameter of 6 cm is made from a circular banner. The scale factor of the reduction was 1/6 .

Let [tex]d[/tex] be the diameter of the original banner.

The scale factor of the reduction was 1/6 . It means,

[tex]\text{New diameter}=\frac{1}{6}\times \text{Original diameter}[/tex]

[tex]6=\frac{1}{6}\times d[/tex]

Multiply both sides by 6.

[tex]36=d[/tex]

Hence, the diameter of the original banner is 36 cm.

The graph of y=(x-1)^2-3 can be transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.

The graph of y=(x-1)^2-3 transformed to produce the graph of y=1/2(x+4)^2 can be done by manipulating the equation and observing its effect on the graph.

Step 1: Identify the transformation of the parent function y=x^2

Step 2: The transformation y=1/2(x+4)^2 indicates a vertical stretch by a scale factor of 1/2 and a horizontal shift to the left by 4 units.

Therefore, the graph of y=(x-1)^2-3 is transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.

A: The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.

B: The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.

C: The graph is translated left 5 units, compressed horizontally by a factor of One-half, and translated down 3 units.

D: The graph is stretched horizontally by a factor of One-half, translated left 5 units, and translated down 3 units.

Answer:

The graph is stretched horizontally by a factor of 1/2, translated left 5 units and up 3 units.

Step-by-step explanation:

I put both equations into a graphing calculator and compared them. Five units left and 3 up agree with answers A and B. The second equation showed a wider parabolic than the first one, which agrees only with answer C. Therefore, it is my opinion that neither answer is correct. I chose D, but since this is a unit test I can't go in and see if I was correct or not.

Answer:

5 hours

Step-by-step explanation:

The total amount of the repair is $265 and includes parts and an hourly rate. We are told the parts are $90. Subtract the price of the parts, $90, from the total of $265.

$265 - $90 = $175

The $175 is only due to the hourly rate.

Now we divide the total due to the hours by the hourly rate to find the number of hours.

175/35 = 5

Answer: 5 hours

Answer:

The function that shows total sales, including the first hour is

[tex]S(x)=15(x-1)+120[/tex]  or [tex]S(x)=15x+105[/tex]  

Step-by-step explanation:

Let

s(x) -----> function that represent the sales after the first hour

S(x) ----> function that represent the total sales (including the first hour)

x -----> the  number of hours

we know that

The linear equation that represent the total sales is equal to

[tex]S(x)=s(x)+120[/tex] -----> equation A

we have

[tex]s(x)=15(x-1)[/tex] -----> equation B

substitute equation B in equation A

[tex]S(x)=15(x-1)+120[/tex]

[tex]S(x)=15x-15+120[/tex]

[tex]S(x)=15x+105[/tex]  

Therefore

The function that shows total sales, including the first hour is

[tex]S(x)=15(x-1)+120[/tex]  or [tex]S(x)=15x+105[/tex]  

Answer:

The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down

Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

  problem

- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

* Lets solve the problem

- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)

- Lets find the mid-poits of PQ called A

∵ Point P is (x1 , y1) and point Q is (x2 , y2)

∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0

∵ A is the mid-point of PQ

∴ [tex]A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)[/tex]

- Lets find the mid-poits of PR which called B

∵ Point P is (x1 , y1) and point R is (x2 , y2)

∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c

∵ B is the mid-point of PR

∴ [tex]B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)[/tex]

- The parallel line have equal slopes, so lets find the slopes of AB and

  QR to prove that they have same slopes then they are parallel

# Slope of AB

∵ Point A is (x1 , y1) and point B is (x2 , y2)

∵ Point A = (a , 0) and point B = (b , c)

∴ x1 = a , x2 = b and y1 = 0 and y2 = c

∴ The slope of AB is [tex]m=\frac{c-0}{b-a}=\frac{c}{b-a}[/tex]

# Slope of QR

∵ Point Q is (x1 , y1) and point R is (x2 , y2)

∵ Point Q = (2a , 0) and point R = (2b , 2c)

∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c

∴ The slope of AB is [tex]m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}[/tex]

∵ The slopes of AB and QR are equal

∴ AB // QR

∵ AB is the line containing the midpoints of PQ and PR of Δ PQR

∵ QR is the third side of the triangle

∴ The line containing the midpoints of two sides of a triangle is parallel

  to the third side

Answer:

b,c

Step-by-step explanation:

That guy above took so long

Answer:

The amount of salads sold that day were 93.

Step-by-step explanation:

Information to note:

Salad = $6.50

Drinks = $2.00

Total amount sold = 209

Total amount of money gained = $836.50

Set the system of equation. Let salad = s, and drinks = d

s + d = 209

6.50s + 2d = 836.50

Isolate the variable s in the first equation. Note the equal sign, what you do to one side, you do to the other. Subtract d from both sides:

s + d = 209

s + d (-d) = 209 (-d)

s = 209 - d

Plug in the new expression for s into the second equation:

s = 209 - d

6.50s + 2d = 836.50

6.50(209 - d) + 2d = 836.50

Simplify. Isolate the variable, d. First, distribute 6.50 to all terms within the parenthesis:

6.50(209 - d) = 1358.5 - 6.50d

1358.5 - 6.50d + 2d = 836.50

Simplify. Combine like terms:

1358.5 + (-6.50d + 2d) = 836.50

1358.5 - 4.50d = 836.50

Isolate the variable, d. Note the equal sign, what you do to one side, you do to the other.

Subtract 1358.5 from both sides:

1358.5 (-1358.5) - 4.50d = 836.50 (-1358.5)

-4.50d = 836.50 - 1358.50

-4.50d = -522

Isolate the variable, d. Divide -4.50 from both sides:

(-4.50d)/-4.50 = (-522)/-4.50

d = -522/-4.50

d = 116

The amount of drinks sold were 116.

Plug in 116 for d in one of the equations:

s + d = 209

s + (116) = 209

Isolate the variable, s. Subtract 116 from both sides:

s + 116 (-116) = 209 (-116)

s = 209 - 116

s = 93

The amount of salads sold that day were 93.

~

Answer:68

Step-by-step explanation:

In an isosceles triangle with angle BCA equal to 44 degrees, the measure of angle CXA is also 44 degrees because the sum of the two bisected base angles is 44 degrees.

In an Isosceles Triangle, the base angles are always equal. Therefore, if m∠BCA (angle BAC) is 44 degrees, then m∠ABC is also 44 degrees.

Because BFAD and CE are bisectors, they split ∠ABC and ∠ACB into two equal angles. So, ∠ABF (or ∠ABX) and ∠ACD (or ∠ACX) are each 22 degrees.

m∠CXA is the sum of ∠ABX and ∠ACX. Therefore, m∠CXA is 22 degrees + 22 degrees = 44 degrees.

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A. obtuse. The angle R is obtuse.

An obtuse angle is an angle greater than 90° and less than 180°. So, in the image attached we can see that the angle R is greater than 90° and less than 180°.

Answer:

the order is

2,4,1,3

(the 1st answer is the 2nd option)

Answer:

1. (a² - b)/(a³b²)= 1/ab² - 1/a²b

2. (b - a)/a³b³ = 1/a³b² - 1/a²b³

3. (2 - ab²)/(a²b³) = 2/a²b³ - 1/ab

4. (2 - a)/a³b³ = 2/a³b³ - 1/a²b³

Step-by-step explanation:

To do this we'll break down fraction to least term through division.

The solution is as follows

1. (a² - b)/(a³b²)

Splitting the fraction;

a²/a³b² - b/a³b²

= 1/ab² - 1/a²b

2. (b - a)/a³b³

Splitting the fraction.

b/a³b³ - a/a³b³

1/a³b² - 1/a²b³

3. (2 - ab²)/(a²b³)

Splitting the fraction.

2/a²b³ - ab²/a²b³

2/a²b³ - 1/ab

4. (2 - a)/a³b³

Splitting the fraction

2/a³b³ - a/a³b³

2/a³b³ - 1/a²b³

Answer:

its the second choice 2 + n< 14

Answer:

90

Step-by-step explanation:

90 is where the middle line is

please mark brainliest :)

Answer:

90.

Step-by-step explanation:

The median is the point near the middle of the box.  It is 90.

Answer:

-2 + i

Step-by-step explanation:

The midpoint is the average:

[ (-7 + 4i) + (3 − 2i) ] / 2

Combine like terms:

(-4 + 2i) / 2

Divide:

-2 + i

Answer:

[tex]\large\boxed{\bigg(4\times10^8\bigg)^2=1.6\times10^{17}}[/tex]

Step-by-step explanation:

[tex]\text{The sicientific notation:}\ a\times10^k,\ \text{where}\ 1\leq a<10\ \text{and}\ k\in\mathbb{Z}.\\\\\bigg(4\times10^8\bigg)^2\qquad\text{use}\ (ab)^n=a^nb^n\\\\=4^2\times\left(10^8\right)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=16\times10^{16}\ -\ \text{this is not a scientific notation yet}\ a=16>10\\\\=1.6\times10\times10^{16}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=1.6\times10^{17}[/tex]

Answer:

1.6 x 1017

Step-by-step explanation: