rectangle ABCD is reflected over the x-axis. What rule shows the input and output of the reflection, and what is the new coordinate of A'?

A. (x, y) -> (y, -x) A' is at (1, 5)

B. (x, y) -> (-y, x) A' is at (-1, -5)

C. (x, y) -> (-x, y) A' is at (5, 1)

D. (x, y) -> (x, -y) A' is at (-5, -1)​

Answer:

$65720

Step-by-step explanation:

The job pays a starting salary of $62000, and raises $3720 per year. In one year, Carlos will be earning $62000 + $3720 =  $65720

Final answer:

Carlos's salary in one year will be $65720, which is the sum of his starting salary, $62000, and the promised annual raise of $3720.

Explanation:

After graduating from college, Carlos has received two different job offers, both offering a starting salary of $62000, and one includes a promise of a $3720 raise per year. To calculate his salary in one year, we need to add this annual raise to his starting salary.

Starting salary: $62000

Raise after one year: $3720

Carlos's salary in one year: $62000 + $3720 = $65720

This computation shows that with the promised annual raise, Carlos's salary for the next year would be $65720.

[tex]\bf 4csc(x)+6=-2\implies 4csc(x)=-8\implies csc(x)=\cfrac{-8}{4}\implies csc(x)=-2 \\\\\\ \cfrac{1}{sin(x)}=-2\implies \cfrac{1}{-2}=sin(x)\implies sin^{-1}\left( -\cfrac{1}{2} \right)=x\implies x= \begin{cases} \frac{7\pi }{6}\\\\ \frac{11\pi }{6} \end{cases}[/tex]

Answer:

11. r^2 + 12r + 27 = (r+3)(r+9)

12. g^2-9 = (g+3)(g-3)

13. 2p^3 + 6p^2 + 3p + 9 = (2p^2+3)(p+3)

Step-by-step explanation:

[tex]11.\ r^2 + 12r + 27\\Factorizing\\= r^2+9r+3r+27\\=r(r+9)+3(r+9)\\=(r+3)(r+9)\\\\12. g^2-9\\The\ expression\ will\ be\ factorized\ using\ the\ formula\\(a+b)(a-b)=a^2-b^2\\So,\\g^2-9\\=(g)^2-(3)^2\\=(g+3)(g-3)\\\\13. 2p^3 + 6p^2 + 3p + 9\\=2p^2(p+3)+3(p+3)\\=(2p^2+3)(p+3)[/tex] ..

Answer:

y=2x-3

Step-by-step explanation:

The slope-intercept form of a linear equation is y=mx+b where m is the slope and b is the y-intercept.

The y-intercept is where it crosses the y-axis.  It cross the y-axis in your picture at -3 so b=-3.

Now the slope=rise/run.  So starting at (0,-3) we need to find another point that crosses nicely on the cross-hairs and count the rise to and then the run to it.  So I see (1,-1) laying nicely.  So the rise is 2 and the run is 1.

If you don't like counting.  You could just use the slope formula since we already identified the two points as (-1,1) and (0,-3).

The way I like to use the formula is line up the points and subtract vertically then put 2nd difference over 1st difference.

(0,-3)

-(1,-1)

----------

-1     -2

So the slope is -2/-1 or just 2.

We have that m is 2 and b is -3.

Plug them into y=mx+b and you are done.

y=2x-3.

Slope intercept equation of the line is y = 2x - 3.

Slope intercept form gives the graph of a straight line and is represented in the form of y=mx + c.

By checking the graph by drawing manually.

From that we get the equation

y = 2x - 3

Comparing above equation with the standard slope-intercept form y = mx +c, we get

Slope : m = 2

Now, given equation can be re-written as :

2x - y = 3

Divide by 3 on both sides

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

[tex]\frac{x}{\frac{3}{2} } -\frac{y}{3} =1[/tex]

Comparing above equation with intercept form:

[tex]\frac{x}{a}+\frac{y}{b}=1[/tex], we get

x-intercept : [tex]a=\frac{3}{2}[/tex]

y-intercept : [tex]b=-3[/tex]

Now the given straight line intersects the coordinate axes at [tex](\frac{3}{2} ,0)[/tex] and [tex](0,-3)[/tex]. Specify these plots on XY-plane & join by a straight line to get a plot.

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Answer:

Second option:

[tex]d = 15.6\ mm,\ C = 49.01\ mm[/tex]

Step-by-step explanation:

We can observe that the radius of the circle is given. This is:

[tex]r = 7.8\ mm[/tex]

And the missing measures are the diameter of the circle and the circumference.

Since the diameter of a circle is twice the radius, we get that this is:

[tex]d=2r\\\\d=2(7.8\ mm)\\\\d=15.6\ mm[/tex]

To find the circumference of the circle, we can use this formula:

[tex]C=2\pi r[/tex]

Where "r" is the radius of the circle.

Substituting the radius into the formula, we get:

[tex]C=2\pi r\\\\C=2\pi (7.8\ mm)\\\\C=49.01\ mm[/tex]

Answer:

125

Step-by-step explanation:

500 ÷ 4 = 125

I think this is the right answer. sorry if I'm wrong.

Answer:

x=5 assuming that x is the radius.

x is the radius?

Step-by-step explanation:

[tex]V=\frac{4}{3} \pi r^3[/tex] is the volume of a sphere.

We are given [tex]V=\frac{500}{3} \pi[/tex] cubic units.

We are asked to find the value of x.  If x is not the radius, please correct me:

[tex]V=\frac{4}{3}\pi r^3[/tex] with  [tex]V=\frac{500}{3} \pi[/tex]  and the assumption that x is r.

[tex]\frac{500}{3}\pi=\frac{4}{3}\pi x^3[/tex]

If you multiply both sides by 3, then you would have:

[tex]500 \pi=4 \pi x^3[/tex]

If you divide both sides by [tex]\pi[/tex] you will have:

[tex]500=4x^3[/tex]

If you divide both sides by 4, you will have:

[tex]125=x^3[/tex]

The last step would be to take the cube root of both sides:

[tex]\sqrt[3]{125}=x[/tex]

[tex]5=x[/tex]

[tex]x=5[/tex]

Answer:

Step-by-step explanation:

(X+5)(X+1) = x²+x+5x+5 = x² +6x+5

(X+5)(X+1)

Use the FOIL method to expand.

This means multiply each term in the first set of parenthesis by each term in the second set.

x *x = x^2

x*1 = x

5*x = 5x

5*1 = 5

Now you have x^2 + x + 5x + 5

Now simplify by combining like terms:

x^2 + 6x + 5

Answer:

Option D y=3

Step-by-step explanation:

The question in English is

Which of the following functions is a constant function?

we know that

A constant function is a function whose output value is the same for every input value

so

Verify each case

case A) y=x+1

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case B) y=x+2

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case C) x=y+3

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case D) y=3

This is a constant function

Is a function whose output value is the same for every input value

Answer:

x =96 degree.

Step-by-step explanation:

Given : Triangle .

To find : The value of x is

Solution : We have given triangle

Exterior Angle sum property of triangle : Sum of all exterior angle of triangle is 360.

130 + 134 + x = 360 .

264 + x = 360.

On subtracting both sides by 264 .

x = 360 - 264 .

x = 96.

Therefore, x =96 degree.

Using Exterior Angle sum property of the triangle, The value of x will be 96 degree.

Exterior Angle sum property of the triangle states that the Sum of all exterior angles of the triangle is 360.

Given: Two exterior angles measure of 130 and 134 degrees.

To find: The value of x is

So,

130 + 134 + x = 360 .

264 + x = 360.

x = 360 - 264 .

x = 96.

Using Exterior Angle sum property of the triangle, The value of x will be 96 degrees.

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Answer:

73°

Step-by-step explanation:

Since WX = WZ then ΔWXZ is isosceles and WY is perpendicular to XZ

Hence ∠XYW = 90°

YW bisects XWZ, hence ⇒ ∠ YWX = ∠YWZ = 17°

The sum of the 3 angles in ΔWXY = 180°, hence

∠WXY = 180° - (90 + 17)° = 180° - 107° = 73°

[tex]f(x) = x^2(x^2 + 9)(x^3 + 2x)\\\\f(-x) = (-x)^2((-x)^2 + 9)((-x)^3 + 2\cdot(-x))\\f(-x)=x^2(x^2+9)(-x^3-2x)\\f(-x)=-x^2(x^2+9)(x^3+2x)\\\Large f(-x)\not =f(x)\implies\text{not even}\\\\-f(x)=-x^2(x^2+9)(x^3+2x)\\ -f(x)=f(-x)\implies \text{odd}[/tex]

Answer:

y=(6(x+6)(x-3))/((x-2)(x+3))

Step-by-step explanation:

The vertical asymptote should be in the denominator. The x-interceps should be in the numerator. Because we have horizontal asymptote y=6, then we have to put 6 in the numerator. the horizontal asymptote is the leading coefficient of the numerator ÷ the leading coefficient of the denominator, when the degree of the numerator and denominator are the same.

Given the horizontal asymptote, vertical asymptotes and x intercepts, the equation of the rational function is y = 6((x+6)(x-3))/((x-2)(x+3)). The vertical asymptotes are found by setting the function's denominator equal to zero, while the x-intercepts come from setting the numerator to zero.

In this question, we are asked to write the equation of a rational function based on given conditions. The function's vertical asymptotes are located at x = 2 and x = -3, and has x-intercepts at (-6,0) and (3,0), with a horizontal asymptote at y = 6.

The general form of a rational function is y = (ax+b)/(cx+d). Asymptotes help define the behavior and boundaries of the function. In this situation, we can set the denominator of our function equal to zero to find our vertical asymptotes, giving us (x-2)(x+3). To achieve our stated x-intercepts, we set the numerator equal to zero, providing (x+6)(x-3). Combining these, the function becomes y = ((x+6)(x-3))/((x-2)(x+3)). The output of the function approaches the horizontal asymptote as x approaches infinity. Thus to have y = 6 as our horizontal asymptote, we adjust our function to maintain this behaviour, settling on y = 6((x+6)(x-3))/((x-2)(x+3)).

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Answer:

=800 km

Step-by-step explanation:

Let the distance traveled by train be y and by bus be x.

Bus -x

Train -y

y=x+150 (since they traveled by train for a distance of 150 km more than by bus.)

The sum of the two is equal to 1450

x+y=1450

y=x+150

These two form simultaneous equations.

y+x=1450..............i

y-x=150.................ii

Adding ii to i gives:

2y=1600

Divide both sides by two

y=800

Distance traveled by train =y=800 km

Answer:

800

Step-by-step explanation:

For the first row, where x is equal to 7, to find y plug 7 in for x like so...

y = 7 - 3

y = 4

For the second row, where y is equal to 1, to find x plug 1 in for y like so...

1 = x - 3

To solve for x add 3 to both sides. This will cancel 3 from the right side:

1 + 3 = x - 3 + 3

4 = x + 0

x = 4

For the third row, where y is equal to 7, to find x plug 7 in for y like so...

7 = x - 3

To solve for x add 3 to both sides. This will cancel 3 from the right side:

7 + 3 = x - 3 + 3

10 = x + 0

x = 10

First row: y is 4

Second row: x is 4

Third row: x is 10

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

(x-3)² + (y-2)² = 25

Step-by-step explanation:

A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².

So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.

Answer:

[tex]\large\boxed{\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}=\dfrac{1}{64}}[/tex]

Step-by-step explanation:

[tex]\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=4^{-\frac{11}{3}-\left(-\frac{2}{3}\right)}=4^{-\frac{11}{3}+\frac{2}{3}}=4^{-\frac{9}{3}}=4^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{4^3}=\dfrac{1}{64}[/tex]

The simplification of the expression is [tex]\dfrac{1}{64}[/tex].

Exponentiation(the process of raising some number to some power) have some basic rules as:

[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\[/tex]

Given ;

[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})}[/tex]

We know that

[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]

[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})} = 4^({-11/3 + 2/3})\\\\\\= 4 ^{-9/3}\\\\= 4^{-3}\\\\[/tex]

Hence, [tex]\dfrac{1}{4^3} = \dfrac{1}{64}[/tex]

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Answer:

D is correct option

Step-by-step explanation:

The correct option is D.

The standard quadratic equation is ax²+bx+c=0

Where a and b are coefficients and c is constant.

It means that constant are on the L.H.S and there is 0 on the right hand side.

Therefore to make it a quadratic equation first of all you have to add 11 at both sides so that the R.H.S becomes 0.

The given equation is:

2x2-x+ 2 = -11

If we add 11 on both sides the equation will be:

2x2-x+ 2 +11= -11+11

2x^2-x+13=0

Thus the correct option is D

You can further solve it by applying quadratic formula....

Final answer:

The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to set up smaller equations using the zero product rule and then applthe quadratic formula. The correct option is c.

Explanation:

The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to:

C. Set up smaller equations using the zero product rule.

Once the equation is rearranged, apply the quadratic formula to determine the values of x.

Using the quadratic formula yields the solutions by substituting the values of a, b, and c correctly.

Answer:

The correct option is 3.

Step-by-step explanation:

The given equation is

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

It can be written as

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

Taking out the common factor form the parenthesis.

[tex]2(x^2+6x)-14=0[/tex]

If an expression is defined as [tex]x^2+bx[/tex] then we add [tex](\frac{b}{2})^2[/tex] to make it perfect square.

In the above equation b=6.

Add and subtract 3^2 in the parenthesis.

[tex]2(x^2+6x+3^2-3^2)-14=0[/tex]

[tex]2(x^2+6x+3^2)-2(3^2)-14=0[/tex]

[tex]2(x+3)^2-18-14=0[/tex]

[tex]2(x+3)^2-32=0[/tex]             .... (1)

Add 32 on both sides.

[tex]2(x+3)^2=32[/tex]

The vertex from of a parabola is

[tex]p(x)=a(x-h)^2+k[/tex]        .... (2)

If a>0, then k is minimum value at x=h.

From (1) and (2) in is clear that a=2, h=-3 and k=-32. It means the minimum value is -32 at x=-3.

The equation [tex]2(x+3)^2=32[/tex] reveals the minimum value for the given equation.

Therefore the correct option is 3.

The correct answer is option 3. [tex]2(x + 3)^2 = 32[/tex].

To find the minimum value of the quadratic equation [tex]2x^2 + 12x - 14[/tex] = 0, we can rewrite it in vertex form, which reveals the minimum or maximum value of a quadratic function.

The given options are attempts at rewriting the quadratic equation in vertex form. Let’s rewrite the equation:

First, complete the square:

1. Start with the equation: [tex]2x^2 + 12x - 14[/tex]

2. Factor out the coefficient of x² from the first two terms: [tex]2(x^2 + 6x) - 14[/tex]

3. Complete the square inside the parentheses:
- Take [tex](\frac{6}{2})^2 =9[/tex] - Add and subtract 9 inside the parentheses: [tex]2(x^2 + 6x + 9 - 9) - 14[/tex]
- Simplify inside the square: [tex]2((x + 3)^2 - 9) - 14[/tex]

4. Distribute and simplify: [tex]2(x + 3)^2 - 18 - 14 = 2(x + 3)^2 - 32[/tex]

Comparing this with the options, we have [tex]2(x + 3)^2 = 32[/tex].

The correct answer is: [tex]2(x + 3)^2 = 32[/tex].

Answer:

The length is 9 and the width is 6.

Step-by-step explanation:

6*9 = 54 and 9 is 3 greater than 6.

Answer:

x = -2, x = 0, and x = 3

Step-by-step explanation:

it was right lol

Answer:

The original price of a skateboard is $64

Step-by-step explanation:

Let

x ----> the original price of a skateboard

y ----> the new price of a skateboard

we know that

The linear equation that represent this problem is equal to

y=x-15 ----> equation A

y=49 ---> equation B

substitute equation B in equation A and solve for x

49=x-15

Adds 15 both sides

49+15=x

64=x

Rewrite

x=$64

Answer:

m < A = 101 degrees.

Step-by-step explanation:

The transverse line crosses 2 parallel lines (opposite angles of a rectangle are parallel) ,  so the same side angles add up to 180 degrees.

m < A + 79 = 180

m < A = 101 degrees.

Answer:

A=101°

Step-by-step explanation:

The two lengths of the rectangle are parallel and therefore the sides of the path form two parallel transversals.

The angle marked 79° and the angle marked A are supplementary ( they add up to 180°)

A+79=180°

A=180-79

=101°

Answer:

2 is your slope

Step-by-step explanation:

Find the slope. Use the slope-formula:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (-1 , 1)

(x₂ , y₂) = (2 , 7)

Plug in the corresponding numbers to the corresponding variables:

m = (7 - 1)/(2 - (-1))

Simplify:

m = (6)/(2 + 1)

m = 6/3

m = 2

2 is your slope (or rise 2, run 1).

~

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (2, 7)

m = [tex]\frac{7-1}{2+1}[/tex] = [tex]\frac{6}{3}[/tex] = 2

Answer:

g(3)=11 I think

Step-by-step explanation:

Since x is 3, you substitute it in for the x. So it would be 3 squared +2.

I'm not sure if this is right but I tried helping.

Answer:

g(3) =11

Step-by-step explanation:

g(x) = x^2 +2

Let x =3

g(3) = 3^2 +2

      = 9+2

      = 11

Answer:

sum of angles of triamgle is 180 degree

the half base× hight ue1/2×b×h

use the formula for all qusetions

Answer:

[tex]y=x^{2}+3[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex

In this problem we have the vertex at point (0,3)

substitute

[tex]y=a(x-0)^{2}+3[/tex]

[tex]y=ax^{2}+3[/tex]

therefore

The option [tex]y=x^{2}+3[/tex] is the answer

In this case the coefficient a is equal to 1

Answer:

Circle A and circle B are similar

Step-by-step explanation:

* Lets explain similarity of circles

- Figures can be proven similar if one, or more, similarity transformations

 reflections, translations, rotations, dilations can be found that map one

 figure onto another

- To prove all circles are similar, a translation and a scale factor from a

  dilation will be found to map one circle onto another

* Lets solve the problem

∵ Circle A has center (-1 , 1) and radius 1

∵ The standard form of the equation of the circle is:

   (x - h)² + (y - k)² = r² , where (h , k) are the coordinates the center

   and r is the radius

∴ Equation circle A is (x - -1)² + (y - 1)² = (1)²

∴ Equation circle A is (x + 1)² + (y - 1)² = 1

∵ Circle B has center (-3 , 2) and radius 2

∴ Equation circle B is (x - -3)² + (y - 2)² = (2)²

∴ Equation circle B is (x + 3)² + (y - 2)² = 4

- By comparing between the equations of circle A and circle B

# Remember:

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

∵ -3 - -1 = -2 and 2 - 1 = 1

∴ The center of circle A moves 2 units to the left and 1 unit up to

  have the same center of circle B

∴ Circle A translate 2 units to the left and 1 unit up

∵ The radius of circle A = 1 and the radius of circle B = 2

∴ Circle A dilated by scale factor 2/1 to be circle B

∴ Circle B is the image of circle A after translation 2 units to the left

  and 1 unit up followed by dilation with scale factor 2

- By using the 2nd fact above

∴ Circle A and circle B are similar

Answer:

Answer is Circle

Step-by-step explanation:

Check the picture below.

notice, all points are equidistant from the center of it, wherever the center happens to be.

Answer:

4:3

Step-by-step explanation:

Given that P divides segment MN into 4/7, let MN to be x units in length then

MP = 4/7 x =4x/7 --------(i)

But MN =MP+PN so;

x=4x/7 +PN

x- 4X/7 =PN

3x/7 =PN ----------(ii)

To get the ratio of MP:PN

MP: PN

4x/7:3x/7

MP/PN = 4x/7 / 3x/7

MP/PN =4/3

MP:PN = 4:3

Answer: 4:3

Step-by-step explanation:

Given : A point P is 4/7 of the distance from M to N.

∴ Let the distance between M to N be d.

[tex]\Rightarrow\ MP=\dfrac{4}{7}\times d=\dfrac{4d}{7}[/tex]

Also,  the point P partition the directed line segment from M to N .

Thus , MN = MP+PN

[tex]\Rightarrow\ d=\dfrac{4d}{7}+PN\\\\\Rightarrow\ PN= d-\dfrac{4d}{7}=\dfrac{7d-4d}{7}\\\\\Rightarrow\ PN=\dfrac{3}{7}d[/tex]

Now, the ration of MP to PN will be :-

[tex]\dfrac{MP}{PN}=\dfrac{\dfrac{4d}{7}}{\dfrac{3d}{7}}=\dfrac{4}{3}[/tex]

∴ Point P partitioned the line segment MN into 4:3.

To solve the equation 3x - 2 = 37, you add 2 to both sides to get 3x = 39. Then, you divide by 3 to solve for x, obtaining x = 13.

To solve the equation

3x − 2 = 37

for x, you start by moving the -2 to the other side of the equation by adding 2 to both sides. This gives you

3x = 39

. Then, you isolate x by dividing every term by 3. After dividing, you find that

x = 13

. So the solution to the equation 3x - 2 = 37 is x = 13.

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To solve the equation, add 2 to both sides and then divide by 3 to isolate the variable x. The solution is x = 13.

To solve the equation 3x - 2 = 37, we need to isolate the variable x. Here are the steps:

Therefore, the solution to the equation is x = 13.

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