Point P has coordinates P(-3,5).
What are the coordinates of the image P" after I translate point P: 2
units to the right 3 units up and then I reflect its image across the x-
axis?

Answer:

I hope you will get help from these...

Answer:

Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Step-by-step explanation:

The formula for average rate of change of f(x) over [a,b] is

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

The given function is

[tex]r(x)=x^2+2x-5[/tex]

[tex]r(0)=(0)^2+2(0)-5=-5[/tex]

[tex]r(3)=(3)^2+2(3)-5=10[/tex]

Now,

[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]

[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]

From the graph it is clear that q(0)=-4 and q(3)=5.

[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]

[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]

It is given that  function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.

[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]

[tex]m_3=\dfrac{0-6}{3}=-2[/tex]

From the given table it is clear that s(0)=-13 and s(3)=5.

[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]

[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]

Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Answer: B. He loses 1/5 of his points in the next crash

Plug in x = 0 to get y = 100(4/5)^0 = 100. He starts with 100 points

After x = 1 crash happens, he has y = 100(4/5)^1 = 80 points left. He lost 20/100 = 1/5 of his points after one crash.

Answer:

x=10 cm

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

x^2 + ( sqrt(200) )^2 = (sqrt(300))^2

x^2 +200 = 300

Subtract 200 from each side

x^2 +200-200 = 300-200

x^2 = 100

Take the square root of each side

sqrt(x^2) = sqrt(100)

x = 10

Answer:

The answer is

negative 12 s squared + 11 s t minus 2 t squared

Step-by-step explanation:

( - 3s + 2t)( 4s - t)

Expand the terms

We have

- 12s² + 3st + 8st - 2t²

Simplify

We have the final answer as

Hope this helps you

Answer:

D. -12s^2+11st-2t^2

Answer:

Step-by-step explanation:

(0+2)/(0-10)= 2/-10 = -1/5

y - 0 = -1/5(x - 0)

y = -1/5x

solution is D

Since HJ is tangent to circle G, it forms a right angle with the radius that intersects it.

This means HG and HG are perpendicular and we have a right angle.

We have a (right) triangle with angle measurements 43 and 90, and we want to find the value of the last angle.

All the angles in a triangle must add up to 180, thus we can create the following equation to find the measurement of the last angle:

[tex]180-90-43[/tex]

[tex]=47[/tex]

The measure of angle G is 47 degrees. Let me know if you need any clarifications, thanks!

Answer:

<G = 47 degrees

Step-by-step explanation:

For this problem, we need to understand two things.  This tangent on the circle, with a line drawn to the center, forms a right angle at H.  Additionally, the sum of the angles of a triangle is 180.  Now with these two things, let's solve.

<G = 180 - (43 + 90)

<G = 180 - 133

<G = 47 degrees

Hope this helps.

Cheers.

Answer:

2x - y = 3

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

x + 2y = - 2 ( subtract x from both sides )

2y = - x - 2 ( divide all terms by 2 )

y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

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}{-\frac{1}{2} }[/tex] = 2 , thus

y = 2x + c ← is the partial equation

To find c substitute (2, 1) into the partial equation

1 = 4 + c ⇒ c = 1 - 4 = - 3

y = 2x - 3 ← equation in slope- intercept form

add 3 to both sides

y + 3 = 2x ( subtract y from both sides )

3 = 2x - y, thus

2x - y = 3 ← equation in standard form

]

Answer:

25,217,091

Step-by-step explanation:

4551 * 5541 = 25,217,091

Answer:

4551*5541=25217091

Step-by-step explanation:

Answer:

44°

Step-by-step explanation:

The secant- secant angle y is half the difference of the measure of its intercepted arcs, that is

[tex]\frac{1}{2}[/tex](BHF - CGJ ) = y , that is

[tex]\frac{1}{2}[/tex](156 - CGH) = 56° ( multiply both sides by 2 )

156 - CGH = 112° , thus

CGH = 156° - 112° = 44°

Answer:

24.5 oz

Step-by-step explanation:

First lets calculate the blood tests, 3/4 oz of solution.

3/4 multiplied by four tests= 3. (.75*4=3)

So 3 oz of Blood Tests were performed, now lets calculate the amount of tissue staining tests for performed.

1/2 multiplied by five tests= 5/2 or 2.5 oz of tests. (.5*5=2.5)

3oz+2.5=5.5oz

Now let's subtract that amount by 30.

30-5.5=24.5

Answer:

The number of students that would have a test score between 61 and 71 are 154 students

Step-by-step explanation:

The given information are;

The mean test score, μ = 61

The standard deviation, σ = 10

The sample size, n = 450

The z score is given as follows;

[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]

We therefore have at x = 61,

[tex]Z=\dfrac{61-61 }{10 } = 0[/tex]

P(x > 61) = P(Z > 0) = 1 - 0.5 = 0.5

For x = 71, we  have;

[tex]Z=\dfrac{71-61 }{10 } = 1[/tex]

P(x < 71) = P(Z < 1) = 0.84134

The probability that the score will be between 61 and 71 is the difference between the two probabilities, which is 0.84134 - 0.5 = 0.34134

Given that the probability is equivalent to  the proportion of the students that would have a test score between 61 and 71, we have;

The number of students that would have a test score between 61 and 71 = 0.34134 × 450 = 153.6 ≈ 154 to the nearest whole number.

Answer: The fifth piece of paper could have any number 9 and less or 14 and greater.

Step-by-step explanation:  The list of choices is not given in the question, but it makes sense that the new number would not be a duplicate of any of the numbers 10, 11, 12, 13. Otherwise that would change the probability to 5/5.

So any other number could be a possibility.

Answer:

[tex]\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4[/tex]

The foci c is at +/-2√5, using c² = a² + b²:

[tex]c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2[/tex]

Substituting the value of a and b to get the equation of the hyperbola:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]

Answer:

7.1 km

Step-by-step explanation:

Bien, este es un problema de conversión de unidades.

Procedemos de la siguiente manera;

Convirtamos todas las alturas que tenemos a metros.

Comenzamos con 23,000 decímetros a metros Matemáticamente, 1 metro = 10 decímetros Entonces 23,000 decímetros = 23,000 / 10 = 2,300 metros

En segundo lugar, convertimos 54 hectómetros a metros.

Matemáticamente; 1 hectómetro = 100 metros Entonces 54 hectómetros = 54 * 100 = 5400 metros Por lo tanto, su nueva altura sería; 14,800-2300-5400 = 7,100 metros Ahora, procedemos a convertir 7.100 metros a kilómetros.

Matemáticamente 1000 m = 1 km Entonces 7,100 m serán = 7100/1000 = 7.1 km

Responder:

Explicación paso a paso:

Altura inicial del avión = 14.800 m.

Como se redujo en 23,000 decímetros y luego en 54 hectómetros, la caída total de altura se obtiene al agregar 23,000 decímetros y 54 hectómetros

Antes de agregarlos, necesitamos convertir ambos valores a metros

1 decímetro = 0.1m

23,000 decímetros = x

x = 23,000 * 0.1

x = 2,300 metros

Además, si 1 hectómetro = 100 m

54 hectómetros = y

y = 54 * 100

y = 5400 metros.

Sumando ambas alturas;

x + y = 2300m + 5400m = 7700 metros

Esto significa que el avión cae por una altura total de 7700 metros

Para calcular la altura a la que volará el avión después de la caída, tomaremos la diferencia entre la altura inicial y la altura total caída.

La altura que el avión está volando ahora será 14,800 - 7,700 = 7,100 metros

Convirtiendo la respuesta final a kilómetros.

1000m = 1km

7.100m = z

z = 7100/1000

z = 7.1 km

Esto significa que el avión está volando a una altura de 7.1 kilómetros después de la caída.

Answer:

Step-by-step explanation:

Let the first number be x

Let the second number be y

For the first equation

One number is 7 less than 3 times the second number is written as

x = 3y - 7

For the second equation

The sum of the two numbers is 29

So we have

x + y = 29

Substitute the first equation into the second one

That's

3y - 7 + y = 29

4y = 29 + 7

4y = 36

Divide both sides by 4

Substitute y = 9 into x = 3y - 7

That's

x = 3(9) - 7

x = 27 - 7

The numbers are 20 and 9

Hope this helps you

Answer:

x² - 20 = 0

Using the quadratic formula

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

a = 1 b = 0 c = -20

So we have

[tex]x = \frac{ - 0 ± \sqrt{ {0}^{2} - 4(1)( -20)} }{2(1)} \\ \\ x = \frac{± \sqrt{80} }{2} \\ \\ x = \frac{±4 \sqrt{5} }{2} \\ \\ \\ x = ±2 \sqrt{5} \\ \\ \\ x = 2 \sqrt{5} \: \: \: or \: \: \: x = - 2 \sqrt{5} [/tex]

Hope this helps you.

Answer:

50

Step-by-step explanation:

Answer:

The answer is b

Step-by-step explanation:

since 2*9=18 and (x)(2x+3)=2x^2+3x

Answer: B

Step-by-step explanation:

Answer:

1. [tex]\bold{S=f(P) = 0.07P}[/tex]

2. x = 16

3. Part 1: P is the independent variable and S is the dependent variable.

Part 2: x is the independent variable and y is the dependent variable.

Step-by-step explanation:

1. To write the function notation for:

Sales tax is 7% of the total price.

Let the total price be [tex]P[/tex].

And sales tax be [tex]S[/tex].

As per the given statement:

[tex]S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P[/tex]

Writing it in the function notation:

[tex]\bold{S=f(P) = 0.07P}[/tex]

2. To find the value of x such that [tex]f(x) = 14[/tex] and

[tex]f(x) = \dfrac{1}4x + 10[/tex]

Putting the value of [tex]f(x) = 14[/tex]

[tex]14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}[/tex]

3. To find the dependent and independent variable.

Independent variables are those whose value is not dependent on the other variable's values.

Dependent variables are dependent on the value of other variables.

In question 1:

[tex]\bold{S=f(P) = 0.07P}[/tex]

P is the independent variable.

S is the dependent variable.

In question 2:

If we write it as follows:

[tex]y=f(x) = \dfrac{1}4x + 10[/tex]

x is the independent variable and y is the dependent variable.

Answer:

2

Step-by-step explanation:

green

Answer: 2

Step-by-step explanation:

Answer:

t = -(25/112)

Answer:

388.5yd²

Step-by-step explanation:

We have Triangle TUV

In the question, we are given already

Angle U = 32°

Angle T = 38°

Angle V = ???

Side t = 31yd

Side u = ?

Side v = ?

Area of the triangle= ?

Step 1

We find the third angle = Angle V

Sum of angles in a triangle = 180°

Third angle = Angle V = 180° - (32 + 38)°

= 180° - 70°

Angle V = 110°

Step 2

Find the sides u and v

We find these sides using the sine rule

Sine rule or Rule of Sines =

a/ sin A = b/ Sin B

Hence for triangle TUV

t/ sin T = u/ sin U = v/ sin V

We have the following values

Angle T = 38°

Angle U = 32°

Angle V = 110°

We are given side t = 31y

Finding side u

u/ sin U= t/ sin T

u/sin 32 = 31/sin 38

Cross Multiply

sin 32 × 31 = u × sin 38

u = sin 32 × 31/sin 38

u = 26.68268yd

u = 26.68yd

Finding side x

v / sin V= t/ sin T

v/ sin 110 = 31/sin 38

Cross Multiply

sin 110 × 31 = v × sin 38

v = sin 110 × 31/sin 38

v = 47.31573yd

v = 47.32yd

To find the area of triangle TUV

We use heron formula

= √s(s - t) (s - u) (s - v)

Where S = t + u + v/ 2

s = (31 + 26.68 + 47.32)/2

s = 52.5

Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)

Area of the triangle = √150967.6032

Area of the triangle = 388.5454973359yd²

Approximately to the nearest tenth =388.5yd²

Answer: [tex]U_{n} =(40)+(n-1)(10)[/tex]

Step-by-step:

[tex]U_{n} =a+(n-1)d[/tex]

a = 40

d = 10

[tex]U_{n} =(40)+(n-1)(10)[/tex] is the formula for nth hour

Answer:

84 squared units.

Step-by-step explanation:

In order to find the surface area of the pyramid, you use the following formula:

[tex]S=b^2+\frac{1}{2}ps[/tex]           (1)

b: base of the pyramid = 6

p: perimeter of the base = 6*4 = 24

s: slant height

Then, you first calculate the slant height, by using the Pythagoras' theorem:

[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]

Thus, you replace the values of b, p and s in the equation (1):

[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]

The surface area of the pyramid is 84 squared units.

Answer:

Step-by-step explanation:

wrong

Answer:

117 R=0

Step-by-step explanation:

819:7= 117 R=0

Answer:

95

Step-by-step explanation:

a=3,b=2

3^2+3(2)-2^2

a=11,b=13

11^2+11(13)-13^2

= 95

Answer:

95

Step-by-step explanation:

If a ∆ b = a² + ab - b²,

Then (3 ∆ 2) ∆ 13:

a = 3

b = 2

3 ∆ 2 = 3² + 3 × 2 - 2² = 11

a = 11

b = 13

11 ∆ 13 = 11² + 11 × 13 - 13² = 95

The answer is 95.

Answer:

length=25m

breadth=10m

Step-by-step explanation:

2.5units+2.5units+1unit+1unit=7units

70/7=10

length=10x2.5=25

breadth=10

(sorryy im not really sure but i hope it helps :D)

Answer:

Length = 25 cm

Breadth = 10 cm

Step-by-step explanation:

Let breadth of the room be 'x'

Let length of the room be ''

Perimeter ( P ) = 70 cm

Now, let's find the breadth of the room 'x '

Perimeter of rectangle =  2(l+b)

plug the values

70=2(2.5x+x)

Collect the like terms

70=2x3.5x

Calculate the product

70=7x

Swap the sides of the equation

7x=70

Divide both sides of the equation by 7

7x / 7= 70/7

Calculate

x=10cm

Breadth = 10 cm

Now, Let's find the length of the room ' 2.5x '

Length of the room =  2.5x

Plug the value of X

2.5x10

Calculate the product

25cm

Thus , The length and breadth of the room is 25 cm and 10 cm respectively.

Hope this helps..

Best regards!!

Answer:

a). x = 12

b). m∠H = 90°

    m∠I = 58°

    m∠J = 62°

Step-by-step explanation:

a). Use the property of a triangle,

  " Sum of all the angles in a triangle is 180°"

  (2x + 34)° + (4x + 14)° = 180°

  (2x + 4x) + (34 + 14) = 180

  6x + 48 = 180

  6x = 180 - 48

  6x = 132

   x = [tex]\frac{132}{6}[/tex]

   x = 12

b). m∠H = 90° [Given]

   m∠I = (2x + 34)° = [(2 × 12) + 34]°

   m∠I = 58°

   m∠J = (4x + 14)° = [(4 × 12) + 14]°

  m∠J = 62°

Answer:

x < 7

Step-by-step explanation:

-6x > -42

Divide each side by -6, remembering to flip the inequality

-6x/-6 < -42/-6

x < 7

Answer:

[tex]\boxed{x<7}[/tex]

Step-by-step explanation:

[tex]-6x > -42[/tex]

Divide both sides by -6 (flip sign).

[tex]\displaystyle \frac{-6x}{-6} < \frac{-42}{-6}[/tex]

[tex]x<7[/tex]