You are in a panic! You forgot to buy your little brother a birthday present. You start with $60 in your wallet. You buy him several toys, t, that are $5 each. You know have $45 leftover. How many toys did you buy your little brother for his birthday? (set up the equation)

Answer:

[tex]p=- \frac{15}{2}[/tex]

[tex]p=2[/tex]

Step-by-step explanation:

[tex]2p^2+11p=30[/tex]

Subtract 30 on both sides.

[tex]2p^2+11p-30=30-30[/tex]

[tex]2p^2+11p-30=0[/tex]

Factor left side of the equation.

[tex](2p + 15)(p-2)=0[/tex]

Set factors equal to 0.

[tex]2p+15=0[/tex]

[tex]2p=-15[/tex]

[tex]p=\frac{-15}{2}[/tex]

[tex]p-2=0[/tex]

[tex]p=2[/tex]

Answer:

A) [tex]1<x<\infty[/tex]

Step-by-step explanation:

Given:

A graph of a function.

When we analyze the given graph, it is of a parabola.

To find:

The interval of values of [tex]x[/tex] where the function is increasing.

Solution:

First of all, let us learn about the meaning of increasing and decreasing functions.

1. A function [tex]y=f(x)[/tex] is known as increasing  in an interval [tex]a<x<b[/tex] when

Value of y keeps on increasing when we move from the value of x from a to b.

2. A function [tex]y=f(x)[/tex] is known as decreasing  in an interval [tex]a<x<b[/tex] when

Value of y keeps on decreasing when we move from the value of x from a to b.

On analyzing the given graph , we can see that the graph is decreasing on the interval: [tex]-\infty<x<1[/tex]

and is increasing on the interval: [tex]1<x<\infty[/tex]

When we choose from the options,

The correct answer is option A) [tex]1<x<\infty[/tex]

Complete question:

Para ingresar a la Universidad del Chocó se aplica una prueba de razonamiento que consta de 30 preguntas. Por cada respuesta correcta se asignan 5 puntos y por cada incorrecta (o no contestada) se restan 2 puntos. Si un participante obtuvo un puntaje de 94 puntos, ¿cuantas preguntas respondió bien?

Responder:

número de respuestas correctas = 22

Explicación paso a paso:

Dado lo siguiente:

Número total de preguntas = 30

Deje respuestas correctas = y; Respuestas incorrectas = n

Marca otorgada por y = 5

Marca deducida por n = 2

Si el total de preguntas = 30; luego

y + n = 30 - - - - (1)

Puntuación total obtenida = 94; luego

5y - 2n = 94 - - - (2)

De 1),

y + n = 30

y = 30 - n

Sustituya y = 30 - n en equ (2)

5 (30 - n) - 2n = 94

150 - 5n - 2n = 94

150 - 7n = 94

-7n = 94-150

-7n = - 56

n = 56/7

n = 8

Sustituir n = 8 en (1)

y + n = 30

y + 8 = 30

y = 30 - 8

y = 22

y = número de respuestas correctas = 22

n = número de respuestas incorrectas = 8

Usando un sistema de ecuaciones, se encuentra que el participante obtuve 22 respuestas correctas.

En el sistema, x es el número de respuestas correctas, con y siendo el número de respuestas incorrectas.

Total de 30 preguntas, o sea:

[tex]x + y = 30 \rightarrow y = 30 - x[/tex]

5 puntos asignados por cada respuesta correcta, 2 restados por cada respuesta incorrecta. Puntaje de 94 puntos, o sea:

[tex]5x - 2y = 94[/tex]

Considerando [tex]y = 30 - x[/tex]

[tex]5x - 60 + 2x = 94[/tex]

[tex]7x = 154[/tex]

[tex]x = \frac{154}{7}[/tex]

[tex]x = 22[/tex]

El participante obtuve 22 respuestas correctas.

Un problema similar es dado en https://brainly.com/question/24646137

Answer:

Step-by-step explanation:

f(x) = 3x - 1

g(x) = 2x + 1

To find (f +g)(3) , first find (f + g)(x)

To find (f + g)(x) add g(x) to f(x)

That's

(f + g)(x) = 3x - 1 + 2x + 1

= 3x + 2x + 1 - 1

(f + g)(x) = 5x

Now to find (f + g)(3) substitute 3 into

(f + g)(x)

That's

(f +g)(3) = 5(3)

Hope this helps you

Answer:

[tex] \boxed{\sf (a + 3)(a + 1)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 4a + 3 \\ \\ \sf The \: factors \: of \: 3 \: that \: sum \: to \: 4 \\ \sf are \: 3 \: and \: 1. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 + 1)a + 3 \\ \\ \sf \implies {a}^{2} + 3a + a + 3 \\ \\ \sf \implies a(a + 3) + 1(a + 3) \\ \\ \sf \implies (a + 3)(a + 1) [/tex]

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

p < 2

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

9p < 18

p < 2

w is the width and it is the independent variable. You can pick any positive whole number you want (within reason of course; you can't go to infinity or go beyond some set boundary). Whatever you picked for w, the expression 2w-5 will be dependent on it. So the length is dependent on the width.

For instance, if the width is w = 10 feet, then 2w-5 = 2*10-5 = 20-5 = 15 feet is the length. The choice of 10 feet for the width directly affects the length being 15 feet.

Answer:

12*3*2=72

10*3*2=60

12*10*2=240

240+72+60=312+60=372

hope this helps

Step-by-step explanation:

Answer:

Answer is c 480 in2

Step-by-step explanation:

Answer:

18 meters

Step-by-step explanation:

If the width is w, the length is w + 7.

Perimeter = 2(width + length), therefore:

86 = 2(w + w + 7)

86 = 2(2w + 7)

43 = 2w + 7

36 = 2w

w = 18

Answer:

Step-by-step explanation:

Given,

Let length of a rectangle be ' x + 7 ' meters

Let width of a rectangle be ' x ' meters

Perimeter = 86 meters

Now, let's find the width of the rectangle:

Perimeter of rectangle = [tex]2(l + b)[/tex]

plug the values

[tex]86 = 2(x + 7 + x)[/tex]

Collect like terms

[tex]86 = 2(2x + 7)[/tex]

Distribute 2 through the parentheses

[tex]86 = 4x + 14[/tex]

Move constant to R.H.S and change its sign

[tex]86 - 14 = 4x[/tex]

Calculate the difference

[tex]72 = 4x[/tex]

Swipe the sides of the equation

[tex]4x = 72[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{72}{4} [/tex]

Calculate

[tex]x = 18[/tex] meters

Hope this helps..

Best regards!!

Answer:

answer is D

Step-by-step explanation:

f(x) = -2(-5) + 7

f(x) = 10 + 7 = 17

the solution is 17

Answer: The store must sell 40 bikes.

Step-by-step explanation:

y=60x+2400

y=120x

120x=60x+2400

-60x on both sides

60x=2400

divide 60 on both sides

2400/60=40

x=40  

Answer:

2√3

Step-by-step explanation:

Since this is a 30-60-90 triangle, we can find s by finding the short leg (bottom), then the hypotenuse (s).

To find the short leg, we can divide the long leg (which is 3mm) by sqrt 3 (also  √3, as any of them are fine), and we will have 3/√3. Since we don't want the square root on the bottom, we can multiply √3 on both sides, giving us 3√3/3, which is technically √3 because of simplifying.

Since you have the short leg now, you can find s. By finding s, you can multiply the short leg by 2, which will be √3 * 2 which is 2√3.

Answer: it is =4176000000000000

Step-by-step explanation:

(2.9)(100000)(7.2)(10^2)

5(10^−8)

=

(290000)(7.2)(10^2)

5(10^−8)

=

2088000(10^2)

5(10^−8)

=

(2088000)(100)

5(10^−8)

=

208800000

5(10^−8)

=

208800000

5(1/100000000)=

208800000/1

20000000

=4176000000000000

hope i helped

-lvr

Answer:Domain is (-infiniti,infiniti) and Range is (-infiniti,10.45)

Step-by-step explanation:

Answer:

B) $10.00

Step-by-step explanation:

10 × 18 = 180

10 + 2 = 12

12 × 15 = 180

Answer:

Step-by-step explanation:

x - Earl's earnings per hour

The equation:

18x = 15(x + 2)         use the distributive property

18x = (15)(x) + (15)(2)

18x = 15x + 30        subtract 15x from both sides

18x - 15x = 15x - 15x + 30

3x = 30        divide both sides by 3

3x : 3 = 30 : 3

x = 10

Answer:

7.5kilometer

Step-by-step explanation:

for 30mins semin runs 5kilometer

then for 1min: (1min×5kilometer)÷30mins,

therefore, for 45mins: (45mins×5kilometer)÷30mins=7.5kilometer

From the given information:

We are being informed that Samin can run for 5 kilometers in 30 minutes;

If Samin can run such a kilometer in 30 minutes;

5 kilometers = 30 minutes

∴

In x kilometers = 45 minutes

By cross multiplying;

(x × 30 minutes) = 5 kilometers × 45 minutes

30x = 225 kilometer/minutes

[tex]x = \dfrac{225 \ kilometer/minutes}{30 minutes}[/tex]

[tex]\mathbf{x = 7.5 \ kilometers}[/tex]

Therefore, we can conclude that the Samin can run 7.5 kilometers in 45 minutes.

Learn more about word problems here:

https://brainly.com/question/23542499?referrer=searchResults

Answer:

8685 butterflies

Step-by-step explanation:

Given the logistics growth function expressed as ​f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t which describes the population of a species of butterflies t months after they are introduced to a​ non threatening habitat, to know the number of butterflies expected butterflies are expected in the habitat after 20 ​months, we will substitute t = 20 into the function.

f(20) = 440/1+13.7exp-(0.28×20)

f(20) = 440/1+13.7exp-(5.60)

f(20) = 440/1+(13.7× 0.003698)

f(20) = 440/1+0.05066

f(20) = 440/1.05066

f(20) = 8684.9

This means there will be approximately 8685 butterflies in the habitat after 20months.

Answer:

x = - 1/18

Step-by-step explanation:

Move all terms not containing  x to the right side of the equation

Divide each term by 18 and simplify

The result can be shown in multiple forms

x = -1/18

Decimal form= -0.05

Answer: x=-1/18

Step-by-step explanation:

18x+18=17

you subtract 18 from both sides

18x=-1

then you divide by 18 on both sides

x=-1/18

Answer:

first one

Step-by-step explanation:

Answer:

Your ans is. a12 = 47/12

Step-by-step explanation:

First, you need to find if the series has a common ratio or a common difference between each term. Based from observation, there is a common difference of 1/3 so the series is an arithmetic series.

The solution for this problem goes like this

an=a1+(n-1)d

a12=1/n+(12-1)(1/3)

a12=47/12

Hope it helped you.. Please mark BRAINLIEST

Tysm

Answer:

x² + 4x + y² + 10y + 20 = 0

Step-by-step explanation:

Step 1: Expand (x + 2)²

x² + 2x + 2x + 4 + (y + 5)² = 9

Step 2: Combine like terms

x² + 4x + 4 + (y + 5)² = 9

Step 3: Expand (y + 5)²

x² + 4x + 4 + y² + 5y + 5y + 25 = 9

Step 4: Combine like terms

x² + 4x + 4 + y² + 10y + 25 = 9

Step 5: Move 9 over

x² + 4x + 4 + y² + 10y + 25 - 9 = 0

Step 6: Combine like terms

x² + 4x + y² + 10y + 20 = 0

Answer:

x^2+y^2+4x+10y+20=0

Step-by-step explanation:

(x+2)^2+(y+5)^2=9

x^2+4x+4+y^2+10y+25-9=0

general form: x^2+y^2+4x+10y+20=0

Answer:

D: As the x-values go to negative infinity, the function's values go to positive infinity.

Step-by-step explanation:

Since we are dealing with end behavior, we look at the graph infinitely:

When x-values go to negative infinity, we see that f(x) values go to positive infinity.

When x-values go to positive infinity, we see that f(x) values also go to positive infinity.

Therefore. our only correct answer is D.

Answer:

150

Step-by-step explanation:

Answer:

150  =  half of 300

± 180

230

soooo 230 students

Step-by-step explanation:

Answer:

72° and 45°

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Since the given polygons are regular, then

Pentagon (5 sides ) has

exterior angle = 360° ÷ 5 = 72°

Octagon ( 8 sides ) has

exterior angle = 360° ÷ 8 = 45°

Step-by-step explanation:

The exterior angle of a polygon is given by

360/n

where n is the number of sides

First figure

For the first shape it has five sides

That's it's a pentagon

The measure of one exterior angle of the shape is

360 / 5

= 72°

Second figure

For the second shape it has 8 sides that's it's an octagon

So the measure of one exterior angle of the shape is

360 / 8

= 45°

Hope this helps you

Answer:

Option (B)

Step-by-step explanation:

There are two lines on the graph representing the system of equations.

First line passes through two points (-3, 1) and (-2, 3).

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

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

                       m = 2

Equation of the line passing through (x', y') and slope = m is,

y - y' = m(x - x')

Equation of the line passing through (-3, 1) and slope = 2 will be,

y - 1 = 2(x + 3)

y = 2x + 7 ----------(1)

Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.

Let the equation of this line is,

y = mx + b

Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

               = [tex]\frac{4-1}{-1-0}[/tex]

               = -3

Here 'b' = 1

Therefore, equation of the line will be,

y = -3x + 1 ---------(2)

From equation (1) and (2),

2x + 7 = -3x + 1

5x = -6

x = [tex]-\frac{6}{5}[/tex]

x = [tex]-1\frac{1}{5}[/tex]

From equation (1),

y = 2x + 7

y = [tex]-\frac{12}{5}+7[/tex]

  = [tex]\frac{-12+35}{5}[/tex]

  = [tex]\frac{23}{5}[/tex]

  = [tex]4\frac{3}{5}[/tex]

Therefore, exact solution of the system of equations is [tex](-1\frac{1}{5},4\frac{3}{5})[/tex].

Option (B) will be the answer.

Answer:

B. (-1 1/5, 4 3/5)

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

[tex]x^3 - 4[/tex]

[tex](3)^3 - 4[/tex]

step 2 - solve the exponent

[tex](3)^3 - 4[/tex]

[tex]27 - 4[/tex]

step 3 - subtract

[tex]27 - 4[/tex]

[tex]23[/tex]

therefore, the value of the expression is 23.

Answer: 42w

Step-by-step explanation:

Subtracting a negative is like adding.

Answer:

[tex]\dfrac{10}{4} \ hour[/tex]

Step-by-step explanation:

Given that :

Jack had 4 hours of school.

He spent 45 minutes in the library

1/2 hour on a science lecture  and;

had a lunch break of 25 minutes

The objective is to determine how much time is left for the school to get over and we are to write the answer as a fraction.

In order to do that, we will have to convert the minutes into hours,

we all know that; 60 minutes = 1 hour.

Then,

45 minutes = (45/60)hour = 3/4 hour

25/60 minutes = 1/4 hour

Therefore, the amount of time left  for the school to get over is:

= [tex]4 - (\dfrac{3}{4}+\dfrac{1}{2}+ \dfrac{1}{4})[/tex]

=  [tex]\dfrac{16-(3+2+1)}{4}[/tex]

= [tex]\dfrac{16-6}{4}[/tex]

= [tex]\dfrac{10}{4} \ hour[/tex]

Answer:

Volume of a pyramid is

[tex] \frac{1}{3 } \times (area \: \: of \: base) \times height[/tex]

Since it's a square pyramid the base is a square

So we have

Area of a square = l²

where l is the length of one side

Area of square = 22²

= 484 cm²

So volume of the pyramid is

[tex] = \frac{1}{3} \times 484 \times 8 = 1290.7 {cm}^{3} [/tex]

Hope this helps you

Answer:

Check the answer below.

Step-by-step explanation:

This is a very trivial but professional question. Note that all of millimetre, centimetre and metres are acceptable metric units but the millimetre is more preferable by builders and architects because:

1. It is easier to work with integer values on building and architectural plans, an advantage given by measuring and recording in millimetre.

2. working in millimetre allows for precision. The builder will record values that are very close to the true value

3. The measurement will be easily readable by anybody that sees it.