B. In each of the following questions, find the smallest number by which it should be multiplied to get
a perfect square. Find the square root of the perfect squares so obtained.
(a) 392
(b) 216
(c) 11.045
(d) 3,698 (e) 11,094​

Answer:

10

Step-by-step explanation:

12 total and 3 whites

there is 10 11 and 12.

Answer:

C

Step-by-step explanation:

Given

f(x) = 2x³ + 3x² - 3x - 2

Note that

f(1) = 2 + 3 - 3 - 2 = 0 , thus

(x - 1) is a factor

Dividing f(x) by (x - 1) gives

f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)

To find the roots equate f(x) to zero, that is

(x - 1)(x + 2)(2x + 1) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x + 2 = 0 ⇒ x = - 2

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

The solution set is therefore

{ - 2, - [tex]\frac{1}{2}[/tex], 1 } → C

Answer:

1.9cm

Step-by-step explanation:

The density d of a material is related to its mass m and volume V as follows;

d = [tex]\frac{m}{V}[/tex]             ------------------(i)

The material in question here is the lead ball.

Now, from known experiment;

the density of lead is 11.34g/cm³

From the question, the weight/mass of the lead ball is 326g

Substitute these values into equation (i) as follows;

11.34 = [tex]\frac{326}{V}[/tex]

V = [tex]\frac{326}{11.34}[/tex]

V = 28.75cm³

Now, since the ball is of course spherical, we can get the radius by using the following relation from the volume of a sphere;

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

V = 28.75cm³

=> 28.75 = [tex]\frac{4}{3} \pi r^3[/tex]

=> 3 x 28.75 = 4 π r³

=> 86.25 = 4 π r³

=> 21.5625 = π r³      [Take π = 3.142]

=> 21.5625 = (3.142) r³      [divide both sides by 3.142]

=> 6.86 = r³              [Take the cube root of both sides]

=> ∛6.86 = ∛r³

=> 1.90 = r

Therefore, the radius is 1.9cm to the nearest tenth

Answer:

(0.5, 8.5)

Step-by-step explanation:

use this formula ((x1+x2/2), (y1+y2/2)) if you use desmos graphing calculator and you type this formula in, all you have to do it put in the correct numbers and you get your midpoint.

Hope this helped :)

The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)

We have given that, the points (−5,13) and (6,4)

We have to determine the midpoints

((x1+x2/2), (y1+y2/2))

x1=-5,x2=6,y1=13 and y2=4

-5+6/2=1/2=0.5

and next is,

13+4/2=17/2=8.5

The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)

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Answer:

The linear system shown on the graph is consistent and independent

Step-by-step explanation:

The linear system shown on the graph is consistent because it has at least one solution which satisfy both linear graphs. The solution is at the point of interception of the two line graphs.

The linear system shown on the graph is independent because the two line graphs are distinct and not parallel or dependent on one another.

Therefore, The linear system shown on the graph is consistent and independent

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.

Step-by-step explanation:

An example of a mathematical expression with a variable is 2x + 3. All variables must have a coefficient, a number that is multiplied by the variable. In the expression 2x + 3, the coefficient of x is the number 2, and it means 2 times x plus 3. ... For example, 2x + 3 could also be expressed as 2(x) + 3 or 2 * x + 3. are you talking about this

Answer:

a. See Attachment 1

b. [tex]PT = 12.3\ m[/tex]

c. [tex]HT = 31.1\ m[/tex]

d. [tex]OH = 28.4\ m[/tex]

Step-by-step explanation:

Calculating PT

To calculate PT, we need to get distance OT and OP

Calculating OT;

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

[tex]tan50 = \frac{OT}{20}[/tex]

Multiply both sides by 20

[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]

[tex]20 * tan50 = OT[/tex]

[tex]20 * 1.1918 = OT[/tex]

[tex]23.836 = OT[/tex]

[tex]OT = 23.836[/tex]

Calculating OP;

We have to consider angle 30, distance OH and distance OP

The relationship between these parameters is;

[tex]tan30 = \frac{OP}{20}[/tex]

Multiply both sides by 20

[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]

[tex]20 * tan30 = OP[/tex]

[tex]20 * 0.5774= OP[/tex]

[tex]11.548 = OP[/tex]

[tex]OP = 11.548[/tex]

[tex]PT = OT - OP[/tex]

[tex]PT = 23.836 - 11.548[/tex]

[tex]PT = 12.288[/tex]

[tex]PT = 12.3\ m[/tex] (Approximated)

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

Calculating the distance between H and the top of the tower

This is represented by HT

HT can be calculated using Pythagoras theorem

[tex]HT^2 = OT^2 + OH^2[/tex]

Substitute 20 for OH and [tex]OT = 23.836[/tex]

[tex]HT^2 = 20^2 + 23.836^2[/tex]

[tex]HT^2 = 400 + 568.154896[/tex]

[tex]HT^2 = 968.154896[/tex]

Take Square Root of both sides

[tex]HT = \sqrt{968.154896}[/tex]

[tex]HT = 31.1\ m[/tex] (Approximated)

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

Calculating the position of H

This is represented by OH

See Attachment 2

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

[tex]tan50 = \frac{OH}{OT}[/tex]

Multiply both sides by OT

[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]

[tex]OT * tan50 = {OH[/tex]

[tex]OT * 1.1918 = OH[/tex]

Substitute [tex]OT = 23.836[/tex]

[tex]23.836 * 1.1918 = OH[/tex]

[tex]28.4= OH[/tex]

[tex]OH = 28.4\ m[/tex] (Approximated)

Answer:

27.8%

Step-by-step explanation:

P(male | Spanish) = P(male and Spanish) / P(Spanish)

P(male | Spanish) = 0.05 / 0.18

P(male | Spanish) = 0.278

The probability of the student being a male is 27.8%

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that in a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%.

The probability of the student being a male will be calculated as below:-

P(male | Spanish) = P(male and Spanish) / P(Spanish)

P(male | Spanish) = 0.05 / 0.18

P(male | Spanish) = 0.278

Therefore, the probability of the student being a male is 27.8%

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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]

Step-by-step explanation:

Hi, there!!!!

The main purpose of developing si unit is to have standard unit of measurements and to bring uniformity in whole world in terms of measurements.

I hope it helps you...

Answer:

first one

Step-by-step explanation:

Answer:

answer is D

Step-by-step explanation:

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

f(x) = 10 + 7 = 17

the solution is 17

Answer:

p = 1

Step-by-step explanation:

Given that the system intersect at (4, q) then this point satisfies both equations, that is

q = 4² - 4(4) + 3

q = [tex]\frac{1}{2}[/tex] (4) + p

Equating both gives

16 - 16 + 3 = 2 + p, that is

3 = 2 + p ( subtract 2 from both sides )

p = 1

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:

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

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:

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.

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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]

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.

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Answer:

4 liters

Step-by-step explanation:

Let's assume that the side lengths of the cubical block are 2 inches.

This means that one of the sides area is 4 in².

Multiplying this by 6 (for there are 6 sides) gets us 24 in².

So one liter of paint covers 24 in².

Now if the side lengths (edge) of the second block is doubled, that means that the side lengths are [tex]2\cdot2 = 4[/tex] inches.

So the area of one side is 16 in².

Multiplying this by 6 (as there are 6 sides) gets us 96 in².

To find how many liters of paint this will take, we divide 96 by 24.

[tex]96\div24=4[/tex]

So 4 liters of paint will be needed for the second cubical block.

Hope this helped!

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] \frac{5 {x}^{2} + 20xy + 20 {y}^{2} }{x ^{2} - xy - {6y}^{2} } [/tex]

To simplify first factorize both the numerator and the denominator

For the numerator

5x² + 20xy + 20y²

Factor 5 out

5 ( x² + 4xy + 4y²)

Using a² + 2ab + b² = ( a + b)²

The numerator is

5( x + 2y)²

For the denominator

x² - xy - 6y²

Rewrite -xy as a difference

x² + 2xy - 3xy - 6y²

Factorize

We have the denominator as

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

So we now have

Simplify

We have the final answer as

Hope this helps you

Answer:

[tex] (0, 8\sqrt{3}) [/tex]  and  [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).

Step-by-step explanation:

distance formula

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

We want the distance, d, from points (-2, 0) and (2, 0) to be 14.

Point (-2, 0):

[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]

[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]

Point (2, 0):

[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]

[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]

We have a system of equations:

[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]

[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]

Since the right sides of both equations are equal, we set the left sides equal.

[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]

Square both sides:

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

Square the binomials and combine like terms.

[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]

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

[tex] 8x = 0 [/tex]

[tex] x = 0 [/tex]

Now we substitute x = 0 in the first equation of the system of equations:

[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]

[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]

[tex] \sqrt{4 + y^2} = 14 [/tex]

Square both sides.

[tex] y^2 + 4 = 196 [/tex]

[tex] y^2 = 192 [/tex]

[tex] y = \pm \sqrt{192} [/tex]

[tex] y = \pm \sqrt{64 \times 3} [/tex]

[tex] y = \pm 8\sqrt{3} [/tex]

The points are:

[tex] (0, 8\sqrt{3}) [/tex]  and  [tex] (0, -8\sqrt{3}) [/tex]

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:

Step-by-step explanation:

First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)

To find the zeros, you set the equation equal to 0 and solve for x

x^3+2x^2-8x=0

x(x^2+2x-8)=0

x(x+4)(x-2)=0

x=0   x=-4   x=2

So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)

And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.

Plugging in a -5 gets us -35

-1 gets us 9

1 gets us -5

3 gets us 21

So now you know end behavior, zeroes, and signs of intervals

Hope this helps

The zeroes of the function are -4, 0 and 2.

The intervals where the function is positive is [tex]-4 < x < 2, \ \ x >2[/tex].

The intervals where the function is negative is [tex]x < -4[/tex].

The given parameters:

The zeroes of a function is the possible values of the unknown that makes the entire function to be zero.

The zeroes of the cubic equation is calculated as follows;

f(x) = 0

x³ + 2x² - 8x

factorize as follows;

[tex]x(x^2 + 2x -8) = 0\\\\x(x^2 + 4x - 2x -8) = 0\\\\x[x (x + 4 )-2(x + 4)]= 0\\\\x(x + 4)(x -2)=0\\\\x = 0, \ \ x = -4 \ \ x = 2[/tex]

The intervals where the function is positive and negative is determined as follows;

[tex]x(x + 4) (x - 2)\\\\[/tex]

[tex]when, \ x = -5, \ f(x) = -ve\\\\when, \ x = -4, \ f(x) =0\\\\when , \ x = -3, \ f(x) = +ve[/tex]

The intervals where the function is positive is determined as;

[tex]-4 < x < 2, \ \ x >2[/tex]

The intervals where the function is negative is determined as;

[tex]x < -4[/tex]

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Answer:

Her annual salary is approximately $41,667

Step-by-step explanation:

Hello,

This question deals with percentage of a number and it's very easy :)

First of all, get the data and understand what's required of us.

Pam spends $7500 yearly on expenses

But this amount represents 18% of her annual income.

Let her annual income be represented by x

18% = 7500 / x

18÷100 = 7500÷x

cross multiply and solve for x

18 × x = 7500 × 100

18x = 750,000

divide both sides by 18

18x / 18 = 750,000 / 18

x = $41,666.67

x = $41,667

Her annual salary is approximately $41,667

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:

[tex]\boxed{4^{-2}}[/tex]

Step-by-step explanation:

[tex]4^6 \times 4^{-8}[/tex]

When bases are same for exponents and it is multiplication, then add the exponents.

[tex]4^{6+-8}[/tex]

[tex]4^{-2}[/tex]

Explanation: Since these two powers have the same base of 4, you can multiply them together by simply adding their exponents to get 4⁻².

When applying your exponent rules, the bases don't change!

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.