Self Practice 5.3
1. Find the sum of the following arithmetic progression.

(a) -20, -15, -10, ..., 100

Answer:

13

Step-by-step explanation:

Calculate the length using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 5, 4) and (x₂, y₂ ) = (7, - 1)

d = [tex]\sqrt{(7-(-5))^2+(-1-4)^2}[/tex]

   = [tex]\sqrt{(7+5)^2+(-5)^2}[/tex]

   = [tex]\sqrt{12^2+25}[/tex]

   = [tex]\sqrt{144+25}[/tex]

   = [tex]\sqrt{169}[/tex]

   = 13

Answer:

Volume of paint required is 3.125 litres.

Step-by-step explanation:

It would be noted that each side walls would have the shape of a trapezium. So that the areas of each wall can be determined as:

wall 1 = [tex]\frac{1}{2}[/tex](a + b) h

         =  [tex]\frac{1}{2}[/tex](0.5 + 1.5)2

        = 2 [tex]m^{2}[/tex]

wall 2 = [tex]\frac{1}{2}[/tex](a + b) h

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

          = 4 [tex]m^{2}[/tex]

wall 3 = [tex]\frac{1}{2}[/tex](a + b) h

         =  [tex]\frac{1}{2}[/tex](0.5 + 1.5)2

        = 2 [tex]m^{2}[/tex]

wall 4 = [tex]\frac{1}{2}[/tex](a + b) h

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

          = 4 [tex]m^{2}[/tex]

Total area of the walls = 2 + 2 + 4 + 4

                            = 12 [tex]m^{2}[/tex]

Area of the bottom base = l x b

                          = 1 x 0.5

                          = 0.5 [tex]m^{2}[/tex]

Total area to be painted = 12 + 0.5

                           = 12.5 [tex]m^{2}[/tex]

But to paint one square meter of a gap surface, we need 0.25 litres of a green paint color. Thus, to paint 12.5 [tex]m^{2}[/tex] of the gap surface:

12.5 x 0.25 = 3.125

The litres of paint required is 3.125.

Answer:

Step-by-step explanation:

Equations

x + y = 29

x^2 + y^2 = 425

Solution

y = 29 - x

x^2 + (29 - x)^2 = 425

x^2 + (841 - 58x + x^2 ) = 425

x^2 - 58x + x^2 + 841 - 425 = 0

2x^2 - 58x +416 = 0

a = 2

b = - 58

c = 416

You get two answers that look valid

2x^2 - 58x + 416 = 0

x^2 - 29x + 208 = 0           This factors

(x - 16)(x - 13) = 0

x = 16

y = 13

Now check it

16^2 + 13^2 = ? 425

256 + 169 =  425

Answer:

first one

Step-by-step explanation:

Answer:

3km/h

Step-by-step explanation:

total distance ÷ total time = average speed

6 ÷ 2 = 3

Hello,

If the question is simplify then

we suppose x not equal to 5 and x not equal to -5

[tex]\dfrac{x^2-10x+25}{(x-5)(x+5)} \\\\=\dfrac{(x-5)^2}{(x-5)(x+5)} \\\\=\dfrac{x-5}{x+5} \\\\[/tex]

else

if the question is to find the euclidian 's quotient then

[tex]\dfrac{x^2-10x+25}{(x-5)(x+5)} \\\\= 1 + \dfrac{-10x+30}{x^2-25} \\\\=1-\frac{10}{x+5} \\[/tex]

euclian's quotient is 1

remainder is -10/(x+5)

Answer:

5⁷

Step-by-step explanation:

5³×5⁴

when bases are same powers are added

so..

5(³+⁴)

5⁷

Answer:

5^7

Step-by-step explanation:

Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)

You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!

Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.

数学思维是如何建立的？ 怎样才能有数学思维？

Answer:

Added

Step-by-step explanation:

For example, take the arithmetic sequence of 3, 5, 7, 9...

Here, the number that gets us from the first number to the second (from 3 to 5), is 2. Meaning, we need to add 2 to 3 in order to get 5. I believe that makes "addition" or "added" the answer. Please let me know if I misunderstood and I will change my answer! Thank you!

Answer:

added or subtracted

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

h(8) is given so D can't be true and A and B do not follow the domain and range restrictions

Answer:

Slope is 1/3

Y intercept is -4

Answer:

answer

Step-by-step explanation:

h+2 ≥ 10

h ≥ 10 - 2

h ≥ 8

The square root of 256 = X^2

X ^2 = X x X

A) 16 x 16 = 256

The answer is a) 16

Answer:

A. ) 16

Step-by-step explanation:

[tex] \small \sf \: \sqrt{256} [/tex]

Write 256 in the exponential form with the base of 16

[tex] \small \sf \: \sqrt{16 {}^{2} } [/tex]

Reduce the index of the radical and exponent with 2

16

it may be 12...........

Answer:

B) RS=5

Step-by-step explanation:

(2x-6)+(1)+(x-4)=18

2x-6+1+x-4=18

3x-9=18

3x=18+9

3x=27

x=9

Find RS

x-4

9-4

=5

Answer:

[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex] would ensure that at least one real root exists for this equation when solving for [tex]x[/tex].

Step-by-step explanation:

Apply the Pythagorean identity [tex]1 - \sin^{2}(x) = \cos^{2}(x)[/tex] to replace the cosine this equation with sine:

[tex](1 - \sin^{2}(x)) - (m^2 - 3)\, \sin(x) + 2\, m^2 - 3 = 0[/tex].

Multiply both sides by [tex](-1)[/tex] to obtain:

[tex]-1 + \sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 3 = 0[/tex].

[tex]\sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 2 = 0[/tex].

If [tex]y = \sin(x)[/tex], then this equation would become a quadratic equation about [tex]y[/tex]:

[tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex].

However, [tex]-1 \le \sin(x) \le 1[/tex] for all real [tex]x[/tex].

Hence, the value of [tex]y[/tex] must be between [tex](-1)[/tex] and [tex]1[/tex] (inclusive) for the original equation to have a real root when solving for [tex]x[/tex].

Determinant of this quadratic equation about [tex]y[/tex]:

[tex]\begin{aligned} & b^{2} - 4\, a\, c \\ =\; & (m^{2} - 3)^{2} - 4 \cdot (-2\, m^{2} + 2) \\ =\; & m^{4} - 6\, m^{2} + 9 - (-8\, m^{2} + 8) \\ =\; & m^{4} - 6\, m^{2} + 9 + 8\, m^{2} - 8 \\ =\; & m^{4} + 2\, m^{2} + 1 \\ =\; &(m^2 + 1)^{2} \end{aligned}[/tex].

Hence, when solving for [tex]y[/tex], the roots of [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] in terms of [tex]m[/tex] would be:

[tex]\begin{aligned}y_1 &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) + \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) + (m^{2} + 1)}{2} = 2\end{aligned}[/tex].

[tex]\begin{aligned}y_2 &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) - \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) - (m^{2} + 1)}{2} \\ &= \frac{-2\, m^{2} + 2}{2} = -m^{2} + 1\end{aligned}[/tex].

Since [tex]y = \sin(x)[/tex], it is necessary that [tex]-1 \le y \le 1[/tex] for the original solution to have a real root when solved for [tex]x[/tex].

The first solution, [tex]y_1[/tex], does not meet the requirements. On the other hand, simplifying [tex]-1 \le y_2 \le 1[/tex], [tex]-1 \le -m^{2} + 1 \le 1[/tex] gives:

[tex]-2 \le -m^{2} \le 0[/tex].

[tex]0 \le m^{2} \le 2[/tex].

[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

In other words,  solving [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] for [tex]y[/tex] would give a real root between [tex]-1 \le y \le 1[/tex] if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

On the other hand, given that [tex]y = \sin(x)[/tex] for the [tex]x[/tex] in the original equation, solving that equation for [tex]x\![/tex] would give a real root if and only if [tex]-1 \le y \le 1[/tex].

Therefore, the original equation with [tex]x[/tex] as the unknown has a real root if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

Answer:

5%

.35x = 2800

x = 8000

p(160,000)=8000

p=.05 = 5%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope this helps u !!

Answer:

( 1 , 2 )

Step-by-step explanation:

x + 4y = 9

x = 9 - 4y .... ( 1)

2x - 4y = -6 ...( 2)

substitute the 9 - 4y as x in the second equation

2( 9 - 4y ) - 4y = -6

distribute 2

18 - 8y - 4y = -6

combine like terms

18 - 12y = -6

Subtract 18 from both sides

18 - 18 - 12y = -6 - 18

- 12y = - 24

divide both sides by -12

-12y / -12 = -24/-12

y = 2

Now , substitute the 2 as y in the second equation

2x - 4y = -6

2x - 4 ( 2 ) = -6

2x - 8 = -6

add 8 to both sides

2x - 8 + 8 = -6 + 8

2x = 2

divide both sides by 2

2x / 2 = 2/2

x = 1.

Answer:

[tex] \blue{b = \dfrac{2A}{h}} [/tex]

Step-by-step explanation:

[tex] A = \dfrac{1}{2}bh [/tex]

Step 1. Switch sides.

[tex] \dfrac{1}{2}bh = A [/tex]

Step 2. Since the fraction 1/2 multiplies b, multiply both sides by the reciprocal of 1/2 which is 2.

[tex] 2 \times \dfrac{1}{2}bh = 2 \times A [/tex]

[tex] bh = 2A [/tex]

Step 3. Since h is multiplying b, and you want b alone, divide both sides by h.

[tex] \dfrac{bh}{h} = \dfrac{2A}{h} [/tex]

Answer:

[tex] b = \dfrac{2A}{h} [/tex]

Answer:

From top to bottom;

1,1,3,3

Step-by-step explanation:

mathematically, for an even function;

f(x) = f(-x)

what this mean is that;

f(-1) = f(1)

f(-3) = f(3)

f(-5) = f(5)

f(-6) = f(6)

so we have it that;

f(-1) = 1

f(-3) = 1

f(-5) = 3

f(-7) = 3

Comolete question is;

One national survey found that 86 percent of those who were unhappily married but who stayed with the marriage were, when re-interviewed five years later,

A) preparing to divorce

B) resigned to the situation

C) mostly "very" or "quite" happy

D) mostly "very" happy

Answer:

C) mostly "very" or "quite" happy

Step-by-step explanation:

From social psychology, we know that;

Sometimes people could be happy about something but later on as things progress they become satisfied and are happy about that same thing or person.

The same is the case here with marriage and more importantly in this research.

It says they were unhappily married but they stayed in the marriage and were interviewed 5 years after that. Thus, for them to stay that long even after being unhappy, it means that they began to become a bit happy along the line.

Thus, they would gradually become happy or mostly happy.

Answer:

35 2/3 dollars per hour

Step-by-step explanation:

The unit rate in dollars per hour is 6.8 dollars per hour.

To find the unit rate in dollars per hour, we need to divide the amount earned by the time taken.

The person earns 17/5 dollars in 1/2 hours. To calculate the unit rate in dollars per hour, we divide the amount earned (17/5 dollars) by the time taken (1/2 hours):

Unit rate = (Amount earned) / (Time taken) = (17/5 dollars) / (1/2 hours)

To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction:

Unit rate = (17/5 dollars) x (2/1 hours)

Simplifying the expression:

Unit rate = (17 x 2) / (5 x 1) = 34/5 = 6.8

Therefore, the unit rate in dollars per hour is 6.8 dollars per hour.

To know more about an expression follow

https://brainly.com/question/28699958

#SPJ2

Answer:

(- 2, - [tex]\frac{1}{3}[/tex] )

Step-by-step explanation:

Given the 2 equations

2x + 3y + 5 = 0 → (1)

5x - 3y + 9 = 0 → (2)

Rearrange (1) expressing 3y in terms of x by subtracting 2x + 5 from both sides

3y = - 2x - 5

Substitute 3y = - 2x - 5 into (2)

5x - (- 2x - 5) + 9 = 0 ← distribute parenthesis on left side and simplify

5x + 2x + 5 + 9 = 0

7x + 14 = 0 ( subtract 14 from both sides )

7x = - 14 ( divide both sides by 7 )

x = - 2

Substitute x = - 2 into either of the 2 equations and solve for y

Substituting into (1)

2(- 2) + 3y + 5 = 0

- 4 + 3y + 5 = 0

1 + 3y = 0 ( subtract 1 from both sides )

3y = - 1 ( divide both sides by 3 )

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

solution is (- 2, - [tex]\frac{1}{3}[/tex] )

Answer:

65 percent certain to get the job

Step-by-step explanation:

The given parameters are;

The chance that she gets the job if she receives a strong recommendation, P(J|S) = 80 percent = 0.8

The chance that she gets the job if she receives a moderately good recommendation, P(J|M) = 40 percent = 0.4

The chance that she gets the job if she receives a weak recommendation = 10 percent, P(J|W) = 0.1

The probability that the recommendation will be strong, P(S) = 0.7

The probability that the recommendation will be moderate, P(M) = 0.2

The probability that the recommendation will be weak, P(W) = 0.1

Therefore, the probability that she gets the job given any condition, is given as follows;

P(J) = P(J|S)×P(S) + P(J|M)×P(M) + P(J|W)×P(W)

∴ P(J) = 0.8 × 0.7 + 0.4×0.2 + 0.1×0.1 = 0.65

Therefore, she is 65 percent certain to get the job

Answer:

opo

Step-by-step explanation:

kung Hindi kayo sure sa sagot ko sorry po

Answer:

2.32*10^-10

Step-by-step explanation:

n will change its position with 32

(1/2)^32=n

n=2.32*10^-10

Answer:

The answer is 12 %R

Step-by-step explanation:

Answer:

[tex]\text{C. }\cos R=21/29[/tex]

Step-by-step explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse.

From the diagram, we know:

Therefore, the cosine of angle R must be [tex]\boxed{\frac{21}{29}}[/tex]

Answer:

5.6 days

Step-by-step explanation:

We are given;

Initial Mass; N_o = 25 g

Mass at time(t); N_t = 25/2 = 12.5 (I divide by 2 because we are dealing with half life)

k = 0.1229

Formula is given as;

N_t = N_o•e^(-kt)

Plugging in the relevant values;

12.5 = 25 × e^(-0.1229t)

e^(-0.1229t) = 12.5/25

e^(-0.1229t) = 0.5

(-0.1229t) = In 0.5

-0.1229t = -0.6931

t = -0.6931/-0.1229

t = 5.6 days

Answer:  43.1 degrees (choice B)

==================================================

Work Shown:

Use the law of sines

sin(A)/a = sin(C)/c

sin(A)/20 = sin(82)/29

sin(A) = 20*sin(82)/29

sin(A) = 0.68294349

A = arcsin(0.68294349)

A = 43.074088

A = 43.1 degrees

Answer:

43.1°

Step-by-step explanation:

Hello, just finished the quiz and the correct answer is 43.1 degrees.