Determine if the ordered pair (1/2,-1/2) is a solution to linear system
4x + y = -1
7x - 3y = 4

Answer:

(- 2, 4 )

Step-by-step explanation:

Given the 2 equations

3x + 5y = 14 → (1)

y = [tex]\frac{1}{2}[/tex] x + 5 → (2)

Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)

3x + 5([tex]\frac{1}{2}[/tex] x + 5) = 14

3x + [tex]\frac{5}{2}[/tex] x + 25 = 14

[tex]\frac{11}{2}[/tex] x + 25 = 14 ( subtract 25 from both sides )

[tex]\frac{11}{2}[/tex] x = - 11 ( multiply both sides by 2 )

11x = - 22 ( divide both sides by 11 )

x = - 2

Substitute x = - 2 into (2) for corresponding value of y

y = [tex]\frac{1}{2}[/tex] × - 2 + 5 = - 1 + 5 = 4

solution is (- 2, 4 )

Answer:

314

Step-by-step explanation:

First, find the diameter which is 10 and square it. Then, multiply by pi or 3.14 to get 314.

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Answer:

14mm×20mm=280mm²

14mm×12mm/2=84mm²

3.14×10²mm=314mm²

280m²+84mm²+314mm²=678mm²

Answer:

521mm^2

Step-by-step explanation:

First, separate the shapes.

-Half circle= diameter of 20, radius 10

-Rectangle= 14x20

-Triangle= (32-20)x14= 12x14

Then, calculate

Circle equation= (pi)r^2= (pi)(10)^2= 314.16    -> divide by 2 for half circle= 157.1

Rectangle= 14x20=280

Triangle= (12x14)=168   ->  Divide by two because it's a triangle= 84

Add 157 + 280 + 84 and you get  521

Answer:

[tex]P(t) = 1460(1.06)^t[/tex]

Step-by-step explanation:

Exponential equation for population growth:

The exponential equation for a population after t years is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

Currently, there are 1,460 wolves in Scataway National Park.

This means that [tex]P(0) = 1460[/tex]

Growing at a rate of 6% every year:

This means that [tex]r = 0.06[/tex]. So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = 1460(1+0.06)^t[/tex]

[tex]P(t) = 1460(1.06)^t[/tex]

Answer:

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Answer:

g(x) is not the inverse of f(x)

Step-by-step explanation:

If f(x)=5x-25 and g(x) = 5x+5, which expression could be used to verify g(x) is the inverse of fx)

We need to show that f(g(x)) = g(f(x))

f(g(x)) = f(5x+5)

f(5x+5) = 5(5x+5) - 25

f(5x+5) =25x+25 - 25

f(5x+5) = 25x

f(g(x)) = 25x

Similarly;

g(f(x)) = g(5x-25)

g(5x-25) = 5(5x-25) + 5

g(5x-25) = 25x - 125 + 5

g(5x-25) = 25x - 120

This shows that g(x) is not the inverse of f(x)

Answer:

5

Step-by-step explanation:

Answer:

1200 was is interested in the first 4years

Answer:

1. (28-2)x

2.(12+6)x

3.(15+1)x

Step-by-step explanation:

Answer:

here is the right answer

C- (2,4)

Answer:

Mixed Fraction

Step-by-step explanation:

A mixed fraction is a fraction with a whole number attached to it like 5 1/5 or 3 1/2

[tex]1\frac{4}{5}[/tex] is an example of a mixed fraction.

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

A mixed number is a whole number, and a proper fraction represented together.  It generally represents a number between any two whole numbers.

A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Properties of Mixed Numbers :

1. It is partly a whole number.  

2. It is partly a fraction.

[tex]1\frac{4}{5}[/tex] is an example of a mixed fraction.

In [tex]1\frac{4}{5}[/tex] , 2 is the quotient, 4 is the remainder.

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Answer:

? = 9.2

Step-by-step explanation:

The angle between a tangent and radius at the point of contact is 90°

Then the triangle shown is right with legs ? , 6.9 and hypotenuse = (6.9 + 4.2) = 11.5

Using Pythagoras' identity in the right triangle

?² + 6.9² = 11.5²

?² + 47.61 = 132.25 ( subtract 47.61 from both sides )

?² = 84.64 ( take the square root of both sides )

? = [tex]\sqrt{84.64}[/tex] = 9.2

Answer:

Solution given:

BC=BD=6.9 units

AD=4.6units

Now

AB=4.6+6.9=11.5units.

we have

<C=90°[the line from the tangent is perpendicular to the radius of circle]

we know that ∆ABC is a right angled triangle.

hypotenuse [h]=AB=11.5units

base[b]=BC=6.9 units

perpendicular [p]=x units

By using Pythagoras law

h²=p² +b²

11.5²=x²+6.9²

x²=11.5²-6.9²

x²=84.64

x=[tex] \sqrt{86.64} [/tex]=9.2

Sothe segment length indicated is 9.2 units.

Answer: See explanation

Step-by-step explanation:

1 . 61

2 124

3 27

4 29

Answer:

120

Step-by-step explanation:

Sold = 36

remaining = x - 36

Evening = 2/7 × (x - 36)

(2x - 72)/7

36 + (2x - 72)/7 = x/2

2x + 180)/7 = x/2

4x + 360 = 7x

4x - 7x = -360

x = 120

Answer:

x = 2.

Step-by-step explanation:

If its a parallelogram then the diagonal will be bisected so:

4x + 7 = 10x - 5

7 + 5 = 10x - 4x

12 = 6x

x = 2.

Answer:

The correct answer is "0.0000039110".

Step-by-step explanation:

The given values are:

[tex]Y_n\rightarrow N(\mu, \sigma^2)[/tex]

[tex]\mu = 40n[/tex]

[tex]\sigma^2=100n[/tex]

[tex]n=20[/tex]

then,

The required probability will be:

= [tex]P(Y_{20}>1000)[/tex]

= [tex]P(\frac{Y_{20}-\mu}{\sigma} >\frac{1000-40\times 20}{\sqrt{100\times 20} } )[/tex]

= [tex]P(Z>\frac{1000-800}{44.7214} )[/tex]

= [tex]P(Z>\frac{200}{44.7214} )[/tex]

= [tex]P(Z>4.47)[/tex]

By using the table, we get

= [tex]0.0000039110[/tex]

Answer:

0.9 = 90% probability that it arrived during the last 30 seconds of the 5-minute period.

Step-by-step explanation:

The car is equally as likely to arrive during each second of the interval, which means that the uniform distribution is used to solve this question.

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the probability of finding a value higher than x is given by:

[tex]P(X \geq x) = \frac{b - x}{b - a}[/tex]

5-minute period

This means that [tex]a = 0, b = 5*60 = 300[/tex]

Find the probability that it arrived during the last 30 seconds of the 5-minute period.

300 - 30 = 270. So

[tex]P(X \geq 270) = \frac{300 - 270}{300 - 0} = 0.9[/tex]

0.9 = 90% probability that it arrived during the last 30 seconds of the 5-minute period.

Answer:

125 percent

Step-by-step explanation:

25 percent *500.00 =

(25:100)*500.00 =

(25*500.00):100 =

12500:100 = 125

Now we have: 25 percent of 500.00 = 125

Question: What is 25 percent of 500.00?

Percentage solution with steps:

Step 1: Our output value is 500.00.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$500.00=100\%$.

Step 4: Similarly, $x=25\%$.

Step 5: This results in a pair of simple equations:

$500.00=100\%(1)$.

$x=25\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{500.00}{x}=\frac{100\%}{25\%}$

Step 7: Again, the reciprocal of both sides gives

{x}/{500.00}={25}/{100}$

$Rightarrow x=125$

Therefore, $25\%$ of $500.00$ is $125$

Answer:

You bought 5 books for $60 and 2 movies for $30

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The attached number lines show the domains of each function.

  x > 3 — both number lines are included

  x < 3 — only the g(x) domain is included

  x = 3 — only the f(x) domain is included

  x ≠ 3 — only the g(x) domain is included in the entire region

Answer:

5/12 ton

Step-by-step explanation:

Y1 ( uniform random variable ) : ( 0, 1 )

Y2 ( uniform distribution ) ; ( 0, y1 )

supplier stocked ; 5/6 ton

Determine the amount of tons expected to be sold

F ( y2 | y1 ) = 1 / y1

E ( y2 | y1 = 5/6 )

The number of tons expected to be sold = 5/12 ton

attached below is the detailed solution

Answer:

Eric

Step-by-step explanation:

At 5 days (the x axis), the y axis is 60 which is how much lemonade he sold.

sarah sold 10x or 10 x 5 days=50 cups.

‘Eric sold 60, Sarah sold 50

Finding x,

We will use Pythagoras theorem to determine the value of x:

[tex]9^{2} = {8}^{2} + {x}^{2} \\ 81 = 64 + {x}^{2} \\ 81 - 64 = {x}^{2} \\ {x}^{2} = 17 \\ x = \sqrt{17} [/tex]

Finding y,

We have to determine the angle, at the bottom left of the bigger triangle.

Using sine rule,

[tex] \frac{9}{sin(90)} = \frac{8}{sin(z)} \\ sin(z) = 0.8889 \\ z = {sin}^{ - 1} (0.8889) \\ z = 62.73[/tex]

To find the angle on the smaller triangle,

[tex]a = 90 - 62.73 \\ a = 27.27[/tex]

Finding the missing length of y,

[tex] \frac{ \sqrt{17} }{sin(62.73)} = \frac{m}{sin(27.27)} \\ m = 2[/tex]

So y = 2 + 8, y = 10

Answer:

A

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

9604 American adults must be interviewed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How many adults must be interviewed for the margin of error to be 0.01?

This is n, which is found for M = 0.01.

We have no estimate for the proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample size will be needed.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.01 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.01}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.01})^2[/tex]

[tex]n = 9604[/tex]

9604 American adults must be interviewed.

Answer:

option A is the answer.......

The remainder is 40 if the polynomial function f(x) = x³-2x²+ax-8 has (x-2) value of a is 4 option (D) is correct.

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial function:

[tex]\rm f(x)= x^3-2x^2+ax-8[/tex]

(x-2) is a factor of the above polynomial

To get the value of a put x = 2 in the polynomial and equate to zero.

[tex]\rm 2^3-2(2)^2+a(2)-8=0[/tex]

[tex]\rm a = 4[/tex]

[tex]\rm f(x)= x^3-2x^2+4x-8[/tex]

From the remainder theorem:

Put x = 4 in the polynomial to get the remainder

[tex]\rm R =f(4)= (4)^3-2(4)^2+4(4)-8[/tex]

[tex]\rm R = 64-32+16-8\\\\R = 40[/tex]

Thus, the remainder is 40 if the polynomial function f(x)=x³-2x²+ax-8 has(x-2) value of a is 4 option (D) is correct.

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Answer:

the 600 bags of cement would weigh 25.5826 tonnes

Answer:

600-90 lb bags of cement weigh 27 tons

Step-by-step explanation:

You don't say how much each bag weighs.  Let's suppose that that weight is 90 lb.

Then:

 90 lb         1 ton

----------- * -------------- = 9/200 ton/bag

  1 bag      2000 lb

Now multiply this by 600 bags:

  9 tons         600 bags

--------------- * ------------------ = 27 tons

200 bags             1

600-90 lb bags of cement weigh 27 tons

Answer:

We can not use ASA property of congruence.

Step-by-step explanation:

In ΔHML and ΔHMK,

HL ≅ HK [Given]

LM ≅ KM [Given]

HM ≅ HM [Reflexive property]

m∠L ≅ m∠K [Given]

ASA property of congruence,

Angle-Side-Angle property of congruence.

False

SSS property of congruence,

Side-Side-Side property of congruence,

True

SAS property of congruence,

Side-Included Angle-Side property of congruence,

True.

Therefore, we can not use ASA property of congruence.

Answer:

B

Step-by-step explanation:

Answer:

B is the answer 98 square units