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Integers are numbers such as

And odd numbers are

5x + 2y = -12 (a)

3y + 5x =-8 (b)

First, write (b) in the ax+by=c form:

5x + 3y = -8 (b)

Now, subtract (b) to (a) to eliminate x

5x + 2y = -12

-

5x + 3y = -8

__________

-y = -4

solve for y:

Multiply both sides by -1

y=4

Replace y=4 on (a) and solve for x:

5x + 2 (4) = -12

5x + 8 = -12

5x = -12-8

5x = -20

x = -20/5

x = -4

Solution: (-4,4)

Given the expression

express in sen and cos terms

then the correct answer is option C

Cos (angle)

Given

$152,000

52% assessment rate

$48 per $1,000

Procedure

First, let's calculate the assessment rate.

Now let's calculate the taxes

Property taxes are equal to $3,793.92.

The Solution:

Given:

By formula,

From the z-score tables:

Convert to percent by multiplying with 100.

Thus, the number of people that have an IQ score less than 90 is 25.25%

Therefore, the correct answer si 25.25%

The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}

Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.

Given data form the question

99% confidence interval

30 randomly selected students

mean sample = 84

Standard deviation = 12.2

Definition of variables

confidence level, CI = 99%

mean sample, X = 84

standard deviation, SD = 12.2

Z score, z = 2.576

sample size, n = 30

The formula for the confidence interval is given by

[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex]    OR    [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]  

[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]

=[tex]=84+2.576*2.2274[/tex]

= 84 + 5.7378     OR       84 - 5.7378

= 89.7378           OR        78.2622

=  89.73 to 78.26  

The confidence interval for the mean score of all students is 78.26 to 89.78

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Answer: Width =14, Length = 18

Step-by-step explanation:

L = W + 4

2W + 2L = 64

W+ L = 32

2W+ 4 = 32

2W = 28

W = 14

Value of x and y are -51 and 8 respectively

What is Algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.

Let,

X+27+32 = 8

X+ 3y +32 = 10

X + 2y +42 = 9

Be, equation 1, 2 and 3 respectively

X+27+32 = 8 -----(1)

X+ 3y +32 = 10 -----(2)

X + 2y +42 = 9 -----(3)

From equation we can find the value of x

X+27+32 = 8

X + 59 = 8

X = 8 - 59

X = - 51

Substituting the value of x in equation 3

X + 2y +42 = 9

(-51) + 2y + 42 = 9

-51 + 42 + 2y = 9

-9 + 2y = 9

2y = 9 + 9

2y = 18

y = 18/2

y = 9

Hence, the value of x = -51 and y = 9

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Explanation

Step 1

Let

then

I hope this helps you

a)The vertex of the function is (3, -1)

b)The line of symmetry is  x= 3

c) The maximum is no maximum and  minimum is  (3, -1)

a) What is the vertex of the function of the parabola ?

[tex]f(x) = x^{2} -6x+8[/tex]

Transforming the function in the vertex form,

[tex]f(x) = a(x-h)^{2} +k[/tex]

[tex]f(x)=(x-3)^{2} -1[/tex]

The vertex of the function  is given by,

(h, k) =  (3, -1)

So ,the vertex of the function of the parabola is (3, -1)

b) What is the line of symmetry in the function?

In a parabola , the axis of symmetry  is x = h.

Here, x = 3

So, the line of symmetry of the function of the parabola is x= 3

c) What is the maximum and minimum?

What is a function of a parabola?

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we have the following:

Therefore:

To complete the perfect square ((x-h)²) we add and subtract constants:

For statement one:

We need to add up to complex numbers and their sum must give us equal to 10.

Also, we need to use the complex numbers:

5+i√15 and 5-i√15.

Then, we can use:

(5+i√15)+( 5-i√15) =

5+i√15+5-i√15 =

5+5+ i√15-i√15 =

= 10 + 0

= 10

For the second statement:

We need to show the product of complex numbers:

Then, we use:

(5+i√15)(5-i√15))=

5*5 - 5*i√15) +5*i√15) +√15*√15=

25 + 0 + 15=

40

Answer

The least likely to occur is Event C

Explanation

A.

P(spade card) = 13/52

P(queen) = 4/51 Note: Without replacement

⇒ 13/52 x 4/51

= 52/2652

= 0.0196

B.

P(a spade) = 13/52

P( another spade) = 12/51 Note: Without replacement

⇒ 13/52 x 12/51

= 156/2652

= 0.0588

C.

P(an ace) = 4/52

P(king) = 4/51

⇒ 4/52 x 4/51

= 16/2652

= 0.006

∴ The least likely to occur is Event C

The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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Answer:

B. 1

Explanation:

Given the inequality:

To find the critical number, first, change the inequality sign to the equality sign :

Next, solve for x:

Therefore, from the options, 1 is the critical number.

The correct option is B.

We need to know how to calculate compound interest to solve this problem. The present value is $2577.32

Compound interest is the interest that is earned on interest. Inorder to calculate the compound interest we need to know the principal amount, the rate of interest, the time period and how many times the interest is applied in per time period. In this question we know the amount after 9 years and the rate of interest is 9.5% and the interest is compounded quarterly. We will use the formula for compound interest get the principal value.

A=P[tex](1+\frac{r}{n}) ^{nt}[/tex]

where A= amount, P= principal, t=time period, n= number of times interest applied per time period, r=rate of interest

A=$6000

r=9.5%

t=9 yrs

n=4

6000=P[tex](1+\frac{9.5}{400} )^{36}[/tex]

6000= P x 2.328

P=6000/2.328=2577.32

Therefore the present value that will grow to $6000 in 9 years is $2577.32

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x = 0,1 are the real solutions of the equation .

What are real solutions in math?

 4x³ - 8x² + 4x = 0

x( 4x² - 8x + 4 ) = 0

x( 4x² - 4x - 4x + 4 ) = 0

x ( 4x ( x - 1) -4 ( x - 1 )) = 0

x ( ( 4x - 4 ) ( x - 1 ) ) = 0

x = 0

4x - 4 = 0 ⇒ x = 1

x - 1 = 0 ⇒ x = 1

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The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour

Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.

In other words, 1 km / h is equal to 54.6807 feet per minute.

If there are 880 ft / minute therefore, the number of kilometers per hour is:

= Speed in feet per minute / feet per minute per kilometer per hour

= 880 / 54.6807

= 16.09 kilometers per hour

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We are given two functions:

h(x) = x^2 + 1

and k(x) = x - 2

We are asked to find the value of:

(h - k) (3) (the value of the difference of the two functions at the point x = 3

So we performe the difference of the two functions:

(h - k) (x) = x^2 + 1 - (x - 2) = x^2 + 1 - x + 2 = x^2 - x + 3

So, this expression evaluated at 3 gives:

(h-k)(3) = 3^2 - 3 + 3 = 9

One could also evaluate what was asked by evaluating each function independently and subtracting the results of such evaluation:

h(3) = 3^2 + 1 = 10

k(3) = 3 - 2 = 1

Then, the difference is : h(3) - k(3) = 10 - 1 = 9

So use whatever method feels more comfortable for you.

Multiply both sides by t:

Multiply both sides by 10:

Divide both sides by 12:

Answer:

The coefficients of the terms in the algebraic expression are 1 and -3

Explanation:

The coefficients are the number that multiplies an algebraic term in an algebraic expression.

for example; the coefficient of 3x is 3.

For the question;

given the expression;

The coefficient of x^2 is 1

while the coefficient of x is -3

Therefore, the coefficients of the terms in the algebraic expression are 1 and -3

To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.

So let's calculate our first prime factorization:

As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).

Now, for the second number we have:

And both prime factorizations are our final answers.

If x is uniformly distributed over the interval [ a , b ] then,

Also ,

It is given that ,

Therefore,

(a)The distribution is as follows :

(b)The mean is calculated as,

Standard deviation is calculated as,

(c) The probability is calculated as,

(d) The probability is calculated as,

We will have the following:

The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:

In order to have a linear function, the rate of change needs to be the same in each point

For

(-18,2)=(x1,y1)

(-14,4)=(x2,y2)

for

(-14,4)=(x1,y1)

(-12,5)=(x2,y2)

for

(-12,5)=(x1,y1)

(0,12)=(x2,y2)

as we can see here are the two numbers so we will obtain the equation in order to know the number that needs to be change

therefore if x=0

the number we need to change is 12 and need to be changed for 11

(0,11)

a. The number that needs to be changed in order to create a linear function is 12

b. That number needs to be changed to 11 in order for the function to be linear

50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.

10m = 90 - 50

10m = 40

m = 40/10

m = 4

We will see that the function f(x) is:

f(x) = 15*(x - 3)

Evaluating it in x = -3 we can see that:

f(-3) =  -90

We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)

so we can write the equation:

f(x)/(x - 3) = 15

And we can solve this for f(x) as if it were a variable, then we get:

f(x) = 15*(x - 3)

Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:

f(-3) = 15*(-3 - 3) = 15*(-6) = -90

So the statement:

f(-3) = 15

Is false

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Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is the number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$2,000

t=5 years

r=6%=6/100=0.06

n=12

substitute the given values in the above formula

therefore

There is quadrilateral, means it has 4 lines

Is a rhombus