The perimeter of a rectangle is 82 cm the length is 1 cm more than three times the width find the length and the width of the rectangle

1. x - 3 is not a factor

2. The remainder is 32.

Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.

So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then

p(3) = 0

So, substituting x = 3 into the equation, we have

p(3) = 2x³ - 4x² - 6

= 2(3)³ - 4(2)² - 6

= 2(27) - 4(4) - 6

= 54 - 16 - 6

= 54 - 22

= 32

Since p(3) ≠ 0.

x - 3 is not a factor

Since p(3) = 32,

The remainder is 32.

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The variable x is 9 and the two adjacent angles have measures of 117° and 63°, respectively.

Parallelograms are quadrilaterals with two pairs of parallel sides of equal length. According to Euclidean geometry, the measures of two adjacent angles in a parallelogram are supplementary. Thus,

13 · x + 7 · x = 180°

Now we clear the variable x:

20 · x = 180°

x = 9

And the missing angles are:

13 · 9 = 117°

7 · 9 = 63°

The value of the variable x is 9 and the measures of the two adjacent angles are 117° and 63°, respectively.

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Answer:

23

Step-by-step explanation:

4h = 92

Divide both sides by 4 to get h by itself

h = 23

Neither parallel nor perpendicular

The points are:

A(3, 1), B(3,-4), C(-4,1), D (-4,5)

The slope of a line is given as:

The slope of the line AB, m(AB), with gthe points A(3, 1), B(3,-4) is given as:

The slope of the line CD, m(CD), with the points C(-4,1), D (-4,5) is given as:

A line that has an infinite slope is a vertical line

For the two lines to be parallel, m(AB) should be equal to m(CD)

For the two lines to be perpendicular, m(AB) = -1 / m(CD)

None of the conditions for paralleleism and perpendicularity is met, the lines AB and CD are neither parallel nor perpendicular

Answer:

27

Step-by-step explanation:

Divide 270 by 10

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

−3x−9=−15

Step 1: Add 9 to both sides.

−3x−9+9=−15+9

−3x=−6

Step 2: Divide both sides by -3.

−3x/−3 = −6/−3

x=2

The hypotenuse of a right triangle = 19.31cm

What is Hypotenuse?

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Let the measure be,

Perpendicular = 18cm

Base = 7cm

Hypotenuse = ?

To find the Hypotenuse we can Pythagoras Theorem:

Hypotenuse² = Perpendicular²+ Base²

H² = (18)² + (7)²

H² = 324 + 49

H² = 373

H = [tex]\sqrt{373}[/tex]

H = 19.31cm

Hence, The measure of the other leg is²

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Answer:

92 over 100

Step-by-step explanation:

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

The lines aren't parallel since they intersect at point B.

Parallel lines never intersect.

The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma([tex]\alpha ,\beta[/tex])

E(X)= [tex]\alpha \beta[/tex]                 [tex]\beta[/tex]= [tex]12^{2}/24[/tex]=6 weeks

V(x)= [tex]\alpha \beta ^{2}[/tex]                [tex]\alpha[/tex]=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X, [tex]\alpha[/tex], [tex]\beta[/tex], False)

P([tex]12\leq X\leq 24[/tex])

P([tex]12/6\leq G\leq 24/6[/tex])

P([tex]2\leq G\leq 4[/tex])

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

Step-by-step explanation:

0.424 is the probability that the transistor will last between 12 and 24 weeks.

X= lifetime of the transistor in weeks E(X)= 24 weeks

Standard deviation= 12 weeks

Finding the parameters alpha and beta X~gamma(αβ)

E(X)= αβ             β =6 weeks

V(x)=αβ^2           α =24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,α,β,False)

P(12≤X≤24)

P(12/6≤G≤24/6)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:Given : f(x)=x

4

−3x

2

+4

f(2)=(2)

4

−3(2)

2

+4

=16−12+4=8

This can also be verified by the actual divison

The largest possible whole-number length for the third side of the triangle is 23.

The total of any two sides in a triangle with sides a, b, and c MUST be less than the length of the third side.  

You have a line segment, not a triangle if the third side's length equals the sum of the other two sides' lengths.  

Here, the sum of the two sides of the triangle is 12 + 12 = 24.  

Therefore, the length of the third side should be less than 24, and the whole number which is less than 24 is 23.  

Hence, the length of the third side is 23.

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Answer:

2

Step-by-step explanation:

512÷2=256

256÷2=128

128÷2=64

64÷2=32

32÷2=16

16÷2=8

8÷2=4

4÷2=2

2÷2=1

=(2^2)+(2^2)+(2^2)+(2^2)+2

When 2 is multiplied it will make it a perfect square.

512×2=1024

√1024

=32

No, the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

In the question ,

an equation y=(1/2)x-3 is given ,

if the ordered pair (-8,1) is a solution of the equation , then it should satisfy the equation .

Substituting x=-8 and y=1 in the equation y=(1/2)x-3 , we get

y=(1/2)x-3

1 = (1/2)(-8) -3

1 = -8/2 -3

1 = -4-3

1 ≠ -7

Since 1≠7 , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3 .

Therefore , No , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

The given question is incomplete , the complete question is

Is the ordered pair (-8,1) a solution to the equation y=1/2x-3  ?

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I WILL USE THE LAWS OF EXPONENTS

[tex] {x}^{n} \times {x}^{m} \\ = {x}^{n + m} [/tex]

AND

[tex] \frac{{x}^{n}}{ {x}^{m} } \\ = {x}^{n - m} [/tex]

[tex] \frac{3 {x}^{ - 2 + 5} }{ {x}^{8} } \\ = \frac{3 {x}^{3} }{ {x}^{8} } \\ = 3 {x}^{3 - 8} \\ = 3 {x}^{ - 5} [/tex]

ATTACHED IS THE SOLUTION.

Answer:

i hope this one is good for you

The cost for a year is cheaper in Gym A.

The value of k for the cheaper membership is $10.

An equation in the form y = kx is known as a linear equation. A linear equation is an equation that increases at a constant rate.

In the equation : y = kx

k = y/x

Cost per month at Gym A = $50 / 5 = $10

Cost per month at Gym B = $40 / 3 = $13.33

Membership cost at Gym A for a year = $10 x 12 = $120

Membership cost at Gym B for a year = $13.33 x 12 = $160

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Answer: is 72 people to 27 animals

Step-by-step explanation:

I can find the ratio by cross multiplying

40/15 to x/27

15x = 1080

x = 72

you can also divide 40/15 for a ratio percent = 8/3

multiply 27 animals x 8/3 = 72

two ways to solve for ratios

The area of the region within the square and without the circle is equal to 13.7 square inches.

In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:

A = L² - 0.25π · D²

Where:

If we know that D = L = 8 in, then the area of the region is:

A = (8 in)² - 0.25π · (8 in)²

A = 64 in² - 50.265 in²

A = 13.735 in²

The area of the region is equal to 13.7 square inches.

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The decimal figure that would be added to 1/5 to give 3/6 = 0.3

A decimal form is defined as the expression of figures that are more than a whole number with the use of decimal point.

Examples of figures that are in decimal form include the following: 0.2, 0.3, 0.4, 0.5, 1.2, 2.2,3.3 and 4.4.

To represent the given fractions in decimal form;

1/5 = 0.2

3/6 = 0.5

Therefore, X + 0.2 = 0.5

make X the subject of formula,

X = 0.5 - 0.2

X= 0.3

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The shows the expression below simplified 0.0042 - (1.2 x 10-6) as D. 4.1988 x 10^-3.

The concept that is been used is subtraction of the first expression from second expression.

The given expression is 0.0042 - (1.2 x 10-6) and this can be expressed in standard form as ( 4.2 *10^-3) - (1.2 x 10-6)

Then then the subtraction can be done as [ ( 4.2 *10^-3) ] - [ (1.2 x 10^-6) ] = 4.1988 x 10^-3

In conclusion, iif we go through the options., then we can see that the forth option is the best option that match the expression.

Therefore, option D is correct.

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Mei Mei's age if the sum of Mei Mei's age and 5 times Xin's age is 143. is 23 years.

Let the ages be x and x+1 since they're consecutive numbers.

In this case the sum of Mei Mei's age and 5 times Xin's age is 143. This will be:

x + 5(x + 1) = 143

x + 5x + 5 = 143

Collect like terms

6x + 5 = 143

6x = 143 - 5

6x = 138

Divide

x = 138 / 6

x= 23

Mei Mei is 23 years.

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Answer:

See below

Step-by-step explanation:

The  equation is

y = [tex]x^{2}[/tex] + x

x equals the step

We see steps: 1, 2,3 and 4

y equals the number of squares that you see in each step.

If you look at step 1, you see [tex]1^{2}[/tex] + 1 = 2

Step 2: [tex]2^{2}[/tex] + 2 = 6

Step 3: [tex]3^{2}[/tex] + 3 = 12

Step 4: [tex]4^{2}[/tex] + 4 = 20

Can you see at each step there is a square of the number and then a little extra?  That little extra equals the number of the stop.

In the equation

y = 4x -2

Step 1

y = 4(1) -2

y = 2  It works!

Step 2:

y = 4x -2

y = 4(2)  - 2

y = 8 - 2

y = 6  It works!

Step 3:

y = 4x -2

y = 4(3) - 2

y = 12 - 2

y = 10  It does not work!

Step 4:

y = 4x -2

y  = 4(4) - 2

y = 16 - 2

y = 14  It does not work!

The equation y= 4x -2  only worked for the first 2 steps.

a. The equation for h is h = 100/x²

b. The function for the volume of the box V, in terms of x is:

v(x) = x²×h

Given, the prism has a square base and a total surface area of 100 cm².

A) let x = the side length of the base and

h = the height of the prism.

equation for h = ?

Volume = b × h

100 cm² = x² × h

h = 100/x²

B) a function for the volume of the box, V, in terms of x.

we know that x is the base and h is the height.

So, volume in terms of x :

v = b×h

v = x² × h

Hence we get the required answers.

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EXPLANATION

Let's see the facts:

The increasing rate is:

The increasing rate is 1.67

In percentage this is:

The percentage of increasing is of 60%.

The equation of the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

The given parameters are

Leading coefficient = 1

Zeros =  − 2 , − 4 , 3 , and 3 .

Polynomial equations have their multiplicities to add up to their degree.

This means that the multiplicity of the zeros is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

From the question, the polynomial is to be factored

This means that we represent it as

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

Hence, the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

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Polynomial is an expression consisting of indeterminates and coefficients the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3)

Polynomial is an expression consisting of indeterminates and coefficients, which involves  the operations like addition, subtraction, multiplication, and positive-integer powers of variables

Factors are the numbers which divide the expression or number with a remainder zero.

We need to write the factored form of the polynomial functions with real; coefficients and zeros minus two comma  minus four comma three and 3.

The leading coefficient of the polynomial is 1. Leading coefficient means coefficient of leading term.

Zeros =  − 2 , − 4 , 3 , and 3 .

Let the polynomial is of variable x.

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

(x-(-2))=x+2

(x-(-4))=x+4

(x-3)=x-3

So the factored form is (x+2)(x+4)(x-3)(x-3)

the polynomial is P(x)=(x+2)(x+4)(x-3)(x-3)

Hence the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3).

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Answer:

No, it is not.

Step-by-step explanation:

A function only has exactly one output for each input. In other words, for each X input, there is only one Y output. In the given set of coordinates, 3 is repeated as an input, which makes this set of coordinates not a function.