The diameter of a circle 18cm

(x • (y³)) - 32xyz²

Pull out like factors :

xy³ - 9xyz² = xy • (y² - 9z²)

Factoring: y² - 9z²

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B² =

A² - B²

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check : y² is the square of y¹

Check : z² is the square of z¹

Factorization is : (y + 3z) • (y - 3z)

Final result :

xy • (y + 3z) • (y - 3z)

Answer:

addition property of equality

Step-by-step explanation:

This is because the addition property of equality means

if [tex]a=b[/tex] then [tex]a+c=b+c[/tex]

So if, [tex]x=2[/tex] then [tex]x+8=2+8[/tex]

Answer:

Step-by-step explanation:

Translate the given into two pairs of coordinates:

Work out the equation of the line passing through both of the points.

Find the slope:

Find the y-intercept:

The line is:

Find the value of y when x = 1500:

The next number in the sequence is the sum of the two note ious numbers.

The next number would be 99 + 160 = 259

Answer:

∠7    . However ∠7 and ∠8 are vertical angles which are equal,

Step-by-step explanation:

Angle ∠7, but because ∠7 and ∠8 are vertical angles and they are equal also.

 ∠5 corresponds to ∠7

m ∠7  = m ∠8    vertical angles are =

I will say ∠7 and ∠8.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000e^{0.08\cdot 4}\implies A=2000e^{0.32}\implies \boxed{A\approx 2754.26}[/tex]

Answer:

  411

Step-by-step explanation:

Put the values where the variables are and do the arithmetic.

  3s³ +4t² = 3(5³) +4(3²)

  = 3(125) +4(9) = 375 +36 = 411

Answer:

angle m1 = 40°

Step-by-step explanation:

The first angel presented to the left is 40° if you take that and flip it its the same as M1 therefore its 40°.

Answer:

12 have a bicycle

Step-by-step explanation:

There are 30 students and 40% have a bicycle

30 * .40

12

12 have a bicycle

Answer: 12

40% of 30 is 12.

Answer:

70% of people did not order popcorn at the movie theater on Saturday.

Step-by-step explanation:

first, add to get the total amount of people

150 + 350 = 500

now that we have the total, divide the people that did not buy popcorn by the total amount of people

350/500 = 0.7

then, multiply that by 100

0.7 x 100 = 70

your final answer would be 70%

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(3*x+7)^2+5-((7*x-9)^2*x+5)=0

Step by step solution :

STEP1:

Equation at the end of step 1

(((3x+7)2)+5)-(x•(7x-9)2+5) = 0

STEP2:

Checking for a perfect cube

2.1 -49x3+135x2-39x+49 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: -49x3+135x2-39x+49

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -39x+49

Group 2: -49x3+135x2

Pull out from each group separately :

Group 1: (-39x+49) • (1) = (39x-49) • (-1)

Group 2: (49x-135) • (-x2)

Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

Find roots (zeroes) of : F(x) = -49x3+135x2-39x+49

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is -49 and the Trailing Constant is 49.

The factor(s) are:

of the Leading Coefficient : 1,7 ,49

of the Trailing Constant : 1 ,7 ,49

Let us test ....

Equation at the end of step

2

:

-49x3 + 135x2 - 39x + 49 = 0

STEP

3

:

Cubic Equations:

3.1 Solve -49x3+135x2-39x+49 = 0

Future releases of Tiger-Algebra will solve equations of the third degree directly.

Meanwhile we will use the Bisection method to approximate one real solution.

Approximating a root using the Bisection Method :

We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).

The function is F(x) = -49x3 + 135x2 - 39x + 49

At x= 3.00 F(x) is equal to -176.00

At x= 2.00 F(x) is equal to 119.00

Intuitively we feel, and justly so, that since F(x) is negative on one side of the interval, and positive on the other side then, somewhere inside this interval, F(x) is zero

Procedure :

(1) Find a point "Left" where F(Left) < 0

(2) Find a point 'Right' where F(Right) > 0

(3) Compute 'Middle' the middle point of the interval [Left,Right]

(4) Calculate Value = F(Middle)

(5) If Value is close enough to zero goto Step (7)

Else :

If Value < 0 then : Left <- Middle

If Value > 0 then : Right <- Middle

(6) Loop back to Step (3)

(7) Done!! The approximation found is Middle

Next Middle will get us close enough to zero:

F( 2.596896529 ) is 0.000000414

The desired approximation of the solution is:

x ≓ 2.596896529

Note, ≓ is the approximation symbol

One solution was found :

x ≓ 2.596896529

Answer:

You: 3, 6, 9, 12

Friend:4, 8, 12, 16

Step-by-step explanation:

You/Friend ratio is 3/4

Missing numbers:

Numbers:

You      3, 6, 9, 12

Friend  4, 8, 12, 16

Answer:

10:1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The unit rate is found by dividing.

2/3 = 0.(6)

1/15 = 0.(6)

Answer:

x = 42

Step-by-step explanation:

2x + 8 + 2x + 4 = 180

4x + 12 = 180

4x = 168

x = 42

Answer:

C) y + 1 = -5(x - 1)

Step-by-step explanation:

Given:

m = -5

(1, -1)

We just simply use the point-slope formula and plug in:

y - y1 = m(x - x1)

y - (-1) = -5(x - 1)

y + 1 = -5(x - 1)

Check the picture below.

Answer:

x=11

Step-by-step explanation:

We know that angles on a straight line equal 180 degrees, so we know that 8x+10+7x+5 = 180.

Simplify

15x+15=180

Solve

Take away 15 from both sides

15x = 165

Divide 165 by 15

x = 11

I'm sorry if I'm wrong

Testing the hypothesis, it is found that the appropriate test statistic is z = 0.54.

At the null hypothesis, it is tested if the proportion of women physics majors in your college is the same as the national average of 19%, that is:

[tex]H_0: p = 0.19[/tex]

At the alternative hypothesis, it is tested if the proportion is different, that is:

[tex]H_1: p \neq 0.19[/tex]

The test statistic is given by:

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

In which:

For this problem, the parameters are:

[tex]p = 0.19, n = 50, \overline{p} = \frac{11}{50} = 0.22[/tex]

Hence, the value of the test statistic is:

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

[tex]z = \frac{0.22 - 0.19}{\sqrt{\frac{0.19(0.81)}{50}}}[/tex]

[tex]z = 0.54[/tex]

A similar problem is given at https://brainly.com/question/24166849

Answer:

Flower stick hahhhahaHaha

The total interest on the loan and monthly payments are $64,000 and $ 1,333.3 respectively

The formula for calculating the simple interest is expressed as:

I = PRT

Get the interest;

I = 16,000 * 0.8 * 5

I = $64000

Amount after 5 years = 16000 + 64000

Amount after 5 years  = $80,000

Monthly payment  = 80000/60months

Monthly payment = $1,333.33

Hence the total interest on the loan and monthly payment are $64,000 and $ 1,333.3 respectively

Learn more on interest here: https://brainly.com/question/10488979

Answer:

x2 the left side and x3 the right side of the equation

Answer:

X = -2

First you cross multiply, and then you expand to get 15x+6

after that its basic algebra with adding/subtracting from each side, simplifying, and then divide both sides by -13.

[tex]10(-7y-2z) +4z -2(-8z+6y)\\\\=-70y -20z +4z +16z - 12y\\\\=-82y -4z+4z \\\\=-82y[/tex]

Answer:

Step-by-step explanation:

926/71 = 13 Remainder 3

Answer:

Enlargement (aka: Dilation)

Step-by-step explanation:

As the triangle's scale factor is 3, The triangle P enlarges by 3 onto triangle Q.

Answer:

dilation by a scale factor by 3 about (1, 0)

Step-by-step explanation:

it is dilation by a scale factor of 3

see the below picture to find the center of dilation formula

(2, 1)  (4, 3) points of transformation

center = (3*2 - 4 / 3 - 1,  3*1 - 3 / 3 - 1)

= ( 6 - 4 / 2,  0)

= (1, 0)

so single transformation is  dilation by a scale factor by 3 about (1, 0)

Answer:

Range is 7 to 42

Step-by-step explanation:

Answer:

X > -11/10

Step-by-step explanation:

Answer:

b. 3

Step-by-step explanation:

find equation of g(x):

(-16-(-10))/(-3-(-1))=-6/-2=3

apply a point

-16=3(-3)+n

-16=-9+n

n=-7

g(x)=3x-7

find equation of f(x):

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

simplify

f(x)=-2x-10

subtract y intercepts

-7-10=3

3