What is the length of BC in the right triangle below?
B
00
A
15
с
A. 17
B. 60
C. 17
D. 289

Answer:

[tex]\boxed{-3(x+3)(x^2-6x+10)}[/tex]

Step-by-step explanation:

Hello,

As the polynomial has only real coefficients, it means that 3-i is a zero too, because we apply the Conjugate Zeros Theorem.

It means that we can write the expression as below, k being a real number that we will have to identify.

[tex]k(x+3)(x-3-i)(x-3+i)=k(x+3)((x-3)^2-i^2)\\\\=k(x+3)(x^2-6x+9+1)\\\\=k(x+3)(x^2-6x+10)[/tex]

And for x = 0, y = -90 so we can write

-90=k*3*10, meaning that k=-3

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Step-by-step explanation:

=The difference between a number and 6

the term difference is used in mathmatics as subtraction

let x = a number

x - 6 = the difference between that unknown number and 6

Answer:

Step-by-step explanation:

difference means subtract. Difference is always worded the same way. What you have written means that you start with an algebraic letter and then comes the minus sign and then the number

Let the number = x

x - 6

If it was worded as difference between 6 and a number, you would write it this way

6 - x

Answer:

  3x +4 = -2x -1

Step-by-step explanation:

The line that goes up to the right has a y-intercept of +4. This is where it crosses the y-axis. It's slope (rise/run) is 3/1 = 3, so its equation in slope-intercept form is ...

  y = mx +b . . . . where m is the slope, b is the y-intercept

  y = 3x +4

The other line has a negative slope and a y-intercept of -1. The slope of that line is rise/run = -2/1 = -2, so its equation is ...

  y = -2x -1

__

The solution point will have the x-coordinate that is the solution of the equation ...

  y = y

  3x +4 = -2x -1 . . . . . . substituting the above expressions for y.

Answer:

b is your answer hope it is helpful

Answer:

b is the correct answer

Step-by-step explanation:

the answer is b

Answer:

C

Step-by-step explanation:

Answer:

f^6h^6

Step-by-step explanation:

f^9 h^23

-----------------

f^3 h^17

We know a^b / a^c = a^(b-c)

f^9 / f^3 = f^(9-3) = f^6

h^23 / h^17 = h^(23-17) = h^6

f^6h^6

Step-by-step explanation:

When θ is very small, θ ≈ sin θ ≈ tan θ.

θ (sin θ)² / (2 tan θ)

θ³ / (2θ)

θ² / 2

90/-10

= 9/-1

= -9

So, -9 is the quotient.

Answer:

missing side length is 12

Step-by-step explanation:

similar means that all correlating pairs of sides have the same ratio (old side length) / (new side length).

so, when we know the ratio of one pair, we can apply it to any other side to calculate the correlating side.

we see, when we go from small to large, that we have the ratio 32/40 = 4/5.

so, multiplying the larger side by this, we get the shorter side.

15 × 4/5 = 3 × 4 = 12

the proportion part in your picture is a bit confusing :

yes,

x/15 = 32/40 = 32/40

I don't know, why this last expression was repeated.

x/15 = 32/40

x = 15×32/40 = 15×4/5 = 3×4 = 12

as you see we get of course the same result doing it that way.

Answer:

Hello,

Answer C: -40

Step-by-step explanation:

[tex]\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\[/tex]

Answer:

n = -10

Step-by-step explanation:

1 / 8^n  = 8^5^2

We know that 1/a^b = a^-b

We also know that a^b^c = a^(b*c)

8^-n = 8^(5*2)

8^-n = 8^(10)

Since the bases are the same, the exponents are the same

-n = 10

n = -10

Answer:

None of the above.

1.86p + 0.7

Step-by-step explanation:

Step 1: Write expression

0.7 + p + 0.86p

Step 2: Combine like terms

0.7 + 1.86p

None of those answer choices are correct unless you wrote the problem incorrectly.

Answer:

3

Step-by-step explanation:

Y is given by sin(theta). sin(-60)=-sqrt(3)/2

Answer:

The P-Value is  0.07186  

Step-by-step explanation:

GIven that :

Mean = 70

standard deviation = 3.5

sample size n = 49

sample mean = 69.1

The null hypothesis and the alternative hypothesis can be computed as follows;

[tex]H_o : \mu = 70 \\ \\ H_1 : \mu \neq 70[/tex]

The standard z score formula can be expressed as follows;

[tex]\mathtt{z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]

[tex]\mathtt{z = \dfrac{69.1 - 70}{\dfrac{3.5}{\sqrt{49}}}}[/tex]

[tex]\mathtt{z = \dfrac{-0.9}{\dfrac{3.5}{7}}}[/tex]

z = -1.8

Since the test is two tailed and using the Level of significance = 0.05

P- value = 2 × P( Z< - 1.8)

From normal tables

P- value = 2 × (0.03593)

The P-Value is  0.07186  

Answer:

Step-by-step explanation:

Given that:

p = 0.61

If X is the the number of students in a randomly selected group  of a sample size n = 50

The expected value and the standard deviation can be computed as follows:

The expected value E(X) = np

The expected value E(X) =  50 × 0.61

The expected value E(X) = 30.5

The required standard deviation = [tex]\sqrt{np(1-p)}[/tex]

The required standard deviation = [tex]\sqrt{30.5(1-0.61)}[/tex]

The required standard deviation = [tex]\sqrt{30.5(0.39)}[/tex]

The required standard deviation = [tex]\sqrt{11.895}[/tex]

The required standard deviation = 3.4489

The required standard deviation =  3.45

(b) Fill in the missing quantity. (Round your answer to the nearest whole number.)

There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.

From the given information:

Now, we can deduce that:

the mean = 30.5

standard deviation = 3.45

Using the empirical rule:

At 95% confidence interval;

[μ - 2σ,  μ + 2σ] = [ 30.5 - 2(3.45) , 30.5 + 2(3.45)]

[μ - 2σ,  μ + 2σ] =  [ 30.5 - 6.9 , 30.5 + 6.9]

[μ - 2σ,  μ + 2σ] = [ 23.6, 37.4]

The 2.5% of the observations are less than 95% confidence interval and 2.5% observations are greater than 95% confidence interval.

The required number of teenagers is = the upper limit of the 95% confidence interval = 37

There is an approximately 2.5% chance that __37___ or more teenagers in the group will shop at the mall during the next week.

The answer would be the first image.

Step-by-step explanation:

From context, it appears that to be circumscribed is to be drawn about; thus the square circumscribed about the circle is the first graph.

Answer:

The first image which is a circle in a square

Answer:

x^2+6x+9= (x+3)^2

Step-by-step explanation:

x^ 2 +6x+__ =(_)^ 2

The formula is a^2+2ab+b^2= (a+b)^2

x^2= a^2

x=a

6x=2ab where a=x

6x=2x*b

b=3

b^2=9

x^2+6x+9= (x+3)^2

[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]

$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$

$=(3+0.5+0.6+0.1)(4+0.1)$

$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$

$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$

$=16+0.4+0.8+0.02=17.22$

Answer:n-6=168

Step-by-step explanation:

The statement starts with the variable first.

Answer:

n - 6 = 168.

Step-by-step explanation:

Let's say that the value of the number is n.

n minus 6 is 168, so n - 6 = 168.

n - 6 = 168

n = 174.

Hope this helps!

Answer:

The Width = 65.44 inches

The Height = 36.81 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Using Pythagoras Theorem we known that:

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 75²

We are given ratio: 16:9 as aspect ratio

Width = 16x

Height = 9x

(16x)² +(9x)² = 75²

= 256x² + 81x² = 75²

337x² = 5625

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately x = 4.09

For the newer 75 inch tv set

The Height = 9x

= 9 × 4.09

= 36.81 inches

The Width = 16x

= 16 × 4.09

= 65.44 inches.

Answer:

A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.

Step-by-step explanation:

Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.

Answer:

Step-by-step explanation:

Given:

x = 2cost,

t = (1/2)arccosx

y = 2sint

dy/dx = dy/dt . dt/dx

dy/dt = 2cost

dt/dx = -1/√(1 - x²)

dy/dx = -2cost/√(1 - x²)

Differentiate again to obtain d²y/dx²

d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)

At t = π/4, we have

(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)

Answer:

-15

Step-by-step explanation:

Let a = 2 and c = -7.

[tex]c-4a\\(-7)-4(2)\\-7-8\\-15[/tex]

we know that the value of a is 2 and c is -7

Expression-

c-4a

= (-7)-4×2

= (-7)-8

= -15

Answer:

The formula for the probability distribution is:

P(X = n) = q^(n - 1)p

= [0.2^(n - 1)]0.8

Step-by-step explanation:

This is a geometric probability distribution.

The probability of success p = 80% = 0.8

The probability of failure is q = 1 - p = 0.2

The formula is:

P(X = n) = q^(n - 1)p

= [0.2^(n - 1)]0.8

Answer:

Hello,

Step-by-step explanation:

[tex]\overline{x}=3262\\\sigma=1100\\\\P(x\geq 1000)=P(x\leq 3262+(3262-1000))=P(x\leq 5524)\\\\z=\dfrac{x-\overline{x}}{\sigma} =\dfrac{5524-3262}{1100} =2.05\overline{63}\\\\\\P(z\leq 2.05)=0.9789\\\\P(z\leq 2.06)=0.9803\\\\\\\boxed{0.9789\leq P\leq 0.9803}\\\\\\[/tex]

[tex]P(x\leq 4000)=P(z\leq \dfrac{4000-3262}{1100} )=P(z\leq 0.67\overline{09})\\\\P(z\leq 0.67)=0.7486\\P(z\leq 0.68)=0.7517\\\\0.7486\leq P\leq 0.7517\\[/tex]

Answer:

w = 124/15 = 8 4/15

Step-by-step explanation:

[tex]-\frac{7}{3}+\frac{1}{2}w=-\frac{9}{5}\\\\\frac{1}{2}w=\frac{62}{15}\\\\w=\frac{124}{15}=8\frac{4}{15}[/tex]

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer:

x = -3

Step-by-step explanation:

12 - 4x-5x = 39

Combine like terms

12 - 9x = 39

subtract 12 from each side

12 -9x-12 = 39-12

-9x = 27

Divide by -9

-9x/-9 = 27/-9

x = -3

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges