The radius of the circle whose equation is (x - 3)² + (y + 1)² = 16 is
A). 4
B). 8
C). 16

Answer:Solution

(

−

4

)

(

7

2

+

3

)

Step-by-step explanation:

7

3

−

2

8

2

+

3

−

1

2

7x^{3}-28x^{2}+3x-12

7x3−28x2+3x−12

Grouping

1

Find one factor

Factor by grouping

Factor by grouping

Factor by grouping

(

−

4

)

(

7

2

+

3

)

{\color{#c92786}{({\color{#c92786}{x-4}})({\color{#c92786}{7x^{2}+3}})}}

(x−4)(7x2+3)

Answer:

-3

Step-by-step explanation:

4^x = (1/8)^(x+5)

(2^2)^x =  (2^-3)^(x+5)

2^2x = 2^(-3x - 15)

Since both sides have the same base of 2, then the exponents are equal

So

2x = - 3x - 15

5x = -15

 x = -3

Answer:

-3

Step-by-step explanation:

see attached

Answer:

[tex]\large\boxed{x=\dfrac{8}{3}}[/tex]

Step-by-step explanation:

[tex]-3(-x)-6=-3x+10\\\\3x-6=-3x+10\qquad\text{add 6 to both sideS}\\\\3x=-3x+16\qquad\text{add}\ 3x\ \text{to both sides}\\\\6x=16\qquad\text{divide both sides by 6}\\\\x=\dfrac{16}{6}\\\\x=\dfrac{8}{3}[/tex]

Answer:

2(3x-2(3x+2)

Step-by-step explanation:

1) 18x^2-8

2) 2(9x^2-4)

3) 2(3x-2)(3x+2)

Answer:

2(3x-2(3x-2) instead of the + 2

Step-by-step explanation:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

y = 1 - 3x = -3x + 1

slope = -3

y-intercept at 1

y = 3x - 1

slope = 3

y-intercept at -1

x - 3 = y → y = 1x - 3

slope = 1

y-intercept at -3

x + 3 = y → y = 1x + 3

slope = 1

y-intercept at 3

Answer:

m=-1

Step-by-step explanation:

9m+13 =4

Subtract 13 from each side

9m+13-13 =4-13

9m = -9

Divide each side by 9

9m/9 = -9/9

m = -1

Answer:

m=-1

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

To find your answer, plug in 4 for r.

[tex]-3r+8\\-3(4)+8[/tex]

You can start by multiplying -3 by 4.

[tex]-3(4)+8\\-12+8[/tex]

Next, add -12 to 8 and you'll have your answer.

[tex]-12+8\\-4[/tex]

Answer:

-4.

Step-by-step explanation:

Substitute r = 4 into the given expression:

= -3(4) + 8

= -12 + 8

= -4.

Answer: About 99.7% of sixth-grade students will have

heights between 51.1 inches and 64.9 inches.

Step-by-step explanation:

According to the empirical rule, 99.7% of data falls within the three standard deviations from the mean.

Given : Mean: [tex]\mu=58\text{ inches}[/tex]

Standard deviation:=  [tex]\sigma=2.3\text{ inches}[/tex]

Then, the  99.7% of sixth-grade students will have  heights between

[tex]\mu-3\sigma[/tex] inches and [tex]\mu+3\sigma[/tex] inches

i.e. [tex]58-3(2.3)[/tex] inches and [tex]58+3(2.3)[/tex] inches

i.e. 51.1 inches and 64.9 inches.

Answer:

About 99.7% of sixth-grade students will have

heights between 51.1 inches and 64.9 inches.

Step-by-step explanation:

Got it right :/

Answer:

The x-intercepts are x = 1 , x = 2 , x = 3

The y-intercept is -6

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the x-intercept of a function substitute f(x) by 0

- To find the y-intercept of a function substitute x by 0

- To find the factors of quadratic function use the long division

* Lets solve the problem

∵ f(x) = x³ - 6x² + 11x - 6

∵ (x - 3) is one of its factors

- Use the long division to find the other factors

∵ x³ - 6x² + 11x - 6 ⇒ dividend

∵ x - 3 ⇒ divisor

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ x³ ÷ x = x²

# Multiply x² by the divisor (x - 3)

∵ x²(x - 3) = x³ - 3x²

# subtract it from the dividend

∵ (x³ - 6x² + 11x - 6) - (x³ - 3x²) = (x³ - x³) + (-6x² + 3x²) +11x - 6

∴ The dividend is -3x² + 11x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ -3x² ÷ x = -3x

# Multiply -3x by the divisor (x - 3)

∴ -3x(x - 3) = -3x² + 9x

# subtract it from the dividend

∵ (-3x² + 11x - 6) - (-3x² + 9x) = (-3x² - 3x²) + (11x - 9x) - 6

∴ The dividend is 2x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ 2x ÷ x = 2

# Multiply 2 by the divisor (x - 3)

∴ 2(x - 3) = 2x - 6

# subtract it from the dividend

∴ (2x - 6) - (2x - 6) = (2x - 2x) + (-6 + 6) = 0

∴ (x³ - 6x² + 11x - 6) ÷ (x - 3) = x² - 3x + 2

∴ The factors of f(x) are (x - 3)( x² - 3x + 2)

- The factor (x² - 3x + 2) can factorize into two bracket

∵ The last term is positive and the middle term is negative than the

   two brackets have the middle sign (-)

∵ x × x = x² ⇒ 1st terms in the two brackets

∵ 2 × 1 = 2 ⇒ 2nd terms in the two brackets

∵ 2 × x = 2x

∵ 1 × x = x

∵ 2x + x = 3x

∴  (x² - 3x + 2) = (x - 2)(x - 1)

∴ f(x) = (x - 3)(x - 2)(x - 1)

- To find the x-intercept put f(x) = 0

∴ (x - 3)(x - 2)(x - 1) = 0

- That means each bracket = 0

∵ x - 3 = 0 ⇒ add 3 for both sides

∴ x = 3

∵ x - 2 = 0 ⇒ add 2 for both sides

∴ x = 2

∵ x - 1 = 0 ⇒ add 1 for both sides

∴ x = 1

∴ The x-intercepts are x = 1 , x = 2 , x = 3

- To find the y-intercept put x = 0

∵ f(x) = x³ - 6x² + 11x - 6

∵ x = 0

∴ f(0) = 0 - 0 + 0 - 6 = -6

∴ The y-intercept is -6

Answer:  dilation and translation

Step-by-step explanation:

Here Δ ABC and ΔA'B'C' are similar triangles (By AAA similarity postulate), so one of the transformation used here is dilation and also the there is some distance between the triangles without any change in its orientation , so the other transformation used here is translation.

Answer:

Step-by-step explanation:

let angle [tex]B[/tex] . be [tex]y[/tex]   then,

using angle sum property,

x+y+90=180 (angle c is 90 because its given)

hence you have the equation

Answer:

Cos() = AC / AB

So in this case: Cos() = 5 / 13

Answer:

x = pi/12, 5pi/12, 13pi/12, 17pi/12.

Step-by-step explanation:

Note that cos (4x) =  1 - 2sin^2 (2x)

Substituting we have:

1 - 2sin^2 (2x) - 9 sin(2x) + 4 = 0

2 sin^2 (2x) + 9 sin(2x) - 5 = 0

(2 sin 2x - 1 )(sin 2x + 5 ) = 0

sin 2x = 1/2 and sin 2x = -5.

sin 2x = 1/2,   gives 2x = pi/6, 5pi/6, 13pi/6, 17pi/6.

There are no solutions to sin 2x = -5  because the range of sin x  is -1 to +1.

So x = pi/12, 5pi/12, 13pi/12, 17pi/12.

To solve the trigonometric equation cos(4x) - 9 sin(2x) + 4 = 0, we can use trigonometric identities and algebraic manipulation. The steps to solve the equation are writing it as a quadratic equation, substituting with sin(x), solving the quadratic equation, and substituting back to solve for x.

To solve the trigonometric equation cos(4x) - 9 sin(2x) + 4 = 0 for 0 to 2pi, we can use trigonometric identities and algebraic manipulation. Here are the steps to solve the equation:

The solutions to the equation will be the values of x that make the equation true.

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Answer:

f[g(6)] = 0

Step-by-step explanation:

f(x) = 6x + 12

g(x) = x - 8

f[g(6)]

First lets find g(6)

g(6) = 6-8 = -2

Then we substitute -2 in for g(6)

Putting -2 into f(x)

f[g(6)] = f(-2) = 6(-2)+12 = -12+12 =0

Answer:

here is

Step-by-step explanation:

Answer:

Option 3 and 4

Step-by-step explanation:

We have to find the solutions represented by point A on graph

The point A is represented by (-6,7i)

Lets check all options one by one

1.

[tex]2(1-2i)-(4+3i)\\= (2-4i)-(4+3i)\\=2-4i-4-3i\\=2-4-4i-3i\\=-2-7i[/tex]

This option is not correct

2.

[tex]2(1+2i)+(-4-3i)\\=(2+4i)-4-3i\\=2+4i-4-3i\\=2-4+4i-3i\\=-2+i[/tex]

This option is also not correct

3.

[tex]2(-1+2i)-(4-3i)\\=(-2+4i)-4+3i\\=-2+4i-4+3i\\=-2-4+4i+3i\\=-6+7i[/tex]

This solution is same as point A so this option is correct

4.

[tex](-2+4i)+(-4+3i)\\=-2+4i-4+3i\\=-2-4+4i+3i\\=-6+7i[/tex]

Solution same as point A so this is correct option.

5.

[tex](-2-4i)+(4-3i)\\=-2-4i+4-3i\\=-2+4-4i-3i\\=2-7i[/tex]

Not correct

The correct options are option no 3 and 4 ..

In the complex plane, complex numbers are represented as points with the real part as the x-coordinate and the imaginary part as the y-coordinate. Therefore, various complex number operations like addition, subtraction, multiplication, or division could result in point A, depending on the specific numbers and operations involved.

To understand which operations involving complex numbers would have solutions represented by point A on a graph, we need to firstly understand that in the complex plane, complex numbers are represented as points. The x-axis corresponds to the real part of the number and the y-axis corresponds to the imaginary part. For example, complex number a + bi would correspond to a point at coordinates (a, b) on the graph.

Various operations involving complex numbers could potentially yield the given point A, such as addition, subtraction, multiplication, or division of two complex numbers. However, without the specific coordinates of point A or other pertinent information (such as the specific complex numbers involved in the operation or the nature of the operation), we cannot definitively say which operation would result in point A output.

For instance, addition of two complex numbers can be visually depicted as adding the vectors for the two numbers together. Depending on what the two initial numbers are, their sum could land at point A.

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7-4x= 31

Bring over 7 to the other side

Positive 7 changes into negative 7

7-7-4x= 31-7

-4x= 24

Divide by -4 for -4x and 24

-4x/-4= 24/-4

x= -6

Check answer by using substitution method

7-4x= 31

7-4(-6)= 31

7+24= 31

31= 31

Answer : C. x= -6

Answer:

C. x = -6

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 7 from both sides:

7 - 4x = 31

7 (-7) - 4x = 31 (-7)

-4x = 31 - 7

-4x = 24

Divide -4 from both sides to isolate the variable, x:

(-4x)/-4 = (24)/-4

x = 24/-4

x = -6

x = -6, or C. is your answer.

~

so we know she has sculptures and paintings, if she sold twice as many paintings as sculptures, that means that for every 2 paintings, she sold 1 sculpture, so the paintings and sculptures are on a 2:1 ratio.

we know she sold a total of 57, so we'll need to split 57 in a 2:1 ratio, we'll simply divide the whole amount of 57 by (2+1) and distribute accordingly.

[tex]\bf \cfrac{paintings}{sculptures}\qquad 2:1\qquad \cfrac{2}{1}\qquad \qquad \cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}\implies \cfrac{2\cdot 19}{1\cdot 19}\implies \cfrac{\boxed{38}}{19}[/tex]

Answer:

10 units

Step-by-step explanation:

Points R and S both have y-coordinate 4, so they are on the same horizontal line. The distance between them is the absolute value of the difference of the x-coordinates.

RS = |-2 - 3| = |-5| = 5

Points S and T both have x-coordinate 3, so they are on the same vertical line. The distance between them is the absolute value of the difference of the y-coordinates.

ST = |-1 - 4| = |-5| = 5

The total length of the trail is the sum of the two distances.

total length = 5 + 5 = 10

Answer:

Step-by-step explanation:

Using the formula for distance, D given 2 coordinates (see attached)

Given

R(-2,4)  S(3,4)   T(3,-1)

Distance RS = √ { [ (-2) -3]² + [4-4]² } = √25 =5 units

Distance ST = √ { [ (3 -3]² + [4-(-1)]² } = √25 = 5 units

Total distance = RS + ST = 5 + 5 = 10 units

Answer:

d. no real solutions

Step-by-step explanation:

3p − 9p² = 6

0 = 9p² − 3p + 6

0 = 3p² − p + 2

The discriminant of ax² + bx + c is b² − 4ac.

If the discriminant is negative, there are no real roots.

If the discriminant is zero, there is 1 real root.

If the discriminant is positive, there are 2 real roots.

If the discriminant is a perfect square, the root(s) are rational.

If the discriminant isn't a perfect square, the root(s) are irrational.

Finding the discriminant:

a = 3, b = -1, c = 2

(-1)² − 4(3)(2) = -23

The discriminant is negative, so there are no real roots.

Final answer:

After rewriting the equation 3p-9p²=6 in standard quadratic form and calculating the discriminant, we find that the discriminant is negative, indicating the equation has d. no real solutions.

Explanation:

To determine the number and type of solutions the equation 3p-9p²=6 has using the discriminant, we first need to rewrite the equation in standard quadratic form, which is ax² + bx + c = 0. Moving all terms to one side gives us -9p² + 3p - 6 = 0, where a = -9, b = 3, and c = -6. The discriminant of a quadratic equation is defined as b² - 4ac.

A discriminant greater than zero indicates two real solutions, equal to zero indicates one real solution, and less than zero indicates no real solutions. Calculating the discriminant for our equation: (3)² - 4(-9)(-6)=9-216=-207, which is less than zero. Therefore, the equation -9p²+ 3p - 6 = 0 has d. no real solutions.

Answer:

20 movies

Step-by-step explanation:

no of movies= 80

action movies percentage=25%

no of action movies=25/100*80(25% of 80)

Answer:

Step-by-step explanation:

The most general form of this, without seeing any of the options, would be:

[tex]y=(x+3)^2+6[/tex]

Again, there might have been a value outside the parenthesis that may or may not have been negative, but either way, this is the most basic translation of the parabola.

Answer: Choice D

Step-by-step explanation: Why? Because (d-21) is what how many days she was late. The problem is asking what (d-21) presents and Choice D says 'The number of days the book is late'. If the problem did have the 0.10 before (d-21) THEN it would've been Choice C.

In the expression 0.10(d-21), the term (d-21) represents the number of days the book is late, beyond the initial 21-day borrowing period.

The expression (d-21) in the context of the late fee calculation represents the number of days the book is late. Since the library charges a late fee only if the book is returned more than 21 days after it was borrowed, subtracting 21 from the total days borrowed, which is represented by 'd,' gives us the number of days Camilla returned the book late. Multiplying this by the per-day late fee of $0.10 gives us the total late fee owed.

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Answer:

7/4

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

To answer this, take the negative reciprocal of -7/4, obtaining 4/7.  

seventy five thousand

Answer:

Step-by-step explanation:

I can't add much to this. The answer is 75 thousand.

Answer:

see explanation

Step-by-step explanation:

Using the identity

(a + b + c)³ = a³ + b³ + c³ + 3 [ (a + b + c)(ab + bc + ac) - abc ], then

5³ = a³ + b³ + c³ + 3(5 × 10) - 3abc, that is

125 = a³ + b³ + c³ + 150 - 3abc, hence

a³ + b³ + c³ - 3abc = 125 - 150 = - 25

Using the cubic identity equation and the values given in the question, we can prove that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc equals -25.

The equation required to prove is derived from the expansion of the cubic identity (a+b+c)³. The equation is a³+b³+c³-3abc = (a+b+c)[(a+b+c)²-3(ab+bc+ac)]. Let's use the values given in the question which are (a+b+c) = 5 and ab+bc+ac = 10.

Therefore, we have proved that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc indeed equals -25.

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Answer:

C. x =3

Step-by-step explanation:

Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.

Let's solve the equation first

[tex]\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6[/tex]

Hence, we can conclude that x=3 is an extraneous solution of the equation ..

Answer:

C

Step-by-step explanation:

Answer:

f(x) = 0.2x - 4  (incorrect)

f(x) = 0.5x + 2  (correct)

f(x) = 1/2x + 2      (correct)

y – 3 = 1/2(x – 2)     (correct)

y – 1 = 0.5(x + 2)

Step-by-step explanation:

Step 1 : Find two coordinates

(0, 2) (-4, 0)

Step 2 : Find the slope

Slope = m = Y2-Y1/X2-X1

m = 0-2/-4-0

m = -2/-4

m = 1/2 or 0.5

Step 3 : Find the y-intercept

Y-intercept is where the line intersects the y-axis

c = 2

Step 4 : Form the equation y=mx + c

Given Equations and their slope intercept forms:

1) f(x) = 0.2x - 4

This is incorrect because slope is 1/2 or 0.5 and y intercept is 2

2) f(x) = 1/2x + 2

y = 1/2x + 2

This is correct because slope is 1/2 or 0.5 and y intercept is 2

3) f(x) = 0.5x + 2

y= 0.5x + 2 (As m=0.5)

This is correct because slope is 1/2 or 0.5 and y intercept is 2

4) y – 3 = 1/2(x – 2)

Rearranging in slope intercept form:

y-3=1/2x - 1

y = 1/2x-1+3

y = 1/2x + 2

This is correct because slope is 1/2 or 0.5 and y intercept is 2

5) y – 1 = 0.5(x + 2)

y -1 = 0.5x+1

y = 0.5x +1+1

y = 0.5x + 2

This is correct because slope is 1/2 or 0.5 and y intercept is 2

!!

first off, let's notice something on this line, the graph touches the y-axis at 2, namely when x = 0, y = 2, so that's the y-intercept for this line.

now, let's notice something else, as the line moves from x = -4, to the right towards x = 0, the run is 4 units, the rise is 2 units, so its slope is rise/run or  2/4 or 1/2, that said, that gives us an equation of

[tex]\bf y=\cfrac{1}{2}x+2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\implies y=0.5x+2[/tex]

[tex]\bf y-3 = \cfrac{1}{2}(x-2)\implies y-3=\cfrac{1}{2}x-1\implies y=\cfrac{1}{2}x+2\qquad \textit{\Large\checkmark} \\\\\\ y-1=0.5(x+2)\implies y-1=0.5x+1\implies y=0.5x+2\qquad \textit{\Large\checkmark} \\\\\\ f(x) = 0.2x-4\qquad \bigotimes[/tex]

Answer:

$30 down  

and 10 installments of $10 each

Step-by-step explanation:

paying $30 down means the left price to divide into installments is : 130-30 = 100

since he will pay the rest in equal installments, we divide  by the number of installments to get how much each one will be :

100/10 = $10

Answer:

(X - 4)(x - 4)

Step-by-step explanation:

x2 - 8x + 16

What two numbers multiply to 16 and add to -8

-4 * -4 = 16

-4 +-4 = -8

(x-4) (x-4)

(x-4)^2

Answer:

B

Step-by-step explanation:

(x - 4)(x - 4)

To find the area, you multiply b×h. (Base × height) b=20 and h=9. Multiply it and you will get 180. The answer is 180 cm².

The area of the parallelogram is equal to 180 square meters.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called as the area of the parallelogram.

Given that a parallelogram has a base of 20 cm and a height of 9 cm. The area of the parallelogram is calculated by the formula,

Area of the parallelogram = Base x Height

Area of the parallelogram = 20 x 9

Area of the parallelogram = 180 square meters

Therefore, the area of the parallelogram is equal to 180 square meters.

To know more about an area follow

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