In the image, point A is the center of the circle. Which two line segments must be equal in length?

Step-by-step explanation:

X-2y=5 ; 2x-4y=10

• x - 2y = 5 • 2x -4y = 10

-2y = -x+5 -4y= -2x +10

y1 = ½x - 5/2 y2 = ½x -5/2

• => y1 = y2

½x -5/2 = ½x -5/2

the systems have no solution

• graph as attached

Answer:

[tex]\textsf{Equation 1}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]

[tex]\textsf{Equation 2}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]

True for all x (infinitely many solutions)

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]y = mx + b[/tex]

(where m is the slope and b is the y-intercept)

Given equations:

[tex]\begin{cases}x-2y=5\\2x-4y=10\end{cases}[/tex]

To put both equations in slope-intercept form, rearrange both equations to make y the subject:

Equation 1

[tex]\implies x-2y=5[/tex]

[tex]\implies x-2y+2y=5+2y[/tex]

[tex]\implies x=5+2y[/tex]

[tex]\implies x-5=5+2y-5[/tex]

[tex]\implies 2y=x-5[/tex]

[tex]\implies 2y \div 2=(x-5) \div 2[/tex]

[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]

Equation 2

[tex]\implies 2x-4y=10[/tex]

[tex]\implies 2x-4y+4y=10+4y[/tex]

[tex]\implies 2x=10+4y[/tex]

[tex]\implies 2x-10=10+4y-10[/tex]

[tex]\implies 4y=2x-10[/tex]

[tex]\implies 4y \div 4=(2x-10) \div 4[/tex]

[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]

Therefore, both equations are the same as they have the same slope and y-intercept.

As both equations are the same, this system of equations is called an equivalent system.

To solve a system of equations by substitution, substitute one equation into the other:

[tex]\implies \dfrac{1}{2}x-\dfrac{5}{2}= \dfrac{1}{2}x-\dfrac{5}{2}[/tex]

As both sides are equal, the solution is true for all x.

The solution to a graphed system of equations is the point(s) of intersection.

When graphing the given system of equations, as the lines are the same, they will be on top of each other. They are called coincident lines and have infinitely many solutions since the lines have the same slope and same y-intercept.

Learn more about systems of equations here:

https://brainly.com/question/21447811

https://brainly.com/question/27357423

Answer:

a = -2

Step-by-step explanation:

Given that,

-1 is a zero of the polynomial. i.e. x = -1.

The polynomial is :

p(x) = ax²-x²+x+4

We need to find the value of a.

Put x = -1 in the above polynomial.

p(1) = a(-1)²-(-1)²+(-1)+4

For zeroes,

p(1) = 0

a(-1)²-(-1)²+(-1)+4 = 0

a-1-1+4 = 0

a = -2

So, the value of a is equal to -2.

Answer:

Always

Assumption:

At least how I know it.

Answer:

1. 5.75 * 33 = $189.75

The bakers income is $189.75

2. 2 * y - 8 / 4 when y = 7

  2 * 7 - 8 / 4 = 12

3. 76 + 4 * y^2 + 1 when y = 3

   76 + 4 * 3^2 + 1 = 113

Answer:

Has a slope of [tex]\frac{3}{4}[/tex] and passes through the point (0,1)

Step-by-step explanation:

We can eliminate half the answer choices by finding whether the line passes through (1,0) or (0,1). Coordinates are read as (x,y), therefore the line passes through (0,1). The slope of the line y=x has a slope of 1. Looking at the graph, we can see that the increasing interval of the line is tilted down ever so slightly, therefore the slope must be less than one.

Therefore, the answer is has a slope of [tex]\frac{3}{4}[/tex] and passes through the point (0,1).

Answer:

Its C, or the third option.

Step-by-step explanation:

Rise/run on this graph is 3/4

and y-intercept is (0, 1)

so C, or third option is correct.

Answer:

f(x) = - 2(x - 3)² + 2

Step-by-step explanation:

Given

f(x) = - 2x² + 12x - 16 ( factor out - 2 from the first 2 terms )

      = - 2(x² - 6x) - 16

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = - 2(x² + 2(- 3)x + 9 - 9) - 16

     = - 2(x - 3)² + 18 - 16

     = - 2(x - 3)² + 2

Answer:

AB ≈ 2.62 cm

Step-by-step explanation:

The arc AB is calculated as

AB = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{15}{360}[/tex]

     = 2π × 10 × [tex]\frac{1}{24}[/tex]

     = [tex]\frac{20\pi }{24}[/tex]

     ≈ 2.62 cm ( to the nearest hundredth )

Answer:

y = (1/2)x - 2

Step-by-step explanation:

Slope intercept form: y = mx + c

x - 2y = 4

    -2y = -x + 4

[tex]\frac{-2y}{-2}=\frac{-x}{-2}+\frac{4}{-2}\\\\y = \frac{1}{2}x - 2[/tex]

Answer:.

Answer:1.we have dividend =divisor*quotient+remainder=

(x²+2x-1)(x²-2x+1)+(-4x+1)

=x²(x²-2x+1)+2x(x²-2x+1)-1(x²-2x+1)-4x+1

=x⁴-2x³+x²+2x³-4x²+2x-x²+2x-1-4x+1

=x⁴-4x²

Dividend is x⁴-4x².

2.

Multiplier is a-a²+1.

Answer:

[tex]i \: hope \: the \: above \: picture \\ helps[/tex]

[tex]have \: a \: nice \: day \: [/tex]

[tex]#Liliflim[/tex]

Answer:

b = 6 sqrt(2)

Step-by-step explanation:

Since this is right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

3^2 + b^2 = 9^2

9+b^2 = 81

b^2 = 81-9

b^2 = 72

Take the square root of each side

sqrt(b^2) = sqrt(72)

b = sqrt(36*2)

b = 6 sqrt(2)

The answer:

(x+2)²+(y–1)²=9

Answer:

4f + 3g

Step-by-step explanation:

g + 3f + f + g + g

3f + f = 4f

g + g = 2g + g = 3g

4f + 3g

Answer:

5.97

Step-by-step explanation:

Answer:

5.97

Step-by-step explanation:

5.946 = 5.94

5.97>5.94

Answer:

cot(x)=-sqrt(3)/3

Step-by-step explanation:

I'm going to use the Pythagorean Identity sin^2(x)+cos^2(x)=1 to find the sine value since cotangent value is the cosine value over sine value.

Plug in:

sin^2(x)+(-1/2)^2=1

Simplify:

sin^2(x)+1/4=1

Subtract 1/4 on both sidea:

sin^2(x)=3/4

Square root both sides:

sin(x)=sqrt(3)/2. [Sine is positive since x is in 2nd quadrant]

cot(x)=(-1/2)/(sqrt(3)/2))

cot(x)=-1/sqrt(3)

Rationalize denominator by multiplying by sqrt(3)/sqrt(3):

cot(x)=-sqrt(3)/3

cot(x)=

======================================================

Explanation:

Think of 25 as 25/1 and 5 as 5/1

Choice E is really saying [tex]\frac{25}{1} \div \frac{5}{1}[/tex] which becomes [tex]\frac{25}{1} \times \frac{1}{5}[/tex]. Note the second fraction flips and we change to a multiplication sign.

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

Or you could think of it like this:

[tex]25 \times \frac{1}{5} = \frac{25}{1} \times \frac{1}{5} = \frac{25*1}{1*5} = \frac{25}{5} = 25 \div 5[/tex]

to help see why the answer is E.

Answer:

E

Step-by-step explanation:

Answer:

[tex]Q_3 = 56.45[/tex] --- The third quartile

[tex]Var = 370.18[/tex] -- Variance

Step-by-step explanation:

Given

[tex]Q_1 = 30.8[/tex] -- First quartile

[tex]Q_2 = 48.5[/tex] --- Median

[tex]\bar x = 42[/tex] --- Mean

[tex]Skp = -0.38[/tex] --- Coefficient of skewness

Solving (9): The third quartile [tex]Q_3[/tex]

This is calculated from

[tex]Skp = \frac{Q_1 + Q_3 - 2Q_2}{Q_3 - Q_1}[/tex]

So, we have:

[tex]-0.38 = \frac{30.8 + Q_3- 2*48.5}{Q_3 - 30.8}[/tex]

Cross Multiply

[tex]-0.38 (Q_3 - 30.8)= 30.8 + Q_3- 2*48.5[/tex]

Open bracket

[tex]-0.38Q_3 + 11.704= 30.8 + Q_3- 97.0[/tex]

Collect like terms

[tex]-0.38Q_3 -Q_3= 30.8 - 97.0- 11.704[/tex]

[tex]-1.38Q_3= -77.904[/tex]

Divide both sides -1.38

[tex]Q_3 = \frac{-77.904}{-1.38}[/tex]

[tex]Q_3 = 56.45[/tex] --- approximated

Solving (b): The variance

First, calculate the standard deviation from:

[tex]3IQR = 4SD[/tex]

[tex]IQR= Q_3 - Q_1[/tex]

So:

[tex]3IQR = 4SD[/tex]

[tex]3(Q_3 - Q_1) = 4SD[/tex]

Make SD the subject

[tex]SD = \frac{3}{4}(Q_3 - Q_1)[/tex]

[tex]SD = \frac{3}{4}(56.45 - 30.8)[/tex]

[tex]SD = \frac{3}{4}*25.65[/tex]

[tex]SD = \frac{3*25.65}{4}[/tex]

[tex]SD = \frac{76.95}{4}[/tex]

[tex]SD = 19.24[/tex]

So, the variance is:

[tex]Var = SD^2[/tex]

[tex]Var = 19.24^2[/tex]

[tex]Var = 370.18[/tex]

Answer:

a) (-1,4.5)

b)10.63 units

c)7/8

Step-by-step explanation:

a) To find this, we use the midpoint formula

(x,y) = (x1 + x2)/2 , (y1 + y2)/2

(x1,y1) = (3,8)

(x2,y2) = (-5,1)

(x,y) = (3 -5)/2 , (8 + 1)/2 = (-1, 4.5)

b) To calculate the distance D between two points, we use the formula;

D = √(x2-x1)^2 + (y2-y1)^2

D = √(-5-3)^2 + (1-8)^2

D = √(-8)^2 + (-7)^2

D = √64 + 49

D = √113

D = 10.63 units

C) We use the slope formula here

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

m = (1-8)/(-5-3) = -7/-8 = 7/8

Answer:

[tex] {x}^{0} y + 9 \\ = y + 9[/tex]

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

We require the fractions to have the same common denominator

The LCM of 4 and 3 is 12 , then

[tex]\frac{3(3)}{4(3)}[/tex] - [tex]\frac{2(4)}{3(4)}[/tex]

= [tex]\frac{9}{12}[/tex] - [tex]\frac{8}{12}[/tex]

= [tex]\frac{1}{12}[/tex]

The formula for the circumference of a circle is 2 x 3.14 x radius

2 x 3.14 x 6 = 37.68

Answer:

answer is 1

Step-by-step explanation:

3 and 3 gets cancel .when you divide the same number answer is always 1

Answer:

100+0.30p

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

I think the answer is 11 because 244140625/(5^3*5^(-2)*5^11)

m=11

[tex] \huge \bf\pink{a} \purple{n} \pink{s} \purple{w} \pink{e} \purple{r}[/tex]

[tex]5m = 60 \\ m = \frac{60}{5} = 12[/tex]

Answer:

lincth times with times hight

Step-by-step explanation:

Cubcivtiv tyk ok givyog Answer: gg

Step-by-step explanation:

Answer:

Of is a keyword for multiplication.

So, your equation is really 2 X 1,800,000÷3=?

Final answer: 1,200,000

Step-by-step explanation:

Hope that this helps! :)

Have a great rest of your day/night!