Factor the expression below x^2-12x+36

In a 30-60-90 triangle, the longer leg is sqrt(3) times the hypotenuse. Therefore, the correct ratios provided are A. sqrt(3) : 2 and D. 3sqrt(3) : 6, with the latter simplifying to the correct ratio when reduced.

The ratio of the length of the longer leg to the hypotenuse in a 30-60-90 triangle is determined by the properties of this special right triangle. In such a triangle, the sides are in a fixed ratio: the shorter leg is 1 times the length of the hypotenuse, the longer leg is sqrt(3) times the length of the hypotenuse, and the hypotenuse itself is 2 times the length of the shorter leg.

Using this knowledge, we can evaluate the options given:

Options B, C, E, and F do not represent the correct ratio of the longer leg to the hypotenuse of a 30-60-90 triangle. Therefore, options A and D are correct.

Answer:

46

Step-by-step explanation:

Replace k with (-8)

30-2(-8)    Substitution

30-(-16)     Multiplication 2(-8)=-16

30+16        

46              

Answer: The answer is 46

Step-by-step explanation: If you plug in -8 for k in the problem 30-2k then multiply -8 by 2 you get -16. Then you have to do 30 - -16 which results in 46.

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

When we have a point (a,b) on the unit circle, we can say that

[tex]a^2+b^2=1[/tex]

This is a property of the unit circle.

From the point given  [tex](x,\frac{\sqrt{3} }{2})[/tex] , now we can write the equation shown below and solve for x:

[tex]x^2+(\frac{\sqrt{3} }{2})^2=1\\x^2+\frac{3}{4}=1\\x^2=1-\frac{3}{4}\\x^2=\frac{1}{4}\\x=\frac{\sqrt{1}}{\sqrt{4} } \\x=\frac{1}{2}[/tex]

So, x = 1/2

Answer: x = 1/2

Step-by-step explanation:

We have that the point (x, (√3)/2)) is on the unit circle.

we can define a circle of radius R centered in the (0,0) as:

x^2 + y^2 = R^2

This means that:

x^2 + (√(3)/2)^2 = 1

x^2 + 3/4 = 1

x^2 = 1 - 3/4 = 1/4

x = √(1/4) = 1/2

So we have that x is equal to 1/2

Answer:You haven't attached a picture but this is what your line should look like

Step-by-step explanation:

For this equation you simply have to graph it.

First, you have to remember that these equations follow a formula: y=mx+b. m is the slope of you line and b is the y-intercept.

Next, you need to graph it. First, graph your b, in this case 2. You would go up 2 on you graph (graph (0,2)). Then, you would graph your slope which is 3.

Now, remember that slope equals y/x, so think of the number 3 being like 3/1. You would start at (0,2) and go up 3 points in the graph, then over 1 point (graph where you end up). You repeat that from each new point you make until you have enough points to create a straight line.

Hope this helps a bit,

Flips

Answer:

is there a graph

Step-by-step explanation:

Answer:

The statement most accurately describes the relationship between

segments of the triangles formed by the beam is AC < DF

Step-by-step explanation:

* Lets study the figure to answer the problem

- There are two triangles ABC and DEF

- AB = BC

- DE = EF

- AB = DE

∴ AB = BC = DE = EF

- m∠ABC = 45°

- m∠DEF = 60°

∵ The measure of angle ABC is smaller than the measure of

   angle DEF

∴ The opposite side to the angle ABC is shorter than the opposite

   side of angle DEF

∵ AC is the opposite side to angle ABC

∵ DF is the opposite side to angle DEF

∴ AC is shorter than DF

∴ DF > AC

∴ AC < DF

* The statement most accurately describes the relationship between

  segments of the triangles formed by the beam is AC < DF

Answer:

21.99 units

164.93 units²

Step-by-step explanation:

given radius r = 15 units

angle of sector = 84°

Length of sector = [tex]\frac{84}{360}[/tex] x 2 x π x r

= [tex]\frac{84}{360}[/tex] x 2 x 3.14 x 15

= 21.99 units

Area of sector = [tex]\frac{84}{360}[/tex] x π x r²

= [tex]\frac{84}{360}[/tex] x 3.14 x 15²

= 164.93 units²

for similar shapes, their corresponding sides will form the same proportion or ratio for any pair of corresponding sides, now, let's check the ratio of each corresponding side on these two.

[tex]\bf \cfrac{\textit{small triangle}}{\textit{large triangle}}\qquad \qquad \cfrac{12}{45}\implies \cfrac{4}{15}~\hfill \cfrac{25}{75}\implies \cfrac{1}{3}~\hfill \cfrac{15}{36}\implies \cfrac{5}{12} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{the triangles are \underline{not} similar}}{\cfrac{4}{15}\ne \cfrac{1}{3}\ne \cfrac{5}{12}}~\hfill[/tex]

Answer:

(1,1);(11,1);(6,6);(6-4)

Step-by-step explanation:

The easiest way to do is add or subtract 5 to the x or y value.

The answer is:

The solutions to the system of equations are:

[tex]x=0\\y=1\\z=0[/tex]

To solve the system of equations by the easiest way, we need to use the reduction method. The reduction method consist of reducing the variables applying different math operations in order to be able to isolate the variables.

So, we are given the system:

[tex]4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3[/tex]

Let's work with the first and the third equation:

[tex]4x+3y+6z=3\\6x+3y+6z=3[/tex]

Then, multiplying the first equation by -1, we have:

[tex]-4x-3y-6z=-3\\6x+3y+6z=3[/tex]

[tex]-4x+6x-3y+3y-6z+6z=-3+3[/tex]

[tex]2x=0[/tex]

[tex]x=0[/tex]

Now, working with the first and the second equation, we have:

[tex]4x+3y+6z=3\\5x+5y+6z=5[/tex]

Then, multiplying the first equation by -1, we have:

[tex]-4x-3y-6z=-3\\5x+5y+6z=5[/tex]

[tex]5x-4x+5y-3y-6z+6z=-3+5[/tex]

[tex]x+2y=2[/tex]

Then, substituting "x" into the equation, we have:

[tex]0+2y=2[/tex]

[tex]y=\frac{2}{2}=1[/tex]

Finally, working with the first equation and substituting "x" and "y", we have:

[tex]4x+3y+6z=3[/tex]

[tex]4*0+3*1+6z=3[/tex]

[tex]0+3+6z=3[/tex]

[tex]6z=3-3=0[/tex]

[tex]6z=0[/tex]

[tex]z=\frac{0}{6}=0[/tex]

Hence, we have that the solutions to the system of equations are:

[tex]x=0\\y=1\\z=0[/tex]

Have a nice day!

Answer:

[tex]x=0\\y=1\\z=0[/tex]

Step-by-step explanation:

Multiply the first equation by -1:

[tex](-1)(4x+3y+6z)=3(-1)\\\\-4x-3y-6z=-3[/tex]

Add the new equation and the third equation an solve for "x":

[tex]\left \{ {{-4x-3y-6z=-3\ \atop {6x+3y+6z=3} \right.\\...........................\\2x=0\\x=0[/tex]

Substitute the value of "x" into the first equation and solve for "y":

[tex]4(0)+3y+6z=3\\\\3y=3-6z\\\\y=\frac{3-6z}{3}\\\\y=1-2z[/tex]

Substitute the value of "x" and [tex]y=1-2z[/tex] into the second equation and solve for "z":

[tex]5(0)+5(1-2z)+6z=5\\\\5-10z+6z=5\\\\-4z=0\\\\z=0[/tex]

Knowing the values of "x" and "z", you can substitute them into any original equation and solve for "y". Then:

[tex]4(0)+3y+6(0)=3\\\\3y=3\\\\y=\frac{3}{3}\\\\y=1[/tex]

Hello!

The answer is 127,000%

The statement that best describes the spread of these data is 79 is an outlier, which would affect the standard deviation of these data

An outlier is a piece of data that is an abnormal distance from other points.

In other words, an outlier is any value that is numerically distant from most of the other data points in a set of data.

The outlier in the set of data is 79 because it is quite distance from the other numerical value

Generally, outliers significantly affects the standard deviation of data.

Therefore, 79 is an outlier, which would affect the standard

deviation of these data

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Answer:

Option D.

Step-by-step explanation:

Given: See the diagram.

Prove: DC = DB

Perpendicular bisector theorem : If a point lies on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.

Proof:

Statement 1:  [tex]\overleftrightarrow{DG}\perp \overline{AC}[/tex]

Reason: Given.

Statement 2: AG=GC

Reason: Given

Statement 3: [tex]\overleftrightarrow{DG}[/tex] is perpendicular bisector of [tex]\overline{AC}[/tex].

Reason: Deduced from steps 1 and 2

Statement 4: DA=DC

Reason: Perpendicular bisector theorem

Statement 5: [tex]\overleftrightarrow{DH}\perp \overline{AB}[/tex]

Reason: Given

Statement 6:AH=HB

Reason:Given

Statement 7: [tex]\overleftrightarrow{DH}[/tex] is perpendicular bisector of [tex]\overline{AB}[/tex].

Reason: By definition of perpendicular bisector.

Statement 8: DA=DB

Reason : Perpendicular bisector theorem

Statement 9: DC=DB

Reason: Transitive property of equality.

Hence proved.

Therefore, the correct option is D.

Answer:

8

Step-by-step explanation:

Plug in a =4 and b=3 into  6+4/a +b/3

6 + 4/4 + 3/3

= 6 + 1 + 1

= 8

Answer:

The answer would be 8.

Step-by-step explanation:

Here the given expression,

[tex]6+\frac{4}{a}+\frac{b}{3}[/tex]

By substituting a = 4 and b = 3 in the above expression,

We get,

[tex]6+\frac{4}{4}+\frac{3}{3}[/tex]

[tex]=6+1+1[/tex]

[tex]=8[/tex]

Therefore, the value of the given expression would be 8.

Answer: use a ruler and measure each side multiply by 30 then multiply all of them by each other

hope this helps and if I'm wrong hope you for give me here is some memes

Answer:

50 degrees

Step-by-step explanation:

since angle bac is bisected, bae and eac are equal measurement. therefore:

x+30 = 3x-10

now isolate the variable

x-3x=-10-30

-2x=-40

2x=40

x=20

mEAC =3x-10

=3(20)-10

60-10

=50

this can be proven because BAE is the same measurement as EAC (because of the bisector): x +30

20+30

=50

Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

[tex]\frac{7\pi }{6}[/tex] is an angle in the third quadrant

To find the reference angle subtract π from it

reference angle = [tex]\frac{7\pi }{6}[/tex] - π = [tex]\frac{\pi }{6}[/tex]

Answer:

Option C [tex]-7x-5y=-48[/tex]

Step-by-step explanation:

step 1

Find the slope of AB

we have

A(-3,-1) and B(4,4)

The slope m is equal to

[tex]m=(4+1)/(4+3)[/tex]

[tex]m=5/7[/tex]

step 2

Find the slope of BC

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

[tex]m1*m2=-1[/tex]

we have

[tex]m1=5/7[/tex]

substitute

[tex]5/7*m2=-1[/tex]

[tex]m2=-7/5[/tex]

step 3

Find the equation of the line into slope point form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-7/5[/tex]

[tex]B(4,4)[/tex]

substitute

[tex]y-4=-(7/5)(x-4)[/tex]

Multiply by 5 both sides

[tex]5y-20=-7x+28[/tex]

[tex]7x+5y=28+20[/tex]

[tex]7x+5y=48[/tex]

Multiply by -1 both sides

[tex]-7x-5y=-48[/tex]

The slope-intercept form of the equation for this line is y = 58x + 460.

Given:

Slope (m) = 58

Point [tex](x_1, y_1)[/tex] = (-8, -4)

Using the point-slope form of the equation, which is

[tex](y - y_1) = m(x - x_1)[/tex]

Substitute the values into the equation:

(y - (-4)) = 58(x - (-8))

(y + 4) = 58(x + 8)

To convert this equation into slope-intercept form

y + 4 = 58x + 464

y = 58x + 464 - 4

y = 58x + 460

Therefore, the slope-intercept form is y = 58x + 460.

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Answer:

Step-by-step explanation:

Assuming the problem is: 3/4  x +5/8=4x

Or .75 x+5/8=4x

Subtract .75 on both sides: 5/8=3.25x

Then divide both sides by 3.25:       (5/8)/3.25=x

So x=5/26

Step-by-step explanation:

hihi, so given a statistic, a sample standard deviation, and the sample size, we can create a 99% confidence interval for this distribution. Given the equations for confidence interval and Margin of Error, all we have to calculate initially is t* (invT(.995, 85-1)) and Standard error (34/sqrt(85)). Once we have these numbers, it's as easy as plugging in and doing some simple calculations to reaching our upper and lower fences of our interval. (136.28, 155.72). Any value below the lower fence or any value above the upper fence is not in our interval

The 99% confidence interval for the given random sample is between 136.5 and 155.5. The critical value for a 99% of confidence interval is 2.58.

The formula for the confidence interval is

C.I = μ ± Margin error

Where Margin error = critical value × Standard error and μ - mean

Standard error = δ/[tex]\sqrt{n}[/tex]

δ - standard deviation and n is the sample space.

The critical value (z) is obtained from the percentage confidence interval table.

Given that,

Sample space n = 85

Mean μ = 146 and δ = 34

Calculating the standard error:

S.E = δ/[tex]\sqrt{n}[/tex]

      = 34/√85

      = 3.68

The critical value for the 99% of the confidence interval is 2.58

Calculating the Margin error:

Margin error = 2.58 × 3.68

                     = 9.49

                     = 9.5

Then the 99% of the confidence interval is calculated as follows:

C.I = μ - Margin error (lower interval)

    = 146 - 9.5

    = 136.5

C.I = μ + Margin error (upper interval)

    = 146 + 9.5

    = 155.5

Thus, the 99% confidence interval is 136.5 - 155.5.

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Answer:

Step-by-step explanation:

//  12

// -12

//-11

//88

[tex]\bf \begin{cases} f(x)=2x+3\\ g(x)=x^2+1 \end{cases}\qquad \qquad g(3)=(3)^2+1\implies g(3)=\boxed{10} \\\\\\ f(~~g(3)~~)\implies f\left( ~~\boxed{10}~~ \right)=2(10)+3\implies \stackrel{f(g(3))}{f(10)}=23[/tex]

Answer:

There is a 1/64 possibility.

Step-by-step explanation:

Since the probability of selecting student 1's number is 1/8 and then replacing it leaves us with still 8 numbers to choose from, so student 8's probability of being selected is also 1/8. Multiplying these two gives P=1/64, since (1/8)^2 = 1/64.

Hope this helps!

Answer:

1/64 possibility

Explanation:

Multiply the numbers by the number of students(8x8) to get 64. That means there is 1 in 64 chances. 1/64

have a great day

Answer:

x = 1.25

y = 0.75

Step-by-step explanation:

Let $x be the cost per pound of apples

Let $y be the cost per pound of bananas

5x + 3y = 8.5  --- (1)

3x + 2y = 5.25  --- (2)

From (1),

3x + 1.8y = 5.1  --- (1a)

Subtract (1a) from (2),

(3x + 2y) - (3x + 1.8y) = 5.25 - 5.1

3x - 3x + 2y - 1.8y = 0.15

0.2y = 0.15

y = 0.15 / 0.2 = 0.75

x = [ 5.25 - 2(0.75) ] / 3 = 1.25

The coordinates of the roots of the given quadratic equation x^2 + 4x + 3 = 0 are -1 and -3.

The given equation is a quadratic equation in the form of ax² + bx + c = 0, where a = 1, b = 4, and c = 3. To find the coordinates of the roots, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the given values, we get:

x = (-4 ± √(4² - 4(1)(3))) / (2(1))

Simplifying further, we have:

x = (-4 ± √(16 - 12)) / 2

x = (-4 ± √4) / 2

x = (-4 ± 2) / 2

Therefore, the two roots of the equation are:

x₁ = (-4 + 2) / 2 = -1

x₂ = (-4 - 2) / 2 = -3

Hello There!

14 + 5x - 40 = -36

5x - 26 = -36

5x = -10

x = -2

Answer:

Step-by-step explanation:

14+4(x-8)=-36

19(x-8)=-36

x-8= -36-19

-8x=-55

6.875

Answer:

[tex]x=8.1[/tex]

Step-by-step explanation:

we have that

[tex]tan(48\°)=\frac{9}{x}[/tex]

Solve for x

[tex]x=\frac{9}{tan(48\°)}[/tex]

[tex]x=8.1[/tex]

Answer:

3

Step-by-step explanation:

7÷2 hope this is the correct answer enjoy this help.