Determine the length of AB. Write your answer in simplest form.

Answer:

x = 25

Step-by-step explanation:

The mistake here is the squaring. When you square one side, you have to do the same on the other side:

[tex]\sqrt{3x+6}[/tex] = 9

[tex](\sqrt{3x+6}) ^{2}[/tex] = [tex]9^{2}[/tex]

3x + 6 = 81

3x = 75

x = 25

[tex]\huge\boxed{x=25}[/tex]

The mistake is in Step 1. The solver should have also squared [tex]9[/tex] when squaring the other side of the equation.

[tex]\begin{aligned}\sqrt{3x+6}&=9\\(\sqrt{3x+6})^2&=9^2\\3x+6&=81\\3x+6-6&=81-6\\3x&=75\\\frac{3x}{3}&=\frac{75}{3}\\x&=25\end{aligned}[/tex]

Step-by-step explanation:

The expression square root of 25/49 can be given as 5/7

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is the non equal comparison of two or more numbers and variables.

The solution to the system of inequalities x – 4y < 4 and y < x + 1 is shown in the graph.

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Answer:

its c

Step-by-step explanation:

The statement which the diagram shows is that the length of GH is half of the length of KL . Option B

The midsegment theorem holds that any segment that forms the joining midpoints of two sides of a triangle is parallel to half the length of the third side.

It can be seen that the length of GH is half of the length of KL as deduced from the diagram

Therefore, the statement which the diagram shows is that the length of GH is half of the length of KL . Option B

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The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

An equation is an expression that shows the relationship between two or more variables and numbers.

Step 1:

ax² + bx + c = 0

Step 2:

ax² + bx = -c

Step 3:

x² + (b/a)x = -c/a

Step 4:

x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

The next step to derive the quadratic formula is x² + (b/a)x + (b²/2a²)= -c/a + (b²/2a²)

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Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

We know that the sum of angles of a triangle is always. In ΔXYZ,

[tex]\angle A + \angle B + \angle C=180^0[/tex]

[tex]35^0+\angle Y+47^0=180^0[/tex]

[tex]\angle y=98^0[/tex]

In both triangles, it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A=\angle X=35^0[/tex]and.[tex]\angle B = \angle Y =98^0[/tex]

By the AAS rule of congruence, ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having the same angle and rotate the triangle to align the sides and angles.

Since vertex X and vertex A have the same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.

Hence the correct option is d.

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Answer:

D: Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

Step-by-step explanation:

edge 2022

Answer:

a = 8.1

Step-by-step explanation:

Use the cosine rule:

[tex]a = \sqrt{b^2 + c^2 -2 bc \space\ cosA }[/tex]

Substituting the values:

[tex]a = \sqrt{10^2 + 12^2 -2(10)(12) \space\ cos 42 \textdegree\ }[/tex]

⇒ [tex]a = \sqrt{4 \space\ cos 42\textdegree\ }[/tex]

⇒ [tex]a = 8.1[/tex]

Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.

Which composition of transformations will create a pair of similar, not congruent triangles?

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.

Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.

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Answer:

D. a rotation, then a dilation

Step-by-step explanation:

got it right on edge 23

Answer: 20

Step-by-step explanation:

     We will set up a proportion to solve.

[tex]\displaystyle \frac{?}{16}=\frac{15}{12}[/tex]

   Now, we will cross-multiply.

12 * ? = 16 * 15

12? = 240

? = 20

Answer:

Step-by-step explanation:

4.8 x 10^3   heartbeats/day

Answer: A humans heart average per minute is 80 then you got one hour 60 x 80 equals 4800

which would be 4.8x 10 over 3 which is your answer

Step-by-step explanation:

Some habits that you can engage in that would increase your risk of being victim of fraud or identity theft are:

You can be less at risk of fraud or identity theft if you:

When you use the same password for various accounts, all those accounts are at risk if the password is stolen. So using multiple passwords is best.

You should also regularly monitor your credit card statements and bank reports to check for unfamiliar expenses which can be flagged immediately.

Also update your apps regularly as they come with security patches to protect your data. Avoid sharing too much information on social media as these can be used to predict your passwords.

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Answer:

x = 2 ± [tex]\sqrt{15}[/tex]

Step-by-step explanation:

x² - 4x - 11 = 0 ( add 11 to both sides )

x² - 4x = 11

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2)x + 4 = 11 + 4

(x - 2)² = 15 ( take square root of both sides )

x - 2 = ± [tex]\sqrt{15}[/tex] ( add 2 to both sides )

x = 2 ± [tex]\sqrt{15}[/tex]

Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

Cost price is the amount we pay to buy an item at which it is available.

Here,

Selling price of a cake = 200 cedis

Discount because of sale = 10% on each unit.

                                              (Only if 4 cakes purchased at a time)

Amanda purchased 8 cakes

So, Amanda need to pay only 90 percent of the total amount.

Total cost price of 8 cakes for Amanda = (200 X 90%) X 8

                                                                  = 180 X 8

                                                                  = 1440

Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

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The question is incomplete. Please read below to find the missing content.

D) cumulative is an argument that should be set to FALSE.

If we use cumulative =fake then we are able to get a precise probability

If we use cumulative= genuine, we will get less than or equal to possibility.

A sequence of actions wherein the effects are always unsure. I was tossing a coin, deciding on a card from a deck of playing cards, and throwing a cube. occasion. It is a single final result of a test. Getting a Head at the same time as tossing a coin is an occasion.

When using BINOM.DIST to calculate a probability mass function, which argument should be set to FALSE? Select an answer

A) number_s

B) probability_s

C) trials

D) cumulative

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Answer:

x=−9 and y=8

Step-by-step explanation:

Let's solve your system by elimination.

2x+3y=6;4x−y=−44

Multiply the first equation by -2,and multiply the second equation by 1.

−2(2x+3y=6)

1(4x−y=−44)

Becomes:

−4x−6y=−12

4x−y=−44

Add these equations to eliminate x:

−7y=−56

Then solve−7y=−56for y:

−7y=−56

-7y/-7 = = -56/-7

(Divide both sides by -7)

y=8

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

2x+3y=6

Substitute8 for y in 2x+3y=6:

2x+(3)(8)=6

2x+24=6(Simplify both sides of the equation)

2x+24+−24=6+−24(Add -24 to both sides)

2x=−18

2x/2 = -18/2 (Divide both sides by 2)

x=−9

Answer:

x=−9 and y=8

Answer:

x = -9

y = 8

Step-by-step explanation:

(using substitution)

4x-y = -44

4x + 44 = y

substitute (4x+44) as y in the other equation

2x + 3(4x+44) = 6

2x+12x+132 = 6

14x = -126

x = -9

then plug -9 as x into one of the equations to find y

4(-9) - y = -44

-36-y=-44

-y=-8

y=8

then check the answer by plugging in the values of x and y (-9 and 8) for x and y in one of the equations

4(-9) - (8) = -44

you get: -44 = -44, which is true, so the x and y values are correct

The gradient of line A is -2. 67

Gradient = slope = Δy/ Δx

We have,

y2 = 3

y1 = -5

x2 = -3

x1 = 0

Substitute the values

Gradient = [tex]\frac{3 - (-5)}{-3 -0}[/tex]

Gradient = [tex]\frac{3 + 5}{-3}[/tex]

Gradient = [tex]\frac{8}{-3}[/tex]

Gradient = -2. 67

Thus, the gradient of line A is -2. 67

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Answer:

40.1

Step-by-step explanation:

Because the order of operations (Bodmas or Pedmas) tells you to add from left to right. So you would do 18.79 + 2.11 = 20.9, then you would do 20.90 + 1.92 (Add 0 at the end of 20.9) = 22.81. Then you will add 22.81 + 17.28 = 40.1. So your answer is 40.1. Hope this helps!

The Sample mean,Sample Variance, Standard deviation is mathematically given as

Generally, the equation for Sample mean is  mathematically given as

[tex]x = \frac{1}{N}(\sum xifi )[/tex]

Where

[tex]\sum xifi=80+135+220+145+72+258[/tex]

[tex]\sum xifi=910[/tex]

Therefore

x=1/42 (910)

x=21.66

Sample Variance

[tex]\sigma = \frac{1}{N-1}(\sum xi^2fi-(\frac{1}{N}(\sum xifi^2 )) )[/tex]

Where

[tex]\sum xi^2fi=640+2025+4840+4205+2592+11094[/tex]

[tex]\sum xi^2fi=25396[/tex]

Therefore

[tex]\sigma = \frac{1}{41}(25396-(\frac{1}{42}(910^2 )) )[/tex]

[tex]\sigma=138.52[/tex]

Standard deviation.

[tex]\mu=\sqrt{\sigma^2}\\\\\mu=\sqrt{138.52}[/tex]

[tex]\mu=11.769[/tex]

In conclusion,

x=21.66

[tex]\sigma=138.52[/tex]

[tex]\mu=11.769[/tex]

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The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x). The correct option is C.

A straight line equation is represented by y = mx+c, where m is the slope and c is the y-intercept.

m is given by (y₂-y₁)/(x₂-x₁)

From the graph , the y-intercept is 4 and the two points on the line are    ( 0,4) and ( 1,1).

m = -3

c =4

The equation of the function g(x) is g(x) = -3x+4

The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x).

Therefore, the correct option is C.

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Step-by-step explanation:

To reflect a function about the vertical axis, just negate the variable.

For example, if we want to reflect this function

[tex] y = log(x) [/tex]

about the y axis or vertical axis, we just make the x negative

[tex]y = log( - x) [/tex]

Another example,

[tex]y = |x| [/tex]

To reflect about y axis or vertical axis,

[tex]y = | - x| [/tex]

So here l,the answer with negative variables are function that are reflected about the y axis.

The options are the first and the fifth option.

Answer:

cylinder to cone = 3:1

sphere to cylinder = 4r:3h

cone to sphere = h:4r

hemisphere to cylinder = 2r:3h

Step-by-step explanation:

Answer:

[tex](x + 5) {}^{2} = - 12(y - 1)[/tex]

By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].

Trigonometric functions are trascendent functions, these are, that cannot be described algebraically. Herein we must utilize trigonometric formulae to calculate the exact value of a trigonometric function:

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2} }{2} }[/tex]

[tex]\sin \frac{5\pi}{12} = \sqrt{\frac{2+\sqrt{3}}{4} }[/tex]

[tex]\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

By using properties for trigonometric functions and trigonometric expressions, we find that the exact value of the sine of the angle 5π/12 radians is [tex]\frac{\sqrt{2+\sqrt{3}}}{2}[/tex].

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Answer:

(f + g)(x) = x² + 4x - 4  

Step-by-step explanation:

The statement (f + g)(x) is the same as f(x) + g(x). In other words, the question simply wants you to add the two functions together.

f(x) = 4x + 1

g(x) = x² - 5

(f + g)(x)                                  <----- Original statement

f(x) + g(x)                                <----- Rewrite

(4x + 1) + (x² - 5)                     <----- Substitute the equations in f(x) and g(x)

4x + x² - 4                              <----- Add 1 and -5

x² + 4x - 4                              <----- Rearrange the terms

Step-by-step explanation:

Since we have a vertical major axis, our ellipse is vertical.

The equation of a vertical ellipse is

[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]

where

(h,k) is the center

a is the semi major axis,

b is the semi minor axis

First, let plug in our center

[tex] \frac{(y + 3) {}^{2} }{ {a}^{2} } + \frac{(x + 2) {}^{2} }{ {b}^{2} } = 1[/tex]

Semi means half, so

a is half of 14 which is 7

B is half of 8, which is 4.

[tex] \frac{(y + 3) {}^{2} }{49} + \frac{(x + 2) {}^{2} }{16} = 1[/tex]

By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.

The figure presents a circle, the arc of a circle (s), in inches, is equal to the product of the central angle (θ), in radians, and the radius (r), in inches. Please notice that a complete circle has a central angle of 360°.

If we know that θ = 52π/180 and r = 6 inches, then the length of the arc CD is:

s = [(360π/180) - (52π/180)] · (6 in)

s ≈ 32.254 in

By definition of circumference, the length of the arc EF (radius: 6 in, central angle: 308°) shown in red is approximately equal to 32.254 inches.

The statement has typing mistakes, correct form is shown below:

Find the length of the arc EF shown in red below. Show all the work.

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Answer: C. Y = 5x + 5

Step-by-step explanation:

    We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. See attached for a visual.

    First, we will find our slope. We will use [tex]\frac{rise}{run}[/tex] for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.

     -> Slope = 5

   Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.

     -> Y-intercept = 5

   Lastly, we will write our equation and decide on an answer.

y = mx + b

y = (5)x + (5)

Y = 5x + 5

             C. Y = 5x + 5

The digit on the right side of each equation so that each equation has an integer solution are 2.74, 3.78 and 1986.5 respectively.

35x - 11 = 107

35x = 107 - 11

35x = 96

x = 96/35

x = 2.74

9m + 34 = 68

9m = 68 - 34

9m = 34

m = 34/9

m = 3.78

7965 - 4m = 19

-4m = 19 - 7965

-4m = -7946

m = -7946/-4

m = 1986.5

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Answer:

19 units

Step-by-step explanation:

JM is 40 units, and it is composed of JH and HM. HM is 21 units, and so JH must be the remaining units.

40 - 21 = 19

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