Parallelogram ABCD has diagonal segments AC and BD that intersect at E. if BE is ( x + 8) and ED is (5 x), find the length of BD.

9514 1404 393

Answer:

  \(\displaystyle\sqrt{x+7}-\log{(x+2)}\)

Step-by-step explanation:

It's pretty straightforward. You want ...

  f(x) - g(x)

Substituting the given function definitions gives ...

  \(\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}\)

Answer: 3 i took the test and got it right

Step-by-step explanation:

Answer:

B

Makes the most sense for the question and answer

The correct proof of sin(90-theta)=cos theta is given below.

We have given that

Malia tried to prove that cos(theta) = sin (90 - theta)

The formula for sin(a-b) is sin(a)cos(b)-cos(a)sin(b)

\(Sin(90-\theta)=cos\theta\)

\(sin(90-\theta)=sin(90)cos(\theta)-cos(90)sin(\theta)\\We \ know\\ sin(90)=1 and cos(90)=0\\=(1)cos(\theta)-(0)sin(\theta)\\=cos(\theta)\)

Therefore we get sin(90-theta)=cos theta.

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Answer:

y=4/3+1

Step-by-step explanation:

The y-intercept is positive 1,

The slope form is always rise over run,

Therefore rising from 1 takes us to 5 then we run 3 times, so it takes us to (3,5)

Answer:

392

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

7 men should be able to dig 21 wells in approximately 4.7 days.

From the question, we have the following parameters that can be used in our computation:

We can use the formula:

Number of days = (number of wells * number of days per well) / number of men.

So, we have

Number of days per well for 2 men:

11 days / 7 wells = 1.5714 days per well.

Using the above as a guide, we have the following:

the number of days for 7 men to dig 21 wells:

21 wells * 1.5714 days per well / 7 men = 4.7142days.

Hence, the number of days is 4.7 days.

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Answer:

1) 18

2) P

Step-by-step explanation:

1) Multiply the top number by itself and then reverse the digits!

9*9 = 81 reversed is 18

2) Seems to be the number of line ends a letter has when you write it down. P only has one end, at the bottom.

Answer:

P

Step-by-step explanation:

2.

The number of strokes of the letter that come to an end.

The bottom of the A has two sticks that come to an end.

A = 2

The B has no sticks coming to an end.

B = 0

The C and an upper and a lower stroke coming to an end.

C = 2

D has none.

D = 0

E has 3 sticks coming to an end.

E = 3

etc.

M has 3.

N has 2.

O has 0.

P has 1 stick coming to an end.

Q has none.

R has 2.

S has 2.

T has 3.

U has 2.

V has 2.

W has 3.

X has 4.

Y has 3

Z has 2.

Of all letters after L, only P has exactly 1 stroke coming to an end.

Answer: P

The length of AC in the given triangle is 126.6.

The length of AC in the given triangle can be calculated using the Pythagorean Theorem. The length of AC is the hypotenuse of the right triangle, and can be calculated by taking the square root of the sum of the squares of the other two sides of the triangle. In this case, the length of AC is equal to the square root of (b² + 99.6²). Using the Pythagorean Theorem, the length of AC is equal to 126.6.

To calculate this, we take the square root of (b² + 99.6²). First, we square b, which is 85. This gives us 7225. Then, we square 99.6, which gives us 9920.41. We then add these two values together to get 17145.41. Finally, we take the square root of this value, which gives us 126.6. This is the length of AC in the given triangle.

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The triangles are similar by SSS congruence of triangles.

What is SSS congruence of triangles?

The two triangles are congruent if the three sides of one triangle are the same as the corresponding three sides (SSS) of the other triangle.

We are given two triangle ABC and PQR.

In order to see whether these are similar or not, we will use the SSS congruence of triangles.

The ratio of sides are:

⇒AB : PQ = 8 : 6

⇒AB : PQ = 4 : 3

Similarly,

⇒BC : QR = 12 : 9

⇒BC : QR = 4 : 3

Similarly,

⇒AC : PR = 12 : 9

⇒AC : PR = 4 : 3

Since, the ratio of all the sides is same so, the triangles are similar.

Hence, the triangles are similar by SSS congruence of triangles.

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Since, there are multiple questions so, the question answered above is attached below

Answer:

The measure of the angles:

24°  and   66°

Step-by-step explanation:

Complementary angles sum 90°

then:

(3x + 3) + (10x-4) = 90

3x + 10x + 3 - 4 = 90

13x - 1 = 90

13x = 90+1

13x = 91

x = 91/13

x = 7°

then:

3x+3 = 3*7 + 3 = 21+3 = 24°

10x - 4 = 10*7  - 4 = 70 - 4 = 66°

Check:

66° + 24° = 90°

Answer:

52

Step-by-step explanation:

6ab - 2c =

6(5)(2) - 2(4) =

60 - 8 =

52

Answer:

52

Step-by-step explanation:

6((5)(2)) - 2(4)

6(10) - 2(4)

60 - 8

52

The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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Answer:

d

Step-by-step explanation:

none of the above mhhmm

Answer:

the answer to the question is 231.4 cm^2

Step-by-step explanation:

just got it wrong  

I will assume that we are trying to find the slope between (2,-6) and (-9,-6)

The slope's equation ⇒  \(\frac{y2-y1}{x2-x1}\)

Let's set the variables:

    (x1, y1) --> (2, -6)

    (x2, y2) --> (-9, -6)

Now let's plug them in:

 \(Slope = \frac{-6--6}{-9-2} =\frac{0}{-11} =0\)

Thus the slope of the line is 0.

Hope that helps!

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

Cost of dryer is $250

Cost of washer is $500

Step-by-step explanation:

Let the cost of the dryer be - x

Then, cost of washer = 2x

To find x,

x+2x= $750

3x=$750

x=$750/3

x=$250

Hope this helps you mate.

The required 95% confidence interval for the mean breaking force of acrylic bone cement is approximately 267.29 to 344.85 newtons.

Find the critical value (t*) for a 95% confidence level and (n - 1) degrees of freedom.

The degrees of freedom (df) is equal to the sample size minus 1 (df = 7 - 1 = 6). From a t-table or statistical software, the critical value for a 95% confidence level and df = 6 is approximately 2.447.

Calculate the standard error of the mean (SE).

The standard error of the mean is given by SE = (sample standard deviation) / sqrt(sample size).

\(SE =\dfrac{41.96}{\sqrt{7}}\)

   ≈ 15.85

Calculate the margin of error (MoE).

The margin of error is MoE = (t*) * SE.

MoE ≈ 2.447 * 15.85
        ≈ 38.78

Calculate the confidence interval.

The confidence interval is given by: Mean ± MoE.

Mean ± MoE ≈ 306.07 ± 38.78

Calculate the lower and upper bounds of the confidence interval.

Lower bound ≈ 306.07 - 38.78
                       = 267.29

Upper bound ≈ 306.07 + 38.78
                       = 344.85

Therefore, the 95% confidence interval for the mean breaking force of acrylic bone cement is approximately 267.29 to 344.85 newtons.

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The values of the coordinates x and y is P ( 6 , 3 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( x , y )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = y / x

m₁ = 1/2

So , y/x = 1/2

And , x = 2y

Now , the third point is R ( 7 , 5 )

m₂ = ( 5 - y ) / ( 7 - x )

m₂ = 2

On simplifying , we get

( 5 - y ) / ( 7 - x ) = 2

Multiply by ( 7 - x ) , we get

5 - y = 14 - 2x

Adding 2x and subtracting 5 on both sides , we get

2x - y = 9

Substitute the value of x from m₁ , we get

2 ( 2y ) - y = 0

3y = 9

Divide by 3 on both sides , we get

y = 3

And , the value of x = 6

Hence , the coordinate of the point P is P ( 6 , 3 )

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Answer:

120 : 5 = 24 suy ra 24 x 7,5 = 180

Step-by-step explanation:

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

If  \(U\hat{T}J = 100\), all angles would be equal, resulting in similar triangles. So B is right

The common ratio of the geometric series which satisfies the condition given is; 4.

The given Geometric series has successive terms;

Hence, the common ratio of the geometric series is the quotient of S and C;

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For the following equation, the x-intercept is (3/2, 0) and the y-intercept is (0, 6).

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

y+2=-4(x-2)

for x-intercept=(x,0)

2=-4(x-2)

2=-4x+8

4x=6

x=6/4=3/2

for y-intercept=(0,y)

y+2=-4(*-2)

y=6

The x-intercept is (3/2,0) and y-intercept is (0,6) for given equation.

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1. A reasonable price for my friend to sell the car is $13,480.

2. This price is determined as an average of the prices of similar cars.

An average is a typical value in a dataset.

An average is the mean of a set of numbers.

The average value can be computed by summing the set of numbers and dividing the result by the number of items.

Prices of similar cars:

A. 13,500

B. 12,900

C. 15,300

D. 13,700

E. 12,000

Sum = $67,400

Average = $ 13,480 ($67,400/5)

Thus, a reasonable price for my friend to sell the car is $13,480, which is the average price of similar cars.

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Answer:

Step-by-step explanation: