Elizabeth is 7 years older than her sister
Lauren. Five years ago, Elizabeth was twice
Lauren's age. How old is Lauren now?

Answer:

Step-by-step explanation:

To prove that a quadrilateral ABCD is a trapezium when the diagonals intersect at a point O such that AO/BO=CO/DO, we can use the fact that opposite sides of a trapezium are parallel.

First, let's draw a diagram to represent the given information:

[asy]

pair A, B, C, D, O;

A = (0,0);

B = (2,0);

C = (3,2);

D = (1,2);

O = intersection point(A-C, B--D);

draw(A--B--C--D--cycle);

draw(A-C);

draw(B--D);

label("A", A, W);

label("B", B, E);

label("C", C, E);

label("D", D, W);

label("O", O, N);

label("$\theta_1$", (B+O)/2, NE);

label("$\theta_2$", (O+D)/2, NE);

label("$\theta_3$", (O+C)/2, NW);

label("$\theta_4$", (A+O)/2, NW);

[/asy]

Since the diagonals intersect at point O, the angles formed by the diagonals at O are supplementary (that is, they add up to 180 degrees). In other words, we have:

θ1 + θ2 = 180 degrees

θ3 + θ4 = 180 degrees

Since AO/BO=CO/DO, the triangles AOB and COD are similar. This means that the ratios of their sides are equal. We can write this as:

AO/BO = CO/DO

We can also write this as:

AO/DO = CO/BO

Then, since the angles formed by the diagonals at O are supplementary, we have:

θ1 + θ2 = 180 degrees

θ1 + θ4 = 180 degrees

Subtracting these two equations gives us:

θ2 - θ4 = 0

Since the angles are equal, they are also opposite angles of the quadrilateral ABCD. Therefore, the opposite sides of AB and CD are parallel, which means that ABCD is a trapezium.

Answer:

A.

Step-by-step explanation:

answer A. 14 minutes is your answer

Answer: To determine whether the distance the puck travels per second is constant, we can use the concept of average speed. Average speed is defined as the total distance traveled divided by the time it takes to travel that distance.

If the average speed is constant, then the distance the puck travels per second is also constant. If the average speed is not constant, then the distance the puck travels per second will vary.

To determine the average speed, we need to know the total distance traveled and the time it took to travel that distance. Once we have this information, we can calculate the average speed by dividing the total distance traveled by the time it took to travel that distance. If the resulting value is constant, then the distance the puck travels per second is also constant.

Step-by-step explanation:

Answer:

it is D :)

Step-by-step explanation:

Answer:

120000/600

200 is your answer

Answer:

light

Step-by-step explanation:

it has kinetic energy

Answer:

Step-by-step explanation: Kinetic energy is made because of movement. So Motion would be the correct answer

Answer: it's c

n = 1

Step-by-step explanation:

Answer:

o to http://

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the base is the the big number, the exponent the small one

Answer:

23

Step-by-step explanation:

because m is the midpoint and it divides line uw in two equal parts

This is because for any parallelogram, the diagonals always bisect each other. This means the diagonals cut each other in half. The two halves are the same length. This is why UM = MW. It also means TM = MV.

Answer:

(-1,-3) and (-1,7)

Step-by-step explanation:

The x axis remains at the point -1 so u must see the -3 and 2 or the 7 and 2 which means both are correct . I’m not confident this is right but I tried.

Answer:

(-1,7)

(-1,-3)

(-6,-2)

Step-by-step explanation:

The equation that correctly solves the formula of r is r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

The concept here is the concept of subject of the formula.

The variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own. For instance, the subject of the formula for the area of a rectangle is A = b h (area = base height).

The formula given was A=4πr^2h, then we can r the subject of the formula as

r^2 = A /4π

Then r = [tex]\sqrt{\frac{ A }{4\pi } }[/tex]

Therefore, option B iscorrect.

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missing options:

A) r = 4πA B) r = A 4π C) r = A 4π D) r = A 4π

Answer:

-5

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

negative times negative equals positive

[tex]6(5x-3)[/tex]

Distribute:

[tex](6)(5x)+(6)(-3)[/tex]

[tex]=\fbox{30x - 18}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6(5x - 3)}[/tex]

[tex]\text{DISTRIBUTE 6 WITHIN the PARENTHESES}[/tex]

[tex]\mathsf{= 6(5x) + 6(-3)}[/tex]

[tex]\mathsf{= 30x - 18}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{\mathsf{30x - 18}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

9514 1404 393

Answer:

  (c)  π/2

Step-by-step explanation:

We know the sine of an angle is the cosine of its complement, and vice versa. The complement of angle x is (π/2-x), so ...

  sin(π/2 -x) = cos(x)

This is shown by the attached graph.

Answer:

C

Explanation:

they are in the ratio 1:2

The solution is Option C.

The triangle PRQ with sides 6 cm , 8 cm and 10 cm is similar to the triangle ABC with sides 3 cm , 4 cm and 5 cm and the ratio is 1 : 2

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔABC

Now , the measure of side AB = 3 cm

The measure of side BC = 4 cm

The measure of side AC = 5 cm

Now , let the second triangle be represented as ΔPQR

where , the measure of side PQ = 6 cm

The measure of QR = 8 cm

The measure of PR = 10 cm

The ratio of sides of the triangle is 1 : 2

So , the triangles ΔABC and ΔPQR are similar and the corresponding sides are also in the ratio

Hence , the similar triangle is with the sides 6 cm , 8 cm and 10 cm

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Answer:

The image shows the answer and below I will explain more about it.

Step-by-step explanation:

To draw a line all you need is two points on the graph, and people mainly use the coordinates of the y and x intercepts to draw it (when x=0 and when y=0)

so for these questions all we do is:

y=0+2 (we are putting x=0 into the equation)

y=2, x=0 so this is the first of our set of coords:

0=x+2

x=-2 y=0 (we are putting y=0 into the equation)

so all you do is plot these in and draw a line which passes between both,

now just repeat for the other one :)

Answer:

whats the mass of 1 dog bone

have a good day :)

Step-by-step explanation:

An equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2) is y = 3x - 5.

Mathematically, the standard form of the equation of a straight line (slope-intercept form) is given by this mathematical expression;

y = mx + c

Where:

From the information provided, we have the following points on line g:

Point = (-3, 6)

Point = (0, 5)

Next, we would determine the slope of line g as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (5 - 6)/(0 - (-3))

Slope, m = -1/3

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1/3 × m₂ = -1

m₂ = 3

At point (1, -2), an equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 3(x - 1)

y + 2 = 3x - 3

y = 3x - 3 - 2

y = 3x - 5

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Answer:

385

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

The arithmetic mean will be gotten by adding the numbers together and dividing them by 2. This will be:

= (3 + 7)/2

= 10/2

= 5

Geometric mean will be:

= ✓3 × 7

= ✓21

= 4.59

Answer:

77.40

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The number of hours to fill the pool will be 180. Then the correct option is C.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it.

Flow rate (gal/hr)                   Time (hours)

           x                                          y

         60                                       300

         45                                       400

         36                                       500

         30                                       600

Then the amount of liquid in the pool will be

⇒ 60 x 300

⇒ 18,000 gallons

If this much liquid is filled with hose that has a rate of 40 gallons per hour, then the number of hours will be

⇒ 18,000 / 40

⇒ 450 hours

Then the number of hours if two hoses are used to fill the pool that one has a rate of 40 gallons per hour and one has a rate of 60 gallons per hour will be

1/T = 1/450 + 1/300

1/T = 1 / 180

  T = 180 hours

Then the number of hours to fill the pool will be 180.

Then the correct option is C.

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