The sum of ages of Clayman and Ato is 25 years. In five years' time, the age of Ato will twice the age of Clayman now. a. How old is Clayman? b. How old is Ato?​

Answer:

(1, 1)

Step-by-step explanation:

Given vertices of the parallelogram:

Therefore the parallel sides are:

[tex]\sf \overline{HJ} \parallel \overline{LK}\:\: \textsf{ and }\:\: \overline{LK} \parallel \overline{HL}[/tex]

Therefore, the diagonals of the parallelogram are:

[tex]\sf \overline{LJ} \:\: \textsf{ and }\:\:\overline{HK}[/tex]

To find the coordinates of the intersection of the diagonals, either:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

To find the midpoint of diagonal LJ, define the endpoints:

Substitute the defined endpoints into the formula and solve:

[tex]\begin{aligned} \implies \textsf{Midpoint of LJ} & =\left(\dfrac{3-1}{2},\dfrac{3-1}{2}\right)\\ & =\left(\dfrac{2}{2},\dfrac{2}{2}\right)\\ & =\left(1,1\right) \end{aligned}[/tex]

Therefore, the coordinates off the intersection of the diagonals of parallelogram HJKL are (1, 1).

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Check the order

Means H,J and K,L are adjacent coordinates

Hence HK and JL are diagonals

We know diagonals of a parallelogram bisect each other so midpoint of any diagonal would be the intersection point

Midpoint of HK

Answer:

Rational.

Step-by-step explanation:

[tex]\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}[/tex]

The solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a system of equations:

1st Equation: 4x + y = 7

2nd Equation: 2x + y = 11

Subtract equation 2nd from 1st

(4x + y) - (2x + y) = 7 - 11

2x = -4

x = -2

Now in equation 1st multiply by 2 and in equation 2nd multiply by 4

8x + 2y = 14

8x + 4y = 44

Subtract:

-2y = -30

y = 15

The factor is 2 and 4 for the 1st and 2nd equation respectively.

Thus, the solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.

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If you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x

The standard exponential function is expressed as:

y = ab^x

The value of x determines the nature of a graph whether vertical or horizontal stretch.

If x  > 1, it is a vertical stretch

Given the function f(x) = 2^x, if you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x

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Answer:

D

Step-by-step explanation:

By the distributive property, 5(x+3) is equal to 5x + 15.

The output light frequency of the material used before doubling will be 0.056 Hz.

Frequency is defined as the number of repetitions of a wave occurring waves in 1 second.

Frequency is given by the formula as,

[tex]\rm v = \lambda \times f \\\\\ \rm f = \frac{v}{\lambda} \\\\ \rm f = \frac{3 \times 10^8}{532 \times 10^-9} \\\\ \rm f = 3 \times 10^{12} \\\\ f= 0.056 \ Hz[/tex]

Hence the output light frequency of the material used before doubling will be 0.056 Hz.

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Answer:

They are the same angle.

Step-by-step explanation:

We have a diagonal line and two 180° parallel lines running through it. The x and y values should be identical because of the placement. The diagonal on the right and right above the 180° angle.

Option 2: Corresponding angles.

Hope this helps!

If not, I am sorry.

The general term for the arithmetic sequence is aₙ = 3 + 3n

The general term of an arithmetic sequence is as follows:

aₙ = a + (n - 1)d

where

Therefore,

a = 6

d = 9 - 6 = 3

aₙ = 6 + (n - 1)3

aₙ = 6 + 3n - 3

aₙ = 3 + 3n

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Answer:

a. The mean mark for the test was 20.667.

b. The mean mark as a percentage is 51.6%.

Step-by-step explanation:

a. Calculate the mean mark for the test.

b. Express the mean mark as a percentage.

Answer:

distance = 9.4 units

Step-by-step explanation:

* using the distance formula *

d =

[tex] \sqrt{(x2 - x1 )^{2} + (y2 - y1)^{2} } [/tex]

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

= 9.4 units

From the given expression, the equivalent expression would be 64/25.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

Given;

16÷(2+1/2)²

16÷(5/2)²

16÷(25/4)

16 x (4/25)

= 64 / 25

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Answer:

Area=12x square units;  Perimeter=5x+14 units

Step-by-step explanation:

Recall the formulas for area and perimeter of a triangle:

Area of a triangle is half of the product of a base its corresponding height:

[tex]A=\frac{1}{2}bh[/tex]

Perimeter is the sum of all of the side lengths:

[tex]P=a+b+c[/tex]

In arbitrary triangles ABC, the sides are labeled across from a vertex with a matching lowercase letter.  So, in my diagram, side "b" is the bottom with length "8".  Side "b" is also the base, so the corresponding height is the perpendicular line segment that connects side "b" with vertex "B", which measures "3x"... 3 times some unknown value.

Side "a" is length "4x-3", and side "c" is length "x+9".

In this situation, where the sides have their specific relationship with "x" and the height is exactly triple "x", solving for x (and thus exact numerical values for the Perimeter and Area) involves trying to relate the two equations, possibly done with Heron's formula for area, or with trigonometry.  Ultimately, it involves solving a 4th degree polynomial to get an exact answer, which is not what the question intends, so we'll leave the Area and Perimeter in terms of x (meaning there will still be "x" in our expressions to represent the Area and Perimeter).

Area

[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(8)(3x)\\A=12x[/tex]

So the Area of the triangle equals 12x square units.

Perimeter

[tex]P=a+b+c\\P=(4x-3)+(8)+(x+9)\\P=5x+14[/tex]

So the Perimeter of the triangle equals 5x+14 units

Answer:

-1 and -11

Step-by-step explanation:

"sum" means we're adding.

-1 + -11 = - 12

"product" means we're multiplying.

-1 × -11 = 11

The option that needs to be corrected in this construction of a line parallel to line AB passing through C is C: the second arc should be centered at C.

The second arc should be centered at C because as it crosses passing through Line C, it is seen that it was not touching or intersecting AB and so one can say that it is parallel to it.

Looking at the other lines, we will see that they are all touching AB and are not running parallel to it.

Hence, The option that needs to be corrected in this construction of a line parallel to line AB passing through C is C: the second arc should be centered at C.

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Answer:

2x + 3.

Step-by-step explanation:

x + x + 3

= 2x + 3.

Answer:

2x+3

Step-by-step explanation:

x+x+3=2x+3

sum means to add both expression together and we can see there are 2 x's so we can add them and get 2x+3

Answer:

The median is 3.

Step-by-step explanation:

Since, most of the values presented are 0-8 and median is the middle of any data set. It has to be 3.

Answer:

the answer is 0

Step-by-step explanation:

because anything multiply by 0 is 0.

Can make me the brainliests answerer?Please

See below for the vocabularies and their correct definition

Match the following vocabulary

The terms are given as:

To get the inverse of a conditional, the hypothesis and the conclusion are negated, without interchanging them.

So, we have:

Inverse of a conditional ⇒ A new statement formed by negating both the hypothesis and the conclusion.

To get the contrapositive of a conditional, the hypothesis and the conclusion are negated, after interchanging them.

So, we have:

Contrapositive of a conditional ⇒ Formed by exchanging the hypothesis and the conclusion and negating both of them.

To get the converse of a conditional, we simply interchange the hypothesis and the conclusion, without negating them

So, we have:

Converse of a conditional ⇒ A statement formed by interchanging the hypothesis and the conclusion in a conditional statement.

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Answer:

The answer is Convers because it literally takes the hypothesis and the conclusion and interchanges them.

Step-by-step explanation:

Answer:

y = -3x + 1

Step-by-step explanation:

the line crosses the y-axis at (0,1) then c = 1

The points (0,1) and (1,-2) lie on the line then

m = slope = [(-2)-1]÷(1-0) = [-3]÷(1) = -3÷1 = -3

Therefore,

The equation of the line is : y = -3x + 1

The number of red car altogether is 34

The number of blue cars altogether is 36

The  number of silver car altogether 70

The car manufacturer has parked some cars in 2 car parks .

The first car park has 60 cars.

In the ratio 1 :2:3

Therefore,

red car = 1 / 6 × 60 = 10 cars

blue car = 2 / 6 × 60 = 20 cars

Silver car = 60 - 30 = 30 cars

The second car park has 80 cars.

The ratio are

In the ratio 3:2 5

Therefore,

red cars = 3 / 10 ×80 = 24

blue cars = 2 / 10 × 80 = 16

silver cars = 5 / 10 × 80 = 40

Therefore,

The number of red car altogether is 24 + 10 = 34 red car

The number of blue cars altogether is 20 + 16 = 36 blue cars

The  number of silver car altogether is 30 + 40 = 70 silver cars

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The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).

In this question we know an end and a midpoint of a line segment. The missing end can be found from the following formula:

M(x, y) = G(x, y) + 0.5 · [H(x, y) - G(x, y)]

M(x, y) = 0.5 · G(x, y) + 0.5 · H(x, y)

0.5 · H(x, y) = M(x, y) - 0.5 · G(x, y)

H(x, y) = 2 · M(x, y) - G(x, y)     (1)

If we know that M(x, y) = (5, 3) and G(x, y) = (1, -5), then the coordinates of the point H are:

H(x, y) = 2 · (5, 3) - (1, -5)

H(x, y) = (10, 6) - (1, -5)

H(x, y) = (9, 11)

The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).

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Answer:

its A

Step-by-step explanation:

Answer:

Using the concept of speed-distance-time, we find that the diameter of the circular path is 12 inches.

Step-by-step explanation:

Given that the object completes one revolution in 8 seconds. So, the circular speed of the object is 2πr/8 = πr/4 inches per seconds, where r is the radius of the circular path. The speed can be written as:

πr/4 inches per seconds = 60πr/4 inches per minute = 15πr inches per minute.

But, it is given that the circular speed of the object is 90π inches per minute. So,

90π = 15πr

r = 6 inches

Since, diameter is the double of radius, d = 2r = 12 inches.

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Answer:

r = 290°

Step-by-step explanation:

  In a triangle, exterior angles equals the sum of interior opposite angle.

In triangle A,

   x + 90 = 125   {Exterior angle property}

           x = 125 - 90

           x = 35°

In triangle B,

      y + 90 = 125

             y = 125 - 90

             y = 35°

    x + y + r = 360   {Complete angle}

35 + 35 + r = 360

         70 +r = 360

               r = 360 - 70

               r = 290°

The odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A coin toss is used to determine which team will receive the ball at the beginning of a football game.

The Cougars always choose tails in the toss.

There will total of 8 cases and in 8 cases there will be three cases in which exactly two heads will come so,

3:8

The cases = {TTT, TTH, THT, HTT, HHT, HTH, HHT, HHH}

Thus, the odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.

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Answer:

460

Step-by-step explanation:

if you look at the values you'll notice the next month is just half their value

7360 / 2 = 3680

3680 / 2 = 1840

1840 / 2 = 920

so

920 / 2 = 460 which should be month 5

The statement m∠WXY + m∠YXZ = 180° is true.

From the diagram, m∠WXY > m∠YXZ ⇒ m∠WXY ≠ m∠YXZ. So, option (a) is not true.

From the diagram, m∠WXY > 90° and m∠YZX < 90° ⇒ m∠WXY ≠ m∠YXZ. So, option (b) is not true.

The line WXZ is a straight line so ∠WXY and ∠YXZ are Linear pair. The sum of collinear angles is 180°. So, option (c) is correct.

From the diagram, m∠YXZ ≠ m∠XYZ but since m∠WXY + m∠YXZ = 180° ⇒ m∠WXY + m∠XYZ ≠ 180°. So, option (d) is not correct.

Option (c) is, thus, the correct option.

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Disclaimer: The question was incomplete. Please find the dull content below.

Which statement regarding the attached diagram is true?

m∠WXY = m∠YXZ

m∠WXY < m∠YZX

m∠WXY + m∠YXZ = 180°

m∠WXY + m∠XYZ = 180°

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Step-by-step explanation:

The equation of a exponential function is

[tex]a \times (b) {}^{x} [/tex]

where a is the y value of the y intercept, b is the constant rate of change.

Here the y intercept is (0,4), the y value of the y intercept is 4.

So a=4

The graph passes through point (1,2) so

[tex]h(x) = 4 \times b {}^{x} [/tex]

Plug in 1 for x, 2 for h(x)

[tex]2 = 4 \times {b}^{1} [/tex]

Anything to the first power is itself so

[tex]2 = 4 \times b[/tex]

Isolate b.

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

So our function is

[tex]4 \times ( \frac{1}{2} ) {}^{x} [/tex]

Answer:

[tex]h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]

Step-by-step explanation:

Exponential Function

General form of an exponential function:

[tex]y=ab^x[/tex]

where:

From inspection of the given diagram, the defined points on the curve are:

As one of the defined points is the y-intercept (0, 4) then:

[tex]\implies a=4[/tex]

Substitute the found value of a and the point (1, 2) into the general form of an exponential function and solve for b:

[tex]\begin{aligned}h(x)=ab^x & \\\implies h(1)=4b^1 & = 2\\4b & = 2\\b & = \dfrac{2}{4}\\b & =\dfrac{1}{2} \end{aligned}[/tex]

Finally, substitute the found values of a and b into the general formula to complete the equation for the function h(x):

[tex]\implies h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]

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Answer:

x= 4

y= -2

Step-by-step explanation:

[tex]-3y+5x=26\\-2y-5x=-16[/tex]

Solve by using the Elimination Method.

[tex]-5y=10\\\\\frac{-5y}{-5} =\frac{10}{-5} \\\\y=-2[/tex]

Now plug y into one of the original equation.

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

[tex]-2y-5x=-16[/tex]

[tex](-2*-2)-5x=-16[/tex]

[tex]4-5x=-16[/tex]

[tex]4-5x+5x=-16+5x[/tex]

[tex]4+16=-16+5x+16[/tex]

[tex]20=5x\\\\\frac{20}{5} =\frac{5x}{5} \\\\x=4[/tex]

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

[tex]\left \{ {{x=4} \atop {y=-2}} \right.[/tex]