a deck is shuffled well, what is the probability that the top card is ace of spades and the bottom is queen of hearts?

Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC

Option b) ∠ADE = ∠ABC

According to the figure given in the question,

We can observe that there are two right-angled triangles present and we have to derive the similarities between them

Let one triangle be = ΔADE

Another triangle be = ΔABC

Let us consider the angle arc at point A,

We can conclude that ⇒ ∠BAC = ∠DAE ( according to the property of similar angles )

⇒ ∠ADE = ∠ABC ( by the similar 90° angles )

and both angles are making a total of 180°

So, from the above expressions, we can say that,

⇒ ∠AED = 180° - ∠A - ∠ABC

⇒ ∠ACB = 180° - ∠A - ∠ABC

Hence, ∠AED = ACB ⇒ ΔADE ≅ ΔABC

Therefore,

Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC

Option b) ∠ADE = ∠ABC

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Step-by-step explanation:

When you are looking for a no that DIVIDES the no, then you have to find HCF. When you are looking for a no that is DIVISIBLE, then you have to find LCM (mathematical explaination)

Answer:

0.262 hectares

Step-by-step explanation:

To find the size of each property, you need to divide the total area of the land by the number of properties. In this case, the total area of the land is 1.31 hectares, and it is being divided into 5 properties, so the size of each property is:

Property size = 1.31 hectares / 5 properties = 0.262 hectares/property

Therefore, each property will be 0.262 hectares in size.

The expression to represent the average change in temperature each minute is given as follows:

Mean = (4 x (-4) + 3 x (-3)+2 + 1)/10

Only numerical variables regardless of whether they are discrete or continuous can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.

The average of all values is termed as mean value. Add all values given in data and divide with no. of values to get mean.

According to given condition the expression to represent the average change in temperature each minute is represented as:

Mean = (4 x (-4) + 3 x (-3)+2 + 1)/10

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The solution is Option C.

The number of pints of fresh berries is 6 pints and is calculated by the equation 3 ( f + 2 ) = 24

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pints of fresh berries be represented as f

Now , the number of pints of berries Samantha got initially = 2 pints

So , the total number of berries Samantha got = f + 2

The cost of 1 pint of berries = $ 3

The total amount Samantha paid for the berries = $ 24

Now , the equation will be

Total amount Samantha paid for the berries = cost of 1 pint of berries x ( total number of berries Samantha got )

Substituting the values in the equation , we get

24 = 3 ( f + 2 )   be equation (1)

On simplifying the equation , we get

Divide by 3 on both sides of the equation , we get

f + 2 = 8

Subtracting 2 on both sides of the equation , we get

f = 6 berries

Hence , the equation is 3 ( f + 2 ) = 24

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The system of equations, 2x − 7y = −15 and 4x − 14y = 30, has no solution.

To find the solution to the system of equations, we can plot the line of the two equations on a graph, then find the coordinate of the point where both lines of the equations intersect each other.

Alternatively, we can solve simultaneously as shown below:

2x − 7y = −15 --> eqn. 1

4x − 14y = 30 --> eqn. 2

Rewrite eqn. 1:

2x − 7y = −15

-7y = -15 - 2x

y = 15/7 + 2/7*x

Substitute the value of y into eqn. 2:

4x − 14(15/7 + 2/7*x) = 30

4x - 30 - 4x = 30

0 - 30 = 30

0 - 30 + 30 = 30 + 30

0 = 60 [not true]

This means that the system has no solution. If we graph both lines, the two lines of the equations will not intersect each other at any point.

The graph below shows the graph of both lines of the system of equations, meaning that it has no solution.

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Answer:

area = 27.5625, side length = 5.25

Step-by-step explanation:

21 is the perimeter of a square (given). We know a square has 4 equal sides, so 4s = p, where s is the side length and p is the perimeter of a square. Thus: 4s = 21 → s = 5.25

We also know that a square has a = s², where s is the side length and a is the area. Thus, a = 5.25² → a = 27.5625

Answer:

125.5cm³. (your answer is correct)

Step-by-step explanation:

Volume = cross-sectional area×height

= πr²×h

= (3.14)(2²)×10

= 3.14×4×10

= 125.6cm³

The quadratic function x² + 4x - 5 is factorized to give

(x + 5) (x - 1)

The given quadratic function is x² + 4x - 5

The graph is plotted and the roots of the equation which is the x intercepts that is the points where the graph cuts the x axis is found to be points 1 and -5

Using points 1 and -5 the equation is sort as follows

for 1

x = 1

x - 1 = 0

for -5

x = -5

x + 5 = 0

bringing the solutions together

(x + 5) (x - 1)

The solution is (x + 5) (x - 1)

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Answer:

3/7 ; -7

Step-by-step explanation:

1)

(7-4)/(10-3)

3/7

2) -7 because is the number that multiplies x

Step-by-step explanation:

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

[tex]y - - 5 = 4(x - 2)[/tex]

[tex]y + 5 = 4x - 8[/tex]

[tex]y= 4x - 8 - 5[/tex]

[tex]y = 4x - 13[/tex]

[tex]y = 2x - 13 \div 2[/tex]

In the given angles, the values of R=31⁰, x=34⁰, m<S= 38⁰, m<Y = 111⁰

We know that a triangle is a polygon whose sum of angles is equal to 180 degress , with three sides and three vertices.

The given angles are

31⁰,  (x+4)⁰,  (3x+9)⁰

The sum of angles of the triangle

31+x+4+3x+9=180⁰

44+4x=180⁰

Collecting like terms

4x=136

Dividing by 4

x=34⁰

Substituting the value of x=34 in the given angles we have

R= 31⁰,             given

 (x+4)⁰   = 34+4=38⁰,  (3*34+9)⁰=111⁰

In conclusion the values of R= 31⁰, x=34⁰ , m<S=38⁰, m<T=111⁰

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Answer:

I dont understand

Step-by-step explanation:

Answer:

[tex]5\sqrt{p} ^{11}[/tex]

Explanation:

The equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation is called "point-slope form" because it uses the coordinates of a point on the line (point a) and the slope of the line (m) to describe the line.

The equation has three parts: y, b, and m(x - a).

The y part of the equation represents the y-coordinate of a point on the line. This value can change depending on the x-coordinate of the point.

The b part of the equation is the y-coordinate of a known point on the line. This value is fixed and does not change.

The m(x - a) part of the equation represents the slope of the line and the x-coordinate of the known point on the line. The slope is represented by m, and the x-coordinate of the known point is represented by a.

To use the equation to find the y-coordinate of a point on the line, you first need to know the x-coordinate of the point and the values of b, m, and a. Then, you can substitute these values into the equation and solve for y.

For example, if the x-coordinate of a point on the line is 5, the y-coordinate of a known point on the line is 2, the slope of the line is 3, and the x-coordinate of the known point is 1, then the y-coordinate of the point can be calculated as follows:

y - 2 = 3(x - 1)

y = 3x - 3 + 2

y = 3(5) - 3 + 2

y = 15 - 3 + 2

y = 14

Therefore, the y-coordinate of the point with x-coordinate 5 is 14.

In summary, the equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation uses the coordinates of a known point on the line and the slope of the line to describe the line, and you can use it to find the y-coordinate of a point on the line if you know the x-coordinate of the point and the values of b, m, and a.

Answer:

yellow

Step-by-step explanation:

i can only see one line, and infinitely many points are on it

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x ≥ -26 / (6a - 15)  where a >5/2.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.

Given a equation, (3ax + 2)/ 3  -  (5x / 2) ≥  -8 where a > 5/2

solving for x in terms of a

ax + 2/3  - 5x/2  ≥ -8

x(6a - 15 )  ≥ -26

x ≥ -26 / (6a - 15)

since a is greater than 5/2 let a be 3 than the value of x ≥ -26/3.

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For the given equation of variable condition, the cost of the bench is $450.

What is the equation of variable?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

Given, A garden table and a bench cost $964 combined.

i.e. G + B = $964 .............. (i)

and, the garden table costs $64 more than the bench

i.e. G = B + $64 ............. (ii)

From eq (i) and (ii), we get

B + $64 + B = $964

or, 2B = 964 - 64 = 900

or, B = 900/2 = 450

Hence, the cost of the bench is $450.

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the percent increase in enrollment, and round to the nearest percent is 40%

Given that number of students enrolled in 2010= 2000

Given that number of students enrolled in 2018 = 2800

2800is more than 2000 so that means number of students enrollment is increasing.

increase = 2800-2000= 800

Percent increase is given by formula:

% increase = 800/2000*100= 40

which is approx 40%.

Hence final answer is that enrollment increases by 40%

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Answer:

Line A

Step-by-step explanation:

Any line facing towards the left side of the coordinate plane will have a negative slope.

Line C is facing towards the right

Line D and B doesn't have a slope

A is the only right answer

Using the values provided and a derivative of the cone's volume formula, the result is 0.059 feet per minute.

In mathematics, the rate at which a function changes in relation to a variable.

A cone is a three-dimensional geometric structure that has a smooth transition from a flat base that is typically circular to the point at the top, which is also referred to as the apex or vertex.

The formula for cone volume is:

V=πr2h/3

yields the formula for cone volume:

dv/dt = 2r * h/3 * dr/dt dV/dt = 3 r=2 h=12

dr/dt = 0.059 feet per minute.

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An expression which can be used to determine the total distance in miles that Aisha walked over the 3 days is: C. 3 × 3/4.

In Science, distance can be defined as the amount of ground that is covered (travelled) by a physical object over a particular period of time and speed, irrespective of its direction, starting point or ending point.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities.

From the information provided, we know that Aisha walked three (3) days in a row and three (3) miles out of four (4) miles. Therefore, a mathematical expression that represents the total distance in miles that she walked over the three (3) days is given by;

Total distance = 3/4 + 3/4 + 3/4

Total distance = 3 × 3/4

Total distance = 9/4 or 2.25 miles.

In conclusion, Aisha walked a total distance of 9/4 miles or 2.25 miles over the three (3) days.

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Answer: $355

Step-by-step explanation:

First, find the total of cheques she writes out by taking 558 + 453 = $1011

Then add 78 to it because she is overdrawn by $78 at the end, so we now have $ 1089.

Then we take 1089 - 734 = $355

So, her cheque account balance before she received her pay was $355

The best estimate to get the  total number of times to get a "3" will be 24 times.

This is an expression that simply refers to mathematical statements that have at least two terms which are related by an operator and contain either numbers, variables

In this case, Jimm tossed a die several times and he got the number "3" on 8 of the tosses.

Therefore, when there are 64 tosses, the estimate will be:

= 3/8 × 64

= 3 × 8

= 24

The number of times is 24.

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Answer:

x= 30

Step-by-step explanation:

Angle E

E + F + G = 180

E + 60 + 90 = 180

E + 150 = 180

E = 180-150

E = 30

Angle E  is congruent to angle X so the measures must be the same

E = X = 30

X = 30

Answer:

[tex]E=30[/tex]

Step-by-step explanation:

[tex]E + F + G = 180\\E + 60 + 90 = 180\\E + 150 = 180 \\E= 180-150 = 30[/tex]

Hope this helps u :)

The inequality is 7<x<31.

What is inequality ?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The third side of any triangle must be more than the difference between the other two sides.

x>19-12

x>7 (or) 7<x

The third side of any triangle must be less than the sum of the other two sides.

x<19+12

x<31 (or) 31>x

Put them together.

7<x<31 (or) 31>x>7

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Answer:

Step-by-step explanation:

same as the last one,  hope you are getting these better now.

minor angle (interior angle)  J is the same as angle  t, b/c of the red marks.

180 = 141 = ∠j

39 = ∠j

t = 39

then find s

180 = 2*t +s

180 = 2*39 +s

180 =78 +s

180-78 = s

102 = s

got it better now?