The shortest side of a right angle triangle is 6cm shorter than the hypotenuse. The difference in length of the other two sides is 3cm. If the shortest side is n - 3, show that 2n squared equals 12n. Hence, n.

Answer:

6 gallons per minute

Step-by-step explanation:

54 gallons came out in 9 minutes

54/9 = 6

the rate is 6 gallons per minute

Answer:

Definition. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

The question tests on probability and combinations.

To obtain the probability for selecting exactly two red and 5 white urns is:

If Wi and Ri are events for selecting the ith ball, apply the multiplicative rule to obtain:

=P(W1∩W2∩W3∩W4∩W5∩R1∩R2)

= P(W1)P(W2|W1)P(W3|W1∩W2)P(W4|W1∩W2∩W3)P(W5|W1∩W2∩W3∩ W4)P(R1|W1∩W2∩W3∩W4∩W5)P(R2|W1∩W2∩W3∩W4∩W5∩R1)

=6/10×5/9×4/8×3/7×2/6×4/5×3/4

= 1/10

The probability is 1/10.

Alternatively, use the Bayes theorem. This uses combinations. To get the probability for exactly 5 white and 2 red, obtain the chance for selecting 5 white balls and 2 red balls; 6C5 and 4C2.

(6C5×4C2)/10C7 = 6×6/120 = 1/10

The probability for at least 5 balls is obtained by the probability of either selecting 5 or 6 balls.

Using combination;

(6C6 X6C5)/10C7 = (1x6)/120 = 6/120 = 1/20.

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Answer:

Step-by-step explanation:

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ANSWER:

(3,-4)= -2  (5,6)= -10 and if you need to divide it would be 0.2

Step-by-step explanation:

What I did was get the y- axis number with each other and minus them so that would be (3, - 5) = -2 and then I did (-4 - 6)= -10 and then you can divided -2/-10= 0.2. Hope this helped!

Answer: 2 or 2/1

Step-by-step explanation: the reciprocal of 1/2 is 2/1. in decimal form, 2 is the reciprocal of 0.5.

The solution of the inequality will be;

⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The expression for the inequality will be;

⇒ 3(8 – 4x) < 6(x – 5)

Now, Solve the inequality as;

The expression for the inequality will be;

= 3(8 – 4x) < 6(x – 5)

Divide by 3 both side,

= 8 - 4x < 2 (x - 5)

= 8 - 4x < 2x - 10

Add 4x both side;

= 8 - 4x + 4x < 2x - 10 + 4x

= 8 < 6x - 10

Add 10 both side;

= 18 < 6x

Divide 6 both side;

= 3 < x

So, The solution of the inequality will be;

⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

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Total number of pencils and pens bought by Henry = 35.

What is the unitary method of problem solving?
The unitary technique, in its most basic form, is used to calculate the value of a single unit from a specified multiple. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.

Given, for every 3 pencils, number of pens bought = 2
Therefore, every 1 pencil, number of pens bought = 2/3
Thus, for 21 pencils, number of pens bought = (2/3)*21 = 14
Therefore, total number of pencils and pens bought by Henry = 21 + 14 = 35.

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When compared to the universal setU={1,2,3,4,5,6,7,8,9,10}, the set P=2,4,6,8,10 has a prime that is equal to P'=1,3,5,7,9 as its element.

This is further explained below.

Generally, Assigned the letter A (A prime), The components that are included in the Universal set but are absent from Set A are denoted by the letter A.

U={1,2,3,4,5,6,7,8,9,10}

P={2,4,6,8,10}

Therefore, the prime of the set  P={2,4,6,8,10} in relation to the universal set U={1,2,3,4,5,6,7,8,9,10} is

P'={1,3,5,7,9}

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Suppose U={1,2,3,4,5,6,7,8,9,10} is the universal set, and P={2,4,6,8,10}. What is P'?

Answer:1/2

Step-by-step explanation:

2 heads

2 tails

2 + 2 = 4

heads - 2/4 - total

1/2

Considering the definition of a line, you get:

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Substituting the value of the slope m and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained:

-4= 1/2×0 + b

-4= 0 + b

-4 = b

Finally, the equation of the line is y= 1/2x -4.

In this case, you know:

Substituting the value of the slope m and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained:

2= 1/2×(-5) + b

2= -5/2 + b

2 + 5/2= b

9/2 = b

Finally, the equation of the line is y= 1/2x +9/2.

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)= (2,0) [x-intercept] and (x₂, y₂)= (0,8) [y-intercept] , the slope m can be calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

m= (8- 0)÷ (0 -2)

m= 8÷ (-2)

m= -4

Considering point 2 and the slope m, you obtain:

8= -4×0 + b

8= 0 +b

8=b

Finally, the equation of the line  y=-4x + 8.

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Answer:

x= -9, y= -4

Step-by-step explanation:

Solving a linear equation can be done by two main methods, namely elimination and substitution. Elimination works by making the numerical value of one of the variable's coefficient the same, such that we can subsequently eliminate (or remove) the variable by subtracting or adding the two equations together.

Start by labelling the 2 given equations:

2x -5y= 2-----(1)

3x -7y= 1-----(2)

I will be working to eliminate the x term here, since we would be dealing with smaller numbers in this case. Eliminating the y term would also work.

The lowest common multiple of 2 and 3 is 6, thus multiply equation (1) by 3 and (2) by 2 so that the coefficient of x in both equations is 6. Then label the equations.

(1) ×3:

6x -15y= 6 -----(3)

(2) ×2:

6x -14y= 2 -----(4)

Since the coefficient of x in both equations is positive 6, we can subtract one equation from the other to eliminate the x term. If both coefficients have different signs (e.g. +6 and -6), the addition of the two equations would eliminate the term.

(3) -(4):

6x -15y -(6x -14y)= 6 -2

Expand:

6x -15y -6x +14y= 4

-y= 4

Divide both sides by -1:

y= -4

Then use substitution to find the value of y. Note that at this point, you could work to eliminate the y term from equations (1) and (2) to solve for x but it is commonly understood that when a question states solve by elimination, it is only for the first variable.

Substitute y= -4 into (1):

2x -5(-4)= 2

2x +20= 2

Subtract 20 from both sides:

2x= 2-20

2x= -18

Divide both sides by 2:

x= -9

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The statement that is not true about the angles in the triangle is OPTION C. The measure of ∠K is 89°

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

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

From the diagram:

∠J + ∠K + ∠L = 180° (angles in a triangle)

Substituting:

(7x + 2) + (8x) + (4x + 7) = 180

19x + 9 = 180

x = 9

∠J = 7x + 2 = 7(9) + 2 = 65°

∠K = 8x = 8(9) = 72°

∠L = 4x + 7 = 4(9) + 7 = 43°

∠k ≠ 89°

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Answer:

let the number be x...therefore 1/3 of x equals to 1/3x

1/3x+5=6/5x....collect like terms

1/3x-6/5x=-5

0.3x - 1.2x = -5

-0.9x = -5

Divide both sides by coefficient of x....

X = -5/-0.9

=5.55

=5.6

If two numbers are multiplied, they are written as "a multiplied by b."

The answer is 9 3/7.

Multiplication is the product of 2 or more numbers/things.

Multiplying in math is equivalent to adding like groups.

The quantity of items in the group expands as we multiply.

A multiplication question has two factors, a product, and two factors. The factors and the product in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, respectively.

4 2/7 * 2 1/5 = 30/7 * 11/5

On simplifying,

= 6/7*11

= 66/7

=9 3/7

The answer is 9 3/7.

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

Reason:

Let's check to see if choice A is the answer. We'll replace each x with -1

2x^2 + 4x = 3 + 3x^2

2(-1)^2 + 4(-1) = 3 + 3(-1)^2

2(1) + 4(-1) = 3 + 3(1)

2 - 4 = 3 + 3

-2 = 6

We don't end up with the same thing on both sides, so x = -1 is not a solution to the equation.

--------------

Now try x = 0

2x^2 + 4x = 3 + 3x^2

2(0)^2 + 4(0) = 3 + 3(0)^2

2(0) + 4(0) = 3 + 3(0)

0 = 3

That's false as well, which allows us to rule out choice B.

--------------

Next up plug x = 3 into the equation

2x^2 + 4x = 3 + 3x^2

2(3)^2 + 4(3) = 3 + 3(3)^2

2(9) + 4(3) = 3 + 3(9)

18 + 12 = 3 + 27

30 = 30

We get the same thing on both sides so we have confirmed x = 3 is a solution.

--------------

There may be other solutions. If we tried x = 6, then it leads to 96 on the left hand side and 111 on the right hand side. That rules out x = 6 as a solution.

Answer:

23) 30°

24) 12°

Step-by-step explanation:

23) Lines will be parallel if the co interior angles are supplementary.

               ∠3 + ∠5 = 180°

 3x+ 25 + 4x - 55 = 180

3x + 4x + 25 -55 = 180

Combine like terms,

            7x -  30    = 180

Add 30 to both sides,

                7x = 180 + 30

               7x = 210

Divide both sides by 7,

                x = 210 ÷ 7

                x = 30

24)    If the lines are parallel, then the alternate interior angles are congruent.

                  ∠7 = ∠2

           11x - 36 = 8x

Add 36 to both sides,

                 11x   = 8x + 36

Subtract 8x from both sides,

          11x - 8x  = 36

                  3x = 36

                    x = 36 ÷ 3

x = 12°

Answer: no solution

Step-by-step explanation:

Answer:

$20,000 at 4.5% simple interest

$10,000 at 3% simple interest

Step-by-step explanation:

[tex].045x + .03(30000 - x) = 1200[/tex]

[tex].045x + 900 - .03x = 1200[/tex]

[tex].015x + 900 = 1200[/tex]

[tex].015x = 300[/tex]

[tex]x = 20000[/tex]

$20,000 at 4.5% simple interest

$30,000-$20,000=$10,000 at 3% simple interest

Remember that

We know that:

This way,

Answer:

y=3x=16/3

Step-by-step explanation:

Triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.

In triangle ADT and EDT, we get that:

AD = DE (given)

AT = ET (given)

DT = DT (common)

So, ΔADT ≅ Δ EDT (SSS congruency rule)

In triangle BLG and PFX, we get that:

BL = PF (given)

BG = PX (given)

∠ B = ∠ P (given)

So, ΔBLG ≅ Δ PFX (SAS congruency rule)

Therefore, we get that, triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.

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The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:

50x+80y=1750

y = x+4 ,

where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

We have:

Weight of small box of paper = 50 pounds

Weight of large box of paper = 80 pounds

Total weight of boxes = 1750 pounds

Let us consider that  the number of small boxes of papers be x.

The number of large boxes of papers be y.

Then, according to question

50x+80y=1750

y = x+4  

Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.

where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.

Answer: squared

Step-by-step explanation:

A total of 24 boxes of paper were shipped weighing 1410 pounds altogether, the system of equations are  X + Y =  24, and 45X + 75Y  = 1410 and the variables that you use to write the system X = 13 and Y = 11.

The primary unit of sterling is the pound (sign: £), while the term "pound" is also frequently used to refer to the British pound or pound sterling in foreign settings.

The oldest currency that is still in the circulation and has been used continuously since its origin is sterling. After US dollar, euro, and Japanese yen, it is currently fourth most traded currency on the foreign exchange market. It makes up basket of currencies used to determine the value of IMF special drawing rights along with the other three currencies and the renminbi. Sterling is also fourth-most-held reserve currency in the world's reserves as of mid-2021.

Let X equal  number of small boxes

Let Y equal number of big boxes

The first equation is:  X + Y =  24     ( this shows that total number of boxes = 24)

The second equation is:    45X + 75Y  = 1410    ( this is because small box weighs 24 pounds and big box weighs 75 pounds.  The total weight of small boxes is 45 times weight of each individual box. And the total weight of second boxes is equal to 75Y.  

When you solve system,  X = 13 and Y = 11

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Answer:

19. x=20 y=7 20. x=10 y=25 21. x=12 y=31

Step-by-step explanation:

worksapce thingy

3x+17=5x-7

2x=24 x=12

53

no idea if im right .-.

Answer:

Describe how anthropology challenges more commonly held notions of progress

Step-by-step explanation:

The equation that Joey can use to determine how many months it will take to reach his goal will be 8 + 3x = 50 and the number of months is 14.

From the information, Joey's favorite present is the 8 baseball cards that he got from his dad and he has never owned a baseball card before this gift and he plans to collect 3 baseball cards each month until he has a total of 50 cards.

This will be illustrated as:

8 + 3x = 50

Collect like terms

3x = 50 - 8

3x = 42

Divide through 3

3x / 3 = 42 / 3

x = 14

The number of months is 14.

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Answer:

Grace

Step-by-step explanation:

48 is the LCM, 4 is the GCF

Answer: 400 KL you have to add 300 KL + 100 KL = 400 KL