according to what shortcut are two triangles congruent if all three of their corresponding sides are congruent

Answer:

A) (x +2)(x -3)² = 0

Step-by-step explanation:

Synthetic division by (x-3) gives the quadratic x² -x -6, which has factors (x -3) and (x +2). This is confirmed by another round of synthetic division.

The resulting factorization is ...

... (x +2)(x -3)² = 0

_____

A graph confirms a double zero at x=3 and one at x=-2.

Answer: The bar graph could work.

Answer:

Step-by-step explanation: A box plot takes a large amount of data and clearly identifies the median, first quartile, and third quartile. The first quartile identifies the 25th percentile, and the third quartile identifies the 75th percentile.

To determine how the height of the student compares to 25% of his class, the value of the first quartile of the heights is needed.

Therefore, the best graph type to show how the student compares to 25% of his class is a box plot.

Answer:

Sandwich = 6.75

Soft drink = 2.25

Step-by-step explanation:

9.00/4 = 2.25

2.25*3=6.75

Answer: $16, 666.67

Step-by-step explanation:

Job 1: 0.06x

Job 2: 0.03x + 500

0.06x > 0.03x + 500

-0.03x  -0.03x          

0.03x >              500

÷0.03              ÷0.03

       [tex]x > \dfrac{50000}{3}[/tex]

        x > 16,666.67      rounded to the nearest penny

48

Let x represent the distance OC. Then CD = x+2, and DP = 16-x. The radius of circle P is ...

... CD +DP = (x+2) +(16-x) = 18

The radius of circle O is ..

... OC + CD = (x) + (x +2) = 2x+2

The length OP is ...

... OC + CP = (x) + (18) = x+18.

Now, the perimeter of ΔAOP is ...

... radius of circle O + radius of circle P + OP = 80

... = (2x+2) + 18 + (x+18) = 3x+38 = 80

Then x is ...

... x = (80 -38)/3 = 14

and the radius of circle O is

... 2x +2 = 2·14 +2 = 30

The desired sum is ...

... OB + BP = (radius of circle O) + (radius of circle P) = 30 + 18

... OB + BP = 48

Answer:

d) 9

Step-by-step explanation:

In a kite, the two shorter sides have to be equal.

Therefore

3x-5 = 22

Add 5 to each side

3x-5+5 = 22+5

3x = 27

Divide each side by 3

3x/3 = 27/3

x =9

Answer: SAS congruence (choice C)

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

Explanation:

Let's go through the various answer choices. I'll say whether or not they are used

A) This is used because angle WXZ = angle WYZ and angle WZX = angle ZWY are the two pairs of angles. The pair of sides are WZ = WZ which overlap (aka shared) between the two triangles. Note how the sides are not between the angled mentioned. Eg: for the triangle on the left, WZ is not between angle WXZ and angle WZX. So we can cross choice A off the list. Note: AAS is slightly different from ASA. Make sure not to confuse the two.

B) We use this to prove that the right angles (WXZ and WYZ) are congruent to each other. Both are 90 degrees. This will then feed in to choice A above, to help use AAS. We can cross choice B off the list.

C) We do not use SAS because we use AAS instead. We only have info about one pair of sides (WZ = WZ). We do not have info about another pair of sides. Therefore, this is the answer.

D) We use this fact to help set up that angle WZX = angle ZWY. The segments WY and XZ are parallel. I like to think of them as train tracks. On the inside of the train tracks are the angles WZX and ZWY, and they are on opposite sides of the transversal segment WZ, so this is why the pair of angles are alternate interior angles. They are congruent as long as WY is parallel to XZ. Like with choice B, this helps feed into choice A. We can cross choice D off the list.

Among the listed reasons, the Alternate Interior Angles Theorem would typically not appear in a proof proving that segment WY is congruent to segment ZX, unless the diagram involved parallel lines cut by a transversal. Other postulates might be used if angle and side measurements are congruent.

In proving that segment WY ≅ segment ZX, some postulates or theorems may not appear in the proof depending on the given diagram. The Angel-Angle-Side (AAS) Congruence Theorem, the Side-Angle-Side (SAS) Congruence Postulate, and the Right Angles Congruence Theorem could all potentially appear in the proof if relevant angle and side measurements are given in the diagram.

However, the Alternate Interior Angles Theorem would typically not appear in this proof. This theorem is related to the indication that two lines are parallel when they are cut by a transversal and the alternate interior angles are congruent. This theorem does not directly involve proving the congruity of sides (or segments) as would be necessary for proving segment WY ≅ segment ZX. Unless the diagram specifically involved parallel lines cut by a transversal, this theorem would not be used.

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Answer:

1/5

Step-by-step explanation:

Experimental probability is the actual times it happens divided by the number of trials

Actual times red occurs:2

Trials: 10

Experimental probability: 2/10 = 1/5

Answer:1/5

Step-by-step explanation:Experimental probability is the actual times it happens divided by the number of trials

Actual times red occurs:2

Trials: 10

Experimental probability: 2/10 = 1/5

Answer:

8.14$

Step-by-step explanation:

each pound is for 2.20

2.5 x 2.20 = 5.50$ on Monday

1.2 x 2.20 = 2.64$ on Tuesday

5.50 + 2.64 = 8.14$ in total

1 ║ 4               6                  -1

                      4                  10

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

    4               10                 [tex]\boxed{9}[/tex] 

⇒ The Remainder is 9

[tex]f(x)=\dfrac{x-4}{x+9};\ g(x)=\dfrac{x-9}{x+4}\\\\f(x)+g(x)=\dfrac{x-4}{x+9}+\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)+(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2+x^2-9^2}{(x+9)(x+4)}=\dfrac{2x^2-16-81}{(x+9)(x+4)}=\dfrac{2x^2-97}{(x+9)(x+4)}\\\\f(x)-g(x)=\dfrac{x-4}{x+9}-\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)-(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2-(x^2-9^2)}{(x+9)(x+4)}=\dfrac{x^2-16-x^2+81}{(x+9)(x+4)}=\dfrac{65}{(x+9)(x+4)}[/tex]

[tex]\dfrac{f+g}{f-g}=(f+g):(f-g)=\dfrac{2x^2-97}{(x+9)(x+4)}:\dfrac{65}{(x+9)(x+4)}\\\\=\dfrac{2x^2-97}{(x+9)(x+4)}\cdot\dfrac{(x+9)(x+4)}{65}\\\\Answer:\ \boxed{\dfrac{f+g}{f-g}=\dfrac{2x^2-97}{65}}[/tex]

The value of  f+g / f-g =  (2x² - 97) / 65

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x)= x-4 / x+9 and g(x)= x-9 / x+4

So,  f+g / f-g

f(x)+ g(x)

= x-4 / x+9 + x-9 / x+4

= (x² - 4²) + (x² - 9²) / (x+4)(x+9)

= (2x² - 97) / (x+4)(x+9)

f(x)-g(x)

= x-4 / x+9 - x-9 / x+4

= (x² - 4²) - (x² - 9²) / (x+4)(x+9)

= 65 / (x+4)(x+9)

Then, f+g / f-g

= (2x² - 97) / (x+4)(x+9) x  (x+4)(x+9)/ 65

= (2x² - 97) / 65

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Answer:

Answer is selling price of second horse is Rs 30400.

Step-by-step explanation:

Maulik bought one horse at Rs 40000 and sold it with a gain of 15%

So the selling price of one horse will be 40000+15% of 40000

                                                      = 40000+6000

                                                      = Rs 46000

Second horse is costing Rs 40000 and had suffered a loss of Rs 3600 on selling both so selling price of both will be = 40000×2-3600

                                                                       = 80000-3600

                                                                       = 76400

  Now selling price of second horse will be selling price of both - selling price of first = 76400-46000 = Rs 30400

Answer:

The selling price of the second horse is Rs 30,400.

Step-by-step explanation:

Cost Price of first horse([tex]CP_{1}[/tex])= Rs. 40,000

Cost Price of second horse([tex]CP_{2}[/tex])= Rs. 40,000

Total cost price=[tex]CP_{1}+CP_{2}[/tex]=Rs (40,000+40,000)=Rs 80,000

First horse is sold at 15% gain.

This means selling price of first horse([tex]SP_{1}[/tex])= [tex]\dfrac{115}{100} \times40000[/tex]

                                                              = Rs. 46,000

also total there is a loss of Rs 3600

selling price of both the horses(SP)=80000-3600=Rs 76400

now, [tex]SP=SP_{1}+SP_{2}[/tex]

where [tex]SP_{2}[/tex] is the selling price of the second horse.

[tex]SP_{2}=SP-SP_{1}[/tex]

[tex]SP_{2}=76400-46000[/tex]

[tex]SP_{2}=30400[/tex]

Hence the selling price of the second horse is Rs 30,400.

Answer:

Step-by-step explanation:6*3 7*3 8*3 9*3

Answer:

C / (2pi) = r;  r= 13.9 cm

2A/b = h   ;  h= 5

Step-by-step explanation:

The formula for the circumference of a circle is  C = 2* pi * r.

Solving for r, we need to divide by 2 * pi on each side

C/(2* pi) = 2*pi*r/ (2* pi)

C / (2pi) = r

If the circumference is 87, we can find r by substituting into the equation.

87 / (2 * 3.14) = r

87/ 6.28 = r

13.85350318=r

Rounding to the nearest tenth

r= 13.9 cm

The formula for the area of a triangle is  A = bℎ /2  

To solve the formula for h, we need to multiply each side by 2

2*A = bh

Then divide each side by b

2A/b = bh/b

2A/b = h

If the  area  of a triangle is 25  and the base of 10 , we can substitute in to find the height.

2* 25 /10 = h

50/10 = h

5 =h

So to find the potential roots, we will be using the rational root theorem. The rational root theorem is [tex]\pm \frac{p}{q}[/tex] , with p = factors of the constant and q = factors of the leading coefficient. In this case, our constant is 12 and our leading coefficient is 1:

[tex]p=1,2,3,4,6,12\\q=1\\\\\pm\frac{1,2,3,4,5,6,12}{1}\\\\\pm1,\pm\ 2,\pm\ 3,\pm\ 4,\pm\ 6,\pm\ 12[/tex]

In short, our potential roots are: ± 1, ± 2, ± 3, ± 4, ± 6, and ± 12.

Answer:

2,4,3,6,12

Step-by-step explanation:

i just did it.  

Answer:

The amount of their mortgage loan is $108000

Step-by-step explanation:

we are given

total purchasing amount =$123000

down payment amount = $15000

we know that

Mortgage loan amount =  (total purchasing amount)-(down payment amount)

now, we can plug value

Mortgage loan amount = $123000-$15000

Mortgage loan amount =$108000

Patti Green and her husband need a mortgage loan of $108,000 for their condominium purchase.

The student has asked for the amount of the mortgage loan that Patti Green and her husband would need for purchasing a condominium. To find this, we would subtract their down payment from the total cost of the condominium. Since the condominium costs $123,000 and they have a $15,000 down payment, we do the following calculation:

Total cost of the condominium = $123,000
Down payment = $15,000
Mortgage loan needed = Total cost of the condominium - Down payment
Mortgage loan needed = $123,000 - $15,000
Mortgage loan needed = $108,000

Therefore, the amount of the mortgage loan that Patti Green and her husband would need is $108,000.

Answer:

The value of x is A) 1.5

Step-by-step explanation:

In order to find this, we can first note that if the base is the same, their exponents also must be the same. Since both have a base of 2, then we can eliminate the base and simply compare their exponents.

2x = 3

Now we can solve by simply dividing both by 2.

x = 1.5

Answer:

The answer is false

Step-by-step explanation:

22 quarts is 5.5 gallons

Answer:  FALSE, there are 80 cups in 5 gallons and 88 cups in 22 quarts  

Answer: 4x - 8 ; 12 yrs old

Step-by-step explanation:

sister: x

Ana: 4x - 8

when x = 5, Ana = 4(5) - 8

                           = 20 - 8

                           = 12

Answer:

Final answer is 7.

Step-by-step explanation:

Given that f(x) =7x+8.

Now we need to find the derivative of f(x) at x=5

So let's find derivative first.

[tex]f(x)=7x+8[/tex]

[tex]f'(x)=\frac{d}{dx}(7x+8)[/tex]

[tex]f'(x)=\frac{d}{dx}(7x)+\frac{d}{dx}(8)[/tex]  {Using formula [f+g]'=f'+g'] }

[tex]f'(x)=7\frac{d}{dx}(x)+\frac{d}{dx}(8)[/tex]  {Using formula f'(ax)=a f'(x) }

[tex]f'(x)=7(1)+0[/tex]  {derivative of constant term is 0 }

[tex]f'(x)=7[/tex]

Now plug the given value of x=5

[tex]f'(5)=7[/tex]

Hence final answer is 7.

Answer:

Jane is 12 years old and Harvey's is 36 years old .

Step-by-step explanation:

Given :

Jane is  [tex]a_{0}[/tex]  years old.

Harvey is   [tex]a_{1}[/tex] years old.

Harvey is 3 times as old as Jane.

The sum of their ages is 48 years.

To find : The ages of Harvey and Jane.

Solution :

Jane 's age :

[tex]a_{0}[/tex]

Harvey  's age:

[tex]a_{1}[/tex]  

Since we are given that sum of their ages is 48 years

⇒[tex]a_{1} + a_{0} = 48[/tex]  ----(A)

We are also given that  Harvey is 3 times as old as Jane.

⇒[tex]a_{1} = 3a_{0}[/tex]  --- (B)

Solving (A) and (B) using substitution method

Substitute value of [tex]a_{1}[/tex]  from (B) in (A) :

⇒[tex] 3a_{0}+ a_{0} = 48[/tex]

⇒[tex] 4a_{0} = 48[/tex]

⇒[tex]a_{0} = \frac{48}{4}[/tex]

⇒[tex]a_{0} = 12[/tex]

Thus , Jane 's age is 12 years .

Substitute this value in (B) to find Harvey,s age :

⇒[tex]a_{1} = 3(12)[/tex]

⇒[tex]a_{1} = 36[/tex]

Thus, Harvey,s age is 36 years .

Hence Jane is 12 years old and Harvey's is 36 years old .

Answer:

-3,4

Step-by-step explanation:

The solution to the system of linear equations 2x = y - 10 and x + 7 = y by substitution is (x, y) = (-3, 4).

To solve the system of linear equations 2x = y - 10 and x + 7 = y by substitution, follow these steps:

The solution to the system of equations is (x, y) = (-3, 4).

Let's assume the opposite is the case. So let's assume that a = b is true. If so, then f(a) and f(b) would be the same output. This is because we can replace 'b' with 'a', or vice versa. In other words, f(a) = f(b) would be true. But this contradicts the original inequality that f(b) < f(a)

So that is why 'a' cannot equal b. We don't know if a > b or if a < b (unless we are told if the function is strictly decreasing or increasing on the interval from x = a to x = b), so we just leave it as [tex]a \ne b[/tex]

Answer:

The best answer is C. y = 2/5x + 2

Step-by-step explanation:

You would start at point 2 then rise 2 units then run 5 units. (i got something else) but i went to desmos to make sure and it matched

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b).

Read two points from the graph.

y-intercept = (0, 2) → b = 2

x-intercept = (-5, 0)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute:

[tex]m=\dfrac{0-2}{-5-0}=\dfrac{-2}{-5}=\dfrac{2}{5}[/tex]

Therefore your answer is

[tex]\boxed{C.\ y=\dfrac{2}{5}x+2}[/tex]

Answer:

Step-by-step explanation:

Answer:

12,495 is the answer

Step-by-step explanation:

The total of the two matrices is found by adding corresponding elements:

[tex]\left[\begin{array}{cc}5+2&3+3\\22+17&15+27\\13+15&12+18\end{array}\right] =\left[\begin{array}{cc}7&6\\39&42\\28&30\end{array}\right][/tex]

This matches selection A.