2. Use the diagram and given information to answer the questions and prove the statement.

a. Re-draw the diagram of the overlapping triangles so that the two triangles are separated.

b. What additional information would be necessary to prove that the two triangles, XBY and ZAY , are congruent? What congruency would be applied?

c. Prove (AZ) is congruent to (BX) using a flow chart proof. ( ):both have a line over them
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Answer:

Step-by-step explanation:

[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]

Answer:

7

Step-by-step explanation:

because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7

Answer:

25, 2.45, 8, -0.84, -2

Step-by-step explanation:

negative is a least number

positive is a greater number

Positive number-8, 25, 2.45

Negative number-(-2), -0.84

ordering number from greatest to least:

25, 2.45, 8, -0.84, -2

-2 is smallest then -0.84 because 2 is bigger then 0.84. It is opposite with the positive number.

The bigger the positive number the biggest it is. While the bigger the negative number the smallest it is.

Answer:

Step-by-step explanation:

The numbers are:

● 8

● -2

● 25

● 2.45

● -0.84

To make it easy classify the positive numbers apart and the negatives ones alone

● 2.45<8< 25

● -2 < -0.84

25 is the greatest and -2 is the least

● 25 > 8 > 2.45 > -0.84 > -2

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) [tex]3+x = 27[/tex] Given

2) [tex]x+3 = 27[/tex] Commutative property

3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition

4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property

5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction

6) [tex]x=24[/tex] Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) [tex]\frac{x}{6} = 5[/tex] Given

2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division

3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication

4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property

5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse

6) [tex]x = 30[/tex] Modulative property/Result

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

36×7

=252

Explaination :

First Multiply 6 and 7 we get 42 !

Write 2 and 4 will be added to the product of 3×7

We get 21 and add 4 here

So we get 252

Answer:

[tex]36 \times 7 = 252[/tex]

Step-by-step explanation:

Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.

Hope it helps u mate

Answer:

66 2/3 %

Step-by-step explanation:

First find the students not in the 8th grade

24 - 8 = 16

16 students are not in the 8th grade

Take the fraction of the students not in the 8th grade over the total

16/24 = 2/3

Change to a decimal

.66666666666

Multiply by 100 to change to a percent

66.666666%

66 2/3 %

Answer:

66.67% of students are not in eighth grade

Step-by-step explanation:

8/24=1/3

1/3=0.33333333333

1-0.33333333333=0.66666666667

0.66666666667=66.67%

Answer:

Step-by-step explanation:

Given that:

population mean [tex]\mu[/tex] = 47600

population standard deviation [tex]\sigma[/tex] = 2000

sample size n = 49

Sample mean [tex]\over\ x[/tex] = 48000

Level of significance = 0.05

The null and the alternative hypothesis can be computed as follows;

[tex]H_0 : \mu = 47600 \\ \\ H_1 : \mu \neq 47600[/tex]

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics can be calculated by using the formula:

[tex]z= \dfrac{\overline X - \mu }{\dfrac{\sigma}{ \sqrt{n}}}[/tex]

[tex]z= \dfrac{ 48000-47600 }{\dfrac{2000}{ \sqrt{49}}}[/tex]

[tex]z= \dfrac{400 }{\dfrac{2000}{ 7}}[/tex]

[tex]z= 1.4[/tex]

Conclusion:

Since 1.4 is lesser  than 1.96 , we fail to reject the null hypothesis and  that there is insufficient information to conclude that the   mean gross income is not equal to $47600

The P-value is being calculate as follows:

P -value = 2P(Z>1.4)

P -value =  2 (1 - P(Z< 1.4)

P-value = 2 ( 1 - 0.91924)

P -value = 2 (0.08076 )

P -value = 0.16152

Answer:

24 and 32 ft or 32 and 24 ft

Step-by-step explanation:

Perimeter of rectangle(p)=2(l+b)

or, 112/2=l+b

Therefore, l+b=56

Now,

diagonal(d)=40

By pythogoras theorem,

h^2=p^2+b^2 (d=h here)

40^2=l^2+b^2

Now,

Square l+b=56

(l+b)^2=56^2

l^2+2lb+b^2=3136

2lb=3136-1600

lb=1536/2

Therefore, lb=768

b=768/l

Now,

Perimeter of rectangle(p)=2(l+b)

l+b=56

l+768/l=56

l^2+768=56l

l^2+768-56l=0

Factoring,

(l - 32) (l - 24) = 0

Either l= 32 or l = 24

When l=32,

l+b=56

32+b=56

b=24

When l=24

l+b=56

24+b=56

b=32

So the dimensions of the dance floor are 24 and 32 ft or 32 and 24 ft.

Answer:

24 ft x 32 ft

Step-by-step explanation:

[tex]2x+2y=112[/tex]

[tex]\sqrt{x^{2}+y^{2} } =40[/tex]

Graph the equations

Find the point where they intersect

Answer is 24 ft and 32 ft

Answer:

2 . y=-1

Step-by-step explanation:

m=0  (it is a straight line)

use (-6,-1) in y=mx+b

-1=0(-6)+b

-1=b

equation is now

y=0(x)-1

y=-1

Answer:

7.745

Step-by-step explanation:

Square root of 60 equals X.

Answer:

[tex]D = 42.5\ inch[/tex]

Step-by-step explanation:

Given

[tex]L = Length[/tex] and [tex]W = Width[/tex]

[tex]L:W = 8: 5[/tex]

[tex]Perimeter = 117[/tex]

Required

Determine the Diagonal

First, the dimension of the screen has to be calculated;

Recall that; [tex]L:W = 8: 5[/tex]

Convert to division

[tex]\frac{L}{W} = \frac{8}{5}[/tex]

Multiply both sides by W

[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]

[tex]L = \frac{8W}{5}[/tex]

The perimeter of a rectangle:

[tex]Perimeter = 2(L+W)[/tex]

Substitute [tex]L = \frac{8W}{5}[/tex]

[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]

Take LCM

[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]

[tex]Perimeter = 2(\frac{13W}{5})[/tex]

Substitute 117 for Perimeter

[tex]117 = 2(\frac{13W}{5})[/tex]

[tex]117 = \frac{26W}{5}[/tex]

Multiply both sides by [tex]\frac{5}{26}[/tex]

[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]

[tex]\frac{5 * 117}{26} = W[/tex]

[tex]\frac{585}{26} = W[/tex]

[tex]22.5 = W[/tex]

[tex]W = 22.5[/tex]

Recall that

[tex]L = \frac{8W}{5}[/tex]

[tex]L = \frac{8 * 22.5}{5}[/tex]

[tex]L = \frac{180}{5}[/tex]

[tex]L = 36[/tex]

The diagonal of a rectangle is calculated using Pythagoras theorem as thus;

[tex]D = \sqrt{L^2 + W^2}[/tex]

Substitute values for L and W

[tex]D = \sqrt{36^2 + 22.5^2}[/tex]

[tex]D = \sqrt{1296 + 506.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = 42.4529150943[/tex]

[tex]D = 42.5\ inch[/tex] (Approximated)

Answer:

Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function

g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)?

left 13 units, down 2 units

right 13 units, down 2 units

left 13 units, up 2 units

right 13 units, up 2 units

Answer:

f(x) = x^2 - 3x -10

Step-by-step explanation:

If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).

The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10

Answer:

hope this answer helps.

Answer:

Option A. 4√5

Step-by-step explanation:

To obtain the value of x, we must first obtain the value of y as shown in the attached photo.

The value of y can be obtained by using the pythagoras theory as illustrated below:

In this case y is the longest side i.e the Hypothenus.

y² = 4² + [4√3]²

y² = 4² + [4² × (√3)²]

y² = 4² + [4² × 3]

y² = 16 + [16 × 3]

y² = 16 + 48

y² = 64

Take the square root of both side

y = √64

y = 8

Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.

Note: x is the longest side i.e the Hypothenus in this case.

x² = 4² + 8²

x² = 16 + 64

x² = 80

Take the square root of both side

x = √80

x = √(16 × 5)

x = √16 × √5

x = 4√5

Therefore, the value of x is 4√5.

Answer:

(f+g)(x) = 5x + 3

Step-by-step explanation:

(f+g)(x) is the sum (term by term) of f(x) and g(x):

(f+g)(x) = 2x - 6 + 3x + 9

Combining like terms, we get

(f+g)(x) = 5x + 3

Answer:

(f+g)(x)= 5x+3

Step-by-step explanation:

The question asks us to find (f+g)(x). In other words, the sum of f(x) and g(x).

f(x) + g(x)

We know that f(x)= 2x-6 and g(x)=3x+9. Therefore, we can substitute the expressions in.

(2x-6) + (3x+9)

Now, simplify by combining like terms. Add the terms with variables, then the terms without variables.

(2x+3x) + (-6+9)

Add 2x and 3x.

5x + (-6 + 9)

Add -6 and 9.

5x + 3

If f(x)=2x-6and g(x)=3x+9, then (f+g)(x) is 5x+3

Answer:

Step-by-step explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar  is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using  the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 =  xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295

Answer:

Number 1: A

Number 2:D

Step-by-step explanation:

Let the missing number be x.

=> x + 44587 = 65000

=> x = 65000 - 44587

= 20413

Ans.= The missing number will be 20413.

Hope this answer helps you..

..

..

Select it as the BRAINLIEST..

Answer:

2.8 < x < 5.4

Step-by-step explanation:

Given the triangle with two known sides, 4.1 and 1.3, the range of possible values of the third side, x, can be ascertained by considering the triangle inequality theorem.

According to the theorem, when you add any two of the angles in a triangle, it should give you a value greater than the third side.

If a, b, and c are 3 sides of a triangle, the theorem implies that:

a + b > c.

Therefore, a - b < c < a + b

We can use this logic to find the possibly values of x in the given triangle above.

Thus,

4.1 - 1.3 < x < 4.1 + 1.3

2.8 < x < 5.4

Range of possible sizes of x is 2.8 < x < 5.4

Step-by-step explanation:

Given that,

To find,

Firstly we'll find the base radius of the cylinder.

[tex]\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\[/tex]

According to the question,

[tex]\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\[/tex]

[tex]\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\[/tex]

[tex]\longmapsto\rm{4312 = 88 \times r^2 }\\[/tex]

[tex]\longmapsto\rm{\cancel{\dfrac{4312}{88}} = r^2 }\\[/tex]

[tex]\longmapsto\rm{49 = r^2 }\\[/tex]

[tex]\longmapsto\rm{\sqrt{49} = r }\\[/tex]

[tex]\longmapsto\rm{7 \; cm = r }\\[/tex]

Now,

[tex]\longmapsto\rm{Diameter = 2r }\\[/tex]

[tex]\longmapsto\rm{Diameter = 2(7 \; cm) }\\[/tex]

[tex]\longmapsto\bf{Diameter = 14 \; cm}\\[/tex]

The required answer is 14 cm.

Answer:

About 1.85 seconds and 13.15 seconds.

Step-by-step explanation:

The height (in feet) of the rocket t seconds after launch is given by the equation:

[tex]h = -16t^2 + 240 t[/tex]

And we want to determine how many seconds after launch will be rocket be 390 feet above the ground.

Thus, let h = 390 and solve for t:

[tex]390 = -16t^2 +240t[/tex]

Isolate:

[tex]-16t^2 + 240 t - 390 = 0[/tex]

Simplify:

[tex]8t^2 - 120t + 195 = 0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]

In this case, a = 8, b = -120, and c = 195. Hence:

[tex]\displaystyle t = \frac{-(-120)\pm \sqrt{(-120)^2 - 4(8)(195)}}{2(8)}[/tex]

Evaluate:

[tex]\displaystyle t = \frac{120\pm\sqrt{8160}}{16}[/tex]

Simplify:

[tex]\displaystyle t = \frac{120\pm4\sqrt{510}}{16} = \frac{30\pm\sqrt{510}}{4}[/tex]

Thus, our two solutions are:

[tex]\displaystyle t = \frac{30+ \sqrt{510}}{4} \approx 13.15 \text{ or } t = \frac{30-\sqrt{510}}{4} \approx 1.85[/tex]

Hence, the rocket will be 390 feet above the ground after about 1.85 seconds and again after about 13.15 seconds.

Answer:

A

Step-by-step explanation:

the factored form of the binomial expansion x^3 + 9x^2 + 27x + 27 is (x+3)^3

Answer:

Step-by-step explanation:

x² + 5x - 24

To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24

That's

x² + 8x - 3x - 24

Factorize x out

That's

x( x + 8) - 3(x + 8)

Factor x + 8 out

We have the final answer as

Hope this helps you

Answer:(x-3)(x+8)

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

75                60

------     =      ------

100                x

100 x 60 = 6000

75x = 6000

x =  80

Answer:

Step-by-step explanation:

15-10=5 degrees

Answer:

George has eaten 5/8 of the pizza

Step-by-step explanation:

Step 1: Multiple 1/4 by 2 so it shares a common denominator with 3/8

1.4 x 2 = 2/8

Step 2: Because they share a denominator you can add the numerator together

2/8 + 3/8 = 5/8

Therefore George has eaten 5/8(Five Eigths) of the pizza

George has eaten 5 by 8 of the pizza

Here we have to Multiple 1 by 4 with 2 so it shares a common denominator with 3 by 8

[tex]1.4 \times 2 = 2\div 8[/tex]

Now  

since they share a denominator you can add the numerator together

So,  [tex]\frac{2}{8} + \frac{3}{8} = \frac{5}{8}[/tex]

Learn more: https://brainly.com/question/17429689?referrer=searchResults

Answer:

x = 3/2

Step-by-step explanation:

4/3 ( 3x+9) -2x= 15

Distribute 4/3

4x+12 -2x =15

Combine like terms

2x+12 = 15

Subtract 12 from each side

2x+12-12 =15-12

2x = 3

Divide by 2

2x/2 = 3/2

x = 3/2

Answer:

4/3(3x+9)-2x=15

4x+12+9-2x=15

2x+21=15

2x=-6

x=-3

Let me know if this helps!

Answer:

8[2]×88888

Step-by-step explanation:

[8×8]=8[2]×88888

Answer:

[tex]56[/tex] choices

Step-by-step explanation:

We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.

To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.

Anyways, back to the solving! Remember that the combination formula is

[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.

In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:

[tex]_8C_3=\frac{8!}{3!5!}[/tex]

[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)

[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])

[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)

[tex]=8*7[/tex] (Cancel out [tex]6[/tex])

[tex]=56[/tex]

Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!