What is the congruence correspondence, if any, that will prove the given triangles congruent?
multiple choices on pic

Answer:

plotting the (x,y) coordinates in graph

Step-by-step explanation:

5.

[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]

Simplify both radicals.

[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]

Apply Quadratic Formula

First. find the discramnint.

[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]

Now find the divisor 2a.

[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]

Then,take the square root of the discrimant.

[tex] \sqrt{64} = 8[/tex]

Finally, add -b.

[tex] - (4 + 2 \sqrt{7} )[/tex]

So our possible root is

[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]

Which simplified gives us

[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]

Rationalize the denominator.

[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]

Which simplified gives us

[tex] \frac{6 + \sqrt{7} }{29} [/tex].

6. The answer is 2.

9514 1404 393

Answer:

  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]

__

Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2

Step-by-step explanation:

Answer:

[tex]32[/tex]

Step-by-step explanation:

[tex]x=\dfrac{180-116}{2}=\dfrac{64}{2}=32[/tex]

Answer:

7 and 1 respectively

Step-by-step explanation:

1/7= 7 ) 1 (, the basic definition of division

Answer:

Irrational

Step-by-step explanation:

The constant [tex]\pi[/tex], or "pi", is an irrational mathematic constant that corresponds to a non-terminating (never-ending decimal). Because there are an infinite number of digits in pi, pi cannot be expressed as a fraction and therefore is irrational.

Multiplying or adding a rational number does not make pi rational, and therefore the desired answer is (D) Irrational.

Answer:

P(red, blue) = 1/12

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

because only 48 is dividable by 6

Answer: Third Choice. Thousandths

Step-by-step explanation:

Concept:

Here, we need to know the order and name of each place value.

Please refer to the attachment below for the specified names.

Solve:

STEP ONE: Orde and name each place

2 ⇒ One Thousands

4 ⇒ Hundreds

5 ⇒ Tens

6 ⇒ Ones

.

1 ⇒ Tenths

3 ⇒ Hundredths

8 ⇒ One Thousandths

7 ⇒ Ten Thousandths

STEP TWO: Find the number [8] in the number

As we can see from the list above, 8 is at the right of the decimal point, thus, the place value is Thousandths.

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

-5x + 4y > -24

Plot and draw a graph that's it

Answer:

Step-by-step explanation:

hello

add me on s

ghazalp2186

love xx

and i dont know the answer

Final Answer: 82.2

formula used: a² + b² = c²

a = 66

b = 49

c = x

Solution:

66² + 49² = x²  (note: 66² = 66 × 66 = 4,356 and 49² = 49 × 49 = 2,401)

4,356 + 2,401 = x²

[tex]\sqrt{6,757}[/tex] = [tex]\sqrt{x^2}[/tex]

82.201 = x

rounded to the nearest tenth: 82.2

hope this helps, let me know if its incorrect or not

have a great day ;)

Answer:

When

when x = - 3 then y=. -10

when y = 2 then x =. -1

Answer:

The 80th term is 482

Step-by-step explanation:

8,14,20,26

This is an arithmetic sequence

Find the common difference by taking the second term and subtracting the first term

14-8 = 6

We are adding 6 each time

The formula for an arithmetic sequence is

an =a1+d(n-1)  where a1 is the first term, d is the common difference and n is the term we are looking for

a80 = 8+6(80-1)

       = 8 + 6*79

     = 8+474

    = 482

The 80th term is 482

Answer: 482

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{Rule:} \\\\\boxed{ \huge \boxed{a_n=a_1+(n-1)d }} } \ \ \\\\\\ 8 \underbrace{}_6 14 \underbrace{}_620\underbrace{}_626 ......a_{80}=? \\\\\\a_1=8 \ \ ; \ \ d=6 \\\\\\ a_{80}=8+(80-1)\cdot 6=480+8-6=482 \\\\\\\\ Answer: \boxed{\boldsymbol{ a_{80}=482}}[/tex]

Answer:

7238.23

Step-by-step explanation:

v=4/3πrcubed

solve it and get the answer

Answer: 62

Step-by-step explanation:

[tex]\displaystyle\bf 9x^2-4x-7 =0 \\\\ Synthetic \ \ division\ \ if \ \ x-3 =0 => x=3 \\\\ then \ \ 3| \underline{ \ 9 \ | \ -4 \ | \ -7 \ | } \\\\ . \!\! \qquad\qquad +|3*9| \ \ 23*3 | \\ .\!\!\!\!\!\1 \qquad \qquad \qquad | \ 23 \ | \ \ \ \boxed{62}[/tex]

Answer: A) 1

Answer:

30

Step-by-step explanation:

First, we can say that because the men do 1/3 of the work in 20 days,

for 10 men:

20 days = 1/3 total work

Because we need the house built in 30 days, and 20 days have already passed, we only have 30-20=10 days left. Furthermore, 20/2=10, so in our equation of 20 days = 1/3 total work, we can divide both sides by 2 to get

10 days = 1/6 total work

The amount of work we need to get done in 10 days is (all of it) - (1/3 of total work) = 1 - 1/3 = 2/3 = 4/6

Since 10 men can do 1/6 of the work in 10 days, 10*4 =40 men can do 1/6 * 4 = 4/6 of the work in 10 days. This is the amount of work that needs to get done. Therefore, the contractor needs 40 (total workers) - 10 (current workers) = 30 new workers to finish the remaining work in due time

Answer:

c

Step-by-step explanation:

Answer:

C. y - 7 < 2x - 6

Step-by-step explanation:

A. y + 7 < 2x + 6

0 + 7 < 2(0) + 6

7 < 0 + 6

7 < 6 —————- FALSE

B. y + 7 < 2x - 6

0 + 7 < 2(0) - 6

7 < 0 - 6

7 < -6 —————FALSE

C. y - 7 < 2x - 6

0 - 7 < 2(0) - 6

-7 < 0 - 6

-7 < -6 —————TRUE

D. y - 6 < 2x - 7

0 - 6 < 2(0) - 7

-6 < 0 - 7

-6 < -7 ————— FALSE

Answer:

x =10

y = 10 sqrt(3)/ 3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 60 = 5 sqrt(3) / x

x sin 60 = 5 sqrt(3)

x = 5 sqrt(3)/sin 60

x = 5 sqrt(3) / sqrt(3)/2

x = 5*2

x =10

tan theta = opp /adj

tan 60 = x/y

ytan 60 = 10

y = x/ tan 60

y = 10/ sqrt(3)

y = 10/ sqrt(3)  * sqrt(3)/ sqrt(3)

y = 10 sqrt(3)/ 3

Answer:

12,24 etc

Step-by-step explanation:

4 and 6 both go into 12 evenly

4*3 = 12

6*2 = 12

12 is the least common denominator

We could also use 24

4*6 = 24

It is a common denominator, but not the least common denominator

We can use any multiple of 12

Answer:

see below

Step-by-step explanation:

y = x^2 +2x - 8

Factor

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

The zeros are

x+4 = 0  x-2 = 0    

x= -4    x= 2

(-4,0)  (2,0)

The axis of symmetry is 1/2 way between the zeros

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

x = -1

The x coordinate of the vertex is at the axis of symmetry

The y value is found by substituting x=-1

y = (-1+4) (-1-2)= 3*-3 = -9

Vertex ( -1,-9)

The domain is all real numbers

The range is from -9 up

y≥ -9  since it opens upward

Answer:

A = 16.625

Step-by-step explanation:

Given :-

To rewrite in :-

Answer :-

Hence :-

Answer:

Answer: Option D

Step-by-step explanation:

Hey there!

From the above question;

The line passes through (-3,0) and (0,3).

Use double point formula;

[tex]( y - y1) = \frac{(y2 - y1)}{(x2 - x1)} (x - x1)[/tex]

Keep all values;

[tex](y - 0) = \frac{(3 - 0)}{(0 - ( - 3))} (x + 3)[/tex]

Simplify it;

[tex]y = \frac{3}{3} (x + 3)[/tex]

Therefore, y = x+3.

Hope it helps!

Answer:

D

Step-by-step explanation:

Answer:

x = 67

Step-by-step explanation:

∠ C = ∠ FGD ( corresponding angles )

Consecutive angles in a parallelogram sum to 180° , then

∠ B + ∠  C = 180 , substitute values

73 + x + 40 = 180

x + 113 = 180 ( subtract 113 from both sides )

x = 67

Answer:

Step-by-step explanation:

<B = <GFE                       The parallelograms are similar.

<GFD + <GFE = 180         Consecutive angles in a parallogram = 180

<GFD = x + 40                 Given

FGE = 73                          Step One

x + 40 +   73 = 180           Substitution

x + 113 = 180                     Subtract 113 from both sides

x = 67  

Answer:

6.86 to 2DP.

Step-by-step explanation:

7/12 = 4/DC

Cross multiply:

7DC = 4*12

DC = 48/7

= 6.857.

Answer:

Step-by-step explanation:

x + y = −3

y = 2x + 2

Substitute the y value of the second equation into the top equation

x + 2x + 2 = - 3

3x + 2 = - 3

3x = -3 -2

3x = - 5

x = -5/3

x + y = - 3

-5/3 + y = - 3

y = -3 + 5/3

y = -1 1/3

Answer:

1/25

Step-by-step explanation:

f(x) = 5^x

Let x = -2

f(-2) = 5^-2

We know a^-b = 1/a^b

f(-2) = 1/5^2

      = 1/25

Answer:

[tex]\frac{1}{25} [/tex]

Step-by-step explanation:

[tex]f(x) = {5}^{x} \\ f( - 2) \\ f( - 2) = {5}^{ - 2} \\ = \frac{1}{ {5}^{2} } \\ = \frac{1}{25} [/tex]