(3x + 10) + (3x + 2)

Answer:

SAS theorem

Step-by-step explanation:

Given

[tex]\square ABCD[/tex]

[tex]\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD[/tex]

[tex]\angle BAC = \angle DCA[/tex]

Required

Which theorem shows △ABE ≅ △CDE.

From the question, we understand that:

AC and BD intersects at E.

This implies that:

[tex]\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC[/tex]

and

[tex]\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED[/tex]

So, the congruent sides and angles of △ABE and △CDE are:

[tex]\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD[/tex] ---- S

[tex]\angle BAC = \angle DCA[/tex] ---- A

[tex]\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED[/tex] or [tex]\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC[/tex]  --- S

Hence, the theorem that compares both triangles is the SAS theorem

Answer:

The discount takes $25 dollars off

Step-by-step explanation:

So yes, he'll pay $100 after the discount is applied

Answer:

25 dollars

Step-by-step explanation:

125 - 100= 25

50×100÷110=45.454545r6

#'s 9-14

Base info:   40% are red, 30% are white, 20% are blue, and 10% are green

9) 40% chance to get red, 10% chance to get green. 50% chance to get one of either.

10) getting red: 40%

Getting blue: 20%

11) 80%  (100% - 20% = 80%)

1/8 = 12.5%

12) 12.5% chance

13) 25% chance

14) 12.5 x 5 = 62.5  

62.5% chance

Answer:

Step-by-step explanation:

r=4, w=3, b=2, g=1, t=(4+3+2+1)=10

9) P(r or g)=4/10+1/10=5/10= 1/2

10) P(r or b)=4/10+2/10=6/10= 3/5

11) P(!b)=P(r or w or g)=4/10+3/10+1/10=8/10= 4/5

12) There are six numbers and only one six, P(6)= 1/6

13) The only even numbers less than 5 are 2 and four so

P(e<5)=2/6= 1/3

14) The primes on a die are 2,3,5 so three primes out of six numbers

P(!)=3/6= 1/2

15) 2,3,4,6 are multiples of 2 and three

P(2n or 3n)=4/6= 2/3

16) We want a one half probability so

P(W)=(3+x)/(3+4+2+x)=1/2

(3+x)/(9+x)=1/2

2(3+x)=9+x

6+2x=9+x

x=3

So 3 white marbles have to be added.

17) (3+x)/(9+x)=2/3

3(3+x)=2(9+x)

9+3x=18+2x

x=9

So nine whites need to be added.

Answer:

First option: 336

Step-by-step explanation:

To find the answer, separately solve for each of the shapes.

1. The base is the square so length times width is the formula:

12 x 12 = 144

144 is the area of the square

Next, find the 4 triangles which are congruent(the same).

Triangle area formula: Base x Height divided by 2.

So, the area of 1 triangle is 12 x 8 =96

96/2 = 48

Area =48

Because there are 4 triangles, do 48 x 4=192.

Finally, add the area together and you should get 192+144 =336 ft^2

Surface area = 336 ft^2

Given:

In a triangle, side x has a length of 15 cm and side y has a length of 4 cm.

To find:

The possible value of side z.

Solution:

In a triangle, the sum of two smaller sides must be greater than the largest side otherwise the triangle is not possible.

Case I: Let x be the largest side, then

[tex]y+z>x[/tex]

[tex]4+z>15[/tex]

[tex]z>15-4[/tex]

[tex]z>11[/tex]               ...(i)

It is clear that [tex]y<x[/tex]. So, y cannot be a largest side.

Case II: Let z be the largest side, then

[tex]x+y>z[/tex]

[tex]15+4>z[/tex]

[tex]19>z[/tex]               ...(ii)

From (i) and (ii), we get

[tex]11<z<19[/tex]

It means the value of z lies between 11 and 19.

From the given options, only 17 is the value which lies between 11 and 19. So, the possible length of side z is 17 cm.

Therefore, the correct option is C.

Answer:

See below, please!

Step-by-step explanation:

We know that 6z-31+something is going to be equal to 180 degrees, because it is supplementary. But what is that something? We see 67 degrees. Do you think this is a corresponding angle to the something that we need to find? Yes, it is! So we know that 6z-31+67 is equal to 180. So, z is 24. Now, since we know the value of the something (67 degrees because of corresponding angles) we can find yet another pair of supplementary angles. 67+x=180! Kind of neat, huh? So, x is equal to 113.

Hope this helped!

Answer:

200.96

Step-by-step explanation:

64x3.14=200.96

Answer:

A= 200.96in2

Step-by-step explanation:

8×8=64

64×3.14=200.96

Answer:

90

Step-by-step explanation:

you have to multiply A B and C and you should get 90

i think i'm right

9514 1404 393

Answer:

  f(x) = 2(x -3)² +5

Step-by-step explanation:

For vertex (h, k) and scale factor 'a', the vertex form is ...

  f(x) = a(x -h)² +k

We can fill in the values of h and k from your vertex, and use the values of the extra point to find 'a'.

  55 = a(-2 -3)² +5

  50 = 25a . . . . . . . . subtract 5

  a = 2 . . . . . . . . . . . divide by 25

So, the function is ...

  f(x) = 2(x -3)² +5

__

In standard form, that will be ...

  f(x) = 2x² -12x +23

Answer:

78 OZ (481g)

There are 120 calories in one cup of cereal. So there would be 360 calories of cereal in three cups of cereal. this is the awnser to number two I think thought imma keep working out the problem tell me if its wrong or right

Answer:

X=4

Y=18

I think

Answer:

(- 1, - 2 )

Step-by-step explanation:

Given the 2 equations

y = - 2x - 4 → (1)

y = 4x + 2 → (2)

Substitute y = 4x + 2 into (1)

4x + 2 = - 2x - 4 ( add 2x to both sides )

6x + 2 = - 4 ( subtract 2 from both sides )

6x = - 6 ( divide both sides by 6 )

x = - 1

Substitute x = - 1 into either of the 2 equations and solve for y

Substituting into (2)

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

solution is (- 1, - 2 )

Answer:

8(m⁶ - 8n¹²p¹⁵)

Step-by-step explanation:

Given:

8m⁶ - 64n¹²p¹⁵

The only part that we can factor out is in the coefficients.  Because both terms use different variables, they can not be factored.  However, both terms are divisible by eight, so we can say it equals:

8(m⁶ - 8n¹²p¹⁵)

And that is all the factoring that can be done.

Answer:

$7.98

Step-by-step explanation:

I am not sure if this is right but hopefully this helps!

Answer:

5°C

Step-by-step explanation:

Answer:

There were 343 children and 197 adults.

Step-by-step explanation:

In order to solve this problem, you can use an equation after identifying the important information, like that there were 540 people, the cost for a child is $1.25, the cost for an adult is $2.00, and admission fees totaled $822.75:

where c = number of children, and a = number of adults,

c + a = 540

1.25c + 2a = 822.75

Now, you need to solve this system of equations by isolating one of the variables. I'll isolate c by multiplying the first equation by 2 since it's easier:

  2c + 2a = 1080

- 1.25c + 2a = 822.75

= .75c           = 257.25

Now, you can multiply both sides by 4/3 to find c:

c = 257.25 × 4 ÷ 3

c = 343

So there were 343 children. Now you can find the number of adults by substituting 343 for c in the first equation:

where c + a = 540 and c = 343,

343 + a = 540

a = 197

So, there were 197 adults.

Answer:

44°

Step-by-step explanation:

8x - 4 = 6x + 8 (This is because they are corresponding angles)

8x - 6x = 8 + 4

2x = 12

x = 12 ÷ 2

x = 6

6x + 8 = angle 1 (Vertically opposite angles are equal)

Substitute the value of x in the equation '6x +8' to get the size of the angle.

6 × 6 + 8

36 + 8 = 44°

Angle 1  =  44°

Answer: to get range you subtract the largest and smallest numbers. so 18-3= 15 therefor, 15 is the range.

Hope this helps :)

The inside diameter would be the outside diameter minus 2 of the wall thicknesses.

4 9/32 - (2 x 7/32)

Simplify:

4 9/32 - 14/32

Because 14/32 is larger than 9/32 change one of the hole numbers to a fraction: 1 = 32/32

rewrite 4 9/32 as 3 41/32

Now subtract:

3 41/32 - 14/32 = 3 27/32 inside diameter.

Answer:

12,24,36,60

Step-by-step explanation:

multiples of 4 and 6 less than 61

4 (4,8,12,16,20,24,28,32,36,40,44,48,52,56,60)

6 (6,12,18,24,30,36,42,48,54,60)

common multiples (12,24,36,60)

Answer:

Kindly check explanation

Step-by-step explanation:

To test for Difference in mean times

Null hypothesis, H0 will be, there is no difference in mean times ; m1 = m2

Alternative hypothesis, there is difference in mean times ; m1 ≠ m2

Decision region :

When p value < α ; reject the Null

Here. ;

Pvalue = 2% = 0.02

α = 1% = 0.01

Pvalue > α

0.02 > 0.01

Since, Pvalue > α ; we do not reject the Null ;

Hence, conclusion should be, there is no difference in mean times of bus and car

Answer:

5.3!

Step-by-step explanation:

I took the test on k12 mathematics :)

Answer:

38

Step-by-step explanation:

Answer:

x>9

Step-by-step explanation:

Tamika already has $55, which will stay the same independent of how much time passes. Since she deposits $5 per week, we can assign weeks a variable x. The amount of money in her account after x weeks is equal to 55+5x. If she must save over $100, we can create an inequality to solve for how many weeks must pass: 55+5x>100.

The question also asks to solve the inequality:

This solution tells us that Tamika must save for more than nine weeks to have more than $100 in her account.

lmk if i made an error, hope this helps!!

9514 1404 393

Answer:

  m = 1/3

Step-by-step explanation:

Step 1. Pick a line of the table to use as (x1, y1).

Step 2. Pick a different line of the table to use as (x2, y2).

Step 3. Use the slope formula:

  m = (y2 -y1)/(x2 -x1)

Step 4. Simplify the result.

__

Here are these steps for this problem.

1, 2. use (x1, y1) = (-9, -5) and (x2, y2) = (-3, -3)

3. m = (-3 -(-5))/(-3 -(-9)) = 2/6

4. m = 1/3