Noah has 12 yellow square cards and 18 green ones. All the cards are the same size. He would like to arrange the square cards into two rectangles—one of each color. He wants both the yellow and green rectangles to have the same height and to be as tall as possible. What is the tallest possible height for the two rectangles?

Answer:

[tex]\angle L=\angle S[/tex] using congruence rule

Step-by-step explanation:

Given: ΔSAL, SA = LA and AT is the bisector of [tex]\angle A[/tex]

To prove: [tex]\angle L=\angle S[/tex]

Proof:

Two triangles are congruent if they have same shape and same size.

Consider triangles ALT and AST

AL = AS

As AT bisects [tex]\angle A[/tex], [tex]\angle LAT=\angle SAT\\[/tex]

AT = AT (common side)

So, [tex]\Delta ALT\cong \Delta AST[/tex] ( by SAS congruence rule )

Here, SAS denotes side-angle-side

[tex]\angle L=\angle S[/tex] (using corresponding parts of congruent triangles)

Hence proved

Explanation:

First, we know that △ALT ≅ △AST, because of Side Angle Side Theorem. Next, we know that AL ≅ AS, because it's given.

Since A = A, we can remove A and it gives us m∠L = m∠S.

If you need to show work in math terms, your answer should look something like this:

1. △ ALT ≅ △AST - SAS

2. AL ≅ AS - Given

3. m∠ L ≅ m∠S

Hope this helped!

Answer:

[tex]\frac{rise}{run} =\frac{4}{1} =4[/tex]

Step-by-step explanation:

Answer:

=82%

Step-by-step explanation:

64:78*100=82%

Answer: [tex]-2x^3-14x^2+7x-4[/tex]

Step-by-step explanation:

[tex](3x^3-2x^2+4x-8)-(5x^3+12x^2-3x-4)[/tex]

Distribute the negative sign.

[tex](3x^3-2x^2+4x-8)-5x^3-12x^2+3x+4[/tex]

Remove the other parentheses.

[tex]3x^3-2x^2+4x-8-5x^3-12x^2+3x+4[/tex]

Combine like terms.

[tex]-2x^3-14x^2+7x-4[/tex]

Answer:

2/36

Step-by-step explanation:

There are 36 possibilities when rolling a die

There are 2 that sum to 11

P (sum of 11) =  sum of 11/ total

                      =2/36

                        1/18

As both of the values are equal to each other.

A square root of a number is a value that, when multiplied by itself, gives the number.

Here, given that,

6^(1/2) and √6

Now, we know that both have same value.

6^(1/2)=√6 ≈2.45

Hence, they are equal.

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Answer:

ZY = 14, SQ= 28

Step-by-step explanation:

Because of "ZR=ZS" and "YR=YQ", so we can apply the Thales theorem:

[tex]\frac{x+2}{3x-8}=\frac{RZ}{RS} =\frac{1}{2} \\[/tex]

so 2(x+2)= 3x-8

2x+4 = 3x-8

2x-3x= -8 -4

-x = -12

or x =12

ZY = x+ 2 = 12+ 2 = 14

SQ= 2*ZY= 2*14 = 28

Answer:

You will break even with the cost of your supplies equals your income how many cups of your hot chocolate and less you sell to break even

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

NO is not parallel to ML.

Answer:

13.8

Step-by-step explanation:

Step-by-step explanation:

Start with a point on (0,6) This is because the 6 represents the point on the y - axis

Then, move up 1 and 3 to the right; This should result with a point on (3,7)

Keep repeating this to get your line

Answer:

x intercept = (6,0)

y intercept = (0,-18)

the line is negative so it'll look like that -> /

Step-by-step explanation:

Answer: is there a gra or something to show

Step-by-step explanation:

Answer:

area of a rectangle/front side of the box = 100 cm²

Step-by-step explanation:

The prism box is a rectangular prism and the front side of the box will be made of the clear material. The other sides will be made of cardboard paper. The surface area of the side with clear material is only the area of the front side of the box. The area of only the front side is the area of 1 rectangle.

The box has a length of 20 cm , height of 5 cm and a width of 4 cm. The surface area of only the front side of the box which is the area of one rectangle only deals with the height and the length.

area of a rectangle/front side = length × height

where

length = 20 cm

height = 5 cm

area of a rectangle/front side = 20 × 5

area of a rectangle/front side = 100 cm²

Answer:

D. 100

Step-by-step explanation:

20x5=100

I did the test! Good luck with the rest of your test! Have a good day/night! <3

Answer:

Between -2 and 0

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

x² - 14x = 0

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 7)x + 49 = 0 + 49

(x - 7)² = 49 ( take the square root of both sides )

x - 7 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 7 to both sides )

x = 7 ± 7 , thus

x = 7 + 7 = 14 or x = 7 - 7 = 0

Answer:

Probability that 3 out of the next 5 voters approving the proposal is 0.3125.

Step-by-step explanation:

We are given that the sample probability of the voters approving the proposal is 50% and Political scientists want to determine the probability of exactly 3 out of the next 5 voters they meet approving a proposal.

The above situation can be represented through binomial distribution;

[tex]P(X=r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 5

            r = number of success = exactly 3

            p = probability of success which in our question is probability of

                  the voters approving the proposal, i.e; p = 50%

Let X = Number of voters approving the proposal

So, X ~ Binom(n = 5 , p = 0.50)

Now, Probability that 3 out of the next 5 voters approving the proposal is given by = P(X = 3)

               P(X = 3)  =  [tex]\binom{5}{3} \times 0.50^{3} \times (1-0.50)^{5-3}[/tex]

                              =  [tex]10 \times 0.50^{3} \times 0.50^{2}[/tex]

                              =  0.3125

Answer:

a=he went back home

b=speed=240km/h

Step-by-step explanation:

ps: wouldn't mind brainliest

Answer:

a) Jo moved 1 kn from her starting position at minute 10

b) 0.13 km/min

Step-by-step explanation:

Look at the picture

Answer:

1) Negative (because y value decreases from left to right)

2) Undefined (a vertical line has undefined slope because it fails the vertical line test infinite times)

3) Positive (because y value increases from left to right)

Step-by-step explanation:

Answer:

Three-ninths < One-half < Five-sixths < 1

Step-by-step explanation:

We are supposed to compares Five-sixths, One-half, Three-ninths, and 1

[tex]\frac{5}{6} , \frac{1}{2},\frac{3}{9} , 1[/tex]

Take LCM of denominators

LCM of 6,9,2,1 = 18

[tex]\frac{5}{6} \times \frac{3}{3}=\frac{15}{18}[/tex]

[tex]\frac{1}{2} \times \frac{9}{9}=\frac{9}{18}[/tex]

[tex]\frac{3}{9} \times \frac{2}{2}=\frac{6}{18}[/tex]

[tex]1 \times \frac{18}{18} = \frac{18}{18}[/tex]

[tex]\frac{6}{18}<\frac{9}{18}<\frac{15}{18}<\frac{18}{18}[/tex]

[tex]\frac{3}{9}<\frac{1}{2}<\frac{5}{6} < 1[/tex]

Three-ninths < One-half < Five-sixths < 1

Answer:

Three-ninths < One-half < Five-sixths < 1

Step-by-step explanation:

Answer:

i used calculator and got 1

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Look at the attachment

Answer:

The area of sector is [tex]25.12 miles^2[/tex]

Step-by-step explanation:

Radius of circle = 4 miles

We are supposed to find the area of a sector bounded by a 180 arc

[tex]\theta = 180^{\circ}[/tex]

Area of sector =[tex]\frac{\theta}{360^{\circ}} \pi r^2[/tex]

Area of sector = [tex]\frac{180^{\circ}}{360^{\circ}} \times \frac{22}{7} \times 4^2[/tex]

Area of sector = [tex]25.12 miles^2[/tex]

Hence The area of sector is [tex]25.12 miles^2[/tex]

Answer:

28 hope this helped

Step-by-step explanation:

20+26+26=72

72+28=100

100/4=25

let the number be X

20 + 26 + 26 + X /4 = 25

72 + X /4 = 25

cross multiply

72 + X = 25*4

72 + X = 100

X = 100.- 72 = 28

X = 28

proof

20 + 26 + 26 +28 / 5 = 25

I hope it will help. can I have braainlest

The answer is B. Loan given for a short period of time that is not dependent on credit history

I just took the quiz and I am big brain.

A loan given for a short period of time that is not dependent on credit history is called a easy - access credit.

Credit is the ability to borrow money or access goods or services with the understanding that you'll pay later.

Given is the easy-access credit.

Easy access credit refers to very short-term and usually very high interest loans. It's a fancy way of saying payday loans, pawn shop transactions, or title loans.

Therefore, a loan given for a short period of time that is not dependent on credit history is called a easy - access credit.

To solve more questions on credits, visit the link below-

https://brainly.com/question/29632930

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Answer:

ln(216[tex]x^{4}[/tex] )

Step-by-step explanation:

Using the rules of logarithms

log x + log y = log(xy)

log [tex]x^{n}[/tex] ⇔ n log x

Given

3ln6 + 4lnx

= ln 6³ + ln[tex]x^{4}[/tex]

= ln (216[tex]x^{4}[/tex] )

Answer:

Its D

Step-by-step explanation:

Always substitute variable first !

10(10) - ( 10x6 - 2(6) )

100- ( 60-12)

100 - 48

52!