The length of a rectangle is 12 ft longer than twice the width. If the perimeter is 96 ft, find the length and width of the rectangle

Answer:

Triangle JKL is congruent to triangle

✔ ABC

.

Side LK corresponds to sides

✔ WV and CB

.

Angle JLK corresponds to angles

✔ UWV and ACB

.

Step-by-step explanation:

just did it on edge 2020

Triangle JKL is congruent to triangle ABC.

Side LK corresponds to sides BC.

Angle JLK corresponds to angles BAC.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

As per the given information,

ΔJKL ≅ ΔUVW: This means that triangle JKL is congruent to triangle UVW. Congruent triangles have the same shape and size, so their corresponding angles and sides are equal in measure and length, respectively.

ΔUVW ≅ ΔABC: This means that triangle UVW is congruent to triangle ABC.

Combining these two pieces of information, we can conclude that:

ΔJKL ≅ ΔABC: This is because if two triangles are congruent to the same triangle, then they must be congruent to each other. Therefore, triangle JKL is congruent to triangle ABC.

Side LK corresponds to sides BC: Corresponding sides of congruent triangles are equal in length. In this case, side LK corresponds to side VW (since JKL ≅ UVW), which corresponds to side BC (since UVW ≅ ABC).

Angle JLK corresponds to angles BAC: Corresponding angles of congruent triangles are equal in measure. In this case, angle JLK corresponds to angle UVW (since JKL ≅ UVW), which corresponds to angle BAC (since UVW ≅ ABC).

So, we can say that triangle JKL is congruent to triangle ABC, side LK corresponds to sides BC, and angle JLK corresponds to angles BAC.

To learn more about the congruent;

https://brainly.com/question/12413243

#SPJ7

Answer:

1500

Step-by-step explanation:

Number of boxes = 12

Number of pencils in each box = 125

Total number of pencils

= 12 × 125

= 1500 pencils

1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x

2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x

3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1

4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x

5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x

6.  When we simplify cos x + sin xtan x, the result obtained is sec x

We can simplify the trig identities as follow:

1. Simplification of sec² x + tan² xsec² x

sec² x + tan² xsec² x = sec² x(1 + tan² x)

Recall

sec² x = 1 + tan² x

Thus,

sec² x(1 + tan² x) = sec² x × sec² x

sec² x(1 + tan² x) = sec⁴x

Therefore, the simplified is written as

sec² x + tan² xsec² x = sec⁴x

2. Simplification of (sec² x - 1) / sin² x

(sec² x - 1) / sin² x

Recall,

sec² x - 1 = tan² x

Thus,

(sec² x - 1) / sin² x = tan² x / sin² x

Recall

tan² x = sin² x / cos² x

Thus,

tan² x / sin² x = (sin² x / cos² x) / sin² x

tan² x / sin² x = 1/ cos² x

Recall

1/ cos² x = sec² x

Therefore, the simplified expression is written as:

(sec² x - 1) / sin² x = sec² x

3. Simplification of (1/sec² x) + (1/csc² x)

(1/sec² x) + (1/csc² x)

Recall

sec² x = 1/cos² x

Thus,

cos² x = 1/sec² x

Also,

csc² x = 1/sin² x

Thus,

sin² x = 1/csc² x

Therefore, we have

(1/sec² x) + (1/csc² x) = cos² x + sin² x

Recall

cos² x + sin² x = 1

Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:

(1/sec² x) + (1/csc² x)  = 1

4. Simplification of (sec x / sin x) - (sin x / cos x)

(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x

Recall

sec x = 1/cos x

sinx sinx = sin² x

Thus,

(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x

(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x

Recall

1  - sin² x = cos² x

Thus, we have

[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x

[1 - sin² x] / sinx cos x = cos x / sin x

Recall

cos x / sin x = cot x

Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:

(sec x / sin x) - (sin x / cos x) = cot x

5. Simplification of (1 + sin x)(1 - sin x)

(1 + sin x)(1 - sin x)

Clear bracket

1 - sin x + sin x - sin² x

1 - sin² x

Recall

1 - sin² x = cos² x

Thus, we have

(1 + sin x)(1 - sin x) = cos² x

6. Simplification of cos x + sin xtan x

cos x + sin xtan x

Recall

tan x = sin x / cos x

cos x + sin xtan x = cos x + sin x (sin x / cos x)

cos x + sin xtan x = cos x + (sin² x / cos x)

cos x + sin xtan x = (cos² x + sin² x) / cos x

Recall

cos² x + sin² x = 1

cos x + sin xtan x = 1 / cos x

1/cos x = sec x

Thus,

cos x + sin xtan x = sec x

The simplified expression of cos x + sin xtan x is sec x

Learn more about simplification of trig:

https://brainly.com/question/31193285

#SPJ1

Answer:

because 200 + 200 12 times is equal to 200 x 12Step-by-step explanation:

Answer:

Multiplication is a short way to write repeated addition. So 200 •12 means the same as 200 + 200 + . . . + 200.

Step-by-step explanation:

Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ1

Answer:

7/6 or 1 1/6

Step-by-step explanation:

2/3 = 4/6

1/2 = 3/6

3/6 + 4/6 = 7/6 = 1 1/6

Answer:

A) \( x = 47\sqrt 3,\:\: y = 47\)

Step-by-step explanation:

\( \sin \: 60 \degree = \frac{x}{94} \\ \\ \frac{ \sqrt{3} }{2} = \frac{x}{94} \\ \\ x = \frac{94 \sqrt{3} }{2} \\ \\ \purple{ \bold{ x = 47 \sqrt{3} }} \\ \\ \cos \: 60 \degree = \frac{y}{94} \\ \frac{1}{2} = \frac{y}{94} \\ \\ y = \frac{94}{2} \\ \\ \red{ \bold{ y = 47}}\)

Answer:

£180, £120 and £60.

Step-by-step explanation:

The number of parts = 3 + 2 + 1 = 6.

360 / 6 = 60, so the shares are:

3*60 = 180

2*60 = 120

1 * 60 = 60.

The distribution of £360 in the ratio of 3:2:1 will be  £180, £120 and £60.

What is a ratio?

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

The number of parts = 3 + 2 + 1 = 6.

360 / 6 = 60, so the shares are:

3  x 60 = 180

2 x 60 = 120

1  x 60 = 60.

Hence the distribution of £360 in the ratio of 3:2:1 will be  £180, £120 and £60.

To know more about ratios follow

https://brainly.com/question/2328454

#SPJ2

Answer:

624 pounds

Step-by-step explanation:

If 10 boxes of paper weigh 260 pounds, one box of paper is equal to 26 pounds because 260 divided by 10 is equal to 26. If one box equals 26 pounds, 24 boxes times 26 pounds each is equal to 624 pounds.

Answer:

2x + 1 = y

Step-by-step explanation:

x = Kim

y = Scott's time.

Step-by-step explanation:

150 students overall.

an immediate assumption would be that these 150 students are the universal set of students taking these classes.

but we have to be careful and check. could it be that there are more than these 3 classes for the 150 students ? or that there is an option to be a student and not take any of the classes ?

the last question (c) suggests something like that.

so, these 150 students are the universal set for all these cases.

the sum of all students that took 2 classes contains also the ones that took all 3 classes. each of these students (that took all 3 classes) are then counted three times in these groups - one time for each pair of classes.

so, 26 + 28 + 32 - 22 - 22 = 42 is the number of students that took at least 2 classes (the subtraction of 2×22 eliminates two of the triple counting of the students that took all 3 classes).

since these 42 students contain also the ones with 3 courses, we need to subtract the 22 with 3 classes a third time again to get the number of students that had exactly 2 classes :

42 - 22 = 20.

so, we have 22 students attending all 3 class.

then 20 more attending exactly 2 classes.

in detail it means for these 20

26 - 22 = 4 had taken exactly math and physics.

28 - 22 = 6 had taken exactly math and chemistry.

32 - 22 = 10 had taken exactly chemistry and physics.

and that means for the individual classes

84 - 22 - 4 - 6 = 52 had taken math only.

64 - 22 - 6 - 10 = 26 had taken chemistry only.

48 - 22 - 4 - 10 = 12 had taken physics only.

in total

150 - 52 - 26 - 12 - 20 - 22 = 18

18 students of these 150 have not attended any of these 3 classes.

(a)

so,

52 + 26 + 12 = 90

90 students took one course only.

(b)

so, the number of students that had at most 2 classes is the number of students with exactly one class (90) and exactly 2 classes (20) AND the ones without any of these 3 classes : 90 + 20 + 18 = 128

128 students took at most 2 courses.

we could have gotten this also by saying all the students not taking all 3 classes : 150 - 22 = 128

(c)

the original assumption was that 150 students did at least one of the classes. but that was wrong.

we found that 18 students did not attend any of the classes.

that means that

150 - 18 = 132

132 students took at least one of the courses.

The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.

The concrete can be considered as in the shape of a cuboid.

Length = 18

Breadth = 24'

Height = 4"

Volume of Cuboid = Length * Breadth * Height

Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³

=5.34 cu.yard.

Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

To know more about Cuboid

https://brainly.com/question/19754639

#SPJ1

Answer:

(4, 0).

Step-by-step explanation:

y = 8x - 32

There are many solutions that we can choose from, since any set of coordinates that fit in the equation counts as a solution.

We can have (0, -32), (1, -24), (2, -16), (3, -8), (4, 0), and many more.

Hope this helps!

The solution to this linear equation is x = y + 32. Explanation and answer is in the image below.

Answer:

C. 1/1,000

Step-by-step explanation:

yes or no ?

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

For similar question on probability.

https://brainly.com/question/7965468  

#SPJ8

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

Answer:

66cm is the area of the rectangle

The solution to the equation is 6 and the only restriction is that x cannot be equal to 3.

The steps to solve the given equation are;

1. Find the difference of 2x/x-3 from both sides of the equation. This gives us x+6=2x.

2. Take the difference of 2x from both sides of the equation. This gives us x+6-2x=0.

3. Simplify the left side of the equation. This gives us -x+6=0.

4. Subtract 6 from both sides of the equation. This gives us -x=-6.

5. Divide both sides of the equation by -1. This gives us x=6.

The only restriction on the variable x is that x cannot be equal to 3. This is because the denominator of the fraction x+6/x-3 would be equal to 0 if x were equal to 3.

Here is a summary of the solution:

x = 6

x cannot be equal to 3

Learn more on equation here;

https://brainly.com/question/22688504

#SPJ1

Answer: Circumference of cake board is 35π cm.

Step-by-step explanation:Since we have given that

Diameter of a round cake = 30 cm

Diameter of a cake board is 5 cm longer than the diameter of a round cake.

So, Diameter of a cake board = 30+5=35 cm

So, radius of a cake board will be

As we know the formula for " Circumference of Circle ":

So, According to question, we get,

Hence, Circumference of cake board is 35π cm.

Answer: 35π cm

Step-by-step explanation:

The distance that Mr. Stein drove can be represented by the expression: \(140 - x\)

A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.

Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.

Then, the total distance they traveled is 140 miles.

So, the distance that Mr. Stein drove can be represented by the expression:

140 - x

Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.

Learn more about expression here:

https://brainly.com/question/19864285

#SPJ1

we have that

step 1

Find the probability that selected a baby with a slow heart rate

P=29/42

step 2

Find the probability that selected a baby with brown eyes

P=

The end of the graph is

As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity

The end behavior of function typically says the characteristics of the function at the ends

This is determined by examining the graph and the coordinates.

The end behavior is can be written as

x ⇒ ∞ f(x) ⇒ -∞

x ⇒ -∞ f(x) ⇒ ∞

Learn more about end behavior here:

https://brainly.com/question/28954897

#SPJ1

Answer:

A and D

Step-by-step explanation:

Matched pairs t test is used for paired data.  Data sets are "paired" when the two sets have the same number of data points and each data point in a set is related to only one data point in the other set.

A good example is before/after data.  Each set has the same number of data points, and each data point in the after set is related to one in the before set.

B is not an option because, although the samples are the same size, there is not a paired relationship between the sets.

C is not an option because the samples are not the same size.

The probability of the Doubles" means both dice show the same number is 36.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.

The likelihood of rolling an even number or doubles is thus:

The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.

The odds of rolling an even number or two doubles are 19/36.

Therefore, the probability of the Doubles" means both dice show the same number is 36.

Learn more about probability, here:

https://brainly.com/question/30034780

#SPJ1

Answer:

27,000 feet

Step-by-step explanation:

Let \(x\) be the actual length of the pipeline, in feet.

Set up the following proportion:

\(\displaystyle\\\frac{1}{2,000}=\frac{13.5}{x}\)

Cross-multiplying yields \(x=13.5\cdot 2,000=\boxed{27,000\text{ ft}}\)

The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To study more about Probability:

https://brainly.com/question/13604758

https://brainly.com/question/251701

we have that

Answer:

Step-by-step explanation:

1 )

\(\frac{2}{5}( \frac{5x}{4} - \frac{10}{3})-\frac{4x}{3} \\\frac{x}{2} - \frac{4}{3} - \frac{4x}{3}\\ \frac{-5x}{6}-\frac{4}{3}\)

2 )

\(\frac{17x}{8}+\frac{3x}{4}+\frac{1}{6}-\frac{7x}{12}+\frac{17}{3}\\ \frac{51x}{24}+\frac{18x}{24}-\frac{14x}{24}+\frac{35}{6}\\\frac{55x}{24}+\frac{35}{6}\)