Find missing side length given two similar triangles

Note that given the proof of congruence by SAS, the only thing remaining to know is that "2 corresponding sides and the corresponding included angles of both triangles are equal."

The definition of SAS Congruency is as follows:

The SAS postulate states that two sides and the included angle of one triangle are identical to the corresponding two sides and the included angle of another triangle.

As demonstrated in the triangle, the angles mCAD and mACB are congruent. Thus; m∠CAD ≅ m∠ACB

Because m∠CAD and m∠ACB are congruent, AD and BC must also be congruent. Now, because AC is shared by both triangles ABC and ADC, we get two matching equal sides with the included corresponding equal angles.

As a result, the SAS Congruence postulate is proven.

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answer:

B. -7x2-2

add the numbers and variables together and combine like terms

Answer:

12:1

Step-by-step explanation:

Answer:

12:1

Step-by-step explanation:

Because 12 is the amount of cookies to the ratio of hours which is 1 therfore 12:1

The current weight of the truck is given as follows:

3496 kg.

The current weight of the truck is obtained applying the proportions in the context of the problem.

The initial weight of the truck is given as follows:

3796 kg.

The weight removed from the truck is given as follows:

6 x 50 = 300 kg.

Hence the current weight of the truck is given as follows:

3796 - 300 = 3496 kg.

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140

140-15=125

125÷5=25

answer=25

Answer:

x=12

(90-35)-7/4

Answer:

x=12

Step-by-step explanation:

Since the two angles are complementary, both angles add up to 90°.

So, to find the value of the other angle, simply subtract 35 from 90.

90-35=55

Now we know that the expression is equal to 55.

4x+7=55

Subtract 7 from both sides.

4x=48

Divide both sides by 4.

x = 12

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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The true statement is Statement A which is dogs of breed B typically weigh more than dogs of breed A using histogram in probability concept.

The likelihood of each possible occurrence is displayed on the y-axis of a probability histogram. A histogram is a statistical data display that makes use of rectangles to illustrate the frequency of data items in successive numerical intervals of equal size. The dependent variable is plotted along the vertical axis in the most typical type of histogram, while the independent variable is plotted along the horizontal axis. The distribution of data is depicted graphically in a histogram. A collection of neighboring rectangles, each with a bar that represents a certain type of data, is used to illustrate a histogram. Fill L1 with the values of the random variable (remember to use the class midpoints for continuous random variables). The associated percentages should be entered into L2 with a decimal format.

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Answer:

1.

-3x + 8y = -5

6x + 2y = -8

Set the equations to a common variable.

-3x + 8y = -5 → 8y = 3x - 5 → y = 3/8x - 5/8

6x + 2y = -8 → 2y = -6x - 8 → y = -3x - 4

Set the equations equal to each other.

3/8x - 5/8 = -3x - 4

Combine like terms.

3x + 3/8x = -4 + 5/8

3.375x = -3.375

Divide by 3.375

x = -1

Plug x back in to find y.

-3x + 8y = -5

-3(-1) + 8y = -5

3 + 8y = -5

8y = -8

y = -1

answer: (-1, -1)

2.

3x + 2y = -16

-3x - 8y = 46

Set the equations to a common variable.

3x + 2y = -16 → 2y = -3x - 16 → y = -3/2x - 8

-3x - 8y = 46 → -8y = 3x + 46 → y = -3/8x - 23/4

Set the equations equal to each other.

-3/2x - 8 = -3/8x - 23/4

Combine like terms.

-9/8x = 9/4

or

-1.125x = 2.25

Divide by -1.125

x = -2

Plug x back in to find y.

3(-2) + 2y = -16

-6 + 2y = -16

2y = -10

y = -5

answer: (-2, -5)

Answer:

Combine multiplied terms into a single fraction

13(−6+4)=−112(4+4)

13(−6q+4)=−112(4q+4)\frac{1}{3}(-6q+4)=\frac{-1}{12}(4q+4)31​(−6q+4)=12−1​(4q+4)

1(−6+4)3=−112(4+4)

1(−6q+4)3=−112(4q+4)\frac{1(-6q+4)}{3}=\frac{-1}{12}(4q+4)31(−6q+4)​=12−1​(4q+4)

2

Multiply by 1

3

Combine multiplied terms into a single fraction

4

Distribute

5

Multiply all terms by the same value to eliminate fraction denominators

6

Cancel multiplied terms that are in the denominator

7

Distribute

8

Subtract

16

161616

from both sides of the equation

9

Simplify

10

Add

4

4q4q4q

to both sides of the equation

11

Simplify

12

Divide both sides of the equation by the same term

13

Simplify

Show less

Solution

=1

Step-by-step explanation:

Answer:

q=1

Step 1: Simplify both sides of the equation.

Step 2: Add 1/3q to both sides.

Step 3: Subtract 4/3 from both sides.

Step 4: Multiply both sides by 3/(-5).

Answer:

24.5%

Step-by-step explanation:

Simple Interest = (principal×rate×time)÷100. *Brackets First*

Transpose the formula to make rate the subject: rate= (100×simple interest) ÷ (principal×time).

Plug in values: rate = (100×37975) ÷ (31000×5).

The result is 24.5%.

Yards earned by, Alston = 60, Carlos = 180, Travis =190.

The 5-D Process is an organized method lead to write equations to solve real world problems. The 5-D’s stand for Describe/Draw, Define, Do, Decide, and Declare.

In the first three football games of the season, Carlos gained three times as many yards as Alston.

Travis gained ten yards more than Carlos.

Altogether, the three players gained a total of 430 yards.

Let consider yards gained by Alston as x.

yards earned by Carlos = 3x.

Yards earned by Travis = 3x+10.

The total number of yards earned by them are 430.

⇒x+3x+3x+10 = 430

⇒x=60

Hence, yards earned by Alston = 60, Carlos = 180, Travis =190.

The three trials are determined in the table based on 5-D process.

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Aidan has a total of 48 coins in his pocket.

Let's solve this problem step by step. Since Aidan has an equal number of pennies, nickels, dimes, and quarters,

let's assume he has x coins of each type.

The value of x pennies is x cents, the value of x nickels is 5x cents,

the value of x dimes is 10x cents,

and the value of x quarters is 25x cents.

We know that the total value of all the coins is $4.92,

which is equivalent to 492 cents.

So, we can set up the equation:

x + 5x + 10x + 25x = 492.

Combining like terms,

we get 41x = 492.

Dividing both sides by 41,

we find x = 12.

Since x represents the number of coins of each type,

Aidan has 12 pennies, 12 nickels, 12 dimes, and 12 quarters. To find the total number of coins,

we add up the number of each type of coin: 12 + 12 + 12 + 12 = 48.

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Answer:

1. 8 x 8 ÷ 2

2. 64 ÷ 2 = 32

Step-by-step explanation:

(7+1) becomes 8 and 8 x 8 becomes 64

64 ÷ 2 = 32

Answer: D) Flat area with a large number of plants

The roots of the plants hold in the soil, which prevents/reduces erosion.

The steeper slope means gravity pulls down the soil material faster, since there is less ground in the way to hold it up, so to speak. So flatter areas are less prone to erosion compared to steeper areas.

So that's why overall, flatter areas with lots of plants would have the least erosion.

Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Another solution

The sum of angles in the shape AGBC = 360°

Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

A sample size of at least 43 employees is needed to be 95% confident that the sample mean is within 3 pounds of the true population mean.

To determine the minimal sample size needed to be 95% confident that the sample mean is within 3 pounds of the true population mean, we can use the formula for sample size calculation:

n = (Z * σ / E)^2

where:

n = sample size

Z = Z-score corresponding to the desired level of confidence (95% confidence level corresponds to a Z-score of approximately 1.96)

σ = population standard deviation

E = maximum allowable error (3 pounds in this case)

Plugging in the given values:

n = (1.96 * 10 / 3)^2

n ≈ (19.6 / 3)^2

n ≈ 6.53^2

n ≈ 42.76

Rounding up to the nearest whole number, the minimal sample size required would be 43.

In order to be 95% certain that the sample mean is within 3 pounds of the actual population mean, a sample size of at least 43 employees is required.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

juma->300

anna->450

rose->750

Step-by-step explanation:

j : a : r

2: 3:5

2+3+5=10

10u-> 1500

1u->150

2u->300

3u->450

4u->750

Answer:

The State Department has four main foreign policy goals: Protect the United States and Americans; Advance democracy, human rights, and other global interests; Promote international understanding of American values and policies

Step-by-step explanation:

The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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In linear equation, The number of customers who will pay by debit card will be 44.

Which equation is linear?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

16 + 33 + 6 = 55 customers.

That means that the fraction of the customers, who paid by debit card, was

6/55  

In situations like that, when we use historical data and try to predict future behaviour, we use that past experience and extrapolate to a predicted result.

we simply say that we expect the same fraction, 1/30 if customers use credit cards.

for the absolute number of predicted debit  card customers we multiply the predicted number of customers by the expected fraction

400  × 6/55 = 2400  /55  = 43.63 ≈ 44

Therefore the number of customers who will pay by debit card will be 44.

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A line of symmetry would separate a shape to make multiple shapes that are exactly the same.

The answer is C.2

Option C - y = cos(x + 5π) is the equation that most closely represents the graph. See attached graph.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.

The graph of y = cos(x + 5π) is a cosine function that is shifted horizontally 5 units to the left compared to the standard cosine function.

The function is a periodic function that oscillates between -1 and 1, with each cycle shifted 5 units to the left compared to the standard cosine function.

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Answer:

13,780.8 feet

Step-by-step explanation:

1 mile = 1.609km

1 mile = 5,280ft

Convert 4.2km to miles

1.609km = 1 mile

4.2km = 4.2/1.609 miles

= 2.610 miles

Convert 2.610 miles to feet

1 mile = 5,280ft

2.610 miles = 2.610 × 5,280

= 13,780.8 feet

13,782.47 feet is the correct answer i just did this test DUUUH LOL

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

\(a = 20\) --- tree distance from north gate

\(b =14\) --- movement from south gate

\(c = 1775\) --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

\(\triangle ADE \sim \triangle ACB\) --- similar triangles

So, we have the following equivalent ratios

\(AE:DE = AB:CB\)

Where:

\(AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775\)

Substitute these in the above equation

\(20:x/2 = 20 + x + 14: 1775\)

\(20:x/2 = x + 34: 1775\)

Express as fraction

\(\frac{20}{x/2} = \frac{x + 34}{1775}\)

\(\frac{40}{x} = \frac{x + 34}{1775}\)

Cross multiply

\(x *(x + 34) = 1775 * 40\)

Open bracket

\(x^2 + 34x = 71000\)

Rewrite as:

\(x^2 + 34x - 71000 = 0\)

Expand

\(x^2 + 284x -250x - 71000 = 0\)

Factorize

\(x(x + 284) -250(x + 284)= 0\)

Factor out x + 284

\((x - 250)(x + 284)= 0\)

Split

\(x - 250 = 0 \ or\ x + 284= 0\)

Solve for x

\(x = 250 \ or\ x =- 284\)

x can't be negative;

So:

\(x = 250\)

Answer:

  -1/2

Step-by-step explanation:

You want to know the exact value of sin(-5π/6).

The reference angle is the smallest angle its terminal side makes with the x-axis. The angle -5π/6 is a 3rd-quadrant angle, whose reference angle is ...

  -5π/6 +π = π/6

You know that the signs of the sine and cosine trig functions are negative in the 3rd quadrant. Since you have memorized the short table of trig functions (first attachment), you know the value you're looking for is ...

  sin(-5π/6) = -sin(π/6) = -1/2

__

Additional comment

The second attachment shows the functions that are positive in the different quadrants. The ones not listed are negative.

The third attachment shows the coordinates on the unit circle as (cos, sin). The angle 7π/6 is the same as the angle -5π/6.

The fourth attachment shows you can put your calculator in radian mode and have it tell you the answer.

Answer:

Probabilty of both Black

= 1/6

Step-by-step explanation:

A bag contains five white balls and four black balls.

Total number of balls= 5+4

Total number of balls= 9

Probabilty of selecting a black ball first

= 4/9

Black ball remaining= 3

Total ball remaining= 8

Probabilty of selecting another black ball without replacement

= 3/8

Probabilty of both Black

=3/8 *4/9

Probabilty of both Black

= 12/72

Probabilty of both Black

= 1/6