What is the length of the unknown leg in the right triangle?

A triangle with side 21 centimeters, hypotenuse 29 centimeters, and side a.
8 cm
16 cm
20 cm
40 cm

Answer:

the answer is blank, don't type anything in just f a I l

The two triangles ΔRST and ΔUVW are similar to each other by the SAS property.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that there are two triangles ΔRST and ΔUVW. ΔRST has the angle ∠T = 59° and the sides RT = 15 units and ST = 13 units. The other triangle ΔWVU has the angle ∠W = 59° and the sides WV= 52 units and WU= 60 units.

Firstly the two angles are the same,

∠T= ∠W = 59°

The two sides are dilated by a scale factor of 4,

WV /  ST = 52 / 13 = 4

WU /  RT = 60 / 15 = 4

So these sides are similar.

Hence, from the SAS property, the two triangles are similar.

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Answer:

Step-by-step explanation:

\((a+b)^2=a^2+b^2\\\\a^2+2ab+b^2=a^2+b^2\\\\2ab=0\quad\iff\quad a=0\ \ or\ \ b=0\)

Answer:

Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands. If either a or b equals zero, then the sums would be the same. Since the square root of 0 is 0, adding it to a given radical. Also, adding zero to the radicand would not change the value

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

The answer of the given question of radicals is -1.

What is radicals?
A surd or radical is an unresolved root, particularly one that employs the radical symbol. A radical expression is any expression that contains a radical, whether it is a square root, a cube root, or a higher root, while an algebraic expression is any statement that does not contain any transcendental functions or transcendental numbers. The root test is used to determine the radius of convergence of a power series. The nth roots of 1 are known as roots of unity, and they play an important role in many areas of mathematics, including number theory, equation theory, and the Fourier transform.

Given, ∛-1

if we evaluate this radical then,

∛-1 = -1

because 1 perfect cube.

Hence, the answer is option(a) i.e, -1

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The entry required to account for the change in office supplies would depend on the accounting method used. Assuming the company follows the periodic inventory system, where office supplies are expensed as they are used, the entry would be as follows:

At the beginning of the period:

Debit: Office Supplies Expense - $4,000

Credit: Office Supplies - $4,000

At the end of the period:

Debit: Office Supplies - $3,900

Credit: Office Supplies Expense - $3,900

Explanation:

1. At the beginning of the period, the company records the office supplies as an asset (Office Supplies) and recognizes an expense (Office Supplies Expense) for the same amount. This reduces the value of the asset and reflects the cost of supplies used during the period.

2. At the end of the period, when it is determined that $3,900 worth of supplies remains, the company adjusts the office supplies account by reducing it by the remaining amount. This adjustment is necessary to reflect the correct value of supplies on hand at the end of the period.

The entry ensures that the net effect of the transactions is an expense of $100 ($4,000 - $3,900), which represents the cost of supplies consumed during the period.

The volume of a rectangular pyramid with a congruent base and the same height is 1 1/2 cu.in.

In this question we have been given the volume of a rectangular prism which is  4 1/2 cu.in.

We need to find the volume of a rectangular pyramid with a congruent base and the same height.

Volume of rectangular pyramid = 1/3 * length * width * height

And the volume of rectangular prism = length * width * height

So, the relationship between the volumes of the rectangular prism and pyramid which have the same height and base:

Volume of rectangular pyramid = 1/3 * Volume of rectangular prism  

In this question we ahve been given volume of a rectangular prism = 4 1/2 cu.in.

First we write improper fraction 4 1/2 as proper fraction.

4 1/2 = 9/2

From above equation,

volume of rectangular pyramid = 1/3 * 9/2

Volume of rectangular pyramid = 3/2

Volume of rectangular pyramid = 1 1/2 cu.in.

Therefore, the volume of a rectangular pyramid = 1 1/2 cu.in.    

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The complete question is:

The volume of a rectangular prism is 4 1/2 cu.in. What is the volume of a rectangular pyramid with a congruent base and the same height?

Answer:

n = 10

Step-by-step explanation:

2x = y

2(n)=20

n = 20/2

n = 10

The probability of drawing any two cards in a row from a regular deck of 52 cards is 1/52. If we want to calculate the probability of drawing a specific card twice in a row, we need to multiply the probability of each individual draw, resulting in a probability of 1/2,704

The probability of drawing a particular card from a deck of 52 cards is 1/52. Since the card is put back in the deck after the first draw, the deck is returned to its original 52-card state, and the probability of drawing any specific card on the second draw remains the same at 1/52.

To find the probability of drawing a specific card twice in a row, we multiply the probability of the first draw (1/52) by the probability of the second draw (also 1/52). Therefore, the probability of drawing a specific card twice in a row is (1/52) x (1/52) = 1/2,704.

However, if we are simply looking for the probability of drawing any two cards in a row, the probability of the second card being any card (since the first card was replaced) is 1. Therefore, the probability of drawing any two cards in a row from a deck of 52 cards is (1/52) x 1 = 1/52.

The probability of drawing any two cards in a row from a deck of 52 cards is 1/52. This is because the first card is replaced in the deck, returning the deck to its original 52-card state. Therefore, the probability of drawing any specific card on the second draw remains 1/52. However, the probability of drawing a specific card twice in a row is (1/52) x (1/52) = 1/2,704.

The probability of drawing any two cards in a row from a regular deck of 52 cards is 1/52. If we want to calculate the probability of drawing a specific card twice in a row, we need to multiply the probability of each individual draw, resulting in a probability of 1/2,704. It is important to note that if the first card is not replaced, the probability of the second card being any card will change, and the calculation will be different.

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Answer:

(B) -8

Step-by-step explanation:

Given the 2-column table below:

\(\left|\begin{array}{c|c}x&y\\--&--\\-3&14\\-1&10\\1&6\\4&0\\8&?\\10&-12\end{array}\right|\)

Taking the pair (-3,14) and (-1,10)

\(Slope, m=\dfrac{10-14}{-1-(-3)} =\dfrac{-4}{2} =-2\)

Taking the pair (1,6) and (4,0)

Slope, \(m=\dfrac{0-6}{4-1} =\dfrac{-6}{3} =-2\)

Since the slope is constant, the table represents a linear function whose slope is -2. Therefore:

Taking the pair (8,y) and (4,0)

Slope, \(m=\dfrac{0-y}{4-8} =-2\)

\(\dfrac{-y}{-4} =-2\\y=-2*4=-8\)

Therefore, the value of ? on the y-column is -8.

Answer:

-8

Step-by-step explanation:

Answer: \(x=7\)

Step-by-step explanation:

\(3^x=2187\\\\x=\log_{3} (2187)\\\\x=7\)

So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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Answer

if you mean slope then there is no answer

Step-by-step explanation:

The increase in the minimum wage to $8.00 per hour could potentially lead to an increased demand for clothes due to higher purchasing power and potential shifts in consumer preferences.

We have,

Increasing the minimum wage to $8.00 per hour can have some impact on the demand for clothes.

Here are a few potential effects to consider:

Increased purchasing power:

When the minimum wage is increased, low-wage workers have more disposable income. This extra income can lead to increased consumer spending, including on clothing.

As a result, there could be a boost in the demand for clothes as more people can afford to purchase new clothing items.

A shift in consumer preferences:

With a higher minimum wage, individuals who previously had limited resources may now have the ability to choose higher-quality clothing or purchase from more expensive brands.

This shift in consumer preferences could lead to changes in the demand for different types of clothes and potentially result in an increase in demand for higher-end or premium clothing.

Price sensitivity:

While an increase in the minimum wage may provide workers with more spending power, some individuals may still be price-sensitive and prefer more affordable clothing options.

As a result, there may be continued demand for lower-priced clothing items or a preference for sales and discounts.

Employment and production costs:

An increase in the minimum wage could potentially lead to higher labor costs for clothing manufacturers and retailers.

To mitigate these increased costs, businesses may take steps such as adjusting their pricing strategies, implementing cost-saving measures, or exploring more efficient production methods.

These factors could impact the overall supply of clothes and potentially influence prices.

Thus,

The increase in the minimum wage to $8.00 per hour could potentially lead to an increased demand for clothes due to higher purchasing power and potential shifts in consumer preferences.

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Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

The product of the fractions is 275/20

A fraction can simply be defined as the part of a given whole variable, a whole number or a whole element.

In mathematics, there are different types of fractions, namely;

From the information given, we have that;

To determine the product of the fraction

6 1/4×2 1/5

convert to improper fractions, we get;

25/4 × 11/5

Multiply the numerators

275/4(5)

Multiply the denominator

275/20

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Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

Answer:

Hey!

Your answer is Y= -x + 9

Step-by-step explanation:

hope this helps you!

Answer:

The equation of the line is y = -x + 9.

Step-by-step explanation:

First, you have to find the gradient by choosing any 2 coordinates that lies on the line. I will choose (0,9) and (9,0). Then you have to substitute it the the formula.

\(m = \frac{y2 - y1}{x2 - x1} \)

\(let \: (x1,y1) \: be \: (9,0) \\ let \: (x2,y2) \: be \: (0,9)\)

\(m = \frac{9 - 0}{0 - 9} \)

\(m = \frac{9}{ - 9} \)

\(m = - 1\)

Next, you have to put into the slope-form equation, y = mx + c where m represents gradient which is -1 and c is y-intercept. In order to find c in a faster way, you can look at the graph to see which coordinates touches y-axis. So the value of c is 9 :

\(y = - x + 9\)

Answer:

\(f(x)=-\dfrac{1}{2}x^2+\dfrac{1}{2}x+15\)

Step-by-step explanation:

The given graph is a parabola with:

Therefore, a suitable function that would match the graph is a quadratic function.

\(\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic function}\\\\$f(x)=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

As the parabola opens downwards, a < 0.

\(\implies f(x)=-a(x-p)(x-q)\)

Substitute the x-intercepts into the formula:

\(\implies f(x)=-a(x-(-5))(x-6)\)

\(\implies f(x)=-a(x+5)(x-6)\)

To find the value of a, substitute the y-intercept into the equation:

\(\implies 15=-a(0+5)(0-6)\)

\(\implies 15=-a(5)(-6)\)

\(\implies 15=-a \cdot -30\)

\(\implies 15=30a\)

\(\implies a=\dfrac{15}{30}=\dfrac{1}{2}\)

Therefore the quadratic function that models the given graph in intercept form is:

\(\implies f(x)=-\dfrac{1}{2}(x+5)(x-6)\)

To write the function in standard form, expand the brackets:

\(\implies f(x)=-\dfrac{1}{2}(x^2-x-30)\)

\(\implies f(x)=-\dfrac{1}{2}x^2+\dfrac{1}{2}x+15\)

Answer:

Step-by-step explanation:

8 x 10 to the power of 5

8 x 100000 = ?

800,000

Answer: it should be 22

Step-by-step explanation:

If you put both of them into a TI-84 calculator and look at the equations, the y intercepts are 3 and -19 which are 22 units apart.

Answer:

22/-22

Step-by-step explanation:

First find the equation of graph

m = rise/run = 32-15/6-4 = 17/2 = 8.5

y = mx + b (feel free to use point slope form if you learned it, its much faster)

66 = 8.5(10) + b

66 = 85 + b

-19 = b

y = 8.5x - 19

Distance b/w y-int = -19 - 3 = -22 units or 22 units depending on where you're counting from

The solution to the equation is (a) -2.

To solve the equation log(3x) = log(2) + log(x - 1), we can use the properties of logarithms.

According to the logarithmic property log(a) + log(b) = log(ab), we can rewrite the equation as:

log(3x) = log(2(x - 1))

Since the logarithm function is one-to-one, we can equate the expressions inside the logarithms:

3x = 2(x - 1)

Expanding the equation:

3x = 2x - 2

Bringing all terms to one side:

3x - 2x = -2

x = -2

Therefore, the solution to the equation is x = -2.

The correct answer is (a) -2.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer you have chosen is incorrect. This is derived from the Pythagorean Identity:

\(sin^2x+cos^2x=1\) If we manipulate this and get the 1 over by the sin and then move the cos over, we would have

\(sin^2x-1=-cos^2x\)

The area of land the charity planted was 17000 m². The charity met its target

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

1 km = 1000 m

1 km² = 1000000 m²

An environmental charity set a target to plant trees on 9000 m² of land in September.

In September, it planted trees on 0.017 km² of land. Hence:

Area of land planted = 0.017 km² * 1000000 m² per km² = 17000 m²

17000 m² is greater than 9000m². The charity met its target

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