A right triangle has a leg length of √ and a trypolenuse length of 7. Determine the length of the other leg of the right triangle.
03
O √59
O√43

Yes , the triangles ΔSTU and ΔSRQ are similar triangles

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔSTU

Let the second triangle be ΔSRQ

Now , for the triangles to be similar , the corresponding sides of the triangles should be in the ratio

So , on simplifying , we get

The measure of side ST = 21

The measure of side SU = 35

The measure of side SQ = 6

The measure of side SR = 10

Now , for similar triangles ,

ST / SQ = SU / SR

Substituting the values in the equation , we get

21 / 6 = 35 / 10

3.5 = 3.5

Therefore , the corresponding sides of the triangles are equal

Hence , the pair of triangles are similar triangles

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The equation Sharon can use to find c, the average amount the cable company charges per channel is 300(c - 0.20) = 180.

The cable company charges an average of $0.80 per channel.

An equation involves two expressions or statement on two sides connected with an equal sign.

Total number of channels = 300

Let c be the cable company charges per channel.

Then the charge satellite company charges per channel = c - 0.20

Monthly charge of satellite company = 300(c - 0.20)

Monthly satellite bill = $180

So,  300(c - 0.20) = $180

⇒ c - 0.20 = 180/300

⇒ c - 0.20 = 0.60

⇒ c = 0.60 + 0.20

⇒ c = 0.80

Hence the equation used to find the cable company charge per channel is 300(c - 0.20) = 180 and the cable company charge per channel is $0.80.

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The fraction of the pie left that each friend will receive is; 3/8 of the pie

Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.

The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.

For example, 3/8 divided by 3/4 would be;

3/8 divided by 3/4 = 3/8 * 4/3

Now, we are told that cedric has 3/4 of a pie left.

Now, he wants to share equally among two of his friends, it means that;

Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8

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Complete question is;

Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?

Answer: 0

Step-by-step explanation: The reasoning behind this is that both functions will never intersect which would mean there are no solutions for the system equation.

The value of the numerical expression 70 / (7 - 2) will be 14. Then the correct option is B.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numerical expression is given below.

⇒ 70 / (7 - 2)

Simplify the expression, then we have

⇒ 70 / (7 - 2)

⇒ 70 / 5

⇒ 14

The worth of the mathematical articulation 70/(7 - 2) will be 14. Then the right choice is B.

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The correct expression is given below.

70 / (7 - 2)

Harvey's mistake in this scenario is that he put the pigs on a bed of straw that could infect their belly buttons. Additionally, he did not ensure that they consume colostrum in the first hours of life.

When we have a pregnant sow and we have to manage the postpartum procedure, we must make sure of different necessary procedures so that the piglets are well and their lives are not at risk in the following hours or days.

Among the procedures necessary for the piglets to be well are breathing, feeding and hygiene. In detail, once the piglet is extracted from its mother, we must make sure that it is breathing correctly. Secondly, we must clean it properly and make sure that its navel is completely clean to avoid infections. Finally we must give colostrum as food within the following hours after birth.

Additionally, we must place it in a clean place where it is not exposed to possible bacteria or infections, so the option of putting it on a bed of straw would be ruled out due to hygiene for the pig.

According to the above, Harvey's mistake was that he did not clean the piglets when they were born, did not give them colostrum, and put them on straw. Actually, he made three mistakes.

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Answer:

i think that answer is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alyssa has the money of worth $660

Eric has the money of worth $245

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the amount Alyssa has.

Let y be the amount  Eric has.

alyssa has $75 less than three times eric

=> x= 3y - 75

Together they have $905

=> x + y =905

Substitute x

=> 3y - 75  +y = 905

    4y = 905 +75 = 980

    y = 980 /4 = 245

x= 3y - 75  = 3(245) - 75 = 660

Alyssa has  $660

Eric has  $245

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The coordinate location of the hill halfway between them is  (1, -1).

Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5).  They plan to meet up at the hill located halfway between there two houses.

The coordinate location of the hill can be calculated as follows:

using mid point formula,

(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)

using the end points (-2, 3) and (4, -5)

(x, y) = (-2 + 4 / 2, 3 - 5 / 2)

(x, y) = (2 / 2. -2 / 2)

(x, y) = (1, -1)

Therefore, the coordinate location of the hill is (1, -1).

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Answer:

Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.

Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:

x &= 3y - 4

2x - 2y &= 8

Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12

Answer:

Step-by-step explanation:

11.1

The approximate value of y - x is 17.2°.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given a right triangle LMN.

Using the tangent function,

tan (y) = 19.1 / 14.1

          = 1.3546

y = tan⁻¹ (1.3546) = 53.56°

We know that,

x + y = 90°, since the other angle is 90°.

x = 90 - 53.56° = 36.44°

y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°

Hence the value of y - x is 17.2°.

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Parent function is represented by the graph is

B. The quadratic parent function

What is Parent function?

A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.

A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

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The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.

A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."

Here, we have VAT.

A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.

Value on Rs. 3200 with 13% VAT

= 3200 + 30% of 3200

= 3200 + 960

= 4160 rupees

Now, the less value,

= 4160 - 3820

= 340 rupees.

Therefore, the less value is 340 rupees.

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Answer:

All Real Numbers

Step-by-step explanation:

I assume you are solving for x.
The Interval Notation would be: (-∞,∞)

The number of quizzes still need to be graded is 17quizzes.

There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.

For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.

Algebraic equations in mathematics frequently have one or more variables.

It is given that,

grades of the teacher out of 48 quizzes before school = 16

grades of the teacher of the remaining quizzes after school = 15

Let us assume 'X' as the number of quizzes still need to be graded.

then X= 48-16+15

          =48-31

          =17

Hence, The number of quizzes still need to be graded is 17quizzes.

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The number of quizzes still need to be graded is 17 quizzes.

   then X= 48-=48-31

    =17

Hence, The number of quizzes still need to be graded is 17 quizzes.

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The null and different hypotheses for hypothesis test are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

Null hypotheses

Given that:

sample size (η)= 196

sample proposition (p^) = 114/196

Let p denote the population proportion of people who use a loyalty card.

The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]

Hence, the null and alternative hypothesis are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

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Answer:

144cm²

Step-by-step explanation:

If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.

48/4 = 12cm

Then, to find the area, you need to multiply 12 by 12.

12 cm x 12 cm = 144cm²

Hope this helps :)

The value of y in the isosceles triangle is AC = 6 cm

What Is an Isosceles Triangle?

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the triangle be represented as ABC

Now , the angle ∠ABC = 25°

The angle ∠ACB = 25°

So , the 2 angles of a triangle is 25° so , the third angle is 130°

So , the triangle is an isosceles triangle

And , the two sides of the triangle is AB = AC

The measure of side AB = 6 cm

The measure of side AC = measure of side AB

Therefore , the measure of side AC = 6cm

Therefore , the value of AC is 6 cm

Hence , the measure of side AC of triangle is 6 cm

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Answer: 120 miles

Step-by-step explanation:

If a car goes 60 miles per hour then in two hours (60×2) it will go 120

The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;

Tickets sold by Madelyn is; y = 22 + 30·x

Tickets sold by Kaia is; y = 53 + 20·x

A system of equation obtained from the details in the question can be presented as follows

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.

The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.

An equation consists of two expressions that are joined by the 'equals to' (=) sign.

The number of tickets for the Winter Dance Madelyn sold = 22

Number of tickets per day Madelyn sold after that = 30 per day

Number of tickets Kaia sold on Monday = 53

Number of tickets per day Kaia sold after that = 20 per day

Let x represent the number of days since Monday, and let y represent the number of tickets sold

Therefore;

The number of tickets Madelyn sold, y = 22 + 30·x

The number of tickets Kaia sold, y = 53 + 20·x

The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x

30·x - 20·x = 53 - 22 = 31

10·x = 31

x = 31 ÷ 10 = 3.1

The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days

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Answer:

volume of cube= l^ 3

=(4x)^3

=64x^3 cubic units

Answer:

New price = 0.06 x Original price

New price $1,968

The rocket's height after 3 seconds is 6.3 sec.

The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.

A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.

To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:

h = -5*t2 + 30*t + 10

h = -5(2)2 + 30(2) + 10

h = -5(4) + 30(2) + 10

h = -20 + 60 +10

h = 50 m

The height of the rocket 2 seconds after launching it is 50 meters.

To find the x-coordinate of the vertex of a parabola, we use the formula:

[tex]xvertex = -b / 2a[/tex]

t - 3 = ± √(11)

t = 3 ± √(11)

t = 3 ± 3.3

Solving for t, we get two solutions:

t = 3 - 3.3

t = -0.3 sec

and

t = 3 + 3.3

t = 6.3 sec

Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.

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The number of adult tickets  which were sold that day as calculated from the given data  is 29.

First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.

To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.

This is represented by the following equation,

$8.90A + $5.30C = $928

Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:

3 * C = A

Now we can answer our first problem by substituting 3 * C for A.

8.9 (3C) + 5.3C = 928

26.7C + 5.3C = 928

32C = 928

C = 29

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a. Harold's monthly payment is given as follows: $164.13.

b. The total amount paid is given as follows: $9,847.8.

c. The finance charge is of: $847.8.

The monthly payment formula is defined as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The values of these parameters for this problem are given as follows:

P = 9000, r = 0.036, n = 5 \times 12 = 60.

Then:

r/12 = 0.036/12 = 0.003.

Then the monthly payment is calculated as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]

A = $164.13.

Then the total amount paid is of:

Total = 60 x 164.13 = $9,847.8.

Meaning that the finance charge is given as follows:

9847.8 - 9000 = $847.8.

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The original attendance of the video game club was 28.57 members.

To determine the original attendance of the video game club, you can use the following formula:

Original attendance = (Number of members lost) / (Percent of group that left)

Plugging in the values from the problem, we get:

Original attendance = (8 members) / (28%)

To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:

Original attendance = (8 members) / (0.28)

Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:

Original attendance = 28.57 members

Therefore, the video gaming club had 28.57 members when it first started.

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The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.

2. The insurance company then computes the interquartile range of the prices for each practice.

3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

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Answer:12

Step-by-step explanation:

270/3=90, this is the amount it costs for 1 person to go

1080/90=12

12 people can go for $1080