Triangle ABC is similar to triangle DEF. What is DE?

Answer:

y=x+5;1

Step-by-step explanation:

Hope this helps! =D

Answer:

25 units²

Step-by-step explanation:

Area of a triangle = (1/2)b*h

After graphing the triangle you can see that the two legs are at points

(4,3) and (-2,11) and (4,3) and (0,0). Using the distance formula:

[tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}[/tex]

then plug in the first line

[tex]\sqrt{(-2-4)^{2} + (11-3})^{2}}[/tex]

simplify

[tex]\sqrt{(-6)^{2} + (8})^{2}}[/tex]

[tex]\sqrt{36 +64}[/tex]

[tex]\sqrt{100}[/tex]

10

then the second line

[tex]\sqrt{(4-0)^{2} + (3-0)^{2}}[/tex]

[tex]\sqrt{(4)^{2} + (3)^{2}}[/tex]

[tex]\sqrt{16 + 9}[/tex]

[tex]\sqrt{25\\}[/tex]

=5

5*10=50

50*0.5 =25

so the area is equal to 25 units²

The values of x and y for the tangent segments to the circle A are: 4 and 8.899 respectively.

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

KJ = K L

6x - 3 = 5x + 1

6x - 5x = 1 + 3 {collect like terms}

x = 4

IJ = IH = 11

y² - 10 = 4y + 2

y² - 4y - 2 - 10 = 0

y² - 4y - 8 = 0 {quadratic equation}

using the quadratic formula

y = 8.899 or y = -0.898

Therefore, the values of x and y for the tangent segments to the circle A are: 4 and 8.899 respectively.

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Answer:

(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)

To expand and simplify 5(x + 4) 3(x + 2), we can use the distributive property of multiplication over addition which states that a(b + c) = ab + ac.

So, we have:

5(x + 4) 3(x + 2) = (5x + 20)(3x + 6)

Now, we can use the distributive property again to expand this expression:

(5x + 20)(3x + 6) = 5x * 3x + 5x * 6 + 20 * 3x + 20 * 6

= 15x^2 + 90x + 60

Therefore, the answer is 15x^2 + 90x + 60.

I hope this helps!

(✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿✿)

Hence,The equation that models the height of the roller coaster is  [tex]x^{2} +y^{2}=900[/tex]. and solution of y =[tex]\sqrt{(900-x^{2})}[/tex].

A roller coaster, or roller coaster, is a type of amusement ride that employs a form of elevated railroad track designed with tight turns, steep slopes, and sometimes inversions. Passengers ride along the track in open cars, and the rides are often found in amusement parks and theme parks around the world.

We have given that ,

the Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.

we know that equation of circle ,

[tex]x^{2} +y^{2}=r^{2}[/tex]

Where r is the radius

From given we can say that the radius =30

since the radius is 30 ft

[tex]x^{2} +y^{2}=30^{2}\\x^{2} +y^{2}=900[/tex]

so, the equation that models the height of the roller coaster. [tex]x^{2} +y^{2}=900[/tex].

We have to find the equation that can be represent the height of the roller coaster so find the value of y

[tex]x^{2} +y^{2}=r^{2}[/tex]

⇒[tex]y^{2}=r^{2}-x^{2}[/tex]

⇒[tex]y^{2}=30^{2}-x^{2}[/tex]

⇒[tex]y^{2}=900-x^{2}[/tex]

⇒y =±[tex]\sqrt{(900-x^{2})}[/tex]

⇒y =[tex]\sqrt{(900-x^{2})}[/tex]   ∵according to question choose positive sign only

Therefore the models the height of the roller coaster y =[tex]\sqrt{(900-x^{2})}[/tex].

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Six and forty-seven thousandths.

or six point zero four seven.

the answer depends on what you have to write.

Hope this helps!

Answer:

(-13.82, ∞)

Step-by-step explanation:

To solve this inequality, we need to isolate the variable X on one side of the equation. First, we can subtract 3.8 from both sides of the inequality, which gives us:

X > -10.02 - 3.8

Simplifying this expression, we get:

X > -13.82

Therefore, the solution set for this inequality is all the values of X that are greater than -13.82. In interval notation, we can write the solution set as (-13.82, ∞).

Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.

To factor is to identify the terms that make up an expression when they are multiplied together.

Given quadratic equation:

p² + 14p + 48 = 0

Find the factors of 48 such that on addition 14 will come:

48 = 6*8

So,

p² + 6p + 8p + 48 = 0

Taking p common first two terms:

p(1 + 6) + 8p + 48 = 0

Now, taking 8 common from last two terms

p(p + 6) + 8(p + 6) = 0

taking (p + 6) from both .

(p + 6)(p + 8) = 0

Now,

p + 6 = 0

p = -6 and

p + 8 = 0

p = -8

Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.

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Correct question:

Solve the given quadratic equation using the factorization method:

p² + 14p + 48 = 0

The only number that is a factor of 63 and 6363 is option B: 3,  while the other options are not factors

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

To determine which of the given numbers is a factor of 63 or 6363, we need to check if they divide the given numbers without leaving any remainder.

Option A: 6

63 ÷ 6 = 10 remainder 3

6363 ÷ 6 = 1060 remainder 3

Since both calculations leave a remainder of 3, 6 is not a factor of 63 or 6363.

Option B: 3

63 ÷ 3 = 21

6363 ÷ 3 = 2121

Since both calculations give a whole number without any remainder, 3 is a factor of 63 and 6363.

Option C: 8

63 ÷ 8 = 7 remainder 7

6363 ÷ 8 = 795 remainder 3

Since both calculations leave a remainder, 8 is not a factor of 63 or 6363.

Option D: 2

63 ÷ 2 = 31.5

6363 ÷ 2 = 3181.5

Since both calculations give a non-integer result, 2 is not a factor of 63 or 6363.

Therefore, the only number that is a factor of 63 and 6363 is option B: 3,  while the other options are not factors

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To translate the function y = |x| one unit value downward, we need to subtract 1 from the function: y = |x| - 1.

The function y = |x| is a V-shaped graph that passes through the origin and has a slope of 1 on both sides. It represents the absolute value of x, which means that the function always returns a positive value regardless of whether x is positive or negative.

To translate the function one unit downward, we need to subtract 1 from the function. This means that for any given value of x, the function will return the absolute value of x minus 1. For example, if x = 2, then y = |2| - 1 = 1. If x = -2, then y = |-2| - 1 = 1.

The resulting graph of y = |x| - 1 is still a V-shaped graph, but it is shifted down by one unit compared to the graph of y = |x|.

Thus, the slope of the graph remains the same on both sides, but the minimum value of y is now -1 instead of 0.

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The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

What is meant by days?

Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.

Explain whole numbers

Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.

According to the given information

The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).

In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:

S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)

    ≈ 1200

So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

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Answer:

[tex]15 + 45 = 3(5 + 15)[/tex]

The answer choices which fit into the descriptions as given in the task content are; Squares and Rhombus.

It follows from the task content that the given quadrilateral is such that; FG || HI, GH || IF and FH = GI. However, since the diagonals are perpendicular.

Consequently, it can be inferred that the diagonals of squares and Rhombuses are perpendicular. On this note, the shapes which best align with the given descriptions are; Square and Rhombus.

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Answer:

-60

Step-by-step explanation:

The domain of the function plotted is

In mathematics, the domain of a function is the set of all possible values of the input (independent variable) for which the function is defined.

So we can say that, it is the set of all possible values that we can substitute into the function and get a valid output (dependent variable).

In the graph, watching the x axis which is the input variables we can see that the domain is all real numbers from -4 to 4

In general, the domain of a function depends on the specific form of the function and any restrictions or conditions that may apply to the input values.

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The measurement of the angle labeled (3x)° include the following: 120°.

In Mathematics and Geometry, corresponding angles postulate simply refers to a theorem which states that corresponding angles are always congruent (equal) if the transversal intersects two parallel lines.

This ultimately implies that, the corresponding angles would always be congruent (equal) if a transversal intersects two (2) parallel lines.

60 + y = 180

y = 180 - 60

y = 120°

By applying corresponding angles postulate to both lines a, b, and w, we can reasonably infer and logically deduce that the following angles are congruent:

3x = 120°

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Answer:

Step-by-step explanation: Multiplication first 7x1 = 7, Take 7 and divide it by 10 which gives you 0.7, Do the same but for the other 2 questions,

(9x1/100 = 0.09)

(9x1/1000 = 0.009)

(7x1/10 = 0.7)

Now take the answers and add them up

0.09 + 0.009 + 0.7 = 0.799

Answer: 0.799

According to the price, it will take 3.75 hours for the prices of both stocks to be the same, assuming they continue to increase and decrease at the same rates.

To find out when the prices of both stocks will be the same, we need to set up an equation where the prices of both stocks are equal. Let's call the number of hours it takes for the prices to be equal "t".

For stock A, the price after "t" hours can be expressed as:

Price of stock A = $12.73 + ($0.06 x t)

For stock B, the price after "t" hours can be expressed as:

Price of stock B = $13.48 - ($0.14 x t)

To find the time when the prices of both stocks are equal, we can set the two equations equal to each other and solve for "t".

$12.73 + ($0.06 x t) = $13.48 - ($0.14 x t)

Simplifying this equation, we get:

$0.20 x t = $0.75

Dividing both sides by $0.20, we get:

t = 3.75 hour

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The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The volume of a cone is a third of the volume of a cylinder, hence:

V = πr²h/3.

For both cases, the height variable h has an exponent of one, hence:

If we had doubled the radius for example, the volume would be multiplied by 2² = 4, as the radius is squared.

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The thief stole 22 oranges using algebraic equations.

To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.

According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.

We also know that the thief was left with only 9 oranges. So we can set up the equation:

x - [(1/2)x + 2] = 9

Simplifying this equation:

(1/2)x - 2 = 9
(1/2)x = 11
x = 22

Therefore, the thief stole 22 oranges.

The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.

To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.

In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.

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An adiabatic process is one in which the heat transered between a system and its surroundings is equal to zero( q = 0 ). So, option(e) right one.

In thermodynamics, the adiabatic process is a process in which there is no heat or air exchange between the temperature and the environment. It is different from the isothermal heat flow process. Some important properties are :

Hence, option(e) is right answer.

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Answer:b

Step-by-step explanation:

Answer:

b and c

Step-by-step explanation:

b 5(7+6s—9t)

35+30s—45

c 10×(3.5+3s—4.5t)

10×3.5 +10×3s—10×4.5t

35+30s—45t

Jerel runs 4 km on the sixth day.

Let's call the distance Jerel runs on the sixth day "x". We know that he runs 4.2 km each day for the first 6 days, so the total distance he runs in those 6 days is:

Total distance = 4.2 km/day x 6 days = 25.2 km

We also know that the total distance Jerel runs is 25 km, so we can set up an equation to solve for "x":

4.2 km/day x 5 days + x = 25 km

Simplifying the equation, we get:

21 km + x = 25 km

Subtracting 21 km from both sides, we get:

x = 25 km - 21 km

x = 4 km

Therefore, Jerel runs 4 km on the sixth day.

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Based on the information, we can answer the questions as follows:

An experimental study is a research design in which the researcher manipulates one or more independent variables and measures the effects of those manipulations on one or more dependent variables, while controlling for other potentially relevant factors (known as extraneous variables).

Therefore, he goal of an experimental study is to establish a cause-and-effect relationship between the independent variable(s) and the dependent variable(s).

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The appendix table the point estimate of the difference between the two population means is 2

The difference between the two population means, we need to find the standard error of the difference and use the t-distribution with (n1 + n2 - 2) degrees of freedom. The formula for the standard error of the difference is:

SE = sqrt[ (s1 / n1) + (s2 / n2) ]

Substituting the given values, we get:

SE = sqrt[ (2.4 / 50) + (3 / 35) ] = 0.617

Using a t-distribution with 83 degrees of freedom (50 + 35 - 2), and a 90% confidence level, we find the t-value to be 1.66 (from the t-table or calculator). Therefore, the 90% confidence interval is:

x1 - x2 ± t(α/2) * SE

= 2 ± 1.66 * 0.617

= 0.98 to 3.02

So, we can say with 90% confidence that the true difference between the two population means lies between 0.98 and 3.02.

To calculate the 95% confidence interval:

x1 - x2 ± t(α/2) * SE

= 2 ± 2.00 * 0.617

= 0.79 to 3.21

So, we can say with 95% confidence that the true difference between the two population means lies between 0.79 and 3.21.

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Therefore, the probability of getting a prime number on one die and a composite number on the other die when rolling two dice simultaneously is 1/6 or approximately 0.1667.

Probability theory is a branch of mathematics that deals with the study of random events and the analysis of their outcomes. It is widely used in statistics, science, engineering, finance, and many other fields to model and predict the behavior of complex systems.

Here,

There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled simultaneously. We need to count the number of outcomes where one die shows a prime number and the other die shows a composite number.

Prime numbers in the sample space are 2, 3, and 5. Composite numbers are 4, 6, and any number greater than 1 that is not prime.

So, there are three possible outcomes where one die shows a prime number and the other die shows a 4 or 6:

(2, 4), (2, 6), (3, 4), (3, 6), (5, 4), (5, 6)

Therefore, there are a total of 6 possible outcomes where one die shows a prime number and the other die shows a composite number.

The probability of getting one prime number and one composite number on the two dice is:

P = number of favorable outcomes / total number of possible outcomes

P = 6 / 36

P = 1/6

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Answer:

[tex]6(4x - 3) > 30 \\ divide \: both \: sides \: of \: the \: \\ inequality \: by \: 6 \\ = 4x - 3 > 5 \\ = 4x > 5 + 3 \\ = 4x > 8 \\ = x > \frac{8}{4} \\ = x > 2[/tex]

hope it helps

The answer depends on the rank of A.

If the rank of A is less than 4, then the dimension of its null space is greater than or equal to 4-rank(A).

If the rank of A is 4, then the dimension of its null space is 0.

The dimension of the null space of a matrix A is given by the number of linearly independent vectors that satisfy the equation A x = 0,

where x is a column vector.

Since A is a 6x4 matrix, the equation A x = 0 represents a homogeneous system of 6 linear equations in 4 unknowns.

The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns of the matrix. Therefore, we have:

rank(A) + dim(null(A)) = 4

The rank of A is at most 4, since there are only 4 columns.

If the rank of A is 4, then the dimension of its null space is 0, because there are no linearly independent vectors that satisfy A x = 0. On the other hand, if the rank of A is less than 4, then the dimension of its null space is at least 4-rank(A).

Therefore, the smallest possible dimension of null(A) is:

dim(null(A)) = 4 - rank(A).

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The smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

To determine the smallest possible dimension of the null space (nul A) of a 6x4 matrix A, we need to consider the rank-nullity theorem, which states:

dim(A) = rank(A) + dim(nul A)

Here, dim(A) represents the dimension of the matrix A, rank(A) represents the rank of the matrix A, and dim(nul A) represents the dimension of the null space of A.

For a 6x4 matrix A, the dim(A) is 4 since there are 4 columns. The rank(A) represents the number of linearly independent columns, and it can be at most 4 since there are 4 columns.

To find the smallest possible dimension of the null space, we need to maximize the rank(A). In this case, the maximum possible rank(A) is 4. Now, using the rank-nullity theorem:

4 = 4 + dim(nul A)

Solving for dim(nul A), we get:

dim(nul A) = 4 - 4
dim(nul A) = 0

Therefore, the smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

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The Toy Train Collectors' Club has 140 members who are 42 years of age or younger.

To find the number of members who are 42 years of age or younger, we need to look at the bars in the histogram that represent these age groups. Specifically, we need to add up the heights of the bars that represent members aged 0-42 years old.

The histogram shows that there are 30 members in the age group 0-10,

50 members in the age group 11-20,

40 members in the age group 21-30,

20 members in the age group 31-40, and

15 members in the age group 41-50.

To find the number of members who are 42 years of age or younger, we need to add up the heights of the bars that represent members aged 0-42 years old, which is 30+50+40+20 = 140.

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Answer:

Step-by-step explanation:

4