Which triangles are similar to ΔDEF?

Answer:

To find the value of k and the equation of the line, we can use the slope-intercept form of a line: y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope of the line (m) is given as -⅔. To find the y-intercept (b), we can substitute one of the given points and the value of m into the equation.

Let's use the point (3,k) :

y = mx + b

k = -⅔ * 3 + b

k = -2 + b

b = k + 2

Now we have the equation of the line in the slope-intercept form: y = -⅔x + (k + 2)

To find the value of k we can use the other point (-3, 2k) and substitute into the equation:

2k = -⅔(-3) + (k + 2)

2k = 2 + k + 2

k = -2

So the value of k is -2 and the equation of the line is y = -⅔x + (k + 2) = -⅔x - 2

This line is a straight line with the slope of -⅔ which passes through the points (3, k) and (-3, 2k) and its equation is y = -⅔x - 2

Answer:

Step-by-step explanation:

The height of the triangle which is also called the altitude is; 6.63 cm

The triangle is an Isosceles Triangle that has two congruent sides and we have the parameters as;

Length of congruent sides = 12 cm.

Base length = 10 cm

Half of the base will be 5 cm and as such, we can use the Pythagorean Theorem to find the altitude as;

Altitude² = Hypotenuse² - Base length²

Thus;

A² = 12² - 10²

A = √44

A ≈ 6.63 cm

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Answer:

14

Step-by-step explanation:

f(3) = 3(3) - 5 + 10

f(3) = 9 - 5 + 10

f(3) = 4 + 10

f(3) = 14

Answer:

14

Step-by-step explanation:

Start by finding f(3), which would include plugging in a 3 everywhere you see an x

f(3) = 3(3)-5

f(3) = 9-5

f(3) = 4

Now we can use f(3)+10 because we know what f(3) is, it's 4. So replacing it

f(3) + 10 is now 4+10, which equals 14

Answer:

m < -1 5/8

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Oohh yeah

The probability of an event happening in half an hour cannot be determined simply by multiplying or dividing the probability of the event happening in an hour by a factor of 2.

Probabilities are not linear in that way. The probability of an event happening in half an hour would depend on the specific details of the event and the underlying probability distribution.

The probability of an event happening in half an hour, given an 84% chance of it happening in an hour, cannot be determined without additional information. The probability of an event occurring in half an hour would depend on the specific circumstances of the event and how the 84% probability was determined.

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if there is an 84% chance of an event happening in an hour, then the probability that it happens in half an hour will be 84% = 0.84.

One cannot easily calculate the likelihood of an event occurring in half an hour by multiplying or dividing the chance of the event occurring in an hour by a factor of 2.

In that sense, probabilities are not linear. The likelihood of an event occurring in half an hour is determined by the event's specifics and the underlying probability distribution.

Without further information, the likelihood of an event occurring in half an hour given an 84% chance of occurring in an hour cannot be computed. The likelihood of an event occurring in half an hour is influenced on the event's unique circumstances and how the 84% probability was calculated.

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The logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x is-

  [tex]g(x)[/tex] = ㏑[tex](x) / 0.4[/tex]

The equation can be written as-

[tex]y = f(x) = e x^{0.4x}[/tex]

The natural logarithm is now applied to both sides of the equality after we have isolated y.

[tex]0.4y = ln x[/tex][tex]y = ln x / 0.4[/tex]

This is how the  exponential model as a logarithmic model that calculates the number of years, g(x) can be explained as.

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Answer:

36 cm²

Step-by-step explanation:

Area=Length*Width

so... 9*4 = 36

36 cm²

A mathematical operation which is the same as dividing a number by 1,000 include the following: C. move the decimal 3 places to the left.

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

This ultimately implies that, a quotient in terms of numerical data simply refers to a division of a number (numerator) by another number (denominator).

In terms of determining the decimal place after a division of a number by 1000, we have the following:

Number = 1/1000

Number = 0.001 (3 places to the left.)

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Answer:

Step-by-step explanation:

7

There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

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

The expression is given below.

⇒ 68 ÷ 7

Simplify the expression, then we have

⇒ 68 ÷ 7

⇒ (63 + 5) / 7

⇒ 63 / 7 + 5 / 7

⇒ 9 + 5/7

There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.

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The last D option is missing. The option D is given as,

D. 9 columns which each has 9 blocks and the 10th column will be 5 blocks.

Answer:

group has raised $1680 in the first three months.

Step-by-step explanation:

The students group has raised $1680 in the first three months.

Due of this, The Helping Hands Student Club decided to fundraise $4,000 by the end of the academic year.

How much is a percentage?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

It accomplishes 42% of its goal after three months.

The money raised over the initial three months is

42% of 4000

= 42/100 × 4000

= 42×40

= $1680

Thus, the students' group has raised $1680 in the first three months.

Answer:

a)12:4

Step-by-step explanation:

We know

The ratio is 3:1; we time 4 and get a ratio is 12:4

So, the answer is A

The slope of the Function represents the change in height per day.

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

[tex]m=\frac{dy}{dx}[/tex] = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx

So, the slope of a line is tanΘ.

So as slope represents a change in y per change in x, in the given question as y is height and x is days, slope changes in height per day.

The slope of the Function represents the change in height per day.

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The equation x + (60 + 70)° = 180° is used to solve for the measure of the vertical angle x = 50°

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

The angle y and x form vertical angles, so x = y

Angle y form a straight line with 60° and 70° so we have the equation to solve for x as:

x + 60° + 70° = 180° {sum of angles on a straight line}

x + 130° = 180°

x = 180° - 130° {subtract 139° from both sides}

x = 50°

Therefore, the measure of the vertical angle x is equal to 50° derived with the equation x + (60° + 70°) = 180°.

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The name of the number property matched below with each step from the previous step.

The commutative property of addition:

Let a and b are numbers.

a + b = b + a

The change in the position of two numbers in an addition operation does not change the sum.

Given:

We have an expression,

[-5 + (1/2 + 5)] × 2

Applying commutative property of addition,

= [-5 + (5 + 1/2)] × 2

= [ (-5 + 5) + 1/2] × 2

Applying inverse property of addition,

= [0 + 1/2] × 2

Applying identity property of addition,

= 1/2 x 2

Applying inverse property of multiplication,

= 1

Therefore, the solution is 1.

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Answer:

  D(3.4, 20.8)

Step-by-step explanation:

Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.

The equation for the slope between two points is ...

  m = (y2 -y1)/(x2 -x1)

Using this formula and the given points, we can find D(x, y) to satisfy ...

  2 = (y -10)/(x +2)

  -3 = (y -7)/(x -8)

Putting each of these equations in general form, we have ...

  2(x +2) -(y -10) = 0

  2x -y +14 = 0

and

  -3(x -8) -(y -7) = 0

  3x +y -31 = 0

Adding the two equations eliminates the y-variable:

  (2x -y +14) +(3x +y -31) = 0

  5x -17 = 0 . . . . . . simplify

  x -3.4 = 0 . . . . . . divide by 5

  x = 3.4 . . . . . . . . . add 3.4

Substituting for x in the first equation gives ...

  2(3.4) -y +14 = 0

  y = 6.8 +14 = 20.8 . . . . add y

The point D has coordinates (3.4, 20.8).

__

Additional comment

The graph shows the equations of the lines written in point-slope form.

The inequality involving absolute value is 2 < x < 4 and the graph is attached below.

The term called inequality in math is defined as when two real numbers or two algebraic expressions are represented with symbols like <, > or ≤, ≥.

Here we need to find the inequality involving absolute value for the graph. And here we also need to find the point that is the same distance from 2 as it is from 4.

Here we have consider that x be the number that the inequality is formed than it can be written as

=> 2 < x < 4

And the graph of the inequality is plotted and attached below.

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No, these given system specifications are not consistent.

They present a logical contradiction, also known as a paradox. The first claim claims that "Users cannot access the file system if the system software is changed," while the second claim claims that "Users can store new files if they can access the file system."

The third assertion, which reads, "If users cannot save new files, then the system software is not being upgraded," is in direct opposition to the first. All three of the aforementioned assertions cannot be true at the same time.

Hence, these given system specifications are not consistent.

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Answer: 391.92ft²

Step-by-step explanation:

Answer: 391.92

Step-by-step explanation:

All you simply do in multiply the two numbers together.

The first 8 terms of the sequence are 12, 16, 22, 30, 40, 52, 66, 82 respectively.

(a) The first 8 terms of the sequence are as follows:

a1 = 1 + (1^2) + (2^3) + 2 = 12

a2 = 1 + (2^2) + (2^3) + 3 = 16

a3 = 1 + (3^2) + (2^3) + 4 = 22

a4 = 1 + (4^2) + (2^3) + 5 = 30

a5 = 1 + (5^2) + (2^3) + 6 = 40

a6 = 1 + (6^2) + (2^3) + 7 = 52

a7 = 1 + (7^2) + (2^3) + 8 = 66

a8 = 1 + (8^2) + (2^3) + 9 = 82

(b) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 4n for all n ≥ 3. Hence, a = 3.

(c) We will prove the statement "an > 4n for all integers n ≥ a" using strong induction.

Base case (n=3): a3 = 28 and 28 > 4 * 3 = 12, which is true.

Inductive step: Suppose an > 4n for all integers n = k (k ≥ 3). We need to show that a(k+1) > 4(k+1).

a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 4k + 3 = 4(k+1)

(d) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 45 for all n ≥ 7. Hence, b = 7.

(e) We will prove the statement "an > 5n for all integers n ≥ b" using strong induction.

Base case (n=7): a7 = 120 and 120 > 7 * 5 = 35, which is true.

Inductive step: Suppose an > 5n for all integers n = k (k ≥ 7). We need to show that a(k+1) > 5(k+1).

a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 5k + 3 = 5(k+1)

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The solution for the expression when x= 3 is 75

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

x² + 22x

Also from the question, we have

x = 3

This means that the value of x is 3, and we calculate the value of the expression

Substitute the known values in the above equation, so, we have the following representation

x² + 22x = 3² + 22 * 3

Evaluate

x² + 22x = 75

Hence, the solution is 75

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Possible question

Given x² + 22x, calculate the value when x = 3

The quotient of the expression is 7x² + 8x +  1

From the question, we have the following expression that can be used in solving the quotient

(7x^3-13x^2-23x-5)/(x-3)

Express properly

So, we have

(7x³ - 13x² - 23x - 5)/(x-3)

Set the divisor to 0

x - 3 = 0

So, we have

x = 3

Using a synthetic setup, we have

3 | 7 - 13 - 23 - 5

The synthetic division is then carried out as follows

3 | 7 - 13 - 23 - 5

        21   24    3

    7   8     1    -2

So, we have

Quotient = 7   8   1

Remainder = 2

Introduce the variable

Quotient = 7x² + 8x +  1

Remainder = 2

Hence, the result is 7x² + 8x +  1 remainder 2

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Jessica's speed is 4 mph and Janine's speed is 8 mph

Let us assume that x represents Jessica's speed.

Janine bikes 4 mph faster than her sister, Jessica.

So, Janine's speed would be (x + 4) mph

We know that the formula for the speed is: speed = distance/time

Here, Janine can ride 24 mi in 3 hr less time than Jessica can ride the same distance.

24/(x+4) = (24/x) - 3

24/(x+4) = (24 - 3x)/x

24x = (24 - 3x)(x + 4)

24x = 24x + 96 - 3x² - 12x

3x² + 12x - 96= 0

After solving above quadratic equation we get.

(x - 4) (x + 8) = 0

x = -8 speed is not possible.

So, x = 4 mph

And x + 4 = 8 mph

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Answer: A = shade the square above and below the third square (3 to the right). B = Make a straight line of 4 and put a square below the first square of the line, and above the second square. (Let me know if you need help.)

Step-by-step explanation:

Answer:

X = 37.8

Step-by-step explanation:

Since they stated angle BAC equals angle DEC, makes me believe these sides are just a factor of each other.

Because of that, we can make a proportion, then cross multiply and divide

Making that proportion, you get;

15. 18

---. =. ----

31.5. x

Cross multiply the (15)(x) = (31.5)(18), also known as

15x = 567

Last thing we do is divide both sides by 15 to get that X alone.

567/15 = 37.8

Concluding that x = 37.8

Answer:

10 Slices

Step-by-step explanation:

6x5=30

30 slices in total

We are trying to find 2/3 of 30 slices so we multiply them.

(2x30)/3

=60/3

=20

20 slices were sold out of 30 total slices

This means that 10 slices are left

30-20=10

Answer:

4632/8=579

Step-by-step explanation:

MARK ME BRAINLISIST.

Answer: 579

Hope I'm right

Answer:

5x + 4

Step-by-step explanation:

Base on the given:

[tex]\mathrm{\frac{9}{3}x+4+2x}[/tex]    → Divide 9 by 3. 9 ÷ 3 = 3

[tex]\mathrm{3x+4+2x}[/tex]    → Combine similar term {2x + 3x = 5x}

No farther can be simplify. Hence, 5x + 4 is the answer.

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