What are the 3 types of sides in a right triangle?

Answer:

a) x = 1, x = -7

b) (-3, -48)

c) x = -3

d) upwards

Step-by-step explanation:

Given quadratic equation:

[tex]y=3(x-1)(x+7)[/tex]

Intercept form of a quadratic equation:  

 [tex]y=a(x-p)(x-q)[/tex]

where:

Comparing the formula with the given equation:

⇒ p = 1

⇒ q = -7

Therefore, the x-intercepts of the given equation are x = 1 and x = -7.

The midpoint between the two x-intercepts is the x-coordinate of the vertex.

[tex]\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3[/tex]

Therefore, the x coordinate of the vertex is -3.

To find the y-coordinate of the vertex, substitute this into the given equation:

[tex]\implies y=3(-3-1)(-3+7)=-48[/tex]

Therefore, the coordinates of the vertex are (-3, -48).

The x-coordinate of the vertex is the axis of symmetry.

Therefore, the axis of symmetry is x = -3.

If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.

If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.

From inspection of the given equation, the leading coefficient is 3.

Therefore, the parabola opens upwards.

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The experimental probability of landing on red is 7/20 or 0.35 or 35%

The complete question is added as an attachment

From the question, we have the following outcomes:

Red = 7

Green = 5

Blue = 5

Yellow = 3

The total number of spins is

Total = Red + Green + Blue + Yellow

This gives

Total = 7 + 5 + 5 + 3

Evaluate the sum

Total = 20

The experimental probability of landing on red is the calculated as:

P(Red) = Red/Total

Substitute the known values in the above equation

P(Red) = 7/20

Evaluate

P(Red) = 0.35

Express as percentage

P(Red) = 35%

Hence, the experimental probability of landing on red is 7/20 or 0.35 or 35%

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Answer:

The system of equation y=120+20x and y=30x

Step-by-step explanation:

Let the number of days be x and y be the total number minutes

Jamie has walked 120 mins. She will walk at a rate of 20 mins per day.

y=120+20x

Owen walks 30 mins a day. So

y = 30x

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The area of the shaded face of the cylinder is 1,520 mm².

We can see that the shaded area of the cylinder is circular in shape.

This means that we can find the area of the shaded area by finding the area of the circle.

The radius of the circle is given as 22 mm.

The formula for finding the area of a circle is given as:

Area = πr²

= 3.14 × 22 × 22

= 1,519.76

≈ 1520 mm²

Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².

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Disclaimer: The question was incomplete, the complete question is attached below.

Answer:

x = 8

Step-by-step explanation:

[tex]\frac{9x}{4y}=1[/tex]

[tex]\frac{9x}{4*18} =1[/tex]

9x = 72

x = 8

The inequality to determine the number of runs per inning, p Kim's team could have scored is; 4r + 6 > 17

Let r represent the number of runs per inning. Thus for 4 innings, we have 4r.

The team already has 6 runs. Now add the additional runs to this to get;

4r + 6

The team wants to score more than the other team, this means they need more than 17 and so the inequality required is;

4r + 6 > 17

Subtract 6 from each side to get;

4r + 6 - 6 > 17 - 6

4r > 11

Divide both sides by 4 to get:

r > 2.75

Approximating to a whole number gives;

r > 3

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Answer:

6+4p> 17
3

Step-by-step explanation:

The triangle is illustrated below.

The first thing you should find are the new vertices:

(x, y) ---> (2x, 2y) ---> (x', y')

(0, 0) ---> (2 (0), 2 (0)) ---> (0, 0)

(-4, 4) ---> (2 (-4), 2 (4)) ---> (-8, 8)

(-4, -2) ---> (2 (-4), 2 (-2)) ---> (-8, -4)

Then, you must join the ordered pairs and graph the new triangle.

See the attached graph.

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The quantity with the fewest number of significant figures.

What is significant figures?

When multiplying two measured values the number of significant figures should be equal to the?

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A) The total surface area of the given cylindrical container is 571.76 cm² and B) The volume of the given cylindrical container is 923.62 cm³.

Consider a cylinder with height 'h', and radius 'r'.

The total surface area of the cylinder(TSA) = 2πr (r + h) square units

and

The volume of the cylinder V = πr²h cubic units.

It is given that,

A cylindrical container closed on both ends has a radius r = 7 cm and a height h = 6 cm.

So,

TSA = 2πr (r + h)

       = 2× π × 7 × (7 + 6)

       = 14 × π × 13

      = 571.76 cm²

and

Volume = πr²h

             = π × 7² × 6

             = π × 49 × 6

             = 923.62 cm³

Therefore, the total surface area and volume of the cylindrical container are 571.76 cm² and 923.62 cm³ respectively.

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The solution set to the inequality 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4) gives x > -2.5

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Inequality shows the non equal comparison of two or more numbers and variables.

Given the inequality:

5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)

Simplifying:

15.3 + 11.22x > –14.25 – 10.2x - 24

21.42x > -53.55

x > -2.5

The solution set to the inequality 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4) gives x > -2.5

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The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].

First, we need to determine the value of the vector u by subtracting two vectors whose initial points are at the origin:

[tex]\vec u = (19\,\hat{i} - 8\,\hat{j}) - (21\,\hat{i} + 12\,\hat{j})[/tex]

[tex]\vec u = - 2\,\hat{i} - 20\,\hat{j}[/tex]     (1)

According to the statement, vector v is antiparallel to vector u and its magnitude is five times as the magnitude of vector v, which means that (1) must be multiplied by two scalars:

[tex]\vec v = - 1 \,\cdot \, 5\cdot \vec u[/tex]      (2)

Please notice that antiparallelism is represented by the scalar - 1, whereas the dilation is represented by the scalar 5.

[tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex]

The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].

The statement presents typing mistakes, correct form is shown below:

Vector u has initial points at (21, 12) and its terminal point at (19, - 8). Vector v has a direction opposite that of u, whose magnitud is five times the magnitud of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?

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Answer: A

Step-by-step explanation:

Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.

In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A

The equation of the line that is parallel to the given line and passes through the point (-2,2) is:

[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]

A linear function is modeled by:

y = mx + b

In which:

When two lines are parallel, they have the same slope. In this problem, the given line passes through (-5,-4) and (0,-3), hence the slope is:

m = (-3 - (-4))/(0 - (-5)) = 1/5.

Hence the equation is:

[tex]y = \frac{x}{5} + b[/tex]

When x = -2, y = 2, then:

[tex]y = \frac{x}{5} + b[/tex]

[tex]2 = \frac{-2}{5} + b[/tex]

[tex]b = \frac{12}{5}[/tex]

Hence:

[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]

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Answer:

(0, -5)      (10/3, 0)

Step-by-step explanation:

First, convert the given equation into the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = 10

2y = 3x - 10

y = 3/2x - 5

The y-intercept is -5.

Next, to find the x-intercept, let y = 0 and solve for x. X-intercept is the point where the graph intersects the x-axis, so the y-coordinate of x-intercepts are always 0.

3x - 2*0 = 10

3x - 0 = 10

3x = 10

x = 10/3

X-INTERCEPT

Plug y=0 into the equation and solve the resulting equation 3x=10 for x.

The x-intercept:

[tex]\left(\frac{10}{3},0\right)\approx \left(3.33333333333333,0\right)[/tex]

Y-INTERCEPT

Plug x=0 into the equation and solve the resulting equation −2y=10 for y.

The y-intercept:

[tex]\left(0, -5\right)[/tex]

Answer: Circle lines

Step-by-step explanation:

Hopefully the attached image helps, it is a diagram of all the labeled lines on a circle excluding the radius (BG or GE)

The zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

According to the question,

The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex]. In order to find the zero of polynomials only if we substitute the value and polynomials become zero.

p(-2) = [tex]3(-2)^{3} - 16 (-2) - 8[/tex]

= 3(8) + 32 -8

= 0

Hence, the zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

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Using the quadratic formula, the solutions are:

a) [tex]x = \frac{3 \pm \sqrt{41}}{4}[/tex]

b) [tex]x = 1 \pm 2i[/tex]

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

Item a:

The coefficients are a = 2, b = -3, c = -4, hence:

Item b:

The coefficients are a = 1, b = 2, c = 2, hence:

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The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²

After folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.

An equilateral triangle is a type of triangle where by all the three sides are equal.

To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.

Using the formula for the area of an equilateral triangle,

A = √¾ a²

a= 12 inches

A = √¾ ×12²

A = 62.35 inches ²

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Answer:

Its 78!!!!

Solution:

1/2(12 * 18 - 5 * 12) = 78

The causes of variation that can be identified and eliminated are called; Assignable Causes.

There are two primary causes of variation in the quality of a product or process. These two primary causes are called;

Now, Common causes of variation are defined as random causes that we cannot identify. However, Assignable causes of variation are those that can be identified and eliminated.

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Answer:

[tex]\frac{1}{256}[/tex]

Step-by-step explanation:

So generally a geometric sequence can be defined as: [tex]a_n=a_1(r)^{n-1}[/tex] which is the explicit form. The r, is what each previous term is being multiplied by to get the next value which is evident in the recursive form: [tex]a_n = r(a_{n-1})\\[/tex]. Knowing this we can take two values which are "next" to each other to find what r is. In this case I'll just is 1 and 1/4, given these two values we know that: [tex]\frac{1}{4} = 1 * r[/tex], 1*r is just r... so what each term is being multiplied by is 1/4. So let's plug the values into the explicit formula: [tex]a_n=(\frac{1}{4})^{n-1}[/tex] (I didn't put an a_1 value in front, since it's just 1... so it's a bit redundant). Anyways using this formula we simply plug in 5 as n into the equation to find the 5th term: [tex]a_5 = (\frac{1}{4})^{5-1} = (\frac{1}{4})^4 = \frac{1^4}{4^4} = \frac{1}{256}[/tex]

The equations which are true for the values of x given are; x²-4 =0 and 4x²= 16.

The values of x given according to the task content are; x = –2 and x = 2.

By considering equation; x²-4 =0

x² = 4

x = ±2

Also, by considering 4x²= 16;

x² = 16/4 = 4

x = ±4.

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Answer: The triangles are not similar.

Step-by-step explanation:

Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.

For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.

Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.

[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]

Since we matched corresponding sides, we can now check whether they have the same ratio).

[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]

[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]

Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their

Answer:

Step-by-step explanation:

380 rows in total

bcs

use sense

The distance between David's home and the airport is 210 miles.

let the distance traveled after first 1 hour = y

distance/speed = time

after 1 hour his speed = (35 + 15) = 50 mph

total time after 1 hour and 30 mins = 1.5 hr

y/50 + 1.5 = y/35

multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Thus, the distance between David's home and the airport is 210 miles.

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Answer:

25 miles

Step-by-step explanation:

2 inches represents 10 miles ( divide both parts by 2 )

1 inch represents 5 miles , then

5 inches represents 5 × 5 = 25 miles

The expected value of tournament is $2600.

According to the statement

we have given that the tournament will cost $1000 and if it is sunny, it is expected that the club will collect $4,500 from the participants. And we have to find the expected value of a tournament.

So, we know that the

Cost of hosting the tournament : $1,000

If it rains, the club will lose the investment: $ -1,000

If it is sunny, the club will collect $4,500 ;

From all this the profit they will get

profit: 4,500 - 1000 = 3,500

And

There is a chance of 20% then

The club will loss the investment is

-1000*20 = -200

And

Effect on their profit if there is a rain then

3500*80 = 2800

then

The expected value of tournament is 2800-200=2600.

So,The expected value of tournament is $2600.

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Answer:

C

Step-by-step explanation:

on edge

Answer:

2×sqrt(2) = 2.828427125...

Step-by-step explanation:

x = "a positive number"

x + 56/x = x³

x² + 56 = x⁴

x⁴ - x² - 56 = 0

(x² + 7)(x² - 8) = 0

this is true only for

x² = -7

or

x² = 8

x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.

x² = 8 means

x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...

The criteria which CBR researchers might use to select and specify which units will be sampled as well as the sampling frame and methods to be used is the population.

This is defined as the total number of organisms found in a particular place at any given point in time and varies based on the number of variables present. In some cases, head counts are done to ascertain the exact value of individuals present.

The probability sampling method is ideal for a large population and involves random selection of the organisms so as to find out the statistical features of the group being used such as the range, mean etc. This tool is very important in the area of giving estimates for  ascertain type of activity or job.

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The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

An equation is an expression that shows the relationship between two or more variables and numbers.

An inequality shows the non equal comparison of two or more numbers and variables.

The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

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The worth of the car in 10 years is $1,831.67 using an exponential equation approach.

What is an exponential equation?

An exponential equation is the one with exponents such X^3(the 3 is the exponent)

The exponential equation required here is the one where the future value would be lower than current value because the car reduces in value year-in-year-out.

FV=PV*(1-r)^N

FV=future worth of the car

PV=today's value=$25,000

r=depreciation rate=-23%

N=number of years=10

The fact that r is negative means the car is depreciating not appreciating.

FV=$25,000*(1-23%)^10

FV=$1,831.67

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