Which measurement could represent they side lengths of a right triangle?
a. 3m, 4m, 5m
b. 10m, 12m, 16m
c. 6m, 8m, 12m
d. 4m, 5m, 9m

Answer:

To solve the system of equations:

y = 3x + 5 (Equation 1)

y = 4x^2 + x (Equation 2)

We can substitute Equation 1 into Equation 2, to get:

3x + 5 = 4x^2 + x

Simplifying and rearranging, we get:

4x^2 - 2x - 5 = 0

We can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 4, b = -2, and c = -5.

Substituting these values into the formula, we get:

x = (-(-2) ± √((-2)^2 - 4(4)(-5))) / 2(4)

Simplifying, we get:

x = (2 ± √84) / 8

x ≈ 1.053 or x ≈ -1.193

Substituting each value of x into Equation 1, we can find the corresponding value of y. So, the solutions to the system of equations are:

(x, y) ≈ (1.053, 8.158) or (x, y) ≈ (-1.193, 0.384)

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

The diameter of the circle is 16.66 units.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given a circle,

and two segments intersect at a point and form a right angle,

the length of the segment to the point of intersection is 6 units and 8 units as given in the figure,

and a segment pass from the center of the circle,

let the distance from point of intersection to center be x

so radius of circle be 6 + x from figure,

it forms a right triangle as shown in the figure, with hypotenuse 6 + x, base x, and perpendicular 8 units,

using Pythagoras theorem

h² = b² + p²

(6 + x)² = x² + 8²

36 + x² + 12x = x² + 64

12x = 64 - 36

12x = 28

x = 28/12

x = 2.333

radius of circle = 6 + x = 6 + 2.33 = 8.33

diameter of circle = 2r = 2 x 8.33 = 16.66 units

Hence the diameter is 16.66 units.

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Answer:

Step-by-step explanation:

Because calfornia is right next to Ocean

The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

Answer:.

Step-by-step explanation im not sure

Answer:

Step-by-step explanation:

47.)  sin20 = 6/b

b = 6(sin20) = 17.5

c = √6²+17.5² = 18.5

48.)  tan61 = y/18

y = 18(tan61) = 32.5

z = √18²+32.5² = 37.1

49.)  r = √25²+23² = 34

50).  d = √30²+7² = 30.8

51.)  sin71 = j/19

j = 19(sin71) = 18

k = √19²-18² = 6.2

52.)  y = √4²-1² = √7 = 2.6

53.)  sin49 = f/26

f = 26(sin49) = 19.6

h = √26²-19.6² = 17

54.)  t = √7²+4² = 8.1

Answer:

a) 37.5

b) 52.5

Step by step explanation:

a). Cement : Sand : Gravel = 1 : 2 : 4

2x = 15kg

15/2 = 7.5

7.5 x 5 = 37.5

b). 37.5 + 15 = 52.5

135 in Mayan notation is represented by one dot over four bars, followed by one dot over three bars, and then one dot over five dots.

To convert 135 to Mayan notation, we repeatedly divide by 20 and use the remainders to determine the number of dots and bars in each position. First, we divide 135 by 20 to get a quotient of 6 with a remainder of 15. The remainder of 15 corresponds to 1 dot over 5 dots and 2 bars (10 + 5).

Next, we divide 6 by 20 to get a quotient of 0 with a remainder of 6. The remainder of 6 corresponds to 1 dot over 3 bars (15). Finally, we have a quotient of 0 with a remainder of 6, which corresponds to 1 dot over 4 bars (20).

Putting these together, we get the Mayan representation of 135 as one dot over four bars, followed by one dot over three bars, and then one dot over five dots.

Complete question:

Convert the following numbers to Mayan notation. Show your calculations used to get your answers. 135?

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The time that the ball traveled is given as follows:

1.5 seconds.

The quadratic function determining the ball's height after t seconds is given as follows:

H(t) = -16t² + 24t.

The roots of the quadratic function in this problem are given as follows:

-16t² + 24t = 0.

16t² - 24t = 0

8t(2t - 3) = 0.

Hence we apply the factor theorem as follows:

Hence the time is given as follows:

1.5 - 0 = 1.5 seconds.

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Answer: x=35

Step-by-step explanation:

The expanded form of log4(4 / [7x^2]) is 1 - log4(7) - 2 * log4(x)

To expand the expression log4(4 / [7x^2]), we can use logarithmic properties to simplify it. First, we can rewrite the numerator as a power of the base 4:

log4(4) - log4(7x^2)

Since log4(4) is equal to 1 (since 4 raised to the power of 1 equals 4), the expression becomes:

1 - log4(7x^2)

Next, we can apply the logarithmic property log_a(b^c) = c * log_a(b) to simplify the logarithm of a product:

1 - (log4(7) + log4(x^2))

Using another logarithmic property log_a(b^c) = c * log_a(b), we can simplify the expression further:

1 - (log4(7) + 2 * log4(x))

Therefore, the expanded form of log4(4 / [7x^2]) is:

1 - log4(7) - 2 * log4(x)

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Answer:no idea

Step-by-step explanation:

The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

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Answer:

answer is 4.68$

Step-by-step explanation:

23.40×20/100=4.68

4.68$ is 20% of 23.40$

4.68$

Answer:

18x^2 - 40x / 3

Every three candy bars cost a dollar.

Divide 25 by three.  

$8.33

Answer:

the answer is 0.84

Step-by-step explanation:

Answer: Two numbers have a sum of 1, 212 and a difference of 518. What are the two numbers? Let x represent one number and y represent the other number. The solution is (865,347).

Step-by-step explanation:

The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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Answer:

\(6 \frac{5}{12} \: {ft}^{2} \)

Step-by-step explanation:

\(area \: of \: rectangle = length \times width \\ \\ = 1 \frac{1}{6} \times 5 \frac{1}{2} \\ \\ = \frac{7}{6} \times \frac{11}{2} \\ \\ = \frac{77}{12} \\ \\ = 6 \frac{5}{12} \: {ft}^{2} \)

Answer:

Hi there here is the answer!

Step-by-step explanation:

Out of the 3 main chioces there is a total of 15!

so, it would be a probability of 5/15. or 1/3 / 1:3

The complete factorization of the polynomial is:

h(x) = (x - 3)*(x - 1)*(x + 2)

Here we have the polynomial:

g(x)= x³ - 2x² - 5x + 6

And we know that x = 3 is a zero, then (x - 3) is a factor.

So if f(x) = a*x² + b*x + c

We can write:

h(x) = (x - 3)*f(x)

Let's find f(x).

Expanding that:

x³ - 2x² - 5x + 6 = (x - 3)*(a*x² + b*x + c)

x³ - 2x² - 5x + 6 = ax³ + bx² + cx - 3ax² - 3bx - 3c

x³ - 2x² - 5x + 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c

Comparing like terms, we can see that:

a = 1

b - 3 a = -2

c - 3b = -5

-3c = 6

With the first and last equation we can get:

a = 1

c = 6/-3 = -2

Now with one of these values and the second or third equation we can find the value of b.

b - 3 a = -2

b - 3*1 = -2

b - 3 = -2

b = -2 + 3 = 1

Then:

f(x)  = x² + x - 2

The zeros of this quadratic function are given by:

x = -1±3 / 2

so, we get,

x = (-1 + 3)/2 = 1

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

Then we can factorize this as:

f(x) = (x - 1)*(x + 2)

And then we can write h(x) as:

h(x) = (x - 3)*(x - 1)*(x + 2)

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complete question:

For the polynomial below, 3 is a zero.

g(x)= x³ - 2x² - 5x + 6

Express g (x) as a product of linear factors.

Answer:

a. 2x+3z

b. 7xy

c.   \(\frac{3ab}{2c}\)

d. 10z-6q

e. Subtract xy from the sum of p and q.

f.  Divide the sum of 3 and y by 5.

g. Subtract 2c from the square root of b.

h. 3x ... 4x ...

i. 3y ... y+5 ... 5y+5

j. length ... 3 ... breadth ... 8b ... 3b²

Step-by-step explanation:

Sum means addition. 2x + 3z

Product means multiplication. 7y × x = 7xy

Divide 3ab by 2c. 3ab ÷ 2c = \(\frac{3ab}{2c}\)

Subtract 6q from 10z.  10z-6q

(p+q)-xy : Subtract xy from the sum of p and q.

(3+y)/5: Divide the sum of 3 and y by 5.

\(\sqrt{b}\)- 2c: Subtract 2c from the square root of b.

Let the number of boys be x. Girls are three times more so 3 × x = 3x. The total would be 3x + x = 4x.

Let Nora's age be y. Father is three times more so 3 × y = 3y. Brother is 5 more so would be y+5. The total would be y + 3y + y + 5 = 5y+5

3b is three times more than b, the breadth. Thus, the length is three times more than the breadth since it is 3b. The perimeter would be 3b + b + 3b + b = 8b. The area would be 3b × b = 3b²

The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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Answer:1

Step-by-step explanation: so bro if yo do 5*1/25 u can see

Answer: the probability that I, Samuel Lisa and Andrew are chosen is 0.0003

Step-by-step explanation:

Given that;

Number of 4 employees are to be chosen from 19 of them;

so Number of ways to choose 4 employees from 19 employees = ?

we know that;

c(n,r) = \(\left[\begin{array}{ccc}n\\r\end{array}\right]\) = n! / ( r!(n-r)!)

so we substitute

c(19,4) = \(\left[\begin{array}{ccc}19\\4\end{array}\right]\) = 19! / ( 4!( 19-4 )!) = 3876

so the probability that I, Samuel Lisa and Andrew are chosen will be;

⇒ 1 / 3876 = 0.0002579 ≈ 0.0003

the probability that I, Samuel Lisa and Andrew are chosen is 0.0003

Answer:

Where is the Q?

Step-by-step explanation:

Answer: 9

Step-by-step explanation: