Triangle ABC is a right triangle. Which equation could be used to determine the length of side AC?

Using the counting principle, Fernando can choose from a total of 35 different watch combinations, as he has 5 watch faces and 7 colored bands which can be selected independently.

The question asks about combinations resulting from 5 watch faces and 7 colored bands, this comes from a mathematical concept known as the counting principle. The counting principle states that if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events together can occur in m × n ways.

So, Fernando can choose from 5 watch faces and 7 colored bands independently. Therefore, the total different combinations of watches he can make is 5 × 7 = 35. Thus, Fernando has 35 different watch combinations to choose from.

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Answer:

is there an equation?

Winona's bowling scores have a mean of 204.6, a median and mode both of 195.

To find the mean, median, and mode of Winona's bowling scores, we follow these steps:

The bowling scores are 195, 180, 195, 212, 208, 231, 179, 246, and 195.

Mean: (195 + 180 + 195 + 212 + 208 + 231 + 179 + 246 + 195) / 9 = 1841 / 9 = 204.6

The mean score is 204.6.

To find the median, we first arrange the scores in ascending order: 179, 180, 195, 195, 195, 208, 212, 231, 246.

The median, or the middle score, is the fifth one since there are an equal number of scores on either side of it, which is 195.

The mode is the number that appears most often, which is also 195.

Therefore, Winona's mean score is 204.6, the median score is 195, and the mode is 195.

Answer:

The height of the football is 48 feet after 3 seconds

The first equation y = -16t² + 64t is the best

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation of motion of an object on air without any

 external force is y = ut + 1/2 at², where y is the height of the

 object from the ground, u is the initial velocity, a is the

 acceleration of gravity and t is the time

* Lets solve the problem

- A football is kicked at ground level with an initial velocity of

 64 feet per second

∴ u = 64 feet per seconds

∵ The football is kicked upward

∴ a = -32 feet per seconds²

∵ y = ut + 1/2 at²

∴ y = 64t + 1/2 (-32)t²

∴ y = 64t - 16t²

* We will use the first equation y = -16t² + 64t

∵ y = -16t² + 64t

- We need to find the height of the football after 3 seconds

∵ t = 3 seconds

∴ y = -16(3)² + 64(3)

∴ y = 48

∵ y represents the height of the football

∴ The height of the football is 48 feet after 3 seconds

Answer:

17

Step-by-step explanation:

2x-8=x+9

x=17

ANSWER

BC=17 units

EXPLANATION

The given triangle is an isosceles triangle.

We have

AC=AB

This implies that,

[tex]x + 9 = 2x - 8[/tex]

Group similar terms and simplify to get:

[tex]2x - x = 9 + 8[/tex]

[tex]x = 17[/tex]

Side BC is x units. But x=17

Therefore BC is 17 units.

Answer:

3603 boxes.

Step-by-step explanation:

Rectangular Prism is actually a cuboid.

Volume of cuboid = length * width * height.

It is given that length = 16.5 m,  width = 18.2 m, and height = 12 m. Therefore:

Volume = 16.5 * 18.2 * 12 = 3603.6 cubic meters.

Volume is actually the capacity of the shape. If the box has the volume of 1 cubic meters, then the number of boxes that can fit in the rectangular prism will be:

Number of boxes to be fit = Volume of Large container/Volume of Small Container.

Number of boxes = 3603.6/1 = 3603 boxes.

Therefore, 3603 boxes will fit the rectangular prism and 0.6 cubic meters will be the spare space!!!

Answer:

{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}

Step-by-step explanation:

Any relation having repetitive x-coordinates, is NOT a function.

{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}, is the set of ordered pairs represents a function. So, the option B is correct.

Here, we have,

A set of ordered pairs represents a function if each input (x-value) is associated with exactly one output (y-value).

Let's examine the given options:

O {(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)}: This set does not represent a function because the input value 1 is associated with both 5 and -3.

O {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}: This set represents a function since each input value is associated with a unique output value.

O {(6, 8), (5,2), (-2,-5), (1, -3), (-2, 9)}: This set does not represent a function because the input value -2 is associated with both -5 and 9.

O {(-3, 1), (6,3), (3, 2), (-3, -3), (1, -1)}: This set does not represent a function because the input value -3 is associated with both 1 and -3.

Therefore, the set of ordered pairs that represents a function is:

O {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}

Hence, {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}, is the set of ordered pairs represents a function. So, the option B is correct.

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Answer:

He could increase the sample size

Step-by-step explanation:

In hypothesis testing, the error associated with the test is affected by a number of factors. The first factor is the level of significance, alpha. This is the probability of type 1 error. The probability of rejecting the null hypothesis when it is indeed true.

The second factor is the size of the sample used. The larger the sample, the smaller the error since the characteristics of the sample will be closer to those of the entire population on which inference is being made

Answer:

B is correct just took the test.

Step-by-step explanation:

Answer:

The equation is y = -x + 2.5

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the equation of a line is y = mx + c , where m is the slope

  of the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

- The slope of the line which passes through points (x1 , y1) , (x2 , y2)

  is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

* Lets solve the problem

∵ The line passes through the points (-8.5 , 11) and (5 , -2.5)

- Let point(x1 , y1) = (-8.5 , 11) and point (x2 , y2) = (5 , -2.5)

∴ x1 = -8.5 , x2 = 5 and y1 = 11 , y2 = -2.5

∴ [tex]m=\frac{-2.5-11}{5-(-8.5)}=\frac{-13.5}{5+8.5}=\frac{-13.5}{13.5}=-1[/tex]

∴ The slope of the line is -1

∵ y = mx + c

∴ y = -x + c

- To find c substitute x and y in the equation by the coordinates of

  one of the two points

∵ Point (5 , -2.5) lies on the line

∴ x = 5 at y = -2.5

∵ y = -x + c

∴ -2.5 = -(5) + c

∴ -2.5 = -5 + c

- Add 5 to both sides

∴ c = 2.5

∴ y = -x + 2.5

* The equation is y = -x + 2.5

The slope and y-intercept to get y = -x + 2.5.

The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula, we get m = (-2.5 - 11) / (5 - (-8.5)) = -13.5 / 13.5 = -1.

Next, we use the slope-intercept form of a line, y = mx + b, to find the y-intercept (b). Substituting one of the points and the slope into this equation, for example, (-8.5, 11), gives us 11 = (-1)(-8.5) + b, which simplifies to b = 2.5.

Therefore, the equation of the line is y = -x + 2.5.

Answer:

405.80

Step-by-step explanation:

So, we know Carlos ran 21 miles per week, for 12 weeks....

That makes 21 mi/wk x 12 weeks = 252 miles.

Then we know each km is 0.621 mile.

So, we divide 252 miles by 0.621 mile/km to get= 405.80 km

Dividing miles by miles/km gives us the unit we want (km).

There was a trap in this question, because if instead of dividing the 252 miles by 0.621 you would have multiplied it, you would have gotten another answer listed... just not the right one. :-)

Answer:

Not sure if this is correct but maybe it is 34?

Answer: [tex]tan(x)=\±\frac{3}{4}[/tex]

Step-by-step explanation:

You know that [tex]sin(x)=\frac{3}{5}[/tex] and you can identify that. Then:

[tex]sin^2(x)=(\frac{3}{5})^2[/tex]

[tex]sin^2(x)=\frac{9}{25}[/tex]

Remember that:

[tex]cos^2(x)=1-sin^2(x)[/tex]

Then [tex]cos^2(x)[/tex] is:

[tex]cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}[/tex]

Apply square root to both sides to find cos(x):

[tex]\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}[/tex]

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

Then, this is:

[tex]tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}[/tex]

[tex]tan(x)=\±\frac{3}{4}[/tex]

Answer:

5

Step-by-step explanation:

To write the polynomial in standard form you need to write it in descending order of degree.

Standard form is:

5x^3 + 8x^2 + 9

The leading coefficient is the coefficient of the first term, the highest degree term.

Answer: 5

Therefore, the leading coefficient of the polynomial [tex]\(8x^2 + 9 + 5x^3\)[/tex] is [tex]\(5\)[/tex].

To write the polynomial [tex]\(8x^2 + 9 + 5x^3\)[/tex] in standard form, we arrange the terms in descending order of their degree:

[tex]\[ 5x^3 + 8x^2 + 9 \][/tex]

In this polynomial, the term with the highest degree is [tex]\(5x^3\)[/tex]. The coefficient of this term, which is the number multiplied by [tex]\(x^3\)[/tex], is the leading coefficient.

Answer:6,916

6,916

How to find the number:

The decimal of seven percent is 0.07. Take that times 9880

Answer:

n= -3 and n= -6

Step-by-step explanation:

[tex]n^2 = -18 -9n[/tex]

We need to solve this equation to find the value of n.

Rearranging:

[tex]n^2 +9n +18 =0[/tex]

This is a quadratic equation and we can solve by using factorization method.

We need to make factors of 18n^2 such that their sum is equal to 9n.

So solving,

[tex]n^2 + 9n +18 =0\\n^2 + 6n + 3n +18 =0\\n(n+6) + 3(n+6)=0\\(n+3)(n+6) =0\\=> n+3 =0 \,\, and n+6 =0\\n= -3 \,\,and \,\,n=-6[/tex]

Answer:

f(1) = 2

Step-by-step explanation:

Since y is a function of x, that is;

y = f(x)

f(1) implies the value of y when x = 1.

To obtain this value we draw the vertical line x = 1 and check where the line intersects the graph of f(x).

In this case, the line x = 1 will intersect with the graph of f(x) on the line y = 2. The function f(x) assumes the value 2 between x = 0 and x = 4. Therefore,

f(1) = 2

Answer:

f(1) = 2

Step-by-step explanation:

Answer:

A. ) 125.6 in.

Step-by-step explanation:

Hope I helped :)

Answer:

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=d\pi[/tex]

d - diameter

We have d = 40in. Substitute:

[tex]C=40\pi\ in[/tex]

[tex]\pi\approx3.14\to C\approx(40)(3.14)=125.6\ in[/tex]

ANSWER

[tex](2x-3y) (4x-y) = 8 {x}^{2} -14xy + 3 {y}^{2} [/tex]

EXPLANATION

We want to expand (2x-3y) (4x-y)

We use the distributive property to obtain,

[tex](2x-3y) (4x-y) = 2x(4x-y) -3y(4x-y)[/tex]

We expand to get,

[tex](2x-3y) (4x-y) = 8 {x}^{2} -2xy -12xy + 3 {y}^{2} [/tex]

Combine the middle terms to obtain,

[tex](2x-3y) (4x-y) = 8 {x}^{2} -14xy + 3 {y}^{2} [/tex]

Answer: a

hope this helps

Answer:

The answer is A) rotate 540° clockwise about (5, 3) and reflect across the line y = 3 HOPE I HELP :)

Step-by-step explanation:

D or B Step-by-step explanation:

Answer:

-a^2 -4a +3a +12

-a^2 -1a +12

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

• zero: -4, -4/3, 7

• positive: -4 < x < -4/3 . . . or 7 < x

• negative: x < -4 . . . or -4/3 < x < 7

Step-by-step explanation:

Zeros of the function are at x=-4, -4/3, +7. These are the values that make each of the individual factors be zero. For example, x-7=0 when x=7.

The function will be negative for x-values left of an odd number of zeros. It will be positive for x-values left of an even number of zeros (including left of no zeros, which is to say right of all zeros). This is because the sign of the factor giving rise to the zero changes for x-values on either side of that zero. (This is not true for zeros with even multiplicity, as the sign does not change at those.)

For this case we have the following functions:

[tex]f (x) = - x ^ 2 + 3x + 5\\g (x) = x ^ 2 + 2x[/tex]

We must find (f + g) (x), by definition we have to:

[tex](f + g) (x) = f (x) + g (x)[/tex]

So:

[tex](f + g) (x) = - x ^ 2 + 3x + 5 + (x ^ 2 + 2x)\\(f + g) (x) = - x ^ 2 + 3x + 5 + x ^ 2 + 2x\\(f + g) (x) = 5x + 5[/tex]

ANswer:

See attached image

Answer:

Step-by-step explanation:

see graph below

Answer: 1 5/8 or 13/8. They are the same.

Step-by-step explanation to find the amount of books she reads in 4 1/3 says, first you need to find how much she reads in 1 day.

3/4 divided by 2 = 3/4 x 1/2=3/8.

Now you need to multiply 3/8 by 4 1/3 to find how many books she can reed in a day. 4 1/3= 13/3. 13/3 x 3/8= 39/24 = 13/8 = 1 5/8

Answer: 2.888889

Step-by-step explanation:

3/4 book    4 1/3 book

------------- =  ---------------

2 days          x days

4 1/3= 13/3

3/4= 0.75

1.5x= 13/3

--------- -------

1.5      1.5

 x=  2.888889 books

Answer:

$9426.50

Step-by-step explanation:

let noel's salary = x, robert's salary = y and john's salary = z

y = x - 512.75 ..........(1)

z = 3y = 3(x - 512.75) = 3x - 1538.25 ...............(2)

x + y + z = 47645.25..........................(3)

substitute for y and z

x + (x - 512.75) + (3x - 1538.25) = 47645.25

x + x - 512.75 + 3x - 1538.25 = 47645.25

5x = 47645.75 + 512.75 + 1538.25

5x = 49696.25

divide both sides by 5

x = 9939.25 ..... noel's salary

to get robert's salary substitute x in equation 1

y = 9939.25 - 512.75 = 9426.50

y = $9426.50..... robert's salary

Answer: Fourth Option

[tex]x =4[/tex]

Step-by-step explanation:

First we write the equation

[tex]log_2(x) = 2- log_2(x-3)[/tex]

Now we use the properties of logarithms to simplify the expression

[tex]log_2(x)+log_2(x-3) = 2[/tex]  

The property of the sum of logarithms says that:

[tex]log_a (B) + log_a (D) = log_a (B * D)[/tex]

Then

[tex]log_2[x(x-3)]= 2[/tex]  

Now use the property of the inverse of the logarithms

[tex]a ^ {log_a (x)} = x[/tex]

[tex]2^{log_2[(x)(x-3)]}= 2^2[/tex]  

[tex](x)(x-3))}= 4[/tex]  

[tex]x^2-3x -4=0[/tex]

 [tex]x^2-3x -4=(x-4)(x+1)=0[/tex]

Then the solution are

[tex]x= -1[/tex] and [tex]x= 4[/tex]

We take the positive solution because the logarithm of a negative number does not exist

Finally the solution is:

[tex]x =4[/tex]

Answer:42

Step-by-step explanation:

7 multiplied by 6= 42

Insert 6 in the x place and solve

7x

7(6)

^^^The parentheses is the same as saying 7 × 6

so...

42

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

There were 18 trials recorded

Step-by-step explanation:

Each dot is a trial, the numbers under them is how long each that trial took.

Hope this helps.

The number of  times trials were recorded during the experiment are:

                                    18

We know that the dot plot is nothing but the representation of outcomes of a experiment where the dots represent the value of each outcome.

and the total number of  dots represent the total number of items which are studied or recorded.

Here, the total number of trials that are recorded is equal to the total number of dots in the dot plot i.e. the total frequency of the set.

The data frequency table is as follows:

      Value            Frequency

       15                      2

        17                      3

        19                      2

        20                     2

        21                       1

        23                       4

        24                        1

         25                       3

 Total frequency= 2+3+2+2+1+4+1+3=18

Hence, the answer is: 18                  

Answer: Yes, it does. Because each input value has one and only output value.

Step-by-step explanation:

By definition, a relation is a function when each input value has one and only output value.

Then, to know if the table represents a function, you need to observe if each input value (in other words, each value of the variable "x") has only one output value (the output values are the values of the variable "y").

You can observe that each value of "x" has only one value of "y", therefore, you can conclude that the given table represents a function.

For this case we must find the sum of the given series. For this we must expand the series for each value of k.

[tex](-2 (3) +5) + (- 2 (4) +5) + (- 2 (5) +5) + (- 2 (6) +5) =\\(-6 + 5) + (- 8 + 5) + (- 10 + 5) + (- 12 + 5) =[/tex]

Different signs are subtracted and the sign of the major is placed, while equal signs of sum and the same sign is placed.

[tex]-1-3-5-7 =\\-16[/tex]

The value of the series is -16

ANswer:

-16

Heya!

--------------------

Things to know before we solve:

The "6" at the top means that the the sequence only goes to the 6th term.

k = 3 represents that the sequence starts with the 1st term.

(-2k + 5) represents the rule of the sequence, we can substitute 3, 4, 5, and 6 to solve for the terms of the sequence.

--------------------

Solving for each term:

3rd term:

-2(3) + 5

-6 + 5

-1

4th term:

-2(4) + 5

-8 + 5

-3

5th term:

-2(5) + 5

-10 + 5

-5

6th term:

-2(6) + 5

-12 + 5

-7

--------------------

Simplifying:

Write these terms in expanded form:

(-1) + (-3) + (-5) + (-7)

Find the sum of the series:

(-1) + (-3) + (-5) + (-7) = -16

--------------------

Answer:

The sum of the series is -16

--------------------

Best of Luck!