In a 30 - 60 - 90° triangle x= 7.5 feet
What is the length of the hypotenuse?

Answer:

Graph the parabola y=x2−7x+2 .

Compare the equation with y=ax2+bx+c to find the values of a , b , and c .

Here, a=1,b=−7 and c=2 .

Use the values of the coefficients to write the equation of axis of symmetry .

The graph of a quadratic equation in the form y=ax2+bx+c has as its axis of symmetry the line x=−b2a . So, the equation of the axis of symmetry of the given parabola is x=−(−7)2(1) or x=72 .

Substitute x=72 in the equation to find the y -coordinate of the vertex.

y=(72)2−7(72)+2    =494−492+2    =49 − 98 + 84     =−414

Therefore, the coordinates of the vertex are (72,−414) .

Now, substitute a few more x -values in the equation to get the corresponding y -values.

x y=x2−7x+2

0 2

1 −4

2 −8

3 −10

5 −8

7 2

Plot the points and join them to get the parabola.

[tex]\dfrac 1{\sqrt 7- \sqrt 3}\\\\\\=\dfrac{\sqrt 7 + \sqrt 3}{\left ( \sqrt 7 -\sqrt 3\right) \left( \sqrt 7 + \sqrt 3\right)}\\\\\\=\dfrac{\sqrt 7 + \sqrt 3}{\left(\sqrt 7 \right)^2 - \left(\sqrt 3 \right)^2}\\ \\\\=\dfrac{\sqrt 7 + \sqrt 3}{7-3}\\\\\\=\dfrac 14\left(\sqrt 7 + \sqrt 3\right)[/tex]

The weight of each of the two piles Tineka split the jellybeans in the sack to is 7/24 lb.

Division is when two numbers are grouped into equal parts using another number. The sign used to denote division is ÷.

In order to determine the weight of each pile, divide the weight of the sack by 2.

Weight of each sack = 7/12 ÷ 2

7/12 x 1/2 = 7/24

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Answer:

Use the slider to change the value of k.

Positive values of k shift the graph ✔ up.

Negative values of k shift the graph ✔ down

Step-by-step explanation:

Transformation involves changing the position of a function.

The true statements are:

Positive values of k shift the graph up

Negative values of k shift the graph down

The functions are given as:

The equation of g(x) implies that, f(x) is translated or shifted vertically.

The possible values of k are:

k is greater than 0 i.e. positive

k is less than 0 i.e. negative

When k is positive, then the graph of the function shifts up

If otherwise (i.e. k is negative), then the graph of function shifts down

Changing the value of k in the function g(x) = |x| + k affects the graph by shifting it vertically.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Horizontal translation: g(x)=f(x+c).

The graph is translated as c units to the left if c>0 and c units to the right if c<0.

Vertical translation: g(x)=f(x)+k.

The graph is translated as k units upward if k>0 and k units downward if k<0.

When k is positive, the graph of g(x) is shifted upward by k units compared to the graph of f(x). This is because, for any value of x, g(x) will be greater than f(x) by k units, due to the addition of k to the absolute value of x.

Conversely, when k is negative, the graph of g(x) is shifted downward by k units compared to the graph of f(x). This is because, for any value of x, g(x) will be less than f(x) by k units, due to the subtraction of k from the absolute value of x.

Therefore, changing the value of k in g(x) = |x| + k shifts the graph vertically, either upward or downward, depending on the sign of k.

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Answer:

Hope it helps.....................

Answer:

C

Step-by-step explanation:

a and b add to 180 degrees also known as a straight line

Answer:

supplimentarry

Step-by-step explanation:

add up to be 180

Answer:

Center: (-7,6)

Radius: 4

Step-by-step explanation:

Hope this helps :)

The pie chart of the number of text messages sent by the students represents the stem plot using a circle graph

The stem plot is given as:

0 | 37

1  | 0011223445 77 88 89

2 | 013557

From the above stem plot, we have the following frequency table

SMS        Frequency

0 - 9         2

10 - 19      16

20 - 29    6

Total       24

Next, we determine the relative frequency table

SMS        Frequency    Relative Frequency

0 - 9         2                           2/24 = 8.33%

10 - 19      16                          16/24 = 66.67%

20 - 29    6                            6/24 = 25.0%

Total       24                            100%

Next, we plot the pie chart

See attachment for the pie chart

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The polynomial (a + b)(a² – ab + b²) is reconstructed as (2x + y)(4y² – 2xy + y²), then the correct option is C.

Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Tomas learned that the product of the polynomials (a + b)(a² – ab + b²) was a special pattern that would result in a sum of cubes, a³ + b³.

His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = y.

Then the polynomial equation will be

(2x + y)(4y² – 2xy + y²)

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Answer:

C

Step-by-step explanation:

2022

Answer:

The general formulaa for an arithmetic sequence is:

a(n) = a + d(n - 1)

Step-by-step explanation:

Answer is a(n) = a + d(n - 1)

Answer:

Option A :- V = 301.44

Step-by-step explanation:

Formula= V = (1/3)πr²h

Volume = 1/3 × 22/7 × 36 × 8

⇒ 301.44

[tex]2(3y + 7 + 5) = 180\\\\ \implies 3y+12=\dfrac{180}2 \\ \\ \implies 3y+12 = 90\\\\\implies 3y = 90-12\\\\\implies 3y = 78\\\\\implies y= \dfrac{78}3 \\\\\implies y=26[/tex]

Answer:

y = 26

Step-by-step explanation:

2(3y + 7 + 5) = 180

6y + 14 + 10 = 180

6y + 24 = 180

      -24    -24

6y = 156

÷6     ÷6

y = 26

I hope this helps!

The estimated number of lines of code written by computer programmers per hour when x people are working & the correct option is  y = 27x - 4.

Table  showing the estimated number of lines of code written by computer programmers per hour when x people are working & option given   y= 47 * 1.191ˣ     y= 34 * 1.204ˣ    y=26.9x - 1.3    y = 27x - 4

To Choose the model which best represents the data.

To understand a set of data, it is helpful to organize it and provide summary descriptions of the set.

People Working   lines of code

2                             50

4                             110

6                            160

8                            210

10                           270

12                           320

x      y= 47 * 1.191ˣ    y= 34 * 1.204ˣ    y=26.9x - 1.3   y = 27x - 4

2       66.66               49.3                   52.5                 50

4       94.57               71.44                  106.3                104  

6      134.14                103.57               160.1                 158

8      190.27               150.14                213.9               212

10     269.91              217.64               267.7               266

12     382.85             315.5                  321.5               320.

Below    2              0                         4                        1

on line    0              0                         0                       2  

Above     4               6                         2                       3

Therefore  y = 27x - 4 is the best fit

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Answer:

y = 27x - 4

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Step-by-step explanation:

Answer:

the anwer is 5 cm3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

Triangle C :)

Step-by-step explanation:

On the chart, it shows us that triangle c has the largest base at 5 units long :)

Have an amazing day!!

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Answer:

1/9

Step-by-step explanation:

look up mixed numbers calculator soup , it helps you <3

Answer:

1 37/50

Step-by-step explanation:

4/5÷7/15 =

1.74 =

1 74/100 =

1 37/50

Answer:

1.07142857143 (1 rounded)

Step-by-step explanation:

3/14 of 5 is 1.07142857143

Answer:

[tex]f\left(x\right)=\left(x-1\right)^{2}+3[/tex]

Step-by-step explanation:

The equation for thr function f(x) is [tex]f(x)=\left(x-1\right)^{2}[/tex] . The vertex of this equation is located at (1,0). The vertex of function g(x) is located at (1,3) , meaning that the vertex of g(x) is 3 units higher than that of f(x). This can be represented in the equation using a vertical translation. The final equation for g(x) would be [tex]f\left(x\right)=\left(x-1\right)^{2}+3[/tex] .

Hope this helps! :)

between 30 and 50 is approximately 40

Step-by-step explanation:

[tex] - \frac{1}{5} + \frac{1}{4} \times \frac{1}{20} [/tex]

choice 3

Answer:

  3.9 cm²

Step-by-step explanation:

The area formula for a triangle when sides 'a' and 'b' and angle C are known is ...

  A = 1/2ab·sin(C)

__

The area of the specified triangle is ...

  A = 1/2(3.9 cm)(2.7 cm)sin(133°) ≈ 3.85058 cm²

The area of ΔLMN is about 3.9 square centimeters.

Answer:

1) 27

2) 63

Step-by-step explanation:

cos-1(17/38)= 63.425...= 63= angle C

90-63= 27=angle A

Answer  70 = 7070

Step-by-step explanation: denotes how many times to multiply the base (70)

the answer is around 1.73, so its a little over the 1.5 mark. also, im not sure if this is what you meant, but the phrase is radical 3, or the square root of 3 :)

its the blue line!!!!

The shaded region is the solution of the given functions f(x) = x² – 3 and g(x) = –x² + 2.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The functions f(x) = x² – 3 and g(x) = –x² + 2 are shown on the graph.

Now for the point (0, 0). Then we have

0 ≤ 0² – 3

0 ≤ – 3

which is false

Then the region is opposite to the origin.

Similarly, we have

0 > 0² + 2

0 > 2

which is false

Then the region is opposite to the origin.

Thus, the shaded region is the solution of the given functions f(x) = x² – 3 and g(x) = –x² + 2.

The graph is shown below.

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Answer:x + y = 180

p + q = 180

p = x

Show that y = q

x = 180 - y

p = 180 - q

p = x

180 - q = 180 - y

-q = 180 - y - 180

-q = -y

-q/-1 = -y/-1

q = y  OR y = q

x + y = p + q   CHOICE B.

180 - y + y = 180 - q + q

Step-by-step explanation: your welcome