MATHEMATICS HIGH SCHOOL

Compare using <, >, or =.
11/2____1

Answers

Answer 1
Answer: < Means the number on the right is larger than the left.
> Means the number on the left is larger than the right.

11/2 = 5.5
1 = 1

5.5 Is obviously bigger than 5.
Therefore 5.5 > 1.

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What is the value of b^2 0 4ac for the following equation?2x^2 0 2x 0 1 = 0 04 0 12
Please help . Easy 7th grade work , I’ll give brainliest
Tom conducted a drawing competition at school. He bought 5 boxes of colored pencils and spent $5.25 on drawing paper. However, more contestants entered than he expected, and he had to buy 2 more boxes of colored pencils. The total cost of the paper and pencils was $82.95. Identify the equation and solution that would help to find the cost of each box of pencils.
What is the product of 713 and 82
write an equation with the solution x=20. The equation should have the variable on both sides, a fractional coefficient on the left side, and a fraction anywhere on the right side

If a vector A⃗ has the following components, use trigonometry to find its magnitude and the counterclockwise angle it makes with the +x axis: Ax = 9.00lb , Ay = 5.00lb

Answers

The vector magnitude is 10.29lb and the vector direction is 150.9⁰.

Vector:

As per the given question:

Ay = 5.00 \ lb\n\nAx = 9.00 \ lb\n\n

To find:

magnitude and direction=?

Solution:

Vector representation of the given value:

\to (9i + 5j)

Calculating the vector magnitude:

\to √((9)^2 +(5)^2)\n\n \to √(81+25)\n\n \to √(106) \n\n\to 10.29 \ lb

Calculating the vector direction:

When 90 < \theta < 180

Let's solve the value for \theta\n\n

\tan \theta = (y)/(x)\n\n\tan \theta = (5)/(9)\n\n\tan \theta =0.555\n\n\theta = \tan^(-1)(0.555555556) \n\n\theta= 29.1^(\circ)\n\n

\sin \theta lies in the second quadrant,

\to \theta = 29.1^(\circ) = 180 -29.1 = 150.9^(\circ)\n\n

Find out more information about the angle here:

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True or FalseThe segments shown below could form a triangle.
A_________C is 6
C_____B is 5
B_____________A is 8

Answers

a,b,c-lengths\ sides\ of\ a\ triangle,\ then:\n\na+b > c\na+c > b\nb+c > c\n\nif\ a\leq b\leq c\ then\ a+b > c\n--------------------------\nHere:\na=5;\ b=6;\ c=8\n\na+b=5+6=11 > 8\n\nAnswer:TRUE

Vito is reading a historical fiction novel about Nelson Mandela for his literature class. He needs to identify a theme from the novel. Which statement is an example of a theme?Politicians can become very famous.
Mandela served as president of South Africa for five years.
Challenges can be overcome through hard work and persistence.
Mandela encouraged peace in his country while he was president.

Answers

Answer:

In Nelson Mandela's family he was the first to receive a formal education. At that time, very few black kids attained high school education in South Africa.

A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?

Answers

Given that the range of the signal is a quadratic function: (x-h)^2 = 4a (y - k) (5-4)^2 = 4a (4 - 2) 4a =1/2 therefore, (x -4)^2 = (1/2)(y – 2) The road is a line. Slope of the road is (7 -2)/(-3 -8) =-5/11 Therefore the equation of the line: 5x + 11y = 5(8) + 11(2) 5x + 11y = 62

The system of equations can be used to determine whether the road intersects the boundary of the tower’s signal; y = 2( x - 4 )² + 2 and 5 x + 11 y = 62.

What is the vertex form of a quadratic equation?

If a quadratic equation is written in the form

y = a(x-h)^2 + k

then it is called to be in vertex form.

It is called so because when you plot this equation's graph, you will see the vertex point is on (h,k).

To determine a quadratic function in vertex form:

y = a ( x - 4 )² + 2

4 = a ( 5 - 4 )² + 2

4 = a + 2

a = 2

y = 2 ( x - 4 )² + 2

Then we will determine a linear function in standard form, that passes through the points ( -3, 7 ) and ( 8, 2 ).

7 = -3 m + b

2 = 8 m + b   / ·(-1)

7 = - 3 m + b

- 2 = - 8 m - b

5 = - 11 m

m = -5/11,              

2 = -5/11 · 8 + b,        

b= 2 + 40/11,    

b = 62/11

Substitue,

y = - 5/11 x + 62/11  /  ·11

11 y = - 5 x + 62

5 x + 11 y = 62

Finally the system of equations is:

y = 2( x - 4 )² + 2

5 x + 11 y = 62

Learn more about vertex form of a quadratic equation here:

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How does the graph of y = sqrt(x) + 2 compare to the graph of the parent square root function

Answers

to move te function up z units, add zto the whole equation

from
y=sqrt(x) to
y=sqrt(x)+2

parenth function moved up 2 units
my hands are cold so I don't type well

The graph is a horizontal shift of the function two units to the left.

Given

The graph of the parent squareroot function is;

\rm y= √(x) +2

What is the horizontal shift?

The horizontal shift is obtained by determining the change being made to the x-value. The horizontal shift is C.

If the horizontal shift is positive, the shifting moves to the right.

If the horizontal shift is negative, the shifting moves to the left.

The square root parent function is,

\rm y= √(x) +2

There is a shift in positive x-direction 2 units.

When the constant is negative the shift is to the right in c units, and when the constant is positive (like in this case) the shift is to the left in c units.

Hence, the graph is a horizontal shift of the function two units to the left.

To know more about Horizontal Shift-click the link given below.

brainly.com/question/8740413

Find the quotient by doing long division and show work

Answers