This year, a teacher graded 83 more final exams than last year. If the teacher graded 625 final exams this year, how many final exams did the teacher grade last year?

Distance from the origin to the points  ≈ 0.41.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;

Let OB is the distance from the origin to the point B

Let OA is the distance from the origin to the point A

Using the formula for calculating the distance between two points;

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(4-0)²+(3-0)²+(5-0)²

OA = √(16)+(9)+(25)

OA = √50

OA = 7.071

Similarly;

OB = √(6-0)²+(2-0)²+(-4-0)²

OB = √(6)²+(2)²+(-4)²

OB = √36+4+16

OB = √56

OB = 7.4833

Distance from the origin to the points = 7.4833 - 7.071= 0.4123

Distance from the origin to the points  ≈ 0.41

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Step-by-step explanation:

PART 1:

on the graph you can make a triangle at any point and with any angle measures.

i recommend a smaller right triangle to be easiest.

i recommend the points (0,3) A (3,0) B and (0,0) C

∆ABC angle measurements:

m∠CAB=45°

m∠ABC=45°

m∠ACB=90°

PART 2:

(4,3) D (7,0) E and (4,0) F make an identical right triangle moved 4 squares to the right

m∠FDE=45°

m∠DEF=45°

to find the missing value of the angle EFD we will use subtraction and addition

180-(45+45)

180-90

90

therefore, the m∠EFD=90°

PART 3:

both the angle measures and the shapes of the triangles are the same

PART 4:

i used a 1:1 ratio

sorry for the wait :)

Answer:

1/4

Step-by-step explanation:

Since y/x = 3/12 = 1/4, the answer is 1/4.

Answer:

All its side lengths are equal

(and all the agle of 60°)

Step-by-step explanation:

What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .​

Answer:

is B

Step-by-step explanation:

this is the best possible answer

Answer:

rise over run aka a measure of its steepness

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The slope of a horizontal line, such as that of y= 3, is equal to 0.

This can be proved using the slope formula.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Let's choose 2 points on the line y= 3:

(0, 3) and (2, 3)

Slope

[tex] = \frac{3 - 3}{2 - 0} [/tex]

[tex] = \frac{0}{2} [/tex]

= 0

Thus, the line has a slope of zero.

On the other hand, vertical lines have an undefined slope.

Additional:

To learn more about horizontal lines and their slopes, do check out the following!

Answer:

x=100/7

Step-by-step explanation:

The interior angles will sum to 360 so 72+89+99+7x=360

260+7x=360

7x=100

x=100/7

Answer:

height= 13.2 cm

Step-by-step explanation:

h = 2 × A/b

h = 2 × 33 /5

= 13.2

Answer:

Perimeter = 2(l + b)

= 2(x + 5x³ + 4 - x²)

= 2x + 10x³ + 8 - 2x²

= 10x³ - 2x² + 2x + 8

Hence, ur answer is the first option.

Answer:

A.

Step-by-step explanation:

L = x

W = 5x³ + 4 - x²

P = 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

P(x) 10x³ - 2x² + 2x + 8

L = x

W = 5x³ + 4 - x²

P= 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

= P(x) 10x³ - 2x² + 2x + 8

The function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Given that:-

The cost of the 250 minutes is $25 and if the time extends from 250 minutes then the function will be expressed in the form of.

C(x) = 25 + 0.2 (x)

Here C(x) is the total cost and the x is in minutes.

Hence the function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

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Answer:

Both legs would be 20

Step-by-step explanation:
In the image below, it shows the relationship between the legs and the hypotenuse in every 45 45 90 triangle. If we know that the hypotenuse is 20, then the 2 legs are both 20.

I am slightly confused with the problem since they asked for the "short" leg and the "long" leg. Both legs should be the same length because a 45 45 90 triangle is isosceles, with the two legs being the same length.

Answer:

a=1.66

b=8368.12

Step-by-step explanation:

hope it helps

Answer:

y = x + 4

when x is 5, y is 9

Step-by-step explanation:

the pattern from the table is that the y value is 4 more than the x value, so the equation would be y = x + 4.

if you plug in x = 5, then this would be y = 5 + 4 = 9

The graph is attached with the answer.

When function has different behaviour at different intervals , then it is called a piecewise function.

It is given that

f(x) = - 3x -5 at x ≤ -1

f(x) = -2x +3 at -1 <x<4

f(x) = 2 at x ≥ 4

All the piecewise Function are a straight line.

The table for functions is

f(x) = 3x -5

-1  -8

-2  -11

-3   -14

f(x) = -2x +3

0  3

1    1

2    -1

3   -3

f(x) = 2

4     2

5      2

6     2

7     2

The graph is attached with the answer.

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[tex] \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]

Answer:

Area of smaller square = [tex]\tt\underline{5cm}[/tex][tex]\tt{\times 5cm = }[/tex][tex]\tt\underline\green{25}[/tex] [tex]\tt{sq.cm}[/tex]

Area of bigger square = [tex]\tt{15cm \times}[/tex][tex]\tt\underline{ 15cm }[/tex][tex]\tt{=}[/tex] [tex]\tt\underline\green{225}[/tex] [tex]\tt{sq.cm}[/tex]

Total Area = [tex]\tt\underline\green{25sq.cm}[/tex] [tex]\tt{+}[/tex] [tex]\tt\underline\green{225sq.cm}[/tex] [tex]\tt{=}[/tex] [tex]\normalsize \underline{\boxed{\tt \red{250}}}[/tex] [tex]\tt\underline{sq.cm}[/tex]

[tex]\\[/tex]

Area of square A = [tex]\tt\underline{7m}[/tex][tex]\tt{\times}[/tex][tex]\tt\underline{7m}[/tex][tex]\tt{=}[/tex][tex]\tt\green{49}[/tex] [tex]\tt{sq.m}[/tex]

Area of square B = [tex]\tt{7m}[/tex][tex]\tt{\times}[/tex][tex]\tt{7m}[/tex][tex]\tt{=}[/tex][tex]\tt\underline\green{49}[/tex] [tex]\tt{sq.m}[/tex]

Area of square B = [tex]\tt{14m}[/tex][tex]\tt{\times}[/tex][tex]\tt\underline{14m}[/tex][tex]\tt{=}[/tex][tex]\tt\green{196}[/tex] [tex]\tt{sq.m}[/tex]

Total Area = [tex]\tt\underline\green{49m}[/tex] [tex]\tt{+}[/tex] [tex]\tt\underline\green{49m}[/tex] [tex]\tt{+}[/tex] [tex]\tt\underline\green{196}[/tex] [tex]\tt{=}[/tex][tex] \normalsize \underline{\boxed{\tt \red{294}}}[/tex][tex]\tt{sq.m}[/tex]

====================================

To find the area of square use this formula [tex]\large\tt{A = s \times s}[/tex]. Means side of the square multiply to the same side of the square

[tex] \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]

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Answer: 8x+70

Step-by-step explanation:

[tex]\sum^{5}_{n=2} (2x+5n)=(2x+10)+(2x+15)+(2x+20)+(2x+25)=\boxed{8x+70}[/tex]

Answer:

Step-by-step explanation:

A function is defined so that for each input, there is no more than one output.

We will need to shade the region above f(x) and the region below the function g(x)…

We have:

f(x) = x² - 1

g(x) = -x² + 4

Both of these are already graphed, and we want to transform it into:

y > f(x)

y ≤ g(x)

The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x)…

For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve…

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The triangle is not a right triangle. This is because the sum of the square of the two shorter lengths is not equal to the square of the longest length.

In order to determine if the triangle is a right triangle, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

12 ² + 24²

= 144 + 576 = 720

29² = 841

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Based on the frequency table given, The option that closely matches the histogram I drew is option C but the last one suppose to be 7 and not 6.

Hours online   Frequency

5                           0-3

8                          4-7

10                         8-11

9                          12-15

7                           16-19

Note that in the image attached, you can see how the Hours online were said to be matched with the  Frequency.

So since option A and B was not shown to see which matches the option,  i can say option c is closest but if look at my own image, you can use it to find the right one.

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8) 5 + 4 + 2 = 11

Since there are 5 guavas, the correct answer is B. 5/11

9) 3 + 4 = 7

Since there are 4 blue papers, the correct answer is A. 4/7

10) Count all of the numbers and add them. There are 4 twos, 2 fives, and 1 three:

4 + 2 + 1 = 7

Since there are 4 twos, the correct answer is C. 4/7

Answer:

-51

Step-by-step explanation:

If the limits are reversed, then place a negative sign in front of the integral.

[tex]\int\limits^a_bf ({x}) \, dx =-\int\limits^b_a f({x}) \, dx[/tex]

[tex]\int\limits^a_3 f({x}) \, dx = 51\\[/tex] where [tex]\alpha =10\\[/tex]

[tex]\int\limits^3_\alpha f( {x}) \, dx =-51[/tex]  where[tex]\alpha =10[/tex]

Answer:the equations are

y = x + 4 and y = 3x + 6

Now we can use substitution method to solve the system

So we can substitute value of y from one equation into other

So we get

x+4 = 3x+6

So Option B is correct

Step-by-step explanation:

Answer:

2x + 4 = 3x + 1

Explanation:

Equation A: y = 2x + 4

Equation B: y = 3x + 1

Simultaneously solving :

⇒ y  =  y

⇒ 2x + 4 = 3x + 1

⇒ 2x - 3x = 1 - 4

⇒ -x = -3

⇒ x = 3

Solve for y :

⇒ y = 2x + 4

⇒  y = 2(3) + 4

⇒ y = 10

[tex]y=200(0.5)^2^t[/tex] is Decay

[tex]y=\frac{1}{2}(2.5)^\frac{t}{6}[/tex] is Growth

[tex]y=(0.65)^\frac{t}{4}[/tex] is Decay

The expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, B expression can be simplified by applying identity.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an expression:

Part A)

= 6x¹⁰ - 96x²

= 6x²(x⁸ - 16)

Part B)

[tex]\rm =6x^2(\left(x^4\right)^2-4^2)[/tex]

[tex]\rm =6x^2(\left(x^4+4\right)\left(x^4-4\right))[/tex]

[tex]\rm =6x^2\left(x^2+2x+2\right)\left(x^2-2x+2\right)\left(x^2+2\right)\left(x^2-2\right)[/tex]

Thus, the expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, the B expression can be simplified by applying identity.

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