Answers
Your mouse pointer is covering the number at the hypotenuse, but I assume that it is 10.
We can test to see if the triangle is a right angled triangle by using Pythagoras' Theorem. This is because the Pythagorean Theorem only works with right angled triangles.
The theorem is:
[tex]a^{2} + b^{2} = c^{2}[/tex]
where:
a = length of one leg of the triangle
b = length of the other leg of the triangle
c = the length of the hypotenuse.
If triangle FGH is a right triangle then:
[tex]\sqrt{51}^ {2} + 7 ^{2} = 10^{2}[/tex]
[tex]\sqrt{51} ^{2}[/tex] is just 51
[tex]7^{2}[/tex] is 49
and [tex]10^{2}[/tex] is 100
if we add up 51 and 49 we get 100. And of course, 100 = 100,
Since the theorem works, then the FGH is a right triangle
______________________________________
Answer:
True: FGH is a right angled triangle
Related Questions
Factor completely 5xy3 + 15x3y2 − 30x2y2. 5(xy3 + 3x3y2 − 6x2y2) 5x(y3 + 3x2y2 − 6xy2) 5xy2(y + 3x2 − 6x) Prime
Answers
Answer:
5xy^2(y + 3x^2 - 6x).
Step-by-step explanation:
5xy^3 + 15x^3y^2 − 30x^2y^2
The GCF is 5xy^2 so dividing through by this we get the factors:
= 5xy^2(y + 3x^2 - 6x).
Answer:
[tex]5xy^2(y+ 3x^2- 6x)[/tex]
Step-by-step explanation:
[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]
To factor out an expression, factor out GCF
[tex]5xy^3= 5 \cdot x \cdot y \cdot y \cdot y[/tex]
[tex]15x^3y^2= 5 \cdot 3 \cdot x \cdot x \cdot x \cdot y \cdot y[/tex]
[tex]30x^2y^2= 5 \cdot 2 \cdot 3 \cdot x \cdot x \cdot y \cdot y[/tex]
GCF is 5 times x times y time y
GCF is 5xy^2. Factor out GCF
[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]
[tex]5xy^2(y+ 3x^2- 6x)[/tex]
What is the value of f(6) in the function below?
f(x) = 2x
Answers
Answer:
see below
Step-by-step explanation:
f(x) = 2x
Let x = 6
f(6) = 2*6 = 12
If you meant f(x) = 2^x
Let x = 6
f(6) = 2^6 = 64
What is the general form of the equation of a circle with its center at (-2,1) and passing through (-4,1)
Answers
Answer:
(x + 2)^2 + (y - 1)^2 = 2^2
Step-by-step explanation:
The equation of this circle is
(x + 2)^2 + (y - 1)^2 = r^2, and we are to determine the values of r^2 and r by substituting -4 for x and 1 for y:
(-4 + 2)^2 + (1 - 1)^2 = r^2, or:
(-2)^2 = r^2, or
4 = r^2
Then r = 2.
The desired equation is:
(x + 2)^2 + (y - 1)^2 = 2^2
If p and q prime number greater than 2which of the following is not even integer ? a.p+q b.p×q c.p^2-q^2 d.p-q
Answers
B, because every prime number greater than 2 is odd, and the product of two odd numbers is odd.
Answer: I'm pretty sure its B
Step-by-step explanation:
..
31. A driver
can be charged with Driving While Intoxicated (DWI).
A. under 21 years old only
B. over 21 years old only
c. under 18 years old only
D. of any age
Answers
Answer:
D. of any age
Step-by-step explanation:
A driver can be charged with Driving While Intoxicated of any age.
It doesn't matter how old you are because a crime is a crime. If you are younger there will most likely be less of a punishment as adults.
Use the grouping method to factor the polynomial below completely.
3x3 + 9x2 + 5x + 15
Answers
Answer:
(3x^2+5)(x+3)
Step-by-step explanation:
The given expression is:
3x3 + 9x2 + 5x + 15
First of all group the first two terms and last two terms:
(3x3 + 9x2) + (5x + 15)
Now factor out the greatest common factor from each group:
3x^2(x+3)+5(x+3)
(3x^2+5)(x+3)
Thus the factors of 3x3 + 9x2 + 5x + 15 are:
(3x^2+5)(x+3) ....
Answer:(3x^2 + 5)(x + 3)
Step-by-step explanation:
B.
what is 81-86÷2+(9×2)-50=pmdas
Answers
Answer:
6
Step-by-step explanation:
=81−43+(9)(2)−50
=38+(9)(2)−50
=38+18−50
=56−50
=6
Answer:
6.
Step-by-step explanation:
81-86÷2+(9×2)-50
work out the parentheses first;
= 81 - 86 / 2 + 18 - 50
Now the division:
= 81 - 43 + 18 - 50
= 38 + 18 - 50
= 56 - 50
= 6.
if the point (-4,5) and (0,2) are used to find the slope of the line the slope is -3/4 what is the slope if the points (0,2) and (4,-1) are used
Answers
To find slope you just place the change in y over the change in x.
2- -1=3
0-4= -4
The slope is -3/4 which is the same as before
A certain type of cell can double itself every hour, because it has a growth factor of 2. A laboratory has 15 of these cells.
Which function best models the amount of cells in the laboratory after x hours?
f(x)=2^x+15
f(x)=15⋅2^x
f(x)=2⋅15^x
f(x)=15^x+2
Answers
Answer:
Second one
Step-by-step explanation:
Second choice.
Second one is growing by a factor of 2 because the exponent on 2 tells me that 2 is is being repeated as a factor.
If x=0 then 15*2^0=15(1)=15 which is what we have initially.
Final answer:
The correct option is f(x)=15⋅2^x. The function that best models the cell growth after x hours is f(x) = 15⋅ 2^x, illustrating the exponential nature of cell division starting with 15 cells.
Explanation:
The amount of cells in the laboratory after x hours, when the number of cells doubles every hour, is best represented by the function f(x) = 15⋅ 2^x. This is because the cell population increases exponentially, starting with 15 cells and doubling each hour. The formula represents exponential growth where the original amount of cells (15) is multiplied by two raised to the power of the number of hours elapsed (x).
The first term of a sequence is 4 and the common ratio is –2. What is the formula for the sequence based on term number
Answers
Answer:
its B and the next one is C
Step-by-step explanation:
Formula for the sequence based on term number is
[tex]a_{n} =(4)(2)^{n-1}[/tex].
What is geometric sequence?In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given
First term [tex]a[/tex] = 4
Common ratio r = -2
It is a geometric sequence because we have common ratio
Formula for the sequence based on term number is
[tex]a_{n} =ar^{n-1}[/tex]
[tex]a_{n} =(4)(2)^{n-1}[/tex]
Hence, Formula for the sequence based on term number is
[tex]a_{n} =(4)(2)^{n-1}[/tex].
Find out more information about geometric sequence here
brainly.com/question/11266123
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The slope of the line below is - 1. Write a point-slope equation of the line
using the coordinates of the labeled point.
(3, 3)
- 10+
O A. +3 4(x+3)
OB. y-3--|(x-3)
O C. y-3 - 4(x-3)
O D. +3 --{(x+3)
Answers
Answer:
[tex]\large\boxed{y-3=-(x-3)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = -1 and the point (3, 3).
Substitute:
[tex]y-3=-1(x-3)[/tex]
Erica chops wood in the forest.
The table compares the number of cans of insect repellent Erica uses and the number of mosquito bites she gets each day.
Can the number of mosquito bites be represented as a function of the amount of repellent used?
Answers
Answer:
Yes, the number of mosquito bites can be represented as a function of the amount of repellent used.
Step-by-step explanation:
Let x represents the number of cans of repellent and y represents the number of mosquitos,
If f be the relation from x to y,
Then by the given table,
f(x) = { (0, 11), (1, 8), (5, 2), (4,5), (2, 9), (3, 6)}
∵ If for each input in a relation has exactly one output, the relation is called a function.
Here, for each value of x there is exactly one value of y,
Hence, f(x) is a relation from x to y,
That is, the number of mosquito bites can be represented as a function of the amount of repellent used.
-
[tex] - \sqrt{5 } - 3 \sqrt{5} [/tex]
Answers
Step-by-step explanation:
[tex]-\sqrt5-3\sqrt5=-1\sqrt5-3\sqrt5=(-1-3)\sqrt5=-4\sqrt5[/tex]
How to use substitution? (With picture) thanks!
Answers
Answer: x = 10 y = 6
Step-by-step explanation:
0.1X + 5 = y
0.2X + 4 = y
0.1X + 5 = 0.2X + 4
-0.1X - 4 = -0.1X - 4
1 = .1X
x = 10
0.1(10) + 5 = y
1 +5 = y
6 = y
Question 7
Answers:
Jane's Uber business has the function f(x) = 0.10x+5
Joe's Uber business has the function f(x) = 0.20x+4
x is the number of miles, f(x) is the total cost for the customer
-------------------------
Explanation:
Jane charges $5 no matter how many miles are driven. This is the base fee. On top of this base fee, an additional price is charged based on the number of miles driven. If Jane drives 1 mile, then an additional 0.10*1 = 0.10 dollars is added on. If 2 miles are driven, then 0.10*2 = 0.20 dollars is added on. And so on.
In general, an additional 0.10*x dollars is added on the base fee to get the total cost to be 5 + 0.10x which rearranges to 0.10x + 5. That's how I ended up with f(x) = 0.10x + 5
Joe's equation will be constructed in a similar way. His base fee is $4 and you add on 0.20x dollars (since it costs $0.20 per mile for Joe's company). Overall, we get f(x) = 0.20x + 4 for Joe's company.
Note how your teacher is not asking you to solve for x or f(x). If you want, you can replace f(x) with y; however, this isn't in function notation.
=============================================================
Question 8
Answers:
Function for Joseph's plan is: f(x) = 0.10x + 20
Function for Micki's plan is: f(x) = 0.15x + 10
The plans cost the same when 200 text messages are sent
-------------------------
Explanation:
We'll set up the equations in a similar way done in problem 7. We start with $20 as the base fee for Joseph's plan and then add on 0.10x dollars because $0.10 is charged per text message. We have x represent the number of text messages. Joseph's function is therefore f(x) = 0.10x + 20. Similarly, Micki's function is f(x) = 0.15x + 10
Let's replace f(x) with y and we have these two equations: y = 0.10x + 20 and y = 0.15x + 10
Now use substitution to solve for x and y
y = 0.10x + 20
0.15x + 10 = 0.10x + 20 ... y replaced with 0.15x+10
0.15x-0.10x = 20-10
0.05x = 10
x = 10/0.05
x = 200
This means that the two plans cost the same when 200 messages are sent.
Note plugging x = 200 into each f(x) function leads to
f(x) = 0.10x + 20
f(200) = 0.10*200 + 20
f(200) = 20 + 20
f(200) = 40 <<--- it costs Joseph $40 to send 200 messages
and
f(x) = 0.15x + 10
f(200) = 0.15*200 + 10
f(200) = 30 + 10
f(200) = 40 <<--- it costs Micki $40 to send 200 messages
The area of two rectangles is given by he functions: area of a rectangle A:f(x)= 4x2+6x area of rectangle B:g(x)=3x2-x Which function represents the difference? A.h(x)=7x2-5x B.h(x)=x2-7x C.h(x)=x2+5x D.h(x)=x2+7x
Answers
Answer:
x^2+7x if you are asked to find the difference of a function f and function g
Step-by-step explanation:
We are asked to A-B or f(x)-g(x).
(4x^2+6x)-(3x^2-x)
4x^2+6x-3x^2+x
The like terms I'm going to pair up.
4x^2-3x^2+6x+x
1x^2 +7x
x^2 +7x
The answer is x^2+7x
Answer:
OPTION D: [tex]h(x)=x^2+7x[/tex]
Step-by-step explanation:
You know that the area of Rectangle A is given by :
[tex]f(x)= 4x^2+6x[/tex]
And the area of Rectangle B is given by:
[tex]g(x)=3x^2-x[/tex]
Therefore, in otder to find the function that represents the difference, you need to subtract the functions f(x) and g(x).
Then, you get this function h(x):
[tex]h(x)=f(x)-g(x)\\\\h(x)= (4x^2+6x)-(3x^2-x)\\\\h(x)=4x^2+6x-3x^2+x\\\\h(x)=x^2+7x[/tex]
what is the slope of the line for y = 1/2x + 2 and what is the y intercept of the line
Answers
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
In this case m is 1/2 and b is 2.
This means that the slope of this line is 1/2 and the y-intercept is (0, 2) or simply 2
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 2 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = 2
evaluate the expression 3x + 21 for x=3
Answers
Answer:
30
Step-by-step explanation:
Problem = 3x + 21 for x=3
3(3) +21 --- subsitute the three for the x
9 + 21 ---- multiply the 3s together
30 ----- add
Jim Smith is a salesman who receives a $1,100 draw per week. He receives a 12% commission on all sales. Sales for Jim were $205,000 for the month. Assuming a four-week month. Jim's commission after the draw is
Answers
Answer:
$29,000
Step-by-step explanation:
Given:
Receivable draw per week= $11,00
Commission on all sales= 12%
Sale for the month= $205,000
weeks in a month= 4
Jim's commission after the draw=?
total draws= 11,00 (4)
= 44,00
Commission on the sale= 205000(0.12)
=24600
Jim's commission after the draw= 4400 +24600
=29,000 !
Jim Smith's commission after the draw is calculated by determining his total commission from sales and then subtracting the draw he receives weekly. For a month where he made $205,000 in sales, his commission after the draw is $20,200.
The subject of this question is Jim Smith's commission after the draw, who works as a salesman and receives a draw of $1,100 per week plus a 12% commission on all sales. Considering that Jim made $205,000 in sales for the month, we would first calculate his total commission by multiplying the sales amount by the commission percentage. Next, we deduct the total draw for the month from the total commission to find Jim's commission after the draw.
To calculate the total commission earned, you would use the formula: Commission = Sales x Commission Rate. Therefore, for a sales amount of $205,000 and a commission rate of 12%, the total commission would be $205,000 x 0.12, which equals $24,600. Since a month is considered to have four weeks, Jim's total draw for the month would be $1,100 x 4, totaling $4,400.
To find out how much commission Jim has after accounting for the draw, we subtract the draw from the total commission: Commission after Draw = Total Commission - Total Draw, or $24,600 - $4,400, which equals $20,200.
briana has earned the following test grades: 82%, 75% and 90%. She wants to maintain an 85% average for her test scores. what must she receive on the final test in order to acieve this goal?
Answers
Answer:
93%
Step-by-step explanation:
Formula for calculating average = sum of data/ total number of data
Step 1: Add all percentages
Let the percentage on the last test be x
82% + 75% + 90% + x = 247% + x
Step 2: Apply the formula
Average = sum of percentages/ total number of tests
85 = 247 + x /4
340 = 247 + x
x = 340 - 247
x = 93%
Therefore, Briana must receive 93% on her final test to maintain an average of 85%.
!!
What is LCM of 30 and 62 using Division Method
Answers
Answer:
930
Step-by-step explanation:
To use the division method
Write the given numbers in a horizontal row separated by commas.
Divide them by a suitable prime number
Place the quotient under the numbers in the next row. If a number is not divided exactly then bring it down to the next row.
Repeat the process until only co prime numbers are left in the last row.
Multiply all the prime numbers used as divisors.
The product is the LCM
Given 30 and 62, then
2 | 30, 62
3 | 15, 31
5 | 5, 31
31 | 1, 31
| 1, 1 ← co primes left
Hence LCM = 2 × 3 × 5 × 31 = 930
-2.5y⁰ for y= -1⅔
find the value of the expression
Answers
Solve the equation for x.
the square root of the quantity x plus 5 end quantity minus 3 equals 4
x = 2
x = 12
x = 44
x = 53
Answers
Answer:
x = 44
Step-by-step explanation:
sqrt(x+5) -3 =4
Add 3 to each side
sqrt(x+5) -3+3 =4+3
sqrt(x+5) =7
Square each side
(sqrt(x+5))^2 =7^2
x+5 = 49
Subtract 5 from each side
x+5-5 = 49-5
x=44
Answer:
x is 44
Step-by-step explanation:
[2 -6] - [-2 4] please help
Answers
The answer is 20. The explanation is shown in the picture.
Answer:
[tex]\Huge \boxed{20}[/tex]
Step-by-step explanation:
This question is about order of operations. It stands for parenthesis, exponent, multiply, divide, add, and subtract from left to right.
First thing you do is parenthesis.
[tex]\displaystyle [2-6]=-4[/tex]
[tex]\displaystyle -4-[-24][/tex]
Then, add and subtract numbers from left to right to find the answer.
[tex]\displaystyle -4-[-24][/tex]
[tex]\displaystyle -4-[-24]=-4+24=20[/tex]
20, which is our answer.
Hope this helps!
Which set of polar coordinates are plotted in the graph below
Answers
Answer:
C. (-2,2π/3)
Step-by-step explanation:
Given:
In the given plane, each line represents angles and the circles shows the radii. Now as full circle is of 360 degrees or 2π and there are 12 straight lines that means
every angle is π/6 apart (30 degrees).
As the given red point is on circle 2, this means the radii, r=2
and Ф=300 degrees or 5π/3
r=(2,5π/3)
but above is not given in the options.
Polar coordinates can have positive or negative theta and also have positive or negative radii. In case of negative radii the polar coordinate moves in opposite direction of the pole.
if we consider r=-2 then we have to move in opposite direction of pole of Ф=300 degrees or 5π/3 is 120 degrees or 2π/3.
hence r=-2 andФ=2π/3
Correct option is C:(-2,2π/3)!
(06.04 MC) Find the area of the following shape.
Answers
Check the picture below.
well, the purple trapezoid, has a height of 5, and its bases are of 5 units and 8 units, recall the bases are the parallel sides in a trapezoid.
now, the yellow rectangle, is a 6x5, and it has those two green triangles in it, well, if we simply get the area of the rectangle, 30 anyway, and subtract the areas of those green triangles, what's leftover, is the rest of the shape on points DEFA.
keeping in mind that the green triangles have a base of 4 and a height of 3 for the one atop and base of 5 and height of 2 for the bottom one.
[tex]\bf \stackrel{\textit{purple trapezoid}}{\cfrac{\stackrel{h}{5}(\stackrel{a}{5}+\stackrel{b}{8})}{2}}~~+~~\left[ \stackrel{\textit{yellow square}}{(6\cdot 5)}-\stackrel{\textit{two green triangles}}{\cfrac{1}{2}(4)(3)-\cfrac{1}{2}(5)(2)} \right] \\\\\\ \cfrac{5(13)}{2}+[30-6-5]\implies \cfrac{65}{2}+[19]\implies \cfrac{103}{2}\implies 51\frac{1}{2}[/tex]
What are the coordinates of the point on the directed line segment from K (-5,-4) to L (5,1) that portions the segment into ratio of 3 to 2
Answers
Answer:
4) (1,-1)
Step-by-step explanation:
Let the points be
[tex](x_1,y_1) = K(-5,-4)\\(x_2,y_2) = L(5,1)\\[/tex]
The formula for finding the coordinates of point that divides the line in a:b is:
[tex]x = \frac{bx_1+ax_2}{a+b} \\y = \frac{by_1+ay_2}{a+b}[/tex]
Here x and y are the coordinates of the point that will partition the line into given ratios
Our ratio is 3 to 2,
So,
a=3
b=2
Putting the values in the formula
[tex]x = \frac{(2)(-5)+(3)(5)}{3+2}\\x = \frac{-10+15}{5}\\x =\frac{5}{5}\\ x =1\\y = \frac{(2)(-4)+(3)(1)}{3+2}\\y = \frac{-8+3}{5}\\y = \frac{-5}{5}\\ y = -1[/tex]
Hence, the correct answer is:
4) (1,-1) ..
The coordinate of the point on the directed line segment is (1, -1). Then the correct option is D.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.
The coordinates of the point on the directed line segment from K (-5,-4) to L (5,1) portions the segment into a ratio of 3: 2.
Let the coordinate of the point be (x,y).
We know that the section formula
[tex]\rm (x,y) = (\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ,\dfrac{m_1y_2+m_2y_1}{m_1+m_2})[/tex]
We have
m₁: m₂ = 3: 2
(x₁, y₁) = (-5, -4)
(x₂, y₂) = (5, 1)
Then we have
[tex]\rm (x, y) = (\dfrac{3*5 + 2*(-5)}{3+2} , \dfrac{3*1 + 2*(-4)}{3+2})\\\\\\(x, y) = (\dfrac{5}{5}, \dfrac{-5}{5})\\\\\\(x, y) = (1,-1)[/tex]
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
can someone please help me with this?
Answers
Answer:
A
Step-by-step explanation:
The table of values is linear so we can express the function as
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, - 4) and (x₂, y₂ ) = (- 3, - 2) ← ordered pairs from the table
m = [tex]\frac{-2+4}{-3+6}[/tex] = [tex]\frac{2}{3}[/tex]
Note the ordered pair (0, 0) ⇒ c = 0
y = [tex]\frac{2}{3}[/tex] x → A
Nikita knows the following information about her food club that has 11 members: 3 members like neither fruit nor vegetables. 4 members like fruit but not vegetables. 5 members in total like fruit. Can you help Nikita organize the results into a two-way frequency table?
Answers
Answer:
3 like vegetables but do not like fruit
Step-by-step explanation:
We have 11 total members
There are 5 members that like fruit
11-5=6
That means there are 6 members that do not like fruit
Of those 6 members ,3 do not like vegetables
6-3 =3
That means we have 3 members who do not like fruit who like vegetables
Answer:
3
Step-by-step explanation:
Explain the steps necessary to convert a quadratic function in standard form to vertex form
Answers
Answer:
Sample Response: A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.
Step-by-step explanation:
trust me
To prove a projectile's trajectory is parabolic, we start with the horizontal motion equation, solve for time, and substitute into the vertical motion equation, ending up with a quadratic equation in the form of y = ax + bx², showing parabolic motion.
Explanation:To prove that the trajectory of a projectile is parabolic, we start with the two separate equations for horizontal and vertical motion. The horizontal motion equation is given by x = Voxt, where Vox is the horizontal velocity component. We solve this for time t to get t = x / Vox. We then substitute this expression for t into the vertical motion equation y = Voyt - 1/2gt2, where Voy is the vertical velocity component and g is the acceleration due to gravity.
Substituting t = x / Vox into the vertical equation, we get y = Voy(x / Vox) - (1/2)g(x / Vox)2. This simplifies to y = (Voy/ Vox)x - (g / 2Vox2)x2, which is of the form y = ax + bx2, proving that the trajectory is parabolic with a and b as constants.
Learn more about Projectile Motion here:https://brainly.com/question/29545516
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1800 doubles in value every 7 years
Answers
Answer: 25200
Step-by-step explanation:
I hope that this is helpful, I'm bad at explaining answers so i wont. XD