Step-by-step explanation:
[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]
Factor by grouping,
[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]
Complete the square, with the x variables,
[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]
Factor out 25 for the y variables
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]
Complete the square
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]
Simplify the perfect square trinomial
[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]
Make the right side be 1 so divide everything by 25.
[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]
Here our center is (7,2).
Mr Holmes paid a fixed charge of $125 plus $55 for each kwh of electricity used. how much did he pay for using 75 kwh if electricity?
The table shows the outputs, y, for different inputs, x: Input (x) 2 5 9 12 Output (y) 20 15 12 8 Part A: Do the data in this table represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points) (10 points)
The table is a function and the relation f(x) = 5x + 14 has a greater value when x = 9
Is the table a function?The table of values is given as:
Input (x) 2 5 9 12
Output (y) 20 15 12 8
In the above table of values, each x value have a unique y value.
This means that the table is a one-to-one relation
A one-to-one relation is a function
Hence, the table is a function.
The greater relation at x = 9The function is given as:
f(x) = 5x + 14
This gives
f(9) = 5 * 9 + 14
Evaluate
f(9) = 59
From the table, we have:
y = 12 when x = 9
Hence, the relation f(x) = 5x + 14 has a greater value when x = 9
The value of x if f(x) = 64We have
f(x) = 5x + 14
This gives
5x + 14 = 64
Subtract 14 from both sides
5x = 50
Divide by 5
x = 10
Hence, the value of x when f(x) = 64 is 10
Read more about functions and relations at:
https://brainly.com/question/6904750
#SPJ1
Solve the equation.
7h-5(3h-8)= -72
7h-15h+40=-72
40+72=15h-7h
112=8h
h=14
Quick I need an answer to this Queston:
The functions f(x)= −3/4x + 2 1/4 and g(x)= (1/2)x + 1 are shown in the graph.
What are the solutions to −3/4x + 2 1/4 = (1/2)x + 1?
Select each correct answer.
−1
0
1
2
3
Step-by-step explanation:
[tex] - \frac{3}{4} x + 2 \frac{1}{4 } = \frac{1}{2} x + 1[/tex]
[tex] - \frac{3}{4} x + \frac{9}{4} = \frac{1}{2} x + \frac{2}{2} [/tex]
[tex] \frac{ - 3x + 9}{4} = \frac{2x + 4}{4} [/tex]
[tex] - 3x + 9 = 2x + 4[/tex]
[tex] - 3x - 2x = 4 - 9[/tex]
[tex] - 5x = - 5[/tex]
[tex]x = \frac{ - 5}{ - 5} [/tex]
[tex]x = 1[/tex]
The answer is C.
write an equation for the line that passes through the given point and has the given slope m (4,-5);m= -1/4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -1/4x - 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -1/4, Point through = (4, -5)}[/tex]
Find: [tex]\textsf{Equation for the line that passes through the given point}[/tex]
Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-5) = -1/4(x - 4)}[/tex]Simplify and solve for y
[tex]\textsf{y + 5 = -1/4(x - 4)}[/tex][tex]\textsf{y + 5 = -1/4x + 1}[/tex][tex]\textsf{y + 5 - 5 = -1/4x + 1 - 5}[/tex][tex]\textsf{y = -1/4x - 4}[/tex]Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.
A bookshelf has 96 books. 64 of the books are fiction and the rest are non-fiction. (a) What fraction of the books are fiction? Give your answer in its simplest form. (b) What fraction of the books are non-fiction?
(a) The fraction of books that are fiction is 2/3.
(b) The fraction of books that are non-fiction is 1/3.
To find the fraction of fiction and non-fiction books on a bookshelf:
Given: A bookshelf has 96 books. 64 of the books are fiction and the rest are non-fiction books. (a)Fraction of fiction books =?
(b)Fraction of non-fiction books =?
Now,
As given, we have,
The total number of books on a bookshelf = 96
Out of 96, the total number of fiction books = 64
So,
The remaining number of books = non-fiction books = 96-64 = 32
(a) Fraction of fiction books = fiction books/total books
= 64/96
On simplification,
= 2/3
(b) Fraction of non-fiction books = non-fiction books/total books
= 32/96
= 1/3
Therefore, the fraction of fiction and non-fiction books is 2/3 and 1/3 respectively.
To learn more about fractions, refer:
https://brainly.com/question/78672?utm_source=android&utm_medium=share&utm_campaign=question
#SPJ2
NEED HELP ASAP 1 HOUR LEFT
The number of units that will maximize revenue will be 672 units.
How to calculate the revenue?From the given information, p = 336 - 0.5x. The revenue function will be:
= (336 - 0.5x)x
= 336x - 0.5x²
This will be equated to 0. This will be:
336x - 0.5x² = 0
0.5x² = 336x
0.5x = 336
x = 336/0.5
x = 672
Learn more about revenue on:
brainly.com/question/16232387
#SPJ1
Need help finding the one complete period of a non transformed contangent function
One complete period of a non-transformed cotangent function is π.
The period of the function is defined as the interval after which the function value repeats itself.
For example, f(T+x)=f(x)
where T is the period of the function.
Here given that there is a non-transformed function cotangent function.
We have to find the period of the function in which interval the value of the function will repeat.
So for the function y=f(x)=cot x
the period of the function is π. means after π the value of the cotangent repeats.
cot(π+x)=cot x
Then one cycle of the cotangent graph lies between 0 and π.
Therefore One complete period of a non-transformed cotangent function is π.
Learn more about period of the function
here: https://brainly.com/question/3511043
#SPJ10
Find the remainder when f(X)=2x^3+2x^2-3x-3 is divided by X-2
The remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.
We know that the remainder theorem states that if a polynomial p(x) is divided by a linear polynomial q(x) whose zero is x = a, then the remainder is given by r = p(a).
Here p(x) = f(x) = 2x³ + 2x² - 3x - 3 and q(x) = x - 2. First, we have to find the zero of q(x).
Now, q(x) = 0
i.e. x - 2 = 0
i.e. x = 2.
So, the zero of q(x) is 2, i.e. a = 2.
Then by the remainder theorem,
r = p(a) = f(2) = 2(2)³ + 2(2)² - 3(2) - 3 = 2 × 8 + 2 × 4 - 6 - 3 = 16 + 8 - 9 = 16 - 1 = 15
We can conclude that the remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.
Know more about the remainder theorem here -
https://brainly.com/question/11456067
#SPJ10
Find the range of the function f(x) = 3x² - 2x for the domain (1, 2, 3).
Answer:
Step-by-step explanation:
f(x)=23x−1 and g(x)=−4x+6.
What transformation occurs from function f to function g?
a horizontal stretch by a factor of −6
a horizontal translation 6 units left
a vertical translation 6 units down
a horizontal compression by a factor of −6
The transformation occurs from function g is a vertical translation 6 units down.
What is Transformation?A function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f : X → X.
Given:
g(x) = 4x + 6
g(x) = 0
4x + 6=0
x= -6/4
Now,
f(-6/4) = 2 - 1
=-1
By seeing g(x), we can say that function g is a vertical translation 6 units down.
Learn more about transformation here:
https://brainly.in/question/29403318
#SPJ1
Ariana scored 89% out of 600 in Exam what could be the marks she had scored?
Answer:
534
Step-by-step explanation:
The solution is in the image
What are the zeros of the function f(x) = x4 − x2 − 2?
±3, ±i
±2, ±i
positive or negative square root of 2 comma ±i
positive or negative square root 3, ±i
Answer:
x = ± [tex]\sqrt{2}[/tex] , x = ± i
Step-by-step explanation:
f(x) = [tex]x^{4}[/tex] - x² - 2
to find the zeros , equate f(x) to zero , that is
[tex]x^{4}[/tex] - x² - 2 = 0
using the substitution u = x² , then
u² - u - 2 = 0 ← in standard form
(u - 2)(u + 1) = 0 ← in factored form
equate each factor to zero and solve for u
u - 2 = 0 ⇒ u = 2
u + 1 = 0 ⇒ u = - 1
convert u back into terms of x
x² = 2 ( take square root of both sides )
x = ± [tex]\sqrt{2}[/tex]
x² = - 1 ( take square root of both sides )
x = ± [tex]\sqrt{-1}[/tex] = ± i
Answer: Positive or negative square root of 2, ±i
Proof o fvalidity is shown below.
If a = 2√3, then the exact value of b is...
Answer:
b = 2
Step-by-step explanation:
using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{a}[/tex] = [tex]\frac{b}{2\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
b × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
b = 2
Answer:
C. b = 2Step-by-step explanation:Given that a = 2√3.
Let's find value of b...
[tex]\bf \tan( {30}^{o} ) = \cfrac{b}{a} [/tex][tex] \bf \cfrac{1}{ \sqrt{3} } = \cfrac{b}{2 \sqrt{3} } [/tex][tex]\bf b = 2[/tex]______________________help please I need alot of help
Answer:
HI i no answer of this quetion but what grade are in school
A mapping diagram showing a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 9), (2, negative 6), (negative 5, 4), (1, 2), (6, 0).
What is the domain of the function shown in the mapping?
Answer:
{-3, 2, -5, 1, 6}
Step-by-step explanation:
The domain is the set of input values.
A sign on a roadway at the top of a mountain indicates that for the next 4 miles, the grade is 10.5°. Find the change in elevation over that distance for a car descending the mountain. Round to the nearest hundredth.
the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).
How to find the change in elevation?
To do this, we can think on the situation as a right triangle, where the hypotenuse is 4 miles, the angle that we look at measures 10.5°, and the change in elevation (let's call it x) will be the opposite cathetus to that angle.
Then we can use the relation:
Sin(a) = (opposite cathetus)/(hypotenuse)
Replacing what we know, we get:
sin(10.5°) = x/4mi
x = sin(10.5°)*4mi = 0.73mi
So the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).
If you want to learn more about right triangles:
https://brainly.com/question/2217700
#SPJ1
help please fast grade 5 math help extra points to thooese who explain marking brainliest
11. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x}^2\textsf{ - 14x + 24}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{x = 12 and x = 2}[/tex]
Find: [tex]\textsf{Determine the quadratic equation}[/tex]
Solution: In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.
Move the integers
Solution #1[tex]\textsf{x - 12 = 12 - 12}[/tex][tex]\textsf{x - 12 = 0}[/tex]Solution #2[tex]\textsf{x - 2 = 2 - 2}[/tex][tex]\textsf{x - 2 = 0}[/tex]Create and expression and distribute
[tex]\textsf{(x - 12)(x - 2) = 0}[/tex][tex]\textsf{(x * x) + (x * -2) + (-12 * x) + (-12 * -2) = 0}[/tex][tex]\textsf{x}^2\textsf{ - 2x - 12x + 24 = 0}[/tex][tex]\textsf{x}^2\textsf{ - 14x + 24 = 0}[/tex]Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.
Brian is drawing a scale diagram of a building. for every 10 m of the building he draws a line 5 cm long. Bryn thinks he is using a ratio of 2:1. Alun thinks Bryn is using a ratio of 200:1, is either of them correct? explain your answer
Answer:
200:1, Bryn is correct.
Step-by-step explanation:
Each 10 m is represented by a 5cm length on the diagram. We first note that 100 cm = 1 meter. 5 cm is (0.5 cm)*(1 meter/100 cm) =0.05 meters.
The 0.05 meters on the diagram represents 10 meters on the actual building. The ratio is (10 meters/0.05 meters) or 200:1. This is what Bryn believes is the ratio.
A square with side lengths 12 feet. 4 2 feet by 2 feet squares are cut out of each corner of the square.
Tariq designed the pool shown. The owner of the pool has one square cover to use. Find the area of the space that needs to be covered. (The four corners are squares.)
The area that needs to be covered is
ft2.
A square with side lengths 12 feet. 4 2 feet by 2 feet squares are cut out of each corner of the square.
Find the Area of the Space.[tex] \mathbb{SOLUTION:} [/tex][tex] \bold{A = Length \: x \: Width} [/tex][tex] \bold{A = 12 \: ft \: x \: 4.2 \: ft } [/tex][tex] \blue{\bold{A = 50.4 \: ft} }[/tex][tex] \bold{ A\red{ = 50.4 } \: x \: 2 \: ft} [/tex][tex] \boxed{ \bold{ A = 100.80 ft²}}[/tex]"If the 2 is quantity use multiply it again"
••••••••••••••••••••••••••••••••••••••••••••••••NOTE:The way to solve a square area is by measuring the length and width of your area then multiplying those two numbers together to get the area in feet squared (ft2).
"Problem has been solve"
(ノ^_^)ノ
[tex]\large\bold{SOLUTION} \\ [/tex]
GIVEN :-
A square with side lengths 12 feet.4.2 feet by 2 feet squares are cut out of each corner of the square .FIND :-
Find the area of the space that needs to be covered .By finding the area of the space that needs to be covered we must use multiplication and multiply the given measurements .
[tex] \bold{Formula:}[/tex]
[tex] \qquad \boxed{ \bold{ \: \: Area = Length \times Width \: \: }}[/tex]
Now let's start solving :-
[tex] \quad \sf \implies{Area = Length \times Width} \\ [/tex]
[tex] \quad \sf \implies{Area = 12ft \times 4.2ft} \\ [/tex]
[tex] \quad \sf \implies{Area = 12feet \times 4.2ft = \pmb{50.4 ft}} \\ [/tex]
[tex] \quad \sf \implies{Area = 50.4ft \times 2ft = \pmb{100.80ft^2}} \\ [/tex]
Therefore, the area of the space that needs to be covered is 100.80ft² .
[tex] \underline{ \rule{185pt}{3pt}}[/tex]
Please help!!!!!
The equation of a circle is x² + y² – 8x + 10y + 37 = 0. What is the center and the radius of the circle? Show all your work.
Let's take this problem step-by-step:
Let's convert the equation back into the standard form:
⇒ standard form: (x-h)² +(y-k)² = r²
(h, k): center's coordinater: radius[tex]x^2+y^2-8x+10y + 37 = 0\\\rm \hookrightarrow x^2 - 8x + y^2+10y = -37\\\rm \hookrightarrow (x^2 - 8x) + (y^2 + 10y) = -37\\\rm \hookrightarrow (x^2-8x+16) + (y^2+10y+25) = -37 + 16 +25\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 4\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 2^2[/tex]
Based on the equation found
⇒ center: (4, -5)
⇒ radius: 2
Answer:
center: (4, -5)radius: 2Hope that helps!
#LearnwithBrainly
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
Hey there : y= 3x - 3
Answer:
y = [tex]\frac{3}{2}[/tex] x + 3
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-2)}[/tex] = [tex]\frac{3}{0+2}[/tex] = [tex]\frac{3}{2}[/tex]
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line
How to subtract negative number from 1
when you subtract a negative number from any platitude number the equation changes to addition so you would add the value of the negative number to 1.
To subtract a negative number from one you will need to set it up like this
1- (-x) x equals the negative number you're talking about
so we use the method KCC (keep change change)
So we KEEP the positive one, CHANGE the subtraction sign in to a plus sign "+" then CHANGE the negative number to a positive
lets say the negative number is 2
1-(-2)
1+ (+2)
1+2 = 3
please answer me I will f0ll0w u
Step-by-step explanation:
1. let n=2, then, n+2= 2+2=4 so 2^2= 4 and 4^2=16 then 16-4=12 which is an even number
2. let n=4, the. n+3=4+3=7, and 4^2=16 and 7^2=49 then 49-16 =33 which is an odd number
please follow me
What is the equation if the blue line?
Answer:15
Step-by-step explanation:
Start off using Java. As u progress you cant move over to C and the then transfer to python.
If u get 2 points every 5 minutes, how long will it take to get 3,600 points?
Answer:
9,000 minutes (150 hours)
Step-by-step explanation:
You have 3,600 points total; you need to divide it by 2 points.
3,600 ÷ 2 = 1,800
So, now you need to multiply the 1,800 points by 5 minutes.
1,800 × 5 = 9,000
Another way:
You can figure out how long it takes to get 1 point. If 2 points takes 5 minutes, divide 5 by 2.
5 ÷ 2 = 2.5
Now you need to figure out how long it would take to get 3,600 points. If each point takes 2.5 minutes, just multiply.
3,600 × 2.5 = 9,000
It would take 9,000 minutes (which is equivalent to 150 hours) to get to 3,600 points.
The side of an equilateral triangle is given as 8 cm, correct to the nearest centimetre. What is the least possible length of its perimeter?
[tex]\textsf {21 cm}[/tex]
[tex]\textsf {If it is correct to the nearest centimeter, then the least side length}\\\textsf {would be 8 - 1 = 7 cm. }[/tex]
[tex]\textsf {Then, the least possible perimeter would be :}[/tex]
[tex]\mathsf {7 \times 3}[/tex]
[tex]\textsf {21 cm}[/tex]
HI PLEASE ANSWER THIS QUESTION THANK YOU SO MUCH!
Mr. Avanzado has an underground in his house. What unit ofmeasure will he use to find its volume?
A. mm3
B. cm3
C. dm3
D. m3
2.What is the best unit of measure to use in finding the volumeof a rectangular pencil case?
A. mm3
B. cm3
C. dm3
D. m3
3.What is the formula to be used in finding the volume of a cube?
A. V = s x s or s2
B. V = s x s x s or s3
C. V = l x w x h
D. V = s + s + s
(NO TROLLS PLEASE)
1. m³
2. cm³
3. s³
What is Unit?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
1. Volume is measure in m³
2. volume of a rectangular pencil case in cm³
3. V = s x s x s or s³
Learn more about volume here:
https://brainly.com/question/1324203
#SPJ1
Someone help me as fast as possible!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: length = 11 \: \: in[/tex]
[tex]\qquad \tt \rightarrow \: width = 4 \: \: in[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let the measures be :
width = xlength = x + 7[tex] \textsf{\large Area of rectangle :} [/tex]
[tex]\qquad \tt \rightarrow \: Area = length \sdot width [/tex]
[tex]\qquad \tt \rightarrow \: 44 = x \sdot(x + 7)[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x = 44[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 44 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 11x - 4x - 44 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x(x + 11) - 4(x + 11) = 0[/tex]
[tex]\qquad \tt \rightarrow \: (x + 11)(x - 4) = 0[/tex]
possible values of x = -11 and 4
[tex] \textsf{But the acceptable value of x = 4} [/tex]
[ length or width of rectangle can't be negative ]
[tex]\qquad \tt \rightarrow \: length = x + 7 = 4 + 7 = 11 \: \: in[/tex]
[tex]\qquad \tt \rightarrow \: width = x = 4 \: \: in[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
