Consider the given equation [tex]x^2-8x+14=0[/tex]
We will solve this equation by completing the square method.
Consider the coefficient of 'x', divide it by '2'. then adding and subtracting the square of this number in the given equation.
Coefficient of 'x' = -8
By dividing it by '2', we get -4
Taking the square of '-4' = 16
Adding and subtracting '16' from the given equation.
[tex]x^2-8x+14+16-16=0[/tex]
So, [tex]x^2-8x+16 = -14+16[/tex]
This equation shows one of the step used in solving the equation by completing the square method.
Therefore, option 1 is the correct answer.
For Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]
Jamal was given the equation, [tex]x^2 - 8x + 14 = 0[/tex], to solve by completing the square.
To do this, the first step would be to move the constant, 14 to the other side of the equation by subtracting 14 from both sides of the equation.
Thus:
[tex]x^2 - 8x + 14 - 14 = 0 -14\\\\x^2 - 8x = -14[/tex]
The next step to take is for Jamal to add the square of half of the coefficient of x to both sides of the equation.
Coefficient of 8x = 8Half of the coefficient of 8 is 4Square of 4 = 16Add 16 to both sides of the equation[tex]x^2 - 8x + 16 = - 14 + 16[/tex] (this tallies with the first option given).
Therefore, for Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]
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Use the substitution method to solve the system of equations. 3x + 7y = 1 y = x – 7
A. (3, –4)
B. (4, –3)
C. (2, –5)
D. (5, –2)
Answer:
{x,y} = {12,5}
Step-by-step explanation:
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3x-7y=1;-x+y=-7
Solution :
{x,y} = {12,5}
System of Linear Equations entered :
[1] 3x - 7y = 1
[2] -x + y = -7
Graphic Representation of the Equations :
-7y + 3x = 1 y - x = -7
Solve by Substitution :
// Solve equation [2] for the variable y
[2] y = x - 7
// Plug this in for variable y in equation [1]
[1] 3x - 7•(x -7) = 1
[1] -4x = -48
// Solve equation [1] for the variable x
[1] 4x = 48
[1] x = 12
// By now we know this much :
x = 12
y = x-7
// Use the x value to solve for y
y = (12)-7 = 5
Solution :
{x,y} = {12,5}
A parts distributor's customers always order spark plugs in groups of 4, 6, or 8. Which is the smallest quantity the supplier has that could accommodate every order?
Answer:
24 spark plugs
Step-by-step explanation:
To find smallest quantity that could accommodate every order we will find LCM of 4,6 and 8.
Multiples of 4 are: 4,8,12,16,20, 24,28,..
Multiples of 6 are: 6,12,18,24,30,36,42,..
Multiples of 8 are: 8,16,24,32,40,..
We can see that LCM of 4, 6 and 8 is 24. Therefore, order of 24 spark plugs will accommodate every order.
Identify the terms in the expression 55a + 22b
55a and 22b both are terms in that equation
Complete the square to transform the quadratic equation into the equation form (x – p)2 = q. x2 + 14x + 34 = 5
(x + 7)² = 20
subtract 34 from both sides
x² + 14x = - 29
add (half the coefficient of the x- term )² to both sides
x² + 2(7)x + 49 = - 29 + 49
(x + 7)² = 20
True or false? The circumcenter of a triangle is the center of the only circle that can be circumscribed about it
Answer:
The statement is true.
Step-by-step explanation:
Given the statement we have to tell the statement is true or false.
The statement is
"The circumcenter of a triangle is the center of the only circle that can be circumscribed about it"
The circumcenter of triangle is the point in the triangle where the perpendicular bisectors of sides intersect.
The center of the circumscribed circle is the the point where the perpendicular bisectors of the sides meet.
Hence,
The circumcenter is also center of the triangle's circumcircle - the circle that pass through all three of the triangle's vertices.
Therefore, the given statement is true.
Answer:
True
Step-by-step explanation:
Circumcircle: A circle drawn outside a circle is called circumcircle and its center is called circum-center.
Circum-center of triangle:It is the point where the perpendicular bisectors of a triangle intersect.
The circumcenter of triangle is also the center of triangle's circumcircle.
The circumcenter is equidistant from each vertex of the triangle.
The circumcenter of right triangle falls on the side opposite the right triangle.
Hence, the circumcenter of a triangle is the center of the only circle that can be circumscribed about it.
Answer :True
A triangle has side lengths of 8 inches,12 inches,and 16 inches. Determine whether this is a right triangle and why.
Answer:
the answer is no
Step-by-step explanation:
8²+12²≠16²
Which of the following are ordered pairs for the equation y = -4x + 5?
(0,5) (1,1) (-1,9)
(0,5) (-1,-1) (-1,-9)
(0,5) (1,-1) (-1,9)
(0,5) (-1,1) (-1,-9)
(0, 5), (1, 1 ), ( - 1, 9 )
to test the points substitute the x-coordinate into the equation and if the value is equal to the y- coordinate then it is an ordered pair
(0, 5 ) → y = 0 + 5 = 5 ← ordered pair
(1, 1 ) → y = - 4 + 5 = 1 ← ordered pair
(- 1, 9 ) → y = 4 + 5 = 9 ← ordered pair
( - 1, - 1 ) → y = 4 + 5 = 9 ← not an ordered pair
( - 1, - 9 ) → y = 4 + 5 = 9 ← not an ordered pair
(1, - 1 ) → y = - 4 + 5 = 1 ← not an ordered pair
(- 1, 1 ) → y = 4 + 5 = 9 ← not an ordered pair
What is the area of the shaded region in the diagram? Use the value `pi` = 3.14, and round your answer to two decimal places.
Answer:
Can you attach a picture of the diagram?
Step-by-step explanation:
Answer:
9.42 Square Units
How:
You need to use the sector area formula.
Sector Area = Measure of Arc / 360° × π r²
So then you just plug in the numbers:
Sector Area = 45° / 360° × π 5²
Sector Area = 1/8 × 25π
Sector Area = 9.817477
Sector Area = 45° / 360° × π 7²
Sector Area = 1/8 × 49π
Sector Area = 19.242255
Then all you have to do is subtract them both to find the area.
19.242255 - 9.817477 = 9.42 Square Units
I Hope this helped!
if 1-f=9/10 what is f
Hello there!
[tex]1-f=\frac{9}{10}[/tex]
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓
First you had to subtract by 1 from both sides of the equation.
[tex]1-f-1=\frac{9}{10}-1[/tex]
Simplify
[tex]-f=-\frac{1}{10}[/tex]
Then you divide by -1 from both sides of the equation.
[tex]\frac{-f}{-1}=-\frac{1}{10}/-1[/tex]
Simplify it should the correct answer.
[tex]f=\frac{1}{10}[/tex]
Answer⇒⇒⇒f=1/10
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
A car travels 65km in 45minutes. What is the average speed of the car in km/h
65X60/45=260/3km/hr=86.66km/hr
What is bigger 400 pints or 100 gallons
Which three statements would produce the truth value F when p is true and q is false
p^q , p-> q and ~p ^ q . all these three statements will give false when p is true and q is false
The graph models the function f(x) = 2(1/2)x. What is the domain and range of the function?
A-Domain: x < 0; Range: y > 0
B-Domain: x > 0; Range: all real numbers
C-Domain: all real numbers; Range: y > 0
D-Domain: all real numbers; Range: y ≥ 0
Please explain with the answer !!
Hello!
Given the function, [tex]f(x) = 2(\frac{1}{2})^{x}[/tex], notice that the function f(x) is an exponential function.
All exponential functions have a horizontal asymptote at y = 0, and this means that the graph never goes over the line y = 0. Therefore, the range is less than zero, but never equal to zero.
Also, this means that the domain of the function f(x) is all real numbers because as we substitute positive x-values into the function, the graph goes closer to zero, but never across zero. But, if we substitute negative x-values into the equation, it goes to infinity.
Therefore, the answer is choice C. The domain of f(x) is all real numbers, and the range is y > 0.
We want to find the domain and range of the given equation.
We will see that the correct option is C:
Domain: all real numbers;
Range: y > 0
First, we need to define what these are.
For a given function y = f(x), the domain is the set of all the possible x-values we can input on the function, and the range is the set of the possible outcomes.
We have the exponential equation:
f(x) = 2*(1/2)^x
To get the domain we start by assuming that the domain is the set of all real numbers, and then we see if the equation has a problem for a given value of x, then we remove that from the domain.
But here we have x on the exponent, so there are no value of x that causes problems, thus the domain is the set of all real numbers.
To get the range we can look at the graph, we can see that the range goes from near 0 to infinity, so we can say that:
range = y > 0.
(note that the function tends asymptotically to zero, meaning that it never becomes equal to zero).
Then the correct option is C:
Domain: all real numbers;
Range: y > 0
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Express the number in scientific notation.
0.00341 x 104
A) 3.41 x 10-3
B) 3.41 x 10-1
C) 3.41 x 101
D) 3.41 x 104
Answer:
It's 3.14x10^1
Step-by-step explanation:
A company sells lab equipment. The daily revenue and costs are modeled by the functions below where x is the number of units sold.
Pleeeeaaasssseeeee help! <3 I'm just trying to graduate.thanks.
Subtract the cost from the revenue:
(-0.32x^2+270x) - (70x+52)
270x - 70x = 200x
The answer would be -0.32x^2 + 200x + - 52
Answer:
P(x) = -0.32x² + 200x + (-52)
Step-by-step explanation:
A company sells lab equipment. Daily revenue and costs are modeled by the function as given in the question.
Revenue: R(x) = -0.32x² + 270x
Cost : C(x) = 70x + 52
Here x = Number of units sold.
Now we have to determine the function P(x) for daily profit.
Since Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = (-0.32x² + 270x) - (70x + 52)
= -0.32x² + 270x - 70x - 52
P(x) = -0.32x² + 200x - 52
Therefore, answer will be P(x) = -0.32x² + 200x + (-52)
What is the volume of a cube with edge 5cm
4x + 8 = 2x + 7 + 2x - 20.
PLEASE SHOW WORK!!!
How to get answer:
[tex]\mathrm{Group\:like\:terms}\\4x+8=2x+2x+7-20\\\mathrm{Add\:similar\:elements:}\:2x+2x=4x\\4x+8=4x+7-20\\\mathrm{Add/Subtract\:the\:numbers:}\:7-20=-13\\4x+8=4x-13\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\4x+8-8=4x-13-8\\\mathrm{Simplify}\\4x=4x-21\\\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\4x-4x=4x-21-4x\\Simplify\\0=-21\\The\:sides\:are\:not\:equal\\[/tex]
Steps:
4x + 8 = 2x + 7 + 2x - 20
Group like terms:
4x + 8 = 2x + 2x + 7 - 20
Add similar elements: 2x + 2x = 4x
4x + 8 =4x + 7 - 20
Add/Subtract the numbers: 7 - 20 = -13
4x + 8 = 4x - 13
Subtract 8 from both sides
4x + 8 - 8 = 4x - 13 - 8
Simplify:
4x = 4x - 21
Subtract 4x from both sides:
4x - 4x = 4x - 21 - 4x
Simplify
0 = -21
Hope this helps! :) and Happy Halloween! ~Zane
Math, Not sure how to do this one help me out please?
You need to know the 30-60-90 triangles rules for lengths. (b, b√3, 2b)
the given side length of corresponds to the 30° angle. So, b = 8
side y corresponds to the 60° angle so it is b√3. Since we determined that b = 8, then b√3 is 8√3.
side x corresponds to the 90° angle so it is 2b. Since we determined that b = 8, then 2b = 2(8) = 16
Answer: x = 16, y = 8√3
The skeeters baseball team charges $7. Per ticket plus $3. Processing fee for each order. Is the cost of an order proportional to the number of tickets ordered? Explain how you know.
I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current rate is $129.00 per month." Representative: "We will match any competitive offer. Your adjusted rate will be __________ dollars per month." Read more: I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current rate is $129.00 per ... - I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current rate is $129.00 per month." Representative: "We will match any competitive offer. Your adjusted rate will be __________ dollars per month."
Given my current rate = $129.00 per month.
Savings of 15% over your prices.
Therefore, saving = 15% of $129.00 = 0.15 × 129.00 =$19.35.
Adjusted rate = current rate - saving = 129 - 19.35 = $109.65
Therefore, We can rewrite above expression as :
My current rate is $129.00 per month." Representative: "We will match any competitive offer. Your adjusted rate will be 109.65 dollars per month."
If my current rate is $129.00 per month. Your adjusted rate will be $109.65 dollars per month.
Adjusted rateUsing this formula
Adjusted rate = Current rate - Adjustment
Where:
Current rate=$129
Adjustment=(15%×$129)
Let plug in the formula
Adjusted rate=$129-(15%×$129)
Adjusted rate = $129 - $19.35
Adjusted rate =$109.65 per month
Inconclusion your adjusted rate will be $109.65 dollars per month.
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What is the volume of a box that holds 24 1/2 inch cubes
plzzz help - i will mark brainest
1.-Write the recursive rule of the sequence 9, 3, 3, 9,... −− .
________________________________________
2.-A line has an x-intercept of (4, 0) and a y-intercept of (0, 12). Find the slope of the line.
________________________________________
3.-A horizontal line includes the points (0, -5 ) and ( 2, -5 ) Find the slope of the line.
Answer:
1. You divide by 3 then multiply by 1 and multiply by 3 again
2. Slope of -3
3. Slope of 0
Step-by-step explanation:
Geometry help , only answer if your sure please. The question is in the attached
<7 = 62° ----alternate exterior angle
Answer is C) < 7
The cost of a tyre has increased by 20% to £78. Work out the original price. Please reply ASAP, thank you.
find the value of x for which l is parrell to m
What is the answer to 99.55 divided by 1.1 worked out???
Answer:
90.5
Step-by-step explanation:
0 9 0. 5 0 0
1 1 9 9 5. 5 0 0
− 0
9 9
− 9 9
0 5
− 0
5 5
− 5 5
0 0
− 0
0 0
− 0
0
Question 4 Unsaved
Henry places x marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression shown.
3x + 8
What does the term 8 represent in this expression?
Question 4 options:
the weight of each marble
the weight of the empty bucket
the number of marbles
the total weight of the bucket and marbles
Here in the given equation, 3x + 8 the term 8 represents the weight of the empty bucket.
Its given that the number of marbles is x, and the weight of each marble is same which is 3. So, total weight of marbles is 3x.
Now, if 3x + 8 is the weight of the bucket and marbles, then 8 represents the weight of the empty bucket.
Parabolas A and B both have a focus at (2, 2). Parabola A has a directrix at x = -1 and parabola B has a directrix at x = 5. What is the distance between the vertices of the two parabolas?
A. 1.5
B. 3
C. 4
D. 5
E. 6
Parabola A: directrix is at x = -1 and focus is at (2,2) so the vertex is the midpoint between those. Vertex = (0.5, 2)
Parabola B: directrix is at x = 5 and focus is at (2,2) so the vertex is the midpoint between those. Vertex = (3.5, 2)
Distance between Vertex A and Vertex B is the distance between (0.5, 2) and (3.5, 2) = 3
Answer: B
Joseph owes his older brother $15, so he has a balance of -$15 with his brother . Joseph borrows more money from his brother ,bringing his balance to 5 times of the previous amount what is Joseph's new balance with his brother
Final answer:
Joseph's new balance, after borrowing more money which equals 5 times his initial debt of $15, is -$75.
Explanation:
Joseph initially owes his older brother $15, which can be represented as a balance of -$15. If Joseph's new balance is 5 times the previous amount, we would perform the following calculation:
Previous balance x 5 = New balance
So we would multiply -$15 by 5:
-$15 x 5 = -$75
Therefore, Joseph's new balance with his brother is -$75.
what is the slope for (3,−1) and (4,7)
The values of the slope and y-intercept are m=8 and b=−25
m=8
b=−25
To find the slope you would use the slope formula since you have two point coordinates. The slope formula is:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where y2 and y1 are the y coordinates of the two points and x2 and x1 are the x coordinates of the two points.
Substitute in 7 and -1 for y2 and y1; substitute in 4 and 3 for x2 and x1. Now your expression should look like:
[tex]\frac{7-(-1)}{4-3}[/tex]
Subtract -1 from 7, which is basically the same as 7 + 1. Then subtract 3 from 4. Once you complete these steps you can rewrite your fraction.
[tex]\frac{7+1}{4-3} =\frac{8}{1} =8[/tex]
The final answer is 8 after substituting the appropriate coordinates into the slope formula. This means that the slope of the line passing through the points (3, -1) and (4, 7) is 8.
The answer is: the slope of the line is 8.