Answer:
x=9 and x=-2
Step-by-step explanation:
GFC = 9 => 9(x²-6x-16) =0
9(x-8)(x+2) = 0
x-b=0 x+2= 0
x=8 and x = -2
Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.
What is the quadratic equation for the net income of the company?It is given by:
f(x) = 9x² - 54x - 144.
It can be simplified as follows:
f(x) = 9(x² - 6x - 16)
Then:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, hence:
x + 2 = 0 -> x = -2.x - 8 = 0 -> x = 8.The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.
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asap
pls explain this question about a theater math
A theater can hold 160 giants or 240 elves. If 100 giants are inside, how many elves can also be admitted ?
The answer is 90 elves.
Here's how to find it
100 giants = 100/160 or 5/8
3/8 is left for the elves
3/8 x 240 = 90
PLEASE HELP! What's the value of X?
Answer:
25
Step-by-step explanation:
Pythagorean theorem :
a² + b² = c²
Substitute the values:
24² + 7² = x² (c = x)
576 + 49 = x²
625 = x²
x = √625
x = 25
Solve the system of linear equations by graphing. y = –5/2x – 7 x + 2y = 4 What is the solution to the system of linear equations? A. (–4.5, 4.25) B. (–1.7, –2.8) C. (0, –7) D. (3, 0.5)
ANSWER
(–4.5, 4.25)
EXPLANATION
The first equation is
[tex]y = - \frac{5}{2}x - 7[/tex]
This function is in the slope-intercept form
The second equation is:
x + 2y = 4
2y =-x+ 4
[tex]y = - \frac{1}{2}x + 2[/tex]
The graph of the two functions are shown in the attachment.
The point of intersection represents the solution to the system of equations they represent.
The solution is
(–4.5, 4.25)
Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. Kelly ran at an average speed of 8 miles per hour.
When will Ava and Kelly be 3/4 mile apart?
this is a challenge. please solve.
Answer:
The answer is 22.5
Step-by-step explanation:
The person who answered above me said it was 0.375, but that was in hours. 0.375 hours in min = 22.5.
The person who answered above me is not wrong, it is just that it was in hours.
Welcome! :)
Ava and Kelly will be 3/4 mile apart after 22.5 minutes of running at their respective speeds of 6 mph for Ava and 8 mph for Kelly.
To determine when Ava and Kelly will be 3/4 mile apart in a road race, we must calculate the difference in distance they cover over the same time frame. Ava runs at 6 miles per hour (mph) and Kelly runs at 8 miles per hour (mph). The difference in their speeds is 2 mph (8 mph - 6 mph).
We need to calculate the time it takes for this difference in speed to result in a gap of 3/4 miles. Since speed is distance divided by time, we can use the formula:
Time = Distance / Speed. Substituting the values we have, we get:
Time = (3/4) miles / 2 mph. When we calculate this, we find the time to be 3/8 hours, or 22.5 minutes.
Therefore, Ava and Kelly will be 3/4 mile apart after 22.5 minutes of running at their respective average speeds.
Find the vertex form of y=-x^2-10x-21
Answer:
[tex]\large\boxed{y=-(x+5)^2+4}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of an quadratic equation}\\\\f(x)=ax^2+bx+c=a(x-h)^2+k\\\\h=\dfrac{-b}{2a}\\\\k=f(k)=\dfrac{-(b^2-4ac)}{4a}\\=================================[/tex]
[tex]\text{We have:}\\\\y=-x^2-10x-21\\\\a=-1,\ b=-10,\ c=-21\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)-21=-25+50-21=4\\\\y=-(x-(-5))^2+4=-(x+5)^2+4[/tex]
Final answer:
The vertex form of the quadratic equation [tex]y = -x^2 - 10x - 21[/tex]is [tex]y = -(x + 5)^2 + 4[/tex], with the vertex being (-5, 4).
Explanation:
To find the vertex form of the quadratic equation [tex]y = -x^2 - 10x - 21[/tex], we need to complete the square. Here's a step-by-step guide:
Start with the given quadratic equation: [tex]y = -x^2 - 10x - 21.[/tex]
Factor out the coefficient of the [tex]x^2[/tex]term from the first two terms: [tex]y = -(x^2 + 10x) - 21.[/tex]
Find the number that completes the square for the expression [tex]x^2 + 10x.[/tex]This is [tex](10/2)^2 = 25.[/tex]
Add and subtract this number inside the parentheses, then group the perfect square and the constant terms: y = -[tex](x^2 + 10x + 25 - 25) - 21.[/tex]
Rewrite the equation, recognizing the perfect square trinomial: [tex]y = -[(x + 5)^2 - 25] - 21.[/tex]
Combine the constant terms: [tex]y = -(x + 5)^2 + 4.[/tex]
The vertex form of the equation is [tex]y = -(x + 5)^2 + 4[/tex], where the vertex of the parabola is (-5, 4).
Please help, If I fail this class I have to do it again and this is my last chance to bring up my grade...
(Questions are in the photo(s) provided)
Thank you so much in advance!
I hope this helps. Good luck, I was in the same boat not too long ago.
A quality assurance specialist makes $22 an hour for the first 40 hours she works during a week and $29 an hour for each hour worked over 40 hours. Which piecewise equation models her total week pay y in dollars as it relates to the number of hours x that she has worked during the week?
Answer:
hopes this helps
Step-by-step explanation:
this is a tricky one here
40x X 22= $880
second week
40x X 29=1,160
Answer: Our equation becomes,
[tex]y=22x\ ;\ x\leq 40\\\\and\\\\y=29(x+40)\ ;\ x>40[/tex]
Step-by-step explanation:
Let the number of hours she works for be 'x'.
Let the number of dollars she will be paid in week be 'y'.
Cost per hour for first 40 hours = $22
Cost per hour for over 40 hours = $29
We need to model the piece-wise equation for her total pay in week.
So, our equation becomes,
[tex]y=22x\ ;\ x\leq 40\\\\and\\\\y=29(x+40)\ ;\ x>40[/tex]
PLEASE HELP Arlene claims that the kth root of x can be expressed as x 1/k. Which equation below justifies Arlene's claim?
(x1k)k=x
(x1k)k=1
(x1k)k=0
(x1k)k=k
The k-th root's inverse function is raising to the k-th power.
So, if we raise the k-th root of some number x to the k-th power, we have applied a function and its inverse to x, and we must get x itself as output:
[tex]f(f^{-1}(x))=f^{-1}(f(x))=x\quad\text{for every invertible function f}[/tex]
So, in our case, we have
[tex](\sqrt[k]{x})^k = \left(x^{\frac{1}{k}}\right)^k=x^{k\cdot \frac{1}{k}}=x^1=x[/tex]
The equation that Arlene claim should be [tex]x^{k.\frac{1}{k}} \ = x^1 = x[/tex]
Equation:The k-th root's inverse function should be raising with respect to the k-th power.
Thus, in the case if we raise the k-th root of some number x to the k-th power, so here we used the function and its inverse to x, and we must get x itself in an output:
So,
[tex](k \sqrt x)^k = (x\frac{1}{k})^k = x^{k.\frac{1}{k}} \ = x^1 = x[/tex]
learn more about the expression here: https://brainly.com/question/24686935
a box without a top is made from a rectangular piece of cardboard, with dimensions 6 feet by 8 ft, by cutting out square corners with side length x. which expression can be used to determine the greatest possible volume of the cardboard box?
The answer is:
The second option:
[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]
Why?From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).
So,
Working with the length of the box:
Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(8-(x+x))=(8-2x)[/tex]
Now,
Working with the width of the box:
Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(6-(x+x))=(6-2x)[/tex]
Now that we already know the length and the width of the box, we must remember that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:
[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]
Have a nice day!
Answer: The second option!
Step-by-step explanation:
The resulting R'ST' is an example of what kind of transformation?
rotation
translation
reflecting across y-axis
reflecting across X-axis
Reflection across y-axis
Imagine folding the paper in half with the y-axis being the crease. the triangles would line up perfectly
The resulting transformation is a combination of rotation and translation.
The resulting R'ST' is an example of a Rotation and Translation.
In a rotation, an object is turned or twisted around a fixed point. In this case, R'ST' is rotated around a specific point.
A translation refers to the sliding of an object in a particular direction.
In this case, R'ST' is also shifted or translated in a specific direction.
Therefore, the resulting transformation is a combination of rotation and translation.
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Let the function f be defined as f(x) = 5x² - 7(4x + 3).
What is the value of f(3) ?
Given : f(x) = 5x² - 7(4x + 3)
Now,
f(3) = 5 × 3² - 7(4 × 3 + 3)
= 5 × 9 - 7(12 + 3)
= 45 - 7 × 15
= 45 - 105
= - 60
Hence,
f(3) = - 60
To find f(3) for the function f(x) = 5x² - 7(4x + 3), we substitute 3 into the function and simplify to get f(3) = -60.
Explanation:To evaluate f(3) for the function f(x) = 5x² - 7(4x + 3), we need to substitute the value of 3 into the function:
f(3) = 5(3)² - 7(4(3) + 3)
Now we simplify the expression step by step:
Calculate the square of 3: (3)² = 9.Multiply this result by 5: 5 × 9 = 45.Multiply 4 by 3: 4 × 3 = 12.Add 3 to the result from the previous step: 12 + 3 = 15.Multiply this sum by -7: -7 × 15 = -105.Combine the results of the multiplications: 45 - 105.The final result is:
f(3) = 45 - 105 = -60.
The box-and-whisker plot shows the ages of employees at a video store. What fraction of the employees are 20 years or older?
About
of the employees are 20 years or older.
A rock weighing 15.0 g is
placed in a graduated cylinder,
displacing the volume from
25.0 mL to 36.2 mL. What is
the density of the rock in
grams/cubic centimeter?
Answer: [tex]1.38\frac{g}{cm^3}[/tex]
Step-by-step explanation:
You need to remember the formula for calculate the density:
[tex]density=\frac{mass}{volume}[/tex]
In this case:
[tex]density_{(rock)}=\frac{mass_{(rock)}}{Volume_{(rock)}}[/tex]
You know that:
[tex]mass_{(rock)}=15.5g[/tex]
And when it is placed in a graduated cylinder, the volume is displaced from 25.0 mL to 36.2 mL.
Then, the volume of the rock is:
[tex]Volume_{(rock)}=36.2mL-25.0mL=11.2mL[/tex]
Since [tex]1mL=1cm^3[/tex], you can rewrite the volume as:
[tex]Volume_{(rock)}=11.2cm^3[/tex]
Substituting values into the formula, you get that the density of the rock is:
[tex]density_{(rock)}=\frac{15.5g}{11.2cm^3}=1.38\frac{g}{cm^3}[/tex]
∆ABC and ∆FDE are congruent by the criterion. (Use the three-letter abbreviation without spaces.)
The value of x is , and the value of y is .
Answer:
x = 11, y = 8
Step-by-step explanation:
ΔABC and ΔFDE are congruent by the postulate SSS
Equate the congruent sides in the 2 triangles
BC = ED, that is
x + 3 = 14 ( subtract 3 from both sides )
x = 11
-------------------------------------
DF = AB, that is
x - y = 3 ← substitute x = 11
11 - y = 3 ( subtract 11 from both sides )
- y = 3 - 11 = - 8 ( multiply both sides by - 1 )
y = 8
Answer:
The value of x is 11 and the value of y is 8.
Step-by-step explanation:
It is given that ∆ABC and ∆FDE are congruent.
The corresponding parts of congruent triangle are congruent.
[tex]AB=FD[/tex] (CPCTC)
[tex]3=x-y[/tex] .... (1)
[tex]BC=DE[/tex] (CPCTC)
[tex]x+3=14[/tex]
Subtract 3 from both the sides.
[tex]x=14-3[/tex]
[tex]x=11[/tex]
The value of x is 11.
Put x=11 in equation (1).
[tex]3=11-y[/tex]
Add y on both the sides.
[tex]3+y=11[/tex]
Subtract 3 from both the sides.
[tex]y=11-3[/tex]
[tex]y=8[/tex]
The value of y is 8.
What is another way to express 48+32?
You could express 48+32 by doing 50 + 30 because your adding 2 to the 48 and subtracting 2 from the 32 so that’s not how you could express that.
You could express it by using negatives.
-1(-48-32)
-1(-80)
80
The orginal was:
48+32
=80
Write an expression to match the statement below. Divide the product of 4 and 5 by the sum of 2 and 8.
Answer: (4 x 5)÷(2 + 8)
Step-by-step explanation:
The product is multiplied so the product of 4 and 5 is 20
The sum is adding so the sum of 2 and 8 is 10
Then it wants you to divide them. The 4 * 5 and 2 + 8 are in parenthesis because they are done first.
A square has a perimeter of 258.8 feet. What is the length of each side?
Answer: 64.7
Step-by-step explanation: 258.8 divided by 4
henry had 20 convertibles and 5 trucks in his miniature car collection.After Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertibles .how many trucks did his aunt buy?
Answer:
75
Step-by-step explanation:
Henry started with 20 convertibles and 5 trucks.
His aunt bought him x miniature trucks.
Now, his convertibles represent 1/5 of his collection. How many trucks did her aunt buy?
So, if his convertible represent 1/5 of his collection now, that means his collection is 5 times larger than the number of convertibles. We know he has 20 convertibles... so the collection now counts 100 (5 * 20) items.
Out of 100 items, we remove the 20 convertibles to get a total of 80 trucks.
Then we subtract the initial 5 trucks... so, his aunt bought him 75 trucks.
His aunt bought 75 trucks
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem!
Let :
Number of Additional Miniature Trucks from Henry's Aunt = X
Initial Number of Convertibles = 20
Initial Number of Trucks = 5
Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertible.
[tex]\frac{1}{5}( 20 + 5 + x ) = 20[/tex]
[tex]\frac{1}{5}( 25 + x ) = 20[/tex]
[tex]( 25 + x ) = 20 \div \frac{1}{5}[/tex]
[tex]25 + x = 20 \times \frac{5}{1}[/tex]
[tex]25 + x = \frac{20 \times 5}{1}[/tex]
[tex]25 + x = \frac{100}{1}[/tex]
[tex]25 + x = 100[/tex]
[tex]x = 100 - 25[/tex]
[tex]x = \boxed {75 ~ \texttt{trucks}}[/tex]
Conclusion:Henry's aunt bought him 75 trucks
Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
the price of milk found by dividing its cost in cents by its volume in gallon. what are the units in words?
Answer:
gallons and cents
Step-by-step explanation:
These are the things you can basically measure.
Answer:
gallons and cents
Step-by-step explanation:
These are the things you can basically measure.
39. The equation of a line in standard form is
4x – 2y = 20. Which of the following is the
equation of the same line in slope-intercept
form?
A. y = 2x – 10
B. y = -2x + 10
C. y = 2x – 5
D. y = –2x – 5
Answer:
Let's solve for x.
4x−2y=20
Step 1: Add 2y to both sides.
4x−2y+2y=20+2y
4x=2y+20
Step 2: Divide both sides by 4.
4x/4
= 2y+20/4
x= 1/2y+5
Answer: x= 1/2y+5
I need help please?!!!
Answer:
Step-by-step explanation:
This explains step by step
Hope this helps! <3 -K
math helpp !! :3 will reward :0
The answer is 125° = x because the exterior angle is 55°, from adding up all the exterior angles to ensure they add up to 360°. Then, you would have to use the Supplementary Angeles Theorem to find the obtuse measure beside that 55° exterior angle: 55 + m<x = 180. This is how you get 125° = m<x. You understand?
Answer:
B
Step-by-step explanation:
Two pairs of consecutive sides are congruent, so it can't be C.
At least one pair of opposite sides are parallel, so it can't be A.
The quadrilateral can't be inscribed in a circle, so it can't be D.
Therefore, the quadrilateral is a rhombus. Answer B.
the2,8 slope =4;(2,8) is on the line write the equation
Answer:
The equation of the line is y = 4x
Step-by-step explanation:
* Lets revise how to form an equation of a line from its slope and
a point on the line
- The equation of a line is written as y = mx + b where m is the
slope of the line and b is the y-intercept.
- The line intersect the y-axis at point (0 , b)
* Lets solve the problem
- The line has slope = 4
- The line passes through the point (2 , 8)
∵ The slope = 4
∵ m is the slope of the line in the equation
∴ m = 4
- Substitute the value of m in the equation
∵ y = mx + b
∴ y = 4x + b
- To find the value of b substitute the x-coordinate and the
y-coordinate of the point instead of x and y of the equation
∵ The point (2 , 8) lies on the line
∵ y = 4x + b
- Put x = 2 and y = 8 in the equation to find b
∴ 8 = 4(2) + b ⇒ simplify
∴ 8 = 8 + b ⇒ subtract 8 from both sides
∴ 0 = b
- That means the y-intercept = 0 and the line passing through
the origin point
∴ y = 4x + 0
* The equation of the line is y = 4x
Which of the following has no solution ?
ANSWER
{x|x<0} and {x|x>0}
EXPLANATION
If the two inequalities have an intersection,then it has a solution.
If the two inequalities have no intersection, then there is no solution.
The inequality {x|x<0} and {x|x>0} has no intersection, there is no solution.
The inequalities
{x|x≤0} and {x|x≥0},
{x|x≤0} or {x|x≥0}
both have intersection, therefore have solutions.
How did Wilson believe conquered empires should be treated?
They should be stripped of their wealth.
They should remain occupied by their conquerors.
Their people deserved to determine their own political futures.
Answer:
Their people deserved to determine their own political futures.
Step-by-step explanation:
Answer:
Wilson believed that in conquered empires their people deserved to determine their own political futures
Step-by-step explanation:
Wilson was convinced that democracy was gaining ground allover the world so he declared that he believed "just government must rest upon the consent of the governed" during his taking over of office. he worked with the secretary of state Bryan to sign 22 bilateral treaties to agreed to cooling periods
conquered Latin American states were granted freedom to conduct there own affairs without American interference during this period
What's the surface area?
Answer:
2460 square units
Step-by-step explanation:
Calculate the surface area of the Rectangular Pyramid, calculate the surface area of the Square Prism [Cube], then you add them up.
Helen determined she walks about 1,800 steps per 4/5 mile. How many steps did she take if she walked 2 miles?
Divide 1800 by 1/5 and then add the answer to 1800 (4/5) so you get a whole: then double.
Patrick recorded the daily changes of the value of a stock in dollars : -3.40, -8.09 , -2.47, 1.86, and 3.55. What was the average daily change in the stocks value in dollars?
Plz help!
-$1.71
To find the average of a set of numbers, you add them all together and divide by the amount of numbers.
Start by adding the numbers together to get -8.55.
Since they are 5 numbers, divide -8.55 by 5 to get -1.71.
So, the average daily change of the stock’s value is -$1.71.
estimate each to the nearest integer. square root of 44
The square root of 44 is 6.633249581
If you were going to round to the nearest whole number, it would be seven.
Hope that helps!
The value square root of 44 is 6.63 thus nearest integer of the square root of 44 will be 7.
How do round any digit?To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.
In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep it as it is.
As per the given,
The square root of 44 = √44
√44 = 6.633249581
Since 6 > 5 so it will round up to the nearest integer.
6.633249581 → 7
Hence "The value square root of 44 is 6.63 thus nearest integer of the square root of 44 will be 7".
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which of the following rational functions is graphed below
Answer:
D
Step-by-step explanation:
This graph shows two vertical asymptotes, one at x = +3, the other at x = 4. Thus, we omit the first two answer choices. Next, we substitute 0 for x and determine the y value in Answer Choice C: F(0) = 0. Does the graph go through (0, 0)? Yes, it does. Next, evaluate F at x = 3.5 (halfway between x = 3 and x = 4); that is, evaluate function D at x = 3.5. Does the y value come out to be -4 as shown in the graph? Yes, it does. So D is the correct function to match this graph.
Considering the vertical asymptotes of the function, and it's behavior, it is found that the rational function graphed below is given by:
D. [tex]f(x) = \frac{1}{(x - 3)(x - 4)}[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
In this problem:
There are vertical asymptotes at x = 3 and x = 4, hence the denominator of the function is (x - 3)(x - 4).At x = 3.5, we have that f(x) is approximately 4, hence the numerator is 1.Thus, the correct option is:
D. [tex]f(x) = \frac{1}{(x - 3)(x - 4)}[/tex]
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