The dimensions of a chocolate box are: height=x + 2 inches, length=2x+5 inches, and width=4x-1 inches. If the volume of the chocolate box is 605 cubic inches, what is the value of x?
Answers
I hope this helps you
Answer:
To begin to answer your question you would need to know that the formula for the volume of a rectangular prism is the following: [tex]V=lwh[/tex]. Now its just a manner of substitutions.
Step-by-step explanation:
[tex]V=605 \text{in}^3[/tex]
Then one can also state the following:
[tex]V=(x+2)(4x-1)(2x+5)[/tex]
Following up with this substitution:
[tex]605=(x+2)(4x-1)(2x+5)[/tex]
Proceeding with a FOIL procedure:
[tex]605=(4x^2+8x-x-2)(2x+5)[/tex]
[tex]605=8x^{3}+34x^{2}+31x-10[/tex]
[tex]0=8x^{3}+34x^{2}+31x-615[/tex]
Using PRZs:
[tex]PRZs=\frac{\text{Factors of Constant Term}}{\text{Factors of Highest Power}}=\frac{\pm 1,\pm 3, \pm 5, \pm 41, \pm 615}{\pm 1, \pm 2, \pm 4, \pm 8}[/tex]
By graphing it one can identify that 3 is a solution so plugging it in and using synthetic division.
[tex]\begin{array}{ccccc}3|& 8 & 34 & 31 & -615\\ \ \ |& & 24 & 174 & 615 \\ & 8 & 58 & 205 &0 \end{array}\\[/tex]
Giving the following the polynomial:
[tex]0=(x-3)(8x^2+58x+205)[/tex]
Now one can evaluate the discriminant of that quadratic:
[tex]58^2-4(8)(205)=-3196[/tex]
Because it is negative one knows that it produces imaginary solutions. Therefore the only real solution is [tex]x=3[/tex]. Therefore the dimension of the box is the following: [tex]5\text{in},11\text{in}, 11\text{in}[/tex]
Related Questions
Meagan knits 1/10 of q scarf in 3/4 of annhour.What fraction of a scaf can megan knit in 1 hour
Answers
Answer:
2/15
Step-by-step explanation:
To solve this problem we just need to use a rule of three, relating the fraction of the scarf knitted and the amount of time.
So we have that:
1/10 of the scarf -> 3/4 hour
x of the scarf -> 1 hour
x * (3/4) = 1/10
x = (1/10) / (3/4)
x = (1/10) * (4/3)
x = 4/30 = 2/15
In one hour, Meagan knit 2/15 of the scarf.
A company has been forced to reduce its number of employees. Today the company has 29% fewer employees than it did a year ago. If there are currently 142 employees, how many employees did the company have a year ago?
Answers
250 is not the answer
Step-by-step explanation:
Idk
vvvvvvv help me plzzzzzzzzzzzzzzz
Answers
Answer:
the answer is 0
Step-by-step explanation:
she had -27 in her bank the she added 27
[2x + 3y = 1][5x - 4y = 14]
Answers
Answer:
x = 2
y = - 1
Step-by-step explanation:
Please see the step by step solution in the picture attached below.
Hope it can help you. Have a nice day!
if suresh made a deposit of AED 2700 on the first day of the tear and same amount again after every 4 months at the end of the year how much money will he get if the interest is compounded quarterly and the rate of interest is 7.5% per annum
Answers
Answer:
48.048
Step-by-step explanation:
multiply 77 time 0.60 since 60%in decimal form is 0.60. you then get the answer of that(46.2) and mutiply 0.04 since that the decimal form for 4%. you get 1.848 and add it to 46.2 and get the final answer 48.048. Hope this helped you
you are packing clothes for vacation and don’t want to take any button down shirts. You randomly choose three shirts from a jar containing three T-shirts, three polo shirts, and four button downs.
a) what is the probability that the first three shirts are button downs when you replace each shirt before choosing the next one?
b) what is the probability that the first three shirts are button downs when you do not replace each shirt before choosing the next one?
Answers
a) Because each pick is independent (we pick and then replace), we just have to find the probability of picking it out once, then cube that. This probability is 4/(3+3+4)=2/5. So, it is 8/125.
b) If we replace it, then we can do it in a strategic way:
The probability of picking it out the first time is 2/5. Now, there are 3 button downs and 9 shirts total.
The second time: 3/9=1/3
Now there are 2 and 8
Third time: 2/8=1/4.
The final probability is 2/5*1/3*1/4=1/30
what’s the answer for this
Answers
Answer:
Area of parallelogram A = base x height = 2 x 1 = 2 (in2)
Hope this helps
:)
Expand. Your answer should be a polynomial in standard form. (x-4)(x-6)
Answers
Answer:
x2+10x+24
Step-by-step explanation:
The expanded expression in standard form is: [tex]x^2 - 10x + 24[/tex]
To expand the expression (x - 4)(x - 6), you can use the distributive property to multiply each term in the first parentheses by each term in the second parentheses. Let's do that step by step:
(x - 4)(x - 6)
Step 1: Multiply x from the first parentheses by both terms in the second parentheses:
[tex]x * x = x^2\\x * -6 = -6x[/tex]
Step 2: Multiply -4 from the first parentheses by both terms in the second parentheses:
-4 * x = -4x
-4 * -6 = 24
Now, put everything together: (x - 4)(x - 6) = [tex]x^2 - 6x - 4x + 24[/tex]
Combine like terms: [tex]x^2 - 10x + 24[/tex]
So, the expanded expression in standard form is:
[tex]x^2 - 10x + 24[/tex]
To know more about standard form here
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#SPJ2
What is the volume? Please answer asap.
Answers
Answer:
20
Step-by-step explanation:
i need help i don't understand can someone help me plz :)
Answers
The answer is B. Why?
Terry is buying juice. He needs 3 liters. A half-liter of juice costs $2.39. A 250 -milliliter container of juice cost $ 1.69. What should Terry buy so he gets 3 liters at the lowest price? Explain
Answers
Answer:
Terry should buy half a liter because if he buys 250 millimeters, he will need to pay $20.28, which is more than 14.34.
HELP U GUYS. For a fundraiser, Alex sold large boxes of oranges for $9 each and small boxes of oranges for $5 each. if he sold 17 boxes in all total for 105, how many more small boxes than large boxes did he sell?
A.5
B.7
C.9
D.11
Answers
Answer:
He sold 7 more small boxes than large boxes
Step-by-step explanation:
Let x be the no of small boxes sold .
Cost of 1 small boxes of oranges = $5
Cost of x small boxes of oranges = 5x
Let y be the no. of large boxes sold
Cost of 1 large boxes of oranges = $9
Cost of y large boxes of oranges = 9y
He sold 17 boxes in all total for 105
So,x+y=17 ---1
So,5x+9y=105 ---2
Substitute the value of x from 1 in 2
5x+9(17-x)=105
5x+153-9x=105
153-105=4x
[tex]\frac{153-105}{4}=x[/tex]
12=x
Substitute value of x in 1
12+y=17
y=17-12
y=5
Difference in no. of boxes = 12-5 = 7
So, He sold 7 more small boxes than large boxes
Kia is saving money to buy a Six Flags ticket. She worked for 6 hours at the library and earns the same amount each hour. Her grandmother then gave her $20. In all,she has $53.
Answers
Answer:
She earns 5.5 dollars per hour at the library
Step-by-step explanation:
I am going to assume that the questions is "how much she earns per hour at the library?"
Let's call x the amount of dollars earn by hour at the library. We know that she worked for 6 hours, thus she made 6x dollars.
Later her grandma gave her 20 dollars and she has now 53 dollars.
Let's write the equation and solve it
Amount earned + Amount given by her grandma = 53
[tex]6x+20=53\\6x=33\\x=\frac{33}{6}\\x=5.5[/tex]
Thus, based on this information we would have that Kia earns 5.5 dollars per hour.
Use a net to find the surface area of the prism 8 in 6 in 15 in
Answers
A waitress serves $950. Worth of dinners and recieves &95.00 in tips how much less in tips did she receive if she had gotten her 15% of the cost of meals
Answers
Answer:
She receives $47.5 less
Step-by-step explanation:
Now, the first thing to do here is to calculate what 15% if the total amount is
That would be 15/100 * 950 = $142.5
The amount she receives less is thus $142.5 -$95 = $47.5
Answer:
The amount less that she received than if she had received 15% of the cost of the meal is $47.5
Step-by-step explanation:
Here we have the amount of dinners served by the waitress = $950
Amount received in tips = $95.00
Amount the waitress would have received if she had gotten 15% of the cost of meals served = 15/100 × $950 = $142.5
Therefore, since she received $95.00, the amount less that she received than if she had received 15% of the cost of the meal is thus;
$142.5 - $95 = $47.5.
what is the volume of a hemisphere with a radius of 6?
Answers
V
=
4
3
π
r
3
=
4
3
·
π
·
6
3
≈
904.77863
Which statement about the parabola is not true?A. The focus lies on the axis of symmetry.B.The directrix of the parabola is parallel to the axis of symmetry.C. Each point on the parabola is equidistant from the directrix and the focus
Answers
Answer:
Option B
The directrix of the parabola is parallel to the axis of symmetry
Step-by-step explanation:
The directrix of the parabola is not parallel to the axis of symmetry. It is as a matter of fact, perpendicular to it.
A parabola is actually a set of points that are equidistant from a given point, the focus, and a given line the directrix.
The axis of symmetry is a line that divides the parabola into two equal halves and it always passes through the focus.
The directrix of the parabola is always perpendicular to this axis of symmetry as they always intersect at right angles.
We want to see which one of the given statements is false. We will see that the false one is B: "The directrix of the parabola is parallel to the axis of symmetry"
So in a parabola, we define the axis of symmetry as the vertical line that divides the parabola in two equal parts.
For a general parabola:
y = a*x^2 + b*x + c
The line of symmetry is at:
x = -b/2a
While we know that in a parabola the directrix is a horizontal line.
So the axis of symmetry and the directrix are perpendicular lines.
Then the statement that is false is B: "The directrix of the parabola is parallel to the axis of symmetry"
If you want to learn more, you can read:
https://brainly.com/question/3283347
solve the following
2(X+3)=X-4
Answers
Answer:
2(x+3)=x-4
2x+6=x-4
2x-x=-4-6
x=-10
2x+6=x-4
2x-x=-4-6
x=-10
Clara slept for a total of 126 hours over the cousrve of two weeks.If she sleeps for the same amount of each time each night,how many hours does she sleep per night?
Answers
Answer:
9
Step-by-step explanation:
Answer:
9 hours per night
Step-by-step explanation:
Assuming a week is 7 days
7 * 12 = 14 days
126/14=9
She slept 9 hours per night
Determine if Ginny factored correctly. If not, explain
where she made an error.
Answers
Answer:
The answer is A
Step-by-step explanation:
Which complex number has a distance of the square root of 17 from the origin on the complex plane?
Answers
Hey there! I'm happy to help! :D
-------------------------------------------------------------------
OVERVIEW
A complex number is a real number combined with an imaginary number (such as i, a number that will equal -1 when squared).
The complex plane is an interesting thing we use to graph complex numbers. The horizontal axis is where you plot the real part of the complex number, and the y-axis is where you plot the coefficient of the imaginary number.
For example, if I had the complex number 4+3i, I would plot the point (4,3) on the complex plane.
-------------------------------------------------------------------
MODULI
The modulus (plural is moduli) is the distance of a complex number from the origin on the complex plane. To find the modulus, you take the real number and the coefficient (basically the points of your graph), square them, add the results, and then you find the square root of that! Here's a little checklist so that you can always find the modulus of any complex number!
STEPS TO FIND MODULUS GIVEN COMPLEX NUMBER
STEP 1: PLOT THE COMPLEX NUMBER
Let's use our complex number 4+3i. If we plot it, the point will be (4,3)
STEP 2: TAKE YOUR VALUES OF X AND Y AND SQUARE THEM
4²=16
3²=9
STEP 3: ADD THESE SQUARES
16+9=25
STEP 4: SQUARE ROOT IT
√25=5
Therefore, the modulus (distance from the origin on the complex plane) of 4+3i is 5.
-------------------------------------------------------------------
SOLVING THE PROBLEM
In our case, we are given a modulus but not a point on the line. Our modulus is the square root of seventeen. We are going to have to the steps to find the modulus backwards to find our points. I will put the steps for finding a complex number given the modulus below.
STEPS TO FIND COMPLEX NUMBER GIVEN MODULUS
STEP 1: SQUARE THE MODULUS
√17²=17
STEP 2: FIND THE SQUARES THAT MAKE UP THE NUMBER
Before, we could just add things we found. Now, we have to find the things that were added! How do we know what things were added to find 17? Well, we know that we added two squares to find the modulus, so we will subtract a square of some sort and hopefully come up with another square.
Let's see what squares exist that are less than seventeen.
1, 4, 9, 16
(Note that one is 1², 4 is 2², 9 is 3², and 16 is 4²)
Which of these can we add to get 17?
Well, we can do 1 and 16, so this is our result so far.
STEP 3: SQUARE ROOT THE RESULTS
Now, we just find the square roots of what we found in the last problem!
√1=1
√16=4
STEP 4: PLOT THE GIVEN NUMBERS ON THE PLANE AND FIND THE COMPLEX NUMBER
We can plot these either way because the modulus of 1+4i will be the same distance from the origin as 4+i because we only use the commutative property (adding order doesn't matter) when looking for the modulus. You can also have the negative version of either number because you immediately square it, so it can also be -4+i or 4-i! You can also rearrange the equation in tons of ways to figure it out. You could also have both be negative, flip the coefficient placement, etc.!
-------------------------------------------------------------------
SOLUTION
Therefore, the complex numbers that have a distance of √17 from the origin on the complex plane are ±4±i and ±1±4i. So, why did I write all of these funny plus and minus signs? Well, it's so that I didn't have to write all of the possible equations. I believe those equations actually represent 8 possible points we can create with the solution we got.
4+i
-4+i
4-i
-4-i
1+4i
-1+4i
1-4i
-1-4i
You can plug these complex numbers back in and find the modulus with my instructions to find the modulus given a complex number. Now, you will be able to deal with moduli and complex numbers for the rest of your life!
I hope that this helps! Have a wonderful day! :)
1 1/7 times 3/5 plz answer now
Answers
Answer:
24/35 or 0.6857142
Step-by-step explanation:
Answer:
[tex] \frac{24}{35} [/tex]
alternative form:
[tex] 0.685714286 [/tex]
Step-by-step explanation:
[tex]1 \frac{1}{7} \times \frac{3}{5} \\ multiply \: 1 \: and \: 7 \\ \\ \frac{7 + 1}{7} \times ( \frac{3}{5} ) \\ add \: 7 \: to \: 1 \\ \\ \frac{8}{7} \times ( \frac{3}{5} ) \\ remove \: parenthesis \: and \: put \\numerator \: times \: numerator \: and \\ denominator \: times \: denominator \\ \\ \frac{8 \times 3}{7 \times 5} \\ do \: the \: multiplications \\ \\ \frac{24}{35} [/tex]
Anthony is a high school basketball player. How many points would Anthony score in a game if he made 8 three point shots and 2 two point shots ? How many points would Anthony score in a game if he made x three point shots and y two point shots?
Answers
Answer:
Step-by-step explanation:
x three point shots: 8*3=24
x two point shots: 2*2=4
The point would Anthony score is : 24+4=28
I hope it'll help you much
Thank you for asking
Name a career in which one would have to use the Pythagorean Theorem. Give an example of when, where, and how it would be used.
FULL EXPLANATION NEEDED
Answers
Answer:
Engineers use the Pythagorean Theorem to figure out measurements of objects.
Now move points C, D, and E on the circle, and note the interior angle measurements for the quadrilateral in the table below. Notice that m∠B is predetermined, so set that angle measure first.
Answers
Answer:
Explanation:
Plato
what is a measure of an angle between the perpendicular
bisectors of two adjacent sides of a regular polygon 3
Sides ?
Answers
Answer:
2/5*180=72
360/72=5
as simple as that you just need to read on polygons
Step-by-step explanation:
pls give me brainlyist
Write down all the factors of 15.
Answers
Answer:
1,3,5,15
Step-by-step explanation:
Answer:
Step-by-step explanation:
Factors of 15:
1 , 3 , 5 , 15
How do I Graph y=-2x+5
Answers
Answer:
Slope-Intercept Form y = mx + b
Y = 5
Slope = -2/1
Step-by-step explanation:
Slope-Intercept Form y = mx + b
m = Slope; Rise over Run; Remember there is always an understood 1 in the denominator. If the slope is positive it goes up and to the right and if the slope is negative it goes down and to the right.
b = Y-intercept; This is where the line crosses the y-axis at. If it's positive it's above the x-axis and if negative below.
Complete the point-slope equation of the line through (-9,6)(−9,6)left parenthesis, minus, 9, comma, 6, right parenthesis and (-7,-8)(−7,−8)?
Answers
Answer:
Step-by-step explanation:
hello : here is an solution
The equation of the line in point-slope form is y - 6 = -7(x+9)
The equation of a line in point-slope form is expressed as:
y-y0 = m(x-x0)
m is the slope of the line
(x0, y0) is any point on the line
Given the coordinate points (-9, 6) and (-7, -8)
Get the slope of the line:
slope = -8-6/-7+9
Slope = -14/2
Slope = -7
Using the point (-9, 6), the required slope is expressed as:
y - 6 = -7(x-(-9))
y - 6 = -7(x+9)
Hence the equation of the line in point-slope form is y - 6 = -7(x+9)
Learn more here: https://brainly.com/question/24642959
Question 4 11 point)
Four hundred grocery store shoppers were surveyed to determine their favorite fruit. How many shoppers prefer bananas?
Favorite Fruit
Bananas Apples
32%
35%
Cherries
33%
Os 32
Answers
Answer:
128
Step-by-step explanation:
128 is the right
peanut butter
