The polynomial expression x(3x^2+25)(10x^2+4x+6), where x is in inches, can be used to mod the number of cubic inches of cement that will be needed for a new porch. The cement contractor used 2 for the value of x.
Answers
Since x is given in cubic inches, let's split the expression like this:
[tex]\begin{gathered} h=height=x \\ w=width=(3x^2+25) \\ l=length=(10x^2+4x+6) \end{gathered}[/tex]For x = 2:
[tex]\begin{gathered} h=2in \\ w=3(2)^2+25=37in \\ l=10(2)^2+4(2)+6=54in \end{gathered}[/tex]Related Questions
Which function below has the following domain and range?Domain: {-9, - 5, 2, 6, 10}Range: { -2, 0, 8}
Answers
ANSWER :
A.
EXPLANATION :
From the problem, we have the domain and range :
[tex]\begin{gathered} Domain:\lbrace-9,-5,2,6,10\rbrace \\ Range:\lbrace-2,0,8\rbrace \end{gathered}[/tex]The x coordinates must only have the values of the domain
and the y coordinates must only have the values of the range.
The only option that satisfies this condition is :
[tex]\lbrace(2,0),(-5,-2),(10,8),(6,0),(-9,-2)\rbrace[/tex]Given ARPMAYC. complete each of the following statementsAYC9) AMPKAYAa) A d) 4YEb) CYe) EKc) PAZACYh) Al Aca
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The triangles KMP and AYC, are congruent angles, because we are told that:
[tex]\text{KMP}\cong AYC[/tex]Thus, to find our answers we compare both triangles.
a) KM is approximately equal to AC.
That is because, as we can see in the following image, they are corresponding sides:
[tex]KM\cong AC[/tex]b) CY is approximately equal to MP.
That is because they are corresponding sides, they are the short side of each triangle. And since the triangles are equal, CY and MP are also equal:
[tex]CY\cong MP[/tex]c) for the same reasons as the previous two, PK anf AY, are corresponding sides:
[tex]PK\cong AY[/tex]d) and e)
The corresponding angles of Y and K are represented in the following image:
rrespon
The three sides of a triangle are n, 4n - 2, and 4n - 7. If the perimeter of the triangle is 45 cm, what is the length of each side? Separate multiple entries with a comma.
Answers
6, 22, 17
ExplanationStep 1: writing the equation
We have a triangle with sides n, 4n - 2, and 4n - 7
We obtain its perimeter if we add all its sides:
n + 4n - 2 + 4n - 7
Since the perimeter is 45 cm, then:
n + 4n - 2 + 4n - 7 = 45
combining like terms:
n + 4n +4n = 9n
and
-2 - 7 = -9
then, we have:
n + 4n - 2 + 4n - 7 = 45
↓
9n - 9 = 45
Step 2: finding n
Now we solve the equation:
9n - 9 = 45
↓ taking -9 to the right
9n - 9 + 9 = 45 + 9
9n = 54
↓ taking 9 to the right
n = 54/9 = 6
Then, n = 6
Step 3: sides measure
Since the measure of the first side is given by n,
then its length is
n = 6
SInce the measure of the second side is given by 4n-2,
then its length is
4n - 2 = 4 · 6 - 2
= 24 - 2
= 22
SInce the measure of the third side is given by 4n - 7,
then its length is
4n - 7 = 4 ·6 - 7
= 24 - 7
= 17
That is why the measures are 6, 22 and 17.
Mara bought a bag that contained 16 cups of sugar. She uses two-thirds cup of sugar each time she make a batch of cookies. If the bag now has 10 cups of sugar left, how many batches of cookies has she made?
Answers
From a bag of 16 cups of sugar , Mara used 2/3 cups of sugar to make 1 batch of cookies , then number of baches made by 6 cups of sugar is equal to 9 batches.
As given in the question,
Total number of cups of sugar in a bag = 16
Cups of sugar used to make 1 batch of cookies = 2/3
Number of cups of sugar left in a bag = 10
Number of cups of sugar used = 6
2/3 cups of sugar = 1 batch of cookies
1 cup of sugar = 3/2 batch of cookies
6 cups of sugar = [(3/2) × 6 ]
= 9 batches of cookies
Therefore, from a bag of 16 cups of sugar , Mara used 2/3 cups of sugar to make 1 batch of cookies , then number of baches made by 6 cups of sugar is equal to 9 batches.
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What is the inverse of the given relation?y = 3x + 12I need to understand the step by step breakdown for how to solve this problem.
Answers
Given the function y, we want to find the inverse function y^-1.
Then, replace every x with a y and every y with an x. It yields,
[tex]x=3y+12[/tex]now, solve the equation for y. So, by subtracting 12 to both sides, we have
[tex]x-12=3y[/tex]or equivalently,
[tex]3y=x-12[/tex]and, by dividing both sides by 3, we obtain
[tex]y=\frac{x-12}{3}[/tex]Finally, replace y with y^-1. Then, the inverse function is given by:
[tex]y^{-1}=\frac{x-12}{3}[/tex]Can you please help me
Answers
From the question,
[tex]\begin{gathered} m\angle AFE=m\angle BFC\text{ (Vertically opposite angles)} \\ \therefore \\ m\angle AFE=70^{\circ} \end{gathered}[/tex]We also have
[tex]m\angle AFB=m\angle EFC\text{ (Vertically opposite angl}es)[/tex]Remember that the sum of angles at a point equals 360°. Therefore
[tex]\begin{gathered} m\angle AFB+m\angle BFC+m\angle CFE+m\angle AFE=360 \\ \therefore we\text{ have} \\ 2(m\angle AFB)+2(70)=360 \\ 2(m\angle AFB)=360-140=220 \\ m\angle AFB=\frac{220}{2}=110 \end{gathered}[/tex]Therefore, m(AB) is 110°.
Hence, OPTION B is correct.
The first year shown the number of students per teacher fell below 16 was
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Using the y axis, we want to find when it goes below 16
The x value when y is less than 16 for the first time is 2002
could someone please help :(
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Given from the number line:
D = -2 and F = 13
So, the distance DF = 13 - (-2) = 13 + 2 = 15
1) find E such that, DE : EF = 2 : 1
so,
so, x : (15 - x) = 2 : 1
x = 30 - 2x
3x = 30
x = 10
So, E = -2 + 10 = 8
=========================================================================
2) E is 4/5 of the distance from F to D
So, the distance from F = 4/5 * 15 = 12
So, E = 13 - 12 = 1
=====================================================================
3) the ratio of DE : EF = 2 : 3
So,
3x = 2 ( 15 - x)
3x = 30 - 2x
5x = 30
x = 30/5 = 6
E = -2 + 6 = 4
=================================================
4) E is 1/3 of the distance from D to F
So, the distance DE = 1/3 * 15 = 5
So, E = -2 + 5 = 3
=====================================================
As a summery:
1) E = 8
2) E = 1
3) E = 4
4) E = 3
the radius of a circle is 3 inches long. what is the circumference?
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Given:
a.) A circle with a radius of 3 inches long.
To be able to get the circumference of the circle, we will be using the following formula:
[tex]\text{ C = 2}\pi r[/tex]Where,
C = Circumference
r = radius
We get,
[tex]\begin{gathered} \text{ C = 2}\pi r \\ \text{ = 2(3.14)(3)} \\ \text{ = 6 x 3.14} \end{gathered}[/tex][tex]\text{ C = 18.84 in.}[/tex]Therefore, the circumference of the circle is 18.84 in.
Complete a two-column algebraic proof.Given: x – 4 = (8x+6) + 4xProve: x = -1
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To perform a two column proof, we should give a statement and give a reason of it.
So we start with the initial statement.
1. Statement: x-4 =(1/2)(8x+6)+4x. Reason: Given
Next, we distribute the multiplication (1/2) with(8x+6). If we do so, we get the following statement.
2. Statement x-4 = (4x+3) + 4x. Reason: Distributive property of addition and multiplication.
Now, on the right we can add 4x with 4x, due to the associative property of additon, we get
3. Statement: x-4 = (4x+4x)+3 = 8x+3. Reason: Associative property of addition.
Now, we can subtract x on both sides, so we get
4. Statement: -4 = 7x+3. Reason: Subtraction property of equality.
By the same reason, we should subtract 3 on both sides. We get
5. Statement: -7 = 7x. Reason: Subtraction property of equality.
Finally, we divide by 7 on both sides, so we get
6. Statement: -1=x. Reason: Division property of equality.
7. Statement: x=-1. Reason: Symmetric property of equality.
The graph of which function has a minimum located at (4,-3)
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We need to obtain the first derivate
[tex]\begin{gathered} f\mleft(x\mright)=-\frac{1}{2}x^2+4x-11 \\ f^{\prime}(x)=-x+4 \end{gathered}[/tex][tex]\begin{gathered} f\mleft(x\mright)=-2x^2+16x-35 \\ f^{\prime}(x)=-4x+16 \end{gathered}[/tex][tex]\begin{gathered} \: f\mleft(x\mright)=\frac{1}{2}x^2-4x+5 \\ f^{\prime}(x)=x^{}-4 \end{gathered}[/tex][tex]\begin{gathered} f(x)=2x^2-16x+5 \\ f^{\prime}(x)=4x-16 \end{gathered}[/tex]Answer: B on edge23
Step-by-step explanation:
f(x) = 1/2^x2–4x + 5
How to find postulate
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Note that if plane N and plane M intersects each other in two points (say A and B) it follows that they intersects each other in the line that contains A and B. So they cannot intersect exactly in only two points. Postulate number 10
Are the triangles congruent using AAS?
True
False
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AAS= Angle Angle Side
The singular lines show one pair of congruent angles.
The double lines show another pair of congruent angles.
So, we know that there are 2 angles.
The triangles both share of their sides, the one going down the middle.
So, we know that there is a side as well!
hope this helped!!! <33
help meeeeeeeeeeee pleaseee
Answers
Equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
What exactly are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal.An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.Such as 3x + 5 = 15 as an example.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, (f∙g)(x) and (g∙f)(x):
Where, f(x) = 5x + 1 and g(x) = x - 4:(f∙g)(x):
5x(x - 4) + 1(x - 4)5x² - 20x + x - 45x² - 19x - 4(g∙f)(x):
x(5x + 1) - 4(5x + 1)5x² + x - 20x - 45x² - 19x - 4Therefore, equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
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In the similaritytransformation of AABCto ADEF. ABC was dilatedby a scale factor of 1/2reflected across the !? 1,and moved through thetranslation [1.
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Solution: C. Y-Axis
Analysis: In this case, the triangle is reflected across the Y-Axis. That's the reason why the triangle changes the orientation of the initial triangle.
Example: Point B reflects Point E. X=2 to X=-2. And the value of Y stands.
1.) A gourmet shop wants to mix coffee beans that cost $3.00 per pound with coffee beans that
cost $4.25 per pound to create 25 pounds of a new blend that costs $3.50 per pound. Find the
number of pounds of each needed to produce the new blend.
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Explanation:
3.00 x 15 = 45$ ( old blend )
4.25 x 10 = 42.5$ ( new blend )
25 pound in total cost $87.50
To find the average cost per pound divide total cost by # of pounds.
87.50 divided by 25 pounds is $3.50
One ton (2,000 pounds) is equivalent to 907 kilograms. A baby elephant weighs about 91 kilograms atbirth. Approximately how many pounds (lbs.) is this?A 200 lbs.B 400 lbs.C 600 lbs.D 1,000 lbs.
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Since 2000 pounds = 907 kilograms, use the conversion factor:
[tex]\frac{2000\text{ pounds}}{907\operatorname{kg}}[/tex]To find out what 91 kg are equal to, measured in pounds:
[tex]91\operatorname{kg}=\frac{2000\text{ pounds}}{907\operatorname{kg}}=\frac{91\cdot2000}{907}\text{ pounds =200.66 pounds}[/tex]Therefore, a baby elephant weighs about 200 lbs.
I need help finding the passing adjusted grade of 70A=10R^1/2
Answers
Given:
Passing grade = 70
Formula for adjusted grade, A:
[tex]A=10R^{\frac{1}{2}}[/tex]Given a passing adjusted grade of 70, let's find the raw score, R.
To solve for R, substitute 70 for A and solve for R.
We have:
[tex]\begin{gathered} 70=10R^{\frac{1}{2}} \\ \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{70}{10}=\frac{10R^{\frac{1}{2}}}{10} \\ \\ 7=R^{\frac{1}{2}} \end{gathered}[/tex]Take the square of both sides:
[tex]\begin{gathered} 7^2=(R^{\frac{1}{2}})^2 \\ \\ 7^2=R^{\frac{1}{2}\times2} \\ \\ 49=R^1 \\ \\ 49=R \\ \\ R=49 \end{gathered}[/tex]Therefore, the raw score a student would need to have a passing adjusted grade of 70 is 49
ANSWER:
49
cost to rent a paddle boat at the city park includes a intentral fee of $7.00, plus $3.50 per hour. Which equation models the relationship between the total cost, y, and the number of hours, X, that the paddle boat is rentedA. y = 3.5x + 7. B. y = 7x + 3.5C. y = x/7 + 3.5. D. y = x/3.5 + 7
Answers
The total cost is represented as y, and the number of hours as x.
The intentral fee is $7.00.
Since the cost is $3.50 per hour, the total cost is
y=3.5x+7.
Hence, option A is correct.
Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 12?
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We know we're dealing with two dice. Since each die has 6 different possibilities, the outcomes of rolling two dice are given by:
6 × 6, which is 36. This will be our denominator.
How many ways can we get 9 or 12 with two dices?
For a sum of 9:
3 + 6 = 9
4 + 5 = 9
There are two possibilities.
For a sum of 12:
6 + 6 = 12
There is only one possibility.
Summing it up, there are 3 possibilities to get a sum of 9 or 12 with the two dice.
The events are independent events since neither of them can ever occur at the same time.
Thus, the probability will be:
[tex]\text{ Probability = \lparen Probability of getting 9\rparen + \lparen Probability of getting 12\rparen}[/tex]We get,
[tex]\text{ Probability = }\frac{2}{36}\text{ + }\frac{1}{36}\text{ = }\frac{3}{36}\text{ = }\frac{1}{12}\text{ \lparen simplified\rparen}[/tex]Therefore, the probability is 1/12.
Can you help to solve for number 5. Solving for X.
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We will work at first with the small triangle ADC
[tex]m\angle DAC+m\angle C=m\angle ADB[/tex]mm[tex]m\angle DAC=55-20=35^{\circ}[/tex]We will use the sine rule
[tex]\frac{65}{\sin35}=\frac{AD}{\sin 20}[/tex]By using the cross multiplication
[tex]\begin{gathered} AD\times\sin 35=65\times\sin 20 \\ AD=\frac{65\sin 20}{\sin 35} \end{gathered}[/tex]In triangle ABD
We will use
[tex]\sin 55=\frac{x}{AD}[/tex]Then
[tex]x=AD\sin 55[/tex]Substitute AD by its value above
[tex]undefined[/tex]sorry you have to zoom in to see better. its a ritten response.
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A: height is increasing from 0-2 interval.
B: Height remains the same on 2-4
C: 4-6 the height is decreasing the fastest, because the slope is the steepest on that interval.
D: Baloon would be on the ground at 16 seconds, and will not fall down further. that is the way it is in real-world (constraint).
Looking to receive assistance on the following problem, thank you!
Answers
Given:
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \\ w=5j \end{gathered}[/tex]So the value is:
(a)
[tex]\begin{gathered} u=-2i-7j \\ 2u=2(-2i-7j) \\ 2u=-4i-14j \end{gathered}[/tex][tex]\begin{gathered} 2u-v=-4i-14j-(3i-4j) \\ =-4i-14j-3i+4j \\ =-7i-10j \end{gathered}[/tex](b)
[tex]\begin{gathered} w=5j \\ 3w=3\times5j \\ 3w=15j \end{gathered}[/tex][tex]\begin{gathered} u=-2i-7i \\ 4u=4(-2i-7j) \\ 4u=-8i-28j \end{gathered}[/tex][tex]\begin{gathered} 3w+4u=15j+(-8i-28j) \\ =15j-8i-28j \\ =-8i-13j \end{gathered}[/tex](c)
The dot product of v and u.
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \end{gathered}[/tex]dot product is:
[tex]\begin{gathered} vu=(3i-4j)\cdot(-2i-7j) \\ =-6(i\cdot i)-21(i\cdot j)+8(j\cdot i)+28(j\cdot j) \end{gathered}[/tex]The doat product (i.i = 1) and ( j.j=1) and ( i.j=0) and ( j.i = 0)
[tex]\begin{gathered} =-6(1)-21(0)+8(0)+28(1) \\ =-6+28 \\ =22 \end{gathered}[/tex]Determine the angle of rotation if an image is the result of a composition of two reflections across perpendicular lines.
Answers
The angle of rotation if an image is the result of a composition of two reflections across perpendicular lines is 180 degrees
How to determine the angle of rotation of reflection os perpendicular lineRotation and reflection are forms of transformation as seen in mathematics. The two are related in some forms.
When a reflection is done on a plane perpendicular to the preimage the image is reflected at the perpendicular plane. This is equal to rotation of an angle 90 degrees.
When the reflection is continued again across the perpendicular line, another reflection is noticed and similar rotation however in this case with respect to the initial image, the rotation is now 180 degrees.
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An arctic village maintains a circular cross-country ski trail that has a radius of 2.9 kilometers. A skier started skiing from the position (-1.464, 2.503), measured in kilometers, and skied counter-clockwise for 2.61 kilometers, where he paused for a brief rest. (Consider the circle to be centered at the origin). Determine the ordered pair (in both kilometers and radii) on the coordinate axes that identifies the location where the skier rested. (Hint: Start by drawing a diagram to represent this situation.)(x,y)= ( , ) radii(x,y)= ( , ) kilometers
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The solution to the question is given below.
[tex]\begin{gathered} The\text{ 2.6km is some fraction of the entire Circumference which is: C= 2}\pi r\text{ = 2}\times\text{ }\pi\text{ }\times2.9 \\ \text{ = 5.8}\pi cm \\ \text{ The fraction becomes: }\frac{2.61}{5.8\pi}\text{ = }\frac{0.45}{\pi} \\ \text{The entire circle is: 2 }\pi\text{ radian} \\ \text{ = }\frac{0.45}{\pi}\text{ }\times2\text{ }\times\pi\text{ = 0.9} \\ The\text{ skier has gone 0.9 radian from (-.1.464, 2.503)} \\ \text{The x- cordinate become: =-1.}464\text{ cos}(0.9)\text{ = -1.4625} \\ while\text{ the Y-cordinate becomes: =-1.}464\text{ sin}(0.9)\text{ = -}0.0229 \\ \text{The skier rested at: (-1.4625, -0.0229)} \\ \end{gathered}[/tex]What is the equation of the line that passes through the point (8,-6) and has a
slope of o?
Answers
The equation is y = -6
3) There are 24 applicants for three jobs: computer programmer, software tester, and manager. How many ways can this be done?
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this is a combination, so
[tex]24C3=\frac{24\cdot23\cdot22}{3\cdot2\cdot1}=2024[/tex]answer: 2024 ways
4. You are making guacamole for a familygathering. Your first trip to the store, youpurchased 5 avocados and 3 pounds of tomatoesfor $13.30. The head count changed, and youwent back for an additional 3 avocados and 8pounds of tomatoes, spending another $22.55.What is the price per avocado and pound oftomatoes?
Answers
hello
to solve this question, we need to write an equation expressing the word problem and solve for the price of each item.
let x represent the cost of avocados
let y represent the cost of tomatoes
[tex]\begin{gathered} 5x+3y=13.30\ldots\text{.equation 1} \\ 3x+8y=22.55\ldots\text{.equation 2} \end{gathered}[/tex]from equation 1, let's make xthe subject of formula
[tex]\begin{gathered} 5x+3y=13.30 \\ 5x=13.30-3y \\ \text{divide both sides by 5 to solve for x} \\ x=\frac{13.30-3y}{5} \\ \text{this is equation 3} \end{gathered}[/tex]put equation 3 into equation 2
[tex]\begin{gathered} 3x+8y=22.55 \\ 3(\frac{13.30-3y}{5})+8y=22.55 \\ \frac{39.9-9y}{5}+8y=22.55 \\ \text{solve for y} \\ \frac{39.9-9y+40y}{5}=22.55 \\ \frac{39.9+31y}{5}=22.55 \\ 39.9+31y=22.55\times5 \\ 39.9+31y=112.75 \\ 31y=112.75-39.9 \\ 31y=72.85 \\ y=\frac{72.85}{31} \\ y=2.35 \end{gathered}[/tex]since y = 2.35, let's put that in either equation 1 or 2
from equation 2
3x + 8y = 22.55
put y = 2.35 and solve for x
[tex]\begin{gathered} 3x+8y=22.55 \\ y=2.35 \\ 3x+8(2.35)=22.55 \\ 3x+18.8=22.55 \\ 3x=22.55-18.8 \\ 3x=3.75 \\ x=\frac{3.75}{3} \\ x=1.25 \end{gathered}[/tex]from the calculations above, the price per avocado and pound of tomatoes are $1.25 and $2.35 respectively
Plot the complex number, then write the complex number in polar form. You may express the argument in degrees.
Answers
DEFINITIONS
To represent a complex number we need to address the two components of the number.
Consider the complex number:
[tex]a+bi[/tex]Complex numbers are the points on the plane, expressed as ordered pairs (a, b), where a represents the coordinate for the horizontal axis and b represents the coordinate for the vertical axis.
Note that the imaginary part is plotted out on the vertical axis while the real part is on the horizontal axis.
QUESTION
The complex number is given to be:
[tex]4\sqrt[]{3}-4i[/tex]This means that the ordered pair representing the complex number is given to be:
[tex](a,b)=(4\sqrt[]{3},-4)[/tex]This means that the point will be positive on the real axis and negative on the imaginary axis. Therefore, the point will be in the 4th quadrant.
The correct option is OPTION B.
Assume that when adults with smartphones are randomly selected , 52% use them in meetings or classes. If 7 adults smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes.The probability is:
Answers
From the information available;
The population is 52% and the sample size is 7. The probability that exactly 4 of them use smartphones (if 7 adults are randomly selected) would be calculated by using the formula given;
[tex]\begin{gathered} p=52\text{ \%, OR 0.52} \\ n=7 \\ p(X=x) \\ We\text{ shall now apply;} \\ p(X=4)=\frac{n!}{x!(n-x)!}\times p^x\times(1-p)^{n-x} \end{gathered}[/tex]We shall insert the values as follows;
[tex]\begin{gathered} p(X=4)=\frac{7!}{4!(7-4)!}\times0.52^4\times(1-0.52)^{7-4} \\ =\frac{5040}{24(6)}\times0.07311616\times0.110592 \\ =35\times0.07311616\times0.110592 \\ =0.28301218 \end{gathered}[/tex]Rounded to four decimal places, this becomes;
[tex](\text{selecting exactly 4)}=0.2830[/tex]ANSWER:
The probability of selecting exactly 4 smartphone users is 0.2830
