Answers
Factoring like this is simply the distributive property in reverse. We can check if we did the factoring right by distributing the outer term x back into the inner terms
Let's multiply the outer x by each of the inner terms (a, b and d)
x times a = ax
x times b = bx
x times d = dx <--- the result should be d and not dx
-----------------------------------------------------------------------------
Here is the proper way to solve for x. We first need to move the d over, which is done by subtracting d from both sides. Once all of the x terms are on one side, we can finally factor out the x. Then after that we divide both sides by the quantity (a+b)
k = ax + bx + d
k - d = ax + bx + d - d
k - d = ax + bx
k - d = x(a + b)
(k - d)/(a + b) = x(a + b)/(a + b)
(k - d)/(a + b) = x
x = (k - d)/(a + b)
The final answer is
x = (k - d)/(a + b)
which can be written as
[tex]x=\frac{k-d}{a+b}[/tex]
If you choose to use the first option, then make sure you use parenthesis as shown. The parenthesis are important to make sure that you divide all of "k-d" over all of "a+b" as one big fraction.
Related Questions
A retangular box is 2 cm high, 4 cm wide and 6 cm deep. M packs the box with cubes, each 2 cm by 2 cm by 2 cm with no space left over . How many cubes fit in the box?
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how many times does 8 go into 48? well, that many cubes.
4/25, 13%, 0.28, 7%, 21/100, 0.15 least to greatest
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I think we should turn all of these numbers to decimals so that we can tell which one is least and greatest.
Let's start with 4/25. Let's get the divide 4 by 25 to get the decimal form. 4÷25=.16
Then 13%, move the decimal two places to the left to get it into percentage form. After you move the decimal, it is now .13
0.28 is already in decimal form, let's move to the next one.
7%, again let's move the decimal place two places to the left. After that, it i now .07
21/100, let's divide "21" from "100, 21÷100= 0.21
0.15 is already in decimal form, so now we are ready to order them from least to greatest.
Least to Greatest: 0.7 (7%), 0.13 (13%), 0.15, 0.16 (4/25), and lastly 0.21 (21/100).
Hope this helps!
May
Irving spent the day shopping and made the following purchases: Item Cost ($) Novel 8.75 Shirt 21.66 Lunch 9.13 Potted plant 16.89 When Irving was done, he checked his account balance and found he had a total of $95.06. How much money was in Irving’s account to begin with? a. $56.43 b. $151.49 c. $38.63 d. $142.36
Answers
Solution:
Amount spent by Irving:
Item cost($)
Novel 8.75
Shirt 21.66
Lunch 9.13
Potted plant 16.89
Total money spent = $56.43.
Amount of money In Irving account= $95.06.
Amount of money was in Irving’s account to begin with =$56.43+$95.06=$151.49.
Answer:$151.49.
[tex]r \frac{8}{11} r \frac{10}{11} [/tex] Simplify. Write your answer using a single, positive rational exponent
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[tex]\bf r^{^\frac{8}{11}}\cdot r^{^\frac{10}{11}}\implies r^{^{\frac{8}{11}+\frac{10}{11}}}\implies r^{^\frac{18}{11}}[/tex]
Find (3 × 104) − (5 × 102).
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(3*104) - (5*102)
312 - 510
-198
= 295 x 10^2
= 2.95 x 10^4
hope it helps
A parking garage holds 300 cars on each level. There are 4 levels in the garage. How many cars can the parking garage hold in all?
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The average annual income I in dollars of a lawyer with an age of x years is modeled with the following function I=425x^2+45,500x-650,000
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Also, you made a little (but important) typo.
The right equation for the annual income is: I = - 425x^2 + 45500 - 650000
1) Determine the youngest age for which the average income of a lawyer is $450,000
=> I = 450,000 = - 425x^2 + 45,500x - 650,000
=> 425x^2 - 45,000x + 650,000 + 450,000 = 0
=> 425x^2 - 45,000x + 1,100,000 = 0
You can use the quatratic equation to solve that equation:
x = [ 45,000 +/- √ { (45,000)^2 - 4(425)(1,100,000)} ] / (2*425)
x = 38.29 and x = 67.59
So, the youngest age is 38.29 years
2) Other question is what is the maximum average annual income a layer can earn.
That means you have to find the maximum for the function - 425x^2 + 45500x - 650000
As you are in college you can use derivatives to find maxima or minima.
+> - 425*2 x + 45500 = 0
=> x = 45500 / 900 = 50.55
=> I = - 425 (50.55)^2 + 45500(50.55) - 650000 = 564,021. <--- maximum average annual income
explain...................
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The slopes of all the choices are easy to see because all the choices are in y = mx + b form, slope-intercept form.
If we write our equation in slope-intercept form also, then we can see its slope easily.
We solve -3x + y = 7 for y.
Add 3x to both sides to get
y = 3x + 7
The slope is 3.
We need a negative reciprocal slope to 3, so we need -1/3.
Only choice A has a slope of -1/3.
Answer: Choice A, y = -1/3x + 7
What is the 4th term of the sequence?
a1 = 8 and an = 6 + an – 1
a4 =
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notice, is an arithmetic sequence, simply adding 6 to get the next term's value.
write 18/24 as a percentage
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divide 18 by 24 for a decimal number:
18 / 24 = 0.75
multiply 0.75 by 100 for the percent
0.75 * 100 = 75%
Which choice is the GCF and LCM of 24 and 48? A) GCF = 12, LCM = 12 B) GCF = 24, LCM = 48 C) GCF = 12, LCM = 24 D) GCF = 12, LCM = 48 PLZ HELP FAST
Answers
In how many ways can 3 boys and 3 girls sit in a row if the boys and girls are each to sit together?
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The boys and girls are each to sit together, and there are 3 boys and 3 girls. The total number of ways to arrange them is 36.
Explanation:The boys and girls are each to sit together, meaning that the boys should sit together in one group and the girls should sit together in another group. We can consider these two groups as two separate entities.
The number of ways to arrange the boys within their group is 3! (3 factorial), because there are 3 boys. Similarly, the number of ways to arrange the girls within their group is also 3!. Since these two groups can be arranged independently of each other, the total number of ways to arrange the boys and girls is 3! * 3! = 6 * 6 = 36.
Compute r6r6, l6l6, and m3m3 to estimate the distance traveled over [0, 3] if the velocity at half-second intervals is as follows:
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For R6 and L6, t= (3- 0) / 6= 0.5. For M3, t= (3- 0)/ 3 = 1. Then
For R6 we will add all the velocity given from 12 to 20 and then multiply it by 0.5 seconds
R6 = 0.5 s ( 12 + 18 + 25 + 20 + 14 + 20 ) m/ sec = 0.5 (109) m = 54.5 m,
For L6 we will add all the velocity given from 0 to 14 and then multiply it by 00.5 as well.
L6 = 0.5 sec ( 0 + 12 + 18 + 25 + 20 + 14 ) m/ sec = 0.5 (89 ) m = 44.5 m.
For M3:
M3 = 1 sec (12 + 25 + 14) m/ sec = 51 m.
The question relates to integral calculus and the concept of Riemann sum approximation. The values r6r6, l6l6, and m3m3 need to be calculated given they represent velocities at half-second intervals. The estimated distance travelled would be the sum of these velocities multiplied by their respective time intervals.
Explanation:The task here is to compute the expressions r6r6, l6l6, and m3m3, and use those to estimate the distance traveled over the interval [0,3], if the velocity changes at half-second intervals. From the details, it is indicative this is a problem involving the mathematical concept of integral calculus, specifically the area under velocity-time curve. The overall distance travelled is given by the area under the curve which is the integral of the velocity function over the given interval.
Let's suppose the values r6r6, l6l6, and m3m3 represent velocities at different half-second intervals of time. In order to estimate the total distance travelled, you would need to sum these velocities and multiply by the duration of each interval (0.5 seconds). This concept is also known as Riemann sum approximation in integral calculus.
For example, if r6r6 = 10 m/s, l6l6 = 12 m/s, and m3m3 = 8 m/s, the estimated total distance travelled would be calculated as (10*0.5 + 12*0.5 + 8*0.5) = 5 m + 6 m + 4 m = 15 m.
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Can someone help me with this question?
State the Pythagorean Theorem and tell how you can use it to solve problems
Answers
You can use the Pythagorean theorem to solve for the hypotenuse. For example lets say you have one side (a) equal to 3 and the other side (b) equal to 2. From there you can plug it in and find that the hypotenuse (c) is equal to 3.61
What does it mean? It may help you to draw a right triangle and to draw a square for each side. You can see that the sides of the triangle are the sides of the squares.
Then, if we sum the area of the squares on the sides (because they are equivalent = same area) we get the are of the square on the hypothenuse.
Call "a" and "b" the squares on the sides and "c" the squares on the hypothenuse.
a^2 + b^2 = c^2
Where can this Theorem be used? Of course, where you have to deal with geometry problems, in particular right triangles, rectangles and many more.
For example, we have to find the hypothenuse of a right triangle.
Let's follow the formula and we have that a = 4, b = 3...what's c?
4^2 + 3^2 = c^2
16+9 = c^2
25 = c^2
So, c^2 is 25.
We have c^2 but not c, so how do we solve it?
Simple, do the square root, c = square root of 25 = 5
Of course there are even inverse formulas:
a^2 = c^2 - b^2
b^2 = c^2 - a^2
Which measure of central location is meaningful when the data are categorical?
a. the range
b. the mean
c. the median
d. the mode?
Answers
find the area of the figure (sides meet at right angles)
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18mm
18mm
simplify the expression 2x - 4 + 3x
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I need to have atleast 20 characters so ill add this <3
Divide m2n2/p3 by mp/n2 .
Answers
Hope it helped!
Answer:
The answer is 'm'.
Step-by-step explanation:
Here, the given expression,
[tex]\frac{\frac{m^2n^2}{p^3}}{\frac{mp}{n^2}}[/tex]
[tex]=\frac{m^2n^2\times n^2}{p^3\times mp}[/tex]
[tex]=\frac{m^2n^{2+2}}{p^{3+1}m}[/tex] ( [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=\frac{m^2p^4}{p^4m}[/tex]
[tex]=m^2p^4p^{-4}m^{-1}[/tex] ( [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )
[tex]=m^{2-1}p^{4-4}[/tex]
[tex]=m^1p^0[/tex]
[tex]=m[/tex]
Which set of ordered pairs contains only points that are on the graph of the function y = 12 − 3x?
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Simone paid $12 for an initial years subscription to a magizine. The renewal rate is $8 per year. This situation can be represented by the equation y=8x+12, where x represents the number of years the subscription is renewed and y represents the total cost.
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For example, let x = 0.
y = 8x + 12
y = 8(0) + 12
y = 0 + 12
y = 12
On your table, you have x = 0 and y = 12.
Do the same using other values of x.
The table shows the solution for the linear equation.
What is linear equation?"An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line".
For the given situation,
Cost for initial year subscription = $12
Cost for renewal = $8
The number of years the subscription is renewed be 'x' and
The total cost be 'y'.
This situation can be represented by the equation y = 8x+12.
For this linear equation, we need to make table by substituting different values of x to get y.
For [tex]x=1[/tex]
⇒[tex]y=8(1)+12[/tex]
⇒[tex]y=20[/tex]
For [tex]x=2[/tex]
⇒[tex]y=28[/tex]
For [tex]x=3[/tex]
⇒[tex]y=36[/tex]
For [tex]x=4[/tex]
⇒[tex]y=44[/tex]
For [tex]x=5[/tex]
⇒[tex]y=52[/tex]
The table below shows these interpretations.
Hence we can conclude that the table shows the solution for the linear equation.
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G write the equation in spherical coordinates. (a) 7z2 = 8x2 + 8y2
Answers
Answer:
[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]
General Formulas and Concepts:
Multivariable Calculus
Spherical Coordinate Conversions:
[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle 7z^2 = 8x^2 + 8y^2[/tex]
Step 2: Convert
[Equation] Substitute in Spherical Coordinate Conversions:[tex]\displaystyle 7( \rho \cos \phi )^2 = 8( \rho \sin \phi \cos \theta )^2 + 8( \rho \sin \phi \sin \theta )^2[/tex]Simplify:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi \cos^2 \theta + 8 \rho^2 \sin ^2 \phi \sin^2 \theta[/tex]Factor:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi \bigg( \sin^2 \theta + \cos ^2 \theta \bigg)[/tex]Simplify:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi[/tex]Simplify:
[tex]\displaystyle 7 \cos^2 \phi = 8 \sin^2 \phi[/tex]Rewrite:
[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]
∴ we have found the given equation in terms of spherical coordinates.
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Topic: Multivariable Calculus
Unit: Triple Integrals Applications
When originally purchased, a vehicle costing $24,840 had an estimated useful life of 8 years and an estimated salvage value of $2,600. after 4 years of straight-line depreciation, the asset's total estimated useful life was revised from 8 years to 6 years and there was no change in the estimated salvage value. the depreciation expense in year 5 equals:?
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In bowling you get a spare when you knock down the ten pins in two throws how many possible ways are there to get a spare
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(0,10)
(1,9)
(2,8)
(3,7)
(4,6)
(5,5)
(6,4)
(7,3)
(8,2)
(9,1)
(10,0) <--- doesn't count since that would be a strike!
Counting only the ones that are spares, you'll see there are 10 ways to get a spare (count carefully!)
Answer:
6
Step-by-step explanation:
or more
A right triangle has a hypotenuse of length 20 cm and another side of length 16 cm. what is the length of the third side of the triangle?
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20^2 = 16^2 + x^2 => 400 = 256 + x^2 => 144 = x^2, or x = 12 cm (answer)
In the figure shown, what is the area of the rectangle, if the radius of each circle is 6 cm?
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Thus, the width of the rectangle is 12 cm. and the length is 24 cm.
The area of the rect. is (12 cm)(24 cm) = 288 cm^2
To find the area of the given rectangle with circles at its ends, we need to know the radius of the circles and the length of the rectangle in between. Length of the rectangle would be equal to the diameter of a circle plus the length between the two circles. Then, we multiply this length with the width equivalent to the diameter of the circle.
Explanation:In this Mathematics question, the student is asked to find the area of a rectangle with two circles, each with a radius of 6cm, at its ends.
As we know, the area of a rectangle is found by the formula, Area = Length x Width.
The length of the rectangle can be determined from the radii of the circles, it's equal to the diameter of one of the circles (because the radius of the circle is 6, the diameter would be 2*6=12) plus the length of the rectangle that is between the two circles.
However, the width of the rectangle is smoothly equivalent to the diameter of one of the circles (which is 12cm as calculated).
Once we have both the length and width of the rectangle (assuming the length inside the rectangle is given or predetermined), we can easily determine the area of the rectangle by multiplying these two.
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Compare and contrast Euclidean geometry and spherical geometry. Be sure to include these points:
1. Describe the role of the Parallel Postulate in spherical geometry.
2. How are triangles different in spherical geometry as opposed to Euclidean geometry?
3. Geodesics
4. Applications of spherical geometry
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Final answer:
Euclidean geometry and spherical geometry have distinct characteristics. The Parallel Postulate, triangle properties, geodesics, and applications differ between the two. Euclidean geometry relies on parallel lines, triangles with interior angles summing to 180 degrees, and straight geodesics, while spherical geometry lacks parallel lines, features triangles with angles >180 degrees, and utilizes great circles as geodesics. Spherical geometry finds applications in astronomy, navigation, Earth sciences, and cartography.
Explanation:
Euclidean Geometry vs Spherical Geometry
Euclidean geometry and spherical geometry are two different branches of geometry that have distinct characteristics and applications. Let's compare and contrast them:
1. Role of the Parallel Postulate
In Euclidean geometry: The Parallel Postulate states that given a line and a point not on that line, there is exactly one line that passes through the point and is parallel to the given line.
In spherical geometry: The Parallel Postulate is not true. In fact, there are no parallel lines in spherical geometry. On a sphere, any two lines will eventually intersect.
2. Triangles in Euclidean Geometry vs Spherical Geometry
In Euclidean geometry: Triangles have interior angles that sum up to 180 degrees. The angles of a triangle are classified as acute, obtuse, or right.
In spherical geometry: Triangles have interior angles that add up to more than 180 degrees. In fact, the sum can be greater than 540 degrees. Spherical triangles on a sphere are classified as acute-angled, right-angled, or obtuse-angled based on their angles.
3. Geodesics
In Euclidean geometry: Geodesics are straight lines and shortest paths between two points.
In spherical geometry: Geodesics are great circles or the arcs of circles on the surface of the sphere. They represent the shortest path between two points on a sphere.
4. Applications of Spherical Geometry
Spherical geometry has practical applications in various fields, including:
Astronomy: Spherical coordinates are used to locate celestial objects.
Navigation: Spherical trigonometry helps navigate across the Earth's curved surface.
Earth sciences: Spherical harmonics are used to represent the Earth's gravitational field.
Cartography: Representing the Earth's surface on a map or globe.
PLZ ANSWER I BEG U
An airplane flies to San Francisco from Los Angeles in 4 hours. It flies back in 3 hours. If the wind is blowing from the north at a velocity of 20 mph during both flights, what was the airspeed of the plane (its speed in still air)?
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At a local hospital, 35 babies were born. if 26 were boys, what percentage of the newborns were boys?
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So 26 divided by 35 is 0.7428..... Since the number doesn't end, you round it to the nearest tenth, which is 0.7. Now you multiply that number by 100. And the percentage would be... 70% of the babies would be boys.
I need help with all of them
Answers
I will set up each proportion but you must do the math work.
Part a.
Let s = souvenirs
8/26 = 12/s
Solve for s to find your Part a answer.
Part b.
Let x = snacks
10/x = 20/5
Solve for x to find your Part b answer.
Part c.
Here we must create two proportions.
For Sinea:
Let y = souvenirs
5/40 = 12/y
Solve for y to find how much Sinea spend on souvenirs.
Let k = souvenirs
10/4 = 20/k
Solve for k to find how much Ren spend on souvenirs.
When you find y and k for Part c, subtract the smaller value from the bigger value to find your answer.
Joseph needs to find the quotient of 3.216 ÷8. In what place is the first digit in the quotient?