Answer:
(2a +b)·(13a^2 -5ab +b^2)
Step-by-step explanation:
The factorization of the difference of cubes is a standard form:
(p -q)^3 = (p -q)(p^2 +pq +q^2)
Here, you have ...
p = 3aq = (a-b)so the factorization is ...
(3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q
= (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit
= (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms
Solve the word problem.
Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?
Ron
a0 days
Lee
a1 days
Answer:
Ron: 6+2√5 days ≈ 10.47 days
Lee: 2+2√5 days ≈ 6.47 days
Step-by-step explanation:
Let L represent the number of days it takes Lee to frame a cabin. Then it take L+4 days for Ron to frame it. Working together, they take 4 days. Then their rates, in cabins per day, add up as ...
1/L + 1/(L+4) = 1/4
Multiplying by the product of denominators, we get ...
4(L+4) +4L = L(L+4)
Subtracting the left side gives ...
L^2 -4L -16 = 0
Completing the square, we can write this as ...
L^2 -4L +4 = 20
(L -2)^2 = 20
L = 2 + √20 = 2 +2√5 ≈ 6.47
Lee takes 2+2√5 ≈ 6.47 days to frame a cabin.
Ron takes 6+2√5 ≈ 10.47 days to frame a cabin.
50+50-25*0+2+2=
What is the answer
Answer:
104
Step-by-step explanation:
50+50-25*0+2+2
Order of operations....50+50-0+2+2
This equals to 100+2+2
Then you get the answer of 104.
I hope you understand..
Answer:
104
Step-by-step explanation:
Graph the line passing through the given point and having the indicated slope. through (3, negative 2) with slope minus−three fifths 3/5
Answer:
See the attachment
Step-by-step explanation:
A slope of -3/5 means the line drops 3 units for each 5 units it goes to the right. Then you can find another point on the line by going 5 uints to the left (to x=-2) and 3 units up (to y=1).
Plot the given point and the one just computed and draw the line through them.
You have a coin bank in the shape of a cylinder. It has a radius of 1.5 inches and a height of 5 inches. What is the surface area of the coin bank? Use 3.14 to approximate pi. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
The top and the bottom are easiest to find.
Area_top = pi*r^2
r = 1.5
Area_top = 3.14 * 1.5^2
Area_top = 3.14 * 2.25
Area_top = 7.065
But there are 2 of them (top and bottom) which is 14.13
================
Area of the body of the cylinder
Area body = circumference of the circle * height
C = 2*pi*r
r = 1.5
C = 2 * 3.14 * 1.5
C = 9.42
Area body = 9.42 * 5
Area body = 47.1
===================
The sum of both of these is the answer you want
47.1 + 14.13 = 61.23 square inches.
How can you use a point on the graph of f –1(x) = 9x to determine a point on the graph of f(x) = log9x?
Whenever you can invert a function, you have that the graphs of [tex]f(x)[/tex] and its inverse [tex]f^{-1}(x)[/tex] are reflected with respect to the line [tex]y=x[/tex]
So, given any point on the graph of [tex]f^{-1}(x)[/tex], you can simply swap its coordinates to get the correspondent point on the original function [tex]f(x)[/tex]
As an example, all exponential functions pass through the point [tex](0,1)[/tex], while all the logarithmic functions pass through the point [tex](1,0)[/tex]
Answer: switch x and y coordinates
Step-by-step explanation:
Before it started to rain, Bobby cut 1 8 of the grass in his yard and Danny cut 1 5 of the grass in the yard. Both boys were disappointed because they were not able to cut the entire yard.
Which statement is TRUE?
A)Together the boys didn't even cut half the yard. B) The boys were able to cut more than half the yard. C) The boys cut almost three-fourths of the yard. D) Together the boys cut almost the entire yard.
It’s B. The boys were able to cut more than half the yard.
Answer:
A) Together the boys didn't even cut half the yard.
Step-by-step explanation:
The amount cut was ...
1/8 + 1/5 = 5/40 +8/40 = 13/40
This amount is less than half = 20/40, so choice A is appropriate.
_____
You can reason about these fractions several ways:
1. half is 2 1/2 fifths. 1/8 is less than 1/5, so 1/5+1/8 < (2 1/2)/5.
2. half is 4/8. 1/5 is more than 1/8 but is less than 2/8. 1/8 + 1/5 < 3/8 < 1/2
3. 1/5 < 1/4; 1/8 < 1/4; 1/2 = 2/4, so two amounts less than 1/4 cannot be more than 1/2.
The bear population of yellowstone national park goes from 230 bear to 300 bears. What is the percent of change?
so the difference is 300 - 230 = 70.
now, if we take 230 to be the 100%, what is 70 off of in percentage?
[tex]\bf \hspace{34em}|\\\\ \begin{array}{ccll} amount&\%\\ \cline{1-2} 230&100\\ 70&x \end{array}\implies \cfrac{230}{70}=\cfrac{100}{x}\implies \cfrac{23}{7}=\cfrac{100}{x} \\\\\\ 23x=700\implies x=\cfrac{700}{23}\implies x\approx 30.43[/tex]
Answer:23%
Step-by-step explanation:
300-230=70
70/300=0.23(3 goes on forever)
So 23%
subtract the original with the decreased value, then divide the answer you get with 300. That should equal 0.23 or 23%
A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below.
Which estimate is closest to the volume in cubic millimeters of the part?
A. 65
B. 125
C. 249
D. 446
Answer:
B. 125
Step-by-step explanation:
If you compute the actual volume as the product of the area of the triangle and the length of the piece, you get ...
V = Bh = (1/2)(14.4 mm)(2.1 mm)·(8.25 mm) = 124.74 mm
That is closest to choice B, 125 mm.
___
You can estimate the volume by rounding the dimensions. The triangle can be considered to be a rectangle of the same base width and half the height, so you are looking to estimate the product ...
(8.25 mm)(14.4 mm)(1.05 mm)
That's about 8 × 15 × 1 = 120 . . . . mm³.
Certainly, this is an estimate sufficiently close to allow you to choose the correct answer.
I found the answer!
6 points! Markin Brainliest! 3D Geometry! rectangular prism has a length of 6 cm and a width of 2 cm and a height of 5 cm what is the surface area of the prism enter your answer in the Box.
[ 104 ] cm^2
^
Thats the box btw
The surface area is 104 cm²
Step-by-step explanation:The surface area of rectangular prism is given by
A=2 (wl + hl + hw)
by putting the values we get
A =2 ( 2x6 + 5x6 + 5x2)
A = 104
Read the statement.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Check all that apply.
1)p → q represents the original conditional statement.
2)~p → ~q represents the inverse of the original conditional statement.
3)q → p represents the original conditional statement.
4)~q → ~p represents the converse of the original conditional statement.
5)p → ~q represents the contrapositive of the original conditional statement.
Answer:
1) and 2)
Step-by-step explanation:
Let us see the correction in the rest of the statements.
3) p→q represent the original conditional statement.
4) ~q → ~p represents the contrapositive of the original conditional statement
5) contrapositive of the original conditional statement will be ~q → ~p
There is one more implication called Converse of the original conditional statement . It is represented as q→p
Can someone help me out??
Answer:
see below
Step-by-step explanation:
The figure is completely symmetrical about line RT so ...
ST = UT = 23
RU = RS = 8
SV = UV = 5
SU = SV + UV = 10
Factor form of x^2-x-30
Answer:
(x - 6)(x + 5)
Step-by-step explanation:
You know that in order to get x^2 there has to be two x's so you get:
(x ...)(x...)
Then you also know that two numbers have to multiply together and equal 30 but also have a sume of -1. So you get:
(x - 6)(x + 5)
Answer: [tex](x+5)(x-6)[/tex]
Step-by-step explanation:
To solve the exercise you must keep on mind the following:
- You must find two numbers whose sum is -1 and whose product is -30.
- These numbers would be 5 and -6.
Therefore, you can factor the quadratic equation given in the problem above [tex]x^2-x-30[/tex], as you can see below:
[tex]x^2-x-30\\(x+5)(x-6)[/tex]
The sum of 6 and another number is 23, write and solve an equation to find the other number
Answer: 23 - 6 = x
x = 17
Step-by-step explanation:
6 + x = 23
x = 23 - 6
23 - 6 = 17
x = 17
6 + 17 = 23
Hope this helps!
Answer:
6+x=23
Step-by-step explanation:
So, the number you need to find is x, so x plus 6 equals 23 (the sum of the two numbers).
Hope this helped :)
a survey was given on hours of practice per week and the number of math questions answered correctly. The graph shows the results of the survey. The scatter plot indicates which of the following A.) a positive correlation B.) a negative correlation C.) no correlation
A) a positive correlation
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
v(t) = 32,000(0.95)^t
Find the initial value of the car and the value after 13 years.
Round your answers to the nearest dollar as necessary.
Answer:
v(0) = 32,000 . . . dollars
v(13) = 16,427 . . . dollars
Step-by-step explanation:
The initial value is the value of the function for t=0. Put that into the formula and evaluate.
v(0) = 32,000(0.95^0) = 32,000 . . . . dollars
__
The value after 13 years is the function value for t=13. Put that into the formula and evaluate.
v(13) = 32,000(0.95^13) ≈ 32,000·0.513342 ≈ 16,427 . . . . dollars
If the difference in the values of dependent variables for a function is increasing as values of the independent variable increase, what kind of function does this represent? A) Linear B) Exponential C) Either D) Neither
WILL MARK BRAINLIEST!!!
The answer is b exponential
How do I solve this, and what is the answer? please and thank you.
Answer:
A. (x +8) + (-4x+31)/(x^2+2x+1)
Step-by-step explanation:
When you perform long division of polynomials, the first quotient term is the ratio of the highest-degree terms in the numerator and denominator: x^3/x^2 = x.
This fact eliminates all but choices A and C.
The denominator of the remainder term is the denominator of the original expression, so will be x^2 +2x +1, as shown in choice A.
__
So, simply based on a couple of facts about long division (that you learned in the early elementary grades), you can make the correct choice of answer without actually working the problem in detail.
_____
This is a polynomial long division problem. It is worked in virtually the same way that numerical long division problems are worked: first you find a quotient term, then you multiply that by the divisor and subtract the result from the dividend. The difference is the new dividend. These steps are identical to numerical long division.
For polynomial long division, instead of lining up the digits with the same place value, you line up the terms with the same degree of the variable.
As mentioned above, the quotient term is computed only from the highest-degree terms of dividend and divisor, so that part is actually simpler than for numerical long division.
A dividend that is of lower degree than the divisor is considered to be the remainder. As with numerical long division, it can be expressed as a fraction with the divisor as the denominator.
Numerical example: 18/7 = 2 remainder 4 or 2 4/7.
9x - 4 -6x = 2(x + 1) -5
solve for x and show work, please.
Answer:
x = 1
Step-by-step explanation:
Subtract the right side of the equation and simplify:
9x -4 -6x -2(x +1) +5 = 0
9x -6x -2x -4 -2 +5 = 0 . . . . . eliminate parentheses
x -1 = 0 . . . . . . . . . . . . . . . . . . collect terms
x = 1 . . . . . . . . . . . . . . . . . . . . . add the opposite of the constant
_____
Check
Substitute the value of x where x is found in the equation.
9·1 -4 -6·1 = 2(1 +1) -5
9 - 4 - 6 = 2·2 -5
-1 = 4 -5 . . . . . true. The answer checks OK.
Determine whether the solids are similar.
Answer:
The solids are similar.
Step-by-step explanation:
Every linear dimension of the larger solid is twice that of the smaller solid. Since the scale factor is the same in every direction, the figures are similar.
The Wood family and the Roberts family each used their sprinklers last summer. The water output rate for the Wood family's sprinkler was 25 L
per hour. The water output rate for the Roberts family's sprinkler was15 L
per hour. The families used their sprinklers for a combined total of 60
hours, resulting in a total water output of 1250 L. How long was each sprinkler used?
Answer:
Wood family: 35 hours
Roberts family: 25 hours
Step-by-step explanation:
Let w represent the number of hours the Woods family ran their sprinkler. Then 60-w is the number of hours the Roberts family ran theirs. The total water usage (in liters) was ...
25w + 15(60-w) = 1250
10w = 350
w = 35 . . . . . . Wood family time (hours)
60-w = 25 . . . Roberts family time (hours)
___
Check
(35 h)·(25 L/h) + (25 h)·(15 L/h) = 875 L + 375 L = 1250 L . . . . answer checks OK
Help plz show work please
Alright, so here we have a cone and a cylinder. The cone has a height of 12. The cylinder has a height of 10.5. Both shapes, because they're on top of each other, have a diameter of 26 or a radius of 13.
Equation for a cylinder: [tex]V_{cylinder} = \pi r^{2} h[/tex]
Equation for a cone: [tex]V_{cone} = \frac{1}{3} \pi r^{2} h[/tex]
We're going to add both of the volumes of these shapes as soon as we find them.
Cylinder:
[tex]V_{cylinder} = \pi r^{2} h\\= \pi (13)^{2} (10.5)\\\approx 5574.756[/tex]
Cone:
[tex]V_{cone} = \frac{1}{3} \pi r^{2} h\\= \frac{1}{3} \pi (13)^{2} (12)\\\approx 2123.717[/tex]
Add both values: 2123.717 + 5574.756 = 7698.473 cm³.
Hope this was helpful, let me know if I missed anything!
Answer:
7698.473 cm³.
Step-by-step explanation:
I need to write a 5-paragraph eassy, so please help me it is base on an article name "Schools in Maryland Allow Elementary Students to Carry Cellphones, by Amanda Lenhart, The Washington Post" here are some pic. I just need help writing two paragraph. I already have my Introduction, Body Paragraph #1 and my Body paragraph #2 just need my Body paragraph #3 and my Conclusion I will give brainlis and 30 pnt.
Prompt:
Write an argumentative essay answering the questions: Should students be allowed to carry cellphones on campus? You must support your claim with evidence from the text. You may also use relevant examples from your own experience, observations, and other readings.
Directions:
Before you begin, read the text below, which presents information about the advantages and disadvantages of carrying a cell phone at school. Use the Student Writing Checklist on the back of this page to plan and write a multi-paragraph essay that addresses the prompt. Use your own words, except when quoting directly from the text.
fill 350 milliliter bottles from a 30 liter drum how many bottles
Answer:
85
Step-by-step explanation:
0.350 L × n = 30 L . . . . . where n is the number of bottles.
Divide by 0.350:
n = (30 L)/(0.350 L) ≈ 85.7
85 bottles can be filled, and one can be partially filled.
_____
Of course, you know the SI prefix milli- means 1/1000, so 350 mL = 350/1000 L = 0.350 L. When you do the division indicated above, ...
(30 L)/(0.350 L)
the units of liters cancel, and you are left with the number of bottles.
Plzzz answer all of these questions to get 100 pointd
Answer:
1. 42.8 °C
2. Aceves' class: $133.33; Baca's class: $266.67; Canyon's class: $200.
Step-by-step explanation:
1.) The difference between two numbers is found by subtraction. Since we want to report the positive difference, we can subtract the smaller number from the larger:
-21.2 °C - (-64 °C) = (64 -21.2) °C = 42.8 °C
The temperature must drop 42.8 °C more for the antifreeze to solidify.
_____
2.) We want to divide the prize money in the ratio
1200 : 2400 : 1800 = 2 : 4 : 3
There are 2+4+3 = 9 total ratio units, so each one must stand for $600/9 = $66 2/3.
Then the money to Aceves' class is ...
2 × $66 2/3 = $133 1/3 = $133.33
And the money to Baca's class is ...
4 × $66 2/3 = $266 2/3 = $266.67
Finally, the money to Canyon's class is ...
3 × $66 2/3 = $200.00
___
Note on the division:
The 1/3 cent that Aceves' class should have gotten goes to Baca's class in the above scenario. It might make sense for the classes to donate $6 to the school and divide the remaining $594 as $132 : $264 : $198. If they actually want the pennies, they could donate $0.06 to the school and split the result as $133.32 : $266.64 : $199.98.
Answer:
Step-by-step explanation:
Answer:
1. 42.8 °C
2. Aceves' class: $133.33; Baca's class: $266.67; Canyon's class: $200.
Step-by-step explanation:
1.) The difference between two numbers is found by subtraction. Since we want to report the positive difference, we can subtract the smaller number from the larger:
-21.2 °C - (-64 °C) = (64 -21.2) °C = 42.8 °C
The temperature must drop 42.8 °C more for the antifreeze to solidify.
_____
2.) We want to divide the prize money in the ratio
1200 : 2400 : 1800 = 2 : 4 : 3
There are 2+4+3 = 9 total ratio units, so each one must stand for $600/9 = $66 2/3.
Then the money to Aceves' class is ...
2 × $66 2/3 = $133 1/3 = $133.33
And the money to Baca's class is ...
4 × $66 2/3 = $266 2/3 = $266.67
Finally, the money to Canyon's class is ...
3 × $66 2/3 = $200.00
___
Note on the division:
The 1/3 cent that Aceves' class should have gotten goes to Baca's class in the above scenario. It might make sense for the classes to donate $6 to the school and divide the remaining $594 as $132 : $264 : $198. If they actually want the pennies, they could donate $0.06 to the school and split the result as $133.32 : $266.64 : $199.98.
Suppose f is a differentiable function such that f′(x)≤2 for all x∈[1,3]. If f(1)=4, the Mean Value Theorem says that f(3)≤V for what value of V? (Choose V as small as possible.)
The MVT guarantees the existence of [tex]c\in(1,3)[/tex] such that
[tex]f(c)=\dfrac{f(3)-f(1)}{3-1}=\dfrac{f(3)-4}2[/tex]
Since [tex]f'(x)\le2[/tex] for all [tex]x\in[1,3][/tex], we have
[tex]\dfrac{f(3)-4}2\le2\implies f(3)-4\le4\implies f(3)\le8[/tex]
so that [tex]V=8[/tex].
The mean value theorem is used to link the average rate of change and the derivative of a function.
The value of V is 8.
The given parameters are:
[tex]\mathbf{f'(x) \le 2}[/tex]
[tex]\mathbf{f(1) = 4}[/tex]
[tex]\mathbf{f(3) \le V}[/tex]
[tex]\mathbf{x \in [1,3]}[/tex]
Mean value theorem states that:
If [tex]\mathbf{f(x)\ is\ continuous\ at }[/tex] [a,b] and
[tex]\mathbf{f(x)\ is\ differentiable\ on }[/tex] (a,b),
Then there is a point c in (a,b), such that:
[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
From the question, we understand that: f is differentiable
This means that:
[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]
So, we have:
[tex]\mathbf{f'(c) = \frac{f(3) - f(1)}{3 - 1}}[/tex]
[tex]\mathbf{f'(c) = \frac{f(3) - f(1)}{2}}[/tex]
Substitute 4 for f(1)
[tex]\mathbf{f'(c) = \frac{f(3) -4}{2}}[/tex]
Recall that: [tex]\mathbf{f'(x) \le 2}[/tex]
The equation becomes
[tex]\mathbf{\frac{f(3) -4}{2} \le 2}[/tex]
Cross multiply
[tex]\mathbf{f(3) -4 \le 4}[/tex]
Add 4 to both sides
[tex]\mathbf{f(3) \le 8}[/tex]
From the question, we have: [tex]\mathbf{f(3) \le V}[/tex]
By comparisons;
[tex]\mathbf{V = 8}[/tex]
Hence, the value of V is 8.
Read more about mean value theorems at:
brainly.com/question/3957181
( l = P + P • r • t )
Answer:
$19,720
Step-by-step explanation:
Put the given numbers into the formula and do the arithmetic.
P = principal amount, $17,000
r = interest rate, 8% = 0.08
t = 2 years
"I" = P + Prt
I = $17000 + $17000·0.08·2 = $17000 +2720
I = $19,720
_____
I put "I" in quotes because the variable capital-I is usually used in this context to refer to the amount of interest paid, not the entire repayment amount. However, that is what your formula is. It works for what you want.
Vivian is solving the equation 0=x2−5x−4 0 = x 2 − 5 x − 4 using the quadratic formula. Which value is the negative real number solution to her quadratic equation? Round to the nearest tenth if necessary. -5.7 -4 -1 -0.7
-0.7
steps:the quadratic formula is
[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
substitute the correct values in
[tex] \frac{ - ( - 5) + - \sqrt{ {( - 5)}^{2} - 4(1)( - 4) } }{2(1)} [/tex]
where it says +- you would type this into your calculator with + AND THEN - to get two separate answers.
when you type + you get the answer of: 5.701562119...
when you type - you get the answer of:
-0.7015621187...
when you round to the nearest tenth you get -0.7
hope this helps! :)
have a great day ~ •lipika•
Rich is buying a home for $244,800. He is making a 15% down payment and financing the rest with a 25-year loan a 5.25% interest
A. $1149.02
B. $1216.44
C. $1246.82
D. $1466.84
Answer:
C. $1246.82
Step-by-step explanation:
Using the factor shown in the table for a 25-year loan at 5.25%, the calculated payment is ...
5.992·(244.8·0.85) = 1246.82
The factor of 0.85 on the home price represents the effect of subtracting 15% from the price to get the loan value. Of course, the home price is the number of thousands, so is 244.8 thousand.
_____
If you do the calculation, rather than use a factor from a table, you get a mortgage payment value of $1246.91. This suggests that the numbers in the table need more significant digits for loan values this high.
Answer:
C is your answer
what is the area of this figure
Answer:
54 square units
Step-by-step explanation:
A line (red in the attachment) can divide the figure into two triangles and a trapezoid. The formulas for the areas of these are ...
area of a triangle = (1/2)bh . . . . . where b is the base and h is the height
The triangle on the upper left has a base of 3 and a height of 2, so an area of ...
upper left triangle area = (1/2)(3)(2) = 3 square units . . . . area shown in red
The triangle on the upper right has a base of 6 and a height of 1, so an area of ...
upper right triangle area = (1/2)(6)(1) = 3 square units . . . . area shown in yellow
___
The formula for the area of a trapezoid is ...
area of a trapezoid = (1/2)(b1 +b2)h . . . . where b1 and b2 are the lengths of the parallel bases, and h is the height
The trapezoid has an upper base length of 9 and a lower base length of 7, and a height of 6, so its area is ...
area of bottom trapezoid = (1/2)(9 + 7)(6) = 48 square units . . . . area shown in green
___
Then the total area of the figure is the sum of the areas of its non-overlapping parts:
total area = upper left triangle area + upper right triangle area + trapezoid area
= (3 + 3 + 48) square units = 54 square units
MARKING BRAINLIEST!!!
The graph shows two lines, A and B.
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
(4, 4) is the solution to line A but not to line B.
(4, 4) is the solution to both lines A and B.
(5, 1) is the solution to line B but not to line A.
(0, 2) is the solution to both lines A and B.
Answer:
(4, 4) is the solution to both lines A and B.
Step-by-step explanation:
The solution to a system of equations is the point at which the two lines intersect. Lines A and B intersect at point (4,4). This means (4,4) is the point which makes both equations true for the same values. The correct answer is "(4, 4) is the solution to both lines A and B."
a small baseball stadium 6552 seats the seats are evenly distributed among 18 different section. how many seats are in each section of the stadium
Answer:
3. 364
4. F 11.45
Step-by-step explanation:
3. 1/18 of the total number of seats in the stadium are found in each section. That number is ...
1/18 · 6552 = 364 . . . . seats in one section
__
4. The numbers round to tenths as follows:
F — 11.5
G — 11.6
H — 11.3
J — 12.5
Perhaps you can see that the one that rounds to 11.5 is ...
F 11.45
Answer:
364
Step-by-step explanation:
6552/ 18