Answer:
24p
Step-by-step explanation:
This is the difference of 2 squares:- a^2 - b^2 = (a + b)(a - b).
So here we have:-
(2p + 3)^2 - (2p - 3)^2
= (2p + 3 + (2p - 3))(2p + 3 - (2p - 3))
= (2p + 3 + 2p - 3)(2p + 3 - 2p + 3
= 4p * 6
= 24p (answer)
Final answer:
To simplify the expression (2p+3)² - (2p-3)², apply the difference of squares formula to get ((2p+3) + (2p-3)) * ((2p+3) - (2p-3)), which simplifies to 24p.
Explanation:
To simplify the expression (2p+3)² - (2p-3)², we need to apply the difference of squares formula, which is
a² - b² = (a+b)(a-b).
Here, a is (2p+3) and b is (2p-3). The result will be the product of the sum and difference of a and b.
Let's perform the simplification step-by-step:
Simplify both products:
(4p) * (6)
Finally, multiply the results to get the simplified expression:
24p
The simplified result of the expression (2p+3)² - (2p-3)² is 24p.
A small cruising ship that can hold up to 66 people provides three-day excursions to groups of 42 or more. If the group contains 42 people, each person pays $58. The cost per person for all members of the party is reduced by $1 for each person in excess of 42. Find the size of the group that maximizes income for the owners of the ship.
50 people
Step-by-step explanation:Let x represent the number of people on the cruise. The amount they each must pay is ...
... ($58 -(x -42)) = $100 -x
The revenue from the group is the product of the number of people and the amount each pays:
... r(x) = x·(100 -x)
This describes a downward-opeing parabola with zeros at x=0 and x=100. The vertex (maximum) will be found halfway between those zeros, at x=50.
A group size of 50 maximizes revenue from the cruise.
Which exponential function is represented by the graph?
f(x) = 2(3x)
f(x) = 3(3x)
f(x) = 3(2x)
f(x) = 2(2x)
f(x) = 3·2^x
Step-by-step explanation:When x=0, any exponential term will have a value of 1, so the y-intercept is the multiplier of the exponential function. Here, it is 3.
When x=1, the exponential term will have a value equal to its base, so the multiplier just found will be multiplied by the base value. Here, f(1) = 3·2, so the base of the exponential term is 2.
Given these considerations, the function is ...
... f(x) = 3·2^x
_____
Comment on notation
The caret (^) is used to signify an exponent. When the exponent consists of anything other than a single number or variable, it must be put in parentheses: 2^(1/2), for example.
The expressions you have written all look like linear functions.
(3a^2)^3 in simplest form
Answer:
27 ^6
Step-by-step explanation:
The first step is to split the expression into 2 parts (ab)^x = a^x b^x
(3a^2)^3
3^3 a^2 ^3
27 a^2^3
We can then us the power of power rule to simplify the exponents x^a^b = x^(ab)
27 a^(2*3)
27 ^6
I WILL GIVE THE BRAINLIEST
Answer:
[tex]a=6[/tex], [tex]b=6\sqrt{2}[/tex], [tex]c=2\sqrt{3}[/tex], and [tex]d=6[/tex]
Step-by-step explanation:
Looking at the left triangle, we can solve for [tex]a[/tex] and [tex]c[/tex].
a:
[tex]a[/tex] is to the opposite side of 60° angle, also we know the hypotenuse, [tex]4\sqrt{3}[/tex]. The ratio that relates opposite with hypotenuse is SINE. Thus we can write:
[tex]sin(A)=\frac{opposite}{hypotenuse}\\sin(60)=\frac{a}{4\sqrt{3}}\\[/tex]
Cross multiplying and solving for [tex]a[/tex]:
[tex]sin(60)=\frac{a}{4\sqrt{3} }\\a=sin(60)*4\sqrt{3}\\a=\frac{\sqrt{3}}{2}*4\sqrt{3}\\a=\frac{12}{2}=6[/tex]
( we know [tex]sin(60)=\frac{\sqrt{3}}{2}[/tex] and also [tex]\sqrt{a}*\sqrt{a}=a[/tex] )
c:
[tex]c[/tex] is to the adjacent side of 60° angle, also we know the hypotenuse, [tex]4\sqrt{3}[/tex]. The ratio that relates adjacent with hypotenuse is COS. Thus we can write:
[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(60)=\frac{c}{4\sqrt{3}}[/tex]
Cross multiplying and solving for [tex]c[/tex]:
[tex]cos(60)=\frac{c}{4\sqrt{3}}\\c=cos(60)*4\sqrt{3}\\c=\frac{1}{2}*4\sqrt{3}\\c=2\sqrt{3}[/tex]
( we know [tex]cos(60)=\frac{1}{2}[/tex] )
Looking at the triangle to the right, we can solve for [tex]b[/tex] and [tex]d[/tex].
b:
[tex]a[/tex] is to the opposite side of 45° angle. We have figured out that [tex]a=6[/tex]. Also we know that [tex]b[/tex] is the hypotenuse.The ratio that relates opposite with hypotenuse is SINE. Thus we can write:
[tex]sin(A)=\frac{opposite}{hypotenuse}\\sin(45)=\frac{6}{b}\\b=\frac{6}{sin(45)}\\b=\frac{6}{\frac{1}{\sqrt{2}}}\\b=6*\frac{\sqrt{2}}{1}\\b=6\sqrt{2}[/tex]
( we know [tex]sin(45)=\frac{1}{\sqrt{2}}[/tex] )
d:
To solve for [tex]d[/tex], we can use the pythagorean theorem. Given by:
[tex]a^2+b^2=c^2[/tex]
Where,
[tex]a[/tex] and [tex]b[/tex] are two legs of the right triangle, and [tex]c[/tex] is the hypotenuse (side opposite 90 degree angle)In the triangle on the right, [tex]b[/tex] is the hypotenuse and [tex]a[/tex] and [tex]d[/tex] are the two legs. Using pythagorean theorem and solving for [tex]d[/tex], we get:
[tex]d^2+a^2=b^2\\d^2+(6)^2=(6\sqrt{2})^2\\d^2+36=72\\d^2=72-36\\d^2=36\\d=6[/tex]
( we know that [tex]\sqrt{a}*\sqrt{a}=a[/tex] )
Looking at the answers, 2nd answer choice is right.
Eva left her home and drove for 4.3 hours due north at a rate of 60 miles per hour. After visiting a beach, she drove due south for 3.4 hours at 55 miles per hour.How far is Eva from her home?
Answer:
15
Step-by-step explanation:
i will give brainlest thanks
Answer:
68
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
... Tan = Opposite/Adjacent
For this geometry, this means ...
... tan(x°) = 5/2
Taking the inverse tangent, we can find x.
... x° = arctan(5/2) ≈ 68.199°
... x ≈ 68
Fill in the blank: linear functions grow by equal ____________ over equal intervals.
A. expressions
B. variables
C. factors
D. differences
Answer:
D. differences
Step-by-step explanation:
One way to identify a linear function is by checking the differences over equal intervals. If they are the same, then the function is linear.
Answer:
D. Differences
Step-by-step explanation:
Linear function grow by equal differences over equal intervals as, on a graph, it is shown by a steady increasing line. Exponential functions, on the other hand, do not.
b(1)=-2
b(n)=b(n-1)-7
Find the third term in the sequence
b(3) = -16
Step-by-step explanation:b(2) = b(1) -7 = -2 -7 = -9
b(3) = b(2) -7 = -9 -7 = -16
Answer: b(3)= -16
Step-by-step explanation:
Solve. 3(3x+10)=50−x
Answer:
x=2
Step-by-step explanation:
3(3x+10)=50−x
The first step is to distribute the 3
3*3x + 3*10 = 50-x
9x+30 = 50-x
Add x to each side
9x+x+30 = 50-x+x
10x+30 = 50
Subtract 30 from each side
10x+30-30 = 50-30
10x= 20
Divide each side by 10
10x/10=20/10
x =2
Which pairs of triangles can be shown to be congruent using rigid motions?
Select Congruent or Not Congruent for each pair of triangles.
Answer:
Congruent; Not Congruent; Congruent; Not Congruent; Not Congruent; Congruent
Step-by-step explanation:
We will use the distance formula to find the length of each segment:
[tex]AB=\sqrt{(-4--3)^2+(4-2)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\BC=\sqrt{(-3--1)^2+(4-1)^2}=\sqrt{(-2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\AC=\sqrt{(2-1)^2+(-4--1)^2}=\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
In order for ABC to be congruent to DEF, AB must be congruent to DE, BC must be congruent to EF, and AC must be congruent to DF:
[tex]DE=\sqrt{(4-3)^2+(-2--4)^2}=\sqrt{(1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\EF=\sqrt{(3-1)^2+(-4--1)^2}=\sqrt{(2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}\\\\DF=\sqrt{(4-1)^2+(-2--1)^2}=\sqrt{(3)^2+(-1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
Since AB is congruent to DE, BC is congruent to EF and AC is congruent to DF, the two triangles are congruent.
In order for ABC to be congruent to JKL, AB must be congruent to JK, BC must be congruent to KL, and AC must be congruent to JL. We know the measurements of AB, BC and AC;
[tex]JK=\sqrt{(-4--2)^2+(-1--3)^2}=\sqrt{(-2)^2+(2)^2}=\sqrt{4+4}=\sqrt{8}\\\\KL=\sqrt{(-2--1)^2+(-3-0)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}\\\\JL=\sqrt{(-1--4)^2+(0--1)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
While AC is congruent to JL, the other two corresponding pairs of sides are not congruent. Therefore the triangles are not congruent.
In order for ABC to be congruent to QRS, AB must be congruent to QR, BC must be congruent to RS, and AC must be congruent to QS. We know the measurements of AB, BC and AC;
[tex]QR=\sqrt{(3-4)^2+(3-1)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\RS=\sqrt{(3-1)^2+(3-0)^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\QS=\sqrt{(4-1)^2+(1-0)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
Since AB is congruent to QR, BC is congruent to RS, and AC is congruent to QS, this means that the two triangles are congruent.
Since ABC is congruent to DEF, and ABC is not congruent to JKL, this means that triangle DEF is not congruent to triangle JKL.
Since ABC is congruent to QRS, and QRS is not congruent to JKL, this means that triangle QRS is not congruent to JKL.
Since ABC is congruent to DEF and ABC is congruent to QRS, this means that DEF is congruent to QRS by the transitive property.
In the figure below, figure ABCD is similar to figure WXYZ. What is the length of side XY?
Answer:
XY = 150
Step-by-step explanation:
AB = 8
W Z = 80
SF = 10
8 x 10 = 80
So if BC = 15
XY = 15 x 10 = 150
Answer:
150Step-by-step explanation:
you can solve with a proportion
8 : 15 = 80 : x
x = 15 * 80 : 8
x = 150
or you find the rate from AD and WZ
8 : 80
simplify
1 : 10
15 * 10 = 150
Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the same? Yoga Studio A: Membership: $24.00 Monthly Fee: 21.50. Yoga Studio B: Membership: $41.00 Monthly Fee: $17.25
In 4 months, the total cost of Yoga Studio A would equal that of Yoga Studio B
The cost of Yoga Studio A at any given month can be represented as:
= Membership fee + (Monthly fee x Number of months)
Assuming number of months is x, the formula would be:
= 24 + (21.50 × x)
= 24 + 21.50x
Yoga Studio B would be:
= 41 + (17.25 × x)
= 41 + 17.25x
In order to find the month that these costs would be equal, equate both formulas:
24 + 21.50x = 41 + 17.25x
21.50x - 17.25x = 41 - 24
4.25x = 17
x = 17 / 4.25
x = 4 months
In conclusion, their costs would be the same in the 4th month.
Find out more at https://brainly.com/question/21586729.
convert fractions to a fraction out of 100.
15/60=?
30/60=?
25/75=?
The numerator can be found by multiplying each of these fractions by 100. It can be helpful to reduce these fractions first.
Here, we calculate those numerators.
a) 15/60 · 100 = 1/4 · 100 = 100/4 = 25
b) 30/60 · 100 = 1/2 · 100 = 100/2 = 50
c) 25/75 · 100 = 1/3 · 100 = 100/3 = 33 1/3
Of course, the denominator is 100, so the fractions are ...
... 15/60 = 25/100
... 30/60 = 50/100
... 25/75 = (33 1/3)/100
_____
Comment on this solution
Effectively, we have multiplied each fraction by 1 = 100/100. That is ...
... fraction × (100/100) = (fraction × 100)/100
This changes the form, but not the value.
Someone please help me
Step-by-step explanation:
1. See the attachment for the filled-in diagram. Adding the contents of the figure gives the sum at the bottom, matching selection C.
2. If we let "d" represent the length of the second volyage, then the total length of the two voyages is ...
... (d+43) + d = 1003
... 2d = 960 . . . . . . . subtract 43
... d = 480 . . . . . . . . divide by 2
The second voyage lasted 480 days.
3. 1.9% - 1.9/100 = 0.019. Adding this fraction to the original means the original is multiplied by 1 +0.019 = 1.019. Doing this multiplication each year for t years means the multiplier is (1.019)^t.
Since the starting value (in 1975) is 4 (billion), the population t years after that is ...
... P(t) = 4(1.019)^t
One of the same side angles of two parallel lines is three times the other angle. Find the measures of these two angles.
45° and 135°
Step-by-step explanation:If the smaller is represented by x, then the larger is 3x. The two angles are supplementary, so ...
... x + 3x = 180°
... 4x = 180°
... 180°/4 = x = 45°
... 3x = 135°
The two angles are 45° and 135°.
Answer:
45° and 135°
Step-by-step explanation:
If the smaller is represented by x, then the larger is 3x. The two angles are supplementary, so ...
... x + 3x = 180°
... 4x = 180°
... 180°/4 = x = 45°
... 3x = 135°
The two angles are 45° and 135°.
Step-by-step explanation:
Which is the closest to the value of x?
Answer:
17.9
Step-by-step explanation:
Here we are given a right angled triangle with a known angle of 72°, length of the perpendicular to be 17 feet and we are to find the length of the hypotenuse x.
For that, we can use the formula for sin for which we need an angle and the lengths of base and hypotenuse.
[tex]sin \alpha =\frac{perpendicular}{x}[/tex]
So putting in the given values to get:
[tex]sin 72=\frac{17}{x} [/tex]
[tex]x=\frac{17}{sin 72}[/tex]
[tex]x=17.8[/tex]
Therefore, the length of six cars is the closest to 17.9.
Max wants to know if the following is correct.3+5=6+2. Draw and write to tell how you know.
Answer:
Yes
Step-by-step explanation:
3+5 is 8 and 6+2 is also 8. You can draw 3 apples with 5 other apples, and count that there are 8 of them and draw 6 apples with 2 other apples that make up 8 apples. Or you can rearrange the apples to be 5 and 3 and 6 and 2.
Prove that for any value of x the value of the expression x^4–(x^2–7)(x^2+7) is equal to 49.
Multiplying it out using the distributive property, you have ...
... x^4 -(x^4 -7x^2 +7x^2 -49)
... = x^4 -x^4 +7x^2 -7x^2 +49 . . . . distribute the minus sign
... = x^4(1 -1) +x^2(7 -7) +49 . . . . . . collect like terms
... = 0 +0 + 49 . . . . . . . . . . . . . . . . . .simplify
... = 49
Use the graph to find the solution to this system of linear equations. y = 58x + 18 and y = -12x – 1
To find the solution to the system of linear equations, set the equations equal to each other and solve for x. Then substitute this value back into either of the equations to find y.
Explanation:To find the solution to the system of linear equations, we can set the equations equal to each other:
58x + 18 = -12x - 1
Combining like terms, we get:
70x = -19
Divide both sides by 70:
x = -19/70
Substitute this value back into either of the equations to find y:
y = 58(-19/70) + 18 = -10.2
Therefore, the solution to the system of linear equations is x = -19/70 and y = -10.2.
The graph shows the distance a cyclist traveled in yards (y) as a function of time in seconds (x). The graph is divided into four segments; labeled P, Q, R, and S, respectively.
Which segment did the cyclist complete before stopping for a drink of water?
P
Q
R
S
Answer:
P
Step-by-step explanation:
The distance doesn't change during segment Q, so that is when the cyclist is stopped. The segment before that is labeled P.
The question asks the label of the segment before the one where the cyclist was stopped, so the appropriate choice is P.
Answer:
it is Q
Step-by-step explanation:
Because it is stopped and its a strait line making it look like it is taking a brake.
Solve the equaton for x.
3x = -4y
A. x = -12y
B. x = -12/y
C. x = -3/4y
D. x = -4y/3
3x = -4y
To solve for X, divide both sides by 3:
x = -4y / 3
The answer is D.
True or false: the variable in an exponential function is always the exponent of the power.
Answer:
False
Step-by-step explanation:
It is the exponent of a base.
The variable in an exponential function is always the exponent of the power is false.
What are exponential functions?When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.
Their usual form is specified below. They are written in several such equivalent forms.
The variable in an exponential function is always the exponent of the power is false. It is the exponent of a base.
Learn more about exponential here:
https://brainly.com/question/12608685
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If one card is drawn from a standard 52- card deck and not replaced, what is the probabity of getting an ace on the next draw?
Answer:
The probability is about 7.7%
Step-by-step explanation:
A probability is the ratio of the number of relevant outcomes and the number of all possible outcomes. To answer this question we do some counting first:
Consider two draws. We are interested in the second draw being an Ace, the first draw can either be an Ace or not, so, there are two cases of a relevant outcomes (all without replacement):
(number of relevant oucomes n ) = (number of cases of Ace-Ace draws) + (number of cases of NonAce-Ace draws):
[tex]n=4\cdot 3+{48\cdot4}= 204[/tex]
(number of possible outcomes) = (number of choices at first draw) * (number of choices at second draw) = 52 * 51 = 2652
The probability is then
P = 204/2652 = 0.0769, or about 7.7%
Either Table A or Table B shows a proportional relationship.
Table A:
x −2 −1 0 1
y 2 3 0 5
Table B:
x −1 0 1 2
y −3 0 3 6
nvm you dont have to answer this i just found out the answer
Answer:
Table B shows a proportional relationship.
Step-by-step explanation:
In a proportional relationship two quantities vary directly with each other. It means
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
Where, k is the constant of variation.
The ordered pairs of table A are (-2,2), (-1,3), (0,0) and (1,5).
From these ordered pairs we can conclude that the value of y-coordinate is not changing according to the x-coordinate because the values of x increased by 1 for each ordered pair but the value of y is not increasing in the same proportion..
The ordered pairs of table B are (-1,-3), (0,0), (1,3) and (2,6). The value of y increasing at a constant rate 3 and the value of y-coordinate is 3 times of x-coordinate.
Choose any two ordered pairs of table B. Let the two points are (0,0) and (1,3), then the constant of variation is
[tex]k=\frac{y_2-y_1}{x_2-x_1}=\frac{3-0}{1-0}=3[/tex]
The proportional relationship is defined as
[tex]y=3x[/tex]
Therefore, 3 is the constant of variation and rate of change.
So, Table B shows a proportional relationship.
Answer:
Table B Shows proportional relationship.
Step-by-step explanation:
Correct answers are the green and yellow dots. Hope this helps. The red dot I got wrong.
The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?
Answer:
65550 is the population at the end of 2017
Step-by-step explanation:
Population at the beginning of 2106: 60000
Increased 15% in 2016
Increase = 60000*.15 = 9000
New population = 60000+9000 = 69000
The population at the beginning of 2017: 69000
Decrease by 5% in 2017
Decrease 69000*.05 = 69000*.05 = 3450
New population = 69000-3450=65550
The population at the end of 2017 is 65550
A postal delivery service charges $3.40 per package and then an additional $0.50 per ounce the package weighs. The function can be modeled by f(x)= 0.5 +3.4. Tom ships 4 packages with the following weights: 2 ounces, 3.5 ounces, 15 ounces, and 21.3 ounces. Write four statements using function notation that evaluate the function given each of these weights. Interpret the results in terms of the context of the function.
The function you're to evaluate is
... f(x) = 0.5x +3.40
Using function notation, the value for x = 2 is ...
... f(2)
For x = 3.5, the value is ...
... f(3.5)
and so on.
To actually evaluate the function, you need to put the value where x is in the function definition and do the arithmetic:
... f(2) = 0.5·2 + 3.40 = 1.00 +3.40 = 4.40
_____
The function gives the charge for a package based on its weight in ounces. The result of evaluating the function for the given weights is that you find the charges for delivery of those packages.
Kayla ran L laps around a 14-mile track. The equation d = 0.25L gives the number of miles she ran. If d is 1.5, which statement does NOT describe what L is?
A. The unknown in the equation.
B. The number of laps Kayla ran.
C. The length of one lap.
D. The number of laps needed to run 112 miles.
Answer:
C. The length of one lap.
Step-by-step explanation:
In the first four words, the problem statement tells you that L is the number of laps run. It is not the length of one lap.
_____
Comment on the problem presentation
Appropriate punctuation would be very helpful. Apparently, it is a 1/4-mile track, not a 14-mile track. Apparently, the distance is 1 1/2 miles, not 112 miles. Copying and pasting problem text often leaves out the special symbols used on some web sites. Some editing is usually needed.
Given f '(x) = (x − 4)(6 − 2x), find the x-coordinate for the relative minimum on the graph of f(x).
Answer:
x = 3
Step-by-step explanation:
f'(x) = 0 for x = 3 and x = 4 . . . . by the zero product rule.
The coefficient of x² in f'(x) is negative, so the parabola opens downward.
f''(x) is positive for x < 3.5, so the coordinate x = 3 represents a relative minimum.
estimate 8 2/9- 3 6/7
Answer:
4
Step-by-step explanation:
8 2/9 is close to 8
3 6/7 is close to 4
8 2/9 - 3 6/7 is close to 8-4 = 4
My estimate is 4
Algebra 2 help!
What are the x and y intercepts of the equation?
Round the answers to the nearest hundredth.
y = log(12x + 7) - 3
Answer:
x-intercept: 82.75y-intercept: 2.15Step-by-step explanation:
A graphing calculator can show you the intercepts.
___
Or you can figure them out.
The y-intercept is where x=0, so is ...
y = log(12·0 +7) -3 = log(7) -3 ≈ -2.1549 ≈ -2.15
___
The x-intercept is where y = 0, so is ...
0 = log(12x +7) -3
3 = log(12x +7) . . . . . . add 3
10^3 = 12x +7 . . . . . . . take the antilog
993 = 12x . . . . . . . . . . subtract 7
993/12 = x = 82.75 . . . divide by the coefficient of x