Answer:
Step-by-step explanation:
We have given:
-2x+y=4 ---------equation1
3x+4y=49 ---------equation 2
We will solve the 1st equation for y and substitute the value into the 2nd equation.
-2x+y=4 ---------equation1
Move the values to the R.H.S except y
y = 2x+4
Now substitute the value of y in 2nd equation:
3x+4y=49
3x+4(2x+4)=49
3x+8x+16=49
Combine the like terms:
3x+8x=49-16
11x=33
Now divide both the sides by 11
11x/11 = 33/11
x= 3
Now substitute the value of x in any of the above equations: We will substitute the value in equation 1:
-2x+y=4
-2(3)+y=4
-6+y=4
Combine the constants:
y=4+6
y = 10
Thus the solution set of (x,y) is {(3,10)}....
Find the slope of the vertical line that passes through (2,-4)
Answer:
x=2
Step-by-step explanation:
Vertical lines have the same x value all the time. It is of the form x=
Their slope is undefined
The line passes through the point (2,4) and the x value is 2
x=2
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5. Ir there were 3822 yes votes, what was the total
number of votes?
total votes
Answer:
The total number of votes was [tex]7,007[/tex]
Step-by-step explanation:
Let
x -----> the number of yes votes
y -----> the number of no votes
we know that
[tex]\frac{x}{y} =\frac{6}{5}[/tex]
isolate variable y
[tex]y=\frac{5}{6}x[/tex] -----> equation A
[tex]x=3,822[/tex] -----> equation B
Substitute equation B in equation A and solve for y
[tex]y=\frac{5}{6}(3,822)=3,185[/tex]
therefore
To find out the total number of votes sum the number of yes votes plus the number of no votes
[tex]3,822+3,185=7,007[/tex]
Answer: 7,007 votes :)
Step-by-step explanation:
Hope that helps
You need 300 mL of a 65% alcohol solution. On hand, you have a 50% alcohol mixture. How much of the 50% alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need
____ mL of the 50% solution
and
______ mL of pure alcohol.
Answer:
You will need 220 mL of the 60% solution and 80 mL of pure alcohol.
Step-by-step explanation:
Let 'x' be the amount of 50% alcohol solution and y the amount of pure alcohol.
Therefore:
(0.5x + y)/300 = 0.65 ⇒ 0.5x + y = 190
x + y = 300
Solving the sistem of equations:
x = 220 and y = 080
Therefore, You will need
220 mL of the 60% solution
and 80 mL of pure alcohol.
Which is greater than 4.026?
A. 4.020
B. 4.030
C. 4.021
D. 4.006
Answer:
b
Step-by-step explanation:
Answer:
B. 4.030
Step-by-step explanation:
We need to compare 4.026 with the numbers int he four choices.
All number have the same whole number part, 4.
To compare them, all you need to do is compare the decimal part.
All numbers have 3 places after the decimal point, so the decimal parts are all in thousandths.
A. 4 and 20 thousandths
B. 4 and 30 thousandths
C. 4 and 21 thousandths
D. 4 and 6 thousandths.
The number you are given is 4 and 26 thousandths.
Of all the thousandths in the choices, only 30 thousandths is greater than 26 thousandths, so 4.030 is the only number greater than 4.026.
Koalas absorb only 25% of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. How many ounces of fiber did he eat that day?
42 ounces
Step-by-step explanation:In this question, it is asking how many ounces of fiber did the Koala eat that day.
In order to solve this question, we would need to gather some important information from the question.
Important Information:
Koalas absorb only 25% of fiber they eatKoala absorbed 10.5 ounces of fiber in 1 dayWith the information above, we can solve the question.
We know that koalas only absorb 25% of fiber. We also know that a koala absorbed 10.5 ounces of fiber.
This means that the 10.5 ounces is 25% of fiber. This is 1/4 of the fiber it ate.
Now, we just need to find the other 3/4.
We could just multiply 10.5 by 4 to find how much fiber it ate that day.
[tex]10.5*4=42[/tex]
When you multiply, you should get 42.
This means that the Koala ate 42 ounces of fiber that day.
I hope this helps you out.Good luck on your academics.Have a fantastic day!Answer:
42
Step-by-step explanation:
We seek the answer to the question "10.5 ounces is 25% of what number?" If we call the unknown number of ounces x, we have the equation 10.5=0.25x. Dividing both sides by 0.25, we have x=10.5/0.25=42 ounces of fiber.
Which of the following is a key property of the absolute value parent function? A. It is in quadrants III and IV B. It is U shaped C. It’s vertex is at the origin. D. It has a slope of 1 on the left side
The key property of the absolute value parent function is:
C. It’s vertex is at the origin.
Step-by-step explanation:The absolute value parent function is given by:
[tex]f(x)=|x|[/tex]
The graph of such a function is a V-shaped graph such that the vertex of the graph is located at origin i.e. (0,0) and the function takes non-negative values for all the real numbers.i.e. the graph of the function lie in the first and second quadrant.
Also, to the left side of the y-axis the graph is decreasing continuously i.e. the graph has a negative slope.what is sin 62° ? apexxx
Answer:
D. 15/17
Step-by-step explanation:
Sine is opposite/hypotenuse and the opposite side to 62 degrees is 15 while the hypotenuse is 17
The value of sin 62° will be equal to 15/17.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The formula for sin angle is given as:-
SinФ = Perpendicular / Hypotenuse
From the figure, Perpendicular is 15 and the hypotenuse is 17 so the value will be:-
Sin62° = 15 / 17
Therefore the value of sin 62° will be equal to 15/17.
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ZE is the angle bisector of measure YEX and the perpendicular bisector of GF, GX is the angle bisector of measure YGZ and the perpendicular bisector of EF, FY is the angle bisector of measure ZFX and the perpendicular bisector of EG. Point A is the intersection of EZ, GX, and FY.
Answer:
C
Step-by-step explanation:
The center of inscribed circle into triangle is point of intersection of all interior angles of triangle.
The center of circumscribed circle over triabgle is point of intersection of perpendicular bisectors to the sides.
Circumscribed circle always passes through the vertices of the triangle.
Inscribed circle is always tangent to the triangle's sides.
In your case angles' bisectors and perpendicular bisectors intesect at one point, so point A is the center of inscribed circle and the center of corcumsribed circle. Thus, these circles pass through the points X, Y, Z and G, E, F, respectively.
Round off 600341 to the nearest a) tens b) hundreds c) thousands
a) 600340
b) 600300
c) 600000
Prove that f(x)=x+3/2 and g(x)=2x-3are inverse
To prove that two functions are inverse, we need to show that applying one function and then the other will result in the original input. By evaluating f(g(x)) and g(f(x)), we can confirm that f(x) = x + 3/2 and g(x) = 2x - 3 are inverse functions.
Explanation:To prove that two functions f(x) and g(x) are inverse, we need to show that applying one function and then the other will result in the original input. In other words, f(g(x)) = x and g(f(x)) = x. Let's check if this holds true for the functions given:
First, let's find f(g(x)):Since f(g(x)) = x and g(f(x)) = x, we can conclude that f(x) = x + \frac {3}{2} and g(x) = 2x - 3 are indeed inverses of each other.
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f(x) and g(x) are inverse functions.
To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses, find their compositions and show they equal x, establishing them as inverse functions.
To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses:
Find the composition of f(g(x)) and g(f(x)).Show that f(g(x)) = x and g(f(x)) = x for all x.Thus, f(x) and g(x) are inverse functions.
what is 20% of 50?
A.) Percent=20%, Amount =50, Base =unknown
B.) Percent=50%, Amount =unknown, Base= 20
C.) percent= 20%, Amount=unknown, Base =50
D.) Percent=unknown, Amount =20, Base= 50
20% of 50 is found by multiplying the base (50) by the decimal equivalent of the percent (0.2). The calculation yields an amount of 10, which indicates that 20% of 50 is 10.
Calculating percents involves using the basic equation that relates the percent, the base (also called 'whole' or 'total'), and the amount (or 'part'). The equation can be represented as percent = (amount/base) imes 100. To find what is 20% of 50, we use this equation, where the percent is known (20%) and the base is known (50), but the amount is what we are looking for.
First, let's convert the percent to a decimal to make the calculation easier: 20% = 20/100 = 0.2. Then, we multiply the base (50) by the decimal form of the percent (0.2): 50 x 0.2 = 10. So, 20% of 50 is 10.
Therefore, the correct representation relating the Percent, Amount, and Base in this problem is option A) Percent=20%, Amount=50, Base=unknown, since we're calculating the amount based on the known percent and base.
Answer:
C.) percent= 20%, Amount=unknown, Base =50
Step-by-step explanation:
20% is the percent
50 is the amount
20% of 50 is the unknown. This is the amount.
20% of 50 = 0.2 × 50 = 10
What is a factorial and what is the purpose of it?
Answer:
Step-by-step explanation:
Factorial is used to multiply any natural number with all the numbers smaller than it. It is denoted by n! (n is the natural number)
where n! = n*(n-1)*(n-2)*(n-3)*(n-4) so on....
For example if we take factorial of 5.
Then,
5!= 5*(5-1)*(5-2)*(5-3)*(5-4)
= 5*4*3*2*1
= 120
It is used for the questions which asks us to order a number of things or in how many ways you can arrange something....
Factorial is a key function in mathematics used to calculate permutations and arrangements. It represents the number of ways objects can be arranged within a set number. Factorial is essential in combinatorics and probability theory.
Factorial is a mathematical function denoted as n! and calculated as the product of all positive integers up to n.
The purpose of factorial is to represent the number of ways in which a set of objects can be arranged or permutations can be made within a set number of objects.
Factorial is extensively used in mathematics, especially in combinatorics and probability theory.
1
if f || k and k || m, then blank
Answer:
f || m
Step-by-step explanation:
If f is parallel to k and k is parallel to m
then f must be parallel to m
Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of
10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?
A. 1.7 years
B. 2.0 years
C. 3.1 years
D. 5.0 years
Answer: A) 1.7 Years
Step-by-step explanation:
Answer:
A. 1.7 years
Step-by-step explanation:
Let [tex]P_1[/tex] be the original value of first car,
Since, the car depreciates at an annual rate of 10%,
Let after [tex]t_1[/tex] years the value of car is depreciated to 60%,
That is,
[tex]P_1(1-\frac{10}{100})^{t_1}=60\%\text{ of }P_1[/tex]
[tex]P_1(1-0.1)^{t_1}=0.6P_1[/tex]
[tex]0.9^{t_1}=0.6[/tex]
Taking ln on both sides,
[tex]t_1ln(0.9) = ln(0.6)[/tex]
[tex]\implies t_1=\frac{ln(0.6)}{ln(0.9)}[/tex]
Now, let [tex]P_2[/tex] is the original value of second car,
Since, the car depreciates at an annual rate of 15%
Suppose after [tex]t_2[/tex] years it is depreciated to 60%,
[tex]P_2(1-\frac{15}{100})^{t_2}=60\%\text{ of }P_2[/tex]
[tex]P_2(1-0.15)^{t_2}=0.6P_2[/tex]
[tex]0.85^{t_2}=0.6[/tex]
Taking ln on both sides,
[tex]t_2ln(0.85) = ln(0.6)[/tex]
[tex]\implies t_2=\frac{ln(0.6)}{ln(0.85)}[/tex]
[tex]\because t_1-t_2=\frac{ln(0.6)}{ln(0.90)}-\frac{ln(0.6)}{ln(0.85)}[/tex]
[tex]=1.70518303046[/tex]
[tex]\approx 1.7[/tex]
Hence, the approximate difference in the ages of the two cars is 1.7 years,
Option 'A' is correct.
Which of the pairs of ratios are equivalent? A) 12: 24, 50 :100 B) 16 to 3,27 to 5 C) 22/1, 68/3 D) 3/7, 17/35
Answer:
A
Step-by-step explanation:
equivalent because each are 1:2
Final answer:
After simplifying each pair of ratios, only 12: 24, and 50:100 (Pair A) are equivalent ratios, as both simplify to 1:2. The other pairs are not equivalent since their simplified forms are different.
Explanation:
To determine which of the pairs of ratios are equivalent, we can simplify each ratio or convert them to fractions and simplify to see if they have the same value. Let's look at each pair:
A) 12: 24 simplifies to 1:2. 50 :100 also simplifies to 1:2. Therefore, these ratios are equivalent.B) 16 to 3 is the same as the fraction 16/3. 27 to 5 is the same as the fraction 27/5. These ratios are not equivalent as their simplified forms (16/3 and 27/5) are different.C) 22/1 is simply 22. 68/3 when divided is approximately 22.67. These ratios are not equivalent because 22 does not equal 22.67.D) 3/7 is a fraction and does not simplify further. 17/35 simplifies to 1/2 when divided by 17. These ratios are not equivalent because 3/7 is different from 1/2.From the above, only the pair A) 12: 24, 50:100 are equivalent ratios.
In The Diagram Below, BD is parallel to XY, What is the value of Y?
A.73
B.97
C.83
D.87
Answer: B.97
Step-by-step explanation:
When two parallel lines are intersected by a transversal line then the sum of adjacent angles is 180°.
From the given figure , BD is parallel to XY and a transversal intersecting it making a pair of adjacent angles 83° and y°.
[tex]83^{\circ}+y^{\circ}=180^{\circ}\\\\\Rightarrow\ y^{\circ}=180^{\circ}-83^{\circ}=97^{\circ}[/tex]
Hence, the value of y= 97.
Answer:it is 83
Step-by-step explanation:
Exponential functions have the form f(x)=b^x. What type of an exponential function would you have (increasing or decreasing) if the value of b is greater than one?
Answer:
Increasing
Step-by-step explanation:
Let's see what happens if we choose a value for b greater than 1.
Let's try b=2.
[tex]f(x)=2^x[/tex].
I'm going to keep increasing x. If y increases, the the function is increasing. If y decreases, the function is decreasing.
Let's start with x=1.
[tex]y=2^1=2[/tex]
Now x=2.
[tex]y=2^2=4[/tex]
The y's got higher as you increased x so the function is increasing.
The function keep increasing for the varying value of x, hence the exponential function is increasing
Given the exponential function f(x) = [tex]b^x[/tex]
We are to check if the function is increasing or decreasing if b is greater than 1
Let b = 2 and x = 1
[tex]f(1) = 2^1\\f(1) = 2[/tex]
Let b = 2 when x = 2
[tex]f(2)=2^2\\f(2)=4[/tex]
Let b = 2 when x = 3
[tex]f(3)=2^3\\f(3)=8[/tex]
You can see that the function keep increasing for the varying value of x, hence the exponential function is increasing
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I’m the sixth grade class, 3/7 of the students are boys, and 5/8 of these boys are in mrs. jones’ class. What fraction of the entire sixth grade class are the boys in mrs. jones’ class??
PLEASE SHOW WORK
Answer:
15/56
Step-by-step explanation:
You just multiply 3/7 by 5/8 to get 15/56. Since you cannot simplify it more, that is the fraction of boys in mrs.jones class compared to the whole sixth grade class
Answer:
15/56
Step-by-step explanation:
Let the total number of students be x
Number of boys=[tex]\frac{3}{7}[/tex] of x
Number of boys in Mrs jones' class= [tex]\frac{3}{7}[/tex]of[tex]\frac{5}{8}[/tex]
Fraction of number of boys of Mrs jones' class to total class strength=[tex]\frac{15x/56}{x}[/tex]
Hence, the fraction is[tex]\frac{15}{56}[/tex]
(j-1)(-3) I need help solving the distributive property.
Answer:
Step-by-step explanation:
-3*j = -3j
(-3)(-1) = 3
Answer
-3j + 3 Notice the sign change. Be careful about that when signs are used with the distributive property.
Match the polygons formed by the set of points with their perimetersrounded to the nearest hundredth. Please help ASAP taking a test . Thank you so much in advance
Answer:
Polygon ABCDE = 50 units
Polygon FGHIJ = 23.4 units
Polygon KLMNO = 19.24 units
Polygon UVWXY = 38 units
Step-by-step explanation:
In order to find the perimeter, we have to find lengths of all sides of given points
The distance formula will be used to find the lengths
[tex]d = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]
where (x_1,y_1) are coordinates of first point and (x_2,y_2) are coordinates of second point)
So,
For A(1,1), B(6,13), C(8,13), D(16,-2) and E(1, -2)
AB = 13 units
BC = 2 units
CD = 17 units
DE = 15 units
EA = 3 units
Perimeter of polygon ABCDE = 13+2+17+15+3 = 50 units
For F(14,-10), G(16,-10), H(19,-6), I(14,-2) and J(11,-6)
FG = 2 units
GH = 5 units
HI = 6.40 units
IJ = 5 units
JF = 5 units
Perimeter of polygon FGHIJ = 2+5+6.40+5+5 = 23.4 units
For K(4,2), L(8,2), M(12,5), N(6,5) and O(4,4)
KL = 4 units
LM = 5 units
MN = 6 units
NO = 2.24 units
OK = 2 units
Perimeter of polygon KLMNO = 4+5+6+2.24+2 = 19.24 units
For P(7,2), Q(12,2), R(12,6), S(7,10) and T(4,6)
PQ= 5 units
QR= 4 units
RS=6.40 units
ST= 5 units
TP = 5 units
Perimeter of polygon PQRST = 5+4+6.40+5+5 = 25.40 units
For U(4,-1), V(12, -1), W(20,-7), X(8, -7) and Y(4,-4)
UV = 8 units
VW = 10 units
WX = 12 units
XY = 5 units
YU = 3 units
Perimeter of polygon UVWXY = 8+10+12+5+3 = 38 units
What is 16 percent of 65
Answer:
10.4
Step-by-step explanation:
The way to find percentage is by multiplying the number you want to find the percentage of by the percentage and divide it by 100
So, in the case of 16% of 65
we multiply 65 by 16 =1040
then we divide by 100
Hence 1040/100=10.40
which is same as 10.4
HOPE IT HELPS....
The solution of the expression 16 percent of 65 is 10.4.
A percentage is a ratio that may be written as a fraction of 100.
A fraction is a ratio between two quantities. The upper part is called numerator and the lower part is called denominator.
A collection of constants, variables connected using one or more arithmetic operator is called an expression.
This can be simplified as:
[tex]\dfrac{16}{100} \times65 = 10.4[/tex] in decimal form.
Thus, 16 percent of 65 is 10.4
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Which graph is the solution to lxl > 10?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Note}\rightarrow[/tex] [tex]\leq \& \geq \ = \huge\text{closed circle}\\ < \& > = \huge\text{(o)(p)(e)(n)(e)(d) circle}[/tex]
[tex]\huge\text{So, we know that A or C could be our answer}.[/tex]
[tex]\huge\text{Eliminate option B and D}[/tex]
→ [tex]\huge\text{Find the absolute value of the problem}[/tex]
→ [tex]\huge\text{You can now know that it could be:}[/tex]
[tex]\huge\text{x}\large\huge{\ >}\huge\text{ 10 or x }< \huge\text{ -10}[/tex]
→ [tex]\huge\text{Possible answer \#1: x }>\huge\text{10}\\\\\huge\text{Possible answer \#2: x}<\huge\text{ -10}[/tex]
→ [tex]\boxed{\boxed{\huge\text{Answer: C}}}[/tex]
[tex]\huge\text{Option A. would be too small}[/tex] [tex]\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
a right pyramid with a square base has a base edge length of 24 feet and slant height of 20 feet the height of the pyramid is feet
Answer:
The height of the pyramid is 16 feet.Step-by-step explanation:
Look at the picture.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=12ft,\ leg=H,\ hypotenuse=20ft[/tex]
Substitute:
[tex]12^2+H^2=20^2[/tex]
[tex]144+H^2=400[/tex] subtract 144 from both sides
[tex]H^2=256\to H=\sqrt{156}\\\\H=16\ ft[/tex]
Answer:
16 feet
Step-by-step explanation:
for edg
Which of the following data sets has the mean, median, and mode as the same number?
A. 10,10,12,12,13,13
B. 2,3,4,4,5,7
C. 4,7,11,11,16,17
D. 1,2,3,3,5,6
Answer:
C
Step-by-step explanation:
MEAN:4+7+11+11+16+17=66÷6=11
MEDIAN:11+11=22÷2=11
MODE=11
Answer:
The correct answer is option C
4,7,11,11,16,17
mean = mode = median = 11
Step-by-step explanation:
Check option A
10,10,12,12,13,13
Mean = 12, mode = 12,13 , 14 and median = 12
Check option B
2,3,4,4,5,7
Mean = 4.15, mode = 4 and median = 4
Check option C
4,7,11,11,16,17
Mean = 11, mode = 11 and median = 11
Check option D
1,2,3,3,5,6
Mean = 3.33, mode =3 and median = 3
The correct answer is option C
4,7,11,11,16,17
mean = median = mode = 11
Roger has a 0.250 batting average. If he went up to bat 240 times,how many times did he fail to get any hits?( A 0.250 batting average means that he got hits 0.250 times at bat) please help me
Answer:
lol i need help with the same question
Step-by-step explanation:
Roger, with a batting average of 0.250, recorded 60 successful hits from a total of 240 attempts. Therefore, he failed to get a hit 180 times.
Explanation:In this question, we are dealing with Roger's batting average and his performance. A batting average of 0.250 means that for every 4 at-bats, Roger gets a hit on average 1 time. So, if he has been at bat a total of 240 times, we can expect that he got hits 0.250 times out of these at-bats. So to calculate the number of successful hits, we multiple 240 by 0.250 which equals 60. Therefore, Roger has hit the ball 60 times. To find out how many times he failed to get hits, we subtract his hits from his total tries. So, 240 - 60 = 180. Therefore, Roger failed to get a hit 180 times.
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What is the area of the parallelogram shown below?
A. 88 sq. units
B. 24 sq. units
C. 48 sq. units
D. 42 sq. units
Answer:
48
Let me know if this was right :)
Each of the 27 turtles in the pet store needs to be fed. There is one bag of turtle food that weighs 84 ounces. If each turtle gets the same amount of food, how many ounces of turtle food will each turtle get?
Answer:
[tex]\3.11\ ounces[/tex]
Step-by-step explanation:
we know that
To find the number of ounces of food each turtle will receive, divide the total ounces of food by the total number of turtles
so
[tex]\frac{84}{27}=3.11\ ounces[/tex]
Answer: 3.1
Step-by-step explanation: which is 3.1 with the line on top!
A coffee distributor needs to mix a(n) House coffee blend that normally sells for $10.50 per pound with a Kenya coffee blend that normally sells for $12.80 per pound to create 40 pounds of a coffee that can sell for $10.67 per pound. How many pounds of each kind of coffee should they mix?
Answer: They must mix
______pounds of the House Blend
______pounds of the Kenya Blend.
Round your answers to the nearest whole number of pounds.
Answer:
They must mix
37 pounds of the House Blend
3 pounds of the Kenya Blend.
Step-by-step explanation:
Let 'x' be House coffe and 'y' be Kenya Coffee. Then:
10.50x + 12.80y = 10.67(40)
Also, we knw that:
x + y = 40
Solving the system of equations above, we have that:
x ≈37.0435 ≈ 37 pounds
y ≈2.95652 ≈ 3 pounds
They must mix
37 pounds of the House Blend
3 pounds of the Kenya Blend.
HELP ASAP!!!!!
Pre-calculus
[tex]xy=\log_{5\sqrt5}{125}\cdot\log_{2\sqrt2}64\\\\xy=\dfrac{\log_5125}{\log_5 5\sqrt5}\cdot\dfrac{\log_264}{\log_22\sqrt2}\\\\xy=\dfrac{3}{\log_55^{\tfrac{3}{2}}}\cdot\dfrac{6}{\log_22^{\tfrac{3}{2}}}\\\\xy=\dfrac{3}{\dfrac{3}{2}}\cdot\dfrac{6}{\dfrac{3}{2}}\\\\xy=3\cdot\dfrac{2}{3}\cdot6\cdot\dfrac{3}{2}\\\\xy=18[/tex]
Answer:
The product of x and y is 8.
Step-by-step explanation:
It is given that
[tex]x=\log_{5\sqrt{5}}\left(125\right)[/tex]
[tex]y=\log_{2\sqrt{2}}\left(64\right)[/tex]
We need to find the product of x and y.
[tex]x\cdot y=\log_{5\sqrt{5}}\left(125\right)\cdot\log_{2\sqrt{2}}\left(64\right)[/tex]
It can be written as
[tex]xy=\log_{5\sqrt{5}}\left(5\sqrt{5}\right)^2\cdot\log_{2\sqrt{2}}\left(2\sqrt{2}\right)^4[/tex]
Using the properties of logarithm, we get
[tex]xy=2\cdot 4[/tex] [tex][\because log_aa^x=x][/tex]
[tex]xy=8[/tex]
Therefore the product of x and y is 8.
A hardware store buys 300 feet of nylon rope. The store sells the rope by the inch. A customer can purchase 40 inches of the rope for $1.60. The store sells all of the rope and makes a profit of $54. How much did the store pay for the rope in dollars per inch.
Pls answer this question it’s important..
Answer:
0.025 $/in.
Step-by-step explanation:
The store bought 300 ft of rope.
1 ft = 12 in.
300 ft * 12 in./ft = 3600 in.
The store bought 3600 inches of rope.
The store sells 40 inches of rope for $1.60. We can find the selling unit price of rope in dollars per inch.
($1.60)/(40 in.) = $0.04/in.
The store sells the rope at a price of $0.04 per inch.
The store sold all the rope at $0.04/in.
3600 in. * $0.04/in. = $144
The store sold all the rope for $144.
The profit was $54 for selling ll the rope.
$144 - $54 = $90
The bought the rope for $90.
The cost is dollars per inch is
($90)/(3600 in.) = 0.025 $/in.