Find the values of the variables. Then find the side lengths of the square. Need x=_ , y=_ and the length of the square is _
x = 4; y = 9; length of a side = 5
Step-by-step explanation:Here, you're expected to use the fact that all of the sides of a square are the same length.
The left and right sides both have different expressions only in y, so it is convenient to equate them.
... y -4 = 2y -13
... 0 = y -9 . . . . . subtract the left side
... 9 = y . . . . . . . add 9
This tells us the side of the square (s) is ...
... s = y -4 = 9 -4
... s = 5
And we can use this to find x.
... 5 = 2x -3 . . . . equate the x-expression to the square side length
... 8 = 2x . . . . . . add 3
... 4 = x . . . . . . . . divde by the coefficient of x
x and y are 4 and 9; the square side length is 5.
The values of x and y are not given, so the length of the square cannot be determined.
Explanation:To find the side lengths of the square, we first need to determine the values of x and y. However, the provided information does not give any equations or context to solve for x and y. Without additional information, it is not possible to find the values of x and y, and therefore, we cannot calculate the length of the square. If you have any additional information or equations, please provide them so that we can assist you further.
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The pitney pipe company is one of several large domestic manufacturers of pvc pipe. the quality control department sampled 600 10-foot lengths. at a point 1 foot from the end of the pipe, they measured the outside diameter. the mean was 14 incles and the standard deviation was 0.1 inches. if we assume that the distribution of diameters is symmetrical and bell-shaped, about 95% of the observations will be between what two values?
Answer:
13.8–14.2 inches
Step-by-step explanation:
If you assume the "symmetrical and bell-shaped" distribution is a normal distribution, then 95% of observations will lie within 2 standard deviations of the mean:
... 14 in ±2×(0.1 in) = 13.8 in to 14.2 in
Sin(x+24) = Cos(y-x) ; Tan(z-24) - Tan(y-z)=0
find: Cos(y-z)
Cos(y-z) = Cos(z-24)
Step-by-step explanation:You have two equations in three unknowns, so no solution for the unknowns is possible.
The tangent equation tells you ...
... tan(z -24) = tan(y -z)
... z -24 = y -z . . . . . . take the arctangent
... cos(y -z) = cos(z -24) . . . . take the cosine
keep on getting 10x+12
[tex]\dfrac{13x+10}{2x^2-5x-25}[/tex]
Step-by-step explanation:Multiply the first fraction by (x-5)/(x-5) and the second by (2x+5)/(2x+5). Now, you have both fractions with the common denominator (2x+5)(x-5).
[tex]\dfrac{3}{2x+5}+\dfrac{5}{x-5}=\dfrac{3(x-5)}{(2x+5)(x-5)}+\dfrac{5(2x+5)}{(2x+5)(x-5)}\\\\=\dfrac{3(x-5)+5(2x+5)}{(2x+5)(x-5)}=\dfrac{3x-15+10x+25}{2x^2-5x-25}\\\\=\dfrac{13x+10}{2x^2-5x-25}[/tex]
Notes: Each calculator is $5 dollars and the shipping cost $15. Write a linear relationship between that shows the cost and the number of calculators purchased.
Answer:
y = 5x+15
Step-by-step explanation:
The cost per calculator is 5
The shipping cost is 15
Let y = total cost
Let x = number of calculators
y = 5x+15
Help Please
What is the solution of the system?
Use the elimination method.
-4x - 2y = -12
2x + 4y = -12
Enter your answers in the boxes
(x, y) = (6, -6)
Step-by-step explanation:Divide the first equation by 2 to get equal and opposite coefficients for x.
... -2x -y = -6
Add this to the second equation to eliminate x.
... (2x +4y) +(-2x -y) = (-12) +(-6)
... 3y = -18 . . . . . . . . simplify
... y = -6 . . . . . . . . . . divide by 3
Substitute this vaue into any of the equations to find x. We choose to use the reduced first equation above.
... -2x -(-6) = -6
... -2x = -12 . . . . subtract 6
... x = 6 . . . . . . . divide by -2
The solution to the system is (x, y) = (6, -6).
1. What is 45% of 36 feet?
*Please Show Work*
What is 45% of 36 feet?
ANSWER AND EXPLANATIONTo find the percent of a number, you have to change the percent into a decimal or a fraction and multiply by the number.
DECIMAL
To change a percent into a decimal, remove the percent sign and move the decimal point 2 places to the left.
[tex]45 \% \rightarrow 0.45[/tex]
Now that you have your decimal, multiply by 36:
[tex]0.45 \times 36 = 16.2[/tex]
ANSWER = 16.2 feet
FRACTION
To change a percent into a fraction, make the percent number as the numerator(top number) and 100 as the denominator(bottom number) since fractions are out of 100.
[tex]45 \% \rightarrow \frac{45}{100}[/tex]
Now that you have your fraction, multiply by 36:
[tex]\frac{45}{100} \times 36 = \frac{1620}{100} \rightarrow 16.2[/tex]
ANSWER = 16.2 feet
If you have any questions, feel free to ask in the comments! :)
Answer:
Step-by-step explanation:
36feet=100%
18feet=50%
48.2=45%
Lisa purchased a concert ticket on a web site. The original price of the ticket was $75. She used a coupon code to received a 20% discount. The web site applied a 10% service fee to the discount price. Lisa's ticket was less than the original price by what percent?
12%
Step-by-step explanation:Her discounted price was 100% - 20% = 80% of the original price. The service fee made it be 100% + 10% = 110% of that, so her final price was ...
... 110% × 80% = 88%
of the original ticket price.
This represents a discount of 100% - 88% = 12% from the original.
I am a rectangle. two of my sides are each 7 inches long. My area is 28 square inches. What is the length of each of my other two sides?
Answer:
4
Step-by-step explanation:
The formula for a rectangle is base times height so if one side is 7 inches then you need to figure out what times seven equals 28, which would be four.
If one pair of sides is 7 inches and the area is length times width then the answer would be whatever you multiple by 7 to get 28, so it would be 4 inches for each of the other two sides.
Please I need help Fast!!!!!!!
Equilateral
Step-by-step explanation:An equilateral triangle has medians that are also angle bisectors that are also altitudes.
1. How do you determine whether a function is an inverse of another function?
Add the functions.
Multiply the functions.
Find the composite of the functions.
Apply the vertical line test.
2. Which of the following is the inverse function of f(x) = 3x?
f(x) = x + 3
f(x) = x/3
f(x) = x - 3
f(x) = x3
3. Which of the following statements is true?
A function will always pass the vertical line test.
All the answers are correct.
If the function has an inverse function, then the inverse function will pass the vertical line test.
If a function has an inverse function, then the original function will pass the horizontal line test.
4. What is the inverse function of f(x) = 3(x - 2)3?
5. Which of the following is the inverse function of f(x) = 2x - 3?
f(x) = (2x - 3 + 3)/2
f(x) = x+ 3/2
f(x) = x/2 + 3
f(x) = (x+3)/2
1. If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Finding the composite of the two functions will tell you if they are inverses.
2. To find the inverse of a function, swap x and y, then solve for y.
... x = 3y
... x/3 = y . . . . . matches f(x) = x/3
3. A function will pass the vertical line test. If its inverse is also a function, that, too, will pass the vertical line test. Since the inverse of a function is that function reflected across y=x, any inverse function that passes the vertical line test corresponds to an original function that passes the horizontal line test. (A vertical line reflected across y=x is a horizontal line.)
4. See 2.
... x = 3(y -2)³
... (x/3) = (y -2)³ . . . . divide by 3
... ∛(x/3) = y -2 . . . . .take the cube root
... 2+∛(x/3) = y . . . . .add 2
... f(x) = 2+∛(x/3) . . . . is the inverse
5. See 2.
... x = 2y -3
... x+3 = 2y . . . . . add 3
... (x+3)/2 = y . . . .divide by 2
... f(x) = (x+3)/2 . . . . is the inverse
A composite function is the combination of multiple functions.
The correct answers are:
Find the composite of the functions. The inverse of f(x) = 3x is [tex]f'(x) = \frac x3[/tex].All answers are trueThe inverse of [tex]f(x) = 3(x - 2)^3[/tex] is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]The inverse of [tex]f(x) =2x - 3[/tex] is [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]1. Test for inverse function
To test if two functions are inverse of one another, we simply find their composites.
Assume the functions are g(x) and h(x).
We simply test for [tex]g(h^{-1}(x))[/tex] and [tex]h(g^{-1}(x))[/tex]
If they are equal, then both functions are inverse functions
2. Inverse of f(x) = 3x
Rewrite as:
[tex]y = 3x[/tex]
Swap y and x
[tex]x = 3y[/tex]
Make y the subject
[tex]y = \frac x3[/tex]
Hence, the inverse function is: [tex]f'(x) = \frac x3[/tex]
3. True statements
A function has unique ordered pairs; so, it will pass the vertical line test.
Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.
Hence;
(b) All answers are correct
4. Inverse of [tex]f(x) = 3(x - 2)^3[/tex]
Rewrite as:
[tex]y = 3(x - 2)^3[/tex]
Swap x and y
[tex]x = 3(y - 2)^3[/tex]
Solve for y: Divide both sides by 3
[tex](y -2)^3 = \frac x3[/tex]
Take cube roots of both sides
[tex]y -2 = \sqrt[3]{\frac x3}[/tex]
Add 2 to both sides
[tex]y =2 + \sqrt[3]{\frac x3}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]
5. The inverse of [tex]f(x) =2x - 3[/tex]
Rewrite as:
[tex]y =2x - 3[/tex]
Swap x and y
[tex]x =2y - 3[/tex]
Solve for y: Add 3 to both sides
[tex]2y = x + 3[/tex]
Divide both sides by 2
[tex]y = \frac{x + 3}{2}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]
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Find the number of triangles with c =7, b=11, and B=21 degrees
1
Step-by-step explanation:The given angle is opposite the longest given side, so there will be exactly one solution.
_____
The number of solutions may be 0, 1, or 2 when the given angle is opposite the shortest given side.
classify what type of angle this is
Question
classify what type of angle this is
Answer:
IsoscelesStep-by-step explanation:
2 equal side and 2 equal angles, it is an isosceles.
0=9(k-2/3)+33 solve for k
Answer:
k = -3
Step-by-step explanation:
Simplify, divide by 9, add the opposite of the constant.
0 = 9k -9·2/3 +33
0 = 9k +27
0 = k +3
-3 = k
Which of these statements accurately describes the graph of the function f(x)=x2+14x+49f(x)=x2+14x+49 ? A The graph passes through the x-axis at -7. B The graph touches the x-axis at -7. C The graph passes through the x-axis at 7. D The graph touches the x-axis at 7.
A point belongs to the x axis if its y coordinate equals zero.
The points on a graph are in the form [tex] (x,f(x)) [/tex], so these points are on the x axis if and only if [tex] f(x)=0 [/tex]
In this case, we have
[tex] f(x) = 0 \iff x^2+14x+49=0 [/tex]
You can observe that your expression is actually a squared binomial: using
[tex] (a+b)^2 = a^2+2ab+b^2 [/tex]
you can notice that
[tex] (x+7)^2 = x^2+14x+49 [/tex]
So, you have
[tex] x^2+14x+49=0 \iff (x-7)^2 = 0 \iff x=7 [/tex]
Now, how we decide if this function "touches" or "passes through" the x-axis at x=7? Well, since our function is a square, it is never negative. So, this graph can't cross the x-axis, but rater touch it from above. The parabola has a U shape, and the point of minimum lies on the x axis.
So, the graph touches the x axis at x=7.
The graph of the function f(x)=x^2+14x+49 is a parabola that touches the x-axis at -7, it does not pass through it because the root of the equation -7 is of multiplicity 2.
Explanation:The function f(x)=x^2+14x+49 is a quadratic function, which when factorized becomes f(x) = (x+7)^2. This means that the graph of the function touches the x-axis at -7, but does not pass through it because the root of this equation -7 is of multiplicity 2. Hence, the correct answer is B: The graph touches the x-axis at -7.
To visualize this, remember that a quadratic function like this one forms a parabola. The point where the parabola intersects or touches the x-axis corresponds to the solution(s) of the equation. In this case, because there's only one solution (x=-7), the parabola just touches the x-axis at this point, but doesn't cross it.
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Compare 1⁄2 with 3⁄4 using ( <, >, =). A. 1⁄2 < 3⁄4 B. 1⁄2 > 3⁄4 C. 1⁄2 = 3⁄4 D. None of the abov
Answer:
A. 1⁄2 < 3⁄4
Step-by-step explanation:
1/2 vs 3/4
Get a common denominator of 4
1/2 *2/2 vs 3/4
2/4 vs 3/4
2 is less than 3
2/4 < 3/4
1/2 < 3/4
a certain tv can be purchased from the manufacturer for $160. A certain online retailer gas a standard markup for 30%, and a certain superstore has a standard markup of 40%
what is the price of the tv when purchased online?
Answer:
208
Step-by-step explanation:
basically you can plug this into a calculator, just by pressing 160 + 30(then the percent sign), followed by the equal sign. or you can do it on paper by dividing 160 by 100, which gives you 1.6. then you multiply that by 30, with leaves you with 48. and because 48 is 30% of 160, you do 48 + 160 equals 208.
After its first day of life or baby blue whale started growing. It grew 47.075 inches. If the average baby blue whale grow at a rate of 1.5 inches a day, for how many days did the baby whale grow, to the nearest tenth of a day?
Identify the constant of proportionality in the equation. 3y = 15x A) 1 B) 3 C) 5 D) 15
Answer: The answer is c)5
Answer:
c) 5
Step-by-step explanation:
PM is the median of trapezoid KLNO. If ON = 24 centimeters and KL = 12 centimeters, which is the length of PM?
Answer:
18 cm
Step-by-step explanation:
The length of the median is the average of the two base lengths:
... (24 cm + 12 cm)/2 = 18 cm
the scale on a map is 1 cm for every 400 km .If the Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?
Answer:
8,800
Step-by-step explanation:
400 km
1 cm
=
d
22 cm
In △ABC, AB=8, BC=10, and AC=12. Let M, N, and K be the midpoints of the sides of △ABC. Find length of each side of △MNK.
Answer:
The side lengths are 4, 5, and 6.
Step-by-step explanation:
Each midsegment is half the length of the parallel side, so the side lengths of ΔMNK are 4, 5, and 6.
It isn't clear which point is the midpoint of what segment. If it is true that ...
M is the midpoint of ABN is the midpoint of BCK is the midpoint of ACthen ...
MN = AC/2 = 6NK = AB/2 = 4KM = BC/2 = 5Answer:
4, 5, 6
Step-by-step explanation:
PLEASE HELP!! THANKSS:)
Three dogs barked all night last night. Lola, Patch, and Lady began barking together at 11:00 p.m. Then, Lola barked every 5 minutes, Patch every 8 minutes, and Lady every 12 minutes. Later that night, Ms. Li was awakened when all 3 dogs barked together again. At what time was Ms. Li awakened? Show your work.
1:00 a.m. (and 3:00 a.m., and 5:00 a.m.)
Step-by-step explanation:The problem is to find the least common multiple (LCM) of the barking intervals. One way to find the LCM is to find the product of the factors of the numbers.
... 5 = 5 . . . . a prime number
... 8 = 2³
... 12 = 2²×3
The factor 2³ is a multiple of the factor 2², so we only need 2³ in our final product.
The LCM is then ...
... 2³×3×5 = 120 . . . . minutes
The dogs will all bark together every 120 minutes (2 hours).
2 hours after 11 p.m. is 1 a.m.
_____
The problem statement doesn't say whether Ms. Li was awakened multiple times. The dogs will bark together again at 3 a.m., 5 a.m. and (possibly) 7 a.m.
The time when Ms. Li was awakened by the dogs Lola, Patch and Lady barking together was calculated using the concept of least common multiple (LCM). The LCM of the intervals the dogs bark (5, 8, and 12 minutes) is 120 minutes or 2 hours. Therefore, Ms. Li was awakened at 1:00 am.
Explanation:This problem is a least common multiple (LCM) problem in Mathematics. The dogs Lola, Patch, and Lady started barking together at 11:00 pm. Lola barked every 5 minutes, Patch every 8 minutes, and Lady every 12 minutes. The number that is divisible by all of 5, 8, and 12 is their LCM.
To find the LCM of 5, 8, and 12, list the multiples of each number. The LCM is the smallest number that occurs in each list. In this case, the LCM is 120.
So they all barked together 120 minutes, or 2 hours, after 11:00 pm. Therefore, Ms. Li was awakened at 1:00 am.
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What is the piecewise-defined function that expresses the cost of the order, C(x), in terms of the number of photos ordered, x?
Answer:
See below
Step-by-step explanation:
The values in the table change by $3.80 from one line to the next. Since each change from line to line changes in number of photos by 20, the average cost per photo is $3.80/20 = $0.19. There is apparently a $5.80 -3.80 = $2.00 shipping charge for numbers of photos in the range shown in the table.
Thus, the piecewise function has 3 pieces:
for x < 100: $2.00 + 0.19x
for x < 200: $4.50 + 0.17x
for x ≥ 200: $0.15x
This could be written as ...
[tex]C(x)=\left\{\begin{array}{rcl}\$2.00+0.19x&\text{for}&0\le x<100\\\$4.50+0.17x&\text{for}&100\le x<200\\\$0.15x&\text{for}&x\ge 200\end{array}\right.[/tex]
A three-character code uses the letters C and P. Either of the letters may be repeated. Find the probability of the code PCP.
Answer:
1/8
Step-by-step explanation:
When there are two possiblities for each of 3 positions, the number of possible codes is 2^3 = 8. Your code is one of those, so its probability of occurrence is 1/8.
_____
CCC, CCP, CPC, CPP, PCC, PCP, PPC, PPP
Answer: [tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
Given: A three-character code uses the letters C and P.
If repetition is allowed then the total number of ways to make the three letter character code using two letters C and P is given by :-
[tex]2\times2\times2=8[/tex]
Since the PCP is one of the character code, therefore , the probability of the code PCP is given by :-
[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{1}{8}[/tex]
Hence, the probability of the code PCP = [tex]\dfrac{1}{8}[/tex]
name what type of triangle this is
The answer, I believe, is an Equilateral triangle.
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
I need help with this please
Each of these sequences goes into the classification box above it.
Step-by-step explanation:If the difference of terms is a constant, it is arithmetic.
... (3 -(-1)) = 4 = (7 -3), so the first sequence is arithmetic
If the ratio of terms is a constant, it is geometric.
... 12/36 = 1/3 = 4/12, so the second sequence is geometric
The third sequence has neither constant differences nor constant ratios, so is neither arithmetic nor geometric.
Find the unknown side lengths in similar triangles PQR and ABC
A=
B=
Answer:
A=6
B=8
Step-by-step explanation:
The hypotenuse QR is twice the length of BC, so PQ will be twice the length of AB, 2·3 = 6; and PR will be twice the length of AC, 2·4 = 8.
In similar triangles PQR and ABC:
Side PQ (a) is 40/3 units.
Side PR (b) is 50/3 units.
To find the unknown side lengths in similar triangles PQR and ABC, we can use the properties of similar triangles. Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion.
In this case, we have triangles PQR and ABC:
PQR:
RQ = 10
QP = a
RP = b
ABC:
AB = 3
AC = 4
BC = 5
Since the triangles PQR and ABC are similar, the ratios of corresponding sides must be equal. Specifically, the ratio of the sides in triangle PQR to the sides in triangle ABC should be the same. We can set up proportions to solve for a and b:
RQ / AB = QP / AC = RP / BC
10 / 3 = a / 4 = b / 5
Now, we can solve for a and b separately.
From the first part of the proportion:
10 / 3 = a / 4
Cross-multiply:
10 * 4 = 3 * a
40 = 3a
Now, divide by 3 to solve for a:
a = 40 / 3
From the second part of the proportion:
10 / 3 = b / 5
Cross-multiply:
10 * 5 = 3 * b
50 = 3b
Now, divide by 3 to solve for b:
b = 50 / 3
So, the unknown side lengths are:
a = 40/3
b = 50/3
Therefore, in similar triangles PQR and ABC:
Side PQ (a) is 40/3 units.
Side PR (b) is 50/3 units.
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The heights of two cylinders are in the ratio 3:1 if the volumes of two are same find the ratio of their respective radii
Answer:
[tex]\sqrt{3}[/tex] :1
Step-by-step explanation:
Ratio of height of two cylinders are 3:1
Let C2 has the height x
then height of C1 is 3x
Let r1 is the radius of C1
and r2 is the radius of C2
As given that volume of both are equal
Also we know that formula for the volume of the cylinder is
V= π r²h
for C1
V= π (r1)²h
for C2
V=π (r2)²h
As volume of both are same so equating them
π (r1)²h1 = π (r2)²h2
as h1 =3x and h2=x
putting values
π (r1)²(3x) = π (r2)²(x)
cancelling out π and x from both side of the equation
3(r1)²= (r2)²
Taking square root of both sides give
[tex]\sqrt{3(r1)^{2} }=\sqrt{(r2)^{2} }[/tex]
r1 ( [tex]\sqrt{3}[/tex]) = r2
or
r1 : r2 = [tex]\sqrt{3}[/tex] :1
2x − y = 3
4x = 6 + 2y
a. infinitely many solutions
b. x = 2, y = 1
c. y = 2x - 3
d. x = 4, y = 5
Answer:
a. Infinitely many solutions
Step-by-step explanation:
The given equations are 2x - y = 3
4x = 6 + 2y
We can use substitution method to solve these system of equations.
2x - y = 3
y = 2x - 3
Now plug in y = 2x - 3 in the second equation, we get
4x = 6 + 2(2x - 3)
4x = 6 + 4x - 6
4x = 4x
Here we get infinitely many solution.
Both the equations are the same.
Thank you.