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
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
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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my sides are all the same length. my area is 9 square meters. what is the length of one of my sides?
Answer:
3
Step-by-step explanation:
if the length and width is 3, 3 times 3 is 9
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
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
Change the fraction to a decimal. a. 6⁄100 b. 43⁄100 c. 3⁄10 d. 4 23⁄1,000
6/100 = 0.06
43/100 = 0.43
3/10 = 0.3
23/1,000 = 0.023
Hope this helps!
Final answer:
To convert fractions to decimals, divide the numerator by the denominator and combine with any whole number for mixed numbers, resulting in 0.06, 0.43, 0.3, and 4.023 respectively for the given fractions.
Explanation:
The question asks to change fractions to decimals. Here are the step-by-step conversions:
a. 6⁄100: This fraction means 6 divided by 100, which is 0.06.
b. 43⁄100: Similarly, 43 divided by 100 is 0.43.
c. 3⁄10: Dividing 3 by 10 gives you 0.3.
d. 4 23⁄1,000: For the mixed number, you have the whole number 4 and the fraction 23⁄1,000. The fraction part is 23 divided by 1,000, which is 0.023. So, you combine the whole number and the decimal to get 4.023
Converting fractions to decimals involves dividing the numerator by the denominator and adding any whole number part if it's a mixed number.
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.
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.
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
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]
Please I need help Fast!!!!!!!
Equilateral
Step-by-step explanation:An equilateral triangle has medians that are also angle bisectors that are also altitudes.
Choose all of the unit vectors
To choose unit vectors, one must understand that they have a magnitude of one and are directed along the axes in space. For any point P or S, the unit vectors are (i_p, j_p, k_p) or (i_s, j_s, k_s) respectively, each with a magnitude of one.
Explanation:To determine which vectors are unit vectors, you must know that a unit vector has a magnitude (length) of one and indicates direction in space. The given information states that for a point P in space, the unit vectors are (î_p, â_p, k_p). Each of these vectors has a magnitude of one and points in the direction of increasing x, y, and z coordinates, respectively. Similarly, for point S, you have (i_s, j_s, k_s), also with a magnitude of one.
The special types of unit vectors such as î (i-hat), â (j-hat), and k (k-hat) are always of magnitude one and are parallel to the x, y, and z axes, respectively. The vector dê, represents a vector of length d pointing in the positive x-direction, implying dê is also a unit vector if d equals one.
Therefore, in the context provided, all options (a), (b), (c), and (d) are correct if their vectors have a magnitude of one and adhere to the rules to be considered unit vectors.
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
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.
Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles
Answer:
75 ft
Step-by-step explanation:
Here we are given a right angled triangle with a known angle of 20°, length of the hypotenuse to be 80 and we are to find the length of the base x.
For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.
[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]
So putting in the given values to get:
[tex]cos 20=\frac{x}{80} \\\\x= cos 20*80\\\\x=75.17[/tex]
Therefore, the value of x is the closest to 75 ft.
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
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.
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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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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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
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]
50 POINTS FOR CORRECT ANSWER @PlatoNation
REPORTED IF INCORRECT
Answer:
About 2614 years.
Step-by-step explanation:
We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:
[tex]N=N_0\cdot e^{-kt} \\0.77N_0 = N_0\cdot e^{-kt}\\0.77 = e^{-0.0001 t}[/tex]
and we can solve for t:
[tex]0.77 = e^{-0.0001 t}\\\ln0.77 = \ln e^{-0.0001 t}\\\ln 0.77 = -0.0001 t\implies\\t = -\frac{\ln0.77}{0.0001}=2613.65\approx 2614\,\,\,\mbox{years}[/tex]
The estimated age of the bird skeleton is 2614 years.
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.
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:
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.
Which of the following functions is graphed below ?
See the attachment
Step-by-step explanation:The solid dot on the right-hand portion of the curve means the function is defined for x ≥ 2. Choices A and C have that condition.
The function is linear for x ≥ 2, so matches selection C, not A.
Which expressions are equivalent to 70 × 5.3
Answer:
35 x 10.6, 140 x 2.65 and 371 x 1
Step-by-step explanation:
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.
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).