Answers
9514 1404 393
Answer:
(x, y) = (2, -2)
Step-by-step explanation:
We would normally choose to use substitution when x or y could be easily solved-for without having fractions involved. That is not the case here. However, we observe that the term 3y appears in both equations, so we can substitute for "3y" instead of "y".
From the second equation, ...
3y = 5x -16
Substituting into the first equation, ...
2x +(5x -16) = -2
7x = 14 . . . . . . . . . add 16
x = 2 . . . . . . . . . . divide by 7
Using our equation for y, we get ...
3y = 5(2) -16 = -6
y = -2 . . . . . . . . . divide by 3
The solution is (x, y) = (2, -2).
Related Questions
A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 23 feet less than the height of the pole. If the wire is to be 9 feet longer than the height of the pole, what is the height of the pole?
Answers
9514 1404 393
Answer:
56 feet
Step-by-step explanation:
Let x represent the height of the pole. Then the distance to the anchor point is (x-23), and the length of the wire is (x+9). The Pythagorean theorem tells you the relation between these values is ...
(x+9)² = x² +(x -23)²
0 = x² -64x +448 . . . . . subtract the left side, put in standard form
0 = (x -8)(x -56) . . . . . . factor
The solutions to the quadratic are x=8 and x=56. For our purposes, we require x > 23 so the distances are positive. That means x=56 is the solution of interest.
The pole is 56 feet tall.
Kate is building with blocks. She needs to build a rectangular prism that is 4 meters long by 3 meters wide by 112 meters high. She is building with cubes that have side lengths of 12 meter. What is the volume of the box she needs to build in cubic meters?
Answers
9514 1404 393
Answer:
1344 cubic meters
Step-by-step explanation:
The volume is the product of the dimensions for a rectangular prism:
V = LWH
V = (4 m)(3 m)(112 m) = 1344 m³
Kate needs a volume of 1344 cubic meters.
A rocket is launched vertically from the ground with an initial velocity of 64 ft/sec. A) Write a quadratic function h(t) that shows the height, in feet, of the rocket t seconds after it was launched. B) Graph h (t) on the coordinate plane. C) Use your graph from Part 3 (b) to determine the rocket's maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air. ( Answer options A,B,C) Please don't answer if you don't know how to) Will Mark Brainliest.
Answers
The calculated quadratic function for the height of the rocket is "[tex]h = 64t - 16.085t^2[/tex]" and the further calculation of the given points can be defined as follows:
For point A):
Calculation of the quadratic function:Rocket Initial velocity (u) [tex]= 64 \ \frac{feet}{sec}[/tex]
Considering gravity's acceleration of 32.17 feet/sec2
The rocket's height can be expressed as follows:
[tex]h = ut - \frac{1}{2} \times 32.17 \times t^2 \\\\h = 64 - 16.085 \times t^2 \\\\h = 64t - 16.085t^2[/tex]
For point B):
A y-axis indicates its rocket's height in feet, whereas the x-axis represents the duration in seconds.
Please find the attached file.
For point C):
As seen in the graph, after t = 1.989 seconds, the rocket reaches its highest height of 63.662 feet.maximum height = 63.66 feet, time t = 2 seconds. After 3.979 seconds, the rocket's height returned to zero.It would be in the air for 3.979 seconds. The rocket lingered in the air for 4 seconds.
Find out more information about the velocity here:
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The fourth grade classes are painting designs on tile
squares to make a mural. Mrs. Kirk's class painted 3/10
of the mural. Mr. Becker's class painted 21/100 of the
mural. What part of the mural is painted?
You know how to add fractions with parts that are the
same size. You can use equivalent fractions to add
fractions with parts that are not the same size.
Example 1 Find o + 700
STEP I Write to and 200 as a pair of fractions STEP 2 Add
with a common denominator.
Think: Write using fractions with a common
Think: 100 multiple of 10 ose 100
denominator
the common denominator
30 21
Thinkt already
3 3 x
has 100 in the
100 100 100
10
100 denominator
+
Do
10x
Math
Talk
So
of the mural is painted.
100
MATHEMATICAL PRACTICES
Draw Conclusions When adding
tenths and hundredths, can you
100common
Answers
Answer:
51/100
Step-by-step explanation:
Use the laws of Sines and law of cosines to find missing dimensions
Answers
9514 1404 393
Answer:
11. inconsistent information
12. 26°
Step-by-step explanation:
11. The given numbers are inconsistent. (The first attachment shows one of the 4 possible solutions.)
__
12. In order to find angle C, we need to know side AC. We can find that using the Law of Cosines.
b = √(a² +c² -2ac·cos(B)) = √(19² +15² -2(19)(15)cos(120°)) = √871
b ≈ 29.513
Then angle C is found from the Law of Sines.
C = arcsin(c/b·sin(B)) = arcsin(15/29.513·sin(120°)) ≈ 26.11°
Angle C is about 26°.
The second attachment shows the output of a triangle solver.
For the function y = -1+6 cos (39(x-5) (x-5), what is the minimum value?
Answers
m = 0 , b = - 1+6cos (39)...
What is the profit percent of a shopkeeper buys a footballer of $12 and sells it for $15
Answers
Answer:
25%
Explanation:
the profit made by the shopkeeper would be the difference between the selling price and cost price, which can be found using the equation $15 - $12 = $3.
now, we can find the profit percent using the difference ($3) and the cost price ($12):
$3 ÷ $12 × 100% = 25% (since $3 is 25% of $12, so the $3 increase in price is a 25% increase)
i hope this helps! :D
What is the area of the figure on the coordinate plane below?
Answers
Answer:
-79
Step-by-step explanation:
A regular ice cream cone is 5 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.75 inches.
(a)
Find the volume (in cubic inches) of the regular ice cream cone to the nearest tenth.
cu. in
(b)
Find the volume (in cubic inches) of the waffle cone to the nearest tenth.
cu. in
(c)
How much more ice cream (in cubic inches) fits in the waffle cone compared to the regular cone? Round your answer to the nearest tenth.
cu. in
Answers
Answer:
a) 8.2 in^3 b) 25.8 in^3 c) 17.6 in^3
Step-by-step explanation:
volume of cone=(1/3)π(r^2)*h
a) 8.2 in^3
regular ice cream cone=(1/3)π(1.25^2)*5=8.18=8.2 in^3
b) 25.8 in^3
waffle cone=(1/3)π(1.875^2)*7=25.77=25.8 in^3
c) 17.6 in^3
waffle cone-regular ice cream cone= 25.8-8.2=17.6 in^3
Figure A ~ Figure B
Figure A
R = 4 ft
Figure B
R = 2 ft
V = 352 cu ft
Find the volume of Figure B.
Help please!!
Answers
The volume of figure B that is similar to figure A is: 44 cu. ft.
How to Find the Volume of Similar Figures?If the volumes of two figures are A and B respectively, and their radius is a and b respectively, then, Volume of A/volume of B = a³/b³.
Given that figures A and B are similar, we would have the following ratio:
352/volume of B = 4³/2³
352/volume of B = 64/8
352/volume of B = 8
Volume of B = 352/8
Volume of B = 44 cu. ft.
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What is 5/4 minus 1/3?
Answers
Answer:
11/12
Step-by-step explanation:
5/4 ---- 15/12
1/3------ 4/12
11/12
Answer:
11/12
Step-by-step explanation:
Hello! The answer to this question is 11/12. In this case, we want to make the denominator the same. To make the denominator the same we need to find the lowest common multiple. In this case the lowest common multiple is 12, (because 12 is the smallest number that 3 and 4 are both factors for.) 4x3=12 so now the denominator in 5/4 is 12 but whatever we do the bottom we do to the top. So since we multiplied the bottom (denominator) by 3 we have to multiply the top (numerator) by 3 as well. 5x3=15. Therefore, we now changed 5/4 to 15/12. Now, we have to do the same to the 1/3. 3x4= 12. 1x4=4. Now we have the two numbers, 15/12 and 4/12. 15/12-4/12=11/12! Therefore, your answer is 11/12. Hope this explanation helps! Happy learning!
When you solve x^2 - 8x + 7 = 0 what is the last step of the equation
before you simplify to get the two answers? *
O x = -4 13
O x = 3 + 4
O x = 4 + 3
Answers
Answer:
x = 1 and x = 7
Step-by-step explanation:
The given equation is [tex]x^2 - 8x + 7 = 0[/tex].
We need to solve the equation.
It is a quadratic equation whose solution is given by :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Here, a = 1, b = -8 and c = 7
Put values,
[tex]x=\dfrac{-(-8)\pm \sqrt{(-8)^2-4(1)(7)} }{2(1)}\\\\=\dfrac{8\pm \sqrt{64-28}}{2}\\\\=\dfrac{8\pm 6}{2}\\\\=\dfrac{8+6}{2},\dfrac{8-6}{2}\\\\=7,1[/tex]
So, the values of x are x = 1 and x = 7.
Taxi fare in Tampa cost a base fee of $4 plus an additional $0.85 for each mile traveled how much would a person pay to taxi fare in Tampa cost a base fee of $4 plus an additional $0.85 for each mile traveled how much would a person pay to take a taxi from work to home if the distance is 17 miles
Answers
Answer:
18.45
Step-by-step explanation:
Amare is building a rectangular fence. Originally, he plans to build an 18 ft by 14 ft fence but later decides to increase each dimension by x feet.
Which equation represents the new perimeter of the fence?
P = (18 + x ) + (14 + x )
P = (18 + 2x ) + (14 + 2x )
P = 2(18 + x ) + 2(14 + x )
P = 2(18 + 2x ) + 2(14 + 2x )
Answers
Answer:
P = 2(18 + x ) + 2(14 + x )Step-by-step explanation:
Given,
Dimensions of the fence = 18 ft and 14 ft
Then x ft is increased in both dimensions ,
New dimensions of the fence = (18 + x)ft and (14 + x)ft
Therefore,
Perimeter of the fence = 2 ( l + b)
= 2 l + 2 b
= 2(18 + x) + 2(14 + x) (Ans)
Hence,
Option C is correct.
Use context clues to choose the correct meaning of the italicized word.
Mother asked Mary Jo to care for the baby.
be worried about
pay attention
to take charge of
Answers
Answer:
A.
Step-by-step explanation:
In 1.8 s, a smart and swift dachshund caught his prey that was 8.5 m away what was the dogs speed?
Answers
Does each equation have no solution, one solution, or infinitely many solutions? Place a check in the correct column.
One Solution
No Solution
Infinitely Many Solutions
3(4x - 2) = 12x - 6
3(4x - 2) = -12x - 6
-3(4x - 2) = -12x - 2
Answers
3(4x-2)=-12x-6 has one solution, x=0
-3(4x-2)=-12x-2 has no solution.
PLZ ANSWER, 8 POINTS
Answers
Explanation: Set your percentage up as a fraction
26/100
Simplify
13/50
Hope this helps ;)
Privacy issues: In a Fall 2014 Pew Research survey, 25% of American adults say they are "not at all confident" that the records of their activity maintained by credit card companies will remain private and secure. With numerous data breaches since then, a consumer group is interested in determining whether the proportion has increased this year. They select a random sample of 300 adults and find that 30% state they are not at all confident. After conducting the hypothesis test for p = 0.25 compared to p > 0.25 . we obtain a -value of 0.023. Which of the following interpretations of the -value is correct? There is a % chance that 25% of American adults say they are not at all conħdent that the records of their activity maintained by credit companies will remain private and secure. There is a 2.3% chance that 30% or more of a sample of 300 American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure it 25% of Americans are not at all confident this year. There is a % chance that 30% or more of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if assume 25% of American adults are not at all confident in 2014. There is a 2.3% chance that 30% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secur
Answers
There is a 2.3% chance that 30% or more of a sample of 300 American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if 25% of Americans are not at all confident this year. Answer:
Step-by-step explanation:
The null hypothesis is “the percentage of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure is 25%. If this is true, there is a 2.3% chance that a sample of 300 American adults will have 30% or more who say they are not at all confident.
A square has an area of 100 square meters.
What is the perimeter of the square?
Answers
Answer:
40 square meters
Step-by-step explanation:
Perimeter means to add up all sides.
area means one side times one side
10 times 10 makes 100 so i am guessing each side is 10
10 + 10 + 10 + 10 = 40
What is the volume of the fish tank if the base is 4 feet, the width is 2 feet, and
the height is 3 feet? Be sure to label your units.
Answers
Answer:
24 ft³
Step-by-step explanation:
The volume formula for a rectangular prism is ...
V = LWH
V = (4 ft)(2 ft)(3 ft) = 24 ft³
The volume of the fish tank is 24 cubic feet.
Mr. Taylor arranges some chairs in rows. He puts the same number of chairs in each of the 7 rows and puts 7 chairs in the last row. He sets up 70 chairs. How many chairs does he pt in each of the 7 equal rows?
Choose the equation that can be used to solve the problem.
(7xc) +7=70
(70/7) +7=C
(7xc)-7=70
Answers
Answer:
The first one
Step-by-step explanation:
We need to find out how much chairs there are in each of the 7 rows, so we put it as 7c. The last row has 7 chairs, so we use an addition sign to include that. Since there are 70 chairs in total, the sum is 70.
Hope this helps!
A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the shaded region.
11 yd
13 yd
4 yd
6 yd
Answers
Answer:
34 yd²
Step-by-step explanation:
Area of the shaded region = area of the outer rectangle - area of the inner rectangle
Area of outer rectangle = L*W = 13*6 = 78 yd²
Area of inner rectangle = L*W = 11*4 = 44 yd²
Area of the shaded region = 78 - 44 = 34 yd²
Brennan ate 2 1/4 apples.Then he ate another 1 2/4 apples the next day.How many apples did Brennan eat altogether?Write in simplest.
Answers
Answer:
UwU your welcome!
Step-by-step explanation:
Convert the mixed fractions to a decimal. 2 1/4 is 2.25 1 2/4 is 1.5 2. Add them up. 3. 3.75 as a decimal or 3 3/4 as a mixed fraction or 15/4 as a improper fraction.
a water wheel has a radius of 15 feet. the wheel is rotating at 6 revolutions per minute. find the linear speed of the water. express your answer in terms of n and using units feet per second
Answers
Answer:
25.1333 per second
Step-by-step explanation:
1508 per min
433.54 in terms of pi
Answers
Answer:
138.0700636942675[tex]\pi[/tex]
Step-by-step explanation:
Is the answer
433.54 x π/180.
A magician is filling his underwater escape tank with water. It is being filled by two water hoses. Hose 1 can fill the tank in 4 hours, while both hoses together can fill the tank in 2 hours. How long does it take to fill the underwater escape tank tank using only hose 2? type just the number no words
Answers
Answer:
4 hours
Step-by-step explanation:
how many five-miute segments are in 3\4 of an houre
i need help and fast is 23 points good
Answers
Answer: 9
Step-by-step explanation: because 3/4 of an hour is 45 minutes and 45/5 is 9 and it’s in 5 min segments that’s why you divide 45 by 5
sorry for the first one i read the question wrong
Its me I told u to look for my username to help me with this questions
Answers
Answer:
96
Once again, apologies for the chicken scratch
Answer:
$96
Step-by-step explanation:
→ Work out the discount multiplier
( 100 - 20 ) ÷ 100 = 0.8
→ Multiply answer by price
0.8 × 120 = $96
Element X is a radioactive isotope such that every 11 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 60 grams, how much of the element would remain after 25 years, to the nearest whole number?
Answers
Answer:
Ending Amount = beginning amount / 2^n where "n" is the number of half-lives or elapsed time / half-life
For this problem "n" = 25 / 11 = 2.2727272727
Ending Amount = 60 grams / 2^2.2727272
Ending Amount = 60 / 4.832357534
Ending Amount = 12.4162998242 grams
Source: www.1728.org/halflife.htm
Step-by-step explanation:
A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. The element would remain after 25 years, to the nearest whole number is 2 grams.
What is a radioactive isotope?A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. This surplus energy can be discharged as gamma radiation from the nucleus, transferred to one of its electrons and released as a conversion electron, or used to generate and produce a new particle from the nucleus.
Given the life of radioactive material is stated by the formula,
[tex]N_t = N_o e^{-\lambda t}[/tex]
Now, given the half-life of the comes in 11 years, therefore, the rate of decay will be,
[tex]N_t = N_o e^{-\lambda t}\\\\\dfrac{N_t}{ N_o }=e^{-\lambda t}\\\\0.5 = e^{-\lambda \times 11}\\\\\dfrac{ln(0.5)}{11}=\lambda[/tex]
λ = 0.14631
Given the initial mass is 60 grams, therefore, the amount that will be remaining after 25 years will be,
[tex]N_{25} = 60 \times e^{(-0.14631\times 25)}\\\\N = 1.5474\rm\ grams \approx 2\ grams[/tex]
Hence, the element would remain after 25 years, to the nearest whole number is 2 grams.
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