Which point would be a solution to the system of linear inequalities shown below? {see image for inequalities}
(-10, -2)
(−5,2)
(10,7)
(10,−2)
Answers
Answer:
(10, -2)
Step-by-step explanation:
The inequalities are:
y < x - 7 (1)
y < (1/5)x - 2 (2)
To solve this problem, we have to solve both equations simultaneously and then find the value of x and y that makes the inequality true.
To solve the inequality, subtract inequality (2) from inequality (1) which gives:
0 < (4/5) x - 5
-(4/5)x < -5
Dividing both sides of the equation by -4/5 gives:
-(4/5)x / (-4/5) < -5/ (-4/5)
x > 6.25
Put x > 6.2 in inequality 1
y < 6.25 - 7
y < -0.75
The solution of the inequality is x > 6.25 and y < -0.75
From the list of option, the correct answer is (10, -2) since 10 > 6.25 and -2 < -0.75
Related Questions
what are the order of operations for integers ?
Answers
Answer:
PEMDAS
Step-by-step explanation:
P - Parentheses (Brackets also!)
E - Exponents
M and D - Multiplication and division. Many people think multiplication has to be done first as said in "PEMDAS" but it doesn't. Do multiplication and division according to which ever one is farthest to the left (left to right).
A and S - Addition and subtraction. Same thing applies here, neither addition or subtraction has to be done first, just do them according to which one is farthest to the left when reading the expression from left to right.
If p-1 is a factor of p^4+p^2+p-k,the value of k is ?
Answers
[tex]1^4+1^2+1-k=0\\3-k=0\\k=3[/tex]
Answer:
k=3
Step-by-step explanation:
Hello, if p-1 is a factor of
[tex]f(p)=p^4+p^2+p-k[/tex]
it means that f(1)=0, so
1+1+1-k=0
3-k=0
k=3
thank you
Need help please asap this is not asap but please still give an answer im stuck
Answers
Answer:
135 cubes
Step-by-step explanation:
First, find the volume of the box with the equation V = Bh, where B is the area of the base and h is the height.
V = (2.25)(0.75)(1.25)
V = 2.109375
Next, find the volume of one cube with the side length 1/4 with V = Bh:
V = (0.25)(0.25)(0.25)
V = 0.015625
Then, divide the volume of the box by the volume of one cube:
2.109375 / 0.015625
= 135
What is the perimeter of a square with side length (2x-3)?
Answers
Answer:
Perimeter = 8x - 12
Step-by-step explanation:
The perimeter of a square is:
p = 4(side length)
on this case:
p = 4(2x-3)
p = 4*2x + 4*-3
p = 8x - 12
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answers
Answer:
The third option: x= [tex]\frac{8}{3} \pi[/tex]
Step-by-step explanation:
Arc length formula=[tex]\frac{Central Angle}{360} * 2\pi r[/tex]
Arc length = [tex]\frac{120}{360} *2\pi (4)[/tex]
=[tex]\frac{8}{3}\pi[/tex]
Cheryl earns (p+3) dollars per hour. In 8 hour she earns ___ dollars.
Answers
Answer:
8p + 24 dollars
Step-by-step explanation:
1 hour = (p+3)
8 hours = 8 (p+3)
=> 8p + 24
In 8 hours, Cheryl earns 8p + 24 dollars.
Answer:
[tex]\boxed{8p + 24}[/tex]
Step-by-step explanation:
Hey there!
Well if Cheryl earns p + 3 per hour and it is asking us to find the amount made in 8 hours, we can make the following,
8(p + 3)
8*p = 8p
8*3 = 24
Together,
8p + 24
Hope this helps :)
Combine your expressions from part E (x+2) and part F (y+ (-4) to give the pair of coordinates of any point after a translation two yards East and four yards south.
Answers
Answer:
A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)
Step-by-step explanation:
A transformation is the movement of a point from its initial position to a final position. If an object is transformed all its points are also transformed. Types of transformation are reflection, rotation, translation and dilation.
If a point O(x, y) is translated left by h unit, the new coordinate is O'(x-h, y) while if O(x, y) is translated right by h unit the new coordinate is O'(x+h, y)
If a point O(x, y) is translated up by h unit, the new coordinate is O'(x, y+h) while if O(x, y) is translated down by h unit the new coordinate is O'(x, y-h)
The location of the shape as shown in the diagram is:
A(3, 6), B(3, 3), C(4, 3), D(4, 6)
If the points are translated two yards East and four yards south, it means it is translated 2 unit right and 4 unit down i.e. (x+2, y-4). The new coordinates are:
A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)
Answer:
ombining the expressions from parts E and F, for any given initial point (x, y), the coordinates of the new point after a translation of two yards east and four yards south are (x + 2, y + (-4)).
Step-by-step explanation:
this is more simple
find the area of a sector with a central angle of 150 and a diameter of 7.8 cm
Answers
Answer:
19.9 cm²
Step-by-step explanation:
The following data were obtained from the question:
Angle at the centre (θ) = 150°
Diameter (d) = 7.8 cm
Area of sector =.?
Next, we shall determine the radius.
This can be obtained as illustrated below:
Radius (r) = Diameter (d) /2
r = d/2
Diameter (d) = 7.8 cm
Radius (r) =.?
r = d/2
r = 7.8/2
r = 3.9 cm
Finally, we shall determine the area of the sector as follow:
Angle at the centre (θ) = 150°
Radius (r) = 3.9 cm
Pi (π) = 3.14
Area of sector (A) =.?
A = θ/360 × πr²
A = 150/360 × 3.14 × 3.9²
A = 15/36 × 3.14 × 15.21
A = 19.9 cm²
Therefore, the area of the sector is 19.9 cm²
Add or subtract. Write your answer in scientific notation.
4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5
3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8
8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3
Answers
Answer:
1. 38.3 x 10^5
2. 6.67 x 10^9
3. 4.48 x 10^4
Step-by-step explanation:
4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5
For the above question, we need to make the exponents equal
=> 42 x 10^5 - 1.2 x 10^5 - 2.5 x 10^5
SInce, all the exponents are equal, we can now add and subtract the normally.
=> (42 - 1.2 -2.5) x 10^5
=> (42 - 3.7) x 10^5
=> 38.3 x 10^5
So, the answer to the 1st question is 38.3 x 10^5
Next question:
=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8
=> we need to make the exponents equal
=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9
=> All the exponents are equal, we can now add and subtract the normally.
=> (3.3 + 2.6 + .77) x 10^9
=> 6.67 x 10^9
=> So the answer to the 2nd question is 6.67 x 10^9
Next question,
=> 8 X 10^4 - 3.4 x 10^4 - 1.2 x 10^3
=> we need to make the exponents equal
=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4
=> All the exponents are equal, we can now add and subtract the normally.
=> (8 - 3.4 - .12) x 10^4
=> 4.48 x 10^4
=> So the answer to the 3rd question is 4.48 x 10^4
The solutions to the expressions are:
[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]=[tex]38.3\times 10^5[/tex]
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex] = [tex]6.67\times 10^9[/tex]
[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex] = [tex]4.48 \times 10^4[/tex]
[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]
Combine like terms:
[tex]4.2 \times 10^6 - (1.2+2.5) \times 10^5[/tex]
[tex]4.2 \times 10^6 - 3.7 \times 10^5[/tex]
[tex]42 \times 10^5 - 3.7 \times 10^5[/tex]
[tex](42-3.7)\times 10^5[/tex]
[tex]38.3\times 10^5[/tex]
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex]
Convert all terms with same power:
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9[/tex]
[tex](3.3+2.6+0.77) \times 10^9[/tex]
[tex]6.67\times 10^9[/tex]
[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex]
[tex]8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4[/tex]
[tex](8.0-3.4-0.12) \times 10^4[/tex]
[tex]4.48 \times 10^4[/tex]
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There are 67 bikes in the bike rack outside a school. Out of all the bikes, 33 are silver. Half of the remaining
bikes are red.
Estimate how many bikes are red.
Answers
Answer:
17
Step-by-step explanation:
67 minus 33 leaves 34 red bikes but divided that by half gives you 17
There are approximately 17 red bikes in the bike rack outside the school.
What is Algebra?Algebra is the estimation of mathematical representations, while logic is the manipulation of those symbols.
We can solve this problem by setting up an equation to represent the relationship between the number of bikes in the bike rack, the number of silver bikes, and the number of red bikes.
Let's define a variable, r, to represent the number of red bikes. We know that 33 bikes are silver, so the number of bikes that are not silver is 67 - 33 = 34 bikes.
Half of the remaining bikes are red, so we can say that there are r = 34/2 = 17 red bikes.
Therefore, there are approximately 17 red bikes in the bike rack outside the school.
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Write and solve an equation to answer the question. How many people must attend the third show so that the average attendance per show is 3000?
Answers
Answer:
3250
Step-by-step explanation:
so for the first and 2nd show, the attendance is 2580 and 2920.
The average of both these numbers is 2750
the if the third show had 3000 people, the average attendance would only be 2875.
We need the average number to be 3000.
2750 is 250 less than 3000, so the other number must be 250 more.
3250 is how many people should go to the last show.
=====================================
Explanation:
We have 2580 people attend the first show and 2920 attend the second. So far, that's 2580+2920 = 5500 people. Add on another x people to get 5500+x, which represents the sum of all three days attendance figures. Divide this sum by 3 to get the average attendance
average attendance = (sum of individual attendance values)/(number of days)
average attendance = (5500+x)/3
So that's why (5500+x)/3 goes in the first box. The parenthesis are important to ensure that you divide all of "5500+x" over 3. If you just wrote 5500+x/3, then the computer would think you just want to divide x only over 3.
----------------
We set (5500+x)/3 equal to 3000 as we want the average of the three days to be 3000
(5500+x)/3 = 3000
5500+x = 3*3000
5500+x = 9000
x = 9000-5500
x = 3500
We need 3500 people to show up on day 3 so that the average of all three days is 3000.
3500 goes in the second box.
----------------
Check:
The figures for the three days are 2580, 2920, and 3500
They add to 2580+2920+3500 = 9000
Which divides to 9000/3 = 3000, which is the average we're after. So the answer is confirmed.
The company will be launching a firework from the ground, but you want to increase the time it stays in the air by 2 seconds to build up the suspense. How can the company make this happen without changing the length of the fuse? How will this affect the maximum height of the firework? g(t) = -16t2 + 224t + 120
Answers
Answer: find the answer in the explanation.
Step-by-step explanation:
To increase the time the fireworks stays in the air by 2 seconds to build up the suspense, 2 should be added to the time t.
T + 2 = t
T = t - 2
Substitute T for t in the function g(t)
The company will make this happen without changing the length of the fuse by substituting T for t which will lead to
g(t) = -16(t - 2)^2 + 224(t - 2) + 120
How will this affect the maximum height of the firework?
Initially the function is:
g(t) = -16t2 + 224t + 120
Where the time at maximum height is found by using the formula
t = -b/2a
b = 224, a = -16
Substitutes both into the formula
t = -224/2(-16)
t = -224/-32
t = 7
Substitute 7 for t in the first equation
g(t) = -16(7)^2 + 224(7) + 120
g(t) = -16(49) + 224(7) + 120
g(t) = -784 + 1568 + 120
g(t) = 904 metres
But when the time is delayed by 2 seconds in the air, the maximum height will be
g(t) = -16( 7 - 2 )^2 + 224(7 - 2) + 120
g(t) = -16(5)^5 + 224(5) + 120
g(t) = -16(25) + 224(5) + 120
g(t) = -400 + 1120 + 120
g(t) = 840
The effect will surely reduce the maximum height of the fireworks.
88 feet/second = 60 miles/hour. How many feet per second is 1 mile/hour? (Hintdivide both sides of the equation
by the same amount.)
Round to the nearest thousandth.
One mile per hour is equivalent to
ao feet/second.
Answers
Answer:
1 miles/hour = 1.467·feet/second
Step-by-step explanation:
The given measurement unit are;
88 feet/second = 60 miles/hour
The number of feet per second that is equal to one mile per hour is found as follows;
88 feet/second = 60 miles/hour
To have a unit measure of one mile per hour , we divide both sides of the equation by 60 to get
(88 feet/second)/60 = (60 miles/hour)/60
Which gives;
(88/60 feet/second) = (60/60 miles/hour) = 1 miles/hour
22/15 × feet/second = 1 miles/hour
1.46667·feet/second = 1 miles/hour
Rounding to the nearest thousandth gives;
1.467·feet/second = 1 miles/hour
The number of feet per second that is in 1 mile per hour is 1.467·feet/second.
Which table represents a function?
Answers
Answer:
A
Step-by-step explanation:
it is A for every output y , there is only one input x
Answer:
A
Step-by-step explanation:
Because all the x-intercepts are different. Whereas all the other ones have repeats of numbers in the x-intercepts.
A number “x” increased by 5 is 19?
Answers
Answer:
x+5=19
Step-by-step explanation:
i think that right let me know...:/
Answer:
x= 14
Step-by-step explanation:
a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes
x+5=19
19-5=x
14=x
PLEASE HELP!!!!
The degree of x y 3 + 5 x 2 y − 3 x xy 3 +5x 2 y−3xis 8. True False
Answers
Answer:
it's true
Step-by-step explanation:
inscribed angles. help asap!
Answers
Answer:
20°
Step-by-step explanation:
The measure of the inscribed angle is equal to the half of the arc it sees
Since AC is the diameter the measure of arc ABC is 180°
and since A sees arc BC and C sees the arc AB
A< + C< = 90° so angle C = 20°
find the roots of the following equation X + 1 whole square minus x square equal to 2
Answers
Answer:
x = 1/2
Step-by-step explanation:
Let's represent this in a mathematical way,
(x+1)^2 - x^2 = 2
Ok now we expand,
x^2 + 2x + 1 -x^2 = 2
rearrange,
x^2 - x^2 + 2x + 1 = 2
subtract,
2x + 1 = 2
subtract 1 from both sides,
2x + 1 - 1 = 2 - 1
2x = 1
Now divide 2 from both sides and get your answer,
x = 1/2
Answer:
[tex](x + 1) { }^{2} - x {}^{2} = 2[/tex]
[tex]x {}^{2} + 2x + 1 - x {}^{2} = 2[/tex]
[tex]2x + 1 = 2[/tex]
[tex]x = 1 \div 2[/tex]
what are the roots of the quadratic equation below 2x^2+8x+7=0
Answers
Answer:
x = -1.29 and -2.71
Step-by-step explanation:
Use the quadratic formula, which is [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-8+\sqrt{8^2-4(2)(7)} }{2(2)}[/tex] and [tex]\frac{-8-\sqrt{8^2-4(2)(7)} }{2(2)}[/tex]
[tex]\frac{-8+\sqrt{8} }{4}[/tex] and [tex]\frac{-8-\sqrt{8} }{4}[/tex]
Further reduced down to:
[tex]\frac{-8+2\sqrt{2} }{4}[/tex] and [tex]\frac{-8-2\sqrt{2} }{4}[/tex]
In decimal form, to the hundredths place, both of these are:
-1.29 and -2.71
find six rational numbers between 3 and 4
Answers
Answer:
3.1
3.2
3.3
3.4
3.5
3.6
Hope this answer correct :)
Two trains station at the same time one travels east at 8 miles per hour .The other train traveles east at 8 millas per hour the other train travels west at 11 miles per hour in how many hours will the two trains apart
Answers
helpppppppppppppppp
Express the following English phrase using an algebraic expression.
The product of 12 and a number y.
Represent "The product of 12 and a number y " mathematically.
Answers
Answer:
12y
Step-by-step explanation:
product means multiplycation so twelve times y is 12y
Can someone answer this please? Okay so it says that something is made 3 times than the other item. The other item uses 13 beads. So, what is 13 times 3?
Answers
Answer:
13x3= 39
Step-by-step explanation:
10x3=30
3x3=9
30+9=39
Hope it helps!
The tens digit of a two-digit number is three times greater than the ones digit. The difference between twice the original number and half the number obtained after reversing the digits is 108. What is the original number? Show your work.
Answers
Answer:
Now solve these two equations.ull get andwer
The original number will be "63".
Let,
The ten's digit be "x".One's digit be "y".The equation will be:
→ [tex]x=y+3[/tex]...(equation 1)
Original number will be:
→ [tex]10x+y[/tex]
then,
→ [tex]2 (10x+y)-\frac{(10y+x)}{2} = 108[/tex]
→ [tex]\frac{4(10x+y)}{1} -(10y+x) = 216[/tex]
→ [tex]40x+4y-10y-x = 216[/tex]
→ [tex]39x-6y=216[/tex]...(equation 2)
By using (equation 1) and (equation 2), we get
→ [tex]39(y+3)-6y=216[/tex]
→ [tex]39y+117-6y=216[/tex]
→ [tex]33y=99[/tex]
→ [tex]y = \frac{99}{33}[/tex]
→ [tex]= 3[/tex]
Now,
[tex]x = y+3[/tex]
[tex]=3+3[/tex]
[tex]=6[/tex]
hence,
The original number will be:
= [tex]10x+y[/tex]
= [tex]10\times 6+3[/tex]
= [tex]60+3[/tex]
= [tex]63[/tex]
Thus the above approach is right.
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Answers
Answer:
[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]
Step-by-step explanation:
[tex]2x^2-8x=-7[/tex]
[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]
[tex]2x^2-8x+7=-7+7[/tex]
[tex]2x^2-8x+7=0[/tex]
[tex]ax^2 +bx+c=0[/tex]
[tex]\sf Apply \ quadratic \ formula.[/tex]
[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]
[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]
[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]
[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]
[tex]x=2\pm \frac{\sqrt{2}}{2}[/tex]
Please help ASAP. The question is down below.
Answers
Answer:
2.7 hours
Step-by-step explanation:
We can use the formula
1/a + 1/b = 1/c
where a and b are the times working alone and c is the time working together
1/8 + 1/b = 1/2
Multiply each side by 8b to get rid of the fractions
8b( 1/8 + 1/b = 1/2)
b + 8 = 4b
Subtract b from each side
b+8-b = 4b-b
8 = 3b
Divide each side by 3
8/3 = 3b/3
2.666666repeating = b
Round to 1 decimal place
2.7 = b
Answer:
2.7 hr
Step-by-step explanation:
2/8 +2/x = 1
2x+16 =8
16/8
x=8/3 =2.7
can you make a triangle with 1. 2cm 3cm and 4cm 2. 2cm 3 cm 6 cm 3. 90 degrees 45 degrees 45 degrees 4. 90 degrees 60 degrees 60 degrees?
Answers
Answer:
1. 2cm 3cm and 4cm
yes, because 2+3>4
2. 2cm 3 cm 6 cm
no, 2+3<6
3. 90 degrees 45 degrees 45 degrees
yes, 90+45+45 = 180
4. 90 degrees 60 degrees 60 degrees?
no, 90+60+60=210!=180
The width of a rectangle measures (8.3c-8.4d)(8.3c−8.4d) centimeters, and its length measures (5.3c+4.8d)(5.3c+4.8d) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Answer:
P = 27.2c-7.2d
Step-by-step explanation:
It is given that,
The width of a rectangle is (8.3c-8.4d)
The length of a rectangle is (5.3c+4.8d)
The perimeter of a rectangle is equal to the sum of its all sides i.e.
P = 2(l+b)
P = 2(8.3c-8.4d+5.3c+4.8d)
P = 2[(8.3c+5.3c)+(4.8d-8.4d)]
P = 2(13.6c-3.6d)
⇒P = 27.2c-7.2d
Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.
Plz ans ASAP! Tysm! Pzlllzzz!
Answers
Answer:
Step-by-step explanation:
Number of class intervals = 7
Class width = 5
Class intervals (heights) Frequency (Number of boys)
130 - 135 3
136 - 140 5
141 - 145 3
146 - 150 5
151 - 155 2
156 - 160 1
161 - 165 1
Therefore, frequency table given above will represent the distribution of the heights and number of students.
This composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units. 2 identical pyramids with rectangular bases are connected at their base. The height of the pyramid is 2. The lengths of the sides of the rectangle are 5 and 0.25 units. Which expression represents the volume, in cubic units, of the composite figure? One-half (One-third (5) (0.25) (2) ) One-half (One-third (5) (0.25) (4) ) 2(One-third (5) (0.25) (2) ) 2(One-third (5) (0.25) (4) )
Answers
Answer:
The total volume of the solid is 1.67 cubic units.
Step-by-step explanation:
Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.
1/3 x (area of base) x height
= 1/3 x (5 x 0.25) x 2= 0.833
Therefore, the volume of each pyramid will be
= cubic units.
So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)
Hope it helped ya!
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Tysmm
The total volume of the solid is 1.67 unit³.
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given:
Each pyramid has a height of 2 units.
and the rectangular base with dimensions of 5 units × 0.25 units.
So, the Volume of each Pyramid is
= 1/3 x (area of base) x height
= 1/3 x (5 x 0.25) x 2
= 0.833
and, the total volume of the solid
= (2 × 0.833)
= 1.67 cubic units.
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