The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)
What is a system of equations?A system of equations are two (or more) equations that have common variables.
The system of equation is presented as follows;
20·x + 20·y = -2
2·x + 5·y = -8
The specified possible solution of the equation is; (1, -2)
Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;
20·x + 20·y = -2
20·y = -2 - 20·x
y = (-2 - 20·x)/20
Therefore; y = (-2 - 20 × 1)/20 = -1.1
When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2
Evaluating the second equation, we get;
2·x + 5·y = -8
5·y = -8 - 2·x
y = (-8 - 2·x)/5
Plugging in x = 1, we get;
y = (-8 - 2 × 1)/5 = -2
When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation
The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;
y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5
Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5
-10 - 100·x = -160 - 40·x
60·x = 150
x = 150 ÷ 60 = 2.5
x = 2.5
y = (-2 - 20 × 2.5)/20 = -2.6
y = -2.6
The correct option is therefore, no, the solution to the system of equation is; (2.5, -2.6)Learn more about systems of linear equations here: https://brainly.com/question/11867840
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Activity 1.1 Simplify Me Simplify by removing perfect nth powers: 1. √20 2. √300 3. √128 3 4. √ 5 3 5. √50 3
Answer:
[tex](a)\ \sqrt{20}=2\sqrt{5}[/tex]
[tex](b)\ \sqrt{300} = 10 \sqrt{3}[/tex]
[tex](c)\ \sqrt{128} = 8 \sqrt{2}[/tex]
Step-by-step explanation:
Required
Simplify
[tex](a)\ \sqrt{20}[/tex]
Express 20 as 4 * 5
[tex]\sqrt{20}=\sqrt{4 * 5}[/tex]
Split
[tex]\sqrt{20}=\sqrt{4} * \sqrt{5}[/tex]
This gives:
[tex]\sqrt{20}=2 * \sqrt{5}[/tex]
[tex]\sqrt{20}=2\sqrt{5}[/tex]
[tex](b)\ \sqrt{300[/tex]
Express as 100 * 3
[tex]\sqrt{300} = \sqrt{100} * \sqrt{3}[/tex]
This gives:
[tex]\sqrt{300} = 10 * \sqrt{3}[/tex]
[tex]\sqrt{300} = 10 \sqrt{3}[/tex]
[tex](c)\ \sqrt{128}[/tex]
Express as 64 * 2
[tex]\sqrt{128} = \sqrt{64*2}[/tex]
Split
[tex]\sqrt{128} = \sqrt{64} * \sqrt{2}[/tex]
[tex]\sqrt{128} = 8 * \sqrt{2}[/tex]
[tex]\sqrt{128} = 8 \sqrt{2}[/tex]
Questions 4 and 5 are not clear
Follow the steps in 1 - 3 to solve 4 and 5
(sin 9x)'
what is the derivative of sin 9x
Answer:
[tex]\displaystyle \frac{d}{dx}[\sin(9x)] = 9 \cos(9x)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sin(9x)[/tex]
Step 2: Differentiate
Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \cos(9x)(9x)'[/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = 9 \cos(9x)(x)'[/tex]Basic Power Rule: [tex]\displaystyle y' = 9 \cos(9x)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the sum of the interior angles of a 35-gon?
What is the number of sides of a polygon that has the sum of the interior angles equal to 2340°?
Answer:
5940
number of sides = 15
Step-by-step explanation:
Sum of the interior angles = (n-2)×180
(35-2)×180
=33×180
= 5940
Sum of the interior angles = (n-2)×180
(n-2)×180 = 2340
(n-2) = 2340/180
n-2 = 13
n = 13 + 2 = 15
so total sides are 15
PLEASE HURRY!!
Find the value of x
Answer:
Step-by-step explanation:
3x=24
x=8
Nick mowed about 3.5 of the school lawn yesterday. He mowed another 1/4 of the lawn this morning. How much is left to mow? Answer if you can.
The portion left to mow is 3x+3.5 /4
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here:Nick mowed about 3.5 of the school lawn yesterday. He mowed another 1/4 of the lawn this morning. Let the whole lawn be x then on the first day portion left to be mowed is x-3.5 and on the second day he moved 1/4 of this quantity thus portion of lawn left to be mowed is
x-x-3.5/4
=3x+3.5 /4
Hence, The portion left to mow is 3x+3.5 /4
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Answer needed quick! Problem is attached as a picture. find the surface area of the hemisphere (links and spam will b reported <3)
Answer:
Surface area of hemisphere = 150.72 meter²
Step-by-step explanation:
Given;
Diameter of hemisphere = 8 meter
Find:
Surface area of hemisphere
Computation:
Diameter of hemisphere = 8 meter
Radius of hemisphere = Diameter of hemisphere / 2
Radius of hemisphere = 8 / 2
Radius of hemisphere = 4 meter
Surface area of hemisphere = 3πr²
Surface area of hemisphere = 3(22/7)(4)²
Surface area of hemisphere = 3(22/7)(16)
Surface area of hemisphere = 3(3.14)(16)
Surface area of hemisphere = (9.42)(16)
Surface area of hemisphere = 150.72 meter²
Which of the following numbers is closest to 7?
Answer:
B. √50
Step-by-step explanation:
[tex]7^{2}[/tex] is 49 so √49 is 7
So,
since the closest number to 49 is 50, that is the answer.
[tex]\sqrt{51}[/tex] is the closest square root to 7.
What is square root?The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. If a number is a perfect square, we can easily find the square root of the number. If the given number is not a perfect square number, the square root can be found using the long division method.
[tex]\sqrt{51} = 7.141\\\sqrt{50} = 7.071\\ \sqrt{46} = 6.782\\ \sqrt{47} =6.855[/tex]
(using calculator)
Absolute distance from 7 :
|7.141 - 7| = 0.141
|7.071 - 7| = 0.71
|6.782 - 7| = 0.218
|6.855 - 7| = 0.145
(The absolute value of a number refers to the distance of a number from the origin of a number line. It is represented as |a|, which defines the magnitude of any integer ‘a’. The absolute value of any integer, whether positive or negative, will be the real numbers, regardless of which sign it has. It is represented by two vertical lines |a|, which is known as the modulus of a.)
Since, 0.141 is the least distance. [tex]\sqrt{51}[/tex] is the closest square root to 7.
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Dale has $1,000 to invest. He has a goal to have $2,400 in this investment in 12 years. At what annual rate compounded continuously will Dale reach his goal?
Answer:
7.29%
Step-by-step explanation:
Given data
Principal= $1,000
Final amount= $2,400
TIme= 12 years
The expression for the compound interest is given as
A= P(1+r)^t
Make r subject of fomula
r = ln(A/P) / t
r= ln(2400/1000)/12
r= ln(2.4)/12
r= 0.875/12
r= 0.0729
Hence the rate is 7.29%
what are the missing lengths?
Answer:
U can find it using Cos 60 degree
For what value of a the system of equations Ax Y 2 and 6x 2y 3 has a unique solution?
A = 1, y = -2/3, The value of a for which the system of equations has a unique solution is a = -3.
1. Set the first equation equal to 0:
2x + ay = 2
2. Subtract 2x from both sides of the equation to get:
ay = -2
3. Divide both sides of the equation by a to get:
y = -2/a
4. Substitute this value of y into the second equation to get:
6x + 3(-2/a) = 3
5. Multiply both sides of the equation by a and simplify to get:
6ax - 6 = 3a
6. Add 6 to both sides of the equation to get:
6ax = 3a + 6
7. Divide both sides of the equation by 6 to get:
x = (3a + 6)/6
8. The value of a for which the system of equations has a unique solution is a = -3.
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In the figure below, find the length of AD. Round your answer to the nearest tenth.
B
10
Show Your Work
Answer:
12.4
Step-by-step explanation:
First you need to find the hypotenuse of the other triangle, because it makes up a necessary side for finding AD. Pythagorean theorem states that
a^2 + b^2 = c^2 where a and b are leg lengths and c is the hypotenuse. For the triangle on the left, you're given 2 legs. So you can substitute those into that formula:
a^2 + b^2 = c^2
(10)^2 + (6)^2 = c^2
100 + 36 = c^2
136 = c^2.
Now take the square root of both sides to isolate c.
11.6619038 = c.
11.6619038 rounds to 11.7 so c = 11.7
Now that you have the second leg length for the triangle on the right, you can find its hypotenuse.
Follow the same process. Substitute your values into the equation and then solve for c:
a^2 + b^2 = c^2
(11.7)^2 + (4)^2 = c^2
136.89 + 16 = c^2
152.89 = c^2
Now find the square root of both sides to isolate c
12.3648696 = c.
12.3648696 rounds to 12.4 so c = 12.4
So the distance of AD is 12.4
Please enter the missing number: 4, 8, 14, 22, ?
A. 26
B. 28
C. 32
D. 36
E. 40
Answer:
C) 32
Explanation:
it's adding by 4, 6, 8, and then 10; 22 + 10 = 32, so C will be the answer.
Hope this helps!
The brain volumes ?( cm cubed cm3?) of 20 brains have a mean of 1083. 9 1083. 9 cm cubed cm3 and a standard deviation of 122. 2 122. 2 cm cubed cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such? data, would a brain volume of 1348. 3 1348. 3 cm cubed cm3 be significantly? high?
Therefore , the solution of standard deviation is because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
what is the standard deviation?Standard deviation, often known as variance in a set of data, is a statistical measure of variation. A low standard deviation indicates that the values are more likely to be near the mean of the collection, whereas a high standard deviation indicates that the values are widely distributed. How far the data depart from the mean is expressed by the standard deviation, abbreviated as.
Here,
Considering the details here,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
The much lower results are u-2 = 11169.8-2(126.2) => 917.4.
Reason: According to the range rule of thumb, the required incredibly low values are 91.7 cm3 or less.
Hint: Use the algorithm to identify values that are at least considerably high.
Step: 2
Considering the data supplied,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
Significantly higher values include,
u-2α = 11169.8+ 2(126.2)
=> 1422.2
Justification: According to the range rule of thumb, the necessary significantly high values must be 1422.2 cm3 or higher.
Hint: To determine whether the value 1452.2 cm3 is very high, use the findings of steps (1) and (2).
Step: 3
Using step 1 and step (4),
917.4 is among the significantly low numbers or less.
The significantly high values are 1422.2 or higher.
Yes, 1452.2 cm3 is a noticeably high value.
The apt response is choice (B).
Reason: The value is much higher than expected based on the range rule of thumb because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
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A woman has a ladder that is 13 feet long. If she sets the
base of the ladder on level ground 5 feet from the side of a
house, how many feet above the ground will the top of the
ladder be when it rests against the house?
11
12
8
9
Answer:
8 is the answer
lemme know ——————————-
Answer:
121
Step-by-step explanation:
180 - (56 + 65) = 59
180 - 59 = 121
Riley's dentist has an aquarium in his office with the dimensions 16 in. By 8.5 in. By 10.5 in. What is the volume of the aquarium?
Answer:
1428
Step-by-step explanation:
I did 16 times 8.5 times 10.5. Good Luck!
Pleas help me with #2, thanks
A 30-60-90 triangle has a short leg of 6.
What is the length of the long leg?
Answer:
6√3
Step-by-step explanation:
PLEASE HELP ME ASAP!!!!!!!
At a carnival, Diana sees a balloon shooter game. The ticket cost is $3. The rule is that the first person to shoot 10 balloons from a total 30 balloons wins $10. What is the expected payoff for the winner?
Answer:
$13
Step-by-step explanation:
The expected payoff for the winner would be the ticket cost, $3, plus the prize money, $10, which totals $13. This is the expected value of playing the game. However, it's important to note that this does not guarantee that the winner will receive exactly $13, as the outcome of the game is dependent on chance and the player's skill. There is always a chance that the player could win more or less than the expected value.
Jessica has eaten 3 1/2 hot dogs of the 10 hot dogs she
recently found in her freezer. What percent of the hot
dogs has she eaten?
Answer:
65%
Step-by-step explanation:
100%-> 10
1%->0.1
----------------------------
10 - 3 1/2 = 6 1/2
6 1/2 ÷ 0.1 = 65
The value of y varies directly with x. If x = 3, then y = 4. What is the value of x when y = 120 ?
Answer:
x = 90
Step-by-step explanation:
If x = 3 and y = 4 then when y = 120 just find out what times 4 = 120
which is 30.
so just multiply 30 for x = 3, then the answer will be 90
x = 90
Answer:
x=90
Step-by-step explanation:
x is directly proportional to y
Therefore, if the initial y value was 4 and the final y value is 120. This means that y initial had been multiplied 120/4 times, which is 30.
Same goes for x. If x initial is 3, then the final x value would be x/3=30. This means that x=3×30, which is equal to 90.
The coefficient b and c in the equation x^2bxc=0 are alo the root of that equation (c≠0)
[tex]x^2[/tex] - (b+c)x +bc=0 is the quadratic equation whose roots are b,c.
If the roots of a quadratic equation are given, the equation can be written by factoring the equation using the roots.
Given the roots, let's say r1 and r2, the quadratic equation can be written as (x - r1)(x - r2) = 0.
Expanding the above equation x^2 - (r1 + r2)x + r1r2 = 0
Therefore, if the roots of a quadratic equation are given as r1 and r2, the quadratic equation can be written as:
x^2 - (r1 + r2)x + r1r2 = 0
since we are given that the root of the equation are b,c;
so r1=b,r2=c;
putting the value in the above equation we get the equation with b and c as root:
[tex]x^2[/tex] - (b+c)x +bc=0
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Complete question :
The coefficient b and c in the equation [tex]x^2+bx+c[/tex] is also root of another equation where c≠0 .
please write the equation
Find the product shown below in simplest standard form. (x + 5)(x - 5)
help
Answer:
Step-by-step explanation:
X^2-5^2
X^-25
In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76°, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot. °, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot
The length of OP to the nearest tenth of a foot is 16.9 ft
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
ΔOPQ is right triangle
Tan (p) = opposite/adjacent = OQ/PQ
Tan (76) = OQ/4.1
4.010 = OQ/4.1
OQ = 4.010 * 4.1 = 16.441
OP² = OQ² + PQ² = 16.441 ² + 4.1² = 287.116
=> OP = √ 287.116 = 16.944
OP≅ 16.9 ft
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SOMEONE HELP ME PLSSSS
simplify (pic below)
Answer:
10^11
Step-by-step explanation:
This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.
Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.
10 ^ (8+3)
= 10^11
see image
Mila cuts a sphere with a 13-inch radius in half. Whats the area of the cross section of the sphere in square inches in terms of pi
The area of the cross-section of the sphere in square inches in terms of pi will be 169π inch^2.
The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.
An area is projected onto the plane when a plane slices through a solid object. The axis of symmetry is then perpendicular to that plane. The cross-sectional area refers to its projection.
The cross-section of a sphere is a circle. Hence the area of the cross-section is the area of a circle with a radius of 13, which is given by π*r^2
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Find BC. AB=24 AC=24 BD=15
Answer:
b) BC = 30
Step-by-step explanation:
triangle ACD is equal to ABC so BC = 2xBD = 30
Isabella has already baked 4 pies, and she can bake 2 pies with each additional cup of sugar she buys. Write an equation that shows the relationship between the additional cups of sugar x and the number of pies y.
Answer:
It would be y = 2x+4
Step-by-step explanation:
This is because Isabella has started with 4 baked pies and is gaining additional pies with in amounts of 2 pies.
With this, 4 would be by itself and 2 would be attached to the variable x for the unknown amount of additional pies.
Lastly, you would have this all equaling y, as y is the total amount of pies.
How to find the side of a triangle given two angles and one side?
If you know two angles and one side of a triangle, you can use the Law of Cosines to find the length of the other two sides.
The Law of Cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite to those sides, the following formula holds:
c² = a² + b² - 2ab cos(C)
Where C is the angle opposite to side c.
So, if you know the measures of two angles (A and B) and the length of one side (c), you can use the Law of Cosines to find the lengths of the other two sides (a and b) by using the following formulas:
a = √(c² + b² - 2bc cos(A))
b = √(c² + a² - 2ac cos(B))
You can use the above equations to find the sides of the triangle, if you have the measures of two angles and one side.
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Shelia works at the ice cream shop and makes $8.00 an hour during the day, and one and a half times that rate in the evening. Last week she worked 12 hours during the day and 6 hours at night. How much was her paycheck?