No, If y² varies directly with x², it does not that mean y must vary directly with x
Let's say y² = 16 and x² = 4
Now if y² = 16
Then y = 4 or -4 and same for x = 2 or -2
As the square root can be either negative or positive, if y² varies directly with x², it does not that mean y must vary directly with x .
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Ayudenme a hacer mi tarea es para hoy
Answer:
Pon tu tarea aquí para que podamos ayudarte con ella :)
Please help ASAP and explain the way to get the answer!
Answer:
860.9 m³
Step-by-step explanation:
We can obtain the volume of the composite figure by subtracting the volume of cylinder from the volume of cuboid.
Cuboid or rectangular prism:l = 10 m
w = 10 m
h = 12 m
[tex]\sf \boxed{\text{ \bf Volume of cuboid = l *w * h}}[/tex]
= 10 * 10 * 12
= 1200 m³
Cylinder:r = 3 m
h = height of the cuboid = 12 m
[tex]\sf \boxed{\text{\bf Volume of cylinder = $\pi r^2h$}}[/tex]
= 3.14 * 3 * 3 * 12
= 339.1 m³
Volume of composite figure = 1200 - 339.1
= 860.9 m³
The difference of a number x and 5 is 6
fewer than twice the number x. (hint:
what type of phrase does "fewer than" or
"less than" mean?)
WILL GIVE BRAINLIEST! NEED HELP!!!
Answer: x=1
Step-by-step explanation:
x-5=2x-6
x-5+6=2x-6+6
x+1=2x
x-x+1=2x-x
2x-x=1
x=1
Answer: x = 1
Step-by-step explanation:
fewer or less than means minus -
difference of x and 5 = x - 5
6 fewer = - 6
twice the number of x = 2x
x - 5 = 2x - 6
x = 2x - 6 + 5
x -2x = - 6 + 5
- x = - 1
x = 1
checking
1 - 5 = 2(1) - 6
4 = 2 - 6
4 = 4
kx² 12x +9=0 find the value of K given that each equation has equal roots
Answer:
value of k is 3 to make it perfectly
Write a recursive formula for each sequence. 1,3,6,10, . . . . . . .
The recursive formula for the given sequence is a(n) = 2 a(n-1) - a(n-2) + 1
A recursive formula is an equation that express the nth term as a function of preceding term(s), i.e. as function of (n-1)th term, (n-2)th terms, and so on. Mathematically it can be written as:
a(n) = f(a(n-1), a(n-2), ..., a(1))
The given sequence: 1,3,6,10, . . .
Here a(1) = 1. Notice that:
a(2) = 3 = 1 + 2
a(3) = 6 = 3 + 3
a(4) = 10 = 6 + 4
Notice that the differences between terms increase by 1.
Further, we can write:
a(2) = 3 = 1 + (1 - 0) + 1
= a(1) + a(1) + 1
= 2a(1) + 1
a(3) = 6 = 3 + (3 -1) + 1
= a(2) + a(2) - a(1) + 1
= 2a(2) - a(1) + 1
a(4) = 10 = 6 + (6 - 3) + 1
= a(3) + a(3) - a(2) + 1
= 2 a(3) - a(2) + 1
We can continue this recursive pattern to find a(n),
a(n) = 2 a(n-1) - a(n-2) + 1
We can find next term for n = 5:
a(5) = 2a(4) - a(3) + 1
= 2. 10 - 6 + 1 = 15
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What are the solutions to the equation x² = 169? select each correct answer. −84.5 negative 84.5 −13 negative 13 13 13 84.5
The correct answer is A. 13.
We have been given equation. Now, to find the value of x, we will take square root. So, solving the mathematical expression now -
x = √169
Taking square root to find the value of x
x = 13
Since the number is positive. the square root of the number will also be positive.
Hence, the solution to equation is A. 13.
Further to cross check, we can also square the resultant number.
On squaring the number 13 for validation of our result, we get 169. It is the same number as in mathematical expression provided to us. Thus, our resultant solution to equation is correct.
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The complete question is -
What are the solutions to the equation x² = 169? Choose all answers that are correct. A. 13 B. –13 C. 84.5 D. –84.5
How is the Additive Identity Property similar to the Multiplicative Identity Property? How is it different?
How is the Additive Identity Property similar to the Multiplicative Identity Property?
A number's original value is returned when additive identity is applied to it. The original number is returned when multiplicative identity is multiplied by any number, too.All real numbers have both of these characteristics.How is it different?
Additive Identity is used in addition operation and multiplicative identity is used in multiplication operation.Additive Identity is denoted by a + 0 = a but multiplicative identity is denoted by a x 1 = a.The additive identity for any real number is 0 and multiplicative identity for any real number is 1.To learn more about additive identity property, refer:
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Example 1 Position and label each triangle on the coordinate plane.right ΔA B C with legs AC and AB so that AC is 2 a units long and leg AB is 2 b units long
The right-angle triangle on the coordinate plane will be drawn. Then the third length of the right triangle will be 2√(a² - b²) units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The right triangle ΔABC with legs AC and AB so that AC is 2a units long and leg AB is 2b units long.
We know that the angle ABC is a right angle which means 90°.
Then the third length of the right triangle will be
H² = P² + B²
(2a)² = (2b)² + B²
B² = 4a² - 4b²
B² = 4(a - b²)
B = 2√(a² - b²)
The right-angle triangle on the coordinate plane will be drawn.
The diagram is attached below.
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On olga's 16th birthday, her uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly. how much will olga have in the account when she turns 18? round to the nearest cent. the answer is not $2,071.19 the formula is b=p(1+r/n)^nt b = ending balance p = original balance r = interest rate expressed as a decimal n = number of times interest is compounded annually t = time in number of year
When Olga turns 18, she will have $3032.89 in her account, which earned a monthly compound interest rate of 1.75%.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula of monthly compound interest is:
B = P(1 + r)^t
where B is the ending balance, P is the principal amount or original balance, r is the monthly interest rate in decimal form, and t is the number of months.
If Olga's uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly, using the formula, solve for the ending balance after 2 years.
B = P(1 + r)^t
B = 2000(1+ 0.0175)^24
B = $3032.89
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MODELING REAL LIFE The parabola models the
height y (in feet) of a
snowboarder x seconds
after leaving a jump. Let
the x-axis represent the
base of the jump.
(See Example 4.)
Height (feet)
Height of
Snowboarder
y
20
10
0
(0.75, 18)
a. Write a function f
that models the
height of the
snowboarder over
time. How long is
the snowboarder in the air when he lands 7 feet
below the base of the jump?
-10
(0,9)
1
Time (seconds)
b. What is the average rate of change in the
snowboarder's height over the interval in
which the snowboarder's height is decreasing?
increasing? Compare the average rates of change.
For the given parabola, we have that:
a) The equation is: f(x) = -16(x - 0.75)² + 18.
b) The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (0.75,18), hence:
h = 0.75, k = 18.
f(x) = a(x - 0.75)² + 18.
When x = 0, y = 9, hence:
9 = 0.5625a + 18
a = -9/0.5625
a = -16.
Hence:
f(x) = -16(x - 0.75)² + 18.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
It is increasing between x = 0 and x = 0.75, in which f(0) = 9, f(0.75) = 18, hence:
r = 9/0.75 = 12.
The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.
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find the perimeter of the new similar triangle to the triangle below with a ratio of 3:5, old to new triangle
Answer:
perimeter: 14.5
Step-by-step explanation:
23.7-8.3+4.14=============
ANSWER:
19.54
Step-by-step explanation:
23.7-8.3
=15.4
15.4+4.14
=18.54
graph the solution to the following inequality: 38 - k < 5 - 2k
Answer:
k <−33
Step-by-step explanation:
You had 150 , but you are spending 2 each day. What algebraic expression models this situation?
If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x
Given,
The total amount you had = $150
The amount you spend in each day = $2
Consider the number of days = x
Then the algebraic expression for this situation is 150-2x
Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x
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The monthly minutes on your cell phone can add
up to no more than 700 minutes. You have used
648 minutes. Write an inequality that represents
how many more minutes m you can use during the
rest of the month.
The knowledge of how many more minutes m you can use during the rest of the month is given by the linear inequality 648 + m ≤700, where 'm' is the minutes on the cell phone or simply m ≤ 52
It is given that the monthly minutes on your cell phone can add up to no more than 700 minutes so the highest limit is 700
And You have already used 648 minutes so this is our base for the formation of linear inequality
We are provided to use 'm' for rest of the minutes on the cell phone
Hence, we can form a linear inequality using the three points as the sum of already used minutes and the maximum minutes that can be used in this month is at most 700 minutes is given by 648 + m ≤700
This can also be simplified as
m ≤ 700 - 648
m≤52
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Identify the pattern and find the next three terms.
1,3,5,7, .......
A scientist was in a submarine below sea level studying oceam life. Over the next ten minutes, she ascended 61.9 feet. How many feet had she been below sea level, if she was 21.6 feet below sea level after she ascended?
You can add the distance she travelled upwards to her new distance to get her old distance.
Essentially, 21.6 + 61.9 = 83.5.
This means she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.
Answer: she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.
Step-by-step explanation:
Help me please please
Order the numbers from least to greatest. Put the lowest number on the left. 6.826 6.628 6.286
The ordering of the number is 6.286 , 6.628 , 6.826
According to the question we have been given three numbers which are
6.826 , 6.628 and 6.286
We need to arrange in ascending order that is from least number to the greatest number.
when we arrange number in ascending order for decimal number we first look at the number before the decimal point then if they are all same then we look at the number after the decimal point. After the decimal point the first number is compared which is closest to the decimal point.
If we look into this question the number before decimal points are all same thus we will look the numbers after the decimal point. Therefore we will arrange according to the first number after the decimal that is 8 , 6 and 2
Hence the ordering the number we get:
6.286 , 6.628 , 6.826
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Find the slope of the line from the pair of points. (-2,0) (-4, -3)
A. 3/2
B. 2/3
C. -3/2
D. 2
What is the value of x ?
10 /x(x-2) + 4 / x=5 / x-2
Answer:
ue7e7373777 is is and 88877376363778
Which two decimal numbers are greater than 5.06 and less than 5.13 ?
5.18
5.0
5.21
5.09
5.1
The two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.
How to illustrate the information?It should be noted that decimals simply means.the numbers that aren't whole numbers.
It should be noted that this is a straight forward question.
Here, the two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.
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p=a+b solve for letter b
The value of b is b=p-a.
Given the equation is p=a+b.
A pair of inverse operations is defined as two operations to be performed on a number or. variable, always returns the original number or variable And inverse means opposite.
equation means a mathematical statement with the symbol "equal" between two expressions of equal value. This is represented by '='.
The given equation is p=a+b.
Now, we will apply the inverse operations on both sides.
Subtract a from both sides, we get
p-a=a+b-a
Now, we will simplify the above equation, we get
p-a=b
Hence, the value of b from the given equation p=a+b is b=p-a.
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If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct characters (letters or numbers)? report answer to 3 decimal places.
Using it's concept, there is a 0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
A standard deck is given by 4 suits of 13 cards, each with either a number from 1 to 10 or one letter from A, Q or K, hence:
For the first card, all can be selected.For the second card, 48 out of the remaining 51 cards will be available, removing the three cards with the same letter or number as the first.For the third card, 45 out of the remaining 50 cards will be available, removing the six cards whose letters or numbers have already been chosen.For the fourth card, 42 out of the remaining 49 cards will be available, removing the nine cards whose letters or numbers have already been chosen.Hence the probability is given by:
p = 48/51 x 45/50 x 42/49 = 0.726.
0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).
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In a company, 70% of the workers are men. If 990 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
Step-by-step explanation:
990 x 70% = 693 people
Find the value of A if the 4-digit number 3A5A is divisible by 15.
The value of A in the 4-digit number is 5.
What is the value of A?Given the information provided in the question, the 4-digit number is a multiple of 15. A multiple of a number is the product of an integer and that number.
The multiple of a number is divisible by that number. For example, a multiple of 2 is 20. This is because 2 multiplied by 10 is equal to 20 and 20 is divisible by 2 to yield a value of 10.
The multiplies of 15 either have a unit value of 5 or 0.
If A is 5, the number becomes 3555.
3555 / 15 = 237
If A is 0, the number becomes 3050
3050 / 15 = 203.333
Thus, the value of A is 5 because 3555 is divisible by 15.
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Solve for d.
19d -16d-d-d-1 = 12
Answer:
d = 13
Step-by-step explanation:
19d - 16d - d - d - 1 = 12
19d + (-16 - 1d - 1d) - 1 = 12
19d + (--18d) - 1 = 12
19d - 18d - 1 = 12
1d = 12 + 1
d = 13
Check:
19*13 - 16*13 - 13 - 13 - 1 = 12
247 - 208 - 26 - 1 = 12
39 - 27 = 12
Please help me with this problem! DUE TONIGHT!
Answer:
b=v
Step-by-step explanation:
Answer:
I got b=v so it would be 0
Step-by-step explanation:
I'm sorry if I'm wrong
Write in point-slope form an equation of the line through each pair of points. (-4,10) and (-6,15)
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 10) and (-6 , 15), is y - 10 = -5/2(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , 10) and (-6 , 15).
m = (y2 - y1)/(x2 - x1)
m = (15 - 10)/(-6 - -4)
m = 5/-2
m = -5/2
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -5/2 and (x1 , y1) = (-4 , 10)
(y - 10) = -5/2(x - -4)
y - 10 = -5/2(x + 4)
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(-6)(-8) what is the answer
Answer:
48
Step-by-step explanation:
