Answer:
-15+x+11y
Step-by-step explanation:
How to Solve
-15+x-y+12y < ------ Subtract the values -5 and -10
-15+x+11y < ----- Combining like terms -y−y and 12y12y
An earthquake of magnitude 7.7 occurred in 2001 in Gujarat, India. It was about 4900 times as strong as the greatest earthquake ever to hit Pennsylvania. What is the magnitude of the Pennsylvania earthquake?
The magnitude of the Pennsylvania earthquake is 4.
What is a logarithm function?An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.
The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.
Using the formula,
log I₁ / I₂ = M₁ - M₂
M₁ = 7.7, I₁ / I₂ = 4900
log 4900 = 7.7 - M₂
log 4900 ≈ 3.69
On calculating,
M₂ ≈ 4
The magnitude of the Pennsylvania earthquake is 4.
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Calculate the variance for the data set. Show all of your steps.
{4, 16, 21, 32, 11, 12}
The variance of the data sets is 77.7
How to find variance of a data sets?Variance is the average of the squared differences from the Mean.
Therefore, to find the variance we have to find the mean, Then for each number: subtract the Mean and square the result.
Then work out the average of those squared differences.
Hence,
mean = 4 + 16 + 21 + 32 + 11 + 12 / 6 = 96 / 6 = 16
Therefore, lets find the difference and square it.
(4 - 16)² + (16 - 16)² + (21 - 16)² + (32 - 16)² + (11 - 16)²+ (12 - 16)²
144 + 0 + 25 + 256 + 25 + 16 = 466
Therefore,
variance = 466 / 6
variance = 77.6666666667
variance = 77.7
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How do I write this out and answer it right
The numeric values of the expressions are given as follows:
3. 36.
5. 38.
7. 16/61.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
In item 3, we have that:
4|m - n|, m = -7, n = 2.
Hence the numeric value is:
4|-7 - 2| = 4|-9| = 4 x 9 = 36.
In item 5, we have that:
s²t - 10 with s = -8, t = 3/4.
Hence the numeric value is:
(-8)² x 3/4 - 10 = 48 - 10 = 38.
In item 7, we have that:
(a + b)^5/(a - 2b²), a = 6, b = -8.
Hence the numeric value is:
(-2)^5/(6 - 128)
-32/-122 (negative divided by negative is positive).
32/122 (simplify by 2).
16/61.
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the different between 8 and 4,divided by 2
Answer:
2
Step-by-step explanation:
8-4=4
4/2=2
Answer:
so you take 2×4=8 and 2×2=4 I think that's how to do it
Which of the following is equivalent to
(p3)(2p^2 - 4p)(3p^2 - 1)?
A.(p3)(6p^4 - 12p^3 - 2p^2 + 4p)
B.(p3)(6p^4 + 4p)
C.(2p^6 - 4p^3)(3p^2 - 1)
D.(2p^5 - 4p^4)(3p^5 - p^3)
The equivalent expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).
what is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
(p^3)(2p^2 - 4p)(3p^2 - 1)
Now further solving
(p^3)(2p^2 * 3p^2 - 2p^2 * 1 - 4p * 3p^2 + 4p)
=(p^3) (6p^4 - 2p^2 - 12 P^3 + 4p)
=(p3)(6p^4 - 12p^3 - 2p^2 + 4p)
Hence, the value of expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).
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A figure is multiplied by a scale factor of 1/3. Did the figure get smaller or larger? How do you know?
I will give Brainiest answer
Answer:
Smaller
Step-by-step explanation:
When you multiply something by 1/3, basically what you are doing is multiplying that thing by one and dividing it by 3.
To put it in a better perspective, let's say you have something that is 5 inches long and you multiply it by a scale factor of 1/3. The equation would be: (5*1)/3.
*Please mark brainliest answer
Find the unknown length for the similar rectangles below.
HELP ME PLEASE ITS THE LAST QUESTION
Answer:
10 hours
$352
Step-by-step explanation:
Given costs:
Pleasure Pontoons: $132 per day plus $22 per hour.Water Sportscrafts: $152 per day plus $20 per hour.Define the variables:
Let x = number of hours renting the boat.Let y = total cost (in dollars) of renting the boat.Create a system of equations using the given costs and defined variables:
[tex]\begin{cases}y=132+22x\\y=152+20x \end{cases}[/tex]
To find how many hours Ryan would need to rent the boat in order for the cost of both companies to be the same, substitute equation 1 into equation 2 and solve for x:
[tex]\begin{aligned}132+22x & = 152+20x\\132+22x-20x & = 152+20x-20x\\132+2x & = 152\\132+2x-132 & = 152-132\\2x & = 20\\\dfrac{2x}{2} & = \dfrac{20}{2}\\x & = 10\end{aligned}[/tex]
Therefore, the number of hours Ryan would need to rent the boat in order for the cost of both companies to be the same is 10 hours.
Substitute x = 10 into one of the equations to find the cost at both companies if Ryan rented a boat for this many hours:
[tex]\begin{aligned}x=10 \implies y & = 132+22(10)\\& = 132+220\\& = 352\end{aligned}[/tex]
Therefore, the cost at both companies if Ryan rented a boat for 10 hours would be $352.
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Toby's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion.
The expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).
How to illustrate the information?It should be noted that there are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each and the history museum gave the class 20% off as part of a group promotion.
Therefore, it should be noted that the expression to illustrate this will be:
= 20% × (10 × x) + (20 × y)
= 0.2 (10x + 30y)
Therefore, the expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).
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Toby's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion. What expression will illustrate this?
Steve had the option to buy a new computer at the $4250.00 cash price or to rent it for $595.00 per month for 10 months. after which he will own the computer. What percentage more than the cash price would the rent option cost him?
Answer:
I believe it's 25% .............
Answer:
40%
Step-by-step explanation:
The cash price = $4,250
If Steve rents the computer for $595 for 10 months he would have to spend $595 x 10 = $5,950
The difference in money = 5950 - 4250 =$1700
As a percentage of the cash price this would be
1700/4250 x 100 = 40%
Answer:
Rent option is 40% more than the cash price 40%
We can verify this by noting that if there is an increase of r% in the price of an item then
Increased price = Old price + Increase
= Old price + Old price x r/100
In this case, Old price = 4250
r = 40%, r/100 = 0.04
New price = 4250 + 4250 x 0.04 = 4250(1 + 0.04) = 4250(1.04) = 5950 which tallies with given figures
Answer the questions about the following polynomial
-x^2/4+3x^5+1
(12x^5 + x² + 4) /4.
Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.
Given equation
x²/4+3x^5+1
Find common denominator
x²/4+3x^5 . 4/4+4/4
Combine fractions with common denominator
(x²+3x^5 . 4+4)/4
Multiply the numbers
(x²+12x^5 +4)/4
Rearrange terms
(x²+12x^5 +4)/4
(12x^5 + x² + 4) /4
Thus , solution of the given polynomial is (12x^5 + x² + 4) /4. we can also write it as -
3x^5 + x² / 4 + 1.
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Two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.
SpeedLet r represent the speed of one
Let 2r represent thee speed of the other
Total distance traveled by both the sisters = 30 miles
Time ×rate = Distance
Hence,
2(2r+r) = 30
2(3r)=30
6r=30
r=30/6
r=5 mph
Speed=5 mph and (5 mph×2)
Speed=5 mph and 10 mph
Therefore If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.
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Mrs. Jones decided to buy some pencils for her class. She bought 5 packages of pencils, and each package contained 42 pencils. There are 14 students in her class and she divided up the pencils so that each student had the same amount of pencils. If there were no pencils left over, how many pencils did each student get?
A. 70
B. 15
C. 19
D. 3
Answer:
B, 15 pencils
Step-by-step explanation:
Our equation: (5 x 42)/14
42 x 5 = 210
210/14= 15
What is the gradient y= 12-x
Answer:
-1
Step-by-step explanation:
i just inserted it into an online graphing calculator called desmos.
Given that [tex]sin(x)+cos(x)=\frac{2}{5}[/tex], compute the following.
[tex]sin^4(x)+cos^4(x)[/tex]
Giving 80 points to the person who answers correctly
The function f(t) represents water going into a swimming pool with respect to the number of hours(t) water is flowing in where(t) represents time. f(t)=t squared +8t+9 There is a leak in the pool and it’s losing water at a rate represented by d(t). d(t)=t squared +11t+4
a.Write a function w(t) to represent the amount of water in the pool using the two functions.
b. Use the new function to determine if the pool will leak all of the water
c. If the pool will drain of all water, how much time will it take?
d.Will f(t) and d(t) intersect on a graph? Explain what it means if they do.
e. What is the domain of f(t), d(t), and w(t)? Explain your answer.
Using operations with functions, we have that:
a) w(t) = -3t + 5.
b) The pool will leak all the water in 1.67 hours.
c) 1.67 hours.
d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
e) The domain of the function is 0 ≤ t ≤ 1.67.
What is the amount of water in the pool?The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.
For this problem, these following functions are given:
Flowing: f(t) = t² + 8t + 9.Draining: d(t) = t² + 11t + 4.Hence the amount of water in the pool is given by:
w(t) = f(t) - d(t)
w(t) = t² + 8t + 9 - t² - 11t - 4
w(t) = -3t + 5.
Hence:
The function is: w(t) = -3t + 5.
The pool will have leaked all the water when:
w(t) = 0.
Hence:
-3t + 5 = 0.
3t = 5
t = 1.67.
The pool will leak all the water in 1.67 hours.
Equaling f(t) and d(t), we have that:
t² + 8t + 9 = t² + 11t + 4.
3t = 5.
t = 1.67.
Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:
Time cannot be negative, hence t ≥ 0.When all the water has been drained, everything stops, hence t ≤ 1.67.Hence:
The domain of the function is 0 ≤ t ≤ 1.67.
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Find all the zeros of each function. y=x³-x²+x-1
The required zeros of the polynomial f(x) are 1 and ±√-1.
What are zeros of the polynomial?
All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.
Solving for the zeros of a polynomial
y = x³ - x² + x - 1
Let, f(x) = 0
x³ - x² + x - 1 = 0
Using heat and trial method, we get,
x =1 as one of the zero of the polynomial
It implies that (x-1) is the root of polynomial
Thus, dividing x³ - x² + x - 1 by x - 1, we get
x² + 1, which is then equated to 0 to obtain the zeros of the given polynomial
i.e. x² + 1 = 0
x = 1, ±√-1
Hence, the required zeros of the polynomial y are 1 and ±√-1.
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Identify each function as linear, quadratic, or exponential. Explain your reasoning.
c. y =2x+5
The given function is a linear function because variable have first degree power.
The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
A linear function is a function that represents a straight line on the coordinate plane. As an illustration, the equation y = 3x – 2 represents a linear function because it is a straight line in the coordinate plane.
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A jar contains 0.25 liter of apple juice and 0.30 liter of grape juice. Melissa poured 0.75 liter of pineapple juice into the jar. She then drank 0.20 liter of the mixture
The expression to represent the total amount of juice left in the jar is: (.25 + .30+ .75) -.20 and the property used in each step is addition and extraction of Liquid from the mixture.
ExpressionExpression:
(AJ+GP+PJ)-M
Where:
Apple juice=AJ
Grape juice=GP
Pineapple juice=PJ
Mixture=M
Hence,
(.25 + .30+ .75) -.20
b. Simplifying the expression
(.25 + .30+ .75) -.20
=1.3-.20
=1.10
Therefore the expression to represent the total amount of juice left in the jar is: (.25 + .30+ .75) -.20 and the property used in each step is addition and extraction of Liquid from the mixture.
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Solve the following absolute value equation.
|4x - 12| = 16
The absolute value of the given modulus function are -1 and 7.
What is defined as the modulus function?A modulus function returns this same magnitude of a number regardless of its sign. It's also acknowledged as the absolute value function. This same modulus function, signified by |x| in mathematics, gives the modulus of such a real number x. It returns a non-negative value for x. The modulus but rather absolute value of a number too is known as the number's distance from the origin or zero.The given modulus function is;
|4x - 12| = 16
Removing modulus sign will provide two values;
4x - 12 = ±16
Solve for positive value of modulus function;
4x - 12 = 16
Add 12 on both side;
4x - 12 + 12 = 16 + 12
4x = 28
Dive both side by 4.
x = 7
Now, solve for negative value of modulus function.
4x - 12 = -16
Add 12 on both side;
4x - 12 + 12 = -16 + 12
4x = -4
Divide both side by 4;
x = -1
Thus, the two value of the given modulus function are -1 and 7.
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Evaluate each expression for the given value of x
4ˣ+1 for x=1
The correct answer for the given expression is 5.
A formula is a statement containing at least two numbers/variables and at least one mathematical operation. An expression is a combination of terms combined by mathematical operations such as subtraction, addition, multiplication, and division. The terms that appear in the formula are:Constant: A constant is a fixed number.Variables: Variables are symbols that do not have fixed values.Term: A term can be a single constant, a single variable, or a combination of variables and constants combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.Given,
evaluate the expression 4ˣ + 1
By putting x= 1,
we get 4¹ + 1
= 4+ 1
= 5
So, the the answer for the question, evaluate 4ˣ + 1 is 5.
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Which equation does not belong with the other three? Explain your reasoning.
²³/x+ ²/3=y\
y = 0.5x -0.2
4x + 3 = y
y = x² +6
:: a linear equation
does not belong because it is
while the other three equations are
:: y = 0.5x -0.2 :: 4x +3=y :: y = x² +6
:: not a linear equation
:: not linear equations
x + = y
3/
:: linear equations
Answer:
3 = x ÷ 4
Step-by-step explanation:
Given expressions:
8 = x - 2 ⇒ x = 8 + 2= 10
3 = x ÷ 4 ⇒ x = 3*4 = 12
x - 6 = 5 ⇒ x = 5 + 6 = 11
x - 3 = 9 ⇒ x = 9 + 3 = 12
3 of them involves addition, one of them - multiplication
The second expression doesn't belong
Please HURRY
Describe the trend in the scatter plot.
• positive correlation
no correlation
• negative correlation
O not enough information because the trend line is unclear
Which point is a solution to the following system of inequalities? "-2x+3y>=1" "-5x+6y<=1"
a. (6,6)
b. (7,8)
c. (8,7)
d. (9,7)
By option verification,
i.e., substituting the options by given equation and verifying
Given -2x + 3y > = 1 and - 5x + 6y <= 1
Substituting option A i.e., ( x , y ) = ( 6,6)
-2x + 3y >=1 --> -2 * 6 + 3 * 6 >= 1
--> -12+ 18 >= 1
---> 6>=1
-5x + 6y<=1--> -5 * 6 + 6 *6 <=1
--> -30+ 36 <=1
-->6<=1
False
Substituting option B i.e., (x , y)= (7 ,8)
-2x + 3y>=1 --> -2* 7 + 3 * 8>=1
--> -14 + 24>=1
--> 10>=1
-5x + 6y<=1 --> -5 *7 + 6* 8<=1
--> -35 + 48<=1
--> 13<=1
False
Substituting option C i.e., (x, y) = ( 8 ,7)
-2x + 3y >=1 --> -2* 8 + 3* 7>=1
--> -16 + 21>=1
--> 5>=1
-5x + 6y <=1 --> -5 * 8 + 6 * 7 <=1
--> -40 + 42<=1
--> 2<=1
False
Substituting option D i.e., (x ,y ) = (9, 7)
-2x + 3y >= 1 --> -2* 9 + 3 * 7 >=1
--> -18 +21>=1
--> 3>=1
-5x + 6y <=1 --> -5* 9 + 6 * 7 <=1
--> -45 + 42<=1
--> -3<=1
True
Therefore (x ,y ) = (9, 7) is the solution of the given equation -2x + 3y>=1 and -5x = 6y <=1
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Answer: For the people who were just as confused with the answer above, the answer is D-
Step-by-step explanation:
2-2n=3n+17 solve for n
Answer:
n=-3
Step-by-step explanation:
2-2n=3n+17
-2n=3n+15
-5n=15
n=-3
Question 8 (1 point)
Solve the equation. Check for extraneous solutions.
7|14-8x|= 2x + 2;
Answer:
Step-by-step explanation:
The most appropriate choice for modulus function is given by-
values of [tex]x[/tex] = [tex]\frac{48}{29}[/tex] and [tex]\frac{50}{27}[/tex]
What is modulus function?
Modulus function returns the absolute value of a function.
[tex]|x| = \left \{ {{x, x \geq 0} \atop {-x, x < 0}} \right.[/tex]
Here,
For [tex]14 - 8x \geq 0[/tex]
[tex]7(14-8x) = 2x + 2\\98 - 56x = 2x + 2\\56x + 2x =98 -2\\58 x = 96\\x = \frac{96}{58}\\ \\x = \frac{48}{29}[/tex]
For [tex]14 - 8x < 0[/tex],
[tex]7(8x - 14) = 2x + 2\\56x - 98 = 2x + 2\\56x - 2x =98 +2\\54 x = 100\\x = \frac{100}{54}\\ \\x = \frac{50}{27}[/tex]
So, [tex]x = \frac{48}{29}[/tex] and [tex]x =\frac{50}{27}[/tex]
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DUE TONIGHTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
The estimate for the side length of the square = the width of the rectangle (w) = √44.
What is the Area of a Rectangle?Area of Rectangle = (length)(width)
Given the parameters below:
Width of the rectangle = wLength of the rectangle = 2wArea of the rectangle = 88 square unitsIf this rectangle is divided to form two squares with equal areas, then the side length of each square would be equal to the length of the original rectangle = w.
(2w)(w) = 88
2w² = 88
w² = 88/2
w² = 44
√w² = √44
w = √44
Thus, an estimate of the side length of the square = the width of the rectangle (w) = √44.
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Multiply and simplify. 4√16 x⁸ . 4√x¹⁴
Solving the problem by multiplying and simplifying we have as a result 16x¹⁵
What is simplification?Simplification is a process of reducing terms to expressions, which do not generate changes or values.
What is multiplication?Multiplication is also known as product, and it is a mathematical operation of a successive sum, this operation consists of adding a number a certain number of times:
a x b the number "a" will be added "b" times.
The algebraic expression that we must simplify to its minimum expression is:
4√16 x⁸ . 4√x¹⁴
4×4x⁸ × 4x¹⁴/²
16x⁸× 4x⁷ ; multiply power of equal base
16x⁸⁺⁷
16x¹⁵
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The number of bacteria in a bacterial culture increased by 149% in 110 hours. How many bacteria were there after 55 hours if there were 4850 pcs. from the beginning?
Round the answer to whole tens.
a. 8980 pcs
b. 7650 pcs
c. 7890 pcs
d. 7760 pcs
the angle of elevation to the top of a building in new york is 6° from the ground and 2 miles from the base of the building. use this information to calculate the height of the building.
The height of building is 0.2 miles.
The given points form a right angled triangle. Top of the building to base of building is the perpendicular, base of building to the angle of elevation is base and angle of elevation to top of the building is hypotenuse. So, considering this, tan of angle of elevation related the two sides of triangle as follows -
tan theta = perpendicular ÷ base
tan 6° = perpendicular ÷ 2
Perpendicular = 2 × tan 6°
Keep the value of tan 6°
Perpendicular = 2 × 0.1
Performing multiplication
Perpendicular = 0.2 miles
Hence, the height of the building is 0.2 miles.
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