Answer:
[tex]h = G + \frac pf[/tex]
Step-by-step explanation:
[tex]G = h - \frac pf \text{ / Add }\frac pf \text{ to both sides}\\\\G + \frac pf = h - \frac pf + \frac pf\\\\G + \frac pf = h[/tex]
HELP SOMEONE
A 3-quart container of disinfectant costs $13.56. What is the price per cup?
Answer:
I am not sure but I think its is $1.13
There are 12 cups inside a 3-quart container
Step-by-step explanation:
17. The time it takes Sonia to mow 1 acre of land
is shown in the table. If Sonia has to mow
2.5 acres of land with a push mower, how
long does it take her to mow?
Push Mower
1.25 hours per acre
35 minutes per acre
Gas Mower
The time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .
According to the question we have been given that
Time taken by push mower to mow 1 acre land = 1.25 hours
Time taken by Gas mower to mow 1 acre land = 35 minutes
We need to find how many hours Sonia take to mow 2.5 acre of land with push mower.
To find this we will use unitary method. That is
1 acre = 1.25 hours
2.5 acre = 1.25*2.5 hours
= 3.125 hours.
Hence the time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .
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The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
f(x)-2,0,2,8
The equation y=2x² +8x +8 represents the quadratic function in standard form.
Quadratic Function
The Standard form for a quadratic equation is ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b \± \sqrt{D} }{2a}[/tex] .
You should replace the given values for x and y in the standard form for a quadratic equation is ax²+bx+c=0. When you use x=0, you can find the coefficient c. See below.
y = ax²+ bx + c
8 = 2*0 + b*0 +c
8 = 0 + 0 + c
c =8
Next step, you should find the coefficients a and b from the two given points.
For x =-1 and y=2 and x= -2 and y=0, you will havey = ax²+ bx + c, for (-1,2)
2 = a -b +8
y = ax²+ bx + c, for (-2,0)
0 = 4a -2b +8
Then,
a - b= -8+2
4a - 2b = -8
Here you have a linear system
a - b= -6 (1)
4a-2b = -8 (2)
For solving the linear system, first, you should multiply equation 1 by (-2) and after that sum equations 1 and 2.
Thus,
-2a +2b = +12 (1)
4a - 2b = -8 (2)
The result from sum equations 1 and 2 is
-2a +4a=4
2a=4
a=2
From equation 1 : a-b= -6, if a=2 you have:
a-b= -6
2 - b = -6
-b = -6 -2
-b = -8
b=8
Now you have all data for writing the standard for a quadratic equation: a= 2, b=8 and c=8
y=ax²=bx+c
y=2x²+8x+8
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Nicholas received 100$ for his birthday he decides to spend 20$ per day on whatever he wants
Answer: He would use the money in 5 days.
Step-by-step explanation: 100 divided by 20 is 5.
What are the solutions of each equation? Check your answers.
(a) ln x=2
According to the question, the solution for the equation [tex]ln(x)=2[/tex] is [tex]e^{2}[/tex]. And the procedure for the given equation is as follows:
Expression: [tex]ln(x)=2[/tex]
Removing logarithmic function from the equation, equate it to exponential. Therefore, the expression can be re-written as:
[tex]ln(x)=2\\(x)=e^{2}[/tex]
Therefore, the solution for the equation is :[tex]x=e^{2}[/tex].
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) =-4.9t^2 + 229t + 234. Find the maximum height the rocket attains.
Check the picture below, that one shows the imperial units, however is pretty much the same curve for a metric one, namely using metres, so the maximum point is at the vertex y-coordinate.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+229}t\stackrel{\stackrel{c}{\downarrow }}{+234} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 229}{2(-4.9)}~~~~ ,~~~~ 234-\cfrac{ (229)^2}{4(-4.9)}\right) \implies \left( - \cfrac{ 229 }{ -9.8 }~~,~~234 - \cfrac{ 52441 }{ -19.6 } \right) \\\\\\ \left(\cfrac{1145}{49}~~,~~ 234+\cfrac{262205}{98} \right)\qquad \approx\qquad (\stackrel{seconds}{23.37}~~,~~\underset{\bigtriangleup}{\stackrel{meters}{2909.56}})[/tex]
HELP......................................
Answer:
The equation's result: 32,000 (Rounded)
Goal: Find the closest or equivalent result in another expression
Step-by-step explanation:
A)[tex](1.5^{15})/(0.7^{12})\\(1.5^{15})/(0.7^{12}) = (437.894)/(0.7^{12})\\437.894/(0.014)\\31636.79[/tex]
How we got to 31,636 was by dividing from left to right.
Remember: When dividing decimals, it's like multiplying whole numbers in a way. The number(the quotient, also) ends up bigger instead of being smaller like when dividing whole numbers. If you multiply decimals, they(the product) end up smaller.
Therefore, A is the correct answer.
Evaluate each expression to four decimal places.
e³/₂
The value of e³/₂ is 4.4758
e in here is considered as Euler's number. Euler's number is a numerical constant which is often used in mathematical calculations. the value of e can be taken into consideration as 2.71828.
The given expression e⁽³÷²⁾ can also be written as √e³. First the cube of e is calculated which is then followed by finding the square root of the calculated value.e⁽³÷²⁾ = √e³. The value of e³ when calculated is 2.7182 x 2.7182 x 2.7182 = 20.0855
Now taking the square root of the calculated value is √20.0855 is 4.4816
Therefore the value of e⁽³÷²⁾ up to four decimal places is 4.4816
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Your grandmother gives your little brother 42 coins. Some are dimes and some are
nickels, but they total to $3.00. How many dimes does your little brother have?
Taking into account the definition of a system of linear equations, you little brother has 6 dimes.
System of linear equationsA system of linear equations is a set of equations that have more than one unknown, appearing in several of the equations but necessarily in all of them. The equations relate the unknowns to each other.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In other words, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of dimesIn this case, a system of linear equations must be proposed taking into account that:
"d" is the amount of dimes."n" is the amount of nickels.You know that:
Your grandmother gives your little brother 42 coins. Some are dimes and some are nickels, but they total to $3.00.The system of equations to be solved is
[tex]\left \{ {{d+n=42} \atop {0.1d + 0.05n=3}} \right.[/tex]
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "n" from the first equation:
n= 42 -d
Replacing this expression in the second equation obtained:
0.1d + 0.05×(42 - d)= 3
Solving:
0.1d + 0.05×42 - 0.05d= 3
0.1d + 2.1 - 0.05d= 3
0.15d + 2.1=3
0.15d= 3 -2.1
0.15d= 0.9
d= 0.9÷0.15
d= 6
Finally, you little brother has 6 dimes.
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Factor the sums of two squares. SEE EXAMPLE 5
34. 4x² + 49
35. x² + 1
36.36 + 100a²
38.16² +25
37. 18y² +8
39. x² + y²
A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
factor of 4x² + 49 is (2x)^2+(7)^2
x² + 1 is x^2+(1)^2
36 + 100a² is (6)^2=(10a)^2
16² +25 is (4)^2+(5)^2
18y² +8 is([tex]\sqrt{18}[/tex] y)^2+([tex]\sqrt{8}[/tex])^2
x² + y² is (x)^2+(y)^2
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Three positive integers are (x - 1), x and (x + 1). If their sum is 105, find the numbers.
The three positive integers are 34, 35, 36
Three positive integers are given as (x-1),x and (x+1)
Sum of these three integers are 105,
As we know the total sum of the three positive integers, we can get the value by adding the three integers to the sum value.
Thus,
(x-1) + x + (x+1) = 105
x - 1 + x + x + 1 = 105
3x + 0 = 105
3x = 105
x = 105/3
x = 35
Then, the integers are (35 - 1) , 35 , (35 + 1)
Therefore, the three positive integers are 34, 35, 36
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Students at a high school were polled about their opinion of the food in the school cafeteria. A total of 200 students were chosen randomly from among the student body and asked to fill out a survey. Out of the 200 surveys received, one question had the following responses:
Food is acceptable as it is: 54
Food is terrible and should be improved: 103
Food is excellent and should not be changed: 15
Identify the problem with the study.
A. The relationship between two variables implies one causes the other.
B. Nonresponse
C. Some of the sample data are missing.
D. The conclusion is based on a voluntary response sample.
Based on the poll of the opinion of food by students at a high school, one problem with the study is that B. Nonresponse.
What is a problem with the study?In the question that was asked about how acceptable the food was, the total number of people who responded were:
= 54 + 103 + 15
= 172 responses
This means that the number of people who didn't respond were:
= 200 - 172
= 28 students
This is a problem of nonresponse as 28 students opted not to respond to the question which can affect research conclusions.
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A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?.
Probability of at least one boy and one girl = [tex]\frac{3}{4}[/tex]
The probability of no of boys = 1/2 ×1/2×1/2= 1/8
The probability of no of girls = 1/2×1/2×1/2= 1/8
Now we have to find the probability of at least one girls
Probability of one boy and one girl = 1 - (1/8 + 1/8)
= 1 - 1/4
= 3/4
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The angle below measures _____ degrees.
Kerri got her cell phone bill this month and was charged for her normal plan, but unfortunately she went over her data allowance and was also charged for each gigabyte over her plan limit. Her bill is represented by the following expression: 10x + 65
What does the coefficient represent in this case?
the cost of her normal plan
how many gigabytes she went over
the cost for the gigabytes over her plan
The coefficient in this question represents the cost for the gigabytes over her plan.
What is the coefficient ?A coefficient is a number that is multiplied by a variable. In this question, the coefficient is 10 and the variable is x. 10 here represents the the cost for the gigabytes over her plan.
10x represents the variable cost. Variable cost is the cost that increases with the number of gigabyte used. Fixed cost is the cost that does not change with the gigabyte used. It remains constant regardless of the level of gigabyte used. Total cost is the sum of the fixed cost and the variable cost. The fixed cost is the cost of her normal plan.
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A car travels at a rate of 45 m iles per hour for 5 hours. Let y be the distance in miles that a car travels for a
given amount of time, x, in hours. The situtation can be modeleAndd by a function. Which of these describes how their
domain of the function?
Answer:477.47 revolutions
Step-by-step explanation:
A hot air balloon rises from the ground to 150 feet elevation. But the wind is too strong, so the pilot ascends another 75 feet
Answer: 225
Step-by-step explanation:
I may not be right but I’m taking that ascends is basically adding up the height so 150+75=225
Select all the equations that satisfy this fact.
Answer:
2) SA + AM = SM
3) SA = AM
What is a defined term?
A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them. The number in front of a term is called a coefficient.
What is a midpoint?
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Hope this helped :)
Find the 18th term of the arithmetic sequence whose common difference is d=-5 and whose first term is a₁ = 20.
=================================================
Explanation:
First let's find the nth term denoted as [tex]a_n[/tex]
[tex]a_n = a_1 + d(n-1) \ \text{ ... formula for arithmetic sequences}\\\\a_n = 20 + (-5)(n-1) \\\\a_n = 20 -5n+5 \\\\a_n = -5n+25 \\\\[/tex]
Now we can find the 18th term by plugging in n = 18
[tex]a_n = -5n+25 \\\\a_{18} = -5(18)+25 \\\\a_{18} = -90+25 \\\\a_{18} = \boldsymbol{-65} \\\\[/tex]
The 18th term is -65Answer:
-65
The 18th term in the sequence is -65.
Step-by-step explanation:
an=a1+(n-1)d
d=-5
a1=20
n=18
a18=20+(18-1)(-5)
Simplify.
a18=20+(17)(-5)
a18=20-85
a18=-65
The 18th term in the sequence is -65.
Hope this helps!
Please mark as brainliest if correct!
HLEP NUMBER 3 HELPPOO
Answer:
8.3333333 square & root of 25
Step-by-step explanation:
Determine whether the variable is qualitative or quantitative. explain your reasoning. colors of automobiles
The colors of automobiles are qualitative variables.
Qualitative data deals with traits and qualities that are difficult to quantify but can be perceptually experienced, such as flavors, sensations, looks, and colors. In general, you create quantitative data when you measure something and assign it a numerical value.
A qualitative variable, often known as a categorical variable, classifies a quality of something to characterize it. A wonderful illustration of anything that may be categorized is the hues of the cars in a parking lot: red, green, blue, black, white, etc. As a result, this is a qualitative variable.
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For each function, identify the transformation from the parent function y=b x . y=1/2 (9) x
Transformation of y= bx into [tex]y=\frac{1}{2} 9x[/tex] will take place by vertical dilation by a scale factor of [tex]\frac{9}{2}[/tex] .
A parent function is the simplest form of a particular family of functions. A family of functions is a group of functions that have the same highest degree and therefore the same graph shape. Function transformations "move" or "resize" or "mirror" the graph of the parent function. Mathematically speaking, the transformation of the function y = f(x) is usually y = a f(b(x + c)) + d. where a, b, c, and d are arbitrary real numbers representing transformations. Note that all outer numbers (outside the brackets) represent vertical translations, and all inner numbers represent horizontal translations. Addition and subtraction are translations, and multiplication and division are dilations. Every time a minus sign is multiplied it means it is a reflection here, 'a' stands for vertical stretch , 'b' stands for horizontal stretch , 'c' stands for horizontal movement , 'd' stands for vertical movementWe have given two function y=b x and [tex]y=\frac{1}{2} 9x[/tex] which means that first y changes into [tex]\frac{1}{2} 9x[/tex] i.e., vertical dilation by a scale factor of [tex]\frac{9}{2}[/tex] .
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What is the value of x? (hint: use the measure of XYZ) will mark brainliest
you're playing the lottery, and you buy a ticket with randomly generated numbers. the first three numbers you get are 5, 10, and 15. thus, the next number you get should be 20.
The given statement is of Inductive Reasoning as "the next number you get should be 20" is just a generalization, there is nothing conclusive.
In the Inductive reasoning , if the statements are true then it does not mean that the conclusion will also be true.
In the Deductive reasoning , if the statements are true then the conclusion need to be true.
In the given question ,
We are playing a lottery and buy tickets with randomly generated numbers.
As the numbers are randomly generated we cannot conclude anything concrete/logically about the next number.
It is random that we have found the pattern and found the next number to be 20.
It is just a mere coincidence that the next number is 20 .
There is nothing Logical for the next number to be 20 as the numbers are randomly generated.
Since in this situation we have made a generalization after observing the pattern , "the next number you get should be 20" is mere generalization and thus, it represents Inductive Reasoning .
Therefore , this case is the case of Inductive Reasoning , the correct option is (a) Inductive.
The given question is incomplete , the complete question is
you're playing the lottery, and you buy a ticket with randomly generated numbers. the first three numbers you get are 5, 10, and 15. thus, the next number you get should be 20.
Which type of reasoning does this statement represent ?
(a)Inductive
(b)Deductive
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Work out (7 x 10°) (2 × 10²) 4 Give your answer in standard form.
Answer:
[tex] {1.4 \times 10}^{3} | [/tex]
Step-by-step explanation:
*winks and runs off ;)*
Under his cell phone plan, Ian pays a flat cost of $44.50 per month and $5 per gigabyte. He wants to keep his bill at $61 per month. Which equation could be used to determine xx, the number of gigabytes of data Ian can use while staying within his budget?
Answer:
x<2.1
Step-by-step explanation:
5x<70-59.5
5x<10.5
X<10.5/5
X<2.1
Solve each equation by factoring. Check your answers.
9 x²+15 x+4=0
The factors of the equation are -1/3 and -4/3
Rewriting the equation -
9x² + 15x + 4 = 0
ax² + bx + c = 0
Factorizing the equation such that
sum of the factors should be equal to middle expression (15x in this question)product of the factors should equal to product of (a and c) (9 and 4 in this question)12 and 3 are suitable factors for solving the given expression -
9x² + 3x + 12x+ 4 = 0
Taking common factors -
3x(3x + 1) +4 (3x + 1) = 0
(3x + 1) (3x + 4) = 0
x = -1/3, -4/3
So, the two factors of expression are -1/3 and -4/3
Checking the answers by keeping each value of x in expression
When x = (-1/3)
9x² + 15x + 4 = 0
9(-1/3)² + 15(-1/3) + 4 = 0
1 -5 +4 = 0
5 - 5 = 0
0 = 0
When x = (-4/3)
9x² + 15x + 4 = 0
9(-4/3)² + 15(-4/3) + 4 = 0
16 - 20 +4 = 0
- 4 + 4 = 0
0 = 0
Since for both values of x, Left Hand Side of equation is equal to Right Hand Side of equation, the resultant factors are correct.
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In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
magnitude 7.7 in San Francisco, California, in 1906
1) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.
2) The earthquake at New Madrid was of lesser intensity than earthquake at Valdivia.
3) The earthquake at New Madrid was of greater intensity than earthquake at Charlottesville.
4) The earthquake at New Madrid was of greater intensity than earthquake at Kobe.
In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values. The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle. A typical use of the greater than sign is to compare two values, where the first is greater than the second, or one is greater than the other. The greater than sign is an approximation of a closing square bracket.Learn more about greater sign here
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The question is incomplete. The complete question is
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
1. magnitude 7.7 in San Francisco, California, in 1906
2. magnitude 9.5 in Valdivia, Chile, in 1960
3. magnitude 3.2 in Charlottesville, in 2001
4. magnitude 6.9 in Kobe, Japan, in 1995
Regular hexagon ABCDEF is inscribed in a circle with center H.
Regular hexagon ABCDEF is inscribed in a circle with center point H.
a. What is the image of segment BC after a 120-degree clockwise rotation about point H?
Answer:
Step-by-step explanation:
the image of BC reflecting over FC is DC.
Can someone help plss
Answer:
Yes
Step-by-step explanation:
Replace x with -7 and y with 1 in the original inequality and solve
1 < -7/2 + 9
1 < -3.5 +9
1 < 5.5 (Since this statement is true, the point (-7, 1) is a solution)