Answer:
To approximate the solution to the system of equations, we need to find the point where the two lines intersect. From the second equation, we know that y = (1/2)x + 1. Substituting this expression for y into the first equation gives:
3x + 2[(1/2)x + 1] = -4
Simplifying and solving for x, we get:
3x + x + 2 = -4
4x = -6
x = -1.5
Substituting this value of x back into the second equation gives:
y = (1/2)(-1.5) + 1 = 0.25
Therefore, the solution to the system of equations is approximately (-1.5, 0.25).
So the answer is (−1.5, 0.25).
The height in feet of a toy rocket is modeled by the function y = −16t2 + 128t, where t is the time in seconds after it is launched. Find the maximum height of the rocket and the time it takes the rocket to reach this height. Then find how long the rocket will be in air.
A. 312 ft; 5 s; 10 s
B. 200 ft; 2 s; 4 s
C. 256 ft; 4 s; 8 s
C. 356 ft; 6 s; 12 s
The maximum height of the rocket is 256 feet and the time it takes the rocket to reach this height is 4 seconds.
The rocket will be in the air for 8 seconds.
Option C is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y = -16t² + 128t _____(1)
This can be assumed as an equation of a parabola.
i.e
y = ax² + bx
so,
a = -16 and b = 128
To find the maximum height of the rocket, we need to find the vertex of the parabola.
The vertex is given by the formula.
t = -b/2a
t = -128/(2 x -16)
t = 4
Substitute t = 4 in (1).
y = -16 x 4² + 128 x 4
y = 256 feet
So,
The maximum height of the rocket is 256 feet.
When the rocket is on the ground.
y = 0
-16t² + 128t = 0
t (-16t + 128) = 0
t = 0 or -16t + 128 = 0
t = 0 and -16t = 128
t = 0 and t = -8 (rejected)
Since the rocket is launched at t = 0,
The rocket will be in the air for 8 seconds.
i.e
8 - 0 = 8
Therefore,
The maximum height is 256 feet and it will be in 4 seconds.
The rocket will be in the air for 8 seconds.
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25 points! find the inverse of the function f(x)=4x-2
then graph the function and it's inverse
Answer:
Step-by-step explanation:
To find the inverse of the function f(x) = 4x - 2, we need to switch the roles of x and y, and then solve for y:
x = 4y - 2
x + 2 = 4y
y = (x + 2) / 4
So the inverse of f(x) is g(x) = (x + 2) / 4.
To graph f(x) and g(x), we can plot their points on the same coordinate system. Here is the graph:
Graph of f(x) and g(x)
The blue line represents f(x) = 4x - 2, and the orange line represents g(x) = (x + 2) / 4, which is the inverse of f(x). Notice how the two lines are reflections of each other across the line y = x, which is a characteristic of inverse functions.
The inverse of the function is f-1(x) = (x + 2)/4
How to determine the inverse of the functionInverse functions are pairs of functions that "undo" each other.
Specifically, if a function f maps x to y, its inverse function g maps y back to x such that g(f(x)) = x and f(g(y)) = y for all values of x and y in their respective domains
From the question, we have the following parameters that can be used in our computation:
f(x) = 4x - 2
Rewrite as
y = 4x - 2
Swap x and y
So, we have
x = 4y - 2
This gives
4y = x + 2
Divide by 4
y = (x + 2)/4
This means that the inverse is f-1(x) = (x + 2)/4
See attachment for the graph of the functions
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Find the length of the missing side. Leave your answer in simplest radical form.
The triangle is not drawn to scale.
A.) 25
B.) 144
C.) 5
D.) Square root of 5
The length of the missing side (hypothenuse) is equal to 5
"Information available from the question"
Opposite side of the triangle(y) = 3
Adjacent side of the triangle (z)= 4
Hypothenuse side of the triangle = x
Pythagorean Theorem
This formula is used to find the missing side of a right angle triangle if two sides are given.
[tex]x^{2} =y^2+z^2[/tex]
Let's substitute the values into the formula and solve for the hypothenuse
[tex]x^{2} =3^2+4^2[/tex]
[tex]x^{2}[/tex] = 9 + 16
[tex]x^{2}[/tex] = 25
[tex]x=\sqrt{25}[/tex]
x = 5
The length of the missing side (hypothenuse) is equal to 5.
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Which is the best estimate for the sum of the fractions
5
6
and
5
8
?
A.
about
7
8
B.
about
1
C.
about
1
1
4
D.
about
1
1
2
Answer:
[tex] \frac{5}{6} + \frac{5}{8} = \frac{4 \times 5 + 3 \times 5}{24} = \frac{20 + 15}{24} = \frac{35}{24} = 1 \frac{11}{24} [/tex]
Are the ratios 16:4 and 8:2 equivalent?
The value of the ratios 16: 4 and 8: 2 in the simplest form is 4:1. Then the ratios are equivalent to each other.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The ratios are given below.
16: 4 and 8: 2
Simplify the ratio, then we have
16: 4 = 4: 1
8: 2 = 4: 1
The value of the ratios 16: 4 and 8: 2 in the simplest form is 4:1. Then the ratios are equivalent to each other.
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Mrs Vahey is out buying dinner for the family. She bought a total of 9 hot
dogs or hamburgers. She spent $26. Hot dogs are $1.50 and hamburgers are
$4. How many of each did she purchase?
The number of packages of hot dogs is 4 hot dogs.
The number of packages of hamburgers is 5 hamburgers.
How to write the required system of linear equations?In order to write a system of linear equations to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of hamburgers respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of hot dogs.Let the variable y represent the number of packages of hamburgers.Since Mrs Vahey bought a total of 9 hot dogs or hamburgers, the linear equation to represent this is as follows:
x + y = 9
Additionally, hot dogs are $1.50 and hamburgers are $4, and she spent a total of $26;
1.50x + 4y = 26
Next, we would use an online graphing calculator to plot the above system of linear equations in order to determine the solution (point of intersection) as shown in the graph attached below.
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explain why inequaliies of the form x > or x < c is any rational number have infinitely many solutions
Due to the fact that there are an unlimited number of values that are either more than or less than the variable x.
What personality type is rational?Rationales are intelligent, independent, and capable of both stubbornness and skepticism. Rationales typically spend a lot of time and effort trying to comprehend the manner in which the universe of ideas works.
What in math is reasonable and irrational?Every number that can be stated as a percentage or as a portion of a whole integer is considered rational. (For instance, -7, 2/3, and 3.75) Irrational numbers are those that can't be stated as a ratio of two integers or a fraction. They cannot be expressed in any finite way.
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What is 1177 178.1192 rounded to the nearest
hundreth?
Answer:
1177 178.12
Step-by-step explanation:
Who prepares the questions for grade 7 math worksheets?
The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.
These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.
Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.
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what is 80 days from today?
If today were January 1, 2023, then 80 days from today would be March 22, 2023. Keep in mind that the actual date that is 80 days from today will depend on the current date.
To determine the date that is 80 days from today, you can add 80 days to the current date.
As of my knowledge cutoff date of September 2021, the current date is irrelevant for today. However, I can tell you how to calculate the date that is 80 days from any given date.
Assuming you want to calculate 80 days from today's date, you would add 80 days to today's date. For example, if today were January 1, 2023, then 80 days from today would be:
January 1, 2023 + 80 days = March 22, 2023
So, if today were January 1, 2023, then 80 days from today would be March 22, 2023. Keep in mind that the actual date that is 80 days from today will depend on the current date.
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4. Calculate the surface area of the sphere, to the nearest tenth of a square centimetre. (radius is 12cm)
a. 1809.6 cm²
b. 1809.6 cm³
c. 7238.2 cm²
d. 7238.2 cm³
I will be sure to mark your answer “Brainliest” if it is correct.
Answer:
A. 1809.6 cm²
Step-by-step explanation:
The formula for the surface area of a sphere is:
Surface Area = 4πr^2
where r is the radius of the sphere.
Substituting the given value of radius, r = 12cm, we get:
Surface Area = 4π(12)^2
= 4π(144)
= 576π
≈ 1809.6 cm² (rounded to the nearest tenth)
Therefore, the answer is (a) 1809.6 cm²
Slauson only move about 5 ft./min.. How many minutes would it take a slow to walk across 100 yard foot field
Time taken to walk across 100 yard field is 60 minutes.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Speed of Slauson = 5 ft./min
That is, in 1 minute, Slauson can walk 5 feet.
We have to find the time taken to walk 100 yard.
1 yard = 3 feet
100 yard = 300 feet
Speed = Distance / Time
Time = Distance / Speed
Time = 300 / 5 = 60 minutes
Hence it will take 60 minutes to walk across a 100 yard field.
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Synthetic Division to Find Zeros (Lev 2)
Feb 09, 5:54:37 PM
Watch help video
If f(x) = 4x³ + 12x² + 5x - 6 and x + 2 is a factor of f(x), then find all of the
zeros of f(x) algebraically.
Answer: x=
33
Submit Answer
DELL
M
w
59. Solve the differential equationdy/dr =x-y-1/x+y+3by finding h and k so that the substitutions x = u+h, y = v + k transform it into the homogeneous equationdv /du= u-v/u + vPlease show how to get the following answer belowx2 - 2xy - y2 - 2x - 6y= C
The homogenous equation is
dv/du = -u + v = -(u - v)/u + v = -(x - y)/x + y = -x2 + 2xy + y2 + 2x + 6y = C
Given the differential equation:
dy/dr = x - y - 1/x + y + 3
To make this equation homogeneous, we can make the substitutions:
x = u + h
y = v + k
where h and k are constants. The derivative of y with respect to r becomes:
dy/dr = (du/dr)(v + k) + (du/du)(u + h) = (du/dr)v + (du/dr)k + (du/du)u + (du/du)h
Matching coefficients in the equation above to those in the original differential equation, we have:
(du/dr)k = -1/2 (1/u + v)
(du/du)h = 1/2 (x - y)
Solving for h and k, we have:
h = -x + y
k = -1/2 (1/u + v)
Substituting back into the original equation, we have:
dy/dr = x - y - 1/x + y + 3 = -(u + h) + (v + k) + (u + h) + (v + k) + 3 = 2v + 2k + 3
This is now a homogeneous equation and can be written as:
dv/du = -u + v = -(u - v)/u + v = -(x - y)/x + y = -x2 + 2xy + y2 + 2x + 6y = C
So the general solution to the differential equation is:
x^2 - 2xy - y^2 - 2x - 6y = C
where C is an arbitrary constant of integration.
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A business shipped 138 packages in one day. Customers are charged $2.50 for each standard-delivery package and $8.50 for each express-delivery package. Total shipping charges for the day were $669.00. How many of each kind of package were shipped?
Standard-Delivery:
Express Delivery:
The number of each kind of package that were shipped include the following:
Standard-Delivery: = 61
Express Delivery: = 61
How the calculate the number of packages delivered?The total number of packages that was delivered in a day = 138.
The total cost for the delivery for a day = $669.00
The charges for each standard-delivery package = $2.50
The charges for express-delivery package = $8.50
The total charges for both = $11
The charges for Standard-Delivery
= 2.50/11 × 669.00
= 1672.5/11
= $152.1
The number of Standard-Delivery that was shipped = 152.1/2.5 = 61
The charges for Express Delivery:
= $669.00-$152.1
= $516.9
The number of Express Delivery that was shipped;
=516.9/8.5 = 61.
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the radius of a circle is 6m find it’s area in terms of pi
Answer:
36π cm^2
Step-by-step explanation:
area= πr^2
= 36π cm^2
Geometry question. thanks for the help!
A rectangle is a rhombus =Sometimes
A parallelogram is a rectangle = Always
A quadrilateral is a pentagon = Never
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
A rhombus has four equal sides and its opposite angles are equal.
A rectangle is a rhombus if the rectangle becomes a square.
So,
We can say that a rectangle is sometimes a rhombus.
A parallelogram is always a rectangle.
But not all rectangle is a parallelograms.
A quadrilateral has four sides.
A pentagon has 5 sides.
So,
A quadrilateral is never a pentagon.
Thus,
A rectangle is sometimes a rhombus.
A parallelogram is always a rectangle.
A quadrilateral is never a pentagon.
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The sum of the digits of a two-digit number is 10. When the digits are reversed, the new number is 36 more than the original number. Find the original.
Answer:
Original Number is 37
Step-by-step explanation:
Let
x = First digit
y = Second digit
x + y = 10
∴y = 10 - x
Original Number = 37
3 + 7 = 10
When reversed:
New Number is 36 more than the original Number:
37 + 36 = 73
∴New Number = 73
PLSSSS HURRY AND HELP ME
Sylvie needs $110 for a concert ticket. She already has $16 and she can earn the rest by working 10 hours at her job. If h represents her hourly earnings, which of the following equations can be solved to find Sylvie’s hourly earnings? Select all that apply.
A. 110 – 16 = 10h
B. 110 = 16h + 10
C. 16 = 110 – h
D. 110 = 16 + 10h
E. 110 + 16 = 10h
D) 110 = 16 + 10h
C) 16 = 110 – h
Step-by-step explanation:
Think about it. She NEEDS $110 but she only has $16. So now it's $110=$16 {or C}.
She can EARN the rest {H} by working her hours.
Brand A scooter has a top speed that goes 2 miles per hour faster than Brand B. If after 3 hours, Brand A scooter traveled 24 miles at its top speed, at what rate did Brand B scooter travel at its top speed if traveled the same distance? Write an equation to determine the solution. Identify the if-then moves used in your solution.
HELP ME PLS.
The top speed of Scooter B is calculated and is given by the equation A = 6 miles/hour
What is Speed?Speed is defined as the rate of change of position of an object in any direction. The rate of change of distance over a particular interval of time is known as Speed. The speed is a scalar quantity which has no direction but only magnitude. The SI unit of speed is meter per second or kilometer per hour
Speed = Distance / Time
Given data ,
Let the top speed of Scooter A be represented as = A miles per hour
Let the top speed of Scooter B be = ( A + 2 ) miles per hour
The time traveled = 3 hours
So , Distance = Speed x Time
The distance traveled = 24 miles
So , 24 = ( A + 2 ) 3
On simplifying the equation , we get
24 = 3A + 6
3A = 18
A = 6 miles per hour
Hence , the top speed is 6 miles per hour
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1. A circle is shown. 12 cm What is the diameter of the circle in centimeters? What is the radius of the circle in centimeters?
Answer: B: 113.04cm^2
Step-by-step explanation:
5) Karen deposits $4156 into an investment account that offers 3.45% interest per year, compounded daily. How much will her investment be worth after 6 years?
Answer:
$5111.76
Step-by-step explanation:
compounded daily means 365 times interest is compounded per year, so
A=4156x[tex](1+\frac{0.0345}{365}) ^{365x6}[/tex] ≈ 5111,76
Which of the following rational functions is graphed below?
-10
10-
-10
10
O A. F(x) = (x-1)(x - 5)
X
OB. F(x)= x-5
x-1
O C. F(x) =
OD. F(x)=
X
(x-1)(x-5)
(x + 1)(x+5)
The rational function that is graphed below include the following: A. f(x) = 1/(x - 1)(x - 5).
What is a rational function?In Mathematics, a rational function simply refers to a type of function which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:
NumeratorDenominatorIn order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.
Therefore, when x = 1, the rational function become undefined;
f(x) = 1/(x - 1)(x - 5)
f(x) = 1/(1 - 1)(x - 5)
f(x) = 1/0 (undefined).
Also, when x = 5, the rational function is undefined;
f(x) = 1/(x - 1)(x - 5)
f(x) = 1/(x - 1)(5 - 5)
f(x) = 1/0 (undefined).
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Find the value of x thank you
Answer:
x=166
Step-by-step explanation:
180-14= 166
x=166
Type the value of the expression given int numItems = 5. For any floating-point answer, type answer to tenths. Ex: 8. 0, 6. 5, or 0. 1.
3. 0 / 1. 5
The value of the expression 3.0 / 1.5 is 2.0.
The int() function returns the numeric integer equivalent from a given expression. It converts the specified value into an integer number. Floating point numbers represent real numbers such as 3.14159 or -2.5. The value of the given expression using int() function is 2.0. This is because when you divide 3.0 by 1.5, the result is 2.0. Here are the steps to solving the expression:
1. Start with the numerator (3.0) and the denominator (1.5).
2. Divide the numerator by the denominator.
3. The result is the value of the expression.
So, the value of the expression 3.0 / 1.5 is 2.0.
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if AP = 9 in., AA' = 12 in, and AC = 8.4 in., what is A' C'?
Answer: 11.2 inch
Step-by-step explanation:
In a normal distribution, x = -5 and z=-3.14. This tells you that x = -5 is__standard deviations to the (right or left) of the mean.
-3.14, left
5, left
3.14, left
3.14 right
-3.14, right
In a normal distribution, x = -5 and z = -3.14 means that x = -5 is 3.14 standard deviations to the left of the mean
How to interpret the z-scoresFrom the question, we have the following parameters that can be used in our computation:
Distribution = Normal
z = -3.14
z = -5
In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a z-score of -3.14 indicates that the value is 3.14 standard deviations below the mean.
Since x is given as -5, we know that this value is 3.14 standard deviations below the mean value, which can be determined by multiplying the standard deviation by the z-score.
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how to measure percent error
The absolute amount of the difference between the measured and real value, divided by the actual value, is multiplied by 100 to determine the percent inaccuracy.
1. Divorce the measured value from the true value.
2. Calculate the result's absolute value.
3. Subtract the true value.
4. Increase by 100.
A measure of how closely a measured value matches an actual value is called percent error. By taking the absolute difference between the measured and real values, dividing by the actual values, and multiplying by 100, it is determined. We may determine the percentage difference between our measured value and the real value using this calculation. For instance, the error would be 20% if the real value was 10 and the measured value was 8. It is determined in the following manner step by step: first, deduct the measured value from the real value, then calculate the absolute value of the outcome. Multiply by 100 after dividing the result by the actual value. Percent Error = |Measured Value - Actual Value| Actual Value x 100 is the formula for this problem.
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Determine the independent and dependent variables from the following situation. Delilah was given $50 for her birthday. Every month she saves $15.
Answer:
y is the dependent variable and it is the total amount of money that she has saved.
X is the dependent variable and it is the number of months that she has saved.
Step-by-step explanation:
y = 15x + 50
This is what the equation would look like. If you tell me how many months she has saved, I can tell you how much is in her account.
11+2²-2= [?]. Help please
Answer:
13
Step-by-step explanation:
11+2^2 -2
= 11+4-2
= 15-2
= 13