The y-value of the solution of the system of equations is given as follows:
y = -1.
How to solve the system of equations?The system of equations for this problem is defined as follows:
4x + 3y = 1.-4x + 3y = -7.Adding the two equations, the value of y can be obtained as follows, as the x-variable is eliminated:
6y = -6
y = -6/6
y = -1.
Hence option F is correct.
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The number of passes completed by Brett Favre, quarterback for the Green Bay
Packers, was recorded for each of the 16 regular season games in the fall of 2006
(www.espn.com).
15 31 25 22 22 19 17 28
24 5 22 24 22 20 26 21
a. Draw a stem and leaf plot to describe the data.
b. Calculate the mean and standard deviation for Brett Favre’s per game pass
completions.
c. What proportion of the measurements lie within two standard deviations of
the mean?
2
Calculate the rate of power drainage per hour if the capacity of the cell phone is 3600 mAh
calculate the rate of power drainage per hour if the capacity of the cell phone is 3600 mAh
the parallelogram below has an area of 54 units²
The height of the parallelogram is 5.4 units.
What is area ?
In mathematics, the area is the measure of the size of a two-dimensional surface or region, usually expressed in square units, such as square inches or square meters. The area of a flat shape or planar figure is the amount of space inside its boundary, or the surface of the object, that is covered by a two-dimensional geometric shape.
One way to find the height is to draw a perpendicular line from point B to line segment AD, forming a right triangle. Let's call the length of this perpendicular line h.
Now we can see that the base of the parallelogram is 10 units (from A to D), and the height is h units (from B to the perpendicular line we drew). The area of the parallelogram is given as 54 units², so we can set up the following equation:
Area = base x height
54 = 10h
Solving for h, we get:
h = 54/10 = 5.4
Therefore, the height of the parallelogram is 5.4 units.
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EASY MATH POINTS! Answer from the screenshot :)
The function that is non-linear is function D.
Which of the functions is non-linear?A function is linear if its graph is represented by a straight line, and that line is usually written as:
ax + by = c
Where x is the horizontal variable and y the vertical variable.
For example, here we can see that A, B, and C are represented by straight lines, thus, these are linear functions.
But if you look at graph D, you can see that it is not linear, it's shape is like an "M", so that is the non-linear function.
The correct option is D.
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Martina, Ryan, and Keith sent a total of 77 text messages during the weekend. Ryan sent 7 fewer messages than Martina. Keith sent 2 times as many messages as Martina. How many messages did they each send?
The number of messages are: Martina sent 21 messages, Ryan sent 14 messages, and Keith sent 42 messages.
Why are unknown values represented using variables when solving problems?We may build equations that link unknown values in a problem and describe those numbers using variables. We may modify these equations algebraically to get solutions for the unknowable numbers by employing variables. As a result, issue solving is more effective and we can come up with generic answers that may be used in a variety of situations. Moreover, employing variables enables us to see patterns and trends as well as better grasp the connections between various amounts in a situation.
Given that,
Ryan sent 7 fewer messages than Martina.
R = M - 7
Keith sent 2 times as many messages as Martina.
K = 2M
Martina, Ryan, and Keith sent a total of 77 text messages.
M + R + K = 77
Substitute the value of equation 1 and 2 in equation 3:
M + (M - 7) + 2M = 77
4M - 7 = 77
4M = 84
M = 21
Substitute the value of M in equation 1 and equation2:
R = M - 7 = 21 - 7 = 14
K = 2M = 2(21) = 42
Hence, the number of messages are: Martina sent 21 messages, Ryan sent 14 messages, and Keith sent 42 messages.
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Keenan jumped 3 times every 18 minutes. At that rate, how many would he jump in 24 minutes?
Answer:
4 jumps in 24 minutes
Step-by-step explanation:
Rate: 1 jump every 6 minutes
24/6 = 4
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Step-by-step explanation:
he should have multiplied
The volume of a cone whose height h and base radius is r is given by the formula of the volume of a cone,express r in terms of v,pie and h and find the value of h when the volume of the cone is 660cm raise to power 3,where r is 14cm(pie=22/7)
The formula for the volume of a cone is:
V = (1/3)πr^2h
Solving for r:
V = (1/3)πr^2h
3V = πr^2h
r^2 = (3V)/(πh)
r = sqrt[(3V)/(πh)]
Given that V = 660cm^3, h = 14cm and π = 22/7:
r = sqrt[(3 × 660)/(22/7 × 14)] ≈ 7 cm
So the radius is approximately 7 cm.
To find the value of h:
V = (1/3)πr^2h
660 = (1/3)(22/7)(7^2)h
660 = (22/3)(49/7)h
660 = (22/3)(7)h
h = 660 / [(22/3)(7)]
h = 9.45 cm (rounded to two decimal places)
Therefore, the value of h when the volume of the cone is 660 cm^3 is approximately 9.45 cm.
I NEED HELPI NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP
The diagram shows Triangle ABC. What is the height of Triangle ABC? Show your work.
The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as,
H² = P² + B²
The height of Triangle ΔABC is given as,
17² = h² + 15²
289 = h² + 225
h² = 289 - 225
h² = 64
h = 8 units
The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.
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Solve 9x^2-6x+1=2 using the square root property. Round to the nearest hundredth if necessary.
[tex]9x^2-6x+1=2 \iff (3x)^2-2(3x)+1=2\\[/tex]
[tex](3x - 1)^2 = 2[/tex]
[tex]3x-1=-\sqrt{2} \iff 3x = 1 - \sqrt{2} \implies x_{1} = \dfrac{1-\sqrt{2} }{3}\\[/tex]
[tex]3x-1=\sqrt{2} \iff 3x = 1 + \sqrt{2} \implies x_{2} = \dfrac{1+\sqrt{2} }{3}\\[/tex]
[tex](-0.14, \ 0.8)[/tex]
scatter plot, label each axis, and choose a
Over the last 8 snowstorms, Julian recorded the amount of
snowfall to the nearest inch and the amount of time it took him
to shovel his driveway. He recorded the data in the table.
Snowfall (in.)
2
5
8
18
10
6
12
14
Time Shoveling
1
2
2
5
3
2
4
4
Answer:
Have a good day and time and I6ykjjuu7ttggfszd to the 5tjyyv
I need help please anyone ?!!!!?
Answer:
b
Step-by-step explanation:
3 + 3 = 6 lol
6 how many apples
HELP!!!!!! evaluate and fully simplify each of the following
For function f(x)= -4x²-4x-1, f(x+h)= -4x² - 8xh - 4h² - 4x - 4h - 1, (f(x+h) - f(x))/h= -8x - 4h - 4
Describe function ?The input values of a function are called the domain, and the output values are called the range. The domain can be any set of values, but each input value must have a unique corresponding output value. If there are multiple input values that produce the same output value, the function is not considered to be well-defined. Functions are used to model a wide range of phenomena in many different fields, including science, engineering, and economics. They are also used in calculus to study rates of change and slopes of curves.
To find f(x+h), we need to replace x with (x+h) in the given function:
f(x+h) = -4(x+h)² - 4(x+h) - 1
= -4(x² + 2xh + h²) - 4x - 4h - 1
= -4x² - 8xh - 4h² - 4x - 4h - 1
To find (f(x+h) - f(x))/h, we first need to find f(x):
f(x) = -4x² - 4x - 1
Then we can substitute f(x+h) and f(x) in the formula:
(f(x+h) - f(x))/h = (-4x² - 8xh - 4h² - 4x - 4h - 1 - (-4x² - 4x - 1))/h
= (-4x² - 8xh - 4h² - 4x - 4h - 1 + 4x^2 + 4x + 1)/h
= (-8xh - 4h² - 4h)/h
= -8x - 4h - 4
So, f(x+h) = -4x² - 8xh - 4h² - 4x - 4h - 1, and (f(x+h) - f(x))/h = -8x - 4h - 4.
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A map is drawn on a coordinate plane. The school media center is located at (-20, 22). The school cafeteria is located at (-12,22). The school office is located at (-20,18). The three locations form a triangle. If one using on the cooridnate plane represents 100 feet, what is the distance, in feet, between the media center and the office
The distance between the media center and the office is 4 times 100, or 400 feet.
What is the distance formula?Distance Formula. ⇒ [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] Using this formula in the equation, we get
Using the distance formula, we can find the distance between the media center and the office:
[tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]
where (x1, y1) are the coordinates of the media center (-20, 22) and (x2, y2) are the coordinates of the office (-20, 18).
[tex]d = \sqrt{((-20 - (-20))^2 + (18 - 22)^2)}\\= \sqrt{(0 + (-4)^2)}\\= \sqrt{(16)}\\= 4[/tex]
Since one unit on the coordinate plane represents 100 feet.
Hence, the distance between the media center and the office is 4 times 100, or 400 feet.
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The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190
There is a 2.28% chance that more than 250 books were borrowed in a week.
Describe Probability?Probability can also be calculated using other methods, such as counting techniques and probability distributions. Probability distributions provide a way to model the behavior of random events and describe the likelihood of different outcomes occurring.
Probability has many applications in fields such as statistics, finance, engineering, and science. It is used to make predictions, analyze data, and make decisions based on uncertain information. Understanding probability is an important skill for many professions, as it allows individuals to make informed decisions and assess risk.
To solve this problem, we need to use the standard normal distribution and calculate the z-score.
First, we find the z-score:
z = (x - μ) / σ
z = (250 - 190) / 30
z = 2
We can then use a standard normal distribution table or calculator to find the probability of getting a z-score of 2 or higher.
Using a standard normal distribution table, we find that the probability of getting a z-score of 2 or higher is approximately 0.0228.
To convert this to a percentage, we multiply by 100:
0.0228 x 100 = 2.28%
Therefore, there is a 2.28% chance that more than 250 books were borrowed in a week.
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The complete question is:
The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week.
select all of the expressions that are equivalent to 3²/3-²
Answer:
3 to the power of -4 and -81Step-by-step explanation:
Sven can buy tomatoes for $2.50 a pound at Grandiose Grocers, one block from
his house.
He can get tomatoes for $2.00 a pound at EconoFoods, but he has to spend $3
on bus fare to get there and back.
The graph shows the cost of buying tomatoes from each grocery store.
How should the x-axis be labeled?
The x-axis should be labeled
How should the y-axis be labeled?
The y-axis should be labeled
What does the slope of each line represent?
The slope of each line répresents the
What does the y-intercept of each line represent?
The y-intercept of each line represents the
The x-axis should be the number of pounds of tomatoes bought.
The y-axis should be the total cost of x pounds of tomatoes.
The slope of each line represents the cost of tomatoes/pound.
The y-intercept of each line represents the bus fare.
What is an equation of the line?To determine which point would not be found on the line, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
As per the given data:
Tomatoes from Grandiose Grocers = $2.50/pound
Tomatoes from EconoFoods = $2/pound
Bus fare for EconoFoods = $3
The x-axis should be the number of pounds of tomatoes bought.
The y-axis should be the total cost of x pounds of tomatoes.
For Grandiose Grocers:
y = 2.50x
For EconoFoods:
y = 2x + 3
From comparing with the slope-intercept form of a line, y = mx + c
m(Grandiose Grocers) = 2.50 {cost of tomatoes per pound}
m(EconoFoods) = 2 {cost of tomatoes per pound}
c is the y intercept:
c(Grandiose Grocers) = 0 {bus fare is $0}
c(EconoFoods) = 3 {bus fare is $3}
Hence, The x-axis should be the number of pounds of tomatoes bought.
The y-axis should be the total cost of x pounds of tomatoes. The slope of each line represents the cost of tomatoes/pound. The y-intercept of each line represents the bus fare.
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I need help! Please include an explanation.
Measure of angle B is 40 degree
What is circle ?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.
From the figure,
As △ABC is inscribed in the circle, the points A , B and C lie on the circumference of the circle .
As O is the center of the circle.
Given , angle (BAC) is 50 degree
We know, a triangle drawn from two ends of a diameter of a circle makes an angle of 90° at the circumference.
so, angle (ACB) is 90 degree
Now, in triangle ABC
[tex]\angle ABC +\angle BCA +\angle BAC =180^0\\[/tex]
[tex]\angle B + 90^0 +50^0 = 180^0\\[/tex]
[tex]\angle B =40^0[/tex]
Hence, [tex]\angle B = 40^0[/tex]
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Create a polygon JKLMNOPQ that is a dilation of polygon ABCDEFGH with a scale factor of 3 about the origin
The dilated polygon and polygon are created. And the scale factor of the polygon STUVWXYZ to JKLMNOPQ will be 9.
What is dilation?Dilation is the methodology of expanding the dimensions of an object without impacting its appearance.
The coordinate of the polygon ABCDEFGH is given as,
(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)
a) If the scale factor is 3, then the coordinate of the polygon JKLMNOPQ is given as,
⇒ 3 [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]
⇒ (9, -9), (12, -12), (15, -9), (24, -18), (30, -12), (27, -9), (24, -12), (15, -3)
b) If the scale factor is 1/3, then the coordinate of the polygon STUVWXYZ is given as,
⇒ 1/3 x [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]
⇒ (1, -1), (4/3, -4/3), (5/3, -1), (8/3, -2), (10/3, -4/3), (3, -1), (8/3, -4/3), (5/3, -1/3)
c) The polygon JKLMNOPQ and STUVWXYZ are similar. Then the scale factor is given as,
Scale factor = 9/1
Scale factor = 9
The diagram is given below.
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Given the definitions of f(x) and g(x) below, find the value of f(g(2)).
f(x) = 2x² + x - 13
g(x) = x - 6
Answer:
21 is the value of f(g(2)) in functions.
What is a function, exactly?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). Mathematics is rife with functions , and the sciences depend on them for constructing physical relationships.
f(x) = 2x² + x - 13
g(x) = x - 6
the value of f(g(2))
g(2) = 2 - 6
= -4
f(g(2)) = 2x² + x - 13
= 2(-4)² + 2 - 13
= 32 - 11
= 21
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Rewrite as a single logarithm: log 8 + log 3.
We can rewrite the sum of logarithms as:
log(8) + log(3) = log(24)
How to write this a single logarithm?
Remember that if we have two logarithms of the same base, then we can write:
log(a) + log(b) = log(a*b)
Here the base of the logarithms is the same, then we can use that rule, we can rewrite the given sum as:
log(8) + log(3) = log(8*3) = log(24)
That is the expression rewritten as a single logarithm.
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Hello! 5/6 2/5 in simplest form
Answer:
Step-by-step explanation:
5/6 - 2/5 = 25/30 - 12/30 = 13/30
Answer:
Step-by-step explanation:
To subtract two fractions, we need a common denominator. The smallest number that 6 and 5 both divide into is 30.
Converting the fractions to have 30 as the denominator, we get:
5/6 = 25/30
2/5 = 12/30
Now we can subtract:
25/30 - 12/30 = 13/30
Therefore, 5/6 - 2/5 = 13/30 in simplest form.
55 employees to employees 66
The required, there is a 20% increase from 55 employees to 66 employees.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To calculate the percentage increase from 55 employees to 66 employees, we need to find the difference between the two numbers, divide that difference by the original number, and then multiply by 100 to convert the result to a percentage.
The difference between 66 and 55 is 11.
So, the percentage increase is:
(11/55) x 100% = 20%
Therefore, there is a 20% increase from 55 employees to 66 employees.
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The question seems to be incomplete, the complete question is shown below,
55 employees to employees 66, calculate the percentage increase?
Write the equation of a circle with a center (9,10) and containing the point on the circle (7,4).
Answer: The equation of a circle with center (a,b) and radius r is given by:
(x - a)^2 + (y - b)^2 = r^2
In this case, the center is (9,10) and the point on the circle is (7,4). To find the radius, we can use the distance formula between the center and the point on the circle:
r = sqrt((7 - 9)^2 + (4 - 10)^2) = sqrt((-2)^2 + (-6)^2) = sqrt(40)
So, the equation of the circle is:
(x - 9)^2 + (y - 10)^2 = 40
Alternatively, we can also expand the equation to get:
x^2 - 18x + 81 + y^2 - 20y + 100 = 40
Simplifying and rearranging, we get:
x^2 + y^2 - 18x - 20y + 41 = 0
Therefore, the equation of the circle is either (x - 9)^2 + (y - 10)^2 = 40 or x^2 + y^2 - 18x - 20y + 41 = 0.
Step-by-step explanation:
Camille made a quilt for her cousin's doll. The quilt had an 8 × 8 array of different color square patches. If each patch is 2 2/3 in long, what is the area of the whole quilt?
As a result, the total quilt's area is 512/9 square inches.
What is square used for?Square offers businesses a range of goods and services to help them complete sales deals, use marketing strategies, and control their finances, inventory, and workforce.
The quilt has an 8 x 8 array of square patches, which means it has a total of 8 x 8 = 64 square patches. Each square patch is 2 2/3 inches long.
To find the area of the whole quilt, we need to find the total area covered by all 64 square patches. We can do this by multiplying the length and width of one square patch by the total number of patches:
Area of one square patch = length x width = (2 2/3 in) x (2 2/3 in) = (8/3 in) x (8/3 in) = 64/9 sq in
Total area of all 64 square patches = (64 patches) x (64/9 sq in per patch) = 512/9 sq in
Therefore, the area of the whole quilt is 512/9 square inches.
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A clothing business finds there is a linear relationship between the number of shirts,n, it can sell and the
price,p, it can charge per shirt. In particular, historical data shows that 1000 shirts can be sold at a price
of $19, while 2000 shirts can be sold at a price of $16. Give a linear equation in the form p = mn + b
that gives the price p they can charge for n shirts.
A linear equation in the form p = mn + b that gives the price they can charge for n shirts is p = -0.003x + 22.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (1000, 19), a linear function in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 19 = (16 - 19)/(2000 - 1000)(x - 1,000)
y - 19 = -0.003(x - 1,000)
y = -0.003x + 3 + 19
p = y = -0.003x + 22
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HELP ASAP, WILL GIVE BRAINLIEST, 53 POINTS!!!!
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of three fourths to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
A′(−12, 18), B′(−6, 6), C′(12, −6), D′(12, 12)
A′(3, −4.5), B′(1.5, −1.5), C′(−3, 1.5), D′(−3, −3)
A′(4.5, −3), B′(1.5, −1.5), C′(−1.5, 3), D′(3, 3)
Answer:
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
Step-by-step explanation:
You would take three fourths of each coordinate to get the x and y values.
Answer:
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
Step-by-step explanation:
You would take three fourths of each coordinate to get the x and y values.
What are the solutions to the quadratic equation x2 - 10x + 18 = 0
Answer:
x = 5 + [tex]\sqrt{7}[/tex]
x = 5 - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
The given quadratic equation is:
x^2 - 10x + 18 = 0
We can solve this equation using the quadratic formula, which states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = -10, and c = 18. Substituting these values into the quadratic formula, we get:
x = (-(-10) ± sqrt((-10)^2 - 4(1)(18))) / 2(1)
Simplifying the expression inside the square root, we get:
x = (10 ± sqrt(100 - 72)) / 2
x = (10 ± sqrt(28)) / 2
x = (10 ± 2sqrt(7)) / 2
Simplifying further, we get:
x = 5 ± [tex]\sqrt{7}[/tex]
Help me, please thank you