The equation of the the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]
Equation of the ellipses:
The Equation of the ellipse with center at (h, k)
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]
where,
a = length of semi-major axis
b = length of semi-minor axis
Given,
Here we have the value of center as (1, -3) and the values of a = 7 and b = 5.
Here we need to find the equation of the ellipse.
According to the formula we we have the following values are given,
We know the value of center of ellipses is written as,
(h, k) = (1, -3)
And the values of
a = 7 and b = 5
Therefore, when we apply the values on the formula then we get,
[tex]\frac{(x-1)^2}{7^2}+\frac{(y-(-3))^2}{5^2}[/tex]
When we simplify the term then we get,
[tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]
Therefore, the equation of the ellipse is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex].
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-2x-7 > 1 or x - 2 ≥-1
The inequalities are solved below
What are inequalities?
A connection in mathematics that compares two numbers or other mathematical functions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. To indicate various sorts of inequalities, a variety of notations are employed. The following characteristics control inequalities. Any of these characteristics are also true if monotonic functions are restricted to strictly monotonic functions and all non-strict inequalities ( and ) are replaced by their equivalent strict inequalities ( and >). On each side of an inequality, a common constant c can be added to or removed from.
The inequalities are solved below
-2x-7>1 x-2≥-1
or, -2x>1+7 or, x≥-1+2
or, -x>8/2 or, x≥1
or, x<-4
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Find the value of each variable
Answer:
Step-by-step explanation:
since they are verticle angles:
8x+7=9x-4
subtract 8x and add 4
x=11
if f(x)=2x+a what is the value of A satasfying f(2)=2
Answer:
-2
Step-by-step explanation:
Substitute x with 2 and y with 2
2 = 2 * 2 + a
2 = 4 + a
subtract 4 on both sides
2 = 4 + a
-4 -4
-2 = a
Identify a pair of lines that looks parallel in the diagram.
pls help me
Lines f and g look to be parallel to each other.
Answer:
Lines G and F
Step-by-step explanation:
Parallel means never touching, and they usually run alongside eachother, that's why G and F look parallel.
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What is the area of a triangle whose vertices are J(−2, 1), K(0, 3), and L(4, −1)?
Enter your answer in the box.
Based on the vertices of the triangle, the area of the triangle can be found to be 8 cm²
How to find the area of the triangle?First, find the lengths of JK, KL, and JL. When given vertices, you can find the length of a line by the formula:
= √ ( (x₂ - x₁)² + (y₂ - y₁)²)
The length of JK is therefore 2.83 units
The length of KL is therefore 5.66 units
The length of JL is therefore 6.32 units.
Given these units, the area of the triangle can be found by the formula:
= √ s(s - a) ( s - b) ( s - c)
Where:
s = semi perimeter
a, b, and c are the sides of the triangle which are JK, KL, and JL.
The semi-perimeter can be found by the formula:
= ( a + c + c) / 2
= 15.47 / 2
= 7.74
The area of the triangle is therefore:
= √ s(s - a) ( s - b) ( s - c)
= √ 7.74 (7.74 - 2.83) ( 7.74 - 5.66) ( 7.74 - 6.32)
= 8 cm²
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Jordan and his children went into a restaurant and he bought $26 worth of drinks
and tacos. Each drink costs $2.50 and each taco costs $2. He bought 4 more tacos
than drinks. Write a system of equations that could be used to determine the number
of drinks and the number of tacos that Jordan bought.
The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's assume that number of drinks that Jordan and his children bought is x while the number of tacos is y.
The cost of drinks = 2.50x
Cost of tacos = 2y
Total cost 2.5x + 2y
2.5x + 2y = 26
Given that,
He bought 4 more tacos than drinks.
Therefore,
y = x + 4.
Hence "The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4".
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Don’t get how to do this
Answer:
1. 1.4, 1 5/8, 12/5, 8/8
2. 0.88
3. 1/4 and 8/8
4. 12/5 and 2/100
5. 1 5/8 and 1.625
6. 1 1/2
Find the perimeter and area of the figure, rounding to the nearest tent. Use 3.14 for pie 7 ft 25 ft 4 ft Perimeter = 89.12 feet Area = feet squared
According to the picture, you can find the area of the figure by susbtracting the area of the segments of the circles to the area of the rectangle. We can observe that these segments are a quarter of a circle, together they would be a complete circle, then to find the area of the figure we can substract the area of one of the circles to the area of the rectangle.
1. Find the area of the circle:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(4)^2 \\ A=16(3.14) \\ A=50.24 \end{gathered}[/tex]2. Find the area of the rectangle:
To do it, you need to find the length and the width first, do it this way:
[tex]\begin{gathered} l=25+4+4=33 \\ w=7+4+4=15 \end{gathered}[/tex]Now, find the area of the rectangle:
[tex]\begin{gathered} A=l\cdot w \\ A=33\cdot15 \\ A=495 \end{gathered}[/tex]3. Find the area of the figure:
[tex]\begin{gathered} A=495-50.24 \\ A=444.76 \end{gathered}[/tex]The area of the figure is 444.76 feet squared.
Tommy earned $88.00 working for 5 hours. At this rate, how much will Tommy earn working for 12 hours?
At this rate, Tommy will earn $211.2 working for 12 hours.
The Unitary Method draws a relation between given data. Following the regular trend, information can be calculated. It is also called the 'Mango Method'.
Tommy earned $88.00 working for 5 hours.Tommy will earn $17.6 working for 1 hour.At this rate, Tommy will earn $211.2 working for 12 hours.
The Unitary Method is only valid for regular increases or decreases. Information about unity is drawn from given data, which is multiplied as required. It is widely used in the calculation of prices, amounts, etc.
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The table describes the quadratic function h(x).
x h(x)
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22
What is the equation of h(x) in vertex form?
h(x) = (x + 2)2 − 3
h(x) = (x + 1)2 − 2
h(x) = (x − 1)2 + 2
h(x) = (x − 2)2 + 3
The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that the values of x and h (x) for the quadratic function is given by;
x = -3, -2, -1, 0, 1, 2, 3,
h (x) = -2, -3, -2, 1, 6, 13, 22
Consider the quadratic function as;
h (x) = ax² + bx + c
Now Substitute x = -3 and h (x) = -2 in quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-3)² + b × -3 + c
- 2 = 9a - 3b + c
And, Plug x = -2 and h (x) = -3 in function we get;
h (x) = ax² + bx + c
- 3 = a × (-2)² + b × -2 + c
- 3 = 4a - 2b + c
And, plug x = -1 and h (x) = -2 in function we get;
h (x) = ax² + bx + c
- 2 = a × (-1)² + b × -1 + c
- 2 = a - b + c
After solving we get:
a = 1 , b = 4 and c = 1
Then
h (x) = ax² + bx + c
h (x) = 1 × x² + 4x + 1
h (x) = x² + 4x + 1
h (x) = x² + 4x + 4 - 4 + 1
h (x) = (x + 2)² - 3
Hence, The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3
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Assume that a sample is used to estimate a population mean μ . Find the 99% confidence interval for a sample of size 891 with a mean of 20.8 and a standard deviation of 17.6. Enter your answer as a tri-linear inequality accurate to 3 decimal places.19.281Incorrect < μ < 22.319
Solution:
The confidence interval is expressed as
where
[tex]\begin{gathered} \bar{x}\text{ or }\mu\Rightarrow sample\text{ mean} \\ z\Rightarrow confidence\text{ level value} \\ s\Rightarrow sample\text{ standard deviation} \\ n\Rightarrow sample\text{ size} \end{gathered}[/tex]Given a 99% confidence interval for a sample size of 891 with a mean of 20.8 and a standard deviation of 17.6, this implies that
[tex]\begin{gathered} \bar{x}=20.8 \\ s=17.6 \\ n=891 \\ z=2.576 \end{gathered}[/tex]By substituting these values into the above equation, we have
[tex]\begin{gathered} CI=20.8\pm(2.576\times\frac{17.6}{\sqrt{891}}) \\ =20.8\pm1.518866748 \\ Thus,\text{ } \\ \Rightarrow lower\text{ bound:} \\ 20.8-1.518866748=19.28113325 \\ \Rightarrow upper\text{ bound:} \\ 20.8+1.518866748=22.31886675 \end{gathered}[/tex]Hence, we have
[tex]19.281<\mu<22.319[/tex]When the summer started, Janie needed to fill her empty pool. At first, she used a garden hose to fill the pool, but this was taking too long. She got tired of watching the pool fill so slowly, so she turned off the water and went for a walk. She spotted a truck in the neighborhood that was filling pools and flagged them down to come fill her pool too. They were able to fill the pool at a faster rate. Which graph best represents this situation?
The statement mentions that the pool started empty, which implies that the graph must start at the point (0,0).
Then, the pool slowly filled, so the amount of water in the pool remained constant when Janie turned off the water and went for a walk.
Finally, thanks to a truck in the neighborhood the pool filled up quickly, and when it was filled the amount of water remained constant.
Therefore, the graph that best represents this situation is the one shown in option B.
Describe how to transform the graph of f(x)=x^2 into the graph of g(x)=4(3x-1)^2+5.
Please help me with this question! Thank You
The transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
The given functions are f(x) = x² and g(x)= 4(3x-1)²+5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The transformation is
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 0.333 Units
Vertical Shift: Up 5 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
Therefore, the transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
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Enter a term in the box to make an equation that has infinitely many solutions.
3x+______= 3x+14-6
Answer:
3x+6-14
Step-by-step explanation:
Find the value of $x$ that makes this equation true:
\[2x + 5 = 1.99x + 22.\]
Please help quick!
The value of x that makes the equation 2x+5 = 1.99x + 22 is 1700
The equation is
2x+5 = 1.99x+22
First we have to rearrange the given term and combine the like terms, then we have to find the value of x
Move 1.99x to left hand side of the equation and move 5 to the right hand side of the equation
2x+5 = 1.99x+22
2x-1.99x = 22-5
We have to do the subtraction in like terms
(2-1.99)x = 22-5
0.01x = 17
Move the number 0.01 to the right hand side of the equation
x = 17/0.01
Division
x = 1700
Hence, the value of x that makes the equation 2x+5 = 1.99x + 22 is 1700.
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Find the measure of
Answer:
50 degrees
Step-by-step explanation:
Line CDF is 180 degrees
76 and 54 and some part of the 180 degrees
1. add 76+54 = 130
2. subtract 180-130 = 50
PLEASE HELP! This is due tomorrow!
Determine whether the equation represents a linear or nonlinear function. Explain.
I just need help with these, I have a busy day today :(
The categories of the functions are:
Linear functions: (16) y = 7 - x (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|Nonlinear functions: (15) y = x² + 13 (18) y = x . x . x (20) 7 - y = 2ˣ (22) |x| + 12 = yHow to categorize the functions?The category of the functions are given as
Linear functionsNonlinear functionsAs a general rule, linear functions can take any of the following forms
y = a x = by = xy = mxy = mx + cy - y1 = m(x - x1)Ax + Bx = CWhere the variables a, A, m, b, B, c and C are real numbers
Any equation that do not have the above form is considered a nonlinear function
Using the above forms as a guide, we have the linear equations to be
(16) y = 7 - x (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|
All other equations are nonlinear equations
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The Mendez Family consists of two adults and two children. Their current monthly income is $4800. Calculate the percentage of the total budget for each category.
Percentage spent on transportation is 12%
Percentage spent on Property tax is 11%
Percentage spent on utilities is 9%
Percentage spent on food is 20%
Percentage spent on mortgage payment is 30%
Percentage spent on entertainment is 8%
Percentage spent on miscellaneous is 10%
What are the percentages?
Percentage is the fraction of a number expressed as a number out of 100. In order to convert a number of fraction to percentage, multiiply by 100. The sign that is used to represent percentage is %.
Percentage spent on transportation = (576 / 4800) x 100 = 12%
Percentage spent on Property tax = (528 / 4800) x 100 = 11%
Percentage spent on utilities = (432 / 4800) x 100 = 9%
Percentage spent on food = (960 / 4800) x 100 = 20%
Percentage spent on mortgage payment = (1440 / 4800) x 100 = 30%
Percentage spent on entertainment = (384 / 4800) x 100 = 8%
Percentage spent on miscellaneous = (480 / 4800) x 100 = 10%
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the measure of the angles of a triangle are shown in the figure below. solve for x
64°
x°
40°
Answer:
Sum of angles in a triangle add up to 180°.
x = 180 - 64 - 40
= 76°
a student group plans to donate school supplies for children in an orphanage. if notebooks that are normally 59 cents each are on sale two for 99 cents, how much can be saved by purchasing ten notebooks at the sale price?
The amount that can be saved by purchasing ten notebooks at the sale price is 95 cents.
What will the price be?The information stated that the notebook are in sale for 2 at 99 cents. The cost for each notebook will be:
= 99 cents / 2
= 49.5 cents
The amount they can be saved will be:
= (59 × 10) - (49.5 × 10)
= 590 - 495
= 95 cents
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What is the image of ( − 8 , − 4 ) after a dilation by a scale factor of 1 4 4 1 centered at the origin?
The image of the point after the dilation is (-2, -1)
What is dilation?Dilation is the process of altering the side length of a shape or a function
How to determine the image of the points?From the question, the given parameters are:
Point = (-8, -4)
The scale factor of dilation is given as
Scale factor = 1/4
Mathematically, this transformation can be represented as
(x, y) = k(x, y)
Where k = 1/4 i.e. the scale factor
So, we have
(x, y) = (kx, ky)
This gives
(x, y) = (1/4x, 1/4y)
When represented as an equation, we have
Image = 1/4 * Point
Substitute the equation Point = (-8, -4) in the equation Image = 1/4 * Point
So, we have the following equation
Image = 1/4 * (-8, -4)
Evaluate the product
Image = (-2, -1)
Hence, the image is (-2, -1)
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What is x and y and how do I solve for it in the future?
The values of x and y in the triangle are 15 and 88 degrees.
How to find the angles of a triangle?A triangle is a polygon with 3 sides. The sum of angles in a triangle is 180 degrees.
A triangle can be classified base on its sides and angles as equilateral triangle, isosceles triangle and scalene triangles.
An equilateral triangle has three of its sides and angles equal to each other.
An isosceles triangle has 2 sides and angles equal to each other.
A scalene triangle has no sides equal to each other.
Therefore,
The other triangle on the left side is an equilateral triangle.
Therefore, all it sides and angles are equal.
Hence, each angle of the triangle is 60 degrees.
A traversal line cut across the sides of the parallel lines of the triangles formed.
Therefore,
60° = 4x
x = 60 / 4
x = 15
Therefore,
60 + y + 32 = 180(sum of angles in a triangle)
y = 180 - 92
y = 88°
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ive been struggling pls help
The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.
Given,
A random sample of n = 40
The mean time μ = 21.4
and, standard deviation is σ = 3.6 min
The z score (z) is given by the equation:
z = (x - μ) / σ / [tex]\sqrt{n}[/tex]
Substituting , the values we get
z = (20 - 21.4) / 3.6 /[tex]\sqrt{40}[/tex]
z = -2.45
Using the z table:
P(x < 20) = P(z < -2.45)= 0.00714
Hence, The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.
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5=3+a check
need the answer
The Smiths have decided to put a paved walkway of uniform width around their swimming pool. The pool is a rectangular pool that measures 12 feet by 20 feet. The area of the walkway will be 60 square feet. Find the width of the walkway.
***NOTE*** This is a Quadratic Word Problem, so please the Quadratic Method!! Extra 20 BRAINLIST will be reward if work is shown step by step CORRECTLY!!
Answer:
Step-by-step explanation:
12 times 2 =24 60 into 10 so i think it will be 6
i inserted a picture of the question answers to choices A 5/2B 2/5C -2/5D -5/2
If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. Given a value, a/b, the negative reciprocal of a/b is - b/a.
From the information given, the slope of the red line is 2/5. This means that the slope of the green line which is perpendicular to the red line is - 5/2
Option D is correct
Can someone help me with these two questions, I’m not sure if I’m correct or not.
5. The two triangles are similar. The value of x = 12.
6. The information cannot be used to show that the triangles are similar triangles.
How to Determine if two Triangles are Similar?Two triangles are similar to each other if they have the same shape but different sizes, in order words, they must have the same corresponding angle measures but different corresponding side lengths that are proportional to each other.
5. In the first figure, we see that there are two pairs of corresponding congruent angles (a pair of right angles and a pair of vertical angles in both triangles), but different corresponding side lengths.
Therefore, based on the AA similarity theorem that says two triangles are similar of they have two pairs of congruent sides, we can prove that both triangles are similar to each other.
Therefore:
x/9 = 20/15
15x = (9)(20)
15x = 180
15x/15 = 180/15
x = 12
6. The second image shows that the two triangles share a common side, which means they have a pair of corresponding sides that are congruent. Therefore, the information given cannot be used to prove they are similar triangles.
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yeaa pls help this is past due
Answer: When you graph part a, it has a negative slope.
Step-by-step explanation:
Cost of 100 grams. Cereal=49p
Pasta=14p
Leah buys 400 grams of cereal and 250 grams of pasta.
Work out the total cost in £
what is the name of the function which has the form f(x)=mx+b, where m>0, and how can the graph of the function be described?
The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.
Given,
The function is :
f(x) = mx + b
and, where m> 0
Described the graph of the function and also write the name of the function:
Now, According to the statement is :
f(x) = mx + b , m > 0
It is an increasing line.
So, The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.
What is a increasing line in a graph?
If a linear graph is increasing then its gradient is positive, since when x increases by 1, y changes by a positive number. If a linear graph is decreasing, the gradient is a negative number.
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