Given statement solution is :- The equation of the parabola with a focus at (-5, 5) and a directrix of y = -1.
To derive the equation of a parabola with a focus and directrix, we can use the definition of a parabola.
Let's assume the vertex of the parabola is (h, k), and the distance between the focus and the vertex is denoted as "p." The directrix of the parabola is a horizontal line given by the equation y = k - p.
In this case, the focus is at (-5, 5), so the vertex is at (h, k) = (-5, 5). The directrix is given by y = -1.
Using the definition of a parabola, we can find the distance between the focus and vertex as the same distance between the vertex and the directrix. So, we have:
k - p = -1 (Equation 1)
Since the vertex is (-5, 5), we substitute these values into Equation 1:
5 - p = -1
Solving for p:
p = 5 - (-1)
p = 6
Now we have the value of p, which is the distance between the focus and the vertex.
The equation of a parabola with a vertical axis of symmetry is given by (x - h)^2 = 4p(y - k).
Substituting the values of h, k, and p, we get:
(x + 5)^2 = 4(6)(y - 5)
Simplifying further:
(x + 5)^2 = 24(y - 5)
This is the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1.
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Find the perimeter and area of the polygon shown below.
8ft
15 ft
17ft
16 ft
The perimeter and area of the polygon are 72 feet and 300 feet.
What is a polygon?"A polygon is a plane shape with straight sides. Polygons are 2 - dimensional shapes. They are made of straight lines, and the shape is closed."
From the given polygon
Perimeter of the polygon = Sum of all sides of the polygon
P = 15 + 16 + 8 + 17 + 16
P = 72 feet
Area of the polygon
A = [tex](\frac{16+16+8}{2}[/tex] × [tex]15)[/tex]
A = 20 × 15
A = 300 feet
Hence, the perimeter and area of the polygon are 72 feet and 300 feet.
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Which of the following is not a real number?
А. 1
B. -4
C. 16
D. 13
B is not a real number.
Real number are numbers that are rational (1, 2, 3, -7, -10 etc) and irriational (pi, 9.7582, 1/7, etc), and can be virtually any number, aside from imaginary numbers. Square roots consist of the same number squared, for example the square root of 9, is 3 or the square root of 10 is 3.162... Both of which are real numbers.
A.) The square root of 1, is 1. 1 is a real number.
B.) The square root of -4 is imaginary. There is no real number that can be squared to get -4.
C.) The square root of 16 is 4. 4 is a real number.
D.) The square root of 13 is 3.605... 3.605... is a real number.
Thus meaning your answer is B.
I hope this helps!
Find the slope of the line.
Slope = type your answer...
Answer:
slope= (-1)
...................
Help please! I will mark brainlest. Answer ASAP i have to hand in , in 8 minutes
Answer:
129 degrees
Step-by-step explanation:
So you know that AZC = 90 and CZB = 39, so all you have to do to find AZB is 90 + 39 = 129 degrees.
Find the solution of the system of equations.
10x – 2y = 44
-2x - 9y = 10
Answer:
Merhaba, siz kanadada İngilizcem konuşuyoruz vay canına sjsjs
Answer:
10x=44+2y
x=44+2y/10.....eq(i)
-9y=10+ 2x
-Y=10+2X/9....eq(ii)
Then solve by eq(i) and eq(ii)
The midpoint i need help
Answer:
angle WXU=56 degrees
Step-by-step explanation:
WX || TV so angle WXU is congruent to angle TVU
68-3x=84-7x
simplify by adding 7x to each side
68+4x=84
simply further by subtracting 68 from each side
4x=16
divide both sides by 4
x=4
angle WXU=68-3x
substitute for x
angle WXU=68-3(4)=68-12=56 degrees
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
m = -4/5
b = 7
Negative Slope
Not Proportional
Step-by-step explanation:
Please find the value of x
Answer: x = 118
Step-by-step explanation:
5. Using t = 3.14, what is the circumference of a circle with a diameter of 50 units?
Round your answer to the nearest hundredth.
Answer:
1962.5
Step-by-step explanation:
The equation for the circumference of a circle is Area = pi * r squared. So if the diameter is 50, then the radius is 25. 25*25 = 625. Now we do 625 * 3.14 = 1962.5 So your answer is 1962.5 I hope this helps :)
Here is a list of numbers.
8 9 10 11 12 13 14
From the list write
a a multiple of 7
b a factor of 24
c a prime number
thank you! :))))
Multiply. Give your answer in lowest terms.
3 8
4 11
Answer:
6
11
Step-by-step explanation:
Is it the 2nd and 3rd one? I don't entirely understand
Answer:
Statements 1, 2, or 4 each imply a rectangle. Check all three.
Step-by-step explanation:
A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30 What score is necessary to reach the 75th percentile? Select the closest answer
Answer:
A score of 150.25 is necessary to reach the 75th percentile.
Step-by-step explanation:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30.
This means that [tex]\mu = 130, \sigma = 30[/tex]
What score is necessary to reach the 75th percentile?
This is X when Z has a pvalue of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 130}{30}[/tex]
[tex]X - 130 = 0.675*30[/tex]
[tex]X = 150.25[/tex]
A score of 150.25 is necessary to reach the 75th percentile.
Reduce/Simplify the fraction in its lowest terms.
24/48
[tex] \frac{24}{48} [/tex]
To find:The lowest term of the given fraction by simplifying.
Solution:[tex] \frac{24}{48} [/tex]
[tex] = \frac{24 \div 24}{48 \div 24} [/tex]
[tex] = \frac{1}{2} [/tex]
Which of these tables represents a proportional relationship between x and y choose 2 plz help ASAP
Answer:
b and c
Step-by-step explanation:
.
4 cm What is the volume of this prism? 6 cm 10 cm
Answer:
240 cm³
Step-by-step explanation:
Volume = lwh
10cm • 6cm • 4cm
10cm • 24 cm²
240 cm³
I bought a bag of apples for 500 and sold it for 450 what is the percentage lost
Answer:
10%
Step-by-step explanation:
loss= Cp - Sp
= 500- 450
= 50
loss % = 50/ 500× 100
= 10%
What is the total surface area of the square pyramid in square inches?
Height is 11 in. Base is 7 in. Side Length is 11.5
PLEASE DO THIS QUICKLY
Answer:
Step-by-step explanation:
I assume that "side length" means the slant height of one of the triangular faces.
area of a triangular face = ½(base)(side length) = ½(7)(11.5) = 40.25 in
lateral area = all four triangles = 161 in²
base area = 7² = 49 in²
total surface area = lateral area + base area = 161+49 = 210 in²
The area of the pyramid is 1.4625 ft²
What is a Square Pyramid?If the base of the pyramid is in the shape of a square (base with 4 sides), then it is called a square pyramid. As the square has 4 sides, then the square pyramid has the following properties: No. of Faces: (4+1) = 5 No.of Vertices: (4+1)= 5 No. of Edges: 2(4) = 8
Given here: The height is 11, the base is 7 in, and the side length is 11.5 inches of a pyramid.
The surface area of a square pyramid is the sum of the areas of its square base and four triangular faces:
SA = BA + (4 × FA)
=[tex]a^2+a\sqrt{a^2+4h^2}[/tex]
Where a= base length and height = h
Thus inputting the values we get
SA= 7²+7[tex]\sqrt{7^2+4.11^2}[/tex]
=49+7√533
=210.60 in²
Thus in ft.² we have 1.4625 ft²
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Pls help ..I’ll mark brainly
Answer:
D
Step-by-step explanation:
Answer:
D.33
Step-by-step explanation:
4(7)+[tex]\sqrt{-8\\ (-3)+1[/tex]
First solve inside the radical by multiplying and adding
-8 x -3=24
24+1=25
[tex]\sqrt{25[/tex]=5
Next multiply 7 x 4
28
Then add
28+5=33
Translate the sentence into an equation. Five more than the quotient of a number and 6 is equal to 2. Use the variable w for the unknown number.
Answer:
The equation that represents the sentence is W + 6 + 5 = 2.
Step-by-step explanation:
Since it is required to propose an equation that reflects that five more than the quotient of a number and 6 is equal to 2, using the variable W for the unknown number, the following equation must be performed to determine what the unknown number is:
W + 6 + 5 = 2
W = 2 - 5 - 6
W = -9
Therefore, the unknown number is -9.
29x+2=31
Giving brainliest if do correct..
Explanation also or reported
Answer:
x = 1
Step-by-step explanation:
29x + 2 = 31
-2 -2
29x = 29
----- -----
29 29
x = 1
Please let me know the explanation of the the answer u will tell for this Question..
[tex] \huge \purple{\tt{Answer:}} [/tex]
Area of square = (length)²
[tex] = \sf {(3{\dfrac{1}{2}})^2} \\\\\ = \sf {12.25~cm^2} [/tex]
OR
[tex] \sf{12{\dfrac{1}{4}}} [/tex]
Find the image of (1, 2) after a
reflection about x = 6 followed by a
reflection about x = 4.
(1,2)
reflect across x=6
(11,2)
reflect across x=4
(-3,2)
Done!
The ratio of men to women working for a company is 3 to 4. If there are 161 employees total, how many women work for the company?
(4xy+6y-4x)-5xy-4x+3y STEP explanation pls
Answer:
this is the solution
please follow me and mark it brainliestSelect the correct answer.
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
А -4
B -2.
С -1
D 1
Hong bought 60 CDs that were each the same price. Including sales tax, he paid a total of $100.80. Of that total, $6.60
was tax. What was the price of each CD before tax?
Answer:
$1.57 per CD
Step-by-step explanation:
Subtract the tax from the total then divide by the number of CDs.
100.80-6.60=94.2
94.2/60=1.57
Use the Distributive Property to write –4(7 – 1) as an equivalent expression. What is the value of the expression?
Answer:
Step-by-step explanation:
-4(7-1) = (-4)7 + (-4)(-1) = -24
The volume of a cylinder is 225π cm³ and its height is 9 cm.
What is the length of the cylinder's radius?
Enter your answer in the box.
cm
Answer:
5cm
Step-by-step explanation:
Given data
volume = 225π cm³
Height= 9cm
r= ???
Volume of cylinder
v=πr^2h
substitute
225π= π*r^2*9
225= r^2*9
r^2= 225/9
r^2= 25
r= √25
r= 5cm
Hence the radius is 5cm
The diagram represents a reduction of a triangle by using a scale factor of 0.8.
Answer:
4.8 inches
Step-by-step explanation:
See comment for complete question
Represent the larger triangle with 1 and the smaller with 2.
So, we have:
[tex]H_1 =6\ in[/tex] -- height of 1
Required
Determine H2 --- Height of 2
To do this we apply dilation formula.
[tex]Original * Scale\ Factor = New[/tex]
In this case:
[tex]H_1 * Scale\ Factor = H_2[/tex]
Substitute 6 for H1 and 0.8 for Scale Factor
[tex]6* 0.8 = H_2[/tex]
[tex]4.8= H_2[/tex]
Hence, the height of the smaller triangle is 4.8 inches