Answer:
16
(0,17)
(0,8)
Step-by-step explanation:
i got it right
The length of the transverse axis is the distance between the vertices of the hyperbola. A focus of the hyperbola is a fixed point from which distances to any point on the hyperbola have a constant difference. A vertex of the hyperbola is where it intersects its transverse axis.
Explanation:When analyzing graphs, it is crucial to understand the properties of the figures involved. In this case, we are discussing a hyperbola, which is a set of all points where the difference in the distances from two fixed points, called foci, is constant.
The length of the transverse axis of a hyperbola is the distance between its vertices. For an ellipse as shown in Figure 3.4 (b), the distance between the two vertices on the major axis is 2a, where a is the length of the semimajor axis. However, in the case of a hyperbola, the transverse axis would correspond to the axis that goes through the two vertices of the hyperbola.
A focus of the hyperbola is one of the two fixed points from which the difference in distances to any point on the hyperbola is constant. It is typically denoted as (h ± c, k) in the Cartesian coordinate system, where (h, k) is the center of the hyperbola and c is the distance from the center to each focus.
A vertex of the hyperbola is located at the point on the graph where the hyperbola intersects its transverse axis. This can be expressed as (h ± a, k) for a horizontal hyperbola or (h, k ± a) for a vertical hyperbola, where (h, k) is the center of the hyperbola and a is the length of the semimajor axis.
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Which function has a vertex at (2, –9)? f(x) = –(x – 3)2 f(x) = (x + 8)2 f(x) = (x – 5)(x + 1) f(x) = –(x – 1)(x – 5
Answer:
c
Step-by-step explanation:
The function that has a vertex at (2, -9) is;
C: f(x) = (x - 5)(x + 1)
How to find the vertex of a Function?The formula for x-coordinate of a vertex is;
x = -b/2a
The correct function is Option C with f(x) = (x - 5)(x + 1).
We will expand to get;
f(x) = x² -5x + x - 5
f(x) = x² - 4x - 5
Putting 2 for x gives;
f(2) = 2² - 4(2) - 5
f(2) = -9
Also, x = -b/2a = -(-4)/(2*1) = 2
Thus, it is proved that option C has it's vertex at 2, -9
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An equation that equals 19
Answer:
There are many different types of equations we can use to allow x to equal 19! Below are some examples :) See if you can come up with some on your own based off of these examples:
5x = 95.....................................Divide both sides b 5x = 19.......................................There's one for you :)
1 + x - 5 = 15............................Combine like termsx - 4 = 15..................................Add 4 to both sides
x = 19
2x-y=4 and 7x+3y=27
step by step
Answer:
x=3 y=2
Step-by-step explanation:
2x-y=4
7x+3y=27
Multiply the first equation by 3
3(2x-y)=4*3
6x - 3y+12
Add this to the second equation to eliminate y
6x -3y = 12
7x+3y=27
---------------------
13x +0y = 39
Divide each side by 13
13x/13 = 39/13
x = 3
Now find y
2x-y =4
2(3) -y = 4
6-y=4
Subtract 6 from each side
6-y-6 = 4-6
-y = -2
y=2
During an art show at the local gallery, Joy closely examined 2 pieces of art by each artist whose work was on display there. Each artist had an equal number of pieces on display. Is this sample of the art in the gallery likely to be representative?
Joy's approach to sampling art at the gallery, by examining 2 pieces per artist, can be representative if the selections span the artists' exhibited range. However, the representativeness might be limited if artists have a wide variety of styles or themes not captured by just two pieces.
Explanation:Joy, by examining 2 pieces of art by each artist at the art show, attempts a representative sampling of the gallery's overall offerings. Whether this approach yields a representative sample depends on a few key factors. Primarily, the diversity and range of the artists' works on display must be considered. If each artist displays a wide variety of work and Joy's selections span this variety, her sample could offer a fair representation of the gallery's exhibition. However, if the artists have a vast body of work with significant variations in style, theme, or period not captured by just two pieces per artist, Joy's sample may not accurately represent the entire collection.
Furthermore, the extent to which the selected works reflect the artists’ core themes or periods plays a critical role in determining representativeness. Assuming each artist's work on display has an equal chance of being selected and Joy chooses pieces that span the artists' exhibited range, the sample can be somewhat representative. Nonetheless, a truly comprehensive view would likely require examining a greater number or a more strategically chosen set of artworks.
Joy’s examination provides valuable insights, but for a truly representative view of the gallery, additional observations or data would be beneficial.
Let’s explore the concept of representative samples in the context of Joy’s art gallery experience.
1. Understanding Representative Samples:
o A representative sample is a subset of a larger population that accurately reflects the characteristics of the entire population. In this case, the population consists of all the art pieces displayed in the gallery.
o When we say a sample is “representative,” it means that the selected pieces adequately capture the diversity and essence of the entire collection.
2. Joy’s Situation:
o Joy closely examined 2 pieces of art by each artist. Since each artist had an equal number of pieces on display, Joy effectively observed a balanced representation of the artists’ work.
o By examining multiple pieces from each artist, Joy has a better chance of encountering a variety of styles, themes, and techniques.
3. Likelihood of Representativeness:
o Given that Joy looked at 2 pieces from each artist, we can consider this sample as potentially representative.
o However, there are a few factors to consider:
Artistic Diversity: If the artists’ styles are vastly different, the sample may not fully represent the entire gallery’s range.
Number of Artists: If there are only a few artists in total, the sample might be less representative.
Gallery Size: The larger the gallery, the more challenging it is to capture full representativeness with a limited sample.
4. Conclusion:
o While Joy’s sample is a good start, it’s essential to recognize its limitations.
o To determine true representativeness, we’d need more information about the total number of artists, the overall collection size, and the diversity of artistic approaches.
In summary, Joy’s examination provides valuable insights, but for a truly representative view of the gallery, additional observations or data would be beneficial.
Solve the system of equations 3x + y = 3 and 7x + 2y = 1.
1 Solve for the variable y in the first equation: y = 3 - 3x
2. Substitute the value for y into the second equation: 7x + 2(3 - 3x) = 1
3. Solve for x
Answer: -5
Step-by-step explanation:
Answer:
-5 is right
Step-by-step explanation:
The volume of this cone is 540 pi. Work out the height,h, of the cone
radius is 9
vol=1/3*pi*r^2*h
curved surface area =pi*r*l
Answer:
20
Step-by-step explanation:
The volume of a cone is given as:
[tex]V = \frac{1}{3} \pi r^2 h[/tex]
where r = radius
h = height
The volume of the cone is 540π and its radius is 9.
This implies that:
[tex]540 \pi = \frac{1}{3} \pi * 9^2 * h\\\\h = \frac{540 * 3}{81} \\\\h = 20[/tex]
The height of the cone is 20.
Answer:
The answer is 20 bro
Step-by-step explanation:
1.5 mi = how many ft
Step-by-step explanation:
Step 1: Convert miles to feet
1 mile = 5280 feet
1.5 * 5280
7920 feet
Answer: 7920 feet
Two fair number cubes are rolled. State whether the events are mutually exclusive. Explain your reasoning.
The numbers are the same, the sum is odd.
Are they mutually exclusive?
A. Yes because if one event occurs, the other can’t occur
B. No because they both can’t occur at the same time
C. No because if one event occurs, the other can’t occur
D. Yes, because both events can occur at the same time
Final answer:
When two number cubes are rolled, the events of rolling the same number and getting an odd sum are mutually exclusive, as one excludes the possibility of the other occurring.
Explanation:
Two events are considered mutually exclusive if the occurrence of one event excludes the possibility of the other event occurring simultaneously. When examining whether the events of rolling two number cubes are mutually exclusive, we look at two particular events:
The numbers rolled are the same.
The sum of the numbers rolled is odd.
Two number cubes can simultaneously show the same number, which would be an even number (since the pairs would be (2,2), (4,4), or (6,6)) and not lead to an odd sum. Therefore, if we roll the dice and get two numbers that are the same, we cannot get an odd sum. This means that these two events cannot happen at the same time, so the correct answer is:
A. Yes because if one event occurs, the other can't occur.
Solve for the surface area.
Answer:
382.5
Step-by-step explanation:
9x10=90
9x9=81
13.5x9=121.5
9x10=90
180+81+121.5= 382.5
There are two triangles.
Area of a triangle = 1/2 x 10 x 9 = 45 square in.
45 x 2 = 90 square inches
One side is 9 x 9 = 81 square inches.
One side ix 10 x 9 = 90 square inches.
One side = 9 x 13.5 = 121.5 square inches.
Total surface area = 90 + 81 + 90 + 121.5 = 382.5 square inches.
Find a value of 3a+4b when a=17 and b=9. Then use the formula v=u+at when the initial velocity is 3 m/s, the acceleration is 1.5m/s squared and the time is 7 seconds.
Final answer:
The value of 3a+4b is 87 when a=17 and b=9. Using the kinematics equation v=u+at, the final velocity is calculated as 13.5 m/s given the initial conditions provided.
Explanation:
To find the value of 3a+4b when a=17 and b=9, we substitute the given values into the expression:
3(17) + 4(9) = 51 + 36 = 87.
Thus, the value of 3a+4b is 87.
The next part of the question involves using the kinematics equation v = u + at to find the final velocity v. We are given an initial velocity u = 3 m/s, an acceleration a = 1.5 m/s2, and a time t = 7 seconds. Plugging the values into the formula gives us:
v = 3 m/s + (1.5 m/s2)(7 s) = 3 m/s + 10.5 m/s = 13.5 m/s.
The final velocity after 7 seconds is therefore 13.5 m/s.
Amy’s current grades for her assignments in math class are 85 , 90 , 95 and 80. What grade does she have to earn on her next assignment to attain an average of 90?
Answer:
100
Step-by-step explanation:
100+90+85+95+80= 450,
450/5=90
She has to earn on her next assignment to attain an average of 90 for grade 100.
What is the average value?The average is the middle value of the given data set and is calculated by adding up all the numbers and dividing the result by the total quantity of figures added.
Amy’s current grades for her assignments in math class are 85, 90, 95, and 80.
Let x be the grade she has to earn on her next assignment to attain an average of 90.
The grade does she have to earn on her next assignment to attain an average of 90 is;
[tex]\rm Average =\dfrac{Sum \ of \ all \ grades}{Number \ of \ grades}\\\\ 90 =\dfrac{x+90+85+95+80}{5}\\\\ 90 \times 5 = x+350\\\\450=x+350\\\\x =450-350\\\\x=100[/tex]
Hence, she has to earn on her next assignment to attain an average of 90 for grade 100.
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The graph has lines that are what
I believe you are looking for, intersecting.
Does anyone know the answer to this?
Answer: The height of the monitor is 12 inches.
Step-by-step explanation:
First, you need to acknowledge the Pythagorean Theorum,
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
You already have the c and the b , so you just have to plug them in to find a!
This is what it looks like when you substitute:
a² + 16² = 20²
Then, simplify.
a² + 256 = 400
Now, to isolate the variable, you have to move 256 to the other side. This, of course, means it changes from a positive to a negative number.
a² = 400 - 256
a² = 144
Now, you have to remove the square root from a. But, don’t forget, what you do to one side, you have to do to the other side. So, your equation will now look like this:
√a² = √144
The square root of a squared is obviously just a! And the square root of 144 is 12. Therefore, we now know that:
a = 12
So, the height of the monitor was 12 inches.
2x^2- 5x + 6 when x = -2
Answer:
Step-by-step explanation:
x= -2
2x² - 5x + 6 = 2(-2)² - 5*(-2) + 6
= 2*4 + 10 + 6
= 8 + 10 + 6
= 24
Kayla has 36 yellow stickers, 27 red stickers, and 18 blue stickers. She wants to distribute the stickers into bags so that each bag contains only one color of stickers and every bag has the same number of stickers. How many stickers can Kayla put in each bag?
Answer:
Kayla can put 9 stickers in each bag.
she can distribute it into bags of 9 stickers each of the same colour.
Step-by-step explanation:
Given;
yellow stickers = 36
red stickers = 27
blue stickers = 18
For her to distribute the stickers into bags so that each bag contains only one color of stickers and every bag has the same number of stickers without remainder.
We need to find the highest common factor of the number of the three colours.
36 = 4×9
27 = 3×9
18 = 2×9
We can see that they are all divisible by 9
Therefore, she can distribute it into bags of 9 stickers each
Final answer:
The greatest common divisor of 36, 27, and 18 is 9, so Kayla can put 9 stickers of the same color in each bag.
Explanation:
Kayla wants to distribute her stickers into bags, with each bag containing the same number of stickers of only one color. To find out how many stickers she can put in each bag, we need to find the greatest common divisor (GCD) of the numbers of stickers she has for each color. Kayla has 36 yellow stickers, 27 red stickers, and 18 blue stickers. The GCD of 36, 27, and 18 is 9. Therefore, Kayla can put 9 stickers in each bag.
Step-by-Step Solution
Identify the quantity of each color of stickers: yellow (36), red (27), blue (18).
Calculate the GCD of the three quantities: GCD(36, 27, 18) = 9.
Distribute the stickers into bags with 9 stickers of the same color per bag.
Help ASAP PLZ
Find the equation for this graph
y = 5 * (1/2)^x
Step-by-step explanation:
This is an exponential function
y =ab^x
where a is the initial value ( where x = 0)
a = 5
y = 5 * b^x
Pick a point to determine b
(1,2.5)
2.5 = 5 * b^1
2.5 = 5 *b
Divide each side by 5
2.5/5 = b
b = 1/2
y = 5 * (1/2)^x
What is 18 divided by 10?
Answer: 1.8
Step-by-step explanation:
The division, 18 divided by 10 gives 1.8.
What is 18 divided by 10?Division is one of the basic arithmetic operations in mathematics. It is the opposite of multiplication.
18 divided by 10 means that we are dividing a group of 18 objects into 10 equal groups. That is:
18/10 = 1.8
Note: Since we are dividing by 10, we can move the position of the decimal point to the left by one step.
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What’s the surface area of 20 cm 10 cm and 3 cm
Answer:
200
Step-by-step explanation:
A=b×L
A=20×10
A=200
If (x, y) is a solution to the system of equations, what is the value of y?
x +
1
/8
y = 20
x +
1
/4
y = 4
Answer:
4
Step-by-step explanation:
Which equation can be used to find the volume of the cylinder? A cylinder with a radius of 4 inches and height of 16 inches.
Answer:
V=Bh so Volume = π4.0 2 16.0 = 804.25
Step-by-step explanation:
which geometric figure contains exactly two perpendicular lines
Answer:
Like a square, a rectangle has lines that are perpendicular to two other lines. This means it also has four right angles.
Step-by-step explanation:
Answer:
a right triangle
Step-by-step explanation:
Alfonso scored 18 points during his last basketball game, which was 40% of the points the entire team scored.
Answer:
45
Step-by-step explanation:
What is the volume of this cone?
Answer:
133.97 cubic yard
Step-by-step explanation:
For Cone
radius (r) = 4yd
height (h) = 8yd
Volume of the Cone
= π r^2 * h/3
= 3.14 * 4*4 *8/3 yd
= 133.97 cubic yard
What is the perimeter of ABC with vertices A(-2,9), B(7,-3), and C(-2,-3) and in the coordinate plain?
A. 21 units
B. 15 units
C. 34 units
D. 36 units
Answer:
Step-by-step explanation:
A - C = ( -2, 9) - (- 2 -3)
= ( 0, 12)
AC = 12
B - C = (7 - 3) - ( - 2 -3)
= (9, 0)
BC = 9
ABC is a right -angled triangle with AC as the hypotenuse
AC = sqrt( 9^2 + 12^2)
= sqrt(81 + 144)
= srqt(225)
= 15
Perimeter = 12 + 9 + 15
= 36 units
So the answer is 36 units
Answer:
36unitsStep-by-step explanation: A - C = ( -2, 9) - (- 2 -3)
= ( 0, 12)
AC = 12
B - C = (7 - 3) - ( - 2 -3)
= (9, 0)
BC = 9
ABC is a right -angled triangle with AC as the hypotenuse
AC = sqrt( 9^2 + 12^2)
= sqrt(81 + 144)
= srqt(225)
= 15
Perimeter = 12 + 9 + 15
= 36 units
So the answer is 36 units
Which best describes the error in finding the surface area of the prism?
X
S = 2(5)(3) + 2(3)(4) + 2(5)(3)
= 30 + 24 + 30
= 84 in.2
** 2010
To find the surface area of a prism (or any other geometric solid) we open the solid like a carton box and flatten it out to find all included geometric forms. To find the volume of a prism (it doesn't matter if it is rectangular or triangular) we multiply the area of the base, called the base area B, by the height h.
This info should help you.
Answer:
94
Step-by-step explanation:
the area of the 3 x 5 face is used 4 times rather than twice
A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for π, and round your answer to the nearest hundredth.
Answer:
38.47 square units
Step-by-step explanation:
All we have to do is first find the perimeter of the square (which is equal to the circumference of the circle), then find the radius of the circle and finally the area of the circle.
The square has a side that measures 5.5 units.
The perimeter of a square is given as:
P = 4L
where L = length of side of the square
Therefore, the perimeter of the square is:
P = 4 * 5.5 = 22 units.
This means that the circumference of the circle is 22 units.
The circumference of a circle is given as:
C = 2πR
and the area of a circle is given as:
[tex]A = \pi R^2[/tex]
where R = radius
Therefore:
22 = 2πR
=> R = 22 / (2 * 3.14)
R = 22 / (6.28)
R = 3.50 units
The area is therefore:
[tex]A = \pi * 3.50^2[/tex]
A = 38.47 square units
The area of the circle is 38.47 square units.
The area of the circle is approximately 15.64 square units, calculated using the perimeter of the square and circle formulas.
To find the area of the circle with a circumference equal to the perimeter of the square, we'll first calculate the perimeter of the square using its side length. Then, we'll use the circumference formula to find the radius of the circle. Finally, we'll use the area formula for a circle to find the area.
Step 1:
Calculate the perimeter of the square.
Perimeter of square = 4 * side length = [tex]\(4 \times 5.5 = 22\)[/tex] units.
Step 2:
Set up the equation for the circumference of the circle.
Circumference of circle =[tex]\(2\pi \times\)[/tex] radius = Perimeter of square.
Step 3:
Solve for the radius.
[tex]\[2\pi \times \text{radius} = 22\][/tex]
[tex]\[\text{radius} = \frac{22}{2\pi}\][/tex]
Step 4:
Use the radius to find the area of the circle.
Area of circle = [tex]\(\pi \times \text{radius}^2\)[/tex]
Step 5:
Substitute the value of the radius and calculate.
[tex]\[Area = 3.14 \times \left(\frac{22}{2\pi}\right)^2\][/tex]
[tex]\[Area \approx 15.64\][/tex]
The area of the circle with a circumference equal to the perimeter of the square is approximately [tex]\(15.64\)[/tex] square units.
Solve for x
x2 + 14x + 49 = 0
Answer: X=7
Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term. Solver for X by using this term to complete the square.
X=7
Parallelogram L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. The length of L M is 22 centimeters and the length of M N is 18 centimeters.
What is the perimeter of parallelogram LMNO?
18 cm
22 cm
40 cm
80 cm
Answer:
D. 80
Step-by-step explanation:
edge 2021
The perimeter of the parallelogram LMNO is 80 cm
What is a parallelogram?A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Given that, in a parallelogram LMNO, the length of L M is 22 cm and the length of M N is 18 cm.
Perimeter of a parallelogram = 2(sum of two adjacent sides)
= 2(18+22)
= 2×40
= 80
Hence, the perimeter of the parallelogram LMNO is 80 cm
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2 cm on a map are equal to 3 km in real life. If two points
are 8 cm apart on the map, how far apart are they In real
life?
Answer: 12km
Step-by-step explanation:
2cm=3km
2x4=8
3x4=12
Final answer:
The real-life distance between two points that are 8 cm apart on a map, with a map scale of 2 cm = 3 km, is 12 km. This is calculated using a proportion based on the given scale ratio.
Explanation:
The question asks how to calculate the real-life distance between two points that are 8 cm apart on a map, given that 2 cm on the map are equal to 3 km in real life. To solve this, we can use a proportion where 2 cm on the map corresponds to 3 km of actual distance. The scale ratio is therefore 2 cm : 3 km. If the points are 8 cm apart on the map, we set up the proportion as follows:
2 cm on the map / 3 km in real life = 8 cm on the map / x km in real lifeWe cross multiply to find x:
2 cm * x km = 8 cm * 3 kmx = (8 cm * 3 km) / 2 cmx = 24 km / 2x = 12 kmSo, the real-life distance between the two points is 12 km.
find the measure of an angle between 0 and 360 coterminal with 510
Answer:
150 degrees
Step-by-step explanation:
HOPE THIS HELPED!
The measure of an angle between 0° and 360° coterminal with 510° is 150°. The difference between coterminal angles yields 360°.
Which angles are said to be coterminal?The angles that share a common terminal side are said to be coterminal angles. So, the difference between those angles is 360°.
Calculating the measure of the required angle:The given coterminal angle is 510°.
So, the reference angle = 510° - 360° = 150°
Thus, the angle is required as a measure of 150°.
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