Answer:
From the given expression of parabola, it is clear that the parabola is upward opening.
Step-by-step explanation:
Concept: In the equations of parabolas, when the expression having x variable has the power of 2, then the parabola opens in the y-axis. The equation of parabola is of the form X² = 4aY.
In this case, if a > 0, then the parabola opens in the upward direction.
Given equation is (x - 5)² = 4×3(y + 2). Here the expression of x has the power 2 and a = 3 > 0. So, the parabola is upward opening.
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Final answer:
The given parabolic equation has a positive coefficient for the (y + 2) term, indicating that it opens upward.
Explanation:
The equation given is in the form of a transformed parabolic equation, which can be identified as [tex](x - h)^2 = 4p(y - k),[/tex]where the vertex of the parabola (h,k) and the value of p determine the direction in which the parabola opens.
In the equation [tex](x - 5)^2 = 12(y + 2),[/tex] the presence of the squared term on x and the fact that the coefficient of the (y + 2) term is positive indicates that the parabola opens upward.
In this case, if a > 0, then the parabola opens in the upward direction.
The coefficient of the squared term is 4p, which in this case is positive, confirming the direction of the parabola as opening upwards.
if trapezoid jklm is translated according to the rule (x,y) ,(x+8,y-3) what are the coordinates of point L
With the given translation rule, to find new coordinates of a point L in trapezoid JKLM, apply it to the original coordinates by moving right by 8 units and down by 3 units. If original coordinates of L were (2,5), new coordinates will be (10,2).
Explanation:In geometry, a translation is a type of transformation that slides a figure along a straight line. In this case, the translation rule given is (x, y) -> (x+8, y-3). This means that every point in the trapezoid is being moved 8 units to the right (increase in x-coordinate) and 3 units down (decrease in y-coordinate).
Per your question, to find the new coordinates of point L after the translation, you simply need to apply this rule to the original coordinates of point L. If for example, the original coordinates of point L were (2, 5), its new coordinates after the translation would be calculated as follows: (2+8, 5-3) = (10, 2).
This is how you find the new coordinates of a point after a translation in geometry.
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Please Help! Math Question!
Variable g is 8 more than variable w. Variable g is also 4 less than w. Which pair of equations best models the relationship between g and w?
A) g = w − 8
g = w + 4
B) w = 8g
w = g − 4
C) g = w + 8
g = w − 4
D) w = 8g
w = g + 4
Answer:
The answer is C.
g = w + 8
g = w − 4
Hope This Helps!
A video game sets the points needed to reach the next level based on the function g(x) = 12(2)x − 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 3x. How many points will a player need on the hardest setting of level 6?
A 18 points
B 384 points
C 4020 points
D 6912 points
If csc 0=8÷7 which equation represents cot 0
Answer: [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]
Step-by-step explanation:
Since, given [tex]cosec\theta=\frac{8 }{7}[/tex]
And we know that [tex]Cot\theta=\sqrt{cosec^2\theta-1}[/tex]
Therefore, [tex]Cot\theta=\sqrt{cosec^2\theta-1} = \sqrt{(8/7)^2-1}= \sqrt{64/49-1}[/tex]
⇒[tex]Cot\theta=\sqrt{64-49/49}=\sqrt{15/49}=\sqrt{15}/7[/tex]
Thus, [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]
Answer:
CotA=√15/7
Step-by-step explanation:
cosecA=8/7=hypotenuse/perpendicular
We have to find cotA
We do this by right angled triangle
We use pythagoras theorem to find the base
Base²+Perpendicular²=hypotenuse²
Base²+7²=8²
Base²=15
Base=√15
cotA=Base/Perpendicular
= √15/7
A diagonal of a cube measures 30 inches. The diagonal of a face measures 600 SQUARE ROOTED inches. In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth. HOW MANY? inches
Answer:
The correct answer is 17.3
Step-by-step explanation:
Let me know if it helped you
What is the are of the triangle below??
it is 9 squares high and the base is 6 squares wide
9*6 = 54
54/2 = 27
area = 27 square units
How to find csc theta where theta equals -120
Answer:
[tex]\frac{-2}{\sqrt{3} }[/tex]
Step-by-step explanation:
Cosec of -120 is to be found out
We can do this in steps
cosec (-120) consider only the - sign.
This implies angle lies in IV quadrant and hence cosec is negative
cosec (-120) =-cosec (120)
Now 120 is written as 180-60
cosec (-120) =- cosec(180-60)
=-cosec 60
(since II quadrant cosec is positive)
= [tex]\frac{-2}{\sqrt{3} }[/tex]
A student solved a system of equations by elimination. The answer is not correct. Describe the error made in the part of the solution shown.
The error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .
What is elimination method?The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.
According to the question
5x + 4y= 2 ------------------- (1)
3x + 3y = -3 ------------------- (2)
Now,
solving both equation by elimination method
Multiplying equation (1) by 3 and by 2 to equation (-4)
So, y can be eliminated
3(5x + 4y)=2 * 3
15x + 12y = 6 -------------- (3)
-4(3x + 3y) = -3*-4
-12x - 12y = 12 -----------------(4)
Now,
Adding both eq(3) and (4)
3x = 18
x = 6
Putting value of x in eq(1)
5*6 + 4y = 2
30 + 4y = 2
4y = 2 - 30
4y = - 28
y = -6
Hence, the error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .
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(03.01)
A newly made car will have a model number, a parts number, and a serial number. A model number is assigned by the manufacturer to identify each type of car. A parts number identifies one part of the smaller parts that make up the car. A serial number is unique to each car produced and identifies it.
Which relation is a function?
(parts number, serial number)
(model number, parts number)
(serial number, model number)
(serial number, part number)
Answer:
Hi!
The corrects answers are:
•(serial number, model number)
Step-by-step explanation:
First, you have to understand the meaning of a function, that is an a relation but have the condition:
The input must be relationed with only one output.
The question says:
"A serial number is unique to each car produced and identifies it." so this will be you input, and will be related with only one model number.
Find the coordinates of point l that lies along the directed line segment from N(14,4) to M(2,8) and partitions the segment in the ratio of 1:3
There are 40 vehicles in a parking lot.Twenty percent of the vehicles are pickup trucks.How many pickup trucks are in the parking lot?
Davis electronics manufactures a certain type of radio that requires 15 working resistors per radio. If one out of 25 resistors is defective, are 30,150 resistors enough to assemble 1922 radios?
No, 30,150 resistors are not enough to assemble 1922 radios.
To determine if 30,150 resistors are enough to assemble 1922 radios, we need to calculate the total number of resistors required and then account for the defective resistors.
First, let's calculate the total number of resistors needed for 1922 radios. Since each radio requires 15 resistors, the total number of resistors required is:
[tex]\[ 1922 \text{ radios} \times 15 \text{ resistors/radio} = 28830 \text{ resistors} \][/tex]
Next, we need to account for the defective resistors. Given that one out of every 25 resistors is defective, we can calculate the number of defective resistors in a batch of 28830 resistors. However, to simplify the calculation, we can calculate the number of non-defective resistors we expect to get from every 25 resistors. Since 24 out of 25 are expected to be non-defective, we have:
[tex]\[ \frac{24}{25} \[/tex] { non-defective resistors per 25 resistors}
To find out how many non-defective resistors we would get from 28830 resistors, we multiply the total number of resistors by the ratio of non-defective to total resistors:
[tex]\[ 28830 \times \frac{24}{25} = 28224 \[/tex] { non-defective resistors}
Now, we compare the number of non-defective resistors needed (28830) to the number of non-defective resistors we can expect to have (28224). We find that:
[tex]\[ 28830 - 28224 = 606 \text{ resistors} \][/tex]
This means we are short by 606 non-defective resistors to assemble all 1922 radios. Therefore, 30,150 resistors are not enough.
To confirm this, let's calculate the total number of resistors needed including the defective ones. Since we know that for every 28830 non-defective resistors we need 1/25 more to account for the defective ones, we have:
[tex]\[ 28830 \times \frac{25}{24} = 30156.25 \text{ resistors} \][/tex]
This shows that we actually need more than 30,150 resistors to account for the defective ones and meet the requirement for 1922 radios. Hence, the answer is no, 30,150 resistors are not enough."
James, caleb and abigail bought a pizza. james ate 1/6 of the pizza, caleb ate 1/4 of the pizza what fracion did james and caleb eat together
Find the area of the shaded region.
Given the following geometric sequence, find the common ratio: {225, 45, 9, ...}.
5
-5
1/5
-1/5
Answer:
1/5
Step-by-step explanation:
The difference of twice a number g and 10 is 24
why is a stem and leaf plot called a stem and leaf plot?
A stem-and-leaf plot gets its name from the way the data is structured. The 'stem' represents the highest place value digits of the numbers in the dataset, and the 'leaf' represents the lower place value digits. These plots keep the actual numerical data intact, providing more detail than other data representations like bar graphs or histograms.
Explanation:The term stem-and-leaf plot, also known as a stemplot, originates from the way data is structured in this type of graphical representation. The 'stem' in a stem-and-leaf plot stands for the highest place value digits of the numbers in the dataset, similar to the stem of a plant that holds up the leaves. The 'leaf' stands for the lower place value digits, similar to the leaves that extend from the stem. For example, in a dataset [23, 24, 33, 35], 2 and 3 would be stems, and the various units (3, 4 for 2 and 3, 5 for 3) would be leaves.
One of the main purposes of a stem-and-leaf plot is that it keeps the actual numerical data intact, as opposed to other graphical representations like bar graphs or histograms which group data into classes, thus providing a more detailed view of the data distribution.
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The value of a treadmill bought new for $1000 decreases 5% each year. Use a graph to predict the value of the treadmill in 5 years.
A) ≈ $773.78
B) ≈ $857.38
C) ≈ $902.50
D) ≈ $814.50
The predicted value of the treadmill after 5 years, with an annual depreciation rate of 5%, is approximately $773.78. This calculation uses the exponential decay formula and corresponds to option A).
To predict the value of a treadmill in 5 years that was bought new for $1000 and decreases 5% each year, we can use the formula for exponential decay:
V = [tex]P(1 - r)^t[/tex]
Where:
V is the future value of the treadmill,
P is the original value ($1000),
r is the rate of decay (5% or 0.05), and
t is the time in years (5 years).
By substituting the values we have:
V = $1000(1 - 0.05)⁵
V = $1000(0.95)⁵
V = $1000(0.77378) = $773.78
Therefore, the predicted value of the treadmill after 5 years is approximately $773.78, which corresponds to option A).
Which sequence of transformations will result in an image that maps onto itself?
The correct transformation to get result in an image that maps onto itself will be;
''Reflect over the y axis and then reflect again over the y axis''.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The statement is,
'' A sequence of transformations will result in an image that maps onto itself''.
Now,
Since, We know that after two reflections over the same axis we get the original image.
Thus, we get;
The correct transformation to get result in an image that maps onto itself will be;
''Reflect over the y axis and then reflect again over the y axis''.
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Which inequality describes the graph?
Suppose you add two linear equations that form a system, and you get the result y = −2. how many solutions does the system have?
Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers. Determine which equation represents how much Kayla will spend on sandals after the discount.
The equation represents how much Kayla will spend on sandals after the discount is $13.50 = 0.75x.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers.
The equation can be written as:-
$13.50 = 0.75x.
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Spencer Ward purchased a new riding mower for $1,989. He made a 15% down payment and financed the remainder. What amount did he finance?
Determine the domain of the function. f(x) is equal to four divided by x squared.
A. x ≥ 0
B. All real numbers except 0
C. All real numbers except 3
D. All real numbers
How to divide fractions
Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction. Let's try an example.
[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] can be rewritten as [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex].
Now, we are simply multiplying fractions.
Multiply across the numerators and the denominators
[tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex] = [tex]\frac{9}{10}[/tex]
Therefore, [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] = [tex]\frac{9}{10}[/tex]
What is the solution to the inequality l2n+5l > 1
8 times the total of x and 3
Answer: The expression would be [tex]8x+24[/tex]
Step-by-step explanation:
Since we have given that
8 times the total of x and 3
total of x and 3 means sum of x and 3.
Mathematically it is expressed as
[tex]x+3[/tex]
Now, 8 times the above sum.
Mathematically, it is written as
[tex]8(x+3)\\\\=8x+24[/tex]
Hence, the expression would be [tex]8x+24[/tex]
Identify the x-intercept and y-intercept of the line
4x−2y=−12
4x−2y=−12
.
Select one:
a. The x-intercept is (0,-3) and the y-intercept is (6,0).
b. The x-intercept is (-3,0) and the y-intercept is (0,6).
c. The x-intercept is (4,0) and the y-intercept is (0,-2).
d. The x-intercept is (0,6) and the y-intercept is (-3,0).
The x-intercept is (-3,0) and the y-intercept is (0,6).
The correct option is B,
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Given information:
4x - 2y = -12.
To find the x-intercept, we set y to zero and solve for x:
4x - 2y = -12
4x - 2(0) = -12
4x = -12
x = -3
So the x-intercept is (-3, 0).
To find the y-intercept, we set x to zero and solve for y:
4x - 2y = -12
4(0) - 2y = -12
-2y = -12
y = 6
So the y-intercept is (0, 6).
Therefore, the answer is b. The x-intercept is (-3,0) and the y-intercept is (0,6).
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A rectangular table with sides in the ratio 3:5 has a perimeter equal to 240 inches. what is the area of the table in square inches?
The three sides of sail A are each half the length of the three sides of sail B. How do the areas of the two sails compare?
Answer:
Step-by-step explanation:
It is B