The equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y. (Correct choice: D)
How to determine the best equation of the parabola based on given characteristics
In accordance with the statement, we find that the parabola has its vertex at the origin, therefore it is horizontal and its vertex constant (C) is negative as its focus is in the negative part of the x-axis. Therefore, the equation of the parabola in standard form has the following form:
x² = C · y, for C < 0. (1)
In consequence, the equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y.
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Does this graph show a function? Explain how you know.
• A. Yes; the graph passes the vertical line test.
• B. No; there are y values that have more than one x-value.
• C. No; the graph fails the vertical line test.
• D. Yes; there are no y-values that have more than one x-value.
The graph doesn't show a function as C. No; the graph fails the vertical line test.
What is a graph?It should be noted that a graph is the diagrammatic representation of data.
In this case, the graph doesn't show a function as the graph fails the vertical line test.
The vertical line test is a visual way that's uses to determine if the curve is a graph of the function.
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I need your help :))
Question is:
Make a pattern and explain the rule the pattern follows. Use a minimum of 3 terms within your pattern.
The pattern {1, 3, 5, ...} is an arithmetic sequence with the following rule:
[tex]a_n = 1 + 2(n - 1)[/tex].
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
The pattern {1, 3, 5, ...} has first term and common difference given, respectively, by:
[tex]a_1 = 1, d = 2[/tex]
Hence the rule for the pattern is given by:
[tex]a_n = 1 + 2(n - 1)[/tex].
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Kevin earned $80. Out of his earnings, he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi. Find the remaining amount.
The amount remaining out the money earned is $37.5
Sum of values and proportionGiven the following parameters
Amount earned by kevin = $80
If he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi, the total money spent is given as;
Total money spent = 51/2 + 68/5 + 22/5
Total money spent = 51/2 + 90/5
Total money spent = 25.5 + 18
Total money spent = 43.5
Amount remaining = 80. - 43.5
Amount remaining = 37.5
Hence the amount remaining out the money earned is $37.5
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An exponential growth function represents a quantity that has a constant doubling time true or false
False, An exponential growth function represents a quantity that has a constant doubling time.
It might always be having time, Or 13 times, where I would not double but be unable to receive 2/3. Because the quantity is bigger than one, exponential growth would have a constant time between doublings. The halving time for any exponential decay function is A = Ao * kt1/2 x = x * kt1/2 = ktln(1/2) = t * ln kt = ln(1/2) / ln k.Because the quantity is bigger than one, exponential growth would have a constant time between doublings.What does an exponential growth function represent?
The base b is a constant when describing an exponential function. When the domain is the collection of real numbers, the exponent x is the independent variable. Exponential growth and decay are the two different kinds of exponential functions. When b > 1, the function f (x) = bx represents exponential development.Learn more about exponential growth function brainly.com/question/11811611
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Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground? don’t play if you’re not to continue.
Answer:
28
Step-by-step explanation:
GEOMETRY HELP ME PLS PLS!!!! THE FOLLOWING ROMBUS!!
Answer:
12
Step-by-step explanation:
Diagonals of a rhombus bisect each other at right angles, so in triangle JNK, we have JK=20 and JN=16.
Using the Pythagorean theorem, it follows that KN = 12.
porfaaaaaaa ayudaaaaaaa
Determine el dominio y el rango de la siguiente función.
f(x)=-25-x+50
The domain and the range of f(x) = -25x + 50 are the set of all real numbers
How to determine the domain and the range?The function is given as:
f(x) = -25x + 50
The above function is a linear function.
All linear functions have their domain and range to be the set of all real numbers
Hence, the domain and the range of f(x) = -25x + 50 are the set of all real numbers
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(01.04 LC)Multiply negative 1 over 6 multiplied by negative 1 over 5. negative 1 over 11 negative 1 over 30 1 over 30 1 over 11
The expression is -1/6 x (-1/5) = 1/30.
What is expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given:
negative 1 over 6 multiplied by negative 1 over 5.
As per the data,
if -1/6 is multiplied with -1/5 then the resultant value will be
=-1/6 * -1/5
= 1/5*6
=1/30
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Mathew rolls a number cube labeled with the numbers 1−6. he then flips a fair coin. what is the probability that he rolls a 4 and flips a head? write your answer as a fraction.
The probability that he rolls a 4 and flips a head is 1/12
What is the probability?Probability determines odds that a random event would happen. The odds of the random event happening lie between 0 and 1.
The probability that he rolls a 4 and flips a head = (number of sides that is a 4 / total number of sides) x (number of sides that is a head / total number of sides)
(1/6) x (1/2) = 1/12
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Answer: 1/12
Step-by-step explanation:
just say the answer
pls help me answer this
Diagram 3 shows a composite solid, formed by joining a half m-cylinder with a right prism. ABKJ is the cross - section of the right prism. MK is the diameter of the half - cylinder Given BK 28 cm, AJ = 14 and AE = 20 cm, The volume of the composite solid is 17000 cm³
Using
[tex]\pi = \frac{22}{7} [/tex]
calculate the value of h
Answer: 30 cm
Step-by-step explanation:
The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.
From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus [tex]\frac{1}{2}[/tex] the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of [tex]\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3[/tex].
Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.
The ABKJ is a trapezoid so it's area is [tex]\frac{1}{2}(AJ + BK) \cdot AB[/tex]. Thus the volume of the right prism is [tex]\frac{1}{2}(AJ + BK) \cdot AB \cdot AE[/tex]. This gives us [tex]\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600[/tex], and thus h = 30 cm.
write the equation for the graph given below
Answer: Option (1)
Step-by-step explanation:
The slope of the line is
[tex]\frac{9-6}{4-(-4)}=\frac{3}{8}[/tex]
This eliminates all the options except for (1).
A sock drawer contains 5 different colors of socks. it has 20 white, 10 black, 6 red, and 4 purple. if you reach into the drawer and choose a sock randomly, what is the probability you will get a a black sock? (write your final answer as a fraction.)
The probability of selecting a black sock is 1/4.
What is the required probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. It is more likely that an event will occur if its probability is higher.
Number of white socks=20
Number of black socks=10
Number of red socks=6
Number of purple socks=4
Total number of socks=20+10+6+4
=40
Probability of getting a black sock=Number of black socks/Total number of socks
=10/40
=1/4
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given cos data = 0.7620, approximate the acute angle to the following
a. the nearest 0.01
The acute angle is 40.40 degrees
How to determine the acute angle?The cosine of the angle is given as:
cos(x) = 0.7620
Take the arc cos of both sides
[tex]x = \cos^{-1}(0.7620)[/tex]
Evaluate the arc cos
x = 40.359
Approximate
x = 40.40
Hence, the acute angle is 40.40 degrees
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find the value of 7 + 15 + 23 +...+ 767 + 775 + 783
Answer:
38,710.
Step-by-step explanation:
This is an arithmetic series with common difference 8 , first term a = 7 and last term L = 783.
The number of terms n = (783 - 7) / 8 + 1 = 98
Sum of 98 terms = (n/2)[a + L)
= (98/2)(7 + 783)
= 49 * 790
= 38,710.
4. Use the triangle congruence postulates to prove congruence.
Part I: Fill in the blanks to name each triangle congruence postulate.
a. SSS:
b. SAS:
c. ASA:
AAS:
In the triangle
The triangle congruence postulate is illustrated below
How to illustrate the triangle?It should be noted that two triangles are congruent if they have the same shape and size.
AAS: The angle-angle-side theorem illustrates that two triangles are congruent if the two angles and a side note between the two angles are identical to that of another triangle.
SSS: This illustrates that the three sides of a triangle are congruent to the corresponding three sides of the other triangle.
ASA: This illustrates that the triangles are congruent when the two angles and the side are the same as the corresponding angles and sides of the other triangle.
SAS: When two sides and the included angle of a triangle are congruent to the corresponding sides and the included angle if a second triangle then it follows the side-angle-side theorem.
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Identify the 8th term of the given geometric sequence. 1/2, 2, 8, 32,...
A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).
We have:
[tex]a_1=\dfrac{1}{2}\\\\a_2=2\\\\a_3=8\\\\a_4=32\\\vdots[/tex]
Find the common ratio:
[tex]\boxed{r=\dfrac{a_n}{a_{n-1}}}\Rightarrow r=\dfrac{2}{\frac{1}{2}}=\dfrac{8}{2}=\dfrac{32}{8}=...\\\\\boxed{r=4}[/tex]
The formula of the n-th term of a geometric sequence:[tex]\boxed{a_n=a_1\cdot r^{n-1}}[/tex]
Substitute:
[tex]a_1=\dfrac{1}{2},\ r=4,\ n=8\\\\a_8=\dfrac{1}{2}\cdot4^{8-1}=\dfrac{1}{2}\cdot4^7=\dfrac{1}{2}\cdot16384\\\\\huge\boxed{a_8=8192}[/tex]
Method step by step:[tex]a_4=32,\ r=4\\\\a_5=a_4\cdot r\Rightarrow a_5=32\cdot4=128\\\\a_6=a_5\cdot r\Rightarrow a_6=128\cdot4=512\\\\a_7=a_6\cdot r\Rightarrow a_7=512\cdot4=2048\\\\a_8=a_7\cdot r\Rightarrow a_8=2048\cdot4=8192[/tex]
Rectangle ABCD is congruent to rectangle URST.
Rectangles A B C D and U R S T are congruent. The length of sides A B is 9 millimeters and the length of sides R S is 15 millimeters.
What is the area of rectangle URST?
24 mm
48 mm
135 mm2
The area of the rectangle URST is 135 mm². so the option C is correct.
What are Congruent rectangles?Congruent rectangles have the same lengths of sides, same measures of angles and same areas and same perimeters
The Rectangle ABCD is congruent to rectangle URST
Given; Rectangle ABCD ≅ rectangle URST
AB = UR , BC = RS , CD = ST , AD = UT
AB = 9 millimeters
UR = 9 millimeters
We know that, The area of any rectangle = l × w,
In rectangle URST
∵ UR = 9 millimeters
∵ RS = 15 millimeters
- Assume that UR = l and RS = w
The area of rectangle URST = UR × RS
The area of rectangle URST = 9 × 15 = 135 millimeters²
Hence, The area of rectangle URST is 135 mm²
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Which of the following systems of linear inequalities is represented by the
solution graphed below?
The inequalities represented by the graph are; y > -1 and y <= -x.
What are the inequalities described by the graph?The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.
However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.
Ultimately, the graph represents the inequalities y > -1 and y <= -x.
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Answer:The inequalities represented by the graph are; y > -1 and y <= -x.
What are the inequalities described by the graph?
The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.
However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.
Ultimately, the graph represents the inequalities y > -1 and y <= -x.
Step-by-step explanation:
In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement RQ⎯⎯⎯⎯⎯⎯⎯⎯≅ R Q ¯ ≅ ___
Based on the CPCTC theorem, the complete statement is: RQ ≅ RT.
What is the CPCTC Theorem?According to the CPCTC theorem, if two triangles are said to be congruent, then all the corresponding parts of both triangles are congruent.
Given that ΔPQR ≅ ΔSTR, RQ corresponds to RT. Therefore, both sides are congruent to each other.
Thus, the complete statement is: RQ ≅ RT.
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If a and b are integers such that -6
a x b?
(A)-36
(B)-30
(C)-24
(D)-12
What is the slope of the line represented by the equation y=x/6 −5 ?
−5
1/6
5/6
6
Answer:
slope is the gradient(coefficient of (x) in the equation .We have [tex] \frac{x}{6} [/tex]which can also be written as [tex] \frac{1}{6} x \: therefore \: the \: slope \: is \: \frac{1}{6} [/tex]Answer:
1/6
Step-by-step explanation:
Solution:
The given equation is:y=x/6 -5
arranging the equation :x/6-y=5
Given,
Coefficient of x=1/6
coefficient of y=-1
So,
Slope(m)=-(Coefficient of x/coefficient of y))
= -(1/6 / -1) {minus divided by - becomes plus }
1 by 6 whole divide by 1
= 1/6 ans✓
55. TECHNOLOGY
If f is a linear function, f(0.1) = 11.5, and f(0.4) = -5.9, find an equation for the function.
Considering the expression of a line, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.
Linear equation o lineA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Equation for the function in this caseIn this case, the function f(x) is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9. This is:
(x1, y1)= (0.1, 11.5) (x2, y2)= (0.4, -5.9)So, the slope m can be calculated as:
[tex]m=\frac{-5.9-11.5}{0.4-0.1}[/tex]
Solving:
m= -58
Considering point 1 and the slope m, you obtain:
11.5= -58×0.1 +b
11.5= -5.8 + b
11.5 + 5.8= b
17.3= b
Finally, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.
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suppose g(x)=f(x+2)-3 wich statement best compares the graph of g(x) with the graph of f(x)
Answer:
xyucyxxhc9gohjpbkvicucucuc7vucuc7cucuc7cuvuv8v8
Step-by-step explanation:
q+++
Suppose A and B are 2x2 matrices and that AB = BA =
which of the following statements is correct?
Based on the matrices given, the true statement on matrices AB = BA is A. A⁻¹ = ¹/₃B.
What is true on AB = BA?If:
AB = BA = [3 0]
[0 3]
Then:
AB = BA = 3 [1 0]
[0 1]
This can be further written as:
AB = BA = 3I₂
And again as:
A (¹/₃ B) = I
This then allows us to either write this as:
A⁻¹ = ¹/₃ B
Or:
B⁻¹ = ¹/₃ A
In conclusion, option A is correct.
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-10 -8 -6 -42
10
8
6
41
2
-2
-4
-6
-8
+10
y
2
4 6 8 10
x
Study th
to find its
The equ
Answer: [tex]y=x+2[/tex]
Step-by-step explanation:
The slope is
[tex]\frac{0-2}{-2-0}=1[/tex]
since the y-intercept is 2, the equation is [tex]y=x+2[/tex]
The point-slope form of the equation of of the line that passes through (-4, -3) and (12, 1) is y - 1 = 1/4(x - 12). What
is the standard form of the equation for this line?
O x- 4y = 8
O x-4y=2
O 4x-y= 8
O 4x-y=2
Answer: [tex]\frac{1}{4}[/tex]x - y = 2
Step-by-step explanation:
Standard form is Ax + By = C where A, B, and C, are integers.
Given:
y - 1 = 1/4(x - 12)
Distribute:
y - 1 = [tex]\frac{1}{4}[/tex]x - 3
Add 3 to both sides of the equation:
y + 2 = [tex]\frac{1}{4}[/tex]x
Subtract y from both sides of the equation:
2 = [tex]\frac{1}{4}[/tex]x - y
Apply the reflexive property:
[tex]\frac{1}{4}[/tex]x - y = 2
GIVING BRAINLEST!
Linda collected 1/2 of a stamp album. Becky collected 7 1/3 times as many stamps as Linda. How many
stamp albums were collected by Becky?
O 3 1/3
O 2 1/3
O 3 2/3
O 1 1/3
*
Answer:
3 2/3
Step-by-step explanation:
To do this question, you would need to multiply 7 1/3 with 1/2. The answer is 3 2/3.
Answer:
3 2/3 albums
Step-by-step explanation:
Let's say that the stamp album has 12 stamps (12 is just an arbitrary number used to make calculation easier). If Linda collects half of the album, it means she has 6 stamps. If that is the case, Becky has 6 * 7 1/3 stamps. Since 7 1/3 is equivalent to 22/3, we can determine that Becky has collected 44 stamps (6*22/3). There are 12 stamps in one album, which means there are 44 stamps in 3 2/3 (11/3) albums:
[tex]\frac{12}{1}=\frac{44}{y} \\12y=44\\y=11/3[/tex]
Since the ratio of stamps to albums is constant, the calculation above demonstrates that the number of albums it takes to have 44 stamps is 3 2/3. Please note that the numbers I used are arbitrary. If you substitute 12 for a variable x, you will get the same result.
A man is dealt 4 spade cards from an ordinary deck of 52 cards. If he is given five more, what is the probability that none of them are spades
The probability that none of them are spades is c(39,5) / c(48,5).
Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.
A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final result of an experiment. Getting a Head whilst tossing a coin is an event.
Simple chance is the calculation of an outcome or the chance of an event ever taking place. Coverage companies use possibility statistics to determine the possibility of having to pay out a declaration. A simple chance is calculated by way of dividing a particular outcome by all of the feasible outcomes.
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Checking number 2( Solving inequalities)
1. x < 20
x - 7 < 13
x < 20
2. x > -7
-3(x + 4) < 9
-3x - 12 < 9
-3x < 21
x > -7
Hope this helps!
2x2 – 9x + 2 = –1 discrimiant
By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to 57.
How to determine the discriminant of a quadratic equation
For a quadratic equation of the form a · x² + b · x + c = 0, the discriminant is equal to d = b² - 4 · a · c. In this problem we must transform the polynomial into the canonical form and calculate the discriminant:
2 · x² - 9 · x + 2 = - 1
2 · x² - 9 · x + 3 = 0
d = (-9)² - 4 · (2) · (3)
d = 81 - 24
d = 57
By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to 57.
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