The vertex of the Parabola is (2, -3)
What is a vertex?The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.
From the function f(x) =[tex]-(x-2)^{2}[/tex] - 3
The equation of parabola in vertex form is
y=[tex]a(x-h)^{2}[/tex]+k
where h and k are the coordinates of the vertex
comparing the two equations
h = 2, k = -3
The coordinates of the vertex is (2, -3)
In conclusion, the vertex is (2, -3).
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URGENT PLS HELPPPP!!!!!
Write the point-slope form of the equation of the line with a slope of -2 and an x-intercept of -1.
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.
Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
The equation of the line that has a slope of -2 and x-intercept of -1 in point slope form is y = -2(x + 1).
How to write equation in point slope form?Linear equations can be represented in different form such as point slope form, slope intercept form, general form and standard form.
Therefore, let's represent the equation of the line in point slope form.
Using point slope form,
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the variables.Therefore, the equation of the line has a slope of -2 and an x-intercept of -1.
The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.
hence,
m = -2 and (-1, 0)
x₁ = -1
y₁ = 0
Therefore,
y - 0 = -2(x + 1)
y = -2(x + 1)
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The sum of two numbers is 12. The difference of the two numbers is 6. What are the two numbers?
Answer:
3 and 9
Step-by-step explanation:
x+y=12
y-x=6
y-x=6
+x. +x
y=6+x
x+(6+x)=12
6+2x=12
-6. -6
2x=6
/2. /2
x=3
3+y=12
-3. -3
y=9
Hopes this helps please mark brainliest
5. The corresponding sides of the similar shapes have same
- In the figure given below, what is the value of x? (RED)
2 cm
3 cm
3 cm
2 cm
4 cm
x cm
(GR
4 cm
Using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
What exactly are mathematical operations?An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.
The arity of the operation is influenced by the number of operands.
PEMDAS, parenthesis, exponents, multiplication, and division.
So, the value of x will be:
The given two rectangles have similar sides.
2cm is similar to 4cm.
3cm is similar to xcm.
Now, we can calculate x as follows:
2/4 = 3/x
2x = 4×3
2x = 12
x = 12/x
x = 6
Therefore, using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
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Identify the length of the missing section of each line. Assume that the lines are divided into equal parts.
The identification of the length of the missing section of each line, assuming that the lines are equally divided, is as follows:
a) The missing section is 24 units.
b) The missing section is 18 units.
c) The missing section is 10 units.
How are the missing sections computed?The missing sections can be computed using the mathematical operations of division and multiplication.
The product (quotient) of a division operation involves applying the divisor on the dividend using a division operand (÷).
The product of a multiplication operation applies the multiplier on the multiplicand using the multiplication operand (×).
a) The total units = 36
Division parts = 3
The units of each division = 12 (36/3)
The missing section = 24 (12 x 2)
b) The total units = 36
Division parts = 4
The units of each division = 9 (36/4)
The missing section = 18 (9 x 2)
c) The total units = 16
Division parts = 8
The units of each division = 2 (16/8)
The missing section = 10 (2 x 5)
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The physical plant at the main campus of a large state university recieves daily requests to replace
florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean
of 36 and a standard deviation of 4. Using the 68-95-99.7 rule, what is the approximate percentage
of lightbulb replacement requests numbering between 32 and 36?
Do not enter the percent symbol.
%6
ans =
> Next Question
The percentage of lightbulb replacement requests numbering between 32 and 36 is 34
According to the question,
The distribution of the number of daily request is bell-shapes means Number of daily request follows Normal distribution
Mean of normal distribution : μ = 36
Standard deviation : σ = 4
Let the lightbulb replacement requests number be "x"
So, the probability of lightbulb replacement requests numbering between 32 and 36 = P(32 < x <36)
below 36 i.e. mean of normal
32 = 36 - 4 is probability between one standard deviation and below mean
Percentage between mean ± standard deviation is always 68%
so , percentage of lightbulb replacement requests numbering between 32 and 36 will be half of 68% as mean + standard deviation is excluded
= 68/2
= 34
Hence , 34 percentage of lightbulb replacement requests numbering between 32 and 36.
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HELP ME PLEASE!!!?!!!!!?!!!?!!!!0.0
Answer:
wean positive realtionship
Which point is not a solution of the equation below?
(0, -5)
(2, 1)
(5, 5)
(-2, -9)
(2,1) because if you graph it, the dot won’t be on the line.
NO LINKS! Please help me with this vertex problem
Show work please: step by step
Answer:
[tex]f(x)=6(x-2)^2+18[/tex]
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=6x^2-24x+42[/tex]
To complete the square, begin by grouping the x terms within parentheses:
[tex]\implies f(x)=(6x^2-24x)+42[/tex]
Factor out the coefficient of x²:
[tex]f(x)=6\left(x^2-4x\right)+42[/tex]
Add the square of half the coefficient of the term in x inside the parentheses, and subtract the distributed value outside the parentheses:
[tex]\implies f(x)=6\left(x^2-4x+\left(\dfrac{-4}{2}\right)^2\right)+42-6\left(\dfrac{-4}{2}\right)^2[/tex]
Simplify:
[tex]\implies f(x)=6\left(x^2-4x+\left(-2\right)^2\right)+42-6\left(-2\right)^2[/tex]
[tex]\implies f(x)=6\left(x^2-4x+4\right)+42-6\left(4)[/tex]
[tex]\implies f(x)=6\left(x^2-4x+4\right)+42-24[/tex]
[tex]\implies f(x)=6\left(x^2-4x+4\right)+18[/tex]
Factor the perfect square trinomial inside the parentheses:
[tex]\implies f(x)=6(x-2)^2+18[/tex]
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Comparing the derived equation with the vertex formula, the vertex of the derived equation is (2, 18). Hence the completion of the square is correct.
If the area of a rectangular sign is approximately 4218 sq ft, and the width is approximately 57 ft, what is the height of this sign?
A biologist is studying a particular species of flower. She writes the following equation to
show the length of the flower petal f(w), in cm, after w weeks:
f(w) = 3(1.03)
Part A (3pts): Complete
the table using the
function.
0
1
2
3
4
5
f(w)
Part B (1pt) Highlight the data
needed to solve this from the
table in Part A.
(2pts): What is an average
rate of change of the function
f(w) when w = 2 to
w = 5?
Rate of change formula =
y₂-y₁
x₂-x
3.03
Part C (2pts): What does the y-intercept of
the graph of the function f(w) represent?
(Circle the correct answer.)
a.) initial length of the petal
b.) length of the petal after w weeks
c.) time it took for the flower to stop growing
d.) percentage of growth each week
Part D (2pts): At the end of the study the
length of the petal was 3.48 cm. What is a
reasonable domain to plot the growth
function?
Sws
A. The lengths of the flower petals corresponding to the weeks 0, 1, 2, 3, 4, and 5 are 0, 3.09, 6.18, 9.27, 12.36, and 15.45, respectively.
B. The average rate of change of the function f(w) from week two to week five is 3.09.
C. The y-intercept of the function f(w) represents the initial length of the petal.
D. The reasonable domain to plot the growth function is week 0 to week 2.
The length of the flower petal and the weeks passed are denoted by f(w) and w. The equation of the function is given below.
f(w) = 3(1.03)w
The simplified function is f(w) = 3.09w.
The rate of change of the function from weeks 2 to 5 is calculated below.
R = [f(5) - f(2)]/(5 - 2)
R = [3.09*5 - 3.09*2]/3
R = 3.09*(5 - 2)/3
R = 3.09
The length of the flower petal at the end of the study was 3.48 cm. The length lies between the week 0 and the week 2.
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dentify on which quadratic function is positive.
Y = 2x^2 - 17x + 30
Identify on which quadratic function is negative.
Y = - x^2 - 6x - 8
A explanation on the answers would be appreciated!
(Lots of points!)
Step-by-step explanation:
Let us identify which quadratic function is positive. Yeah, let's start.
Y = [tex]{ \red{ \sf{2 {x}^{2} - 17x + 30}}}[/tex]
By using factorisation method,
[tex]{ \red{ \sf{2 {x}^{2} - 12x - 5x + 30}}}[/tex]
Take common factors
[tex]{ \red{ \sf{2x(x - 6) - 5(x - 6)}}}[/tex]
[tex]{ \red{ \sf{(2x - 5)}}} \: \: \: \: \: \: \: || \: \: \: \: \: { \red{ \sf{(x - 6)}}}[/tex]
[tex]{ \red{ \sf{2x - 5 = 0}}} \: \: || \: \: { \red{ \sf{x - 6 = 0}}}[/tex]
[tex]{ \red{ \sf{2x = 5}}} \: \: \: \: \: \: \: \: \: || \: \: \: \: { \red{ \boxed{ \green{ \sf{x = 6}}}}}[/tex]
[tex]{ \red{ \sf{{ \frac{ \cancel2}{ \cancel2}x}}}} = { \red{ \sf{ \frac{5}{2}}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{5}{2}}}}}} [/tex]
____________________________________
Y = [tex]{ \blue{ \sf {{ - x}^{2} - 6x - 8}}}[/tex]
By using factorisation method,
[tex]{ \blue{ \sf{ - {x}^{2} - 2x - 4x - 8}}}[/tex]
Take common factors
[tex]{ \blue{ \sf{ - x(x + 2) - 4(x + 2)}}}[/tex]
[tex]{ \blue{ \sf{( - x - 4)}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{(x + 2)}}}[/tex]
[tex]{ \blue{ \sf{- x - 4 = 0}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{x + 2 = 0}}}[/tex]
[tex]{ \blue{ \boxed{ \green{ \sf{x = -4}}}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]
Hence, the first quadratic function is positive and second quadratic function is negative.
Answer:
[tex]\textsf{$y = 2x^2 - 17x + 30$: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}[/tex]
[tex]\textsf{$y = - x^2 - 6x - 8$: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}[/tex]
Step-by-step explanation:
A function is positive when it is above the x-axis, and negative when it is below the x-axis.
---------------------------------------------------------------------------------
Given quadratic equation:
[tex]y = 2x^2 - 17x + 30[/tex]
Factor the equation:
[tex]\implies y = 2x^2 - 17x + 30[/tex]
[tex]\implies y = 2x^2 - 5x-12x + 30[/tex]
[tex]\implies y=x(2x-5)-6(2x-5)[/tex]
[tex]\implies y=(x-6)(2x-5)[/tex]
The x-intercepts of the parabola are when y = 0.
To find the x-intercepts, set each factor equal to zero and solve for x:
[tex]\implies x-6=0 \implies x=6[/tex]
[tex]\implies 2x-5=0 \implies x=\dfrac{5}{2}[/tex]
Therefore, the x-intercepts are x = ⁵/₂ and x = 6.
The leading coefficient of the given function is positive, so the parabola opens upwards.
The function is positive when it is above the x-axis.
Therefore, the function is positive for the values of x less than the smallest x-intercept and more than the largest x-intercept:
[tex]\textsf{Solution: \quad $x < \dfrac{5}{2}$ \;and \;$x > 6$}[/tex][tex]\textsf{Interval notation: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}[/tex]---------------------------------------------------------------------------------
Given quadratic equation:
[tex]y = - x^2 - 6x - 8[/tex]
Factor the equation:
[tex]\implies y = - x^2 - 6x - 8[/tex]
[tex]\implies y = -(x^2 +6x +8)[/tex]
[tex]\implies y = -(x^2 +4x +2x+8)[/tex]
[tex]\implies y = -((x(x+4)+2(x+4))[/tex]
[tex]\implies y = -(x+4)(x+2)[/tex]
The x-intercepts of the parabola are when y = 0.
To find the x-intercepts, set each factor equal to zero and solve for x:
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
Therefore, the x-intercepts are x = -4 and x = -2.
The leading coefficient of the given function is negative, so the parabola opens downwards.
The function is negative when it is below the x-axis.
Therefore, the function is negative for the values of x less than the smallest x-intercept and more than the largest x-intercept:
[tex]\textsf{Solution: \quad $x < -4$ \;and \;$x > -2$}[/tex][tex]\textsf{Interval notation: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}[/tex]Circular area rugs are priced at $5 per foot based on the circumference of the carpet used. What is the cost of the largest circular area rug that will fit in Susie’s dining room? Round your answer to the nearest whole number. Do not include the dollar sign in your answer.
A rectangle has length 12 feet and width 7 feet.
Answer:
The area of the room is 34*21 = 714 ft^2
the cost of the carpet is $5 per square foot, so the cost to carpet the whole room will be
5*714 = $3570
Step-by-step explanation:
3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that, Circular area rugs are priced at $5 per foot based on the circumference of the carpet used.
We need to find the cost of the largest circular area rug that will fit in Susie’s dining room.
The area of the room is 34×21 = 714 ft²
The cost of the largest circular area rug that will fit in Susie’s dining room
$5 per foot based on the circumference of the carpet
Multiply 5 with 714
5×714
3570
Hence, 3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.
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A camp counselor and four campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the fourth and a camper who has a tendency to engage in food fights must sit to the counselor's immediate ?
Answer: 6 ways
Step-by-step explanation:
3. Your original purchase price was $825.00 plus 7% sales tax. You enter into an agreement
where the interest (12.5% APR) is waived for the first 12 months provided you make the
required monthly payments; otherwise the interest is accrued from the date of purchase. You
miss the first payment due date. The late fee is $35.00. How much is the interest?
O$103.13
O $110.34
O $8.59
O $9.20
The original price of purchasing is $825 plus 7% sales tax, then the interest will be $9.20. Hence, option D is correct.
What is the Percentage?The Latin term "per centum," which signifies "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship here between a component and a whole, in which the value of the whole is always assumed to be 100.
As per the given data in the question,
The original purchase price = $825
The sales tax = 7% of $825 = 825 × 7/100 = $57.75
Total credit = $825 + $57.75 = $882.75
The monthly interest rate = 12.5%/12 = 1.0417%
Interest = $882.75 × 1.0417/100
Interest = $9.20
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Is 49 prime or composite?
Can Mario organize his marbles into aqual piles?
The number 49 is a composite number because it has more than two factors.
What is a prime number?A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.
Numbers with more than two factors are known as composite numbers. Non-prime numbers are composite numbers because they can be divided by more than two numbers.
A positive integer is a composite number. which is not the case (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes abbreviated as "composites") are 4, 6, 8, 9, 10, 12, 14, 15, and 16.
A composite number is one that can be formed by multiplying two smaller positive integers. It is a positive integer with at least one divisor other than 1 and itself. Every positive integer is either composite, prime, or the unit 1, so composite numbers are those that are neither prime nor a unit.
In this case, the factor of 49 are 1, 7 and 49. Therefore, it's a composite number.
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54 3. Joey opened a new store that sells jars of jelly. Joey sold 3 jars of jelly in his first week of business and 10 jars in his second week. He sold 31 jars in week 3 and 94 jars in week 4. If the number of jars he sells continues to increase in this pattern, how many jars of jelly will Joey sell in the fifth and sixth weeks?
Answer:
7
Step-by-step explanation:
THe answer is 7 because 10-3=7 SOrry if wrong
I NEED HELP PLEASE HELP
Answer:
Step-by-step explanation:
Which of the following could be used as a statement in a two-column proof?
A statement of given information can be used in a two column proof
What is two column proof ?Among the many methods available to mathematicians are proofs, or logical arguments, that begin with premises and reach conclusions through the presentation of facts. The proof is hard to write because you have to put each part in the correct order.While paragraphs and flow charts are enough to outline the various steps, nothing beats a two-column proof for purity and clarity. A two-column proof uses a table to represent a logical argument and assigns a task to each column.The two columns then work in lockstep, leading the reader from the premise to the conclusion. Paragraph proofs tell a story by chronologically listing each fact and reason. This means you have to be very organized and have to rewrite paragraphs over and over until you get it right. Flowchart proofs can be difficult to follow, but at least they provide a clean separation between mathematics and reasoningIn light of the question -The two-column proof is summarized in the statement and reason columns, and each statement must have a verified reason. Two-column proof reasons are usually given information, vocabulary definitions, hypotheses, and previously proven theorems.
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Two data sets and their mean absolute deviations are shown.
Study the plots of each data set, and then use the drop-down menus to answer the questions below?
Answer: you should watch a quick video about it :)
Step-by-step explanation:
I need help with this please help me
From the given figure
a) The value of y = 6
b) The length of the line RS = 39 units
The length of the line ST = 38 units
The length of the line RS = 6y + 3
The length of the line ST = 5y + 8
The length of the line RT = 77
From the line we can say that
RT = RS + ST
77 = 6y + 3 + 5y + 8
Add the like terms
11y + 11 = 77
11y = 77 - 11
11y = 66
y = 66/11
y = 6
The value of y = 6
The length of RS = 6y + 3
= 6×6 + 3
= 36 + 3
= 39 units
The length of the line ST = 5y + 8
= 5×6 + 8
= 30 + 8
= 38 units
Hence, from the given figure
a) The value of y = 6
b) The length of the line RS = 39 units
The length of the line ST = 38 units
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(a - 2b)3 when a = 3 and b = -1/2
Answer:
64
Step-by-step explanation:
Substitute the values so (3-2(-1/2))3
Then distribute so (3-(-1))3
Add since it's a double negative to get (4)3
And 4 cubed is 64
A list of numbers is given below. If x is a number
in this list, which inequality could represent x?
{-5,
-12,-2,-9}
A. x < -13
B. X<-1
C. x>-12
D. X<-2
Answer:
B
Step-by-step explanation:
Since -1 is greater the values given then x is less than -1
what is the value of this expression when x=3 and y=8?
[tex] {3x}^{2} + {2y}^{2} [/tex]
A. 25
B. 155
C. 210
D. 337
Answer:
B
Step-by-step explanation:
3([tex]3^{2}[/tex]) + 2([tex]8^{2}[/tex])
3(9) + 2(64)
27 + 128
155
Find the cardinal number of a set B={Q,R,S,T,U,V}.
Answer:
6
Step-by-step explanation:
The cardinal number of a finite set is the number of elements of the set.
cardinal number = 6
HELP NOW
Which variables would the scatter plot at the right be most likely to represent?
A.The number of people at a concert and the total concession sales
B.The number of guests at a hotel and the total water consumption
C.The number of siblings a person has and the person's GPA
D.The total number of miles driven and the total gallons of gas used
The vertex of the function f(x) = 2x² + 12x + 19 is at the coordinate (x, y), where:
x =
y =
Answer:
x = -3
y = 1
Step-by-step explanation:
Desmos is free and it will graph for you. See picture.
Directions. Answer questions (a – f) based on the following graph.
A: When x = -1, what is the value of y?
B. When y = 7, what is the value of x?
C. What is the y-intercept of the graph?
D. What is the x-intercept of the graph?
E. What is the slope of the line?
F. What is the equation of the line?
A. When x = -1, the value of y is equal to 3.
B. When y = 7, the value of x is equal to 1.
C. The y-intercept of the graph is equal to -2.5.
D. The x-intercept of the graph is equal to 5.
E. The slope of the line is equal to -1.75
F. The equation of the line is equal to y = -1.75x - 2.5
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
How to calculate the slope and equation of this line?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope of a line.x and y are the points on a graph.c represents the y-intercept.Making slope (m) the subject of formula, we have the following:
Slope, m = (y - c)/x
Slope, m = (1 - (-2.5))/-2
Slope, m = (1 + 2.5)/-2
Slope, m = -3.5/2
Slope, m = -1.75.
For the equation of this line, we have:
y = mx + c
y = -1.75x - 2.5
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Piece of rope is 24 1/2 feet long how many 1/4 foot sections will there be?
By taking a quotient between the lengths, we will see that 98 pieces of 1/4 foot can be made.
How many 1/4 foot sections are in the piece of rope?We know that the total length of the rope is (24 + 1/2) ft, to see how many pieces of 1/4 feet we can take from that rope, we need to take the quotient between the total length and the length of the pieces.
It gives:
Q = (24 + 1/2)ft/(1/4)ft = 4*(24 + 1/2)
Q = 4*24 + 4*(1/2)
Q = 96 + 4/2
Q = 96 + 2 = 98
So 98 pieces of 1/4 foot can be made.
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A single serving of hot chocolate requires 0.75 cups of milk. Nina used 7 cups of milk to make hot chocolate for her 9 friends. Did she make enough for each friend to get a serving of hot chocolate?
Answer:
nik
Step-by-step explanation:
if an odd number is added to an even number the result must be
Answer:
an odd number
Step-by-step explanation:
it always will be an odd number when you add an even and an odd number