Answers
The equation from the given graph is y=-2/3 x²+5.
From the given graph the vertex is (h, k)=(0, 5).
What is quadratic equation of graph?A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.
The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.
Here, point on the given line from the graph is (3, -1)
Put (x, y)=(3, -1) and (h, k)=(0, 5) in y = a(x - h)² + k, we get
-1=a(3-0)²+5
⇒ 9a=-6
⇒ a=-2/3
Now, y=-2/3(x-0)²+5
y=-2/3 x²+5
Hence, the equation from the given graph is y=-2/3 x²+5.
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Related Questions
Someone help
Given the function f(x) = 1 + 1/2x³, find the value of f(-4) in simplest form.
Answers
Answer: -62.5
PLEASE GIVE BRAINLIEST THANK YOU!!!
Step-by-step explanation:
Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answers
Answer:
0.86 pounds of fruit is left.
Step-by-step explanation:
If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86
Which statement is true about 67?
A. its a prime number
B. its a composite number
C. its neither prime or composite
Answers
Answer:
a. its a prime number cuz as far as ik 67 has one factor 67x1
Answer:
Number 67 is prime because it doesn't have proper factors. In other words, the only factors of 67 are 1 and itself
Match the following definitions with the correct term.
Answers
Answer:
that's biology but
Step-by-step explanation:
autotrophs make their owner food
heterotrophs can't make their own food
photosynthesis is the 3rd one
photosynthesis happens in the chloroplast
photosynthesis makes glucose
I can go in depth about any of these, ask me if needed
Calculate (8.42 x 109) − (2.35 x 108).
Answers
Answer:
Step-by-step explanation:
663.98
Answer: 663.98
Step-by-step explanation:
(8.42*109)=917.78
(2.35*108)=253.8
917.78-253.8=663.98
Bloomington University charges $53,730 for tuition. If they raise their tuition by 8% each
year, how much will tuition be in 2 years?
If necessary, round your answer to the nearest cent.
$
E
Answers
GHLJ and GSTU are both parallelograms. Why is
∠L ≅ ∠T?
Parallelogram G S T U is inside of larger parallelogram G H L J. Side G S in on side G H, and side G U is on side G J.
Answers
The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that opposite angles of a parallelogram are congruent.
How to identify congruent angles?We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.
Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.
Thus, angle G is congruent to angle T and angle L .
Therefore, ∠L ≅ ∠T
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Answer:
By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Step-by-step explanation:
got it right on edge2
This rectangular design is made from 6 squares. there are 2 small squares surrounded by 4 larger squares. the area of each small square of 1sq.cmwhat is the total area of the design?
Answers
The total Area the design is 8 square cm.
Area of rectangular design is product of length and breadth of rectangular design.
In the given question we have,
Rectangular design is made up from 6 squares .
there is 2 small squares surrounded by 4 large squares.
Area of each small square = 1 sq.cm
let the length of rectangular design be l cm
and breadth is b cm.
Area of rectangular design= l×b sq.cm
from the given statement, we can see that side of small square is 1 cm and small squares surrounded by 4 large squares i.e side of large square is sum of side of small squares or 2cm .
Also , length of rectangular design is sum of sides of two large squares and breadth is same as side of one large square.
so, length of rectangular design= 4 cm
breadth of rectangular design= 2cm
Area of rectangular design= 4×2 = 8sq. cm
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according to a wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (wired magazine website). suppose we randomly select received e-mails. a. what is the expected number of these e-mails that are tracked?
Answers
There should be 12 emails total.
7.200 and 2.683 are the variance and standard deviation, respectively.
What is varience?The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: 2. Both analysts and traders use it to assess market volatility and security.The standard deviation (SD or ), which aids in determining the consistency of an investment's returns over time, is the square root of variance.Calculation of expected number of emails, variance and standard deviation:
Given thatP = 0.40 and n = 30a)The expected value of received e-mails is= n × p= 30 × 0.4= 12 b)The variance of emails received is= n × p × (1 - p)= 30 × 0.4 × 0.6= 7.200NowThe standard deviation of emails received is= sqrt(variance)= 2.683Learn more about variance here:
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x³+10<9 help pls pls pls pls pls pls
Answers
Answer:
x< -1
Step-by-step explanation:
x^3 < 9 - 10
x^3 < -1
x< -1
Answer:
x < -1
Step-by-step explanation:
x³<9-10
x³<-1
x < -1
Please mark as brainliest
Example of a slope intercept form equation with a negative slope and y-intercept of 0
Answers
Answer:
An example would be y = -x.
Step-by-step explanation:
Since the y-intercept is 0, we don't have to write it out. The slope has to be negative, so I chose -1 as the slope. We don't have to write 1 when we use it as a coefficient, so that is why I wrote it as -x. Now to put it all together in slope intercept form, we get y = -x.
Hope this helps.
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What is the value of z where distance of between two point R(6, - 1, - 3) and S(3, 3, z) is 13?
Answers
Answer:
-15, 9
Step-by-step explanation:
Substituting into the distance formula,
[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]
Write an equation of the line in slope-intercept form.
Ay
4
y =
(0, 2)
2
(3, 3)
4
AX
Answers
Equation of line in slope-intercept form is [tex]y = (\frac{1}{3})x + 2[/tex].
Given in graph,
A(0,2) and B(3,3)
Slope-intercept form => y = mx + c
Slope, m = [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{3-2}{3-0}[/tex]
= [tex]\frac{1}{3}[/tex]
Therefore, y = (1/3)x + c
Put A(0,2) in above equation
2 = (1/3)*0 + c
2 = c
Hence, y = (1/3)x + 2.
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What is the
y-intercept of the function f(x)=-2/9x+1/3?
Answers
Answer:
1/3
Step-by-step explanation
We can immediately tell the y-intercept is 1/3.
Slope intercept form:
y = mx + b
m = slope
b = y-intercept.
Answer: the y - intercept is 1/3
Step-by-step explanation: trust
What is the product of (4i-5)(4i+5)
Answers
The product of (4i-5)(4i+5) is -41.
What are complex numbers?
Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.
Here, we have
Given function
= (4i-5) (4i+5)
After applying the product rule, we get
= 16i² + 20i - 20i - 25
= 16i² - 25
after putting i² value, we get
= 16(-1) - 25
= -41
Hence, the product of (4i-5)(4i+5) is -41.
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write the inverse: if the 2 smallest sides sum to be larger than the 3rd side, then it is a triangle.
Answers
Using the properties of conditional statements we can write the inverse of the statement as ": if the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle."
The statement is given as if the sum of two sides is greater than the third side then it is a triangle.
Now for the inverse we have to convert the given line into double negative.
Hence we get:
If the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle
Conditional statements are part of mathematical reasoning, a vital skill that enables students to evaluate a given hypothesis without reference to a particular context or meaning. Simply put, when a scientific research or allegation is studied, the logic isn't truly founded on an individual's perspective. Deductions and evidence must have factual and scientific foundations.
the various types of conditional statements are:
When the conditional statement's hypothesis and conclusion are both untrue, it is referred to as an inversion of the statement.If both a hypothesis and a conclusion are false at the same time, the statement is contrapositive.A statement is said to be biconditional when it is both conditional and converse at the same time, satisfying both conditions as true.Top learn more about inverse of a statement visit:
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What is a counterexample for the conjecture?
If the area of a rectangle is 80 square units, the perimeter must be greater than 35.9 units.
A) A rectangle with length 39.5 units and width 0.5 unit has a perimeter of 80 units and an area of 19.75 square units.
B) A rectangle with length 8 units and width 10 units has a perimeter of 36 units and an area of 80 square units.
C) A rectangle with length 8 units and width 9 units has a perimeter of 34 units and an area of 72 square units.
D) A square with a side length of √80 units has a perimeter of approximately 35.8 units and an area of 80 square units.
Answers
The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.
What is counterexample?An instance or example that refutes the proposition is referred to as a counterexample. To determine if a statement is true or not, logic uses this. Counterexamples typically offer strong arguments in opposition to the assertion under discussion.The goal of the inquiry is to demonstrate any possible relationship between the area and perimeter of a rectangle.acc to our question-
The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.
The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.
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Write an equation for the transformation of y=x; vertical by a factor of 1/10
Answers
The equation the function after the transformation is g(x) = x/10
How to determine the transformation of the function?The equation of the function is given as
y = x
Express as a function
f(x) = x
The sequence of transformations is given as follows:
Vertically stretched by a factor of 1/10
When the above transformations are combined, we have:
Vertically stretched by a factor of 4: g(x) = 1/10f(x)
So, we have
g(x) = 1/10f(x)
Substitute x for f(x)
So, we have
g(x) = 1/10 * x
Evaluate
g(x) = x/10
Hence, the function g(x) is g(x) = x/10
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find the slope through(0,10) and (24, 6)
Answers
Answer:
slope = - [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 10 ) and (x₂, y₂ ) = (24, 6 )
m = [tex]\frac{6-10}{24-0}[/tex] = [tex]\frac{-4}{24}[/tex] = - [tex]\frac{1}{6}[/tex]
Evaluate f(x) = 2|x – 5| for f(–5) and f(0).
Question 20 options:
f(–5) = 10, f(0) = 0
f(–5) = 12, f(0) = 5
f(–5) = –20, f(0) = –2
f(–5) = 20, f(0) = 10
Answers
Answer:
D
Step-by-step explanation:
f(-5) = 2|-5-5|
f(-5) = 2|-10|
f(-5) = 2 * 10
f(-5) = 20
f(0) = 2|0-5|
f(0) = 2|-5|
f(0) = 2 * 5
f(0) = 10
What is the value of x?
1.9x+0.1x=0.6
Enter your answer as a decimal in the box.
x = ???
Answers
2x = 0.6
divide by 2 on both sides
x=0.3
Answer:
x = 0.3
Step-by-step explanation:
[tex] \sf1.9x + 0.1x = 0.6[/tex]
Combine like terms.
[tex] \sf2x = 0.6[/tex]
Divide both sides by 2.
[tex] \sf \: x = 0.3[/tex]
Triangles UVW and VUX are congruent identifier common sides are angles.
Answers
Answer:
Common side: UV
Step-by-step explanation:
The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 side touching. What is the total number of white cubes that were used to build the prism?
Answers
Answer:34?
Step-by-step explanation: not too sure but yeah
Given the following function, find the vertex, y=5x^2-8x+6
Answers
Answer:
The vertex is (0.8, 2.8)------------------------------------
GivenFunction y = 5x² - 8x + 6Find the x-coordinate of the vertexx = - b/(2a)x = - (-8)/(2*5) = 8/10 = 0.8Find the y-coordinate of the vertexy = 5(0.8²) - 8(0.8) + 6 = 2.8in order to estimate the proportion of all credit card holders who pay their credit card bills in full each month a credit counseling bureau took a random sample of 450 credit card holders and found that 127 pay all their credit card bills in full each month. a 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is:
Answers
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
Define confidence interval.Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications. The sample is used to calculate the confidence interval, which represents the range of likely population parameters. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Given,
Number of credit card holders
n = 450
x = 127
p = 127/450
Proportion:
p = 0.2822
99% confidence interval:
C I = 0.2822 ± 2.576 × 0.2122
CI = 0.2822 ± 0.05465
CI = 0.282 + 0.055
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
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Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64
Answers
Answer:
A
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
Then
[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]
= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)
= 12 + 36[tex]\sqrt{3}[/tex] - 40
= - 28 + 36[tex]\sqrt{3}[/tex]
Write the equation of a line in point slope form that has a slope of 1/3 and passes through the point (6,-2)
Answers
The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].
What is point-slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point-slope form is used to determine the equation of a line whose slope is "m" and passes through the point ([tex]x_{1}, y_{1}[/tex]). The equation of a straight line can be expressed in various ways, Point slope shape is one of them. The point slope form's equation is as follows:[tex]y-y_{1} =m(x-x_{1} )[/tex]where (x, y) is a chance point on the line that should be treated as a variable when using the formula.A fixed point on the line is ([tex]x_{1}, y_{1}[/tex]).The slope of the line is m.Calculation
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]
[tex]y+2 =\frac{1}{3} (x-6 )[/tex]
Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]
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help me please
Ayuda pro favor
Answers
The values of x after applying congruency to solve the complete shape is 3.5.
What are congruent shapes?Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. The symbol to represent two congruent shapes is ≅.
To calculate the values of x in the diagram, we need to first join point Q to point H and point G to form ΔQHG also, we join point Q to point E and point F to form ΔQFE.
Comparing ΔQHG and ΔQFE, we can deduce that
ΔQHG ≅ ΔQFETherefore,
x+8 = 3x+13x-x = 8-12x = 7x = 7/2x = 3.5Hence, the values of x in is 3.5.
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The sum of the squares of two consecutive positive numbers is 1,105. Find the numbers.
Answers
Answer:
23 and 24
Step-by-step explanation:
let the 2 consecutive numbers be n and n + 1 , then
n² + (n + 1)² = 1105
n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )
2n² + 2n - 1104 = 0 ( divide through by 2 )
n² + n - 552 = 0 ← in standard form
(n + 24)(n - 23) = 0 ← in factored form
equate each factor to zero and solve for n
n + 24 = 0 ⇒ n = - 24
n - 23 = 0 ⇒ n = 23
However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24
the numbers are 23 and 24
2. The lengths of a certain species of fish was
found to be normally distributed. The mean
length is 78 cm with a standard deviation
of 14 cm. In a school of 370 of these fish,
how many would be longer than than
92 cm
Answers
So, approximately 59 fish in the school would be longer than 92 cm.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, logarithms, etc.
Here,
We can solve this problem using the normal distribution formula, which states:
z = (x - mu) / sigma
where z is the standard score, x is the raw score, mu is the mean, and sigma is the standard deviation.
To find the number of fish longer than 92 cm, we need to find the proportion of fish in the population with lengths greater than 92 cm. We can then multiply this proportion by the total number of fish in the school to get the number of fish longer than 92 cm.
First, we calculate the standard score for 92 cm:
z = (92 - 78) / 14
z = 1
Next, we look up the proportion of the standard normal distribution that corresponds to a z-score of 1. We can use a standard normal distribution table or calculator to find this value. The proportion of the distribution that is greater than z = 1 is approximately 0.1587.
Therefore, the proportion of fish in the population with lengths greater than 92 cm is 0.1587. To find the number of fish longer than 92 cm, we multiply this proportion by the total number of fish in the school:
370 * 0.1587 = 58.8
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