In step 3, he did not subtract –7(9) to keep the function equivalent. Therefore, the correct option is option C among all the given options.
What is mathematical function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a predictor variables (the dependent variable).
In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Paul Dirichlet initially offered the standard concept of function in 1837. When Nick checked his work it did not match the standard form function. In step 3, he did not subtract –7(9) to keep the function equivalent.
Therefore, the correct option is option C.
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Your question is incomplete but most probably your full question was,
Nick wrote the function p(x) = 17 + 42x – 7x2 in vertex form. His work is below.
p(x) = –7x2 + 42x + 17
p(x) = –7(x2 – 6x) + 17
= 9;
p(x) = –7(x2 – 6x + 9) + 17
p(x) = –7(x – 3)2 + 17
When Nick checked his work it did not match the standard form function. Analyze Nick’s work. What was his mistake?
In step 1, he did not put the function in standard form correctly.
In step 2, he should have also factored –7 from the constant term, 17.
In step 3, he did not subtract –7(9) to keep the function equivalent.
In step 4, he did not write the perfect square trinomial correctly as a binomial squared.
Nick made mistakes in converting to standard form, factoring constants correctly, maintaining equivalence, and writing perfect square trinomials. Correcting these steps will yield an accurate transformation of the equation.
Let's break down the steps Nick likely took and identify where he went wrong in putting the quadratic equation into its standard form.
Step 1: Initially converting the equation to standard form. For the equation x² + 4x + 21 = 0, the equation was already in standard form, so no changes were necessary here. It’s possible that Nick incorrectly adjusted coefficients, which led to errors.Step 2: Factoring out terms. If Nick had an equation like -7x² + 17 = 0, he should have factored out -7 from both the x² term and the constant term, resulting in -7(x² - 17/7) = 0. Missing this step would lead to misrepresentation of the equation.Step 3: Ensuring equivalence. Nick should have subtracted -7(9) correctly to maintain the function's equivalence throughout the transformation.Step 4: Writing the perfect square trinomial correctly. To complete the square, for example, (x + 2)² should be correctly represented as a binomial squared. Not doing so indicates an error in the transformation process.In summary, Nick’s mistakes include incorrect standard form conversion, improper factoring of constant terms, failing to maintain equivalence, and incorrect representation of perfect square trinomials.
If a figure has 90° rotational symmetry, what other symmetries must it have?
Answer:
Step-by-step explanation:
The figure must also have the rotational symmetry of 180/270°.
What are symmetries in math?
In geometry, symmetry is defined as a balanced and proportionate similarity that is found in two halves of an object. It means one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
What are the four types of symmetries?Types of symmetries are rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry. These four types of symmetries are examples of different types of symmetry on a flat surface called planar symmetry.
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1. 4 and 4
Find the geometric mean between each pair of numbers
Answer:
2
Step-by-step explanation:
i think bc its on the middle but its ben a min since ive done it
Look at the attached screen shot. The population is 2 while the geometric mean is (Xg):4
need this done please :)
Answer:
y = 11x
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
= (11-0)/(1-0)
= 11/1
=11
We know the y intercept is 0 ( the y value where x is zero)
We can use the slope intercept form of the equation for a line
y = mx+b where m is the slope and b is the y intercept
y = 11x+0
y = 11x
Georgia participated in a sleep study in which scientists found that she fell into REM sleep exactly every 45 minutes while she
was asleep. If Georgia was asleep for 6 hours (390 minutes), how many periods of REM sleep did she have?
The number of periods of REM sleep Georgia has in the 6 hours (390 minutes) as stated in the question is 8.667 periods.
Using the standard time conversion, the number of periods is 8 hours.
How do we determine the number of periods Georgia falls into in REM sleep using word problems.To determine the number of periods of REM sleep that Georgia has, we need to divide the total number of minutes of sleep by the interval at which she falls into the REM sleep.
From the given information:
Georgia was asleep for = 390 minutesNumber of intervals she falls into REM = every 45 minutesThe number of periods of REM sleep she has in 390 minutes of sleep is:
= 390 minutes/ 45 minutes
= 8.667 periods.
NOTE: We have only 360 minutes in 6 hours since 60 minutes = 1 hour.
= 360 minutes/ 45 minutes = 8 periods.
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Consider this right triangle with given measures. A right triangle has a side length of 5 feet and hypotenuse of StartRoot 61 EndRoot feet. What is the length of the missing leg? 6 ft 7 ft StartRoot 51 EndRootft StartRoot 86 EndRootft
Answer:
6ft
Step-by-step explanation:
correct on Edge 2020 :-)
6 feet is the length of the missing leg of the right angles triangle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
A right triangle has a side length of 5 feet and hypotenuse of √61
We need to find the missing length which is x.
By pythagoras theorem we can find this.
√61²=5²+x²
61=25+x²
Substitute 25 from both sides
61-25=x²
36=x²
x=6
6 feet is the length of the missing leg
Hence, 6 feet is the length of the missing leg of the right angles triangle.
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Which are the solutions of the equation x^4 - 5x^2 - 36 = 0
Answer:
x = ± 3, x = ± 2i
Step-by-step explanation:
Given
[tex]x^{4}[/tex] - 5x² - 36 = 0
Use the substitution u = x² then the equation is
u² - 5u - 36 = 0 ← in standard form
(u - 9)(u + 4) = 0 ← in factored form
Equate each factor to zero and solve for u
u - 9 = 0 ⇒ u = 9
u + 4 = 0 ⇒ u = - 4
This indicates there will be 2 real roots and 2 complex roots
Change back to find values of x, that is
u = 9 ⇒ x² = 9 ⇒ x = ± [tex]\sqrt{9}[/tex] = ± 3 ← real roots
u = - 4 ⇒ x² = - 4 ⇒ x = ± [tex]\sqrt{-4}[/tex] = ± 2i ← imaginary roots
What is the average speed of a cheetah that runs 9 km in 10 minutes? Give your answer in km/hr. (Hint: 10 minutes is 1/6 of an hour.)
Answer:
54kph
Step-by-step explanation:
I don’t know how to do the work I just don’t understand
Answer:
1. is -5/7
2. is 6/-9 OR 1/-3 (negative one third)
3. is 2
Step-by-step explanation:
What is the answer? I’m not sure about this one
Answer: Choice A) 3n^2
A monomial has exactly one term. So the answer is between choices A and C based on this fact alone. We can rule out choice C as this has a coefficient of 2. Choice A has a coefficient of 3 and an exponent of 2 (so its degree 2). This is a quadratic monomial.
Find all real square roots of 100
Answer:
square root of 100 is 10
Step-by-step explanation:
The real roots of 100 are 10 and -10.
What are roots?The root of a number x is another number, which, when multiplied by itself a given number of times, equals x.
Roots of 100 = [tex]\sqrt{100}[/tex] = ± 10
Hence, The real roots of 100 are 10 and -10.
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Which is an equation of an asymptote of the hyperbola?
A) y=-3x+8
B) y=3X+10
C) y=-1/3x
D) y=1/3x+2
Answer:
it is 3x+10
Step-by-step explanation:
FOR EASY BRAINLIEST BRAINLIEST!! Do it With a drawn picture!
Answer:
Step-by-step explanation:
The scatter plot below shows the points scored and the points allowed by the bulldogs football teamwork several games . Which association (corrrlation) best describes the data?
Answer: I think it is positive association
Step-by-step explanation:
I am not that sure
Scott has a container of ping pong balls and golf balls. The number of ping pong balls in the container is 8 times as many as the number of golf balls in the container. If there are 10 golf balls in the container, how many ping pong balls are in the container?
a.88
b.80
c.2
d.18
Answer:
b)
Step-by-step explanation:
Number of ping pong balls = 8 * number of golf balls
= 8*10
= 80
HELP i need help with this!!!
Answer:
A=26.75
Step-by-step explanation:
A=1/2(2)(2)=2
A=1/2(5)(2)=5
A=1/2(2+2+5)(3.5)=15.75
A=2+5+15.75=26.75
GIVING BRAINLIEST ..Can somebody help me (explain your answer)
Answer:
13.04 units to the nearest hundredth.
Step-by-step explanation:
Use the Pythagoras theorem:
c^2 = a^2 + b^2 where a, b and c are the sides of a right triangle with c the hypotenuse.
In our triangle ( x = length of the hypotenuse):
x^2 = 13^2 + 1^2
x^2 = 169 + 1 = 170
x = √170
= 13.04.
If we are doing this mentally the best we can do is say that the hypotenuse is a small amount greater than 13.
Can someone answers this please
Answer:
y = - 24
Step-by-step explanation:
[tex]y = (x - 4)(x + 6) \\ plug \: x = 0 \\ y = (0 - 4)(0 + 6) \\ y = ( - 4)(6) \\ y = - 24 \\ \purple{ \bold{ \therefore \: y - intercept = - 24}}[/tex]
ABC bookstore sells packages of books that include both new and used books. New books cost $18 and used books cost $9. The bookstore wants to sell packages that have 36 books total, and the store charges $432 for each package. How many new and used books will each be in the package?
Answer:12 new, 24 used
Step-by-step explanation: i think this is right, sorry if not.
12 x 18= 216
9 x 24 = 216
216 + 216 = 432
what is the volume of a cylinder with a radius of 3 and a hight of 6?
Answer:
Around 169.65.
Step-by-step explanation:
The formula is (pi)r^2*h
(pi)3^2*6
(pi)9*6
54(pi)
169.65
-q/7>-1
Help plz Step-by-step
Answer:
q < 7
Step-by-step explanation:
Given:
[tex]\frac{-q}{7} > -1[/tex]
Required:
Find the value of q.
First, multiply both sides by 7
[tex]7 * \frac{-q}{7} > -1 * 7[/tex]
-q > -7
Then, multiply both sides by -1
q < 7
Note that the sign of the inequality changed.
When multiplying or dividing an inequality by a number less than 0 (in other words, a negative numbers), the sign of the inequality will change.
Hence, the solution to the expression above is
q < 7
Find the sum of the areas of a kite with diagonals of 28 and 32 inches and a rhombus with diagonals of 37 and 63 inches. Round answer to the nearest tenth of a square inch.
Answer:
total area = K + R = 448 + 1,165.5 = $1,613.5 sq. in.
Step-by-step explanation:
Use formulas for area of Kite and area of rhombus.
K = area of Kite
R = area of rhombus
K = (1/2) *(diagonal 1)*(diagonal 2)
R = (1/2)*(diagonal 1)*(diagonal 2)
K = (1/2)*(28 in.)*(32 in.) = 14 * 32 = 448 sq. in.
R = (1/2)*(37 in.)*(63 in.) = 1,165.5 sq. in.
total area = K + R = 448 + 1,165.5 = $1,613.5 sq. in.
The quadratic equation 4x2 + 45x + 24 = 0 was solved using the Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a.
One solution is −10.69. What is the other solution? Round to the hundredths place.
0.51
10.69
−1.12
−0.56
Answer:
The other solution is -0.56
Step-by-step explanation:
Quadratic equation :[tex]4x^2 + 45x + 24 = 0[/tex]
General quadratic equation : [tex]ax^2+bx+c=0[/tex]
Om comparing :
a=4
b = 45
c=24
Formula : [tex]x =\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values in the formula :
[tex]x=\frac{-45 \pm \sqrt{45^2-4(4)(24)}}{2(4)}\\x=\frac{-45 + \sqrt{45^2-4(4)(24)}}{2(4)},\frac{-45 - \sqrt{45^2-4(4)(24)}}{2(4)}\\x=-0.5613,-10.688[/tex]
So, One solution is −10.69.
So, Other solution is −0.56
Hence the other solution is -0.56
The second solution to this equation is −0.56.
Explanation:In the given quadratic equation 4x2 + 45x + 24 = 0, the quadratic formula is used to find the solutions, or roots, of the equation.
This formula is x = [-b ± sqrt(b² - 4ac)] / (2a).
For this specific equation, a is 4, b is 45, and c is 24.
Since it's already given that one root is -10.69, the other root should be obtained by substituting the values into the formula and choosing the alternative sign:
x = [-45 - sqrt(45² - 4*4*24)] / (2*4) this calculation would give −0.56, which is the other solution to the equation.
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Ataut telephone wire extends from the top of a 40-foot tall telephone pole to a stake in the
ground 9 feet away. A bug crawled from the stake in the ground up the wire to the top of the
telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake. How
far did the bug crawl?
feet
The bug crawl in total of 90 feet of distance .
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
According to question
Ataut telephone wire extends from the top of a 40-foot tall telephone pole to a stake in the ground 9 feet away
So, according to diagram
AB= 9 feet
AC = 40 feet
BC =[tex]\sqrt{AB^{2} +AC^{2} }[/tex](Pythagoras theorem)
BC = [tex]\sqrt{9^{2} +40^{2} }[/tex]
BC=[tex]\sqrt{81 + 1600 }[/tex]
BC = [tex]\sqrt{ 1681 }[/tex]
BC= 41 feet
As bug start from the stake in the ground up the wire to the top of the
telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake which means perimeter of right angle triangle.
Perimeter of triangle = AB + BC + AC
= 9 + 41 + 40
= 90 feet
Hence, the total distance travelled by bug is 90 feet .
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a penny is dropped from the top of the building and takes 9 seconds to fall to the ground. What is the height of the building D=distance T=Time
The height of the building is 9x.
What is Distance- time formula?Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance traveled divided by the time.
Given:
Time= 9s
Let the speed of penny be 'x'.
We know,
speed = distance / time
distance = speed* time
distance = x *9
distance = 9x.
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which statement is true?
Answer:
A
Step-by-step explanation:
line 1 is perpendicular to line 2 because of 90°.
line 2 is parallel to line 3 because of corresponding angles
Which term in this expression is a constant?
14x − 10 + 6y − x
A) 14x
B) 6y
C) x
D) 10
Answer:
B
Step-by-step explanation:
i jst did it
Please help me . Find the value of x
Answer:
89
Step-by-step explanation:
1
The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number?
Answer:
0.06 or 6%
Step-by-step explanation:
Both bags have the numbers 5, 6, 7, 8, 9 and 10. Thus, there are 6 similar number in both bags.
The probability of picking the number 5 in both bags is:
P(5)= 1/10 * 1/10= 1/ 100
It is the same probability of picking the number 6 or 7 or 8 or 9 or 10 in both bags.
P ( 6)= 1/100
P ( 7 ) = 1 /100
P (8)= 1 /100
P ( 9 ) = 1 /100
P ( 10 ) = 1 /100
Each time you click the "FLIP" button, the
computer will flip four coins at the same time. For
this experiment, "success" is a head.
Flip 1's number of successes:
Flip 2's number of successes:
Flip 3's number of successes:
Flip 4's number of successes:
DONE
Answer:
2
3
0
2
Step-by-step explanation:
Just did intro
Answer:
2
3
0
2
Step-by-step explanation:
just did it on edg
The equation of a circle is given below.
(x +1.6)2 + (y +9.8)2 = 26
What is its center?
What is its radius?
If necessary, round your answer to two decimal places.
units
As per the equation of the circle, the center of the circle is (-1.6, -9.8) units, and its radius is approximately 5.10 units.
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle, and r is the radius. By comparing the given equation with the standard form, we can easily identify the values of h, k, and r.
Comparing the given equation
=> (x + 1.6)² + (y + 9.8)² = 26
with the standard form, we find that h = -1.6 and k = -9.8.
These values represent the x-coordinate and y-coordinate of the center of the circle, respectively.
To find the radius, we need to take the square root of the constant term on the right side of the equation.
R² = 26
r = √26 ≈ 5.10 (rounded to two decimal places)
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