Answer:
[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
Step-by-step explanation:
Given: The quadratic equation [tex]-3x^2-2x+6=0[/tex]
We have to show the correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
The standard form of quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solution of quadratic equation using quadratic formula is given as [tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Consider the given quadratic equation [tex]-3x^2-2x+6=0[/tex]
Comparing with general quadratic equation, we have
a = -3 , b = -2 , c = 6
Substitute in quadratic formula, we get,
[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex]
Simplify, we have,
[tex]x_{1,2}=\frac{2\pm\sqrt{76} }{-6}[/tex]
Thus, [tex]x_{1}=\frac{2+\sqrt{76} }{-6}[/tex] and x_{2}=\frac{2-\sqrt{76} }{-6}
Simplify, we get,
[tex]x_1=-\frac{1+\sqrt{19}}{3},\:x_2=\frac{\sqrt{19}-1}{3}[/tex]
Thus, [tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
You can use the standard form of quadratic equation to find the correct substitution of the values a, b and c.
The correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]
What is the standard form of quadratic equations?The standard form of quadratic equations is [tex]ax^2 + bx + c = 0[/tex]
What are the solutions of standard quadratic equation?[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
From given equation [tex]0 = -3x^2 -2x + 6[/tex], we deduce that a = -3, b = -2 and c = 6.
Thus, substituting these values in the solutions' equation:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\ \\ x = \dfrac{2 \pm \sqrt{4 + 72}}{-6} = \dfrac{2\pm 2\sqrt{19}}{-6} = \dfrac{-1 \mp 2\sqrt{19}}{3}[/tex]
Thus, the correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]
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What is the approximate volume of a tree trunk is the trunk is 12 feet tall with a circumference of 4.5
An astronomer wishes to measure on a photograph the distance between the image of a certain star and three other star images nearby. If eight images are nearby, how many choices of the three stars does he have?
Answer: 56
Step-by-step explanation:
Given: An astronomer wishes to measure on a photograph the distance between the image of a certain star and three other star images nearby.
The total number of images nearby = 8
The number of images chosen by astronomer = 3
Then, the number of choices of the three stars without being in order is given by :-
[tex]^8C_3=\frac{8!}{3!(8-3)!}=\frac{8\times7\times6\times5!}{3!5!}=56[/tex]
Hence, he has 56 choices .
Describe the change that occurs to the coordinates of a vertex of a figure when it is reflected across the Y axis
The sign of the x-coordinate changes; the y-coordinate stays the same.
evaluate the expression a3 -b/c for a = 3, b = 2 and c = 4. write in simplest form
Final answer:
To evaluate the expression a³ - b/c for a = 3, b = 2, and c = 4, substitute the values and simplify to get 27 - 1/2, which equals 53/2 in simplest form.
Explanation:
To evaluate the expression a³ - b/c when a = 3, b = 2, and c = 4, you need to substitute these values into the expression and simplify.
Step 1: Substitute the given values. The expression becomes 3³ - 2/4.
Step 2: Calculate the power of 3. The expression is now 27 - 2/4.
Step 3: Simplify the fraction 2/4, which is equivalent to 1/2.
Step 4: The expression now reads 27 - 1/2.
Step 5: To subtract, convert 27 to a fraction which has the same denominator as 1/2. This gives us 54/2 - 1/2.
Step 6: Subtract the fractions which results in 53/2, which is the simplest form.
one number is 27 less than twice another. Their sum is 93. What are the numbers?
Andre and Sally are playing a number game. Andre tells Sally, "I'm thinking of a number between 1 and 20. If I take the number and add 5, and then subtract 3, I get 19." What number is Andre thinking of?
a pyramid with a square base of length 3cm and height 16cm
What is the smallest natural number n, greater than 1, for which (1×2×3× . . . ×n) + 01 is not prime?
The smallest natural number is 4 which is not prime.
What are Natural Numbers?Natural numbers are defined as which range from 1 to infinity and are the most fundamental sort of numbers. Commonly known as positive numbers or counting numbers, these numbers. Natural Numbers are represented by the symbol N.
What are Prime numbers?Prime numbers are defined as any number that is any integer with exactly two factors 1 and the number itself. is said to be a prime number.
Given that
⇒ (1×2×3× . . . ×n) + 1
We have to determine the smallest natural number n, greater than 1, for which (1×2×3× . . . ×n) + 1 is not prime.
Here we substitute the value of n = 4 in the given expression,
⇒ (1×2×3×4) + 1
⇒ (24) + 1
⇒ 25
Therefore, the smallest natural number is 4 which is not prime.
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Multiply. (7/5) (−5/4)
Which of these triangle pairs can be mapped to each other using a single reflection?
Answer:
The correct answer should be figure 1 which is also attached in the solution.
Step-by-step explanation:
Reflection of any object is the mirror image of the object about any line or plane. Reflection always shows a congruent figure but inverted.
In first figure, triangle EFG makes a mirror image as triangle FGL. Here, EG is equal to GL, EF is equal to FL and angle E is congruent to angle L.
So, the figure obtained is congruent and inverted. Thus, triangles can be mapped to each other in single reflection in this image.
Figure 2 shows two congruent triangles but the reflection is not a mirror image as it should be inverted.
Figure 3 shows two congruent triangles but here they are aligned in a similar manner and not inverted. So, it is incorrect.
Figure 4 has inverted and congruent triangles but the axis about which the image is taken doesn't match with them. While reflection, they will not overlap each other and hence, it is incorrect.
Therefore, the correct answer should be figure 1 which is also attached in the solution.
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Please help!!
Graph each pair of parametric equations.
x = 2t – 1
y = t^2 + 5, -4 ≤ t ≤ 4
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~
Sorry brainly kept of freezing on me...
Solving this is pretty simple, we plug in what t equals in both equations based upon our lovely given notice -4 ≤ t ≤ 4...
(My work will be attached below)
Now we will have to plot all the points we gathered onto our graph...
(The Graph will be attached below)
And there you are!
Answer:
B
Step-by-step explanation:
100% edge 2021
Which linear system of equations does the matrix represent?
I think it's B
based on the pattern of the drawings which conjecture is reasonable to make?
A. when a pair of parallel lines is intersected by a third line, the corresponding angles are complementary
B. when a pair of parallel lines is intersected by a third line, all of the angles formed are congruent.
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
D. when a pair of parallel lines is intersected by a third line, the corresponding angles are supplementary.
the 2 angles in each picture are the same - meaning they are congruent,
so the answer is:
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
Conjectures are simply opinions from a given information.
The conjecture that can be formed is: C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
From the three diagrams, we can see that:
[tex]\mathbf{30^o = 30^o}[/tex][tex]\mathbf{35^o = 35^o}[/tex][tex]\mathbf{50^o = 50^o}[/tex]From the figures above, we have the following observations
The angles are congruentThe angles are correspondingThe congruence of the angles is based on parallel lines, intersected by a third line (i.e. the transversal)Hence, the conjecture that can be formed is: option (c)
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33% of what number is 1.45
ivied 1.45 by 33%
33% = 0.33
1.45 / 0.33 = 4.3939 ( 39 repeats)
Cindy has 26 nickels. She is getting rolls of nickels from the bank. She has enough money to get up to 10 rolls of nickels and each roll contains 40 nickels. The bank will not give partial rolls. The function that models the number of nickels Cindy will have after leaving the bank is f(r)=40r+26, where r is the number of rolls of nickels she gets.
What is the practical domain of the function?
all real numbers
r>1
all integers from 1 to 10, inclusive
{66, 106, 146, 186, 226, 266, 306, 346, 386, 426}
We know that the domain is actually the number of rolls that she gets because it is the input variable in the equation f (r) = 40 r + 26. The number of rolls that she can get can never be a negative number nor a zero nor a decimal number. However she can only get up to 10 rolls. Therefore the answer is:
all integers from 1 to 10, inclusive
Answer:
all integers from 1 to 10 inclusive
Step-by-step explanation:
took the test and got it correct
A rectangular picture frame measures 83 cm by 42 cm What is the perimeter or distance around the picture frame in meters
Compare 7/8 with 14/16 using (<,>,=)
The required 7/8 is equal to 14/16, or we can write 7/8 = 14/16.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
To compare 7/8 and 14/16, we can first convert both fractions to a common denominator. The least common multiple of 8 and 16 is 16, so we can convert 7/8 to 14/16 by multiplying both the numerator and denominator of 7/8 by 2,
7/8 = (7 × 2) / (8 × 2) = 14/16
Now we can see that both fractions have the same denominator, so we can compare their numerators directly:
7/8 = 14/16
Therefore, 7/8 is equal to 14/16, or we can write 7/8 = 14/16.
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Find the domain of the following piecewise function.
[-4,3)
(-4,3]
[-4,6)
(-4,6]
Answer:
c
Step-by-step explanation:
Jenny earned a 77 on her most recent test. Jenny’s score is no less than 5 points greater than 4/5 of Terrance’s score. If t represents Terrance’s score, which inequality represents the situation?
Answer:
The situation is represented by the following inequality :
[tex]\bf 77\geq \frac{4}{5}\cdot t+ 5[/tex]
Step-by-step explanation:
Score earned by Jenny on her most recent test = 77
Let the Terrance's score is represented by t
[tex]\frac{4}{5}\text{ of the Terrance's score is = }\frac{4}{5}\cdot t[/tex]
If Terrance's score is 5 points greater then the points earned by Terrance's in the test is represented by :
[tex]\bf\frac{4}{5}\cdot t+ 5.......(1)[/tex]
Now, according to the given condition in the question , Jenny's score is not less than the score represented by (1)
⇒ Jenny's score is greater than equal to the score represented by (1)
Hence, The situation is represented by the following inequality :
[tex]\bf 77\geq \frac{4}{5}\cdot t+ 5[/tex]
Answer:
B
Step-by-step explanation:
What is the representation of the third element in an array called a?
What does a negative projected ending inventory value mean? scm?
Bryan is buying notebooks and pens at an office
supply store. Notebooks cost $3.59 each and pens
cost $1.49 each. Bryan spent a total of $13.
Let x represent the number of notebooks and let y
represent the number of pens.
Write an equation that represents this situation.
Haresh is writing a coordinate proof involving an isosceles triangle. Haresh places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis.
What coordinates should he assign to this third vertex of the isoceles triangle?
(2a, b)
(a/2, b/2)
(a/2, b)
(b, 2b)
Answer:- (a/2, b) is coordinates should he assign to the third vertex of the isosceles triangle.
Explanation:-
As the given triangle is isosceles then the median of the triangle divides it into two equal triangles such that the base of the new triangles becomes half of the original triangle[tex]=\frac{1}{2}a[/tex]
[where a is the base of the original isosceles triangle]
Since the median of the given triangle join the third vertex and the mid point of the base thus the x coordinate of the points remains same[tex]=\frac{1}{2}a[/tex] and from the graph it is clear that y coordinate of third point is b .
Thus the coordinates for the third vertex must be [tex](\frac{a}{2},b)[/tex].
A game show contestant must randomly select a door. one door doubles her money while the other three doors leave her bankrupt. what is the probability she selects the door that doubles her money
If a circle of radius 3 is made to roll along the x-axis, with the center above the x-axis, what is an equation for the path of the center of the circle?
According to the number line, what is the distance between points A and B?
6 units
7 units
12 units
14 units
Answer:
D)14 units
Step-by-step explanation:
Just counts how many numbers you get from point A to B. Its pretty simple.
Answer:
The answer is D. 14 units
from -2 add 2 so you can get to 0 which gives you the 12 left add twelve on top of the two you already added and you get 14 units.
Step-by-step explanation:
This year, a hardware store has a profit of -$6.0 million. This profit is 3/4 of last year's profit. What is last year's profit?
What is the y-intercept of y= -5/6x-7
You can get some great new space for $23/square foot per year. You will be leasing 3,200 square feet. What will your MONTHLY rent be? a) $139 b) $3,200
c) $6,133 d) $73,600
The calculation for the monthly rent involves firstly finding the annual rent by multiplying the cost per square foot per year with the total square footage, and then dividing this annual cost by 12 to get the monthly cost. The correct answer is c) $6,133.
Explanation:To calculate the monthly rent, we first need to find out the annual rent and then divide it by 12 months. The annual rent can be found by multiplying the cost per square foot per year with the total number of square feet. So if the cost is $23/square foot per year and you are leasing 3,200 square feet, the calculation becomes: $23 * 3,200 = $73,600 for the annual rent. To calculate the monthly rent, we divide the annual rent by 12: $73,600 / 12 = $6,133.33. Therefore the monthly rent is closest to option c) $6,133.
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Assume f(x) = g(x). Which of the following two functions may be used to represent the function 3x = x – 4? *
1 point
A) f(x) = 3x, g(x) = x – 4
B) f(x) = x – 7, g(x) = x – 4/3
C) f(x) = 3x, g(x) = 3x
D) f(x) = 7, g(x) = 3x
Since we know that the two functions are equal, f (x) = g (x), therefore when we equate the two equations the result should be similar to 3x = x – 4:
A. f(x) = 3x, g(x) = x – 4
Equating the two functions:
3x = x – 4 (correct)
So we now got our answer (A)