Answers
Answer:
a. y-intercept:(0, -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)
b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)
Step-by-step explanation:
a:
So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes [tex]y=(0)^2-0-6[/tex] which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]. In this case a=1, b=-1, c=-6. So plugging those values in you get [tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}[/tex], which simplifies to [tex]x=\frac{1\pm5}{2}[/tex]. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of [tex]y=(x-h)^2+k[/tex] where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be
Move c to the other side
[tex]y+6=x^2-x[/tex]
Complete the square by adding (b/2)^2
[tex]y+6+0.25 = x^2-x+0.25[/tex]
Rewrite as square binomial
[tex]y+6.25 = (x-0.5)^2[/tex]
Isolate y
[tex]y=(x-0.50)^2-6.25[/tex]
(h, k) = 0.50, -6.25 which is the vertex
b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation [tex]y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}[/tex]. which simplifies to [tex]x=\frac{-1\pm5}{-2}[/tex] which gives the values -2 and 3. To find the vertex it's the same process as before
Factor out -1
[tex]y=-(x^2-x-6)[/tex]
Add 6 to both sides (on the left side add -6 since -1 was factored out).
[tex]y-6=-(x^2-x)[/tex]
Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)
[tex]y-6-0.25 = -(x^2-x+0.25)[/tex]
Rewrite as square binomial
[tex]y-6.25=-(x-0.5)^2[/tex]
Add 6.25 to both sides
[tex]y=(x-0.50)^2+6.25[/tex]
(h, k) = (0.50, 6.25)
When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.
Answer:
a) y-intercept (0, -6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, -6.25)
b) y-intercept (0, 6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, 6.25)
Step-by-step explanation:
Related Questions
Question 1 of 20
The volume of a rectangular box is 5x(x+3)(2x - 1).
Height: 2x-1
Length: x + 3
Width: 5x
Which statement is true?
A. The volume is the product of the area of the base, 5x(x + 3), and
the height, 2x - 1.
B. The volume is the sum of the length, x + 3, the width, 5x, and the
height, 2x - 1.
C. The volume is the product of the length, x + 3, and the width, 5x.
D. The volume does not depend on the height, 2x - 1.
Answers
Answer:
A. The volume is the product of the area of the base, 5x(x + 3), and
the height, 2x - 1.
Step-by-step explanation:
Volume is defined as the product of the Length, Width, and Height,
V = L*W*H
The Length x Width is the Area of the Base
L*W = Area Base)
Therefore:
The (L*W) in the equation V = L*W*H can be replaced with [Area of the Base]
[Area of the Base]
[Area of the Base] = (5x)*(x+3) [(or 5x^2 + 15x)]
Volume = [Area of the Base]*H
Volume = [(5x)*(x+3)]*(2x-1)
The volume is the product of the area of the base, 5x(x + 3), and
the height, 2x - 1.
That looks a lot like the answer in A: "The volume is the product of the area of the base, 5x(x + 3), and the height, 2x - 1."
need help with this question , pls help
Answers
Answer:
A = 80g B = 200g
Step-by-step explanation for A:
First, you would find what the serving size is divided by to get the number of people needed to feed 6/3 = 2. Then take that number (3) and divided it by the fish (240g) to get 240/3 = 80.
Step-by-step explanation for B:
You will first need to find how much butter goes into ONE pie by dividing 80 by 6 which is 1.33333333333333. Then do 1.333333333333333 times the number of people to feed (15) to get 200.
At which point in the business cycle would the unemployment rate begin to increase? 1 2 3 4
Answers
Answer:
2 & 3
Step-by-step explanation:
2. High Interest Rates
High-interest rates make it more difficult for businesses to invest. For instance, a small store that is just starting is going to find it hard to make repayments at an interest rate of 20 or 30 percent. It also sucks out money from the economy and re-directs it to the banks. As the interest rates are so high, businesses and consumers reduce their demand for credit. In turn, there is a contraction in the money supply which can lead to deflation.
The effects of high interest rates can be dire if not managed correctly and subtly by central banks. If the interest rates are increased too fast, too high, and too rapidly, we will see the aforementioned effects such as lower business investment and deflation. Therefore, it can contribute to a transition towards an economic contraction in the business cycle.
3. Declining Real Incomes
Inflation can create a drain on consumer incomes as it decreases its value year on year. Therefore, if firms do not increase wages in line with inflation, the average worker will be able to afford less than before.
If real incomes decline, it means consumers have less income to spend on goods and services in the economy. In turn, a prolonged period of decline in real incomes can contribute to an economic contraction in the business cycle.
Answer
is 3 just did it on edge
Step-by-step explanation:
A man walks 4km from point x due east of point Y. The bearing of a flag point x and y are due N80°W and N40°E respectively. Find the distance of the flag pole from point y
Answers
The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sine rule shows the relationship between the sides and angles of a triangle.
The triangle formed has angles A = 10°, B = 50°, C = 120°, c = 4 km, a = distance from point y.
Hence:
a / sinA = c / sinC
a / sin(10) = 4 / sin(120)
a = 0.8 km
The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E
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The starting salary for a particular job is 1.2 million per annum. The salary increases each year by 75000 to a maximum of 1.5million. In which year is the maximum salary reached...... How much money would the person earn in that time
Answers
The maximum salary reached in 5th month.
What is Arithmetic Progression?
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant
For the first year, salary = 1,200,000
For the second year, salary
= 1,200,000 + 75,000 = 1,275,000
For the last year, salary = 1,500,000
We get the AP as
1,200,000, 1,275,000, .... , 1,500,000
a= 1,200,000 and d = 75000
Now using
L = a + (n - 1)d
1,500,000 = 1,200,000 + (n-1) 75,000
300,000 = 75,000(n-1)
300000/75000= n-1
4= n-1
n= 5
Hence, in the 5th year the maximum salary will be reached.
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What is the y-value in the solution to this system of linear equations?
4x + 5y = -12
-2x + 3y = -16
O-4
O-2
O2
O 5
Answers
Step-by-step explanation:
please mark me as brainlest and follow me
In the following situation, determine whether you are asked to determine the number of permutations or combinations. Then do the calculation.
How many ways are there to distribute 8 different books among 21 children if no child gets more than one book?
a.) Combination; Subscript 13 Baseline C Subscript 8 Baseline = 1287
b.) Combination; Subscript 21 Baseline C Subscript 8 Baseline = 203,490
c.) Permutation; Subscript 21 Baseline P Subscript 8 Baseline = 8,204,716,800
d.) Permutation; Subscript 13 Baseline P Subscript 8 Baseline = 51,891,840
Answers
Using the permutation formula, it is found that the number of ways to distribute the books is given by:
c. 8,204,716,800
The order is important, as the books are different, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 8 books are distributed among 21 children, hence the number of ways is given by:
[tex]P_{21,8} = \frac{21!}{13!} = 8,204,716,800[/tex]
Which means that option c is correct.
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PLS HELP ME I WIL MARK BRAINLEST
Answers
Answer: 2. X=-4
A 4-digit combination lock can be opened only if a correct combination of digits from 0-9 is chosen. Find the probability of guessing the correct combination if: none of the digits are repeated, any of the digits can be repeated, any of the digits can be repeated but the 3 and 8 are not in the combination.
Answers
The probabilities are as follows:-
if none of the digits is repeated 0.504If any of the digits can be repeated 1If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability will be calculated as follows:-
Total combinations are = 10⁴ = 10000
A) if none of the digits are repeated:-The combinations will be 10 x 9 x 8 x 7 = 5040
Probability = 5040 / 10000
Probaility = 0.504
B) If any of the digits can be repeated:- The combinations will be 10 x 10 x 10 x 10 = 10000
Probabilityy = 10000 / 10000 = 1
C )If any of the digits can be repeated but the 3 and 8 are not in the combination the combinations will be 7 x 7 x 7 x 7 = 2401
Probability = 2401 / 10000 = 0.24
Therefore if none of the digits is repeated 0.50.If any of the digits can be repeated 1.If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.
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PLS HELP ME OUT THANK YOU I’m studying for my mid-term!!
Answers
Answer:
∠ ABD = 20°
Step-by-step explanation:
since BD bisects ∠ ABC , then
∠ ABD = ∠ CBD ( substitute values )
3x - 1 = 34 - 2x ( add 2x to both sides )
5x - 1 = 34 ( add 1 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Then
∠ ABD = 3x - 1 = 3(7) - 1 = 21 - 1 = 20°
What is the completely factored form of this polynomial? 2x5 + 12x3 − 54x
Answers
Answer:
2x(x^2 - 3)(x^2 + 9)
Step-by-step explanation:
2x^5 + 12x^3 − 54x
2x(x^4 + 6x - 27)
Since -3 + 9 = 6 and -3 x 9 = -27:
2x(x^2 - 3)(x^2 + 9)
Answer:
[tex]2x(x^2-3)(x^2+9)[/tex]
Step-by-step explanation:
Given polynomial:
[tex]2x^5+12x^3-54x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies 2x(x^4+6x^2-27)[/tex]
To factor the trinomial [tex]x^4+6x^2-27[/tex]:
[tex]\textsf{Let }u=x^2 \implies u^2+6u-27[/tex]
Factor the quadratic by finding two numbers that multiply to -27 and sum to 6: 9 and -3
Rewrite the middle term as the sum of these two numbers:
[tex]\implies u^2+9u-3u-27[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+9)-3(u+9)[/tex]
Factor out the common term (u + 9):
[tex]\implies (u-3)(u+9)[/tex]
Substitute back [tex]u=x^2[/tex]:
[tex]\implies (x^2-3)(x^2+9)[/tex]
Therefore, the factored form of the given polynomial is:
[tex]\implies 2x(x^2-3)(x^2+9)[/tex]
Which rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C'?
Answers
The rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).
What is translation?When a line is translated, it means the line is moved from one position to another. The coordinate for triangle ABC are A(-3 ,4) , B(-4,1) and C(-2,1).
The coordinate of triangle A'B'C' is A'(4,-2), B'(3,-5), and C'(5,-5).
From above, it can be seen that the image A'B'C' is obtained from the pre-image ABC by translating the vertices of the image by 7 units to the right and 6 units down.
Therefore, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6)
Hence, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).
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What is the approximate area of the circle shown below?
60 cm C
A. 11,310 cm²
B. 94 cm²
C. 2827 cm²
D. 188 cm²
Answers
Parent Functions
Question 4 of 10
On a piece of paper, graph:
{1 if -1 < x≤0
f(x) = {2 if 0 < x≤1
{3 if 1 < x≤2
Then determine which answer choice matches the graph you drew.
Answers
The graph of the parent function is given below;
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given function is;
1, if -1<x≤0
f(x) = 2, if 0<x≤1
3, if 1<x≤2
Now, the graph of given function is given below.
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Answer:
The correct graph is in the image below
Step-by-step explanation:
-5
-3-2
5
4
3
2
4
-2
بله با
-3
-4
-5
y
1 2 3 4
5
x
The distance between the two points pictured is d =
Use the distance formula to find n.
d = √(x2-x₁)² + (V₂-V₁)²
n =
Answers
Answer:
n = 61
Step-by-step explanation:
The subscripted values of x and y in the formula refer to the coordinates of the points:
[tex](x_1,y_1)=(-3,-2)\qquad(x_2,y_2)=(2,4)[/tex]
Substitute the given values and do the arithmetic.
__
Using these values in the formula gives ...
[tex]d=\sqrt{n}=\sqrt{(2-(-3))^2+(4-(-2))^2}=\sqrt{5^2+6^2}=\sqrt{25+36}\\\\d=\sqrt{n}=\sqrt{61}\\\\\boxed{n=61}[/tex]
Distance
√(2+3)²+(4+2)²√5²+6²√25+36√61√n=√61
n=61
Someone please help with this ::
Answers
Answer:
pi/6
Step-by-step explanation:
honestly just do it in a calculator that is set to radians.
If 1-cosA = 1/2 , Then find the value of sinA.
Answers
Step-by-step explanation:
Given :
1- cosA = 1/2
or, CosA = 1 -1/2
Therefore ; CosA = 1/2 = b/h
According to the Pythagoras theorem,
P = root under h^2 - b^2
= root under (2)^2 - (1)^2
= root under 4 -1
= root 3
Again,
SinA = P/h
= root 3 / 2
find the odds against rolling a number larger than 1 on a die
Answers
Answer:
.833 (83.3%)
Step-by-step explanation:
There are 6 numbers on a normal die. 5 of them are larger than 1. The odds would be 5/6
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
800 grams =
pounds
700 grams =
pounds
Answers
The weight of the full steel bead tire in pounds is 1.76 pounds
The weight of the lighter steel bead tire in pounds is 1.54 pounds.
What are the weights of the tires?Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷.
The weight of the full steel bead tire in pounds = 800 / 453.592 = 1.76
The weight of the lighter steel bead tire in pounds = 700 / 453.592 = 1.54
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Clare has a recipe for yellow cake. She uses 9 1/3 cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c cakes using f cups for flour.
Which of these equations represent the relationship between c and f ?
A. c = 7/3f
B. c = 3/16f
C. c = 16/3f
D. c = 3/7f
Answers
The correct answer is option A which is the equations which represent relationship between c and f is c = 7 / 3f.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division
Given that:-
Clare has a recipe for yellow cake. She uses 9 1/3 cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c cakes using f cups for flour.From the given data we can see that the amount of flour required is [tex]9\dfrac{1}{3}\[/tex] Cups or [tex]\dfrac{28}{3}[/tex] Cups for making 4 cakes.
So the expression will be written as:-
[tex]9\dfrac{1}{3}f = 4c[/tex]
[tex]\dfrac{28}{3\\}f = 4c[/tex]
[tex]c = \dfrac{28}{3\times 4}f[/tex]
c = [tex]\dfrac{7}{3}[/tex]f
Therefore the correct answer is option A which is the equation that represents the relationship between c and f is c = 7 / 3f.
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A university conducted a survey of 383 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. If a survey participant is selected at random, what is the probability that he or she is satisfied or a junior? *Round to 3 decimal places* ( I only need part d.)
Answers
Answer:
62/235 +95/383
Step-by-step explanation:
P(satisfied or junior)= P(satisfied participant that are junior) + P(junior participant)
P(satisfied or junior)= 62/235 + 95/383
P(satisfied or junior)= 46071/90005
tony invest 2000 at a 4.5 percent rate.
Answers
Answer:
$2,999
Step-by-step explanation:
A = P(1 + r) ^ tA = 2000(1 + .045) ^ 9A ≈ 2999PLEASE HELP ( look at ss to answer )
Answers
The direct proportion is shown by table (B)
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.
Here the second table shows the direct proportion relation.
This is because the ratio of x/y remain same.
4/2= 7/3.5= 10/5= 11/5.5= 15/7.5 = 2/1
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what choices are solutions to equation below x^-7x=-24/4
check all that apply
a. x=2
b. x=6
c. x=1
d. x=12
Answers
x^-7x+6=0
(x-6)(x-1)=0
x=6 or x=1
What division problem does this area model represent?
Enter your answer in the boxes.
÷ 75 =
R
Rectangle with left side labeled 75. Vertical lines divide the rectangle into three parts. The left part has 40 above it and 3000 inside it. The middle part has 4 above it and 300 inside it. The right part has 53 inside it and nothing above it.
Answers
The division problem that's illustrated based on the information is 3000/75 = 40 without remainder.
How to calculate the rectangle?
A rectangle is defined as a two-dimensional shape having four-sided and opposite sides equal and parallel.
From the information, it was stated that the rectangle with left side labelled 75 and the middle part has 4 above it and 300 inside it.
Therefore, the division problem that's illustrated based on the information is 3000/75 = 40 without remainder.
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Please Help!!!!!
Write the equation of a parabola with focus (-1, 3) and directrix x = -5. Also include a sketch of the parabola. Show all your work.
Answers
Answer:
Equation of parabola is (x+1)²=20(y-3)
Step-by-step explanation:
And the graph above
(x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given, focus : (-1, 3)
directrix : x + 5 = 0 or x=-5
Let (x ,y) is the point on the parabola .
∴ distance of point from focus = distance of point from directrix
√(x+1)²+(y-3)²=|x+5|
Let (x ,y) is the point on the parabola .
∴ distance of point from focus = distance of point from directrix
√(x+1)²+(y-3)²=|x+5|
squaring both sides,
(x+1)²+(y-3)²=(x+5)²
(x+1)²=20(y-3)
Hence, (x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.
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Point-Slope Form
*See photo*
Answers
Answer:
y = 3x - 5
Step-by-step explanation:
We know that the equation 'y = 3x + ?' intersects the point (1, -2). This means that when x = 1, y = -2 in out equation above. To solve this just plug in the x and y values to get '?'.
[tex]y = 3x + ?\\-2 = 3(1) + ?\\-5 = ?[/tex]
Now that we know '?' is -5, we write it back into slope intercept form, so our final answer is y = 3x - 5
-5/7 x 1/5
please help
Answers
-5/7 x 1/5
-5 x 1 = -5
7 x 5 = 35
-5/35 = -1/7
Happy to help :P
What’s the answer? I don’t know how I got it wrong
Answers
Answer:
C. Line PQ
Step-by-step explanation:
Tangent means touching, not crossing.
Use the law of cosines round to the nearest tenths
Answers
Answer:
x = 11.5
Step-by-step explanation:
Formula
a^2 = b^2 + c^2 - 2*b*c * cos(A) Substitute givens in formula
Givens
b = 31c = 26A = 21oa = x Let a = x to present the formula in it's most normal waySolution
a^2 = 31^2 + 26^2 - 2 * 31 * 26 * cos(21) Find -2*31*26*cos(21)
a^2 = 961 + 676 -1504.93 Combine
a^2 = 1637 -1504.93 Combine again
a^2 = 132.07 Take the √ on both sides
√a^2 = √132.07
a = 11.5 Rounded.
Answer
x = 11.5