Answers
Answer:
-4
+3
12
-0.5, 12.25
x = -0.5
Step-by-step explanation:
The x intercepts are the values of x when y = 0 ie the roots of the equation
[tex]-x^2 -x +12 = 0[/tex]
or
[tex]x^2 + x - 12 = 0[/tex]
We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3
y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12
Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x
Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5
Plugging this value of x into the original function gives the vertex y value
[tex]y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25[/tex]
The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5
The graph of the quadratic function shows these values
Related Questions
On a coordinate plane, the x-axis is labeled minutes and the y-axis is labeled Blocks. Line A goes through points (10, 4), (15, 12), and (20, 20). Line B goes through points (5, 8), (10, 16), (15, 24). Line C goes through points (5, 24), (15, 16), (20, 12).
The table shows Jose’s rate of bicycle riding.
A 2-column table with 3 rows. Column 1 is labeled Minutes with entries 5, 10, 15. Column 2 is labeled Blocks with entries 8, 16, 24.
Which line on the graph shows the proportional relationship in the table?
Line
on the graph shows the proportional relationship.
Answers
Answer:
wait lang yong tppp heheehhehe
Answer:
b is the awancer yw
Step-by-step explanation:
Select all the functions that show an inverse variation...
a) y=6x
b) y=3/x
c) y=1/3x
d) y= -.07x
e) y= 2/x+4
f) xy=-3
Answers
Function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we know, when x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.
a) y=6x
The above function is a linear function
b) y=3/x
or
xy = 3
The above function shows an inverse variation.
c) y=1/3x
or
y = (1/3)x
The above function is a linear function
d) y= -.07x
The above function is a linear function
e) y= 2/x+4
or
y = (2+4x)/x
xy = 2 + 4x
The above function shows an inverse variation.
f) xy=-3
The above function shows an inverse variation.
Thus, function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.
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f(z)=(1/3)
h(z) = z+4/z-2
evaluate (h•f)(0)
Answers
The value of the composite function (h•f)(0) is -2/3
How to solve the composite function?The functions are given as:
f(z)=(1/3)
h(z) = z+4/z-2
Start by calculating f(0) and h(0)
f(0) = 1/3
h(0) = (0+4)/(0-2)
h(0) = -2
The composite function is then calculated as:
(h•f)(0) = h(0) * f(0)
This gives
(h•f)(0) = -2 * 1/3
Evaluate
(h•f)(0) = -2/3
Hence, the value of the composite function (h•f)(0) is -2/3
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Find the x-intercept(s) and the coordinates of the vertex for the parabola y= x^2 -8x + 12. if there is more than one x-intercept, separate them with commas.
Answers
Answer:
(i) x-intercepts: (2, 0), (6, 0)
(ii) vertex : (4, -4)
Explanation:
y = x² - 8x + 12
To find x intercepts, [set y = 0]
x² - 8x + 12 = 0x² - 2x - 6x + 12 = 0x(x - 2) - 6(x - 2) = 0(x - 6)(x - 2) = 0x = 6, x = 2x-intercepts: (2, 0), (6, 0)
To find vertex:
x = -b/2a
= -(-8)/2(1)
= 4
y = x² - 8x + 12
= 4² - 8(4) + 12
= -4
Vertex : (4, -4)
Solve the equation for y=0
x²-8x+12=0x²-6x-2x+12=0x(x-6)-2(x-6)=0(x-2)(x-6)=0x=2,6X inetercepts (2,0) and (6,0)
Vertex :-
x coordinate
-b/2a8/24Y coordinate
4²-8(4)+12-4Verted at (4,-4)
please help in this as well thank !!
Answers
Step-by-step explanation:
4a.
the circumference of a circle is
2×pi×r
we know, r = 6 cm.
so the whole circumference is
2×pi×6 = 12×pi = 37.69911184... cm
4b.
the arc BC is the part of the full circumference that corresponds to 120° out of the 360° of a full circle.
the arc BC is then
12×pi × 120/360 = 12×p × 1/3 = 4×pi = 12.56637061... cm
the perimeter of the shaded area (pie slice) is the arc BC plus 2 radius lengths (from the arc points to the center of the circle)
12.56637061... + 2×6 = 12.56637061... + 12 =
= 24.56637061... cm
4c.
the area of a circle is
pi×r²
in our case
pi×6² = 36pi = 113.0973355... cm²
the area of the shaded area (pie slice) is the 120° part of the full 360° circle area :
36pi × 120/360 = 36pi × 1/3 = 12pi = 37.69911184... cm²
Which of the binomials below is a factor of this trinomial? x2+12x+31
A. x+4 B.x-2 C. x+2 D. x-4
Answers
(x+4) is a factor of this trinomial given , Option A is the right answer.
What is a Factor ?A factor is a number o expression that completely divides the number or the expression and the remainder is equal to zero.
The given trinomial is
x² +12x+32
x² + 8x +4x +32
x(x+8)+4 (x+8)
(x+8)(x+4)
From the given option Option A (x+4) is the right answer.
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Complete the hypothesis about the product of two rational numbers. Select the correct answer from each drop-down menu. The product of two rational numbers is number because multiplying equivalent to the ratio of which is number.
Answers
Answer: I hope this helps you in what you're doing.
Step-by-step explanation: Because multiplying two rational numbers results in the ratio of two integers, which is also a rational number, the product of two rational numbers is also a rational number.
Find the value of x
Find the value of y
Answers
Answer:
x = 9
y = 61
Step-by-step explanation:
let me know if you want an explanation!
What is the simple interest that is missing from the table? Use the formula mc012-1.jp
$375
r
2.2%
t
3 years
$25.00
$24.75
$2,475.75
$2,500.00
Answers
The simple interest is $24.75.
What is the simple interest?The simple interest that is paid on an amount of money is a function of the amount deposited, time and interest rate.
Simple interest = amount deposited x time x interest rate
$375 x 0.022 x 3 = $24.75
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A food production company is choosing between two suppliers of grain. Supplier A sells grain for $5.25 per bushel plus a
delivery fee of $3 per bushel. Supplier B sells B the grain for $6.50 per bushel plus a flat delivery fee of $1,500 each week.
Which supplier would cost more if the production company bought 500 bushels of grain each week?
O Supplier B would cost $625 more than supplier A.
© Supplier B would cost $600 more than supplier A
O Supplier A would cost $875 more than supplier B.
© Supplier A would cost $800 more than supplier B.
Answers
Subtraction is a mathematical operation that reflects the removal of things from a collection. Supplier B would cost $625 more than supplier A. Thus, the correct option is A.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The cost of 500 bushels from supplier A will be,
Cost = ($5.25 × 500) + ($3 × 500)
= $4,125
The cost 500 bushes from supplier B will be,
Cost = $1,500 + ($6.250×500)
= $4,750
Now, the difference between the two suppliers' costs for 500 bushels will be,
Difference = $4,625 - $4,125 = $500
Hence, Supplier B would cost $625 more than supplier A. Thus, the correct option is A.
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What is the quotient of the synthetic division problem below, written in
polynomial form?
3 -2 15
-22
-16
A.2xd 121xr 41
B=
2,219x15
C. 2y 1 9g
40
D
2y7 - 21x 40
Answers
The quotient of the synthetic division problem is "f(x) = -2x² + 9x + 5" (Option C).
What is Synthetic Division?
When a polynomial division is executed using the shorthand method, using a linear factor, one is said to have executed a Synthetic Division.
The synthetic division translates to
- 2 15 -22 -15
3 | -6 27 15
-2 9 5 0
Citing the coefficient of the quotient of the first three numbers:
- 2, 9, 5. The last number is given as the remainder.
Hence the remainder is zero.
Given that the coefficient of the quotient are three, the interpretation is that the polynomial greatest degree is 2.
Thus,
f(x) = -2x² + 9x + 5
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Which of the following have exactly 1 solution?
Choose all answers that apply.
A. -5x + 12 = -12x - 12
B.-5x+12=-5x-12
C. −5x+12=5x+12
D. −5x+12=5x−5
Answers
The equations;
-5x + 12 = -12x - 125x+12=-5x-12−5x+12=5x+12−5x+12=5x−5 all have exactly 1 solution.What is a linear solution?A linear equation is one in which there is only one solution. In a linear solution, the highest power of x is 1.
If we look at the equations listed, we will discover that they are all linear equations, as such;
-5x + 12 = -12x - 125x+12=-5x-12−5x+12=5x+12−5x+12=5x−5Will all have exactly 1 solution.
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students were asked to chose their favorite season if 1/9 of the students chose spring and 3/9 chose summer what fraction chose either spring or summer
Answers
Answer:
4/9 of the students chose summer.
Step-by-step explanation:
Think about it this way. There are 9 students being asked what their favorite season is. 1 chose spring, 3 chose summer. Add those together, and you have 4 people that chose either spring or summer. That number goes on top of the fraction. The total amount of people that were asked goes on the bottom, which is 9.
What is the value of K ?
Answers
Answer:
the answer is A K= -2.5
Step-by-step explanation:
i did the problem
Which quadratic inequality does the graph below represent?
Answers
The quadratic inequality represented by the graph is:
y ≤ 2x² - 8x + 3
Which quadratic inequality does the graph below represent?
First, we can see that the shaded region is below the parabola, and the line of the parabola is solid, which means that the points on the parabola are solutions, then the inequality is:
y ≤ quadratic equation.
Now we need to get the quadratic equation.
Now, if you look at the y-intercept, you can see that it happens at y = 3. Then the constant term of the quadratic equation is 3.
The only one that has that (and the ≤ symbol) y-intercept is the first option:
y ≤ 2x² - 8x + 3
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Given the equation y = x – 2, you substitute 5 for x. Check all true statements below.
Answers
The correct value of the given function at x = 5 is y =3.
What is Equation?An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.
Here, the given equation :
y = x - 2
put x = 5 in the given equation, we get
y = 5 - 2
y = 3
Thus, the correct value of the given function at x = 5 is y =3.
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Kate used 555 grams of wool to knit a sweater, hat, and scarf. She used 5 times less grams for the hat than for the sweater. She used 5 more grams for the hat than for the scarf. How many grams of wool did she use to knit for each?
(Give explanation)
Answers
Answer:
Sweater: 392 [tex]\frac{6}{7}[/tex]
Hat: 78[tex]\frac{4}{7}[/tex]
Scarf: 83[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
Set the sweater = x
The hat = [tex]\frac{1}{5}[/tex] x
The scarf = [tex]\frac{1}{5}[/tex] x + 5
x + [tex]\frac{1}{5}[/tex] x + [tex]\frac{1}{5}[/tex] x + 5 = 555
Combine like terms
1[tex]\frac{2}{5}[/tex] x + 5 = 555
Subtract 5 from both sides
1[tex]\frac{2}{5}[/tex] x = 550
Divide by 1[tex]\frac{2}{5}[/tex]
x = 392 [tex]\frac{6}{7}[/tex] This is how much wool was used for the sweater.
Divide by 5 to get the hat = 78 [tex]\frac{4}{7}[/tex]
Add 5 to that to get the scarf: 83[tex]\frac{4}{7}[/tex]
brainlist kopo yung nag answer ng tama
I. Answer each question. Write the letter of the correct answer in your paper.
Read and analyze the following problems carefully. Then, write your answer on a separate sheet of paper.
_____1. In a given circle, the radius is 9 cm. What is its diameter?
A. 18 m
B.18 cm
C. 4.5 m
D. 4.5 cm
_____2. Which of the following is the formula in solving for the area of a circle?
A. A= 2πr
B. A= πr2
C. A= πd
D. A=2 πr2
_____3. The diameter of a circle is8 cm, what is its area?
A.50.24 cm2
B.200.96 cm2
C.25.12 cm2
D.100.48 cm2
_____4. What is the radius of a circle if the area is 36m2?
A. 0.339 m
B. 3.39 m
C. 33.9 m
D. 339m
_____5. What is the area of a circle if the radius is 5m?
A. 15. 7 m2
B. 31.4 m2
C. 78.5 m2
D. 157 m2
Answers
1) B) 18 cm
Radius (r) = 9 cm
Diameter (d) = 2r = 9 * 2 = 18 cm
2) B) A = πr^2
3) A) 50.24 cm^2
Diameter (d) = 8 cm
Radius (r) = d/2 = 8/2 = 4 cm
Area (A) = πr^2
Therefore,
= πr^2
= 3.14 * 4 * 4
= 3.14 * 16
=> 50.24
Area (A) = 50.24 cm^2
4) B) 3.39 m
Area (A) = πr^2 = 36 m^2
Therefore,
πr^2 = 36
3.14 * (r^2) = 36
r^2 = 36/3.14
r^2 = 3600/314
r^2 = 11.46
r = √11.46
=> r = 3.39
Radius (r) = 3.39 m
5) C) 78.5 m^2
Radius (r) = 5 m
Area (A) = πr^2
Therefore,
= πr^2
= 3.14 * 5 * 5
= 3.14 * 25
=> 78.5
Area (A) = 78.5 m^2
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answers
Answer:
The ordered pair which makes both the inequalities true is = (–2, 2)
Step-by-step explanation:
inequalities are the relationships between two expressions which are not equal to one another.
Inequalities are represented by the following relations:
≤: "less than or equal to"<: "less than"≠: "not equal to">: "greater than"≥: "greater than or equal to"an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
so, the option B(-2,2) satisfies the inequalities expressions given in the question
therefore we can conclude that (-2,2) is the ordered pair which ,makes both the given inequalities true.
so the correct answer is (-2,2)
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Which best describes the orthocenter of a triangle?
O A The point where the three altitudes of the triangle intersect
O B. The point where the three angle bisectors of the triangle intersect
• C. The point where the perpendicular bisectors of the three sides of
the triangle intersect
O D The point where the three medians of the triangle intersect
Answers
Answer:
its A
Step-by-step explanation:
Its a because its A =)
Let x be normal distribution with mean 70 and standard deviation 2. given the following probability, p (x < a) = 0.9147, find the value a.
Answers
The value of a is 72.74.
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that
The mean [tex]\rm \mu[/tex] of the distribution is 70
Standard deviation [tex]\rm \sigma[/tex] is 2
p( x<a) = 0.9147
a = ?
From Z table
For p ( p < 0.9147) , z = 1.37
[tex]\rm Z = \dfrac { X - \mu}{ \sigma}[/tex]
[tex]\rm \rm 1.37 = \dfrac { a - 70}{ 2}[/tex]
a = 70+ 2*1.37
a = 72.74
Therefore the value of a is 72.74.
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A running relay team ran a 400 meter race in a record-setting time of 36 seconds. What was their average speed to the nearest tenth of a meter per second?
Answers
speed = distance/time
time = distance / speed
400m/36s = 11 1/9 m per second
What is the chance of landing on $500 and then Lose A Turn?
Answers
Answer:
B = an event that in the second turn it will land on Lose a Turn. Based from the given wheel, there are 24 equal parts with three $500 and one Lose a Turn. Thus, the probability of landing on $500 then lose a turn is 1921 .
this is possible IF thewheele consists of 24 parts
The chance of landing on $500 and then Lose A Turn will be 1/192. Then the correct option is C.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
The diagram is given below.
The total number of the events will be
Total events = 24
Then the chance of landing on $500 will be
The number of favorable events will be
Favorable events = 3
⇒ 3/24
⇒ 1/8
Then the chance of the Lose A Turn will be
Favorable event = 1
⇒ 1/24
The chance of landing on $500 and then Lose A Turn will be
P = (1/24)(1/8)
P = 1/192
The chance of landing on $500 and then Lose A Turn will be 1/192.
Then the correct option is C.
The question was incomplete, but the complete question is attached below.
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if pound of cheese costs $3.43, what is the cost per pound?
PLS HELP
Answers
Answer:
can you rephrase it? how many pounds are there?
Step-by-step explanation:
1. Choose the description that matches the inequality. x < 1
A line traveling to the left with an closed dot on x=1.
A line traveling to the right with an open dot on x=1.
A line traveling to the right with an closed dot on x=1.
A line traveling to the left with an open dot on x=1.
Answers
Answer:
A line traveling to the left with an open dot on x=1.
Explanation:
The inequality x < 1 basically means "less than 1." On number lines, the further left you go, the smaller the number becomes, and the further right you go, the larger the number becomes. So we know that because it's less or smaller than 1, then the line will be to the left. On the other hand, the inequality does not have a line under it to indicate a "less than or equal to 1," just "less than." Therefore, the dot is open. If there were a line under the inequality, then it would indicate "less than or equal to 1" and the dot would be closed.
given triangle PQR with QR = 8, PQ = 6, and m p = 90 degrees, which of the following choices is used to determine m r
Answers
The value of the angle R in the right triangle PQR is sin⁻¹ 6 / 8
The situation forms a right angle triangle.
How to find an angle in a right triangle?The angle R can be found as follows:
using trigonometric ratios,
sin R = opposite / hypotenuse
Therefore,
opposite sides = 6
hypotenuse = 8
sin R = 6 / 8
R = sin⁻¹ 6 / 8
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One number is 6 more than twice the other number. If the sum of the two numbers is 21, find the two numbers
Answers
Answer:
One number, let's call it x, is 6 more than twice the other number, let's say this number is y.
x= 2y+6
x+y=21
We're left with a system of equations.
If we substitute the first equation in the second we find the value of y.
(2y+6)+y=21
3y+6=21
3y=15
y=5
Now that we have found the value of y, we can take that value and substitute it in the second equation (since it's easier) to find the value of x.
x+ (5)=21
x=16
Now to check if our answers are correct, we plug in both values into any equation and see if they equate.
x+y=21
(16)+(5)=21
21=21
Our solution is correct!
what is the solution to this equation? 8(e)^2x+1=4
Answers
Answer:
Exact Form:
x=3/8e^2
Decimal Form:
x=0.05075073…
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Use the point-slope equation to identify the slope and the coordinates of a point on the line y - 4 = 7 (x-1). The slope of the line is A point on the line is
Answers
Answer:
slope is 7 and point on line is (1, 4 )
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
given line A has equation in point- slope form of
y - 4 = 7(x - 1) , then
slope of line is 7 and a point on the line is (1, 4 )
please help
It is Ms. Smith’s birthday, and her students want to surprise her with a room full of balloons. Use the Fermi process to estimate the number of balloons needed to fill Ms. Smith’s classroom. Assume the classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft. Assume the balloons are spheres with a radius of 0.35 ft. Show your work.
Answers
The number of balloons needed to fill the classroom are 46240 balloons (approx)
Concept: Fermi process is the technique that helps to formulate an answer to a problem based on a series of logical assumptions.
No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)
Given: The classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft, and the balloons are spheres with a radius of 0.35 ft.
No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)
No. of Balloons = 38*52*12/3.14*0.35*0.35*(4/3)
No. of Balloons = 23712/0.5128 = 46240 balloons (approx)
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