Answers
The other root of the given quadratic equation is a = ± 3/√2.
Given that, x=2 and x²+ax+12=0.
What are the roots of quadratic equations?The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
Now, put x=2 in x²+ax+12=0 and find the value of a.
That is, 2²+2a+12=0
⇒4+12+2a=0
⇒16+2a=0
⇒2a=-16
⇒a=-8
So, the value of a is -8.
Put (0, 6) and (4, 6) in the function y=2x²+bx+c and find the value of b and c.
That is, 6=2(0)²+b(0)+c
⇒ c=6
6=2(4)²+b(4)+c
⇒ 6 = 32+4b+c
⇒ -26 = 4b + 6
⇒ 4b = -32
⇒ b = -8
So, the value of b is -8 and the value of c is 6.
Put x=a (root) in the equation 2x + x/a -9 = 0 and find the other root.
That is, 2a²+a/a -9 = 0
⇒ 2a² - 9 = 0
⇒ a²=9/2
⇒ a = ± 3/√2
Therefore, the other root of the given quadratic equation is a = ± 3/√2.
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Related Questions
Before signing a contract, you must review the terms and conditions of the contract. How many terms are there in the surface area formula below?
2(lw + wh + hl)
Answers
How many terms are there in the surface area formula below?2(lw + wh + hl) 3 terms.
What are the three terms ?
The total surface area of a cuboid= 2(lw + wh + hl)
Here, w= width, h= height, l= length
Thus, there are 3 terms in the surface area formula.
What is a total surface area?
There may be numerous flat surfaces throughout an entire object (such as a cube), each of which needs to be measured independently. The total surface area of an object is the sum of all the faces that make up the object.Keep in mind that the total surface area only accounts for the flat exterior of an object, treating it though it were two-dimensional.Even if there are many of them, these many flat surfaces join together to form the three-dimensional entity.Surface area and total surface area do not always represent the amount of space that an object occupies.To learn more about total surface area, refer:
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Which set of points represents a function which is not one-to-one?
choice 1:
{(3, 2), (9, 6), (0, 7), (6, 5), (2, 0)}
Choice 2:
{(9,6), (4,3), (5, 4), (8, 0), (7, 9)}
Choice 3:
{(4,3), (8,5), (8, 7), (0, 2), (1, 6)}
Choice 4:
{(2, 6), (0, 2), (8, 9), (1, 1), (4, 6)}
Answers
Answer:
Choice 4
Step-by-step explanation:
A one to one function has every domain with only one range as their individual output. Choice 4 has the output 6 mentioned twice for both 2 and 4 so therefore it's not a one to one function because the range 6 has two outputs 2 and 4.
Martina has 16 cars available to rent. let c be the number of cars she would have left after renting r of them. write an equation relating c to r. then use this equation to find the number of cars she would have left after renting 14 of them.
Answers
If Martina has 16 cars available to rent, and if c is the number of cars she would have left after renting r of them, then the equation relating c to r will be c = 16 - r, and the number of cars she would have been left with after renting 14 of them is calculated to be 2.
An algebraic expression is a type of expression consisting of both numerals and letters.
If Martina has a total of 16 cars available to rent, then the equation or algebraic expression relating c to r is,
c = total number of cars available to rent - r
c = 16 - r
After renting 14 of the total cars available, then the number of cars left can be calculated using this equation,
c = 16 - r
c = 16 - 14
c = 2
Thus, the number of cars she would have been left with is calculated to be 2.
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The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, which conclusion is accurate?
OA) The triangle is acute.
OB) The triangle is right.
OC) The triangle is obtuse.
OD) The triangle is isosceles.
Answers
The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right. The correct option is B
What is a triangle?A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.
The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right.
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Find the seventh term of each geometric sequence. 1,-3,9, . . . . . . .
Answers
The seventh term of the given geometric progression is: 729.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Now,
Given GP: 1, -3, 9, .....
Here, a₁ = 1
a₂ = a₁ (r)
=> 3 = 1 (r)
=> r = 3
Thus, a₇ = a₁ (r⁷⁻¹) = 1 (3⁶) = 729.
Hence, The seventh term of the given geometric progression is: 729.
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−4 5/9+8/9 pls help and hurry
Answers
exact form:
-11/3decimal form:
-3.6666mixed number form:
-3 2/3Answer:
-11/3
Step-by-step explanation:
Convert −4 5/9 to improper fraction -41/9 and do the math.
-41/9 + 8/9
-33/9
-11/3
Which sequence could be partially defined by the recursive formula f (n 1) = f(n) 2.5 for n ≥ 1?
Answers
The sequence partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 is -10, -7.5, -5, -2.5, …
Given recursive formula is f(n+1) = f(n)+2.5, n ≥ 1.
So the first term of the sequence is f(1) since n ≥ 1.
Given options for the sequences are:
a. 2.5, 6.25, 15.625, 39.0625, …
b. 2.5, 5, 10, 20
c. -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
We compare the first term of each sequence with the given recursive formula.
a. 2.5, 6.25, 15.625, 39.0625, …
In this sequence, the first term, f(1) = 2.5
Using recursive formula, f(2) = f(1) + 2.5 = 2.5 +2.5 = 5.
But the second term in the given sequence is 6.25. So the recursive formula does not match with this sequence.
b.2.5, 5, 10, 20
Here, f(1) = 2.5
By the recursive formula, f(2) = f(1) + 2.5 = 5
f(3) = f(2) + 2.5 = 5 +2.5 = 7.5, which does not match with the third term of the given sequence. So this sequence is not defined by the recursive formula.
c. -10, -7.5, -5, -2.5, …
Here, f(1) = -10
Using recursive formula, f(2) = f(1) + 2.5 = -10 + 2.5 = -7.5
f(3) = f(2) + 2.5 = -7.5 +2.5 = -5
f(4) = f(3) +2.5 = -5 +2.5 = -2.5
So far the recursive formula matches with the given sequence. So the sequence defined partially by the recursive formula, f(n+1) = f(n)+2.5, n ≥ 1 is -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
Here the first term is, f(1) = -10.
But the sequence which matches with the recursive formula and starting with -10 is option c. So this sequence does not need to be verified.
The question is incomplete. Find out the complete question below:
Which sequence could be partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 ?
a. 2.5, 6.25, 15.625, 39.0625, …
b. 2.5, 5, 10, 20
c. -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
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Jim is running a race against his best friend ryan. jim runs at a rate of 18 miles in 3hours while ryan runs at a rate of 11miles in 2 hours. how much further can jim run in an hour compared to his friend ryan
Answers
If Jim is running a race against his best friend Ryan and Jim runs at a rate of 18 miles in 3 hours while Ryan runs at a rate of 11 miles in 2 hours, then Jim can run 0.5 miles further compared to his friend Ryan.
If Jim runs at a speed of 18 miles in 3 hours, it can be represented as,
Speed = distance / time = 18 miles / 3 hours = 6 miles per hour
As Ryan runs at a rate of 11 miles in 2 hours, it can be given as,
Speed = distance / time = 11 miles / 2 hours = 5.5 miles per hour
To determine how much further Jim can run in an hour compared to his friend Ryan,
Distance ( Jim ) = speed x time = 6 x 1 = 6 miles
Distance ( Ryan) = speed x time = 5.5 x 1 = 5.5 miles
The distance that Jim can run further in an hour can be calculated by subtraction.
Distance ( Jim ) - Distance ( Ryan) = 6 - 5.5 = 0.5 miles
Thus, Jim can run 0.5 miles further in an hour compared to his friend Ryan.
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A man who is 6 feet tall is walking at a rate of 4 feet/second, directly away from a light that is located 10 feet above the ground.
How long is the man's shadow t seconds after he starts walking? The answer will be in terms of t.
Answers
Answer:
2.5t
Step-by-step explanation:
Let the man be
x
feet away from the street light, and his shadow length be
y
, Let the tip of the shadow be
l
feet away from the light such that
l
=
x
+
y
and we are given that
d
x
d
t
=
2
By similar triangles:
y
6
=
x
+
y
30
∴
30
y
=
6
(
x
+
y
)
∴
30
y
=
6
x
+
6
y
∴
30
y
−
6
y
=
6
x
∴
24
y
=
6
x
∴
y
=
1
4
x
Now,
l
=
x
+
y
⇒
l
=
x
+
1
4
x
∴
l
=
5
4
x
Differentiating wrt
x
gives;
d
l
d
x
=
5
4
And by the chain rule we have:
d
l
d
t
=
d
l
d
x
d
x
d
t
∴
d
l
d
t
=
5
4
×
2
∴
d
l
d
t
=
2.5
feet/sec
An interior designer is creating a custom coffee table for a client. The top of the table is a glass triangle that needs to balance on a single support. If the coordinates of the vertices of the triangle are at (3,6),(5,2) , and (7,10) , at what point should the support be placed?
Answers
According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.
The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).
What is the rule of centroid?The centroid method is an agglomerative clustering method in which the similarities (or dissimilarities) between clusters are defined in terms of the centroids (i.e., the multidimensional means) of the clusters on the clustering variables.
According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.
The triangle has a balance point at the centroid.
Find the centroid of the triangular coffee table.
Use the centroid formula [tex](x_1+x_2+x_3/3, y_1+y_2+y_3/3)[/tex]
The centroid of the triangle is (3 + 5 + 7/3, 6 + 2 + 10/3) or(5, 6).
Let the points be A(3, 6), B(5, 2), and C(7, 10). The midpoint D of BC is (5 + 7/2, 2 +10/2) OR (6, 6).
Note that AD is a line that connects the vertex A and D, the midpoint of BC. The distance from D(6, 6) to A(3, 6) is 6 – 3 or 3 units.
If P is the centroid of the triangle ABC, then So, the centroid is 2/3(3) or 2 units to the right of A.
The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).
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justin launches a rocket straight up into the air. The table below gives the height(t) of the rocket (in meters) at a few times t (in seconds) during its flight.
FIND THE AVERAGE RATE OF CHANGE!
Answers
Using it's formula, the average rates of change are given as follows:
a) 30 meters per second.
b) -10 meters per second.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the following equation:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, taking the data from the table, we have that:
f(0) = 0.f(4.6) = 138.Hence the rate is given as follows:
r = (138 - 0)/(4.6 - 0) = 30 meters per second.
For item b, taking the data from the table, we have that:
f(9.2) = 23.f(11.5) = 0.Hence the rate is given as follows:
r = (0 - 23)/(11.5 - 9.2) = -10 meters per second.
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Suppose Angel is shooting baskets and makes 40% of the 15 shots. Does he get a prize? Explain your reasoning
Answers
Answer:
Well 40% of 15 is 6
Step-by-step explanation:
It depends on how many shots it takes to win a prize
what is an example of a linear equation that is perpendicular to y = 5?
Answers
Answer:
Step-by-step explanation:
x=5
A cube is a solid figure with six square faces. If the edges of a cube have length 1.5 \mathrm{~cm} , what is the surface area of the cube?
a. What is the relationship between the length of the edges and the area of each face?
Answers
13.5 cm² is the surface area of the cube .
What is surface area of cuboid?
The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.If the edge of a cube have a length = a unit
then, the surface area of the cube = 6a² unit
here, the edge of a cube have length a = 1.5 cm
Therefore , the surface area of the cube 6a² = 6 × 1.5²
= 13.5 cm²
The area of each face = ( the length of the edges)²
The surface area of whole cube = 6 × the area of one face
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Find two pairs of whole numbers with a geometric mean that is also a whole number. What condition must be met in order for a pair of numbers to produce a whole-number geometric mean?
Answers
2 and 18 are the two pairs of whole numbers with a geometric mean that is also a whole number.
The geometric mean is defined as the nth root of the product of n numbers, which means for a set of numbers x1, x2, ..., xn. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.
For example, we multiply them: 2 × 18 = 36
Then (as there are two numbers) take the square root: √36 = 6
Conditions: The square roots of the product of the pair of numbers must be whole-number. These two conditions must be met to have an exact geometric mean
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8 x 10^-3 is how many times greater than 4 x 10^-6
Answers
Answer:
.002 or
2x10^-3
Step-by-step explanation:
make sure the exponents match
8 x 10^-3 =
.008 × 10^-3
(.008 × 10^-6) ÷ (4 x 10^-6)
10^-6 cancels out
.008 ÷ 4 = .002
or
2x10^-3
i need help on this.
Answers
Answer:
what
Step-by-step explanation:
5) Diego had a pizza that was divided into 8 equal slices. He ate 3 of them. Hector has a pizza that
is the same size, but his is divided into 4 equal slices. He ate 3 slices of his pizza. Who ate more
pizza?
Answers
3/4 x 2/2= 6/8 > 3/8
Hector ate more.
Calculate the distance between the following points: F(-9, -14) and G(1,-19)
Answers
The distance between points F and G is 15 units.
How to calculate distance between two points?The length of the line segment connecting two points on a plane is known as the distance between the points. The formula for distance between two points ([tex]x_{1}[/tex],[tex]x_{2}[/tex]) and ([tex]y_{1}[/tex],[tex]y_{2}[/tex]) is given by
distance between two points =[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]
The equation can be used to calculate the distance between any two locations on an x-y plane or coordinate plane.
The point F is (-9,14) and point G is (1,-19)
distance between F and G
=[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]
=[tex]\sqrt{(-9-1)^2+(-14-(-19))^2 } }[/tex]
=[tex]\sqrt{(-9-1)^2+(-14+19)^2 } }[/tex]
=[tex]\sqrt{(-10)^2+(5)^2 } }[/tex]
=[tex]\sqrt{100+25}[/tex]
=[tex]\sqrt{125}[/tex]
=15 units.
Distance between point F and G is 15 units.
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A construction crew is building a straight ramp that rests on two beams. One
3.5 feet tall and the other is 10.5 feet tall. The beams are 40 feet apart. What is the
slope of the ramp?
Answers
According to the solving the slope of the ramp = 0.175.
What exactly is Slope?shows the steepness of an inclination The slope is just the ratio of the rise over the run, or the change there in vertical out over change in the horizontal, as seen below:
How do you calculate slope?find the coordinates of two points on the line. Calculate the difference in y-coordinates between these two places (rise). Determine the x-coordinate difference between these two places (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).
According to the given data:The given values are indeed the heights of a two beams and indeed the distance between them, which are:
Y₁ = 3.5ft
Y₂ = 10.5 ft
ΔX = 40 ft
To get the slope of both the ramp, enter the following values into the slope formula:
m = (Y₂ - Y₁)/ΔX
= (10.5 - 3.5)/40
= 7/40
= 0.175
According to the solving the slope of the ramp = 0.175
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18. If ZW and ZV are supplementary angles and m2V = 49°, find m/W.
19. If 21 and 22 are vertical angles, <2 and <3 are complementary angles,
and m23 = 56°, find m21.
Answers
Answer:
Step-by-step explanation:
18. Supplementary angles add up to 180°therefore
∠W+∠V=180°
∠W+49°=180°
∠W=180°-49°
∠W=131°
19.Complementary angles are angles that add up to 360°
∠2+∠3=90°
∠2+56°=90°
∠2=90°-56°
∠2=34°
Vertical angles are equal therefore this tells us that ∠1 and ∠2 are equal
∠1=∠2
∴∠1=34°
20. Angles which are in a linear pair add up to 180°(supplementary)
Mathematically what the statement is sayin is :
∠1+∠2=180°
and ∠1=5(∠2)-18°
therefore we can plug in ∠1=5(∠2)-18° in ∠1+∠2=180°
(5(∠2)-18°)+∠2=180°
5(∠2)+∠2=180°+18°
6(∠2)=192°
[tex]\frac{6 < 2}{6} =\frac{198}{6} \\ < 2=33[/tex]
∠1=5(33°)-18°
∠1=165°-18°
∠1=147°
a toy rocket is launched from a platform 6.3 meters above the ground in such a way that is a height, h (in meters) after t seconds is given by the equation h=-4.9t^2+43.4t+6.3. how long will it take for the rocket to hit the ground?
Answers
The toy rocket will take a time of 8.999 seconds to hit the ground.
How much time does the rocket take to hit the ground?
The height of the rocket (h), in meters, in terms of time (t), in seconds, is defined by a quadratic equation. In this question we must determine the time needed for the rocket to hit the ground, that is, a time t greater than zero such that the height is zero. Now we proceed to solve the polynomial:
- 4.9 · t² + 43.4 · t + 6.3 = 0
- 4.9 · (t² - 8.857 · t - 1.286) = 0
- 4.9 · (t - 8.999) · (t + 0.143) = 0
Only the first root offers a realistic value as time is a whole number. Hence, the toy rocket will take a time of 8.999 seconds to hit the ground.
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solve each equation(with explanation please)
-4+p=-7
x/10=-6
4-3(8n - 4) = -104
Answers
Answer:
1: P = -3
2: X = -60
3: N = 5
Step-by-step explanation:
Ok, for number one you are going to add 4 on the -4 canceling that out, and adding 4 on the -7 making that -3.
Number 2 you times 10 on the x/10 to cancel out the 10 (making it x) then you do -6 times 10, and then you get -60
Last one is a little tricky here's the equations I used to get the last one
-3 x 8n = -24x
New equation: 4-24x=-104
+4 + 4
___________________________
-24x = -100
___ ___
-24 -24
_
so the answer would be x = 5
Find the value of x to the nearest tenth. 228.4= πx
Answers
x = 73 is the value of x.
What exactly do we mean by a value?A value in mathematics is a number that indicates the result of a calculation or function.So, in the preceding example, you could tell your teacher that 5 x 6 equals 30 or that x + y equals 9 if x = 6 and y = 3.A value is another term for a variable or constant.To find the value of x:
Given: 228.4/x = πAfter we have entered the value of π, we will simplify the given equation to find the value of x.So,
228.4/x = π228.4/x = 3.14159228.4/3.14159 = xx = 72.702039Then rounding to the nearest tenths gives x = 73.
Therefore, x = 73 is the value of x.
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Write an equation of a parabola with vertex at the origin and the given focus.
focus at (-1,0)
Answers
The equation of the parabola that has vertex at (0,0 ) and focus (-1, 0) is
x = -y²What is known as a parabola?A parabola is a quadratic function that can move on any axis, it is composed of:
vertexfocal axisdirectrixThe equation that defines a parabola can be given by:
(x - h)² = 4p(y - k)
(y - k)² = 4p(x - h)
This will depend on its aperture
Since the vertex and the focal axis are on the same axis, we analyze that:
v (0, 0)f (-1, 0) the focus is on the right so the parabola is of the form X = Y².(y - 0)² = 4p(x - 0)
f = (0 + p, 0)
0 + p = -1
p = 0 - 1
p= -1
(y - 0)² = 4*-1(x - 0)
(Y)² = -1(X)
x = -y²
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1.
Solve each equation for the indicated variable.
a+m=n=p,
for a.
Answers
In linear equation, a = (n+p)/m is equation for the indicated variable.
What in mathematics is a linear equation?
A linear equation is an algebraic equation with the formula y=mx+b, . m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."In terms of algebra, writing "am" is the same as writing "a*m" or "a times m"
To undo the multiplication, we use division. We will divide both sides by m to get 'a' all by itself on the left side
So...
am = n+p
a*m = n+p
(a*m)/m = (n+p)/m .... divide both sides by m
a = (n+p)/m ... notice how the 'm's cancel out when we divide on the left side
a = (n+p)/m
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PLEASE HELP PLEASE PLEASE PLEASE!! Please show work for brainliest!!! :)
What is the factored form of the expression over the complex numbers? 16x^2+9y^2
Answers
The factored form of the expression 16x² + 9y² over the complex numbers is; (4x + 3iy)(4x − 3iy)
How to factorize expressions?We want to find the factored form of the expression 16x² + 9y² over the complex numbers.
We can rewrite the given expression 16x² + 9y² as perfect squares;
= (4x)² + (3y)²
Now, from using the difference of squares formula, we know that;
a² - b² = (a + b)(a - b)
Thus;
(4x)² + (3y)² = (4x)² - (√-9)²y²) can be expressed as;
(4x + 3iy)(4x − 3iy)
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Factor the equation.
Answers
Answer: factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Step-by-step explanation:
In a class of 20 students, how many conversations must be had so that every student talks to every other students in the class?
Answers
Answer:
190
Step-by-step explanation:
Similar to the handshake problem, if every student must talk with another person, each student will talk to 19 other students. However, a conversation consists of two people, so we must divide the number of ways we can rearrange the two people. Therefore, our answer is 190
f(x) = -x + 4 and g(x) = x2 - 5, then g(f(3)) = ?
Answers
g(1)=(1)2-5=-3
g(f(3))=-3
