Answers
Answer:
(1) 40 is a common multiple of 6 and 10
False:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42...
Multiples of 10: 10, 20, 30, 40...
(2) The fraction 5/6 is greater than 7/10
True:
Find common denominators. Note that what you multiply to the denominator, you multiply to the numerator.
(5/6) x (5/5) = 25/30
(7/10) x (3/3) = 21/30
25/30 > 21/30 ∴ 5/6 is greater than 7/10
(3) The fraction 42/60 is an equivalent form of 7/10
True:
Find a common denominator. Note that what you multiply to the denominator, you multiply to the numerator.
(7/10) x (6/6) = 42/10
42/10 = 42/10 ∴ 7/10 = 42/10
(4) The only value that can be used as a common denominator is 60.
False:
While 60 is a plausible denominator, there are other denominators that can be used. Remember that what you do to the denominator, you do to the numerator.
(5) Ten is a multiple of 6.
False:
Multiples of 6: 6, 12, 18, 24, 30...
~
The validity of the true or false statements about the fractions 5/6 and 7/10 cannot be determined without the specific statements. In mathematics, comparing fractions requires finding a common denominator or converting them to decimals.
Explanation:The question pertaining to whether the following statements about the fractions 5/6 and 7/10 are true involves understanding these numerical values and their relationships.
Please note that information from different sections that seem to provide contradictory answers cannot be used verbatim to answer your question directly, as the true or false nature of statements about these fractions was not specified in the excerpts provided. In mathematics, it is crucial to consider each expression individually and to apply mathematical principles to determine the validity of each statement.
Given that the statements to be verified are not presented, as a tutor on the Brainly platform, it is important to guide you on how to assess the veracity of statements about these fractions or any other numerical expressions. For instance, you would have to compare the two fractions by finding a common denominator or by converting both of them to decimal forms, to determine which one is greater, if that was part of the statements.
Related Questions
When plucked, the high E string on a guitar has a frequency of 330 cycles per second. What sine function represents this note when it is graphed with an amplitude of 1.5 units? Let x represent the number of seconds. Enter your exact answer in the box.
Answers
Let's analyse the function
[tex]y = f(x) = A\sin(\omega x)[/tex]
The amplitude is A, so we want A=1.5
Now, we start at x=0, and we have [tex]1.5\sin(0)=0[/tex]
After one second, i.e. x=1, we want this sine function to make 330 cycles, i.e. the argument must be [tex]330\cdot 2\pi[/tex]
So, we have
[tex]f(1)=1.5\sin(\omega) = 1.5\sin(660\pi)[/tex]
so, the function is
[tex]f(x) = 1.5\sin(660\pi x)[/tex]
Answer:
f(x) = 1.5\sin(660\pi x)
Step-by-step explanation:
What is the volume of this triangular prism?
Answers
Answer:
5676.16 cm^3
Step-by-step explanation:
The volume of any prism is given by the formula ...
V = Bh
where B is the area of one of the parallel bases and h is the perpendicular distance between them. Here, the base is a triangle, so its area will be ...
B = 1/2·bh
where the b and h in this formula are the base and height of the triangle, 28 cm and 22.4 cm.
Then the volume is ...
V = (1/2·(28 cm)(22.4 cm))·(18.1 cm) = 5676.16 cm^3
_____
You will note that this is half the product of the three dimensions, so is half the volume of a cuboid with those dimensions. Perhaps you can see that if you took another such prism and placed the faces having the largest area against each other, you would have a cuboid of the dimensions shown.
Answer:
[tex]V=5,676.16\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the triangular prism is equal to
[tex]V=BL[/tex]
where
B is the area of the triangular face
L is the length of the triangular prism
Find the area of the triangular face B
[tex]B=\frac{1}{2}(28*22.4)= 313.6\ cm^{2}[/tex]
we have
[tex]L=18.1\ cm[/tex]
substitute the values
[tex]V=313.6*18.1=5,676.16\ cm^{3}[/tex]
Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance between points A and B is 264 miles. What is the speeds of the cars, if one of the cars travels 14 mph faster than the other?
Answers
The answer is:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Why?To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to isolate one in function of the other.
So, let be the first car speed "x" and the second car speed "y", writing the equations we have:
For the first car:
[tex]x_{FirstCar}=x_o+v*t[/tex]
For the second car:
We know that the speed of the second car is the speed of the first car plus 14 mph, so:
[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]
Now, we already know that both cars met after 2 hours and 45 minutes, meaning that positions will be the same at that moment, and the distance between A and B is 264 miles, so, we can calculate the relative speed between them.
If the cars are moving towards each other the relative speed will be:
[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]
Then, since from the statement we know that the cars covered a combined distance which is equal to 264 miles of distance in 2 hours + 45 minutes, we have:
[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]
Writing the equation, we have:
[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]
So, we have that the speed of the first car is equal to 41 mph.
Now, substituting the speed of the first car in the second equation, we have:
[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]
Hence, we have that:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Have a nice day!
An art student wishes to create a clay sphere as part of a sculpture. If the clay’s density is approximately 88 pounds per cubic foot and the sphere’s radius is 2 feet, what is the weight of the sphere to the nearest pound? Use 3.14 for pi, and enter the number only.
Answers
Answer:
The weight of the sphere = 2947 pounds
Step-by-step explanation:
* Lets revise the volume of the sphere
- The volume of the sphere is 4/3 π r³, where r is the radius of
the sphere
- Density = mass ÷ volume
- Mass is the weight and volume is the size, so density is weight
divided through size
- Density = weight ÷ volume
* Now lets solve the problem
∵ The clay's density ≅ 88 pounds/cubic foot
∵ The radius of the sphere is 2 feet
∵ The volume of the sphere = 4/3 π r³
∴ The volume of the sphere = 4/3 π (2)³ = 32/3 π feet³
∵ Density = weight/volume ⇒ by using cross multiply
∴ Weight = density × volume
∵ Density = 88 pounds/foot³
∵ Volume = 32/3 π feet³
∵ π = 3.14
∴ The weight of the sphere = 88 × 32/3 × 3.14 = 2947 pounds
What is the following product?
Answers
Answer: Last Option
[tex]4x^5\sqrt[3]{3x}[/tex]
Step-by-step explanation:
To make the product of these expressions you must use the property of multiplication of roots:
[tex]\sqrt[n]{x^m}*\sqrt[n]{x^b} = \sqrt[n]{x^{m+b}}[/tex]
we also know that:
[tex]\sqrt[3]{x^3} = x[/tex]
So
[tex]\sqrt[3]{16x^7}*\sqrt[3]{12x^9}\\\\\sqrt[3]{16x^3x^3x}*\sqrt[3]{12(x^3)^3}\\\\x^2\sqrt[3]{16x}*x^3\sqrt[3]{12}\\\\x^5\sqrt[3]{16x*12}\\\\x^5\sqrt[3]{2^4x*2^2*3}\\\\x^5\sqrt[3]{2^6x*3}\\\\4x^5\sqrt[3]{3x}[/tex]
What is the lateral area of the cone to the nearest whole number? The figure is not drawn to scale.
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
25,133 m^2
Step-by-step explanation:
The lateral area of a cone is found using the slant height (s) and the radius (r) in the formula ...
A = πrs
So, we need to know the radius and the slant height.
The radius is half the diameter, so is (160 m)/2 = 80 m.
The slant height can be found using the Pythagorean theorem:
s^2 = r^2 + (60 m)^2 = (80 m)^2 +(60 m)^2 = (6400 +3600) m^2
s = √(10,000 m^2) = 100 m
Now, we can put these values into the formula to find the lateral area:
A = π(80 m)(100 m) = 8000π m^2 ≈ 25,133 m^2
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx k S is the part of the paraboloid z = 8 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientation
Answers
Answer:
The flux of F across S is 8.627.
Step-by-step explanation:
Given,
F(x, y, z) = xy i + yz j + zx k
or F=(xy, yz, zx)
S is the part of the paraboloid [tex]z=8-x^{2} -y^{2}[/tex] above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
By differentiating z with respect to x we get:
fx=-2x
By differentiating z with respect to y we get:
fy=-2y
So, Surface integral is given by:
[tex]=\int\limits^1_0\int\limits^1_0( {(xy)*(2x)+y(8-x^{2} -y^{2} *(2y)+x(8-x^{2} -y^{2})} \, )dx \, dy[/tex][tex]=\int\limits^1_0\int\limits^1_0 (2x^{2} y+16y^{2} -2x^{2} y^{2} -2y^{4}+8x-x^{3}-xy^{2} } \,) dx \, dy[/tex]
Integrating with respect y:
[tex]=\int\limits^1_0(x^{2} y^{2} +\frac{16}{3} y^{3} -\frac{2}{3} x^{2} y^{3} -\frac{2}{5} y^{5}+8xy-x^{3}y-\frac{1}{3} xy^{3} } \, )dx \,[/tex]
After Substituting limits of y, we get:
[tex]=\int\limits^1_0(x^{2} +\frac{16}{3} -\frac{2}{3} x^{2} -\frac{2}{5}+8x-x^{3}-\frac{1}{3} x } \,) dx \,[/tex]
Integrating with respect x:
[tex]=(\frac{1}{3} x^{3} +\frac{16}{3}x -\frac{2}{9} x^{3} -\frac{2}{5}x+4 x^{2} -\frac{1}{4} x^{4}-\frac{1}{6} x^{2} } \,)[/tex]
After Substituting limits of x, we get:
[tex]=(\frac{1}{3} +\frac{16}{3} -\frac{2}{9} -\frac{2}{5}+4 -\frac{1}{4} -\frac{1}{6} } \,)\\\\=\frac{1553}{180}[/tex]
[tex]= 8.627[/tex]
Learn more: https://brainly.com/question/3607066
To evaluate the surface integral of the given vector field F across the given surface S, we need to use the formula: Φ = ∫∫S F · dS. In this case, the vector field F(x, y, z) = xy i + yz j + zx k and the surface S is the part of the paraboloid z = 8 - x^2 - y^2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, with upward orientation. We can parametrize the surface S and calculate the normal vector to evaluate the surface integral using the given formula.
Explanation:To evaluate the surface integral of the given vector field F across the given surface S, we need to use the formula:
Φ = ∫∫S F · dS
In this case, the vector field F(x, y, z) = xy i + yz j + zx k and the surface S is the part of the paraboloid z = 8 - x2 - y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, with upward orientation.
We can parametrize the surface S as r(u, v) = (u, v, 8 - u2 - v2), where 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.
Next, we calculate the normal vector to S by taking the cross product of the partial derivatives of r(u, v) with respect to u and v: N = (-∂r/∂u) x (-∂r/∂v) = (2u, 2v, 1).
Now, we can evaluate the surface integral using the formula:
Φ = ∫∫S F · dS = ∫∫R F(r(u, v)) · (N · (∂r/∂u) x (∂r/∂v)) du dv
Substituting the values for F and N, we get:
Φ = ∫∫R (u2v + 4uv + 4uv) (2u, 2v, 1) · (2u, 2v, 1) du dv
Calculating this integral over the region R: 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1, we find the flux of F across S.
Can someone plz help me and show your work I WILL MARK AS BRAINLIEST!!!!
Answers
Answer:
Sheridan is correct.
Step-by-step explanation:
She is correct because there is no B squared listed only A and C are provided, Jayden put 13 cm as B instead of listing it as C but she listed it correctly and answered everything else correctly.
Hope this helps!
Charlie recieved some pocket money,
he used 1/5 of it on shopping,
he used 3/4 to buy a ticket to the cinema.
He was left with £3.80
How much money did Charlie start with?
Answers
Answer:
either 76 or 19
Step-by-step explanation:
76 if it's 1/5 of the original amount as well as 3/4 the original amount
1/5+3/4=19/20
3.80=1/20x
3.80+19/20x=76
3.8*20=76
19 if it's 1/5 of the original amount and 3/4 of the new amount
3.80=1/4y
3.80+3/4y=15.20
15.20=4/5x
15.20+1/5x=19
I’ve been confused on this question! Does anyone know?
Answers
Answer:
I think it is A. But i'm not 100% sure.
Step-by-step explanation:
Hope my answer has helped you!
Given 12x^2-4x=0, which values of x will satisfy the equation?
Answers
Answer:
0, 1/3
Step-by-step explanation:
The equation can be factored as ...
4x(3x -1) = 0
The values of x that will satisfy this equation are the values of x that make the factors be 0.
x = 0 . . . . . . when x=0
3x -1 = 0 . . . when x = 1/3
The values of x that will satisfy the equation are 0 and 1/3.
Answer:
0, 1/3
Step-by-step explanation:
The equation can be factored as ...
4x(3x -1) = 0
The values of x that will satisfy this equation are the values of x that make the factors be 0.
x = 0 . . . . . . when x=0
3x -1 = 0 . . . when x = 1/3
The values of x that will satisfy the equation are 0 and 1/3
square root of 29-12square root of 5
Answers
For this case we have the following expression:
[tex]\sqrt {29-12 \sqrt {5}}[/tex]
The expression can not be simplified, we can write its decimal form.
We have to:
[tex]12 \sqrt {5} = 26.83281572[/tex]
Then, replacing:
[tex]\sqrt {29-26.83281572} =\\\sqrt {2,16718428} =\\1.4721359584[/tex]
If we round up we have:
[tex]\sqrt {29-12 \sqrt {5}} = 1.47[/tex]
ANswer:
[tex]\sqrt {29-12 \sqrt {5}} = 1.47[/tex]
Describe how the graph of g(x) is related to the parent function f(x). f(x) = 4^x g(x) = 4^x – 2
Answers
Answer:
g(x) is translated down 2 units from f(x)
Step-by-step explanation:
Adding -2 to the function value moves it down 2 units.
Answer:
The graph of f(x) is shifted to right by 2 units to get graph of g(x).
Step-by-step explanation:
We have been given two functions [tex]f(x)=4^x[/tex] and [tex]g(x)=4^{x-2}[/tex]. We are asked to find the graph of g(x) is related to the parent function f(x).
Let us recall transformation rules.
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
Upon comparing the graph of f(x) to g(x), we can see that [tex]g(x)=f(x-2)[/tex], therefore, the graph of f(x) is shifted to right by 2 units to get graph of g(x).
please help to identify these equations. thank you, much appreciated!!
Answers
Answer:
the left curve is: y=(x+2)³-1;
the right curve is: y=3(x-2)³-1
Write a quadratic function whose zeros are -3 and -4
Answers
Answer:
f(x) = (x -(-3))(x -(-4))
Step-by-step explanation:
The function can be written as the product of binomial terms whose values are zero at the given zeros.
(x -(-3)) is one such term
(x -(-4)) is another such term
The product of these is the desired quadratic function. In the form easiest to write, it is ...
f(x) = (x -(-3))(x -(-4))
This can be "simplified" to ...
f(x) = (x +3)(x +4) . . . . simplifying the signs
f(x) = x^2 +7x +12 . . . . multiplying it out
If $1000 is invested in an account earning 3% compounded monthly, how long will it take the account to grow in value to $1500?
Answers
Final answer:
To find out how long it will take for an investment to grow with compound interest, we use the formula A = P(1 + r/n)^(nt). Substitute the given values into the formula and solve for t using logarithms to find the time needed for the investment to reach the desired amount.
Explanation:
To determine how long it will take for $1000 invested in an account earning 3% compounded monthly to grow to $1500, we use the formula for compound interest:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where:
We want to solve for t when A is $1500, P is $1000, r is 0.03 (3%), and n is 12 (since interest is compounded monthly). Substituting these values into the formula we have:
Dividing both sides by $1000 and using algebra, we can solve for t:
[tex]1.5 = (1 + \frac{0.03}{12})^{12t}[/tex]
To solve for t, we take the natural logarithm of both sides:
[tex]ln(1.5) = ln((1 + \frac{0.03}{12})^{12t})[/tex]
[tex]ln(1.5) = 12t * ln(1 + \frac{0.03}{12})[/tex]
[tex]t = \frac{ln(1.5)}{12 * ln(1 + \frac{0.03}{12})}[/tex]
After calculating the above expression using a calculator, you will find the value of t, which is the time in years it will take for the investment to grow to $1500.
the population of a small country is modeled by the equation y=525.5e^-0.01t
Where y=population (in thousands)
t=the time (in years) with t=0 for the year 2000.
what was the population in the year 2000?
Answers
ANSWER
The population in 2000 is 525.5
EXPLANATION
The population is modeled by the equation:
[tex]y=525.5e^{-0.01t}[/tex]
Where y=population (in thousands)
t=the time (in years) with t=0 for the year 2000.
To find the population in the year 2000, we substitite t=0 into the equation to get:
[tex]y=525.5e^{-0.01 \times 0}[/tex]
Perform the multiplication in the exponent:
[tex]y=525.5e^{0}[/tex]
Note that any non-zero number exponent zero is 1.
[tex]y=525.5(1)[/tex]
Any number multiplied by 1 is the same number;
[tex]y=525.5[/tex]
The population in 2000 is 525.5
Identify each point as a solution of the system or not a solution of the system.
Options (mark each one below): "Solution" or "Not a solution".
(0, 4)
(-2, 4)
(0, 5)
(–2, 7)
(–4, 1)
(–1, 1)
(–1.5, 3.5)
Thank you in advance, I appreciate the help.
Answers
Answer:
see below
Step-by-step explanation:
Plot the points on the given graph. The ones that fall in on a solid line at the edge of the doubly-shaded area, or fall in the doubly-shaded area, are part of the solution set.
(0, 4) on the dashed line — not a solution
(-2, 4) on red line in blue area — solution
(0, 5) in doubly-shaded area — solution
(–2, 7) in doubly-shaded area — solution
(–4, 1) in blue area — not a solution
(–1, 1) on red line outside blue area — not a solution
(–1.5, 3.5) in doubly-shaded area — solution
Given: m∠ATB = 63°, arc AB = 115° Find: arc DC
Answers
Answer:
The measure of arc DC is [tex]11\°[/tex]
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
[tex]m\angle ATB=\frac{1}{2}[arc\ AB+arc\ DC][/tex]
substitute the given values
[tex]63\°=\frac{1}{2}[115\°+arc\ DC][/tex]
[tex]126\°=[115\°+arc\ DC][/tex]
[tex]arc\ DC=126\°-115\°=11\°[/tex]
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite. Then the arc DC will be 11°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
∠ATB = 1/2 [arc AB + arc DC]
63° = 1/2 [115° + arc DC]
arc DC = 11°
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ5
The measure of a vertex angle of an isosceles triangle is 120°, the length of a leg is 8 cm. Find the length of a diameter of the circle circumscribed about this triangle.
Answers
Answer:
16 cm
Step-by-step explanation:
Consider isosceles triangle ABC with vertex angle ACB of 120° and legs AC=CB=8 cm.
CD is the median of the triangle ABC. Since triangle ABC is isosceles triangle, then median CD is also angle ACB bisector and is the height drawn to the base AB. Thus,
∠DCB=60°
Consider triangle OBC. This triangle is isoscels triangle, because OC=OB=R of the circumscribed about triangle ABC circle. Thus,
∠OCB=∠OBC=60°
So, ∠COB=180°-60°-60°=60°.
Therefore, triangle OCB is equilateral triangle.
This gives that
OC+OB=BC=8 cm.
The diameter of the circumscribed circle is 16 cm.
Answer:
16 cm
Step-by-step explanation:
Edith has nine children at regular intervals of 15 months. If the oldest is now six times as old as the youngest, how old is the youngest child?
MANY POINTS PLEASE QUICK
Answers
Answer:
20 years
Step-by-step explanation:
9=x
8=x+15
7=x+15+15
6=x+15+15+15
5=x+15+15+15+15
4=x+15+15+15+15+15
3=x+15+15+15+15+15+15
2=x+15+15+15+15+15+15+15
1=x+15+15+15+15+15+15+15+15
Xx6=6x
6x=x+15+15+15+15+15+15+15+15
6x=120
divide both sides by 6 to get X as 20
we had written the age of the youngest son as X so the youngest son is 20 years old.
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 8x − x2 x = 0 y = 16
Answers
Completing the square gives
[tex]y=8x-x^2=16-(x-4)^2[/tex]
and
[tex]16=16-(x-4)^2\implies(x-4)^2=0\implies x=4[/tex]
tells us the parabola intersect the line [tex]y=16[/tex] at one point, (4, 16).
Then the volume of the solid obtained by revolving shells about [tex]x=0[/tex] is
[tex]\displaystyle\pi\int_0^4x(16-(8x-x^2))\,\mathrm dx=\pi\int_0^4(x-4)^2\,\mathrm dx[/tex]
[tex]=\pi\dfrac{(x-4)^3}3\bigg|_{x=0}^{x=4}=\boxed{\dfrac{64\pi}3}[/tex]
How many real-number solutions does 4x² + 2x +5=0 have?
a. one
b. two
c. zero
d. infinitely many
I did not get this question so can someone please explain it to me?
Answers
Answer:
c. zero
Step-by-step explanation:
The expression on the left of the equal sign is a polynomial of degree 2. (The highest power of x is 2.) A polynomial of degree 2 is called a "quadratic." Values of the variable (x, in this case) that make the value of the quadratic be zero are called "zeros" or "roots" of the quadratic.
Every polynomial has as many roots as its degree. So, a second degree polynomial (quadratic) will have two roots. The roots may be real numbers, or they may be complex numbers. For polynomials of degree higher than 2, there may be some roots of each kind.
This question is asking, "How many roots of this quadratic are real numbers?"
___
There are several different ways you can figure out the answer to this question. One of the simplest is to graph the quadratic. (See attached.) You can see that the graph of the quadratic never has a y-value of zero, so there are no (real) values of x that will be solutions to this equation.
The two solutions are -0.25±i√1.1875. The "i" indicates that portion of the number is imaginary, and the entire number (real part plus imaginary part) is called a "complex" number. Both solutions for this quadratic are complex, not real.
__
Another way you can answer this question is to compute what is called the "discriminant." The roots of every quadratic of the form ax^2+bx+c can be found using the formula ...
x = (-b±√(b^2-4ac))/(2a)
For this quadratic, the values of a, b, and c are 4, 2, and 5, respectively. Then the formula becomes ...
x = (-2±√(2^2 -4·4·5))/(2·4) = (-2±√-76)/8
The value under the radical sign is the "discriminant." When it is negative, as here, the value of the square root is an imaginary number (not a real number), so the roots are complex. When the discriminant is zero, the two roots have the same value; when it is positive, there are two distinct roots.
There are zero real number solutions to this equation.
A triangle is 20 in tall and 5 in wide. If it is
reduced to a width of 1 in then how tall will
it be?
Answers
Answer:
The triangle should be 4 inches tall
Step-by-step explanation:
We can write a proportion to solve. Put the height over the width
20 x
------- = -----------
5 1
Using cross products
20*1 = 5*x
20 = 5x
Divide by 5
20/5 = 5x/5
4 =x
The triangle should be 4 inches tall
To find the new height when the width of a triangle is reduced, you can use the concept of similar triangles and ratios.
Explanation:To determine the new height of the triangle, we can use the concept of similar triangles. Similar triangles have proportional sides. So, if the width of the triangle is reduced from 5 in to 1 in, the height will also be reduced proportionally. Using the ratio of the new width to the original width, we can find the new height:
New height = (new width / original width) * original height = (1 / 5) * 20 = 4 in
Learn more about Similar triangles here:https://brainly.com/question/32489731
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PLZ HELP I BEGGG 20 POINTS!!!!!!!
Answers
Answer:
i belive its 100
Step-by-step explanation:
Answer:
hes right its 100
Step-by-step explanation:
14. Factor the polynomial by grouping, if possible.
3v2w – 21vw – 3v2 + 21v
A. 3vw(v – 7) – 3(w – 1)
B. 3v(v – 7)(w – 1)
C. It can't be factored.
D. 3v(v – 7)(v + 1)
Answers
Answer:
3 v (v - 7) (w - 1) thus the answer is B:
Step-by-step explanation:
Factor the following:
3 v^2 w - 21 v w - 3 v^2 + 21 v
Factor 3 v out of 3 v^2 w - 21 v w - 3 v^2 + 21 v:
3 v (v w - 7 w - v + 7)
Factor terms by grouping. v w - 7 w - v + 7 = (v w - 7 w) + (7 - v) = w (v - 7) - (v - 7):
3 v w (v - 7) - (v - 7)
Factor v - 7 from w (v - 7) - (v - 7):
Answer: 3 v (v - 7) (w - 1)
When you flip 4 coins, the probability of getting half heads is 0.38. Likewise, the probability is 0.25 of finding that one fourth of the coins is heads. So, with four coins, the most likely outcome (the most probably state) is getting half heads, BUT thechance of getting one head (or one tail and three heads as well) is not all that much smaller, at 0.25. The charts show the probabilities for getting various fractions of heads for flipping four and for flipping eight coins. Describe the differences between the cases of four coins and eight coins with respect to how the probability of getting one-fourth heads compares to one-half heads changes when going from four to eight coins.
Answers
Answer:
Step-by-step explanation:
The probability would be twice as large for eight coins I think
The probability distribution of flipping coins changes as the number of coins increases due to the law of large numbers. The probability of getting half heads is the highest when flipping four coins, whereas the probability distribution broadens with eight coins, making specific outcomes less likely.
Explanation:When analyzing the probability of outcomes when flipping coins, we can compare the cases of flipping four coins to flipping eight coins. When flipping four coins, the most likely outcome is two heads, with a probability of 0.38. The probability of getting one head, which is one-fourth of the coins, has a probability of 0.25. However, these probabilities might change when flipping eight coins because as the number of coin flips increases, the distribution of outcomes tends to become more even due to the law of large numbers.
Tossing a fair coin should theoretically result in 50 percent heads over the long term, as demonstrated by Karl Pearson's experiment which approximated the theoretical probability after 24,000 coin tosses. When moving to eight coins, the probability distribution for getting different fractions of heads will widen, meaning that it's less likely to get a specific outcome (in terms of fractions of heads) because there are more possible combinations (microstates).
Overall, while the exact probabilities for eight coins are not provided, we can expect that the probability of getting exactly half heads will decrease since there are more total combinations possible, and the probability for one-fourth heads will also change but without specific numbers, we cannot determine the precise probabilities.
The equation A = x(x - 7) describes the area, A, of a rectangular flower garden, where x is the width in feet.
What would be the width in feet of the flower garden if the area is 8 square feet?
A. 9
B. 1
C. 8
D. 7
Answers
x(x-7)=8
x^2-7x-8=0
(x-8)(x+1)=0
so x=8 (and -1 but width can’t be negative)
So your answer is C. 8
A 32 gram sample of a substance that’s a by-product of fireworks has a k-value of 0.1368. Find the substance’s half-life, in days. Use formula
N=N0e-kt, t= time in days.
HELP PLS
Answers
Answer:
t=5.1 days
Step-by-step explanation:
We know that the formula is:
[tex]N = N_0e^{-kt}[/tex]
Where N is the amount of substance after a time t, [tex]N_0[/tex] is the initial amount of substance, k is the rate of decrease, t is the time in days.
[tex]k=0.1368\\N_0 =32[/tex]
We want to find the average life of the substance in days
The half-life of the substance is the time it takes for half the substance to disintegrate.
Then we equal N to 16 gr and solve the equation for t
[tex]16= 32e^{-0.1368t}[/tex]
[tex]0.5= e^{-0.1368t}[/tex]
[tex]ln(0.5)= ln(e^{-0.1368t})[/tex]
[tex]ln(0.5)= -0.1368t[/tex]
[tex]t= \frac{ln(0.5)}{-0.1368}\\\\t=5.1\ days[/tex]
Answer:
5.1
PLATO answer
Step-by-step explanation:
Amy makes the following statement:
"There is a 60% chance of snow tomorrow and a 10% chance I will be late for school."
What is the probability that it will snow and Amy will be late for school?
3%
6%
50%
70%
Answers
Answer:
The probability that it will snow and Amy will be late for school is 6%
Step-by-step explanation:
The answer is:
The probability that it will snow and Amy will be late for school is 6%
Step-by-step explanation:
I did the question in the quiz and I got it right soo… ^0^