Answer:
Find the coefficients using ax^2 + bx + c = 0a = 4
b = 7
c = 0
Make the coefficient equal 1. But how do we do that? Division.4n² + 7n = 0
4/4n² + 7n/4 = 0/4
Simplify= n² + 7/4n = 0
a = 1
b = 7/4
c = 0
Complete the square using b/2².b = 7/4
(b/2)² = (7/4 ÷ 2)²
Use fraction rule.
7/4 ÷ 2² = 7/4² / 2²
square the numbers
7/4² / 2² = 49/16 ÷ 4
49/16 ÷ 4 = 49/16 × 1/4
49/16 × 1/4 = 49/64
Add to both sides of the equation using 49/64
b = 7/4
b/2 = 7/4 ÷ 2
simplify
b/2 = 7 ÷ (4 × 2)
simplify(arithmetic)
b/2 = 7/8
n² + 7/4n + 49/64 = 49/64
(n + 7/8)² = 49/64
Solve for the unknown x[tex](n+\frac{7}{8})^2=\frac{49}{64}\\\sqrt{(n+\frac{7}{8})^2}=\sqrt{\frac{49}{64}}\\[/tex]
Next, cancel out the square on the left side.
[tex]n+\frac{7}{8}=+/-\sqrt{\frac{49}{64}}[/tex]
Subtract 7/8 from both of the sides.
[tex]n+\frac{7}{8}-\frac{7}{8}=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}[/tex]
Simplify the left side.
[tex]n=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}\\n=-\frac{7}{8}+/-\frac{\sqrt{49}}{\sqrt{64}}\\n=-\frac{7}{8}+/-\frac{7}{8}\\n_1=0\\n_2=-\frac{7}{4}[/tex]
That wraps it up for this equation. Hope it helped!
Without using a calculator, determine the number of real zeros of the function
f(x) = x3 + 4x2 + x − 6.
PLEASE HELP!!!
The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
How to determine the number of real zeros?The equation of the function is given as:
f(x) = x^3 + 4x^2 + x - 6
Expand the function
f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6
Reorder the terms of the function
f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6
Factor the expression
f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)
Factor out x -1
f(x) = (x^2 + 5x + 6)(x -1)
Expand
f(x) = (x^2 + 3x + 2x + 6)(x -1)
Factorize
f(x) = [x(x + 3) + 2(x + 3)](x - 1)
Factor out x + 2
f(x) = (x + 3)(x + 2)(x- 1)
The function has been completely factored;
And it has 3 linear factors
Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
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Round your answer to the nearest tenth if necessary. Use 3.14 for .
A drum has a diameter of 20 inches and is 16 inches deep. Find the volume of this drum.
The volume of this drum is approximately
in³.
HELP QUICK!!!!
Answer:
[tex] \boxed{\rm \: Volume_{(Drum)} = 5024 \: in {}^{3} }[/tex]
Step-by-step explanation:
Given :
Diameter of a drum = 20 inchesDeep ( height ) of the drum = 16 inchesπ = 3.14To Find:
The volume of the drum.
Solution:
We all know that drum is cylindrical.So we'll use the formulae of the volume of cylinder,to find its volume.
[tex] \boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}[/tex]
Where,
r = radiush = height (deep)π = 3.14The value of radius ain't given,but the diameter is given.We can use the formulae of radius.
[tex] \rm \: Radius = D/2[/tex]
D = diameterSubstitute the value of diameter:
[tex] \rm \: Radius = \cfrac{20}{2} = 10[/tex]
Hence,the radius is 10.
So we could now use the formulae of the volume of cylinder:
[tex] \rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h[/tex]
π = 3.14r =10 inh = 16 in[Firstly bring the answer in terms of π then plug π = 3.14 and then simplify.]
[tex] \rm \: Volume_{(Drum)} = \pi(10) {}^{2} (16)[/tex]
[tex] \rm \: Volume_{(Drum)} =\pi100(16)[/tex]
[tex] \rm \: Volume_{(Drum)} = 1600\pi[/tex]
[tex] \rm \: Volume_{(Drum)} = 1600 \times 3.14[/tex]
[tex] \boxed{\rm \: Volume_{(Cylinder)} = 5024 \: in {}^{3}} [/tex]
Hence, we can conclude that:
The volume of this drum is 5024 in^3.
Peter and Henry went to the movies Peter bought the two Movie tickets for 7 dollars each. How much did he spend for the movie tickets Henry bought two buckets of popcorn for 5 dollars each. How much did Henry spend on popcorn.
Answer:
Peter spent 14 dollars on movie tickets. Henry spent 10 dollars on popcorn.
Step-by-step explanation:
I hope this helps! :)
What are the solutions to this system of
equations?
x² + 2x - 8 = 0
y = x² + 3x + 5
y = x + 13
x = 2 and x = -4
A
(15, 2); (9,-4)
B
(2, 15); (-4, 9)
Answer:
B; because it has two points where x is once 2 and once -4
This venn diagram shows sports played by 10 students let events A = the students plays basketball let event B = the students plays soccer What is P(A|B)
The probability of P(A|B) will be; P(A|B) = 2/5 = 0.4
How to deal with Venn Diagrams?
From the Venn diagram attached, it displays sports played by 10 students.
Let event A = The students play basketball.
Let event B = The student plays soccer.
Then the probability of P(A|B) will be;
P(A|B) = P(A ∩ B)/P(B)
P(A|B) = (2/10)/(5/10)
P(A|B) = 0.40
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please help me with this
Answer:
10π (31.415926)
√101(10.0498756)
9.92749...
0.99853...
Step-by-step explanation:
For 10π, we can simplify π into 3.14 for an approximate amount. 3.14*10=31.4
For the square root of ten, we can estimate it's between 10 and 11 since 10 squared is 100 and 11 squared is 121.
Answer:
See explanation
Step-by-step explanation:
First, we have to put the expressions into numbers. For the square root of 101, it doesn't divide evenly into any whole number. We do know that 10^2 is 100, and 11^2 is 121. That means the square root of 101 is between 10 and 11. Pi is equal to 3.14, so we just multiply 10 by 3.14. If we do this, we get 31.4. From here we can rank the numbers in order from greatest to smallest.
31.4 (10pi) is greater than
The square root of 101 which is greater than
9.92749... which is greater than
0.99853...
Hope this helps!
Expand and simplify: (-7y - 8) (y - 4)
To expand an expression, use FOIL method.
F - FirstMultiply the first term in each expression inside the parentheses.-7y and y are the first terms in each expression.
(-7y)(y) = -7y²
O - Outside Next is to multiply the terms outside. (The first term in the first expression and the last term in the second expression)-7y is the first term in the first expression
-4 is the last term of the second expression
(-7y)(-4) = 28y
I - InsideThe next step is to multiply the terms inside. (The last term in the first expression and the first term in the last expression)-8 is the last term in the first expression
y is the first term in the second expression
(-8)(y) = -8y
L - LastLast step is to multiply the last term in each expression.-8 is the last term of the first expression
-4 is the last term of the second expression
(-8)(-4) = 32
Combine all simplified terms.
-7y² + 28y - 8y + 32-7y + 20y + 32Answer:
-7y + 20y + 32Wxndy~~
what is .3% written as a decimal
Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003
What are decimal numbers?
Decimal numbers are numbers that includes the dot in between. Given the percentage value expressed as:
0.3%
This can be expressed as;
0.3% = 0.3/100
Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003
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a car can travel 340 km with 17 litres of petrol. how much can I travel with 20 litres of petrol?
The car would travel a distance of 400 km using 20 litres of petrol
How to determine the distance travelled?The given parameters can be represented using the following scale ratio :
Scale = 340 km : 17 litres
For 20 litres of petrol, we have:
Distance : 20 = 340 km : 17
Express as fraction
Distance/20 = 340 km/17
Multiply both sides by 20
Distance = 400 km
Hence, the car would travel a distance of 400 km using 20 litres of petrol
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find the measure of the missing angle
In a football tournament, each team plays exactly 19 games.
Teams get 3 points for every win and 1 point for every tie.
At the end of the tournament, team Olympus got a total of 28 points.
From the following options, how many times could team Olympus have tied?
Answer:16 ties
Step-by-step explanation:
there is 19 games if they tied 16 then that 16 points so 28 - 16= 12
then 4 games left so 4 times 3 is 12
At the end of the tournament, team Olympus have tied for 13,10,7,4,1 times
What is inequality?
A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
According to question
In a football tournament, each team plays exactly 19 games.
Points for every win (w) = 3
Points for every tie (t)= 1
Points for every loose = 0
Olympus got a total of 28 points
i.e 3w + t = 28 ---------(1)
And each team plays 19 games
T + W ≤ 19 --------------(2)
and T , W ≥ 0
from equation (1) and (2)
=> 2W ≥ 9
=> W ≥ 4.5
( match can be won in integers only )
=> W ≥ 5
W T Loose
5 13 1
6 10 3
7 7 5
8 4 7
9 1 9
Hence, Olympus have tied for 13,10,7,4,1 times
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ASAP!! HELP!
A) Describe the relationship among the lengts of the segments formed by the secant (DB) and secant (CB) . You may use words and/or an equation.
B) Suppose DB = 18 ft, AB = 3 ft, and CB = 10 ft. Find the lengt of CE. Show all your work.
Given the following parameters DB = 18 ft, AB = 3 ft, and CB = 10 ft. Therefore, The length of the CE is 4.6 ft.
What is Secant-secant rule?The secant-secant rule states that if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant.
Mathematically:
(BA + AD)BA = (BE + EC)BE
Given the following parameters
DB = 18 ft, AB = 3 ft, and CB = 10 ft.
Substitute to check if we can find CE
(BA + AD)BA = (BE + CE)BE
(3+ 15) x 3 = (10 + CE ) x 10
18 x 3 = 100 + 10CE
54 = 100 + 10CE
CE = 4.6
Therefore, The length of the CE is 4.6 ft.
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Translate the following expression to an equation in terms of p: "151.8 is what percent of 69?"
The statement "151.8 is what percent of 69 is expressed as 0.69p = 151.8
Equations and expressionsEquations are expressions separated by an equal sign. Words can be translated to equations.
Let the unknown variable be "p". If p percent of 69is 151.8, this is expressed as;
p% of 69 = 151.8
Convert to decimals
p/100 * 69 = 151.8
0.01p * 69 = 151.8
0.69p = 151.8
Hence the statement "151.8 is what percent of 69 is expressed as 0.69p = 151.8
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reflection across the y-axis
Answer:
A reflection of a point over the y -axis is shown. The rule for a reflection over the y -axis is (x,y)→(−x,y) .
Step-by-step explanation:
Which of the following best describes the graph below?
54 -3 -2 -1
PINT
123 to
3
A. It is not a function.
B. It is a many-to-one function.
C. It is a function, but it is not one-to-one.
D. It is a one-to-one function.
Write the equation of the circle in general form. Show your work.
Answer:
x^2+2x+y^2−2y−7=0
Step-by-step explanation:
The method from converting to standard to general is very simple
this equation in standard form would be
(x+1)^2+(y-1)^2=9
This is because whatever the center of the circle is, you take the negative/positive version of that number
The center is at -1, 1. So it would flip to be put into the equation as 1, -1.
9 is the radius^2.
The radius is 3.
To convert to general form you just simplify
x^2+1+2x = (x+1)^2
y^2 + 1 -2y = (y-1)^2
x^2 - 2x + y^2 - 2y + 2 = 9
get the nine on the left side
x^2 -2x +y^2 - 2y 2 - 9 = 0
x^2+2x+y^2−2y−7=0
Give brainliest, please!
Hope this helps :)
Under what condition is √x > √25?
[tex]\sqrt x > \sqrt{25} \qquad( x\geq 0)\\\sqrt x > 5\\x > 25[/tex]
When [tex]x > 25[/tex].
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Which equation shows p, the price in dollars that she paid for her previous car?
22,500 = 2 p
2 (22,500) = p
22,500 = 2 p minus 8
2 (22,500) = p minus 8
An equation is formed of two equal expressions. The correct option is A.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Therefore, the equation shows p, the price in dollars that she paid for her previous car,
Price of new car = 2 (Price of the previous car)
22,500 = 2p
Hence, the correct option is A.
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Answer: a
Step-by-step explanation:
Given: x - 5> -2.
Choose the solution set.
OxIXER, x> -7}
OxIXER, x> -3}
OxIxER, x> 3}
Answer: [tex]\{x|x \exists \mathbb{R}, x > 3 \}[/tex]
Step-by-step explanation:
Adding 5 to both sides, we get x > 3.
which choices are equivalent to the expression below? check all that apply (image provided)
Answer:
D, E, and A
Step-by-step explanation:
Because 4 is also equivelent to square root of 16 and square root of 16 times square root of 3 is equal to square root of 48 which is D, and E is also correct because square root 24 x square root 2 is also square root 48 and same concept with A.
Use the drop down menus to correctly complete the statement.
1st-
-must be congruent
-Must not be congruent
-Can be either congruent or not congruent
2nd-
-must be perpendicular
-Must not be perpendicular
-Can be either perpendicular or not perpendicular
For a quadrilateral to be a square, the diagonals must be congruent and must be perpendicular.
need help ill be appercaited.
Step-by-step explanation:
mark me brainlist!! hope this helps
Write the equation of the line in slope-intercept form.
The equation of the line in slope-intercept form is ___
Answer:
y = 1/40x + 20
Step-by-step explanation:
Slope-intercept equation format:
y = mx + b
m = slope/ gradient/ constant of variation/ rate of change
b = y-intercept
To find the slope, use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Find two random points:
1 - (0.5, 40) , 2 - (1, 60)
Plug in:
[tex]\frac{60-40}{1-0.5}[/tex]
Solve:
[tex]\frac{20}{0.5}[/tex]
Divide:
[tex]\frac{1}{40}[/tex]
The y-intercept is when the x-coordinate is equal to 0.
The y-intercept is always the beginning.
So observing the graph, the first point is (0, 20)
The x-coordinate is 0.
Y intercept = 20.
Plug in both slope and y-intercept:
y = 1/40x + 20
Write the geometric sequence in function notation.
Answer:
d
Step-by-step explanation:
Which of the following is equidistant from a given directrix and focus?
The term used to describe the equidistance from a given directrix and focus is: C. a locus of points called a parabola.
What is a Parabola?A parabola can be defined as a curve on a plane where any given point is at equal distance from the focus (fixed point), and from a directrix (fixed straight line).
Thus, we can conclude that what is a locus of points called a parabola is equidistant from a given directrix and focus.
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8. Simplify (+2) × (+6) (-3)
Step-by-step explanation:
= ( +2 ) × ( + 6 ) ( -3 )
= + 12 (- 3 )
[tex] = - 36[/tex]
hence - 36 is the answer...
Graph: y+2=-3/4(x+4)
Solve the following equation by factoring.
y²-8y=0
Answer:
y=0, y=8
Step-by-step explanation:
y²-8y=0
y(y-8)=0
so either y=0 or y-8=0
so y=0, y=8
Height of a softball in feet h(t)=3+55+-+16+2
Answer:
18ft
Step-by-step explanation:
i can't lay out the formula
PLS HELP ME ASAP!!!!!
Answer:
c
Step-by-step explanation:
its just the dilate of the triangle which both add up to 180