Solve for x in the equation x squared + 20 x + 100 = 36.
x = –16 or x = –4
x = –10
x = –8
x = 4 or x = 16
Answers
x=-4 if you are in a hurry
The solution of the equation are; x = -16 or x = -4. so option A is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given equation;
x²+ 20 x + 100 = 36.
x²+ 20 x + 100 - 36 = 0
x²+ 20 x + 64 = 0.
x²+ (16 + 4)x + 64 = 0.
x²+ 16x + 4x + 64 = 0.
x(x + 16) +4 (x + 16) = 0.
(x+ 4) (x + 16) = 0
Thus, the solution of the equation are; x = -16 or x = -4.
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Related Questions
a 2-kg block slides down a 3-meter-long, frictionless 30° incline. if the block started from rest at the top of the incline, with what speed does it reach the bottom?
Answers
The block reaches the bottom of the incline with a speed of approximately 7.66 m/s.
The acceleration of the block is given by
a = g sin 30 = 9.8 m/s² × 0.5 = 4.9 m/s²
Where g is the acceleration due to gravity.
The distance travelled by the block is given by
d = 3 m
The initial velocity of the block, u = 0
Using the kinematic equation, v² = u² + 2as
The final velocity of the block,v is given by
v = sqrt(2 × 4.9 × 3) ≈ 7.66 m/s
Therefore, the block reaches the bottom of the incline with a speed of approximately 7.66 m/s.
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What is the simplified form of \(\sqrt{400x ^{100}\)
Answers
Answer:
\(20x^{50}\)
Step-by-step explanation:
This is because you are simplifying the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
There is your answer!
Solve the system of equations using matrices. Use the Gaussian elimination method with back substitution
Answers
The first step is to write the system of equations as an augmented matrix:
\(\begin{bmatrix}{4} & {-5} & {+4|} & {-67} \\ {5} & {-4} & {-3|} & {-12} \\ {1} & {-5} & {+0|} & {-36} \\ {} & {} & {} & {}\end{bmatrix}\)The next step is to let the first number at the mid-row to zero, then let
R2-5/4*R1->R2
\(\begin{bmatrix}{4} & {-5} & {+4|} & {-67} \\ {0} & {9/4} & {-8|} & {287/4} \\ {1} & {-5} & {+0|} & {-36} \\ {} & {} & {} & {}\end{bmatrix}\)Now, let's convert the first number in the last row to 0, then:
R3-1/4*R1->R3
\(\begin{bmatrix}{4} & {-5} & {+4|} & {-67} \\ {0} & {9/4} & {-8|} & {287/4} \\ {0} & {-15/4} & {-1|} & {-77/4} \\ {} & {} & {} & {}\end{bmatrix}\)Let's convert the first number in the first row to 1, then:
1/4*R1->R1
\(\begin{bmatrix}{1} & {-5/4} & {+1|} & {-67/4} \\ {0} & {9/4} & {-8|} & {287/4} \\ {0} & {-15/4} & {-1|} & {-77/4} \\ {} & {} & {} & {}\end{bmatrix}\)Now, let's convert the second number in the last row to zero:
R3-(-5/3)R2->R3
\(\begin{bmatrix}{1} & {-5/4} & {+1|} & {-67/4} \\ {0} & {9/4} & {-8|} & {287/4} \\ {0} & {0} & {-43/3|} & {301/3} \\ {} & {} & {} & {}\end{bmatrix}\)Now let's convert the third number in the last row to 1:
(-3/43)R3->R3
\(\begin{bmatrix}{1} & {-5/4} & {+1|} & {-67/4} \\ {0} & {9/4} & {-8|} & {287/4} \\ {0} & {0} & {+1|} & {-7} \\ {} & {} & {} & {}\end{bmatrix}\)And finally, convert the second number in the mid-row to 1:
(4/9)*R2->R2
\(\begin{bmatrix}{1} & {-5/4} & {+1|} & {-67/4} \\ {0} & {1} & {-32/9|} & {287/9} \\ {0} & {0} & {+1|} & {-7} \\ {} & {} & {} & {}\end{bmatrix}\)Now, we obtained the next equations:
\(\begin{gathered} x-\frac{5}{4}y+z=-67/4\text{ Equation (1)} \\ y-\frac{32}{9}z=287/9\text{ Equation (2)} \\ z=-7\text{ Equation (3)} \end{gathered}\)Replace equation 3 into equation 2 and solve for y:
\(\begin{gathered} y-\frac{32}{9}\cdot(-7)=\frac{287}{9} \\ y+\frac{224}{9}=\frac{287}{9} \\ y=\frac{287}{9}-\frac{224}{9} \\ y=\frac{63}{9} \\ y=7 \end{gathered}\)Now, replace x and y in equation 1 and solve for x:
\(\begin{gathered} x-\frac{5}{4}\cdot7+(-7)=-\frac{67}{4} \\ x-\frac{35}{4}-7=-\frac{67}{4} \\ x=-\frac{67}{4}+\frac{35}{4}+7 \\ x=\frac{-32}{4}+7 \\ x=-8+7 \\ x=-1 \end{gathered}\)Therefore, the solution set is: (-1, 7, -7)
Use the model why 522 is divisible by 9
Answers
Answer:
The rule for divisibility by 9 works because numbers are written in base 10.
Step-by-step explanation:
5 + 2 + 2 = 9
9 is divisible by 9, Therefore, 522 is divisible by 9
Describe IN WORDS how you would solve the equation: 4 + x = -9
Answers
Step-by-step explanation:
4 + x = -9
x = -9 +4
x = - 5
-x = -5
x = 5
Suppose that a product has six parts, each of which must work in order for the product to function correctly. The reliabilities of the parts are 0.82, 0.76, 0.55, 0.62, 0.6, 0.7, respectively. What is the reliability of the product?
a. 0.089
b. 0.98
c. 0.56
d. 3.2
e. 4.05
Answers
Calculating this expression, we find that the reliability of the product is approximately 0.089.
The reliability of a system or product is defined as the probability that it will function correctly over a given period of time. In this case, the reliability of the product is determined by the reliability of its individual parts. To calculate the overall reliability of the product, we multiply the reliabilities of each part together:
Reliability of the product = Reliability of part 1 * Reliability of part 2 * Reliability of part 3 * Reliability of part 4 * Reliability of part 5 * Reliability of part 6Substituting the given values, we have:
Reliability of the product = 0.82 * 0.76 * 0.55 * 0.62 * 0.6 * 0.7
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8. Archie plotted the points on the graph below to show how the amount he owes for tuition decreases as the number of tuition payments increases. What does the rate of change of the points represent? *
Answers
Answer:c
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
Answers
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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What is happening to the x?
Answers
Answer:
If you are talking about mathematics, X is a a variable in an algebraic problem.
Please help!
Solve the inequality for x
#19
Answers
Answer:
Step-by-step explanation:
2x - 13 - 8x + 5 ≥ -7
-6x - 8 ≥ -7
-6x ≥ 1
x ≤ -1/6
4 out of every 7 students in a school eat a packed lunch. The rest eat a school meal.
Which of the following statements is correct?
47% of students eat a school meal
The ratio of school meal to packed lunch is 7 : 4
The ratio of packed lunch to school meal is 4 : 3
56% of students eat a packed lunch
Answers
So the ratio is 4:3
ayuda mañana tengo examen y nesesito saber cuanto es 4 dividido entre 0.93
Answers
\(\displaystyle\\Answer: \frac{400}{93}\approx4.3\)
Step-by-step explanation:
\(\displaystyle\\4:0.93=\\\\\frac{4}{0.93 }=\\\\\frac{4}{\frac{93}{100} } \\\\\frac{4*100}{93} \\\\\frac{400}{93} \approx\\\\4.3\)
A coffee farmer in Costa Rica currently has costs of 70 cents
per kilogram to grow and harvest the coffee, plus $2000 of
fixed costs for land management per year. She can sell her
green, unroasted beans for a guaranteed $1.20 per kilogram.
System of linear equation
PLS HELP ME! THIS IS FOR MY FINAL EXAM!
Answers
The linear equations representing the scenario are:
a) y = 1.20xb) t = 2,000 + 0.7x.What is a system of linear equations?A system of linear equations involves two linear equations with two variables.
One equation represents the total cost function, including fixed and variable costs.
The second equation represents the total revenue function.
The variable cost for growing and harvesting coffee per kilogram = $0.70
The fixed costs for land management per year = $2,000
Let x = the quantity of coffee in kilograms
Total cost, t = 2,000 + 0.7x
Revenue per kilogram = $1.20
Total revenue, y = 1.20x
Thus, the farmer's total revenue and cost functions can be represented by the following two linear equations: a) y = 1.20x and b) t = 2,000 + 0.7x.
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Find the X and Y intercepts and graph the line. Your X and Y must be written as a point. show work plz asap help
Answers
Answer:
14 X+2y=6
0+2y=6
2y=6
2y÷2=6÷2
y=3
x+2y=6
x+2(0)=6
x+0=6
X=6
(13) The x and y intercept of the line x + y = 1 are 1 and 1 respectively.
(14) The x and y intercept of the line x + 2y = 6 are 6 and 3 respectively.
What is the slope intercept form of an equation ?When any equation is represented in the y = mx +c form, it is called the slope intercept from of the equation.
Here m is slope and c is constant.
(13)
The given equation of line,
x + y = 1
x intercept of the line is at y = 0,
x + 0 = 1
x = 1
y intercept of the line is at x = 0,
0 + y = 1
y = 1
The x and y intercept of the line x + y = 1 are 1 and 1 respectively.
(14)
The given equation of line,
x + 2y = 6
x intercept of the line is at y = 0,
x + 0 = 6
x = 6
y intercept of the line is at x = 0,
0 + 2y = 6
y = 3
The x and y intercept of the line x + 2y = 6 are 6 and 3 respectively.
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please helpppppppppp
Answers
Answer:
the popularity keeps going up i wount give the euashions though i dont know them.
Step-by-step explanation:
With regularly distributed data, what percentage of the data points will fall within one standard deviation from the mean?.
Answers
Answer:
68%
Step-by-step explanation:
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
What is the volume of the figure???
Answers
Answer:
1530cm
Step-by-step explanation:
First figure (9x10)x9=810
Second figure (18x10)x4=720
720+810=1530
Given the arithmetic sequence 2, -7, -16, -25, ..., determine the
general term tn.
Answers
Answer:
Step-by-step explanation:
Common difference is -9.
t_1 = 2
t_n = t_1 - (n-1)9
= t_1 - (9n - 9)
= 2 - (9n - 9)
= 11 - 9n
help I will give brainiest
Answers
Answer:
A
Step-by-step explanation:
-2,4
Answer:
Option A (-2,4)
Step-by-step explanation:
It is where the lines intersect
Hope this helped, have a nice day! :)
Ben walks 500 meters from his house to the corner store. He then walks back toward his house, but continues 200 meters past his house to talk to a neighbor. It takes Ben 17 minutes from the time he leaves his house until he stops to talk to his neighbor. What is Ben’s average velocity? Round to the nearest tenth.
Answers
Answer:
0.2
Step-by-step explanation:
Edge 2020
Thanks to the people who commented the correct answer on the wrong answer!
Ben's average speed will be equal to 70.5 meters per minute.
What is an average speed?Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
It is given that Ben walks 500 meters from his house to the corner store. He then walks back toward his house but continues 200 meters past his house to talk to a neighbour. It takes Ben 17 minutes from the time he leaves his house until he stops to talk to his neighbour.
The average speed is calculated as below:-
Average speed = Total distance / Total time
Average speed = ( 500 + 500 + 200 ) / 17
Average speed = ( 1200 ) / 17
Average speed = 70.5 meters per minute.
Therefore, Ben's average speed will be equal to 70.5 meters per minute.
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17. Problem What is the pressure in KPa 1.20 below the surface of a liquid of : 1.50 the gas pressure on the surface is 0.40 atmosphere? a) 42.99 kPa c) 47.04 kPa. d) 63.12 kPa b) 58.20 kPa
100.
Answers
The correct option is c. The pressure in kPa 1.20 below the surface of a liquid is 47.04 kPa.
Given:
Pressure at surface = 0.40 atm
Pressure below the surface = 1.20 m
Density of the liquid = 1500 kg/m³
G = 9.81 m/s²
The pressure due to the weight of the liquid is given as:
P = ρgh
where,ρ is the density of the liquid
h is the depth of the liquid
G is the acceleration due to gravity
At 1.20m below the surface of the liquid, the pressure due to the weight of the liquid is:
P = ρgh
= 1500 kg/m³ × 9.81 m/s² × 1.20m
= 17640 Pa
The total pressure at 1.20m below the surface of the liquid is the sum of the pressure due to the weight of the liquid and the pressure due to the weight of the air. The pressure due to the weight of the air is calculated as follows:
Pa = P0 + ρgh
where,
P0 is the pressure at the surface of the liquid
= 0.40 atm
= 0.40 × 101.325 kPa
= 40.53 kPa
Pa = P0 + ρgh
= 40.53 kPa + 1500 kg/m³ × 9.81 m/s² × 1.20m
= 47.04 kPa
Hence, the pressure in kPa 1.20 below the surface of a liquid is 47.04 kPa.
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PLEASE HELP!!
If you draw a triangle with these measurements, which kind of triangle would it be?
Angles Sides
40∘ 4 cm
50∘ 7 cm
90∘ 8 cm
Answers
Step-by-step explanation:
I think it should be right angle
Find the value of x in the triangle shown below.
Answers
Answer: B square root of 40
Step-by-step explanation:
You're trying to find the length of the hypotenuse so you need to use the formula a^2 + b^2 = c^2
c = x
a = 2
b = 6
So 2^2 + 6^2 = x^2
Which equals: 4 + 36 = x^2
This can be simplified into 40 = x^2
And to get x by itself, just take the square root of each side: Square root of 40 = x
What is the slope and y-intercept of the following equation: y = -4 +2x
Answers
Answer:
slope = 2, y- intercept = - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4 + 2x , that is
y = 2x - 4 ← is in slope- intercept form
with slope m = 2 and y- intercept c = - 4
What is the quotient of (x3 3x2 5x 3) Ă· (x 1)? x2 4x 9 x2 2x x2 2x 3 x2 3x 8.
Answers
The quotient of expression is \(\rm x^2+2x+3\).
Given that,
Expression; \(\rm\dfrac{ (x^3 + 3x^2 + 5x + 3) }{ (x + 1)}\)
We have to determine,
The quotient of expression?
According to the question,
To determine the quotient of expression following all the steps given below.
Simplify the expression,
\(\rm =\dfrac{ (x^3 + 3x^2 + 5x + 3) }{ (x + 1)}\\\\= \dfrac{ (x^3 + 2x^2 + 3x + x^2+2x+ 3) }{ (x + 1)}\\\\ = \dfrac{ x(x^2+ 2x+ 3) + 1(x^2+2x+ 3) }{ (x + 1)}\\= \dfrac{ (x^2+ 2x+ 3) (x+1) }{ (x + 1)}\\\\= x^2+2x+3\)
Hence, The required quotient of expression is \(\rm x^2+2x+3\).
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Find the Sine, cosine, tangent of - 120
Answers
Solution
Find the Sine, cosine, tangent of - 120
\(\sin (-120)\)\(\begin{gathered} \mathrm{Use\: the\: following\: property\colon}\: \sin \mleft(-x\mright)=-\sin \mleft(x\mright) \\ \sin \mleft(-120^{\circ\: }\mright)=-\sin \mleft(120^{\circ\: }\mright) \\ =-\sin \mleft(120^{\circ\: }\mright) \\ =-\frac{\sqrt{3}}{2} \end{gathered}\)\(\cos (-120)\)What is 3m³n² + 4m²n
Answers
Answer:
3m³n² + 4m²n
=3m²mnn+4m²n
=m²n(3mn+4)
Find the value of x.
A 15.0
B. 13.5
C. 9.0
D. 7.5
Answers
Answer:
D
Step-by-step explanation:
The segment inside the triangle is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is
\(\frac{x}{7}\) = \(\frac{15}{14}\) ( cross- multiply )
14x = 105 ( divide both sides by 14 )
x = 7.5 → D
the diagram below, not drawn to scale, shows right angled triangles EDC and ABC. Angle ABC = 30°, BD = 20° cm, AC = 9cm and DE = 8cm.
Calculate, giving your answer correct to 1 dp.
The length of BC, in cm.
The size of angle EDC in degrees.
Answers
The length of side BC is 15.6 cm and the size of angle EDC in degrees is 56.5°
Calculating angles and length of sides of a triangleFrom the question, we are to determine the length of BC
From the given information,
m ∠ABC = 30°
AC = 9 cm
By using SOH CAH TOA, we can write that
tan (m ∠ABC) = AC / BC
tan (30°) = 9 / BC
BC = 9 / tan (30°)
BC = 15.588
BC ≈ 15.6 cm
To determine the measure of angle EDC,
First we will determine the length of CD
From the diagram,
BD = BC + CD
20 = 15.588 + CD
CD = 20 - 15.588
CD = 4.412
Now, using SOH CAH TOA
cos (m ∠EDC) = CD / DE
cos (m ∠EDC) = 4.412 / 8
cos (m ∠EDC) = 0.5515
m ∠EDC = cos⁻¹(0.5515)
m ∠EDC = 56.5300°
m ∠EDC ≈ 56.5°
Hence, the length of BC is 15.6 cm and the measure of EDC is 56.5°
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Which equations can be used to solve for y, the length of the room? Select three options.
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0