Answers
Step-by-step explanation:
since AD is an altitude (height) of ABC, the angle at D must be 90° (that is the definition of an altitude or height).
so,
90 = x² + 6x + 18
72 = x² + 6x
0 = x² + 6x - 72
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-6 ± sqrt(6² - 4×1×-72))/(2×1) =
= (-6 ± sqrt(36 + 288))/2 = (-6 ± sqrt(324))/2 =
= (-6 ± 18)/2 = -3 ± 9
x1 = -3 + 9 = 6
x2 = -3 - 9 = -12
so, the 2 solutions are
x = 6
x = -12
Related Questions
Look at the number line below.
A number line labeled from 0 to 3 with tick marks every one-tenth unit. Tick marks 0, 1, 2, and 3 are labeled. There is a dot at the third tick mark to the right of 2.
Identify the point on the number line and write it as both a fraction and a decimal.
Fraction:
Decimal:
Answers
Answer:
fraction 23/10 that's 2 ³/10
decimal 2.3
A rectangle’s width w, height h, and area A are all functions of time t. At the instant when the rectangle’s area is 20 square inches and the width is 4 inches, the height is decreasing at a rate of 3 inches per second while the area is increasing at a rate of 7 square inches per second. Determine the rate of change of the width of the rectangle at that instant.
Answers
The rate of change of the width of the rectangle at that instant is 3.8 inches/sec.
What is meant by a rectangle?Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).
A crossed rectangle is a crossed quadrilateral made up of two opposing sides and the two diagonals of a rectangle. It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic, with opposite sides of equal length and equal angles that are not right angles.
We have,
W=width of the rectangle
H=height of the rectangle
A=Area of the rectangle
We know that,
A=W×H
A=20, W=4
20=4×H
H=5 inches
dA/dt=7 (inches)²/sec
dH/dt= -3 inches/sec
dA/dt=W.(dH/dt)+H×dW/dt
dA/dt=4(-3)+5(dW/dt)
7=-12+5(dW/dt)
dW/dt=19/5
dW/dt=3.8 inches/sec
Therefore, the rate of change of the width of the rectangle at that instant is 3.8 inches/sec.
To know more about rectangle, visit:
https://brainly.com/question/15019502
#SPJ1
An executive committee consists of 9 members: 5 men and 4 women. 3 members are selected at random to attend a
meeting in Hawaii. The names are drawn from a hat. What is the probability that all 3 selected are men?
Answers
Answer:P(3 men) =
Step-by-step explanation:
18. a. If ΔA B C is rotated 180° about the origin, what are the coordinates of B'
If Δ A B C is to be translated to ΔA'B'C' by the following motion rule:
(x,y)⇒(x-2,y+4)
What will be the coordinates of vertex A'?
Answers
a. The coordinates of vertex B is (-3, -4)
b. The coordinates of vertex A' is (3,8)
What do you mean by rotation 180° about the origin?
The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).
Solution:
a. Current coordinate of vertex B is (3, 4).
After rotating it 180° it becomes B (-3 , -4)
b. After translation the coordinates of vertex A is (5-2,4+4)
Coordinates of vertex A is (3,8)
To learn more about coordinates :
https://brainly.com/question/21548580
#SPJ4
If ΔA B C is rotated 180° about the origin, the coordinates of B' (-3, -4)
b. The coordinates of vertex A' is (3,8)
What do you mean by rotation 180° about the origin?
The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).
Solution:
a. Current coordinate of vertex B is (3, 4).
After rotating it 180° it becomes B (-3 , -4)
b. After translation the coordinates of vertex A is (5-2,4+4)
Coordinates of vertex A is (3,8)
To learn more about coordinates
brainly.com/question/21548580
#SPJ4
A manufacturing company finds that they can sell 250 items at $3.50 per item and 350 items at $2.50 per item.
If the relationship between the number of items sold a and the price per item p is a linear one:
Find a formula that gives a in terms of p: x =
Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell…
items if the price is $1.50.
Answers
Answer:
a = 600 -100pa = 450 for p = 1.50Step-by-step explanation:
You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.
SlopeWe can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...
m = ∆a/∆p = 100/(-1) = -100
InterceptThe y-intercept (b) can be found by solving the slope-intercept equation for b:
y = mx +b
b = y - mx
For (x, y) = (3.50, 250), the value of 'b' is ...
b = 250 -(-100)(3.50) = 600
EquationThe slope-intercept equation for 'a' in terms of p is ...
a = -100p +600
Evaluation
The value of 'a' for p = 1.50 is ...
a = -100(1.50) +600
a = 450
They will sell 450 items if the price per item is $1.50.
Find the missing measures listed below given that the picture below is an incenter.
m∠MJL=__
m∠JLP=__
Answers
The required measures of angles are:
∠MJL = 78°
∠JLP = 28°
What is incenter ?
One of the triangle's centers where the bisectors of the inner angles converge is known as the incline. The incenter is often referred to as the incircle's center in a triangle. An incenter might have several distinct types of characteristics.
The junction point of the central axis, which is the center of the triangle's inscribed circle, places this point at an equal distance from each of the triangle's sides. Since the biggest circle that might fit within a triangle is the incenter, it is also referred to as the center of the triangle's circle.
In the figure,
∠PJL = ∠MJP = 39°
∠MJL = ∠PJL + ∠MJP = 39° + 39° = 78°
∠PLK = 28°
∠JLP =∠PLK = 28°
To learn more about incenter from the link below-
https://brainly.com/question/29630715
#SPJ4
The required measures of angles are:
∠MJL = 78°
∠JLP = 28°
What is the incenter of a triangle?
The inclination is one of the triangle's centers where the inner angles' bisectors converge. The incenter is frequently referred to as the triangle's incircle's center. Multiple different types of features could apply to an incenter.
This point lies at an equal distance from each of the triangle's sides because it is the intersection point of the central axis, which is also the center of the inscribed circle. The incenter is also referred to as the triangle's circle's center since it is the largest circle that could possibly fit inside a triangle.
In the figure,
∠PJL = ∠MJP = 39°
∠MJL = ∠PJL + ∠MJP = 39° + 39° = 78°
∠PLK = 28°
∠JLP =∠PLK = 28°
Learn more about the incenter of a triangle from the link below:
brainly.com/question/29630715
#SPJ4
HELP PLEASE! I WILL GIVE BRAINLIEST
Answers
The maximun value (63) is located at point (1, 2).
Step-by-step explanation:Used method: Graph method from operations research.1. Graph the restrictions.Check attached image 1.
The purple coloured area represents the resulting area of possible answers that meet all the requirements established by the restrictions within the cartesian plane.
2. Find all extreme values.In this step, we need to look for extreme values, these are normally found on the edges and corner of the area drawn by all the restrictions.
Check attached image 2 to see the extreme values.
Point A is located at: (-3, -2)
Point B is located at: (-3, -4)
Point C is located at: (3, -4)
Point D is located at: (1, 2)
3. Evaluate all extreme points using the given function.Given function: [tex]P=10x+6y+41[/tex]
Since we are tryong to obtain the point where there is a maximun value for function "P", we need to evaluate all the extreme points and choose the one that makes the function return the maximum value out of all 4 points.
Evaluating the points:
[tex]P(-3, -2)=10(-3)+6(-2)+41=-1\\ \\P(-3, -4)=10(-3)+6(-4)+41=-13\\ \\P(3, -4)=10(3)+6(-4)+41=47\\ \\P(1, 2)=10(1)+6(2)+41=63[/tex]
4. Conclude.The maximun value (63) is located at point (1, 2).
Note:There's a different method called "Simplex" that can also be used to solve these type of optimization problems. It's more complicated but can be useful when working with more than 2 variables.
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional
questions.
Online Content: Site 1
One of the advantages to an employer of paying employees piece rate or commission is that the employee is paid based solely on
their performance. What is one disadvantage of this type of pay?
BIUS X, X²
ΕΞΩ
I
B
T
Answers
The disadvantage of piece rate pay is that the cost of producing higher quantities of a product can be a reduction in the quality of the items produced.
What is piece rate?Piece rate is any type of job in which a worker is paid a set amount for each unit produced or action performed, regardless of time. Some employees may be paid on a piece rate or on a commission basis.
Employees are paid on a piece rate, and commission payments are based on results rather than an hourly or weekly pay rate. This means that the employee's weekly pay will vary depending on how much work they do. One of the drawbacks of piece rate pay is that the cost of producing larger quantities of a product may result in a decrease in the quality of the items produced.
Learn more about piece rate on:
https://brainly.com/question/12725137
#SPJ1
Determine the probability: There is a 40% chance of rain this weekend.
a. 0.60
b. 0.40
c. 40
d. 4
Answers
Answer:
Step-by-step explanation:
how do i find the inverse of f(x)=[tex]\sqrt[3]{5x+5}[/tex]
Answers
The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
What is inverse of function?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).Change y in for the f(x) :
y = ∛5x + 5
Switch the x and y
x³ = 5y + 5
x³ - 5 = 5y
y = ( x³ - 5 ) / 5
f⁻¹ = ( x³ - 5 ) / 5
Hence, The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
To check more about inverse check the below link:
https://brainly.com/question/3831584
#SPJ1
The lengths of footlong sub sandwiches at a local sub shop follow an approximately normal distribution with unknown mean
and standard deviation 0.2 inch. If 20% of these sandwiches are shorter than 11.7 inches, find the mean length u.
Mean
inches
(Round to 2 decimal
Answers
Answer:
Step-by-step explanation:
simplify 3/7 + 1/7 please answer
Answers
Answer:
2/7 ≈0.285714286
Step-by-step explanation: 3/7−1/7
Since 3/7 and 1/7 have the same denominator, subtract them by subtracting their numerators.
3−1 over 7
Subtract 1 from 3 to get 2.
2/7
the Factor
so 2/7 ≈0.285714286
The Greek letter ___ represents the correlation between two numerical variables for a population.
Answers
The Greek letter rho represents the correlation between two numerical variables for a population.
What is Rho?
The amount of money an option will lose or gain with a 1% change in interest rates is how Rho, which gauges an option's sensitivity to changes in the risk-free rate of interest (the interest rate paid on US Treasury bills), is calculated.
How is rho determined?
Rho's exact formula is challenging. The first derivative of the option's value with regard to the risk-free rate is however used to compute it.
Rho calculates the anticipated change in price of an option for a 1% change in the risk-free rate of a US Treasury bill.
Learn more about Rho
brainly.com/question/14471186
#SPJ4
If cos (0) = -3.29, what is cos (+0)?
A. -3.29
B. 3.29
C. 73.1°
D. -73.1°
Answers
Answer:
A
Step-by-step explanation:
There is no difference between -0 and +0.
So the ans is -3.29 itself.
help. plsss i dont understand so gimme a answer or something
Answers
Which equation best represents a line perpendicular to a line passing through points (–1, 2) and (1, –8)?
Answers
Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0
The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be
y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)
y + 8 = -5x + 5
y = - 5x - 3
The equation that best represents a line perpendicular will be y = - 5x - 3.
You have one type of candy that sells for $2.00/lb and another type of candy that sells for $8.90/lb. You would like to have 55.2 lbs of a candy mixture that sells for $2.50/lb. How much of each candy will you need to obtain the desired mixture?
You will need ___ lbs of the cheaper candy
and ____ lbs of the expensive candy.
Answers
You will need 51.2 lbs of the cheaper candy and 4 lbs of the expensive candy.
What is equation of two variables?A equation is supposed to be straight condition in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight conditions in two factors
According to given information:Let x be number of pounds of cheaper candy and y represent that of expensive candy.
Then, x + y = 55.2----(1)
And
2x + 8.9y = 55.2(2.5) = 138
2x + 8.9y = 138---------(2)
On solving above two equation, we get
x = 51.2
y = 4
Thus, cheaper candy are of 51.2 ib and expensive are of 4 ib
To know more about such problem visit:
brainly.com/question/15255875
#SPJ1
Find the volume of a cone with a radius of 11.5 inches and a height of 15 inches. Enter the answer in terms of pie
Answers
The volume of a cone with diameter 11.5 inches and a height of 15 inches is 519 in³.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreases to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, A cone with a radius of 11.5 inches and a height of 15 inches.
Now, The diameter is 11.5 inches, hence radius is 11.5/2 = 5.75 inches.
We know the volume of a cone is (1/3)πr²h.
∴ The volume of a cone is = (1/3)×π×(5.75)²×15 inch³.
= 519 in³.
learn more about cones here :
https://brainly.com/question/23863102
#SPJ1
Which system of linear inequalities is graphed?
y ≤3x-2
x+ 2y≥4
y≥3x-2
x+2y ≤4
y< 3x-2
x+2y>4
y>3x-2
x+2y <4
Answers
The system of linear inequalities is graphed is y≥3x-2; x+2y ≤4. Hence option b is the correct.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The graph consists of two inequalities.
Since the graph lines are solid, thus the inequality sign either "less than or equal" or "greater than or equal".
First find the equation of line.
One line passes through the points (0,2) and (4,0).
The equation of line that passes through the point (a,0) and (0,b) is
x/a + y/b = 1
The equation of the line is x/4 + y/2 =1
(x + 2y)/4 = 1
x + 2y = 4
The equation of the inequality will be either x + 2y ≤ 4 or x + 2y ≥ 4.
Putting x =0 and y = 0 in x + 2y ≤ 4
0 + 0 ≤ 4
0≤ 4 (true)
In the graph (0,0) includes in the shaded region. Therefore the inequality is x + 2y ≤ 4.
The second line passes through the points (0,-2) and (3,7).
If a line passes through the points (x₁, y₁) and (x₂, y₂), then the equation of line is y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).
The equation of the line is
y - 7 = (7 + 2)/(3 - 0)(x - 3)
y - 7 = 3x -9
y = 3x - 2
The equation of the inequality will be either y ≥ 3x-2 and y ≤ 3x-2:
Putting x =0 and y = 0 in y ≥ 3x-2
0 ≥ 0-2
0 ≥ -2 true
In the graph (0,0) includes in the shaded region. Therefore the inequality is y ≥ 3x-2.
To learn more about system of linear inequalities, click on below link:
https://brainly.com/question/13685981
#SPJ1
The radius of a cylindrical construction pipe is 2.5. If the pipe is 28ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:V = 550 ft^3
Step-by-step explanation:
The volume of a cylinder is
V = pi r^2 h
We know the radius is 2.5 and the height is 28
V = 3.14 * (2.5)^2 * 28
V =549.5 ft^3
Rounding to the nearest whole number
V = 550 ft^3
What is this equal to: (3*2)+6
Answers
Answer:
12
Step-by-step explanation:
(3x2) + 6
6 + 6 = 12
Answer:
12
Step-by-step explanation:
3 × 2 is 6
6 + 6 is 12
thus answer is 12
What is the total number of units (in millions) of electricity produced
each year based on the current extraction rates of coal from all
mines combined assuming all mines have an endless supply of
coal?
Answers
Answer:
Just by multiplying the extraction by the output per kilo for each mine and then summing it. The question asks to express it in millions and you have 8.2 million units
Step-by-step explanation:
Hope it helps
9. RWS congruent to TUV. Find the values of x and y.
Answers
The value of x would be 11° and the value of y would be 6.
What are congruent triangles?
Two triangles are congruent if all of their sides are the same - so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.
ΔRWS ≅ ΔTUV
As both triangles are congruent then we can say that
∠S ≅ ∠V
so ∠S = 29°
Now in ΔRWS,
By using the sum of all angles of the triangle property, we can write
∠R +∠W + ∠S = 180°
(8x - 27)° + 90° + 29° = 180°
8x = 180° - 92°
8x = 88°
x = 88/8
x = 11°
Now Side RS ≅ Side TV
3y + 7 = 25
3y = 25 - 7
3y = 18
y = 18/3
y = 6
Hence, the value of x would be 11° and the value of y would be 6.
To learn more about congruent triangles, visit:
https://brainly.com/question/3999145
#SPJ1
Karen sold 15 hand-made bracelets, earning a total profit of $71.25. She plans to make 25 bracelets for her city’s arts and crafts market. If she sells all 25 bracelets, how much profit can Karen expect to earn?
Answers
Answer: $118.75
Step-by-step explanation: first to see how much one bracelet is, you have to do 71.25/15=4.75. one bracelet is $4.75. so now we multiply 4.75 by 25 to see how much 25 bracelets cost. 4.75x25=118.75. so, if Karen seems all of her bracelets, she can expect to make $118.75.
Please help me
Solve the answer
Arc QR =
Arc RS =
Answers
Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:
Arc QR = 48°
Arc RS = 96°
Arc QPS = 216°
Arc PSR = 186°
Arc SRQ = 144°
What is the Inscribed Angle Theorem?The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.
Find arc PSR:
Arc PSR = 2(93) [based on the inscribed angle theorem]
Arc PSR = 186°
Find arc QR:
Arc QR = 360 - arc PQ - arc PSR
Substitute
Arc QR = 360 - 126 - 186
Arc QR = 48°
The value of ARC QR is 48
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
The value of ARC RS is 96
Arc QPS = 126 + 90
Arc QPS = 216°
Arc PSR = arc PS + arc RS
Arc PSR = 90 + 96
Arc PSR = 186°
Arc SRQ = arc RS + arc QR
Arc SRQ = 96 + 48
Arc SRQ = 144°
Therefore the value of ARC QR is 48° and ARC RS is 96°
To learn more about Inscribed angle refer to :
https://brainly.com/question/3538263
#SPJ1
help me please thank youuuu
Answers
Answer:
g(x)= -x^2 - 3
Step-by-step explanation:
We know the vertex is (0, -3) and the parabola is opening downward that means the a value has to be negative. And if you know the transformation that -3 moves the parabola down by 3 units as f(x) represents the parent function y= x^2
PLEASE HURRY I NEED TO FINISH MY TEST!!
Determine which integer in the solution set will make the equation true.
8x − 4 = 2(2x + 4)
S: {−4, 0, 3, 12}
A.−4
B.12
C.0
D.3
Answers
Answer: x=3
Step-by-step explanation:
When you plug in each number only 3 is the right answer.
A. 8(-4)-4=2(2(-4)+4)
-36=8 False
B. 8(12)-4=2(2(12)+4)
92=56 False
C. 8(0)-4=2(2(0)+4)
-4=8 False
D. 8(3)-4=2(2(3)+4)
20=20 True
Knowledge Check
The graph below shows the numbers of orders received by a company for five months.
Number of orders
3400
3300-
3200-
3100-
3000-
2900+
2800-
March
April
May
Month
une
(a) What was the greatest number of orders in a month?
orders
(b) When did the number of orders have the greatest
decrease?
July
X
Ś
Answers
The Greatest Number of orders were in the month = September
The Numbers of orders increased in month = August to September
What is a graph ?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
According to the given information
From graph
We got to know
In may , orders = 3150
In June , orders = 3050
In July , orders = 2900
In August , orders = 3200
In September , orders = 3250
a) The Greatest Number of orders were in the month = September
b) The Numbers of orders increased in month = August to September
To know more about Graph
https://brainly.com/question/24861666
#SPJ1
A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 90% per year. Estimate the population after one year p 1 = Estimate the population after two years p 2 =
Answers
Answer:
p1 = 95 p2 = 180
Step-by-step explanation:
50 + 90% = 95
95 + 90% = 180
HURRY HELP ME! A group of workers is harvesting berries at a constant rate. The following equation represents the total number of baskets of berries the workers picked over a period of time, in hours y = 10x + 5.
What are the slope and the y-intercept for the equation?
X represents the hours, what does y represent and measure in the context of this situation?
What are the rate of change and the initial amount? Explain the meaning of the rate of change and the initial amount in the context of the situation.
Use graph below to draw a graph for the equation y=10x+5. Label the axes appropriately for the situation.
Answers
Step-by-step explanation:
The equation y=10x+5 is in the y=mx+b format, where m is the slope and b is the y-intercept.
The slope is 10 and the y-intercept is 5.
Since x represent the number of hours picking berries, y would represent the total number of berries picked.
Y-intercept (or the initial amount) is 5, and slope (aka rate of change) is 10.
y=10x+5 replace x to 1 so it means that one hour has passed
y=10(1)+5 simplify
y=10+5
y=15 y represents the total number of berries picked
That means 15 berries would be picked in one hour.
I uploaded an image of how the graph would look like.