Answer:
-1/2, 5/3
Step-by-Step Explanation:
6z^2 - 7z - 5 = 0
=> 6z^2 - 10z + 3z - 5 = 0
=> 2z(3z - 5) + 1(3z - 5) = 0
=> (2z + 1)(3z - 5) = 0
=> z = -1/2, 5/3
Hope it helps.
If you have any query, feel free to ask.
RAMP The height of a ramp can be
modeled by f(x) = -1/2 x − 241 +2,
where f(x) is the height of the ramp, in
feet, and x is the distance from one
side of the ramp. Graph the function
on a separate piece of paper. Find and
interpret the key features of the graph
in the context of the situation.
The vertex is located at ( , )This means that the maximum height of the ramp is _ feet when the distance from one side is _ feet. Because the distance cannot be negative, and the ramp is _ feet long, the relevant domain is {x | 0 ≤ x ≤ __}.
RAMP The height of a ramp can be
modeled by f(x) = -1/2 x − 241 +2,
where f(x) is the height of the ramp, in
feet, and x is the distance from one
side of the ramp. Graph the function
on a separate piece of paper. Find and
interpret the key features of the graph
in the context of the situation.
The vertex is located at ( , )This means that the maximum height of the ramp is _ feet when the distance from one side is _ feet. Because the distance cannot be negative, and the ramp is _ feet long, the relevant domain is {x | 0 ≤ x ≤ __}.
Because the height cannot be negative, and the ramp is _ feet tall, the relevant range is {y | 0 ≤ y ≤ __ }. The graph is symmetric in the line x = _ This means that the height from a distance of 0 to _ feet away from one side of the ramp is the same as the height from a distance of _ to _ feet away from one side of the ramp.
It is a downward parabola, which means the height of the ramp decreases as the distance from one side of the ramp increases.
What is the parabola?
A parabola is a symmetric, U-shaped geometric curve that can be defined as the set of all points that are equidistant to a fixed point (the focus) and a fixed line (the directrix). It is a conic section, which means it is the intersection of a plane and a cone. In algebraic terms, a parabola can be defined as the graph of a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants.
The height of a ramp can be modeled by f(x) = -1/2 x − 241 +2, where f(x) is the height of the ramp, in feet, and x is the distance from one side of the ramp. To find the vertex of the parabola, we need to complete the square.
The vertex is located at (-b/2a, f(x) + (b^2-4ac)/4a) = (-1/2, -241 +2) = (0, -240)
This means that the maximum height of the ramp is -240 feet when the distance from one side is 0 feet.
Because the distance cannot be negative, and the ramp is unknown length, the relevant domain is {x | 0 ≤ x ≤ unknown}.
Because the height cannot be negative, and the ramp is unknown tall, the relevant range is {y | 0 ≤ y ≤ unknown }.
The graph is symmetric in the line x = 0. This means that the height from a distance of 0 to an unknown feet away from one side of the ramp is the same as the height from a distance of an unknown to an unknown feet away from one side of the ramp.
It is a downward parabola, which means the height of the ramp decreases as the distance from one side of the ramp increases.
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16. If AABC-ADBE, find the values of x and y.
The values of x and y for the given similar triangles are 3 and 10 respectively.
Define the term similarity of the triangle?If two figures have the same shape, they are termed to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name given to this usual ratio.For the stated question-
Using the similarity for the triangle ABC and DBE,
Taking the ratios of the sides.
x/9 = 4/12
x = 9/3 = 3
And,
5/y = 4/(12 - 4)
5/y = 4/8
y = 5*2 = 10
Thus, the values of x and y for the given similar triangles are 3 and 10 respectively.
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(-6 , -6 ) and ( -9 , - 5 )
Answer:
15
Step-by-step explanation:
(-6,-6)and (-9,-5) =15
2(3b+6) =78 : Answer is 11
-2(6c-3) = -72 : Answer is 6.5
Check Right and Left side of the equation
The right side of the first equation is 78 and the right side of the second equation is -72. Both sides of the equations are constants (numbers with no variable in them)
The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.
To find the value of b and c in the equation, you need to solve the equation.
For the first equation:
2(3b + 6) = 78
3b + 6 = 39
3b = 33
b = 11
For the second equation:
-2(6c - 3) = -72
6c - 3 = 36
6c = 39
c = 6.5
So, the value of b is 11 and the value of c is 6.5
Surface Area and Volume
Z
X
X
Note: Figure not drawn to scale.
Height has been rounded for computational ease.
If X = 13 units, Y = 11 units, and Z = 15 units, then what is the surface area of the right triangular pyramid shown above?
OA.
390 square units
OB. 266.5 square units
OC. 435.5 square units
OD. 364 square units
The surface area of the right triangular pyramid is 435.5 square units.
What is a surface area of a triangle?
A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees. It is the polygon with the fewest sides.
Here, we have
Given: X = 13 units, Y = 11 units, and Z = 15 units
We have to determine the surface area of the right triangular pyramid.
Surface area = base area + 1/2 (perimeter × slant height)
A = xy + 1/2 (3x × z)
A = 13 × 11 + 1/2 (3× 13 × 15)
A = 143 + 292.5
A = 435.5 square units.
Hence, the surface area of the right triangular pyramid is 435.5 square units.
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What will be the solution of linear equation 3x 4y 10 and 2x 2y 2?.
The solutions of the system of linear equations 3x+ 4y= 10 2x+ 2y= 2 can be found by using the method of substitution or elimination.Solve one of the equations for one of the variables in terms of the other variable.
Let's solve the first equation for x: 3x + 4y = 10 3x = -4y + 10 x = -4/3y + 10/3
Substitute this expression into the other equation and solve for the remaining variable.
2(-4/3y + 10/3) + 2y = 2 -8/3y + 20/3 + 2y = 2 -8/3y + 2y = -20/3 + 2 -2/3y = -18/3 y = 9
Use the value of y to find the value of x.
x = -4/3y + 10/3 x = -4/3(9) + 10/3 x = -4 + 10/3 x = -4 + 10/3
The solution of the system of equations is (x,y) = (-4 + 10/3, 9)
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Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
The three angles of the triangle can be found by using the formula for the sum of angles of a triangle, which is 180°. Then, the measure of angle A + angle B + angle C = 180°.
1. Using the sum of angles formula, angle A + angle B + angle C = 180°
2. Use the Law of Cosines to calculate the angle between two sides of the triangle.
3. Subtract the sum of those two angles from 180° to find the measure of the third angle.
The three angles of a triangle can be found using the sum of angles formula, which states that the sum of the angles of a triangle equals 180°. This means that angle A + angle B + angle C = 180°. To find the individual angles, we can use the Law of Cosines which states that c2 = a2 + b2 - 2ab cos C, where C is the angle between two sides of the triangle. This formula allows us to calculate the angle between two sides of the triangle. Once we have calculated the sum of the two angles, we can subtract this sum from 180° to find the measure of the third angle. For example, if the sum of the two angles is 120°, then the third angle would be 180° - 120° = 60°. This method allows us to find the three angles of the triangle with the given vertices.
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How do you solve an algebraic equation with 3 variables?.
Answer:
using the linear combination method
Step-by-step explanation:
hope this helps
A student says x^2+36=(x+6)^2
Answer:
x=0
Step-by-step explanation:
-Use (a+b)^2=a^2+2ab+b to expand the expression.
-Cancel equal terms on both sides of the equation
-Swap the sides of the equation
-Divide both sides of the equation by 12
-Solution
x=0
find sin2x, cos2x, and tanx2x if sinx= 15/17 and x terminates in quadrant 2
The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
What is trigonometric?Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles and circles. Trigonometry is used to calculate the measurements of angles, lengths, and areas of different geometric figures. It is also used to solve problems involving forces, motion, and velocity.
Sin2x = (2*15/17)*(-12/17) = -30/289
Cos2x = (2*15/17)*(-5/17) = -30/289
Tan2x = (2*15/17)/(-12/17) = -5/12
Since sinx = 15/17 and x terminates in quadrant 2, then x = -3π/17. The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
Sin2x = 2*sinx*cosx = 2*(15/17)*(-12/17) = -30/289
Cos2x = 2*cosx*cosx - 1 = 2*(-12/17)*(-12/17) - 1 = -5/289
Tan2x = (2*sinx*cosx)/(cosx*cosx - sinx*sinx) = (2*(15/17)*(-12/17))/((-12/17)*(-12/17) - (15/17)*(15/17)) = -5/12
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Autumn is a teacher and takes home 83 papers to grade over the weekend. She can grade at a rate of 9 papers per hour. How many papers would Autumn have remaining to grade after working for 8 hours?
After working 8 hours and grading 9 papers per hour, it is expected Autumn has 11 papers left.
How many paper will Autumn be able to grade in 9 hours?To calculate the number of papers she can grade during this time, let's use the rate provided:
9 papers per hour x 8 = 72 papersThis means in 9 hours she can grade 72 papers.
How many papers will she have left?Now, let's calculate the number of papers left:
83-72 = 11Based on this, the total of papers left after working for 8 hours is 11 papers.
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A Cylinder The lateral surface of a cylinder has an area of 824 m². The cylinder has a height of 40 m. a) Determine the circumference of the cylinder's circular face.
The circumference of cylinder's circular face is 20.09 pi units.
What is circumference?The cylinder's lateral surface area is equal to the circumference of the circular base multiplied by the height. A circle's circumference is 2r and its height is h, so the lateral area is 2rh.
That is LSA = 2 × π × r × h where, r = base radius, and h = height of the cylinder.
Here given,
LSA = 824m²
Height = 40 m
By substituting
824 = 2 x 3.14 x r x 40
824 / 2 x 3.14 x 40 = r
r = 3.2m
Circumference of circular face = 2 π r
By substituting the values,
Circumference = 2 x 3.14 x 3.2
Circumference = 20.09 pi units.
Therefore the circumference of a cylinder with circular face is 20.09 pi units.
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What are the 3 rules to solving an equation?.
The Golden Rule to Solve an Equation are:-
Simplify both sides of the equation.Move all parts of the equation that contain the variable you're solving for to the same side.Isolate the variable using multiplication, division, exponentiation, or by taking roots.Check your solution!In arithmetic, an equation is a system that expresses the equality of two expressions, by connecting them with the equals signal =. The phrase equation and its cognates in different languages may additionally have subtly one-of-a-kind meanings; as an example, in French, an équation is defined as containing one or more variables, whilst in English, any well-formed method together with expressions associated with an equals signal is an equation.
solving an equation containing variables includes figuring out which values of the variables make the equality real. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that fulfill the equality are called answers to the equation. There are kinds of equations: identities and conditional equations. An identity is real for all values of the variables. A conditional equation is handiest authentic for particular values of the variables.
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The Ahmad family uses propane gas to heat their home in the winter. The cost to fill their
propane tank varies directly with the number of gallons of propane they buy. The Ahmads have a
budget of $750 to buy propane for their tank this winter, and the gas costs $3.83 per gallon. Give
the direct variation equation that describes how much propane the Ahmads can purchase with
their $750 budget and state the meaning of the variables x, y, and k for this situation.
The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.
what is equation ?Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 and 14 apart. The relationship between two sentences on either side of a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 = 2, for instance.
given
Let the direct variation equation
be x + $3.83y = 750,
Let the direct variation equation be x + $3.83y = 750,
The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.
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What is the slope of 4x 2y =- 12?.
After solving, the slope of equation 4x + 2y = -12 is -2.
In the given question, we have to find the slope of 4x + 2y = -12.
The given equation is 4x + 2y = -12.
The general equation of line is y = mx + c, where m is the slope of the line and c is the y-intercept of the line.
To find the slope of the line we have to convert the given equation in the form of general equation.
We have to isolate y.
4x + 2y = -12
Subtract 4x on both side, we get
2y = -4x - 12
Divide by 2 on both side, we get
y = -4/2 x - 12/2
y = -2x - 6
On comparing the equation by general equation, we get
m = -2
Hence, the slope of the equation 4x + 2y = -12 is -2.
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The complete question is:
What is the slope of 4x + 2y = -12?
my mother purchased 8 pepsi products at Bi-Lo for $14.00 what is the price per product
Answer:
$1.75
Step-by-step explanation:
We take
14 / 8 = $1.75
So, one product cost $1.75
Help is very much appreciated need this by tmr.
A triangle has vertices A (2,-3), B (-2,1) and C (1,2). Find the midpoint of the side AB.
Step-by-step explanation:
let the mid point be (x, y)
x= (-2-2)/2; y=(1-(-3))/2
please comletd the rest by yourself
Answer: I believe the midpoint of the side AB would be (0.3,0)
Step-by-step explanation:
I hope that helps!
Can someone help? Stuck on it
Step-by-step explanation:
(6×(-4) - 1 )/ 4=-24-1/4= -25/4= -6.2
Please help! I’m really bad at math
Answer:
14.6
Step-by-step explanation:
In the example
x =kh
k is the constant of proportionality
please help im very confused how to do this.
Step-by-step explanation:
(a)
[tex] \frac{b + x}{3} = \frac{b - x}{4} \\ 4b + 4x = 3b - 3x \\ b = - 7x[/tex]
(b)
[tex]p = \frac{y}{1 + y \\ } \\ p + py = y \\ y - py = p \\ y = \frac{p}{1 - p} [/tex]
(c)
[tex] \frac{1}{a} = \frac{1}{b} - \frac{1}{c} \\ \frac{1}{c } = \frac{1}{b} - \frac{1}{a} \\ \frac{1}{c} = \frac{a - b}{ab} \\ c = \frac{ab}{a - b} [/tex]
A business owner wants to have the front window of her store painted and is considering two
artists for the job. Britney has quoted a flat rate of $63 for the job. Quincy's quote is $8 per
hour, plus $47 to cover the cost of materials. Depending on how long it takes Quincy to paint
the window, these two could end up charging the same amount. How long would Quincy have
to take? How much would it cost?
If the job takes Quincy
hours, the cost would be $
with either artist.
It would take Lisa 3 hours to complete the painting as both Brennan and Lisa could end up charging the same amount of $63.
What is an hour?An hour is a unit of time that is traditionally calculated as 124 of a day and is scientifically estimated to last between 3,599 and 3,601 seconds, depending on how quickly the Earth rotates. There are 60 minutes in an hour and 24 hours in a day.
The concept of the hour was first developed in the ancient Near East as a flexible measurement of 1/12 of the night or day. Such seasonal, temporal, or uneven hours varied with latitude.
Equal or equinoctial hours were defined as 124 of the day, measured from noon to noon; the minor seasonal variations of this unit were eventually smoothed out by making it 124 of the mean solar day.
Flat rate quoted by Brennan = $63
Rate quoted by Lisa = $8 h + $47
The number of hours for Lisa to finish the painting = ($63 - $47)/$8
= 2 hours
The total cost that Lisa would charge is = ($8 x 2 + $47)
= $63
Thus, It would take Lisa 3 hours to complete the painting as both Brennan and Lisa could end up charging the same amount of $63.
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2/3 x 22/7 x 5.25 x 5.25 x 5.25 =?
Please explain this step by step because i am weak at math.
Answer:
Step-by-step explanation:
step 1: NUMERATOR:
2 x 22 x (5.25)³
= 44 x 144.703125
Numerator = 6366.9375
step 2: DENOMINATOR:
= 3 x 7
Denominator = 21
step 3: CALCULATION:
= numenator / denominator
= 6366.9375 / 21
Answer = 303.1875
Jacob picks a 5-digit even number.
The first digit is a prime number.
The third digit is odd.
The four digit is 8
How many different 5-digit number could he pick
Answer:
Total no ways can be taken
Step-by-step explanation:
A weight attached to the end of a long spring is bouncing up and down. As it bounces, its distance from the floor varies sinusoidally with time. You start a stopwatch. When the stopwatch reads 1.7 seconds the spring is 58 cm above the floor and is on a downward path. It takes 4.4 seconds for the spring to bounce from a distance of 36 cm to 80 cm above the ground.
A. Write an equation expressing distance from the floor in terms of the number of seconds the stopwatch reads
B. Predict the distance from the floor when the stopwatch reads 6 seconds
C. What was the distance from the floor when you started the stopwatch?
The answers to all parts are shown below.
what is wave Equation?One of the most crucial equations in mechanics is the wave equation. It describes the movement of fluid surfaces, such as water waves, in addition to the movement of strings and wires.
Define constants:
t0 = 1.7seconds h0 = 58cm highest point
t1 = 4.4 seconds h1 = 44 cm lowest point
t2 = 6 seconds h2 = (h0 + h1)/2 = 51 cm center height
Half a cycle passes between t0 and t1, so the period T is
T = 2(t1 - t0) = 2(4.4-1.7) seconds = 5.4 seconds
The amplitude A is half the total height change between h0 and h1:
A = (h0 - h1)/2 = 7 cm
a) Equation of motion in terms of height H above the floor is
H(t) = h2 + A Co s[2π(t - t0)/T]
H(t) = 51 cm + (7cm) Cos[0.1775(t - 1.7second)/second]
b) Let t = 6 seconds in the equation:
H(t) = 51 cm + (7cm) Cos[0.1775(6 - 1.7second)/second]
= 51 + 7 x (-0.4008)
= 48.1944 cm
c) Let t = 0 seconds in the equation:
H(0 seconds) = 51 cm + (7cm) Cos[0.1775(0 - 1.7second)/second]
= (51+ 7[0.99999986]) cm
= 57.99cm
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What are the 4 inverse operations in math?.
The four main inverse operations in math are addition, subtraction, multiplication, and division. These are the operations that reverse the effects of the operation.
When you use the word "inverse," you want to move backward in time or space. The Latin term "inversus," which means to turn inside out or upside down, is where the word's name originates. An inverse operation in mathematics is a procedure that reverses the effects of a preceding one.
Multiplication, division, subtraction, and addition are the four fundamental mathematical operations. Subtraction, and vice versa, are the opposites of addition. Division and vice versa are the opposites of multiplication.
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What are the four rules of multiplication?.
The four rules of multiplication is explained below.
The term multiplication in math is defined as the process of when you take one number and add it together a number of times
Here we need to define the four rules of multiplication.
Here the first rule of multiplication is written as that any number times zero is always zero.
And the next rule is that any number times one is always the same number.
And the another rule is written as add a zero onto the original number when multiplying by 10.
And if the order of factors does not affect the product then switching the roles of multiplier and multiplicand results in the same answer.
Where the other rule is that products are always positive when multiplying numbers with the same signs.
And the final rule is the products are always negative when multiplying numbers with different signs.
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A polar vortex causes the temperature to decrease from 3°C at 3 PM to -2°C at 4 PM the temperature continues to change by the same amount each hour until 8 PM find the total change in temperature for 3 PM to 8 PM
The total change in temperature from 3 PM to 8 PM is 25°C.
The first step is to calculate the temperature difference.
Temperature at 3 PM = 3°C
The temperature at 4 The period2°C
The difference = 3 - (-2) = 3 + 2 =5°C
The second step is to calculate the difference time.
Period from 3 PM to 8 PM:
To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.
So,
8-3 = 5 hours
The third step is to calculate the total temperature change.
5°C × 5 hours = 25°C.
The total change in temperature from 3 PM to 8 PM is 25°C.
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A school is arranging a field trip to the zoo. The school spends 633.85 dollars on passes for 31 students and 4 teachers. The school also spends 300.08 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Total money spent on a pass and lunch for each student = $29.9
What is a field trip?A field trip is a journey by a group of people to a place away from their normal environment.
Given :
School spends $633.85 on passes for 31 students and 4 teachers.
School spends $300.08 on lunch for 31 students.
Calculation :
School spends on a pass for each student,
633.85
35
=20.22$
School spends on a lunch for each student,
300.08
31
=9.68$
Therefore, total money spent on a pass and lunch for each student
20.22 + 9.68
= $29.9
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Please help me again
Answer:83
Step-by-step explanation: sum of the angles should be 180
44+53+x=180
x=180-97
x=83
Answer:
Step-by-step explanation:
The addition of three angles in a triangle is 180°.
Therefore, if we add all the angles, it's
180° = x + 53° +44 °
180° - ( 53°+44° ) = x
180°-97° = x
83 ° = x
Then the answer is obvious, it's 83°.
5.
For the exponential function f(x)= a(b)' we know that f(3) =17 and f(7)=3156. Which of the
following is closest to the value of b?
The closest to the value of b is 3.6912.
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b
Set up both equations with values
When x = 3, f(3) = 17, so we have a(b)^3 = 17
When x = 7, f(7) = 3156, so we have a(b)^7 = 3156
Isolate a in each equation
a = 17/(b)^3
a = 3156/(b)^7
Now set them equal to each other
17/(b)^3 = 3156/(b)^7
Cross Multiply
17b^7 = 3156b^3
Divide each side by b^3
17b^4 = 3156
Divide each side by 17
b^4 = 185.6471
b = 3.6912
Therefore, the closest to the value of b is 3.6912.
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