Answer:
19 - 3(x - 2)²
Step-by-step explanation:
7 + 12x - 3x² ( rearrange terms in x )
7 - 3x² + 12x ( factor out - 3 from each of the x- terms )
= 7 - 3(x² - 4x)
using the method of completing the square on x² - 4x
add/subtract ( half the coefficient of the x- term )² to x² - 4x
= 7 - 3(x² + 2(- 2)x + 4 - 4)
= 7 - 3(x - 2)² - 3(- 4)
= 7 - 3(x - 2)² + 12
= 19 - 3(x - 2)² ← in the form a + b(x + c)²
with a = 19 , b = - 3 , c = - 2
A student is overheard saying: "I don't need to learn the Primary Trig Ratios. I am just going to use the Sine
and Cosine Laws to solve problems." Show by example that the student is right. Explain the advantages and
disadvantages to this approach. Step by step. Thank you!
The sine and cosine rule is typically used to find the measure of angles in trigonometry.
How to illustrate the trigonometry?It should be noted that the sine rule is used when we are given:
two angles and one side.two sides and a non included angle.The cosine rule is used when we are given:
there sides two sides and the included angle.The advantage is that it can help us understand the connections between the sides and their angles.
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If the function 5x+y=1 has the domain (-2,1,6) then what is the corresponding range?
The corresponding range of the domain is (11, -4, -29)
How to determine the range?The function is given as:
5x + y = 1
Make y the subject
y = 1 - 5x
The domain is given as:
(-2,1,6)
Substitute these values in y = 1 - 5x
y = 1 - 5(-2) = 11
y = 1 - 5(1) = -4
y = 1 - 5(6) = -29
Hence, the corresponding range of the domain is (11, -4, -29)
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Help with these two problems and show work please having trouble solving them !
Answer:
see explanation
Step-by-step explanation:
to find the zeros let f(x) = 0
1
f(x) = 0 , that is
x(x + 10) = 0
equate each factor to zero and solve for x
x = 0
x + 10 = 0 ⇒ x = - 10
2
f(x) = 0 , that is
x(x - 3) - 4(x - 3) = 0 ← factor out (x - 3) from each term on the left side
(x - 3)(x - 4) = 0
equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 4 = 0 ⇒ x = 4
Answer:
1) x₁ = 0, x₂ = -10
2) x₁ = 3, x₂ = 4
Step-by-step explanation:
Given functions:
[tex]1)\ f(x)=x(x+10)[/tex]
[tex]2)\ f(x)=x(x-3)-4(x-3)[/tex]
.................................................................................................................................................
Zero Product Property: If m • n = 0, then m = 0 or n = 0.
Distributive Property: a(b + c) = ab + ac.
Standard Form of a Quadratic: ax² + bx + c = 0.
.................................................................................................................................................
The Zero Product Property
1) f(x) = x(x + 10)
Step 1: Set the function to zero.
[tex]\implies 0=x(x+10)[/tex]
Step 2: Apply the Zero Product Property.
[tex]\boxed{x_1=0}[/tex]
[tex]x+10=0\implies \boxed{x_2=-10}[/tex]
The solutions to this quadratic are: [tex]x_1=0,\ x_2=-10[/tex].
.................................................................................................................................................
The Zero Product Property
2. f(x) = x(x - 3) - 4(x - 3)
Step 1: Set the function to zero.
[tex]\implies 0 = x(x - 3) - 4(x - 3)[/tex]
Step 2: Factor out [tex]x- 3[/tex].
[tex]\implies 0 = (x - 3)(x - 4)[/tex]
Step 3: Apply the Zero Product Property.
[tex]x-3=0\implies \boxed{x_1=3}[/tex]
[tex]x-4=0 \implies \boxed{x_2=4}[/tex]
The solutions to this quadratic are: [tex]x_1=3,\ x_2=4[/tex].
.................................................................................................................................................
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Which of the following shows 2x^3Y - 3x^2 + 7y^2x - 12y written in standard form? Answers in photo thank you
Answer:
[tex] \large{ \boxed{\tt{2 {x}^{3}y + 7 {y}^{2} x - 3 {x}^{2} - 12y}}}[/tex]
- All you gotta do is writing the polynomial in the descending order of the power of the variable.
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One of the legs of a right triangle measures 10 cm and the other leg measures 7 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
12.2 cm
Step-by-step explanation:
we are going to use the formula (below).
Our a and b are going to be our two legs: 10cm and 7cm
[tex]C^{2} =10^{2} +7^{2} \\C^{2}=100+49\\C^{2}=149\\C=\sqrt{149} \\C=12.2cm[/tex]
Instructions: Find the measure of the indicated angle to the nearest degree.
Answer:
15.78°
Step-by-step explanation:
Let the angle be x.
From the x, the known sides are the opposite side, O(13) and the adjacent side, A(46)
Therefore, The trigonometric ratio is the tangent ratio.
tan x = O/A
tan x =13/46
x = 15.78°
Using the table below, find the mean and median of the set of data.
Note: Round all numbers to the nearest tenth.
Using their concepts concept, we have that:
a) The mean of the data-set is of 81.6.
b) The median of the data-set is of 80.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, there are 2 + 8 + 6 + 3 + 9 = 28 observations, hence the mean is:
M = (70 x 2 + 75 x 8 + 80 x 6 + 85 x 3 + 90 x 9)/28 = 81.6.
What is the median?The median of a data-set is the 50th percentile, the value that separates the median in two halfs.
This data-set has an even number of elements, hence the median is the mean of the 14th and 15th elements, as 28/2 = 14. Both elements are 80, hence the median is of 80.
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4. You read an article in your local newspaper about a discussion between the owner of a popular business and a group
of community members. The business owner keeps a flag raised on an outdoor flagpole during nighttime hours, but
the community members are calling for the flag to be properly illuminated at night. The business owner says that the
flag cannot be illuminated because the only power source available for the spotlights is solar power, but there is too
much shade on the ground for solar-powered spotlights to charge sufficiently during the day.
You realize that you can offer a solution to the problem by suggesting that the solar-powered spotlights be mounted
on the roof of the building where it can be charged by sufficient sunlight. You decide to contact the business owner to
suggest angling the spotlight down to the raised flag from the roof instead of angling it up to the raised flag from the
ground. The business owner informs you that the flagpole is located 55 feet from the building. If the building is 45 feet
high and the flagpole is 25 feet high, at what angle should you tell the business owner to angle a spotlight mounted on
the roof? Please show all your work.
य
The business owner should be told to angle a spotlight mounted on the roof at the angle of =39°
Calculation of angleThe distance of the flagpole from the building = 55ft
The building has the height of = 45ft
The flagpole has the height of = 25ft
The angle can be calculated using the formula;
Tan θ = opposite/adjacent
Where opposite= 45ft
adjacent = 55ft
Tan θ = 45/55 = 0.82
θ = Tan–¹0.82
θ = 39°
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(HELP!) now consider 0=-120. Draw the angle 0=-120 on the circle below. Make sure you rotate clockwise for the negative angle. It needs to be approximate, but not precise.
The reference angle after rotating the unit circle anti-clockwise is; π/3 Radians
How to draw a Unit Circle?To draw the angle θ = -120° in the unit circle, we will move clockwise 90°, and thereafter another angle of 30°.
This tells us that we pass the fourth quadrant and stop in the third quadrant.
The reference angle of an angle theta in the third quadrant, is; θ + 180°.
Thus, the reference angle of -120° is; -120° + 180° = 60°.
Converting 60° to radians gives; (60/360) * 2π Radians = π/3 Radians
Thus, the Reference angle is π/3 Radians
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PLEASE HELP Which answer provides a counterexample to the following statement: "If a figure has an endpoint,
then it is a line segment"?
Answer:
ray
Step-by-step explanation:
Rays only have one endpoint, so it continues infinitely in one direction. Segments have TWO endpoints.
In which diagram do angles 1 and 2 form a linear pair?
2 lines intersect and form 4 angles. Labeled clockwise from the top: blank, 2, blank, 1.
3 lines extend from a point and form 2 angles, labeled 1 and 2. Both angles add up to 90 degrees.
A horizontal line has 2 lines extending from a midpoint forming 3 angles. Labeled from left to right: 1, 2, 3.
A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.
Mark this and return
The diagram where angles 1 and 2 form a linear pair is D. A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.
What is a linear pair?It should be noted that a linear pair simply means angles that are formed when two lines intersect each other at a single point.
In this case, when a horizontal line has 1 line extending from it. Angles 1 and 2 are formed. This depicts a linear pair
In conclusion, the correct option is D.
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Model the situation with the sum of polynomials. Simplify their sun.
A rectangular picture frame has the dimensions shown in the figure. Write a polynomial that represents the perimeter of the frame.
Answer:
16x-2
Step-by-step explanation:
Perimeter is 2w+2l
so we plug it in
2(3x+1) + 2(5x-2)
now we distribute
6x+2 + 10x -4
now we add like terms
6x+10x+2-4
16x-2
Which equation is equivalent to: 3r = 78 + 14 ?
A. −3r =−78+14
B. 3r =78−14
C. 3r−14 =78
D. −3r =78−14
Answer:
Step-by-step explanation:
B is the answer
Some bacteria double in every hour. if there were 2 bacteria in the beginning, how many bacteria will be there after 6 hours? how many bacteria will be there after 24 hours?
Using an exponential function, it is found that:
After 6 hours, there will be 256 bacteria.After 24 hours, there will be 33,554,432 bacteria.What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the growth rate.The parameters for this problem are given as follows:
a = 2, b = 2.
Hence the number of bacteria after x hours is given by:
[tex]y = 2(2)^x[/tex]
After 6 hours, the amount is:
[tex]y = 2(2)^6 = 2^7 = 128[/tex]
After 24 hours, the amount is:
[tex]y = 2(2)^{24} = 2^{25} = 33554432[/tex]
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what is 7+6-8x5=????
Answer:
Step-by-step explanation:
7+6-8x5=
7+6-40=
13-40=
-37
if the x is multiplying
The gas co2 is diffusin at steady state through a tube 20 cm long having a diameter of 1 cm and containing n2 at 350 k . the total pressur is constant at 101.3kpa . the partial pressure of co2 at one end is 456 mmhg and 76 mmhg at the end . the diffusivity is 0.167 cm2 /s at 298 k . calculate the mass rate of co2 if the partial pressure remains constant.
The value is J = 1.71*10^-6 kmol/m^2.s
According to the given conditions we get,
The length the tube l= 0.20m
The diameter of the tube d= 0.01m
The total pressure inside the tube P= 101.32kPa
The partial pressure of CO2 at the first end is
P1= 456mm Hg = 60794.832 Pa
The partial pressure of CO2 at the other end is
P2= 76mm Hg = 10132.472 Pa
The temperature is T = 298 K
The diffusion coefficient D= 1.67* 10^-5 m^2/s
Generally the molar flux of CO2 is mathematically represented as
J= D{p1-p2} / R.T
Here R is the gas constant with value R= 8.314 j/kmol
So we get J= 1.71 * 10^-3 mol/m^2.sec
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make x the subject! w/ show work
write 5 consecutive odd integers preceding -31
Based on the given task content; the five consecutive odd integers preceding -31 are: -21, -23, -25, -27, -29
Odd integerAn integer can either be a positive value or negative value.Odd integers are integers which can not be divided by 2 without a remainder.Examples of odd integers are; 1, 3, 5, 7, 9 etc.Preceding means before a particular thing.Odd integers preceding -31
= -1, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21, -23, -25, -27, -29
Therefore, Five consecutive odd integers preceding -31 are: -21, -23, -25, -27, -29
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What is the y-intercept of the function f(x)=-2/9x + 1/3?
Answer:
y-intercept = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the coefficient is the slope (slope = -2/9x)
the constant is the y-intercept (y-intercept=1/3)
this is true for all functions like this
Answer:
The y-intercept is
c) 1/3
Step-by-step explanation:
If you borrow $800 for 10 years at an annual interest rate of 12%, how much will you pay altogether?
Answer:
the principal amount is 10000 is the rate of interest is 10 and the number of years is 10 you can calculate the simple interest a is equal to 10000 1 + 0 is equal to 1.6 is equal to 16000 interest is equal to a - b is equal to 6000 - 1000
Answer:
$1,760
Step-by-step explanation:
So I'm assuming the interest is simple interest rate which means that the interest applied each year is 12% of the original amount.
So this means that we can find the interest rate from one year by finding 12% of 800, and to do this we convert 12% to a decimal by dividing by 100 to get 0.12 and then use this decimal value to multiply by 800 to get: 0.12 * 800 = 96.
This means annually $96 will be charged in interest. To find how much interest there is after 100 years, simply multiply by 10, to get $96 * 10 = $960.
This is only the interest rate, it's like a fee, you still have to pay back the original amount, so all together you pay: $ borrowed + interest
So we add the interest rate 960 to the amount borrowed 800 to get: 960 + 800 = 1,760
what are the solutions to 5x^2 - x - 1 < 0
The shape of f(x) = √ x, but shifted nine units to the left and then reflected in both the x-axis and the y-axis
Answer:
g(x) = -√(-x +9)
Step-by-step explanation:
The relevant transformations are ...
f(x -h) . . . . . shifts the graph of f(x) right h unitsf(x) +k . . . . . shifts the graph of f(x) up k units-f(x) . . . . . . . reflects the graph of f(x) over the x-axisf(-x) . . . . . . . reflects the graph of f(x) over the y-axisApplicationApplying the transformations in the specified order, we have ...
f(x) = √x
f(x +9) = √(x +9) . . . . . . . shifted 9 units to the left
-f(x +9) = -√(x +9) . . . . . . shifted 9 left, reflected in the x-axis
-f(-x +9) = -√(-x +9) . . . . shifted 9 left, reflected in x-axis, reflected in y-axis
The shifted, reflected function is ...
g(x) = -√(-x +9)
__
Additional comment
The graph shows the original f(x) = √x function in red. The shifted, reflected function is shown in blue. Note that the initial left shift changes appearance to a right shift when it is reflected over the y-axis.
Help help pls, ASAP!!! (Geometry)
“Complete the proof”
1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)
2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)
3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)
4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. during week 10 of the recall, the manufacturer fixed 200 cars. in week 15, the manufacturer fixed 175 cars. assume that the reduction in the number of cars each week is linear. write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 5x 250 f(x) = −5x 250 f(x) = 10x 200 f(x) = −10x 200
The linear function that shows that the number of cars seen each week by the mechanic is:
f(x) = -5x + 200.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.During the first week analyzed, the amount of cars was of 200, hence the y-intercept is of 200. In 5 weeks, the amount decayed by 25, hence the slope is given by:
m = -25/5 = -5.
Thus the linear function that shows that the number of cars seen each week by the mechanic is:
f(x) = -5x + 200.
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Answer:
f(x) = −5x + 250
Step-by-step explanation:
First, we must find the slope. We can take 2 points. (10, 100) and (15,175)
Using y2-y1/x2-x1=m, we find that the slope =-5. to find the y-intercept, we have to find that y= when x=0. Since 10 weeks passed since the begining, we can inverse the slope to find 5(cars)x10(weeks)=50.
so, 200(week10)+50(week 1)=250
f(x)=-5x+250.
WILL GIVE BRAINLIEST! I’m desperate for help! This assignment is due today I’m stuck! Pls help!
Which expression represents the following statement? Multiply 6 by 3, and then subtract the quotient of 18 and 9.
6 x (3 ÷ 18) + 9
6 + 3 + (18 ÷ 9)
(6 x 3) − 18 ÷ 9
6 x (3 + 18) + 9
Answer:
Step-by-step explanation:
the third one is correct
[tex]6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)[/tex]
Divide the following polynomials. Then place the answer in the proper location on the grid. Write the quotient and remainder as a sum in this format: quotient, remainder/ divisor. Do not include parentheses in your answer. 8y square- 4y+1 over 2y-1
For the division of the given polynomials, quotient = 4y and remainder =1
What is a polynomial?Algebraic expressions called polynomials include constants and indeterminates.
A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.
A polynomial is written in its standard form when its descending power of the variable is used.
[tex]\frac{8y^{2}-4y+1 }{2y-1}[/tex]
Quotient = 4y
Remainder = 1
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Find the mean and standard deviation for the set of data. {22,21,20,4,19,6,24,11,26} A. mean: 17; standard deviation: 8.1 B. mean: 17; standard deviation: 7.53 C. mean: 20; standard deviation: 8.1 D. mean: 20; standard deviation: 7.53
Using it's concepts, the mean and the standard deviation of the data-set are given as follows:
B. mean: 17; standard deviation: 7.53.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean for this problem is:
M = (22 + 21 + 20 + 4 + 19 + 6 + 24 + 11 + 26)/9 = 17
The standard deviation is:
[tex]S = \sqrt{\frac{(22-17)^2+(21-17)^2+(20-17)^2+(4-17)^2+(19-17)^2+(6-17)^2+(24-17)^2+(11-17)^2+(26-17)^2}{9}} = 7.53[/tex]
Hence option B is correct.
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Kira is trying to drink more water and juice each day. The difference in the amount of water in a jug and the amount of juice in the bottle she is drinking from is 192 ounces. She has consumed a total of 42 ounces, which is StartFraction 3 Over 32 EndFraction of the bottle of juice and StartFraction 9 Over 64 EndFraction of the jug of water. Which system of equations can be used to determine the total number of ounces in the jug of water, x, and the total number of ounces in the bottle of juice, y?
The required system of equations that can be used to determine the total number of ounces in the jug of water (x), and the total number of ounces in the bottles of juice (y) is
[tex]x - y = 192[/tex]
[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]
How to write an equation?To write an equation,
Observe the variable term in the given informationConsider more or less as addition or subtraction of the termsEquate the terms with the given valuesThus, the expression formed is called an equation.Calculation:It is given that,
The difference between the jug of water and the bottle of juice that Kira is drinking is 192 ounces
Kira has consumed a total of 42 ounces, which is 3/32 of the bottle of juice and 9/64 of the jug of water.
Consider,
The total number of ounces in the jug of water = x
The total number of ounces in the bottle of juice = y
Applying these variables in the above sentences,
[tex]x-y=192[/tex]
[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]
Therefore, these two equations are used to determine the total number of ounces in the jug of water and the bottle of juice.
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What is another name for XW?
Name a ray with an endpoint X.
Give another name for WX.
What’s another name for AXW?
Double points
Another name for AXW is <X
What is another name for XW?The arrow on XW implies that the segment XW is a ray, such that any of the points X or W can be the starting point
Hence, another name for XW is WX
Name a ray with an endpoint X.A ray with an endpoint X is a ray that ends at point X
An example of such ray is XY
Give another name for WX.The arrow on WX implies that the segment WX is a ray, such that any of the points X or W can be the starting point
Hence, another name for WX is XW
What’s another name for AXW?The name AXW represents an angle
An angle can be named after its middle point
Hence, another name for AXW is <X
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You always have to tell us to sign and we need the answers so bad why don't you close this website because you don't even give us the answer f u