g( x ) = 2x² + 12x + 22 is the standard form of the the function g( x ) = 2( x + 3 )² + 4.
What is the standard form of the function?Polynomials in standard forms are written in a way that arrange the terms in descending order.
Given the data in the question.
g( x ) = 2( x + 3 )² + 4
First, we expand; ( x + 3 )² → ( x + 3 )( x + 3 )
g( x ) = 2( ( x + 3 )( x + 3 ) ) + 4
Using FOIL Method
g( x ) = 2( x² + 3x + 3x + 9 ) + 4
g( x ) = 2( x² + 6x + 9 ) + 4
Apply distributive property
g( x ) = 2( x² + 6x + 9 ) + 4
g( x ) = ( 2x² + 12x + 18 ) + 4
Add 18 and 4
g( x ) = 2x² + 12x + 18 + 4
g( x ) = 2x² + 12x + 22
Therefore, the function in standard form is g( x ) = 2x² + 12x + 22
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PLEASE ASAP HELP MEEEEThe longer leg of a right triangle is 3 inches longer than the shorter leg. The hypotenuse is 6 inches longer than the shorter leg. Find the side lengths of thetriangle.Length of the shorter leg:inchesLength of the longer leg:inchesinchesLength of the hypotenuse:
In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.
h: hypotenuse
c1: shorter leg
c2: longer leg
Longer leg c2 is 3 inches longer than c1:
c2 = c1 + 3
hypotenuse h is 6 inches longer than c1:
h = c1 + 6
The formula for the calculation of the hypotenuse is:
h² = c1² + c2²
you replace for h and c2 in terms of c1:
(c1 + 6)² = c1² + (c1 + 3)²
You solve the previous equation for c1:
c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9
c1² - 6c1 - 27 = 0
the roots of the previous equation are:
(c1 - 9 )(c1 + 3) = 0
c1 = 9
c1 = -3
You take the positive number because there is no length of sides with negative values.
Then, c2 and h are:
c2 = c1 + 3 = 9 + 3 = 12
h = c1 + 6 = 9 + 6 = 15
Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches
[tex]3 {}^{2} + ( - 4 {}^{2} ) + 5 {}^{2} [/tex]I'm confused on that can you help me please?
We have to replace the values in the equation
[tex]x^2+y^2+z^2=(3)^2+(-4)^2+(5)^2=9+16+25=50[/tex]Since the square of a negative number is a positive number, (-4)^2 = +16
Alvin paddled for 2 hours with a 5-km/h current to reach a campsite. The returntrip against the same current took 7 hours. Find the speed of the boat in stillwater.
Given:
Alvin paddled for 2 hours with a 5-km/h current to reach a campsite.
Let n be the speed of boat.
Distance is calculated as,
[tex]\begin{gathered} d=rt \\ d=2\mleft(n+5\mright) \end{gathered}[/tex]The return trip against the same current took 7 hours.
[tex]\begin{gathered} d=rt \\ d=7(n-5) \end{gathered}[/tex]Equate both the equations,
[tex]\begin{gathered} 2(n+5)=7(n-5) \\ 2n+10=7n-35 \\ 7n-2n=10+35 \\ 5n=45 \\ n=\frac{45}{5} \\ n=9 \end{gathered}[/tex]Answer: the speed of the boat is 9 mph.
Two companies are competing for a contract to make the programs for middle school gymnastics meets. Nadia’s Printing charges a $19.99 fee for printing and $0.25 for each program printed. Simone’s Stylish Print charges a $29.99 fee for printing and $0.10 for each program printed. For the most recent meet, Nadia’s Printing charged more than Simone’s Stylish Print.
Which inequality models this situation?
Answer:
the second answer
Step-by-step explanation:
Can someone help me on this pleaser
Answer: it should be the third one down
Step-by-step explanation:
4. the probability that an engine overheats is 0.12. the probability that an engine leaks oil is .08. (a) if overheating and leaking oil are independent, what is the probability that an engine overheats and leaks oil?
The probability that the engine over heats and leaks is 0.0096
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
Engine leaks oil AND overheats,
hence P(Engine overheats) = P(Engine overheats) X P(Engine leaks oil) = 0.12 X 0.08 = 0.0096
Hence the probability of leaking of engine due to over heating is 0.0096
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Tom bought 10 cans of Coca cola drink at a cost of USD26.00. How much he will need to pay for 36 cans of Coca Cola?
(20 Points) Working Step
Tom will need to pay $93.60 for 36 cans of Coca-Cola.
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=3x+2.
The question gives:
Tom bought 10 cans of Coca-cola drink at a cost of USD26.00. Here you can convert this text into an algebraic expression, see:
10x = 26, where x represents the unit cost.
You can find x, solving the previous algebraic expression. Thus,
10x=26
x=26/10
x=2.6
So, 1 can of Coca-Cola costs $2.60.
For knowing the cost total for 36 cans of Coca-Cola, you need to multiply 36 units by the unit cost ($2.6). See below:
36*2.6= $93.60
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Hey!
New question 4 today
Nadia is walking a 3.4-mile trail. She stops to take a break after walking 1.6 miles. Which explains whether the distance Nadia already walked is greater than, less than, or equal to the distance she has left to walk?
!PLEASE!
Don't give wrong answers. (its not very nice)
Only use one of the answer options. (other answers are wrong)
Based on the distance walked by Nadia when she took her break, the statement that explains the distance already walked is C. The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8.
How to find the distance?Nadia had already walked 1.6 miles by the time she took her break. This means that the distance she was still left to walk in the mile trail was:
= 3.4 - 1.6
= 1.8 miles
The distance that Nadia had already walked was 1.6 miles and yet she was left to walk 1.8 miles.
We can therefore conclude that the distance that Nadia already walked is less than the distance still to be walked.
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The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8 which is the correct answer would be an option (C).
What is the distance?Distance is calculated as the product of a person's movement and time.
Nadia took a rest after covering 1.6 miles of walking.
This indicates that she had the following distance to cover on the mile trail:
⇒ 3.4 - 1.6 = 1.8 miles
Nadia had already walked 1.6 miles, but she still had another 1.8 miles to go.
Therefore, the distance Nadia has already traveled is less than the distance that needs to be covered.
Hence, the correct answer would be an option (C).
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Select all ratios equivalent to 13:14
52:56. 39:42. 3:4
Answer:
52:56 and 39:42
Step-by-step explanation:
The ratios equivalent to 13:14 are:
52:56
39:42
3:4 is not equivalent to 13:14 because 3 is not a multiple of 13.
Multiply and write in standard form: 10x + 3)(2x - 1) Show all work
Explanation
[tex](10x+3)(2x+1)[/tex]Step 1
apply distributive property
[tex]\begin{gathered} (10x+3)(2x+1)=(10x\cdot2x)+(10x\cdot1)+(3\cdot2x)+(3\cdot1) \\ (10x+3)(2x+1)=20x^2+10x+6x+3 \end{gathered}[/tex]Step 2
add similar terms and order
[tex]\begin{gathered} (10x+3)(2x+1)=20x^2+10x+6x+3 \\ (10x+3)(2x+1)=20x^2+16x+3 \\ \text{the standard form is} \\ ax^2+bx+c,so \\ ax^2+bx+c\Rightarrow20x^2+16x+3 \end{gathered}[/tex]so, the answer is
[tex]20x^2+16x+3[/tex]I hope this helps you
Julia has a mask collection consisting of 255 masks she keeps on the wall and 45 she keeps in a display case. What percentage of Julias mask collection does she keep on her wall?
We are told that Julia keeps 255 masks on the wall and 45 on the display case, this means in total the number of masks she has is
[tex]255+45=300\text{masks}[/tex]The number of masks Julia keeps on the wall is 255 masks; therefore, the percentage of fo masks on the wall is
[tex]\frac{255}{300}\times100[/tex][tex]=85.\text{ }[/tex]Hence, Julia keeps 85% of her mask collection on her wall.
a school nurse can give 25 eye tests in a two-hour period. how long will it take the nurse to give eye tests to all 600 stuents in her school.
1. Is 26 divisible by 2? (1 point)
ONO
O Yes, because 2 +6=8 and 8 is divisible by 2.
O Yes, because the last digit is 6, which is divisible by 2.
Answer:
Yes, because the last digit is 6, which is divisible by 2.
Step-by-step explanation:
The solution is, Yes, because the last digit is 6, which is divisible by 2.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
26 divisible by 2
i.e. 26/2 = 13
so, it is divisible.
now, we know that,
because the last digit is 6, which is divisible by 2.
Hence, The solution is, Yes, because the last digit is 6, which is divisible by 2.
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1) Find the volume of each cone.a. Estimate using 22 꼭 for n. Express theanswer as a fraction.
Volume of the cone = 50.29 mm³
Explanation:[tex]\text{Volume = 1/3}\pi r^2\text{ h}[/tex]radius = r = ?
height = 3mm
slant height = 5mm
To get the radius, we would apply pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse = 5mm
opposite = 3mm
adjacent = radius = ?
5² = 3² + radius²
25 = 9 + radius²
25 - 9 = radius²
16 = radius²
radius = √16
radius = 4
[tex]\text{Volume of the cone = }\frac{1}{3}\times\frac{22}{7}\times4^2\times3[/tex][tex]\text{Volume of the cone = }50.29mm^3[/tex]Given the polynomial f(x)=x⁴+3x³-3x²-x, which of the following is true?
a) (x+1) is a factor since f(-1)=0.
b) (x-1) is a factor since f(-1)=0.
c) (x+1) is a factor since f(1)=0.
d) (x-1) is a factor since f(1)=0.
The new figure that is produced in a transformation is called the
Let:
[tex]\begin{gathered} P=(x1,y1)=(-3,4) \\ P^{\prime}=(x2,y2)=(4,0) \end{gathered}[/tex][tex]\begin{gathered} x1+a=x2 \\ -3+a=4 \\ so\colon \\ a=4+3 \\ a=7 \\ ---- \\ y1+b=y2 \\ 4+b=0 \\ b=-4 \end{gathered}[/tex]Therefore:
[tex](x,y)\to(x+7,y-4)[/tex]I need help 9th grade math
Answer:
D
Step-by-step explanation:
PLEASE HELP I AM GROUNDED AND NEED A BETTER GEOMETRY GRADE ASAP
Answer:
w = 9
Step-by-step explanation:
This is a 90-degree angle, so if you add both equations together, they will equal 90.
First, write the equation:
(4w - 7) + (7w - 2) = 90
Then you solve for w:
- add like factors
11w - 9 = 90
- add 9 to both sides
11w = 99
- divide both sides by 11
w = 9
So, the value of w is 9.
To check, plug your answer into the equation to check if it's true:
(4(9) - 7) + (7(9) - 2) = 90
(36-7) + (63-2) = 90
29 + 61 = 90
90 = 90
How can I work out the size of angle y?
Answer:
180 degrees converted is 3.14159 i think
Step-by-step explanation:
Answer:
< y = 17 degrees.
Step-by-step explanation:
x + y = 180 - 112 = 68 (as there are 180 degrees in a triangle)
Also, x = 3y, so substituting for x in the first equation:
3y + y = 68
4y = 68
y = 17.
So,
x = 3*17 = 51,
Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
The intervals on which the function is increasing, decreasing and constant are (-5,-3) and (2,5) on increasing (-3,0) on decreasing and (0,2) on constant.
What is intervals?
An interval in math is the measured in terms of the numbers. An interval to includes all the numbers that come between two of particular numbers. This is the range includes all of the realistic numbers between those two of numbers. Real numbers are the any kind of number you can definitely think of.
Sol-by showing in the figure the function is increasing on the (-3,0)
Decreasing on (-5,-3) and (2,5)
Constant on (0,2)
Thus, the correct option is A
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can you help solve for y?
Answer:
Go ahead and color the nose red!
The solution is
[tex]y = \dfrac{n-9}{x}[/tex]
Step-by-step explanation:
[tex]\text{We have: }\\\\[/tex]
[tex]\rightarrow\; \dfrac{x}{y} + 9 = n\\\\\\\text{Subtract 9 from both sides:}\\\\\rightarrow\;\dfrac{x}{y} + 9 - 9 = n - 9\\\\[/tex]
[tex]\rightarrow\;\dfrac{x}{y} = n - 9\\\\[/tex]
Multiply both sides by y:
[tex]\rightarrow\; y \cdot \dfrac{x}{y} = y (n-9)\\\\\rightarrow\; x = y(n-9)\\\\\\[/tex]
[tex]\text{Divide both sides by (n-9)}:\\\\\\\rightarrow\; \dfrac{x}{n-9} = \dfrac{y (n-9)}{n-9}\\\\\\\rightarrow\; \dfrac{x}{n-9} = y\\\\\\[/tex]
By switching sides without changing the meaning, this can be re-written as :
[tex]y = \dfrac{x}{n-9} \\\\[/tex]
which of course means you can color the nose red
:)
according to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
About twice as likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers.A 16 or 17-year-old driver has a higher risk of dying every mile they drive compared to operating a vehicle alone. increases by 44% when one of the passengers is under the age of 21. while transporting two passengers who are under 21 in doubles.
Are 16 year olds more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.To learn more about crash with two passengers refer to:
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16-year-old driver to crash with two passengers as opposed to with no passengers is about twice as likely.
Are 16 year old's more likely to crash?Teenagers between the ages of 16 and 19 had the highest crash risk of any age group. Teen drivers in this age range have a roughly three times higher risk of being in a fatal collision per mile traveled than drivers who are at least 20 years old.According to CDC research, there are a few main factors that increase the likelihood of young drivers being in auto accidents: insufficient experience Due in part to their inability to identify and avoid road dangers, teen drivers have a fatal crash risk that is three times higher than that of older drivers.The complete question is,
According to the chart, approximately how many times more likely is a 16-year-old driver to crash with two passengers as opposed to with no passengers?
just as likely
about twice as likely
about three times more likely
about four times more likely
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suppose an opaque jar contains 4 red marbles and 11 green marbles. this exercise refers to the experiment of picking two marbles from the jar without replacing the first one. what is the probability of getting a green marble first and a red marble second?
The probability of getting a green marble first and a red marble second exists 5/26.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Red marbles = 3
Green marbles = 10
So, the total marbles = 3 + 10 = 13
Probability = Favorable outcomes / Total outcomes
Since, here replacement is not allowed,
Therefore, the probability of getting a green marble and a red marble
= first red and second green + first green second red
= 3/13 × 10/12+ 10/13 × 3/12
= 2 × 3/13 × 10/12
= 30/78
= 5/13
The probability of getting a green marble first and a red marble second
= 10/13 × 3/12
= 30/156
= 5/26
Therefore, the probability of getting a green marble first and a red marble second exists 5/26.
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2. What is the slope-intercept form of 9x + 3y = 15?
y = 3x - 5
y = 3x + 5
y=-3x - 5
y=-3x+5
Answer:
y=3x+5
Step-by-step explanation:
A hiker descended 450 feet down to an elevation of 2300 feet. Which equation models this scenario?
The equation models this scenario regarding the hiker is x - 450 = 2300.
Whet is elevation?Elevation is simply used to illustrate the height above the sea level.
In this case, the hiker descended 450 feet down to an elevation of 2300 feet.
The equation that can model the scenario will be x - 450 = 2300
where x = Initial elevation
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What’s the answer plss
Answer:
B.15.9
Step-by-step explanation:
Trigonometry
7.7/SIN(29)=15.9
Answer:
3.7 cm
Step-by-step explanation:
See attached worksheet
a box is constructed out of two different types of metal. the metal for the top and bottom, which are both square, costs 1/ft2 and the metal for teh sides costs 2 ft find the dimensions that minimize cost if the box has a volume of 20 ft 3
The cost function of the box is C(x) = 2. x² + 160/x and the dimension that lead to the minimum cost is length = ∛40 ft., width = ∛40 ft., height = ∛5 ft.
Let:
x = the bottom's side length
h = the height of the box
Then, the surface area of top and bottom:
A1 = 2. x²
The surface area of vertical sides:
A2 = 4 x. h
The cost function is:
C(x) = 2. x² . 1 + 4 x. h . 2
C(x) = 2. x² + 8 x. h
The volume of the box is:
V = x² . h
20 = x² . h
h = 20 / x²
Substitute h = 20 / x² into the cost function:
C(x) = 2. x² + 8 x. h
C(x) = 2. x² + 8 x. 20 / x²
C(x) = 2. x² + 160/x
At the minimum point, the derivative of a function is equal to zero. Hence,
C'(x) = 4x -160 / x² = 0
x³ = 40
x = ∛40
Substitute x = ∛40 to find the height:
h = 20 / x²
= 2 . 10 / (∛4² . ∛10²)
= ∛10 / ∛2 = ∛5
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Marilyn wants to use a non-price competitive marketing strategy to gain more customers. Which of the following might she use?
As Marilyn wants to use a non-price competitive marketing strategy to gain more customers, the strategy that she might use is offering a promotion.
What is a Non-price competition in marketing?In marketing, the non-price competition refers to a marketing strategy in which a firm tries to distinguish its product or service from competing products on the basis of attributes like design and workmanship.
This competition most often occurs in an imperfectly competitive markets because it exists between producers that sell goods and services at same prices but competes to increase their respective market shares through different non-price measures such as marketing schemes and greater quality.
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Tell whether the given situation is an example of Direct Variation or Inverse Variation. Write DV if it is a Direct Variation and IV for Inverse Variation. (NEED THE ANSWER ASAP)7. The height of a person and his weight
Given,
The statement is "The height of a person and his weight".
Required/
Identify the statement is inverse or direct variation.
As the height of the person increase then its their weight is also increased.
Similarly,
The height of the person decrease then its their weight is also decreased.
Hence, it is direct variation.
I need to find the value of x in this figure.
Please explain how to do so.
Answer: 2x^2
Step-by-step explanation:
(x+5)
x (2x - 9)
-----------------
X times 2x = 2x^2