The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.
How to find the roots of an equation?The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
The equation to find the roots, is a quadratic equation.
Hence,
2x² + 7x + 6
2x² + 3x + 4x + 6
x(2x + 3) + 2(2x + 3)
Hence,
(x + 2)(2x + 3) = 0
Therefore,
x + 2 = 0 or 2x + 3 = 0
x = -2 or x = -3 / 2
The roots of the equation is x = -2 and x = -3 / 2
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The sum of the first k positive integers is 990. What is k?
Pls give explaintion
Answer:
k=44
Step-by-step explanation:
1 + 2 + 3 + 4......+ k = 990
Arithmetic sequence with d = 1 a1 = 1
1 + 1+ 1 + 1 +2 ...... 1+ (k-1) = 990
ak = a1 + (k-1) <====formula for sequence
Sum of a sequence formula = Sk = k ( a1+ak)/2
990 = k ( 1 + (1 + k-1) /2
1980 = k^2 + k
k^2 + k - 1980 = 0 Use quadratic formula a = 1 b = 1 c = - 1980
to find k = 44
What is the solution to this system of equations?
3b + 4c = 3
8b+ 5c = 27
2b + 6c = 1
Here ya are hope this helps! :]]
The data to the right represent the cost of living for 20
states. The cost of living is a measure of the average
price paid for housing, utilities, groceries, healthcare,
transportation, and miscellaneous expenses. The
national average cost of living is 100. The data can be
used to compare a state to the national average and
to other states.
T
Use these data to construct a frequency distribution with a first class of 85.0-94.9. Fill in the missing classes and the frequency for each class belo
Cost of living
Number of states
9
85.0-94.9
125.0134.9
8-8
20
(Type integers or decimals. Do not round.)
151.2121.3 99.4 94.5 89.7
138.7120.1 96.7 94.5 89.6
132.1106.5 95.3 90.9 89.4
124.9101.6 95.2 90.1 89.2
The frequency distribution based on the information given is illustrated below.
What is the frequency distribution of table?
A frequency distribution table is the chart that summarizes all the data under two columns - variables/categories, and their frequency.
It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.
Given the above information the frequency distribution table is:
Cost of living[tex]\begin{table}[]\begin{tabular}{ll}Cost of living & Number of States \\85.0 - 94.9 & 9 \\95.0 - 104.9 & 5 \\105.0 - 114.9 & 0 \\115.0 - 124.9 & 2 \\125.0 - 134.9 & 2 \\135.0 - 144.9 & 1 \\145.0 = 154.9 & 1 \end{tabular}\end{table}[/tex] Number of states
85.0 - 94.9 9
95.0 - 104.9 5
105.0 - 114.9 0
115.0 - 124.9 2
125.0 - 134.9 2
135.0 - 144.9 1
145.0 - 154.9 1
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Solve The Problem
All the students in grades 3, 4 and 5 are going on a field trip to Coney Island
Each grade has 125 students. The cafeteria needs to pack lunches. About how
many students are going on the trip? Represent the exact amount of student
in all three grades using an array, How many students are there altogether?
The number of Students going on the trip is 375.
In the question,
It is given that:
There are 125 students in Grade 3.
There are 125 students in Grade 4.
There are 125 students in Grade 5.
So, Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5
= 125 + 125 + 125 = 375.
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Solve for x.
please help asap!
Which of the following choices would move this curve to the RIGHT 17 units and up 4 units: y=(x+6)^2 - 2
If we start with the parent quadratic function, then the transformation is:
g(x) = (x - 17)^2 + 4
Which transformations move the graph in the desired way?The definitions of translations are:
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.
Then if the parent function is:
f(x) = x^2
The translation of 17 units to the right and 4 units up is:
g(x) = f(x - 17) + 4 = (x - 17)^2 + 4
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20 points Describe another way you could have solved the equation. Tell which of these two ways of solving the equation you prefer and why.
In the equation 2[(4m * 3.5) / 400] = 171.5, the value of m is 2450
EquationsEquations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.
In the equation given;
2[(4m * 3.5) / 400] = 171.5
To solve for m, we have to expand the bracket and make m the subject of formula.
2[(4m * 3.5) / 400] = 171.5
2[14m/400] = 171.5
28m / 400 = 171.5
28m = 400 * 171.5
28m = 68600
m = 68600 / 28
m = 2450
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perpendicular bisector of the line segment whose endpoints are 7,4) and (−9,−4).
Answer:
y=-2x-2
Step-by-step explanation:
If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:
[tex]\frac{-4-4}{-9-7}[/tex] = [tex]\frac{-8}{-16}[/tex]=[tex]\frac{1}{2}[/tex]. For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of [tex]\frac{1}{2}[/tex], which is -[tex]2[/tex]. The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.
Now we find the equation!
y=mx+b. Plug in -[tex]2[/tex] as the "m", or slope:
y=-[tex]2[/tex]x+b
Now, plug in the point (-1, 0):
0=-[tex]2[/tex]*-1+b
0=[tex]2[/tex]+b
b=-[tex]2[/tex]
So, we have m=-[tex]2[/tex] and b=-[tex]2[/tex] and we can form our equation!
y=-[tex]2[/tex]x-[tex]2[/tex]
Hope this helps!! :D
Use a table of areas to obtain the shaded area under the standard normal curve.
The shaded area under the standard normal curve is 2.58%.
According to z-score table,
Area for < 2.23 = 0.9871
Area for >2.23 = 1 - 0.9871
= 0.0129
Area for < 2.23 = 0.0129
Total area = 0.0129 + 0.0129
= 0.0258
Area percent = 0.0258*100
= 2.58%
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In an ecology experiment, a number of mosquitoes are placed in a container with water and vegetation. The population of mosquitoes, P, increases and can be modelled by the function:
P9T)=24*4^0.385t, t is greater than or equal to 0
Where t is the time, in days, since the mosquitoes were placed in the container.
(a) find the number of mosquitoes in the container after 5 days
The maximum capacity of the container is 5000 mosquitoes
(b) Find the number of days until the container reaches its maximum capacity.
Using the given exponential function, it is found that:
a) The number of mosquitoes in the container after 5 days is of: 346.
b) The number of days until the container reaches the maximum capacity is of: 10 days.
What is the exponential function?The exponential function that models this problem is presented as follows:
P(t) = 24(4)^(0.385t).
Hence, after five days, the number of mosquitoes is of:
P(5) = 24(4)^(0.385 x 5) = 346 mosquitoes.
The number of days that it takes for the container to reach it's maximum capacity of 5000 is obtained solving the exponential function with logarithms as follows:
[tex]5000 = 24(4)^{0.385t}[/tex]
[tex](4)^{0.385t} = \frac{5000}{24}[/tex]
[tex](4)^{0.385t} = 208.3[/tex]
[tex]\log{(4)^{0.385t}} = \log{208.3}[/tex]
Applying the power property of logarithms, we have that:
[tex]0.385t\log{4} = \log{208.3}[/tex]
[tex]t = \frac{\log{208.3}}{0.385\log{4}}[/tex]
t = 10 days.
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A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.24t2 + 12t feet per second after t seconds (for 0 ≤ t < 30).
a.
Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time
t = 0.]
b.
Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.)
The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.
What is the relation between speed and distance?Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.
The speed formula is speed = distance/time.
We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).
Then the distance that it will travel from its starting point in the first t seconds is;
[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]
At zero it will be 12 feet.
b. the distance (in ft) that the car will travel in the first 10 seconds.
-0.48(10) + 12 = 16.8 feet.
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Please help me! Much needed ASAP!
The correct option regarding whether the linear functions are parallel is given as follows:
C. The slope of f(x) is of 2 and of g(x) is of 5. Since they are different, the lines are not parallel.
What are parallel linear functions?First, we start with the definition of a linear function, in slope-intercept format, which is given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope of the function.b is the y-intercept of the function.If two linear functions are parallel, they have the same slope.
The slope is given by the change in y when x is increased by one, hence the slopes of the functions are given as follows:
Slope of f(x) = 2, as when x increases by one, y increased by 2.Slope of g(x) = 5, as when x increases by one, y increased by 5.Due to the different slopes, the two lines are not parallel, hence option C is correct.
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2007 Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700 Tim Tradesman had a taxable income of $82,500. He figured his tax from the table above.
Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The given Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700
Earned income is said to be $35,000.
Base tax amount at that level is $4386.
The amount over $31850 is $35000-31850 = $3150
Line 3 is multiplied by 25%: $3150×0.25 = $787.50
The sum of lines 2 and 4 is $4386 +787.50 = $5173.50
This amount divided by 12 is ... $5173.50/12 ≈ $431.13
Hence, Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.
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Graph the function with the given domain. Then identify the range of the function.
1) y = -6; domain: x ≥ 5
2) y = -x - 1; domain: -1 ≤ x ≤ 3
If A = 1
a.
-2 6 1
b.
-5
9 -6 and B= -2 -7
1
10
-99-9
-22 30 32
-16 -78 48
42 24 30
-32 72 30
-2
26 -20
-50
94 -58
9 6
4
-1
Ń
find-4A + 6B.
C.
d.
38
8
30
-78
-40
6 0
42
58
-96
8 0 -18
14
82 -52
The answer is option (a)
Hope this answer helps you
Please only answer if you know the answer for sure,
URGENT
MIXED REVIEW
Directions: Arrange the numbers in order from least to greatest.
21) 32%, pi, 2 1/2 √9
22) -3.4, -4, -3, -2 1/2, -pi
23) 250%, 3.4, -%, 0
The solution is
a) The ascending order is 32 % < 2 1/2 < √9 < π
b) The ascending order is -4 < -3.4 < -3 < -2 1/2 < π
c) The ascending order is -5/8 < 0 < 250% < 3.4
What is Ascending Order?
When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.
Given data ,
A)
32 % , π , 2 1/2 , √9
32 % = 32 / 100
= 0.32
π = 3.14
2 1/2 = 2.5
√9 = 3
So , arranging the numbers in ascending order we get ,
0.32 < 2.5 < 3 < 3.14
Hence , the ascending order is 32 % < 2 1/2 < √9 < π
B)
-3.4 , -4 , -3 , -2 1/2 , π
Hence , the ascending order is -4 < -3.4 < -3 < -2 1/2 < π
C)
250 % , 3.4 , -5/8 , 0
250 % = 2.5
-5/8 = -0.625
So , arranging the numbers in ascending order we get
-0.625 < 0 < 2.5 < 3.4
Hence , the ascending order is -5/8 < 0 < 250% < 3.4
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Solve for the value of T
Step-by-step explanation:
4t - 7 + 83 = 180
4t + 76 = 180
4t = 104
t = 26
What numbers are elements? -7, -4, 2, 14, 21, 34, 42
The answer is [14, 42].
The number 14 is even.
7 x 2 = 14
An even number, 42.
7 x 6 = 42
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What do you observe? What do you wonder? What are 2 things you know and 1 thing that you're missing?
The observation of the graphing speed versus time is given below.
What is acceleration?The rate at which the speed is changing is known as acceleration.
From the graph, the line segment OA and DE have linear acceleration which increases the velocity.
Similarly, from the graph, the line segment BC and EF have linear deacceleration which decreases the velocity.
From the graph, line segment AB has constant acceleration which increases the velocity.
And from the graph, the line segment CD has zero acceleration which makes the velocity to be constant.
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help me out thanks 10 ponits
Answer:
yes yes ...................
A student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30. How many
more monthly payments must be maid to pay off the loan?
The number of months required to pay off the loan will be 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30.
The number of the months will be calculated as,
N = ( 1178.8 - 547.30) / 42.10
N = 631.5 / 42.10
N = 15
Therefore, the number of months required to pay off the loan will be 15.
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A standard toilet uses 1.6 gallons per flush. If a toilet is flushed two times per day, how much water will be used in a week (7 days)?
Total Water Used by a standard flush in a week i.e. 7 days is 22.4 gallons.
What is Multiplication?
In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply.
Solution:
Given that,
The standard toilet uses 1.6 gallons of water per flush
Also, it is flushed twice a day
To Find, Total water used in a week i.e. 7 days
Since, flush uses 1.6 gallons water per flush
Total water used in a day is 2*1.6 = 3.2 gallons
This implies,
Total water used in 7 days = 7 * 3.2 = 22.4 gallons
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His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas
mileage in his new car?
The Xavier is not getting better mileage with his new car .
In the question ,
it is given that
distance travelled by Xavier's new car in 25 gallons = 528 miles
the mileage can be calculated using the formula = (distance travelled)/( gallons of fuel used) .
So , mileage of the new car = 528/25 = 21.12 miles per gallon ,
the milage of Xavier's former car = 20.28 miles per gallon .
From the above data , we can see that the mileage of former car is greater than new car .
Therefore , The Xavier is not getting better mileage with his new car .
The given question is incomplete , the complete question is
Xavier's new car uses 25 gallons for 528 miles , His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?
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Please help me with this thank you :)))
Answer:
Step-by-step explanation:
Use the graph below to answer the following questions.
⦁ Estimate the available territory at 20 years
⦁ Estimate the available territory at 15 years
⦁ Does this graph represent exponential growth or decay?
⦁ As the time decreases the available territory _______________
Answer:
a) about 190 acres
b) around 240 acres
c) exponential decay because the amount of land available is decreasing at an increasingly rapid rate over time.
The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in cm2/min) is the surface area of the ball increasing when the radius is 6 cm?
The rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.
Surface area of SphereThe surface area of a sphere with radius r is given by4π[tex]r^{2}[/tex]
Given;
S = surface area at time t, and r = radius at time t
radius of a spherical ball is increasing at a rate of 2 cm/min
radius: 6cm
Area of a sphere is A = 4π[tex]r^{2}[/tex]
Step 1: Differentiate area of a spherical ball
A = 4π[tex]r^{2}[/tex]
[tex]\frac{dA}{dt}[/tex] =[tex]\frac{d}{dt}[/tex](4π[tex]r^{2}[/tex])
=4π [tex]\frac{d}{dt}[/tex]([tex]r^{2}[/tex])
=4π2r [tex]\frac{dr}{dt}[/tex]
[tex]\frac{dA}{dt}[/tex] = 8πr
since we have that dr/dt = 2 cm/min. Thus, the radius of the ball is 6cm, we have;
[tex]\frac{dA}{dt}[/tex]= 8π(6)(2) =96π
So, the rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.
Note that measuring area unit is cm2/min
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A rectangular fish tank has a base that is 4 inches by 9 inches. How much water will it take to fill the tank to a depth of 3 inches? A 150 cubic inches B 685 cubic inches C 108 cubic inches 16 cubic inches
Answer:
C: 108 cubic inches
Step-by-step explanation:
This problem is simply asking us to calculate volume, and in a rectangular shape can be calculate as: length * width * height
Since we know that the base is 4 inches by 9 inches, we already have the length and width.
We're also given that the depth, which in this case is our height, as 3 inches.
So we multiply these three numbers: [tex]4 \text{ in} * 9 \text{ in} * 3\text{ in} = 108\text{ in}^3[/tex]
So our answer is 108 cubic inches
Differentiate the function with respect to x.
The differentiation of the given function is 12[tex]x^3[/tex](5[tex]x^2[/tex] +2).
In the given question we have to differentiate the given function with respect to x.
The given function is f(x) = [tex]2x^4(5x^2+3)[/tex]
Before differentiating the function we first simplify the given expression.
To simplify the expression we multiply the 2x^4 to each term under the bracket.
Now the function;
f(x) = [tex]2x^4\cdot5x^2+3\cdot2x^4[/tex]
As we know that if the base is same en power get added.
f(x) = [tex]10x^{4+2}+6x^4[/tex]
f(x) = [tex]10x^{6}+6x^4[/tex]
Now differentiating the function with respect to x.
f'(x) = d/dx([tex]10x^{6}+6x^4[/tex])
f'(x) = 10d/dx([tex]x^6[/tex]) + 6d/dx([tex]x^4[/tex])
As we know that d/dx of x^n =nx^(n-1). So
f'(x) = 10∙6 [tex]x^5[/tex] + 6∙4 [tex]x^3[/tex]
f'(x) = 60[tex]x^5[/tex]+24[tex]x^3[/tex]
Now taking 12x^3 common
f'(x) = 12[tex]x^3[/tex](5[tex]x^2[/tex] +2)
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Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine,
2.51 ⨯ 10−5
watts/cm2
The 2.51 × 10⁻⁵ Watts/cm² sound intensity of the sound from the rocket engine has a decibel level of 114 dB
What is a decibel?A decibel is a unit to measure the relative loudness of sound or to express the ratio electrical or acoustic power.
The intensity of the sound of the rocket engine = 2.51 × 10⁻⁵ Watts/cm²
Converting the unit of the sound intensity to Watts/m² gives;
1 cm² = 0.0001 m²
10,000 cm² = 1 m²
2.51 × 10⁻⁵ Watts/cm² = 10000 × 2.51 × 10⁻⁵ Watts/m² = 0.251 Watts/m²
The equation for the decibel from the power of sound is presented as follows;
[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{I}{I_0} \right)[/tex]
Where;
I₀ = 10⁻¹² W/m²
Which gives;
[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{0.251 }{10^{-12}} \right) = 113.9967373215 \approx 114[/tex]
The number of decibels for the power of the sound given to the nearest decibel by the rocket engine is 114 decibels
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