Answer:
3x^2 - 48 = 0
Step-by-step explanation:
The roots of a quadratic equation whose roots are -4 and 4, means that valid solutions for the quadratic equation are -4 and 4.
The two forms we know for the quadratic equation are the factored binomials:
(ax + cy)(bx + dz) = 0
and the full equation
ax^2 + bx + c = 0
We will start with the factored form:
(x + 4) ( x - 4) = 0
Note that if we solve this, we get the roots: x + 4 = 0 ==> -4 && x - 4 = 0 ==> 4
Now we apply foil to get the unfactored form:
(x + 4) (x - 4) = 0
x * x + x * -4 + 4 * x + 4 * -4 = 0
x^2 + -4x + 4x + -16 = 0
x^2 - 16 = 0
And now we want the leading coefficient to be 3.
3x^2 - 16 = 0
This looks like what we want; however, now with the leading 3, our solutions are no long +4 and -4. So, we need to re-evaluate.
Going back to the binomials with the idea of a leading 3, let's rewrite them to still give us the solutions 4 and -4, but with the 3 included:
(3x + 12) (x - 4) = 0
Note, we simply multipled one binomial by 3 to maintain the roots of the original, but also incorporate the leading 3.
3x + 12 = 0 x - 4 = 0
3x = -12 x = 4
x = -4
So now, we simply apply foil to this new equation of binomials to get our final quadratic equation:
(3x + 12) (x - 4) = 0
3x * x + 3x * -4 + 12 * x + 12 * -4 = 0
3x^2 + -12x + 12x + -48 = 0
3x^2 - 48 = 0
This is our quadratic equation we wish to use.
Note, we could have gotten this same equation by simply multiplying the original (x^2 - 16) = 0 by 3.
Cheers.
Prove the statement using the ε, δ definition of a limit. lim x → 1 4 + 2x 3 = 2
Given ε > 0, we need δ ---Select--- such that if 0 < |x − 3| < δ, then 2 + 1 3 x − 3 ---Select--- . But 2 + 1 3 x − 3 < ε ⇔ 1 3 x − 1 < ε ⇔ 1 3 |x − 3| < ε ⇔ |x − 3| < ---Select--- . So if we choose δ = ---Select--- then 0 < |x − 3| < δ ⇒ 2 + 1 3 x − 3 < ε. Thus, lim x → 3 2 + 1 3 x = 3 by the definition of a limit.
You want to prove
[tex]\displaystyle\lim_{x\to1}\frac{4+2x}3=2[/tex]
By the definition of the limit, this means that for any [tex]\varepsilon>0[/tex], we can find [tex]\delta>0[/tex] such that
[tex]|x-1|<\delta\implies\left|\dfrac{4+2x}3-2\right|<\varepsilon[/tex].
In order to get the inequality we want, we need to have
[tex]\left|\dfrac{4+2x}3-2\right|=\left|\dfrac{2x-2}3\right|=\dfrac23|x-1|<\varepsilon\implies|x-1|<\dfrac{3\varepsilon}2[/tex]
so we can pick [tex]\delta=\frac{3\varepsilon}2[/tex].
So here's the proof: Let [tex]\varepsilon>0[/tex] be given, and let [tex]\delta=\frac{3\varepsilon}2[/tex]. Then
[tex]|x-1|<\delta=\dfrac{3\varepsilon}2[/tex]
[tex]\implies\dfrac23|x-1|<\varepsilon[/tex]
[tex]\implies\left|\dfrac{2x-2}3\right|=\left|\dfrac{2x+4}3-1\right|<\varepsilon[/tex]
as required.
6.009 in expanded form
Answer:
6.009 = (6 x 1) . (0/10) + (0/100) + (9/1000)
Step-by-step explanation:
If A and B are 4 * 6 matrices and C is a 7 * 4 matrix, which of the following are defined?
1. CA.2. B^T * C^T.3. AC.4. A-B.5. B-C.6. B^T.
Answer:
1. CA is defined
2. B^T * C^T defined
3. AC is NOT defined
4. A - B is defined
5. B - C is NOT defined
6. B^T is defined
Hence, 1,2,4, and 6 are defined
Step-by-step explanation:
Order of the matrices:
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
To determine which are defined
1. CA
CA means product of Matrix C and Matrix A
To determine the product of two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. For example, given that matrix X is a (m × n) matrix, matrix Y is a (n × k) matrix and matrix Z is (k × n) matrix. From the definition above,
XY can be determined because number of columns in X equals number of rows in Y
XZ cannot be determine because number of columns in X is not equal to the number of rows in Z.
YZ can be determined because number of columns in Y equals number of rows in Z
(NOTE: A matrix of order (m × n) means the matrix has m rows and n columns)
Hence, for CA
Matrix C is a (7 × 4) matrix
Matrix A is a (4 × 6) matrix
Number of columns in C equals number of rows in A, hence CA is defined
2. B^T * C^T
B^T means transpose of matrix B
Transpose of a matrix is defined as a new matrix whose rows are the same as the columns of the original matrix and whose columns are the rows of the original matrix. Hence, for a matrix of order (m × k), the transpose of the matrix will have an order (k × m).
Hence,
Matrix B is a (4 × 6) matrix
∴B^T gives a matrix of order (6 × 4)
Matrix C is a (7 × 4) matrix
∴ C^T gives a matrix of order (4 × 7)
Since the number of columns in B^T equals the number of rows in C^T, then B^T * C^T defined
3. AC
Matrix A is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
The number of columns in A is NOT equal to the number of rows in C, hence AC is NOT defined
4. A - B
To find the difference between two matrices, the matrices must have the same order.
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Since matrices A and B have the same order [(4 × 6)], hence A - B is defined
5. B - C
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
Since matrices B and C are of different orders [(4 × 6) and (7 × 4) respectively], then B - C is NOT defined
6. B^T
B^T means the transpose of matrix B
Matrix B is a (4 × 6) matrix
From the above definition
B^T gives a (6 × 4) matrix
Hence, B^T is defined
please someone help me, i will give brainliest
Answer:
Both of them are the same measure: 45 degrees.
Step-by-step explanation:
You plug in 15 for the xin both of the equations they give.
3(15) +17=45
75-2(15)=45
Draw a figure to represent the following information: T
is between S and U, ST = 7x, SU = 45, and TU = 5x –
3.
Answer:
ST = 28 unit
TU = 17 units
Step-by-step explanation:
Given:
ST = 7x
SU = 45
TU = 5x – 3
Find:
Each value
Computation:
SU = ST + TU
45 = 7x + 5x - 3
48 = 12x
x = 4
So,
ST = 7x
ST = 7(4)
ST = 28 unit
TU = 5x – 3
TU = 5(4) – 3
TU = 17 units
A company recently replaced its 9-oz cup of yogurt with a 7-oz cup and reduced the suggested retail price from 87 cents to 75 cents. Was the price per ounce reduced by the same percent as the size of the cup? If not, find the price difference per ounce in terms of a percent.
Answer:
Question 1
Was the price per ounce reduced by the same percent as the size of the cup? No it's not the same
Question 2
If not, find the price difference per ounce in terms of a percent.
13.8%
Step-by-step explanation:
The first yoghurt cup size = 9 oz
The second and recent yoghurt cup size = 7 oz
The difference in ounces = 9 oz - 7 oz
= 2 oz
Converting this difference to percentage
= 2 oz/ 9 oz × 100%
= 22.222222222%
The percent reduction in cup size is approximately
22.2%.
The first retail price per ounce = 87 cents
The second and recent retail price per ounce =75 cents
The difference in prices = 87 cents - 75 cents
= 12 cents
Converting this difference to percentage
= 12 cents / 87 cents × 100%
= 13.793103448%
The percent reduction in yoghurt price per ounce is approximately
13.8%.
Question 1
Was the price per ounce reduced by the same percent as the size of the cup?
From the above calculation,
Percent reduction in price per ounce =
13.8%
Percent reduction in the size of the cup = 22.2%
13.8% ≠ 22.2%
Therefore, it is not the same
Question 2
If not, find the price difference per ounce in terms of a percent.
Therefore, the price difference per ounce in terms of percent is
13.793103448%.
Approximately ≈ 13.8%
A point lies in the _____ of an angle if it lies between the rays that form the angle. *
Answer:
I believe it is the vertex, of an angle.
Step-by-step explanation:
It is the vertex, because that is what you would call the bottom point of an angle.
An angle is a figure created by two rays, known as the angles' sides, that share a common terminus, known as the angle's vertex. A point lies in the interior of an angle if it lies between the rays that form the angle.
What is an angle?An angle is a figure created by two rays, known as the angles' sides, that share a common terminus, known as the angle's vertex. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles.
An angle has two rays and the area that lies between the two rays is known as the interior of the angle, while the area that is not between the two rays is the exterior of the angle.
Therefore, A point lies in the interior of an angle if it lies between the rays that form the angle.
Learn more about Angle:
https://brainly.com/question/7116550
#SPJ5
WhAt is the value of y
6√3 is the value of y...
8(1 + 5x) + 5= 13 + 5x
Answer:
0 will be answer as shown in image
What is
2+2?
I been trying to figure it out, but I’m stuck on this question
Answer:
4
Step-by-step explanation:
three subtracted from twice a number ?
How much shorter is the handle than the top of the screwdriver?
Answer:
Hey There! Here's Ur Answer
Step-by-step explanation:
one at their standard length of 45-3/4 inches, the other two inches shorter.
Happy to Help!
Write the following sentence using mathematical symbols. The sum of 10 and x is -13. "The sum of 10 and x is -13" in mathematical symbols is..
Answer:
10 + x = -13
Step-by-step explanation:
The sum of 10 and x is -13.
10 + x = -13
The larger of two numbers is 7 less than twice the
smaller number. If the sum of the numbers is 47,
find both numbers.
Answer:
larger number=29;smaller number=18
Step-by-step explanation:
let assume the two numbers are X and Y
where X is the larger number and Y is the smaller number.
From the question the larger number is 7 less than twice the smaller number. in mathematical terms this can be denoted as;
X=2Y - 7→→→→→→ equation 1
Also it was stated in the question that the sum of the two numbers is 47 which can be denoted as;
X + Y = 47→→→→→→ equation 2
Now from equation 1, X is mathematically expressed as 2Y - 7. Having known this we substitute X as 2Y - 7 into equation 2 then we have 2Y - 7 + Y = 47.
collecting like terms we have
2Y + Y = 47 + 7
solving arithmetically we have;
3Y = 54
divide both sides by 3 we have;
Y = 18.
Now if you recall from equation 1;
X = 2Y - 7;
since we now know Y as 18 we substitute Y as 18 in equation one then we have;
X = 2(18) - 7;
X =36 - 7
X = 29.
Carries first three children were boys. If she has more children, they will all be boys. Is this deductive or inductive reasoning?
Answer:
Inductive reasoning
Step-by-step explanation:
Inductive reasoning is when you make a false assumption based on previous knowledge you had before. The previous fact will often be referring to just a certain amount/set of things.
Deductive reasoning is when you have previous knowledge and you make a claim that is correct based on the knowledge before. The previous fact will often be referring to a whole set of things, not limited to a certain number.
The fact here is that Carrie's first three children were boys. This doesn't necessarily mean all of her upcoming children will be boys. So this is inductive reasoning.
Hope this helped!
Answer:
inductive
Step-by-step explanation:
Inductive
7/9 as a decimal please
Answer:
0.77777778
Step-by-step explanation:
...
Hi there!
~
[tex]\frac{7}{9} = 0.77777778[/tex]
Hope this helped you!
I NEED HELP ASAP please
Answer:
A
Step-by-step explanation:
Find the least whole number that can replace ? To make the statement true
? ÷9>700
Answer:
6301.
Step-by-step explanation:
First we find the integer such that ? / 9 = 700.
? = 700 * 9 = 6300.
Therefore the least whole number for ? / 9 > 700 should be 6301.
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.2 million cells per microliter and a standard deviation of 0.5 million cells per microliter. What is the minimum red blood cell count that can be in the top 24% of counts? What is the maximum red blood cell count that can be in the bottom 15% of counts? can somebody help me?
Answer:
5.55 million cells per microliter
4.68 million cells per microliter
Step-by-step explanation:
First, use a chart or calculator to find the z-score for reach percentage.
P(Z > z) = 0.24
P(Z < z) = 1 − 0.24 = 0.76
z = 0.706
Next, use definition of z-score to find the value.
z = (x − μ) / σ
0.706 = (x − 5.2) / 0.5
x = 5.55
Repeat for the other percentage.
P(Z < z) = 0.15
z = -1.036
z = (x − μ) / σ
-1.036 = (x − 5.2) / 0.5
x = 4.68
find the position vectors of the points which trisect the line joining the points whose position vectors are i+2j+7k and 3i+j-k
Answer:
Step-by-step explanation:
you should have to find two position vectors between the given positional vectors . to find the first position vector take the ratio 1:2 internally and for the second positon vector take the ratio 2:1 as it is trisectedusing the position vector formula we get the respective answer'swhat's the answer for the question find the following Figure angle x and y angle z
from the degrees and go 47 degrees
where is figure????????????????????
2. "three times the sum of a number and 7”.
Answer:
3 * (7 + n)
Step-by-step explanation:
Three times - '3 *'
The sum of a number and 7 - '(7 + n)'
"Three times the sum of a number and 7” would be '3 * (7 + n)'.
Hope this helps.
The required equation is 3*(n + 7).
It is required to find the equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
Let the number be n.
The sum of a number and 7 is n + 7
Three times the sum of a number and 7 is
3*(n + 7).
Therefore, the required equation is 3*(n + 7).
Learn more about equation here:
brainly.com/question/17351613
#SPJ2
i need help understanding this problem, any help is appreciated :)
Answer:
B = 31.467 °
Step-by-step explanation:
Sides:
a = 13 cm
b = 9 cm
c = 17 cm
Angles:
A = 48.939 °
B = 31.467 °
C = 99.5941 °
Other:
P = 39 cm
s = 19.5 cm
K = 57.6818 cm2
r = 2.95804 cm
R = 8.62057 cm
Agenda:
A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
Formula: SSS is Side, Side, Side
Given the sizes of the 3 sides, you can calculate the sizes of all 3 angles in the triangle. Use The Law of Cosines to solve for the angles. You could also use the Sum of Angles Rule to find the final angle once you know 2 of them.
simplify the fraction 34%
The questions asks us to simplify the fraction 34%, first convert that into a decimal which would be .34, then change that as a fraction which would be [tex]\frac{17}{50}[/tex]
Answer:
brainliest plssssss
Step-by-step explanation:
answer is in the img below
Help immediate... What are the like terms and to simplify fully. -7y^2-6-2-6x+x
Answer:
the fully simplified expression is: [tex]-7y^2+7x-8[/tex]
Step-by-step explanation:
The like terms are:
-6 and -2, which combined give -8
and 6 x and x, which combine give 7 x
So the simplified form of this is:
[tex]-7y^2+7x-8[/tex]
The function f(x) = 4x – 0.1x2 is used to model the curve of a bridge over a small river, where x is the distance from one side of the river and the x-axis represents the ground. The mathematical range for the function is the set of real numbers.
Which statement describes the limitation for the reasonable range compared to the mathematical range
Answer:
The limitation for the resonable range restricts it to postive ral numbers
Step-by-step explanation:
Which number is IRRATIONAL?
Answer:
A
Step-by-step explanation:
because no square root in in 12
Answer:
[tex]\sqrt{12}[/tex]
If a square root is not a perfect square, then it is an irrational number
[tex]ANSWER =\\\sqrt{12} \\\\=2\sqrt{3}[/tex]
Step-by-step explanation:
SOME ONE HELP ME PLZ FAST it's already late
Question Example Step by Step Calculate the minimum and maximum possible areas. Round your answers to the nearest whole square unit. Sara wants to paint a wall. The length and width of the wall are 3 meters and 1.8 meters, respectively. The minimum possible area is about m2. The maximum possible area is about m?
Answer:
4
Step-by-step explanation:
Write these numbers in order of size,
smallest first:
a 8810 m, 8.9 km, 8901 m, 8.821 km,
8812 m, 8.8 km
Answer:8.8 km, 8810 m, 8812 m, 8.821 km, 8.9 km, 8901 m
Step-by-step explanation:
8810 m, 8.9 km, 8901 m, 8.821 km, 8812 m, 8.8 km
which mean
8810 m, 8900 m, 8901 m, 8821 m, 8812 m, 8800 m
arrange accordingly
8800 km, 8810 m, 8812 m, 8821 m, 8900 m, 8901 m
convert back
8.8 km, 8810 m, 8812 m, 8.821 km, 8.9 km, 8901 m
Answer:
8.8km , 8810m , 8812m , 8.821km , 8.9km , 8901m
Step-by-step explanation:
1km = 1000m
Convert values in km to m by multiplying them by 1000
8.8km × 1000 = 8800m
8.821km × 1000 = 8821m
8.9km × 1000 = 8900m
What is the difference in kilowatt hours of monthly energy production between an a erage local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour?
Answer:
The difference in energy production in kilowatt hours of monthly energy produced between an average local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour is approximately 9 kWh
Step-by-step explanation:
We note that the energy produced is given by the formula;
Energy = 1/2 × m × v²
From which we have the energy per unit mass = 1/2 × v²
The energy produced by the wind traveling at 15 miles per hour is given as follows;
15 mph = 6.705 m/s
The energy per unit mass produced in a month of 30 days is therefore;
1/2×6.705²×60×60×24×30 = 58264304.4 J/kg
We note that 1 Kilowatt hour = 3.6 × 10⁶ Joules
Therefore;
58264304.4 J = 58264304.4 J/(3.6 × 10⁶) kWh = 16.184529 kWh
The energy produced by the wind traveling at 10 miles per hour is given as follows;
10 mph = 4.47 m/s
The energy per unit mass produced in a month of 30 days is therefore;
1/2×4.47²×60×60×24×30 = 25,895,246.4 J/kg
We note that 1 Kilowatt hour = 3.6 × 10⁶ Joules
Therefore;
25,895,246.4 J = 25,895,246.4 J/(3.6 × 10⁶) kWh = 7.193124 kWh
The difference in energy production in kilowatt hours of monthly energy produced between an average local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour is therefore;
16.184529 kWh - 7.193124 kWh = 8.991405 kWh. ≈ 9 kWh