The mass of the frying pan in grams is 52 grams.
What is a conversion factor?In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are one (1) kilogram in one hundred (100) grams. This ultimately implies that, a proportion or ratio for the conversion of 0.52 kilogram to grams would be written as follows;
Conversion:
1 kilogram = 100 grams
0.52 kilogram = x grams
By cross-multiplying, we have the following:
x = 0.52 × 100
x = 52 grams.
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Complete Question:
The mass of Stewart's favorite frying pan is 0.52 kilograms. What is the mass of the frying pan in grams?
Which of the following statements are true?
Select all that apply.
A. 4 is a perfect cube.
B. 16 is a perfect square.
C. 2,197 is both a perfect square and a perfect cube.
D. 8 is a perfect cube.
E. 18 is neither a perfect square nor a perfect cube.
Answer:
B and D
Step-by-step explanation:
4²= 16
it's a perfect square
2³= 8
it's a perfect cube
Write the number 0.08 in scientific notation
The scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex] where 10 raised to an exponent (-2).
In scientific notation, a number is expressed as the product of a coefficient and a power of 10.
To write the number 0.08 in scientific notation, it as a decimal number multiplied by a power of 10.
So, 0.08 can be written in scientific notation as 8 x [tex]10^{(-2)[/tex].
In scientific notation, the number is written as the product of a coefficient (8) and a power of 10 raised to an exponent (-2), indicating the decimal's position relative to the coefficient.
Therefore, the scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex].
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Which inequality represents the values of x for which triangle ABC exists
After considering all the given options we come to the conclusion that the inequality that represents the values of x for the give triangle ABC is 15/11 < x < 17/5, which is Option A.
Here, the sides of a triangle should gradually satisfy the triangle inequality theorem which projects that the summation of the lengths considering any two sides of a triangle should be bigger than or equivalent towards the length of the third side.
Then, for the given sides of triangle ABC,
3x+1 + 16 > 8x
Applying this inequality,
x > 15/11
So,
16 + 8x > 3x+1
Applying simplification
x < 17/5
Hence , the inequality that represents the values of x for which triangle ABC exists is 15/11 < x < 17/5.
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The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
OC) 3 years
D) 308 years
Answer:
31 years
Step-by-step explanation:
A = P(interest rate)^number of years (n)
if the money is to quadruple, A = 4 X 22,000 = 88,000.
P = investment amount = 22,000.
interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.
n is number of years.
22,000 (1.045)^n = 88, 000
divide both sides by 22, 000:
(1.045)^n = 4
take logs for both sides:
log (1.045)^n = log 4
simplify using log laws (by bringing down the n):
n log (1.045) = log 4
divide both sides by log (1.045):
n = (log 4) / log (1.045)
= 31.49 (31 years to nearest year)
An archaeologist finds a barren land with a large number of fossils of Dinosaurs. The number N(t) of fossils that can be found per cubic meter after t years can be determined by solving the equation:
Assuming that the initial number of fossils is 100, estimate the number of fossils after 10 years.
The assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.
To estimate the number of fossils after 10 years, we need to solve the given equation. However, since the equation is not provided, we'll assume a simple exponential decay model for the population of fossils.
Let's assume the equation for the population of fossils is:
N(t) = N0 * e^(-kt)
where:
N(t) is the number of fossils after t years,
N0 is the initial number of fossils,
k is a decay constant, and
e is the base of the natural logarithm (approximately 2.71828).
Since the initial number of fossils is given as 100, we have N0 = 100. Now, we need to find the value of the decay constant (k) to estimate the number of fossils after 10 years.
Without further information, it's challenging to determine the exact decay constant. However, let's assume a hypothetical value of k = 0.1 for this example.
Plugging the values into the equation, we get:
N(10) = 100 * e^(-0.1 * 10)
= 100 * e^(-1)
≈ 100 * 0.36788
≈ 36.788
So, with the assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.
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Answer:
B. 2333.59
Step-by-step explanation:
We have been given the following differential equation:
[tex]\dfrac{dN}{dt}=\dfrac{5000}{6+5t}[/tex]
To find the number of fossils N(t) after t = 10 years, we first need to solve the differential equation using integration and the given parameters to create an equation for N(t) in terms of t.
Solving a differential equation means using it to find an equation in terms of the two variables, without a derivative term.
Rearrange the equation so that all the terms containing N are on the left-hand side, and all the terms containing t are on the right-hand side:
[tex]1\;dN=\dfrac{5000}{6+5t}\; dt[/tex]
Integrate both sides:
[tex]\displaystyle \int 1 \;dN=\int \dfrac{5000}{6+5t}\; dt[/tex]
Use the following integration rules:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Integration rulest}\\\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\;\;(where $n$ is any constant value)\\\\\\$\displaystyle \int \dfrac{n}{a+bx}\:\text{d}x=\dfrac{n}{b}\ln |a+bx|+\text{C}$\\\\ \end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int 1\;dN&=\int \dfrac{5000}{6+5t}\; dt\\\\\implies N&=\frac{5000}{5}\ln \left|6+5t\right|+C\\\\N&=1000\ln \left|6+5t\right|+C\end{aligned}[/tex]
As the initial number of fossils is 100, then N = 100 when t = 0.
Substitute these values into the equation and solve for C:
[tex]100=1000\ln \left|6+5(0)\right|+C[/tex]
[tex]C=100-1000\ln (6)[/tex]
Therefore, the equation for N in terms of t is:
[tex]N=1000\ln \left|6+5t\right|+100-1000\ln(6)[/tex]
Use the quotient log rule to simplify:
[tex]N=1000\ln \left|6+5t\right|-1000\ln(6)+100[/tex]
[tex]N=1000\ln \left(\dfrac{\left|6+5t\right|}{6}\right)+100[/tex]
To estimate the number of fossils after 10 years, substitute t = 10 into the equation:
[tex]N=1000\ln \left(\dfrac{\left|6+5(10)\right|}{6}\right)+100[/tex]
[tex]N=1000\ln \left(\dfrac{56}{6}\right)+100[/tex]
[tex]N=2333.59\; \sf (2\;d.p.)[/tex]
Therefore, the number of fossils after 10 years is 2333.59.
An end behavior model for f(x) = [tex](8x^6-16x^3+8)/4x^2-4x-24)[/tex]
2x^2.
2x^3.
2x^4.
2x^6.
This given function does not have an end behavior since it is not a polynomial.
What is the end behavior of a function?The end behavior of a function describes the behavior or trend of the function as the input values (x) approach positive or negative infinity. It helps us understand what happens to the function's values as x becomes very large or very small.
We have three possible cases of end behavior of a function which are;
When the value of x approaches positive infinityWhen the value of x approaches negative infinityWhen a function may have different behaviors for positive and negative infinity. In such cases, we specify the end behavior separately for positive and negative infinity.The end behavior of a function is often determined by using the leading term of the function, which is the term with the highest power of x.
In the given problem;
[tex]f(x) = \frac{8x^6 - 16x^3 + 8}{4x^2 - 4x - 24}[/tex]
The end behavior of this function does not exist because this function is not a polynomial
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18.3% of the animals in the local shelter are neither cats nor dogs. 2% of those animals that are not cats or dogs are rabbits. If there are 267 animals in the shelter, approximately how many of them are rabbits? Do not round any numbers until you finish the problem
I need some help with this problem please
(a) The result of row 1 and row 2 interchange is [3 -2 3]
[2 3 1]
(b) The result of multiplying and adding the matrix is [-1 5 -2]
[3 -2 3]
What is the row operation of the matrix?
The row operation of the matrix is calculated as follows;
The given matrix;
[2 3 1]
[3 -2 3]
To interchange row 1 and row 2, we determine it as follows;
R₁ ↔ R₂ = [3 -2 3]
[2 3 1]
The product of row 2 and -1 is calculated as;
-1 (R₂) = [-3 2 -3]
The addition of -1(R₂) + R₁ is calculated as;
-1(R₂) + R₁ = [-3 2 -3] + [2 3 1]
-1(R₂) + R₁ = [-1 5 -2]
new matrix = [-1 5 -2]
[3 -2 3]
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What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 18 yd 9 yd
The surface area of the given cylinder is approximately 1758.4 square yards.
To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface (lateral surface area) and its two circular bases.
Given:
Height (h) = 18 yards
Radius (r) = 10 yards
π (pi) ≈ 3.14
Lateral Surface Area:
The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius and h is the height.
Lateral Surface Area = 2πrh
Substituting the given values, we have:
Lateral Surface Area = 2 × 3.14 × 10 × 18
Lateral Surface Area = 1130.4 square yards (rounded to the nearest hundredth)
Circular Bases:
The area of a circle can be calculated using the formula πr^2, where r is the radius.
Area of a Circular Base = π[tex]r^2[/tex]
Substituting the given radius, we have:
Area of a Circular Base = 3.14 × [tex]10^2[/tex]
Area of a Circular Base = 314 square yards
To find the total surface area, we need to add the lateral surface area and the areas of the two circular bases.
Total Surface Area = Lateral Surface Area + 2 × Area of a Circular Base
Substituting the values, we get:
Total Surface Area = 1130.4 + 2 × 314
Total Surface Area = 1758.4 square yards (rounded to the nearest hundredth)
Therefore, the surface area of the given cylinder is approximately 1758.4 square yards.
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Question
'What is the surface area of this cylinder? What is the surface area of this cylinder? Use I ~ 3.14 and round your answer to the nearest hundredth_ 18 yd 10 yd square yards'
Find the volume of a cylinder with a diameter of 20 km and a height of 5 km in terms of pie.
what is the volume of the cylinder?
Answer:
The volume of the cylinder is 500 π cubic kilometers.
Step-by-step explanation:
Formula: V = πr²h
r = d/2
r = 20km/2
r = 10 km
h = 5km
Solve for the volume using the formula.
Substitute the given
V = π(10km)²(5km)
V = 500π km³
I hope this helps you
Exponent
T-Table
Coincident (Consistent
Dependent)
Systems of Equations
Inconsistent
Consistent Independent
1.
2.
3.
4.
5.
6.
A set of two or more equations
with the same variables.
A system of linear equations with
EXACTLY ONE solution.
A system of linear equations with
INFINITELY MANY solutions.
A system of equations with NO
solution.
A number representing how many
times the Base number should be
multiplied by itself.
A chart of the different values for
an equation or graph.
A set of two or more equations with the same variables.
A system of linear equations with EXACTLY ONE solution.
A system of linear equations with INFINITELY MANY solutions.
A system of equations with NO solution.
A number representing how many times the Base number should be multiplied by itself.
A chart of the different values for an equation or graph.
Systems of Equations:
A set of two or more equations with the same variables.
These equations are solved simultaneously to find the values of the variables.
Consistent Independent:
A system of linear equations with EXACTLY ONE solution.
This means that the lines represented by the equations intersect at a single point.
Consistent Dependent (Coincident):
A system of linear equations with INFINITELY MANY solutions.
In this case, the equations represent the same line or overlapping lines, and every point on the line is a solution.
Inconsistent:
A system of equations with NO solution.
This occurs when the lines represented by the equations are parallel and never intersect.
Exponent:
A number representing how many times the base number should be multiplied by itself.
For example, in the expression[tex]2^3,[/tex] the exponent is 3, which means 2 should be multiplied by itself 3 times [tex](2 \times 2 \times 2 = 8).[/tex]
T-Table:
A chart of the different values for an equation or graph.
It typically includes two columns: one for the input values (usually x) and one for the corresponding output values (usually y).
T-tables are helpful for understanding the relationship between the variables in an equation and for plotting points on a graph.
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Find the probability that a randomly
selected point within the square falls in the
red-shaded square.
1
1
3
P = [?]
3
Enter as a decimal rounded to the nearest hundredth.
The probability that a randomly selected point within the square falls in the red-shaded square is 0.11
Finding the probabilityFrom the question, we have the following parameters that can be used in our computation:
Red square of length 1White square of length 3The areas of the above shapes are
Red square = 1² = 1
White square = 3² = 9
The probability is then calculated as
P = Red square/White square
So, we have
P = 1/9
Evaluate
P = 0.11
Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.11
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factorise P(x)=2x*3-5.6x+1
After applying factorization of the given functions the evaluated expression comes out to be (2x + 1)(x² - x - 4.8), under the condition the given function is P(x)=2x × 3- 5.6x +1
In order to factorize the given polynomial P(x) = 2x³ - 5.6x + 1, we can apply the Rational Root Theorem. The theorem projects that in an incident when a polynomial has integer coefficients, then any rational roots must have a numerator that divides the constant term and a denominator that divides the leading coefficient.
For the given case, the leading coefficient is 2 and the constant term is 1.
Hence, any rational roots must be of the form p/q where p divides 1 and q divides 2. This elaborates that the possible rational roots are ±1/2 and ±1.
We can observe these roots applying synthetic division. Using synthetic division with root -1/2 gives us:
-1/2 | 2 0 -5.6 1
| -1 0.8 -0.5
-------------------
2 -1 -4.8 0.5
This means that P(x) can be factored as:
P(x) = (2x + 1)(x² - x - 4.8)
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pls answer me fast rapidly:
You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What are the balances for each account by the end of the third year and the total gain on your original saved amount?
Answer:
Step-by-step explanation:
Amount in 4.6% acct= 15000*(1/3)= 5000
Amount in bonds = 1/4*15000= 3750
Amount in stock= 15000-(5000+3750)= 6250
Amount in each account at the end of three years
5000*(1.046)^3= 5722.22668
3750*(1.052)^3=4365.94728
6250*1.03*(1-.08)*1.06= 6277.85
total: 5722.22668+4365.94728+6277.85=16366.02396
gain= 16366.02396-15000=1366.02396
or (16366.02396/15000)-1= 9.1068264%
What is the approximate perimeter of the triangle shown below?
Last question is 19.8…
The perimeter of the given triangle is: 19.2 units
What is the Perimeter of the Triangle?The formula for the distance between two coordinates is:
D = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus: (0, 3)(4, -2)
Slant distance on left side of triangle = √[(-2 - 3)² + (-3 - 0)²] = 5.8 units
Slant distance on right side of triangle = √[(-2 - 3)² + (4 - 0)²] = 6.40 units
Length of horizontal part of triangle = 7 units
Thus:
Perimeter of triangle = 5.83 + 6.40 + 7 = 19.2 units
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the diagram shows a right triangle and the lengths of two of its sides in 11.9in and 7.9 and d what measurement is closest to the value of d inches
The measurement is closest to the value of d inches is 14. 28
How to determine the valueIt is important to note that the Pythagorean theorem is stated as;
The Pythagorean theorem states that the square of the longest leg or hypotenuse side of a triangle is equal to the sum of the squares of the other two sides.
This is represented as;
x²= y²+ z²
Now, substitute the values, we get;
x² = 11. 9² + 7.9²
Find the square values, we have;
x² = 141. 61 + 62. 41
add the values, we have;
x² = 204. 02
Now, find the square root of both sides, we get;
x = √204. 02
x = 14.28
Know that d = x = 14. 28
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A lion can run 1.89 miles in distance. If 1 mile is the
same as 5,280 feet, what is the distance that a lion
can run in feet?
Precalculus > M.12 Trigonometric ratios: find a side length 62D Find BC. B C BC= 00 12/31 √ 30° Write your answer in simplified, rationalized form. Do not round. D Learn with an example
PLEASE HELP ME
The length of BC is determined as 6√31 by applying trigonometry ratio.
What is the length of BC?The length of BC is calculated by applying the following formulas for trig ratios.
The trig ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The hypothenuse side of the right triangle is given as 12√31 and the opposite side is length BC.
The length of BC is calculated as follows;
sin 30 = BC / 12√31
BC = 12√31 x sin (30)
BC = 12√31 x ¹/₂
BC = 6√31
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I'm giving the brainiest to the correct answer.
Answer:
$15,200
Step-by-step explanation:
You want to know the amount deposited at 1.5% that will earn the same simple interest in a year as $12,000 deposited at 1.9%.
InterestThe interest amount is given by the formula ...
I = Prt
For the two accounts, the interest and the time are the same, so we have ...
P1·r1 = P2·r2
12000·1.9% = P2·1.5% . . . . . . . . . . . equate interest amounts for t=1
P2 = 1.9/1.5·12000 = 15200 . . . . . . divide by 1.5%
Ruth deposited $15,200.
<95141404393>
please help i cant fail this
Answer:20%
Step-by-step explanation:
Bookwork code: K27
,Calculator
allowed
A pendulum of length 18 cm is swinging from a fixed point, as shown.
Calculate the distance that the end of the pendulum travels when it swings
through an angle of 87°.
Give your answer in centimetres (cm) to 1 d.p.
87°
18 cm
The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm
Given data ,
A pendulum of length 18 cm is swinging from a fixed point
Now , it swings through an angle of 87°
So , Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
Now , D = ( θ/360 ) x 2πr
On simplifying , we get
D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )
D = ( 0.241667 ) ( 113.04 )
D = 27.3 cm
Hence , the pendulum travels a distance of 27.3 cm
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The next day you take Zeek to the Arizona State Fair. His mom gives him $30 to
spend. It costs $13 to get in and the $2 for every ride. How many rides can he ride?
● Define a variable, ex: x = ________.
● Write an equation to model this situation.
● Solve the equation for your variable.
● Write your answer in a complete sentence.
● Give the page a relevant title.
Answer:
Step-by-step explanation:
Let’s define the number of rides that Zeek can ride as “r”.
To determine how many rides Zeek can ride, we need to first subtract the cost of admission from his total budget:
$30 - $13 = $17
This means that Zeek has $17 left to spend on rides. Since each ride costs $2, we can set up the following equation:
$2r = $17
To solve for “r”, we divide both sides of the equation by $2:
r = $8.50
So Zeek can ride a maximum of 8 rides with the $17 he has left after paying for admission. However, since he cannot ride a fraction of a ride, he may be limited to only 8 rides or fewer.
=
A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number less than 7.
The probability of rolling a number less than 7 is
(Type an integer or a simplified fraction.)
After considering all the given data we conclude that the the probability of rolling a number less than 7 is 1/2, under the condition that the set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12).
The evaluated probability of rolling a number less than 7 on a 12-sided die is the number of outcomes that are less than 7 divided by the total number of possible outcomes.
The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). There are 6 numbers less than 7 in this set (1,2,3,4,5,6) and 12 possible outcomes.
Hence , the probability of rolling a number less than 7 is:
6/12 = 1/2
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Given WX is tangent to ⊙S at point V, select all the statements that must be true.
A. m∠TVX =m∠TVX
B. m∠TSV =m∠UVX
C. m∠TVW = m∠TSV
D. m∠TUV =m∠TVW
E. m∠UVX =m∠VTU
Given WX is tangent to OS at point V, the statements that must be true include:
A. m∠TVX =m∠TVX
C. m∠TVW = m∠TSV
D. m∠TUV =m∠TVW
How to explain the tangentIn mathematics, a tangent is a line that touches a curve at exactly one point, without intersecting it at that point. The tangent line at a point on a curve represents the slope of the curve at that point. The concept of tangent is important in calculus, where it is used to calculate derivatives of functions.
TUV = 1/2MTU = TVW
TUV = TVW
Also, MTV = TSV = 2TVW
TVW = TSV
The correct options are A, C and D.
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Which is a whole number?
0.86
2/5
98
35%
Answer:
98 is a whole number
Step-by-step explanation:
0.86 is a decimal
2/5 is a fraction
35% is a percentage
Is x-1
a factor of
x^5-3x^4-2x^3-5x^2+5x+12?
Correct The remainder when you divide is
The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8
What is the remainder theorem?The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point
The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;
f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8
The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8
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Is the relation a function? Explain.
A. No because for each input there is not exactly one output.
B. No because for each output there is not exactly one input.
C. Yes because for each input there is exactly one output.
D. Yes because for each output there is exactly one input.
The relation is a function because (d) Yes because for each output there is exactly one input.
Determining if the relation is a functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph can be represented as
x g(x)
-5 1
-2 0
-1 -1
0 2
1 3
5 1
The above table of values is a function
This is so because each output values have different input values.
i.e. it would pass the vertical line test when represented on a graph
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Use substitution to solve the system of equations. How many solutions are there? 12 x − 13 y = 5 x = 23 y + 10 There are no solutions. There is one solution. There are infinitely many solutions.
Answer: there is one solution
Step-by-step explanation:
12x − 13y = 5
x = 23y + 10
lets substitute x into the first equation.
12(23y + 10) - 13y = 5
276y + 120 - 13y = 5
263y = -115
y = -115/263
substituting for x:
x = 23(-115/263) + 10
x = -2645/263 + 10
x = -15/263
As we can see, we get one value of x;
this means there is one solution