The solutions of the given polynomial equation p⁴+32=12 p² is p = {-2√2, 2√2, -2, 2}.
The given polynomial equation is:
p⁴+32=12 p²
Subtract both sides by 12 p²
p⁴ + 32 -12 p² = 12 p² 12 p²
p⁴ -12 p² + 32 = 0 ...... (1)
Let x = p², then equation (1) becomes
x² -12x + 32 = 0
This is a quadratic equation.
Factorize:
x² -12x + 32 = 0
⇔ (x - 8 ) (x - 4) = 0
Take:
x - 8 = 0
x = 8
p² = 8
p = ±√8 = ±2√2
Take:
x - 4 = 0
x = 4
p² = 4
p = ±√4 = ±2
Hence the solution is p = {-2√2, 2√2, -2, 2}
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Write an explicit formula for each sequence. 2,4,8,16, . . . .
The explicit formula for the given geometric sequence is: [tex]a_n=2^n[/tex].
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now, Given sequence: 2, 4, 8, 16, ...
=> 2¹, 2², 2³, 2⁴, ....
Thus, the explicit formula for this geometric sequence will be given by: [tex]a_n=2^n[/tex].
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Katy’s favorite rides at the amusement park are the roller coaster and water slide. The wait time for the roller coaster is 25 minutes and the wait time for the water slide is 10 minutes. If she went on 12 rides total and waited three hours in line, how many times did she go on each ride?
Katty rode the roller coaster four times after riding the slide eight times.
What number times did she go on each ride?Let R be the number of times she rode the roller coaster
Let S be the number of slides
The following mathematical equation can be created using the information provided:
R + S = 12. ........(i)
25R + 10S = 180 .......(ii)
From equation i, R = 12 - S.
Therefore, 25(12 - s) + 10s = 180
300 - 25s + 10s = 180
300 - 15s = 180
15s = 300 - 180
15s = 120
S = 120/15
S = 8 ,
Therefore R = 12 - S = 12 - 8 = 4
Katty rode the roller coaster four times after riding the slide eight times.
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For the geometric sequence 3,12,48,192, . . . . . , find the indicated term. n th term
The nth term of the given geometric sequence, 3, 12, 48, 192, . . . , is a(n) = 3[4^(n - 1)], where a(n) is the nth term.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
a = first term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Substitute the value or r and the first term to the formula to determine expression for the nth term.
a(n) = a r^(n-1)
a(n) = 3[4^(n - 1)]
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Help. Ill give 20 points and brainliest
Answer:
EF = 10
Step-by-step explanation:
DE + EF = DF
So, x + 22 + x + 23 = 21
2x + 47 = 21
2x = -26
x = -13
EF = x + 23
EF = 10
The area of a rectangle is 85 yd 2 . If both the length and the width of the rectangle are doubled, what is the area of the new (bigger) rectangle?
The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length and y represent the width of the rectangle. The area is 85 yd², hence:
xy = 85
If both the length and the width of the rectangle are doubled:
new length = 2x; new width = 2y
new area = 2x * 2y = 4xy = 4(85) = 340 yd²
The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²
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Shawna works for a company that makes frozen pizzas. She cooked a sample of pizzas in
different ovens and let them cool in different rooms. She noticed an exponential relationship
between cooling times and pizza temperatures after cooking.
Shawna took the base 10 logarithm for the temperatures only, and she noticed a linear
relationship between the cooling times and the transformed temperatures.
Here's the least-squares regression equation for the transformed data, where "time"
represents minutes spent cooling, and "temp" is the pizza's temperature in degrees Celsius.
log(temp) = 2.390 -0.004(time)
According to this model, what is the predicted temperature of a pizza that cools for 20
minutes?
You may round your answer to the nearest whole degree.
Answer:
204 °C
Step-by-step explanation:
You want the predicted temperature of a pizza that has cooled for 20 minutes, as predicted by the formula ...
log(temp) = 2.39 -0.004·time
where temp is in degrees Celsius, and time is in minutes.
Evaluating the formulaUsing time = 20 in the formula, we find ...
log(temp) = 2.39 - 0.004·20 = 2.39 -0.08 = 2.31
Taking the antilog, we find the temperature to be ...
temp = 10^2.31 ≈ 204.2 . . . . . degrees C
The predicted temperature of the pizza is 204 °C.
State the property that justifies each statement.
If X Y+20=Y W and X Y+20=D T , then Y W=D T .
The characteristic that justifies each assertion Property of substitution
Briefing:The substitution property asserts that if a=b, then one can of replacing b in quite an expression or equation.
X Y+20=Y W and X Y+20=D T
then Y W=D T
What is the Substitution Property?The replacement property of equality states that "If a variable x is equal towards another variable y, then x may be substituted in place of y in whatsoever equation/expression and y can indeed be substituted throughout the place of x in any equation/expression."
Why is substitution significant in mathematics?Substitution connects many aspects of mathematics and hence aids in viewing mathematics as an entire discipline.
How do they solve through substitution?Three phases are involved in the substitution method: Solve this equation for a single of the variables. Substitute (plug-inin) this equation into a different equation and solve. Replace the value inside this original equation to obtain the equivalent variable.
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5) La Varianza es la raíz cuadrada de la desviación típica
O Falso
O Verdadero
Answer:
la correcta es verdadero
Samara preferences are expressed by the utility function u(x, y) = x2y2. if her utility level is at 3136 and the slope of her indifference curve is -0.875, what is her consumption of x?
Her consumption of x is mathematically given as
x=8
What is her consumption of x?Generally, the equation for Slope is mathematically given as
u=x^2y^2 ....1
Therefore
[tex]$ slope=-\frac{m u x}{m v_y}=\frac{-2 x y^2}{2 x^2 y}$[/tex]
slope=-y/x
y=0.875 x
Substitute in (1)
[tex]u=x^2(0.875 x)^2=3136 \\[/tex]
[tex]0.875^2 x^4=3136 \\[/tex]
[tex]x^4=4096[/tex]
x=8
y=7
In conclusion,
x=8
y=7
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-2(x+4)+3x=x-8solve the equation
Step-by-step explanation:
-2(x+4)=-3x+x-8
Movemos todos los términos a la izquierda:
-2(x+4)-(-3x+x-8)=0
Sumamos todos los números, y todos los variables
-2(x+4)-(-2x-8)=0
Multiplicamos paréntesis
-2x-(-2x-8)-8=0 Eliminamos
paréntesis
-2x+2x+8-8=0
Sumamos todos los numeros juntos, y todas las variables
=0
x=0/1
x=0
The circumference
of the circle shown above
is 108. The length of the minor arc AB is a pi. What is the value of a
Answer:
Thus, the length of the arc AB will be 5/18 of the circumference of the circle, which equals 2πr, according to the formula for circumference. length of arc AB = (5/18)(2πr) = (5/18)(2π(18)) = 10π. Thus, the length of arc AB is 10π.
Step-by-step explanation:
What is the slop and standard form (image here)
The slope of the line is - 2 / 5
The equation in standard form is as follows:
2x + 5y = -15
How to find the slope and standard form equation of the line?The slope of the line can be found as follows;
using (0, - 3)(5, - 5)
m = -5 + 3 / 5 - 0
m = -2 / 5
slope = -2 / 5
The slope intercept form representation of an equation is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = -2 / 5 x + b
using (0, -3),
-3 = - 2 / 5 (0) + b
b = -3
Hence,
y = - 2 / 5 x - 3
The standard form is as follows:
Ax + By = C
Therefore, the equation in standard form is as follows:
2 / 5 x + y = - 3
2x + 5y = -15
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Determine which property is being used below. 18x1
Multiplicative Identity Property
Step-by-step explanation:Using math properties like the multiplicative identity property we can solve different expressions and equations.
Definition of Multiplicative Identity Property
The multiplicative identity property states that any number multiplied by 1 equals itself. This means that 18 x 1 = 18. Of course, since this is a property we can apply this idea to any equation.
-56 x 1 = -561 x π = π∞ x 1 = ∞All of the statements above are true because of the multiplicative identity property.
Uses of the Multiplicative Identity Property
While being able to do simple operations with this property is helpful, there are other uses as well. One of the most prominent uses is finding a great common factor. When adding or subtraction fractions, you must have a GCF. We can use the multiplicative identity property to do this.
Take the expression
[tex]\displaystyle\frac{5}{6}-\frac{2}{3}[/tex]To solve this we must multiply [tex]\frac{2}{3}[/tex] by [tex]\frac{2}{2}[/tex]. The multiplicative identity property tells us that since 2/2 = 1, this will not affect the value of the expression (remember that anything times 1 is still equal to itself).
[tex]\displaystyle\frac{2}{3}*\frac{2}{2} =\frac{4}{6}[/tex]Then, we can solve the expression.
[tex]\displaystyle\frac{5}{6} -\frac{4}{6} =\frac{1}{6}[/tex]Explain why...
x2 + 7x + 8
does not factorise
Step-by-step explanation:
because you need 2 numbers that
(+)=7
and
(x)=8
no 2 whole numbers work
it will have to be decimals
so you can't factorise
so you have to use the quadratic formula
hope this helps :)
Answer:
Step-by-step explanation:
if a quadratic of this form can be factorised the factors are
(x + a)(x + b).
In this case a*b would be = + 8 and a + b would be + 7.
There are no integer values which will give these 2 results so x^2 + 7x + 8 cannot be factorised.
An example of a quadratic that can be factories is x^2 + 8x + 7,
because ab = 7 *1 and a + b = 7 + 1 = 8 so the factors are:
(x + 1)(x + 7).
Number 6 help please thanks
Answer:
im guessing c?
Step-by-step explanation:
adam can rent an apartment in the city and walk to work for $615 per month. He can rent an apartment in the suburbs for $500 per month and take the train to work for $5 per day. How many days will he have to work per month to make either choice equal financially?
The 7 days will he have to work per month to make either choice equal financially.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Adam can rent an apartment in the city and walk to work for $615 per month.
He can rent for $500 per month and take the train to work for $5 per day.
According to given question we have
Total rent =$615 per month.
Rent an apartment in the suburbs = $500 per month
train to work= $5 per day
train to work in a month=$5*30= $150 per month
So, total Rent an apartment in the suburbs
=$500 per month+$150 per month
=$650 per month
Difference
=$650 per month- $615 per month.
=$ 35 per month
$5day==$ 35 month
1 day= $ 35 /5 = $ 7 per month
To work per month to make either choice equal financially in 7 days.
Therefore, the 7 days will he have to work per month to make either choice equal financially.
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The diagram below shows the dimensions of a pool in a waterpark. Point "O" shown in the diagram is the center of the circular portion of the pool. If a cover is needed for the pool, what is the area of the cover? (Assume pi = 3.14)
Answer:
10,168 sq m
Step-by-step explanation:
The are of the cover is
the area of the circular portion of the pool + area of square portion - area common to both circular and square portions
The common portion is 1/4the the area of the circle
The radius of the circular portion = 80-40 = 40m
Area of circular portion = πr² = π (40)³ = 1600π sq m
1/4 this is 160/4 = 400 sq m
Area of square = 80² = 6400 sq m
Total area = 1600π + 6400 - 400π = 1200π + 6400 = 1200 x 3.14 + 6400
= 10,168 sq m
Answer:
hihihihi
Step-by-step explanation:
Which is the ratio of the number of months that begin with the letter J to the total number of months in a year?
Answer:1:4
Step-by-step explanation:there are 3 months with the letter j and 12 months so 1:4
Answer:
Ratio of the number of months that begin with the letter J to the total number of months in a year is:
1:4
Step-by-step explanation:
Total number of months in a year=12
Months starting with J are:
January June July
Total months starting with J=3
Ratio= 3:12
=1:4
Hence, ratio of the number of months that begin with the letter J to the total number of months in a year is:
1:4
A company advertises that their juice boxes contain 20 \% more juice than their competitor's. If the base dimensions of the boxes are the same, how much taller are the larger boxes?
The boxes will be 1.2 times taller than old boxes.
We are given that increase in amount of juice is achieved by keeping the base same but increasing the height only. So, we are aware that length and width are part of base but height is not. Now, there will 20% increase in volume, so finding the increase in height when volume of boxes is increased.
V₁ = V₂
L₁×B₁×H₁ = L₂×B₂×H₂
We know, L₁B₁ = L₂B₂
So, relating the height of boxes -
H₂ = H₁ (1 + 20%)
H₂ = H₁ (1 + 0.2)
H₂ = H₁×1.2
H₂ =1.2 H₁
Hence, the larger boxes will be 1.2 times taller than old boxes.
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which best describes how to solve the equation below?
26x = 74
A. divide both sides by 74
B. divide both sides by 26
C. Multiply both sides by 26
D. multiply both sides by 74
Answer:
B. Divide both sides by 26
Explanation:
When doing a one step equation you basically want to get the x alone. To do that you need to divide 26x by 26.
26x = 74
26 26
x = 2.8
1. Evaluate: 3x³- 2x² + 7y for x = -3 and y = -7.
A -148
B 14
C 112
D -112
Answer:
A. -148
Step-by-step explanation:
3x³ - 2x² + 7y
3(-3)³ - 2(-3)² + 7(-7)
3(-27) - 2(9) - 49
-81 - 18 - 49
-148
I hope this helps!
Problem
The following graph shows y=m(x)y=m(x)y, equals, m, left parenthesis, x, right parenthesis.
Which of the following shows the graph of y=m^{-1}(x)y=m
−1
(x)y, equals, m, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The inverse of a function is a mirror image of a graph around y = x thus graph in (A) will be the inverse of a function y = m(x).
What is the inverse of a function?The inverse of a function is basically a reverse function or undo of the function.
It means in the inverse function we need to interchange x and y.
Let's consider a function y = 2x + 3
The inverse of y is ⇒ y = (x - 3)/2
Now,
If we draw both graphs, both are mirror images of each other about x = y (as shown below).
Therefore y = m⁻¹(x) will be the mirror image of y = m(x) about y = x.
In option (A) the graph is the only mirror image of graph y = m(x).
Hence "The graph in option (A) shows the inverse of function y = m(x)".
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Consider y - 8 = - x a.
Complete the table for the equation.
X y
0 ?
1 ?
2 ?
Answer:
(0, 8)
(1, 7)
(2, 6)
(3, 5)
(4, 4)
(5, 2)
(6, 1)
Step-by-step explanation:
y - 8 = -x
+8 +8
y = -x + 8
Slope: -1
8(*)
7 - *
6 - *
5 - *
4 - *
3 - *
2 -
1 -
----|-----|-----|---|----|---|--|----|-
0 1 2 3 4 5
I hope this helps!
Find the x - and y -intercepts of each line.
y=6x
The equation of the line y = 6x has 0 and 0 as its x- and y-intercept, respectively.
The equation of a line is an equation containing variable(s) and constant(s) and can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The x-intercept of a line is the value of x when y = 0 while the y-intercept of a line is the value of y when x = 0.
For an equation written in standard form ax + by = c, the x- and y-intercept is as follows:
x-intercept = c/a
y-intercept = c/b
If the equation of the line is y = 6x, then its x- and y-intercept is as follows:
x-intercept = c/a = 0/6 = 0
y-intercept = c/b = 0/1 = 0
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Forty two is the sun of twelve and the product of a number and 3. What is the number. (Show work)
Answer:
10
Step-by-step explanation:
First write out the equation: 42 = 12 + 3x
42 - 12 = 12 - 12 + 3x
30 = 3x
30/3 = 3x/3
x = 10
Solve each equation. Check your answers. x/2 + x/3 =15
The solution of the given equation x/2 + x/3 = 15 is x = 18
In this question,
We have been given an equation.
x/2 + x/3 =15
We need to find the solution of given equation.
First we simplify the LHS of given equation.
x/2 + x/3
= (3x + 2x) / (2)(3)
= 5x / 6
So given equation would be,
⇒ x/2 + x/3 = 15
⇒ 5x / 6 = 15
⇒ 5x = (15)(6)
⇒ 5x = 90
⇒ x = 18
We need to check above solution.
Substitute x = 18 in LHS of given equation.
= 18/2 + 18/3
= 9 + 6
= 15
= RHS
Therefore, the solution of the given equation x/2 + x/3 = 15 is x = 18
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Three cards are selected from a standard deck of 52 cards. What is the probability that all three cards are diamonds if neither the first nor the second card is replaced?
The probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132
In this question,
We have been given a standard deck of 52 cards.
Three cards are selected from a standard deck of 52 cards.
Sample space n(S) = 52
We need to find the probability that all three cards are diamonds if neither the first nor the second card is replaced.
We know that, in a standard deck of 52 cards, there are 13 diamond cards.
The probability that the first card is diamond,
P1 = 13/52
The card is not replaced, so the total number of cards in a standard deck = 51
And the number of diamonds = 12
Now the probability that second card would be diamond,
P2 = 12/51
Similarly the probability that the third card is diamond,
P3 = 11/50
So, the probability that all three cards are diamonds if neither the first nor the second card is replaced:
⇒ P = P1 × P2 × P3
⇒ P = 13/52 × 12/51 × 11/50
⇒ P = 0.25 × 0.24 × 0.22
⇒ P = 0.0132
Therefore, the probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132
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Dalvin runs a farm stand that sells strawberries and
blueberries. Each pound of strawberries sells for $2
and each pound of blueberries sells for $3.50. Dalvin
sold twice as many pounds of blueberries as
pounds of strawberries and he made $225
altogether. Write a system of equations that could be
used to determine the number of pounds of
strawberries sold and the number of pounds of
blueberries sold. Define the variables that you use to
write the system.find the system of equation.
2x + 3.50y = 225
To make $225, Dalvin had to sell 25 pounds strawberries and 50 pounds of blueberries.Given that:
Dalvin has a farm stand where strawberries and blueberries are for sale.Blueberries cost $3.50 per pound, while strawberries cost $2 per pound.Dalvin made $225 total by selling twice as many pounds of blueberries as strawberries.To find:
Write an system of equation that might be utilized to calculate the quantity of strawberries and blueberries sold in pounds.Calculate the amount of blueberries and strawberries that were sold in pounds.So, according the question,
Let's assume Delvin sold x pound of strawberries and y pound of blueberries to make $225.
From question,
if, 1 pound of strawberries = $2
So, x pound of strawberries = $2 × x = $2x.
Similarly,
if, 1 pound of blueberries = $3.50
So, y pound of blueberries = $3.50 × y = $3.50y.
Now, we can say that,
x pound of strawberries + y pound of blueberries = $225.
2x + 3.50y = 225 -------------(1)
Equation (1) is the system of equation of the question.
In comparison to strawberries, Dalvin sold twice as many pounds of blueberries.
So,
y = 2x -----------(2)
Now, putting the value of y from eq(2) in the system of equation of the question.
So, we will we get
2x + 3.50y = 225 -------------(1)
2x + 3.50 × 2x = 225
2x + 7x = 225
9x = 225
x = 225/9
x = 25
Now, putting the value of x in eq(2)
So, we will we get
y = 2x -----------(2)
y = 2 × 25
y = 50
Answer:
The system of equation is2x + 3.50y = 225
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Suppose J is between H and K. use the segment addition postulate to solve for x. then find the length of the segment. HJ = 4x + 9, JK = 3x + 3, HK = 33
As we are told that J is between H and K on line segment HK so HJ and JK becomes two different line segments on the same line segment HK
Using the segment addition postulate and the given values of line segments HJ, JK & HK, we first need to find out the value x first
As we know HJ + JK= HK
4x+9 + 3x+3 = 33
7x +12 = 33
7x= 33-12
7x=21
x= 21/7
x= 3
Hence the values of
Line segment HJ = 4x + 9 = 4× 3+ 9=21
Line segment HJ = 3x + 3 = 3× 3+ 3=12
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Describe the Domain
f(x)=-3x²+2
Answer:
X€R or x€(-&, +&)......
