Test II Solve the given equations using the method of Extracting the square roots. Show your solution(5 points each)
1. x²=16
2. (x-4)²=169
3. 4 x²-225=0
Answers
The quadratic functions x² = 16, (x - 4)² = 169 and 4x² - 225 = 0 have solutions 4, (17 or -9) and (7.5 or -7.5) respectively.
Quadratic EquationsA quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x² term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.
In the first function;
1. x² = 16
take the square roots of both sides;
x = √16
x = 4
2. (x - 4)² = 169
Open the bracket
x² - 8x + 16 = 169
Solving for x
x = 17 or x = - 9
3. 4x² - 225 = 0
4x² = 225
x = 7.5 or x = -7.5
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Related Questions
The population of a country was 64 million in 1993 and the continuous exponential growth rate was
estimated at 2.7% per year. Assuming that the population of the country continues to follow an
exponential growth model, find the projected population in 2008. Round your answer to 1 decimal
place.
The approximate population in 2008 is
million people
Answers
Answer: 104.1
Step-by-step explanation:
If [tex]P(t)[/tex] represents the initial population in millions. [tex]t[/tex] years after 1990, then [tex]P(t)=64e^{0.027t}[/tex].
2008 is 18 years after 1990, so [tex]P(18)=64e^{0.027 \cdot 18} \approx 104.1[/tex]
The exponential growth of population in 2008 is 95.4 million
What is exponential growth factor?
The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the population of the country in 1993 be = 64 million
The exponential growth rate r = 2.7 %
So , the population of the country in 2008 is calculated by
The time t in years = 2008 - 1993
= 15 years
So , the equation for exponential growth rate is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
And substituting the values in the equation , we get\
x ( 15 ) = 64 × ( 1 + 0.027 )¹⁵
x ( 15 ) = 64 × ( 1.027 )¹⁵
x ( 15 ) = 64 × 1.49127
x ( 15 ) = 95.4413
So , the value of x ( 15 ) = 95.4 million
Hence , The exponential growth of population in 2008 is 95.4 million
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Find the AGI and taxable income.
O $19,007 and $7,822
O $19,007 and $6,362
O $20,222 and $7,822
$20,222 and $6,362
Gross income
Adjustments
1 Exemption
Deduction
$20,467
$245
$12,400
$1460
Answers
Answer:
406$
Step-by-step explanation:
Answer:
$20,222 and $6,362
Step-by-step explanation:
I took the test
Help please answer the question.
Answers
The graph of the function g(x) is described as 5 units translation down.
What is a graph?A visual representation or diagram that represents data or values is known as a graph.
The function equations are provided as
f(x) = 1/3x+1
f(x) - 1 = 1/3x
g(x) = 1/3(6x) + 1
g(x) = (1/3x)6 + 1
In the equation g(x) = (1/3x), replace f(x) with f(x) - 1 = 1/3x.
6 + 1
Thus, we have
g(x) = (f(x) - 1)
6 + 1
g(x) = 6f(x) - 6 + 1
g(x) = 6f(x) - 5
The rule mentioned above means that:
A translation of the function f is the function g(x) (x)
As a result, the translation's unit is 5 and its direction is downward.
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A ( x ) = 4 − ( x + 3 )^5
Answers
The solution for A(3) in the function when the function A(x) = 4 − (x + 3)⁵ is -772
How to determine the solution for A(x) in the function?From the question, we have the following equation that can be used in our computation:
A ( x ) = 4 − ( x + 3 )^5
To make the equation legible, we need to rewrite it
So, we have the following representation
A(x) = 4 − (x + 3)⁵
Also from the question, we have
A(3)
This means that the value of x is 3, and we calculate A(x) when x = 3
Substitute the known values in the above equation, so, we have the following representation
A(3) = 4 − (x + 3)⁵
So, we have the following equation
A(3) = 4 − (3 + 3)⁵
There are constants to add or subtract to both sides of the equation
However, there is no factor to multiply or divide from both sides of the equation
So, we have the following representation
A(3) = 4 − (6)⁵
Solving further, we have
A(3) = 4 − 7776
Evaluate the difference
A(3) = −7772
Hence, the solution is −7772
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Possible question
Given A ( x ) = 4 − ( x + 3 )^5, find A(3).
Use the give information to find the value of x.
Answers
30 = x + 25
subtract 25 from both sides
x = 5
hope this helps !
[tex]7*3^x=189[/tex]
Answers
7*3^3=189
Good luck
Hope this helps
A relation that shows that one expression equals another expression is a(n) __________. equation function rate inequality
Answers
Answer:
Equation.
Step-by-step explanation:
The term equation state that the two expression are equal that means left hand side of the expression and right hand side of expression are equal.
Whereas if the two equation are not equal then it is known as inequality.
Thus, the given statement is correctly filled with equation.
sarah invests $8200 in a new savings account which earns 5.8% annual interest, compounded semi-annually.
what will be the value of her investment after four years?
Answers
Answer:
The value after 4 years is $10307.11--------------------------------
GivenInvested amount P = $8200,Interest rate r = 5.8% = 0.058,Compound number n = 2,Time t = 4 years.Find the future amount[tex]A = P(1+r/n)^{nt}[/tex][tex]A = 8200(1+0.058/2)^{2*4}=8200*1.029^8=10307.11[/tex]Answer:
$10,307.11
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given:
P = $8,200r = 5.8% = 0.058n = 2 (semi-annually)t = 4 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=8200\left(1+\dfrac{0.058}{2}\right)^{2 \times 4}[/tex]
[tex]\implies \sf A=8200\left(1+0.029\right)^{8}[/tex]
[tex]\implies \sf A=8200\left(1.029\right)^{8}[/tex]
[tex]\implies \sf A=8200\left(1.25696445...\right)[/tex]
[tex]\implies \sf A=10307.10856...[/tex]
Therefore, the value of Sarah's investment after four years is $10,307.11 (nearest cent).
(2.9X10^5)X(3.4X10^3 in standard form
Answers
By using exponent, it can be verified that
[tex](2.9 \times 10^5) \times (3.4 \times 10^3)[/tex] in standard form is [tex]9.86 \times 10^8[/tex]
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a ... \times a[/tex] (m times), a is the base and m is the index.
The laws of index are
[tex]a^{m + n} = a^m \times a^n\\a^{m - n} = \frac{a^m}{a^n}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\(ab)^m = a^m b^m\\a^0 = 1\\a^{-n} = \frac{1}{a^n}[/tex]
The given exponent is
[tex](2.9 \times 10^5) \times (3.4 \times 10^3)\\9.86 \times 10^{5+ 3}\\9.86 \times 10^8[/tex]
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There are three times as many orange pumpkins at the pumpkin patch as there are white pumpkins. What percentage of the pumpkins are white?
Responses
4%
4%
10%
10%
25%
25%
75%
Answers
The percentage of white pumpkin is 25%.
How to find the percentage of white pumpkin?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.
There are three times as many orange pumpkins at the pumpkin patch as there are white pumpkins.
Hence,
let
x = Number of white pumpkin
orange pumpkin = 3x
The percentage of pumpkin that are whiter can be calculated as follows:
The full percentage is 100%.
Therefore, percentage of white pumpkin is 25%.
Orange pumpkin = 25%(3) = 75
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A table is on sale for 100.80 , which is 76% less than the regular price. What is the regular price?
Answers
The regular price of the table based on the information is $177.41.
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Let the regular price be x.
Since the table is on sale for 100.80, which is 76% less than the regular price, that will be illustrated as:
x = 100.80 × (100% + 76%)
x = 100.80 × 1.76
x = 177.408
The value is $177.41.
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The equation c = 8m represents how many ice cream cones (c) are sold within a certain number of minutes (m) at a certain ice cream shop.
Determine the constant of proportionality.
8
1
one-eighth
16
Answers
The constant of proportionality in the equation c = 8m is 8.
What is a variation?A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
since C = 8m is an equation and the relationship between c and m is direct.
It means that dividing both sides of the equation by m we have
C/m = 8m/m
c/m = 8
Therefore the constant of proportionality is 8
In conclusion the constant of proportionality for which c = 8m is 8.
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A metallurgist has one alloy containing 35% titanium and another containing 52% titanium. How many pounds of each alloy must be use to make 45 pounds of a third alloy containing 47% titanium
Answers
Step-by-step explanation:
% in calculations are always represented as hundredths, as 100% represents the whole, and n% = n/100 of the whole.
x = pounds of 35% alloy.
y = pounds of 52% alloy.
x + y = 45
0.35x + 0.52y = 0.47(x + y)
from the first equation we get e.g.
x = 45 - y
now we use this in the second equation :
0.35(45 - y) + 0.52y = 0.47((45 - y) + y)
15.75 - 0.35y + 0.52y = 0.47(45 - y + y)
15.75 + 0.17y = 0.47×45 = 21.15
0.17y = 5.4
y = 5.4/0.17 = 31.76470588... pound
x = 45 - y = 13.23529412... pound
he needs to use
31.76470588... pounds of the 52% alloy
13.23529412... pounds of the 35% alloy.
Find the slope of the following line.
4x - y = 0
Answers
Answer:
4
Step-by-step explanation:
slope intercept form is y=Mx+b
4x-y=0
+y. +y
4x=y
y=4x
So slope is 4
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008
Clear all
Find the quotient.
12a² - 3
ба - 3
Enter the correct answer.
ADO
?
DONE
Answers
Answer:
6a - 3
Step-by-step explanation:
Dividend: A number/expression that is divided by the divisor.
Divisor: The number/expression that divides the dividend.
Quotient: The result obtained by the division.
Remainder: The number/expression left behind.
Long division method
Divide the first term of the dividend by the first term of the divisor, and put that in the answer.Multiply the divisor by that answer, put that below the dividend.Subtract to create a new dividend.Repeat.The solution is the quotient plus the remainder divided by the divisor.
Given dividend:
12a² - 3Given divisor:
6a - 3[tex]\large \begin{array}{r}2a+1\phantom{)}\\6a-3{\overline{\smash{\big)}\,12a^2\phantom{))..)))}-3\phantom{)}}}\\{-~\phantom{(}\underline{(12a^2-6a)\phantom{)))))}}\\6a-3\phantom{)}\\-~\phantom{()}\underline{(6a-3)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]
Therefore, the quotient is 6a - 3.
Select the correct answer. What does it mean when the correlation coefficient has a positive value? A. When x increases, y decreases, and when x decreases, y increases. B. When x increases, y increases, and when x decreases, y decreases. C. When x increases, y decreases, and when x is constant, y equals zero. D. When x increases, y increases, and when x is constant, y decreases.
Answers
when the correlation coefficient has a positive value , it means that when x increases , y increases and when x decreases , y decreases , the correct option is (b) .
in the question ,
it is given that
the value of correlation coefficient has a positive value .
it means that the variables have a direct relation with each other,
which means when one variable increases , the other variable also increases and when one variable decreases , the other variable also decreases ,
Therefore , the positive value of correlation coefficient means that When x increases, y increases, and when x decreases, y decreases.
The given question is incomplete , the complete question is
Select the correct answer. What does it mean when the correlation coefficient has a positive value?
(a) When x increases, y decreases, and when x decreases, y increases.
(b) When x increases, y increases, and when x decreases, y decreases.
(c) When x increases, y decreases, and when x is constant, y equals zero.
(d) When x increases, y increases, and when x is constant, y decreases.
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i need help in this question plsss
Answers
Answer:
a) (-9)/10
Step-by-step explanation:
Given number,
→ -(9/10)
Now the equivalent number is,
→ -(9/10)
→ -9/10
→ (-9)/10
Hence, the answer is (-9)/10.
need help ASAP please
Answers
B.) It is a flat and closed shape. A rectangle is a quadrilateral.
The opposite sides are parallel and equal to each other.
Answer:
Step-by-step explanation:
know it isnt the best but here gives
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answers
2. Vertical
3. Alternating exterior
4. Corresponding
5. Supplementary
5/9 of the animals in the pet show are dogs 3/5 of the dogs are poodles what fraction of the animals in the pet show are poodles
Answers
Answer:
1/3
Step-by-step explanation:
You want to know the fraction that are poodles when 5/9 of animals are dogs, and 3/5 of dogs are poodles.
SubstitutionWe can write the equations ...
dogs = (5/9)·(animals)
poodles = (3/5)·(dogs)
Using the first equation to substitute into the second, we get ...
poodles = (3/5)·(5/9)·(animals) = 3/9·animals = 1/3·animals
FractionThen the fraction that are animals is found by dividing by "animals":
poodles/animals = 1/3
1/3 of the animals in the pet show are poodles.
find the slope. help please
Answers
Answer:
-2
Step-by-step explanation:
Look at the bottom right point. To get to the point above it only moving vertical and horizontally, you would move 2 units up (or vertically) and one unit left (or horizontally).
The slope is negative. Imagine a person starting on the very left side of the line and he starts walking. As he walks on the line, he is going down hill. That tells us that the slope is negative.
Give m || n, find the value of x.
Answers
The value of x, given the angles m and n can be found to be 30.
How to find the angles?Given the fact that m || n, it means that when m and n are added, they equate to 180 degrees.
The reason for this is that m and n are supplementary angles and such angles will always add up to 180 degrees.
This means the value of x can be found as:
180 = m + n
180 = (6x - 5 ) + ( x - 25 )
180 = 6x + x - 5 - 25
180 = 7x - 30
180 + 30 = 7x
x = 210 /7
x = 30
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Working simultaneously, six fudge machines complete a big order in 36 hours. All the machines at the fudge factory work at the same pace. How many hours would it take to complete the order with twice the number of working machines?
Answers
Answer: 18 hours
Step-by-step explanation: There are 6 working machines at first, and it takes 36 hours to complete this.
If there are double the machines, it takes half the time to complete the order, because double the amount of fudgemaking is being done per hour.
36 divided by 2 = 18 hours with twice the machines.
Part A: A bakery sells specialty pumpkin pies during the month of October. One pumpkin pie contains 187.64 grams of sugar. The bakery wants each slice of pie to contain less than 22 grams of sugar. What is the minimum number of slices the bakery will have to cut the pie into in order for each slice to contain less than 22 grams of sugar ? Show your work. Part B: If the bakery cuts the pie into that minimum number of slices, how much sugar, in grams, will each slice of pumpkin pie contain? Round your answer to the nearest hundredth.
Answers
Answer:
9 slices20.85 gStep-by-step explanation:
You want the minimum number of pie slices and the amount of sugar in each such that the sugar in each slice is less than 22 grams when the whole pie has 187.64 grams of sugar.
A: SlicesThe sugar in each of n slices is 1/n times the sugar in the whole pie. You want ...
(187.64 g)/n < 22 g
Multiply by n/(22 g) to get
n > 187.64/22
n > 8.53
The smallest whole number that satisfies this inequality is n = 9.
The minimum number of pie slices is 9.
B: SugarWhen the sugar in the pie is divided into 9 equal parts, each part is ...
(187.64 g)/(9 slices) = 20.85 g/slice
Each slice of pumpkin pie will contain about 20.85 grams of sugar.
Answer:
Step-by-step explanation:
the answer is 9
Are the linear expressions equivalent?
Drag the choices to the boxes to correctly complete the table.
3x-2(2,3x+2.5)=-1.6x-5
5-3(-1.6x-2.1)=4.8x-1.3
Answers
Comparing the linear expressions it shows that
3x - 2(2,3x + 2.5) = -1.6x - 5 - equivalent
5 - 3(-1.6x - 2.1) = 4.8x - 1.3 - not equivalent
How to check if the expressions are equivalentInformation given in the question include
3x - 2(2,3x + 2.5) = -1.6x - 5
5 - 3(-1.6x - 2.1) = 4.8x - 1.3
The equations are equivalent if the values on the left hand side of the equation is equal to the values on the right hand side of the equation
3x - 2(2,3x + 2.5) = -1.6x - 5
expending gives
3x - 4.6x - 5 = -1.6x - 5
-1.6x - 5 = -1.6x - 5
The expression above is equivalent
5 - 3(-1.6x - 2.1) = 4.8x - 1.3
expending gives
5 + 4.8x + 6.3 = 4.8x - 1.3
4.8x + 11.3 = 4.8x - 1.3
The expression above is not equivalent
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27
Question
A hula hoop has a diameter of 44 inches. What is the circumference of the hula hoop? Use 3.14 for pi
Answers
Answer:
138.16 inches
Step-by-step explanation:
C=Circumference. r=radius. d=diameter
C=2πr
C=2π(d/2) ==> a radius is half of a diameter
C=2(d/2)π
C=dπ ==> simplify
C=44π
C=44*3.14
C=138.16 inches
!!PLEASE HURRY!!
Find the missing length indicated.
Answers
Answer:
Step-by-step explanation:
17
Explanation step - by -step
15/12 = x/28
Rewrite equation
x/28 = 15/12
Multiply both sides of equation 28
28(x/28) = 28(15/12)
Cancel common factor
x = 28(15/12)
x = 28 ( 5/4)
x = 7•5
x = 35
Pete's Convenience Store has a beginning inventory of 12 cans of soup at a cost of $.85 each. During the year, the store purchased 4 at $.95, 6 at $1.05, 7 at $1.35, and 8 at $1.50. By the end of the year, 18 cans were sold. Calculate (A) the number of cans of soup ending inventory and (B) the cost of ending inventory under LIFO, FIFO, and weighted average. (Round your final answers to the nearest cent.)
Answers
A) The number of unsold cans of soup (ending inventory) is 19.
B) The various costs of the ending inventory under LIFO, FIFO, and the weighted average are as follows:
Ending Inventory
LIFO $17.15
FIFO $25.65
Weighted average $21.47
How are the inventory methods different?FIFO assumes that the physical flow of goods sold should follow the chronological sequence of purchases or production.
LIFO assumes that the first goods acquired are the last to be sold.
The Weighted Average uses an average to determine the cost of ending inventory and the cost of goods sold.
Description Units Unit Cost Total
Beginning inventory 12 $0.85 $10.20
Purchases 4 $0.95 $3.80
Purchases 6 $1.05 $6.30
Purchases 7 $1.35 $9.45
Purchases 8 $1.50 $12.00
Total 37 $41.75
Sales 18
Ending inventory 19 (37 - 18)
Average cost = $1.13 ($41.75/37)
LIFO:
Ending inventory = $17.15 ($10.20 + $3.80 + 3 x $1.05)
Cost of goods sold = $24.60 ($41.75 - $17.15)
FIFO:
Ending inventory = $25.65 (4 x $1.05 + $9.45 + $12.00)
Cost of goods sold = $16.10 ($41.75 - $25.65)
Weighted Average:
Ending inventory = $21.47 (19 x $1.13)
Cost of goods sold = $20.34 (18 x $1.13)
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The height of a building is proportional to the number of floors. The figure shows the height of a building with 8 floors. Complete parts a and b.
Answers
a. The ratio of the height of the building to the number of floor is 14:1
b. the unit rate is 14ft per floor and this means that each floor is 14ft high.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.
if h is the height of the building and n is the number of floor.
Therefore h:n= h/n
h:n = 112/8
divide through by 8
h:n= 14/1=14:1
the unit rate is therefore 14feet per floor and this means that one floor has a height of 14 feet.
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please help if u can
Game Station 2: Amazing Race- Each team has to match 9 of the 20 banners with the word “Hello” in different languages with the 9 countries that speak that language
9/20
A. Determine the number of ways of selecting and matching nine banners with a country.
B. Determine the number of ways of selecting nine banners without having to match them with a
Answers
the number of ways of selecting and matching nine banners with a country is 36.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
Given, 9 of the 20 banners with the word “Hello” in different languages with the 9 countries
Toatl ways for arranging the 9 banners will be 9C2
And as the matching nine banner with the country is 9/20
So the number of ways of selecting is 9c2 = 36.
Hence the number of ways to select and matching the banner is 36.
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