[tex]2x^2=-8\\x^2=-4[/tex]
No real solutions.
Complex solutions:
[tex]x=\sqrt{-4} \vee x=-\sqrt{-4}\\x=2i \vee x=-2i[/tex]
landon invested 110 in an account with an interest rate of 4.1 how much would be there after 5 years
As it only told interest i asume its simple interest for compound interest the answer would be different
The values in the table represent a linear relationship between x and y.
x -8.5 -6.5 -2.5 -1
y -92 -72 -32 -17
What is the rate of change of y with respect to x?
The rate of change of y with respect to x for the given linear relationship is 10.
To determine the rate of change of y with respect to x, we can calculate the slope of the linear relationship between x and y using the formula:
slope = (change in y) / (change in x)
Given the values in the table:
x: -8.5, -6.5, -2.5, -1
y: -92, -72, -32, -17
We can calculate the change in y and change in x between any two points.
For example, between the first two points (-8.5, -92) and (-6.5, -72), the change in y is:
change in y = -72 - (-92) = -72 + 92 = 20
And the change in x is
change in x = -6.5 - (-8.5) = -6.5 + 8.5 = 2
Using the formula for slope:
slope = (change in y) / (change in x) = 20 / 2 = 10.
Therefore, the rate of change of y with respect to x is 10.
This means that for every unit increase in x, y increases by 10 units.
We can perform the same calculations for the other points in the table and observe that the rate of change of y with respect to x remains constant at 10.
Hence, the rate of change of y with respect to x for the given linear relationship is 10.
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Thianga buys a car for $75 000. The value of the car depreciates at 15% per year. After 1 year the car is worth 85% of its original value.
How many years will the car be worth less than $15000? without using log
Answer: 6 years
Step-by-step explanation:
75,000*15% = 11,250
11,250*6 = 67,500
75,000-67,500 = 7500
7500 is worth less than 15,000
5 years would have been 18,750; more than 15,000
Find the missing side
By using trigonometry, the missing sides are
Example 1: x = 16.7
Example 2: x = 3.2
Example 3: x = 23.5
Example 4: x = 9.3
Trigonometry: Determining the values of the missing sidesFrom the question we are to determine the value of the missing sides in the given triangles
We can determine the value of the missing sides by using SOH CAH TOA
Example 1
Angle = 42°
Opposite side = x
Hypotenuse = 25
Thus,
sin (42°) = x / 25
x = 25 × sin (42°)
x = 16.7
Example 2
Angle = 75°
Opposite side = 12
Adjacent side = x
Thus,
tan (75°) = 12 / x
x = 12 / tan (75°)
x = 3.2
Example 3
Angle = 36°
Hypotenuse side = x
Adjacent side = 19
Thus,
cos (36°) = 19 / x
x = 19 / cos (36°)
x = 23.5
Example 4
Angle = 53°
Opposite side = x
Adjacent side = 7
Thus,
tan (53°) = x / 7
x = 7 × tan (53°)
x = 9.3
Hence,
The missing sides are 16.7, 3.2, 23.5 and 9.3
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Which function equation is represented by the graph?
f(x)=40(2.5)x
f(x)=40(1.5)x
f(x)=40(3.25)x
f(x)=40(2.25)x
Answer:
f(x)=40(2.25)^x
Step-by-step explanation:
You want the equation of the exponential function that goes through points (0, 40) and (1, 90).
Exponential functionThe exponential function can be written ...
f(x) = a·b^x
ParametersWhen x = 0, this is ...
f(0) = a·b^0 = a·1 = a
Using the given point, we have a = 40.
When x = 1, this is ...
f(1) = 40·b^1 = 40b
Using the given point, we have ...
90 = 40b
b = 90/40 = 2.25
The function equation is ...
f(x) = 40(2.25^x)
<95141404393>
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
subsidiaries hi sus
Step-by-step explanation:
scientific 2 is the answer
A scientist has two solutions what she has labeled solution a and solution b each contains salt she knows that solution a is 60% salt and solution b is 85% salt she wants to obtain 70 ounces of a mixture that is 80% salt how many ounces of each solution should she use
Solving a system of equations we can see that:
She needs to use 56 oz of the 85% solution.She needs to use 14 oz of the 60% solution.How many ounces of each solution should she use?We can use the variables:
x = mass of the 60% solution.
y = mass of the 85% solution.
We can write a system of equations.
x + y = 70
x*0.6 + y*0.85 = 70*0.8
We can isolate x on the first equation to get:
x = 70 - y
Replace that in the other one:
(70 - y)*0.6 + y*0.85 = 70*0.8
Now we can solve this for y.
y*0.25 = 70*0.8 - 70*0.6
y = 14/0.25 = 56
Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.
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Which sign makes the statement true?
67.18% ?
7
22
64
V
||
(Please NEED THIS AASP!)
The required sign that makes the statement true is "||".
The given options are 7, 22, 64, and V.
To express a percentage in mathematical notation, we divide the number by 100. In this case, 67.18% can be written as 0.6718.
Using the "||" symbol, we can write the equation as: 0.6718 || 7 = 22.
This equation represents the statement "0.6718 is to 7 as 22 is to 100." The vertical bar "||" signifies the ratio or proportion between the numbers. The double vertical bars "||" typically represent the symbol for "is equivalent to" or "is parallel to" in various contexts.
Therefore, the sign "||" makes the statement true.
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An increase from $27 to $35.10 what percent of increase?
Answer:
30% increase
Step-by-step explanation:
percentage increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase = $35.10 - $27 = $8.10 , then
percentage increase = [tex]\frac{8.10}{27}[/tex] × 100% = 0.3 × 100% = 30%
Answer:
Step-by-step explanation:
step 1: 35.10-27 =8.1
step 2: 8.1/27 x 100 = 30%
so therefore = 30% increase
need help can someone help me
Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;
Statement Reason
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
∠BCA ≅ ∠DCA Congruent angles of a triangle (SAS).
AC ≅ AC Reflexive property
ΔABC ≅ ΔADC AAS postulate
What is an angle bisector?In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
By applying the angle bisector theorem to the given triangle, the variable y can be calculated by using the following mathematical equation (formula):
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can logically deduce that ∠BCA is congruent to ∠DCA
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Help please will Mark brainliest
Answer: B =[tex]x^{\frac{4}{5} }[/tex]
Step-by-step explanation:
Rules needed:
When you have a root, you can write it in exponented form. It becomes a fraction.
EX.
[tex]\sqrt[5]{x} =x^{\frac{1}{5} }[/tex]
When you have a number that is multiplied to another number both have exponents and same bases, you can combine the two by adding the exponents
EX.
[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } = x^{\frac{2}{5} }[/tex]
Your problem:
[tex]\sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}[/tex] >convert to exponent form
=[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} }[/tex] >add all exponents [tex](\frac{1}{5} +\frac{1}{5} +\frac{1}{5}+\frac{1}{5})[/tex]
=[tex]x^{\frac{4}{5} }[/tex]
B
Is the relation a function?
Yes or No
!PLEASE HELP!
Answer:
Is the relation a function?
no
Step-by-step explanation:
please make brainlist
In a club there are 8 women and 5 men. A committee of 4 women and 3 men is to be chosen. How many different ways are there to select the committee?
The number of ways of selecting a committee of 4 women and 3 men from 8 women and 5 men is 700 ways
How do i determine the number of ways of selecting the committee?First, we shall obtain the number of ways to choosing a committee of 4 women from 8 women. This is given below:
Number of items (n) = 8Number of items selected (r) = 4Selecting 4 women from 8 women [C(8, 4)] = ?C(n, r) = n! / [r!(n - r)!]
C(8, 4) = 8! / [4!(8 - 4)!]
C(8, 4) = 70 ways
Next, we shall obtain the number of ways to choosing a committee of 3 men from 5 men. This is given below:
Number of items (n) = 5Number of items selected (r) = 3Selecting 3 men from 5 men [C(5, 3)] = ?C(n, r) = n! / [r!(n - r)!]
C(5, 3) = 5! / [3!(5 - 3)!]
C(5, 3) = 10 ways
Finally, we shall determine the Total ways of selecting the committee. Details below:
Selecting 4 women from 8 women [C(8, 4)] = 70 waysSelecting 3 men from 5 men [C(5, 3)] = 10 waysTotal ways of selecting =?Total ways of selecting = [C(8, 4)] × C(5, 3)]
Total ways of selecting = 70 × 10
Total ways of selecting = 700 ways
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need some help can anyone help me
The measure of side TR is given as follows:
TR = 6.7.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.As the triangles in this problem are similar, the proportional relationship for the side lengths is given as follows:
TR/35 = 5/26.
Hence the length of side TR is given as follows:
TR = 35 x 5/26
TR = 6.7.
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Given P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41. Find P(G|N).
The probability P(G|N) value is 0.585 when P(G∩N)=0.24, P(G)=0.37, and P(N)=0.41.
To find P(G|N), which represents the probability of event G given event N, we can use the formula:
P(G|N) = P(G∩N) / P(N)
Given that P(G∩N) = 0.24 and P(N) = 0.41
we can substitute these values into the formula:
P(G|N) = 0.24 / 0.41
Calculating the division:
P(G|N) = 0.585
Therefore, the value of P(G|N) is 0.585.
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the sum of 9 and x is at least -23. Translate the sentence into an inequality
Answer:
9 + x ≥ -23
Step-by-step explanation:
'At least' here means the lowest possibility of the sum 9 + x can equal -23, which means 9 + x can also be greater than -23. So the sum is either equal to -23 or greater than -23.
Find the curvature of the curve
Note that the curvature of the curve defined by the function y = 3x² - 2x +4 at point x = 2 is approximately 0.0002.
How did we arrive at this ?To find the curvature of the curve defined by the function, we need to first find the second derivative of the function.
y = 3x² - 2x + 4
Taking the first derivative of y with respect to x
y' = 6x - 2
Taking the second derivative of y with respect to x:
y'' = 6
So the second derivative of y is a constant 6.
To find the curvature of the curve at point x = 2, we need to evaluate the following formula:
k = |y''| / [1 + (y')²][tex]^{(3/2)}[/tex]
Substituting x = 2 and y'' = 6, we get:
k = |6| / [1 + (6x2 - 2)²][tex]^{(3/2)}[/tex]
= 6 / [1 + (22)²][tex]^{(3/2)}[/tex]
= 6 / [1 + 484][tex]^{(3/2)}[/tex]
= 6 / 485[tex]^{(3/2)}[/tex]
k ≈ 0.0002
Hence, the curvature of the curve defined by the function y = 3x² - 2x + 4 at point x = 2 is approximately 0.0002.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Find the curvature of the curve defined by the function
y=3x^2 -2x + 4
at point x =2
Question A survey asked 10 boys and 10 girls how many text messages they sent the previous day. The number of texts are given in the line plots. Select from the drop-down menus to complete each statement. The data set with the greater range is Choose... . The median Choose... .
The data set with the greater range is greater for girls. The median is greater for girls.
The range of a dataset is the difference between the maximum and minimum values in the set.
The median is the middle value in a sorted dataset, or the average of the two middle values if the set has an even number of elements.
To determine which dataset has a greater range, you need to compare the difference between the highest and lowest values of the two datasets.
To determine which dataset has a larger median, you need to sort the datasets and find the middle value(s).
The range for boys is 60 as for girls the range is 80. The median for boys is 90 and for girl 110.
Hence, the data set with the greater range is greater for girls. The median is greater for girls.
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Calculate the average Budget across the four quarters.
Next year, it is estimated that there will be an average
budget of £6,032 per quarter. How much more is this, as a
percentage?
6,500
5,500
4,500
3,500
2,500
1.500
Budget and Project Costs
(£GBP)
5,623
1,670
Quarter 1
5,892
1,903
Quarter 2
Costs
6,382
2,104
Quarter 3
Budget
Q Search
5,325
1,790
Quarter 4
a
Please select the correct answer from the options
shown.
a. 2.9%
b. 3.1%
c. 3.7%
d. 3.9%
Answer:
d
Step-by-step explanation:
To calculate the average budget across the four quarters, we need to add the budget for each quarter and divide by 4:
Average budget = (5623 + 5892 + 6382 + 5325) / 4 = 5805.5
Next year's estimated budget is £6,032 per quarter.
To calculate the percentage difference, we can use the following formula:
Percentage difference = (new value - old value) / old value x 100%
Percentage difference = (6032 - 5805.5) / 5805.5 x 100% = 3.9%
Therefore, the answer is (d) 3.9%.
According to United States Census Bureau, in 2013 the four states shown in the table had the highest population density of all states, measured in population per square mile
(mi^2). Which state had the greatest population density in 2013?
New Jersey has the greatest population density in 2013
Since we know that,
Population density is defined as the number of people per square at any given point in time.
Total people / total area = population density
In emerging countries, population density is higher than in developed countries.
Now for the state : Connecticut
Population = 3596080
Area = 4842
Therefore,
Density = 3596080/4842
= 742.68
Now for the state : Massachusetts
Population = 6692824
Area = 7800
Therefore,
Density = 6692824/7800
= 858.05
Now for the state : New Jersey
Population = 8899339
Area = 7354
Therefore,
Density = 8899339/7354
= 1210.13
Now for the state : New Jersey
Population = 1051511
Area = 1034
Therefore,
Density = 8899339/7354
= 1016.93
Hence population Density of New Jersey is greatest.
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Please I need this answer
Answer:
FE = 12
DE = 20
Step-by-step explanation:
Part A
We can solve for FE by equating the ratios of the triangles' sides. Remember we can only do this because the triangles are similar, so the scale factor between the side lengths is the same.
[tex]HE : GH = FE : DF[/tex]
↓ plugging in the given values
[tex]9 : 12 = FE : 16[/tex]
↓ representing as fractions
[tex]\dfrac{9}{12} = \dfrac{FE}{16}[/tex]
↓ multiplying both sides by 16
[tex]\boxed{FE = 12}[/tex]
Part B
We can solve for DE using the same technique.
[tex]GE : GH = DE : DF[/tex]
↓ plugging in the given values
[tex]15 : 12 = DE : 16[/tex]
↓ representing as fractions
[tex]\dfrac{15}{12}= \dfrac{DE}{16}[/tex]
↓ multiplying both sides by 16
[tex]\boxed{DE = 20}[/tex]
Acme toy company prints baseball cards. The company claims that 30% of the cards are
rookies, 60% veterans but not All-Stars, and 10% are veteran All-Stars. Suppose a random
sample of 100 cards has 50 rookies, 45 veteran, and 5 All starts. Is this consistent with
Acme’s claim? Use a 0.05 level of significance to perform a complete hypothesis test. Show
all work.
1. Calculate the Expected values for opening a sample of 100 cards:
2. State the null and alternative hypotheses.
3. Calculate the degrees of freedom.
4. Complete your hypothesis test using the procedures covered in the lecture for
Chapter 11. What are the results?
5. State your conclusions
6. Supposed you got a larger sample, and performed another hypothesis test. What
would you expect to happen, based on your findings?
7. Now, we will think like a sociologist. We are interested in determining whether
there is a relationship (i.e. independent or dependent variables) between gender
and getting in trouble at school. Below is the table documenting the frequency
counts of boys and girls and their respective behavior issues (or lack thereof):
Got in
Trouble
Did Not
Get in
Trouble
Total
Boys 46 71 117
Girls 37 83 120
Total 83 154 237
Show your work here, and come up with a conclusion about these variables using the
methods discussed
Answer:
1 calculate the Expected values for opening a sample of 100 cards
literally struggling so hard
Answer: I think question two is Adjacent angles and complimentary angles.
Step-by-step explanation: Complementary angles are two acute angles that add to form a right angle.
Adjacent angles are two angles that share a common side.
Michelle orders 200 T-shirts to sell at the school carnival. She pays $6.50 per shirt, plus 5% of the total order for shipping. How much does she pay in all?
A $6.83
B $65.00
C $1,235.00
D $1,365.00
Michelle pays $1365 in total.
Option D is the correct answer.
We have,
To calculate the total amount Michelle pays for the T-shirts, we need to consider the cost per shirt and the shipping fee.
The cost per shirt is $6.50, and she ordered 200 shirts, so the cost of the shirts alone is:
= $6.50 x 200
= $1300
The shipping fee is 5% of the total order, which is:
= 5% x $1300
= $65
To find the total amount Michelle pays, we add the cost of the shirts and the shipping fee:
= $1300 + $65 = $1365
Therefore,
Michelle pays $1365 in total.
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Can someone please help:(
Thank you all
There were 172 children and 165 adults admitted to the amusement park.
Given that the admission fee for children is $1.50, so the total amount collected from children is 1.5c.
Similarly, the admission fee for adults is $4, so the total amount collected from adults is 4a.
We are also given that the total number of people admitted to the park is 337, so we can write the following equation based on the number of people:
c + a = 337
The total admission fees collected is $918.
1.5c + 4a = 918
Now we have a system of two equations.
From the first equation, we can express 'c' in terms of 'a':
c = 337 - a
Substituting this value of 'c' into the second equation:
1.5(337 - a) + 4a = 918
505.5 - 1.5a + 4a = 918
2.5a = 918 - 505.5
2.5a = 412.5
a = 412.5 / 2.5
a = 165
Substituting the value of 'a' back into the first equation:
c + 165 = 337
c = 337 - 165
c = 172
Therefore, there were 172 children and 165 adults admitted to the amusement park.
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
The coordinates in the solution to the systems of inequalities graphically is (-5, 1)
Solving the systems of inequalities graphicallyFrom the question, we have the following parameters that can be used in our computation:
y < 1/2x + 5
y ≤ -3x - 2
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (-5, 1)
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Answer:
(-5, -5)
Step-by-step explanation:
Given system of linear inequalities:
[tex]\begin{cases}y < \dfrac{1}{2}x+5\\\\y\leq-3x-2\end{case}[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.To graph linear inequalities, treat them as equations (swap the inequality sign for an "equals" sign). Plug in two values of x to find two points on the line to help draw the lines.
Graphing the line y < (1/2)x + 5Substitute x = 0 and x = 6 into the equation of the inequality to find two points on the line.
[tex]\begin{aligned}x=0 \implies y&=\dfrac{1}{2}(0)+5\\y&=5\end{aligned}[/tex] [tex]\begin{aligned}x=6 \implies y&=\dfrac{1}{2}(6)+5\\y&=8\end{aligned}[/tex]
Plots points (0, 5) and (6, 8).
As the inequality sign is <, draw a dashed line through the plotted points and shade below the line.
Graphing the line y ≤ -3x - 2Substitute x = 0 and x = 2 into the equation of the inequality to find two points on the line.
[tex]\begin{aligned}x=0 \implies y&=-3(0)-2\\y&=-2\end{aligned}[/tex] [tex]\begin{aligned}x=2 \implies y&=-3(2)-2\\y&=-8\end{aligned}[/tex]
Plots points (0, -2) and (2, -8).
As the inequality sign is ≤, draw a solid line through the plotted points and shade below the line.
SolutionThe solution set is the set of points contained within the overlapping shaded region and on the solid line.
Therefore, a point in the solution set is (-5, -5).
Matthew invested $8,000 in an account paying an interest rate of 3 1/8% compounded
continuously. Parker invested $8,000 in an account paying an interest rate of 2 3/4%
compounded annually. To the nearest dollar, how much money would Parker have in
his account when Matthew's money has tripled in value?
Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.
We have,
For Matthew's investment, the continuous compounding formula can be used:
[tex]A = P \times e^{rt}[/tex]
Where:
A = Final amount
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time (in years)
In this case,
Matthew's money has tripled,
So A = 3P.
For Parker's investment, the formula for compound interest compounded annually is used:
[tex]A = P \times (1 + r)^t[/tex]
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
t = Time (in years)
We need to find t when Matthew's money has tripled in value.
Let's set up the equation:
[tex]3P = P \times e^{rt}[/tex]
Dividing both sides by P, we get:
[tex]3 = e^{rt}[/tex]
Taking the natural logarithm of both sides:
ln(3) = rt
Now we can solve for t
t = ln(3) / r
For Matthew's investment,
r = 3 1/8% = 3.125% = 0.03125 (as a decimal).
For Parker's investment,
r = 2 3/4% = 2.75% = 0.0275 (as a decimal).
Now we can calculate t for Matthew's investment:
t = ln(3) / 0.03125
Using a calculator, we find t ≈ 22.313 years.
Now, we can calculate how much money Parker would have in his account at that time:
[tex]A = P \times (1 + r)^t[/tex]
[tex]A = $8,000 \times (1 + 0.0275)^{22.313}[/tex]
Using a calculator, we find A ≈ $13,774.
Therefore,
Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.
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Answer:
20,763
Step-by-step explanation:
I saw the answer after I got it wrong
Can someone please provide a step-by-step explanation for the answer? I would really appreciate it.
Let f(x)= 2(x-1) / x²-2x-3 - 1/ x-3, x ЄR, x > 3.
(a) Show that f(x) = 1/ x+1
(b) Find the inverse function of ƒ (x).
(c) Find the domain of ƒ−¹(x).
(d) Given that g(x) = 2x² – 3, where x Є R. Solve (ƒ o g)(x) = 1/8.
b) The inverse function of ƒ(x) is given by: ƒ⁻¹(x) = (1 - x) / x
c) The domain of ƒ⁻¹(x) is all real numbers except for 1.
d) The solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.
(a) To show that f(x) = 1 / (x + 1), we need to simplify the expression f(x) and demonstrate that it is equivalent to 1 / (x + 1):
f(x) = [2(x - 1) / (x² - 2x - 3)] - (1 / (x - 3))
f(x) = [2(x - 1) / (x - 3)(x + 1)] - (1 / (x - 3))
f(x) = [2(x - 1) - (x + 1)] / (x - 3)(x + 1)
f(x) = [2x - 2 - x - 1] / (x - 3)(x + 1)
f(x) = (x - 3) / (x - 3)(x + 1)
f(x) = 1 / (x + 1)
Therefore, we have shown that f(x) = 1 / (x + 1).
(b) To find the inverse function of ƒ(x), we interchange the roles of x and y and solve for y:
x = 1 / (y + 1)
xy + x = 1
xy = 1 - x
y = (1 - x) / x
Therefore, the inverse function of ƒ(x) is given by:
ƒ⁻¹(x) = (1 - x) / x
(c) The domain of ƒ⁻¹(x) can be determined by looking at the domain of the original function f(x), which is x > 3.
For ƒ(x), the range is all real numbers except for 1 (since f(x) = 1 / (x + 1)).
Therefore, the domain of ƒ⁻¹(x) is all real numbers except for 1.
(d) Given g(x) = 2x² - 3, we are asked to solve (ƒ o g)(x) = 1/8.
(ƒ o g)(x) means we need to substitute g(x) into ƒ(x):
ƒ(g(x)) = 1 / (g(x) + 1)
Substituting g(x) = 2x² - 3:
ƒ(2x² - 3) = 1 / (2x² - 3 + 1)
ƒ(2x² - 3) = 1 / (2x² - 2)
1 / (2x² - 2) = 1 / 8
8 = 2x² - 2
2x² = 10
x² = 5
x = ±√5
Therefore, the solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.
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Tamika Clark is the county superintendent. She travels to the
3 schools in her district every month. This month her travel
expenses include: 246 miles traveled at $0.55 per mile; meals,
$180.70; miscellaneous, $46.90. What is her total travel expense
this month?
Tamika Clark's total travel expense this month is $362.90.
Given that the supervisor for the county is Tamika Clark.
Every month, she makes the trip to the three schools in her district.
Her travel costs for this month include 246 miles at a cost of $0.55 per mile, $180.70 for meals, and $46.10 for other expenses.
We must determine the whole cost of her.
To calculate Tamika Clark's total travel expenses this month, we need to add up her expenses for miles traveled, meals, and miscellaneous items.
Miles traveled:
246 miles x $0.55 per mile = $135.30
Meals: $180.70
Miscellaneous: $46.90
Total travel expenses:
$135.30 (miles traveled) + $180.70 (meals) + $46.90 (miscellaneous) = $362.90
Therefore, Tamika Clark's total travel expense this month is $362.90.
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A solid figure is composed of a cube and a right triangular
prism. The figure and some of its dimensions are shown in
this diagram.
-8 cm
What is the volume of the figure?
A
6 cm
B
560 cubic centimeters
704 cubic centimeters
The volume of the figure is 704 cubic centimeters.The correct option is B. 704 cubic centimeters.
The volume of the figure, need to calculate the volumes of the cube and the right triangular prism separately, and then add them together.
Volume of the cube:
The length of each side of the cube is given as 8 cm. The formula for the volume of a cube is V_cube = [tex]side^3.[/tex] Substituting the given value, we have V_cube = [tex]8^3[/tex] = 512 cubic centimeters.
Volume of the right triangular prism:
The base of the right triangular prism is a right triangle with one side measuring 8 cm and the other side measuring 6 cm. The height of the prism is given as 8 cm.
The formula for the volume of a right triangular prism is V_prism = base area * height. The base area of a right triangle is [tex](1/2) * base * height[/tex]Substituting the given values, we have V_prism = [tex](1/2) * 8 cm * 6 cm * 8[/tex]cm = 192 cubic centimeters.
Add the volumes of the cube and the right triangular prism:
V_figure = V_cube + V_prism = 512 cubic centimeters + 192 cubic centimeters = 704 cubic centimeters.
The volume of the figure is 704 cubic centimeters.
The correct option is B. 704 cubic centimeters.
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