FOR EQUATION INVERSES IT MEANS ... x and y swap positions.
[tex]x = (f(x))^{2} - 9 \\ (f(x))^{2} = x + 9 \\ \sqrt{(f(x))^{2} } = \sqrt{x + 9} \\ f(x) = \sqrt{x + 9} [/tex]
ATTACHED IS THE SOLUTION.
Solving systems of inequalities
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y < 6x + 9 eq. 1
Step 02:
systems of inequalities
y > 6x + 7 eq. 1
<9
Graph
y = 6x + 9 eq. 2
Unlimited/Infinite solutions
The answer is:
(-4 , 32)
(3 , 25)
Complete the factoring.
x^2 + 8x + 15
Answer:
(x+3) (x+5)
Step-by-step explanation:
1) When factorising a quadratic like this the first step is to put x in front of two brackets:
(x ) (x )
2) Next check if all numbers in your question is positive (+). In this case it is so we put + after both x in bracket.
(x+ ) (x+ )
3) now the last number in your question is 15 so we find all factors of 15:
1 and 15
3 and 5
4) to know which pair of factors to use we look at owr second number in the question which is 8x. The factors that add up to 8 is 3 and 5.
Voilà
1. 2 million is ______
thousands.
Answer: 2 million is 2,000 thousands.
Step-by-step explanation:
2,000,000 = 2 million
1,000 = 1 thousand
2,000 thousands = 2 million
Discussion forum---reply to this post
There is no one right answer to why statistics is misleading. There can be many factors at work that have hidden variables that affect the outcome of the data. It’s up to us to see the data and come up with factors that could be hidden but still at work that we don’t see. It’s important to study the data, to see if there are hidden variables in the data or not.
But I still think, any statistics is good to help the decision-making process. It's good to see data before making the final decision. Any sort of data, good or bad is still useful to see trends. Data should be considered when making decisions, but more analysis should be done before any final decision can be made. Data at face value can be right but we should make sure if there is any hidden information that we don’t know about.
Statistics can be misleading by faulty sampling and inaccurate graphs
What is statistics?The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
Given Data
Statistics can be misleading.
Statistics is quite powerful. So much so that some of the most significant decisions made by individuals and organizations were based on statistics. The adage that "statistics don't lie" may actually be true. However, statistics can occasionally be deceptive, and depending on how they are used, the same type of data can demonstrate the opposite tendency.
Sometimes inaccurate information is purposefully supplied in order to influence individuals and forward a goal. Similarly, it can also occur as a result of negligence or just failing to comprehend the data.
Knowing the various ways statistics can be abused will help you spot them and avoid making decisions based on skewed or inaccurate information.
1)Faulty sampling
The info can due to the sampling strategy employed to gather the data, be deceptive. For instance, the size and kind of the sample used in any statistics has a big impact. Since many surveys and polls are directed at specific groups of people who give particular answers, the sample sizes tend to be tiny and skewed.
2)Inaccurate graphs
Data manipulation can be done in a variety of ways, not just by using descriptive statistics incorrectly. You can identify them if you are aware of them.
3)Chooser Data Display
This type of data visualization might be perplexing and exaggerate differences. If you look at the data and consider how much variety there is in the numbers, you can spot false graphs in the media.
4)Absence of Baseline
Checking to see if the start-at-zero criteria has been adhered to is another approach to spot a deceptive graph. In a graph, The New York Times demonstrated that its sales are double those of The Daily Telegraph. However, if you look at the scale, you can see that the sales difference is just about 10%.
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Let f(x)=x2−12 and g(x)=13−x.
Perform the composition or operation indicated. (fg)(4)
Answer:
The answer would be 36.
Step-by-step explanation:
I linked the steps I used to get this answer in the image, I hope this helps :)
I am z years old, and my brother is 6 years younger than I am. How old will I be in 10 years? How old will my brother be in 10 years?
Answer:
In ten year you will be 10 years older than you are now and so will your brother. The 6 years difference will remain if no one dies.
Step-by-step explanation:
You are z years old
Your brother is 6 years younger than z years; z - 6 years
In 10 years time, you will be z + 10 years
Your brother will be z - 6 years + 10 years = z + 4 years
OR
In 10 years time, you will be z + 10 years
You brother is still 6 years younger than you, so is z + 10 years - 6 years = z + 4 years
Zoie is painting a picture that is 15 by 27 inches. She plans to frame it in a frame x inches wide.
1) Write a polynomial that will be the area of the framed picture.
2) What will be the area of the picture with the frame if x=3?
The polynomial area of the framed picture is (27 + 2x) * (15 + 2x) and the value is 693 square units
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the framed picture?The given parameters are
Width = 15
Length = 27
Also, we have
Length of the frame = x
This means that the area of the framed picture is
Area = (Length + 2 * Length of the frame) * (Width + 2 * Length of the frame)
Substitute the known values in the above equation
Area = (27 + 2x) * (15 + 2x)
The value of the area when x = 3In (a), we have
Area = (27 + 2x) * (15 + 2x)
When x = 3, we have
Area = (27 + 2 x 3) * (15 + 2 x 3)
Evaluate
Area = 693
Hence, the area is 693 square units
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In May, Jacalyn opens a savings account with an initial balance of $200 and deposits about the same amount each month. write a linear equation in slope intercept form
The linear equation in slope intercept form is y = 200x + 200
where y represents the amount in the savings account of Jacalyn at the end of x months beginning from May.
In the slope intercept form, slope (the numerical coefficient of variable x) is having a numerical value of 200 and vertical intercept is the constant of term of the equation i.e. 200. The positive value of slope indicates that the gradient of straight line representing this linear equation is positive. Positive value of vertical intercept indicates that the linear equation's graph plot shall not pass through the origin but will intercept the y-axis at 200.
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Stishen is running late for class one morning and randomly grabs two socks from a drawer that has 8 blue and 6 black. If you select four socks at random, what is the probability at most three are blue?
If you select four socks at random, the probability that at most three are blue is 42.9%.
What is probability?Probability is the likelihood of an expected outcome occurring when many possible events can happen.
Probability is represented in percentages, fractions, and decimals to show that it describes what is likely from many outcomes.
The total number of socks in the drawer = 14
The number of blue socks = 8
The number of black socks = 6
The probability of getting a blue sock = 8/14
The probability of getting 3 out of 4 = 3/4
The combined probability = 8/14 x 3/4
= 42.86%
= 42.9%
Thus, when you randomly select four socks, you can probably get blue socks 42.9% of the time.
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What is 4/5 Times 10/16 in simplist form
Answer: 4/5 × 10/16 = 1/2
Step-by-step explanation:
Multiply the numerators and then multiply the denominators to get: 4/5 * 10/16 = 40/80
Simplify with the GCF (40): 40/80 / 40/40 = 1/2
And that's your simplified answer :)
Graph both lines and plot the point of intersection of the system. -x+y=1 and 2x+y=10
The point of intersection of the system of equations is (3, 4) and this is plotted in the graph shown below.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In conclusion, the coordinate (3, 4) is the point of intersection of the given system of equations.
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i need help with question 15
A rational number is a number that can be written in the form:
[tex]\frac{p}{q}[/tex]Where p and q are coprimes. We are asked for finite sets, we can rule out options 3 and 4. In the set in option 2 the first element is:
[tex]\sqrt{3}[/tex]This number cannot be written a ratio. We can rule out option 2.
All the elements in the set from option 1 can be written in the form p/q.Thus, the answer is the first option.
3. Grace is thinking of a number. She states that
free times the number increased by six is
twenty-four
Which choice can be used to find
(1) 3(2-6) = 24
(3)3-6=24
(4) 3m +6 = 24
9x2=18+6=2
X
The choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.
What are expressions?A group of numbers or variables combined with the operations +, -,×, or ÷ form an expression. Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that only contain numbers and mathematical operators.So, three times the number increased by six is twenty-four:
The equation can be: 3x + 6 = 24Which is similar to the option (C) that is 3m + 6 = 24.Therefore, the choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.
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The correct question is given below:
Grace is thinking of a number. She states that three times the number increased by six is twenty-four. Which choice can be used to find
(A) 3(2-6) = 24
(B)3-6=24
(C) 3m + 6 = 24
(D) 9x2=18+6=2
Bill is 6 years older than Tom. Three years ago bulls age was four times toms age. Find the age of each boy now
Answer:
Tom is currently 5 and Bill is currently 11
Step-by-step explanation:
Let b = Bill's current age
Let t = Tom's current age
We have 2 unknowns so we need to equations to solve for this.
b = t + 6
(b-3) = 4(t-3) We have to subtract 3 from both Tom and Bill's current age
b- 3 = 4t - 12 Distribute the 4 and then substitute in t + 6 for b.
t + 6 -3 = 4t -12 Combine like terms
t + 3 = 4t -12 Subtract t from both sides of the equation
3 = 3t - 12 Add 12 to both sides of the equation
15 = 3t Divide both sides by 3
5 = t Tom is 5. Since Bill is 6 years old, her is 11.
Check:
11 = 5+ 6
Three years ago, Tom would have been 2 and Bill would have been 8. Bill is four times older than Tom. 2x4 = 8.
the point on 0 on the number line represents what?
Accordig to the given line, City P is above sea level, and City R is below sea level because they are above and below zero, respectively.
Hence, the right answer is D.The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The water pressure on the submerged object is given by d = P ÷ 64
Pressure is the force applied perpendicularly to an object's surface in relation to the area across which it is applied (symbol: p or P).
Gauge pressure, also spelled gage pressure, is the pressure in relation to the surrounding air.Various units are used to express pressure. The pound-force per square inch (psi), which is equivalent to one newton per square meter (N/m2) in the SI, is the standard unit of pressure in the imperial and U.S. customary systems. Some of these results arise from dividing a unit of force by a unit of area.a. The given formula is is P=64d
or , d = P ÷ 64
b. at a pressure of 672
d = 672 ÷ 64
or, d = 10.5 feet
Hence the pressure is 672 pounds per square foot at a depth of 10.5 feet.
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I could use some help solving these two problems if possible. Thank you.
Solution:
iven the figure below:
Where
[tex]\begin{gathered} S\Rightarrow satellite \\ B\Rightarrow Bora-Bora \\ G\Rightarrow Greenland \\ R\Rightarrow Rapa\text{ Nui} \\ H\Rightarrow St.\text{ Helen} \end{gathered}[/tex]Using the secant-secant theorem expressed as
[tex]SB\left(SB+BG\right)=SR\left(SR+RH\right)\text{ ----- equation 1}[/tex]Given that th e satellite signal reaches Bora-Bora at 38,000 km and Greenland which is an additional 20,000km, this implies that
[tex]\begin{gathered} SB=38000 \\ BG=20000 \end{gathered}[/tex]If the distance from the satellite to Rapa Nui is 45,000 km, this implies that
[tex]SR=45000[/tex]The total distance from the satelite to St. Helen is expressed as
[tex]SH=SR+RH\text{ ----- equation 2}[/tex]From equation 1,
[tex]\begin{gathered} \begin{equation*} SB\left(SB+BG\right)=SR\left(SR+RH\right)\text{ } \end{equation*} \\ substitute\text{ equation 2 into equation 1} \\ thus,\text{ we have} \\ SB\left(SB+BG\right)=SR\left(SH\right)\text{ ---- equation 3} \end{gathered}[/tex]Substituting the values, we have
[tex]\begin{gathered} 38000\left(38000+20000\right)=45000\left(SH\right) \\ \Rightarrow38000\times58000=45000\left(SH\right) \end{gathered}[/tex]divide both sides by 45000,
[tex]\begin{gathered} SH=\frac{38000\times58000}{45000} \\ \Rightarrow SH=48977.77777 \end{gathered}[/tex]Hence, the signal will travel a distance of 48977.77777 km from the satellite to St. Helen.
HELP IF U CAN ILL GIVE BRAINLIESt AND 20 POINTS SHOW UR WORKK!!!!
Answer:
9
Step-by-step explanation:
→ Multiply by every value to see
735 - ( 24.99 × 9 ) = 510.09
∴ He has to add money in the 9th month otherwise he will be charged
Answer:
9
Step-by-step explanation:
24.99 x 9 = 224.91
735 - 224.91 = 510.09
if a=4 b=6 and c=10 what is the volume of the three prisms above
Because the prisms are stacked onto one another, they have a total volume of 320 cubic units
How to determine the volume of the figure?The possible question is added at the end of the solution and as an attachment
From the attached figure, we have the following parameters
Shape 1: Cube of dimension aShape 2: A cuboid of dimension a, a and bShape 2: A cuboid of dimension a, a and cThe volume of a prism is the prodict of its dimensions
This means that
Cube = Length^2
Cuboid = Base area * Height
So, we have the following equations
Shape 1 = a^3
Shape 2 =a^2b
Shape 3 =a^2c
Substitute the known values in the above equation
So, we have
Shape 1 = a^3 = 4^3 = 64
Shape 2 =a^2b = 4^2 * 6 = 96
Shape 3 =a^2c = 4^2 * 10 = 160
Add the above values
Prism volume =64 + 96 + 160
Evaluate the sum
So, we have
Prism volume = 320
Hence, the volume of the three prisms is 320 cubic units
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a light flashes every 2 minutes, a second light flashes every 3.5 minutes and a third light flashes every 4 minutes. if all three lights flash together at 8 p.m what is the next time of the day they will all flash together?
Answer:
take the LCM of the three numbers. Since 2 is a multiple of 4, you can ignore the two and just take the LCM of 4 and 3.5. Since 3.5 is a decimal, the LCM is just 3.5*4 which is 14. That is how many minutes after 8:00 they will flash together again.
Step-by-step explanation:
a rectangular poster is 3 times as long as it is wide. it has an area of 27 square inches. what is the length and width of the poster
The dimensions of the rectangular poster are:
Width = 3 inches.
Length = 9 inches.
How to Find the Dimensions of a Rectangle?A rectangle usually has a long side called the length, and a shorter side called the width.
The area of the rectangle is calculated by multiplying the length and the width together. Therefore, formula for the area of a rectangle is:
Area = (length)(width).
The rectangular poster has the following parameters:
Let x represent the width of the rectangular poster.
Width of the rectangular poster = x
Length of the rectangular poster = 3x
Area of the rectangular poster = 27 in.².
Plug in the values
(x)(3x) = 27
3x² = 27
Divide both sides by 3
3x²/3 = 27/3 [division property of equality]
x² = 9
Take the square root of both sides
√x² = √9
x = 3
Width of the rectangular poster = x = 3 inches.
Length of the rectangular poster = 3x = 3(3) = 9 inches.
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3 Find the coordinates of the vertices of each figure after the given transformation
3) reflection across the x-axis
Enter Question Text
A U'(1,3),V'(4,3), W'(5,4),T'(1,4)
B U'(3,1),V'(3,4,), W'(4,5),T'(4,1)
D U'(-1,3),V'(-4,3), W'(-5,4),T'(-1,4)
(3)(4-3);W(Sp-4)T(4)
U
T
X
The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes
U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.
Solution:When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, y reflection )'s across the x-axis is (x, -y).the point (x , y)→ (x , -y).In the question given 4 coordinates,
U(1 , -3)
V(4 , -3)
T(1 , -4)
W(5 , -4)
the reflection across x-axis
U(1 , -3) →U' (1, 3)
V(4 , -3) → V'(4 , 3)
T(1 , -4) → T'(1 , 4)
W(5 , -4) → W'(5 , 4)
so after the reflection across the x axis the coordinates of the vertices becomes ,
U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)
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After attending a major league baseball game, the patrons often purchase souvenirs. If a family purchases
4 t-shirts, a cap and 1 stuffed animal their total is $135. A couple buys 2 t-shirts, a cap and 3 stuffed animals
for their nieces and spends $115. Another couple buys 2 t-shirts, a cap and 1 stuffed animal and their total is
$85. What is the cost of each item?
The cost of a t-shirt is $25, the cap costs $20 and the stuffed animal costs $15
Let t-shirts be represented by x, the cap is represented by y and stuffed animals are represented by z
Items purchased by family:
4 t-shirts + 1 cap + 1 stuffed animal
The total cost of the items was = $135
Equation: 4x+y+z=135--------(1)
Items purchased by couple 1:
2 t-shirts + 1 cap + 3 stuffed animals
The total cost of the items was = $115
Equation: 2x+y+3z=115------(2)
Items purchased by couple 2:
2 t-shirts + 1 cap + 1 stuffed animals = $85
Equation: 2x+y+z=85------(3)
Subtracting equation (3) from (2) we get:
2z = 30
z = 15
Substituting the value of z=15 in equations (1) and (3) we get the following equations:
4x+y+15=135
4x+y=120------(4)
And, 2x+y+15=85
2x+y=70-------(5)
Multiplying equation (5) with 2 and subtracting equation (4) we get:
4x+2y=140
4x+y=120
y = 20
So, x = 25
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how do you factor 12b-30
The factored expression of the expression given as 12b - 30 is 6(2b - 5)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to factor the expression by grouping?The expression is given as
12b - 30
Factor out the common factor from the expression
So, we have
12b - 30 = 3 * 4b - 3 * 10
Factor out 3 from the expression
So, we have
12b - 30 = 3(4b - 10)
Factor out 3 from the expression
So, we have
12b - 30 = 6(2b - 5)
The expression above cannot be further simplified
This means that the expression has been completely factored and cannot be further factored
Hence, the equivalent expression of the expression given as 12b - 30 when it is factored by grouping is 6(2b - 5)
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The answer is in red, i just need someone to show me why/how
thankssss!!
Given a series discount of 20/10/10/20 what is the net cost equivalent?
The net cost equivalent is the price the customer pays after deducting all the discounts. To find the net cost equivalent given an amount n of discounts, we use the following formula
[tex]N=(1-d_1)(1-d_2)\ldots(1-d_n)[/tex]Where d is the discount written as a decimal.
In our problem, we have a series discount of 20/10/10/20, therefore, the net cost equivalent is
[tex]\begin{gathered} N=(1-0.20)(1-0.10)(1-0.10)(1-0.20) \\ =(0.8)(0.9)(0.9)(0.8) \\ =0.5184 \end{gathered}[/tex]I have failed this question a lot and I don't know what I'm doing wrong,
Find the vertex of:
Answer:
(-2,-7)
Step-by-step explanation:
Rewrite in vertex form and use this form to find the vertex (h,k).
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-15}x^2\stackrel{\stackrel{b}{\downarrow }}{-60}x\stackrel{\stackrel{c}{\downarrow }}{-67} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -60}{2(-15)}~~~~ ,~~~~ -67-\cfrac{ (-60)^2}{4(-15)}\right) \implies \left( - \cfrac{ -60 }{ -30 }~~,~~-67 - \cfrac{ 3600 }{ -60 } \right) \\\\\\ (-2~~,~~-67+60)\implies {\Large \begin{array}{llll} (-2~~,~~-7) \end{array}}[/tex]
Addition and what are operations you can use to join what
Answer: The correct answer is:
Addition and multiplication are operations you can use to join equal groups.
Step-by-step explanation: Confirmed correct.
monroe's teacher wants each students to draw a sketch of the longest specimen which specimen is the longest
The most appropriate choice for tabular data will be given by-
Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B
What is tabular data?
Data given in the form of rows and columns is known as tabular data.
Here,
Size of specimen A = 0.008 cm
Size of specimen B = 0.011 cm
Size of specimen C = 0.0025 cm
Size of specimen D = 0.004 cm
Size of the longest specimen = 0.011 cm
Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B
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Complete Question
The table has been attached
Specimen Actual length(cm) Size seen under microscope (cm)
A 0.008
B 0.011
C 0 .0025
D 0.0040
Find the maturity value of a loan of $17104 after 4 months. The loan carries a simple interest rate of 12.5% peryear: Round to the nearest cent.O A. $17,639 50O B. $17.822.66OC. $17.816.67OD. $17.994.83
Answer: maturity value = $17816.67
Explanation:
The formula for calculating simple interest is expressed as
I = PRT
where
I is the interest
P is the principal or initial amount
R is the interest rate
T is the time in years
From the information given,
P = 17104
R = 12.5% = 12.5/100 = 0.125
We would convert 4 months to years. Recall
12 months = 1 year
4 months = 4/12 = 1/3
Thus, the interest is calculated as follows
I = 17104 x 0.125 x 1/3 = 712.67
maturity value = principal + interest
maturity value = 17104 + 712.67
maturity value = $17816.67