Answer:
x2- 2x+1 =x2-x-x+1
=x(x-1) -1(x-1)
=(x-1)(x-1)
We need to keep it this way as this is the simplest way of expressing its factors.
-1
How can the equation 3*= 4x + 1 be used to check any solutions indicated by the graphs of y= f(x) and y= g(x)?
Answer:
shook
Step-by-step explanation:
The x-coordinate of each point where the graphs of y = f(x) and y = g(x) intersect corresponds to a solution of the equation. To check the solutions, first substitute x = 0 and then substitute x = 2 into the equation and verify the statement is true when x equals each of those values.
Trapezoid area calculations
#1
1/2(Sum of parallel sides)Height=AreaArea
1/2(6+14)(5.5)1/2(20)(5.5)10(5.5)55in²#2
Apply Pythagorean theorem
B²=14²-12²=196-144=52B\approx 7Area
1/2(52+8)(12)6(60)360yd²#3
Area
1/2(Diagonals)1/2(6+6)(9+3)1/2(12)12)6(12)72ft²Answer:
Formulas Used
[tex]\textsf{Area of a Trapezoid}=\dfrac{1}{2}(a+b)h[/tex]
where:
a and b are the bases (parallel sides)h is the height (perpendicular to the parallel sides)[tex]\textsf{Pythagoras' Theorem}: \quad a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side, opposite the right angle)[tex]\textsf{Area of a Kite}=\dfrac{1}{2}pq[/tex]
where:
p and q are the diagonals-----------------------------------------------------------------------------------------
Question g (Trapezoid)
[tex]\textsf{Formula}: \quad A=\dfrac{1}{2}(a+b)h[/tex]
[tex]\textsf{Substitution}: \quad A=\dfrac{1}{2}(6+14)5.5[/tex]
[tex]\textsf{Answer}: \quad A=55\:\: \sf in^2[/tex]
Question h (Trapezoid)
[tex]\textsf{Formula}: \quad A=\dfrac{1}{2}(a+b)h[/tex]
Find the missing side length of the right triangle using Pythagoras' Theorem:
[tex]\implies a=\sqrt{14^2-12^2}=\sqrt{52}[/tex]
Therefore, top edge of trapezoid = √52 + 8
[tex]\textsf{Substitution}: \quad A=\dfrac{1}{2}(\sqrt{52}+8+8)12[/tex]
[tex]\textsf{Answer}: \quad A=96+12\sqrt{13}=139.3\:\: \sf yd^2\:(nearest\:tenth)[/tex]
Question i (Kite)
[tex]\textsf{Formula}: \quad A=\dfrac{1}{2}pq[/tex]
[tex]\textsf{Substitution}: \quad A=\dfrac{1}{2}(6+6)(3+9)[/tex]
[tex]\textsf{Answer}: \quad A=72\:\: \sf ft^2[/tex]
Solve for the surface area of the shape 6m 6m 6m 6m 4m
Answer:
28
Step-by-step explanation: add all sides together
if M is the midpoint of AB, and O is the any point, find an expression for OM in terms of OA and OB
The expression for OM in terms of OA and OB when M is the midpoint of AB, and O is any point, is OM=OA-OB.
What is midpoint?For a line segment, mid-point is the middle point of it which divides the line segment into the two equal parts.
The M is the midpoint of line segment AB. Thus, it divides the AB in two equal parts.
[tex]AB=MA+MB[/tex]
O is any point on the line segment AB. An expression for OM in terms of OA and OB has to be found out.
The length of OM is the difference of OA and OB as shown in the figure attached below.
[tex]OM=OA-OB[/tex]
Thus, the expression for OM in terms of OA and OB when M is the midpoint of AB, and O is any point, is OM=OA-OB.
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please help with this
what does the solution to a system of equations mean?
Answer:
The solution to a system of equations means the point must work. In both equations in the system, if you are asked if a point is a solution to an equation, you replace the variables with the given values and see if the two sides of the equation is equal "so is a solution"
Investment question Part 2: $3,500 is invested at 7%. How much money
will be in the account after 17 years?
Answer:
$7665
Explanation:
simple interest: principal * rate (%) * time (years)
Given:
principal: $3,500
rate: 7%
time: 17 years
Solve for interest received:
3,500 * 7% * 17
$4165
Total money in account:
$4165 + $3,500
$7665
Find the inverse function answer to the question in the image attached.
The inverse function is:
[tex]g(x) = 27*x^3 - 4[/tex]
And g(2) = 212.
How to get the inverse function?
We need to find g(x) such that:
g(h(x)) = x.
We know that:
[tex]h(x) = \frac{\sqrt[3]{x + 4} }{3}[/tex]
Then our function must be a cubic, multiplied by 3^3 = 27, and then subtracts 4, it is:
[tex]g(x) = 27*x^3 - 4[/tex]
As you can see, if you evaluate in h(x), the outcome is x.
Now we can evaluate this in x = 2, we get:
[tex]g(2) = 27*2^3 - 4 = 212[/tex]
The correct option is C.
If you want to learn more about inverses.
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PLEASE HELP!!!!! WILL MARK BRAINLIEST!!!
Answer:
either 1/3 chance or 1/6 chance
Step-by-step explanation:
not exactly sure...
7,614 is closer to ___ than it is to ____
Answer:
closer to 8000 than it is to 7000
Answer:
Hope this helps :)
7,614 is closer to 8,000 than it is to 7,000
This is because if the number has the hundreds place with 500 or more than it would be round up. If it's less than 500 than round down.
Also 7,614 rounded to the nearest thousand is 8,000 because the 6 in the hundreds place is more than 5 so we round up in the thousands place. The final answer would be 8,000.
there are 672 eggs in 6 identical boxes. How many eggs are in each box.
Answer:
112
Step-by-step explanation:
672/6 = 112
Answer:
112
Step-by-step explanation:
672 divided by 6 is 112. There are 112 eggs in each box.
I NEED THIS ASAP ( Look at the picture).
Answer:
r ≈ 4
Step-by-step explanation:
circle = 360 degrees
360 / 90 = 4
let's call the area of triangle XYZ + the shaded area portion A
because ∠XYZ = 90°, and 360 / 90 = 4, A = 1/4th of the area
total area of circle = πr²
XY = YZ = radius
thus, as ∠XYZ = 90° and two sides are the same, this forms a 45-45-90 triangle, with base YZ and height XY (base/height are interchangeable here)
thus, area of triangle XYZ = r*r/2 = r²/2
area A = r²/2 + 4.64
4 * A = total area of circle
4(r²/2+4.64) = πr²
2r²+18.56 = πr²
subtract 2r² from both sides to put all the variables on one side
(π-2)r² = 18.56
divide both sides by (π-2) to isolate r²
18.56/(π-2) = r² ≈ 16.258
r ≈ 4.032 ≈ 4
A survey asks teachers and students whether they would like the new school mascot to be a Viking or a Patriot. This table shows the results. Vikings Patriots Total Students 80 20 100 23 Teachers 5 20 25 Total 85 40 125 A person is randomly selected from those surveyed. Are being a student and preferring "Viking" independent events? Why or why not? = A. No, they are not independent because P(student) = 0.80 and P(student|Viking) =0.94. B. Yes, they are independent because P(student) = 0.80 and P(student|Viking) = 0.94 C. No, they are not independent because P(student) = 0.80 and A(student|Viking) = 0.68. KOTID D. Yes, they are independent because P(student) = 0.80 and P(student|Viking) = 0.68.
Using conditional probability, it is found that the correct option regarding whether the events are independent is given by:
A. No, they are not independent because P(student) = 0.80 and P(student|Viking) =0.94.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.An event B is classified as independent if:
P(B|A) = P(B).
In this problem, 100 out of the 125 people sampled are students, hence the probability is given by:
P(student) = 100/125 = 0.8.
Out of the people that prefer to be a Viking, 80 out of 85 people are students, hence:
P(student|Viking) = 80/85= 0.94.
The probabilities are different, hence the events are not independent, and option A is correct.
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This season, the probability that the Yankees will win a game is 0.57 and the probability that the Yankees will score 5 or more runs in a game is 0.46. The probability that the Yankees lose and score fewer than 5 runs is 0.33. What is the probability that the Yankees would score 5 or more runs when they lose the game? Round your answer to the nearest thousandth.
The probability that the Yankees would score fewer than 5 runs when they lose the game is 0.44.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability that the Yankees will win a game P(win) = 0.57
The probability that the Yankees will score 5 or more runs in a game is:
P(s>5) = 0.46
The probability that the Yankees lose and score fewer than 5 runs is:
P(s<5) = 0.33
To find the probability that the Yankees would score fewer than 5 runs when they win the game:
This is the case of probabilities of one event and another event together we will multiply the respective probabilities of the event:
= 0.57 + 0.33 - 0.46
= 0.44
Thus, the probability that the Yankees would score fewer than 5 runs when they lose the game is 0.44.
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Help me with this problem
Answer:
Looking at the given points we know that it is going to be a triangle because it only have 3 points. Therefore the figure is a triangle and the area formula would be [tex]A=\frac{1}{2}*b*h[/tex].
You can look at the attached graph and what we see is that our height of the triangle is from [tex]y=-3[/tex] to [tex]y=4[/tex] which means that our height is 7 units high. We can also see that our base starts at [tex]x=-4[/tex] and ends at [tex]x=4[/tex] making us have a base of 8 units.
We then plug in the values and solve
[tex]A = \frac{1}{2}*7\ units * 8\ units[/tex]
[tex]A = \frac{1}{2}*56\ units^2[/tex]
[tex]A = 28\ units^2[/tex]
Therefore, the area of our triangle is [tex]28\ units^2[/tex]
Hope this helps! Let me know if you have any questions
What is the measure of YVZ in degrees
Answer:
the answer is 56
Step-by-step explanation:
2x+3x+5=90
5x=90-5
5x=85
x=85/5
x=17
YVZ= 3(17)+5
YVZ=51+5
YVZ=56
Can someone help me please?
I’ll give you brainliest ^^
The sample space that represents all possible buses and boats combinations is given by:
{(D,1), (D,2), (D,3), (E,1), (E,2), (E,3), (F,1), (F,2), (F,3)}.
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
In this problem, for each the bus and the boat, there are 3 outcomes, hence the cardinality of the sample space is given by:
3 x 3 = 9.
Considering that one letter from D, E and F, and one number for 1, 2 and 3 are chosen, the sample space is given by:
{(D,1), (D,2), (D,3), (E,1), (E,2), (E,3), (F,1), (F,2), (F,3)}.
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help me pleaseeeeeeeeee, much appreciated!!!!!!!!!!
Step-by-step explanation:
that is quite a lot of failing TVs.
if 5% are failing, this means you have a "chance" of 5/100 = 1/20 that your TV is among them.
that means the expected costs for replacement in the next 3 years are
1750 × 1/20 = 175/2 = $87.50
minus the $200 replacement plan the expected value is of course negative :
87.5 - 200 = -$112.50
and if your TV breaks after more than 3 years, the expected value is actually -1750 - 200 = -$1,950
which is the principle of replacement plans, and why I never buy one.
but sure, for the 5% with broken TVs this pays off big time (it is kind of a lottery).
Mrs hernandez is taking her children and their friends to the movies. She will pay $10 for her adult ticket and $7 for each child ticket. Mrs hernandez does not want to spend more than $40. Which inequality can be used to find c, the number of child tickets Mrs hernandez can purchase
Answer:
The inequality is
10+7x\leq 4010+7x≤40
Step-by-step explanation:
Let
x-----> the number of child tickets
we know that
10+7x\leq 4010+7x≤40 -----> inequality that represent the situation
Solve for x
7x\leq 40-107x≤40−10
7x\leq 307x≤30
x\leq 4.3x≤4.3
The maximum number of child tickets is 4
Help me solve pls don’t know the equation
The graph below represents the number of pieces of paper that are found in boxes. What is the constant of proportionality?
Answer:
12.5
Step-by-step explanation:
It is equal to the slope of the line = 50/4 = 12.5
4x - 8y = 16 solve for y
Answer:
y=1/2x-2
Step-by-step explanation:
4x - 8y = 16
-8y = 16-4x
y=-2+ 1/2x
y=1/2x-2
mark brainliest pls
If the right triangle's dimensions are enlarged by 3 units, the new area would be *blank* square units. Just write the numerical answer.
Your answer
15 points!!
Answer:
If each of the dimensions was enlarged by 3 units then the new length would be 5 and the new width would be 6. To find the area of the triangle we use the formula: A = L x W ÷ 2.
6 x 5 = 30ft2
30 ÷ 2 = 15ft2
Therefore the new area of the triangle would be 15ft2.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Can someone help me with this question please
Answer:
∠A≅∠Y AB≅YZ
∠B≅∠Z AC≅YX
∠C≅∠X BC≅ZX
ΔABC≅ΔYZX
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
pls help me sovle i cant heck this app and answer the test so i heck brainly to give me answer im seruos pls if i fail i die i have 13mins pls hurry
Answer:
3/16
Step-by-step explanation:
you do length x width x height, and get 3/16
true or false each triangular face has the same base and height
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
1 and 1/5 is the answer to this problem
Please help me yall
A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the accompanying
table. Write the linear regression equation that represents this set of data, rounding
all coefficients to the nearest tenth. Using this equation, find the projected test grade,
to the nearest integer, for a student with a homework grade of 45.
Homework Grade (x) Test Grade (y)
78
66
89
76
54
42
86
90
74
68
73
73
86
84
63
54
64
54
Answers in bold:
Regression equation: y = 1.2x - 21.3Final Answer: 33=======================================================
Explanation:
I'm not sure how your calculator works, but I'm assuming you can copy/paste the given numbers into the calculator somehow to have it determine the regression equation.
The tool I used is GeoGebra and the regression equation it produced was
y = 1.2x - 21.3
Each decimal value is approximate and rounded to the nearest tenth.
---------------------------
Once we determine the regression line, plug the homework grade x = 45 to find the associated test grade (y). This is a predicted test grade.
y = 1.2x - 21.3
y = 1.2*45 - 21.3
y = 32.7
y = 33
If a student got a 45 on a homework, then we predict their test grade should be around 33.
Strawberries cost $2.14 per pound and Annie purchased 1.3 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?
simplify the following radical expression
Answer:
[tex]2\sqrt{6} -13\sqrt{3} +4\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{24} -5\sqrt{12} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=\sqrt{4\times 6} -5\sqrt{4\times 3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=\sqrt{4} \times \sqrt{6} -5\times\sqrt{4} \times \sqrt{3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=2\sqrt{6} -5\times2\sqrt{3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=2\sqrt{6} -10\sqrt{3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=2\sqrt{6} -13\sqrt{3} +4\sqrt{2}[/tex]
Answer:
[tex] \boxed{ \tt 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2} }[/tex]
or
[tex] \boxed{ \tt \approx - 12.1}[/tex]
Step-by-step explanation:
Simplify:
[tex] = \tt \sqrt{ {2}^{2} \times 6} −5 \sqrt{12} +4√2−3√3[/tex]
[tex] = \tt \: 2 \sqrt{6} - 5 \sqrt{12} + 4 \sqrt{2 } - 3 \sqrt{3} [/tex]
[tex] = \tt2 \sqrt{6} - \sqrt{ {2}^{2} \times 3} + 4 \sqrt{2} - 3 \sqrt{3} [/tex]
[tex] = \tt \: 2√6−5(2√3)+4√2−3√3[/tex]
[tex] \tt = 2√6−10√3+4√2−3√3[/tex]
[tex] \tt = 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2} [/tex]
[tex] \tt \approx \: - 12.1[/tex]
[tex] \rule{225pt}{2pt}[/tex]