Answer: Relative frequency and probability are similar terms and the answer to both of them are the same. What I mean is that, even if the question asks for probability or relative frequency, the answer will remain the same. The basic difference is that relative frequency is used when probability is being estimated using the outcomes of an experiment or trial, when theoretical probability cannot be used.
We can write the probability in the help of a normal formula,
P(A) is the probability of an event “A” n(B) is the number of favorable outcomes. n(S) is the total number of events in the sample space.
One more thing you might need to know is that, in probability, and means multiplication and or means addition.
And = multiplication
Or = addtion
So from the above equation, n(S) , the total number " 10 + 7 + 3" is 20.
i) 2/20 and in simplified terms, 1/10
ii) 7/20 * 3/20 = 21/400
iii) 1/20
iv) 13/20
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
what is the factor expression of x2 + 7x + 10
Answer:
[tex](x+5)(x+2)[/tex]
Step-by-step explanation:
[tex]\textbf{Given that,}\\\\~~~~x^2 +7x +10\\\\=x^2 +5x +2x +10~~~~~~~~~~~~~~~~~~~~;\textbf{Rewrite}~ 7x ~ \textbf{as}~ 5x +2x\\\\=x(x+5) +2(x+5)\\\\=(x+5)(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Take out the common factor}~ x+5[/tex]
Using a standard deck of cards, find the probability of selecting a jack, replacing the card, and then selecting a king.
please explain
The probability of selecting a jack, replacing the card, and then selecting a king is 1/169
How to determine the probability?In a standard deck of cards, we have:
Total = 52
Jack = 4
King = 4
The probability of each is:
P(Jack) = 4/52
P(King) = 4/52
So, we have:
P = 4/52 * 4/52
Simplify
P = 1/13 * 1/13
Evaluate
P = 1/169
Hence, the probability is 1/169
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find the arc length of a sector with a radius of 4 feet and a central angle of 6°
Answer:
24 ft.
Step-by-step explanation:
Radius = 4 ft
Central angle = 6°
Arc length = radius × central angle
= 4 × 6°
= 24 ft.
Solve for x using quadratic formula :
abx^2 + (b^2 - ac)x - bc = 0
[tex]\boxed{\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}}[/tex]
Explanation:
Given expression: (ab)x^2 + (b^2 - ac)x + (-bc) = 0
Here given:
a = abb = b² - acc = -bcApply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \ ax^2 + bx + c = 0[/tex]
Insert values:
[tex]\sf x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
Apply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\\ \sf\Rrightarrow x= \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
x(3y - 2)
Multiply this problem
Answer:
3xy-2x
Step-by-step explanation:
Distribute x to both 3y and -2: 3y*x-2*x.
Order these fractions from smallest to lowest
1[tex]\frac{1}{2} \frac{7}{12} \frac{2}{17}[/tex]
Answer: [tex]\frac{1}{2} \frac{2}{17} \frac{7}{12}[/tex]
Step-by-step explanation:
!!! TIME SENSITIVE !!! Determine the period.
Answer:
A wave period is the measure of the time it takes for the wave cycle to complete.
The period of the wave is 2 seconds.
Suppose you know the slope of a linear relationship and one of the points that it’s graph passes through how can you determine if the relationship is proportional or not?
Answer:
I exactly don't have or know the answer
Deon has bought 18 pounds of dog food. He feeds his dog
Write your answer in simplest form.
2|3
pounds for each meal. For how many meals will the food last?
Answer:
6 to 9 meals
Step-by-step explanation:
9 If he feeds 2 pounds per meal. 18÷2 =9
6 if he feeds 3 pounds per meal. 18÷3=6
True or false: The factor by which a row operation changed the determinant is equal to the determinant of the elementary matrix corresponding to that row operation.
The given statement is false.
What is the effect of a row operation on a determinant?
The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.
Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.
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What is the results of
4-³ × (¼)²
Answer:
4^-3*(1/4)^2
(1/64)*(1/16)
=(1/1024)
Answer:
0.00025
Step-by-step explanation:
hope it'll help I'll ask . if you feel that it's not that correct please comment so that I can ask my sister who I'm sure she'll help although she's far good day.
HELP NOW PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASE
Answer:
-3/2
Step-by-step explanation:
First, you divide by taking the reciprocal of -2/5 which is -5/2.
Second, you get the answer which is -5/4.
Add that with -1/4 and you will get -6/4.
Simplify to get the answer which is -3/2.
Answer:
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{\dfrac{1}{2}}{-\dfrac{2}{5}}+\left(-\dfrac{1}{4}\right)[/tex]
To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:
[tex]\implies \dfrac{1}{2} \times -\dfrac{5}{2}+\left(-\dfrac{1}{4}\right)[/tex]
To multiply the fractions, multiply the numerators and multiply the denominators:
[tex]\implies \dfrac{1 \times (-5)}{2 \times 2} +\left(-\dfrac{1}{4}\right)[/tex]
[tex]\implies -\dfrac{5}{4} +\left(-\dfrac{1}{4}\right)[/tex]
Apply the rule -a + (-b) = -a - b :
[tex]\implies -\dfrac{5}{4} -\dfrac{1}{4}[/tex]
As the denominators are the same, subtract the numerators and put the answer over the same denominator:
[tex]\implies \dfrac{-5-1}{4}[/tex]
[tex]\implies -\dfrac{6}{4}[/tex]
Simplify by dividing the numerator and denominator by the highest common factor:
[tex]\implies -\dfrac{6 \div 2}{4 \div 2}[/tex]
[tex]\implies -\dfrac{3}{2}[/tex]
(-4,3)
-5-4-3
24
5
432
-14
-2
-3-
A
(0,1)
1 2
(4,-1)
Which linear function is represented by the graph?
Of(x) = -2x + 1
Of(x)=x+1
O f(x) = x+1
Of(x)=2x+1
Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.
Linear function that is represented by the graph is f(x)= -1/2 x+1.
Here, we have,
From the graph,
y - intercept of the linear function is 1 , i.e. c = 1
and there are two points on the line (-4, 3), (4, -1)
We can get the equation of line by applying slope-intercept formula,
Slope of the line,
m = y₂ -y₁ / x₂-x₁
so, we get,
m = -1 -3 / 4 + 4
= -4/8
= -1/2
Now applying slope-intercept formula,
y = mx+c
Putting the values,
=> y = -1/2 x + 1
=>f(x) = -1/2 x + 1.
Therefore, linear function that is represented by the graph is
f(x) = -1/2 x + 1.
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Emily works at a local restaurant. She made $200 in tips last night. She shared 15 percent of her tips with the crew that cleans the tables. How much did she give to the clean-up crew?
$
A percentage is a way to describe a part of a whole. The amount Emily shared is $30.
What are percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Emily works at a local restaurant. She made $200 in tips last night. She shared 15% of her tips with the crew that cleans the tables. The amount Emily shared is,
15% of $200
= 0.15 × $200
= $30
The amount Emily shared is $30.
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Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 point is deducted. Desiree did not leave any question unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
and the equation will have
.
Total number of multiple-choice questions that Desiree has to answer in Aptitude test = 50
Points given for every correct Answer = +3
Points deducted for every Incorrect Answer = -1
For every question unanswered ,
points Deducted = -0.5
Total Points Obtained by Desiree after Answering all the questions = 110
Number of Answers that Desiree answered correctly = x questions
Number of Incorrect Answers = (50 - x) questions
Then,the Equation representing above situation
→ 3 × x + ( -1 ) × ( 50 - x ) = 110
⇒3x - 50 + x = 110 ----------- equation that represents the given situation
⇒ 4x - 50 = 110
Adding 50, on both sides
→ 4x - 50 + 50 = 110 + 50
⇒ 4x = 160
Dividing both sides by, 4 we get
x = 40
Number of correct answers given by Desiree= 40 questions
Number of Incorrect Answers = 50 - 40
= 10 Questions .
Answer:
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 points is deducted. Desiree did not leave any questions unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
3(50 - x) + x = 110
and the equation will have
no solution
.
Step-by-step explanation:
Which statement about the polynomial function g(x) is true?
1If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
2If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
3If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
4If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.
When leading coefficient is 1 , the root will be an integer for g(x) = 0
Option 4 is the right answer.
What is a Polynomial Function ?Functions of independent variable in which the variable can appear more than once with different powers.
[tex]\rm g(x) = a_n x^n + a_{n-1}x^{n-1} + ................+ a_o[/tex]
Let this represents the polynomial function
where [tex]\rm a_n \; is\;the \;leading \; coefficient \; a_o \; is \;the\;last \;term[/tex]
Then the according to rational root theorem ,
The root of the function is given by
[tex]\rm \dfrac{p}{q} = \dfrac{factor \;of\; the\; last\; term}{factor \;of \;the\; leading coefficient}[/tex]
So when leading coefficient is 1 , the root will be an integer for g(x) = 0
Option 4 is the right answer.
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Find the simplified product 2 square root 5x^3(-3 square root 10x^2
The simplified product of [tex]2\sqrt{5x^{3} }[/tex] and -3[tex]\sqrt{10x^{2} }[/tex] is -30[tex]x^{5/2} \sqrt{2}[/tex].
Given Two expressions: -3[tex]\sqrt{10x^{2} }[/tex] and 2[tex]\sqrt{5x^{3} }[/tex].
We have to multiply both the expressions and it can be done as under:
-3[tex]\sqrt{10x^{2} }[/tex] *2[tex]\sqrt{5x^{3} }[/tex]
Firstly we have to multiply -3 with 2 to get
=-6[tex]\sqrt{10x^{2} }\sqrt{5x^{3} }[/tex]
Then we have to find square root of x cube and x square which is x to the power 3/2 and x to the power 1.
=[tex]-6x^{3/2} x\sqrt{10}\sqrt{5}[/tex]
Now we have to multiply both the numbers in the root to get the answer;
=-6[tex]x^{5/2} \sqrt{50}[/tex]
Square root of 50 is 5 root 2.
=-6*5[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]
=-30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]
Hence the simplified product is -30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex].
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how many sets of 5 students can be selected out of 30 students?
Answer:
142 506
Step-by-step explanation:
here the order does not matter
Then
we the number of sets is equal to the number of combinations.
Using the formula :
the number of sets is 30C5
[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]
[tex]=142506[/tex]
There are 142506 ways in which 5 students can be selected out of 30 students.
How can a certain number of individuals be selected using a combination?The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.
By using the formula:
[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]
where;
n = total number of individual in the set = 30r = number of chosing individuals to be selected = 5[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]
[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]
[tex]\mathbf{^nC_r = 142506}[/tex]
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(c) (i) A new truck costs $15 000 and loses 23% of its value each year. Calculate the value of the truck after three years. ( c ) ( i ) A new truck costs $ 15 000 and loses 23 % of its value each year . Calculate the value of the truck after three years .
Answer:
$6847.955
Explanation:
Use the compound interest formula, but the value decreases over time.
[tex]\sf A = P(1 - \dfrac{r}{100} )^t[/tex]
where 'A' is final amount, r is rate, t is time
Inserting P = $15,000, r = 23, t = 3 years
[tex]\sf A = 15000(1- \dfrac{23}{100} )^3[/tex]
[tex]\sf A = 6847.995[/tex]
Hence the value of truck after three years will be $6847.955.
The graph of a system of inequalities shown
How many square feet of outdoor carpet will we need for this hole.
Step-by-step explanation:
area of rectangle= 12×6
=72ft^2
A2=9ft^2 whereby the base of the hole is 3ft
height is 6ft
therefore the square is 18 ft
Alex, jas and stef each get a student loan to help with living expenses. they decide to allocate two fifths of their loans for food, and one-sixth for travel. what fraction of their student loan will be left to spend?
The fraction of their student loan will be left to spend is half of their loan.
A number expressed quotient, in which numerator is divided by denominator is called a fraction.
Let the loan amount be $100.
Expenses for food is given that two fifths of their loan
i.e.
= 2/5 × 100
= $40
Now,
Remaining part will be = $100- $40 = $60
So,
Expenses for travel are given that one sixth of their loan,
i.e.
= 1/6 × 60
= $10
So,
Remaining part will be = $60 - $10 = $50
Hence, the fraction of their student loan will be left to spend is half of their loan.
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Describe the solution of f(x) shown in the graph. a parabola opening up passing through 0 comma 2, 1 comma zero and 2 comma zero All real solutions All solutions that lie on f(x) All positive solutions All whole number solutions
A quadratic equation is in the form of ax²+bx+c. The correct option is C, All the positive solutions.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The graph of the question is given below. Since a quadratic equation has only two solutions, and this two solutions can be found by observing the graph. The coordinate at which the graph of the equation intersect the x-axis are the solution of the equation.
As it can be observed in this graph, that the graph intersect the x-axis at (1,0) and (2,0).Therefore, the solutions of the graph are 1 and 2.
Thus, both the solutions are positive or it can be concluded that all the solutions are positive.
Hence, the correct option is C, All the positive solutions.
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Answer:
B. All solutions that lie on f(x)
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
Can someone help me with this algebra two assignment I will give brainilest
Answer:
The answer is incorrect because the slope formula was used incorrectly in step 1 (parentheses weren't used during the substitution and/or the wrong values were substituted).
y=4x-6
Step-by-step explanation:
The equation we're looking for in slope intercept form looks like [tex]y=mx+b[/tex], where "m" is the slope, "b" is the y-coordinate of the y-intercept, and "x" and "y" are variables that have a certain mathematical relationship through this equation.
To find the equation itself, it usually is easier to find slope before finding the y-intercept.
Finding the slopeThere are many ways to represent slope (usually represented by the letter m), and while they all mean the same thing, they look different, some examples are shown below:
[tex]m=\frac{rise}{run} =\frac{\text{horizontal change}}{\text{vertical change}}=\frac{\Delta{y}}{\Delta{x}} =\frac{\text{change in }y}{\text{change in }x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
For this problem, since we are given ordered pairs, probably the most useful version will be the last one:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the values from the ordered pairs, it's important to remember that the ordered pairs are (x,y)... that the first coordinate is an x (and will go into the denominator, or bottom, of the fraction), and the second coordinate is a y (and will go into the numerator, or top of the fraction).
It actually doesn't matter which point we choose to be point 1, and which point we choose to be point 2. For the least amount of confusion, I choose the first point they gave to be point 1, and the second point they gave to be point 2.
So, [tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex]
If I could give only one piece of advice, it would be "ANY time you substitute, use parentheses." You can always simplify later, but for the initial substitution, keep them (this is why the "mistake" happened in this problem, and is the thing we need to fix).
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{(6)-(-2)}{(3)-(1)}[/tex]
Simplifying...
[tex]m=\frac{(6)+(2)}{(3)-(1)}[/tex]
[tex]m=\frac{8}{2}[/tex]
[tex]m=4[/tex]
Thus, the equation we want in slope intercept form, with the new information we know plugged in, looks like this:
[tex]y=(4)x+b\\y=4x+b[/tex]
"b" is still the y-coordinate of the y-intercept (which we don't know yet), and "x" and "y" are variables related through this mathematical equation.
Finding the y-interceptWith "m" solved for, we can solve for the "b" by using the relationship in the equation we have so far.
We know that every "x" and "y" ordered pair is an "x" related to the "y" by this specific equation. Even though we don't know the specific value of "b", we know that the equation must be true for every ordered pair on the line.
While we don't know many associated "y" values and "x" values (for instance, we don't know what the "y" value is when the x is 10, and we don't know what the x value is the "y" is 26), we do know two associations for sure... from the two ordered pairs
[tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex], so
[tex]x=1 \text{ is related to } y=-2[/tex], and [tex]x=3 \text{ is related to } y=6[/tex]
... and they're related through this equation that we've almost found!
Now, in our equation, there is only room to associate one x and y value at a time, so we need to pick one known association, and substitute those values in. Since this equation is supposed to relate the x to the y, it should be true for both points (so, we can try both, and it should work out the same. If you don't want to try both, if you see one ordered pair that has numbers that look easier, use that one):
Substituting Point 1 to find b
[tex]y=4x+b[/tex]
[tex](-2)=4(1)+b[/tex]
simplifying the right side, 4*1 is 4...
[tex](-2)=4+b[/tex]
subtracting 4 from both sides of the equation, and simplifying the left hand side
[tex]-2-4=b\\-2+-4=b\\-6=b[/tex]
Substituting Point 2 to find b (not necessary, but a good double-check)
[tex]y=4x+b[/tex]
[tex](6)=4(3)+b[/tex]
simplifying the right side, 4*3 is 12...
[tex]6=12+b[/tex]
subtracting 4 from both sides of the equation, and simplifying the left hand side
[tex]6=12+b\\6-12=b\\6+-12=b\\-6=b[/tex]
So, as a verification, we get the same value of b (which we should have, because this equation is supposed to work for every pair of (x,y) that has this relationship, and those were the only two points that we knew that did).
The Final equation in slope intercept formSubstituting the value we found for b:
[tex]y=4x+(-6)[/tex]
...and simplifying...
[tex]y=4x-6[/tex]
Need Help Fast!!!!!! The graph of the piecewise function f(x) is shown. f(x) What is the range of f(x)?
Answer:
The second option
Step-by-step explanation:
If you look at the graph, it appears that from negative infinity to 0, the line is just constant, so the range of that would simply be the constant value or in this case 4. from 0 to infinity it appears the line is decreasing at a constant rate and should go towards negative infinity as x goes towards infinity. So the range would be -infinity < f(x) <= 4
Which of the following is a Recursive Formula for an Arithmetic Sequence?
an = 6n – 9
an = -3 + 6(n – 1)
a1 = -3, an = an-1 + 6
a1 = -3, an = 6an-1
Pls I require assistance.
The Recursive formula for an Arithmetic Sequence is a1 = -3, an = an-1 + 6.
What is Arithmetic sequence ?An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.
Given:
an = -3 + 6(n – 1)
a1= -3
a2= 3
a3 = 9
Here the common difference is 6 and first term is -3
Hence, the recursive formula is a1 = -3, an = an-1 + 6.
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Hi! So, I know I got this answer wrong, but I wasn't sure how to solve an equation with signs like: [brackets] in it, I've included my problem as an example, but can someone please teach me what those brackets mean, and how do I go about solving an equation (using this problem as an example) with brackets like these?
Step-by-step explanation:
Brackets is the bigger version of parentheses, you first solve the questions inside the parentheses, then move onto brackets.
For example, this question:
[tex]x=-1\\y=-2\\z=3[/tex]
[tex]5x-y[7-4(z-y)][/tex]
plug in x, y, and z.
[tex]5(-1)-(-2)[7-4(3-(-2))][/tex]
[tex]5(-1)-(-2)[7-4(5)][/tex]
[tex]5(-1)-(-2)[7-20][/tex]
[tex]5(-1)-(-2)[-13][/tex]
[tex]-5-(-2)[-13][/tex]
[tex]-5-26[/tex]
[tex]-31[/tex]
I hope you understand better now.
Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds:
Answer:
4 secs
Step-by-step explanation:
Since they have to be synchronized, their parabolic equations must be equal to one another
3(t^2 + 9 - 6t) - (t^2 + 25 - 10t) - t + 2 = 0
2t^2 - 9t + 4
(2t - 1)(t - 4) = 0
t = 1/2, 4
From the options, the answer is 4
The gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
so, correct option is: C.
Here, we have,
To determine when the gymnasts will be at the same height during their flips, we need to find the time (x) at which the equations for y are equal.
The given equations are:
y = –(x – 5)² + 3
y = –3(x – 3)² + x + 1
Setting the two equations equal, we have:
–(x – 5)² + 3 = –3(x – 3)² + x + 1
Expanding the squared terms:
–(x² – 10x + 25) + 3 = –3(x² – 6x + 9) + x + 1
Simplifying the equation:
–x² + 10x – 25 + 3 = –3x² + 18x – 27 + x + 1
Combining like terms:
–x² + 10x – 22 = –3x² + 19x – 26
Rearranging the equation:
2x² - 9x + 4 = 0
To solve this quadratic equation, we can factor it:
(2x - 1)(x - 4) = 0
Setting each factor equal to zero:
2x - 1 = 0 or x - 4 = 0
Solving for x:
2x = 1 or x = 4
Dividing by 2:
x = 1/2 or x = 4
Therefore, the gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
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please help need it asap
Answer:
195
Step-by-step explanation:
87+38+40=165
360-165=195
Hope this helps!
If not, I am sorry.
If u(x) = -2x²+3 and v(x)=
X'
what is the range of (uv)(x)?
The answer is option D which is the range will be ( -∞, ∞ ).
What is the range?After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).
Given function is
u(x) = -2x²+3 and v(x) = ( 1 / x ).
The product of the function will give uv(x).
uv(x) = (-2x²+3 ) x [tex]\dfrac{1}{x}[/tex]
uv(x) = [tex]\dfrac{-2x^2+3}{x}[/tex]
When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.
Therefore the answer is option D which is the range will be ( -∞, ∞ ).
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