You have that the perimeter of the rectangle is given by the following formula:
[tex]P=2l\text{ + 2w}[/tex]l: length of the rectangle
w: width of the rectangle
[tex]\begin{gathered} l=3x^2+x+2 \\ w=-x^2-5x+1 \end{gathered}[/tex]Then, you replace the pevious expression for l and w in the formula for the perimeter, just as follow:
[tex]\begin{gathered} P=2(3x^2+x+2)+2(-x^2-5x+1) \\ P=2(3x^2)+2(x)+2(2)+2(-x^2)+2(-5x)+2(1) \\ P=6x^2+2x+4-2x^2-10x+2 \\ P=4x^2-8x+6 \end{gathered}[/tex]Hence, the perimeter of the rectangle is P = 4x2 - 8x + 6
find the absolute extrema for the function on the given internal
Given the function;
[tex]f(x)=-3x^2-24x+3[/tex]The first derivative of the function is;
[tex]f^{\prime}(x)=-6x-24[/tex]At critical points;
[tex]\begin{gathered} -6x-24=0 \\ -6x=24 \\ x=\frac{24}{-6} \\ x=-4 \end{gathered}[/tex]Thus, the f(x) at x=-4 is;
[tex]\begin{gathered} f(-4)=-3(-4)^2-24(-4)+3 \\ f(-4)=-48+96+3 \\ f(-4)=51 \end{gathered}[/tex]Thus, the absolute maxima on the given point is;
[tex](-4,51)[/tex]The absolute minima on the given points is;
[tex](4,-141)[/tex]I believed I solved correctly but want a double check pls
We have the original price P and it will increase a rate r%, we can express is as
[tex]P+P\cdot r[/tex]As we can see, P is the original price and P*r is what's going to be added to the original price, we can even simplify it to
[tex]P(1+r)[/tex]That's a generic expression to find it, so here we have P = 153 and r = 19% = 0.19, then
[tex]\begin{gathered} P(1+r)=153(1+0.19) \\ \\ 153(1+0.19)=153\cdot1.19 \\ \\ 153\cdot1.19=182.07 \end{gathered}[/tex]The price will be $182.07
Find two values of angle A between 2pi where sin A = [tex] \frac{ - \sqrt{2 } }{2} [/tex]
Answer:
Explanation:
First of all, we know that
[tex]\sin \frac{\pi}{4}=\frac{\sqrt[]{2}}{2}[/tex]And knowing the unit circle, we know that the sine takes negative values in 3rd and 4th quadrants. Therefore, from the above value of the angle, If we go π radians counterclockwise, we encounter negative values of sine; hence,
[tex]\sin \lbrack\frac{\pi}{4}+\pi\rbrack=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{5\pi}{4}=\frac{-\sqrt[]{2}}{2}[/tex]The second value of the angle that yields the above value for sine is found by adding π/2 radians to the angle above (we are now in the 4th quadrant)
[tex]\sin \frac{5\pi}{4}+\frac{\pi}{2}=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{7\pi}{4}=-\frac{\sqrt[]{2}}{2}[/tex]Hence, the two values of angles between 0 and 2π are 5π/4 and 7π/4.
A chicken soup recipe calls for 15 cups of chicken stock. How much is this in quarts?Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer
Recall the conversion
1 quarts = 4 cup
Given that there is 15 cups, multiply it by the ratior of quarts to cup, making sure that the cup is in the denominator
[tex]\begin{gathered} 15\text{ cups}\times\frac{1\text{ quarts}}{4\text{ cups}} \\ =15\cancel{\text{cups}}\times\frac{1\text{ quarts}}{4\cancel{\text{cups}}} \\ =\frac{15\times1\text{ quarts}}{4} \\ =\frac{15\text{ quarts}}{4} \\ =3\text{ }\frac{3}{4}\text{ quarts} \end{gathered}[/tex]Therefore, 15 cups is equivalent to 3 and 3/4 quarts.
Every ten minutes, Frankie follows a pattern in creating a new group of drawings. Below, you can see how many total drawings Frankie has created by the end of each ten-minute interval.
If he continues to follow this pattern, at the end of seventy minutes, how many total drawings will Frankie have created?
will give 199 points
Answer: 54 patterns
Step-by-step explanation:
12+17=19+14=33+21=54
YOU BE THE TEACHER Your friend solves the equation 9x2 = 36. Is your friend correct? 9x2 = 36 x = 4 x= 14 x= +2 O yes O no Explain your reasoning.
ANSWER
Yes
EXPLANATION
Your friend is correct.
First he divided both sides by 9: 36 divided by 9 is 4
Then he did the square root, which has two results: one positive and one negative. This gives +2 and -2.
Another way to check the result is to replace it into the equation. If the equation is true, then the result is correct:
[tex]\begin{gathered} 9(2)^2=36 \\ 9\cdot4=36 \\ 36=36\text{ }\rightarrow\text{ true} \\ \\ 9(-2)^2=36 \\ 9\cdot4=36 \\ 36=36\text{ }\rightarrow\text{ true} \end{gathered}[/tex]i really need help can you help me?
1. Madison's work is correct. Her there is no mistake
2. Kaleb's work is not correct. His mistake was when he divided by 4
Find the midpoint of the segment with the following endpoints.(4,5) and (9, 2)
Answer: (6.5, 3.5)
Explanation:
The midpoint between two points can be found by taking the mean of the x coordinates, and the mean of the y coordinates.
The points we have are:
(4, 5) where we will call
[tex]x_1=4,y_1=5[/tex]and also the point
(9, 2) where we will call
[tex]x_2=9,y_2=2[/tex]Now, the midpoint will be at
[tex](x_m,y_m)[/tex]Where xm is the mean of the x coordinates, and ym is the mean of the y coordinates:
[tex]x_m=\frac{x_1+x_2}{2}[/tex]subtituting the values:
[tex]x_m=\frac{4+9}{2}=\frac{13}{2}=6.5[/tex]we have xm, now we need ym:
[tex]y_m=\frac{y_1+y_2}{2}[/tex]Substituting the values
[tex]y_m=\frac{5+2}{2}=\frac{7}{2}=3.5[/tex]Thus, the midpoint is at:
[tex](x_m,y_m)=(6.5,3.5)[/tex]Solve for y:6y -4 = 3y +2
1) Solving for y, the following expression
6y -4 = 3y +2 Add 4 to both sides
6y = 3y +2+4
6y = 3y +6 Subtract 3y from both sides
6y -3y = 6
3y = 6 Divide both sides by 3
y= 2
S={2}
2) So the solution for this is y=2
I need to know what a cordanate plain is
A coordinated plane is
10. In July, Ariel recorded the height of a pine tree and how quickly it was expected to grow in thenext several monthsQ. Write an equation for the table.Height ofTree (inches)b. What does theторе represent608c. What does the y-intercept represent?
Using the table to find the equation:
Let x is the number of months, and y is the height of the tree
The general form of the line y = mx + c
where m is the slope and c is the y-intercept
So, at the beginning at x = 0 , y = 600
So,
600 = m * 0 + c
c = 600
When x = 3 , y = 602
so,
602 = 3m + 600
solve to find m
602 - 600 = 3m
3m = 2
m = 2/3
So,
[tex]y=\frac{2}{3}x+600[/tex]b. What does the slope represent?
The slope represents the rate of growth each month
which mean the tree grow (2/3) inches per month
c. What does the y-intercept represent?
y-intercept represents the first height of the tree
Simplify the expression showed question … which is the correct answer
Okay, here we have this:
We need to simplify the following expression:
[tex]\begin{gathered} (5^{-4}(25)^4)^2 \\ =(5^{-4}(5^2)^4)^2 \\ =(5^{-4}\cdot5^8)^2 \\ =(5^{-4+8})^2 \\ =(5^4)^2 \\ =5^8 \end{gathered}[/tex]Finally we obtain that the correct answer is the option B.
A plater holds 24 strawbers,2 aplles,16 oranges.What fraction of all the fruits are strawberiias?Fracion of apples?Fraction of oranges?
The fraction for strawberries, apples, and oranges is 12/21, 1/21, and 8/21 respectively.
What are fractions?A fraction depicts a portion of an entire. This entire could be a location or a group of things. The Latin word "fraction," which means "to break," is where the word "fraction" comes from. In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. The numerator displays how many pieces the whole has been divided into. It is positioned at the top of the fraction, beneath the fractional bar is the denominator.
Given,
Number of strawberries = 24
Number of apples = 2
Number of oranges = 16
So, the total number of fruits is given as
= 24 + 2 + 16
= 42
The fraction for strawberries = 24/42
=12/21
The fraction for apples = 2/42
= 1/21
The fraction for oranges = 16/42
=8/21
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Could you please help me out with figuring out how to do this 216 into a scientific notation
In order to express a small number (less than zero) in scientific notation we just have to move the decimal point until we reach the last digit, the exponent we use must be a negative number and it represents the number of times we moved the dot.
In this case, we initially had the number 0.216, as you can see, we have three digits on the right of the point, then we must move the dot 3 times, then the representation in the scientific notation of this number is:
0.216 = 216×10⁻³
12. A bag of peanuts could be divided among 6 children, 9 children, or 10 children with each bag getting the same number, of peanuts. What is the smallest number of peanuts that could be in the bag?A.72 B.90 C.108 D.120
the numbers of children we have
6 children group , 9 children group or 10 children group
for equal quantity of peanuts among these groups will be LCM of these groups
so LCM of 6 , 9 , 10 is
6 = 2 x3
9 = 3 x 3
10 = 2 x 5
so, the LCM is 2 x 3 x 3 x 5 = 90
so smallest number of the peanuts will be 90
please help ASAP!!!!!
The first question
[tex]\frac{5x^2-28x-12}{x-6}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
The 2nd question
[tex]\frac{x^2+11x+28}{x+4}=\frac{(x+7)(x+4)}{x+4}=x+7[/tex]so, it can be solved by inspection.
The 3rd question
[tex]\frac{6x^2+2x+7}{3x-2}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
Finally, 4th question
[tex]\frac{x^2-x-35}{x-6}[/tex]can be rewritten by polynomial division.
can you show me like on a same graph like mine
Given the general quadratic equation:
[tex]ax^2+bx+c=0[/tex]The general solution of the quadratic equation is given by the expression:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the problem, we have the quadratic equation:
[tex]3x{}^2+2x-225=0[/tex]Identifying the coefficients:
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-225 \end{gathered}[/tex]Then, using the general solution formula:
[tex]\begin{gathered} x=\frac{-2\pm\sqrt{4+2700}}{6}=\frac{-2\pm52}{6} \\ \\ \Rightarrow x_1=\frac{25}{3} \\ \\ \Rightarrow x_2=-9 \end{gathered}[/tex]And the solutions on the number line are:
Given:• PQRS is a rectangle.• mZ1 = 50°PeNSRWhat is mZ2?130°85°70°65°
We can start answering this having that a rectangle is a parallelogram. The diagonals of a parallelogram bisect each other. Therefore, we have that the sides Q to the point where the diagonals intersect each other of the rectangle is congruent to R to this point. Then, we have two congruent sides.
The angles opposite to these sides are congruent too. They have the same measure. Since we have a triangle, and the sum of the internal angles of a triangle is equal to 180, we can say that:
[tex]m\angle1+2\cdot m\angle2=180[/tex]Then, we have:
[tex]50+2\cdot m\angle2=180[/tex]Subtracting 50 from both sides of the equation, and then dividing this equation by 2, we have:
[tex]50-50+2\cdot m\angle2_{}=180-50\Rightarrow2\cdot m\angle2=130[/tex][tex]2\cdot\frac{m\angle2}{2}=\frac{130}{2}\Rightarrow m\angle2=65[/tex]Therefore, the measure of angle 2 (m<2) is equal to 65 (degrees) (last option).
How much sales tax will Justin pay on a computer priced at $1,723.42 if the sales tax rateis 9.25 percent?
Given : the price of the computer = $1,723.42
The sales tax = 9.25% = 9.25/100 = 0.0925
The sales tax = 9.25% of $1,723.42 = 0.0925 * $1,723.42 = $159.42 (to the nearest cent)
So,
The sales tax = $159.42
Use the change of base formula to evaluate the expression then convert it to a logarithm in base eight round to the nearest thousandth
Recall that the change of base formula for logarithms is:
[tex]\log_a(b)=\frac{\log_x(b)}{\log_x(a)}.[/tex]Using the change of base formula for logarithms to the given logarithm we get:
[tex]\log_354=\frac{\log_8(54)}{\log_8(3)}.[/tex]Therefore:
[tex]\log_3(54)=3.631.[/tex]And:
[tex]undefined[/tex]Given the function f(x), whose graph is shown, place the black dot at the point the corresponds to f^-1(-1)
Given: Graph of a function f(x) is provided.
Required: To find the inverse of the function
[tex]f^{-1}(-1)[/tex]Explanation: The inverse of a function is determined by interchanging the domain and the range. The domain is the input values, and the range is the output values where the function is defined.
Hence, to find the inverse of the function at x=-1, we need to look at the graph and find out at which value of x, the value of f(x), is -1. Since if
[tex]\begin{gathered} f(a)=-1 \\ then,f^{-1}(-1)=a \end{gathered}[/tex]Hence we need to look at which point on the x-axis of the given function we have f(x)=-1. This is the point (-3,-1) as
[tex]\begin{gathered} f(-3)=-1 \\ \Rightarrow f^{-1}(-1)=-3 \end{gathered}[/tex]Hence the point corresponding to the inverse is (-1,-3). The point is shown below in the graph-
Final Answer: The point corresponding to the inverse of f at x=-1 is (-1,-3).
Lottery: I buy one of 5000 raffle tickets for $1. The sponsors then randomly select one grand prize worth $500, two second prizes worth $200 each, and three third prizes at $100 each. Create the probability distribution for this raffle and calculate my expected value. Enter each row of your table as a separate line, but don't worry too much about formatting. Tables should look similar to those given in questions 1 and 3. Don't forget to give your expected value.
To give the probability distribution, we need to calculate the probability of each possible outcome and the value of this outcome.
We have 5000 raffle, 1 will win the first prize, 2 will win the second prize, 3 will win the third prize and the rest 4994 will win no prize.
The first prize is $500, but the raffle cost $1, so the outcome is actually $499.
The second prizes are $200 each, minus the cost we have an outcome of $199.
The third prizes are $100 each, minus the cost we have an outcome of $99.
The others will not receive prizes, but they will still have the cost of $1, so the outcome is -$1.
The first prize is 1 in 5000, so the probability is 1/5000
The second prizes are 2 in 500, so the probability is 2/5000
The third prizes are 3 in 5000, so the probability is 3/5000
The lost is the rest of the 4994 in 500, so the probability is 4994/5000
So, the table for the probability distributions is:
Value gained | P(x)
$499 | 1/5000
$199 | 2/5000
$99 | 3/5000
-$1 | 4994/5000
To calculate the expected value, we multiply the value by its probability and add them:
[tex]\begin{gathered} E(x)=499\cdot\frac{1}{5000}+199\cdot\frac{2}{5000}+99\cdot\frac{3}{5000}-1\cdot\frac{4994}{5000}_{} \\ E(x)=\frac{499}{5000}+\frac{398}{5000}+\frac{297}{5000}-\frac{4994}{5000} \\ E(x)=\frac{499+398+297-4994}{5000} \\ E(x)=-\frac{3800}{5000} \\ E(x)=-0.76 \end{gathered}[/tex]So, the expected value if -$0.76.
I need help on prime factorization just describe how to do it for me
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself.
For example, if we take the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.
Let us take another example and solve for its prime factorization
Prime factorization of 72
Hence, the prime factorization of 72 = 2³×3².
Finally,
You want to walk from home to a grocery store that is 1/2 miles away. You stop for a rest after 1/4 miles. How much farther do you have to walk? Write your answer as a fraction in simplest form.
Answer: 1/4
Step-by-step explanation:
1/2-1/4=1/4 because 1/4x2=2/4 and 2/4=1/2
Answer: 1/4 mile
Step-by-step explanation: so 1/2 = 2/4. You stop after 1/4, so subtract. You get 1/4, meaning you have to walk 1/4 mile. Also, r u sure you're in college, cuz this problem is pretty easy.
Please help will mark Brainly
Using the properties of a linear function we get the value of y as 2 when x is 0.
A linear function is of the form: y = mx + c , where m is the slope
Now the function satisfies (-4,3) and (4,5)
So we substitute these values in the function.
At (-4,3) we get 3 = -4m + c
At (4,5) we get 5 = 4m + c
Adding the two equation we get:
2c = 8
or, c = 4
Now at c = 4 , and at (4,5) we get
5 = 4m + 2
or, m = 3/4
So the linear function is of the form :
y = 3/4 x + 2
or, 4y = 3x + 8
Now at x = 0 ,
4y = 8
or, y = 2
A function which graph (in Cartesian coordinates) is a non-vertical straight in the plane is known as a linear function as from real numbers to the real numbers in calculus and related mathematical fields. When the input variable is modified, the output often changes in a manner that is proportionate to the input variable's change.
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Using the identity sin? 0 + cos²0 1, find the value of sin 0, to the nearesthundredth, if cos 0 = 0.52 and 3
we have that
sin^2(x)+cos^2(x)=1
we have
cos(x)=0.52
the angle lie in the IV quadrant
substitute
sin^2(x)+0.52^2=1
sin^2(x)=0.7296
sin(x)=(+/-)0.85
but
the angle lie in IV quadrant
so
is negative
sin(x)=-0.85Part 2
cos(x)=-0.54
III quadrant
the sine is negative too
substitute
sin^2(x)+(-0.54)^2=1
sin^2(x)=0.7084
sin(x)=-0.84Find the sum of all multiples of 7 between 1 to 200, inclusive.
Answer:
2842
Explanation:
The first multiple of 7 =7
The last multiple of 7 before 200 = 196
This problem forms an arithmetic sequence where:
• The first term, a= 7
,• The last term, l = 196
To determine the sum, we find first the number of multiples of 7 between 7 and 196.
[tex]\begin{gathered} \text{Number of multiples=}\frac{196}{7} \\ =28 \end{gathered}[/tex]For a sequence with first and last terms, its sum is:
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ =\frac{28}{2}(7+196) \\ =14\times203 \\ =2842 \end{gathered}[/tex]The sum of all multiples of 7 between 1 to 200 is 2842.
•
Write the expression without a negative exponent.1/a^-4
Explanation
We are given the expression below:
[tex]\frac{1}{a^{-4}}[/tex]We are required to rewrite the expression without a negative exponent.
This can be achieved thus:
[tex]\begin{gathered} \frac{1}{a^{-4}} \\ We\text{ }know\text{ }from\text{ }indices\text{ }that\text{ }a^{-x}=\frac{1}{a^x} \\ \therefore\frac{1}{a^{-4}}=1\div a^{-4}=1\div\frac{1}{a^4} \\ =1\times\frac{a^4}{1}=a^4 \end{gathered}[/tex]Hence, the answer is a⁴.
Paul is planning to sell bottled water at the local carnival. Paul's profit (in dollars) from selling b bottles of water is given by the formula P=1.05b-151.
Explanation :
• The standard linear function takes the form of y = mx +c
• Since the Pauls profit is given by the formula ,P = 1.05b -151,, The curve of this profit is in line with the slope ,m = 1.05, as comparing with the standard linear fuction.
,• Therefore, Paul profit is increasing at a rate of 1.05 dollar per bottle.,
A person places $531 in an investment account earning an annual rate of 6.1%,compounded continuously. Using the formula V = Pe", where V is the value of theaccount in t years, P is the principal initially invested, e is the base of a naturallogarithm, and ris the rate of interest, determine the amount of money, to thenearest cent, in the account after 16years.
This is the solution, Qxk:
Step 1: Let's review the information provided to us to answer the problem correctly:
Principal = $ 531
Interest rate = 6.1% (0.061) compounded continously
Term = 16 years
Step 2: Let's find the future value of this investment, as follows:
V = Pe^t*r
V