Answer:
l = 7x - 9
Step-by-step explanation:
The length of the rectangle is represented by the expression "7x - 9".
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 (length + width)
Therefore, we can set up the equation:
20x - 18 = 2 (length + (3x - 1))
Expanding the parentheses and combining like terms, we get:
20x - 18 = 2 × length + 6x - 2
Moving all the terms to one side, we get:
14x - 18 = 2 × length
Dividing both sides by 2, we get:
7x - 9 = length
Thus, the rectangle's length is expressed by the expression "7x - 9".
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WILL GIVE BRAINLIEST ‼️ The graph represents the piecewise function:
Answer:
[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]
Step-by-step explanation:
You can find the first function if you know the general form of a line:
[tex]y = mx + b[/tex]
where [tex]m[/tex] is the slope and [tex]b[/tex] the intercept point with the [tex]y[/tex]-axis.
So in the first case the slope is 1 because the next formula
[tex]m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-0}{-1+3} = 1[/tex]
And you can find the interception point if extend the line, then in our case is 3.
So the function is:
[tex]f(x) = x + 5[/tex]
In the other case is constant function that's mean that the function has the next form
[tex]f(x) = k[/tex]
Where [tex]k[/tex] is a constant.
So you only have to observe what is the value for each point in the interval, in this occasion is 5.
So the final answer is:
[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]
Translate and solve using proportions: What number is 30% of 60
Answer: 18
Step-by-step explanation:
The question is asked to know 30% of 60, we get
60 x 30% = 60 x 0.3 = 18
Answer:
18
Step-by-step explanation:
We know that 30% means 30/100
30/100 multiplied by 60
hence, the answer is 18
Compare -8 and 3. Which statement is not true?
Answer:
B
Step-by-step explanation:
it is the opposite of A, which is true, as |-8| = 8
y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence relation that the coefficients must satisfy
Let
[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots[/tex]
Differentiating twice gives
[tex]\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots[/tex]
[tex]\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n[/tex]
When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.
Substitute these into the given differential equation:
[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0[/tex]
Then the coefficients in the power series solution are governed by the recurrence relation,
[tex]\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}[/tex]
Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.
• If n is even, then n = 2k for some integer k ≥ 0. Then
[tex]k=0 \implies n=0 \implies a_0 = a_0[/tex]
[tex]k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}[/tex]
[tex]k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}[/tex]
[tex]k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]
It should be easy enough to see that
[tex]a_{n=2k} = \dfrac{a_0}{(2k)!}[/tex]
• If n is odd, then n = 2k + 1 for some k ≥ 0. Then
[tex]k = 0 \implies n=1 \implies a_1 = a_1[/tex]
[tex]k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}[/tex]
[tex]k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}[/tex]
[tex]k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}[/tex]
so that
[tex]a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}[/tex]
So, the overall series solution is
[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)[/tex]
[tex]\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}[/tex]
The price of a video game is $32.99 before tax. Andre bought the video game for 20% off. He then paid 8% sales tax on the discounted price. Part A: How much did Andre pay in sales tax? Show all work and steps in your solution. (5 points) Part B: What is the total amount that Andre paid for the video game? Show all work and steps in your solution. (5 points)
Answer:
the answer is 24.23 $ thats what i got
Answer:
A. 2.11 and B. 26.39+2.11=28.50
Step-by-step eplanation:
A Chevrolet Sonic Hatchback costs $14,845.00. With a 15% down payment, you can have an amortized loan for 6 years at a rate of 4.5%.
A) What will the monthly payment be?
B) How much will the car cost, in total?
C) How much money will be paid in interest?
Using simple interest, it is found that:
a) The monthly payment will be of $222.57.
b) In total, the car will cost $18,251.9275.
c) $16,025.1775 will be paid in interest.
The amount of money accrued after t years, using simple interest, with an initial value of P and a decimal rate of r is given by:
[tex]A(t) = P(1 + rt)[/tex]
In this problem:
Total cost of $14,845.00, with a down payment of 15%, hence the initial value that will accrue interest is [tex]P = 0.85(14845) = 12618.25[/tex].Loan for 6 years, hence [tex]t = 6[/tex]Rate of 4.5%, hence [tex]r = 0.045[/tex].Item a:
The amount of money accrued will be of:
[tex]A(6) = 12618.25[1 + 0.045(6)] = 16025.1775 [/tex]
Payment over 6 x 12 = 72 months, hence, the monthly payment will be of:
[tex]m = \frac{16025.1775}{72} = 222.57[/tex]
The monthly payment will be of $222.57.
Item b:
The total cost is composed by:
Down payment of 15%, out of the amount of $14,845.00.Interest of $16,025.1775.Hence:
[tex]T = 0.15(14845) + 16025.1775 = 18251.9275[tex]
In total, the car will cost $18,251.9275.
Item c:
As found in item a, $16,025.1775 will be paid in interest.
A similar problem is given at https://brainly.com/question/13176347
Simplify: 7√(1/3) + 2 1/3√(1/3) + 3√(147)
Step-by-step explanation:
7 √(1/3) - 2 1/3 √(1/3) +3√147
→7(1/√3) - (7/3)(1/√3) +3√(3×7×7)
→ (7/√3) - (7/3√3) +3×7√3
→ (7/√3) - (7/3√3) + 21√3
On Rationalising the denominators then
→ [ 7√3/(√3×√3)]-[7√3/(3×√3×√3) +21√3
The Rationalising factor of√3 =√3
→ (7√3/3)-[7√3/(3×3)]+21√3
→ (7√3/3)-(7√3/9)+21√3
LCM of 3 and 9 = 9
→ [(3×7√3)-(7√3)+(9×21√3)]/9
→ (21√3-7√3+189√3)/9
→[(21-7+189)√3]/9
→ [(210-7)√3]/9
→ 203√3/9 Ans.
Hope this helps.
Valentine's Day is coming up, so Sweet Dreams chocolate shop is ordering ribbon to decorate gift boxes. Small gift boxes use 20 inches of ribbon, while large ones use 30 inches. Sweet Dreams expects to sell 225 small boxes and 180 large boxes. If the ribbon they use is sold by the yard, how many yards of ribbon should they order?
Answer:
i think 9900
Step-by-step explanation:
225x20 = 4500
180x30 = 5400
5400+4500 = 9900
what is the absolute value for 115 and 15
12
rectia
14. Ne
10.) Lars has a current annual salary of $38,650.
If he gets a raise of $3,280, what percent is
the raise of his current annual salary? Round
to the nearest whole percent.
(1) 6%
(2) 7%
2 %
8%
(4) 9%
10%
Answer:
3,280/38650 x 100% = 8%
Use synthetic division to find the result when 3x^3 + 4x^2 - 5x - 2 is divided by x + 2
Check the picture below.
a dance club had 3 times as many members as an art club. The art club has 3598 fewer members than the dance club. How many members did the art club have? show bar graph
Answer:
1799 members in the art club i think but i don't have a bar graph
Step-by-step explanation:
^^
Which expression is NOT equal to 729?
3 × 3 × 3 × 3 × 3 × 3
63
9 × 9 × 9
36
Answer:
6^3
Step-by-step explanation:
3 × 3 × 3 × 3 × 3 × 3=729
6^3=216
3 × 3 × 3 × 3 × 3 × 3=729
3^6=729
Hope this helps :)
3 × 3 × 3 × 3 × 3 × 3
63
9 × 9 × 9
36
The profits in hundreds of dollars, Pc), that a company can make from a product is modeled by a function of the price, c,
they charge for the product: P(c) = -20c2 + 320C + 5,120. What is the maximum profit the company can make from the
product?
$540,000
$640,000
$800,000
$896,000
What are the solutions to the quadratic function. f(x) = x^2+4x-12
Answer:
2, -6
Step-by-step explanation:
x^2 + 4x - 12
A = 1
B = 4
C = -12
i used the "X" method to solve for the solutions. i think it's easier than using the quadratic formula but it doesn't always work
for the "X" method you have to multiply your A value and your C value together so 1 x (-12) = -12. that is going to be the top part of the X
the bottom part of the x will be your B value which is 4
we have to find multiples of -12 that will also add to 4
so -2 and 6 multiply to -12 but also add to 4 so we know these numbers will work
i added added two drawings to show how i found the solutions using the "X" method and the quadratic formula
Find the indefinite integral|(12x+5)dx
[tex]\int {12x+5} \, dx[/tex]
For this problem, let's first apply the intergral sum rule.
[tex]\int {12x+5} \, dx = \int{12x} \, dx + \int{5}x \,dx[/tex]
Then, we'll use the reverse power rule on each of these integrals.
[tex]\int{12x} \,dx = 6x^2+C[/tex]
[tex]\int{5} \,dx = 5x+C[/tex]
So the indefinite integral of [tex]\int{12x+5} \,dx[/tex] is [tex]6x^2+5x+C[/tex].
Remember that we need our constant of integration, [tex]C[/tex], because of if we take the derivative of a constant, it'll be 0.
Hope this helps!
Hi there!
[tex]\int\limits {12x+5} \, dx[/tex]
Recall the following rules:
[tex]\int\limits {x^n} \, dx = \frac{x^{n+1}}{n+1}[/tex]
Use this rule to evaluate. Remember to include the constant:
[tex]\int\limits {12x+5} \, dx = \frac{12x^{1+1}}{1+1} + 5x +C[/tex]
[tex]\int\limits {12x+5} \, dx = 6x^2 + 5x + C[/tex]
-
Find the equation of the line that
is parallel to y = 2x – 7 and
contains the point (-3,6).
Step-by-step explanation:
The first step is to Know the condition for two lines be parallel is that have the same slope, and this form the slope given is 2, therefore the new function has its slope too
2) with the slope and the two points givens, you can find the equation
Y-Y1 = m( X-X1) , Y-6 = 2[(X-(-3)] ⇒Y-6 = 2X+6 ⇒Y = 2X+12, AND THIS IS THE EQUATION PARALLEL TO THE LINE Y = 2X-7
What is 5m + 5n where m = 10 and n = -5?
A. 25
B. 26
C. 62
D. 52
ADD EXPLANATION IF NECESSARY. TYSM! :D
Answer:
A
Step-by-step explanation:
5 times 10= 50
5 times -5= -25
50-25=25
A school needs to buy new notebook and desktop computers for its computer lab. The
notebook computers cost $325 each, and the desktop computers cost $250 each. How
many total computers would someone buy if they get 20 notebooks and 17 desktop
computers? How many total computers would someone buy if they get n notebooks
and d desktop computers?
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You buy clothing at a sale. You buy a sweater at
7
10
of its original price of $35. Answer each question and show all your work.
a. How much money did you spend?
b. How much money did you save?
c. What fraction of the total original price did you save?
The amount that will be spent is $24.50, the amount saved will be $10.50, and the percentage saved will be 30%.
The amount that will be spent will be:
= 7/10 × $35 = $24.50
The amount that will be saved will be:
= $35 - $24.50 = $10.50
The fraction of the original price that is saved will be:
= 10.50/35 × 100
= 30%
Read related link on:
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Identify a pattern in each list of numbers. Then use this pattern to find the next number.
-3, 12, -33, 102, -303, ___
[tex]\begin{array}{cccccccc}\\ \underline{-3}&,&12&,&-33&,&102\\ \cline{1-7} &&(-3)(\underline{-3})+3&&(-3)(12)+3&&(-3)(-33)+3 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccc} -303&,&912\\ \cline{1-3} (-3)(102)+3&&(-3)(-303)+3 \end{array}[/tex]
The diameter of a circle is 6.8 m. Find the circumference to the nearest tenth
Answer:
21.4m
Step-by-step explanation:
Circumference : x diameter
is approximately 3.142
3.142 x 6.8 = 21.3656
Nearest tenth = 21.4m
Which element should be used to help clarify a complicated idea in a text? (1 point) O a new topic O a bibliography O a visual O a research question w
The element which should be used to help clarify a complicated idea in a text is ; A research question.
According to the question;
We are required to determine which element should be used to help clarify a complicated idea in a text.A research question is the best fit which should be used to help clarify a complicated idea in a text.
This is so because; a research question provides a basis for accessing all perspectives there is to the complicated idea.
Read more:
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Answer:
D
Step-by-step explanation:
how is this math? 0-0
Naomi can run 1/4 mile in 2 minutes. Does Amal or Naomi run faster? How do you know
Answer: Yes
Step-by-step explanation:
A: 12 minutesAnswer to B: 36 minutesAnswer to C:
solve using quadratic formula
3n^2-2n-5=0
=5/3 =−1
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
Please help!
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
Answer:
it would be c because its moved 2x up
Step-by-step explanation:
Order the side lengths.
Check the picture below.
now, we know, the wider the angle, the longer the opposite side.
so, let's just look at all 5 sides and check the angle that's opposite to them, or namely, making the side.
[tex]\stackrel{DF}{46^o}\qquad \stackrel{CD}{55^o}\qquad \stackrel{CE}{74^o}\qquad \stackrel{EF}{45^o}\qquad \stackrel{DE}{89^o} \\\\\\ \stackrel{\textit{in ascending order}}{\stackrel{EF}{45^o}~~ < ~~\stackrel{DF}{46^o}~~ < ~~ \stackrel{CD}{55^o}~~ < ~~ \stackrel{CE}{74^o}~~ < ~~ \stackrel{DE}{89^o}}[/tex]
If a deck of cards is 7/10 of an inch tall, how tall is the package of 6 decks of cards?
reflect the quadrilateral graph on the x axis graph
is the X-axis reflection right?
Answer:
Step-by-step explanation:
No . B' (reflection of B) and C' (reflection of C) are in the right position, but D' should be at (4, 1) and A' should be at (-2,-4).
solve for x
2/x -2 = 3/2x +3
Step-by-step explanation: